Subgroups — C₂₃×#36697 #19184323

Order 5888.

1484 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2843	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2839	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2838	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2837	C₂	1	2	yes	maximal
5	C₂₃×#2836	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2833	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2832	C₂	1	1	yes	maximal, characteristic
8	C₂₃×#2831	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2823	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#2821	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2402	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2401	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2398	C₂	1	1	yes	maximal, characteristic
15	C₂₃×#2396	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2396	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2395	C₂	1	2	yes	maximal
18	C₄×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₂₃×#126	C₂	1	2	yes	maximal, complemented
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#126	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#117	C₂²	1	2	yes	—
27	C₂₃×#401	C₂²	1	2	yes	—
28	C₂₃×#400	C₂²	1	1	yes	characteristic
29	C₂₃×#400	C₂²	1	1	yes	characteristic
30	C₂₃×#400	C₂²	1	2	yes	—
31	C₂₃×#400	C₂²	1	2	yes	—
32	C₂₃×#400	C₂²	1	2	yes	—
33	C₂₃×#400	C₂²	1	2	yes	—
34	C₂₃×#400	C₂²	1	2	yes	—
35	C₂₃×#400	C₂²	1	2	yes	—
36	C₂₃×#400	C₂²	1	2	yes	—
37	C₂₃×#400	C₂²	1	2	yes	—
38	C₂₃×#400	C₂²	1	2	yes	—
39	C₂₃×#400	C₂²	1	2	yes	—
40	C₂₃×#399	C₂²	1	2	yes	—
41	C₂₃×#399	C₂²	1	2	yes	—
42	C₂₃×#399	C₂²	1	2	yes	—
43	C₂₃×#398	C₂²	1	1	yes	characteristic
44	C₂₃×#398	C₂²	1	1	yes	characteristic
45	C₂₃×#398	C₂²	1	2	yes	—
46	C₂₃×#398	C₂²	1	2	yes	—
47	C₂₃×#398	C₂²	1	2	yes	—
48	C₂₃×#398	C₂²	1	2	yes	—
49	C₂₃×#398	C₂²	1	2	yes	—
50	C₂₃×#398	C₂²	1	2	yes	—
51	C₂₃×#398	C₂²	1	2	yes	—
52	C₂₃×#398	C₂²	1	2	yes	—
53	C₂₃×#398	C₂²	1	2	yes	—
54	C₂₃×#398	C₂²	1	2	yes	—
55	C₂₃×#397	C₂²	1	2	yes	—
56	C₂₃×#397	C₂²	1	2	yes	—
57	C₂₃×#397	C₂²	1	2	yes	—
58	C₂₃×#397	C₂²	1	2	yes	—
59	C₂₃×#397	C₂²	1	2	yes	—
60	C₂₃×#397	C₂²	1	2	yes	—
61	C₂₃×#397	C₂²	1	2	yes	—
62	C₂₃×#396	C₂²	1	2	yes	—
63	C₂₃×#396	C₂²	1	2	yes	—
64	C₂₃×#396	C₂²	1	2	yes	—
65	C₂₃×#396	C₂²	1	2	yes	—
66	C₂₃×#396	C₂²	1	2	yes	—
67	C₂₃×#395	C₂²	1	2	yes	—
68	C₂₃×#395	C₂²	1	1	yes	characteristic
69	C₂₃×#395	C₂²	1	1	yes	characteristic
70	C₂₃×#395	C₂²	1	2	yes	—
71	C₂₃×#395	C₂²	1	2	yes	—
72	C₂₃×#394	C₂²	1	1	yes	characteristic
73	C₂₃×#394	C₂²	1	1	yes	characteristic
74	C₂₃×#394	C₂²	1	2	yes	—
75	C₂₃×#394	C₂²	1	2	yes	—
76	C₂₃×#393	C₂²	1	2	yes	—
