Subgroups — C₂₃×#61440 #19209066

Order 5888.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3480	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3346	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3320	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3316	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3270	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3172	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3108	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3107	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×#137	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#137	C₂²	1	2	yes	—
25	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#559	—	2	1	no	—
27	C₂₃×#559	C₂²	1	1	yes	characteristic
28	Q₈²×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#557	—	2	1	no	—
30	C₂₃×#557	C₂²	1	1	yes	characteristic
31	C₂₃×#557	C₂²	1	1	yes	characteristic
32	C₂₃×#556	—	2	1	no	—
33	C₂₃×#556	C₂²	1	1	yes	characteristic
34	C₂₃×#554	—	2	2	no	—
35	C₂₃×#554	—	2	1	no	—
36	C₂₃×#554	C₂²	1	2	yes	—
37	C₂₃×#554	C₂²	1	1	yes	characteristic
38	C₂₃×#553	—	2	2	no	—
39	C₂₃×#553	C₂²	1	2	yes	—
40	C₂₃×#550	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
42	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
43	C₂₃×#548	C₂²	1	2	yes	—
44	C₂₃×#533	—	2	1	no	—
45	C₂₃×#533	—	2	2	no	—
46	C₂₃×#533	C₂²	1	1	yes	characteristic
47	C₂₃×#533	C₂²	1	2	yes	—
48	C₂₃×#532	—	2	1	no	—
49	C₂₃×#532	C₂²	1	1	yes	characteristic
50	C₂₃×#529	—	2	2	no	—
51	C₂₃×#529	C₂²	1	2	yes	—
52	C₄×#41×C₂₃	—	2	1	no	—
53	C₄×#41×C₂₃	—	2	1	no	—
54	C₄×#41×C₂₃	C₂²	1	2	yes	—
55	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
59	C₂₃×#501	C₂²	1	2	yes	—
60	C₂₃×#498	C₂²	1	1	yes	characteristic
61	C₂₃×#497	C₂²	1	2	yes	—
62	C₂₃×#492	C₂²	1	1	yes	characteristic
63	C₂₃×#491	C₂²	1	2	yes	—
64	C₂₃×#489	C₂²	1	2	yes	—
65	C₂₃×#487	C₂²	1	1	yes	characteristic
66	C₂₃×#486	C₂²	1	1	yes	characteristic
67	C₂₃×#485	C₂²	1	2	yes	—
68	C₂₃×#485	C₂²	1	2	yes	—
69	C₂₃×#484	C₂²	1	2	yes	—
70	C₂₃×#483	C₂²	1	2	yes	—
71	C₂₃×#481	C₂²	1	2	yes	—
72	C₂₃×#480	C₂²	1	2	yes	—
73	C₂₃×#479	C₂²	1	2	yes	—
74	C₂₃×#479	C₂²	1	2	yes	—
75	C₂₃×#477	C₂²	1	1	yes	characteristic
76	C₂₃×#477	C₂²	1	1	yes	characteristic
77	C₂₃×#475	C₂²	1	2	yes	—
78	C₂₃×#475	C₂²	1	1	yes	characteristic
79	C₂₃×#475	C₂²	1	1	yes	characteristic
80	C₂₃×#474	C₂²	1	2	yes	—
81	C₂₃×#470	C₂²	1	2	yes	—
82	C₂₃×#470	C₂²	1	2	yes	—
83	C₂₃×#468	C₂²	1	2	yes	—
84	C₂₃×#468	C₂²	1	2	yes	—
85	C₂₃×#465	C₂²	1	2	yes	—
86	C₂₃×#465	C₂²	1	2	yes	—
87	C₂₃×#464	C₂²	1	2	yes	—
88	C₂₃×#464	C₂²	1	2	yes	—
89	C₂₃×#462	C₂²	1	2	yes	—
90	C₂₃×#462	C₂²	1	1	yes	characteristic
91	C₂₃×#462	C₂²	1	1	yes	characteristic
92	C₂₃×#461	C₂²	1	2	yes	—
93	C₂₃×#460	C₂²	1	1	yes	characteristic
94	C₂₃×#460	C₂²	1	1	yes	characteristic
95	C₂₃×#452	C₂²	1	2	yes	—
96	C₂₃×#452	C₂²	1	2	yes	—
97	C₂₃×#451	C₂²	1	2	yes	—
98	C₂₃×#451	C₂²	1	2	yes	—
99	C₂₃×#448	C₂²	1	2	yes	—
100	C₂₃×#448	C₂²	1	2	yes	—
101	C₂₃×#446	C₂²	1	1	yes	characteristic
102	C₂₃×#446	C₂²	1	1	yes	characteristic
103	C₂₃×#441	C₂²	1	2	yes	—
104	C₂₃×#441	C₂²	1	2	yes	—
105	C₂₃×#440	C₂²	1	2	yes	—
106	C₂₃×#440	C₂²	1	2	yes	—
107	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
108	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
109	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
113	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
120	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
121	C₂₃×#436	C₂²	1	1	yes	characteristic
122	C₂₃×#436	C₂²	1	1	yes	characteristic
