Subgroups — C₂₃×#61734 #19209360

Order 5888.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1148 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	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3350	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3349	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3317	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3309	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3231	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×#3093	C₂	1	2	yes	maximal, complemented
22	C₂₃×#3091	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#559	—	2	2	no	—
25	C₂₃×#556	C₂²	1	1	yes	characteristic
26	C₂₃×#556	C₂²	1	2	yes	—
27	C₂₃×#555	C₂²	1	1	yes	characteristic
28	C₂₃×#555	C₂²	1	1	yes	characteristic
29	C₂₃×#555	C₂²	1	1	yes	characteristic
30	C₂₃×#554	C₂²	1	1	yes	characteristic
31	C₂₃×#553	—	2	1	no	—
32	C₂₃×#553	—	2	1	no	—
33	C₂₃×#553	C₂²	1	2	yes	—
34	C₂₃×#552	—	2	1	no	—
35	C₂₃×#552	C₂²	1	2	yes	—
36	C₂₃×#551	—	2	2	no	—
37	C₂₃×#550	C₂²	1	2	yes	—
38	C₂₃×#547	C₂²	1	1	yes	characteristic
39	C₂₃×#547	C₂²	1	1	yes	characteristic
40	C₂₃×#547	C₂²	1	1	yes	characteristic
41	C₂₃×#546	—	2	1	no	—
42	C₂₃×#538	—	2	2	no	—
43	C₂₃×#535	—	2	1	no	—
44	C₂₃×#533	C₂²	1	1	yes	characteristic
45	C₂₃×#533	C₂²	1	1	yes	characteristic
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#529	—	2	2	no	—
48	C₂₃×#529	—	2	1	no	—
49	C₂₃×#525	C₂²	1	2	yes	—
50	C₂₃×#525	C₂²	1	2	yes	—
51	C₂₃×#525	C₂²	1	2	yes	—
52	C₂₃×#520	—	2	1	no	—
53	C₄×#41×C₂₃	—	2	1	no	—
54	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#117	C₂²	1	2	yes	—
57	C₂₃×#501	C₂²	1	2	yes	complemented
58	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#490	C₂²	1	2	yes	complemented
61	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#485	C₂²	1	2	yes	—
64	C₂₃×#485	C₂²	1	2	yes	—
65	C₂₃×#485	C₂²	1	2	yes	—
66	C₂₃×#485	C₂²	1	2	yes	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×#484	C₂²	1	2	yes	complemented
71	C₂₃×#483	C₂²	1	2	yes	complemented
72	C₂₃×#482	C₂²	1	2	yes	—
73	C₂₃×#482	C₂²	1	2	yes	—
74	C₂₃×#482	C₂²	1	1	yes	characteristic
75	C₂₃×#482	C₂²	1	1	yes	characteristic
76	C₂₃×#482	C₂²	1	2	yes	complemented
77	C₂₃×#482	C₂²	1	2	yes	complemented
78	C₂₃×#482	C₂²	1	2	yes	complemented
79	C₂₃×#482	C₂²	1	2	yes	complemented
80	C₂₃×#481	C₂²	1	2	yes	complemented
81	C₂₃×#480	C₂²	1	2	yes	complemented
82	C₂₃×#479	C₂²	1	2	yes	complemented
83	C₂₃×#479	C₂²	1	2	yes	complemented
84	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#470	C₂²	1	2	yes	complemented
93	C₂₃×#469	C₂²	1	2	yes	complemented
94	C₂₃×#468	C₂²	1	2	yes	complemented
95	C₂₃×#468	C₂²	1	2	yes	complemented
96	C₂₃×#467	C₂²	1	2	yes	complemented
97	C₂₃×#466	C₂²	1	2	yes	complemented
98	C₂₃×#465	C₂²	1	2	yes	complemented
99	C₂₃×#465	C₂²	1	2	yes	complemented
100	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#452	C₂²	1	2	yes	—
105	C₂₃×#452	C₂²	1	2	yes	complemented
106	C₂₃×#452	C₂²	1	2	yes	complemented
107	C₂₃×#449	C₂²	1	1	yes	characteristic
108	C₂₃×#449	C₂²	1	1	yes	characteristic
109	C₂₃×#449	C₂²	1	2	yes	complemented
110	C₂₃×#449	C₂²	1	2	yes	complemented
111	C₂₃×#441	C₂²	1	2	yes	complemented
112	C₂₃×#440	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₂₃×#436	C₂²	1	1	yes	characteristic
118	C₂₃×#436	C₂²	1	1	yes	characteristic
119	C₂₃×#435	C₂²	1	2	yes	—
120	C₂₃×#435	C₂²	1	2	yes	—
121	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
123	C₂₃×#432	C₂²	1	1	yes	characteristic
124	C₂₃×#431	C₂²	1	1	yes	characteristic
125	C₂₃×#428	C₂²	1	2	yes	complemented
126	C₂₃×#428	C₂²	1	2	yes	complemented
127	C₂₃×#427	C₂²	1	2	yes	complemented
128	C₂₃×#427	C₂²	1	2	yes	complemented
129	C₂₃×#417	C₂²	1	2	yes	complemented
130	C₂₃×#417	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	—
134	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	—	2	1	no	—
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂×#41×C₂₃	C₂³	1	2	yes	—
139	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