77	C₂₃×#393	C₂²	1	2	yes	—
78	C₂₃×#393	C₂²	1	2	yes	—
79	C₂₃×#391	C₂²	1	1	yes	characteristic
80	C₂₃×#391	C₂²	1	1	yes	characteristic
81	C₂₃×#389	C₂²	1	2	yes	—
82	C₂₃×#389	C₂²	1	2	yes	—
83	C₂₃×#388	C₂²	1	2	yes	—
84	C₂₃×#388	C₂²	1	2	yes	—
85	C₂₃×#388	C₂²	1	2	yes	—
86	C₂₃×#387	C₂²	1	2	yes	—
87	C₂₃×#387	C₂²	1	2	yes	—
88	C₂₃×#387	C₂²	1	2	yes	—
89	C₂₃×#384	C₂²	1	1	yes	characteristic
90	C₂₃×#383	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
104	C₂₃×#376	C₂²	1	1	yes	characteristic
105	C₂₃×#376	C₂²	1	1	yes	characteristic
106	C₄³×C₂₃	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
112	C₂₃×C₄⋊Q₈	—	2	4	no	—
113	C₂₃×#126	—	2	8	no	—
114	C₄×Q₈×C₂₃	—	4	2	no	—
115	C₄×Q₈×C₂₃	—	4	2	no	—
116	C₄×Q₈×C₂₃	—	4	2	no	—
117	C₄×D₄×C₂₃	—	4	2	no	—
118	C₂₃×#117	—	4	4	no	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
159	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
169	C₂₃×#95	C₂³	1	2	yes	—
170	C₂₃×#95	C₂³	1	1	yes	characteristic
171	C₂₃×#95	C₂³	1	1	yes	characteristic
172	C₂₃×#95	C₂³	1	1	yes	characteristic
173	C₂₃×#95	C₂³	1	2	yes	—
174	C₂₃×#95	C₂³	1	1	yes	characteristic
175	C₂₃×#95	C₂³	1	2	yes	—
176	C₂₃×#95	C₂³	1	2	yes	—
177	C₂₃×#95	C₂³	1	2	yes	—
178	C₂₃×#95	C₂³	1	2	yes	—
179	C₂₃×#95	C₂³	1	2	yes	—
180	C₂₃×#95	C₂³	1	2	yes	—
181	C₂₃×#95	C₂³	1	2	yes	—
182	C₂₃×#95	C₂³	1	2	yes	—
183	C₂₃×#95	C₂³	1	2	yes	—
184	C₂₃×#95	C₂³	1	2	yes	—
185	C₂₃×#95	C₂³	1	2	yes	—
186	C₂₃×#95	C₂³	1	2	yes	—
187	C₂₃×#95	C₂³	1	2	yes	—
188	C₂₃×#95	C₂³	1	2	yes	—
189	C₂₃×#95	C₂³	1	2	yes	—
190	C₂₃×#95	C₂³	1	2	yes	—
191	C₂₃×#95	C₂³	1	2	yes	—
192	C₂₃×#95	C₂³	1	2	yes	—
193	C₂₃×#95	C₂³	1	2	yes	—
194	C₂₃×#95	C₂³	1	2	yes	—
195	C₂₃×#95	C₂³	1	2	yes	—
196	C₂₃×#95	C₂³	1	2	yes	—
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
202	C₂×Q₈×C₂₃	—	2	2	no	—
203	C₂×Q₈×C₂₃	—	2	2	no	—
204	C₂×Q₈×C₂₃	—	4	1	no	—
205	C₂×Q₈×C₂₃	—	4	1	no	—
206	C₂×Q₈×C₂₃	—	4	1	no	—
207	C₂×Q₈×C₂₃	—	4	1	no	—
208	C₂×Q₈×C₂₃	—	4	1	no	—
209	C₂×Q₈×C₂₃	—	4	2	no	—
210	C₂×D₄×C₂₃	—	4	1	no	—
211	C₂×D₄×C₂₃	—	4	2	no	—
212	C₂²×C₄×C₂₃	—	2	4	no	—
213	C₂²×C₄×C₂₃	—	2	4	no	—
214	C₂²×C₄×C₂₃	—	2	4	no	—
215	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₄⋊C₄×C₂₃	—	2	4	no	—
234	C₄⋊C₄×C₂₃	—	2	4	no	—
235	C₄⋊C₄×C₂₃	—	2	4	no	—
236	C₄⋊C₄×C₂₃	—	2	4	no	—
237	C₄⋊C₄×C₂₃	—	2	4	no	—
238	C₄⋊C₄×C₂₃	—	4	2	no	—
239	C₄⋊C₄×C₂₃	—	4	2	no	—
240	C₄⋊C₄×C₂₃	—	4	2	no	—
241	C₄⋊C₄×C₂₃	—	4	2	no	—
242	C₄⋊C₄×C₂₃	—	4	2	no	—
243	C₄⋊C₄×C₂₃	—	4	2	no	—
244	C₄⋊C₄×C₂₃	—	4	2	no	—
245	C₄⋊C₄×C₂₃	—	4	2	no	—
246	C₄⋊C₄×C₂₃	—	4	2	no	—
247	C₄⋊C₄×C₂₃	—	4	2	no	—
248	C₄⋊C₄×C₂₃	—	4	2	no	—
249	C₄⋊C₄×C₂₃	—	4	2	no	—
250	C₄⋊C₄×C₂₃	—	4	2	no	—
251	C₄⋊C₄×C₂₃	—	4	1	no	—
252	C₄⋊C₄×C₂₃	—	4	1	no	—