123	C₂₃×#435	C₂²	1	2	yes	—
124	C₂₃×#435	C₂²	1	2	yes	—
125	C₂₃×#431	C₂²	1	1	yes	characteristic
126	C₂₃×#431	C₂²	1	2	yes	—
127	C₂₃×#428	C₂²	1	2	yes	—
128	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
129	C₂₃×#419	C₂²	1	2	yes	—
130	C₂₃×#417	C₂²	1	2	yes	—
131	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
132	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
141	C₂₃×#137	—	2	8	no	—
142	C₂×Q₁₆×C₂₃	—	2	4	no	—
143	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
157	C₂₃×C₄⋊Q₈	—	2	1	no	—
158	C₂₃×C₄⋊Q₈	—	2	1	no	—
159	C₂₃×C₄⋊Q₈	—	2	2	no	—
160	C₂₃×C₄⋊Q₈	—	2	1	no	—
161	C₂₃×C₄⋊Q₈	—	2	2	no	—
162	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₂₃×#127	—	2	1	no	—
168	C₂₃×#127	C₂³	1	1	yes	characteristic
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#126	—	2	2	no	—
172	C₂₃×#125	—	2	2	no	—
173	C₂₃×#125	—	2	1	no	—
174	C₂₃×#125	—	2	2	no	—
175	C₂₃×#125	—	2	1	no	—
176	C₂₃×#125	—	2	2	no	—
177	C₂₃×#125	—	2	2	no	—
178	C₂₃×#125	—	2	1	no	—
179	C₂₃×#125	C₂³	1	2	yes	—
180	C₂₃×#124	—	2	1	no	—
181	C₂₃×#124	—	2	1	no	—
182	C₂₃×#124	—	2	2	no	—
183	C₂₃×#124	—	2	1	no	—
184	C₂₃×#124	C₂³	1	2	yes	—
185	C₂₃×#123	—	2	2	no	—
186	C₂₃×#123	—	2	2	no	—
187	C₂₃×#123	—	2	2	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	—	2	2	no	—
195	C₂₃×C₂²⋊Q₈	—	2	2	no	—
196	C₂₃×C₂²⋊Q₈	—	2	2	no	—
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×#121	—	2	2	no	—
202	C₂₃×#121	—	2	2	no	—
203	C₂₃×#121	—	2	1	no	—
204	C₂₃×#121	—	2	2	no	—
205	C₂₃×#121	C₂³	1	2	yes	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₄×Q₈×C₂₃	—	2	1	no	—
208	C₄×Q₈×C₂₃	—	2	1	no	—
209	C₄×Q₈×C₂₃	—	2	1	no	—
210	C₄×Q₈×C₂₃	—	2	1	no	—
211	C₄×Q₈×C₂₃	—	2	2	no	—
212	C₄×Q₈×C₂₃	—	2	1	no	—
213	C₄×Q₈×C₂₃	—	2	1	no	—
214	C₄×Q₈×C₂₃	—	2	1	no	—
215	C₄×Q₈×C₂₃	—	2	2	no	—
216	C₄×Q₈×C₂₃	—	2	1	no	—
217	C₄×Q₈×C₂₃	—	2	2	no	—
218	C₄×Q₈×C₂₃	—	2	1	no	—
219	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
220	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
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×D₄×C₂₃	—	2	2	no	—
234	C₄×D₄×C₂₃	—	2	1	no	—
235	C₄×D₄×C₂₃	—	2	2	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	2	no	—
244	C₄×D₄×C₂₃	—	2	1	no	—
245	C₄×D₄×C₂₃	D₄	1	2	yes	—
246	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
247	C₄×D₄×C₂₃	C₂³	1	2	yes	—
248	C₄×D₄×C₂₃	C₂³	1	2	yes	—
249	C₄×D₄×C₂₃	C₂³	1	2	yes	—
250	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
251	C₂₃×#117	—	2	2	no	—
252	C₂₃×#117	—	2	1	no	—
253	C₂₃×#117	—	2	2	no	—
254	C₂₃×#117	—	2	2	no	—
255	C₂₃×#117	D₄	1	1	yes	characteristic
256	C₂₃×#117	D₄	1	2	yes	—
257	C₂₃×#117	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
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	2	yes	—
264	C₂×C₄²×C₂₃	—	2	1	no	—
265	C₂×C₄²×C₂₃	—	2	2	no	—
266	C₂×C₄²×C₂₃	—	2	1	no	—
267	C₂×C₄²×C₂₃	—	2	2	no	—
268	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
270	C₂₃×#107	C₂³	1	1	yes	characteristic
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	2	yes	—
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×C₄⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂₃×#103	C₂³	1	1	yes	characteristic
285	C₂₃×#103	C₂³	1	1	yes	characteristic
286	C₂₃×#103	C₂³	1	1	yes	characteristic
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	1	yes	characteristic
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#103	C₂³	1	1	yes	characteristic
291	C₂₃×#103	C₂³	1	1	yes	characteristic
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#103	C₂³	1	2	yes	—
