Subgroups — C₂₃×#61271 #19208897

Order 5888.

1806 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3492	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3356	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3351	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3350	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3344	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3344	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3343	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3336	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3335	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×#3097	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#137	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	C₂²	1	2	yes	—
28	C₂₃×#554	—	2	1	no	—
29	C₂₃×#554	C₂²	1	2	yes	—
30	C₂₃×#554	C₂²	1	2	yes	—
31	C₂₃×#553	—	2	1	no	—
32	C₂₃×#553	C₂²	1	2	yes	—
33	C₂₃×#552	—	2	2	no	—
34	C₂₃×#552	—	2	1	no	—
35	C₂₃×#552	C₂²	1	2	yes	—
36	C₂₃×#552	C₂²	1	2	yes	—
37	C₂₃×#552	C₂²	1	2	yes	—
38	C₂₃×#551	—	2	2	no	—
39	C₂₃×#547	—	2	1	no	—
40	C₂₃×#547	C₂²	1	2	yes	—
41	C₂₃×#544	C₂²	1	1	yes	characteristic
42	C₂₃×#544	C₂²	1	1	yes	characteristic
43	C₂₃×#542	—	2	1	no	—
44	C₂₃×#541	—	2	1	no	—
45	C₂₃×#539	—	2	2	no	—
46	C₂₃×#537	C₂²	1	1	yes	characteristic
47	C₂₃×#536	C₂²	1	1	yes	characteristic
48	C₂₃×#533	—	2	1	no	—
49	C₂₃×#529	—	2	1	no	—
50	C₂₃×#525	—	2	2	no	—
51	C₂₃×#525	C₂²	1	1	yes	characteristic
52	C₂₃×#525	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×C₂²⋊Q₈	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×#519	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	1	yes	characteristic
65	C₂₃×#485	C₂²	1	1	yes	characteristic
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×#484	C₂²	1	1	yes	characteristic
70	C₂₃×#484	C₂²	1	2	yes	complemented
71	C₂₃×#483	C₂²	1	2	yes	—
72	C₂₃×#483	C₂²	1	1	yes	characteristic
73	C₂₃×#483	C₂²	1	2	yes	—
74	C₂₃×#483	C₂²	1	2	yes	—
75	C₂₃×#483	C₂²	1	2	yes	—
76	C₂₃×#483	C₂²	1	2	yes	complemented
77	C₂₃×#483	C₂²	1	2	yes	complemented
78	C₂₃×#482	C₂²	1	1	yes	characteristic
79	C₂₃×#482	C₂²	1	1	yes	characteristic
80	C₂₃×#482	C₂²	1	2	yes	complemented
81	C₂₃×#481	C₂²	1	1	yes	characteristic
82	C₂₃×#481	C₂²	1	2	yes	complemented
83	C₂₃×#480	C₂²	1	1	yes	characteristic
84	C₂₃×#479	C₂²	1	2	yes	complemented
85	C₂₃×#479	C₂²	1	2	yes	complemented
86	C₂₃×#479	C₂²	1	2	yes	complemented
87	C₂₃×#478	C₂²	1	2	yes	complemented
88	C₂₃×#477	C₂²	1	2	yes	complemented
89	C₂₃×#476	C₂²	1	2	yes	complemented
90	C₂₃×#475	C₂²	1	2	yes	complemented
91	C₂₃×#475	C₂²	1	2	yes	complemented
92	C₂₃×#470	C₂²	1	2	yes	—
93	C₂₃×#470	C₂²	1	2	yes	complemented
94	C₂₃×#468	C₂²	1	2	yes	—
95	C₂₃×#468	C₂²	1	2	yes	complemented
96	C₂₃×#467	C₂²	1	2	yes	—
97	C₂₃×#467	C₂²	1	2	yes	complemented
98	C₂₃×#465	C₂²	1	2	yes	—
99	C₂₃×#465	C₂²	1	2	yes	complemented
100	C₂₃×#441	C₂²	1	2	yes	complemented
101	C₂₃×#440	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
104	C₂₃×#436	C₂²	1	2	yes	—
105	C₂₃×#435	C₂²	1	2	yes	—
106	C₂₃×#435	C₂²	1	2	yes	—
107	C₈×D₄×C₂₃	C₂²	1	2	yes	—
108	C₂₃×#428	C₂²	1	1	yes	characteristic
109	C₂₃×#428	C₂²	1	1	yes	characteristic
110	C₂₃×#428	C₂²	1	1	yes	characteristic
111	C₂₃×#428	C₂²	1	1	yes	characteristic
112	C₂₃×#428	C₂²	1	2	yes	—
113	C₂₃×#428	C₂²	1	2	yes	—
114	C₂₃×#428	C₂²	1	1	yes	characteristic
115	C₂₃×#428	C₂²	1	2	yes	complemented
116	C₂₃×#428	C₂²	1	2	yes	complemented
117	C₂₃×#427	C₂²	1	1	yes	characteristic
118	C₂₃×#427	C₂²	1	1	yes	characteristic
119	C₂₃×#427	C₂²	1	2	yes	complemented
120	C₂×C₂₃×#107	C₂²	1	2	yes	—
121	C₂×C₂₃×#106	C₂²	1	2	yes	—
122	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
123	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
124	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
125	C₂₃×#424	C₂²	1	1	yes	characteristic
