Subgroups — C₂₃×#61599 #19209225

Order 5888.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3313	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3311	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3271	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3268	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3197	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3191	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3005	C₂	1	2	yes	maximal, complemented
22	C₂₃×#3002	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	2	yes	—
25	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
26	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
28	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
29	C₂₃×#559	—	2	2	no	—
30	C₂₃×#556	C₂²	1	2	yes	complemented
31	C₂₃×#555	C₂²	1	1	yes	characteristic
32	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#553	—	2	1	no	—
34	C₂₃×#553	—	2	1	no	—
35	C₂₃×#550	C₂²	1	1	yes	characteristic
36	C₂₃×#550	C₂²	1	2	yes	complemented
37	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂₃×#548	C₂²	1	2	yes	—
39	C₂₃×#547	—	2	1	no	—
40	C₂₃×#547	C₂²	1	1	yes	characteristic
41	C₂₃×#547	C₂²	1	1	yes	characteristic
42	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#546	—	2	2	no	—
44	C₂₃×#546	C₂²	1	2	yes	—
45	D₄²×C₂₃	—	2	1	no	—
46	D₄²×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#538	—	2	2	no	—
48	C₂₃×#535	—	2	1	no	—
49	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#532	—	2	1	no	—
51	C₂₃×#532	C₂²	1	1	yes	characteristic
52	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#525	—	2	2	no	—
54	C₂₃×#525	C₂²	1	2	yes	—
55	C₂₃×#525	C₂²	1	2	yes	complemented
56	C₂₃×#525	C₂²	1	2	yes	complemented
57	C₂₃×#520	—	2	1	no	—
58	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
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×#494	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×#485	C₂²	1	2	yes	complemented
68	C₂₃×#485	C₂²	1	2	yes	complemented
69	C₂₃×#485	C₂²	1	2	yes	complemented
70	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#482	C₂²	1	2	yes	complemented
72	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#482	C₂²	1	2	yes	complemented
74	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#470	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×#467	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×#464	C₂²	1	2	yes	complemented
87	C₂₃×#464	C₂²	1	2	yes	complemented
88	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#460	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×#452	C₂²	1	2	yes	—
97	C₂₃×#452	C₂²	1	2	yes	complemented
98	C₂₃×#452	C₂²	1	2	yes	complemented
99	C₂₃×#452	C₂²	1	2	yes	complemented
100	C₂₃×#452	C₂²	1	2	yes	complemented
101	C₂₃×#452	C₂²	1	2	yes	complemented
102	C₂₃×#452	C₂²	1	2	yes	complemented
103	C₂₃×#451	C₂²	1	2	yes	complemented
104	C₂₃×#450	C₂²	1	2	yes	complemented
105	C₂₃×#449	C₂²	1	1	yes	characteristic
106	C₂₃×#449	C₂²	1	1	yes	characteristic
107	C₂₃×#449	C₂²	1	2	yes	complemented
108	C₂₃×#449	C₂²	1	2	yes	complemented
109	C₂₃×#449	C₂²	1	2	yes	complemented
110	C₂₃×#449	C₂²	1	2	yes	complemented
111	C₂₃×#449	C₂²	1	2	yes	complemented
112	C₂₃×#449	C₂²	1	2	yes	complemented
113	C₂₃×#448	C₂²	1	2	yes	complemented
114	C₂₃×#447	C₂²	1	2	yes	complemented
115	C₂₃×#441	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
122	C₂₃×#436	C₂²	1	1	yes	characteristic
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×#419	C₂²	1	2	yes	complemented
130	C₂₃×#418	C₂²	1	2	yes	complemented
131	C₂₃×#416	C₂²	1	2	yes	complemented
132	C₂₃×#416	C₂²	1	2	yes	complemented
133	C₂₃×#407	C₂²	1	2	yes	complemented
134	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₂×#41×C₂₃	—	2	2	no	—
136	C₂×#41×C₂₃	—	2	2	no	—
137	C₂×#41×C₂₃	—	2	1	no	—
138	C₂×#41×C₂₃	—	4	4	no	—
139	C₂×#41×C₂₃	—	4	4	no	—
140	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₂₃	C₂³	1	2	yes	—
142	C₂×#41×C₂₃	C₂³	1	2	yes	—
143	C₂×#41×C₂₃	C₂³	1	2	yes	—
144	C₂×#41×C₂₃	C₂³	1	2	yes	—
145	C₂×#41×C₂₃	C₂³	1	2	yes	—
146	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
147	C₂²×D₄×C₂₃	—	2	2	no	—
148	C₂²×D₄×C₂₃	—	2	1	no	—
149	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
150	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
151	C₂³×C₄×C₂₃	—	2	2	no	—
152	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
153	C₂₃×#137	—	4	4	no	—
154	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
155	C₂₃×#135	—	4	4	no	—
156	C₂₃×#135	—	4	4	no	—
157	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
167	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
168	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×D₈×C₂₃	C₂³	1	2	yes	—
170	C₂×D₈×C₂₃	C₂³	1	2	yes	—
171	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
174	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
175	C₂₃×C₄⋊Q₈	—	2	1	no	—
176	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