296	C₂₃×#103	C₂³	1	2	yes	—
297	C₂₃×#103	C₂³	1	2	yes	—
298	C₂₃×#103	C₂³	1	2	yes	—
299	C₂₃×#103	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×#97	C₂³	1	2	yes	—
308	C₂₃×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₂₃	C₂³	1	2	yes	—
314	#41×C₂₃	—	2	4	no	—
315	#41×C₂₃	—	2	4	no	—
316	#41×C₂₃	—	4	2	no	—
317	#41×C₂₃	—	4	4	no	—
318	C₂×Q₈×C₂₃	—	2	1	no	—
319	C₂×Q₈×C₂₃	—	2	2	no	—
320	C₂×Q₈×C₂₃	—	2	1	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	2	2	no	—
323	C₂×Q₈×C₂₃	—	2	1	no	—
324	C₂×Q₈×C₂₃	—	2	2	no	—
325	C₂×Q₈×C₂₃	—	2	2	no	—
326	C₂×Q₈×C₂₃	—	2	4	no	—
327	C₂×Q₈×C₂₃	—	4	1	no	—
328	C₂×Q₈×C₂₃	—	4	1	no	—
329	C₂×Q₈×C₂₃	—	4	2	no	—
330	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	—	2	2	no	—
339	C₂×D₄×C₂₃	—	2	1	no	—
340	C₂×D₄×C₂₃	—	2	1	no	—
341	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₂₃	—	2	1	no	—
345	C₂²×C₄×C₂₃	—	2	2	no	—
346	C₂²×C₄×C₂₃	—	2	1	no	—
347	C₂²×C₄×C₂₃	—	2	1	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	2	1	no	—
350	C₂²×C₄×C₂₃	—	2	2	no	—
351	C₂²×C₄×C₂₃	—	2	2	no	—
352	C₂²×C₄×C₂₃	—	2	2	no	—
353	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
354	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
359	Q₁₆×C₂₃	—	2	2	no	—
360	Q₁₆×C₂₃	—	2	2	no	—
361	Q₁₆×C₂₃	—	2	4	no	—
362	Q₁₆×C₂₃	—	2	2	no	—
363	Q₁₆×C₂₃	—	4	2	no	—
364	Q₁₆×C₂₃	#41	1	4	yes	complemented
365	SD₁₆×C₂₃	—	2	4	no	—
366	SD₁₆×C₂₃	—	2	4	no	—
367	SD₁₆×C₂₃	—	4	2	no	—
368	SD₁₆×C₂₃	—	4	2	no	—
369	M₁₆×C₂₃	—	2	4	no	—
370	M₁₆×C₂₃	—	4	2	no	—
371	C₂×C₈×C₂₃	—	2	2	no	—
372	C₂×C₈×C₂₃	—	4	1	no	—
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	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
377	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
379	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	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	2	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	1	no	—
389	C₄⋊C₄×C₂₃	—	2	1	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	2	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	1	no	—
399	C₄⋊C₄×C₂₃	—	2	2	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	1	no	—
404	C₄⋊C₄×C₂₃	—	2	2	no	—
405	C₄⋊C₄×C₂₃	—	2	2	no	—
406	C₄⋊C₄×C₂₃	—	2	2	no	—
407	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₂₃	C₂×D₄	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	1	yes	characteristic
414	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	2	no	—
420	C₂²⋊C₄×C₂₃	—	2	2	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	2	no	—
423	C₂²⋊C₄×C₂₃	—	2	2	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	2	no	—
428	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
431	C₄²×C₂₃	—	2	2	no	—
432	C₄²×C₂₃	—	2	2	no	—
433	C₄²×C₂₃	—	2	1	no	—
434	C₄²×C₂₃	—	2	2	no	—
435	C₄²×C₂₃	—	2	1	no	—
436	C₄²×C₂₃	—	2	1	no	—
437	C₄²×C₂₃	—	2	2	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	1	no	—
440	C₄²×C₂₃	—	2	1	no	—
441	C₄²×C₂₃	—	2	1	no	—
442	C₄²×C₂₃	—	2	2	no	—
443	C₄²×C₂₃	—	2	1	no	—
444	C₄²×C₂₃	C₂×D₄	1	2	yes	—
445	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₂₃	C₂×D₄	1	2	yes	—
447	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₂₃	C₂⁴	1	2	yes	—
449	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
451	#61440	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂³×C₂₃	—	2	2	no	—
453	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
454	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
455	Q₈×C₂₃	—	2	2	no	—
456	Q₈×C₂₃	—	2	1	no	—
457	Q₈×C₂₃	—	2	1	no	—
458	Q₈×C₂₃	—	2	2	no	—
459	Q₈×C₂₃	—	2	1	no	—