126	C₂₃×#419	C₂²	1	1	yes	characteristic
127	C₂₃×#417	C₂²	1	1	yes	characteristic
128	C₂₃×#416	C₂²	1	1	yes	characteristic
129	C₂₃×#416	C₂²	1	1	yes	characteristic
130	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
131	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
132	C₂₃×#408	C₂²	1	1	yes	characteristic
133	C₂×C₂₃×C₂²⋊C₈	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	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₂₃	—	2	1	no	—
140	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂₃×#137	—	2	4	no	—
142	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂₃×#131	—	2	4	no	—
145	C₂×M₁₆×C₂₃	—	2	4	no	—
146	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
154	C₂₃×C₄⋊Q₈	—	2	1	no	—
155	C₂₃×C₄⋊Q₈	—	2	1	no	—
156	C₂₃×C₄⋊Q₈	—	2	1	no	—
157	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
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×#126	—	2	2	no	—
165	C₂₃×#125	—	2	2	no	—
166	C₂₃×#125	—	2	2	no	—
167	C₂₃×#125	—	2	1	no	—
168	C₂₃×#125	—	2	2	no	—
169	C₂₃×#125	—	2	2	no	—
170	C₂₃×#125	—	2	2	no	—
171	C₂₃×#125	—	2	1	no	—
172	C₂₃×#125	C₂³	1	2	yes	—
173	C₂₃×#125	C₂³	1	2	yes	—
174	C₂₃×#124	—	2	2	no	—
175	C₂₃×#124	—	2	1	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	1	no	—
181	C₂₃×#123	—	2	2	no	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×#123	—	2	2	no	—
184	C₂₃×#123	D₄	1	2	yes	—
185	C₂₃×C₂²⋊Q₈	—	2	1	no	—
186	C₂₃×C₂²⋊Q₈	—	2	1	no	—
187	C₂₃×C₂²⋊Q₈	—	2	1	no	—
188	C₂₃×C₂²⋊Q₈	—	2	2	no	—
189	C₂₃×C₂²⋊Q₈	—	2	2	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	—	2	2	no	—
192	C₂₃×C₂²⋊Q₈	—	2	2	no	—
193	C₂₃×C₂²⋊Q₈	—	2	2	no	—
194	C₂₃×C₂²⋊Q₈	—	2	2	no	—
195	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
196	C₂₃×C₂²⋊Q₈	D₄	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	2	yes	—
201	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
203	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂₃×#121	—	2	1	no	—
205	C₂₃×#121	—	2	2	no	—
206	C₂₃×#121	—	2	2	no	—
207	C₂₃×#121	D₄	1	1	yes	characteristic
208	C₂₃×#121	D₄	1	1	yes	characteristic
209	C₂₃×#121	C₂³	1	1	yes	characteristic
210	C₂₃×#121	C₂³	1	2	yes	—
211	C₂₃×#121	C₂³	1	1	yes	characteristic
212	C₂₃×#120	—	2	1	no	—
213	C₂₃×#120	D₄	1	2	yes	—
214	C₄×Q₈×C₂₃	—	2	1	no	—
215	C₄×Q₈×C₂₃	—	2	1	no	—
216	C₄×Q₈×C₂₃	—	2	2	no	—
217	C₄×Q₈×C₂₃	—	2	1	no	—
218	C₄×Q₈×C₂₃	—	2	1	no	—
219	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
222	C₄×D₄×C₂₃	—	2	1	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	1	no	—
228	C₄×D₄×C₂₃	—	2	1	no	—
229	C₄×D₄×C₂₃	—	2	1	no	—
230	C₄×D₄×C₂₃	—	2	2	no	—
231	C₄×D₄×C₂₃	—	2	2	no	—
232	C₄×D₄×C₂₃	C₂³	1	2	yes	—
233	C₄×D₄×C₂₃	C₂³	1	2	yes	—
234	C₄×D₄×C₂₃	C₂³	1	2	yes	—
235	C₂₃×#117	—	2	1	no	—
236	C₂₃×#117	—	2	1	no	—
237	C₂₃×#117	—	2	1	no	—
238	C₂₃×#117	—	2	2	no	—
239	C₂₃×#117	—	2	2	no	—
240	C₂₃×#117	—	2	2	no	—
241	C₂₃×#117	—	2	2	no	—
242	C₂₃×#117	C₂³	1	1	yes	characteristic
243	C₂₃×#117	C₂³	1	2	yes	—
244	C₂₃×#117	C₂³	1	2	yes	—
245	C₂₃×#117	C₂³	1	1	yes	characteristic
246	C₂₃×#117	C₂³	1	1	yes	characteristic
247	C₂₃×#117	C₂³	1	1	yes	characteristic
248	C₂₃×#117	C₂³	1	1	yes	characteristic
249	C₂₃×#117	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
251	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
252	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
253	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
266	C₂×C₄²×C₂₃	—	2	1	no	—
267	C₂₃×#107	C₂³	1	2	yes	—
268	C₂₃×#107	C₂³	1	2	yes	—
269	C₂₃×#107	C₂³	1	2	yes	—
270	C₂₃×#107	C₂³	1	2	yes	—
271	C₂₃×#107	C₂³	1	1	yes	characteristic
272	C₂₃×#107	C₂³	1	1	yes	characteristic
273	C₂₃×#107	C₂³	1	1	yes	characteristic
274	C₂₃×#107	C₂³	1	1	yes	characteristic
275	C₂₃×#107	C₂³	1	2	yes	—
276	C₂₃×#106	C₂³	1	2	yes	—
277	C₂₃×#106	C₂³	1	2	yes	—
278	C₂₃×#106	C₂³	1	2	yes	—
