Subgroups — C₂₃×#62605 #19210231

Order 5888.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3375	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3370	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3319	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3314	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3308	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3294	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3224	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3180	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3175	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3136	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#563	—	2	2	no	—
21	C₂₃×#562	—	2	1	no	—
22	C₂₃×H(3,𝔽₄)	—	2	1	no	—
23	C₂₃×#559	C₂²	1	2	yes	—
24	Q₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
27	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#552	—	2	1	no	—
29	C₂₃×#552	C₂²	1	2	yes	complemented
30	C₂₃×#548	C₂²	1	2	yes	—
31	C₂₃×#547	—	2	1	no	—
32	C₂₃×#547	C₂²	1	2	yes	complemented
33	C₂₃×#546	—	2	2	no	—
34	C₂₃×#546	C₂²	1	2	yes	—
35	D₄²×C₂₃	C₂²	1	2	yes	—
36	C₂₃×#544	—	2	1	no	—
37	C₂₃×#544	C₂²	1	2	yes	complemented
38	C₂₃×#542	—	2	1	no	—
39	C₂₃×#542	C₂²	1	2	yes	—
40	C₂₃×#542	C₂²	1	2	yes	complemented
41	C₂₃×#538	—	2	2	no	—
42	C₂₃×#538	—	2	1	no	—
43	C₂₃×#536	—	2	2	no	—
44	C₂₃×#535	C₂²	1	2	yes	—
45	C₂₃×#534	—	2	1	no	—
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#529	C₂²	1	1	yes	characteristic
49	C₂₃×#529	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
51	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#500	C₂²	1	2	yes	complemented
53	C₂₃×#496	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#495	C₂²	1	2	yes	complemented
55	C₂₃×#490	C₂²	1	2	yes	—
56	C₂₃×#490	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#489	C₂²	1	2	yes	complemented
59	C₂₃×#489	C₂²	1	2	yes	complemented
60	C₂₃×#489	C₂²	1	2	yes	complemented
61	C₂₃×#489	C₂²	1	2	yes	complemented
62	C₂₃×#489	C₂²	1	2	yes	complemented
63	C₂₃×#488	C₂²	1	2	yes	complemented
64	C₂₃×#488	C₂²	1	2	yes	complemented
65	C₂₃×#486	C₂²	1	2	yes	—
66	C₂₃×#486	C₂²	1	2	yes	complemented
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#484	C₂²	1	2	yes	complemented
69	C₂₃×#482	C₂²	1	2	yes	—
70	C₂₃×#480	C₂²	1	2	yes	—
71	C₂₃×#480	C₂²	1	2	yes	complemented
72	C₂₃×#480	C₂²	1	2	yes	complemented
73	C₂₃×#479	C₂²	1	2	yes	complemented
74	C₂₃×#478	C₂²	1	2	yes	complemented
75	C₂₃×#477	C₂²	1	2	yes	complemented
76	C₂₃×#474	C₂²	1	2	yes	complemented
77	C₂₃×#474	C₂²	1	2	yes	complemented
78	C₂₃×#474	C₂²	1	2	yes	complemented
79	C₂₃×#468	C₂²	1	2	yes	—
80	C₂₃×#468	C₂²	1	2	yes	complemented
81	C₂₃×#467	C₂²	1	2	yes	complemented
82	C₂₃×#466	C₂²	1	2	yes	—
83	C₂₃×#466	C₂²	1	2	yes	complemented
84	C₂₃×#465	C₂²	1	2	yes	complemented
85	C₂₃×#464	C₂²	1	2	yes	complemented
86	C₂₃×#464	C₂²	1	2	yes	complemented
87	C₂₃×#463	C₂²	1	2	yes	complemented
88	C₂₃×#463	C₂²	1	2	yes	complemented
89	C₂₃×#460	C₂²	1	2	yes	—
90	C₂₃×#459	C₂²	1	2	yes	—
91	C₂₃×#452	C₂²	1	2	yes	complemented
92	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#450	C₂²	1	1	yes	characteristic
94	C₂₃×#450	C₂²	1	2	yes	complemented
95	C₂₃×#449	C₂²	1	2	yes	complemented
96	C₂₃×#448	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#447	C₂²	1	1	yes	characteristic
98	C₂₃×#447	C₂²	1	2	yes	complemented
99	C₂₃×#446	C₂²	1	2	yes	complemented
100	C₂₃×#442	C₂²	1	2	yes	complemented
101	C₂₃×#440	C₂²	1	2	yes	complemented
102	C₂₃×#440	C₂²	1	2	yes	complemented
103	C₂₃×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
105	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
106	C₂₃×#435	C₂²	1	2	yes	complemented
107	C₂₃×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
109	C₂₃×#433	C₂²	1	2	yes	complemented
110	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#418	C₂²	1	2	yes	complemented
112	C₂₃×#417	C₂²	1	2	yes	complemented
113	C₂₃×#416	C₂²	1	2	yes	complemented
114	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
115	C₂×C₂₃×#102	C₂²	1	2	yes	—
116	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
117	C₂₃×#405	C₂²	1	2	yes	complemented
118	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₂₃	—	2	2	no	—
120	C₂×#41×C₂₃	—	2	1	no	—
121	C₂×#41×C₂₃	C₂³	1	2	yes	—
122	C₂²×Q₈×C₂₃	—	2	1	no	—
123	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₂₃	—	2	2	no	—
