Subgroups — C₂₃×#61492 #19209118

Order 5888.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3349	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3302	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3269	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3178	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3127	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3124	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2947	C₂	1	2	yes	maximal, complemented
23	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#137	C₂²	1	2	yes	—
25	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
26	Q₈²×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#557	C₂²	1	1	yes	characteristic
28	C₂₃×#556	—	2	2	no	—
29	C₂₃×#556	—	2	1	no	—
30	C₂₃×#556	C₂²	1	1	yes	characteristic
31	C₂₃×#556	C₂²	1	2	yes	—
32	C₂₃×#555	—	2	1	no	—
33	C₂₃×#555	C₂²	1	1	yes	characteristic
34	C₂₃×#554	C₂²	1	1	yes	characteristic
35	C₂₃×#554	C₂²	1	1	yes	characteristic
36	C₂₃×#553	—	2	1	no	—
37	C₂₃×#552	—	2	2	no	—
38	C₂₃×#552	—	2	1	no	—
39	C₂₃×#552	C₂²	1	2	yes	—
40	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
41	C₂₃×#548	C₂²	1	2	yes	—
42	C₂₃×#547	C₂²	1	2	yes	—
43	C₂₃×#547	C₂²	1	1	yes	characteristic
44	C₂₃×#542	—	2	2	no	—
45	C₂₃×#542	C₂²	1	2	yes	—
46	C₂₃×#541	C₂²	1	2	yes	—
47	C₂₃×#539	—	2	2	no	—
48	C₂₃×#533	—	2	1	no	—
49	C₂₃×#533	C₂²	1	1	yes	characteristic
50	C₂₃×#533	C₂²	1	1	yes	characteristic
51	C₂₃×#529	—	2	1	no	—
52	C₂₃×#529	—	2	1	no	—
53	C₂₃×#529	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×#125	—	2	1	no	—
55	C₂₃×#520	C₂²	1	2	yes	—
56	C₂₃×#519	C₂²	1	2	yes	—
57	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
58	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#501	C₂²	1	2	yes	—
60	C₂₃×#500	C₂²	1	1	yes	characteristic
61	C₂₃×#497	C₂²	1	2	yes	—
62	C₂₃×#494	C₂²	1	1	yes	characteristic
63	C₂₃×#488	C₂²	1	2	yes	—
64	C₂₃×#487	C₂²	1	1	yes	characteristic
65	C₂₃×#487	C₂²	1	1	yes	characteristic
66	C₂₃×#487	C₂²	1	2	yes	—
67	C₂₃×#485	C₂²	1	2	yes	—
68	C₂₃×#485	C₂²	1	2	yes	—
69	C₂₃×#485	C₂²	1	2	yes	—
70	C₂₃×#485	C₂²	1	2	yes	—
71	C₂₃×#484	C₂²	1	2	yes	—
72	C₂₃×#480	C₂²	1	2	yes	—
73	C₂₃×#479	C₂²	1	2	yes	—
74	C₂₃×#479	C₂²	1	2	yes	—
75	C₂₃×#477	C₂²	1	1	yes	characteristic
76	C₂₃×#477	C₂²	1	2	yes	—
77	C₂₃×#477	C₂²	1	1	yes	characteristic
78	C₂₃×#476	C₂²	1	1	yes	characteristic
79	C₂₃×#476	C₂²	1	1	yes	characteristic
80	C₂₃×#474	C₂²	1	2	yes	—
81	C₂₃×#470	C₂²	1	2	yes	—
82	C₂₃×#468	C₂²	1	2	yes	—
83	C₂₃×#467	C₂²	1	2	yes	—
84	C₂₃×#467	C₂²	1	2	yes	—
85	C₂₃×#467	C₂²	1	2	yes	—
86	C₂₃×#465	C₂²	1	2	yes	—
87	C₂₃×#464	C₂²	1	2	yes	—
88	C₂₃×#463	C₂²	1	2	yes	—
89	C₂₃×#462	C₂²	1	2	yes	—
90	C₂₃×#462	C₂²	1	1	yes	characteristic
91	C₂₃×#462	C₂²	1	1	yes	characteristic
92	C₂₃×#462	C₂²	1	2	yes	—
93	C₂₃×#461	C₂²	1	1	yes	characteristic
94	C₂₃×#461	C₂²	1	1	yes	characteristic
95	C₂₃×#452	C₂²	1	2	yes	—
96	C₂₃×#452	C₂²	1	2	yes	—
97	C₂₃×#452	C₂²	1	2	yes	—
98	C₂₃×#451	C₂²	1	2	yes	—
99	C₂₃×#451	C₂²	1	2	yes	—
100	C₂₃×#449	C₂²	1	2	yes	—
101	C₂₃×#446	C₂²	1	1	yes	characteristic
102	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
103	C₂₃×#441	C₂²	1	2	yes	—
104	C₂₃×#441	C₂²	1	2	yes	—
105	C₂₃×#441	C₂²	1	2	yes	—
106	C₂₃×#440	C₂²	1	2	yes	—
107	C₂₃×#440	C₂²	1	2	yes	—
108	C₂₃×#440	C₂²	1	2	yes	—
109	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
110	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
113	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