279	C₂₃×#106	C₂³	1	2	yes	—
280	C₂₃×#106	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	1	yes	characteristic
285	C₂₃×#106	C₂³	1	2	yes	—
286	C₂₃×#106	C₂³	1	1	yes	characteristic
287	C₂₃×#106	C₂³	1	1	yes	characteristic
288	C₂₃×#106	C₂³	1	1	yes	characteristic
289	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
290	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
296	C₂₃×#103	C₂³	1	1	yes	characteristic
297	C₂₃×#103	C₂³	1	1	yes	characteristic
298	C₂₃×#103	C₂³	1	1	yes	characteristic
299	C₂₃×#103	C₂³	1	2	yes	—
300	C₂₃×#103	C₂³	1	2	yes	—
301	C₂₃×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
306	C₂₃×#102	C₂³	1	2	yes	—
307	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	—	8	4	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	2	2	no	—
323	C₂×Q₈×C₂₃	—	2	2	no	—
324	C₂×Q₈×C₂₃	—	2	2	no	—
325	C₂×Q₈×C₂₃	—	2	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×D₄×C₂₃	—	2	1	no	—
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
335	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₂₃	—	2	2	no	—
339	C₂²×C₄×C₂₃	—	2	2	no	—
340	C₂²×C₄×C₂₃	—	2	1	no	—
341	C₂²×C₄×C₂₃	—	2	1	no	—
342	C₂²×C₄×C₂₃	—	2	2	no	—
343	C₂²×C₄×C₂₃	—	2	1	no	—
344	C₂²×C₄×C₂₃	—	2	1	no	—
345	C₂²×C₄×C₂₃	—	2	1	no	—
346	C₂²×C₄×C₂₃	—	2	2	no	—
347	C₂²×C₄×C₂₃	—	2	1	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	2	2	no	—
350	C₂²×C₄×C₂₃	—	2	1	no	—
351	C₂²×C₄×C₂₃	—	2	2	no	—
352	C₂²×C₄×C₂₃	—	8	2	no	—
353	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
360	Q₁₆×C₂₃	—	2	4	no	—
361	SD₁₆×C₂₃	—	2	4	no	—
362	M₁₆×C₂₃	—	2	2	no	—
363	M₁₆×C₂₃	—	2	4	no	—
364	M₁₆×C₂₃	—	2	4	no	—
365	M₁₆×C₂₃	#41	1	4	yes	complemented
366	C₂×C₈×C₂₃	—	2	2	no	—
367	C₂×C₈×C₂₃	—	2	2	no	—
368	C₂×C₈×C₂₃	—	2	4	no	—
369	C₂×C₈×C₂₃	—	2	4	no	—
370	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
373	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₂₃	—	2	1	no	—
377	C₄⋊C₄×C₂₃	—	2	1	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	2	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	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	2	no	—
395	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
401	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
407	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
414	C₂²⋊C₄×C₂₃	—	2	1	no	—
415	C₂²⋊C₄×C₂₃	—	2	1	no	—
416	C₂²⋊C₄×C₂₃	—	2	1	no	—
417	C₂²⋊C₄×C₂₃	—	2	1	no	—
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	2	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	1	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	1	no	—
431	C₂²⋊C₄×C₂₃	—	2	1	no	—
432	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
437	C₄²×C₂₃	—	2	1	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	1	no	—
440	C₄²×C₂₃	—	2	1	no	—
441	C₄²×C₂₃	—	2	2	no	—
442	C₄²×C₂₃	—	2	2	no	—
443	C₄²×C₂₃	—	2	2	no	—
444	C₄²×C₂₃	—	2	2	no	—
445	C₄²×C₂₃	—	2	2	no	—
446	C₄²×C₂₃	—	2	1	no	—
447	C₄²×C₂₃	C₂⁴	1	2	yes	—
448	#61271	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₂₃	—	2	2	no	—
450	C₂³×C₂₃	—	2	2	no	—
451	C₂³×C₂₃	—	2	1	no	—
452	C₂³×C₂₃	—	4	1	no	—
453	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
454	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
455	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
456	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
457	Q₈×C₂₃	—	2	2	no	—
458	Q₈×C₂₃	—	2	2	no	—
459	Q₈×C₂₃	—	2	1	no	—
460	Q₈×C₂₃	—	2	2	no	—
461	Q₈×C₂₃	—	2	1	no	—
462	Q₈×C₂₃	—	4	2	no	—
463	Q₈×C₂₃	—	8	2	no	—
464	Q₈×C₂₃	—	8	2	no	—
465	D₄×C₂₃	—	2	4	no	—
466	D₄×C₂₃	—	2	4	no	—
467	D₄×C₂₃	—	2	2	no	—
468	D₄×C₂₃	—	2	1	no	—
469	D₄×C₂₃	—	2	1	no	—
470	D₄×C₂₃	—	4	2	no	—
471	D₄×C₂₃	—	4	2	no	—
472	D₄×C₂₃	—	4	2	no	—
473	D₄×C₂₃	—	4	2	no	—
474	D₄×C₂₃	—	8	2	no	—
475	C₂×C₄×C₂₃	—	2	2	no	—
476	C₂×C₄×C₂₃	—	2	2	no	—
477	C₂×C₄×C₂₃	—	2	2	no	—
478	C₂×C₄×C₂₃	—	2	1	no	—
