Subgroups — C₂₃×#61598 #19209224

Order 5888.

2392 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3308	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3306	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3265	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3006	C₂	1	2	yes	maximal, complemented
22	C₂×C₂₃×#449	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×H(5,𝔽₂)	—	2	1	no	—
25	C₂²×#41×C₂₃	C₂²	1	2	yes	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	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
29	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
30	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
31	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#548	C₂²	1	2	yes	complemented
33	C₂₃×#547	—	2	1	no	—
34	C₂₃×#547	C₂²	1	1	yes	characteristic
35	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#547	C₂²	1	2	yes	complemented
37	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#546	—	2	1	no	—
39	C₂₃×#546	—	2	2	no	—
40	C₂₃×#546	—	2	1	no	—
41	C₂₃×#546	—	2	2	no	—
42	C₂₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₂₃	—	2	1	no	—
44	D₄²×C₂₃	C₂²	1	1	yes	characteristic
45	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
46	D₄²×C₂₃	C₂²	1	2	yes	complemented
47	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#537	—	2	1	no	—
49	C₂₃×#534	—	2	2	no	—
50	C₂₃×#532	—	2	1	no	—
51	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#525	—	2	2	no	—
55	C₂₃×#525	C₂²	1	2	yes	complemented
56	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
57	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
58	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×D₄×C₂₃	—	2	1	no	—
60	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
61	C₂₃×#496	C₂²	1	2	yes	complemented
62	C₂₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#489	C₂²	1	2	yes	complemented
65	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#484	C₂²	1	2	yes	complemented
68	C₂₃×#483	C₂²	1	2	yes	complemented
69	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#482	C₂²	1	2	yes	complemented
71	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#481	C₂²	1	2	yes	complemented
73	C₂₃×#480	C₂²	1	2	yes	complemented
74	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#469	C₂²	1	2	yes	complemented
79	C₂₃×#469	C₂²	1	2	yes	complemented
80	C₂₃×#468	C₂²	1	2	yes	complemented
81	C₂₃×#468	C₂²	1	2	yes	complemented
82	C₂₃×#466	C₂²	1	2	yes	complemented
83	C₂₃×#466	C₂²	1	2	yes	complemented
84	C₂₃×#465	C₂²	1	2	yes	complemented
85	C₂₃×#465	C₂²	1	2	yes	complemented
86	C₂₃×#463	C₂²	1	2	yes	complemented
87	C₂₃×#463	C₂²	1	2	yes	complemented
88	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#450	C₂²	1	2	yes	complemented
97	C₂₃×#450	C₂²	1	2	yes	complemented
98	C₂₃×#449	C₂²	1	2	yes	complemented
99	C₂₃×#449	C₂²	1	2	yes	complemented
100	C₂₃×#449	C₂²	1	2	yes	complemented
101	C₂₃×#449	C₂²	1	2	yes	complemented
102	C₂₃×#449	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#449	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×#449	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#448	C₂²	1	2	yes	complemented
110	C₂₃×#448	C₂²	1	2	yes	complemented
111	C₂₃×#447	C₂²	1	2	yes	complemented
112	C₂₃×#447	C₂²	1	2	yes	complemented
113	C₂₃×#447	C₂²	1	2	yes	complemented
114	C₂₃×#447	C₂²	1	2	yes	complemented
115	C₂₃×#442	C₂²	1	2	yes	complemented
116	C₂₃×#440	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
121	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#435	C₂²	1	2	yes	complemented
124	C₂₃×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
128	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#417	C₂²	1	2	yes	complemented
130	C₂₃×#417	C₂²	1	2	yes	complemented
131	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
132	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
133	C₂₃×#407	C₂²	1	2	yes	complemented
134	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₂₃×H(5,𝔽₂)	—	4	8	no	—
136	C₂×#41×C₂₃	—	2	1	no	—
137	C₂×#41×C₂₃	—	2	2	no	—
138	C₂×#41×C₂₃	—	2	1	no	—
139	C₂×#41×C₂₃	—	2	2	no	—
140	C₂×#41×C₂₃	—	2	2	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	—	4	4	no	—
145	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×#41×C₂₃	C₂³	1	2	yes	—
147	C₂×#41×C₂₃	C₂³	1	2	yes	—
148	C₂×#41×C₂₃	C₂³	1	2	yes	—
149	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
150	C₂²×D₄×C₂₃	—	2	2	no	—
151	C₂²×D₄×C₂₃	—	2	2	no	—
152	C₂²×D₄×C₂₃	—	2	2	no	—
153	C₂²×D₄×C₂₃	—	2	1	no	—
154	C₂²×D₄×C₂₃	—	2	2	no	—
155	C₂²×D₄×C₂₃	—	2	1	no	—
156	C₂²×D₄×C₂₃	—	2	1	no	—
157	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
158	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
159	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
160	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
161	C₂³×C₄×C₂₃	—	2	2	no	—
162	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
163	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
164	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
165	C₂×SD₁₆×C₂₃	—	4	4	no	—
166	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
170	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
171	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
172	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
173	C₂×D₈×C₂₃	—	4	4	no	—
174	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×D₈×C₂₃	C₂³	1	2	yes	—
176	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
177	C₂×D₈×C₂₃	C₂³	1	2	yes	—
178	C₂×D₈×C₂₃	C₂³	1	2	yes	—
179	C₂×D₈×C₂₃	C₂³	1	2	yes	—
180	C₂×D₈×C₂₃	C₂³	1	2	yes	—
181	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
182	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
183	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
184	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
