Subgroups — C₂₃×#61786 #19209412

Order 5888.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3546	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3351	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3337	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3323	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3296	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3201	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3200	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3099	C₂	1	2	yes	maximal, complemented
22	C₂₃×#3096	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#560	—	2	2	no	—
25	C₂₃×#559	—	2	1	no	—
26	C₂₃×#557	—	2	1	no	—
27	C₂₃×#556	—	2	2	no	—
28	C₂₃×#556	C₂²	1	1	yes	characteristic
29	C₂₃×#556	C₂²	1	1	yes	characteristic
30	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#554	C₂²	1	1	yes	characteristic
32	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#553	C₂²	1	2	yes	—
34	C₂₃×#552	C₂²	1	2	yes	complemented
35	C₂₃×#552	C₂²	1	2	yes	complemented
36	C₂₃×#550	—	2	1	no	—
37	C₂₃×#550	C₂²	1	1	yes	characteristic
38	C₂₃×#547	C₂²	1	1	yes	characteristic
39	C₂₃×#546	—	2	1	no	—
40	C₂₃×#546	C₂²	1	2	yes	—
41	D₄²×C₂₃	C₂²	1	1	yes	characteristic
42	C₂₃×#542	—	2	1	no	—
43	C₂₃×#539	—	2	2	no	—
44	C₂₃×#538	—	2	2	no	—
45	C₂₃×#537	C₂²	1	2	yes	—
46	C₂₃×#536	C₂²	1	2	yes	complemented
47	C₂₃×#535	—	2	1	no	—
48	C₂₃×#535	C₂²	1	2	yes	—
49	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#532	C₂²	1	1	yes	characteristic
51	C₂₃×#532	C₂²	1	1	yes	characteristic
52	C₂₃×#529	—	2	1	no	—
53	C₂₃×#529	—	2	1	no	—
54	C₂₃×#529	C₂²	1	1	yes	characteristic
55	C₂₃×#520	C₂²	1	2	yes	complemented
56	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#499	C₂²	1	2	yes	complemented
59	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#488	C₂²	1	2	yes	—
61	C₂₃×#486	C₂²	1	1	yes	characteristic
62	C₂₃×#486	C₂²	1	1	yes	characteristic
63	C₂₃×#485	C₂²	1	2	yes	complemented
64	C₂₃×#485	C₂²	1	2	yes	complemented
65	C₂₃×#485	C₂²	1	2	yes	complemented
66	C₂₃×#485	C₂²	1	2	yes	complemented
67	C₂₃×#484	C₂²	1	2	yes	complemented
68	C₂₃×#483	C₂²	1	2	yes	complemented
69	C₂₃×#483	C₂²	1	2	yes	complemented
70	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#482	C₂²	1	2	yes	—
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×#482	C₂²	1	2	yes	complemented
77	C₂₃×#481	C₂²	1	2	yes	—
78	C₂₃×#481	C₂²	1	2	yes	—
79	C₂₃×#481	C₂²	1	2	yes	complemented
80	C₂₃×#480	C₂²	1	1	yes	characteristic
81	C₂₃×#480	C₂²	1	2	yes	complemented
82	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#478	C₂²	1	2	yes	complemented
85	C₂₃×#478	C₂²	1	2	yes	complemented
86	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#476	C₂²	1	1	yes	characteristic
88	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#474	C₂²	1	1	yes	characteristic
92	C₂₃×#470	C₂²	1	2	yes	complemented
93	C₂₃×#468	C₂²	1	2	yes	—
94	C₂₃×#468	C₂²	1	2	yes	—
95	C₂₃×#468	C₂²	1	2	yes	complemented
96	C₂₃×#467	C₂²	1	2	yes	complemented
97	C₂₃×#465	C₂²	1	2	yes	—
98	C₂₃×#465	C₂²	1	2	yes	—
99	C₂₃×#465	C₂²	1	2	yes	complemented
100	C₂₃×#464	C₂²	1	1	yes	characteristic
101	C₂₃×#464	C₂²	1	1	yes	characteristic
102	C₂₃×#460	C₂²	1	1	yes	characteristic
103	C₂₃×#460	C₂²	1	1	yes	characteristic
104	C₂₃×#452	C₂²	1	2	yes	complemented
105	C₂₃×#452	C₂²	1	2	yes	complemented
106	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#450	C₂²	1	2	yes	—
108	C₂₃×#450	C₂²	1	2	yes	—
109	C₂₃×#448	C₂²	1	1	yes	characteristic
110	C₂₃×#448	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
117	C₂₃×#436	C₂²	1	1	yes	characteristic
118	C₂₃×#436	C₂²	1	2	yes	complemented
119	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
120	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
121	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