119	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
121	C₂₃×#436	C₂²	1	1	yes	characteristic
122	C₂₃×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₂₃	C₂²	1	2	yes	—
125	C₂₃×#433	C₂²	1	2	yes	—
126	C₂₃×#432	C₂²	1	1	yes	characteristic
127	C₂₃×#428	C₂²	1	2	yes	—
128	C₂₃×#427	C₂²	1	1	yes	characteristic
129	C₂₃×#416	C₂²	1	1	yes	characteristic
130	C₂₃×#416	C₂²	1	1	yes	characteristic
131	C₂₃×#416	C₂²	1	2	yes	—
132	C₂×C₂₃×#103	C₂²	1	2	yes	—
133	C₂₃×#405	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×#41×C₂₃	C₂³	1	2	yes	—
137	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
139	C₂₃×#137	—	2	8	no	—
140	C₂₃×#135	—	2	4	no	—
141	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
155	C₂₃×C₄⋊Q₈	—	2	1	no	—
156	C₂₃×C₄⋊Q₈	—	2	1	no	—
157	C₂₃×C₄⋊Q₈	—	2	2	no	—
158	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₂₃×#126	—	2	2	no	—
165	C₂₃×#126	—	2	2	no	—
166	C₂₃×#126	—	2	2	no	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#126	D₄	1	2	yes	—
172	C₂₃×#125	—	2	2	no	—
173	C₂₃×#125	—	2	2	no	—
174	C₂₃×#125	—	2	1	no	—
175	C₂₃×#125	—	2	2	no	—
176	C₂₃×#125	—	2	1	no	—
177	C₂₃×#125	—	2	2	no	—
178	C₂₃×#125	—	2	1	no	—
179	C₂₃×#125	—	2	1	no	—
180	C₂₃×#125	D₄	1	1	yes	characteristic
181	C₂₃×#125	C₂³	1	2	yes	—
182	C₂₃×#124	—	2	2	no	—
183	C₂₃×#124	—	2	2	no	—
184	C₂₃×#124	—	2	2	no	—
185	C₂₃×#124	—	2	2	no	—
186	C₂₃×#124	D₄	1	1	yes	characteristic
187	C₂₃×#124	C₂³	1	2	yes	—
188	C₂₃×#123	—	2	2	no	—
189	C₂₃×#123	—	2	2	no	—
190	C₂₃×#123	—	2	2	no	—
191	C₂₃×#123	—	2	2	no	—
192	C₂₃×#123	—	2	2	no	—
193	C₂₃×#123	D₄	1	2	yes	—
194	C₂₃×C₂²⋊Q₈	—	2	1	no	—
195	C₂₃×C₂²⋊Q₈	—	2	1	no	—
196	C₂₃×C₂²⋊Q₈	—	2	1	no	—
197	C₂₃×C₂²⋊Q₈	—	2	1	no	—
198	C₂₃×C₂²⋊Q₈	—	2	2	no	—
199	C₂₃×C₂²⋊Q₈	—	2	2	no	—
200	C₂₃×C₂²⋊Q₈	—	2	2	no	—
201	C₂₃×C₂²⋊Q₈	—	2	2	no	—
202	C₂₃×C₂²⋊Q₈	—	2	2	no	—
203	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
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×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂₃×#121	—	2	1	no	—
210	C₂₃×#121	—	2	2	no	—
211	C₂₃×#121	—	2	2	no	—
212	C₂₃×#121	—	2	1	no	—
213	C₂₃×#121	D₄	1	1	yes	characteristic
214	C₂₃×#121	C₂³	1	2	yes	—
215	C₄×Q₈×C₂₃	—	2	1	no	—
216	C₄×Q₈×C₂₃	—	2	1	no	—
217	C₄×Q₈×C₂₃	—	2	2	no	—
218	C₄×Q₈×C₂₃	—	2	2	no	—
219	C₄×Q₈×C₂₃	—	2	2	no	—
220	C₄×Q₈×C₂₃	—	2	1	no	—
221	C₄×Q₈×C₂₃	—	2	1	no	—
222	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
231	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	—	2	1	no	—
234	C₄×D₄×C₂₃	—	2	1	no	—
235	C₄×D₄×C₂₃	—	2	1	no	—
236	C₄×D₄×C₂₃	—	2	1	no	—
237	C₄×D₄×C₂₃	—	2	1	no	—
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	—	2	2	no	—
240	C₄×D₄×C₂₃	—	2	2	no	—
241	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₂₃	C₂³	1	2	yes	—
243	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₂₃	C₂³	1	2	yes	—
247	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
248	C₂₃×#117	—	2	1	no	—
249	C₂₃×#117	—	2	1	no	—
250	C₂₃×#117	—	2	2	no	—
251	C₂₃×#117	—	2	1	no	—
252	C₂₃×#117	—	2	1	no	—
253	C₂₃×#117	—	2	2	no	—
254	C₂₃×#117	—	2	2	no	—
255	C₂₃×#117	—	2	2	no	—
256	C₂₃×#117	—	2	1	no	—
257	C₂₃×#117	—	2	1	no	—
258	C₂₃×#117	C₂³	1	1	yes	characteristic
259	C₂₃×#117	C₂³	1	2	yes	—
260	C₂₃×#117	C₂³	1	1	yes	characteristic
261	C₂₃×#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
264	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
265	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
266	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