185	C₂₃×C₄⋊Q₈	—	2	1	no	—
186	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
187	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
188	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
189	C₂₃×#127	—	2	1	no	—
190	C₂₃×#127	C₂³	1	1	yes	characteristic
191	C₂₃×#127	C₂³	1	1	yes	characteristic
192	C₂₃×#127	C₂³	1	1	yes	characteristic
193	C₂₃×#124	—	2	2	no	—
194	C₂₃×#124	—	2	1	no	—
195	C₂₃×#124	—	2	1	no	—
196	C₂₃×#124	C₂³	1	2	yes	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×#123	—	2	2	no	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×#123	—	2	2	no	—
203	C₂₃×#123	—	2	2	no	—
204	C₂₃×C₂²⋊Q₈	—	2	2	no	—
205	C₂₃×C₂²⋊Q₈	—	2	1	no	—
206	C₂₃×C₂²⋊Q₈	—	2	1	no	—
207	C₂₃×C₂²⋊Q₈	—	2	2	no	—
208	C₂₃×C₂²⋊Q₈	—	2	2	no	—
209	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂₃×#121	—	2	1	no	—
212	C₂₃×#121	—	2	2	no	—
213	C₂₃×#121	—	2	1	no	—
214	C₂₃×#121	—	2	2	no	—
215	C₂₃×#121	—	2	2	no	—
216	C₂₃×#121	—	2	2	no	—
217	C₂₃×#121	—	2	2	no	—
218	C₂₃×#121	—	2	1	no	—
219	C₂₃×#121	—	2	1	no	—
220	C₂₃×#121	—	2	1	no	—
221	C₂₃×#121	—	2	1	no	—
222	C₂₃×#121	—	2	1	no	—
223	C₂₃×#121	—	2	1	no	—
224	C₂₃×#121	—	2	2	no	—
225	C₂₃×#121	—	2	2	no	—
226	C₂₃×#121	—	2	2	no	—
227	C₂₃×#121	C₂³	1	2	yes	—
228	C₂₃×#121	C₂³	1	2	yes	—
229	C₂₃×#121	C₂³	1	2	yes	—
230	C₂₃×#121	C₂³	1	2	yes	—
231	C₂₃×#121	C₂³	1	2	yes	—
232	C₂₃×#121	C₂³	1	2	yes	—
233	C₂₃×#121	C₂³	1	2	yes	—
234	C₂₃×#121	C₂³	1	1	yes	characteristic
235	C₂₃×#121	C₂³	1	1	yes	characteristic
236	C₂₃×#120	—	2	2	no	—
237	C₂₃×#120	—	2	2	no	—
238	C₂₃×#120	—	2	2	no	—
239	C₂₃×#120	—	2	2	no	—
240	C₂₃×#120	—	2	2	no	—
241	C₂₃×#120	—	2	2	no	—
242	C₂₃×#120	—	2	2	no	—
243	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₂₃	—	2	1	no	—
246	C₄×D₄×C₂₃	—	2	1	no	—
247	C₄×D₄×C₂₃	—	2	2	no	—
248	C₄×D₄×C₂₃	—	2	1	no	—
249	C₄×D₄×C₂₃	—	2	2	no	—
250	C₄×D₄×C₂₃	—	2	1	no	—
251	C₄×D₄×C₂₃	—	2	2	no	—
252	C₄×D₄×C₂₃	—	2	1	no	—
253	C₄×D₄×C₂₃	—	2	1	no	—
254	C₄×D₄×C₂₃	—	2	1	no	—
255	C₄×D₄×C₂₃	—	2	1	no	—
256	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
257	C₄×D₄×C₂₃	D₄	1	2	yes	—
258	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
259	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₂₃	C₂³	1	2	yes	—
263	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₂₃	C₂³	1	2	yes	—
267	C₂₃×#117	—	2	1	no	—
268	C₂₃×#117	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
272	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
276	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
277	C₂×C₄²×C₂₃	—	2	1	no	—
278	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
279	C₂₃×#107	C₂³	1	1	yes	characteristic
280	C₂₃×#107	C₂³	1	1	yes	characteristic
281	C₂₃×#107	C₂³	1	2	yes	—
282	C₂₃×#106	C₂³	1	1	yes	characteristic
283	C₂₃×#106	C₂³	1	1	yes	characteristic
284	C₂₃×#106	C₂³	1	2	yes	—
285	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	1	yes	characteristic
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#103	C₂³	1	2	yes	—
296	C₂₃×#102	C₂³	1	1	yes	characteristic
297	C₂₃×#102	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	1	yes	characteristic
304	C₂₃×#102	C₂³	1	1	yes	characteristic
305	C₂₃×#102	C₂³	1	1	yes	characteristic
306	C₂₃×#102	C₂³	1	1	yes	characteristic
307	C₂₃×#102	C₂³	1	2	yes	—
308	C₂₃×#102	C₂³	1	2	yes	—
309	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
314	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₂₃×#97	C₂³	1	2	yes	—
317	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
318	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
319	C₂⁴×C₂₃	—	2	2	no	—
320	C₂⁴×C₂₃	—	2	2	no	—
321	C₂⁴×C₂₃	—	2	2	no	—
322	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
323	#41×C₂₃	—	2	2	no	—
324	#41×C₂₃	—	2	2	no	—
325	#41×C₂₃	—	2	4	no	—
326	#41×C₂₃	—	2	4	no	—
327	#41×C₂₃	—	4	2	no	—
328	#41×C₂₃	—	4	2	no	—
329	#41×C₂₃	—	4	2	no	—
330	#41×C₂₃	—	4	2	no	—
331	#41×C₂₃	—	4	8	no	—
332	#41×C₂₃	—	4	4	no	—
333	#41×C₂₃	—	4	4	no	—
334	#41×C₂₃	—	4	8	no	—
335	#41×C₂₃	—	4	8	no	—
336	#41×C₂₃	—	4	4	no	—
337	#41×C₂₃	—	4	4	no	—
338	C₂×Q₈×C₂₃	—	2	2	no	—
339	C₂×Q₈×C₂₃	—	2	1	no	—
340	C₂×Q₈×C₂₃	—	2	1	no	—
341	C₂×Q₈×C₂₃	—	2	4	no	—
342	C₂×Q₈×C₂₃	—	4	2	no	—
343	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
344	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₂₃	—	2	1	no	—
346	C₂×D₄×C₂₃	—	2	4	no	—
347	C₂×D₄×C₂₃	—	2	4	no	—
348	C₂×D₄×C₂₃	—	2	2	no	—
349	C₂×D₄×C₂₃	—	2	2	no	—
350	C₂×D₄×C₂₃	—	2	2	no	—
351	C₂×D₄×C₂₃	—	2	2	no	—
352	C₂×D₄×C₂₃	—	2	2	no	—
353	C₂×D₄×C₂₃	—	2	2	no	—
354	C₂×D₄×C₂₃	—	2	2	no	—
355	C₂×D₄×C₂₃	—	2	1	no	—
356	C₂×D₄×C₂₃	—	2	2	no	—
357	C₂×D₄×C₂₃	—	2	1	no	—
358	C₂×D₄×C₂₃	—	2	2	no	—
359	C₂×D₄×C₂₃	—	2	2	no	—
360	C₂×D₄×C₂₃	—	2	1	no	—
361	C₂×D₄×C₂₃	—	2	2	no	—
362	C₂×D₄×C₂₃	—	2	1	no	—
363	C₂×D₄×C₂₃	—	2	1	no	—
364	C₂×D₄×C₂₃	—	2	1	no	—
365	C₂×D₄×C₂₃	—	2	1	no	—
366	C₂×D₄×C₂₃	—	2	1	no	—
367	C₂×D₄×C₂₃	—	2	2	no	—
368	C₂×D₄×C₂₃	—	2	2	no	—
369	C₂×D₄×C₂₃	—	4	2	no	—
370	C₂×D₄×C₂₃	—	4	2	no	—
371	C₂×D₄×C₂₃	—	4	2	no	—
372	C₂×D₄×C₂₃	—	4	2	no	—
373	C₂×D₄×C₂₃	—	4	2	no	—
374	C₂×D₄×C₂₃	—	4	8	no	—
375	C₂×D₄×C₂₃	—	4	8	no	—
376	C₂×D₄×C₂₃	—	4	4	no	—
377	C₂×D₄×C₂₃	—	4	8	no	—
378	C₂×D₄×C₂₃	—	4	8	no	—
379	C₂×D₄×C₂₃	—	4	4	no	—
380	C₂×D₄×C₂₃	—	4	4	no	—
381	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
382	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
385	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
387	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
388	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₂₃	—	2	1	no	—
390	C₂²×C₄×C₂₃	—	2	2	no	—
391	C₂²×C₄×C₂₃	—	2	2	no	—
392	C₂²×C₄×C₂₃	—	2	2	no	—
393	C₂²×C₄×C₂₃	—	2	1	no	—
394	C₂²×C₄×C₂₃	—	2	2	no	—
395	C₂²×C₄×C₂₃	—	2	2	no	—
396	C₂²×C₄×C₂₃	—	2	2	no	—
397	C₂²×C₄×C₂₃	—	2	2	no	—
398	C₂²×C₄×C₂₃	—	2	1	no	—
399	C₂²×C₄×C₂₃	—	2	1	no	—