141	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
152	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₂₃×#127	—	2	2	no	—
158	C₂₃×#127	C₂³	1	1	yes	characteristic
159	C₂₃×#126	—	2	2	no	—
160	C₂₃×#126	—	2	2	no	—
161	C₂₃×#126	—	2	2	no	—
162	C₂₃×#126	—	2	2	no	—
163	C₂₃×#126	—	2	2	no	—
164	C₂₃×#125	—	2	2	no	—
165	C₂₃×#125	—	2	1	no	—
166	C₂₃×#125	—	2	1	no	—
167	C₂₃×#125	C₂³	1	2	yes	—
168	C₂₃×#124	—	2	2	no	—
169	C₂₃×#124	—	2	1	no	—
170	C₂₃×#124	—	2	2	no	—
171	C₂₃×#124	—	2	2	no	—
172	C₂₃×#124	—	2	2	no	—
173	C₂₃×#124	—	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	—	2	2	no	—
182	C₂₃×C₂²⋊Q₈	—	2	1	no	—
183	C₂₃×C₂²⋊Q₈	—	2	1	no	—
184	C₂₃×C₂²⋊Q₈	—	2	1	no	—
185	C₂₃×C₂²⋊Q₈	—	2	1	no	—
186	C₂₃×C₂²⋊Q₈	—	2	2	no	—
187	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₂₃×#121	—	2	1	no	—
193	C₂₃×#121	—	2	1	no	—
194	C₂₃×#121	—	2	1	no	—
195	C₂₃×#121	—	2	1	no	—
196	C₂₃×#121	—	2	2	no	—
197	C₂₃×#121	—	2	1	no	—
198	C₂₃×#121	—	2	1	no	—
199	C₂₃×#121	—	2	2	no	—
200	C₂₃×#121	—	2	2	no	—
201	C₂₃×#121	C₂³	1	2	yes	—
202	C₂₃×#121	C₂³	1	2	yes	—
203	C₂₃×#121	C₂³	1	2	yes	—
204	C₂₃×#121	C₂³	1	2	yes	—
205	C₂₃×#121	C₂³	1	1	yes	characteristic
206	C₂₃×#121	C₂³	1	1	yes	characteristic
207	C₂₃×#120	—	2	2	no	—
208	C₂₃×#120	—	2	2	no	—
209	C₂₃×#120	—	2	2	no	—
210	C₄×Q₈×C₂₃	—	2	1	no	—
211	C₄×Q₈×C₂₃	—	2	2	no	—
212	C₄×Q₈×C₂₃	—	2	1	no	—
213	C₄×Q₈×C₂₃	—	2	1	no	—
214	C₄×Q₈×C₂₃	—	2	1	no	—
215	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₂₃	—	2	1	no	—
219	C₄×D₄×C₂₃	—	2	1	no	—
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	—	2	2	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	2	no	—
224	C₄×D₄×C₂₃	—	2	2	no	—
225	C₄×D₄×C₂₃	—	2	2	no	—
226	C₄×D₄×C₂₃	—	2	2	no	—
227	C₄×D₄×C₂₃	—	2	2	no	—
228	C₄×D₄×C₂₃	—	2	2	no	—
229	C₄×D₄×C₂₃	—	2	1	no	—
230	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
231	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
232	C₄×D₄×C₂₃	D₄	1	2	yes	—
233	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₂₃	C₂³	1	2	yes	—
240	C₂₃×#117	—	2	2	no	—
241	C₂₃×#117	—	2	2	no	—
242	C₂₃×#117	—	2	1	no	—
243	C₂₃×#117	—	2	1	no	—
244	C₂₃×#117	—	2	1	no	—
245	C₂₃×#117	—	2	1	no	—
246	C₂₃×#117	—	2	2	no	—
247	C₂₃×#117	—	2	1	no	—
248	C₂₃×#117	C₂³	1	2	yes	—
249	C₂₃×#117	C₂³	1	2	yes	—
250	C₂₃×#117	C₂³	1	2	yes	—
251	C₂₃×#117	C₂³	1	2	yes	—
252	C₂₃×#117	C₂³	1	1	yes	characteristic
253	C₂₃×#117	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
255	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
259	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
261	C₂×C₄²×C₂₃	—	2	2	no	—
262	C₂×C₄²×C₂₃	—	2	1	no	—
263	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
264	C₂₃×#107	C₂³	1	1	yes	characteristic
265	C₂₃×#107	C₂³	1	2	yes	—
266	C₂₃×#107	C₂³	1	2	yes	—
267	C₂₃×#107	C₂³	1	2	yes	—
268	C₂₃×#107	C₂³	1	1	yes	characteristic
269	C₂₃×#107	C₂³	1	2	yes	—
270	C₂₃×#107	C₂³	1	2	yes	—
271	C₂₃×#106	C₂³	1	1	yes	characteristic
272	C₂₃×#106	C₂³	1	2	yes	—
273	C₂₃×#106	C₂³	1	2	yes	—
274	C₂₃×#106	C₂³	1	2	yes	—
275	C₂₃×#106	C₂³	1	1	yes	characteristic
276	C₂₃×#106	C₂³	1	2	yes	—
277	C₂₃×#106	C₂³	1	2	yes	—
278	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₃×#103	C₂³	1	2	yes	—
283	C₂₃×#103	C₂³	1	2	yes	—
284	C₂₃×#103	C₂³	1	2	yes	—
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	2	yes	—
291	C₂₃×#102	C₂³	1	1	yes	characteristic
292	C₂₃×#102	C₂³	1	1	yes	characteristic
293	C₂₃×#102	C₂³	1	2	yes	—
294	C₂₃×#102	C₂³	1	2	yes	—
295	C₂₃×#102	C₂³	1	1	yes	characteristic
296	C₂₃×#102	C₂³	1	1	yes	characteristic
297	C₂₃×#102	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	1	yes	characteristic
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂₃×C₂²⋊C₈	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	1	yes	characteristic
307	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₂₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
312	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
313	#41×C₂₃	—	4	1	no	—
314	#41×C₂₃	—	4	1	no	—
