Subgroups — C₂₃×#61266 #19208892

Order 5888.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3356	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3355	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3354	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3352	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3350	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3348	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3346	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3343	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#556	—	2	1	no	—
28	C₂₃×#556	C₂²	1	2	yes	—
29	C₂₃×#555	—	2	1	no	—
30	C₂₃×#555	C₂²	1	2	yes	—
31	C₂₃×#554	—	2	1	no	—
32	C₂₃×#554	C₂²	1	2	yes	—
33	C₂₃×#553	—	2	1	no	—
34	C₂₃×#553	—	2	1	no	—
35	C₂₃×#553	C₂²	1	2	yes	—
36	C₂₃×#553	C₂²	1	2	yes	—
37	C₂₃×#552	—	2	1	no	—
38	C₂₃×#552	—	2	1	no	—
39	C₂₃×#552	C₂²	1	2	yes	—
40	C₂₃×#552	C₂²	1	2	yes	—
41	C₂₃×#547	—	2	1	no	—
42	C₂₃×#547	C₂²	1	2	yes	—
43	C₂₃×#544	C₂²	1	1	yes	characteristic
44	C₂₃×#544	C₂²	1	1	yes	characteristic
45	C₂₃×#539	—	2	2	no	—
46	C₂₃×#538	—	2	2	no	—
47	C₂₃×#537	C₂²	1	1	yes	characteristic
48	C₂₃×#537	C₂²	1	1	yes	characteristic
49	C₂₃×#529	—	2	2	no	—
50	C₂₃×#525	—	2	2	no	—
51	C₂₃×#525	C₂²	1	1	yes	characteristic
52	C₂₃×#525	C₂²	1	1	yes	characteristic
53	C₂₃×#525	C₂²	1	1	yes	characteristic
54	C₂₃×#520	C₂²	1	1	yes	characteristic
55	C₂₃×#520	C₂²	1	1	yes	characteristic
56	C₂₃×#520	C₂²	1	1	yes	characteristic
57	C₂₃×#520	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
59	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
60	C₂₃×#501	C₂²	1	2	yes	complemented
61	C₂₃×#501	C₂²	1	2	yes	complemented
62	C₂₃×#499	C₂²	1	2	yes	complemented
63	C₂₃×#498	C₂²	1	2	yes	complemented
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×#484	C₂²	1	2	yes	—
69	C₂₃×#484	C₂²	1	2	yes	complemented
70	C₂₃×#483	C₂²	1	2	yes	—
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	2	yes	complemented
75	C₂₃×#482	C₂²	1	2	yes	complemented
76	C₂₃×#481	C₂²	1	2	yes	—
77	C₂₃×#481	C₂²	1	2	yes	complemented
78	C₂₃×#480	C₂²	1	2	yes	—
79	C₂₃×#480	C₂²	1	2	yes	complemented
80	C₂₃×#479	C₂²	1	2	yes	complemented
81	C₂₃×#479	C₂²	1	2	yes	complemented
82	C₂₃×#478	C₂²	1	2	yes	complemented
83	C₂₃×#478	C₂²	1	2	yes	complemented
84	C₂₃×#477	C₂²	1	2	yes	complemented
85	C₂₃×#476	C₂²	1	2	yes	complemented
86	C₂₃×#475	C₂²	1	2	yes	complemented
87	C₂₃×#474	C₂²	1	2	yes	complemented
88	C₂₃×#470	C₂²	1	1	yes	characteristic
89	C₂₃×#470	C₂²	1	1	yes	characteristic
90	C₂₃×#470	C₂²	1	2	yes	complemented
91	C₂₃×#469	C₂²	1	1	yes	characteristic
92	C₂₃×#469	C₂²	1	1	yes	characteristic
93	C₂₃×#469	C₂²	1	2	yes	complemented
94	C₂₃×#468	C₂²	1	1	yes	characteristic
95	C₂₃×#468	C₂²	1	1	yes	characteristic
96	C₂₃×#468	C₂²	1	1	yes	characteristic
97	C₂₃×#468	C₂²	1	1	yes	characteristic
98	C₂₃×#465	C₂²	1	2	yes	complemented
99	C₂₃×#465	C₂²	1	2	yes	complemented
100	C₂₃×#440	C₂²	1	2	yes	complemented
101	C₂₃×#440	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
103	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
104	C₂₃×#436	C₂²	1	2	yes	—
105	C₂₃×#436	C₂²	1	2	yes	—
106	C₂₃×#435	C₂²	1	2	yes	—
107	C₂₃×#435	C₂²	1	2	yes	—
108	C₂₃×#428	C₂²	1	2	yes	—
109	C₂₃×#428	C₂²	1	2	yes	—
110	C₂₃×#428	C₂²	1	2	yes	—
111	C₂₃×#428	C₂²	1	2	yes	—
112	C₂₃×#428	C₂²	1	1	yes	characteristic
113	C₂₃×#428	C₂²	1	1	yes	characteristic
114	C₂₃×#428	C₂²	1	1	yes	characteristic
115	C₂₃×#428	C₂²	1	1	yes	characteristic
116	C₂₃×#428	C₂²	1	2	yes	complemented
117	C₂₃×#428	C₂²	1	2	yes	complemented
118	C₂₃×#427	C₂²	1	1	yes	characteristic
119	C₂₃×#427	C₂²	1	2	yes	complemented
120	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
121	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
122	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
123	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
124	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