479	C₂×C₄×C₂₃	—	2	2	no	—
480	C₂×C₄×C₂₃	—	2	1	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	2	1	no	—
483	C₂×C₄×C₂₃	—	2	2	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	1	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	1	no	—
488	C₂×C₄×C₂₃	—	2	1	no	—
489	C₂×C₄×C₂₃	—	2	2	no	—
490	C₂×C₄×C₂₃	—	2	1	no	—
491	C₂×C₄×C₂₃	—	2	2	no	—
492	C₂×C₄×C₂₃	—	2	2	no	—
493	C₂×C₄×C₂₃	—	2	1	no	—
494	C₂×C₄×C₂₃	—	2	2	no	—
495	C₂×C₄×C₂₃	—	4	2	no	—
496	C₂×C₄×C₂₃	—	4	2	no	—
497	C₂×C₄×C₂₃	—	4	4	no	—
498	C₂×C₄×C₂₃	—	4	2	no	—
499	C₂×C₄×C₂₃	—	8	2	no	—
500	C₂×C₄×C₂₃	—	8	2	no	—
501	C₂×C₄×C₂₃	—	8	1	no	—
502	C₂×C₄×C₂₃	—	8	1	no	—
503	C₂×C₄×C₂₃	—	8	1	no	—
504	C₂×C₄×C₂₃	—	8	2	no	—
505	C₂×C₄×C₂₃	—	8	1	no	—
506	C₂×C₄×C₂₃	—	8	2	no	—
507	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
514	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
515	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
516	C₈×C₂₃	—	2	1	no	—
517	C₈×C₂₃	—	2	1	no	—
518	C₈×C₂₃	—	2	2	no	—
519	C₈×C₂₃	—	2	1	no	—
520	C₈×C₂₃	—	2	1	no	—
521	C₈×C₂₃	C₂×#41	1	4	yes	—
522	#3495	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#3492	C₂×C₂₃	1	1	yes	characteristic
524	#3356	C₂×C₂₃	1	2	yes	complemented
525	#3351	C₂×C₂₃	1	2	yes	complemented
526	#3350	C₂×C₂₃	1	2	yes	complemented
527	#3344	C₂×C₂₃	1	2	yes	complemented
528	#3344	C₂×C₂₃	1	2	yes	complemented
529	#3343	C₂×C₂₃	1	2	yes	complemented
530	#3336	C₂×C₂₃	1	2	yes	complemented
531	#3335	C₂×C₂₃	1	2	yes	complemented
532	#3163	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3099	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3097	C₂×C₂₃	1	1	yes	characteristic, complemented
535	#3091	C₂×C₂₃	1	1	yes	characteristic, complemented
536	C₂×#483	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3084	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3082	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#3063	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3056	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#2947	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#2933	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#2912	C₂×C₂₃	1	1	yes	characteristic, complemented
544	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
545	C₂²×C₂₃	—	2	1	no	—
546	C₂²×C₂₃	—	2	1	no	—
547	C₂²×C₂₃	—	2	1	no	—
548	C₂²×C₂₃	—	2	1	no	—
549	C₂²×C₂₃	—	2	2	no	—
550	C₂²×C₂₃	—	2	1	no	—
551	C₂²×C₂₃	—	2	1	no	—
552	C₂²×C₂₃	—	2	2	no	—
553	C₂²×C₂₃	—	2	1	no	—
554	C₂²×C₂₃	—	2	2	no	—
555	C₂²×C₂₃	—	4	4	no	—
556	C₂²×C₂₃	—	4	1	no	—
557	C₂²×C₂₃	—	4	1	no	—
558	C₂²×C₂₃	—	4	1	no	—
559	C₂²×C₂₃	#547	1	2	yes	—
560	C₂²×C₂₃	#577	1	2	yes	—
561	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₂₃	—	2	2	no	—
563	C₄×C₂₃	—	2	1	no	—
564	C₄×C₂₃	—	2	1	no	—
565	C₄×C₂₃	—	2	2	no	—
566	C₄×C₂₃	—	2	2	no	—
567	C₄×C₂₃	—	4	1	no	—
568	C₄×C₂₃	—	4	2	no	—
569	C₄×C₂₃	—	4	1	no	—
570	C₄×C₂₃	—	4	1	no	—
571	C₄×C₂₃	—	4	1	no	—
572	C₄×C₂₃	—	4	2	no	—
573	C₄×C₂₃	—	4	1	no	—
574	C₄×C₂₃	—	4	1	no	—
575	C₄×C₂₃	—	4	2	no	—
576	C₄×C₂₃	—	4	2	no	—
577	C₄×C₂₃	—	4	1	no	—
578	C₄×C₂₃	#547	1	2	yes	—
579	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
580	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
581	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
582	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
583	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
584	#556	C₂²×C₂₃	1	2	yes	—
585	#554	—	2	1	no	—
586	#554	C₂²×C₂₃	1	2	yes	—
587	#554	C₂²×C₂₃	1	2	yes	—
588	#553	—	2	1	no	—
589	#553	C₂²×C₂₃	1	2	yes	—
590	#552	—	2	2	no	—
591	#552	—	2	1	no	—
592	#552	C₂²×C₂₃	1	2	yes	—
593	#552	C₂²×C₂₃	1	2	yes	—
594	#552	C₂²×C₂₃	1	2	yes	—
595	#551	—	2	2	no	—
596	#547	—	2	1	no	—
597	#547	C₂²×C₂₃	1	2	yes	—
598	#544	C₂²×C₂₃	1	1	yes	characteristic
599	#544	C₂²×C₂₃	1	1	yes	characteristic