267	C₂×C₄²×C₂₃	—	2	1	no	—
268	C₂×C₄²×C₂₃	—	2	1	no	—
269	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
270	C₂₃×#107	C₂³	1	1	yes	characteristic
271	C₂₃×#107	C₂³	1	1	yes	characteristic
272	C₂₃×#107	C₂³	1	2	yes	—
273	C₂₃×#107	C₂³	1	2	yes	—
274	C₂₃×#107	C₂³	1	2	yes	—
275	C₂₃×#107	C₂³	1	2	yes	—
276	C₂₃×#106	C₂³	1	1	yes	characteristic
277	C₂₃×#106	C₂³	1	1	yes	characteristic
278	C₂₃×#106	C₂³	1	2	yes	—
279	C₂₃×#106	C₂³	1	2	yes	—
280	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₂₃×#103	C₂³	1	1	yes	characteristic
285	C₂₃×#103	C₂³	1	2	yes	—
286	C₂₃×#103	C₂³	1	2	yes	—
287	C₂₃×#103	C₂³	1	2	yes	—
288	C₂₃×#103	C₂³	1	1	yes	characteristic
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#103	C₂³	1	1	yes	characteristic
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	2	yes	—
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×#103	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	1	yes	characteristic
299	C₂₃×#102	C₂³	1	1	yes	characteristic
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×#97	C₂³	1	2	yes	—
308	C₂₃×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₂₃	C₂³	1	2	yes	—
314	#41×C₂₃	—	2	2	no	—
315	#41×C₂₃	—	2	2	no	—
316	#41×C₂₃	—	2	4	no	—
317	#41×C₂₃	—	4	2	no	—
318	#41×C₂₃	—	4	1	no	—
319	#41×C₂₃	—	4	1	no	—
320	C₂×Q₈×C₂₃	—	2	2	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	2	1	no	—
323	C₂×Q₈×C₂₃	—	2	2	no	—
324	C₂×Q₈×C₂₃	—	2	4	no	—
325	C₂×Q₈×C₂₃	—	4	2	no	—
326	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₂₃	—	2	2	no	—
340	C₂²×C₄×C₂₃	—	2	2	no	—
341	C₂²×C₄×C₂₃	—	2	1	no	—
342	C₂²×C₄×C₂₃	—	2	1	no	—
343	C₂²×C₄×C₂₃	—	2	1	no	—
344	C₂²×C₄×C₂₃	—	2	1	no	—
345	C₂²×C₄×C₂₃	—	2	2	no	—
346	C₂²×C₄×C₂₃	—	2	1	no	—
347	C₂²×C₄×C₂₃	—	2	1	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
353	Q₁₆×C₂₃	—	2	2	no	—
354	Q₁₆×C₂₃	—	2	4	no	—
355	Q₁₆×C₂₃	—	2	4	no	—
356	Q₁₆×C₂₃	—	4	2	no	—
357	Q₁₆×C₂₃	—	4	2	no	—
358	SD₁₆×C₂₃	—	2	4	no	—
359	SD₁₆×C₂₃	—	2	2	no	—
360	SD₁₆×C₂₃	—	4	2	no	—
361	SD₁₆×C₂₃	#41	1	4	yes	—
362	D₈×C₂₃	—	2	2	no	—
363	M₁₆×C₂₃	—	2	4	no	—
364	C₂×C₈×C₂₃	—	2	2	no	—
365	C₂×C₈×C₂₃	—	4	2	no	—
366	C₂×C₈×C₂₃	—	4	1	no	—
367	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
370	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
371	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₂₃	—	2	2	no	—
374	C₄⋊C₄×C₂₃	—	2	1	no	—
375	C₄⋊C₄×C₂₃	—	2	1	no	—
376	C₄⋊C₄×C₂₃	—	2	2	no	—
377	C₄⋊C₄×C₂₃	—	2	2	no	—
378	C₄⋊C₄×C₂₃	—	2	2	no	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	2	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	2	no	—
383	C₄⋊C₄×C₂₃	—	2	1	no	—
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	—	2	1	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	1	no	—
389	C₄⋊C₄×C₂₃	—	2	2	no	—
390	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	2	no	—
393	C₄⋊C₄×C₂₃	—	2	2	no	—
394	C₄⋊C₄×C₂₃	—	2	1	no	—
395	C₄⋊C₄×C₂₃	—	2	2	no	—
396	C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₄⋊C₄×C₂₃	—	2	2	no	—
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
411	C₂²⋊C₄×C₂₃	—	2	2	no	—
412	C₂²⋊C₄×C₂₃	—	2	2	no	—
413	C₂²⋊C₄×C₂₃	—	2	2	no	—
414	C₂²⋊C₄×C₂₃	—	2	2	no	—
415	C₂²⋊C₄×C₂₃	—	2	1	no	—
416	C₂²⋊C₄×C₂₃	—	2	1	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	1	no	—
420	C₂²⋊C₄×C₂₃	—	2	1	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	1	no	—
423	C₂²⋊C₄×C₂₃	—	2	1	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
432	C₄²×C₂₃	—	2	1	no	—
