Subgroups — C₂₃×#61592 #19209218

Order 5888.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3322	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3319	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3314	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3297	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3280	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3273	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3268	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3264	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3194	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3193	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3190	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
28	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
29	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
30	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#553	—	2	1	no	—
33	C₂₃×#553	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#553	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#546	—	2	1	no	—
37	C₂₃×#546	—	2	1	no	—
38	C₂₃×#546	—	2	1	no	—
39	C₂₃×#546	—	2	1	no	—
40	C₂₃×#546	—	2	1	no	—
41	C₂₃×#546	—	2	1	no	—
42	C₂₃×#546	C₂²	1	2	yes	—
43	C₂₃×#546	C₂²	1	2	yes	complemented
44	C₂₃×#546	C₂²	1	2	yes	complemented
45	C₂₃×#546	C₂²	1	2	yes	complemented
46	C₂₃×#546	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#546	C₂²	1	1	yes	characteristic, complemented
48	D₄²×C₂₃	—	2	1	no	—
49	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#540	—	2	1	no	—
51	C₂₃×#538	—	2	1	no	—
52	C₂₃×#538	—	2	1	no	—
53	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#529	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#525	C₂²	1	1	yes	characteristic
57	C₂₃×#525	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₂₃×#123	—	2	1	no	—
59	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂₃×#121	—	2	1	no	—
61	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₂₃×#120	—	2	1	no	—
65	C₂₃×#518	—	2	1	no	—
66	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
67	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
68	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
69	C₂₃×#496	C₂²	1	2	yes	complemented
70	C₂₃×#495	C₂²	1	2	yes	complemented
71	C₂₃×#489	C₂²	1	2	yes	complemented
72	C₂₃×#488	C₂²	1	2	yes	complemented
73	C₂₃×#485	C₂²	1	2	yes	complemented
74	C₂₃×#484	C₂²	1	2	yes	complemented
75	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#482	C₂²	1	2	yes	complemented
77	C₂₃×#480	C₂²	1	2	yes	complemented
78	C₂₃×#480	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#480	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#480	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#478	C₂²	1	2	yes	complemented
82	C₂₃×#474	C₂²	1	2	yes	complemented
83	C₂₃×#469	C₂²	1	2	yes	complemented
84	C₂₃×#468	C₂²	1	2	yes	complemented
85	C₂₃×#468	C₂²	1	2	yes	complemented
86	C₂₃×#468	C₂²	1	2	yes	complemented
87	C₂₃×#467	C₂²	1	2	yes	complemented
88	C₂₃×#466	C₂²	1	2	yes	complemented
89	C₂₃×#466	C₂²	1	2	yes	complemented
90	C₂₃×#465	C₂²	1	2	yes	complemented
91	C₂₃×#464	C₂²	1	2	yes	complemented
92	C₂₃×#463	C₂²	1	2	yes	complemented
93	C₂₃×#463	C₂²	1	2	yes	complemented
94	C₂₃×#463	C₂²	1	2	yes	complemented
95	C₂₃×#463	C₂²	1	2	yes	complemented
96	C₂₃×#459	C₂²	1	2	yes	complemented
97	C₂₃×#452	C₂²	1	2	yes	complemented
98	C₂₃×#452	C₂²	1	2	yes	complemented
99	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#450	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#450	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#450	C₂²	1	2	yes	complemented
103	C₂₃×#450	C₂²	1	2	yes	complemented
104	C₂₃×#449	C₂²	1	2	yes	complemented
105	C₂₃×#449	C₂²	1	2	yes	complemented
106	C₂₃×#449	C₂²	1	2	yes	complemented
107	C₂₃×#449	C₂²	1	2	yes	complemented
108	C₂₃×#448	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#448	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#448	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#447	C₂²	1	1	yes	characteristic
112	C₂₃×#447	C₂²	1	1	yes	characteristic
113	C₂₃×#447	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#447	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#447	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#447	C₂²	1	2	yes	complemented
117	C₂₃×#447	C₂²	1	2	yes	complemented
118	C₂₃×#447	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×#447	C₂²	1	2	yes	complemented
120	C₂₃×#447	C₂²	1	2	yes	complemented
121	C₂₃×#442	C₂²	1	2	yes	complemented
122	C₂₃×#440	C₂²	1	2	yes	complemented
123	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
124	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
125	C₂₃×#436	C₂²	1	2	yes	complemented
126	C₂₃×#435	C₂²	1	2	yes	complemented
127	C₂₃×#435	C₂²	1	2	yes	complemented
128	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
129	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
130	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
131	C₂₃×#418	C₂²	1	2	yes	complemented
132	C₂₃×#417	C₂²	1	2	yes	complemented
133	C₂₃×#416	C₂²	1	2	yes	complemented
134	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
135	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
136	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
139	C₂⁵×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	—	2	1	no	—
141	C₂×#41×C₂₃	—	2	1	no	—
142	C₂×#41×C₂₃	—	2	1	no	—
143	C₂×#41×C₂₃	—	4	4	no	—
144	C₂×#41×C₂₃	C₂³	1	2	yes	—
145	C₂×#41×C₂₃	C₂³	1	2	yes	—
146	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic, complemented
148	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₂₃	—	2	1	no	—
150	C₂²×D₄×C₂₃	—	2	1	no	—
151	C₂²×D₄×C₂₃	—	2	1	no	—
152	C₂²×D₄×C₂₃	—	2	1	no	—
153	C₂²×D₄×C₂₃	—	2	1	no	—
154	C₂²×D₄×C₂₃	—	2	1	no	—
155	C₂²×D₄×C₂₃	—	2	1	no	—
156	C₂²×D₄×C₂₃	—	2	1	no	—
157	C₂²×D₄×C₂₃	—	4	4	no	—
158	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
159	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
160	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
161	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
162	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
163	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
164	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
165	C₂³×C₄×C₂₃	—	2	1	no	—
166	C₂³×C₄×C₂₃	—	2	1	no	—
167	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
169	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
170	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
171	C₂₃×#135	—	4	4	no	—
172	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	complemented
173	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
174	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	complemented
176	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	complemented
177	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	complemented
178	C₂×D₈×C₂₃	—	4	4	no	—
179	C₂×D₈×C₂₃	C₂³	1	2	yes	—
180	C₂×D₈×C₂₃	C₂³	1	2	yes	—
181	C₂×D₈×C₂₃	C₂³	1	2	yes	—
182	C₂×D₈×C₂₃	C₂³	1	2	yes	—
183	C₂×D₈×C₂₃	C₂³	1	2	yes	—
184	C₂×D₈×C₂₃	C₂³	1	2	yes	—
185	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
186	C₂×M₁₆×C₂₃	C₂³	1	2	yes	complemented
187	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
188	C₂²×C₈×C₂₃	C₂³	1	2	yes	complemented
189	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
190	C₂₃×#127	—	2	1	no	—