600	#542	—	2	1	no	—
601	#541	—	2	1	no	—
602	#539	—	2	2	no	—
603	#537	C₂²×C₂₃	1	1	yes	characteristic
604	#536	C₂²×C₂₃	1	1	yes	characteristic
605	#533	—	2	1	no	—
606	#529	—	2	1	no	—
607	#525	—	2	2	no	—
608	#525	C₂²×C₂₃	1	1	yes	characteristic
609	#525	C₂²×C₂₃	1	1	yes	characteristic
610	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
611	#520	C₂²×C₂₃	1	1	yes	characteristic
612	#520	C₂²×C₂₃	1	1	yes	characteristic
613	#520	C₂²×C₂₃	1	1	yes	characteristic
614	#519	C₂²×C₂₃	1	1	yes	characteristic
615	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
616	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
617	#501	C₂²×C₂₃	1	2	yes	complemented
618	#501	C₂²×C₂₃	1	2	yes	complemented
619	#499	C₂²×C₂₃	1	2	yes	complemented
620	#498	C₂²×C₂₃	1	2	yes	complemented
621	#485	C₂²×C₂₃	1	1	yes	characteristic
622	#485	C₂²×C₂₃	1	1	yes	characteristic
623	#485	C₂²×C₂₃	1	2	yes	complemented
624	#485	C₂²×C₂₃	1	2	yes	complemented
625	#485	C₂²×C₂₃	1	2	yes	complemented
626	#484	C₂²×C₂₃	1	1	yes	characteristic
627	#484	C₂²×C₂₃	1	2	yes	complemented
628	#483	C₂²×C₂₃	1	2	yes	—
629	#483	C₂²×C₂₃	1	1	yes	characteristic
630	#483	C₂²×C₂₃	1	2	yes	—
631	#483	C₂²×C₂₃	1	2	yes	—
632	#483	C₂²×C₂₃	1	2	yes	—
633	#483	C₂²×C₂₃	1	2	yes	complemented
634	#483	C₂²×C₂₃	1	2	yes	complemented
635	#482	C₂²×C₂₃	1	1	yes	characteristic
636	#482	C₂²×C₂₃	1	1	yes	characteristic
637	#482	C₂²×C₂₃	1	2	yes	complemented
638	#481	C₂²×C₂₃	1	1	yes	characteristic
639	#481	C₂²×C₂₃	1	2	yes	complemented
640	#480	C₂²×C₂₃	1	1	yes	characteristic
641	#479	C₂²×C₂₃	1	2	yes	complemented
642	#479	C₂²×C₂₃	1	2	yes	complemented
643	#479	C₂²×C₂₃	1	2	yes	complemented
644	#478	C₂²×C₂₃	1	2	yes	complemented
645	#477	C₂²×C₂₃	1	2	yes	complemented
646	#476	C₂²×C₂₃	1	2	yes	complemented
647	#475	C₂²×C₂₃	1	2	yes	complemented
648	#475	C₂²×C₂₃	1	2	yes	complemented
649	#470	C₂²×C₂₃	1	2	yes	—
650	#470	C₂²×C₂₃	1	2	yes	complemented
651	#468	C₂²×C₂₃	1	2	yes	—
652	#468	C₂²×C₂₃	1	2	yes	complemented
653	#467	C₂²×C₂₃	1	2	yes	—
654	#467	C₂²×C₂₃	1	2	yes	complemented
655	#465	C₂²×C₂₃	1	2	yes	—
656	#465	C₂²×C₂₃	1	2	yes	complemented
657	#441	C₂²×C₂₃	1	2	yes	complemented
658	#440	C₂²×C₂₃	1	2	yes	complemented
659	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
660	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
661	#436	C₂²×C₂₃	1	2	yes	—
662	#435	C₂²×C₂₃	1	2	yes	—
663	#435	C₂²×C₂₃	1	2	yes	—
664	C₈×D₄	C₂²×C₂₃	1	2	yes	—
665	#428	C₂²×C₂₃	1	1	yes	characteristic
666	#428	C₂²×C₂₃	1	1	yes	characteristic
667	#428	C₂²×C₂₃	1	2	yes	—
668	#428	C₂²×C₂₃	1	2	yes	—
669	#428	C₂²×C₂₃	1	1	yes	characteristic
670	#428	C₂²×C₂₃	1	1	yes	characteristic
671	#428	C₂²×C₂₃	1	1	yes	characteristic
672	#428	C₂²×C₂₃	1	2	yes	complemented
673	#428	C₂²×C₂₃	1	2	yes	complemented
674	#427	C₂²×C₂₃	1	1	yes	characteristic
675	#427	C₂²×C₂₃	1	1	yes	characteristic
676	#427	C₂²×C₂₃	1	2	yes	complemented
677	C₂×#107	C₂²×C₂₃	1	2	yes	—
678	C₂×#106	C₂²×C₂₃	1	2	yes	—
679	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
680	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
681	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
682	#424	C₂²×C₂₃	1	1	yes	characteristic
683	#419	C₂²×C₂₃	1	1	yes	characteristic
684	#417	C₂²×C₂₃	1	1	yes	characteristic
685	#416	C₂²×C₂₃	1	1	yes	characteristic
686	#416	C₂²×C₂₃	1	1	yes	characteristic
687	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
688	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
689	#408	C₂²×C₂₃	1	1	yes	characteristic
690	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
691	#405	C₂²×C₂₃	1	1	yes	characteristic
692	C₂×C₂₃	—	2	2	no	—
693	C₂×C₂₃	—	2	2	no	—
694	C₂×C₂₃	—	4	2	no	—
695	C₂×C₂₃	—	4	1	no	—
696	C₂×C₂₃	—	8	1	no	—
697	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
698	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