460	Q₈×C₂₃	—	2	1	no	—
461	Q₈×C₂₃	—	2	1	no	—
462	Q₈×C₂₃	—	2	2	no	—
463	Q₈×C₂₃	—	2	1	no	—
464	Q₈×C₂₃	—	4	4	no	—
465	Q₈×C₂₃	—	4	2	no	—
466	Q₈×C₂₃	—	4	2	no	—
467	Q₈×C₂₃	—	4	2	no	—
468	Q₈×C₂₃	—	8	2	no	—
469	Q₈×C₂₃	—	8	1	no	—
470	Q₈×C₂₃	C₂×#41	1	2	yes	—
471	Q₈×C₂₃	C₂×#41	1	2	yes	—
472	D₄×C₂₃	—	2	4	no	—
473	D₄×C₂₃	—	2	2	no	—
474	D₄×C₂₃	—	2	2	no	—
475	D₄×C₂₃	—	2	2	no	—
476	D₄×C₂₃	—	4	4	no	—
477	D₄×C₂₃	—	4	4	no	—
478	D₄×C₂₃	—	4	2	no	—
479	D₄×C₂₃	—	8	1	no	—
480	D₄×C₂₃	—	8	2	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	2	1	no	—
483	C₂×C₄×C₂₃	—	2	4	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	2	no	—
488	C₂×C₄×C₂₃	—	2	1	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	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	1	no	—
495	C₂×C₄×C₂₃	—	2	2	no	—
496	C₂×C₄×C₂₃	—	2	1	no	—
497	C₂×C₄×C₂₃	—	4	2	no	—
498	C₂×C₄×C₂₃	—	4	1	no	—
499	C₂×C₄×C₂₃	—	4	4	no	—
500	C₂×C₄×C₂₃	—	4	2	no	—
501	C₂×C₄×C₂₃	—	4	2	no	—
502	C₂×C₄×C₂₃	—	4	4	no	—
503	C₂×C₄×C₂₃	—	4	4	no	—
504	C₂×C₄×C₂₃	—	8	2	no	—
505	C₂×C₄×C₂₃	—	8	1	no	—
506	C₂×C₄×C₂₃	—	8	1	no	—
507	C₂×C₄×C₂₃	—	8	2	no	—
508	C₂×C₄×C₂₃	#137	1	4	yes	complemented
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	2	yes	—
512	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
518	C₈×C₂₃	—	2	1	no	—
519	C₈×C₂₃	—	2	2	no	—
520	C₈×C₂₃	—	2	1	no	—
521	C₈×C₂₃	—	2	1	no	—
522	C₈×C₂₃	—	2	2	no	—
523	C₈×C₂₃	C₂×#41	1	2	yes	—
524	#3480	C₂×C₂₃	1	1	yes	characteristic
525	Q₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
526	#3400	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#3387	C₂×C₂₃	1	1	yes	characteristic, complemented
528	#3375	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3374	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3356	C₂×C₂₃	1	1	yes	characteristic, complemented
531	#3346	C₂×C₂₃	1	2	yes	complemented
532	#3333	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3328	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3320	C₂×C₂₃	1	2	yes	complemented
535	#3316	C₂×C₂₃	1	2	yes	complemented
536	#3278	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3270	C₂×C₂₃	1	2	yes	complemented
538	#3172	C₂×C₂₃	1	2	yes	complemented
539	#3167	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3108	C₂×C₂₃	1	2	yes	complemented
541	#3107	C₂×C₂₃	1	2	yes	complemented
542	#3104	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#3103	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
545	C₄×#137	C₂×C₂₃	1	2	yes	complemented
546	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
547	C₂²×C₂₃	—	2	1	no	—
548	C₂²×C₂₃	—	2	1	no	—
549	C₂²×C₂₃	—	2	2	no	—
550	C₂²×C₂₃	—	2	2	no	—
551	C₂²×C₂₃	—	2	2	no	—
552	C₂²×C₂₃	—	4	2	no	—
553	C₂²×C₂₃	—	4	2	no	—
554	C₂²×C₂₃	—	4	2	no	—
555	C₂²×C₂₃	C₂×#137	1	2	yes	—
556	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
557	C₄×C₂₃	—	2	1	no	—
558	C₄×C₂₃	—	2	2	no	—
559	C₄×C₂₃	—	2	1	no	—
560	C₄×C₂₃	—	2	2	no	—
561	C₄×C₂₃	—	2	1	no	—
562	C₄×C₂₃	—	2	2	no	—
563	C₄×C₂₃	—	2	2	no	—
564	C₄×C₂₃	—	2	2	no	—
565	C₄×C₂₃	—	4	1	no	—
566	C₄×C₂₃	—	4	1	no	—
567	C₄×C₂₃	—	4	1	no	—
568	C₄×C₂₃	—	4	1	no	—
569	C₄×C₂₃	—	4	2	no	—
570	C₄×C₂₃	—	4	1	no	—
571	C₄×C₂₃	—	4	2	no	—
572	C₄×C₂₃	—	4	1	no	—
573	C₄×C₂₃	—	4	2	no	—
574	C₄×C₂₃	C₂×#137	1	2	yes	—
575	C₄×C₂₃	C₂×#137	1	2	yes	—
576	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
577	C₄×C₂₃	#585	1	1	yes	characteristic
578	C₂×#137	C₂²×C₂₃	1	2	yes	—
579	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
580	#559	—	2	1	no	—
581	#559	C₂²×C₂₃	1	1	yes	characteristic