125	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
127	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×D₈×C₂₃	C₂³	1	2	yes	—
132	C₂×D₈×C₂₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
134	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
135	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
136	C₂₃×C₄⋊Q₈	—	2	1	no	—
137	C₂₃×C₄⋊Q₈	—	2	2	no	—
138	C₂₃×C₄⋊Q₈	—	2	2	no	—
139	C₂₃×C₄⋊Q₈	—	2	1	no	—
140	C₂₃×C₄⋊Q₈	—	2	1	no	—
141	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
145	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
146	C₂₃×#127	C₂³	1	2	yes	—
147	C₂₃×#127	C₂³	1	1	yes	characteristic
148	C₂₃×#126	—	2	2	no	—
149	C₂₃×#126	—	2	2	no	—
150	C₂₃×#126	—	2	2	no	—
151	C₂₃×#126	—	2	1	no	—
152	C₂₃×#126	D₄	1	2	yes	—
153	C₂₃×#125	—	2	1	no	—
154	C₂₃×#125	—	2	2	no	—
155	C₂₃×#125	—	2	2	no	—
156	C₂₃×#125	D₄	1	1	yes	characteristic
157	C₂₃×#125	C₂³	1	2	yes	—
158	C₂₃×#125	C₂³	1	1	yes	characteristic
159	C₂₃×#124	—	2	2	no	—
160	C₂₃×#124	—	2	2	no	—
161	C₂₃×#124	—	2	2	no	—
162	C₂₃×#124	—	2	2	no	—
163	C₂₃×#124	—	2	2	no	—
164	C₂₃×#124	—	2	1	no	—
165	C₂₃×#124	—	2	1	no	—
166	C₂₃×#124	—	2	1	no	—
167	C₂₃×#124	D₄	1	1	yes	characteristic
168	C₂₃×#124	C₂³	1	2	yes	—
169	C₂₃×#124	C₂³	1	2	yes	—
170	C₂₃×#124	C₂³	1	2	yes	—
171	C₂₃×#124	C₂³	1	1	yes	characteristic
172	C₂₃×#123	—	2	2	no	—
173	C₂₃×#123	—	2	1	no	—
174	C₂₃×#123	—	2	2	no	—
175	C₂₃×#123	—	2	2	no	—
176	C₂₃×#123	—	2	2	no	—
177	C₂₃×#123	—	2	2	no	—
178	C₂₃×#123	—	2	2	no	—
179	C₂₃×#123	—	2	2	no	—
180	C₂₃×#123	—	2	2	no	—
181	C₂₃×#123	D₄	1	2	yes	—
182	C₂₃×C₂²⋊Q₈	—	2	1	no	—
183	C₂₃×C₂²⋊Q₈	—	2	2	no	—
184	C₂₃×C₂²⋊Q₈	—	2	2	no	—
185	C₂₃×C₂²⋊Q₈	—	2	2	no	—
186	C₂₃×C₂²⋊Q₈	—	2	2	no	—
187	C₂₃×C₂²⋊Q₈	—	2	2	no	—
188	C₂₃×C₂²⋊Q₈	—	2	2	no	—
189	C₂₃×C₂²⋊Q₈	—	2	2	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
192	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
194	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂₃×#121	—	2	1	no	—
196	C₂₃×#121	—	2	2	no	—
197	C₂₃×#121	—	2	1	no	—
198	C₂₃×#121	—	2	2	no	—
199	C₂₃×#121	—	2	2	no	—
200	C₂₃×#121	—	2	2	no	—
201	C₂₃×#121	—	2	2	no	—
202	C₂₃×#121	D₄	1	1	yes	characteristic
203	C₂₃×#121	C₂³	1	1	yes	characteristic
204	C₂₃×#121	C₂³	1	2	yes	—
205	C₂₃×#121	C₂³	1	2	yes	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₂₃×#120	—	2	2	no	—
208	C₂₃×#120	—	2	2	no	—
209	C₂₃×#120	—	2	2	no	—
210	C₂₃×#120	—	2	2	no	—
211	C₂₃×#120	—	2	2	no	—
212	C₄×Q₈×C₂₃	—	2	1	no	—
213	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₂₃	—	2	1	no	—
218	C₄×D₄×C₂₃	—	2	1	no	—
219	C₄×D₄×C₂₃	—	2	2	no	—
220	C₄×D₄×C₂₃	—	2	2	no	—
221	C₄×D₄×C₂₃	—	2	1	no	—
222	C₄×D₄×C₂₃	C₂³	1	2	yes	—
223	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₂₃	C₂³	1	2	yes	—
225	C₄×D₄×C₂₃	C₂³	1	2	yes	—
226	C₄×D₄×C₂₃	C₂³	1	2	yes	—
227	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
228	C₂₃×#117	—	2	1	no	—
229	C₂₃×#117	—	2	2	no	—
230	C₂₃×#117	—	2	1	no	—
231	C₂₃×#117	C₂³	1	2	yes	—
232	C₂₃×#117	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
240	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
241	C₂₃×#107	C₂³	1	2	yes	—
242	C₂₃×#107	C₂³	1	2	yes	—
243	C₂₃×#107	C₂³	1	2	yes	—
244	C₂₃×#107	C₂³	1	2	yes	—
245	C₂₃×#107	C₂³	1	2	yes	—
246	C₂₃×#106	C₂³	1	2	yes	—
247	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
248	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₂₃×#103	C₂³	1	2	yes	—
251	C₂₃×#103	C₂³	1	2	yes	—
252	C₂₃×#103	C₂³	1	2	yes	—
253	C₂₃×#103	C₂³	1	2	yes	—
254	C₂₃×#103	C₂³	1	2	yes	—
255	C₂₃×#103	C₂³	1	2	yes	—
256	C₂₃×#103	C₂³	1	2	yes	—
257	C₂₃×#102	C₂³	1	2	yes	—
258	C₂₃×#102	C₂³	1	2	yes	—
259	C₂₃×#102	C₂³	1	2	yes	—
260	C₂₃×#102	C₂³	1	2	yes	—
261	C₂₃×#102	C₂³	1	2	yes	—
262	C₂₃×#102	C₂³	1	2	yes	—
263	C₂₃×#102	C₂³	1	2	yes	—
264	C₂₃×#102	C₂³	1	2	yes	—
265	C₂₃×#102	C₂³	1	2	yes	—
266	C₂₃×#102	C₂³	1	2	yes	—
267	C₂₃×#102	C₂³	1	2	yes	—
268	C₂₃×#102	C₂³	1	2	yes	—
269	C₂₃×#102	C₂³	1	2	yes	—
270	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₂₃×#97	C₂³	1	1	yes	characteristic
275	C₂₃×#97	C₂³	1	1	yes	characteristic
276	C₂₃×#97	C₂³	1	2	yes	—
277	C₂₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₂₃	C₂³	1	2	yes	—
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	C₂⁴×C₂₃	—	2	1	no	—
281	C₂⁴×C₂₃	—	2	2	no	—
282	#41×C₂₃	—	4	2	no	—
283	#41×C₂₃	—	4	2	no	—
284	#41×C₂₃	—	8	2	no	—
285	#41×C₂₃	—	8	4	no	—
286	C₂×Q₈×C₂₃	—	2	1	no	—
287	C₂×Q₈×C₂₃	—	2	1	no	—