191	C₂₃×#127	C₂³	1	1	yes	characteristic, complemented
192	C₂₃×#126	—	2	1	no	—
193	C₂₃×#126	—	2	1	no	—
194	C₂₃×#126	—	2	1	no	—
195	C₂₃×#125	—	2	1	no	—
196	C₂₃×#125	C₂³	1	1	yes	characteristic, complemented
197	C₂₃×#124	—	2	1	no	—
198	C₂₃×#124	—	2	1	no	—
199	C₂₃×#124	—	2	1	no	—
200	C₂₃×#124	—	2	1	no	—
201	C₂₃×#124	—	2	1	no	—
202	C₂₃×#124	C₂³	1	2	yes	—
203	C₂₃×#124	C₂³	1	2	yes	—
204	C₂₃×#124	C₂³	1	1	yes	characteristic, complemented
205	C₂₃×#123	—	2	1	no	—
206	C₂₃×#123	—	2	1	no	—
207	C₂₃×#123	—	2	1	no	—
208	C₂₃×#123	—	2	1	no	—
209	C₂₃×#123	—	2	1	no	—
210	C₂₃×#123	—	2	2	no	—
211	C₂₃×#123	—	2	2	no	—
212	C₂₃×#123	—	2	2	no	—
213	C₂₃×#123	—	2	2	no	—
214	C₂₃×#123	—	2	1	no	—
215	C₂₃×#123	—	2	1	no	—
216	C₂₃×C₂²⋊Q₈	—	2	1	no	—
217	C₂₃×C₂²⋊Q₈	—	2	1	no	—
218	C₂₃×C₂²⋊Q₈	—	2	1	no	—
219	C₂₃×C₂²⋊Q₈	—	2	1	no	—
220	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic, complemented
225	C₂₃×#121	—	2	1	no	—
226	C₂₃×#121	—	2	1	no	—
227	C₂₃×#121	—	2	1	no	—
228	C₂₃×#121	—	2	1	no	—
229	C₂₃×#121	—	2	1	no	—
230	C₂₃×#121	—	2	1	no	—
231	C₂₃×#121	—	2	1	no	—
232	C₂₃×#121	—	2	1	no	—
233	C₂₃×#121	—	2	1	no	—
234	C₂₃×#121	—	2	1	no	—
235	C₂₃×#121	—	2	1	no	—
236	C₂₃×#121	—	2	1	no	—
237	C₂₃×#121	—	2	1	no	—
238	C₂₃×#121	—	2	2	no	—
239	C₂₃×#121	—	2	2	no	—
240	C₂₃×#121	—	2	2	no	—
241	C₂₃×#121	—	2	2	no	—
242	C₂₃×#121	—	2	1	no	—
243	C₂₃×#121	—	2	1	no	—
244	C₂₃×#121	C₂³	1	1	yes	characteristic
245	C₂₃×#121	C₂³	1	1	yes	characteristic
246	C₂₃×#121	C₂³	1	1	yes	characteristic
247	C₂₃×#121	C₂³	1	1	yes	characteristic
248	C₂₃×#121	C₂³	1	1	yes	characteristic
249	C₂₃×#121	C₂³	1	1	yes	characteristic
250	C₂₃×#121	C₂³	1	2	yes	—
251	C₂₃×#121	C₂³	1	2	yes	—
252	C₂₃×#121	C₂³	1	1	yes	characteristic, complemented
253	C₂₃×#121	C₂³	1	1	yes	characteristic, complemented
254	C₂₃×#121	C₂³	1	1	yes	characteristic, complemented
255	C₂₃×#120	—	2	1	no	—
256	C₂₃×#120	—	2	1	no	—
257	C₂₃×#120	—	2	2	no	—
258	C₂₃×#120	—	2	2	no	—
259	C₂₃×#120	—	2	2	no	—
260	C₂₃×#120	—	2	2	no	—
261	C₂₃×#120	—	2	1	no	—
262	C₂₃×#120	—	2	1	no	—
263	C₂₃×#120	—	2	1	no	—
264	C₂₃×#120	—	2	1	no	—
265	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
266	C₄×D₄×C₂₃	—	2	1	no	—
267	C₄×D₄×C₂₃	—	2	1	no	—
268	C₄×D₄×C₂₃	—	2	1	no	—
269	C₄×D₄×C₂₃	—	2	1	no	—
270	C₄×D₄×C₂₃	—	2	1	no	—
271	C₄×D₄×C₂₃	—	2	1	no	—
272	C₄×D₄×C₂₃	—	2	1	no	—
273	C₄×D₄×C₂₃	—	2	1	no	—
274	C₄×D₄×C₂₃	—	2	1	no	—
275	C₄×D₄×C₂₃	—	2	1	no	—
276	C₄×D₄×C₂₃	—	2	1	no	—
277	C₄×D₄×C₂₃	—	2	1	no	—
278	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
279	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
280	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
281	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
282	C₄×D₄×C₂₃	C₂³	1	2	yes	—
283	C₄×D₄×C₂₃	C₂³	1	2	yes	—
284	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
289	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
290	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
291	C₂₃×#117	—	2	1	no	—
292	C₂₃×#117	—	2	1	no	—
293	C₂₃×#117	C₂³	1	1	yes	characteristic
294	C₂₃×#117	C₂³	1	1	yes	characteristic, complemented
295	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
296	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
297	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
300	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
301	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
302	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
303	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
304	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
305	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
306	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
308	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
312	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
313	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
314	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
315	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
316	C₂₃×#107	C₂³	1	2	yes	complemented
317	C₂₃×#107	C₂³	1	2	yes	complemented
318	C₂₃×#107	C₂³	1	2	yes	complemented
319	C₂₃×#106	C₂³	1	2	yes	complemented
320	C₂₃×C₄⋊C₈	C₂³	1	2	yes	complemented
321	C₂₃×C₄⋊C₈	C₂³	1	2	yes	complemented
322	C₂₃×#103	C₂³	1	2	yes	complemented
323	C₂₃×#103	C₂³	1	2	yes	complemented
324	C₂₃×#103	C₂³	1	2	yes	complemented
325	C₂₃×#103	C₂³	1	2	yes	complemented
326	C₂₃×#103	C₂³	1	2	yes	complemented
327	C₂₃×#102	C₂³	1	2	yes	—
328	C₂₃×#102	C₂³	1	2	yes	—
329	C₂₃×#102	C₂³	1	2	yes	—
330	C₂₃×#102	C₂³	1	2	yes	—
331	C₂₃×#102	C₂³	1	2	yes	—
332	C₂₃×#102	C₂³	1	2	yes	—
333	C₂₃×#102	C₂³	1	2	yes	—
334	C₂₃×#102	C₂³	1	2	yes	—
335	C₂₃×#102	C₂³	1	2	yes	complemented
336	C₂₃×#102	C₂³	1	2	yes	complemented
337	C₂₃×#102	C₂³	1	2	yes	complemented
338	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
339	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
340	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
341	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
342	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
343	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
344	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	complemented
345	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	complemented
346	C₂₃×#97	C₂³	1	2	yes	complemented
347	C₄×C₈×C₂₃	C₂³	1	2	yes	complemented
348	C₂⁴×C₂₃	—	2	1	no	—
349	C₂⁴×C₂₃	—	2	1	no	—
350	C₂⁴×C₂₃	—	2	2	no	—
351	C₂⁴×C₂₃	—	2	2	no	—
352	C₂⁴×C₂₃	—	2	1	no	—
353	C₂⁴×C₂₃	—	2	1	no	—
354	C₂⁴×C₂₃	—	4	4	no	—
355	C₂⁴×C₂₃	—	4	4	no	—
356	C₂⁴×C₂₃	—	8	2	no	—
357	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
358	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
359	#41×C₂₃	—	2	4	no	—
360	#41×C₂₃	—	2	4	no	—
361	#41×C₂₃	—	4	2	no	—
362	#41×C₂₃	—	4	2	no	—
363	#41×C₂₃	—	4	2	no	—
364	#41×C₂₃	—	4	2	no	—
365	#41×C₂₃	—	4	4	no	—
366	#41×C₂₃	—	4	4	no	—
367	#41×C₂₃	—	8	2	no	—
368	C₂×Q₈×C₂₃	—	2	1	no	—
369	C₂×Q₈×C₂₃	—	2	1	no	—
370	C₂×Q₈×C₂₃	—	4	2	no	—
371	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
372	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₂₃	—	2	4	no	—
374	C₂×D₄×C₂₃	—	2	4	no	—
375	C₂×D₄×C₂₃	—	2	4	no	—
376	C₂×D₄×C₂₃	—	2	1	no	—
377	C₂×D₄×C₂₃	—	2	1	no	—
378	C₂×D₄×C₂₃	—	2	1	no	—
379	C₂×D₄×C₂₃	—	2	1	no	—
380	C₂×D₄×C₂₃	—	2	1	no	—
381	C₂×D₄×C₂₃	—	2	2	no	—
382	C₂×D₄×C₂₃	—	2	2	no	—
383	C₂×D₄×C₂₃	—	2	2	no	—
384	C₂×D₄×C₂₃	—	2	2	no	—
385	C₂×D₄×C₂₃	—	2	1	no	—
386	C₂×D₄×C₂₃	—	2	1	no	—
387	C₂×D₄×C₂₃	—	2	1	no	—
388	C₂×D₄×C₂₃	—	2	1	no	—
389	C₂×D₄×C₂₃	—	2	1	no	—
390	C₂×D₄×C₂₃	—	2	1	no	—
391	C₂×D₄×C₂₃	—	2	1	no	—
392	C₂×D₄×C₂₃	—	2	1	no	—
393	C₂×D₄×C₂₃	—	2	2	no	—
394	C₂×D₄×C₂₃	—	2	2	no	—
395	C₂×D₄×C₂₃	—	2	1	no	—
396	C₂×D₄×C₂₃	—	2	1	no	—
397	C₂×D₄×C₂₃	—	2	1	no	—
398	C₂×D₄×C₂₃	—	2	1	no	—
399	C₂×D₄×C₂₃	—	4	2	no	—
400	C₂×D₄×C₂₃	—	4	2	no	—
401	C₂×D₄×C₂₃	—	4	2	no	—
402	C₂×D₄×C₂₃	—	4	2	no	—
403	C₂×D₄×C₂₃	—	4	2	no	—
404	C₂×D₄×C₂₃	—	4	2	no	—
405	C₂×D₄×C₂₃	—	4	4	no	—
406	C₂×D₄×C₂₃	—	4	4	no	—
407	C₂×D₄×C₂₃	—	4	4	no	—
408	C₂×D₄×C₂₃	—	4	4	no	—
409	C₂×D₄×C₂₃	—	4	4	no	—
410	C₂×D₄×C₂₃	—	8	2	no	—
411	C₂×D₄×C₂₃	—	8	2	no	—
412	C₂×D₄×C₂₃	—	8	2	no	—
413	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
414	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
415	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
416	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
417	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