400	C₂²×C₄×C₂₃	—	2	1	no	—
401	C₂²×C₄×C₂₃	—	4	2	no	—
402	C₂²×C₄×C₂₃	—	4	2	no	—
403	C₂²×C₄×C₂₃	—	4	8	no	—
404	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
407	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
408	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
409	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
411	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
412	SD₁₆×C₂₃	—	2	2	no	—
413	SD₁₆×C₂₃	—	2	4	no	—
414	SD₁₆×C₂₃	—	2	2	no	—
415	SD₁₆×C₂₃	—	4	2	no	—
416	SD₁₆×C₂₃	—	4	2	no	—
417	SD₁₆×C₂₃	—	4	2	no	—
418	SD₁₆×C₂₃	—	4	2	no	—
419	D₈×C₂₃	—	2	2	no	—
420	D₈×C₂₃	—	2	4	no	—
421	D₈×C₂₃	—	2	2	no	—
422	D₈×C₂₃	—	4	2	no	—
423	D₈×C₂₃	—	4	2	no	—
424	D₈×C₂₃	—	4	2	no	—
425	D₈×C₂₃	—	4	2	no	—
426	M₁₆×C₂₃	—	4	2	no	—
427	M₁₆×C₂₃	—	4	2	no	—
428	C₂×C₈×C₂₃	—	4	2	no	—
429	C₂×C₈×C₂₃	—	4	2	no	—
430	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
431	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
432	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
433	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
434	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
435	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₂₃	—	2	1	no	—
437	C₄⋊C₄×C₂₃	—	2	2	no	—
438	C₄⋊C₄×C₂₃	—	2	2	no	—
439	C₄⋊C₄×C₂₃	—	2	2	no	—
440	C₄⋊C₄×C₂₃	—	2	1	no	—
441	C₄⋊C₄×C₂₃	—	2	1	no	—
442	C₄⋊C₄×C₂₃	—	2	1	no	—
443	C₄⋊C₄×C₂₃	—	2	2	no	—
444	C₄⋊C₄×C₂₃	—	2	1	no	—
445	C₄⋊C₄×C₂₃	—	2	1	no	—
446	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
449	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
453	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
454	C₂²⋊C₄×C₂₃	—	2	2	no	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	2	no	—
457	C₂²⋊C₄×C₂₃	—	2	1	no	—
458	C₂²⋊C₄×C₂₃	—	2	2	no	—
459	C₂²⋊C₄×C₂₃	—	2	1	no	—
460	C₂²⋊C₄×C₂₃	—	2	2	no	—
461	C₂²⋊C₄×C₂₃	—	2	2	no	—
462	C₂²⋊C₄×C₂₃	—	2	2	no	—
463	C₂²⋊C₄×C₂₃	—	2	2	no	—
464	C₂²⋊C₄×C₂₃	—	2	2	no	—
465	C₂²⋊C₄×C₂₃	—	2	2	no	—
466	C₂²⋊C₄×C₂₃	—	2	1	no	—
467	C₂²⋊C₄×C₂₃	—	2	1	no	—
468	C₂²⋊C₄×C₂₃	—	2	2	no	—
469	C₂²⋊C₄×C₂₃	—	2	2	no	—
470	C₂²⋊C₄×C₂₃	—	2	2	no	—
471	C₂²⋊C₄×C₂₃	—	2	1	no	—
472	C₂²⋊C₄×C₂₃	—	2	1	no	—
473	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
474	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
475	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
476	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
477	C₄²×C₂₃	—	2	1	no	—
478	C₄²×C₂₃	—	2	1	no	—
479	C₄²×C₂₃	—	2	1	no	—
480	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
481	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
483	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
484	#61598	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
485	C₂³×C₂₃	—	2	1	no	—
486	C₂³×C₂₃	—	2	4	no	—
487	C₂³×C₂₃	—	2	2	no	—
488	C₂³×C₂₃	—	2	1	no	—
489	C₂³×C₂₃	—	2	2	no	—
490	C₂³×C₂₃	—	2	1	no	—
491	C₂³×C₂₃	—	4	2	no	—
492	C₂³×C₂₃	—	4	2	no	—
493	C₂³×C₂₃	—	4	4	no	—
494	C₂³×C₂₃	—	4	4	no	—
495	C₂³×C₂₃	—	4	4	no	—
496	C₂³×C₂₃	—	4	4	no	—
497	C₂³×C₂₃	—	8	2	no	—
498	C₂³×C₂₃	—	8	2	no	—
499	C₂³×C₂₃	—	8	2	no	—
500	C₂³×C₂₃	—	8	2	no	—
501	C₂³×C₂₃	—	8	2	no	—
502	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
503	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
505	Q₈×C₂₃	—	2	1	no	—
506	Q₈×C₂₃	—	2	2	no	—
507	Q₈×C₂₃	—	2	2	no	—
508	Q₈×C₂₃	—	4	4	no	—
509	Q₈×C₂₃	—	4	2	no	—
510	Q₈×C₂₃	—	4	2	no	—
511	Q₈×C₂₃	H(5,𝔽₂)	1	2	yes	complemented
512	D₄×C₂₃	—	2	4	no	—
513	D₄×C₂₃	—	2	4	no	—
514	D₄×C₂₃	—	2	2	no	—
515	D₄×C₂₃	—	2	1	no	—
516	D₄×C₂₃	—	2	1	no	—
517	D₄×C₂₃	—	2	2	no	—
518	D₄×C₂₃	—	2	1	no	—
519	D₄×C₂₃	—	2	1	no	—
520	D₄×C₂₃	—	2	2	no	—
521	D₄×C₂₃	—	2	2	no	—
522	D₄×C₂₃	—	2	2	no	—
523	D₄×C₂₃	—	2	1	no	—
524	D₄×C₂₃	—	4	4	no	—
525	D₄×C₂₃	—	4	4	no	—
526	D₄×C₂₃	—	4	2	no	—
527	D₄×C₂₃	—	4	4	no	—
528	D₄×C₂₃	—	4	4	no	—
529	D₄×C₂₃	—	4	2	no	—
530	D₄×C₂₃	—	4	2	no	—
531	D₄×C₂₃	—	4	4	no	—
532	D₄×C₂₃	—	4	4	no	—
533	D₄×C₂₃	—	4	4	no	—
534	D₄×C₂₃	—	4	4	no	—
535	D₄×C₂₃	—	4	4	no	—
536	D₄×C₂₃	—	4	4	no	—
537	D₄×C₂₃	—	4	2	no	—
538	D₄×C₂₃	—	4	2	no	—
539	D₄×C₂₃	—	8	1	no	—
540	D₄×C₂₃	—	8	1	no	—
541	D₄×C₂₃	—	8	1	no	—
542	D₄×C₂₃	—	8	2	no	—
543	D₄×C₂₃	—	8	2	no	—
544	D₄×C₂₃	—	8	2	no	—
545	D₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	complemented
546	D₄×C₂₃	H(5,𝔽₂)	1	2	yes	complemented
547	C₂×C₄×C₂₃	—	2	4	no	—
548	C₂×C₄×C₂₃	—	2	1	no	—
549	C₂×C₄×C₂₃	—	2	2	no	—
550	C₂×C₄×C₂₃	—	2	2	no	—
551	C₂×C₄×C₂₃	—	2	2	no	—
552	C₂×C₄×C₂₃	—	2	2	no	—
553	C₂×C₄×C₂₃	—	2	2	no	—
554	C₂×C₄×C₂₃	—	2	1	no	—
555	C₂×C₄×C₂₃	—	2	1	no	—
556	C₂×C₄×C₂₃	—	2	1	no	—
557	C₂×C₄×C₂₃	—	2	1	no	—
558	C₂×C₄×C₂₃	—	2	2	no	—
559	C₂×C₄×C₂₃	—	2	2	no	—
560	C₂×C₄×C₂₃	—	2	1	no	—
561	C₂×C₄×C₂₃	—	2	1	no	—
562	C₂×C₄×C₂₃	—	4	2	no	—
563	C₂×C₄×C₂₃	—	4	2	no	—
564	C₂×C₄×C₂₃	—	4	2	no	—
565	C₂×C₄×C₂₃	—	4	1	no	—
566	C₂×C₄×C₂₃	—	4	4	no	—
567	C₂×C₄×C₂₃	—	4	4	no	—
568	C₂×C₄×C₂₃	—	4	4	no	—
569	C₂×C₄×C₂₃	—	4	4	no	—
570	C₂×C₄×C₂₃	—	4	4	no	—
571	C₂×C₄×C₂₃	—	4	4	no	—
572	C₂×C₄×C₂₃	—	4	4	no	—
573	C₂×C₄×C₂₃	—	4	2	no	—
574	C₂×C₄×C₂₃	—	4	2	no	—
575	C₂×C₄×C₂₃	—	4	2	no	—
576	C₂×C₄×C₂₃	—	8	1	no	—
577	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
582	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
583	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
585	C₈×C₂₃	—	2	1	no	—
586	C₈×C₂₃	—	2	1	no	—
587	C₈×C₂₃	—	2	2	no	—
588	C₈×C₂₃	—	2	2	no	—
589	C₈×C₂₃	—	2	1	no	—
590	C₈×C₂₃	—	2	1	no	—
591	#3496	C₂×C₂₃	1	1	yes	characteristic, complemented
592	D₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#3332	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#3330	C₂×C₂₃	1	1	yes	characteristic, complemented
595	#3308	C₂×C₂₃	1	2	yes	complemented
596	#3306	C₂×C₂₃	1	2	yes	complemented
597	#3298	C₂×C₂₃	1	1	yes	characteristic, complemented
598	#3294	C₂×C₂₃	1	1	yes	characteristic, complemented