315	#41×C₂₃	—	4	4	no	—
316	#41×C₂₃	—	4	2	no	—
317	#41×C₂₃	—	4	2	no	—
318	#41×C₂₃	—	4	2	no	—
319	#41×C₂₃	—	4	2	no	—
320	#41×C₂₃	—	4	4	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	2	1	no	—
323	C₂×Q₈×C₂₃	—	2	1	no	—
324	C₂×Q₈×C₂₃	—	2	1	no	—
325	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₂₃	—	2	1	no	—
328	C₂×D₄×C₂₃	—	2	1	no	—
329	C₂×D₄×C₂₃	—	2	1	no	—
330	C₂×D₄×C₂₃	—	2	2	no	—
331	C₂×D₄×C₂₃	—	2	2	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	1	no	—
337	C₂×D₄×C₂₃	—	2	1	no	—
338	C₂×D₄×C₂₃	—	4	2	no	—
339	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₂₃	—	2	2	no	—
346	C₂²×C₄×C₂₃	—	2	2	no	—
347	C₂²×C₄×C₂₃	—	2	1	no	—
348	C₂²×C₄×C₂₃	—	2	1	no	—
349	C₂²×C₄×C₂₃	—	2	1	no	—
350	C₂²×C₄×C₂₃	—	2	1	no	—
351	C₂²×C₄×C₂₃	—	2	1	no	—
352	C₂²×C₄×C₂₃	—	2	2	no	—
353	C₂²×C₄×C₂₃	—	2	2	no	—
354	C₂²×C₄×C₂₃	—	4	2	no	—
355	C₂²×C₄×C₂₃	—	4	2	no	—
356	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
360	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
361	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
364	Q₁₆×C₂₃	—	4	2	no	—
365	SD₁₆×C₂₃	—	4	1	no	—
366	SD₁₆×C₂₃	—	4	2	no	—
367	SD₁₆×C₂₃	—	4	1	no	—
368	D₈×C₂₃	—	4	1	no	—
369	D₈×C₂₃	—	4	1	no	—
370	M₁₆×C₂₃	—	4	2	no	—
371	M₁₆×C₂₃	—	4	2	no	—
372	C₂×C₈×C₂₃	—	4	2	no	—
373	C₂×C₈×C₂₃	—	4	2	no	—
374	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
375	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
377	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₂₃	—	2	1	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	2	no	—
383	C₄⋊C₄×C₂₃	—	2	2	no	—
384	C₄⋊C₄×C₂₃	—	2	2	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	—	2	1	no	—
387	C₄⋊C₄×C₂₃	—	2	2	no	—
388	C₄⋊C₄×C₂₃	—	2	2	no	—
389	C₄⋊C₄×C₂₃	—	2	1	no	—
390	C₄⋊C₄×C₂₃	—	2	1	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	1	no	—
393	C₄⋊C₄×C₂₃	—	2	2	no	—
394	C₄⋊C₄×C₂₃	—	2	2	no	—
395	C₄⋊C₄×C₂₃	—	2	1	no	—
396	C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₄⋊C₄×C₂₃	—	2	2	no	—
398	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂⁴	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	2	yes	—
408	C₂²⋊C₄×C₂₃	—	2	1	no	—
409	C₂²⋊C₄×C₂₃	—	2	2	no	—
410	C₂²⋊C₄×C₂₃	—	2	2	no	—
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	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	2	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	2	no	—
420	C₂²⋊C₄×C₂₃	—	2	2	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	1	no	—
425	C₂²⋊C₄×C₂₃	—	2	1	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	1	no	—
428	C₂²⋊C₄×C₂₃	—	2	1	no	—
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	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
433	C₄²×C₂₃	—	2	1	no	—
434	C₄²×C₂₃	—	2	2	no	—
435	C₄²×C₂₃	—	2	1	no	—
436	C₄²×C₂₃	—	2	2	no	—
437	C₄²×C₂₃	—	2	2	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	2	no	—
440	C₄²×C₂₃	—	2	2	no	—
441	C₄²×C₂₃	—	2	2	no	—
442	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
445	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
446	#61734	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₂₃	—	2	1	no	—
448	C₂³×C₂₃	—	2	1	no	—
449	C₂³×C₂₃	—	2	1	no	—
450	C₂³×C₂₃	—	4	2	no	—
451	C₂³×C₂₃	—	4	2	no	—
452	C₂³×C₂₃	—	4	2	no	—
453	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
454	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
455	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
456	Q₈×C₂₃	—	2	1	no	—
457	Q₈×C₂₃	—	2	2	no	—
458	Q₈×C₂₃	—	2	1	no	—
459	Q₈×C₂₃	—	2	2	no	—
460	Q₈×C₂₃	—	4	2	no	—
461	Q₈×C₂₃	—	4	2	no	—
462	Q₈×C₂₃	—	8	1	no	—
463	Q₈×C₂₃	—	8	1	no	—
464	D₄×C₂₃	—	2	2	no	—
465	D₄×C₂₃	—	2	2	no	—
466	D₄×C₂₃	—	2	1	no	—
467	D₄×C₂₃	—	2	1	no	—
468	D₄×C₂₃	—	2	1	no	—
469	D₄×C₂₃	—	2	1	no	—
470	D₄×C₂₃	—	2	1	no	—
471	D₄×C₂₃	—	2	1	no	—
472	D₄×C₂₃	—	4	2	no	—
473	D₄×C₂₃	—	4	2	no	—
474	D₄×C₂₃	—	4	2	no	—
475	D₄×C₂₃	—	4	2	no	—
476	D₄×C₂₃	—	4	2	no	—
477	D₄×C₂₃	—	4	4	no	—
478	D₄×C₂₃	—	8	1	no	—
479	D₄×C₂₃	—	8	2	no	—
480	D₄×C₂₃	—	8	2	no	—
481	D₄×C₂₃	—	8	2	no	—