433	C₄²×C₂₃	—	2	1	no	—
434	C₄²×C₂₃	—	2	1	no	—
435	C₄²×C₂₃	—	2	1	no	—
436	C₄²×C₂₃	—	2	1	no	—
437	C₄²×C₂₃	—	2	1	no	—
438	C₄²×C₂₃	—	2	2	no	—
439	C₄²×C₂₃	—	2	2	no	—
440	C₄²×C₂₃	—	2	2	no	—
441	C₄²×C₂₃	—	2	2	no	—
442	C₄²×C₂₃	—	2	2	no	—
443	C₄²×C₂₃	—	2	2	no	—
444	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
447	C₄²×C₂₃	C₂⁴	1	2	yes	—
448	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
449	#61492	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
450	C₂³×C₂₃	—	2	1	no	—
451	C₂³×C₂₃	—	2	1	no	—
452	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
453	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
454	Q₈×C₂₃	—	2	2	no	—
455	Q₈×C₂₃	—	2	1	no	—
456	Q₈×C₂₃	—	2	2	no	—
457	Q₈×C₂₃	—	2	1	no	—
458	Q₈×C₂₃	—	2	2	no	—
459	Q₈×C₂₃	—	2	2	no	—
460	Q₈×C₂₃	—	2	2	no	—
461	Q₈×C₂₃	—	2	1	no	—
462	Q₈×C₂₃	—	4	4	no	—
463	Q₈×C₂₃	—	8	1	no	—
464	Q₈×C₂₃	—	8	1	no	—
465	Q₈×C₂₃	—	8	2	no	—
466	Q₈×C₂₃	C₂×#41	1	2	yes	—
467	D₄×C₂₃	—	2	2	no	—
468	D₄×C₂₃	—	2	1	no	—
469	D₄×C₂₃	—	2	1	no	—
470	D₄×C₂₃	—	2	1	no	—
471	D₄×C₂₃	—	4	2	no	—
472	D₄×C₂₃	—	4	2	no	—
473	D₄×C₂₃	—	4	4	no	—
474	D₄×C₂₃	—	4	2	no	—
475	D₄×C₂₃	—	8	2	no	—
476	D₄×C₂₃	C₂×#41	1	2	yes	—
477	C₂×C₄×C₂₃	—	2	1	no	—
478	C₂×C₄×C₂₃	—	2	2	no	—
479	C₂×C₄×C₂₃	—	2	1	no	—
480	C₂×C₄×C₂₃	—	2	2	no	—
481	C₂×C₄×C₂₃	—	2	2	no	—
482	C₂×C₄×C₂₃	—	2	1	no	—
483	C₂×C₄×C₂₃	—	2	1	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	2	no	—
488	C₂×C₄×C₂₃	—	2	1	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	2	no	—
491	C₂×C₄×C₂₃	—	2	2	no	—
492	C₂×C₄×C₂₃	—	4	1	no	—
493	C₂×C₄×C₂₃	—	4	2	no	—
494	C₂×C₄×C₂₃	—	4	4	no	—
495	C₂×C₄×C₂₃	—	4	2	no	—
496	C₂×C₄×C₂₃	—	4	4	no	—
497	C₂×C₄×C₂₃	—	4	2	no	—
498	C₂×C₄×C₂₃	—	4	2	no	—
499	C₂×C₄×C₂₃	—	8	1	no	—
500	C₂×C₄×C₂₃	—	8	1	no	—
501	C₂×C₄×C₂₃	—	8	2	no	—
502	C₂×C₄×C₂₃	—	8	2	no	—
503	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
512	C₈×C₂₃	—	2	1	no	—
513	C₈×C₂₃	—	2	2	no	—
514	C₈×C₂₃	—	2	1	no	—
515	C₈×C₂₃	—	2	2	no	—
516	C₈×C₂₃	—	2	1	no	—
517	C₈×C₂₃	C₂×#41	1	2	yes	—
518	#3518	C₂×C₂₃	1	1	yes	characteristic, complemented
519	#3515	C₂×C₂₃	1	1	yes	characteristic, complemented
520	#3398	C₂×C₂₃	1	1	yes	characteristic, complemented
521	#3385	C₂×C₂₃	1	1	yes	characteristic, complemented
522	#3363	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#3360	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#3357	C₂×C₂₃	1	1	yes	characteristic, complemented
525	#3349	C₂×C₂₃	1	2	yes	complemented
526	#3303	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#3302	C₂×C₂₃	1	2	yes	complemented
528	#3300	C₂×C₂₃	1	2	yes	complemented
529	#3299	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3276	C₂×C₂₃	1	1	yes	characteristic, complemented
531	#3269	C₂×C₂₃	1	2	yes	complemented
532	#3178	C₂×C₂₃	1	2	yes	complemented
533	#3170	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3127	C₂×C₂₃	1	2	yes	complemented
535	#3124	C₂×C₂₃	1	2	yes	complemented
536	#3116	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3116	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#2947	C₂×C₂₃	1	2	yes	complemented
540	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
541	C₂²×C₂₃	—	2	1	no	—
542	C₂²×C₂₃	—	2	2	no	—
543	C₂²×C₂₃	—	2	2	no	—
544	C₂²×C₂₃	—	2	1	no	—
545	C₂²×C₂₃	—	2	2	no	—
546	C₂²×C₂₃	—	2	1	no	—
547	C₂²×C₂₃	—	2	2	no	—
548	C₂²×C₂₃	—	4	1	no	—
549	C₂²×C₂₃	—	4	1	no	—
550	C₂²×C₂₃	—	4	1	no	—
551	C₂²×C₂₃	—	4	1	no	—
552	C₂²×C₂₃	—	4	1	no	—
553	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