418	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
419	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
420	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
421	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
422	C₂²×C₄×C₂₃	—	2	1	no	—
423	C₂²×C₄×C₂₃	—	2	1	no	—
424	C₂²×C₄×C₂₃	—	2	1	no	—
425	C₂²×C₄×C₂₃	—	2	1	no	—
426	C₂²×C₄×C₂₃	—	2	2	no	—
427	C₂²×C₄×C₂₃	—	2	2	no	—
428	C₂²×C₄×C₂₃	—	2	1	no	—
429	C₂²×C₄×C₂₃	—	2	2	no	—
430	C₂²×C₄×C₂₃	—	2	2	no	—
431	C₂²×C₄×C₂₃	—	2	1	no	—
432	C₂²×C₄×C₂₃	—	2	1	no	—
433	C₂²×C₄×C₂₃	—	2	1	no	—
434	C₂²×C₄×C₂₃	—	2	1	no	—
435	C₂²×C₄×C₂₃	—	4	2	no	—
436	C₂²×C₄×C₂₃	—	4	2	no	—
437	C₂²×C₄×C₂₃	—	4	4	no	—
438	C₂²×C₄×C₂₃	—	8	2	no	—
439	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
440	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
441	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
442	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
443	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
444	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
445	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
446	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
447	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	Q₁₆×C₂₃	—	4	2	no	—
453	SD₁₆×C₂₃	—	2	4	no	—
454	SD₁₆×C₂₃	—	4	2	no	—
455	SD₁₆×C₂₃	—	4	2	no	—
456	SD₁₆×C₂₃	—	4	2	no	—
457	SD₁₆×C₂₃	—	4	2	no	—
458	D₈×C₂₃	—	2	4	no	—
459	D₈×C₂₃	—	2	4	no	—
460	D₈×C₂₃	—	2	4	no	—
461	D₈×C₂₃	—	4	2	no	—
462	D₈×C₂₃	—	4	2	no	—
463	D₈×C₂₃	—	4	2	no	—
464	M₁₆×C₂₃	—	4	2	no	—
465	M₁₆×C₂₃	—	4	2	no	—
466	C₂×C₈×C₂₃	—	4	2	no	—
467	C₂×C₈×C₂₃	—	4	2	no	—
468	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
469	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
470	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
471	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
472	C₄⋊C₄×C₂₃	—	2	2	no	—
473	C₄⋊C₄×C₂₃	—	2	2	no	—
474	C₄⋊C₄×C₂₃	—	2	1	no	—
475	C₄⋊C₄×C₂₃	—	2	1	no	—
476	C₄⋊C₄×C₂₃	—	2	1	no	—
477	C₄⋊C₄×C₂₃	—	2	1	no	—
478	C₄⋊C₄×C₂₃	—	2	1	no	—
479	C₄⋊C₄×C₂₃	—	2	1	no	—
480	C₄⋊C₄×C₂₃	—	2	1	no	—
481	C₄⋊C₄×C₂₃	—	2	1	no	—
482	C₄⋊C₄×C₂₃	—	2	1	no	—
483	C₄⋊C₄×C₂₃	—	2	1	no	—
484	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
485	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
486	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
487	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
488	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
489	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
490	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
491	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
492	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
493	C₂²⋊C₄×C₂₃	—	2	2	no	—
494	C₂²⋊C₄×C₂₃	—	2	2	no	—
495	C₂²⋊C₄×C₂₃	—	2	1	no	—
496	C₂²⋊C₄×C₂₃	—	2	1	no	—
497	C₂²⋊C₄×C₂₃	—	2	1	no	—
498	C₂²⋊C₄×C₂₃	—	2	1	no	—
499	C₂²⋊C₄×C₂₃	—	2	1	no	—
500	C₂²⋊C₄×C₂₃	—	2	2	no	—
501	C₂²⋊C₄×C₂₃	—	2	2	no	—
502	C₂²⋊C₄×C₂₃	—	2	2	no	—
503	C₂²⋊C₄×C₂₃	—	2	2	no	—
504	C₂²⋊C₄×C₂₃	—	2	1	no	—
505	C₂²⋊C₄×C₂₃	—	2	1	no	—
506	C₂²⋊C₄×C₂₃	—	2	1	no	—
507	C₂²⋊C₄×C₂₃	—	2	1	no	—
508	C₂²⋊C₄×C₂₃	—	2	1	no	—
509	C₂²⋊C₄×C₂₃	—	2	1	no	—
510	C₂²⋊C₄×C₂₃	—	2	1	no	—
511	C₂²⋊C₄×C₂₃	—	2	1	no	—
512	C₂²⋊C₄×C₂₃	—	2	2	no	—
513	C₂²⋊C₄×C₂₃	—	2	2	no	—
514	C₂²⋊C₄×C₂₃	—	2	2	no	—
515	C₂²⋊C₄×C₂₃	—	2	2	no	—
516	C₂²⋊C₄×C₂₃	—	2	1	no	—
517	C₂²⋊C₄×C₂₃	—	2	1	no	—
518	C₂²⋊C₄×C₂₃	—	2	1	no	—
519	C₂²⋊C₄×C₂₃	—	2	1	no	—
520	C₂²⋊C₄×C₂₃	—	2	1	no	—
521	C₂²⋊C₄×C₂₃	—	2	1	no	—
522	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
523	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
524	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
525	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
526	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
527	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
528	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
529	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
530	C₄²×C₂₃	—	2	1	no	—
531	C₄²×C₂₃	—	2	1	no	—
532	C₄²×C₂₃	—	2	1	no	—
533	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
534	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
535	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
536	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
537	#61592	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
538	C₂³×C₂₃	—	2	4	no	—
539	C₂³×C₂₃	—	2	2	no	—
540	C₂³×C₂₃	—	2	2	no	—
541	C₂³×C₂₃	—	2	2	no	—
542	C₂³×C₂₃	—	2	2	no	—
543	C₂³×C₂₃	—	2	1	no	—
544	C₂³×C₂₃	—	2	2	no	—
545	C₂³×C₂₃	—	2	1	no	—
546	C₂³×C₂₃	—	2	1	no	—
547	C₂³×C₂₃	—	4	1	no	—
548	C₂³×C₂₃	—	4	1	no	—
549	C₂³×C₂₃	—	4	1	no	—
550	C₂³×C₂₃	—	4	4	no	—
551	C₂³×C₂₃	—	4	4	no	—
552	C₂³×C₂₃	—	4	2	no	—
553	C₂³×C₂₃	—	4	2	no	—
554	C₂³×C₂₃	—	4	2	no	—
555	C₂³×C₂₃	—	4	4	no	—
556	C₂³×C₂₃	—	4	2	no	—
557	C₂³×C₂₃	—	4	2	no	—
558	C₂³×C₂₃	—	4	4	no	—
559	C₂³×C₂₃	—	4	2	no	—
560	C₂³×C₂₃	—	4	2	no	—
561	C₂³×C₂₃	—	8	2	no	—
562	C₂³×C₂₃	—	8	2	no	—
563	C₂³×C₂₃	—	8	1	no	—
564	C₂³×C₂₃	—	8	1	no	—
565	C₂³×C₂₃	—	8	1	no	—
566	C₂³×C₂₃	—	8	1	no	—
567	C₂³×C₂₃	—	8	16	no	—
568	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
569	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
570	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
571	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
572	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
573	Q₈×C₂₃	—	2	2	no	—
574	Q₈×C₂₃	—	2	2	no	—
575	Q₈×C₂₃	—	2	2	no	—
576	Q₈×C₂₃	—	4	2	no	—
577	Q₈×C₂₃	—	8	1	no	—
578	D₄×C₂₃	—	2	4	no	—
579	D₄×C₂₃	—	2	2	no	—
580	D₄×C₂₃	—	2	2	no	—
581	D₄×C₂₃	—	2	2	no	—
582	D₄×C₂₃	—	2	2	no	—
583	D₄×C₂₃	—	2	2	no	—
584	D₄×C₂₃	—	2	2	no	—
585	D₄×C₂₃	—	2	2	no	—
586	D₄×C₂₃	—	2	2	no	—
587	D₄×C₂₃	—	4	1	no	—
588	D₄×C₂₃	—	4	1	no	—
589	D₄×C₂₃	—	4	4	no	—
590	D₄×C₂₃	—	4	4	no	—
591	D₄×C₂₃	—	4	2	no	—
592	D₄×C₂₃	—	4	2	no	—
593	D₄×C₂₃	—	4	4	no	—
594	D₄×C₂₃	—	4	4	no	—
595	D₄×C₂₃	—	4	2	no	—
596	D₄×C₂₃	—	4	2	no	—
597	D₄×C₂₃	—	4	2	no	—
598	D₄×C₂₃	—	4	2	no	—
599	D₄×C₂₃	—	4	2	no	—
600	D₄×C₂₃	—	8	1	no	—
601	D₄×C₂₃	—	8	1	no	—
602	D₄×C₂₃	—	8	1	no	—
603	D₄×C₂₃	—	8	2	no	—
604	D₄×C₂₃	—	8	2	no	—
605	D₄×C₂₃	—	8	1	no	—
606	D₄×C₂₃	—	8	1	no	—
607	D₄×C₂₃	—	8	1	no	—
608	D₄×C₂₃	—	8	1	no	—
609	D₄×C₂₃	—	8	1	no	—
610	D₄×C₂₃	—	8	1	no	—
611	D₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
612	C₂×C₄×C₂₃	—	2	2	no	—
613	C₂×C₄×C₂₃	—	2	2	no	—
614	C₂×C₄×C₂₃	—	2	2	no	—
615	C₂×C₄×C₂₃	—	2	2	no	—
616	C₂×C₄×C₂₃	—	2	2	no	—
617	C₂×C₄×C₂₃	—	2	2	no	—
618	C₂×C₄×C₂₃	—	2	1	no	—
619	C₂×C₄×C₂₃	—	2	1	no	—
620	C₂×C₄×C₂₃	—	2	1	no	—
621	C₂×C₄×C₂₃	—	2	1	no	—
622	C₂×C₄×C₂₃	—	2	1	no	—
623	C₂×C₄×C₂₃	—	2	2	no	—
624	C₂×C₄×C₂₃	—	2	2	no	—
625	C₂×C₄×C₂₃	—	4	1	no	—
626	C₂×C₄×C₂₃	—	4	1	no	—
627	C₂×C₄×C₂₃	—	4	1	no	—
628	C₂×C₄×C₂₃	—	4	1	no	—
629	C₂×C₄×C₂₃	—	4	1	no	—
630	C₂×C₄×C₂₃	—	4	1	no	—
631	C₂×C₄×C₂₃	—	4	1	no	—
632	C₂×C₄×C₂₃	—	4	4	no	—
633	C₂×C₄×C₂₃	—	4	4	no	—
634	C₂×C₄×C₂₃	—	4	2	no	—
635	C₂×C₄×C₂₃	—	4	2	no	—
636	C₂×C₄×C₂₃	—	4	2	no	—
637	C₂×C₄×C₂₃	—	8	2	no	—
638	C₂×C₄×C₂₃	—	8	2	no	—
639	C₂×C₄×C₂₃	—	8	1	no	—
640	C₂×C₄×C₂₃	—	8	1	no	—
641	C₂×C₄×C₂₃	—	8	1	no	—
642	C₂×C₄×C₂₃	—	8	1	no	—
643	C₂×C₄×C₂₃	—	8	1	no	—
644	C₂×C₄×C₂₃	—	8	1	no	—
645	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
649	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
650	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
651	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
652	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