599	D₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
600	D₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
601	#3274	C₂×C₂₃	1	1	yes	characteristic, complemented
602	#3272	C₂×C₂₃	1	1	yes	characteristic, complemented
603	#3265	C₂×C₂₃	1	2	yes	complemented
604	#3264	C₂×C₂₃	1	2	yes	complemented
605	#3214	C₂×C₂₃	1	1	yes	characteristic, complemented
606	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
607	#3194	C₂×C₂₃	1	2	yes	complemented
608	#3188	C₂×C₂₃	1	2	yes	complemented
609	#3115	C₂×C₂₃	1	1	yes	characteristic, complemented
610	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
611	#3006	C₂×C₂₃	1	2	yes	complemented
612	C₂×#449	C₂×C₂₃	1	2	yes	complemented
613	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
614	C₂²×C₂₃	—	2	2	no	—
615	C₂²×C₂₃	—	2	2	no	—
616	C₂²×C₂₃	—	2	1	no	—
617	C₂²×C₂₃	—	2	2	no	—
618	C₂²×C₂₃	—	2	1	no	—
619	C₂²×C₂₃	—	2	2	no	—
620	C₂²×C₂₃	—	2	2	no	—
621	C₂²×C₂₃	—	2	1	no	—
622	C₂²×C₂₃	—	2	2	no	—
623	C₂²×C₂₃	—	4	1	no	—
624	C₂²×C₂₃	—	4	1	no	—
625	C₂²×C₂₃	—	4	2	no	—
626	C₂²×C₂₃	—	4	1	no	—
627	C₂²×C₂₃	—	4	2	no	—
628	C₂²×C₂₃	—	4	1	no	—
629	C₂²×C₂₃	—	4	2	no	—
630	C₂²×C₂₃	—	4	1	no	—
631	C₂²×C₂₃	—	4	2	no	—
632	C₂²×C₂₃	—	4	1	no	—
633	C₂²×C₂₃	—	4	2	no	—
634	C₂²×C₂₃	—	4	1	no	—
635	C₂²×C₂₃	—	4	1	no	—
636	C₂²×C₂₃	—	4	2	no	—
637	C₂²×C₂₃	—	8	4	no	—
638	C₂²×C₂₃	—	8	8	no	—
639	C₂²×C₂₃	—	16	4	no	—
640	C₂²×C₂₃	—	16	4	no	—
641	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
642	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
643	C₄×C₂₃	—	2	1	no	—
644	C₄×C₂₃	—	2	1	no	—
645	C₄×C₂₃	—	2	1	no	—
646	C₄×C₂₃	—	2	2	no	—
647	C₄×C₂₃	—	2	2	no	—
648	C₄×C₂₃	—	2	2	no	—
649	C₄×C₂₃	—	2	1	no	—
650	C₄×C₂₃	—	4	1	no	—
651	C₄×C₂₃	—	4	2	no	—
652	C₄×C₂₃	—	4	2	no	—
653	C₄×C₂₃	—	4	1	no	—
654	C₄×C₂₃	—	4	1	no	—
655	C₄×C₂₃	—	4	1	no	—
656	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
657	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
658	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
659	C₂×H(5,𝔽₂)	—	2	1	no	—
660	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
661	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
662	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
663	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
664	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
665	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
666	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
667	#548	C₂²×C₂₃	1	2	yes	complemented
668	#547	—	2	1	no	—
669	#547	C₂²×C₂₃	1	1	yes	characteristic
670	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
672	#547	C₂²×C₂₃	1	2	yes	complemented
673	#546	—	2	1	no	—
674	#546	—	2	2	no	—
675	#546	—	2	1	no	—
676	#546	—	2	2	no	—
677	#546	C₂²×C₂₃	1	2	yes	complemented
678	D₄²	—	2	1	no	—
679	D₄²	C₂²×C₂₃	1	1	yes	characteristic
680	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	D₄²	C₂²×C₂₃	1	2	yes	complemented
682	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
683	#537	—	2	1	no	—
684	#534	—	2	2	no	—
685	#532	—	2	1	no	—
686	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
687	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
688	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
689	#525	—	2	2	no	—
690	#525	C₂²×C₂₃	1	2	yes	complemented
691	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
692	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
693	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
694	C₂×C₄×D₄	—	2	1	no	—
695	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
696	#496	C₂²×C₂₃	1	2	yes	complemented
697	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
699	#489	C₂²×C₂₃	1	2	yes	complemented
700	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
701	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
702	#484	C₂²×C₂₃	1	2	yes	complemented
703	#483	C₂²×C₂₃	1	2	yes	complemented
704	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
705	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
706	#482	C₂²×C₂₃	1	2	yes	complemented
707	#481	C₂²×C₂₃	1	2	yes	complemented
708	#480	C₂²×C₂₃	1	2	yes	complemented
709	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
710	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
711	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
712	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
713	#469	C₂²×C₂₃	1	2	yes	complemented
714	#469	C₂²×C₂₃	1	2	yes	complemented
715	#468	C₂²×C₂₃	1	2	yes	complemented
716	#468	C₂²×C₂₃	1	2	yes	complemented
717	#466	C₂²×C₂₃	1	2	yes	complemented
718	#466	C₂²×C₂₃	1	2	yes	complemented
719	#465	C₂²×C₂₃	1	2	yes	complemented
720	#465	C₂²×C₂₃	1	2	yes	complemented
721	#463	C₂²×C₂₃	1	2	yes	complemented
722	#463	C₂²×C₂₃	1	2	yes	complemented
723	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
724	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
725	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
726	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
727	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
728	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
729	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
730	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
731	#450	C₂²×C₂₃	1	2	yes	complemented
732	#450	C₂²×C₂₃	1	2	yes	complemented
733	#449	C₂²×C₂₃	1	2	yes	complemented
734	#449	C₂²×C₂₃	1	2	yes	complemented
735	#449	C₂²×C₂₃	1	1	yes	characteristic, complemented
736	#449	C₂²×C₂₃	1	1	yes	characteristic, complemented
737	#449	C₂²×C₂₃	1	2	yes	complemented
738	#449	C₂²×C₂₃	1	2	yes	complemented
739	#449	C₂²×C₂₃	1	2	yes	complemented
740	#449	C₂²×C₂₃	1	2	yes	complemented
741	#449	C₂²×C₂₃	1	2	yes	complemented
742	#449	C₂²×C₂₃	1	2	yes	complemented
743	#449	C₂²×C₂₃	1	2	yes	complemented
744	#448	C₂²×C₂₃	1	2	yes	complemented