554	C₄×C₂₃	—	2	1	no	—
555	C₄×C₂₃	—	2	1	no	—
556	C₄×C₂₃	—	2	2	no	—
557	C₄×C₂₃	—	2	1	no	—
558	C₄×C₂₃	—	2	2	no	—
559	C₄×C₂₃	—	2	2	no	—
560	C₄×C₂₃	—	2	1	no	—
561	C₄×C₂₃	—	2	2	no	—
562	C₄×C₂₃	—	4	1	no	—
563	C₄×C₂₃	—	4	2	no	—
564	C₄×C₂₃	—	4	1	no	—
565	C₄×C₂₃	—	4	2	no	—
566	C₄×C₂₃	—	4	1	no	—
567	C₄×C₂₃	—	4	2	no	—
568	C₄×C₂₃	—	4	2	no	—
569	C₄×C₂₃	—	4	1	no	—
570	C₄×C₂₃	—	4	1	no	—
571	C₄×C₂₃	#578	1	2	yes	—
572	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
573	C₄×C₂₃	#585	1	1	yes	characteristic
574	C₂×#137	C₂²×C₂₃	1	2	yes	—
575	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
576	Q₈²	C₂²×C₂₃	1	1	yes	characteristic
577	#557	C₂²×C₂₃	1	1	yes	characteristic
578	#556	—	2	2	no	—
579	#556	—	2	1	no	—
580	#556	C₂²×C₂₃	1	1	yes	characteristic
581	#556	C₂²×C₂₃	1	2	yes	—
582	#555	—	2	1	no	—
583	#555	C₂²×C₂₃	1	1	yes	characteristic
584	#554	C₂²×C₂₃	1	1	yes	characteristic
585	#554	C₂²×C₂₃	1	1	yes	characteristic
586	#553	—	2	1	no	—
587	#552	—	2	2	no	—
588	#552	—	2	1	no	—
589	#552	C₂²×C₂₃	1	2	yes	—
590	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
591	#548	C₂²×C₂₃	1	2	yes	—
592	#547	C₂²×C₂₃	1	2	yes	—
593	#547	C₂²×C₂₃	1	1	yes	characteristic
594	#542	—	2	2	no	—
595	#542	C₂²×C₂₃	1	2	yes	—
596	#541	C₂²×C₂₃	1	2	yes	—
597	#539	—	2	2	no	—
598	#533	—	2	1	no	—
599	#533	C₂²×C₂₃	1	1	yes	characteristic
600	#533	C₂²×C₂₃	1	1	yes	characteristic
601	#529	—	2	1	no	—
602	#529	—	2	1	no	—
603	#529	C₂²×C₂₃	1	1	yes	characteristic
604	C₂×#125	—	2	1	no	—
605	#520	C₂²×C₂₃	1	2	yes	—
606	#519	C₂²×C₂₃	1	2	yes	—
607	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
608	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
609	#501	C₂²×C₂₃	1	2	yes	—
610	#500	C₂²×C₂₃	1	1	yes	characteristic
611	#497	C₂²×C₂₃	1	2	yes	—
612	#494	C₂²×C₂₃	1	1	yes	characteristic
613	#488	C₂²×C₂₃	1	2	yes	—
614	#487	C₂²×C₂₃	1	1	yes	characteristic
615	#487	C₂²×C₂₃	1	1	yes	characteristic
616	#487	C₂²×C₂₃	1	2	yes	—
617	#485	C₂²×C₂₃	1	2	yes	—
618	#485	C₂²×C₂₃	1	2	yes	—
619	#485	C₂²×C₂₃	1	2	yes	—
620	#485	C₂²×C₂₃	1	2	yes	—
621	#484	C₂²×C₂₃	1	2	yes	—
622	#480	C₂²×C₂₃	1	2	yes	—
623	#479	C₂²×C₂₃	1	2	yes	—
624	#479	C₂²×C₂₃	1	2	yes	—
625	#477	C₂²×C₂₃	1	2	yes	—
626	#477	C₂²×C₂₃	1	1	yes	characteristic
627	#477	C₂²×C₂₃	1	1	yes	characteristic
628	#476	C₂²×C₂₃	1	1	yes	characteristic
629	#476	C₂²×C₂₃	1	1	yes	characteristic
630	#474	C₂²×C₂₃	1	2	yes	—
631	#470	C₂²×C₂₃	1	2	yes	—
632	#468	C₂²×C₂₃	1	2	yes	—
633	#467	C₂²×C₂₃	1	2	yes	—
634	#467	C₂²×C₂₃	1	2	yes	—
635	#467	C₂²×C₂₃	1	2	yes	—
636	#465	C₂²×C₂₃	1	2	yes	—
637	#464	C₂²×C₂₃	1	2	yes	—
638	#463	C₂²×C₂₃	1	2	yes	—
639	#462	C₂²×C₂₃	1	1	yes	characteristic
640	#462	C₂²×C₂₃	1	2	yes	—
641	#462	C₂²×C₂₃	1	1	yes	characteristic
642	#462	C₂²×C₂₃	1	2	yes	—
643	#461	C₂²×C₂₃	1	1	yes	characteristic
644	#461	C₂²×C₂₃	1	1	yes	characteristic
645	#452	C₂²×C₂₃	1	2	yes	—
646	#452	C₂²×C₂₃	1	2	yes	—
647	#452	C₂²×C₂₃	1	2	yes	—
648	#451	C₂²×C₂₃	1	2	yes	—
649	#451	C₂²×C₂₃	1	2	yes	—
650	#449	C₂²×C₂₃	1	2	yes	—
651	#446	C₂²×C₂₃	1	1	yes	characteristic
652	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
653	#441	C₂²×C₂₃	1	2	yes	—
654	#441	C₂²×C₂₃	1	2	yes	—
655	#441	C₂²×C₂₃	1	2	yes	—
656	#440	C₂²×C₂₃	1	2	yes	—
657	#440	C₂²×C₂₃	1	2	yes	—
658	#440	C₂²×C₂₃	1	2	yes	—
659	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
660	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
661	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