653	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
654	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
655	C₈×C₂₃	—	2	2	no	—
656	C₈×C₂₃	—	2	2	no	—
657	C₈×C₂₃	—	2	2	no	—
658	C₈×C₂₃	—	2	2	no	—
659	#3519	C₂×C₂₃	1	1	yes	characteristic, complemented
660	C₂×#546	C₂×C₂₃	1	1	yes	characteristic, complemented
661	#3322	C₂×C₂₃	1	2	yes	complemented
662	#3319	C₂×C₂₃	1	2	yes	complemented
663	#3314	C₂×C₂₃	1	2	yes	complemented
664	#3297	C₂×C₂₃	1	2	yes	complemented
665	#3280	C₂×C₂₃	1	2	yes	complemented
666	#3273	C₂×C₂₃	1	2	yes	complemented
667	#3268	C₂×C₂₃	1	2	yes	complemented
668	#3264	C₂×C₂₃	1	2	yes	complemented
669	#3213	C₂×C₂₃	1	1	yes	characteristic, complemented
670	#3211	C₂×C₂₃	1	1	yes	characteristic, complemented
671	#3194	C₂×C₂₃	1	1	yes	characteristic, complemented
672	#3193	C₂×C₂₃	1	1	yes	characteristic, complemented
673	#3190	C₂×C₂₃	1	1	yes	characteristic, complemented
674	#3186	C₂×C₂₃	1	1	yes	characteristic, complemented
675	#3114	C₂×C₂₃	1	1	yes	characteristic, complemented
676	#3100	C₂×C₂₃	1	1	yes	characteristic, complemented
677	#3006	C₂×C₂₃	1	1	yes	characteristic, complemented
678	#3003	C₂×C₂₃	1	1	yes	characteristic, complemented
679	#3002	C₂×C₂₃	1	1	yes	characteristic, complemented
680	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
681	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
682	C₂²×C₂₃	—	2	1	no	—
683	C₂²×C₂₃	—	2	1	no	—
684	C₂²×C₂₃	—	2	1	no	—
685	C₂²×C₂₃	—	2	1	no	—
686	C₂²×C₂₃	—	2	1	no	—
687	C₂²×C₂₃	—	2	1	no	—
688	C₂²×C₂₃	—	2	1	no	—
689	C₂²×C₂₃	—	2	4	no	—
690	C₂²×C₂₃	—	2	1	no	—
691	C₂²×C₂₃	—	2	1	no	—
692	C₂²×C₂₃	—	2	1	no	—
693	C₂²×C₂₃	—	2	1	no	—
694	C₂²×C₂₃	—	2	1	no	—
695	C₂²×C₂₃	—	2	1	no	—
696	C₂²×C₂₃	—	4	4	no	—
697	C₂²×C₂₃	—	4	8	no	—
698	C₂²×C₂₃	—	4	2	no	—
699	C₂²×C₂₃	—	4	2	no	—
700	C₂²×C₂₃	—	4	1	no	—
701	C₂²×C₂₃	—	4	1	no	—
702	C₂²×C₂₃	—	4	2	no	—
703	C₂²×C₂₃	—	4	1	no	—
704	C₂²×C₂₃	—	4	1	no	—
705	C₂²×C₂₃	—	4	1	no	—
706	C₂²×C₂₃	—	4	1	no	—
707	C₂²×C₂₃	—	4	2	no	—
708	C₂²×C₂₃	—	4	1	no	—
709	C₂²×C₂₃	—	4	1	no	—
710	C₂²×C₂₃	—	4	1	no	—
711	C₂²×C₂₃	—	4	2	no	—
712	C₂²×C₂₃	—	8	2	no	—
713	C₂²×C₂₃	—	8	8	no	—
714	C₂²×C₂₃	—	8	4	no	—
715	C₂²×C₂₃	—	8	8	no	—
716	C₂²×C₂₃	—	16	2	no	—
717	C₂²×C₂₃	—	16	2	no	—
718	C₂²×C₂₃	#575	1	2	yes	—
719	C₂²×C₂₃	#576	1	2	yes	—
720	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
721	C₄×C₂₃	—	2	1	no	—
722	C₄×C₂₃	—	2	1	no	—
723	C₄×C₂₃	—	2	1	no	—
724	C₄×C₂₃	—	2	1	no	—
725	C₄×C₂₃	—	2	1	no	—
726	C₄×C₂₃	—	2	1	no	—
727	C₄×C₂₃	—	2	1	no	—
728	C₄×C₂₃	—	2	1	no	—
729	C₄×C₂₃	—	2	1	no	—
730	C₄×C₂₃	—	4	2	no	—
731	C₄×C₂₃	—	4	1	no	—
732	C₄×C₂₃	—	4	1	no	—
733	C₄×C₂₃	—	4	2	no	—
734	C₄×C₂₃	—	4	1	no	—
735	C₄×C₂₃	—	4	1	no	—
736	C₄×C₂₃	—	4	1	no	—
737	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
738	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
739	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
740	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
741	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
742	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
743	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
744	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
745	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
746	#553	—	2	1	no	—
747	#553	C₂²×C₂₃	1	1	yes	characteristic, complemented
748	#553	C₂²×C₂₃	1	1	yes	characteristic, complemented
749	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
750	#546	—	2	1	no	—
751	#546	—	2	1	no	—
752	#546	—	2	1	no	—
753	#546	—	2	1	no	—
754	#546	—	2	1	no	—
755	#546	—	2	1	no	—
756	#546	C₂²×C₂₃	1	2	yes	—
757	#546	C₂²×C₂₃	1	2	yes	complemented
758	#546	C₂²×C₂₃	1	2	yes	complemented
759	#546	C₂²×C₂₃	1	2	yes	complemented
760	#546	C₂²×C₂₃	1	1	yes	characteristic, complemented
761	#546	C₂²×C₂₃	1	1	yes	characteristic, complemented
762	D₄²	—	2	1	no	—
763	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
764	#540	—	2	1	no	—
765	#538	—	2	1	no	—
766	#538	—	2	1	no	—
767	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
768	#529	C₂²×C₂₃	1	1	yes	characteristic, complemented
769	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
770	#525	C₂²×C₂₃	1	1	yes	characteristic
771	#525	C₂²×C₂₃	1	1	yes	characteristic, complemented
772	C₂×#123	—	2	1	no	—
773	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
774	C₂×#121	—	2	1	no	—
775	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
776	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
777	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
778	C₂×#120	—	2	1	no	—
779	#518	—	2	1	no	—
780	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
781	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
782	C₂²×C₂²⋊C₄	—	2	1	no	—
783	#496	C₂²×C₂₃	1	2	yes	complemented
784	#495	C₂²×C₂₃	1	2	yes	complemented
785	#489	C₂²×C₂₃	1	2	yes	complemented
786	#488	C₂²×C₂₃	1	2	yes	complemented
787	#485	C₂²×C₂₃	1	2	yes	complemented
788	#484	C₂²×C₂₃	1	2	yes	complemented
789	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
790	#482	C₂²×C₂₃	1	2	yes	complemented
791	#480	C₂²×C₂₃	1	1	yes	characteristic, complemented
792	#480	C₂²×C₂₃	1	1	yes	characteristic, complemented
793	#480	C₂²×C₂₃	1	1	yes	characteristic, complemented
794	#480	C₂²×C₂₃	1	2	yes	complemented
795	#478	C₂²×C₂₃	1	2	yes	complemented
796	#474	C₂²×C₂₃	1	2	yes	complemented
797	#469	C₂²×C₂₃	1	2	yes	complemented
798	#468	C₂²×C₂₃	1	2	yes	complemented
799	#468	C₂²×C₂₃	1	2	yes	complemented
800	#468	C₂²×C₂₃	1	2	yes	complemented
801	#467	C₂²×C₂₃	1	2	yes	complemented
802	#466	C₂²×C₂₃	1	2	yes	complemented
803	#466	C₂²×C₂₃	1	2	yes	complemented
804	#465	C₂²×C₂₃	1	2	yes	complemented
805	#464	C₂²×C₂₃	1	2	yes	complemented
806	#463	C₂²×C₂₃	1	2	yes	complemented
807	#463	C₂²×C₂₃	1	2	yes	complemented
808	#463	C₂²×C₂₃	1	2	yes	complemented
809	#463	C₂²×C₂₃	1	2	yes	complemented
810	#459	C₂²×C₂₃	1	2	yes	complemented
811	#452	C₂²×C₂₃	1	2	yes	complemented
812	#452	C₂²×C₂₃	1	2	yes	complemented
813	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
814	#450	C₂²×C₂₃	1	1	yes	characteristic, complemented
815	#450	C₂²×C₂₃	1	1	yes	characteristic, complemented
816	#450	C₂²×C₂₃	1	2	yes	complemented
817	#450	C₂²×C₂₃	1	2	yes	complemented
818	#449	C₂²×C₂₃	1	2	yes	complemented
819	#449	C₂²×C₂₃	1	2	yes	complemented
820	#449	C₂²×C₂₃	1	2	yes	complemented
821	#449	C₂²×C₂₃	1	2	yes	complemented
822	#448	C₂²×C₂₃	1	1	yes	characteristic, complemented
823	#448	C₂²×C₂₃	1	1	yes	characteristic, complemented
824	#448	C₂²×C₂₃	1	1	yes	characteristic, complemented
825	#447	C₂²×C₂₃	1	1	yes	characteristic
826	#447	C₂²×C₂₃	1	1	yes	characteristic
827	#447	C₂²×C₂₃	1	1	yes	characteristic, complemented
828	#447	C₂²×C₂₃	1	1	yes	characteristic, complemented
829	#447	C₂²×C₂₃	1	1	yes	characteristic, complemented
830	#447	C₂²×C₂₃	1	1	yes	characteristic, complemented
831	#447	C₂²×C₂₃	1	2	yes	complemented
832	#447	C₂²×C₂₃	1	2	yes	complemented
833	#447	C₂²×C₂₃	1	2	yes	complemented
834	#447	C₂²×C₂₃	1	2	yes	complemented
835	#442	C₂²×C₂₃	1	2	yes	complemented
836	#440	C₂²×C₂₃	1	2	yes	complemented
837	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
838	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
839	#436	C₂²×C₂₃	1	2	yes	complemented
840	#435	C₂²×C₂₃	1	2	yes	complemented
841	#435	C₂²×C₂₃	1	2	yes	complemented
842	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
843	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