177	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₂₃×#127	—	2	1	no	—
181	C₂₃×#127	—	2	2	no	—
182	C₂₃×#127	C₂³	1	1	yes	characteristic
183	C₂₃×#127	C₂³	1	1	yes	characteristic
184	C₂₃×#126	—	2	2	no	—
185	C₂₃×#126	—	2	2	no	—
186	C₂₃×#125	—	2	1	no	—
187	C₂₃×#124	—	2	2	no	—
188	C₂₃×#124	—	2	2	no	—
189	C₂₃×#124	—	2	2	no	—
190	C₂₃×#124	—	2	2	no	—
191	C₂₃×#124	—	2	1	no	—
192	C₂₃×#124	C₂³	1	2	yes	—
193	C₂₃×#123	—	2	2	no	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	2	no	—
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×C₂²⋊Q₈	—	2	1	no	—
201	C₂₃×C₂²⋊Q₈	—	2	2	no	—
202	C₂₃×C₂²⋊Q₈	—	2	2	no	—
203	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂₃×#121	—	2	1	no	—
209	C₂₃×#121	—	2	1	no	—
210	C₂₃×#121	—	2	1	no	—
211	C₂₃×#121	—	2	2	no	—
212	C₂₃×#121	—	2	1	no	—
213	C₂₃×#121	—	2	1	no	—
214	C₂₃×#121	—	2	1	no	—
215	C₂₃×#121	—	2	1	no	—
216	C₂₃×#121	—	2	1	no	—
217	C₂₃×#121	—	2	1	no	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	C₂³	1	2	yes	—
223	C₂₃×#121	C₂³	1	2	yes	—
224	C₂₃×#121	C₂³	1	2	yes	—
225	C₂₃×#121	C₂³	1	2	yes	—
226	C₂₃×#121	C₂³	1	1	yes	characteristic
227	C₂₃×#121	C₂³	1	1	yes	characteristic
228	C₂₃×#120	—	2	2	no	—
229	C₂₃×#120	—	2	2	no	—
230	C₂₃×#120	—	2	2	no	—
231	C₂₃×#120	—	2	2	no	—
232	C₂₃×#120	—	2	2	no	—
233	C₄×Q₈×C₂₃	—	2	2	no	—
234	C₄×Q₈×C₂₃	—	2	1	no	—
235	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
238	C₄×D₄×C₂₃	—	2	1	no	—
239	C₄×D₄×C₂₃	—	2	1	no	—
240	C₄×D₄×C₂₃	—	2	2	no	—
241	C₄×D₄×C₂₃	—	2	2	no	—
242	C₄×D₄×C₂₃	—	2	2	no	—
243	C₄×D₄×C₂₃	—	2	1	no	—
244	C₄×D₄×C₂₃	—	2	2	no	—
245	C₄×D₄×C₂₃	—	2	2	no	—
246	C₄×D₄×C₂₃	—	2	2	no	—
247	C₄×D₄×C₂₃	—	2	1	no	—
248	C₄×D₄×C₂₃	—	2	2	no	—
249	C₄×D₄×C₂₃	—	2	2	no	—
250	C₄×D₄×C₂₃	—	2	1	no	—
251	C₄×D₄×C₂₃	—	2	1	no	—
252	C₄×D₄×C₂₃	—	2	1	no	—
253	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
254	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
255	C₄×D₄×C₂₃	D₄	1	2	yes	—
256	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₂₃	C₂³	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	C₂₃×#117	—	2	1	no	—
264	C₂₃×#117	—	2	1	no	—
265	C₂₃×#117	—	2	1	no	—
266	C₂₃×#117	—	2	1	no	—
267	C₂₃×#117	C₂³	1	2	yes	—
268	C₂₃×#117	C₂³	1	2	yes	—
269	C₂₃×#117	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
272	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
276	C₂×C₄²×C₂₃	—	2	1	no	—
277	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
278	C₂₃×#107	C₂³	1	1	yes	characteristic
279	C₂₃×#107	C₂³	1	1	yes	characteristic
280	C₂₃×#107	C₂³	1	2	yes	—
281	C₂₃×#106	C₂³	1	1	yes	characteristic
282	C₂₃×#106	C₂³	1	1	yes	characteristic
283	C₂₃×#106	C₂³	1	2	yes	—
284	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	1	yes	characteristic
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	1	yes	characteristic
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#103	C₂³	1	2	yes	—
296	C₂₃×#103	C₂³	1	2	yes	—
297	C₂₃×#102	C₂³	1	1	yes	characteristic
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
308	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
313	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₂₃×#97	C₂³	1	2	yes	—
316	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
318	C₂⁴×C₂₃	—	2	2	no	—
319	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
320	#41×C₂₃	—	2	2	no	—
321	#41×C₂₃	—	2	2	no	—
322	#41×C₂₃	—	2	4	no	—
323	#41×C₂₃	—	2	4	no	—
324	#41×C₂₃	—	4	2	no	—
325	#41×C₂₃	—	4	2	no	—
326	#41×C₂₃	—	4	2	no	—
327	#41×C₂₃	—	4	2	no	—
328	#41×C₂₃	—	4	4	no	—
329	#41×C₂₃	—	4	8	no	—
330	#41×C₂₃	—	4	2	no	—
331	#41×C₂₃	—	4	2	no	—
332	#41×C₂₃	—	4	2	no	—
333	#41×C₂₃	—	4	2	no	—
334	#41×C₂₃	—	4	8	no	—
335	C₂×Q₈×C₂₃	—	2	1	no	—
336	C₂×Q₈×C₂₃	—	2	2	no	—
337	C₂×Q₈×C₂₃	—	2	1	no	—
338	C₂×Q₈×C₂₃	—	2	4	no	—
339	C₂×Q₈×C₂₃	—	4	2	no	—
340	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
341	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
342	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₂₃	—	2	1	no	—
344	C₂×D₄×C₂₃	—	2	4	no	—
345	C₂×D₄×C₂₃	—	2	2	no	—
346	C₂×D₄×C₂₃	—	2	1	no	—
347	C₂×D₄×C₂₃	—	2	1	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	2	no	—
356	C₂×D₄×C₂₃	—	2	1	no	—
357	C₂×D₄×C₂₃	—	2	1	no	—
358	C₂×D₄×C₂₃	—	2	2	no	—
359	C₂×D₄×C₂₃	—	2	1	no	—
360	C₂×D₄×C₂₃	—	2	1	no	—
361	C₂×D₄×C₂₃	—	4	2	no	—
362	C₂×D₄×C₂₃	—	4	2	no	—
363	C₂×D₄×C₂₃	—	4	4	no	—
364	C₂×D₄×C₂₃	—	4	8	no	—
365	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
369	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
370	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₂₃	—	2	1	no	—
373	C₂²×C₄×C₂₃	—	2	2	no	—
374	C₂²×C₄×C₂₃	—	2	1	no	—
375	C₂²×C₄×C₂₃	—	2	2	no	—
376	C₂²×C₄×C₂₃	—	2	1	no	—
377	C₂²×C₄×C₂₃	—	2	1	no	—
378	C₂²×C₄×C₂₃	—	2	2	no	—
379	C₂²×C₄×C₂₃	—	2	2	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	2	no	—
382	C₂²×C₄×C₂₃	—	2	2	no	—
383	C₂²×C₄×C₂₃	—	4	2	no	—
384	C₂²×C₄×C₂₃	—	4	2	no	—
385	C₂²×C₄×C₂₃	—	4	8	no	—