122	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
124	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
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	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
129	C₂₃×#418	C₂²	1	2	yes	—
130	C₂₃×#417	C₂²	1	2	yes	complemented
131	C₂₃×#416	C₂²	1	2	yes	complemented
132	C₂×C₂₃×#102	C₂²	1	2	yes	—
133	C₂₃×#408	C₂²	1	2	yes	complemented
134	C₂₃×#408	C₂²	1	2	yes	complemented
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	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₂₃	—	2	1	no	—
141	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
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	—	2	2	no	—
153	C₂₃×C₄⋊Q₈	D₄	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	1	no	—
158	C₂₃×#127	—	2	2	no	—
159	C₂₃×#127	D₄	1	1	yes	characteristic
160	C₂₃×#127	C₂³	1	1	yes	characteristic
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×#126	—	2	2	no	—
166	C₂₃×#126	—	2	2	no	—
167	C₂₃×#126	—	2	1	no	—
168	C₂₃×#125	—	2	2	no	—
169	C₂₃×#125	—	2	2	no	—
170	C₂₃×#125	—	2	1	no	—
171	C₂₃×#125	—	2	1	no	—
172	C₂₃×#125	C₂³	1	2	yes	—
173	C₂₃×#125	C₂³	1	1	yes	characteristic
174	C₂₃×#124	—	2	2	no	—
175	C₂₃×#124	—	2	2	no	—
176	C₂₃×#124	—	2	1	no	—
177	C₂₃×#124	—	2	1	no	—
178	C₂₃×#124	—	2	1	no	—
179	C₂₃×#124	—	2	1	no	—
180	C₂₃×#124	D₄	1	2	yes	—
181	C₂₃×#124	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
187	C₂₃×#123	—	2	2	no	—
188	C₂₃×#123	—	2	2	no	—
189	C₂₃×#123	—	2	2	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	—	2	1	no	—
192	C₂₃×C₂²⋊Q₈	—	2	1	no	—
193	C₂₃×C₂²⋊Q₈	—	2	1	no	—
194	C₂₃×C₂²⋊Q₈	—	2	2	no	—
195	C₂₃×C₂²⋊Q₈	—	2	2	no	—
196	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
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	1	yes	characteristic
202	C₂₃×#121	—	2	2	no	—
203	C₂₃×#121	—	2	2	no	—
204	C₂₃×#121	—	2	2	no	—
205	C₂₃×#121	—	2	2	no	—
206	C₂₃×#121	—	2	1	no	—
207	C₂₃×#121	—	2	1	no	—
208	C₂₃×#121	—	2	2	no	—
209	C₂₃×#121	—	2	2	no	—
210	C₂₃×#121	D₄	1	1	yes	characteristic
211	C₂₃×#121	D₄	1	2	yes	—
212	C₂₃×#121	D₄	1	1	yes	characteristic
213	C₂₃×#121	C₂³	1	2	yes	—
214	C₂₃×#121	C₂³	1	2	yes	—
215	C₂₃×#121	C₂³	1	2	yes	—
216	C₂₃×#121	C₂³	1	1	yes	characteristic
217	C₂₃×#121	C₂³	1	2	yes	—
218	C₂₃×#120	—	2	2	no	—
219	C₂₃×#120	—	2	2	no	—
220	C₂₃×#120	—	2	2	no	—
221	C₂₃×#120	—	2	2	no	—
222	C₄×Q₈×C₂₃	—	2	2	no	—
223	C₄×Q₈×C₂₃	—	2	1	no	—
224	C₄×Q₈×C₂₃	—	2	1	no	—
225	C₄×Q₈×C₂₃	—	2	1	no	—
226	C₄×Q₈×C₂₃	—	2	1	no	—
227	C₄×Q₈×C₂₃	—	2	1	no	—
228	C₄×Q₈×C₂₃	—	2	1	no	—
229	C₄×Q₈×C₂₃	—	2	1	no	—
230	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₂₃	—	2	1	no	—
236	C₄×D₄×C₂₃	—	2	1	no	—
237	C₄×D₄×C₂₃	—	2	2	no	—
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	—	2	2	no	—
240	C₄×D₄×C₂₃	—	2	1	no	—
241	C₄×D₄×C₂₃	—	2	1	no	—
242	C₄×D₄×C₂₃	—	2	2	no	—
243	C₄×D₄×C₂₃	—	2	1	no	—
244	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₂₃	C₂³	1	2	yes	—
246	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₂₃	C₂³	1	2	yes	—
248	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
249	C₂₃×#117	—	2	2	no	—
250	C₂₃×#117	—	2	2	no	—
251	C₂₃×#117	—	2	1	no	—
252	C₂₃×#117	C₂³	1	2	yes	—
253	C₂₃×#117	C₂³	1	2	yes	—
254	C₂₃×#117	C₂³	1	2	yes	—
255	C₂₃×#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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×C₂²⋊C₄×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	1	yes	characteristic
267	C₂₃×#107	C₂³	1	2	yes	—
268	C₂₃×#107	C₂³	1	2	yes	—
269	C₂₃×#107	C₂³	1	2	yes	—
270	C₂₃×#106	C₂³	1	1	yes	characteristic
271	C₂₃×#106	C₂³	1	2	yes	—
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	1	yes	characteristic
283	C₂₃×#103	C₂³	1	2	yes	—
284	C₂₃×#103	C₂³	1	1	yes	characteristic
285	C₂₃×#103	C₂³	1	2	yes	—
286	C₂₃×#103	C₂³	1	1	yes	characteristic