745	#448	C₂²×C₂₃	1	2	yes	complemented
746	#447	C₂²×C₂₃	1	2	yes	complemented
747	#447	C₂²×C₂₃	1	2	yes	complemented
748	#447	C₂²×C₂₃	1	2	yes	complemented
749	#447	C₂²×C₂₃	1	2	yes	complemented
750	#442	C₂²×C₂₃	1	2	yes	complemented
751	#440	C₂²×C₂₃	1	2	yes	complemented
752	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
753	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
754	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
755	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
756	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
757	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
758	#435	C₂²×C₂₃	1	2	yes	complemented
759	#435	C₂²×C₂₃	1	2	yes	complemented
760	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
761	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
762	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
763	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
764	#417	C₂²×C₂₃	1	2	yes	complemented
765	#417	C₂²×C₂₃	1	2	yes	complemented
766	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
767	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
768	#407	C₂²×C₂₃	1	2	yes	complemented
769	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
770	C₂×C₂₃	—	2	4	no	—
771	C₂×C₂₃	—	4	1	no	—
772	C₂×C₂₃	—	4	2	no	—
773	C₂×C₂₃	—	4	2	no	—
774	C₂×C₂₃	—	8	2	no	—
775	C₂×C₂₃	—	8	1	no	—
776	C₂×C₂₃	—	8	2	no	—
777	C₂×C₂₃	—	8	1	no	—
778	C₂×C₂₃	#3484	1	1	yes	characteristic
779	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
780	C₂×C₂₃	#3584	1	1	yes	characteristic
781	H(5,𝔽₂)	—	4	8	no	—
782	C₂×#41	—	2	1	no	—
783	C₂×#41	—	2	2	no	—
784	C₂×#41	—	2	1	no	—
785	C₂×#41	—	2	2	no	—
786	C₂×#41	—	2	1	no	—
787	C₂×#41	—	2	1	no	—
788	C₂×#41	—	2	2	no	—
789	C₂×#41	—	4	4	no	—
790	C₂×#41	—	4	4	no	—
791	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
792	C₂×#41	C₂³×C₂₃	1	2	yes	—
793	C₂×#41	C₂³×C₂₃	1	2	yes	—
794	C₂×#41	C₂³×C₂₃	1	2	yes	—
795	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
796	C₂²×D₄	—	2	2	no	—
797	C₂²×D₄	—	2	2	no	—
798	C₂²×D₄	—	2	2	no	—
799	C₂²×D₄	—	2	1	no	—
800	C₂²×D₄	—	2	1	no	—
801	C₂²×D₄	—	2	2	no	—
802	C₂²×D₄	—	2	1	no	—
803	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
804	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
805	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
806	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
807	C₂³×C₄	—	2	2	no	—
808	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
809	AGL(1,ℤ/8)	—	4	4	no	—
810	AGL(1,ℤ/8)	—	4	4	no	—
811	C₂×SD₁₆	—	4	4	no	—
812	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
813	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
814	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
815	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
816	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
817	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
818	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
819	C₂×D₈	—	4	4	no	—
820	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
821	C₂×D₈	C₂³×C₂₃	1	2	yes	—
822	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
823	C₂×D₈	C₂³×C₂₃	1	2	yes	—
824	C₂×D₈	C₂³×C₂₃	1	2	yes	—
825	C₂×D₈	C₂³×C₂₃	1	2	yes	—
826	C₂×D₈	C₂³×C₂₃	1	2	yes	—
827	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
828	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
829	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
830	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
831	C₄⋊Q₈	—	2	1	no	—
832	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
833	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
834	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
835	#127	—	2	1	no	—
836	#127	C₂³×C₂₃	1	1	yes	characteristic
837	#127	C₂³×C₂₃	1	1	yes	characteristic
838	#127	C₂³×C₂₃	1	1	yes	characteristic
839	#124	—	2	2	no	—
840	#124	—	2	1	no	—
841	#124	—	2	1	no	—
842	#124	C₂³×C₂₃	1	2	yes	—
843	#123	—	2	2	no	—
844	#123	—	2	2	no	—
845	#123	—	2	2	no	—
846	#123	—	2	2	no	—
847	#123	—	2	2	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	C₂²⋊Q₈	—	2	2	no	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	—	2	1	no	—
853	C₂²⋊Q₈	—	2	2	no	—
854	C₂²⋊Q₈	—	2	2	no	—
855	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
856	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
857	#121	—	2	2	no	—
858	#121	—	2	1	no	—
859	#121	—	2	2	no	—
860	#121	—	2	2	no	—
861	#121	—	2	2	no	—
862	#121	—	2	2	no	—
863	#121	—	2	1	no	—
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	—	2	1	no	—
867	#121	—	2	1	no	—
868	#121	—	2	1	no	—
869	#121	—	2	1	no	—
870	#121	—	2	2	no	—
871	#121	—	2	2	no	—
872	#121	—	2	2	no	—
873	#121	C₂³×C₂₃	1	1	yes	characteristic
874	#121	C₂³×C₂₃	1	2	yes	—
875	#121	C₂³×C₂₃	1	1	yes	characteristic
876	#121	C₂³×C₂₃	1	2	yes	—
877	#121	C₂³×C₂₃	1	2	yes	—
878	#121	C₂³×C₂₃	1	2	yes	—
879	#121	C₂³×C₂₃	1	2	yes	—
880	#121	C₂³×C₂₃	1	2	yes	—
881	#121	C₂³×C₂₃	1	2	yes	—
882	#120	—	2	2	no	—
883	#120	—	2	2	no	—
884	#120	—	2	2	no	—
885	#120	—	2	2	no	—
886	#120	—	2	2	no	—
887	#120	—	2	2	no	—
888	#120	—	2	2	no	—
889	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
890	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	2	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	2	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	2	no	—
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
903	C₄×D₄	D₄×C₂₃	1	2	yes	—
904	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
905	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
906	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
908	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
909	C₄×D₄	C₂³×C₂₃	1	2	yes	—
910	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
911	C₄×D₄	C₂³×C₂₃	1	2	yes	—