288	C₂×Q₈×C₂₃	—	2	1	no	—
289	C₂×Q₈×C₂₃	—	2	2	no	—
290	C₂×Q₈×C₂₃	—	2	2	no	—
291	C₂×Q₈×C₂₃	—	2	1	no	—
292	C₂×Q₈×C₂₃	—	4	2	no	—
293	C₂×Q₈×C₂₃	—	8	2	no	—
294	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
295	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
296	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
297	C₂×D₄×C₂₃	—	2	2	no	—
298	C₂×D₄×C₂₃	—	2	1	no	—
299	C₂×D₄×C₂₃	—	2	2	no	—
300	C₂×D₄×C₂₃	—	2	2	no	—
301	C₂×D₄×C₂₃	—	2	2	no	—
302	C₂×D₄×C₂₃	—	2	2	no	—
303	C₂×D₄×C₂₃	—	2	1	no	—
304	C₂×D₄×C₂₃	—	2	1	no	—
305	C₂×D₄×C₂₃	—	2	1	no	—
306	C₂×D₄×C₂₃	—	2	2	no	—
307	C₂×D₄×C₂₃	—	2	2	no	—
308	C₂×D₄×C₂₃	—	4	2	no	—
309	C₂×D₄×C₂₃	—	4	2	no	—
310	C₂×D₄×C₂₃	—	4	2	no	—
311	C₂×D₄×C₂₃	—	8	4	no	—
312	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
313	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
314	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
315	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
316	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₂₃	—	2	2	no	—
318	C₂²×C₄×C₂₃	—	2	1	no	—
319	C₂²×C₄×C₂₃	—	2	2	no	—
320	C₂²×C₄×C₂₃	—	2	1	no	—
321	C₂²×C₄×C₂₃	—	2	2	no	—
322	C₂²×C₄×C₂₃	—	2	2	no	—
323	C₂²×C₄×C₂₃	—	2	2	no	—
324	C₂²×C₄×C₂₃	—	2	2	no	—
325	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
329	Q₁₆×C₂₃	—	4	2	no	—
330	SD₁₆×C₂₃	—	4	2	no	—
331	SD₁₆×C₂₃	—	4	2	no	—
332	SD₁₆×C₂₃	—	4	2	no	—
333	D₈×C₂₃	—	4	2	no	—
334	D₈×C₂₃	—	4	2	no	—
335	M₁₆×C₂₃	—	4	2	no	—
336	C₂×C₈×C₂₃	—	4	2	no	—
337	C₂×C₈×C₂₃	—	4	2	no	—
338	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
339	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
340	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
341	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₂₃	—	2	1	no	—
343	C₄⋊C₄×C₂₃	—	2	1	no	—
344	C₄⋊C₄×C₂₃	—	2	2	no	—
345	C₄⋊C₄×C₂₃	—	2	2	no	—
346	C₄⋊C₄×C₂₃	—	2	2	no	—
347	C₄⋊C₄×C₂₃	—	2	2	no	—
348	C₄⋊C₄×C₂₃	—	2	2	no	—
349	C₄⋊C₄×C₂₃	—	2	2	no	—
350	C₄⋊C₄×C₂₃	—	2	1	no	—
351	C₄⋊C₄×C₂₃	—	2	1	no	—
352	C₄⋊C₄×C₂₃	—	2	2	no	—
353	C₄⋊C₄×C₂₃	—	2	1	no	—
354	C₄⋊C₄×C₂₃	—	2	1	no	—
355	C₄⋊C₄×C₂₃	—	2	2	no	—
356	C₄⋊C₄×C₂₃	—	2	2	no	—
357	C₄⋊C₄×C₂₃	—	2	1	no	—
358	C₄⋊C₄×C₂₃	—	2	2	no	—
359	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
370	C₂²⋊C₄×C₂₃	—	2	2	no	—
371	C₂²⋊C₄×C₂₃	—	2	1	no	—
372	C₂²⋊C₄×C₂₃	—	2	2	no	—
373	C₂²⋊C₄×C₂₃	—	2	2	no	—
374	C₂²⋊C₄×C₂₃	—	2	2	no	—
375	C₂²⋊C₄×C₂₃	—	2	2	no	—
376	C₂²⋊C₄×C₂₃	—	2	2	no	—
377	C₂²⋊C₄×C₂₃	—	2	2	no	—
378	C₂²⋊C₄×C₂₃	—	2	2	no	—
379	C₂²⋊C₄×C₂₃	—	2	1	no	—
380	C₂²⋊C₄×C₂₃	—	2	2	no	—
381	C₂²⋊C₄×C₂₃	—	2	1	no	—
382	C₂²⋊C₄×C₂₃	—	2	2	no	—
383	C₂²⋊C₄×C₂₃	—	2	2	no	—
384	C₂²⋊C₄×C₂₃	—	2	2	no	—
385	C₂²⋊C₄×C₂₃	—	2	1	no	—
386	C₂²⋊C₄×C₂₃	—	2	2	no	—
387	C₂²⋊C₄×C₂₃	—	2	2	no	—
388	C₂²⋊C₄×C₂₃	—	2	2	no	—
389	C₂²⋊C₄×C₂₃	—	2	1	no	—
390	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
395	C₄²×C₂₃	—	2	2	no	—
396	C₄²×C₂₃	—	2	1	no	—
397	C₄²×C₂₃	—	2	2	no	—
398	C₄²×C₂₃	—	2	2	no	—
399	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
402	C₄²×C₂₃	C₂⁴	1	2	yes	—
403	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
404	#62605	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₂³×C₂₃	—	2	1	no	—
406	C₂³×C₂₃	—	2	2	no	—
407	C₂³×C₂₃	—	2	2	no	—
408	C₂³×C₂₃	—	4	2	no	—
409	C₂³×C₂₃	—	8	1	no	—
410	C₂³×C₂₃	—	8	2	no	—
411	C₂³×C₂₃	—	8	2	no	—
412	C₂³×C₂₃	—	8	1	no	—
413	C₂³×C₂₃	—	8	2	no	—
414	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
415	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
416	Q₈×C₂₃	—	2	2	no	—
417	Q₈×C₂₃	—	2	2	no	—
418	Q₈×C₂₃	—	2	2	no	—
419	Q₈×C₂₃	—	4	1	no	—
420	Q₈×C₂₃	—	8	1	no	—
421	Q₈×C₂₃	—	8	1	no	—
422	Q₈×C₂₃	—	8	1	no	—
423	Q₈×C₂₃	—	8	2	no	—
424	Q₈×C₂₃	—	8	1	no	—
425	Q₈×C₂₃	—	8	2	no	—
426	D₄×C₂₃	—	2	4	no	—
427	D₄×C₂₃	—	2	2	no	—
428	D₄×C₂₃	—	2	2	no	—
429	D₄×C₂₃	—	2	2	no	—
430	D₄×C₂₃	—	2	2	no	—
431	D₄×C₂₃	—	2	2	no	—
432	D₄×C₂₃	—	4	1	no	—
433	D₄×C₂₃	—	4	4	no	—
434	D₄×C₂₃	—	4	2	no	—
435	D₄×C₂₃	—	8	1	no	—
436	D₄×C₂₃	—	8	2	no	—
437	D₄×C₂₃	—	8	2	no	—
438	D₄×C₂₃	—	8	1	no	—
439	D₄×C₂₃	—	8	2	no	—
440	D₄×C₂₃	—	8	1	no	—
441	D₄×C₂₃	—	8	2	no	—
442	D₄×C₂₃	—	8	2	no	—
443	D₄×C₂₃	—	8	2	no	—
444	C₂×C₄×C₂₃	—	2	2	no	—
445	C₂×C₄×C₂₃	—	2	2	no	—
446	C₂×C₄×C₂₃	—	2	2	no	—
447	C₂×C₄×C₂₃	—	2	2	no	—
448	C₂×C₄×C₂₃	—	2	1	no	—
449	C₂×C₄×C₂₃	—	2	1	no	—
450	C₂×C₄×C₂₃	—	2	2	no	—
451	C₂×C₄×C₂₃	—	2	2	no	—
452	C₂×C₄×C₂₃	—	2	2	no	—
453	C₂×C₄×C₂₃	—	2	1	no	—
454	C₂×C₄×C₂₃	—	2	2	no	—