386	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
389	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
390	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
391	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
394	Q₁₆×C₂₃	—	2	4	no	—
395	Q₁₆×C₂₃	—	4	2	no	—
396	Q₁₆×C₂₃	—	4	2	no	—
397	SD₁₆×C₂₃	—	2	2	no	—
398	SD₁₆×C₂₃	—	2	2	no	—
399	SD₁₆×C₂₃	—	2	4	no	—
400	SD₁₆×C₂₃	—	4	2	no	—
401	SD₁₆×C₂₃	—	4	2	no	—
402	SD₁₆×C₂₃	—	4	2	no	—
403	SD₁₆×C₂₃	—	4	2	no	—
404	D₈×C₂₃	—	2	2	no	—
405	D₈×C₂₃	—	2	2	no	—
406	D₈×C₂₃	—	4	2	no	—
407	D₈×C₂₃	—	4	2	no	—
408	M₁₆×C₂₃	—	4	2	no	—
409	M₁₆×C₂₃	—	4	2	no	—
410	C₂×C₈×C₂₃	—	4	2	no	—
411	C₂×C₈×C₂₃	—	4	2	no	—
412	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
416	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
417	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₂₃	—	2	1	no	—
419	C₄⋊C₄×C₂₃	—	2	1	no	—
420	C₄⋊C₄×C₂₃	—	2	2	no	—
421	C₄⋊C₄×C₂₃	—	2	2	no	—
422	C₄⋊C₄×C₂₃	—	2	2	no	—
423	C₄⋊C₄×C₂₃	—	2	1	no	—
424	C₄⋊C₄×C₂₃	—	2	1	no	—
425	C₄⋊C₄×C₂₃	—	2	1	no	—
426	C₄⋊C₄×C₂₃	—	2	2	no	—
427	C₄⋊C₄×C₂₃	—	2	1	no	—
428	C₄⋊C₄×C₂₃	—	2	2	no	—
429	C₄⋊C₄×C₂₃	—	2	1	no	—
430	C₄⋊C₄×C₂₃	—	2	1	no	—
431	C₄⋊C₄×C₂₃	—	2	2	no	—
432	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
433	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
435	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₂₃	—	2	2	no	—
441	C₂²⋊C₄×C₂₃	—	2	2	no	—
442	C₂²⋊C₄×C₂₃	—	2	1	no	—
443	C₂²⋊C₄×C₂₃	—	2	2	no	—
444	C₂²⋊C₄×C₂₃	—	2	2	no	—
445	C₂²⋊C₄×C₂₃	—	2	2	no	—
446	C₂²⋊C₄×C₂₃	—	2	2	no	—
447	C₂²⋊C₄×C₂₃	—	2	2	no	—
448	C₂²⋊C₄×C₂₃	—	2	2	no	—
449	C₂²⋊C₄×C₂₃	—	2	2	no	—
450	C₂²⋊C₄×C₂₃	—	2	2	no	—
451	C₂²⋊C₄×C₂₃	—	2	2	no	—
452	C₂²⋊C₄×C₂₃	—	2	1	no	—
453	C₂²⋊C₄×C₂₃	—	2	1	no	—
454	C₂²⋊C₄×C₂₃	—	2	1	no	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	2	no	—
457	C₂²⋊C₄×C₂₃	—	2	2	no	—
458	C₂²⋊C₄×C₂₃	—	2	1	no	—
459	C₂²⋊C₄×C₂₃	—	2	1	no	—
460	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
464	C₄²×C₂₃	—	2	1	no	—
465	C₄²×C₂₃	—	2	1	no	—
466	C₄²×C₂₃	—	2	1	no	—
467	C₄²×C₂₃	—	2	2	no	—
468	C₄²×C₂₃	—	2	2	no	—
469	C₄²×C₂₃	—	2	2	no	—
470	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
473	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
474	#61599	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂³×C₂₃	—	2	1	no	—
476	C₂³×C₂₃	—	2	1	no	—
477	C₂³×C₂₃	—	2	1	no	—
478	C₂³×C₂₃	—	2	2	no	—
479	C₂³×C₂₃	—	4	2	no	—
480	C₂³×C₂₃	—	4	2	no	—
481	C₂³×C₂₃	—	4	2	no	—
482	C₂³×C₂₃	—	4	4	no	—
483	C₂³×C₂₃	—	4	4	no	—
484	C₂³×C₂₃	—	8	2	no	—
485	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
486	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
487	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
488	Q₈×C₂₃	—	2	1	no	—
489	Q₈×C₂₃	—	2	2	no	—
490	Q₈×C₂₃	—	2	2	no	—
491	Q₈×C₂₃	—	2	2	no	—
492	Q₈×C₂₃	—	2	2	no	—
493	Q₈×C₂₃	—	4	4	no	—
494	Q₈×C₂₃	—	4	2	no	—
495	Q₈×C₂₃	—	8	1	no	—
496	Q₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
497	D₄×C₂₃	—	2	4	no	—
498	D₄×C₂₃	—	2	2	no	—
499	D₄×C₂₃	—	2	2	no	—
500	D₄×C₂₃	—	2	1	no	—
501	D₄×C₂₃	—	2	1	no	—
502	D₄×C₂₃	—	2	1	no	—
503	D₄×C₂₃	—	2	1	no	—
504	D₄×C₂₃	—	2	2	no	—
505	D₄×C₂₃	—	2	2	no	—
506	D₄×C₂₃	—	2	1	no	—
507	D₄×C₂₃	—	4	2	no	—
508	D₄×C₂₃	—	4	4	no	—
509	D₄×C₂₃	—	4	4	no	—
510	D₄×C₂₃	—	4	2	no	—
511	D₄×C₂₃	—	4	4	no	—
512	D₄×C₂₃	—	4	4	no	—
513	D₄×C₂₃	—	4	4	no	—
514	D₄×C₂₃	—	4	2	no	—
515	D₄×C₂₃	—	4	2	no	—
516	D₄×C₂₃	—	4	2	no	—
517	D₄×C₂₃	—	8	1	no	—
518	D₄×C₂₃	—	8	1	no	—
519	D₄×C₂₃	—	8	2	no	—
520	D₄×C₂₃	—	8	2	no	—
521	D₄×C₂₃	—	8	2	no	—
522	D₄×C₂₃	—	8	2	no	—
523	D₄×C₂₃	—	8	2	no	—
524	D₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
525	C₂×C₄×C₂₃	—	2	4	no	—
526	C₂×C₄×C₂₃	—	2	1	no	—
527	C₂×C₄×C₂₃	—	2	2	no	—
528	C₂×C₄×C₂₃	—	2	2	no	—
529	C₂×C₄×C₂₃	—	2	2	no	—
530	C₂×C₄×C₂₃	—	2	2	no	—
531	C₂×C₄×C₂₃	—	2	2	no	—
532	C₂×C₄×C₂₃	—	2	1	no	—
533	C₂×C₄×C₂₃	—	2	1	no	—
534	C₂×C₄×C₂₃	—	2	2	no	—
535	C₂×C₄×C₂₃	—	2	1	no	—
536	C₂×C₄×C₂₃	—	2	1	no	—
537	C₂×C₄×C₂₃	—	2	1	no	—
538	C₂×C₄×C₂₃	—	2	1	no	—
539	C₂×C₄×C₂₃	—	2	2	no	—
540	C₂×C₄×C₂₃	—	2	2	no	—
541	C₂×C₄×C₂₃	—	4	2	no	—
542	C₂×C₄×C₂₃	—	4	2	no	—
543	C₂×C₄×C₂₃	—	4	2	no	—
544	C₂×C₄×C₂₃	—	4	1	no	—
545	C₂×C₄×C₂₃	—	4	4	no	—
546	C₂×C₄×C₂₃	—	4	4	no	—
547	C₂×C₄×C₂₃	—	4	4	no	—
548	C₂×C₄×C₂₃	—	4	4	no	—
549	C₂×C₄×C₂₃	—	4	2	no	—
550	C₂×C₄×C₂₃	—	4	2	no	—
551	C₂×C₄×C₂₃	—	4	2	no	—
552	C₂×C₄×C₂₃	—	8	1	no	—
553	C₂×C₄×C₂₃	—	8	2	no	—
554	C₂×C₄×C₂₃	—	8	2	no	—
555	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
563	C₈×C₂₃	—	2	1	no	—
564	C₈×C₂₃	—	2	1	no	—
565	C₈×C₂₃	—	2	2	no	—
566	C₈×C₂₃	—	2	2	no	—
567	C₈×C₂₃	—	2	1	no	—
568	C₈×C₂₃	—	2	1	no	—
569	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
570	D₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
571	#3329	C₂×C₂₃	1	1	yes	characteristic, complemented
572	#3325	C₂×C₂₃	1	1	yes	characteristic, complemented
573	#3313	C₂×C₂₃	1	2	yes	complemented
574	#3311	C₂×C₂₃	1	2	yes	complemented
575	#3305	C₂×C₂₃	1	1	yes	characteristic, complemented