253	C₄⋊C₄×C₂₃	—	4	1	no	—
254	C₄⋊C₄×C₂₃	—	4	1	no	—
255	C₄⋊C₄×C₂₃	—	4	1	no	—
256	C₄⋊C₄×C₂₃	—	4	2	no	—
257	C₄⋊C₄×C₂₃	—	4	2	no	—
258	C₄⋊C₄×C₂₃	—	4	1	no	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₂²⋊C₄×C₂₃	—	2	4	no	—
262	C₂²⋊C₄×C₂₃	—	4	2	no	—
263	C₂²⋊C₄×C₂₃	—	4	2	no	—
264	C₂²⋊C₄×C₂₃	—	4	2	no	—
265	C₂²⋊C₄×C₂₃	—	4	2	no	—
266	C₂²⋊C₄×C₂₃	—	4	2	no	—
267	C₂²⋊C₄×C₂₃	—	4	2	no	—
268	C₂²⋊C₄×C₂₃	—	4	2	no	—
269	C₂²⋊C₄×C₂₃	—	4	2	no	—
270	C₂²⋊C₄×C₂₃	—	4	2	no	—
271	C₂²⋊C₄×C₂₃	—	4	2	no	—
272	C₄²×C₂₃	—	2	4	no	—
273	C₄²×C₂₃	—	2	4	no	—
274	C₄²×C₂₃	—	2	2	no	—
275	C₄²×C₂₃	—	2	2	no	—
276	C₄²×C₂₃	—	2	2	no	—
277	C₄²×C₂₃	—	2	4	no	—
278	C₄²×C₂₃	—	2	4	no	—
279	C₄²×C₂₃	—	2	4	no	—
280	C₄²×C₂₃	—	4	2	no	—
281	C₄²×C₂₃	—	4	1	no	—
282	C₄²×C₂₃	#41	1	4	yes	—
283	#36697	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂³×C₂₃	—	2	2	no	—
285	C₂³×C₂₃	—	2	2	no	—
286	C₂³×C₂₃	—	2	2	no	—
287	C₂³×C₂₃	—	2	2	no	—
288	C₂³×C₂₃	—	2	2	no	—
289	C₂³×C₂₃	—	2	2	no	—
290	C₂³×C₂₃	—	2	2	no	—
291	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
292	Q₈×C₂₃	—	4	4	no	—
293	Q₈×C₂₃	—	4	4	no	—
294	Q₈×C₂₃	—	4	4	no	—
295	D₄×C₂₃	—	4	4	no	—
296	C₂×C₄×C₂₃	—	2	1	no	—
297	C₂×C₄×C₂₃	—	2	2	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	1	no	—
313	C₂×C₄×C₂₃	—	2	1	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	1	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	1	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	4	8	no	—
343	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
344	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
345	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
346	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
347	#2843	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#2839	C₂×C₂₃	1	2	yes	complemented
349	#2838	C₂×C₂₃	1	2	yes	complemented
350	#2837	C₂×C₂₃	1	2	yes	—
351	#2836	C₂×C₂₃	1	2	yes	complemented
352	#2833	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#2832	C₂×C₂₃	1	1	yes	characteristic
354	#2831	C₂×C₂₃	1	2	yes	complemented
355	#2823	C₂×C₂₃	1	1	yes	characteristic
356	#2821	C₂×C₂₃	1	2	yes	complemented
357	#2402	C₂×C₂₃	1	2	yes	complemented
358	#2401	C₂×C₂₃	1	2	yes	complemented
359	#2399	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#2398	C₂×C₂₃	1	1	yes	characteristic
361	#2396	C₂×C₂₃	1	2	yes	complemented
362	#2396	C₂×C₂₃	1	2	yes	complemented
363	#2395	C₂×C₂₃	1	2	yes	—
364	C₄×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
365	C₄×#126	C₂×C₂₃	1	2	yes	complemented
366	C₂²×C₂₃	—	4	2	no	—
367	C₂²×C₂₃	—	4	2	no	—
368	C₂²×C₂₃	—	4	2	no	—
369	C₂²×C₂₃	—	4	2	no	—
370	C₂²×C₂₃	—	4	2	no	—
371	C₂²×C₂₃	—	4	2	no	—
372	C₂²×C₂₃	—	4	2	no	—