125	C₂₃×#424	C₂²	1	1	yes	characteristic
126	C₂₃×#417	C₂²	1	1	yes	characteristic
127	C₂₃×#417	C₂²	1	1	yes	characteristic
128	C₂₃×#417	C₂²	1	1	yes	characteristic
129	C₂₃×#417	C₂²	1	1	yes	characteristic
130	C₂₃×#416	C₂²	1	1	yes	characteristic
131	C₂₃×#416	C₂²	1	1	yes	characteristic
132	C₂₃×#408	C₂²	1	1	yes	characteristic
133	C₂₃×#407	C₂²	1	1	yes	characteristic
134	C₂₃×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	—	2	2	no	—
136	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
138	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₂₃	—	2	1	no	—
140	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂₃×#135	—	2	4	no	—
142	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
146	C₂₃×#131	—	2	4	no	—
147	C₂×M₁₆×C₂₃	—	2	4	no	—
148	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
157	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
158	C₂₃×C₄⋊Q₈	—	2	1	no	—
159	C₂₃×C₄⋊Q₈	—	2	1	no	—
160	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₂₃×#126	—	2	2	no	—
163	C₂₃×#126	—	2	2	no	—
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×#125	—	2	2	no	—
169	C₂₃×#125	—	2	1	no	—
170	C₂₃×#125	—	2	1	no	—
171	C₂₃×#125	—	2	2	no	—
172	C₂₃×#125	—	2	2	no	—
173	C₂₃×#125	C₂³	1	2	yes	—
174	C₂₃×#125	C₂³	1	2	yes	—
175	C₂₃×#124	—	2	2	no	—
176	C₂₃×#124	—	2	2	no	—
177	C₂₃×#124	—	2	2	no	—
178	C₂₃×#123	—	2	2	no	—
179	C₂₃×#123	—	2	2	no	—
180	C₂₃×#123	—	2	1	no	—
181	C₂₃×#123	—	2	1	no	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×#123	—	2	2	no	—
184	C₂₃×#123	—	2	2	no	—
185	C₂₃×#123	—	2	2	no	—
186	C₂₃×#123	D₄	1	2	yes	—
187	C₂₃×C₂²⋊Q₈	—	2	1	no	—
188	C₂₃×C₂²⋊Q₈	—	2	1	no	—
189	C₂₃×C₂²⋊Q₈	—	2	2	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	—	2	2	no	—
192	C₂₃×C₂²⋊Q₈	—	2	2	no	—
193	C₂₃×C₂²⋊Q₈	—	2	2	no	—
194	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
195	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
196	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
197	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
198	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
201	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
202	C₂₃×#121	—	2	1	no	—
203	C₂₃×#121	—	2	2	no	—
204	C₂₃×#121	—	2	1	no	—
205	C₂₃×#121	—	2	2	no	—
206	C₂₃×#121	—	2	2	no	—
207	C₂₃×#121	—	2	2	no	—
208	C₂₃×#121	—	2	2	no	—
209	C₂₃×#121	D₄	1	1	yes	characteristic
210	C₂₃×#121	D₄	1	1	yes	characteristic
211	C₂₃×#121	C₂³	1	1	yes	characteristic
212	C₂₃×#121	C₂³	1	2	yes	—
213	C₂₃×#121	C₂³	1	1	yes	characteristic
214	C₂₃×#121	C₂³	1	1	yes	characteristic
215	C₂₃×#121	C₂³	1	2	yes	—
216	C₂₃×#121	C₂³	1	1	yes	characteristic
217	C₂₃×#120	—	2	1	no	—
218	C₂₃×#120	—	2	1	no	—
219	C₂₃×#120	D₄	1	2	yes	—
220	C₄×Q₈×C₂₃	—	2	1	no	—
221	C₄×Q₈×C₂₃	—	2	1	no	—
222	C₄×Q₈×C₂₃	—	2	2	no	—
223	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
225	C₄×D₄×C₂₃	—	2	1	no	—
226	C₄×D₄×C₂₃	—	2	2	no	—
227	C₄×D₄×C₂₃	—	2	1	no	—
228	C₄×D₄×C₂₃	—	2	2	no	—
229	C₄×D₄×C₂₃	—	2	2	no	—
230	C₄×D₄×C₂₃	—	2	1	no	—
231	C₄×D₄×C₂₃	—	2	1	no	—
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	—	2	1	no	—
234	C₄×D₄×C₂₃	—	2	2	no	—
235	C₄×D₄×C₂₃	—	2	2	no	—
236	C₄×D₄×C₂₃	—	2	2	no	—
237	C₄×D₄×C₂₃	—	2	2	no	—
238	C₄×D₄×C₂₃	C₂³	1	2	yes	—
239	C₄×D₄×C₂₃	C₂³	1	2	yes	—
240	C₄×D₄×C₂₃	C₂³	1	2	yes	—
241	C₄×D₄×C₂₃	C₂³	1	2	yes	—
242	C₂₃×#117	—	2	1	no	—
243	C₂₃×#117	—	2	1	no	—
244	C₂₃×#117	—	2	1	no	—
245	C₂₃×#117	—	2	2	no	—
246	C₂₃×#117	—	2	1	no	—
247	C₂₃×#117	—	2	2	no	—
248	C₂₃×#117	—	2	2	no	—
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	2	yes	—
253	C₂₃×#117	C₂³	1	1	yes	characteristic
254	C₂₃×#117	C₂³	1	1	yes	characteristic
255	C₂₃×#117	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
258	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
270	C₂×C₄²×C₂₃	—	2	1	no	—
271	C₂₃×#107	C₂³	1	2	yes	—
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	1	yes	characteristic
276	C₂₃×#107	C₂³	1	2	yes	—
277	C₂₃×#107	C₂³	1	2	yes	—
278	C₂₃×#107	C₂³	1	1	yes	characteristic