912	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
913	#117	—	2	1	no	—
914	#117	C₂³×C₂₃	1	1	yes	characteristic
915	C₂×C₄⋊C₄	—	2	1	no	—
916	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
918	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
919	C₂×C₂²⋊C₄	—	2	2	no	—
920	C₂×C₂²⋊C₄	—	2	2	no	—
921	C₂×C₂²⋊C₄	—	2	2	no	—
922	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
923	C₂×C₄²	—	2	1	no	—
924	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
925	#107	C₂³×C₂₃	1	1	yes	characteristic
926	#107	C₂³×C₂₃	1	1	yes	characteristic
927	#107	C₂³×C₂₃	1	2	yes	—
928	#106	C₂³×C₂₃	1	1	yes	characteristic
929	#106	C₂³×C₂₃	1	1	yes	characteristic
930	#106	C₂³×C₂₃	1	2	yes	—
931	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
932	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
933	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
934	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
935	#103	C₂³×C₂₃	1	1	yes	characteristic
936	#103	C₂³×C₂₃	1	2	yes	—
937	#103	C₂³×C₂₃	1	2	yes	—
938	#103	C₂³×C₂₃	1	2	yes	—
939	#103	C₂³×C₂₃	1	1	yes	characteristic
940	#103	C₂³×C₂₃	1	2	yes	—
941	#103	C₂³×C₂₃	1	2	yes	—
942	#102	C₂³×C₂₃	1	1	yes	characteristic
943	#102	C₂³×C₂₃	1	2	yes	—
944	#102	C₂³×C₂₃	1	2	yes	—
945	#102	C₂³×C₂₃	1	2	yes	—
946	#102	C₂³×C₂₃	1	1	yes	characteristic
947	#102	C₂³×C₂₃	1	2	yes	—
948	#102	C₂³×C₂₃	1	2	yes	—
949	#102	C₂³×C₂₃	1	1	yes	characteristic
950	#102	C₂³×C₂₃	1	1	yes	characteristic
951	#102	C₂³×C₂₃	1	1	yes	characteristic
952	#102	C₂³×C₂₃	1	1	yes	characteristic
953	#102	C₂³×C₂₃	1	2	yes	—
954	#102	C₂³×C₂₃	1	2	yes	—
955	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
956	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
957	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
958	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
959	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
960	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
961	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
962	#97	C₂³×C₂₃	1	2	yes	—
963	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
964	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
965	C₂₃	#61598	1	1	yes	characteristic, direct product factor, Sylow
966	C₂⁴	—	2	2	no	—
967	C₂⁴	—	2	2	no	—
968	C₂⁴	—	2	2	no	—
969	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
970	#41	—	2	2	no	—
971	#41	—	2	2	no	—
972	#41	—	2	4	no	—
973	#41	—	2	4	no	—
974	#41	—	4	2	no	—
975	#41	—	4	2	no	—
976	#41	—	4	2	no	—
977	#41	—	4	2	no	—
978	#41	—	4	8	no	—
979	#41	—	4	4	no	—
980	#41	—	4	4	no	—
981	#41	—	4	8	no	—
982	#41	—	4	8	no	—
983	#41	—	4	4	no	—
984	#41	—	4	4	no	—
985	C₂×Q₈	—	2	2	no	—
986	C₂×Q₈	—	2	1	no	—
987	C₂×Q₈	—	2	1	no	—
988	C₂×Q₈	—	2	4	no	—
989	C₂×Q₈	—	4	2	no	—
990	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
991	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	4	no	—
994	C₂×D₄	—	2	4	no	—
995	C₂×D₄	—	2	2	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	4	2	no	—
1017	C₂×D₄	—	4	2	no	—
1018	C₂×D₄	—	4	2	no	—
1019	C₂×D₄	—	4	2	no	—
1020	C₂×D₄	—	4	2	no	—
1021	C₂×D₄	—	4	8	no	—
1022	C₂×D₄	—	4	8	no	—
1023	C₂×D₄	—	4	4	no	—
1024	C₂×D₄	—	4	8	no	—
1025	C₂×D₄	—	4	8	no	—
1026	C₂×D₄	—	4	4	no	—
1027	C₂×D₄	—	4	4	no	—
1028	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1029	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1030	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1031	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1032	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1033	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1034	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1035	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	2	2	no	—
1043	C₂²×C₄	—	2	2	no	—
1044	C₂²×C₄	—	2	2	no	—
1045	C₂²×C₄	—	2	1	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	4	2	no	—
1049	C₂²×C₄	—	4	2	no	—
1050	C₂²×C₄	—	4	8	no	—
1051	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1052	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1053	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1054	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1055	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1056	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1057	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1058	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1059	SD₁₆	—	2	2	no	—
1060	SD₁₆	—	2	4	no	—
1061	SD₁₆	—	2	2	no	—
1062	SD₁₆	—	4	2	no	—
1063	SD₁₆	—	4	2	no	—
1064	SD₁₆	—	4	2	no	—
1065	SD₁₆	—	4	2	no	—
1066	D₈	—	2	2	no	—
1067	D₈	—	2	4	no	—
1068	D₈	—	2	2	no	—
1069	D₈	—	4	2	no	—
1070	D₈	—	4	2	no	—
1071	D₈	—	4	2	no	—
1072	D₈	—	4	2	no	—
1073	M₁₆	—	4	2	no	—
1074	M₁₆	—	4	2	no	—
1075	C₂×C₈	—	4	2	no	—
1076	C₂×C₈	—	4	2	no	—
1077	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1078	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1079	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1080	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1081	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1082	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1094	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1095	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1096	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1097	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1098	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1100	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1121	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1122	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1123	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1128	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1129	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1130	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1131	C₂³	—	2	1	no	—