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	1	yes	characteristic
291	C₂₃×#103	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	2	yes	—
296	C₂₃×#102	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	C₂⁴×C₂₃	—	2	2	no	—
313	#41×C₂₃	—	4	2	no	—
314	#41×C₂₃	—	4	2	no	—
315	#41×C₂₃	—	4	2	no	—
316	#41×C₂₃	—	4	2	no	—
317	#41×C₂₃	—	8	2	no	—
318	#41×C₂₃	—	8	2	no	—
319	C₂×Q₈×C₂₃	—	2	1	no	—
320	C₂×Q₈×C₂₃	—	2	1	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	2	1	no	—
323	C₂×Q₈×C₂₃	—	4	1	no	—
324	C₂×Q₈×C₂₃	—	4	1	no	—
325	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
336	C₂×D₄×C₂₃	—	2	1	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	—	4	2	no	—
339	C₂×D₄×C₂₃	—	4	2	no	—
340	C₂×D₄×C₂₃	—	8	2	no	—
341	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₂₃	—	2	1	no	—
350	C₂²×C₄×C₂₃	—	2	1	no	—
351	C₂²×C₄×C₂₃	—	2	2	no	—
352	C₂²×C₄×C₂₃	—	2	2	no	—
353	C₂²×C₄×C₂₃	—	2	2	no	—
354	C₂²×C₄×C₂₃	—	2	1	no	—
355	C₂²×C₄×C₂₃	—	2	2	no	—
356	C₂²×C₄×C₂₃	—	2	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	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
362	Q₁₆×C₂₃	—	4	1	no	—
363	Q₁₆×C₂₃	—	4	1	no	—
364	SD₁₆×C₂₃	—	4	1	no	—
365	SD₁₆×C₂₃	—	4	2	no	—
366	SD₁₆×C₂₃	—	4	1	no	—
367	SD₁₆×C₂₃	—	4	2	no	—
368	M₁₆×C₂₃	—	4	2	no	—
369	M₁₆×C₂₃	—	4	2	no	—
370	C₂×C₈×C₂₃	—	4	2	no	—
371	C₂×C₈×C₂₃	—	4	2	no	—
372	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₂₃	—	2	1	no	—
379	C₄⋊C₄×C₂₃	—	2	1	no	—
380	C₄⋊C₄×C₂₃	—	2	1	no	—
381	C₄⋊C₄×C₂₃	—	2	1	no	—
382	C₄⋊C₄×C₂₃	—	2	1	no	—
383	C₄⋊C₄×C₂₃	—	2	2	no	—
384	C₄⋊C₄×C₂₃	—	2	2	no	—
385	C₄⋊C₄×C₂₃	—	2	2	no	—
386	C₄⋊C₄×C₂₃	—	2	2	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	1	no	—
389	C₄⋊C₄×C₂₃	—	2	2	no	—
390	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	1	no	—
392	C₄⋊C₄×C₂₃	—	2	1	no	—
393	C₄⋊C₄×C₂₃	—	2	1	no	—
394	C₄⋊C₄×C₂₃	—	2	2	no	—
395	C₄⋊C₄×C₂₃	—	2	2	no	—
396	C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₄⋊C₄×C₂₃	—	2	2	no	—
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	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	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	1	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	1	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	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	1	no	—
435	C₄²×C₂₃	—	2	1	no	—
436	C₄²×C₂₃	—	2	1	no	—
437	C₄²×C₂₃	—	2	2	no	—
438	C₄²×C₂₃	—	2	2	no	—
439	C₄²×C₂₃	—	2	1	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	#61786	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₂₃	—	2	1	no	—
448	C₂³×C₂₃	—	2	2	no	—
449	C₂³×C₂₃	—	8	2	no	—
450	C₂³×C₂₃	—	8	2	no	—
451	C₂³×C₂₃	—	8	2	no	—
452	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
453	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
454	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
455	Q₈×C₂₃	—	2	1	no	—
456	Q₈×C₂₃	—	2	1	no	—
457	Q₈×C₂₃	—	2	1	no	—
458	Q₈×C₂₃	—	2	1	no	—
459	Q₈×C₂₃	—	2	1	no	—
460	Q₈×C₂₃	—	2	1	no	—
461	Q₈×C₂₃	—	4	2	no	—
462	Q₈×C₂₃	—	4	2	no	—
463	Q₈×C₂₃	—	4	2	no	—
464	Q₈×C₂₃	—	4	2	no	—
465	Q₈×C₂₃	—	8	1	no	—
466	D₄×C₂₃	—	2	2	no	—
467	D₄×C₂₃	—	2	2	no	—
468	D₄×C₂₃	—	2	1	no	—
469	D₄×C₂₃	—	2	1	no	—
470	D₄×C₂₃	—	2	2	no	—
471	D₄×C₂₃	—	2	2	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	—	8	1	no	—
478	D₄×C₂₃	—	8	2	no	—
479	D₄×C₂₃	—	8	1	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	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	2	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	1	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	—	4	1	no	—
503	C₂×C₄×C₂₃	—	4	2	no	—
504	C₂×C₄×C₂₃	—	4	2	no	—
505	C₂×C₄×C₂₃	—	8	2	no	—
506	C₂×C₄×C₂₃	—	8	2	no	—
507	C₂×C₄×C₂₃	—	8	1	no	—
508	C₂×C₄×C₂₃	—	8	2	no	—
509	C₂×C₄×C₂₃	—	8	2	no	—
510	C₂×C₄×C₂₃	—	8	2	no	—