482	D₄×C₂₃	—	8	2	no	—
483	D₄×C₂₃	—	8	2	no	—
484	C₂×C₄×C₂₃	—	2	2	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	2	2	no	—
487	C₂×C₄×C₂₃	—	2	2	no	—
488	C₂×C₄×C₂₃	—	2	2	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	1	no	—
491	C₂×C₄×C₂₃	—	2	1	no	—
492	C₂×C₄×C₂₃	—	2	1	no	—
493	C₂×C₄×C₂₃	—	2	2	no	—
494	C₂×C₄×C₂₃	—	2	1	no	—
495	C₂×C₄×C₂₃	—	2	1	no	—
496	C₂×C₄×C₂₃	—	2	1	no	—
497	C₂×C₄×C₂₃	—	2	2	no	—
498	C₂×C₄×C₂₃	—	2	2	no	—
499	C₂×C₄×C₂₃	—	2	2	no	—
500	C₂×C₄×C₂₃	—	4	2	no	—
501	C₂×C₄×C₂₃	—	4	2	no	—
502	C₂×C₄×C₂₃	—	4	2	no	—
503	C₂×C₄×C₂₃	—	4	1	no	—
504	C₂×C₄×C₂₃	—	4	2	no	—
505	C₂×C₄×C₂₃	—	4	4	no	—
506	C₂×C₄×C₂₃	—	4	2	no	—
507	C₂×C₄×C₂₃	—	4	2	no	—
508	C₂×C₄×C₂₃	—	4	2	no	—
509	C₂×C₄×C₂₃	—	8	1	no	—
510	C₂×C₄×C₂₃	—	8	2	no	—
511	C₂×C₄×C₂₃	—	8	2	no	—
512	C₂×C₄×C₂₃	—	8	2	no	—
513	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
521	C₈×C₂₃	—	2	1	no	—
522	C₈×C₂₃	—	2	1	no	—
523	C₈×C₂₃	—	2	2	no	—
524	C₈×C₂₃	—	2	2	no	—
525	C₈×C₂₃	—	2	1	no	—
526	C₈×C₂₃	—	2	1	no	—
527	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
528	#3475	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3357	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3354	C₂×C₂₃	1	1	yes	characteristic, complemented
531	#3350	C₂×C₂₃	1	2	yes	complemented
532	#3349	C₂×C₂₃	1	2	yes	complemented
533	#3341	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3340	C₂×C₂₃	1	1	yes	characteristic, complemented
535	#3331	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3330	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3317	C₂×C₂₃	1	2	yes	complemented
538	#3309	C₂×C₂₃	1	2	yes	complemented
539	#3303	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3302	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3235	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#3231	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#3197	C₂×C₂₃	1	2	yes	complemented
544	#3191	C₂×C₂₃	1	2	yes	complemented
545	#3116	C₂×C₂₃	1	1	yes	characteristic, complemented
546	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
547	#3093	C₂×C₂₃	1	2	yes	complemented
548	#3091	C₂×C₂₃	1	2	yes	complemented
549	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
550	C₂²×C₂₃	—	2	1	no	—
551	C₂²×C₂₃	—	2	2	no	—
552	C₂²×C₂₃	—	2	2	no	—
553	C₂²×C₂₃	—	2	1	no	—
554	C₂²×C₂₃	—	2	2	no	—
555	C₂²×C₂₃	—	2	2	no	—
556	C₂²×C₂₃	—	2	1	no	—
557	C₂²×C₂₃	—	2	2	no	—
558	C₂²×C₂₃	—	2	2	no	—
559	C₂²×C₂₃	—	4	1	no	—
560	C₂²×C₂₃	—	4	1	no	—
561	C₂²×C₂₃	—	4	1	no	—
562	C₂²×C₂₃	—	4	1	no	—
563	C₂²×C₂₃	—	4	1	no	—
564	C₂²×C₂₃	—	4	1	no	—
565	C₂²×C₂₃	—	4	1	no	—
566	C₂²×C₂₃	—	4	1	no	—
567	C₂²×C₂₃	—	4	1	no	—
568	C₂²×C₂₃	—	8	4	no	—
569	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
570	C₄×C₂₃	—	2	1	no	—
571	C₄×C₂₃	—	2	1	no	—
572	C₄×C₂₃	—	2	1	no	—
573	C₄×C₂₃	—	2	2	no	—
574	C₄×C₂₃	—	2	2	no	—
575	C₄×C₂₃	—	2	1	no	—
576	C₄×C₂₃	—	4	1	no	—
577	C₄×C₂₃	—	4	2	no	—
578	C₄×C₂₃	—	4	2	no	—
579	C₄×C₂₃	—	4	1	no	—
580	C₄×C₂₃	—	4	2	no	—
581	C₄×C₂₃	—	4	1	no	—
582	C₄×C₂₃	—	4	1	no	—
583	C₄×C₂₃	—	4	1	no	—
584	C₄×C₂₃	—	4	2	no	—
585	C₄×C₂₃	#575	1	2	yes	—
586	C₄×C₂₃	#585	1	1	yes	characteristic
587	C₄×C₂₃	#585	1	1	yes	characteristic
588	#559	—	2	2	no	—
589	#556	C₂²×C₂₃	1	1	yes	characteristic
590	#556	C₂²×C₂₃	1	2	yes	—
591	#555	C₂²×C₂₃	1	1	yes	characteristic
592	#555	C₂²×C₂₃	1	1	yes	characteristic
593	#555	C₂²×C₂₃	1	1	yes	characteristic
594	#554	C₂²×C₂₃	1	1	yes	characteristic
595	#553	—	2	1	no	—
596	#553	—	2	1	no	—
597	#553	C₂²×C₂₃	1	2	yes	—
598	#552	—	2	1	no	—
599	#552	C₂²×C₂₃	1	2	yes	—
600	#551	—	2	2	no	—
601	#550	C₂²×C₂₃	1	2	yes	—
602	#547	C₂²×C₂₃	1	1	yes	characteristic
603	#547	C₂²×C₂₃	1	1	yes	characteristic
604	#547	C₂²×C₂₃	1	1	yes	characteristic
605	#546	—	2	1	no	—
606	#538	—	2	2	no	—
607	#535	—	2	1	no	—
608	#533	C₂²×C₂₃	1	1	yes	characteristic
609	#533	C₂²×C₂₃	1	1	yes	characteristic
610	#532	C₂²×C₂₃	1	1	yes	characteristic
611	#529	—	2	2	no	—
612	#529	—	2	1	no	—
613	#525	C₂²×C₂₃	1	2	yes	—
614	#525	C₂²×C₂₃	1	2	yes	—
615	#525	C₂²×C₂₃	1	2	yes	—