1132	C₂³	—	2	4	no	—
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	1	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	4	2	no	—
1138	C₂³	—	4	2	no	—
1139	C₂³	—	4	4	no	—
1140	C₂³	—	4	4	no	—
1141	C₂³	—	4	4	no	—
1142	C₂³	—	4	4	no	—
1143	C₂³	—	8	2	no	—
1144	C₂³	—	8	2	no	—
1145	C₂³	—	8	2	no	—
1146	C₂³	—	8	2	no	—
1147	C₂³	—	8	2	no	—
1148	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1149	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1150	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1151	Q₈	—	2	1	no	—
1152	Q₈	—	2	2	no	—
1153	Q₈	—	2	2	no	—
1154	Q₈	—	4	4	no	—
1155	Q₈	—	4	2	no	—
1156	Q₈	—	4	2	no	—
1157	Q₈	C₂₃×H(5,𝔽₂)	1	2	yes	complemented
1158	D₄	—	2	4	no	—
1159	D₄	—	2	4	no	—
1160	D₄	—	2	2	no	—
1161	D₄	—	2	1	no	—
1162	D₄	—	2	1	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	1	no	—
1165	D₄	—	2	1	no	—
1166	D₄	—	2	2	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	4	4	no	—
1171	D₄	—	4	4	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	4	4	no	—
1174	D₄	—	4	4	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	4	no	—
1178	D₄	—	4	4	no	—
1179	D₄	—	4	4	no	—
1180	D₄	—	4	4	no	—
1181	D₄	—	4	4	no	—
1182	D₄	—	4	4	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	8	2	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	1	no	—
1188	D₄	—	8	1	no	—
1189	D₄	—	8	1	no	—
1190	D₄	—	8	2	no	—
1191	D₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	complemented
1192	D₄	C₂₃×H(5,𝔽₂)	1	2	yes	complemented
1193	C₂×C₄	—	2	4	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	1	no	—
1212	C₂×C₄	—	4	4	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	4	no	—
1215	C₂×C₄	—	4	4	no	—
1216	C₂×C₄	—	4	4	no	—
1217	C₂×C₄	—	4	4	no	—
1218	C₂×C₄	—	4	4	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1225	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1226	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1228	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1229	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1230	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1231	C₈	—	2	1	no	—
1232	C₈	—	2	1	no	—
1233	C₈	—	2	2	no	—
1234	C₈	—	2	2	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	2	2	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	2	no	—
1241	C₂²	—	2	2	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	2	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	2	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	2	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	2	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	2	no	—
1259	C₂²	—	4	1	no	—
1260	C₂²	—	8	4	no	—
1261	C₂²	—	8	8	no	—
1262	C₂²	—	16	4	no	—
1263	C₂²	—	16	4	no	—
1264	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
1265	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1266	C₄	—	2	1	no	—
1267	C₄	—	2	2	no	—
1268	C₄	—	2	2	no	—
1269	C₄	—	2	2	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	2	1	no	—
1273	C₄	—	4	2	no	—
1274	C₄	—	4	2	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	1	no	—
1279	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
1280	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1281	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1282	C₂	—	2	4	no	—
1283	C₂	—	4	1	no	—
1284	C₂	—	4	2	no	—
1285	C₂	—	4	2	no	—
1286	C₂	—	8	2	no	—
1287	C₂	—	8	1	no	—
1288	C₂	—	8	2	no	—
1289	C₂	—	8	1	no	—
1290	C₂	C₂₃×#3484	1	1	yes	characteristic
1291	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
1292	C₂	C₂₃×#3584	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×#3496	C₂	semidirect
2. D₄×#41×C₂₃	C₂	semidirect
3. C₂₃×#3332	C₂	semidirect
4. C₂₃×#3330	C₂	semidirect
5. C₂₃×#3308	C₂	semidirect
6. C₂₃×#3306	C₂	semidirect
7. C₂₃×#3298	C₂	semidirect
8. C₂₃×#3294	C₂	semidirect
9. D₄×SD₁₆×C₂₃	C₂	semidirect
10. D₄×D₈×C₂₃	C₂	semidirect
11. C₂₃×#3274	C₂	semidirect
12. C₂₃×#3272	C₂	semidirect
13. C₂₃×#3265	C₂	semidirect
14. C₂₃×#3264	C₂	semidirect
15. C₂₃×#3214	C₂	semidirect
16. C₂₃×#3207	C₂	semidirect
17. C₂₃×#3194	C₂	semidirect
18. C₂₃×#3188	C₂	semidirect
19. C₂₃×#3115	C₂	semidirect
20. C₂₃×#3106	C₂	semidirect
21. C₂₃×#3006	C₂	semidirect
22. C₂×C₂₃×#449	C₂	semidirect
23. C₂₃×#2974	C₂	semidirect
25. C₂²×#41×C₂₃	C₂²	semidirect
26. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂²×SD₁₆×C₂₃	C₂²	semidirect
29. C₂²×D₈×C₂₃	C₂²	semidirect
30. C₂₃×#550	C₂²	semidirect
31. D₄×Q₈×C₂₃	C₂²	semidirect
32. C₂₃×#548	C₂²	semidirect
35. C₂₃×#547	C₂²	semidirect
36. C₂₃×#547	C₂²	semidirect
37. C₂₃×#547	C₂²	semidirect
42. C₂₃×#546	C₂²	semidirect
45. D₄²×C₂₃	C₂²	semidirect
46. D₄²×C₂₃	C₂²	semidirect
47. D₄²×C₂₃	C₂²	semidirect
51. C₂₃×#532	C₂²	semidirect
52. C₂₃×#532	C₂²	semidirect
53. C₂₃×#532	C₂²	semidirect
55. C₂₃×#525	C₂²	semidirect
56. C₂×C₂₃×#121	C₂²	semidirect
57. C₂×C₂₃×#121	C₂²	semidirect
58. C₄×#41×C₂₃	C₂²	semidirect
61. C₂₃×#496	C₂²	semidirect
62. C₂₃×#493	C₂²	semidirect
63. C₂₃×#492	C₂²	semidirect
64. C₂₃×#489	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
66. C₂₃×#486	C₂²	semidirect
67. C₂₃×#484	C₂²	semidirect
68. C₂₃×#483	C₂²	semidirect
69. C₂₃×#482	C₂²	semidirect
70. C₂₃×#482	C₂²	semidirect
71. C₂₃×#482	C₂²	semidirect
72. C₂₃×#481	C₂²	semidirect
73. C₂₃×#480	C₂²	semidirect
74. C₂₃×#477	C₂²	semidirect
75. C₂₃×#476	C₂²	semidirect
76. C₂₃×#475	C₂²	semidirect
77. C₂₃×#474	C₂²	semidirect
78. C₂₃×#469	C₂²	semidirect
79. C₂₃×#469	C₂²	semidirect
80. C₂₃×#468	C₂²	semidirect
81. C₂₃×#468	C₂²	semidirect
82. C₂₃×#466	C₂²	semidirect
83. C₂₃×#466	C₂²	semidirect
84. C₂₃×#465	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#463	C₂²	semidirect
87. C₂₃×#463	C₂²	semidirect
88. C₂₃×#461	C₂²	semidirect