373	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
374	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
376	C₂²×C₂₃	#585	1	1	yes	characteristic
377	C₂²×C₂₃	#585	1	2	yes	—
378	C₄×C₂₃	—	2	2	no	—
379	C₄×C₂₃	—	2	4	no	—
380	C₄×C₂₃	—	4	2	no	—
381	C₄×C₂₃	—	4	1	no	—
382	C₄×C₂₃	—	4	2	no	—
383	C₄×C₂₃	—	4	1	no	—
384	C₄×C₂₃	—	4	2	no	—
385	C₄×C₂₃	—	4	2	no	—
386	C₄×C₂₃	—	4	2	no	—
387	C₄×C₂₃	—	4	2	no	—
388	C₄×C₂₃	—	4	1	no	—
389	C₄×C₂₃	—	4	1	no	—
390	C₄×C₂₃	—	4	2	no	—
391	C₄×C₂₃	—	4	1	no	—
392	C₄×C₂₃	—	4	2	no	—
393	C₄×C₂₃	—	4	2	no	—
394	C₄×C₂₃	—	4	2	no	—
395	C₄×C₂₃	#563	1	4	yes	—
396	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×#126	C₂²×C₂₃	1	2	yes	—
398	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
402	C₂×#117	C₂²×C₂₃	1	2	yes	—
403	#401	C₂²×C₂₃	1	2	yes	—
404	#400	C₂²×C₂₃	1	2	yes	—
405	#400	C₂²×C₂₃	1	2	yes	—
406	#400	C₂²×C₂₃	1	2	yes	—
407	#400	C₂²×C₂₃	1	2	yes	—
408	#400	C₂²×C₂₃	1	2	yes	—
409	#400	C₂²×C₂₃	1	2	yes	—
410	#400	C₂²×C₂₃	1	2	yes	—
411	#400	C₂²×C₂₃	1	2	yes	—
412	#400	C₂²×C₂₃	1	1	yes	characteristic
413	#400	C₂²×C₂₃	1	2	yes	—
414	#400	C₂²×C₂₃	1	2	yes	—
415	#400	C₂²×C₂₃	1	1	yes	characteristic
416	#399	C₂²×C₂₃	1	2	yes	—
417	#399	C₂²×C₂₃	1	2	yes	—
418	#399	C₂²×C₂₃	1	2	yes	—
419	#398	C₂²×C₂₃	1	2	yes	—
420	#398	C₂²×C₂₃	1	2	yes	—
421	#398	C₂²×C₂₃	1	1	yes	characteristic
422	#398	C₂²×C₂₃	1	2	yes	—
423	#398	C₂²×C₂₃	1	2	yes	—
424	#398	C₂²×C₂₃	1	2	yes	—
425	#398	C₂²×C₂₃	1	2	yes	—
426	#398	C₂²×C₂₃	1	1	yes	characteristic
427	#398	C₂²×C₂₃	1	2	yes	—
428	#398	C₂²×C₂₃	1	2	yes	—
429	#398	C₂²×C₂₃	1	2	yes	—
430	#398	C₂²×C₂₃	1	2	yes	—
431	#397	C₂²×C₂₃	1	2	yes	—
432	#397	C₂²×C₂₃	1	2	yes	—
433	#397	C₂²×C₂₃	1	2	yes	—
434	#397	C₂²×C₂₃	1	2	yes	—
435	#397	C₂²×C₂₃	1	2	yes	—
436	#397	C₂²×C₂₃	1	2	yes	—
437	#397	C₂²×C₂₃	1	2	yes	—
438	#396	C₂²×C₂₃	1	2	yes	—
439	#396	C₂²×C₂₃	1	2	yes	—
440	#396	C₂²×C₂₃	1	2	yes	—
441	#396	C₂²×C₂₃	1	2	yes	—
442	#396	C₂²×C₂₃	1	2	yes	—
443	#395	C₂²×C₂₃	1	2	yes	—
444	#395	C₂²×C₂₃	1	2	yes	—
445	#395	C₂²×C₂₃	1	1	yes	characteristic
446	#395	C₂²×C₂₃	1	1	yes	characteristic
447	#395	C₂²×C₂₃	1	2	yes	—
448	#394	C₂²×C₂₃	1	1	yes	characteristic
449	#394	C₂²×C₂₃	1	2	yes	—
450	#394	C₂²×C₂₃	1	2	yes	—
451	#394	C₂²×C₂₃	1	1	yes	characteristic
452	#393	C₂²×C₂₃	1	2	yes	—
453	#393	C₂²×C₂₃	1	2	yes	—
454	#393	C₂²×C₂₃	1	2	yes	—
455	#391	C₂²×C₂₃	1	1	yes	characteristic
456	#391	C₂²×C₂₃	1	1	yes	characteristic
457	#389	C₂²×C₂₃	1	2	yes	—
458	#389	C₂²×C₂₃	1	2	yes	—
459	#388	C₂²×C₂₃	1	2	yes	—
460	#388	C₂²×C₂₃	1	2	yes	—
461	#388	C₂²×C₂₃	1	2	yes	—
462	#387	C₂²×C₂₃	1	2	yes	—
463	#387	C₂²×C₂₃	1	2	yes	—
464	#387	C₂²×C₂₃	1	2	yes	—
465	#384	C₂²×C₂₃	1	1	yes	characteristic