699	C₂×C₂₃	#3586	1	1	yes	characteristic
700	C₂×#41	—	2	2	no	—
701	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
702	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
703	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
704	C₂³×C₄	—	2	1	no	—
705	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
706	#137	—	2	4	no	—
707	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
709	#131	—	2	4	no	—
710	C₂×M₁₆	—	2	4	no	—
711	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
712	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
713	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
714	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
715	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
716	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
717	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
718	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	—	2	1	no	—
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#125	—	2	1	no	—
731	#125	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	1	no	—
737	#125	C₂³×C₂₃	1	2	yes	—
738	#125	C₂³×C₂₃	1	2	yes	—
739	#124	—	2	1	no	—
740	#124	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	1	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	D₄×C₂₃	1	2	yes	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	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	D₄×C₂₃	1	1	yes	characteristic
762	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	—	2	1	no	—
772	#121	D₄×C₂₃	1	1	yes	characteristic
773	#121	D₄×C₂₃	1	1	yes	characteristic
774	#121	C₂³×C₂₃	1	1	yes	characteristic
775	#121	C₂³×C₂₃	1	1	yes	characteristic
776	#121	C₂³×C₂₃	1	2	yes	—
777	#120	—	2	1	no	—
778	#120	D₄×C₂₃	1	2	yes	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	2	no	—
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×D₄	—	2	2	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	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	C₂³×C₂₃	1	2	yes	—
798	C₄×D₄	C₂³×C₂₃	1	2	yes	—
799	C₄×D₄	C₂³×C₂₃	1	2	yes	—
800	#117	—	2	1	no	—
801	#117	—	2	1	no	—
802	#117	—	2	1	no	—
803	#117	—	2	2	no	—
804	#117	—	2	2	no	—
805	#117	—	2	2	no	—
806	#117	—	2	2	no	—
807	#117	C₂³×C₂₃	1	1	yes	characteristic
808	#117	C₂³×C₂₃	1	1	yes	characteristic
809	#117	C₂³×C₂₃	1	1	yes	characteristic
810	#117	C₂³×C₂₃	1	1	yes	characteristic
811	#117	C₂³×C₂₃	1	1	yes	characteristic
812	#117	C₂³×C₂₃	1	2	yes	—
813	#117	C₂³×C₂₃	1	2	yes	—
814	#117	C₂³×C₂₃	1	1	yes	characteristic
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
821	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
822	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
823	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
824	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
825	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
828	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
829	C₂×C₂²⋊C₄	—	2	1	no	—
830	C₂×C₂²⋊C₄	—	2	1	no	—
831	C₂×C₄²	—	2	1	no	—
832	#107	C₂³×C₂₃	1	2	yes	—
833	#107	C₂³×C₂₃	1	2	yes	—
834	#107	C₂³×C₂₃	1	2	yes	—
835	#107	C₂³×C₂₃	1	2	yes	—
836	#107	C₂³×C₂₃	1	1	yes	characteristic
837	#107	C₂³×C₂₃	1	1	yes	characteristic
838	#107	C₂³×C₂₃	1	1	yes	characteristic
839	#107	C₂³×C₂₃	1	1	yes	characteristic
840	#107	C₂³×C₂₃	1	2	yes	—
841	#106	C₂³×C₂₃	1	2	yes	—
842	#106	C₂³×C₂₃	1	2	yes	—
843	#106	C₂³×C₂₃	1	2	yes	—
844	#106	C₂³×C₂₃	1	2	yes	—
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	2	yes	—
849	#106	C₂³×C₂₃	1	1	yes	characteristic
850	#106	C₂³×C₂₃	1	2	yes	—
851	#106	C₂³×C₂₃	1	1	yes	characteristic
852	#106	C₂³×C₂₃	1	1	yes	characteristic
853	#106	C₂³×C₂₃	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
855	C₄⋊C₈	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	1	yes	characteristic