616	#520	—	2	1	no	—
617	C₄×#41	—	2	1	no	—
618	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
619	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
620	C₂×#117	C₂²×C₂₃	1	2	yes	—
621	#501	C₂²×C₂₃	1	2	yes	complemented
622	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
623	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
624	#490	C₂²×C₂₃	1	2	yes	complemented
625	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
626	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
627	#485	C₂²×C₂₃	1	2	yes	—
628	#485	C₂²×C₂₃	1	2	yes	—
629	#485	C₂²×C₂₃	1	2	yes	—
630	#485	C₂²×C₂₃	1	2	yes	complemented
631	#485	C₂²×C₂₃	1	2	yes	complemented
632	#485	C₂²×C₂₃	1	2	yes	complemented
633	#485	C₂²×C₂₃	1	2	yes	complemented
634	#484	C₂²×C₂₃	1	2	yes	complemented
635	#483	C₂²×C₂₃	1	2	yes	complemented
636	#482	C₂²×C₂₃	1	1	yes	characteristic
637	#482	C₂²×C₂₃	1	2	yes	—
638	#482	C₂²×C₂₃	1	1	yes	characteristic
639	#482	C₂²×C₂₃	1	2	yes	—
640	#482	C₂²×C₂₃	1	2	yes	complemented
641	#482	C₂²×C₂₃	1	2	yes	complemented
642	#482	C₂²×C₂₃	1	2	yes	complemented
643	#482	C₂²×C₂₃	1	2	yes	complemented
644	#481	C₂²×C₂₃	1	2	yes	complemented
645	#480	C₂²×C₂₃	1	2	yes	complemented
646	#479	C₂²×C₂₃	1	2	yes	complemented
647	#479	C₂²×C₂₃	1	2	yes	complemented
648	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
649	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
651	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
652	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
653	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
654	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
656	#470	C₂²×C₂₃	1	2	yes	complemented
657	#469	C₂²×C₂₃	1	2	yes	complemented
658	#468	C₂²×C₂₃	1	2	yes	complemented
659	#468	C₂²×C₂₃	1	2	yes	complemented
660	#467	C₂²×C₂₃	1	2	yes	complemented
661	#466	C₂²×C₂₃	1	2	yes	complemented
662	#465	C₂²×C₂₃	1	2	yes	complemented
663	#465	C₂²×C₂₃	1	2	yes	complemented
664	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
665	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
666	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
667	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
668	#452	C₂²×C₂₃	1	2	yes	—
669	#452	C₂²×C₂₃	1	2	yes	complemented
670	#452	C₂²×C₂₃	1	2	yes	complemented
671	#449	C₂²×C₂₃	1	1	yes	characteristic
672	#449	C₂²×C₂₃	1	1	yes	characteristic
673	#449	C₂²×C₂₃	1	2	yes	complemented
674	#449	C₂²×C₂₃	1	2	yes	complemented
675	#441	C₂²×C₂₃	1	2	yes	complemented
676	#440	C₂²×C₂₃	1	2	yes	complemented
677	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
679	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
680	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	#436	C₂²×C₂₃	1	1	yes	characteristic
682	#436	C₂²×C₂₃	1	1	yes	characteristic
683	#435	C₂²×C₂₃	1	2	yes	—
684	#435	C₂²×C₂₃	1	2	yes	—
685	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
686	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
687	#432	C₂²×C₂₃	1	1	yes	characteristic
688	#431	C₂²×C₂₃	1	1	yes	characteristic
689	#428	C₂²×C₂₃	1	2	yes	complemented
690	#428	C₂²×C₂₃	1	2	yes	complemented
691	#427	C₂²×C₂₃	1	2	yes	complemented
692	#427	C₂²×C₂₃	1	2	yes	complemented
693	#417	C₂²×C₂₃	1	2	yes	complemented
694	#417	C₂²×C₂₃	1	2	yes	complemented
695	#416	C₂²×C₂₃	1	2	yes	complemented
696	#416	C₂²×C₂₃	1	2	yes	complemented
697	#407	C₂²×C₂₃	1	2	yes	—
698	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
699	C₂×C₂₃	—	4	2	no	—
700	C₂×C₂₃	—	4	2	no	—
701	C₂×C₂₃	—	4	1	no	—
702	C₂×C₂₃	—	8	1	no	—
703	C₂×C₂₃	—	8	1	no	—
704	C₂×C₂₃	—	8	1	no	—
705	C₂×C₂₃	#3485	1	1	yes	characteristic
706	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
707	C₂×C₂₃	#3584	1	1	yes	characteristic
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
711	C₂×#41	C₂³×C₂₃	1	2	yes	—
712	C₂×#41	C₂³×C₂₃	1	2	yes	—
713	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
714	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