466	#383	C₂²×C₂₃	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
473	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
474	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
477	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
478	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
479	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
480	#376	C₂²×C₂₃	1	1	yes	characteristic
481	#376	C₂²×C₂₃	1	1	yes	characteristic
482	C₄³	C₂²×C₂₃	1	1	yes	characteristic
483	C₂×C₂₃	—	8	2	no	—
484	C₂×C₂₃	#3460	1	1	yes	characteristic
485	C₂×C₂₃	#3461	1	2	yes	—
486	C₂×C₂₃	C₂×#563	1	1	yes	characteristic
487	C₂×C₂₃	#3529	1	1	yes	characteristic
488	C₂×C₂₃	#3531	1	2	yes	—
489	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
491	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
492	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
494	C₄⋊Q₈	—	2	4	no	—
495	#126	—	2	8	no	—
496	C₄×Q₈	—	4	2	no	—
497	C₄×Q₈	—	4	2	no	—
498	C₄×Q₈	—	4	2	no	—
499	C₄×D₄	—	4	2	no	—
500	#117	—	4	4	no	—
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
540	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
541	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
542	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
546	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
547	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
548	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
549	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
551	#95	C₂³×C₂₃	1	2	yes	—
552	#95	C₂³×C₂₃	1	1	yes	characteristic
553	#95	C₂³×C₂₃	1	1	yes	characteristic
554	#95	C₂³×C₂₃	1	1	yes	characteristic
555	#95	C₂³×C₂₃	1	2	yes	—
556	#95	C₂³×C₂₃	1	1	yes	characteristic
557	#95	C₂³×C₂₃	1	2	yes	—
558	#95	C₂³×C₂₃	1	2	yes	—
559	#95	C₂³×C₂₃	1	2	yes	—
560	#95	C₂³×C₂₃	1	2	yes	—
561	#95	C₂³×C₂₃	1	2	yes	—
562	#95	C₂³×C₂₃	1	2	yes	—
563	#95	C₂³×C₂₃	1	2	yes	—
564	#95	C₂³×C₂₃	1	2	yes	—
565	#95	C₂³×C₂₃	1	2	yes	—
566	#95	C₂³×C₂₃	1	2	yes	—
567	#95	C₂³×C₂₃	1	2	yes	—
568	#95	C₂³×C₂₃	1	2	yes	—
569	#95	C₂³×C₂₃	1	2	yes	—
570	#95	C₂³×C₂₃	1	2	yes	—
571	#95	C₂³×C₂₃	1	2	yes	—
572	#95	C₂³×C₂₃	1	2	yes	—
573	#95	C₂³×C₂₃	1	2	yes	—
574	#95	C₂³×C₂₃	1	2	yes	—
575	#95	C₂³×C₂₃	1	2	yes	—
576	#95	C₂³×C₂₃	1	2	yes	—
577	#95	C₂³×C₂₃	1	2	yes	—
578	#95	C₂³×C₂₃	1	2	yes	—
579	#95	C₂³×C₂₃	1	2	yes	—
580	#95	C₂³×C₂₃	1	2	yes	—
581	#95	C₂³×C₂₃	1	2	yes	—
582	#95	C₂³×C₂₃	1	2	yes	—
583	C₂₃	#36697	1	1	yes	characteristic, direct product factor, Sylow
584	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	4	1	no	—
588	C₂×Q₈	—	4	1	no	—
589	C₂×Q₈	—	4	1	no	—
590	C₂×Q₈	—	4	1	no	—
591	C₂×Q₈	—	4	1	no	—
592	C₂×Q₈	—	4	2	no	—