662	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
663	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
664	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
665	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
666	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
668	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
669	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
670	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
671	#436	C₂²×C₂₃	1	1	yes	characteristic
672	#435	C₂²×C₂₃	1	2	yes	—
673	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
674	C₈×D₄	C₂²×C₂₃	1	2	yes	—
675	#433	C₂²×C₂₃	1	2	yes	—
676	#432	C₂²×C₂₃	1	1	yes	characteristic
677	#428	C₂²×C₂₃	1	2	yes	—
678	#427	C₂²×C₂₃	1	1	yes	characteristic
679	#416	C₂²×C₂₃	1	1	yes	characteristic
680	#416	C₂²×C₂₃	1	1	yes	characteristic
681	#416	C₂²×C₂₃	1	2	yes	—
682	C₂×#103	C₂²×C₂₃	1	2	yes	—
683	#405	C₂²×C₂₃	1	2	yes	—
684	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
685	C₂×C₂₃	—	4	1	no	—
686	C₂×C₂₃	—	4	2	no	—
687	C₂×C₂₃	—	4	2	no	—
688	C₂×C₂₃	—	8	1	no	—
689	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
690	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
691	C₂×C₂₃	#3584	1	1	yes	characteristic
692	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
693	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
694	C₂×#41	C₂³×C₂₃	1	2	yes	—
695	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
696	#137	—	2	8	no	—
697	#135	—	2	4	no	—
698	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
699	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
700	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
701	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
702	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
704	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
707	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
708	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
709	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
710	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
711	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	—	2	1	no	—
714	C₄⋊Q₈	—	2	2	no	—
715	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
718	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	D₄×C₂₃	1	2	yes	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	—	2	1	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	—	2	1	no	—
737	#125	D₄×C₂₃	1	1	yes	characteristic
738	#125	C₂³×C₂₃	1	2	yes	—
739	#124	—	2	2	no	—
740	#124	—	2	2	no	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	D₄×C₂₃	1	1	yes	characteristic
744	#124	C₂³×C₂₃	1	2	yes	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	D₄×C₂₃	1	2	yes	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
761	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
766	#121	—	2	1	no	—
767	#121	—	2	1	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	D₄×C₂₃	1	1	yes	characteristic
771	#121	C₂³×C₂₃	1	2	yes	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	2	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	—	2	2	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
784	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
787	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
788	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₂₃	1	2	yes	—
803	C₄×D₄	C₂³×C₂₃	1	2	yes	—
804	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	—	2	1	no	—