582	Q₈²	C₂²×C₂₃	1	1	yes	characteristic
583	#557	—	2	1	no	—
584	#557	C₂²×C₂₃	1	1	yes	characteristic
585	#557	C₂²×C₂₃	1	1	yes	characteristic
586	#556	—	2	1	no	—
587	#556	C₂²×C₂₃	1	1	yes	characteristic
588	#554	—	2	2	no	—
589	#554	—	2	1	no	—
590	#554	C₂²×C₂₃	1	1	yes	characteristic
591	#554	C₂²×C₂₃	1	2	yes	—
592	#553	—	2	2	no	—
593	#553	C₂²×C₂₃	1	2	yes	—
594	#550	C₂²×C₂₃	1	1	yes	characteristic
595	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
596	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
597	#548	C₂²×C₂₃	1	2	yes	—
598	#533	—	2	1	no	—
599	#533	—	2	2	no	—
600	#533	C₂²×C₂₃	1	1	yes	characteristic
601	#533	C₂²×C₂₃	1	2	yes	—
602	#532	—	2	1	no	—
603	#532	C₂²×C₂₃	1	1	yes	characteristic
604	#529	—	2	2	no	—
605	#529	C₂²×C₂₃	1	2	yes	—
606	C₄×#41	—	2	1	no	—
607	C₄×#41	—	2	1	no	—
608	C₄×#41	C₂²×C₂₃	1	2	yes	—
609	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
610	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
611	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
612	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
613	#501	C₂²×C₂₃	1	2	yes	—
614	#498	C₂²×C₂₃	1	1	yes	characteristic
615	#497	C₂²×C₂₃	1	2	yes	—
616	#492	C₂²×C₂₃	1	1	yes	characteristic
617	#491	C₂²×C₂₃	1	2	yes	—
618	#489	C₂²×C₂₃	1	2	yes	—
619	#487	C₂²×C₂₃	1	1	yes	characteristic
620	#486	C₂²×C₂₃	1	1	yes	characteristic
621	#485	C₂²×C₂₃	1	2	yes	—
622	#485	C₂²×C₂₃	1	2	yes	—
623	#484	C₂²×C₂₃	1	2	yes	—
624	#483	C₂²×C₂₃	1	2	yes	—
625	#481	C₂²×C₂₃	1	2	yes	—
626	#480	C₂²×C₂₃	1	2	yes	—
627	#479	C₂²×C₂₃	1	2	yes	—
628	#479	C₂²×C₂₃	1	2	yes	—
629	#477	C₂²×C₂₃	1	1	yes	characteristic
630	#477	C₂²×C₂₃	1	1	yes	characteristic
631	#475	C₂²×C₂₃	1	1	yes	characteristic
632	#475	C₂²×C₂₃	1	1	yes	characteristic
633	#475	C₂²×C₂₃	1	2	yes	—
634	#474	C₂²×C₂₃	1	2	yes	—
635	#470	C₂²×C₂₃	1	2	yes	—
636	#470	C₂²×C₂₃	1	2	yes	—
637	#468	C₂²×C₂₃	1	2	yes	—
638	#468	C₂²×C₂₃	1	2	yes	—
639	#465	C₂²×C₂₃	1	2	yes	—
640	#465	C₂²×C₂₃	1	2	yes	—
641	#464	C₂²×C₂₃	1	2	yes	—
642	#464	C₂²×C₂₃	1	2	yes	—
643	#462	C₂²×C₂₃	1	1	yes	characteristic
644	#462	C₂²×C₂₃	1	1	yes	characteristic
645	#462	C₂²×C₂₃	1	2	yes	—
646	#461	C₂²×C₂₃	1	2	yes	—
647	#460	C₂²×C₂₃	1	1	yes	characteristic
648	#460	C₂²×C₂₃	1	1	yes	characteristic
649	#452	C₂²×C₂₃	1	2	yes	—
650	#452	C₂²×C₂₃	1	2	yes	—
651	#451	C₂²×C₂₃	1	2	yes	—
652	#451	C₂²×C₂₃	1	2	yes	—
653	#448	C₂²×C₂₃	1	2	yes	—
654	#448	C₂²×C₂₃	1	2	yes	—
655	#446	C₂²×C₂₃	1	1	yes	characteristic
656	#446	C₂²×C₂₃	1	1	yes	characteristic
657	#441	C₂²×C₂₃	1	2	yes	—
658	#441	C₂²×C₂₃	1	2	yes	—
659	#440	C₂²×C₂₃	1	2	yes	—
660	#440	C₂²×C₂₃	1	2	yes	—
661	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
662	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
663	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
664	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
665	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
666	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
667	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
668	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
669	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
670	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
672	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
673	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
674	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
675	#436	C₂²×C₂₃	1	1	yes	characteristic
676	#436	C₂²×C₂₃	1	1	yes	characteristic
677	#435	C₂²×C₂₃	1	2	yes	—
678	#435	C₂²×C₂₃	1	2	yes	—