844	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
845	#418	C₂²×C₂₃	1	2	yes	complemented
846	#417	C₂²×C₂₃	1	2	yes	complemented
847	#416	C₂²×C₂₃	1	2	yes	complemented
848	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
849	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
850	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
851	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
852	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
853	C₂×C₂₃	—	2	2	no	—
854	C₂×C₂₃	—	2	2	no	—
855	C₂×C₂₃	—	4	1	no	—
856	C₂×C₂₃	—	4	1	no	—
857	C₂×C₂₃	—	4	1	no	—
858	C₂×C₂₃	—	4	4	no	—
859	C₂×C₂₃	—	8	2	no	—
860	C₂×C₂₃	—	8	1	no	—
861	C₂×C₂₃	—	8	1	no	—
862	C₂×C₂₃	—	8	1	no	—
863	C₂×C₂₃	#3484	1	1	yes	characteristic
864	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
865	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
866	C₂⁵	—	2	1	no	—
867	C₂×#41	—	2	1	no	—
868	C₂×#41	—	2	1	no	—
869	C₂×#41	—	2	1	no	—
870	C₂×#41	—	4	4	no	—
871	C₂×#41	C₂³×C₂₃	1	2	yes	—
872	C₂×#41	C₂³×C₂₃	1	2	yes	—
873	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
874	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic, complemented
875	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
876	C₂²×D₄	—	2	1	no	—
877	C₂²×D₄	—	2	1	no	—
878	C₂²×D₄	—	2	1	no	—
879	C₂²×D₄	—	2	1	no	—
880	C₂²×D₄	—	2	1	no	—
881	C₂²×D₄	—	2	1	no	—
882	C₂²×D₄	—	2	1	no	—
883	C₂²×D₄	—	2	1	no	—
884	C₂²×D₄	—	4	4	no	—
885	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
886	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
887	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
888	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
889	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
890	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
891	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic, complemented
892	C₂³×C₄	—	2	1	no	—
893	C₂³×C₄	—	2	1	no	—
894	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
895	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
896	AGL(1,ℤ/8)	—	4	4	no	—
897	AGL(1,ℤ/8)	—	4	4	no	—
898	#135	—	4	4	no	—
899	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	complemented
900	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
901	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
902	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	complemented
903	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	complemented
904	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	complemented
905	C₂×D₈	—	4	4	no	—
906	C₂×D₈	C₂³×C₂₃	1	2	yes	—
907	C₂×D₈	C₂³×C₂₃	1	2	yes	—
908	C₂×D₈	C₂³×C₂₃	1	2	yes	—
909	C₂×D₈	C₂³×C₂₃	1	2	yes	—
910	C₂×D₈	C₂³×C₂₃	1	2	yes	—
911	C₂×D₈	C₂³×C₂₃	1	2	yes	—
912	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
913	C₂×M₁₆	C₂³×C₂₃	1	2	yes	complemented
914	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
915	C₂²×C₈	C₂³×C₂₃	1	2	yes	complemented
916	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
917	#127	—	2	1	no	—
918	#127	C₂³×C₂₃	1	1	yes	characteristic, complemented
919	#126	—	2	1	no	—
920	#126	—	2	1	no	—
921	#126	—	2	1	no	—
922	#125	—	2	1	no	—
923	#125	C₂³×C₂₃	1	1	yes	characteristic, complemented
924	#124	—	2	1	no	—
925	#124	—	2	1	no	—
926	#124	—	2	1	no	—
927	#124	—	2	1	no	—
928	#124	—	2	1	no	—
929	#124	C₂³×C₂₃	1	2	yes	—
930	#124	C₂³×C₂₃	1	2	yes	—
931	#124	C₂³×C₂₃	1	1	yes	characteristic, complemented
932	#123	—	2	1	no	—
933	#123	—	2	1	no	—
934	#123	—	2	1	no	—
935	#123	—	2	2	no	—
936	#123	—	2	2	no	—
937	#123	—	2	2	no	—
938	#123	—	2	2	no	—
939	#123	—	2	1	no	—
940	#123	—	2	1	no	—
941	#123	—	2	1	no	—
942	#123	—	2	1	no	—
943	C₂²⋊Q₈	—	2	1	no	—
944	C₂²⋊Q₈	—	2	1	no	—
945	C₂²⋊Q₈	—	2	1	no	—
946	C₂²⋊Q₈	—	2	1	no	—
947	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
948	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
949	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
950	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
951	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
952	#121	—	2	1	no	—
953	#121	—	2	1	no	—
954	#121	—	2	1	no	—
955	#121	—	2	1	no	—
956	#121	—	2	1	no	—
957	#121	—	2	1	no	—
958	#121	—	2	1	no	—
959	#121	—	2	1	no	—
960	#121	—	2	1	no	—
961	#121	—	2	1	no	—
962	#121	—	2	1	no	—
963	#121	—	2	2	no	—
964	#121	—	2	2	no	—
965	#121	—	2	2	no	—
966	#121	—	2	2	no	—
967	#121	—	2	1	no	—
968	#121	—	2	1	no	—
969	#121	—	2	1	no	—
970	#121	—	2	1	no	—
971	#121	C₂³×C₂₃	1	1	yes	characteristic
972	#121	C₂³×C₂₃	1	1	yes	characteristic
973	#121	C₂³×C₂₃	1	1	yes	characteristic
974	#121	C₂³×C₂₃	1	1	yes	characteristic
975	#121	C₂³×C₂₃	1	1	yes	characteristic
976	#121	C₂³×C₂₃	1	2	yes	—
977	#121	C₂³×C₂₃	1	2	yes	—
978	#121	C₂³×C₂₃	1	1	yes	characteristic
979	#121	C₂³×C₂₃	1	1	yes	characteristic, complemented
980	#121	C₂³×C₂₃	1	1	yes	characteristic, complemented
981	#121	C₂³×C₂₃	1	1	yes	characteristic, complemented
982	#120	—	2	1	no	—
983	#120	—	2	1	no	—
984	#120	—	2	2	no	—
985	#120	—	2	2	no	—
986	#120	—	2	2	no	—
987	#120	—	2	2	no	—
988	#120	—	2	1	no	—
989	#120	—	2	1	no	—
990	#120	—	2	1	no	—
991	#120	—	2	1	no	—
992	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
993	C₄×D₄	—	2	1	no	—
994	C₄×D₄	—	2	1	no	—
995	C₄×D₄	—	2	1	no	—
996	C₄×D₄	—	2	1	no	—
997	C₄×D₄	—	2	1	no	—
998	C₄×D₄	—	2	1	no	—
999	C₄×D₄	—	2	1	no	—
1000	C₄×D₄	—	2	1	no	—
1001	C₄×D₄	—	2	1	no	—
1002	C₄×D₄	—	2	1	no	—
1003	C₄×D₄	—	2	1	no	—
1004	C₄×D₄	—	2	1	no	—
1005	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
1006	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
1007	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
1008	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
1009	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1010	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1011	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1012	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1013	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1014	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1015	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic, complemented
1016	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic, complemented
1017	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic, complemented
1018	#117	—	2	1	no	—
1019	#117	—	2	1	no	—
1020	#117	C₂³×C₂₃	1	1	yes	characteristic
1021	#117	C₂³×C₂₃	1	1	yes	characteristic, complemented
1022	C₂×C₄⋊C₄	—	2	1	no	—
1023	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
1024	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1025	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1026	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic, complemented
1027	C₂×C₂²⋊C₄	—	2	1	no	—
1028	C₂×C₂²⋊C₄	—	2	1	no	—
1029	C₂×C₂²⋊C₄	—	2	1	no	—
1030	C₂×C₂²⋊C₄	—	2	1	no	—
1031	C₂×C₂²⋊C₄	—	2	1	no	—
1032	C₂×C₂²⋊C₄	—	2	1	no	—
1033	C₂×C₂²⋊C₄	—	2	1	no	—
1034	C₂×C₂²⋊C₄	—	2	2	no	—
1035	C₂×C₂²⋊C₄	—	2	2	no	—
1036	C₂×C₂²⋊C₄	—	2	2	no	—
1037	C₂×C₂²⋊C₄	—	2	2	no	—
1038	C₂×C₂²⋊C₄	—	2	1	no	—
1039	C₂×C₂²⋊C₄	—	2	1	no	—
1040	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
1042	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1043	#107	C₂³×C₂₃	1	2	yes	complemented
1044	#107	C₂³×C₂₃	1	2	yes	complemented
1045	#107	C₂³×C₂₃	1	2	yes	complemented
1046	#106	C₂³×C₂₃	1	2	yes	complemented
1047	C₄⋊C₈	C₂³×C₂₃	1	2	yes	complemented
1048	C₄⋊C₈	C₂³×C₂₃	1	2	yes	complemented