279	C₂₃×#107	C₂³	1	2	yes	—
280	C₂₃×#107	C₂³	1	2	yes	—
281	C₂₃×#106	C₂³	1	2	yes	—
282	C₂₃×#106	C₂³	1	2	yes	—
283	C₂₃×#106	C₂³	1	2	yes	—
284	C₂₃×#106	C₂³	1	2	yes	—
285	C₂₃×#106	C₂³	1	1	yes	characteristic
286	C₂₃×#106	C₂³	1	1	yes	characteristic
287	C₂₃×#106	C₂³	1	2	yes	—
288	C₂₃×#106	C₂³	1	2	yes	—
289	C₂₃×#106	C₂³	1	2	yes	—
290	C₂₃×#106	C₂³	1	2	yes	—
291	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
292	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	1	yes	characteristic
294	C₂₃×#103	C₂³	1	1	yes	characteristic
295	C₂₃×#103	C₂³	1	1	yes	characteristic
296	C₂₃×#103	C₂³	1	1	yes	characteristic
297	C₂₃×#103	C₂³	1	2	yes	—
298	C₂₃×#103	C₂³	1	2	yes	—
299	C₂₃×#103	C₂³	1	2	yes	—
300	C₂₃×#103	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×#102	C₂³	1	1	yes	characteristic
303	C₂₃×#102	C₂³	1	1	yes	characteristic
304	C₂₃×#102	C₂³	1	1	yes	characteristic
305	C₂₃×#102	C₂³	1	2	yes	—
306	C₂₃×#102	C₂³	1	2	yes	—
307	C₂₃×#102	C₂³	1	2	yes	—
308	C₂₃×#102	C₂³	1	2	yes	—
309	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂₃×#97	C₂³	1	2	yes	—
314	C₄×C₈×C₂₃	C₂³	1	2	yes	—
315	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
316	#41×C₂₃	—	2	2	no	—
317	#41×C₂₃	—	2	2	no	—
318	#41×C₂₃	—	2	2	no	—
319	#41×C₂₃	—	2	2	no	—
320	#41×C₂₃	—	2	2	no	—
321	#41×C₂₃	—	2	2	no	—
322	#41×C₂₃	—	8	4	no	—
323	C₂×Q₈×C₂₃	—	2	2	no	—
324	C₂×Q₈×C₂₃	—	2	2	no	—
325	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₂₃	—	2	1	no	—
329	C₂×D₄×C₂₃	—	2	1	no	—
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	—	2	1	no	—
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₂₃	—	2	2	no	—
343	C₂²×C₄×C₂₃	—	2	2	no	—
344	C₂²×C₄×C₂₃	—	2	2	no	—
345	C₂²×C₄×C₂₃	—	2	1	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	—	2	1	no	—
350	C₂²×C₄×C₂₃	—	2	2	no	—
351	C₂²×C₄×C₂₃	—	2	2	no	—
352	C₂²×C₄×C₂₃	—	2	1	no	—
353	C₂²×C₄×C₂₃	—	2	1	no	—
354	C₂²×C₄×C₂₃	—	2	2	no	—
355	C₂²×C₄×C₂₃	—	2	2	no	—
356	C₂²×C₄×C₂₃	—	8	2	no	—
357	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
364	Q₁₆×C₂₃	—	2	2	no	—
365	SD₁₆×C₂₃	—	2	2	no	—
366	SD₁₆×C₂₃	—	2	2	no	—
367	D₈×C₂₃	—	2	2	no	—
368	M₁₆×C₂₃	—	2	2	no	—
369	M₁₆×C₂₃	—	2	2	no	—
370	M₁₆×C₂₃	—	2	2	no	—
371	M₁₆×C₂₃	—	2	2	no	—
372	M₁₆×C₂₃	—	2	2	no	—
373	M₁₆×C₂₃	—	2	2	no	—
374	M₁₆×C₂₃	—	2	4	no	—
375	C₂×C₈×C₂₃	—	2	2	no	—
376	C₂×C₈×C₂₃	—	2	4	no	—
377	C₂×C₈×C₂₃	#41	1	4	yes	complemented
378	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
381	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
382	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	—	2	2	no	—
387	C₄⋊C₄×C₂₃	—	2	2	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	1	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	2	no	—
397	C₄⋊C₄×C₂₃	—	2	2	no	—
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	—	2	1	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	2	no	—
403	C₄⋊C₄×C₂₃	—	2	2	no	—
404	C₄⋊C₄×C₂₃	—	2	1	no	—
405	C₄⋊C₄×C₂₃	—	2	2	no	—
406	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	2	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	1	no	—
427	C₂²⋊C₄×C₂₃	—	2	1	no	—
428	C₂²⋊C₄×C₂₃	—	2	1	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	1	no	—
431	C₂²⋊C₄×C₂₃	—	2	2	no	—
432	C₂²⋊C₄×C₂₃	—	2	2	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	no	—
434	C₂²⋊C₄×C₂₃	—	2	1	no	—
435	C₂²⋊C₄×C₂₃	—	2	2	no	—
436	C₂²⋊C₄×C₂₃	—	2	1	no	—
437	C₂²⋊C₄×C₂₃	—	2	1	no	—
438	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
443	C₄²×C₂₃	—	2	2	no	—
444	C₄²×C₂₃	—	2	2	no	—
445	C₄²×C₂₃	—	2	2	no	—
446	C₄²×C₂₃	—	2	2	no	—
447	C₄²×C₂₃	—	2	2	no	—
448	C₄²×C₂₃	—	2	2	no	—
449	C₄²×C₂₃	—	2	1	no	—
450	C₄²×C₂₃	—	2	1	no	—
451	C₄²×C₂₃	C₂⁴	1	2	yes	—
452	#61266	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂³×C₂₃	—	2	2	no	—
454	C₂³×C₂₃	—	2	1	no	—
455	C₂³×C₂₃	—	2	1	no	—
456	C₂³×C₂₃	—	4	1	no	—
457	C₂³×C₂₃	—	4	1	no	—
458	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
460	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