511	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
518	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
519	C₈×C₂₃	—	2	1	no	—
520	C₈×C₂₃	—	2	2	no	—
521	C₈×C₂₃	—	2	1	no	—
522	C₈×C₂₃	—	2	2	no	—
523	C₈×C₂₃	—	2	1	no	—
524	C₈×C₂₃	—	2	1	no	—
525	#3546	C₂×C₂₃	1	1	yes	characteristic
526	#3507	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#3356	C₂×C₂₃	1	1	yes	characteristic, complemented
528	#3353	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3351	C₂×C₂₃	1	2	yes	complemented
530	#3342	C₂×C₂₃	1	1	yes	characteristic, complemented
531	#3337	C₂×C₂₃	1	2	yes	complemented
532	#3335	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3333	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3324	C₂×C₂₃	1	1	yes	characteristic, complemented
535	#3323	C₂×C₂₃	1	2	yes	complemented
536	#3304	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3296	C₂×C₂₃	1	2	yes	complemented
538	#3295	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#3233	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3228	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3201	C₂×C₂₃	1	2	yes	complemented
542	#3200	C₂×C₂₃	1	2	yes	complemented
543	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#3103	C₂×C₂₃	1	1	yes	characteristic, complemented
545	#3099	C₂×C₂₃	1	2	yes	complemented
546	#3096	C₂×C₂₃	1	2	yes	complemented
547	#2979	C₂×C₂₃	1	1	yes	characteristic, complemented
548	C₂²×C₂₃	—	2	1	no	—
549	C₂²×C₂₃	—	2	2	no	—
550	C₂²×C₂₃	—	2	2	no	—
551	C₂²×C₂₃	—	2	1	no	—
552	C₂²×C₂₃	—	2	2	no	—
553	C₂²×C₂₃	—	2	2	no	—
554	C₂²×C₂₃	—	2	1	no	—
555	C₂²×C₂₃	—	2	2	no	—
556	C₂²×C₂₃	—	2	2	no	—
557	C₂²×C₂₃	—	4	2	no	—
558	C₂²×C₂₃	—	4	1	no	—
559	C₂²×C₂₃	—	4	2	no	—
560	C₂²×C₂₃	—	4	1	no	—
561	C₂²×C₂₃	—	4	1	no	—
562	C₂²×C₂₃	—	4	2	no	—
563	C₂²×C₂₃	—	16	4	no	—
564	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
565	C₄×C₂₃	—	2	1	no	—
566	C₄×C₂₃	—	2	1	no	—
567	C₄×C₂₃	—	2	2	no	—
568	C₄×C₂₃	—	2	1	no	—
569	C₄×C₂₃	—	2	2	no	—
570	C₄×C₂₃	—	2	1	no	—
571	C₄×C₂₃	—	4	1	no	—
572	C₄×C₂₃	—	4	1	no	—
573	C₄×C₂₃	—	4	2	no	—
574	C₄×C₂₃	—	4	1	no	—
575	C₄×C₂₃	—	4	1	no	—
576	C₄×C₂₃	—	4	1	no	—
577	C₄×C₂₃	—	4	1	no	—
578	C₄×C₂₃	—	4	1	no	—
579	C₄×C₂₃	—	4	2	no	—
580	C₄×C₂₃	—	4	2	no	—
581	C₄×C₂₃	#577	1	2	yes	—
582	C₄×C₂₃	#585	1	1	yes	characteristic
583	C₄×C₂₃	#585	1	1	yes	characteristic
584	#560	—	2	2	no	—
585	#559	—	2	1	no	—
586	#557	—	2	1	no	—
587	#556	—	2	2	no	—
588	#556	C₂²×C₂₃	1	1	yes	characteristic
589	#556	C₂²×C₂₃	1	1	yes	characteristic
590	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
591	#554	C₂²×C₂₃	1	1	yes	characteristic
592	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
593	#553	C₂²×C₂₃	1	2	yes	—
594	#552	C₂²×C₂₃	1	2	yes	complemented
595	#552	C₂²×C₂₃	1	2	yes	complemented
596	#550	—	2	1	no	—
597	#550	C₂²×C₂₃	1	1	yes	characteristic
598	#547	C₂²×C₂₃	1	1	yes	characteristic
599	#546	—	2	1	no	—
600	#546	C₂²×C₂₃	1	2	yes	—
601	D₄²	C₂²×C₂₃	1	1	yes	characteristic
602	#542	—	2	1	no	—
603	#539	—	2	2	no	—
604	#538	—	2	2	no	—
605	#537	C₂²×C₂₃	1	2	yes	—
606	#536	C₂²×C₂₃	1	2	yes	complemented
607	#535	—	2	1	no	—
608	#535	C₂²×C₂₃	1	2	yes	—
609	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
610	#532	C₂²×C₂₃	1	1	yes	characteristic
611	#532	C₂²×C₂₃	1	1	yes	characteristic
612	#529	—	2	1	no	—
613	#529	—	2	1	no	—
614	#529	C₂²×C₂₃	1	1	yes	characteristic
615	#520	C₂²×C₂₃	1	2	yes	complemented
616	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
617	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
618	#499	C₂²×C₂₃	1	2	yes	complemented
619	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
620	#488	C₂²×C₂₃	1	2	yes	—
621	#486	C₂²×C₂₃	1	1	yes	characteristic
622	#486	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	#485	C₂²×C₂₃	1	2	yes	complemented