1049	#103	C₂³×C₂₃	1	2	yes	complemented
1050	#103	C₂³×C₂₃	1	2	yes	complemented
1051	#103	C₂³×C₂₃	1	2	yes	complemented
1052	#103	C₂³×C₂₃	1	2	yes	complemented
1053	#103	C₂³×C₂₃	1	2	yes	complemented
1054	#102	C₂³×C₂₃	1	2	yes	—
1055	#102	C₂³×C₂₃	1	2	yes	—
1056	#102	C₂³×C₂₃	1	2	yes	—
1057	#102	C₂³×C₂₃	1	2	yes	—
1058	#102	C₂³×C₂₃	1	2	yes	—
1059	#102	C₂³×C₂₃	1	2	yes	—
1060	#102	C₂³×C₂₃	1	2	yes	—
1061	#102	C₂³×C₂₃	1	2	yes	—
1062	#102	C₂³×C₂₃	1	2	yes	complemented
1063	#102	C₂³×C₂₃	1	2	yes	complemented
1064	#102	C₂³×C₂₃	1	2	yes	complemented
1065	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1066	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1067	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1068	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1069	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1070	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1071	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	complemented
1072	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	complemented
1073	#97	C₂³×C₂₃	1	2	yes	complemented
1074	C₄×C₈	C₂³×C₂₃	1	2	yes	complemented
1075	C₂₃	#61592	1	1	yes	characteristic, direct product factor, Sylow
1076	C₂⁴	—	2	1	no	—
1077	C₂⁴	—	2	1	no	—
1078	C₂⁴	—	2	2	no	—
1079	C₂⁴	—	2	2	no	—
1080	C₂⁴	—	2	1	no	—
1081	C₂⁴	—	2	1	no	—
1082	C₂⁴	—	4	4	no	—
1083	C₂⁴	—	4	4	no	—
1084	C₂⁴	—	8	2	no	—
1085	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
1086	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
1087	#41	—	2	4	no	—
1088	#41	—	2	4	no	—
1089	#41	—	4	2	no	—
1090	#41	—	4	2	no	—
1091	#41	—	4	2	no	—
1092	#41	—	4	2	no	—
1093	#41	—	4	4	no	—
1094	#41	—	4	4	no	—
1095	#41	—	8	2	no	—
1096	C₂×Q₈	—	2	1	no	—
1097	C₂×Q₈	—	2	1	no	—
1098	C₂×Q₈	—	4	2	no	—
1099	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1100	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1101	C₂×D₄	—	2	4	no	—
1102	C₂×D₄	—	2	4	no	—
1103	C₂×D₄	—	2	4	no	—
1104	C₂×D₄	—	2	1	no	—
1105	C₂×D₄	—	2	1	no	—
1106	C₂×D₄	—	2	1	no	—
1107	C₂×D₄	—	2	1	no	—
1108	C₂×D₄	—	2	1	no	—
1109	C₂×D₄	—	2	2	no	—
1110	C₂×D₄	—	2	2	no	—
1111	C₂×D₄	—	2	2	no	—
1112	C₂×D₄	—	2	2	no	—
1113	C₂×D₄	—	2	1	no	—
1114	C₂×D₄	—	2	1	no	—
1115	C₂×D₄	—	2	1	no	—
1116	C₂×D₄	—	2	1	no	—
1117	C₂×D₄	—	2	1	no	—
1118	C₂×D₄	—	2	1	no	—
1119	C₂×D₄	—	2	1	no	—
1120	C₂×D₄	—	2	1	no	—
1121	C₂×D₄	—	2	2	no	—
1122	C₂×D₄	—	2	2	no	—
1123	C₂×D₄	—	2	1	no	—
1124	C₂×D₄	—	2	1	no	—
1125	C₂×D₄	—	2	1	no	—
1126	C₂×D₄	—	2	1	no	—
1127	C₂×D₄	—	4	2	no	—
1128	C₂×D₄	—	4	2	no	—
1129	C₂×D₄	—	4	2	no	—
1130	C₂×D₄	—	4	2	no	—
1131	C₂×D₄	—	4	2	no	—
1132	C₂×D₄	—	4	2	no	—
1133	C₂×D₄	—	4	4	no	—
1134	C₂×D₄	—	4	4	no	—
1135	C₂×D₄	—	4	4	no	—
1136	C₂×D₄	—	4	4	no	—
1137	C₂×D₄	—	4	4	no	—
1138	C₂×D₄	—	8	2	no	—
1139	C₂×D₄	—	8	2	no	—
1140	C₂×D₄	—	8	2	no	—
1141	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1142	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1143	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1144	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1145	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1146	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1147	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1148	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1149	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1150	C₂²×C₄	—	2	1	no	—
1151	C₂²×C₄	—	2	1	no	—
1152	C₂²×C₄	—	2	1	no	—
1153	C₂²×C₄	—	2	1	no	—
1154	C₂²×C₄	—	2	2	no	—
1155	C₂²×C₄	—	2	2	no	—
1156	C₂²×C₄	—	2	1	no	—
1157	C₂²×C₄	—	2	2	no	—
1158	C₂²×C₄	—	2	2	no	—
1159	C₂²×C₄	—	2	1	no	—
1160	C₂²×C₄	—	2	1	no	—
1161	C₂²×C₄	—	2	1	no	—
1162	C₂²×C₄	—	2	1	no	—
1163	C₂²×C₄	—	4	2	no	—
1164	C₂²×C₄	—	4	2	no	—
1165	C₂²×C₄	—	4	4	no	—
1166	C₂²×C₄	—	8	2	no	—
1167	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1168	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1169	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1170	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1171	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1172	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1173	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1174	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1175	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1176	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1177	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1178	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1179	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1180	Q₁₆	—	4	2	no	—
1181	SD₁₆	—	2	4	no	—
1182	SD₁₆	—	4	2	no	—
1183	SD₁₆	—	4	2	no	—
1184	SD₁₆	—	4	2	no	—
1185	SD₁₆	—	4	2	no	—
1186	D₈	—	2	4	no	—
1187	D₈	—	2	4	no	—
1188	D₈	—	2	4	no	—
1189	D₈	—	4	2	no	—
1190	D₈	—	4	2	no	—
1191	D₈	—	4	2	no	—
1192	M₁₆	—	4	2	no	—
1193	M₁₆	—	4	2	no	—
1194	C₂×C₈	—	4	2	no	—
1195	C₂×C₈	—	4	2	no	—
1196	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1197	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1198	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1199	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1200	C₄⋊C₄	—	2	2	no	—
1201	C₄⋊C₄	—	2	2	no	—
1202	C₄⋊C₄	—	2	1	no	—
1203	C₄⋊C₄	—	2	1	no	—
1204	C₄⋊C₄	—	2	1	no	—
1205	C₄⋊C₄	—	2	1	no	—
1206	C₄⋊C₄	—	2	1	no	—
1207	C₄⋊C₄	—	2	1	no	—
1208	C₄⋊C₄	—	2	1	no	—
1209	C₄⋊C₄	—	2	1	no	—
1210	C₄⋊C₄	—	2	1	no	—
1211	C₄⋊C₄	—	2	1	no	—
1212	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1213	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1214	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1215	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1216	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1217	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1218	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1219	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1220	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1221	C₂²⋊C₄	—	2	2	no	—
1222	C₂²⋊C₄	—	2	2	no	—
1223	C₂²⋊C₄	—	2	1	no	—
1224	C₂²⋊C₄	—	2	1	no	—
1225	C₂²⋊C₄	—	2	1	no	—
1226	C₂²⋊C₄	—	2	1	no	—
1227	C₂²⋊C₄	—	2	1	no	—
1228	C₂²⋊C₄	—	2	2	no	—
1229	C₂²⋊C₄	—	2	2	no	—
1230	C₂²⋊C₄	—	2	2	no	—
1231	C₂²⋊C₄	—	2	2	no	—
1232	C₂²⋊C₄	—	2	1	no	—
1233	C₂²⋊C₄	—	2	1	no	—
1234	C₂²⋊C₄	—	2	1	no	—
1235	C₂²⋊C₄	—	2	1	no	—
1236	C₂²⋊C₄	—	2	1	no	—
1237	C₂²⋊C₄	—	2	1	no	—
1238	C₂²⋊C₄	—	2	1	no	—
1239	C₂²⋊C₄	—	2	1	no	—
1240	C₂²⋊C₄	—	2	2	no	—
1241	C₂²⋊C₄	—	2	2	no	—
1242	C₂²⋊C₄	—	2	2	no	—
1243	C₂²⋊C₄	—	2	2	no	—
1244	C₂²⋊C₄	—	2	1	no	—
1245	C₂²⋊C₄	—	2	1	no	—
1246	C₂²⋊C₄	—	2	1	no	—
1247	C₂²⋊C₄	—	2	1	no	—
1248	C₂²⋊C₄	—	2	1	no	—
1249	C₂²⋊C₄	—	2	1	no	—
1250	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1251	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1252	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1253	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1254	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1255	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1256	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1257	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1258	C₄²	—	2	1	no	—
1259	C₄²	—	2	1	no	—
1260	C₄²	—	2	1	no	—
1261	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1262	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1263	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1264	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1265	C₂³	—	2	4	no	—
1266	C₂³	—	2	2	no	—