679	#431	C₂²×C₂₃	1	1	yes	characteristic
680	#431	C₂²×C₂₃	1	2	yes	—
681	#428	C₂²×C₂₃	1	2	yes	—
682	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
683	#419	C₂²×C₂₃	1	2	yes	—
684	#417	C₂²×C₂₃	1	2	yes	—
685	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
686	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
687	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
688	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
689	C₂×C₂₃	—	2	2	no	—
690	C₂×C₂₃	—	4	2	no	—
691	C₂×C₂₃	—	8	2	no	—
692	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
693	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
694	C₂×C₂₃	#3584	1	1	yes	characteristic
695	C₂×#41	—	2	1	no	—
696	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
697	C₂×#41	C₂³×C₂₃	1	2	yes	—
698	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
699	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
700	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
701	#137	—	2	8	no	—
702	C₂×Q₁₆	—	2	4	no	—
703	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
704	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
705	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
706	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
707	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
708	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
711	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
713	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
714	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
715	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
716	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	—	2	2	no	—
720	C₄⋊Q₈	—	2	1	no	—
721	C₄⋊Q₈	—	2	2	no	—
722	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
726	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
727	#127	—	2	1	no	—
728	#127	C₂³×C₂₃	1	1	yes	characteristic
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	—	2	1	no	—
734	#125	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	C₂³×C₂₃	1	2	yes	—
740	#124	—	2	1	no	—
741	#124	—	2	1	no	—
742	#124	—	2	2	no	—
743	#124	—	2	1	no	—
744	#124	C₂³×C₂₃	1	2	yes	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	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	C₂³×C₂₃	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
761	#121	—	2	2	no	—
762	#121	—	2	2	no	—
763	#121	—	2	1	no	—
764	#121	—	2	2	no	—
765	#121	C₂³×C₂₃	1	2	yes	—
766	#121	C₂³×C₂₃	1	2	yes	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	2	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	2	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
787	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
790	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
792	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	D₄×C₂₃	1	2	yes	—
806	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₂₃	1	2	yes	—
808	C₄×D₄	C₂³×C₂₃	1	2	yes	—
809	C₄×D₄	C₂³×C₂₃	1	2	yes	—
810	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
811	#117	—	2	2	no	—
812	#117	—	2	1	no	—
813	#117	—	2	2	no	—
814	#117	—	2	2	no	—
815	#117	D₄×C₂₃	1	1	yes	characteristic
816	#117	D₄×C₂₃	1	2	yes	—
817	#117	C₂³×C₂₃	1	2	yes	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	—	2	2	no	—
821	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
822	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
823	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
824	C₂×C₄²	—	2	1	no	—
825	C₂×C₄²	—	2	2	no	—
826	C₂×C₄²	—	2	1	no	—
827	C₂×C₄²	—	2	2	no	—