715	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
717	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
718	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
719	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
720	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
721	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
722	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
723	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
724	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
725	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
730	#127	—	2	2	no	—
731	#127	C₂³×C₂₃	1	1	yes	characteristic
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	—	2	1	no	—
740	#125	C₂³×C₂₃	1	2	yes	—
741	#124	—	2	1	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	1	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
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	#121	—	2	2	no	—
766	#121	—	2	1	no	—
767	#121	—	2	1	no	—
768	#121	—	2	1	no	—
769	#121	—	2	1	no	—
770	#121	—	2	1	no	—
771	#121	—	2	1	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	C₂³×C₂₃	1	1	yes	characteristic
775	#121	C₂³×C₂₃	1	1	yes	characteristic
776	#121	C₂³×C₂₃	1	2	yes	—
777	#121	C₂³×C₂₃	1	2	yes	—
778	#121	C₂³×C₂₃	1	2	yes	—
779	#121	C₂³×C₂₃	1	2	yes	—
780	#120	—	2	2	no	—
781	#120	—	2	2	no	—
782	#120	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	2	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	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	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
804	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
805	C₄×D₄	D₄×C₂₃	1	2	yes	—
806	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₂₃	1	2	yes	—
813	#117	—	2	2	no	—
814	#117	—	2	2	no	—
815	#117	—	2	1	no	—
816	#117	—	2	1	no	—
817	#117	—	2	1	no	—
818	#117	—	2	1	no	—
819	#117	—	2	2	no	—
820	#117	—	2	1	no	—
821	#117	C₂³×C₂₃	1	1	yes	characteristic
822	#117	C₂³×C₂₃	1	2	yes	—
823	#117	C₂³×C₂₃	1	2	yes	—
824	#117	C₂³×C₂₃	1	2	yes	—
825	#117	C₂³×C₂₃	1	2	yes	—
826	#117	C₂³×C₂₃	1	2	yes	—
827	C₂×C₄⋊C₄	—	2	1	no	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
830	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
831	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
832	C₂×C₂²⋊C₄	—	2	2	no	—
833	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
834	C₂×C₄²	—	2	2	no	—
835	C₂×C₄²	—	2	1	no	—
836	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
837	#107	C₂³×C₂₃	1	1	yes	characteristic
838	#107	C₂³×C₂₃	1	2	yes	—
839	#107	C₂³×C₂₃	1	2	yes	—
840	#107	C₂³×C₂₃	1	2	yes	—
841	#107	C₂³×C₂₃	1	1	yes	characteristic
842	#107	C₂³×C₂₃	1	2	yes	—
843	#107	C₂³×C₂₃	1	2	yes	—
844	#106	C₂³×C₂₃	1	1	yes	characteristic
845	#106	C₂³×C₂₃	1	2	yes	—
846	#106	C₂³×C₂₃	1	2	yes	—
847	#106	C₂³×C₂₃	1	2	yes	—
848	#106	C₂³×C₂₃	1	1	yes	characteristic
849	#106	C₂³×C₂₃	1	2	yes	—
850	#106	C₂³×C₂₃	1	2	yes	—
851	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
855	#103	C₂³×C₂₃	1	2	yes	—
856	#103	C₂³×C₂₃	1	2	yes	—
857	#103	C₂³×C₂₃	1	2	yes	—
858	#103	C₂³×C₂₃	1	2	yes	—
859	#103	C₂³×C₂₃	1	2	yes	—
860	#103	C₂³×C₂₃	1	2	yes	—
861	#103	C₂³×C₂₃	1	1	yes	characteristic
862	#103	C₂³×C₂₃	1	1	yes	characteristic
863	#103	C₂³×C₂₃	1	2	yes	—
864	#102	C₂³×C₂₃	1	1	yes	characteristic
865	#102	C₂³×C₂₃	1	1	yes	characteristic
866	#102	C₂³×C₂₃	1	2	yes	—
867	#102	C₂³×C₂₃	1	2	yes	—
868	#102	C₂³×C₂₃	1	1	yes	characteristic
869	#102	C₂³×C₂₃	1	1	yes	characteristic
870	#102	C₂³×C₂₃	1	2	yes	—
871	#102	C₂³×C₂₃	1	2	yes	—
872	#102	C₂³×C₂₃	1	1	yes	characteristic
873	#102	C₂³×C₂₃	1	1	yes	characteristic
874	#102	C₂³×C₂₃	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
880	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
882	#97	C₂³×C₂₃	1	2	yes	—
883	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
885	C₂₃	#61734	1	1	yes	characteristic, direct product factor, Sylow
886	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
887	#41	—	4	1	no	—
888	#41	—	4	1	no	—