810	#117	—	2	2	no	—
811	#117	—	2	2	no	—
812	#117	—	2	2	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	C₂³×C₂₃	1	1	yes	characteristic
816	#117	C₂³×C₂₃	1	1	yes	characteristic
817	#117	C₂³×C₂₃	1	2	yes	—
818	#117	C₂³×C₂₃	1	2	yes	—
819	C₂×C₄⋊C₄	—	2	2	no	—
820	C₂×C₄⋊C₄	—	2	1	no	—
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
824	C₂×C₄²	—	2	1	no	—
825	C₂×C₄²	—	2	1	no	—
826	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
827	#107	C₂³×C₂₃	1	1	yes	characteristic
828	#107	C₂³×C₂₃	1	1	yes	characteristic
829	#107	C₂³×C₂₃	1	2	yes	—
830	#107	C₂³×C₂₃	1	2	yes	—
831	#107	C₂³×C₂₃	1	2	yes	—
832	#107	C₂³×C₂₃	1	2	yes	—
833	#106	C₂³×C₂₃	1	1	yes	characteristic
834	#106	C₂³×C₂₃	1	1	yes	characteristic
835	#106	C₂³×C₂₃	1	2	yes	—
836	#106	C₂³×C₂₃	1	2	yes	—
837	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
840	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
841	#103	C₂³×C₂₃	1	1	yes	characteristic
842	#103	C₂³×C₂₃	1	2	yes	—
843	#103	C₂³×C₂₃	1	2	yes	—
844	#103	C₂³×C₂₃	1	2	yes	—
845	#103	C₂³×C₂₃	1	1	yes	characteristic
846	#103	C₂³×C₂₃	1	1	yes	characteristic
847	#103	C₂³×C₂₃	1	1	yes	characteristic
848	#103	C₂³×C₂₃	1	2	yes	—
849	#103	C₂³×C₂₃	1	2	yes	—
850	#103	C₂³×C₂₃	1	2	yes	—
851	#103	C₂³×C₂₃	1	2	yes	—
852	#103	C₂³×C₂₃	1	2	yes	—
853	#103	C₂³×C₂₃	1	2	yes	—
854	#103	C₂³×C₂₃	1	2	yes	—
855	#102	C₂³×C₂₃	1	1	yes	characteristic
856	#102	C₂³×C₂₃	1	1	yes	characteristic
857	#102	C₂³×C₂₃	1	1	yes	characteristic
858	#102	C₂³×C₂₃	1	1	yes	characteristic
859	#102	C₂³×C₂₃	1	2	yes	—
860	#102	C₂³×C₂₃	1	2	yes	—
861	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
864	#97	C₂³×C₂₃	1	2	yes	—
865	#97	C₂³×C₂₃	1	2	yes	—
866	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
869	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₂₃	1	2	yes	—
871	C₂₃	#61492	1	1	yes	characteristic, direct product factor, Sylow
872	#41	—	2	2	no	—
873	#41	—	2	2	no	—
874	#41	—	2	4	no	—
875	#41	—	4	2	no	—
876	#41	—	4	1	no	—
877	#41	—	4	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	4	no	—
883	C₂×Q₈	—	4	2	no	—
884	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
885	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
886	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
887	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
888	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
894	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
895	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
896	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
908	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
911	Q₁₆	—	2	2	no	—
912	Q₁₆	—	2	4	no	—
913	Q₁₆	—	2	4	no	—
914	Q₁₆	—	4	2	no	—
915	Q₁₆	—	4	2	no	—
916	SD₁₆	—	2	4	no	—
917	SD₁₆	—	2	2	no	—
918	SD₁₆	—	4	2	no	—
919	SD₁₆	#41×C₂₃	1	4	yes	—
920	D₈	—	2	2	no	—
921	M₁₆	—	2	4	no	—
922	C₂×C₈	—	2	2	no	—
923	C₂×C₈	—	4	2	no	—
924	C₂×C₈	—	4	1	no	—
925	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
927	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
928	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
929	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
930	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
962	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
986	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
987	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