455	C₂×C₄×C₂₃	—	4	1	no	—
456	C₂×C₄×C₂₃	—	4	2	no	—
457	C₂×C₄×C₂₃	—	4	4	no	—
458	C₂×C₄×C₂₃	—	8	2	no	—
459	C₂×C₄×C₂₃	—	8	2	no	—
460	C₂×C₄×C₂₃	—	8	2	no	—
461	C₂×C₄×C₂₃	—	8	2	no	—
462	C₂×C₄×C₂₃	—	8	1	no	—
463	C₂×C₄×C₂₃	—	8	2	no	—
464	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
473	C₈×C₂₃	—	2	2	no	—
474	C₈×C₂₃	—	2	2	no	—
475	C₈×C₂₃	—	2	2	no	—
476	C₈×C₂₃	—	2	2	no	—
477	#3558	C₂×C₂₃	1	1	yes	characteristic, complemented
478	#3544	C₂×C₂₃	1	1	yes	characteristic, complemented
479	#3375	C₂×C₂₃	1	2	yes	complemented
480	#3370	C₂×C₂₃	1	2	yes	complemented
481	#3319	C₂×C₂₃	1	2	yes	complemented
482	#3314	C₂×C₂₃	1	2	yes	complemented
483	#3310	C₂×C₂₃	1	2	yes	complemented
484	#3308	C₂×C₂₃	1	2	yes	complemented
485	#3300	C₂×C₂₃	1	2	yes	complemented
486	#3294	C₂×C₂₃	1	2	yes	complemented
487	#3243	C₂×C₂₃	1	2	yes	complemented
488	#3226	C₂×C₂₃	1	1	yes	characteristic, complemented
489	#3224	C₂×C₂₃	1	2	yes	complemented
490	#3211	C₂×C₂₃	1	1	yes	characteristic, complemented
491	#3180	C₂×C₂₃	1	1	yes	characteristic, complemented
492	#3175	C₂×C₂₃	1	2	yes	complemented
493	#3136	C₂×C₂₃	1	2	yes	complemented
494	C₂×#489	C₂×C₂₃	1	1	yes	characteristic, complemented
495	#2968	C₂×C₂₃	1	1	yes	characteristic, complemented
496	C₂²×C₂₃	—	2	1	no	—
497	C₂²×C₂₃	—	2	1	no	—
498	C₂²×C₂₃	—	2	2	no	—
499	C₂²×C₂₃	—	2	2	no	—
500	C₂²×C₂₃	—	2	2	no	—
501	C₂²×C₂₃	—	4	1	no	—
502	C₂²×C₂₃	—	4	2	no	—
503	C₂²×C₂₃	—	4	2	no	—
504	C₂²×C₂₃	—	4	2	no	—
505	C₂²×C₂₃	—	4	2	no	—
506	C₂²×C₂₃	—	4	1	no	—
507	C₂²×C₂₃	—	4	1	no	—
508	C₂²×C₂₃	—	4	2	no	—
509	C₂²×C₂₃	—	4	2	no	—
510	C₂²×C₂₃	—	16	2	no	—
511	C₂²×C₂₃	—	16	4	no	—
512	C₂²×C₂₃	#576	1	2	yes	—
513	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
514	C₄×C₂₃	—	2	1	no	—
515	C₄×C₂₃	—	2	1	no	—
516	C₄×C₂₃	—	2	2	no	—
517	C₄×C₂₃	—	2	2	no	—
518	C₄×C₂₃	—	2	1	no	—
519	C₄×C₂₃	—	2	1	no	—
520	C₄×C₂₃	—	2	1	no	—
521	C₄×C₂₃	—	2	2	no	—
522	C₄×C₂₃	—	4	1	no	—
523	C₄×C₂₃	—	4	2	no	—
524	C₄×C₂₃	—	4	1	no	—
525	C₄×C₂₃	—	4	2	no	—
526	C₄×C₂₃	—	4	2	no	—
527	C₄×C₂₃	—	4	2	no	—
528	C₄×C₂₃	—	4	1	no	—
529	C₄×C₂₃	#585	1	2	yes	—
530	#563	—	2	2	no	—
531	#562	—	2	1	no	—
532	H(3,𝔽₄)	—	2	1	no	—
533	#559	C₂²×C₂₃	1	2	yes	—
534	Q₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
535	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
536	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
537	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
538	#552	—	2	1	no	—
539	#552	C₂²×C₂₃	1	2	yes	complemented
540	#548	C₂²×C₂₃	1	2	yes	—
541	#547	—	2	1	no	—
542	#547	C₂²×C₂₃	1	2	yes	complemented
543	#546	—	2	2	no	—
544	#546	C₂²×C₂₃	1	2	yes	—
545	D₄²	C₂²×C₂₃	1	2	yes	—
546	#544	—	2	1	no	—
547	#544	C₂²×C₂₃	1	2	yes	complemented
548	#542	—	2	1	no	—
549	#542	C₂²×C₂₃	1	2	yes	—
550	#542	C₂²×C₂₃	1	2	yes	complemented
551	#538	—	2	2	no	—
552	#538	—	2	1	no	—
553	#536	—	2	2	no	—
554	#535	C₂²×C₂₃	1	2	yes	—
555	#534	—	2	1	no	—
556	#532	C₂²×C₂₃	1	1	yes	characteristic
557	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
558	#529	C₂²×C₂₃	1	1	yes	characteristic
559	#529	C₂²×C₂₃	1	1	yes	characteristic, complemented
560	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
561	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
562	#500	C₂²×C₂₃	1	2	yes	complemented
563	#496	C₂²×C₂₃	1	1	yes	characteristic, complemented
564	#495	C₂²×C₂₃	1	2	yes	complemented
565	#490	C₂²×C₂₃	1	2	yes	—
566	#490	C₂²×C₂₃	1	1	yes	characteristic, complemented
567	#489	C₂²×C₂₃	1	2	yes	complemented
568	#489	C₂²×C₂₃	1	2	yes	complemented
569	#489	C₂²×C₂₃	1	2	yes	complemented
570	#489	C₂²×C₂₃	1	2	yes	complemented
571	#489	C₂²×C₂₃	1	2	yes	complemented
572	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
573	#488	C₂²×C₂₃	1	2	yes	complemented
574	#488	C₂²×C₂₃	1	2	yes	complemented
575	#486	C₂²×C₂₃	1	2	yes	—
576	#486	C₂²×C₂₃	1	2	yes	complemented
577	#485	C₂²×C₂₃	1	2	yes	complemented
578	#484	C₂²×C₂₃	1	2	yes	complemented
579	#482	C₂²×C₂₃	1	2	yes	—
580	#480	C₂²×C₂₃	1	2	yes	—
581	#480	C₂²×C₂₃	1	2	yes	complemented
582	#480	C₂²×C₂₃	1	2	yes	complemented
583	#479	C₂²×C₂₃	1	2	yes	complemented
584	#478	C₂²×C₂₃	1	2	yes	complemented
585	#477	C₂²×C₂₃	1	2	yes	complemented
586	#474	C₂²×C₂₃	1	2	yes	complemented
587	#474	C₂²×C₂₃	1	2	yes	complemented
588	#474	C₂²×C₂₃	1	2	yes	complemented
589	#468	C₂²×C₂₃	1	2	yes	—
590	#468	C₂²×C₂₃	1	2	yes	complemented
591	#467	C₂²×C₂₃	1	2	yes	complemented