461	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
462	Q₈×C₂₃	—	2	2	no	—
463	Q₈×C₂₃	—	2	1	no	—
464	Q₈×C₂₃	—	2	1	no	—
465	Q₈×C₂₃	—	2	1	no	—
466	Q₈×C₂₃	—	2	1	no	—
467	Q₈×C₂₃	—	8	2	no	—
468	Q₈×C₂₃	—	8	2	no	—
469	D₄×C₂₃	—	2	4	no	—
470	D₄×C₂₃	—	2	2	no	—
471	D₄×C₂₃	—	2	1	no	—
472	D₄×C₂₃	—	2	1	no	—
473	D₄×C₂₃	—	2	1	no	—
474	D₄×C₂₃	—	2	1	no	—
475	D₄×C₂₃	—	4	2	no	—
476	D₄×C₂₃	—	4	2	no	—
477	D₄×C₂₃	—	4	2	no	—
478	D₄×C₂₃	—	4	2	no	—
479	D₄×C₂₃	—	4	2	no	—
480	D₄×C₂₃	—	4	2	no	—
481	D₄×C₂₃	—	8	1	no	—
482	D₄×C₂₃	—	8	2	no	—
483	D₄×C₂₃	—	8	1	no	—
484	D₄×C₂₃	—	8	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	2	no	—
495	C₂×C₄×C₂₃	—	2	1	no	—
496	C₂×C₄×C₂₃	—	2	1	no	—
497	C₂×C₄×C₂₃	—	2	1	no	—
498	C₂×C₄×C₂₃	—	2	1	no	—
499	C₂×C₄×C₂₃	—	2	2	no	—
500	C₂×C₄×C₂₃	—	2	2	no	—
501	C₂×C₄×C₂₃	—	2	1	no	—
502	C₂×C₄×C₂₃	—	2	1	no	—
503	C₂×C₄×C₂₃	—	2	2	no	—
504	C₂×C₄×C₂₃	—	4	4	no	—
505	C₂×C₄×C₂₃	—	4	2	no	—
506	C₂×C₄×C₂₃	—	4	2	no	—
507	C₂×C₄×C₂₃	—	8	2	no	—
508	C₂×C₄×C₂₃	—	8	2	no	—
509	C₂×C₄×C₂₃	—	8	1	no	—
510	C₂×C₄×C₂₃	—	8	2	no	—
511	C₂×C₄×C₂₃	—	8	1	no	—
512	C₂×C₄×C₂₃	—	8	1	no	—
513	C₂×C₄×C₂₃	—	8	2	no	—
514	C₂×C₄×C₂₃	—	8	1	no	—
515	C₂×C₄×C₂₃	—	8	2	no	—
516	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
523	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
524	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
525	C₈×C₂₃	—	2	1	no	—
526	C₈×C₂₃	—	2	1	no	—
527	C₈×C₂₃	—	2	2	no	—
528	C₈×C₂₃	—	2	2	no	—
529	C₈×C₂₃	C₂×#41	1	2	yes	—
530	C₈×C₂₃	C₂×#41	1	2	yes	—
531	#3493	C₂×C₂₃	1	1	yes	characteristic, complemented
532	#3492	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3356	C₂×C₂₃	1	2	yes	complemented
534	#3355	C₂×C₂₃	1	2	yes	complemented
535	#3354	C₂×C₂₃	1	2	yes	complemented
536	#3352	C₂×C₂₃	1	2	yes	complemented
537	#3350	C₂×C₂₃	1	2	yes	complemented
538	#3348	C₂×C₂₃	1	2	yes	complemented
539	#3346	C₂×C₂₃	1	2	yes	complemented
540	#3343	C₂×C₂₃	1	2	yes	complemented
541	#3163	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#3099	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#3098	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#3093	C₂×C₂₃	1	1	yes	characteristic, complemented
545	#3092	C₂×C₂₃	1	1	yes	characteristic, complemented
546	#3084	C₂×C₂₃	1	1	yes	characteristic, complemented
547	#3083	C₂×C₂₃	1	1	yes	characteristic, complemented
548	#3060	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#3054	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#2951	C₂×C₂₃	1	1	yes	characteristic, complemented
551	#2930	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#2913	C₂×C₂₃	1	1	yes	characteristic, complemented
553	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
554	C₂²×C₂₃	—	2	1	no	—
555	C₂²×C₂₃	—	2	1	no	—
556	C₂²×C₂₃	—	2	1	no	—
557	C₂²×C₂₃	—	2	2	no	—
558	C₂²×C₂₃	—	2	1	no	—
559	C₂²×C₂₃	—	2	1	no	—
560	C₂²×C₂₃	—	2	2	no	—
561	C₂²×C₂₃	—	2	1	no	—
562	C₂²×C₂₃	—	2	1	no	—
563	C₂²×C₂₃	—	2	1	no	—
564	C₂²×C₂₃	—	2	2	no	—
565	C₂²×C₂₃	—	4	4	no	—
566	C₂²×C₂₃	—	4	1	no	—
567	C₂²×C₂₃	—	4	1	no	—
568	C₂²×C₂₃	—	4	1	no	—
569	C₂²×C₂₃	—	4	1	no	—
570	C₂²×C₂₃	—	4	1	no	—
571	C₂²×C₂₃	—	4	1	no	—
572	C₂²×C₂₃	#547	1	2	yes	—
573	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
574	C₄×C₂₃	—	2	2	no	—
575	C₄×C₂₃	—	2	2	no	—
576	C₄×C₂₃	—	2	1	no	—
577	C₄×C₂₃	—	2	1	no	—
578	C₄×C₂₃	—	2	2	no	—
579	C₄×C₂₃	—	4	2	no	—
580	C₄×C₂₃	—	4	2	no	—
581	C₄×C₂₃	—	4	2	no	—
582	C₄×C₂₃	—	4	1	no	—
583	C₄×C₂₃	—	4	1	no	—
584	C₄×C₂₃	—	4	2	no	—
585	C₄×C₂₃	—	4	1	no	—
586	C₄×C₂₃	—	4	1	no	—
587	C₄×C₂₃	—	4	1	no	—
588	C₄×C₂₃	—	4	1	no	—
589	C₄×C₂₃	#547	1	2	yes	—
590	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
591	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
592	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
593	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
594	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
595	#556	—	2	1	no	—
596	#556	C₂²×C₂₃	1	2	yes	—