627	#484	C₂²×C₂₃	1	2	yes	complemented
628	#483	C₂²×C₂₃	1	2	yes	complemented
629	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
630	#483	C₂²×C₂₃	1	2	yes	complemented
631	#482	C₂²×C₂₃	1	2	yes	—
632	#482	C₂²×C₂₃	1	2	yes	—
633	#482	C₂²×C₂₃	1	2	yes	—
634	#482	C₂²×C₂₃	1	2	yes	complemented
635	#482	C₂²×C₂₃	1	2	yes	complemented
636	#482	C₂²×C₂₃	1	2	yes	complemented
637	#481	C₂²×C₂₃	1	2	yes	—
638	#481	C₂²×C₂₃	1	2	yes	—
639	#481	C₂²×C₂₃	1	2	yes	complemented
640	#480	C₂²×C₂₃	1	1	yes	characteristic
641	#480	C₂²×C₂₃	1	2	yes	complemented
642	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
643	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
644	#478	C₂²×C₂₃	1	2	yes	complemented
645	#478	C₂²×C₂₃	1	2	yes	complemented
646	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
647	#476	C₂²×C₂₃	1	1	yes	characteristic
648	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
649	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
651	#474	C₂²×C₂₃	1	1	yes	characteristic
652	#470	C₂²×C₂₃	1	2	yes	complemented
653	#468	C₂²×C₂₃	1	2	yes	—
654	#468	C₂²×C₂₃	1	2	yes	—
655	#468	C₂²×C₂₃	1	2	yes	complemented
656	#467	C₂²×C₂₃	1	2	yes	complemented
657	#465	C₂²×C₂₃	1	2	yes	—
658	#465	C₂²×C₂₃	1	2	yes	—
659	#465	C₂²×C₂₃	1	2	yes	complemented
660	#464	C₂²×C₂₃	1	1	yes	characteristic
661	#464	C₂²×C₂₃	1	1	yes	characteristic
662	#460	C₂²×C₂₃	1	1	yes	characteristic
663	#460	C₂²×C₂₃	1	1	yes	characteristic
664	#452	C₂²×C₂₃	1	2	yes	complemented
665	#452	C₂²×C₂₃	1	2	yes	complemented
666	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
667	#450	C₂²×C₂₃	1	2	yes	—
668	#450	C₂²×C₂₃	1	2	yes	—
669	#448	C₂²×C₂₃	1	1	yes	characteristic
670	#448	C₂²×C₂₃	1	2	yes	complemented
671	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
672	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
675	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
676	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
677	#436	C₂²×C₂₃	1	1	yes	characteristic
678	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
679	#436	C₂²×C₂₃	1	2	yes	complemented
680	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
681	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
683	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
684	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	#428	C₂²×C₂₃	1	2	yes	complemented
686	#428	C₂²×C₂₃	1	2	yes	complemented
687	#427	C₂²×C₂₃	1	2	yes	complemented
688	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
689	#418	C₂²×C₂₃	1	2	yes	—
690	#417	C₂²×C₂₃	1	2	yes	complemented
691	#416	C₂²×C₂₃	1	2	yes	complemented
692	C₂×#102	C₂²×C₂₃	1	2	yes	—
693	#408	C₂²×C₂₃	1	2	yes	complemented
694	#408	C₂²×C₂₃	1	2	yes	complemented
695	C₂×C₂₃	—	4	1	no	—
696	C₂×C₂₃	—	4	2	no	—
697	C₂×C₂₃	—	4	2	no	—
698	C₂×C₂₃	—	8	2	no	—
699	C₂×C₂₃	—	8	1	no	—
700	C₂×C₂₃	#3485	1	1	yes	characteristic
701	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
702	C₂×C₂₃	#3584	1	1	yes	characteristic
703	C₂×#41	—	2	1	no	—
704	C₂×#41	—	2	1	no	—
705	C₂×#41	C₂³×C₂₃	1	2	yes	—
706	C₂×#41	C₂³×C₂₃	1	2	yes	—
707	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
708	C₂²×D₄	—	2	1	no	—
709	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
711	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
716	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
717	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
718	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
719	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
720	C₄⋊Q₈	—	2	2	no	—
721	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
725	#127	—	2	1	no	—
726	#127	—	2	2	no	—
727	#127	D₄×C₂₃	1	1	yes	characteristic
728	#127	C₂³×C₂₃	1	1	yes	characteristic
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	1	no	—
736	#125	—	2	1	no	—