576	#3303	C₂×C₂₃	1	1	yes	characteristic, complemented
577	#3284	C₂×C₂₃	1	1	yes	characteristic, complemented
578	#3283	C₂×C₂₃	1	1	yes	characteristic, complemented
579	#3276	C₂×C₂₃	1	1	yes	characteristic, complemented
580	#3272	C₂×C₂₃	1	1	yes	characteristic, complemented
581	#3271	C₂×C₂₃	1	2	yes	complemented
582	#3268	C₂×C₂₃	1	2	yes	complemented
583	#3214	C₂×C₂₃	1	1	yes	characteristic, complemented
584	#3210	C₂×C₂₃	1	1	yes	characteristic, complemented
585	#3197	C₂×C₂₃	1	2	yes	complemented
586	#3191	C₂×C₂₃	1	2	yes	complemented
587	#3116	C₂×C₂₃	1	1	yes	characteristic, complemented
588	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
589	#3005	C₂×C₂₃	1	2	yes	complemented
590	#3002	C₂×C₂₃	1	2	yes	complemented
591	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
592	C₂²×C₂₃	—	2	1	no	—
593	C₂²×C₂₃	—	2	2	no	—
594	C₂²×C₂₃	—	2	2	no	—
595	C₂²×C₂₃	—	2	2	no	—
596	C₂²×C₂₃	—	2	1	no	—
597	C₂²×C₂₃	—	2	2	no	—
598	C₂²×C₂₃	—	2	2	no	—
599	C₂²×C₂₃	—	2	1	no	—
600	C₂²×C₂₃	—	2	2	no	—
601	C₂²×C₂₃	—	2	2	no	—
602	C₂²×C₂₃	—	4	1	no	—
603	C₂²×C₂₃	—	4	1	no	—
604	C₂²×C₂₃	—	4	1	no	—
605	C₂²×C₂₃	—	4	1	no	—
606	C₂²×C₂₃	—	4	2	no	—
607	C₂²×C₂₃	—	4	2	no	—
608	C₂²×C₂₃	—	4	1	no	—
609	C₂²×C₂₃	—	4	1	no	—
610	C₂²×C₂₃	—	4	1	no	—
611	C₂²×C₂₃	—	4	1	no	—
612	C₂²×C₂₃	—	4	2	no	—
613	C₂²×C₂₃	—	8	4	no	—
614	C₂²×C₂₃	—	8	8	no	—
615	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
616	C₄×C₂₃	—	2	1	no	—
617	C₄×C₂₃	—	2	1	no	—
618	C₄×C₂₃	—	2	1	no	—
619	C₄×C₂₃	—	2	2	no	—
620	C₄×C₂₃	—	2	2	no	—
621	C₄×C₂₃	—	2	2	no	—
622	C₄×C₂₃	—	2	1	no	—
623	C₄×C₂₃	—	4	1	no	—
624	C₄×C₂₃	—	4	2	no	—
625	C₄×C₂₃	—	4	2	no	—
626	C₄×C₂₃	—	4	2	no	—
627	C₄×C₂₃	—	4	1	no	—
628	C₄×C₂₃	—	4	1	no	—
629	C₄×C₂₃	—	4	1	no	—
630	C₄×C₂₃	#575	1	2	yes	—
631	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
632	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
633	C₂²×#41	C₂²×C₂₃	1	2	yes	—
634	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
635	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
636	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
637	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
638	#559	—	2	2	no	—
639	#556	C₂²×C₂₃	1	2	yes	complemented
640	#555	C₂²×C₂₃	1	1	yes	characteristic
641	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
642	#553	—	2	1	no	—
643	#553	—	2	1	no	—
644	#550	C₂²×C₂₃	1	1	yes	characteristic
645	#550	C₂²×C₂₃	1	2	yes	complemented
646	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
647	#548	C₂²×C₂₃	1	2	yes	—
648	#547	—	2	1	no	—
649	#547	C₂²×C₂₃	1	1	yes	characteristic
650	#547	C₂²×C₂₃	1	1	yes	characteristic
651	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
652	#546	—	2	2	no	—
653	#546	C₂²×C₂₃	1	2	yes	—
654	D₄²	—	2	1	no	—
655	D₄²	C₂²×C₂₃	1	1	yes	characteristic
656	#538	—	2	2	no	—
657	#535	—	2	1	no	—
658	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	#532	—	2	1	no	—
660	#532	C₂²×C₂₃	1	1	yes	characteristic
661	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
662	#525	—	2	2	no	—
663	#525	C₂²×C₂₃	1	2	yes	—
664	#525	C₂²×C₂₃	1	2	yes	complemented
665	#525	C₂²×C₂₃	1	2	yes	complemented
666	#520	—	2	1	no	—
667	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
668	C₂×C₄×D₄	—	2	1	no	—
669	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
670	#496	C₂²×C₂₃	1	2	yes	complemented
671	#494	C₂²×C₂₃	1	1	yes	characteristic, complemented
672	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	#489	C₂²×C₂₃	1	2	yes	complemented
674	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
675	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	#485	C₂²×C₂₃	1	2	yes	complemented
677	#485	C₂²×C₂₃	1	2	yes	complemented
678	#485	C₂²×C₂₃	1	2	yes	complemented
679	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
680	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	#482	C₂²×C₂₃	1	2	yes	complemented
682	#482	C₂²×C₂₃	1	2	yes	complemented
683	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
684	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
687	#470	C₂²×C₂₃	1	2	yes	complemented
688	#469	C₂²×C₂₃	1	2	yes	complemented
689	#468	C₂²×C₂₃	1	2	yes	complemented
690	#468	C₂²×C₂₃	1	2	yes	complemented
691	#467	C₂²×C₂₃	1	2	yes	complemented
692	#466	C₂²×C₂₃	1	2	yes	complemented
693	#465	C₂²×C₂₃	1	2	yes	complemented
694	#465	C₂²×C₂₃	1	2	yes	complemented
695	#464	C₂²×C₂₃	1	2	yes	complemented
696	#464	C₂²×C₂₃	1	2	yes	complemented
697	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
699	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
700	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
701	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
702	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
703	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
704	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
705	#452	C₂²×C₂₃	1	2	yes	—
706	#452	C₂²×C₂₃	1	2	yes	complemented