597	#555	—	2	1	no	—
598	#555	C₂²×C₂₃	1	2	yes	—
599	#554	—	2	1	no	—
600	#554	C₂²×C₂₃	1	2	yes	—
601	#553	—	2	1	no	—
602	#553	—	2	1	no	—
603	#553	C₂²×C₂₃	1	2	yes	—
604	#553	C₂²×C₂₃	1	2	yes	—
605	#552	—	2	1	no	—
606	#552	—	2	1	no	—
607	#552	C₂²×C₂₃	1	2	yes	—
608	#552	C₂²×C₂₃	1	2	yes	—
609	#547	—	2	1	no	—
610	#547	C₂²×C₂₃	1	2	yes	—
611	#544	C₂²×C₂₃	1	1	yes	characteristic
612	#544	C₂²×C₂₃	1	1	yes	characteristic
613	#539	—	2	2	no	—
614	#538	—	2	2	no	—
615	#537	C₂²×C₂₃	1	1	yes	characteristic
616	#537	C₂²×C₂₃	1	1	yes	characteristic
617	#529	—	2	2	no	—
618	#525	—	2	2	no	—
619	#525	C₂²×C₂₃	1	1	yes	characteristic
620	#525	C₂²×C₂₃	1	1	yes	characteristic
621	#525	C₂²×C₂₃	1	1	yes	characteristic
622	#520	C₂²×C₂₃	1	1	yes	characteristic
623	#520	C₂²×C₂₃	1	1	yes	characteristic
624	#520	C₂²×C₂₃	1	1	yes	characteristic
625	#520	C₂²×C₂₃	1	1	yes	characteristic
626	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
627	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
628	#501	C₂²×C₂₃	1	2	yes	complemented
629	#501	C₂²×C₂₃	1	2	yes	complemented
630	#499	C₂²×C₂₃	1	2	yes	complemented
631	#498	C₂²×C₂₃	1	2	yes	complemented
632	#485	C₂²×C₂₃	1	2	yes	—
633	#485	C₂²×C₂₃	1	2	yes	—
634	#485	C₂²×C₂₃	1	2	yes	complemented
635	#485	C₂²×C₂₃	1	2	yes	complemented
636	#484	C₂²×C₂₃	1	2	yes	—
637	#484	C₂²×C₂₃	1	2	yes	complemented
638	#483	C₂²×C₂₃	1	2	yes	—
639	#483	C₂²×C₂₃	1	2	yes	complemented
640	#482	C₂²×C₂₃	1	2	yes	—
641	#482	C₂²×C₂₃	1	2	yes	—
642	#482	C₂²×C₂₃	1	2	yes	complemented
643	#482	C₂²×C₂₃	1	2	yes	complemented
644	#481	C₂²×C₂₃	1	2	yes	—
645	#481	C₂²×C₂₃	1	2	yes	complemented
646	#480	C₂²×C₂₃	1	2	yes	—
647	#480	C₂²×C₂₃	1	2	yes	complemented
648	#479	C₂²×C₂₃	1	2	yes	complemented
649	#479	C₂²×C₂₃	1	2	yes	complemented
650	#478	C₂²×C₂₃	1	2	yes	complemented
651	#478	C₂²×C₂₃	1	2	yes	complemented
652	#477	C₂²×C₂₃	1	2	yes	complemented
653	#476	C₂²×C₂₃	1	2	yes	complemented
654	#475	C₂²×C₂₃	1	2	yes	complemented
655	#474	C₂²×C₂₃	1	2	yes	complemented
656	#470	C₂²×C₂₃	1	1	yes	characteristic
657	#470	C₂²×C₂₃	1	1	yes	characteristic
658	#470	C₂²×C₂₃	1	2	yes	complemented
659	#469	C₂²×C₂₃	1	1	yes	characteristic
660	#469	C₂²×C₂₃	1	1	yes	characteristic
661	#469	C₂²×C₂₃	1	2	yes	complemented
662	#468	C₂²×C₂₃	1	1	yes	characteristic
663	#468	C₂²×C₂₃	1	1	yes	characteristic
664	#468	C₂²×C₂₃	1	1	yes	characteristic
665	#468	C₂²×C₂₃	1	1	yes	characteristic
666	#465	C₂²×C₂₃	1	2	yes	complemented
667	#465	C₂²×C₂₃	1	2	yes	complemented
668	#440	C₂²×C₂₃	1	2	yes	complemented
669	#440	C₂²×C₂₃	1	2	yes	complemented
670	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
671	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
672	#436	C₂²×C₂₃	1	2	yes	—
673	#436	C₂²×C₂₃	1	2	yes	—
674	#435	C₂²×C₂₃	1	2	yes	—
675	#435	C₂²×C₂₃	1	2	yes	—
676	#428	C₂²×C₂₃	1	1	yes	characteristic
677	#428	C₂²×C₂₃	1	1	yes	characteristic
678	#428	C₂²×C₂₃	1	2	yes	—
679	#428	C₂²×C₂₃	1	2	yes	—
680	#428	C₂²×C₂₃	1	1	yes	characteristic
681	#428	C₂²×C₂₃	1	1	yes	characteristic
682	#428	C₂²×C₂₃	1	2	yes	—
683	#428	C₂²×C₂₃	1	2	yes	—
684	#428	C₂²×C₂₃	1	2	yes	complemented
685	#428	C₂²×C₂₃	1	2	yes	complemented
686	#427	C₂²×C₂₃	1	1	yes	characteristic
687	#427	C₂²×C₂₃	1	2	yes	complemented
688	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
689	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
690	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
691	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
692	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
693	#424	C₂²×C₂₃	1	1	yes	characteristic
694	#417	C₂²×C₂₃	1	1	yes	characteristic
695	#417	C₂²×C₂₃	1	1	yes	characteristic
696	#417	C₂²×C₂₃	1	1	yes	characteristic
697	#417	C₂²×C₂₃	1	1	yes	characteristic
698	#416	C₂²×C₂₃	1	1	yes	characteristic
699	#416	C₂²×C₂₃	1	1	yes	characteristic
700	#408	C₂²×C₂₃	1	1	yes	characteristic
701	#407	C₂²×C₂₃	1	1	yes	characteristic
702	#405	C₂²×C₂₃	1	1	yes	characteristic