1267	C₂³	—	2	2	no	—
1268	C₂³	—	2	2	no	—
1269	C₂³	—	2	2	no	—
1270	C₂³	—	2	1	no	—
1271	C₂³	—	2	2	no	—
1272	C₂³	—	2	1	no	—
1273	C₂³	—	2	1	no	—
1274	C₂³	—	4	1	no	—
1275	C₂³	—	4	1	no	—
1276	C₂³	—	4	1	no	—
1277	C₂³	—	4	4	no	—
1278	C₂³	—	4	4	no	—
1279	C₂³	—	4	2	no	—
1280	C₂³	—	4	2	no	—
1281	C₂³	—	4	2	no	—
1282	C₂³	—	4	4	no	—
1283	C₂³	—	4	2	no	—
1284	C₂³	—	4	2	no	—
1285	C₂³	—	4	4	no	—
1286	C₂³	—	4	2	no	—
1287	C₂³	—	4	2	no	—
1288	C₂³	—	8	2	no	—
1289	C₂³	—	8	2	no	—
1290	C₂³	—	8	1	no	—
1291	C₂³	—	8	1	no	—
1292	C₂³	—	8	1	no	—
1293	C₂³	—	8	1	no	—
1294	C₂³	—	8	16	no	—
1295	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1296	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1297	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1298	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1299	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1300	Q₈	—	2	2	no	—
1301	Q₈	—	2	2	no	—
1302	Q₈	—	2	2	no	—
1303	Q₈	—	4	2	no	—
1304	Q₈	—	8	1	no	—
1305	D₄	—	2	4	no	—
1306	D₄	—	2	2	no	—
1307	D₄	—	2	2	no	—
1308	D₄	—	2	2	no	—
1309	D₄	—	2	2	no	—
1310	D₄	—	2	2	no	—
1311	D₄	—	2	2	no	—
1312	D₄	—	2	2	no	—
1313	D₄	—	2	2	no	—
1314	D₄	—	4	1	no	—
1315	D₄	—	4	1	no	—
1316	D₄	—	4	4	no	—
1317	D₄	—	4	4	no	—
1318	D₄	—	4	2	no	—
1319	D₄	—	4	2	no	—
1320	D₄	—	4	4	no	—
1321	D₄	—	4	4	no	—
1322	D₄	—	4	2	no	—
1323	D₄	—	4	2	no	—
1324	D₄	—	4	2	no	—
1325	D₄	—	4	2	no	—
1326	D₄	—	4	2	no	—
1327	D₄	—	8	1	no	—
1328	D₄	—	8	1	no	—
1329	D₄	—	8	1	no	—
1330	D₄	—	8	2	no	—
1331	D₄	—	8	2	no	—
1332	D₄	—	8	1	no	—
1333	D₄	—	8	1	no	—
1334	D₄	—	8	1	no	—
1335	D₄	—	8	1	no	—
1336	D₄	—	8	1	no	—
1337	D₄	—	8	1	no	—
1338	D₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
1339	C₂×C₄	—	2	2	no	—
1340	C₂×C₄	—	2	2	no	—
1341	C₂×C₄	—	2	2	no	—
1342	C₂×C₄	—	2	2	no	—
1343	C₂×C₄	—	2	2	no	—
1344	C₂×C₄	—	2	2	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	2	no	—
1351	C₂×C₄	—	2	2	no	—
1352	C₂×C₄	—	4	1	no	—
1353	C₂×C₄	—	4	1	no	—
1354	C₂×C₄	—	4	1	no	—
1355	C₂×C₄	—	4	1	no	—
1356	C₂×C₄	—	4	1	no	—
1357	C₂×C₄	—	4	1	no	—
1358	C₂×C₄	—	4	1	no	—
1359	C₂×C₄	—	4	4	no	—
1360	C₂×C₄	—	4	4	no	—
1361	C₂×C₄	—	4	2	no	—
1362	C₂×C₄	—	4	2	no	—
1363	C₂×C₄	—	4	2	no	—
1364	C₂×C₄	—	8	2	no	—
1365	C₂×C₄	—	8	2	no	—
1366	C₂×C₄	—	8	1	no	—
1367	C₂×C₄	—	8	1	no	—
1368	C₂×C₄	—	8	1	no	—
1369	C₂×C₄	—	8	1	no	—
1370	C₂×C₄	—	8	1	no	—
1371	C₂×C₄	—	8	1	no	—
1372	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1373	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1374	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1375	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1376	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1377	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1378	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1379	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1380	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1381	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1382	C₈	—	2	2	no	—
1383	C₈	—	2	2	no	—
1384	C₈	—	2	2	no	—
1385	C₈	—	2	2	no	—
1386	C₂²	—	2	1	no	—
1387	C₂²	—	2	1	no	—
1388	C₂²	—	2	1	no	—
1389	C₂²	—	2	1	no	—
1390	C₂²	—	2	1	no	—
1391	C₂²	—	2	1	no	—
1392	C₂²	—	2	1	no	—
1393	C₂²	—	2	4	no	—
1394	C₂²	—	2	1	no	—
1395	C₂²	—	2	1	no	—
1396	C₂²	—	2	1	no	—
1397	C₂²	—	2	1	no	—
1398	C₂²	—	2	1	no	—
1399	C₂²	—	2	1	no	—
1400	C₂²	—	4	4	no	—
1401	C₂²	—	4	8	no	—
1402	C₂²	—	4	2	no	—
1403	C₂²	—	4	2	no	—
1404	C₂²	—	4	1	no	—
1405	C₂²	—	4	1	no	—
1406	C₂²	—	4	2	no	—
1407	C₂²	—	4	1	no	—
1408	C₂²	—	4	1	no	—
1409	C₂²	—	4	1	no	—
1410	C₂²	—	4	1	no	—
1411	C₂²	—	4	2	no	—
1412	C₂²	—	4	1	no	—
1413	C₂²	—	4	1	no	—
1414	C₂²	—	4	1	no	—
1415	C₂²	—	4	2	no	—
1416	C₂²	—	8	2	no	—
1417	C₂²	—	8	8	no	—
1418	C₂²	—	8	4	no	—
1419	C₂²	—	8	8	no	—
1420	C₂²	—	16	2	no	—
1421	C₂²	—	16	2	no	—
1422	C₂²	C₂₃×#575	1	2	yes	—
1423	C₂²	C₂₃×#576	1	2	yes	—
1424	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1425	C₄	—	2	1	no	—
1426	C₄	—	2	1	no	—
1427	C₄	—	2	1	no	—
1428	C₄	—	2	1	no	—
1429	C₄	—	2	1	no	—
1430	C₄	—	2	1	no	—
1431	C₄	—	2	1	no	—
1432	C₄	—	2	1	no	—
1433	C₄	—	2	1	no	—
1434	C₄	—	4	2	no	—
1435	C₄	—	4	1	no	—
1436	C₄	—	4	1	no	—
1437	C₄	—	4	2	no	—
1438	C₄	—	4	1	no	—
1439	C₄	—	4	1	no	—
1440	C₄	—	4	1	no	—
1441	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1442	C₂	—	2	2	no	—
1443	C₂	—	2	2	no	—
1444	C₂	—	4	1	no	—
1445	C₂	—	4	1	no	—
1446	C₂	—	4	1	no	—
1447	C₂	—	4	4	no	—
1448	C₂	—	8	2	no	—
1449	C₂	—	8	1	no	—
1450	C₂	—	8	1	no	—
1451	C₂	—	8	1	no	—
1452	C₂	C₂₃×#3484	1	1	yes	characteristic
1453	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1454	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3519	C₂	semidirect
2. C₂×C₂₃×#546	C₂	semidirect
3. C₂₃×#3322	C₂	semidirect
4. C₂₃×#3319	C₂	semidirect
5. C₂₃×#3314	C₂	semidirect
6. C₂₃×#3297	C₂	semidirect
7. C₂₃×#3280	C₂	semidirect
8. C₂₃×#3273	C₂	semidirect
9. C₂₃×#3268	C₂	semidirect
10. C₂₃×#3264	C₂	semidirect
11. C₂₃×#3213	C₂	semidirect
12. C₂₃×#3211	C₂	semidirect
13. C₂₃×#3194	C₂	semidirect
14. C₂₃×#3193	C₂	semidirect
15. C₂₃×#3190	C₂	semidirect
16. C₂₃×#3186	C₂	semidirect
17. C₂₃×#3114	C₂	semidirect
18. C₂₃×#3100	C₂	semidirect
19. C₂₃×#3006	C₂	semidirect
20. C₂₃×#3003	C₂	semidirect
21. C₂₃×#3002	C₂	semidirect
22. C₂×C₂₃×#447	C₂	semidirect
23. C₂₃×#2974	C₂	semidirect
24. C₂²×#41×C₂₃	C₂²	semidirect
25. C₂³×D₄×C₂₃	C₂²	semidirect
26. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₂₃×#135	C₂²	semidirect
29. C₂²×D₈×C₂₃	C₂²	semidirect
30. C₂₃×#555	C₂²	semidirect
31. C₂₃×#554	C₂²	semidirect
33. C₂₃×#553	C₂²	semidirect
34. C₂₃×#553	C₂²	semidirect
35. C₂₃×#550	C₂²	semidirect
43. C₂₃×#546	C₂²	semidirect
44. C₂₃×#546	C₂²	semidirect
45. C₂₃×#546	C₂²	semidirect
46. C₂₃×#546	C₂²	semidirect
47. C₂₃×#546	C₂²	semidirect
49. D₄²×C₂₃	C₂²	semidirect
53. C₂₃×#532	C₂²	semidirect
54. C₂₃×#529	C₂²	semidirect
55. C₂×C₂₃×#124	C₂²	semidirect
57. C₂₃×#525	C₂²	semidirect
59. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₂₃×#121	C₂²	semidirect
63. C₂×C₂₃×#121	C₂²	semidirect
67. C₂×C₄×D₄×C₂₃	C₂²	semidirect
69. C₂₃×#496	C₂²	semidirect
70. C₂₃×#495	C₂²	semidirect
71. C₂₃×#489	C₂²	semidirect
72. C₂₃×#488	C₂²	semidirect
73. C₂₃×#485	C₂²	semidirect
74. C₂₃×#484	C₂²	semidirect
75. C₂₃×#483	C₂²	semidirect
76. C₂₃×#482	C₂²	semidirect
77. C₂₃×#480	C₂²	semidirect
78. C₂₃×#480	C₂²	semidirect
79. C₂₃×#480	C₂²	semidirect
80. C₂₃×#480	C₂²	semidirect
81. C₂₃×#478	C₂²	semidirect
82. C₂₃×#474	C₂²	semidirect
83. C₂₃×#469	C₂²	semidirect
84. C₂₃×#468	C₂²	semidirect
85. C₂₃×#468	C₂²	semidirect
86. C₂₃×#468	C₂²	semidirect
87. C₂₃×#467	C₂²	semidirect
88. C₂₃×#466	C₂²	semidirect
89. C₂₃×#466	C₂²	semidirect
90. C₂₃×#465	C₂²	semidirect
91. C₂₃×#464	C₂²	semidirect
92. C₂₃×#463	C₂²	semidirect
93. C₂₃×#463	C₂²	semidirect
94. C₂₃×#463	C₂²	semidirect
95. C₂₃×#463	C₂²	semidirect
96. C₂₃×#459	C₂²	semidirect
97. C₂₃×#452	C₂²	semidirect
98. C₂₃×#452	C₂²	semidirect
99. C₂₃×#451	C₂²	semidirect
100. C₂₃×#450	C₂²	semidirect
101. C₂₃×#450	C₂²	semidirect
102. C₂₃×#450	C₂²	semidirect
103. C₂₃×#450	C₂²	semidirect
104. C₂₃×#449	C₂²	semidirect
105. C₂₃×#449	C₂²	semidirect
106. C₂₃×#449	C₂²	semidirect
107. C₂₃×#449	C₂²	semidirect
108. C₂₃×#448	C₂²	semidirect
109. C₂₃×#448	C₂²	semidirect
110. C₂₃×#448	C₂²	semidirect
113. C₂₃×#447	C₂²	semidirect
114. C₂₃×#447	C₂²	semidirect
115. C₂₃×#447	C₂²	semidirect
116. C₂₃×#447	C₂²	semidirect
117. C₂₃×#447	C₂²	semidirect