889	#41	—	4	4	no	—
890	#41	—	4	2	no	—
891	#41	—	4	2	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	4	4	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
900	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
914	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
915	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
916	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
917	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
918	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	4	2	no	—
929	C₂²×C₄	—	4	2	no	—
930	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
932	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
933	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
934	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
938	Q₁₆	—	4	2	no	—
939	SD₁₆	—	4	1	no	—
940	SD₁₆	—	4	2	no	—
941	SD₁₆	—	4	1	no	—
942	D₈	—	4	1	no	—
943	D₈	—	4	1	no	—
944	M₁₆	—	4	2	no	—
945	M₁₆	—	4	2	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	—	4	2	no	—
948	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
950	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
953	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
979	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1017	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1018	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1019	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	4	2	no	—
1024	C₂³	—	4	2	no	—
1025	C₂³	—	4	2	no	—
1026	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1027	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1028	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	2	2	no	—
1031	Q₈	—	2	1	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	4	2	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	1	no	—
1036	Q₈	—	8	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	4	4	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	4	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	1	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1093	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1094	C₈	—	2	1	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	2	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	1	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	8	4	no	—
1119	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	2	no	—
1135	C₄	C₂₃×#575	1	2	yes	—
1136	C₄	C₂₃×#585	1	1	yes	characteristic
1137	C₄	C₂₃×#585	1	1	yes	characteristic
1138	C₂	—	4	1	no	—
1139	C₂	—	4	2	no	—
1140	C₂	—	4	2	no	—
1141	C₂	—	8	1	no	—
1142	C₂	—	8	1	no	—
1143	C₂	—	8	1	no	—
1144	C₂	C₂₃×#3485	1	1	yes	characteristic
1145	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1146	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. C₂₃×#3475	C₂	semidirect
3. C₂₃×#3357	C₂	semidirect
4. C₂₃×#3354	C₂	semidirect
5. C₂₃×#3350	C₂	semidirect
6. C₂₃×#3349	C₂	semidirect
7. C₂₃×#3341	C₂	semidirect
8. C₂₃×#3340	C₂	semidirect
9. C₂₃×#3331	C₂	semidirect
10. C₂₃×#3330	C₂	semidirect
11. C₂₃×#3317	C₂	semidirect
12. C₂₃×#3309	C₂	semidirect
13. C₂₃×#3303	C₂	semidirect
14. C₂₃×#3302	C₂	semidirect
15. C₂₃×#3235	C₂	semidirect
16. C₂₃×#3231	C₂	semidirect
17. C₂₃×#3197	C₂	semidirect
18. C₂₃×#3191	C₂	semidirect
19. C₂₃×#3116	C₂	semidirect
20. C₂₃×#3106	C₂	semidirect
21. C₂₃×#3093	C₂	semidirect
22. C₂₃×#3091	C₂	semidirect
23. C₂₃×#2974	C₂	semidirect
57. C₂₃×#501	C₂²	semidirect
58. C₂₃×#500	C₂²	semidirect
59. C₂₃×#498	C₂²	semidirect
60. C₂₃×#490	C₂²	semidirect
61. C₂₃×#487	C₂²	semidirect
62. C₂₃×#487	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#485	C₂²	semidirect
69. C₂₃×#485	C₂²	semidirect
70. C₂₃×#484	C₂²	semidirect
71. C₂₃×#483	C₂²	semidirect
76. C₂₃×#482	C₂²	semidirect
77. C₂₃×#482	C₂²	semidirect
78. C₂₃×#482	C₂²	semidirect
79. C₂₃×#482	C₂²	semidirect
80. C₂₃×#481	C₂²	semidirect
81. C₂₃×#480	C₂²	semidirect
82. C₂₃×#479	C₂²	semidirect
83. C₂₃×#479	C₂²	semidirect
84. C₂₃×#477	C₂²	semidirect
85. C₂₃×#477	C₂²	semidirect