703	C₂×C₂₃	—	2	2	no	—
704	C₂×C₂₃	—	4	2	no	—
705	C₂×C₂₃	—	4	1	no	—
706	C₂×C₂₃	—	4	1	no	—
707	C₂×C₂₃	—	8	1	no	—
708	C₂×C₂₃	—	8	1	no	—
709	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
710	C₂×C₂₃	#3585	1	1	yes	characteristic
711	C₂×C₂₃	#3586	1	1	yes	characteristic
712	C₂×#41	—	2	2	no	—
713	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
714	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
715	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
716	C₂³×C₄	—	2	1	no	—
717	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
718	#135	—	2	4	no	—
719	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
721	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
722	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
723	#131	—	2	4	no	—
724	C₂×M₁₆	—	2	4	no	—
725	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
727	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
728	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
730	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
731	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
732	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
733	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
734	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
738	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	2	no	—
747	#125	—	2	2	no	—
748	#125	—	2	1	no	—
749	#125	—	2	1	no	—
750	#125	C₂³×C₂₃	1	2	yes	—
751	#125	C₂³×C₂₃	1	2	yes	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	1	no	—
758	#123	—	2	1	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	D₄×C₂₃	1	2	yes	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
772	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
773	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	D₄×C₂₃	1	1	yes	characteristic
787	#121	D₄×C₂₃	1	1	yes	characteristic
788	#121	C₂³×C₂₃	1	1	yes	characteristic
789	#121	C₂³×C₂₃	1	1	yes	characteristic
790	#121	C₂³×C₂₃	1	1	yes	characteristic
791	#121	C₂³×C₂₃	1	1	yes	characteristic
792	#121	C₂³×C₂₃	1	2	yes	—
793	#121	C₂³×C₂₃	1	2	yes	—
794	#120	—	2	1	no	—
795	#120	—	2	1	no	—
796	#120	D₄×C₂₃	1	2	yes	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	2	no	—
800	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
801	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	C₂³×C₂₃	1	2	yes	—
816	C₄×D₄	C₂³×C₂₃	1	2	yes	—
817	C₄×D₄	C₂³×C₂₃	1	2	yes	—
818	C₄×D₄	C₂³×C₂₃	1	2	yes	—
819	#117	—	2	1	no	—
820	#117	—	2	1	no	—
821	#117	—	2	1	no	—
822	#117	—	2	1	no	—
823	#117	—	2	2	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	C₂³×C₂₃	1	2	yes	—
827	#117	C₂³×C₂₃	1	2	yes	—
828	#117	C₂³×C₂₃	1	1	yes	characteristic
829	#117	C₂³×C₂₃	1	1	yes	characteristic
830	#117	C₂³×C₂₃	1	2	yes	—
831	#117	C₂³×C₂₃	1	2	yes	—
832	#117	C₂³×C₂₃	1	1	yes	characteristic
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
841	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
842	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
845	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
846	C₂×C₂²⋊C₄	—	2	1	no	—
847	C₂×C₄²	—	2	1	no	—
848	#107	C₂³×C₂₃	1	2	yes	—
849	#107	C₂³×C₂₃	1	2	yes	—
850	#107	C₂³×C₂₃	1	2	yes	—
851	#107	C₂³×C₂₃	1	2	yes	—
852	#107	C₂³×C₂₃	1	1	yes	characteristic
853	#107	C₂³×C₂₃	1	2	yes	—
854	#107	C₂³×C₂₃	1	2	yes	—
855	#107	C₂³×C₂₃	1	1	yes	characteristic
856	#107	C₂³×C₂₃	1	2	yes	—
857	#107	C₂³×C₂₃	1	2	yes	—
858	#106	C₂³×C₂₃	1	2	yes	—
859	#106	C₂³×C₂₃	1	2	yes	—
860	#106	C₂³×C₂₃	1	2	yes	—
861	#106	C₂³×C₂₃	1	2	yes	—
862	#106	C₂³×C₂₃	1	1	yes	characteristic
863	#106	C₂³×C₂₃	1	1	yes	characteristic
864	#106	C₂³×C₂₃	1	2	yes	—
865	#106	C₂³×C₂₃	1	2	yes	—
866	#106	C₂³×C₂₃	1	2	yes	—
867	#106	C₂³×C₂₃	1	2	yes	—
868	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
869	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
870	#103	C₂³×C₂₃	1	1	yes	characteristic
871	#103	C₂³×C₂₃	1	1	yes	characteristic
872	#103	C₂³×C₂₃	1	1	yes	characteristic