592	#466	C₂²×C₂₃	1	2	yes	—
593	#466	C₂²×C₂₃	1	2	yes	complemented
594	#465	C₂²×C₂₃	1	2	yes	complemented
595	#464	C₂²×C₂₃	1	2	yes	complemented
596	#464	C₂²×C₂₃	1	2	yes	complemented
597	#463	C₂²×C₂₃	1	2	yes	complemented
598	#463	C₂²×C₂₃	1	2	yes	complemented
599	#460	C₂²×C₂₃	1	2	yes	—
600	#459	C₂²×C₂₃	1	2	yes	—
601	#452	C₂²×C₂₃	1	2	yes	complemented
602	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
603	#450	C₂²×C₂₃	1	1	yes	characteristic
604	#450	C₂²×C₂₃	1	2	yes	complemented
605	#449	C₂²×C₂₃	1	2	yes	complemented
606	#448	C₂²×C₂₃	1	1	yes	characteristic, complemented
607	#447	C₂²×C₂₃	1	1	yes	characteristic
608	#447	C₂²×C₂₃	1	2	yes	complemented
609	#446	C₂²×C₂₃	1	2	yes	complemented
610	#442	C₂²×C₂₃	1	2	yes	complemented
611	#440	C₂²×C₂₃	1	2	yes	complemented
612	#440	C₂²×C₂₃	1	2	yes	complemented
613	#440	C₂²×C₂₃	1	2	yes	complemented
614	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
615	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
616	#435	C₂²×C₂₃	1	2	yes	complemented
617	#435	C₂²×C₂₃	1	2	yes	complemented
618	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
619	#433	C₂²×C₂₃	1	2	yes	complemented
620	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
621	#418	C₂²×C₂₃	1	2	yes	complemented
622	#417	C₂²×C₂₃	1	2	yes	complemented
623	#416	C₂²×C₂₃	1	2	yes	complemented
624	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
625	C₂×#102	C₂²×C₂₃	1	2	yes	—
626	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
627	#405	C₂²×C₂₃	1	2	yes	complemented
628	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
629	C₂×C₂₃	—	2	2	no	—
630	C₂×C₂₃	—	4	2	no	—
631	C₂×C₂₃	—	8	1	no	—
632	C₂×C₂₃	—	8	2	no	—
633	C₂×C₂₃	—	8	2	no	—
634	C₂×C₂₃	#3500	1	1	yes	characteristic
635	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
636	C₂×C₂₃	#3586	1	1	yes	characteristic
637	C₂×#41	—	2	2	no	—
638	C₂×#41	—	2	1	no	—
639	C₂×#41	C₂³×C₂₃	1	2	yes	—
640	C₂²×Q₈	—	2	1	no	—
641	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
642	C₂²×D₄	—	2	2	no	—
643	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
644	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
645	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
646	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
647	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
648	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
649	C₂×D₈	C₂³×C₂₃	1	2	yes	—
650	C₂×D₈	C₂³×C₂₃	1	2	yes	—
651	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
652	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
653	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
654	C₄⋊Q₈	—	2	2	no	—
655	C₄⋊Q₈	—	2	2	no	—
656	C₄⋊Q₈	—	2	1	no	—
657	C₄⋊Q₈	—	2	1	no	—
658	C₄⋊Q₈	—	2	1	no	—
659	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
660	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
661	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
662	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
663	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
664	#127	C₂³×C₂₃	1	1	yes	characteristic
665	#127	C₂³×C₂₃	1	2	yes	—
666	#126	—	2	2	no	—
667	#126	—	2	2	no	—
668	#126	—	2	2	no	—
669	#126	—	2	1	no	—
670	#126	D₄×C₂₃	1	2	yes	—
671	#125	—	2	1	no	—
672	#125	—	2	2	no	—
673	#125	—	2	2	no	—
674	#125	D₄×C₂₃	1	1	yes	characteristic
675	#125	C₂³×C₂₃	1	1	yes	characteristic
676	#125	C₂³×C₂₃	1	2	yes	—
677	#124	—	2	2	no	—
678	#124	—	2	2	no	—
679	#124	—	2	2	no	—
680	#124	—	2	2	no	—
681	#124	—	2	2	no	—
682	#124	—	2	1	no	—
683	#124	—	2	1	no	—
684	#124	—	2	1	no	—
685	#124	D₄×C₂₃	1	1	yes	characteristic
686	#124	C₂³×C₂₃	1	2	yes	—
687	#124	C₂³×C₂₃	1	2	yes	—
688	#124	C₂³×C₂₃	1	1	yes	characteristic
689	#124	C₂³×C₂₃	1	2	yes	—
690	#123	—	2	2	no	—
691	#123	—	2	1	no	—
692	#123	—	2	2	no	—
693	#123	—	2	2	no	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	—	2	2	no	—
698	#123	—	2	2	no	—
699	#123	D₄×C₂₃	1	2	yes	—
700	C₂²⋊Q₈	—	2	1	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	—	2	2	no	—
709	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
710	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
711	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
712	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
713	#121	—	2	2	no	—
714	#121	—	2	1	no	—
715	#121	—	2	1	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	D₄×C₂₃	1	1	yes	characteristic
721	#121	C₂³×C₂₃	1	1	yes	characteristic