86. C₂₃×#476	C₂²	semidirect
87. C₂₃×#476	C₂²	semidirect
88. C₂₃×#476	C₂²	semidirect
89. C₂₃×#476	C₂²	semidirect
90. C₂₃×#474	C₂²	semidirect
91. C₂₃×#474	C₂²	semidirect
92. C₂₃×#470	C₂²	semidirect
93. C₂₃×#469	C₂²	semidirect
94. C₂₃×#468	C₂²	semidirect
95. C₂₃×#468	C₂²	semidirect
96. C₂₃×#467	C₂²	semidirect
97. C₂₃×#466	C₂²	semidirect
98. C₂₃×#465	C₂²	semidirect
99. C₂₃×#465	C₂²	semidirect
100. C₂₃×#462	C₂²	semidirect
101. C₂₃×#461	C₂²	semidirect
102. C₂₃×#460	C₂²	semidirect
103. C₂₃×#459	C₂²	semidirect
105. C₂₃×#452	C₂²	semidirect
106. C₂₃×#452	C₂²	semidirect
109. C₂₃×#449	C₂²	semidirect
110. C₂₃×#449	C₂²	semidirect
111. C₂₃×#441	C₂²	semidirect
112. C₂₃×#440	C₂²	semidirect
113. C₄×SD₁₆×C₂₃	C₂²	semidirect
114. C₄×SD₁₆×C₂₃	C₂²	semidirect
115. C₄×D₈×C₂₃	C₂²	semidirect
116. C₄×D₈×C₂₃	C₂²	semidirect
125. C₂₃×#428	C₂²	semidirect
126. C₂₃×#428	C₂²	semidirect
127. C₂₃×#427	C₂²	semidirect
128. C₂₃×#427	C₂²	semidirect
129. C₂₃×#417	C₂²	semidirect
130. C₂₃×#417	C₂²	semidirect
131. C₂₃×#416	C₂²	semidirect
132. C₂₃×#416	C₂²	semidirect
446. #61734	C₂₃	direct (N × H)
527. #3506	C₂×C₂₃	semidirect
528. #3475	C₂×C₂₃	semidirect
529. #3357	C₂×C₂₃	semidirect
530. #3354	C₂×C₂₃	semidirect
531. #3350	C₂×C₂₃	semidirect
532. #3349	C₂×C₂₃	semidirect
533. #3341	C₂×C₂₃	semidirect
534. #3340	C₂×C₂₃	semidirect
535. #3331	C₂×C₂₃	semidirect
536. #3330	C₂×C₂₃	semidirect
537. #3317	C₂×C₂₃	semidirect
538. #3309	C₂×C₂₃	semidirect
539. #3303	C₂×C₂₃	semidirect
540. #3302	C₂×C₂₃	semidirect
541. #3235	C₂×C₂₃	semidirect
542. #3231	C₂×C₂₃	semidirect
543. #3197	C₂×C₂₃	semidirect
544. #3191	C₂×C₂₃	semidirect
545. #3116	C₂×C₂₃	semidirect
546. #3106	C₂×C₂₃	semidirect
547. #3093	C₂×C₂₃	semidirect
548. #3091	C₂×C₂₃	semidirect
549. #2974	C₂×C₂₃	semidirect
621. #501	C₂²×C₂₃	semidirect
622. #500	C₂²×C₂₃	semidirect
623. #498	C₂²×C₂₃	semidirect
624. #490	C₂²×C₂₃	semidirect
625. #487	C₂²×C₂₃	semidirect
626. #487	C₂²×C₂₃	semidirect
630. #485	C₂²×C₂₃	semidirect
631. #485	C₂²×C₂₃	semidirect
632. #485	C₂²×C₂₃	semidirect
633. #485	C₂²×C₂₃	semidirect
634. #484	C₂²×C₂₃	semidirect
635. #483	C₂²×C₂₃	semidirect
640. #482	C₂²×C₂₃	semidirect
641. #482	C₂²×C₂₃	semidirect
642. #482	C₂²×C₂₃	semidirect
643. #482	C₂²×C₂₃	semidirect
644. #481	C₂²×C₂₃	semidirect
645. #480	C₂²×C₂₃	semidirect
646. #479	C₂²×C₂₃	semidirect
647. #479	C₂²×C₂₃	semidirect
648. #477	C₂²×C₂₃	semidirect
649. #477	C₂²×C₂₃	semidirect
650. #476	C₂²×C₂₃	semidirect
651. #476	C₂²×C₂₃	semidirect
652. #476	C₂²×C₂₃	semidirect
653. #476	C₂²×C₂₃	semidirect
654. #474	C₂²×C₂₃	semidirect
655. #474	C₂²×C₂₃	semidirect
656. #470	C₂²×C₂₃	semidirect
657. #469	C₂²×C₂₃	semidirect
658. #468	C₂²×C₂₃	semidirect
659. #468	C₂²×C₂₃	semidirect
660. #467	C₂²×C₂₃	semidirect
661. #466	C₂²×C₂₃	semidirect
662. #465	C₂²×C₂₃	semidirect
663. #465	C₂²×C₂₃	semidirect
664. #462	C₂²×C₂₃	semidirect
665. #461	C₂²×C₂₃	semidirect
666. #460	C₂²×C₂₃	semidirect
667. #459	C₂²×C₂₃	semidirect
669. #452	C₂²×C₂₃	semidirect
670. #452	C₂²×C₂₃	semidirect
673. #449	C₂²×C₂₃	semidirect
674. #449	C₂²×C₂₃	semidirect
675. #441	C₂²×C₂₃	semidirect
676. #440	C₂²×C₂₃	semidirect
677. C₄×SD₁₆	C₂²×C₂₃	semidirect
678. C₄×SD₁₆	C₂²×C₂₃	semidirect
679. C₄×D₈	C₂²×C₂₃	semidirect
680. C₄×D₈	C₂²×C₂₃	semidirect
689. #428	C₂²×C₂₃	semidirect
690. #428	C₂²×C₂₃	semidirect
691. #427	C₂²×C₂₃	semidirect
692. #427	C₂²×C₂₃	semidirect
693. #417	C₂²×C₂₃	semidirect
694. #417	C₂²×C₂₃	semidirect
695. #416	C₂²×C₂₃	semidirect
696. #416	C₂²×C₂₃	semidirect
885. C₂₃	#61734	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
C₂₃×#3475	2
C₂₃×#3357	2
C₂₃×#3354	2
C₂₃×#3350	2
C₂₃×#3349	2
C₂₃×#3341	2
C₂₃×#3340	2
C₂₃×#3331	2
C₂₃×#3330	2
C₂₃×#3317	2
C₂₃×#3309	2
C₂₃×#3303	2
C₂₃×#3302	2
C₂₃×#3235	2
C₂₃×#3231	2
C₂₃×#3197	2
C₂₃×#3191	2
C₂₃×#3116	2
C₂₃×#3106	2
C₂₃×#3093	2
C₂₃×#3091	2
C₂₃×#2974	2
#61734	23

Subgroups — C23×#61734 #19209360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61734 #19209360