737	#125	—	2	1	no	—
738	#125	—	2	2	no	—
739	#125	—	2	2	no	—
740	#125	C₂³×C₂₃	1	1	yes	characteristic
741	#125	C₂³×C₂₃	1	2	yes	—
742	#124	—	2	2	no	—
743	#124	—	2	1	no	—
744	#124	—	2	1	no	—
745	#124	—	2	1	no	—
746	#124	—	2	2	no	—
747	#124	—	2	1	no	—
748	#124	D₄×C₂₃	1	2	yes	—
749	#124	C₂³×C₂₃	1	1	yes	characteristic
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	1	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
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	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	1	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	D₄×C₂₃	1	1	yes	characteristic
779	#121	D₄×C₂₃	1	1	yes	characteristic
780	#121	D₄×C₂₃	1	2	yes	—
781	#121	C₂³×C₂₃	1	1	yes	characteristic
782	#121	C₂³×C₂₃	1	2	yes	—
783	#121	C₂³×C₂₃	1	2	yes	—
784	#121	C₂³×C₂₃	1	2	yes	—
785	#121	C₂³×C₂₃	1	2	yes	—
786	#120	—	2	2	no	—
787	#120	—	2	2	no	—
788	#120	—	2	2	no	—
789	#120	—	2	2	no	—
790	C₄×Q₈	—	2	2	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₂₃	1	2	yes	—
814	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₂₃	1	2	yes	—
816	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
817	#117	—	2	2	no	—
818	#117	—	2	2	no	—
819	#117	—	2	1	no	—
820	#117	C₂³×C₂₃	1	2	yes	—
821	#117	C₂³×C₂₃	1	2	yes	—
822	#117	C₂³×C₂₃	1	2	yes	—
823	#117	C₂³×C₂₃	1	2	yes	—
824	C₂×C₄⋊C₄	—	2	1	no	—
825	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
827	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
828	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
829	C₂×C₂²⋊C₄	—	2	2	no	—
830	C₂×C₄²	—	2	1	no	—
831	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
832	#107	C₂³×C₂₃	1	1	yes	characteristic
833	#107	C₂³×C₂₃	1	2	yes	—
834	#107	C₂³×C₂₃	1	1	yes	characteristic
835	#107	C₂³×C₂₃	1	2	yes	—
836	#107	C₂³×C₂₃	1	2	yes	—
837	#107	C₂³×C₂₃	1	2	yes	—
838	#106	C₂³×C₂₃	1	1	yes	characteristic
839	#106	C₂³×C₂₃	1	2	yes	—
840	#106	C₂³×C₂₃	1	2	yes	—
841	#106	C₂³×C₂₃	1	2	yes	—
842	#106	C₂³×C₂₃	1	2	yes	—
843	#106	C₂³×C₂₃	1	1	yes	characteristic
844	#106	C₂³×C₂₃	1	2	yes	—
845	#106	C₂³×C₂₃	1	2	yes	—
846	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
849	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
850	#103	C₂³×C₂₃	1	1	yes	characteristic
851	#103	C₂³×C₂₃	1	2	yes	—
852	#103	C₂³×C₂₃	1	1	yes	characteristic
853	#103	C₂³×C₂₃	1	2	yes	—
854	#103	C₂³×C₂₃	1	1	yes	characteristic
855	#103	C₂³×C₂₃	1	1	yes	characteristic
856	#103	C₂³×C₂₃	1	2	yes	—
857	#103	C₂³×C₂₃	1	2	yes	—
858	#103	C₂³×C₂₃	1	1	yes	characteristic
859	#103	C₂³×C₂₃	1	1	yes	characteristic
860	#102	C₂³×C₂₃	1	1	yes	characteristic
861	#102	C₂³×C₂₃	1	2	yes	—
862	#102	C₂³×C₂₃	1	2	yes	—
863	#102	C₂³×C₂₃	1	2	yes	—
864	#102	C₂³×C₂₃	1	2	yes	—
865	#102	C₂³×C₂₃	1	2	yes	—
866	#102	C₂³×C₂₃	1	2	yes	—
867	#102	C₂³×C₂₃	1	1	yes	characteristic
868	#102	C₂³×C₂₃	1	2	yes	—
869	#102	C₂³×C₂₃	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
877	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₂₃	1	2	yes	—
880	C₂₃	#61786	1	1	yes	characteristic, direct product factor, Sylow
881	C₂⁴	—	2	2	no	—
882	#41	—	4	2	no	—
883	#41	—	4	2	no	—
884	#41	—	4	2	no	—
885	#41	—	4	2	no	—
886	#41	—	8	2	no	—
887	#41	—	8	2	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	4	1	no	—
893	C₂×Q₈	—	4	1	no	—
894	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
895	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	2	no	—
909	C₂×D₄	—	8	2	no	—
910	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
911	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
912	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
913	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
914	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
916	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