722	#121	C₂³×C₂₃	1	2	yes	—
723	#121	C₂³×C₂₃	1	2	yes	—
724	#121	C₂³×C₂₃	1	2	yes	—
725	#120	—	2	2	no	—
726	#120	—	2	2	no	—
727	#120	—	2	2	no	—
728	#120	—	2	2	no	—
729	#120	—	2	2	no	—
730	C₄×Q₈	—	2	1	no	—
731	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
732	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
733	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
734	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
735	C₄×D₄	—	2	1	no	—
736	C₄×D₄	—	2	1	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	2	no	—
739	C₄×D₄	—	2	1	no	—
740	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
741	C₄×D₄	C₂³×C₂₃	1	2	yes	—
742	C₄×D₄	C₂³×C₂₃	1	2	yes	—
743	C₄×D₄	C₂³×C₂₃	1	2	yes	—
744	C₄×D₄	C₂³×C₂₃	1	2	yes	—
745	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
746	#117	—	2	1	no	—
747	#117	—	2	2	no	—
748	#117	—	2	1	no	—
749	#117	C₂³×C₂₃	1	2	yes	—
750	#117	C₂³×C₂₃	1	2	yes	—
751	C₂×C₄⋊C₄	—	2	1	no	—
752	C₂×C₄⋊C₄	—	2	1	no	—
753	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
755	C₂×C₂²⋊C₄	—	2	1	no	—
756	C₂×C₂²⋊C₄	—	2	1	no	—
757	C₂×C₂²⋊C₄	—	2	2	no	—
758	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
759	#107	C₂³×C₂₃	1	2	yes	—
760	#107	C₂³×C₂₃	1	2	yes	—
761	#107	C₂³×C₂₃	1	2	yes	—
762	#107	C₂³×C₂₃	1	2	yes	—
763	#107	C₂³×C₂₃	1	2	yes	—
764	#106	C₂³×C₂₃	1	2	yes	—
765	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
766	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
767	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
768	#103	C₂³×C₂₃	1	2	yes	—
769	#103	C₂³×C₂₃	1	2	yes	—
770	#103	C₂³×C₂₃	1	2	yes	—
771	#103	C₂³×C₂₃	1	2	yes	—
772	#103	C₂³×C₂₃	1	2	yes	—
773	#103	C₂³×C₂₃	1	2	yes	—
774	#103	C₂³×C₂₃	1	2	yes	—
775	#102	C₂³×C₂₃	1	2	yes	—
776	#102	C₂³×C₂₃	1	2	yes	—
777	#102	C₂³×C₂₃	1	2	yes	—
778	#102	C₂³×C₂₃	1	2	yes	—
779	#102	C₂³×C₂₃	1	2	yes	—
780	#102	C₂³×C₂₃	1	2	yes	—
781	#102	C₂³×C₂₃	1	2	yes	—
782	#102	C₂³×C₂₃	1	2	yes	—
783	#102	C₂³×C₂₃	1	2	yes	—
784	#102	C₂³×C₂₃	1	2	yes	—
785	#102	C₂³×C₂₃	1	2	yes	—
786	#102	C₂³×C₂₃	1	2	yes	—
787	#102	C₂³×C₂₃	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
789	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
790	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
792	#97	C₂³×C₂₃	1	1	yes	characteristic
793	#97	C₂³×C₂₃	1	1	yes	characteristic
794	#97	C₂³×C₂₃	1	2	yes	—
795	#97	C₂³×C₂₃	1	2	yes	—
796	C₄×C₈	C₂³×C₂₃	1	2	yes	—
797	C₄×C₈	C₂³×C₂₃	1	2	yes	—
798	C₂₃	#62605	1	1	yes	characteristic, direct product factor, Sylow
799	C₂⁴	—	2	1	no	—
800	C₂⁴	—	2	2	no	—
801	#41	—	4	2	no	—
802	#41	—	4	2	no	—
803	#41	—	8	2	no	—
804	#41	—	8	4	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	2	no	—
809	C₂×Q₈	—	2	2	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	4	2	no	—
812	C₂×Q₈	—	8	2	no	—
813	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
814	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
815	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	2	1	no	—
824	C₂×D₄	—	2	1	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	8	4	no	—
831	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
832	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
833	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
834	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
835	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
845	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
848	Q₁₆	—	4	2	no	—
849	SD₁₆	—	4	2	no	—
850	SD₁₆	—	4	2	no	—
851	SD₁₆	—	4	2	no	—
852	D₈	—	4	2	no	—
853	D₈	—	4	2	no	—
854	M₁₆	—	4	2	no	—
855	C₂×C₈	—	4	2	no	—
856	C₂×C₈	—	4	2	no	—
857	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
858	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
859	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
860	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
879	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
880	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
881	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
882	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
883	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
884	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
885	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
886	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
887	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