593	C₂×D₄	—	4	1	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	1	no	—
624	C₄⋊C₄	—	4	1	no	—
625	C₄⋊C₄	—	4	1	no	—
626	C₄⋊C₄	—	4	1	no	—
627	C₄⋊C₄	—	4	1	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	1	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	2	4	no	—
663	C₄²	—	4	2	no	—
664	C₄²	—	4	1	no	—
665	C₄²	#41×C₂₃	1	4	yes	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
674	Q₈	—	4	4	no	—
675	Q₈	—	4	4	no	—
676	Q₈	—	4	4	no	—
677	D₄	—	4	4	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	4	8	no	—
725	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
726	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
727	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
728	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
737	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
738	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
739	C₂²	C₂₃×#585	1	1	yes	characteristic
740	C₂²	C₂₃×#585	1	2	yes	—
741	C₄	—	2	2	no	—
742	C₄	—	2	4	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	C₂₃×#563	1	4	yes	—
759	C₂	—	8	2	no	—
760	C₂	C₂₃×#3460	1	1	yes	characteristic
761	C₂	C₂₃×#3461	1	2	yes	—
762	C₂	C₂×C₂₃×#563	1	1	yes	characteristic
763	C₂	C₂₃×#3529	1	1	yes	characteristic
764	C₂	C₂₃×#3531	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂⁵
prime radical	C₂²×D₄×C₂₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2843	C₂	semidirect
2. C₂₃×#2839	C₂	semidirect
3. C₂₃×#2838	C₂	semidirect
5. C₂₃×#2836	C₂	semidirect
6. C₂₃×#2833	C₂	semidirect
8. C₂₃×#2831	C₂	semidirect
10. C₂₃×#2821	C₂	semidirect
11. C₂₃×#2402	C₂	semidirect
12. C₂₃×#2401	C₂	semidirect
13. C₂₃×#2399	C₂	semidirect
15. C₂₃×#2396	C₂	semidirect
16. C₂₃×#2396	C₂	semidirect
18. C₄×C₂₃×C₄⋊Q₈	C₂	semidirect
19. C₄×C₂₃×#126	C₂	semidirect
283. #36697	C₂₃	direct (N × H)
347. #2843	C₂×C₂₃	semidirect
348. #2839	C₂×C₂₃	semidirect
349. #2838	C₂×C₂₃	semidirect
351. #2836	C₂×C₂₃	semidirect
352. #2833	C₂×C₂₃	semidirect
354. #2831	C₂×C₂₃	semidirect
356. #2821	C₂×C₂₃	semidirect
357. #2402	C₂×C₂₃	semidirect
358. #2401	C₂×C₂₃	semidirect
359. #2399	C₂×C₂₃	semidirect
361. #2396	C₂×C₂₃	semidirect
362. #2396	C₂×C₂₃	semidirect
364. C₄×C₄⋊Q₈	C₂×C₂₃	semidirect
365. C₄×#126	C₂×C₂₃	semidirect
583. C₂₃	#36697	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×#2843	2
C₂₃×#2839	2
C₂₃×#2838	2
C₂₃×#2837	2
C₂₃×#2836	2
C₂₃×#2833	2
C₂₃×#2832	2
C₂₃×#2831	2
C₂₃×#2823	2
C₂₃×#2821	2
C₂₃×#2402	2
C₂₃×#2401	2
C₂₃×#2399	2
C₂₃×#2398	2
C₂₃×#2396	2
C₂₃×#2395	2
C₄×C₂₃×C₄⋊Q₈	2
C₄×C₂₃×#126	2
#36697	23

Subgroups — C23×#36697 #19184323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36697 #19184323