118. C₂₃×#447	C₂²	semidirect
119. C₂₃×#447	C₂²	semidirect
120. C₂₃×#447	C₂²	semidirect
121. C₂₃×#442	C₂²	semidirect
122. C₂₃×#440	C₂²	semidirect
123. C₄×D₈×C₂₃	C₂²	semidirect
124. C₄×D₈×C₂₃	C₂²	semidirect
125. C₂₃×#436	C₂²	semidirect
126. C₂₃×#435	C₂²	semidirect
127. C₂₃×#435	C₂²	semidirect
128. C₈×D₄×C₂₃	C₂²	semidirect
129. C₂₃×#432	C₂²	semidirect
130. C₂₃×#431	C₂²	semidirect
131. C₂₃×#418	C₂²	semidirect
132. C₂₃×#417	C₂²	semidirect
133. C₂₃×#416	C₂²	semidirect
134. C₂×C₂₃×#102	C₂²	semidirect
135. C₂₃×#407	C₂²	semidirect
136. C₂₃×#407	C₂²	semidirect
137. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
138. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
147. C₂×#41×C₂₃	C₂³	semidirect
164. C₂²×D₄×C₂₃	C₂³	semidirect
172. C₂×Q₁₆×C₂₃	C₂³	semidirect
175. C₂×SD₁₆×C₂₃	C₂³	semidirect
176. C₂×SD₁₆×C₂₃	C₂³	semidirect
177. C₂×SD₁₆×C₂₃	C₂³	semidirect
186. C₂×M₁₆×C₂₃	C₂³	semidirect
188. C₂²×C₈×C₂₃	C₂³	semidirect
189. C₂₃×C₄⋊Q₈	C₂³	semidirect
191. C₂₃×#127	C₂³	semidirect
196. C₂₃×#125	C₂³	semidirect
204. C₂₃×#124	C₂³	semidirect
224. C₂₃×C₂²⋊Q₈	C₂³	semidirect
252. C₂₃×#121	C₂³	semidirect
253. C₂₃×#121	C₂³	semidirect
254. C₂₃×#121	C₂³	semidirect
265. C₄×Q₈×C₂₃	C₂³	semidirect
288. C₄×D₄×C₂₃	C₂³	semidirect
289. C₄×D₄×C₂₃	C₂³	semidirect
290. C₄×D₄×C₂₃	C₂³	semidirect
294. C₂₃×#117	C₂³	semidirect
299. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
316. C₂₃×#107	C₂³	semidirect
317. C₂₃×#107	C₂³	semidirect
318. C₂₃×#107	C₂³	semidirect
319. C₂₃×#106	C₂³	semidirect
320. C₂₃×C₄⋊C₈	C₂³	semidirect
321. C₂₃×C₄⋊C₈	C₂³	semidirect
322. C₂₃×#103	C₂³	semidirect
323. C₂₃×#103	C₂³	semidirect
324. C₂₃×#103	C₂³	semidirect
325. C₂₃×#103	C₂³	semidirect
326. C₂₃×#103	C₂³	semidirect
335. C₂₃×#102	C₂³	semidirect
336. C₂₃×#102	C₂³	semidirect
337. C₂₃×#102	C₂³	semidirect
344. C₂₃×C₂²⋊C₈	C₂³	semidirect
345. C₂₃×C₂²⋊C₈	C₂³	semidirect
346. C₂₃×#97	C₂³	semidirect
347. C₄×C₈×C₂₃	C₂³	semidirect
537. #61592	C₂₃	direct (N × H)
659. #3519	C₂×C₂₃	semidirect
660. C₂×#546	C₂×C₂₃	semidirect
661. #3322	C₂×C₂₃	semidirect
662. #3319	C₂×C₂₃	semidirect
663. #3314	C₂×C₂₃	semidirect
664. #3297	C₂×C₂₃	semidirect
665. #3280	C₂×C₂₃	semidirect
666. #3273	C₂×C₂₃	semidirect
667. #3268	C₂×C₂₃	semidirect
668. #3264	C₂×C₂₃	semidirect
669. #3213	C₂×C₂₃	semidirect
670. #3211	C₂×C₂₃	semidirect
671. #3194	C₂×C₂₃	semidirect
672. #3193	C₂×C₂₃	semidirect
673. #3190	C₂×C₂₃	semidirect
674. #3186	C₂×C₂₃	semidirect
675. #3114	C₂×C₂₃	semidirect
676. #3100	C₂×C₂₃	semidirect
677. #3006	C₂×C₂₃	semidirect
678. #3003	C₂×C₂₃	semidirect
679. #3002	C₂×C₂₃	semidirect
680. C₂×#447	C₂×C₂₃	semidirect
681. #2974	C₂×C₂₃	semidirect
738. C₂²×#41	C₂²×C₂₃	semidirect
739. C₂³×D₄	C₂²×C₂₃	semidirect
740. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
741. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
742. C₂×#135	C₂²×C₂₃	semidirect
743. C₂²×D₈	C₂²×C₂₃	semidirect
744. #555	C₂²×C₂₃	semidirect
745. #554	C₂²×C₂₃	semidirect
747. #553	C₂²×C₂₃	semidirect
748. #553	C₂²×C₂₃	semidirect
749. #550	C₂²×C₂₃	semidirect
757. #546	C₂²×C₂₃	semidirect
758. #546	C₂²×C₂₃	semidirect
759. #546	C₂²×C₂₃	semidirect
760. #546	C₂²×C₂₃	semidirect
761. #546	C₂²×C₂₃	semidirect
763. D₄²	C₂²×C₂₃	semidirect
767. #532	C₂²×C₂₃	semidirect
768. #529	C₂²×C₂₃	semidirect
769. C₂×#124	C₂²×C₂₃	semidirect
771. #525	C₂²×C₂₃	semidirect
773. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
776. C₂×#121	C₂²×C₂₃	semidirect
777. C₂×#121	C₂²×C₂₃	semidirect
781. C₂×C₄×D₄	C₂²×C₂₃	semidirect
783. #496	C₂²×C₂₃	semidirect
784. #495	C₂²×C₂₃	semidirect
785. #489	C₂²×C₂₃	semidirect
786. #488	C₂²×C₂₃	semidirect
787. #485	C₂²×C₂₃	semidirect
788. #484	C₂²×C₂₃	semidirect
789. #483	C₂²×C₂₃	semidirect
790. #482	C₂²×C₂₃	semidirect
791. #480	C₂²×C₂₃	semidirect
792. #480	C₂²×C₂₃	semidirect
793. #480	C₂²×C₂₃	semidirect
794. #480	C₂²×C₂₃	semidirect
795. #478	C₂²×C₂₃	semidirect
796. #474	C₂²×C₂₃	semidirect
797. #469	C₂²×C₂₃	semidirect
798. #468	C₂²×C₂₃	semidirect
799. #468	C₂²×C₂₃	semidirect
800. #468	C₂²×C₂₃	semidirect
801. #467	C₂²×C₂₃	semidirect
802. #466	C₂²×C₂₃	semidirect
803. #466	C₂²×C₂₃	semidirect
804. #465	C₂²×C₂₃	semidirect
805. #464	C₂²×C₂₃	semidirect
806. #463	C₂²×C₂₃	semidirect
807. #463	C₂²×C₂₃	semidirect
808. #463	C₂²×C₂₃	semidirect
809. #463	C₂²×C₂₃	semidirect
810. #459	C₂²×C₂₃	semidirect
811. #452	C₂²×C₂₃	semidirect
812. #452	C₂²×C₂₃	semidirect
813. #451	C₂²×C₂₃	semidirect
814. #450	C₂²×C₂₃	semidirect
815. #450	C₂²×C₂₃	semidirect
816. #450	C₂²×C₂₃	semidirect
817. #450	C₂²×C₂₃	semidirect
818. #449	C₂²×C₂₃	semidirect
819. #449	C₂²×C₂₃	semidirect
820. #449	C₂²×C₂₃	semidirect
821. #449	C₂²×C₂₃	semidirect
822. #448	C₂²×C₂₃	semidirect
823. #448	C₂²×C₂₃	semidirect
824. #448	C₂²×C₂₃	semidirect
827. #447	C₂²×C₂₃	semidirect
828. #447	C₂²×C₂₃	semidirect
829. #447	C₂²×C₂₃	semidirect
830. #447	C₂²×C₂₃	semidirect
831. #447	C₂²×C₂₃	semidirect
832. #447	C₂²×C₂₃	semidirect
833. #447	C₂²×C₂₃	semidirect
834. #447	C₂²×C₂₃	semidirect
835. #442	C₂²×C₂₃	semidirect
836. #440	C₂²×C₂₃	semidirect
837. C₄×D₈	C₂²×C₂₃	semidirect
838. C₄×D₈	C₂²×C₂₃	semidirect
839. #436	C₂²×C₂₃	semidirect
840. #435	C₂²×C₂₃	semidirect
841. #435	C₂²×C₂₃	semidirect
842. C₈×D₄	C₂²×C₂₃	semidirect
843. #432	C₂²×C₂₃	semidirect
844. #431	C₂²×C₂₃	semidirect
845. #418	C₂²×C₂₃	semidirect
846. #417	C₂²×C₂₃	semidirect
847. #416	C₂²×C₂₃	semidirect
848. C₂×#102	C₂²×C₂₃	semidirect
849. #407	C₂²×C₂₃	semidirect
850. #407	C₂²×C₂₃	semidirect
851. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
852. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
874. C₂×#41	C₂³×C₂₃	semidirect
891. C₂²×D₄	C₂³×C₂₃	semidirect
899. C₂×Q₁₆	C₂³×C₂₃	semidirect
902. C₂×SD₁₆	C₂³×C₂₃	semidirect
903. C₂×SD₁₆	C₂³×C₂₃	semidirect
904. C₂×SD₁₆	C₂³×C₂₃	semidirect
913. C₂×M₁₆	C₂³×C₂₃	semidirect
915. C₂²×C₈	C₂³×C₂₃	semidirect
916. C₄⋊Q₈	C₂³×C₂₃	semidirect
918. #127	C₂³×C₂₃	semidirect
923. #125	C₂³×C₂₃	semidirect
931. #124	C₂³×C₂₃	semidirect
951. C₂²⋊Q₈	C₂³×C₂₃	semidirect
979. #121	C₂³×C₂₃	semidirect
980. #121	C₂³×C₂₃	semidirect
981. #121	C₂³×C₂₃	semidirect
992. C₄×Q₈	C₂³×C₂₃	semidirect
1015. C₄×D₄	C₂³×C₂₃	semidirect
1016. C₄×D₄	C₂³×C₂₃	semidirect
1017. C₄×D₄	C₂³×C₂₃	semidirect
1021. #117	C₂³×C₂₃	semidirect
1026. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
1043. #107	C₂³×C₂₃	semidirect
1044. #107	C₂³×C₂₃	semidirect
1045. #107	C₂³×C₂₃	semidirect
1046. #106	C₂³×C₂₃	semidirect
1047. C₄⋊C₈	C₂³×C₂₃	semidirect
1048. C₄⋊C₈	C₂³×C₂₃	semidirect
1049. #103	C₂³×C₂₃	semidirect
1050. #103	C₂³×C₂₃	semidirect
1051. #103	C₂³×C₂₃	semidirect
1052. #103	C₂³×C₂₃	semidirect
1053. #103	C₂³×C₂₃	semidirect
1062. #102	C₂³×C₂₃	semidirect
1063. #102	C₂³×C₂₃	semidirect
1064. #102	C₂³×C₂₃	semidirect
1071. C₂²⋊C₈	C₂³×C₂₃	semidirect
1072. C₂²⋊C₈	C₂³×C₂₃	semidirect
1073. #97	C₂³×C₂₃	semidirect
1074. C₄×C₈	C₂³×C₂₃	semidirect
1075. C₂₃	#61592	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3519	2
C₂×C₂₃×#546	2
C₂₃×#3322	2
C₂₃×#3319	2
C₂₃×#3314	2
C₂₃×#3297	2
C₂₃×#3280	2
C₂₃×#3273	2
C₂₃×#3268	2
C₂₃×#3264	2
C₂₃×#3213	2
C₂₃×#3211	2
C₂₃×#3194	2
C₂₃×#3193	2
C₂₃×#3190	2
C₂₃×#3186	2
C₂₃×#3114	2
C₂₃×#3100	2
C₂₃×#3006	2
C₂₃×#3003	2
C₂₃×#3002	2
C₂×C₂₃×#447	2
C₂₃×#2974	2
#61592	23

Subgroups — C23×#61592 #19209218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61592 #19209218