707	#452	C₂²×C₂₃	1	2	yes	complemented
708	#452	C₂²×C₂₃	1	2	yes	complemented
709	#452	C₂²×C₂₃	1	2	yes	complemented
710	#452	C₂²×C₂₃	1	2	yes	complemented
711	#452	C₂²×C₂₃	1	2	yes	complemented
712	#451	C₂²×C₂₃	1	2	yes	complemented
713	#450	C₂²×C₂₃	1	2	yes	complemented
714	#449	C₂²×C₂₃	1	1	yes	characteristic
715	#449	C₂²×C₂₃	1	1	yes	characteristic
716	#449	C₂²×C₂₃	1	2	yes	complemented
717	#449	C₂²×C₂₃	1	2	yes	complemented
718	#449	C₂²×C₂₃	1	2	yes	complemented
719	#449	C₂²×C₂₃	1	2	yes	complemented
720	#449	C₂²×C₂₃	1	2	yes	complemented
721	#449	C₂²×C₂₃	1	2	yes	complemented
722	#448	C₂²×C₂₃	1	2	yes	complemented
723	#447	C₂²×C₂₃	1	2	yes	complemented
724	#441	C₂²×C₂₃	1	2	yes	complemented
725	#440	C₂²×C₂₃	1	2	yes	complemented
726	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
727	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
728	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
729	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
730	#436	C₂²×C₂₃	1	1	yes	characteristic
731	#436	C₂²×C₂₃	1	1	yes	characteristic
732	#435	C₂²×C₂₃	1	2	yes	complemented
733	#435	C₂²×C₂₃	1	2	yes	complemented
734	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
735	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
736	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
737	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
738	#419	C₂²×C₂₃	1	2	yes	complemented
739	#418	C₂²×C₂₃	1	2	yes	complemented
740	#416	C₂²×C₂₃	1	2	yes	complemented
741	#416	C₂²×C₂₃	1	2	yes	complemented
742	#407	C₂²×C₂₃	1	2	yes	complemented
743	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
744	C₂×C₂₃	—	4	2	no	—
745	C₂×C₂₃	—	4	1	no	—
746	C₂×C₂₃	—	4	2	no	—
747	C₂×C₂₃	—	4	2	no	—
748	C₂×C₂₃	—	8	1	no	—
749	C₂×C₂₃	—	8	1	no	—
750	C₂×C₂₃	—	8	2	no	—
751	C₂×C₂₃	#3484	1	1	yes	characteristic
752	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
753	C₂×C₂₃	#3584	1	1	yes	characteristic
754	C₂×#41	—	2	1	no	—
755	C₂×#41	—	2	2	no	—
756	C₂×#41	—	2	2	no	—
757	C₂×#41	—	4	4	no	—
758	C₂×#41	—	4	4	no	—
759	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
760	C₂×#41	C₂³×C₂₃	1	2	yes	—
761	C₂×#41	C₂³×C₂₃	1	2	yes	—
762	C₂×#41	C₂³×C₂₃	1	2	yes	—
763	C₂×#41	C₂³×C₂₃	1	2	yes	—
764	C₂×#41	C₂³×C₂₃	1	2	yes	—
765	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
766	C₂²×D₄	—	2	2	no	—
767	C₂²×D₄	—	2	1	no	—
768	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
769	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
770	C₂³×C₄	—	2	2	no	—
771	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
772	#137	—	4	4	no	—
773	AGL(1,ℤ/8)	—	4	4	no	—
774	#135	—	4	4	no	—
775	#135	—	4	4	no	—
776	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
777	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
778	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
780	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
781	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
782	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
786	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
787	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
788	C₂×D₈	C₂³×C₂₃	1	2	yes	—
789	C₂×D₈	C₂³×C₂₃	1	2	yes	—
790	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
791	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
792	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
793	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
794	C₄⋊Q₈	—	2	1	no	—
795	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
797	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
798	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
799	#127	—	2	1	no	—
800	#127	—	2	2	no	—
801	#127	C₂³×C₂₃	1	1	yes	characteristic
802	#127	C₂³×C₂₃	1	1	yes	characteristic
803	#126	—	2	2	no	—
804	#126	—	2	2	no	—
805	#125	—	2	1	no	—
806	#124	—	2	2	no	—
807	#124	—	2	2	no	—
808	#124	—	2	2	no	—
809	#124	—	2	2	no	—
810	#124	—	2	1	no	—
811	#124	C₂³×C₂₃	1	2	yes	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	2	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
823	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
827	#121	—	2	2	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	1	no	—
835	#121	—	2	1	no	—
836	#121	—	2	1	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	C₂³×C₂₃	1	2	yes	—
842	#121	C₂³×C₂₃	1	2	yes	—
843	#121	C₂³×C₂₃	1	1	yes	characteristic
844	#121	C₂³×C₂₃	1	1	yes	characteristic
845	#121	C₂³×C₂₃	1	2	yes	—
846	#121	C₂³×C₂₃	1	2	yes	—
847	#120	—	2	2	no	—
848	#120	—	2	2	no	—
849	#120	—	2	2	no	—
850	#120	—	2	2	no	—
851	#120	—	2	2	no	—
852	C₄×Q₈	—	2	2	no	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
855	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
856	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
873	C₄×D₄	D₄×C₂₃	1	2	yes	—
874	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
876	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