888	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	1	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	1	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	1	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	1	no	—
909	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
910	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
911	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
912	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
913	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	1	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	2	no	—
918	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
919	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
920	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
921	C₄²	C₂⁴×C₂₃	1	2	yes	—
922	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
923	C₂³	—	2	1	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	4	2	no	—
927	C₂³	—	8	1	no	—
928	C₂³	—	8	2	no	—
929	C₂³	—	8	2	no	—
930	C₂³	—	8	1	no	—
931	C₂³	—	8	2	no	—
932	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
933	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
934	Q₈	—	2	2	no	—
935	Q₈	—	2	2	no	—
936	Q₈	—	2	2	no	—
937	Q₈	—	4	1	no	—
938	Q₈	—	8	1	no	—
939	Q₈	—	8	1	no	—
940	Q₈	—	8	1	no	—
941	Q₈	—	8	2	no	—
942	Q₈	—	8	1	no	—
943	Q₈	—	8	2	no	—
944	D₄	—	2	4	no	—
945	D₄	—	2	2	no	—
946	D₄	—	2	2	no	—
947	D₄	—	2	2	no	—
948	D₄	—	2	2	no	—
949	D₄	—	2	2	no	—
950	D₄	—	4	1	no	—
951	D₄	—	4	4	no	—
952	D₄	—	4	2	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	1	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	1	no	—
957	D₄	—	8	1	no	—
958	D₄	—	8	2	no	—
959	D₄	—	8	2	no	—
960	D₄	—	8	2	no	—
961	D₄	—	8	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	4	1	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	8	2	no	—
977	C₂×C₄	—	8	2	no	—
978	C₂×C₄	—	8	2	no	—
979	C₂×C₄	—	8	2	no	—
980	C₂×C₄	—	8	1	no	—
981	C₂×C₄	—	8	2	no	—
982	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
983	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
984	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
985	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
986	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
988	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
989	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
990	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
991	C₈	—	2	2	no	—
992	C₈	—	2	2	no	—
993	C₈	—	2	2	no	—
994	C₈	—	2	2	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	16	2	no	—
1010	C₂²	—	16	4	no	—
1011	C₂²	C₂₃×#576	1	2	yes	—
1012	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1013	C₄	—	2	2	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	2	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	1	no	—
1028	C₄	C₂₃×#585	1	2	yes	—
1029	C₂	—	2	2	no	—
1030	C₂	—	4	2	no	—
1031	C₂	—	8	2	no	—
1032	C₂	—	8	2	no	—
1033	C₂	—	8	1	no	—
1034	C₂	C₂₃×#3500	1	1	yes	characteristic
1035	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
1036	C₂	C₂₃×#3586	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 ◁ C₂₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3558	C₂	semidirect
2. C₂₃×#3544	C₂	semidirect
3. C₂₃×#3375	C₂	semidirect
4. C₂₃×#3370	C₂	semidirect
5. C₂₃×#3319	C₂	semidirect
6. C₂₃×#3314	C₂	semidirect
7. C₂₃×#3310	C₂	semidirect
8. C₂₃×#3308	C₂	semidirect
9. C₂₃×#3300	C₂	semidirect
10. C₂₃×#3294	C₂	semidirect
11. C₂₃×#3243	C₂	semidirect
12. C₂₃×#3226	C₂	semidirect
13. C₂₃×#3224	C₂	semidirect
14. C₂₃×#3211	C₂	semidirect
15. C₂₃×#3180	C₂	semidirect
16. C₂₃×#3175	C₂	semidirect
17. C₂₃×#3136	C₂	semidirect
18. C₂×C₂₃×#489	C₂	semidirect
19. C₂₃×#2968	C₂	semidirect
24. Q₈²×C₂₃	C₂²	semidirect
25. C₂₃×#555	C₂²	semidirect
26. C₂₃×#554	C₂²	semidirect
27. C₂₃×#554	C₂²	semidirect
29. C₂₃×#552	C₂²	semidirect
32. C₂₃×#547	C₂²	semidirect
37. C₂₃×#544	C₂²	semidirect
40. C₂₃×#542	C₂²	semidirect
47. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
49. C₂₃×#529	C₂²	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#500	C₂²	semidirect
53. C₂₃×#496	C₂²	semidirect
54. C₂₃×#495	C₂²	semidirect
56. C₂₃×#490	C₂²	semidirect
57. C₂₃×#489	C₂²	semidirect
58. C₂₃×#489	C₂²	semidirect
59. C₂₃×#489	C₂²	semidirect
60. C₂₃×#489	C₂²	semidirect
61. C₂₃×#489	C₂²	semidirect
62. C₂₃×#489	C₂²	semidirect
63. C₂₃×#488	C₂²	semidirect