917	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
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	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
927	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
928	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
931	Q₁₆	—	4	1	no	—
932	Q₁₆	—	4	1	no	—
933	SD₁₆	—	4	1	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	1	no	—
936	SD₁₆	—	4	2	no	—
937	M₁₆	—	4	2	no	—
938	M₁₆	—	4	2	no	—
939	C₂×C₈	—	4	2	no	—
940	C₂×C₈	—	4	2	no	—
941	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
945	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	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	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	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	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	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	2	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	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1012	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	8	2	no	—
1018	C₂³	—	8	2	no	—
1019	C₂³	—	8	2	no	—
1020	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1021	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1022	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	4	2	no	—
1032	Q₈	—	4	2	no	—
1033	Q₈	—	8	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	2	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	1	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	2	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1086	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1087	C₈	—	2	1	no	—
1088	C₈	—	2	2	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	2	no	—
1092	C₈	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	16	4	no	—
1109	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1110	C₄	—	2	2	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	C₂₃×#577	1	2	yes	—
1127	C₄	C₂₃×#585	1	1	yes	characteristic
1128	C₄	C₂₃×#585	1	1	yes	characteristic
1129	C₂	—	4	2	no	—
1130	C₂	—	4	1	no	—
1131	C₂	—	4	2	no	—
1132	C₂	—	8	1	no	—
1133	C₂	—	8	2	no	—
1134	C₂	C₂₃×#3485	1	1	yes	characteristic
1135	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1136	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3507	C₂	semidirect
3. C₂₃×#3356	C₂	semidirect
4. C₂₃×#3353	C₂	semidirect
5. C₂₃×#3351	C₂	semidirect
6. C₂₃×#3342	C₂	semidirect
7. C₂₃×#3337	C₂	semidirect
8. C₂₃×#3335	C₂	semidirect
9. C₂₃×#3333	C₂	semidirect
10. C₂₃×#3324	C₂	semidirect
11. C₂₃×#3323	C₂	semidirect
12. C₂₃×#3304	C₂	semidirect
13. C₂₃×#3296	C₂	semidirect
14. C₂₃×#3295	C₂	semidirect
15. C₂₃×#3233	C₂	semidirect
16. C₂₃×#3228	C₂	semidirect
17. C₂₃×#3201	C₂	semidirect
18. C₂₃×#3200	C₂	semidirect
19. C₂₃×#3108	C₂	semidirect
20. C₂₃×#3103	C₂	semidirect
21. C₂₃×#3099	C₂	semidirect
22. C₂₃×#3096	C₂	semidirect
23. C₂₃×#2979	C₂	semidirect
30. C₂₃×#556	C₂²	semidirect
32. C₂₃×#554	C₂²	semidirect
34. C₂₃×#552	C₂²	semidirect
35. C₂₃×#552	C₂²	semidirect
46. C₂₃×#536	C₂²	semidirect
49. C₂₃×#533	C₂²	semidirect
55. C₂₃×#520	C₂²	semidirect
56. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
57. C₂₃×#500	C₂²	semidirect
58. C₂₃×#499	C₂²	semidirect
59. C₂₃×#498	C₂²	semidirect
63. C₂₃×#485	C₂²	semidirect
64. C₂₃×#485	C₂²	semidirect
65. C₂₃×#485	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#484	C₂²	semidirect
68. C₂₃×#483	C₂²	semidirect
69. C₂₃×#483	C₂²	semidirect
70. C₂₃×#483	C₂²	semidirect
74. C₂₃×#482	C₂²	semidirect
75. C₂₃×#482	C₂²	semidirect
76. C₂₃×#482	C₂²	semidirect
79. C₂₃×#481	C₂²	semidirect
81. C₂₃×#480	C₂²	semidirect
82. C₂₃×#479	C₂²	semidirect
83. C₂₃×#479	C₂²	semidirect
84. C₂₃×#478	C₂²	semidirect
85. C₂₃×#478	C₂²	semidirect
86. C₂₃×#477	C₂²	semidirect
88. C₂₃×#475	C₂²	semidirect