877	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
878	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
879	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
880	C₄×D₄	C₂³×C₂₃	1	2	yes	—
881	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
882	#117	—	2	1	no	—
883	#117	—	2	1	no	—
884	#117	—	2	1	no	—
885	#117	—	2	1	no	—
886	#117	C₂³×C₂₃	1	1	yes	characteristic
887	#117	C₂³×C₂₃	1	2	yes	—
888	#117	C₂³×C₂₃	1	2	yes	—
889	C₂×C₄⋊C₄	—	2	1	no	—
890	C₂×C₄⋊C₄	—	2	1	no	—
891	C₂×C₄⋊C₄	—	2	1	no	—
892	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
893	C₂×C₂²⋊C₄	—	2	2	no	—
894	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
895	C₂×C₄²	—	2	1	no	—
896	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
897	#107	C₂³×C₂₃	1	1	yes	characteristic
898	#107	C₂³×C₂₃	1	1	yes	characteristic
899	#107	C₂³×C₂₃	1	2	yes	—
900	#106	C₂³×C₂₃	1	1	yes	characteristic
901	#106	C₂³×C₂₃	1	1	yes	characteristic
902	#106	C₂³×C₂₃	1	2	yes	—
903	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
904	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
905	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
906	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
907	#103	C₂³×C₂₃	1	1	yes	characteristic
908	#103	C₂³×C₂₃	1	2	yes	—
909	#103	C₂³×C₂₃	1	2	yes	—
910	#103	C₂³×C₂₃	1	2	yes	—
911	#103	C₂³×C₂₃	1	1	yes	characteristic
912	#103	C₂³×C₂₃	1	2	yes	—
913	#103	C₂³×C₂₃	1	2	yes	—
914	#103	C₂³×C₂₃	1	2	yes	—
915	#103	C₂³×C₂₃	1	2	yes	—
916	#102	C₂³×C₂₃	1	1	yes	characteristic
917	#102	C₂³×C₂₃	1	2	yes	—
918	#102	C₂³×C₂₃	1	2	yes	—
919	#102	C₂³×C₂₃	1	2	yes	—
920	#102	C₂³×C₂₃	1	1	yes	characteristic
921	#102	C₂³×C₂₃	1	2	yes	—
922	#102	C₂³×C₂₃	1	2	yes	—
923	#102	C₂³×C₂₃	1	1	yes	characteristic
924	#102	C₂³×C₂₃	1	1	yes	characteristic
925	#102	C₂³×C₂₃	1	1	yes	characteristic
926	#102	C₂³×C₂₃	1	1	yes	characteristic
927	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
931	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
932	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
933	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
934	#97	C₂³×C₂₃	1	2	yes	—
935	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
936	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
937	C₂₃	#61599	1	1	yes	characteristic, direct product factor, Sylow
938	C₂⁴	—	2	2	no	—
939	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
940	#41	—	2	2	no	—
941	#41	—	2	2	no	—
942	#41	—	2	4	no	—
943	#41	—	2	4	no	—
944	#41	—	4	2	no	—
945	#41	—	4	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	8	no	—
949	#41	—	4	4	no	—
950	#41	—	4	2	no	—
951	#41	—	4	2	no	—
952	#41	—	4	2	no	—
953	#41	—	4	2	no	—
954	#41	—	4	8	no	—
955	C₂×Q₈	—	2	1	no	—
956	C₂×Q₈	—	2	2	no	—
957	C₂×Q₈	—	2	1	no	—
958	C₂×Q₈	—	2	4	no	—
959	C₂×Q₈	—	4	2	no	—
960	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
961	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
962	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	4	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	4	2	no	—
982	C₂×D₄	—	4	2	no	—
983	C₂×D₄	—	4	8	no	—
984	C₂×D₄	—	4	4	no	—
985	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
986	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
987	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
988	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
989	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
990	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
991	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	4	2	no	—
1004	C₂²×C₄	—	4	2	no	—
1005	C₂²×C₄	—	4	8	no	—
1006	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1007	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1009	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1010	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1011	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1013	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1014	Q₁₆	—	2	4	no	—
1015	Q₁₆	—	4	2	no	—
1016	Q₁₆	—	4	2	no	—
1017	SD₁₆	—	2	2	no	—
1018	SD₁₆	—	2	2	no	—
1019	SD₁₆	—	2	4	no	—
1020	SD₁₆	—	4	2	no	—
1021	SD₁₆	—	4	2	no	—
1022	SD₁₆	—	4	2	no	—
1023	SD₁₆	—	4	2	no	—
1024	D₈	—	2	2	no	—
1025	D₈	—	2	2	no	—
1026	D₈	—	4	2	no	—
1027	D₈	—	4	2	no	—
1028	M₁₆	—	4	2	no	—
1029	M₁₆	—	4	2	no	—
1030	C₂×C₈	—	4	2	no	—
1031	C₂×C₈	—	4	2	no	—
1032	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1033	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1034	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1035	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1036	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1053	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1054	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1058	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1059	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1081	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1082	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1083	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1091	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1092	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1093	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	1	no	—