828	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
829	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
830	#107	C₂³×C₂₃	1	1	yes	characteristic
831	#107	C₂³×C₂₃	1	1	yes	characteristic
832	#107	C₂³×C₂₃	1	1	yes	characteristic
833	#107	C₂³×C₂₃	1	1	yes	characteristic
834	#107	C₂³×C₂₃	1	2	yes	—
835	#107	C₂³×C₂₃	1	2	yes	—
836	#106	C₂³×C₂₃	1	2	yes	—
837	#106	C₂³×C₂₃	1	2	yes	—
838	#106	C₂³×C₂₃	1	2	yes	—
839	#106	C₂³×C₂₃	1	2	yes	—
840	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
841	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
842	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
844	#103	C₂³×C₂₃	1	1	yes	characteristic
845	#103	C₂³×C₂₃	1	1	yes	characteristic
846	#103	C₂³×C₂₃	1	1	yes	characteristic
847	#103	C₂³×C₂₃	1	1	yes	characteristic
848	#103	C₂³×C₂₃	1	1	yes	characteristic
849	#103	C₂³×C₂₃	1	1	yes	characteristic
850	#103	C₂³×C₂₃	1	1	yes	characteristic
851	#103	C₂³×C₂₃	1	1	yes	characteristic
852	#103	C₂³×C₂₃	1	2	yes	—
853	#103	C₂³×C₂₃	1	2	yes	—
854	#103	C₂³×C₂₃	1	2	yes	—
855	#103	C₂³×C₂₃	1	2	yes	—
856	#103	C₂³×C₂₃	1	2	yes	—
857	#103	C₂³×C₂₃	1	2	yes	—
858	#103	C₂³×C₂₃	1	2	yes	—
859	#103	C₂³×C₂₃	1	2	yes	—
860	#102	C₂³×C₂₃	1	2	yes	—
861	#102	C₂³×C₂₃	1	2	yes	—
862	#102	C₂³×C₂₃	1	2	yes	—
863	#102	C₂³×C₂₃	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
867	#97	C₂³×C₂₃	1	2	yes	—
868	#97	C₂³×C₂₃	1	2	yes	—
869	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₂₃	1	2	yes	—
874	C₂₃	#61440	1	1	yes	characteristic, direct product factor, Sylow
875	#41	—	2	4	no	—
876	#41	—	2	4	no	—
877	#41	—	4	2	no	—
878	#41	—	4	4	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	2	4	no	—
888	C₂×Q₈	—	4	1	no	—
889	C₂×Q₈	—	4	1	no	—
890	C₂×Q₈	—	4	2	no	—
891	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
893	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
894	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
903	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
904	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
915	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
916	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
917	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
920	Q₁₆	—	2	2	no	—
921	Q₁₆	—	2	2	no	—
922	Q₁₆	—	2	4	no	—
923	Q₁₆	—	2	2	no	—
924	Q₁₆	—	4	2	no	—
925	Q₁₆	#41×C₂₃	1	4	yes	complemented
926	SD₁₆	—	2	4	no	—
927	SD₁₆	—	2	4	no	—
928	SD₁₆	—	4	2	no	—
929	SD₁₆	—	4	2	no	—
930	M₁₆	—	2	4	no	—
931	M₁₆	—	4	2	no	—
932	C₂×C₈	—	2	2	no	—
933	C₂×C₈	—	4	1	no	—
934	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
938	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
939	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	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	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	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	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
978	C₂²⋊C₄	—	2	2	no	—
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	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
990	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1006	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1007	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1008	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1011	C₄²	C₂⁴×C₂₃	1	2	yes	—
1012	C₂³	—	2	2	no	—
1013	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1014	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	4	4	no	—
1025	Q₈	—	4	2	no	—