89. C₂₃×#475	C₂²	semidirect
90. C₂₃×#475	C₂²	semidirect
92. C₂₃×#470	C₂²	semidirect
95. C₂₃×#468	C₂²	semidirect
96. C₂₃×#467	C₂²	semidirect
99. C₂₃×#465	C₂²	semidirect
104. C₂₃×#452	C₂²	semidirect
105. C₂₃×#452	C₂²	semidirect
106. C₂₃×#451	C₂²	semidirect
110. C₂₃×#448	C₂²	semidirect
111. C₄×Q₁₆×C₂₃	C₂²	semidirect
112. C₄×Q₁₆×C₂₃	C₂²	semidirect
115. C₄×SD₁₆×C₂₃	C₂²	semidirect
116. C₄×SD₁₆×C₂₃	C₂²	semidirect
118. C₂₃×#436	C₂²	semidirect
119. C₂₃×#436	C₂²	semidirect
121. C₈×D₄×C₂₃	C₂²	semidirect
122. C₈×D₄×C₂₃	C₂²	semidirect
123. C₂₃×#431	C₂²	semidirect
124. C₂₃×#431	C₂²	semidirect
125. C₂₃×#428	C₂²	semidirect
126. C₂₃×#428	C₂²	semidirect
127. C₂₃×#427	C₂²	semidirect
128. C₂×C₂₃×#106	C₂²	semidirect
130. C₂₃×#417	C₂²	semidirect
131. C₂₃×#416	C₂²	semidirect
133. C₂₃×#408	C₂²	semidirect
134. C₂₃×#408	C₂²	semidirect
446. #61786	C₂₃	direct (N × H)
526. #3507	C₂×C₂₃	semidirect
527. #3356	C₂×C₂₃	semidirect
528. #3353	C₂×C₂₃	semidirect
529. #3351	C₂×C₂₃	semidirect
530. #3342	C₂×C₂₃	semidirect
531. #3337	C₂×C₂₃	semidirect
532. #3335	C₂×C₂₃	semidirect
533. #3333	C₂×C₂₃	semidirect
534. #3324	C₂×C₂₃	semidirect
535. #3323	C₂×C₂₃	semidirect
536. #3304	C₂×C₂₃	semidirect
537. #3296	C₂×C₂₃	semidirect
538. #3295	C₂×C₂₃	semidirect
539. #3233	C₂×C₂₃	semidirect
540. #3228	C₂×C₂₃	semidirect
541. #3201	C₂×C₂₃	semidirect
542. #3200	C₂×C₂₃	semidirect
543. #3108	C₂×C₂₃	semidirect
544. #3103	C₂×C₂₃	semidirect
545. #3099	C₂×C₂₃	semidirect
546. #3096	C₂×C₂₃	semidirect
547. #2979	C₂×C₂₃	semidirect
590. #556	C₂²×C₂₃	semidirect
592. #554	C₂²×C₂₃	semidirect
594. #552	C₂²×C₂₃	semidirect
595. #552	C₂²×C₂₃	semidirect
606. #536	C₂²×C₂₃	semidirect
609. #533	C₂²×C₂₃	semidirect
615. #520	C₂²×C₂₃	semidirect
616. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
617. #500	C₂²×C₂₃	semidirect
618. #499	C₂²×C₂₃	semidirect
619. #498	C₂²×C₂₃	semidirect
623. #485	C₂²×C₂₃	semidirect
624. #485	C₂²×C₂₃	semidirect
625. #485	C₂²×C₂₃	semidirect
626. #485	C₂²×C₂₃	semidirect
627. #484	C₂²×C₂₃	semidirect
628. #483	C₂²×C₂₃	semidirect
629. #483	C₂²×C₂₃	semidirect
630. #483	C₂²×C₂₃	semidirect
634. #482	C₂²×C₂₃	semidirect
635. #482	C₂²×C₂₃	semidirect
636. #482	C₂²×C₂₃	semidirect
639. #481	C₂²×C₂₃	semidirect
641. #480	C₂²×C₂₃	semidirect
642. #479	C₂²×C₂₃	semidirect
643. #479	C₂²×C₂₃	semidirect
644. #478	C₂²×C₂₃	semidirect
645. #478	C₂²×C₂₃	semidirect
646. #477	C₂²×C₂₃	semidirect
648. #475	C₂²×C₂₃	semidirect
649. #475	C₂²×C₂₃	semidirect
650. #475	C₂²×C₂₃	semidirect
652. #470	C₂²×C₂₃	semidirect
655. #468	C₂²×C₂₃	semidirect
656. #467	C₂²×C₂₃	semidirect
659. #465	C₂²×C₂₃	semidirect
664. #452	C₂²×C₂₃	semidirect
665. #452	C₂²×C₂₃	semidirect
666. #451	C₂²×C₂₃	semidirect
670. #448	C₂²×C₂₃	semidirect
671. C₄×Q₁₆	C₂²×C₂₃	semidirect
672. C₄×Q₁₆	C₂²×C₂₃	semidirect
675. C₄×SD₁₆	C₂²×C₂₃	semidirect
676. C₄×SD₁₆	C₂²×C₂₃	semidirect
678. #436	C₂²×C₂₃	semidirect
679. #436	C₂²×C₂₃	semidirect
681. C₈×D₄	C₂²×C₂₃	semidirect
682. C₈×D₄	C₂²×C₂₃	semidirect
683. #431	C₂²×C₂₃	semidirect
684. #431	C₂²×C₂₃	semidirect
685. #428	C₂²×C₂₃	semidirect
686. #428	C₂²×C₂₃	semidirect
687. #427	C₂²×C₂₃	semidirect
688. C₂×#106	C₂²×C₂₃	semidirect
690. #417	C₂²×C₂₃	semidirect
691. #416	C₂²×C₂₃	semidirect
693. #408	C₂²×C₂₃	semidirect
694. #408	C₂²×C₂₃	semidirect
880. C₂₃	#61786	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×#3546	2
C₂₃×#3507	2
C₂₃×#3356	2
C₂₃×#3353	2
C₂₃×#3351	2
C₂₃×#3342	2
C₂₃×#3337	2
C₂₃×#3335	2
C₂₃×#3333	2
C₂₃×#3324	2
C₂₃×#3323	2
C₂₃×#3304	2
C₂₃×#3296	2
C₂₃×#3295	2
C₂₃×#3233	2
C₂₃×#3228	2
C₂₃×#3201	2
C₂₃×#3200	2
C₂₃×#3108	2
C₂₃×#3103	2
C₂₃×#3099	2
C₂₃×#3096	2
C₂₃×#2979	2
#61786	23

Subgroups — C23×#61786 #19209412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61786 #19209412