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	2	no	—
1098	C₂³	—	4	2	no	—
1099	C₂³	—	4	2	no	—
1100	C₂³	—	4	2	no	—
1101	C₂³	—	4	4	no	—
1102	C₂³	—	4	4	no	—
1103	C₂³	—	8	2	no	—
1104	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1105	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1106	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	2	no	—
1109	Q₈	—	2	2	no	—
1110	Q₈	—	2	2	no	—
1111	Q₈	—	2	2	no	—
1112	Q₈	—	4	4	no	—
1113	Q₈	—	4	2	no	—
1114	Q₈	—	8	1	no	—
1115	Q₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1116	D₄	—	2	4	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	2	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	2	1	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	2	2	no	—
1125	D₄	—	2	1	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	4	no	—
1128	D₄	—	4	4	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	4	no	—
1131	D₄	—	4	4	no	—
1132	D₄	—	4	4	no	—
1133	D₄	—	4	2	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	8	1	no	—
1137	D₄	—	8	1	no	—
1138	D₄	—	8	2	no	—
1139	D₄	—	8	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	2	no	—
1143	D₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1144	C₂×C₄	—	2	4	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	4	2	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	4	no	—
1165	C₂×C₄	—	4	4	no	—
1166	C₂×C₄	—	4	4	no	—
1167	C₂×C₄	—	4	4	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	4	2	no	—
1171	C₂×C₄	—	8	2	no	—
1172	C₂×C₄	—	8	2	no	—
1173	C₂×C₄	—	8	1	no	—
1174	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1175	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1177	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1178	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1179	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1180	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1181	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	2	no	—
1185	C₈	—	2	2	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	1	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	2	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	2	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	2	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	2	no	—
1209	C₂²	—	8	4	no	—
1210	C₂²	—	8	8	no	—
1211	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1212	C₄	—	2	1	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	2	2	no	—
1216	C₄	—	2	1	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	2	no	—
1226	C₄	C₂₃×#575	1	2	yes	—
1227	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1228	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1229	C₂	—	4	2	no	—
1230	C₂	—	4	1	no	—
1231	C₂	—	4	2	no	—
1232	C₂	—	4	2	no	—
1233	C₂	—	8	2	no	—
1234	C₂	—	8	1	no	—
1235	C₂	—	8	1	no	—
1236	C₂	C₂₃×#3484	1	1	yes	characteristic
1237	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1238	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×#3506	C₂	semidirect
2. D₄×#41×C₂₃	C₂	semidirect
3. C₂₃×#3329	C₂	semidirect
4. C₂₃×#3325	C₂	semidirect
5. C₂₃×#3313	C₂	semidirect
6. C₂₃×#3311	C₂	semidirect
7. C₂₃×#3305	C₂	semidirect
8. C₂₃×#3303	C₂	semidirect
9. C₂₃×#3284	C₂	semidirect
10. C₂₃×#3283	C₂	semidirect
11. C₂₃×#3276	C₂	semidirect
12. C₂₃×#3272	C₂	semidirect
13. C₂₃×#3271	C₂	semidirect
14. C₂₃×#3268	C₂	semidirect
15. C₂₃×#3214	C₂	semidirect
16. C₂₃×#3210	C₂	semidirect
17. C₂₃×#3197	C₂	semidirect
18. C₂₃×#3191	C₂	semidirect
19. C₂₃×#3116	C₂	semidirect
20. C₂₃×#3106	C₂	semidirect
21. C₂₃×#3005	C₂	semidirect
22. C₂₃×#3002	C₂	semidirect
23. C₂₃×#2974	C₂	semidirect
25. C₂×C₂₃×#137	C₂²	semidirect
26. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₂₃×#135	C₂²	semidirect
28. C₂×C₂₃×#135	C₂²	semidirect
30. C₂₃×#556	C₂²	semidirect
32. C₂₃×#555	C₂²	semidirect
36. C₂₃×#550	C₂²	semidirect
42. C₂₃×#547	C₂²	semidirect
49. C₂₃×#533	C₂²	semidirect
52. C₂₃×#532	C₂²	semidirect
55. C₂₃×#525	C₂²	semidirect
56. C₂₃×#525	C₂²	semidirect
61. C₂₃×#496	C₂²	semidirect
62. C₂₃×#494	C₂²	semidirect
63. C₂₃×#492	C₂²	semidirect
64. C₂₃×#489	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
66. C₂₃×#486	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#485	C₂²	semidirect
69. C₂₃×#485	C₂²	semidirect
70. C₂₃×#482	C₂²	semidirect
71. C₂₃×#482	C₂²	semidirect
72. C₂₃×#482	C₂²	semidirect
73. C₂₃×#482	C₂²	semidirect
74. C₂₃×#477	C₂²	semidirect
75. C₂₃×#477	C₂²	semidirect
76. C₂₃×#476	C₂²	semidirect
77. C₂₃×#476	C₂²	semidirect
78. C₂₃×#470	C₂²	semidirect
79. C₂₃×#469	C₂²	semidirect
80. C₂₃×#468	C₂²	semidirect