873	#103	C₂³×C₂₃	1	1	yes	characteristic
874	#103	C₂³×C₂₃	1	2	yes	—
875	#103	C₂³×C₂₃	1	2	yes	—
876	#103	C₂³×C₂₃	1	2	yes	—
877	#103	C₂³×C₂₃	1	2	yes	—
878	#102	C₂³×C₂₃	1	1	yes	characteristic
879	#102	C₂³×C₂₃	1	1	yes	characteristic
880	#102	C₂³×C₂₃	1	1	yes	characteristic
881	#102	C₂³×C₂₃	1	1	yes	characteristic
882	#102	C₂³×C₂₃	1	2	yes	—
883	#102	C₂³×C₂₃	1	2	yes	—
884	#102	C₂³×C₂₃	1	2	yes	—
885	#102	C₂³×C₂₃	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
890	#97	C₂³×C₂₃	1	2	yes	—
891	C₄×C₈	C₂³×C₂₃	1	2	yes	—
892	C₂₃	#61266	1	1	yes	characteristic, direct product factor, Sylow
893	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	2	2	no	—
897	#41	—	2	2	no	—
898	#41	—	2	2	no	—
899	#41	—	2	2	no	—
900	#41	—	8	4	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
905	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
916	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
917	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
918	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	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	1	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	8	2	no	—
935	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
936	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
937	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
939	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
942	Q₁₆	—	2	2	no	—
943	SD₁₆	—	2	2	no	—
944	SD₁₆	—	2	2	no	—
945	D₈	—	2	2	no	—
946	M₁₆	—	2	2	no	—
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	2	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	2	2	no	—
951	M₁₆	—	2	2	no	—
952	M₁₆	—	2	4	no	—
953	C₂×C₈	—	2	2	no	—
954	C₂×C₈	—	2	4	no	—
955	C₂×C₈	#41×C₂₃	1	4	yes	complemented
956	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
957	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
958	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	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	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
988	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1019	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1020	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	C₂⁴×C₂₃	1	2	yes	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	4	1	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1036	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1037	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1038	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	8	2	no	—
1045	Q₈	—	8	2	no	—
1046	D₄	—	2	4	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	1	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	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	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	4	4	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	1	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	1	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1094	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1098	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1099	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1100	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1101	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1102	C₈	—	2	1	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	2	2	no	—
1105	C₈	—	2	2	no	—
1106	C₈	C₂×#41×C₂₃	1	2	yes	—
1107	C₈	C₂×#41×C₂₃	1	2	yes	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	4	4	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	C₂₃×#547	1	2	yes	—
1127	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1128	C₄	—	2	1	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	C₂₃×#547	1	2	yes	—
1144	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1145	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1146	C₂	—	2	2	no	—
1147	C₂	—	4	1	no	—
1148	C₂	—	4	1	no	—
1149	C₂	—	4	2	no	—
1150	C₂	—	8	1	no	—
1151	C₂	—	8	1	no	—