861	#103	C₂³×C₂₃	1	1	yes	characteristic
862	#103	C₂³×C₂₃	1	1	yes	characteristic
863	#103	C₂³×C₂₃	1	1	yes	characteristic
864	#103	C₂³×C₂₃	1	2	yes	—
865	#103	C₂³×C₂₃	1	2	yes	—
866	#103	C₂³×C₂₃	1	2	yes	—
867	#102	C₂³×C₂₃	1	1	yes	characteristic
868	#102	C₂³×C₂₃	1	1	yes	characteristic
869	#102	C₂³×C₂₃	1	1	yes	characteristic
870	#102	C₂³×C₂₃	1	1	yes	characteristic
871	#102	C₂³×C₂₃	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
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	#97	C₂³×C₂₃	1	2	yes	—
879	C₄×C₈	C₂³×C₂₃	1	2	yes	—
880	C₂₃	#61271	1	1	yes	characteristic, direct product factor, Sylow
881	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
882	#41	—	2	2	no	—
883	#41	—	2	2	no	—
884	#41	—	2	2	no	—
885	#41	—	2	2	no	—
886	#41	—	8	4	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	2	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
893	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
894	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
900	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
901	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
902	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
903	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	8	2	no	—
919	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
920	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
921	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
926	Q₁₆	—	2	4	no	—
927	SD₁₆	—	2	4	no	—
928	M₁₆	—	2	2	no	—
929	M₁₆	—	2	4	no	—
930	M₁₆	—	2	4	no	—
931	M₁₆	#41×C₂₃	1	4	yes	complemented
932	C₂×C₈	—	2	2	no	—
933	C₂×C₈	—	2	2	no	—
934	C₂×C₈	—	2	4	no	—
935	C₂×C₈	—	2	4	no	—
936	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
941	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	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	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
970	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	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	C₂×D₄×C₂₃	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	C₂⁴×C₂₃	1	2	yes	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	4	1	no	—
1018	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1019	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1020	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1021	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	2	no	—
1029	Q₈	—	8	2	no	—
1030	D₄	—	2	4	no	—
1031	D₄	—	2	4	no	—
1032	D₄	—	2	2	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	2	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	8	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	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	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	4	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	1	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	1	no	—
1068	C₂×C₄	—	8	2	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	—	8	1	no	—
1072	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1075	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1078	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1079	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1080	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	2	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₈	C₂×#41×C₂₃	1	4	yes	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	4	4	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	C₂₃×#547	1	2	yes	—
1102	C₂²	C₂₃×#577	1	2	yes	—
1103	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	C₂₃×#547	1	2	yes	—
1121	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1122	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1123	C₂	—	2	2	no	—
1124	C₂	—	2	2	no	—
1125	C₂	—	4	1	no	—
1126	C₂	—	4	2	no	—
1127	C₂	—	8	1	no	—