988	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1003	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₂₃	1	2	yes	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1010	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	2	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	4	4	no	—
1020	Q₈	—	8	1	no	—
1021	Q₈	—	8	1	no	—
1022	Q₈	—	8	2	no	—
1023	Q₈	C₂×#41×C₂₃	1	2	yes	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	4	2	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	8	2	no	—
1033	D₄	C₂×#41×C₂₃	1	2	yes	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	4	1	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	8	1	no	—
1057	C₂×C₄	—	8	1	no	—
1058	C₂×C₄	—	8	2	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1061	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1064	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1065	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1068	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1069	C₈	—	2	1	no	—
1070	C₈	—	2	2	no	—
1071	C₈	—	2	1	no	—
1072	C₈	—	2	2	no	—
1073	C₈	—	2	1	no	—
1074	C₈	C₂×#41×C₂₃	1	2	yes	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1088	C₄	—	2	1	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	C₂₃×#578	1	2	yes	—
1106	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1107	C₄	C₂₃×#585	1	1	yes	characteristic
1108	C₂	—	4	2	no	—
1109	C₂	—	4	1	no	—
1110	C₂	—	4	2	no	—
1111	C₂	—	8	1	no	—
1112	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
1113	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
1114	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 ◁ C₂₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3518	C₂	semidirect
2. C₂₃×#3515	C₂	semidirect
3. C₂₃×#3398	C₂	semidirect
4. C₂₃×#3385	C₂	semidirect
5. C₂₃×#3363	C₂	semidirect
6. C₂₃×#3360	C₂	semidirect
7. C₂₃×#3357	C₂	semidirect
8. C₂₃×#3349	C₂	semidirect
9. C₂₃×#3303	C₂	semidirect
10. C₂₃×#3302	C₂	semidirect
11. C₂₃×#3300	C₂	semidirect
12. C₂₃×#3299	C₂	semidirect
13. C₂₃×#3276	C₂	semidirect
14. C₂₃×#3269	C₂	semidirect
15. C₂₃×#3178	C₂	semidirect
16. C₂₃×#3170	C₂	semidirect
17. C₂₃×#3127	C₂	semidirect
18. C₂₃×#3124	C₂	semidirect
19. C₂₃×#3116	C₂	semidirect
20. C₂₃×#3116	C₂	semidirect
21. C₂₃×#2966	C₂	semidirect
22. C₂₃×#2947	C₂	semidirect
23. C₄×C₂₃×#135	C₂	semidirect
449. #61492	C₂₃	direct (N × H)
518. #3518	C₂×C₂₃	semidirect
519. #3515	C₂×C₂₃	semidirect
520. #3398	C₂×C₂₃	semidirect
521. #3385	C₂×C₂₃	semidirect
522. #3363	C₂×C₂₃	semidirect
523. #3360	C₂×C₂₃	semidirect
524. #3357	C₂×C₂₃	semidirect
525. #3349	C₂×C₂₃	semidirect
526. #3303	C₂×C₂₃	semidirect
527. #3302	C₂×C₂₃	semidirect
528. #3300	C₂×C₂₃	semidirect
529. #3299	C₂×C₂₃	semidirect
530. #3276	C₂×C₂₃	semidirect
531. #3269	C₂×C₂₃	semidirect
532. #3178	C₂×C₂₃	semidirect
533. #3170	C₂×C₂₃	semidirect
534. #3127	C₂×C₂₃	semidirect
535. #3124	C₂×C₂₃	semidirect
536. #3116	C₂×C₂₃	semidirect
537. #3116	C₂×C₂₃	semidirect
538. #2966	C₂×C₂₃	semidirect
539. #2947	C₂×C₂₃	semidirect
540. C₄×#135	C₂×C₂₃	semidirect
871. C₂₃	#61492	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×#3518	2
C₂₃×#3515	2
C₂₃×#3398	2
C₂₃×#3385	2
C₂₃×#3363	2
C₂₃×#3360	2
C₂₃×#3357	2
C₂₃×#3349	2
C₂₃×#3303	2
C₂₃×#3302	2
C₂₃×#3300	2
C₂₃×#3299	2
C₂₃×#3276	2
C₂₃×#3269	2
C₂₃×#3178	2
C₂₃×#3170	2
C₂₃×#3127	2
C₂₃×#3124	2
C₂₃×#3116	2
C₂₃×#2966	2
C₂₃×#2947	2
C₄×C₂₃×#135	2
#61492	23

Subgroups — C23×#61492 #19209118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61492 #19209118