1026	Q₈	—	4	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	2	no	—
1029	Q₈	—	8	1	no	—
1030	Q₈	C₂×#41×C₂₃	1	2	yes	—
1031	Q₈	C₂×#41×C₂₃	1	2	yes	—
1032	D₄	—	2	4	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	4	4	no	—
1037	D₄	—	4	4	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	8	1	no	—
1040	D₄	—	8	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	4	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	4	no	—
1063	C₂×C₄	—	4	4	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	1	no	—
1066	C₂×C₄	—	8	1	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	C₂₃×#137	1	4	yes	complemented
1069	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1077	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1078	C₈	—	2	1	no	—
1079	C₈	—	2	2	no	—
1080	C₈	—	2	1	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	2	no	—
1083	C₈	C₂×#41×C₂₃	1	2	yes	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	C₂×C₂₃×#137	1	2	yes	—
1093	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1094	C₄	—	2	2	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	C₂×C₂₃×#137	1	2	yes	—
1112	C₄	C₂×C₂₃×#137	1	2	yes	—
1113	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1114	C₄	C₂₃×#585	1	1	yes	characteristic
1115	C₂	—	2	2	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	8	2	no	—
1118	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
1119	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
1120	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
prime radical	C₂₃×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×#41×C₂₃	C₂	semidirect
3. C₂₃×#3400	C₂	semidirect
4. C₂₃×#3387	C₂	semidirect
5. C₂₃×#3375	C₂	semidirect
6. C₂₃×#3374	C₂	semidirect
7. C₂₃×#3356	C₂	semidirect
8. C₂₃×#3346	C₂	semidirect
9. C₂₃×#3333	C₂	semidirect
10. C₂₃×#3328	C₂	semidirect
11. C₂₃×#3320	C₂	semidirect
12. C₂₃×#3316	C₂	semidirect
13. C₂₃×#3278	C₂	semidirect
14. C₂₃×#3270	C₂	semidirect
15. C₂₃×#3172	C₂	semidirect
16. C₂₃×#3167	C₂	semidirect
17. C₂₃×#3108	C₂	semidirect
18. C₂₃×#3107	C₂	semidirect
19. C₂₃×#3104	C₂	semidirect
20. C₂₃×#3103	C₂	semidirect
21. C₂₃×#2965	C₂	semidirect
22. C₄×C₂₃×#137	C₂	semidirect
23. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
364. Q₁₆×C₂₃	#41	semidirect
451. #61440	C₂₃	direct (N × H)
508. C₂×C₄×C₂₃	#137	semidirect
525. Q₈×#41	C₂×C₂₃	semidirect
526. #3400	C₂×C₂₃	semidirect
527. #3387	C₂×C₂₃	semidirect
528. #3375	C₂×C₂₃	semidirect
529. #3374	C₂×C₂₃	semidirect
530. #3356	C₂×C₂₃	semidirect
531. #3346	C₂×C₂₃	semidirect
532. #3333	C₂×C₂₃	semidirect
533. #3328	C₂×C₂₃	semidirect
534. #3320	C₂×C₂₃	semidirect
535. #3316	C₂×C₂₃	semidirect
536. #3278	C₂×C₂₃	semidirect
537. #3270	C₂×C₂₃	semidirect
538. #3172	C₂×C₂₃	semidirect
539. #3167	C₂×C₂₃	semidirect
540. #3108	C₂×C₂₃	semidirect
541. #3107	C₂×C₂₃	semidirect
542. #3104	C₂×C₂₃	semidirect
543. #3103	C₂×C₂₃	semidirect
544. #2965	C₂×C₂₃	semidirect
545. C₄×#137	C₂×C₂₃	semidirect
546. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
874. C₂₃	#61440	direct (N × H)
925. Q₁₆	#41×C₂₃	semidirect
1068. C₂×C₄	C₂₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3480	2
Q₈×#41×C₂₃	2
C₂₃×#3400	2
C₂₃×#3387	2
C₂₃×#3375	2
C₂₃×#3374	2
C₂₃×#3356	2
C₂₃×#3346	2
C₂₃×#3333	2
C₂₃×#3328	2
C₂₃×#3320	2
C₂₃×#3316	2
C₂₃×#3278	2
C₂₃×#3270	2
C₂₃×#3172	2
C₂₃×#3167	2
C₂₃×#3108	2
C₂₃×#3107	2
C₂₃×#3104	2
C₂₃×#3103	2
C₂₃×#2965	2
C₄×C₂₃×#137	2
C₂×C₄×Q₁₆×C₂₃	2
#61440	23

Subgroups — C23×#61440 #19209066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61440 #19209066