1128	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
1129	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1130	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3492	C₂
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×#3495	C₂	semidirect
3. C₂₃×#3356	C₂	semidirect
4. C₂₃×#3351	C₂	semidirect
5. C₂₃×#3350	C₂	semidirect
6. C₂₃×#3344	C₂	semidirect
7. C₂₃×#3344	C₂	semidirect
8. C₂₃×#3343	C₂	semidirect
9. C₂₃×#3336	C₂	semidirect
10. C₂₃×#3335	C₂	semidirect
11. C₂₃×#3163	C₂	semidirect
12. C₂₃×#3099	C₂	semidirect
13. C₂₃×#3097	C₂	semidirect
14. C₂₃×#3091	C₂	semidirect
15. C₂×C₂₃×#483	C₂	semidirect
16. C₂₃×#3084	C₂	semidirect
17. C₂₃×#3082	C₂	semidirect
18. C₂₃×#3063	C₂	semidirect
19. C₂₃×#3056	C₂	semidirect
20. C₂₃×#2947	C₂	semidirect
21. C₂₃×#2933	C₂	semidirect
22. C₂₃×#2912	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
68. C₂₃×#485	C₂²	semidirect
70. C₂₃×#484	C₂²	semidirect
76. C₂₃×#483	C₂²	semidirect
77. C₂₃×#483	C₂²	semidirect
80. C₂₃×#482	C₂²	semidirect
82. C₂₃×#481	C₂²	semidirect
84. C₂₃×#479	C₂²	semidirect
85. C₂₃×#479	C₂²	semidirect
86. C₂₃×#479	C₂²	semidirect
87. C₂₃×#478	C₂²	semidirect
88. C₂₃×#477	C₂²	semidirect
89. C₂₃×#476	C₂²	semidirect
90. C₂₃×#475	C₂²	semidirect
91. C₂₃×#475	C₂²	semidirect
93. C₂₃×#470	C₂²	semidirect
95. C₂₃×#468	C₂²	semidirect
97. C₂₃×#467	C₂²	semidirect
99. C₂₃×#465	C₂²	semidirect
100. C₂₃×#441	C₂²	semidirect
101. C₂₃×#440	C₂²	semidirect
102. C₄×Q₁₆×C₂₃	C₂²	semidirect
103. C₄×SD₁₆×C₂₃	C₂²	semidirect
115. C₂₃×#428	C₂²	semidirect
116. C₂₃×#428	C₂²	semidirect
119. C₂₃×#427	C₂²	semidirect
124. C₂×C₂₃×#106	C₂²	semidirect
365. M₁₆×C₂₃	#41	semidirect
448. #61271	C₂₃	direct (N × H)
522. #3495	C₂×C₂₃	semidirect
524. #3356	C₂×C₂₃	semidirect
525. #3351	C₂×C₂₃	semidirect
526. #3350	C₂×C₂₃	semidirect
527. #3344	C₂×C₂₃	semidirect
528. #3344	C₂×C₂₃	semidirect
529. #3343	C₂×C₂₃	semidirect
530. #3336	C₂×C₂₃	semidirect
531. #3335	C₂×C₂₃	semidirect
532. #3163	C₂×C₂₃	semidirect
533. #3099	C₂×C₂₃	semidirect
534. #3097	C₂×C₂₃	semidirect
535. #3091	C₂×C₂₃	semidirect
536. C₂×#483	C₂×C₂₃	semidirect
537. #3084	C₂×C₂₃	semidirect
538. #3082	C₂×C₂₃	semidirect
539. #3063	C₂×C₂₃	semidirect
540. #3056	C₂×C₂₃	semidirect
541. #2947	C₂×C₂₃	semidirect
542. #2933	C₂×C₂₃	semidirect
543. #2912	C₂×C₂₃	semidirect
544. C₂×#428	C₂×C₂₃	semidirect
617. #501	C₂²×C₂₃	semidirect
618. #501	C₂²×C₂₃	semidirect
619. #499	C₂²×C₂₃	semidirect
620. #498	C₂²×C₂₃	semidirect
623. #485	C₂²×C₂₃	semidirect
624. #485	C₂²×C₂₃	semidirect
625. #485	C₂²×C₂₃	semidirect
627. #484	C₂²×C₂₃	semidirect
633. #483	C₂²×C₂₃	semidirect
634. #483	C₂²×C₂₃	semidirect
637. #482	C₂²×C₂₃	semidirect
639. #481	C₂²×C₂₃	semidirect
641. #479	C₂²×C₂₃	semidirect
642. #479	C₂²×C₂₃	semidirect
643. #479	C₂²×C₂₃	semidirect
644. #478	C₂²×C₂₃	semidirect
645. #477	C₂²×C₂₃	semidirect
646. #476	C₂²×C₂₃	semidirect
647. #475	C₂²×C₂₃	semidirect
648. #475	C₂²×C₂₃	semidirect
650. #470	C₂²×C₂₃	semidirect
652. #468	C₂²×C₂₃	semidirect
654. #467	C₂²×C₂₃	semidirect
656. #465	C₂²×C₂₃	semidirect
657. #441	C₂²×C₂₃	semidirect
658. #440	C₂²×C₂₃	semidirect
659. C₄×Q₁₆	C₂²×C₂₃	semidirect
660. C₄×SD₁₆	C₂²×C₂₃	semidirect
672. #428	C₂²×C₂₃	semidirect
673. #428	C₂²×C₂₃	semidirect
676. #427	C₂²×C₂₃	semidirect
681. C₂×#106	C₂²×C₂₃	semidirect
880. C₂₃	#61271	direct (N × H)
931. M₁₆	#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×#3495	2
C₂₃×#3492	2
C₂₃×#3356	2
C₂₃×#3351	2
C₂₃×#3350	2
C₂₃×#3344	2
C₂₃×#3343	2
C₂₃×#3336	2
C₂₃×#3335	2
C₂₃×#3163	2
C₂₃×#3099	2
C₂₃×#3097	2
C₂₃×#3091	2
C₂×C₂₃×#483	2
C₂₃×#3084	2
C₂₃×#3082	2
C₂₃×#3063	2
C₂₃×#3056	2
C₂₃×#2947	2
C₂₃×#2933	2
C₂₃×#2912	2
C₂×C₂₃×#428	2
#61271	23

Subgroups — C23×#61271 #19208897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61271 #19208897