81. C₂₃×#468	C₂²	semidirect
82. C₂₃×#467	C₂²	semidirect
83. C₂₃×#466	C₂²	semidirect
84. C₂₃×#465	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#464	C₂²	semidirect
87. C₂₃×#464	C₂²	semidirect
88. C₂₃×#462	C₂²	semidirect
89. C₂₃×#461	C₂²	semidirect
90. C₂₃×#461	C₂²	semidirect
91. C₂₃×#461	C₂²	semidirect
92. C₂₃×#460	C₂²	semidirect
93. C₂₃×#459	C₂²	semidirect
94. C₂₃×#459	C₂²	semidirect
95. C₂₃×#459	C₂²	semidirect
97. C₂₃×#452	C₂²	semidirect
98. C₂₃×#452	C₂²	semidirect
99. C₂₃×#452	C₂²	semidirect
100. C₂₃×#452	C₂²	semidirect
101. C₂₃×#452	C₂²	semidirect
102. C₂₃×#452	C₂²	semidirect
103. C₂₃×#451	C₂²	semidirect
104. C₂₃×#450	C₂²	semidirect
107. C₂₃×#449	C₂²	semidirect
108. C₂₃×#449	C₂²	semidirect
109. C₂₃×#449	C₂²	semidirect
110. C₂₃×#449	C₂²	semidirect
111. C₂₃×#449	C₂²	semidirect
112. C₂₃×#449	C₂²	semidirect
113. C₂₃×#448	C₂²	semidirect
114. C₂₃×#447	C₂²	semidirect
115. C₂₃×#441	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
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×#419	C₂²	semidirect
130. C₂₃×#418	C₂²	semidirect
131. C₂₃×#416	C₂²	semidirect
132. C₂₃×#416	C₂²	semidirect
133. C₂₃×#407	C₂²	semidirect
134. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
474. #61599	C₂₃	direct (N × H)
569. #3506	C₂×C₂₃	semidirect
570. D₄×#41	C₂×C₂₃	semidirect
571. #3329	C₂×C₂₃	semidirect
572. #3325	C₂×C₂₃	semidirect
573. #3313	C₂×C₂₃	semidirect
574. #3311	C₂×C₂₃	semidirect
575. #3305	C₂×C₂₃	semidirect
576. #3303	C₂×C₂₃	semidirect
577. #3284	C₂×C₂₃	semidirect
578. #3283	C₂×C₂₃	semidirect
579. #3276	C₂×C₂₃	semidirect
580. #3272	C₂×C₂₃	semidirect
581. #3271	C₂×C₂₃	semidirect
582. #3268	C₂×C₂₃	semidirect
583. #3214	C₂×C₂₃	semidirect
584. #3210	C₂×C₂₃	semidirect
585. #3197	C₂×C₂₃	semidirect
586. #3191	C₂×C₂₃	semidirect
587. #3116	C₂×C₂₃	semidirect
588. #3106	C₂×C₂₃	semidirect
589. #3005	C₂×C₂₃	semidirect
590. #3002	C₂×C₂₃	semidirect
591. #2974	C₂×C₂₃	semidirect
634. C₂×#137	C₂²×C₂₃	semidirect
635. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
636. C₂×#135	C₂²×C₂₃	semidirect
637. C₂×#135	C₂²×C₂₃	semidirect
639. #556	C₂²×C₂₃	semidirect
641. #555	C₂²×C₂₃	semidirect
645. #550	C₂²×C₂₃	semidirect
651. #547	C₂²×C₂₃	semidirect
658. #533	C₂²×C₂₃	semidirect
661. #532	C₂²×C₂₃	semidirect
664. #525	C₂²×C₂₃	semidirect
665. #525	C₂²×C₂₃	semidirect
670. #496	C₂²×C₂₃	semidirect
671. #494	C₂²×C₂₃	semidirect
672. #492	C₂²×C₂₃	semidirect
673. #489	C₂²×C₂₃	semidirect
674. #487	C₂²×C₂₃	semidirect
675. #486	C₂²×C₂₃	semidirect
676. #485	C₂²×C₂₃	semidirect
677. #485	C₂²×C₂₃	semidirect
678. #485	C₂²×C₂₃	semidirect
679. #482	C₂²×C₂₃	semidirect
680. #482	C₂²×C₂₃	semidirect
681. #482	C₂²×C₂₃	semidirect
682. #482	C₂²×C₂₃	semidirect
683. #477	C₂²×C₂₃	semidirect
684. #477	C₂²×C₂₃	semidirect
685. #476	C₂²×C₂₃	semidirect
686. #476	C₂²×C₂₃	semidirect
687. #470	C₂²×C₂₃	semidirect
688. #469	C₂²×C₂₃	semidirect
689. #468	C₂²×C₂₃	semidirect
690. #468	C₂²×C₂₃	semidirect
691. #467	C₂²×C₂₃	semidirect
692. #466	C₂²×C₂₃	semidirect
693. #465	C₂²×C₂₃	semidirect
694. #465	C₂²×C₂₃	semidirect
695. #464	C₂²×C₂₃	semidirect
696. #464	C₂²×C₂₃	semidirect
697. #462	C₂²×C₂₃	semidirect
698. #461	C₂²×C₂₃	semidirect
699. #461	C₂²×C₂₃	semidirect
700. #461	C₂²×C₂₃	semidirect
701. #460	C₂²×C₂₃	semidirect
702. #459	C₂²×C₂₃	semidirect
703. #459	C₂²×C₂₃	semidirect
704. #459	C₂²×C₂₃	semidirect
706. #452	C₂²×C₂₃	semidirect
707. #452	C₂²×C₂₃	semidirect
708. #452	C₂²×C₂₃	semidirect
709. #452	C₂²×C₂₃	semidirect
710. #452	C₂²×C₂₃	semidirect
711. #452	C₂²×C₂₃	semidirect
712. #451	C₂²×C₂₃	semidirect
713. #450	C₂²×C₂₃	semidirect
716. #449	C₂²×C₂₃	semidirect
717. #449	C₂²×C₂₃	semidirect
718. #449	C₂²×C₂₃	semidirect
719. #449	C₂²×C₂₃	semidirect
720. #449	C₂²×C₂₃	semidirect
721. #449	C₂²×C₂₃	semidirect
722. #448	C₂²×C₂₃	semidirect
723. #447	C₂²×C₂₃	semidirect
724. #441	C₂²×C₂₃	semidirect
725. #440	C₂²×C₂₃	semidirect
726. C₄×SD₁₆	C₂²×C₂₃	semidirect
727. C₄×SD₁₆	C₂²×C₂₃	semidirect
728. C₄×D₈	C₂²×C₂₃	semidirect
729. C₄×D₈	C₂²×C₂₃	semidirect
732. #435	C₂²×C₂₃	semidirect
733. #435	C₂²×C₂₃	semidirect
734. C₈×D₄	C₂²×C₂₃	semidirect
735. C₈×D₄	C₂²×C₂₃	semidirect
736. #432	C₂²×C₂₃	semidirect
737. #431	C₂²×C₂₃	semidirect
738. #419	C₂²×C₂₃	semidirect
739. #418	C₂²×C₂₃	semidirect
740. #416	C₂²×C₂₃	semidirect
741. #416	C₂²×C₂₃	semidirect
742. #407	C₂²×C₂₃	semidirect
743. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
937. C₂₃	#61599	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×#3506	2
D₄×#41×C₂₃	2
C₂₃×#3329	2
C₂₃×#3325	2
C₂₃×#3313	2
C₂₃×#3311	2
C₂₃×#3305	2
C₂₃×#3303	2
C₂₃×#3284	2
C₂₃×#3283	2
C₂₃×#3276	2
C₂₃×#3272	2
C₂₃×#3271	2
C₂₃×#3268	2
C₂₃×#3214	2
C₂₃×#3210	2
C₂₃×#3197	2
C₂₃×#3191	2
C₂₃×#3116	2
C₂₃×#3106	2
C₂₃×#3005	2
C₂₃×#3002	2
C₂₃×#2974	2
#61599	23

Subgroups — C23×#61599 #19209225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61599 #19209225