64. C₂₃×#488	C₂²	semidirect
66. C₂₃×#486	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#484	C₂²	semidirect
71. C₂₃×#480	C₂²	semidirect
72. C₂₃×#480	C₂²	semidirect
73. C₂₃×#479	C₂²	semidirect
74. C₂₃×#478	C₂²	semidirect
75. C₂₃×#477	C₂²	semidirect
76. C₂₃×#474	C₂²	semidirect
77. C₂₃×#474	C₂²	semidirect
78. C₂₃×#474	C₂²	semidirect
80. C₂₃×#468	C₂²	semidirect
81. C₂₃×#467	C₂²	semidirect
83. C₂₃×#466	C₂²	semidirect
84. C₂₃×#465	C₂²	semidirect
85. C₂₃×#464	C₂²	semidirect
86. C₂₃×#464	C₂²	semidirect
87. C₂₃×#463	C₂²	semidirect
88. C₂₃×#463	C₂²	semidirect
91. C₂₃×#452	C₂²	semidirect
92. C₂₃×#451	C₂²	semidirect
94. C₂₃×#450	C₂²	semidirect
95. C₂₃×#449	C₂²	semidirect
96. C₂₃×#448	C₂²	semidirect
98. C₂₃×#447	C₂²	semidirect
99. C₂₃×#446	C₂²	semidirect
100. C₂₃×#442	C₂²	semidirect
101. C₂₃×#440	C₂²	semidirect
102. C₂₃×#440	C₂²	semidirect
103. C₂₃×#440	C₂²	semidirect
104. C₄×Q₁₆×C₂₃	C₂²	semidirect
105. C₄×D₈×C₂₃	C₂²	semidirect
106. C₂₃×#435	C₂²	semidirect
107. C₂₃×#435	C₂²	semidirect
108. C₈×D₄×C₂₃	C₂²	semidirect
109. C₂₃×#433	C₂²	semidirect
110. C₂₃×#431	C₂²	semidirect
111. C₂₃×#418	C₂²	semidirect
112. C₂₃×#417	C₂²	semidirect
113. C₂₃×#416	C₂²	semidirect
114. C₂×C₂₃×#103	C₂²	semidirect
116. C₂×C₂₃×#102	C₂²	semidirect
117. C₂₃×#405	C₂²	semidirect
118. C₂×C₂₃×#97	C₂²	semidirect
404. #62605	C₂₃	direct (N × H)
477. #3558	C₂×C₂₃	semidirect
478. #3544	C₂×C₂₃	semidirect
479. #3375	C₂×C₂₃	semidirect
480. #3370	C₂×C₂₃	semidirect
481. #3319	C₂×C₂₃	semidirect
482. #3314	C₂×C₂₃	semidirect
483. #3310	C₂×C₂₃	semidirect
484. #3308	C₂×C₂₃	semidirect
485. #3300	C₂×C₂₃	semidirect
486. #3294	C₂×C₂₃	semidirect
487. #3243	C₂×C₂₃	semidirect
488. #3226	C₂×C₂₃	semidirect
489. #3224	C₂×C₂₃	semidirect
490. #3211	C₂×C₂₃	semidirect
491. #3180	C₂×C₂₃	semidirect
492. #3175	C₂×C₂₃	semidirect
493. #3136	C₂×C₂₃	semidirect
494. C₂×#489	C₂×C₂₃	semidirect
495. #2968	C₂×C₂₃	semidirect
534. Q₈²	C₂²×C₂₃	semidirect
535. #555	C₂²×C₂₃	semidirect
536. #554	C₂²×C₂₃	semidirect
537. #554	C₂²×C₂₃	semidirect
539. #552	C₂²×C₂₃	semidirect
542. #547	C₂²×C₂₃	semidirect
547. #544	C₂²×C₂₃	semidirect
550. #542	C₂²×C₂₃	semidirect
557. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
559. #529	C₂²×C₂₃	semidirect
561. #501	C₂²×C₂₃	semidirect
562. #500	C₂²×C₂₃	semidirect
563. #496	C₂²×C₂₃	semidirect
564. #495	C₂²×C₂₃	semidirect
566. #490	C₂²×C₂₃	semidirect
567. #489	C₂²×C₂₃	semidirect
568. #489	C₂²×C₂₃	semidirect
569. #489	C₂²×C₂₃	semidirect
570. #489	C₂²×C₂₃	semidirect
571. #489	C₂²×C₂₃	semidirect
572. #489	C₂²×C₂₃	semidirect
573. #488	C₂²×C₂₃	semidirect
574. #488	C₂²×C₂₃	semidirect
576. #486	C₂²×C₂₃	semidirect
577. #485	C₂²×C₂₃	semidirect
578. #484	C₂²×C₂₃	semidirect
581. #480	C₂²×C₂₃	semidirect
582. #480	C₂²×C₂₃	semidirect
583. #479	C₂²×C₂₃	semidirect
584. #478	C₂²×C₂₃	semidirect
585. #477	C₂²×C₂₃	semidirect
586. #474	C₂²×C₂₃	semidirect
587. #474	C₂²×C₂₃	semidirect
588. #474	C₂²×C₂₃	semidirect
590. #468	C₂²×C₂₃	semidirect
591. #467	C₂²×C₂₃	semidirect
593. #466	C₂²×C₂₃	semidirect
594. #465	C₂²×C₂₃	semidirect
595. #464	C₂²×C₂₃	semidirect
596. #464	C₂²×C₂₃	semidirect
597. #463	C₂²×C₂₃	semidirect
598. #463	C₂²×C₂₃	semidirect
601. #452	C₂²×C₂₃	semidirect
602. #451	C₂²×C₂₃	semidirect
604. #450	C₂²×C₂₃	semidirect
605. #449	C₂²×C₂₃	semidirect
606. #448	C₂²×C₂₃	semidirect
608. #447	C₂²×C₂₃	semidirect
609. #446	C₂²×C₂₃	semidirect
610. #442	C₂²×C₂₃	semidirect
611. #440	C₂²×C₂₃	semidirect
612. #440	C₂²×C₂₃	semidirect
613. #440	C₂²×C₂₃	semidirect
614. C₄×Q₁₆	C₂²×C₂₃	semidirect
615. C₄×D₈	C₂²×C₂₃	semidirect
616. #435	C₂²×C₂₃	semidirect
617. #435	C₂²×C₂₃	semidirect
618. C₈×D₄	C₂²×C₂₃	semidirect
619. #433	C₂²×C₂₃	semidirect
620. #431	C₂²×C₂₃	semidirect
621. #418	C₂²×C₂₃	semidirect
622. #417	C₂²×C₂₃	semidirect
623. #416	C₂²×C₂₃	semidirect
624. C₂×#103	C₂²×C₂₃	semidirect
626. C₂×#102	C₂²×C₂₃	semidirect
627. #405	C₂²×C₂₃	semidirect
628. C₂×#97	C₂²×C₂₃	semidirect
798. C₂₃	#62605	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×#3558	2
C₂₃×#3544	2
C₂₃×#3375	2
C₂₃×#3370	2
C₂₃×#3319	2
C₂₃×#3314	2
C₂₃×#3310	2
C₂₃×#3308	2
C₂₃×#3300	2
C₂₃×#3294	2
C₂₃×#3243	2
C₂₃×#3226	2
C₂₃×#3224	2
C₂₃×#3211	2
C₂₃×#3180	2
C₂₃×#3175	2
C₂₃×#3136	2
C₂×C₂₃×#489	2
C₂₃×#2968	2
#62605	23

Subgroups — C23×#62605 #19210231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62605 #19210231