89. C₂₃×#461	C₂²	semidirect
90. C₂₃×#460	C₂²	semidirect
91. C₂₃×#460	C₂²	semidirect
92. C₂₃×#459	C₂²	semidirect
93. C₂₃×#459	C₂²	semidirect
94. C₂₃×#459	C₂²	semidirect
95. C₂₃×#459	C₂²	semidirect
96. C₂₃×#450	C₂²	semidirect
97. C₂₃×#450	C₂²	semidirect
98. C₂₃×#449	C₂²	semidirect
99. C₂₃×#449	C₂²	semidirect
100. C₂₃×#449	C₂²	semidirect
101. C₂₃×#449	C₂²	semidirect
102. C₂₃×#449	C₂²	semidirect
103. C₂₃×#449	C₂²	semidirect
104. C₂₃×#449	C₂²	semidirect
105. C₂₃×#449	C₂²	semidirect
106. C₂₃×#449	C₂²	semidirect
107. C₂₃×#449	C₂²	semidirect
108. C₂₃×#449	C₂²	semidirect
109. C₂₃×#448	C₂²	semidirect
110. C₂₃×#448	C₂²	semidirect
111. C₂₃×#447	C₂²	semidirect
112. C₂₃×#447	C₂²	semidirect
113. C₂₃×#447	C₂²	semidirect
114. C₂₃×#447	C₂²	semidirect
115. C₂₃×#442	C₂²	semidirect
116. C₂₃×#440	C₂²	semidirect
117. C₄×SD₁₆×C₂₃	C₂²	semidirect
118. C₄×SD₁₆×C₂₃	C₂²	semidirect
119. C₄×D₈×C₂₃	C₂²	semidirect
120. C₄×D₈×C₂₃	C₂²	semidirect
121. C₂₃×#436	C₂²	semidirect
122. C₂₃×#436	C₂²	semidirect
123. C₂₃×#435	C₂²	semidirect
124. C₂₃×#435	C₂²	semidirect
125. C₈×D₄×C₂₃	C₂²	semidirect
126. C₈×D₄×C₂₃	C₂²	semidirect
127. C₂₃×#432	C₂²	semidirect
128. C₂₃×#431	C₂²	semidirect
129. C₂₃×#417	C₂²	semidirect
130. C₂₃×#417	C₂²	semidirect
131. C₂×C₂₃×#103	C₂²	semidirect
132. C₂×C₂₃×#102	C₂²	semidirect
133. C₂₃×#407	C₂²	semidirect
134. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
484. #61598	C₂₃	direct (N × H)
511. Q₈×C₂₃	H(5,𝔽₂)	semidirect
545. D₄×C₂₃	AGL(1,ℤ/8)	semidirect
546. D₄×C₂₃	H(5,𝔽₂)	semidirect
591. #3496	C₂×C₂₃	semidirect
592. D₄×#41	C₂×C₂₃	semidirect
593. #3332	C₂×C₂₃	semidirect
594. #3330	C₂×C₂₃	semidirect
595. #3308	C₂×C₂₃	semidirect
596. #3306	C₂×C₂₃	semidirect
597. #3298	C₂×C₂₃	semidirect
598. #3294	C₂×C₂₃	semidirect
599. D₄×SD₁₆	C₂×C₂₃	semidirect
600. D₄×D₈	C₂×C₂₃	semidirect
601. #3274	C₂×C₂₃	semidirect
602. #3272	C₂×C₂₃	semidirect
603. #3265	C₂×C₂₃	semidirect
604. #3264	C₂×C₂₃	semidirect
605. #3214	C₂×C₂₃	semidirect
606. #3207	C₂×C₂₃	semidirect
607. #3194	C₂×C₂₃	semidirect
608. #3188	C₂×C₂₃	semidirect
609. #3115	C₂×C₂₃	semidirect
610. #3106	C₂×C₂₃	semidirect
611. #3006	C₂×C₂₃	semidirect
612. C₂×#449	C₂×C₂₃	semidirect
613. #2974	C₂×C₂₃	semidirect
660. C₂²×#41	C₂²×C₂₃	semidirect
661. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
662. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
663. C₂²×SD₁₆	C₂²×C₂₃	semidirect
664. C₂²×D₈	C₂²×C₂₃	semidirect
665. #550	C₂²×C₂₃	semidirect
666. D₄×Q₈	C₂²×C₂₃	semidirect
667. #548	C₂²×C₂₃	semidirect
670. #547	C₂²×C₂₃	semidirect
671. #547	C₂²×C₂₃	semidirect
672. #547	C₂²×C₂₃	semidirect
677. #546	C₂²×C₂₃	semidirect
680. D₄²	C₂²×C₂₃	semidirect
681. D₄²	C₂²×C₂₃	semidirect
682. D₄²	C₂²×C₂₃	semidirect
686. #532	C₂²×C₂₃	semidirect
687. #532	C₂²×C₂₃	semidirect
688. #532	C₂²×C₂₃	semidirect
690. #525	C₂²×C₂₃	semidirect
691. C₂×#121	C₂²×C₂₃	semidirect
692. C₂×#121	C₂²×C₂₃	semidirect
693. C₄×#41	C₂²×C₂₃	semidirect
696. #496	C₂²×C₂₃	semidirect
697. #493	C₂²×C₂₃	semidirect
698. #492	C₂²×C₂₃	semidirect
699. #489	C₂²×C₂₃	semidirect
700. #487	C₂²×C₂₃	semidirect
701. #486	C₂²×C₂₃	semidirect
702. #484	C₂²×C₂₃	semidirect
703. #483	C₂²×C₂₃	semidirect
704. #482	C₂²×C₂₃	semidirect
705. #482	C₂²×C₂₃	semidirect
706. #482	C₂²×C₂₃	semidirect
707. #481	C₂²×C₂₃	semidirect
708. #480	C₂²×C₂₃	semidirect
709. #477	C₂²×C₂₃	semidirect
710. #476	C₂²×C₂₃	semidirect
711. #475	C₂²×C₂₃	semidirect
712. #474	C₂²×C₂₃	semidirect
713. #469	C₂²×C₂₃	semidirect
714. #469	C₂²×C₂₃	semidirect
715. #468	C₂²×C₂₃	semidirect
716. #468	C₂²×C₂₃	semidirect
717. #466	C₂²×C₂₃	semidirect
718. #466	C₂²×C₂₃	semidirect
719. #465	C₂²×C₂₃	semidirect
720. #465	C₂²×C₂₃	semidirect
721. #463	C₂²×C₂₃	semidirect
722. #463	C₂²×C₂₃	semidirect
723. #461	C₂²×C₂₃	semidirect
724. #461	C₂²×C₂₃	semidirect
725. #460	C₂²×C₂₃	semidirect
726. #460	C₂²×C₂₃	semidirect
727. #459	C₂²×C₂₃	semidirect
728. #459	C₂²×C₂₃	semidirect
729. #459	C₂²×C₂₃	semidirect
730. #459	C₂²×C₂₃	semidirect
731. #450	C₂²×C₂₃	semidirect
732. #450	C₂²×C₂₃	semidirect
733. #449	C₂²×C₂₃	semidirect
734. #449	C₂²×C₂₃	semidirect
735. #449	C₂²×C₂₃	semidirect
736. #449	C₂²×C₂₃	semidirect
737. #449	C₂²×C₂₃	semidirect
738. #449	C₂²×C₂₃	semidirect
739. #449	C₂²×C₂₃	semidirect
740. #449	C₂²×C₂₃	semidirect
741. #449	C₂²×C₂₃	semidirect
742. #449	C₂²×C₂₃	semidirect
743. #449	C₂²×C₂₃	semidirect
744. #448	C₂²×C₂₃	semidirect
745. #448	C₂²×C₂₃	semidirect
746. #447	C₂²×C₂₃	semidirect
747. #447	C₂²×C₂₃	semidirect
748. #447	C₂²×C₂₃	semidirect
749. #447	C₂²×C₂₃	semidirect
750. #442	C₂²×C₂₃	semidirect
751. #440	C₂²×C₂₃	semidirect
752. C₄×SD₁₆	C₂²×C₂₃	semidirect
753. C₄×SD₁₆	C₂²×C₂₃	semidirect
754. C₄×D₈	C₂²×C₂₃	semidirect
755. C₄×D₈	C₂²×C₂₃	semidirect
756. #436	C₂²×C₂₃	semidirect
757. #436	C₂²×C₂₃	semidirect
758. #435	C₂²×C₂₃	semidirect
759. #435	C₂²×C₂₃	semidirect
760. C₈×D₄	C₂²×C₂₃	semidirect
761. C₈×D₄	C₂²×C₂₃	semidirect
762. #432	C₂²×C₂₃	semidirect
763. #431	C₂²×C₂₃	semidirect
764. #417	C₂²×C₂₃	semidirect
765. #417	C₂²×C₂₃	semidirect
766. C₂×#103	C₂²×C₂₃	semidirect
767. C₂×#102	C₂²×C₂₃	semidirect
768. #407	C₂²×C₂₃	semidirect
769. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
965. C₂₃	#61598	direct (N × H)
1157. Q₈	C₂₃×H(5,𝔽₂)	semidirect
1191. D₄	C₂₃×AGL(1,ℤ/8)	semidirect
1192. D₄	C₂₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3496	2
D₄×#41×C₂₃	2
C₂₃×#3332	2
C₂₃×#3330	2
C₂₃×#3308	2
C₂₃×#3306	2
C₂₃×#3298	2
C₂₃×#3294	2
D₄×SD₁₆×C₂₃	2
D₄×D₈×C₂₃	2
C₂₃×#3274	2
C₂₃×#3272	2
C₂₃×#3265	2
C₂₃×#3264	2
C₂₃×#3214	2
C₂₃×#3207	2
C₂₃×#3194	2
C₂₃×#3188	2
C₂₃×#3115	2
C₂₃×#3106	2
C₂₃×#3006	2
C₂×C₂₃×#449	2
C₂₃×#2974	2
#61598	23

Subgroups — C23×#61598 #19209224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61598 #19209224