1152	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
1153	C₂	C₂₃×#3585	1	1	yes	characteristic
1154	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3493	C₂	semidirect
2. C₂₃×#3492	C₂	semidirect
3. C₂₃×#3356	C₂	semidirect
4. C₂₃×#3355	C₂	semidirect
5. C₂₃×#3354	C₂	semidirect
6. C₂₃×#3352	C₂	semidirect
7. C₂₃×#3350	C₂	semidirect
8. C₂₃×#3348	C₂	semidirect
9. C₂₃×#3346	C₂	semidirect
10. C₂₃×#3343	C₂	semidirect
11. C₂₃×#3163	C₂	semidirect
12. C₂₃×#3099	C₂	semidirect
13. C₂₃×#3098	C₂	semidirect
14. C₂₃×#3093	C₂	semidirect
15. C₂₃×#3092	C₂	semidirect
16. C₂₃×#3084	C₂	semidirect
17. C₂₃×#3083	C₂	semidirect
18. C₂₃×#3060	C₂	semidirect
19. C₂₃×#3054	C₂	semidirect
20. C₂₃×#2951	C₂	semidirect
21. C₂₃×#2930	C₂	semidirect
22. C₂₃×#2913	C₂	semidirect
23. C₂×C₂₃×#428	C₂	semidirect
60. C₂₃×#501	C₂²	semidirect
61. C₂₃×#501	C₂²	semidirect
62. C₂₃×#499	C₂²	semidirect
63. C₂₃×#498	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
69. C₂₃×#484	C₂²	semidirect
71. C₂₃×#483	C₂²	semidirect
74. C₂₃×#482	C₂²	semidirect
75. C₂₃×#482	C₂²	semidirect
77. C₂₃×#481	C₂²	semidirect
79. C₂₃×#480	C₂²	semidirect
80. C₂₃×#479	C₂²	semidirect
81. C₂₃×#479	C₂²	semidirect
82. C₂₃×#478	C₂²	semidirect
83. C₂₃×#478	C₂²	semidirect
84. C₂₃×#477	C₂²	semidirect
85. C₂₃×#476	C₂²	semidirect
86. C₂₃×#475	C₂²	semidirect
87. C₂₃×#474	C₂²	semidirect
90. C₂₃×#470	C₂²	semidirect
93. C₂₃×#469	C₂²	semidirect
98. C₂₃×#465	C₂²	semidirect
99. C₂₃×#465	C₂²	semidirect
100. C₂₃×#440	C₂²	semidirect
101. C₂₃×#440	C₂²	semidirect
102. C₄×Q₁₆×C₂₃	C₂²	semidirect
103. C₄×D₈×C₂₃	C₂²	semidirect
116. C₂₃×#428	C₂²	semidirect
117. C₂₃×#428	C₂²	semidirect
119. C₂₃×#427	C₂²	semidirect
122. C₂×C₂₃×#107	C₂²	semidirect
377. C₂×C₈×C₂₃	#41	semidirect
452. #61266	C₂₃	direct (N × H)
531. #3493	C₂×C₂₃	semidirect
532. #3492	C₂×C₂₃	semidirect
533. #3356	C₂×C₂₃	semidirect
534. #3355	C₂×C₂₃	semidirect
535. #3354	C₂×C₂₃	semidirect
536. #3352	C₂×C₂₃	semidirect
537. #3350	C₂×C₂₃	semidirect
538. #3348	C₂×C₂₃	semidirect
539. #3346	C₂×C₂₃	semidirect
540. #3343	C₂×C₂₃	semidirect
541. #3163	C₂×C₂₃	semidirect
542. #3099	C₂×C₂₃	semidirect
543. #3098	C₂×C₂₃	semidirect
544. #3093	C₂×C₂₃	semidirect
545. #3092	C₂×C₂₃	semidirect
546. #3084	C₂×C₂₃	semidirect
547. #3083	C₂×C₂₃	semidirect
548. #3060	C₂×C₂₃	semidirect
549. #3054	C₂×C₂₃	semidirect
550. #2951	C₂×C₂₃	semidirect
551. #2930	C₂×C₂₃	semidirect
552. #2913	C₂×C₂₃	semidirect
553. C₂×#428	C₂×C₂₃	semidirect
628. #501	C₂²×C₂₃	semidirect
629. #501	C₂²×C₂₃	semidirect
630. #499	C₂²×C₂₃	semidirect
631. #498	C₂²×C₂₃	semidirect
634. #485	C₂²×C₂₃	semidirect
635. #485	C₂²×C₂₃	semidirect
637. #484	C₂²×C₂₃	semidirect
639. #483	C₂²×C₂₃	semidirect
642. #482	C₂²×C₂₃	semidirect
643. #482	C₂²×C₂₃	semidirect
645. #481	C₂²×C₂₃	semidirect
647. #480	C₂²×C₂₃	semidirect
648. #479	C₂²×C₂₃	semidirect
649. #479	C₂²×C₂₃	semidirect
650. #478	C₂²×C₂₃	semidirect
651. #478	C₂²×C₂₃	semidirect
652. #477	C₂²×C₂₃	semidirect
653. #476	C₂²×C₂₃	semidirect
654. #475	C₂²×C₂₃	semidirect
655. #474	C₂²×C₂₃	semidirect
658. #470	C₂²×C₂₃	semidirect
661. #469	C₂²×C₂₃	semidirect
666. #465	C₂²×C₂₃	semidirect
667. #465	C₂²×C₂₃	semidirect
668. #440	C₂²×C₂₃	semidirect
669. #440	C₂²×C₂₃	semidirect
670. C₄×Q₁₆	C₂²×C₂₃	semidirect
671. C₄×D₈	C₂²×C₂₃	semidirect
684. #428	C₂²×C₂₃	semidirect
685. #428	C₂²×C₂₃	semidirect
687. #427	C₂²×C₂₃	semidirect
690. C₂×#107	C₂²×C₂₃	semidirect
892. C₂₃	#61266	direct (N × H)
955. C₂×C₈	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3493	2
C₂₃×#3492	2
C₂₃×#3356	2
C₂₃×#3355	2
C₂₃×#3354	2
C₂₃×#3352	2
C₂₃×#3350	2
C₂₃×#3348	2
C₂₃×#3346	2
C₂₃×#3343	2
C₂₃×#3163	2
C₂₃×#3099	2
C₂₃×#3098	2
C₂₃×#3093	2
C₂₃×#3092	2
C₂₃×#3084	2
C₂₃×#3083	2
C₂₃×#3060	2
C₂₃×#3054	2
C₂₃×#2951	2
C₂₃×#2930	2
C₂₃×#2913	2
C₂×C₂₃×#428	2
#61266	23

Subgroups — C23×#61266 #19208892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61266 #19208892