Subgroups — #15686880

Order 2944.

1648 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#67288	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093085	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093080	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093077	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093073	C₂	1	1	yes	maximal, characteristic, complemented
7	#13093069	C₂	1	1	yes	maximal, characteristic, complemented
8	#13093065	C₂	1	2	yes	maximal, complemented
9	#13093064	C₂	1	1	yes	maximal, characteristic, complemented
10	#13093059	C₂	1	2	yes	maximal, complemented
11	#13093058	C₂	1	1	yes	maximal, characteristic, complemented
12	#13093054	C₂	1	2	yes	maximal, complemented
13	#13093051	C₂	1	1	yes	maximal, characteristic, complemented
14	#13093049	C₂	1	2	yes	maximal, complemented
15	#13092964	C₂	1	2	yes	maximal, complemented
16	#13092963	C₂	1	1	yes	maximal, characteristic, complemented
17	#13092929	C₂	1	1	yes	maximal, characteristic, complemented
18	#13092926	C₂	1	2	yes	maximal, complemented
19	#13092926	C₂	1	2	yes	maximal, complemented
20	#13092885	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×C₂²⋊D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₂₃	C₂	1	2	yes	maximal, complemented
23	C₂₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
28	#41×D₂₃	—	2	8	no	—
29	C₂×#67292	C₂²	1	1	yes	characteristic, complemented
30	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#67290	C₂²	1	2	yes	complemented
32	C₂×#67290	C₂²	1	1	yes	characteristic, complemented
33	C₂×D₄×D₂₃	C₂²	1	2	yes	—
34	C₂×D₄×D₂₃	C₂²	1	2	yes	complemented
35	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#67288	—	2	8	no	—
37	C₂×#67288	C₂²	1	1	yes	characteristic
38	C₂×#67288	C₂²	1	2	yes	complemented
39	C₂×#67288	C₂²	1	2	yes	complemented
40	C₂×#67288	C₂²	1	1	yes	characteristic, complemented
41	C₂×#67288	C₂²	1	2	yes	complemented
42	C₂×#67288	C₂²	1	1	yes	characteristic, complemented
43	C₂×#67288	C₂²	1	1	yes	characteristic, complemented
44	C₂²×D₉₂	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
46	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
48	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#123	C₂²	1	2	yes	complemented
50	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#120	C₂²	1	2	yes	complemented
55	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
56	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
57	C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
59	#10625118	C₂²	1	1	yes	characteristic, complemented
60	#10625115	C₂²	1	1	yes	characteristic, complemented
61	#10625111	C₂²	1	1	yes	characteristic, complemented
62	#10625111	C₂²	1	2	yes	complemented
63	#10625110	C₂²	1	2	yes	complemented
64	#10625110	C₂²	1	2	yes	complemented
65	#10625110	C₂²	1	2	yes	complemented
66	#10625110	C₂²	1	2	yes	complemented
67	#10625109	C₂²	1	2	yes	complemented
68	#10625108	C₂²	1	2	yes	complemented
69	#10625108	C₂²	1	2	yes	complemented
70	#10625107	C₂²	1	1	yes	characteristic, complemented
71	D₄×Dic₂₃	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
82	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
83	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
85	#10625068	C₂²	1	1	yes	characteristic, complemented
86	#10625068	C₂²	1	1	yes	characteristic, complemented
87	#10625067	C₂²	1	2	yes	complemented
88	#10625067	C₂²	1	2	yes	complemented
89	#10625066	C₂²	1	1	yes	characteristic, complemented
90	#10625066	C₂²	1	1	yes	characteristic, complemented
91	#10625066	C₂²	1	2	yes	complemented
92	#10625065	C₂²	1	2	yes	complemented
93	#10625065	C₂²	1	2	yes	complemented
94	#10625064	C₂²	1	2	yes	complemented
95	#10625064	C₂²	1	1	yes	characteristic, complemented
96	#10625064	C₂²	1	1	yes	characteristic, complemented
97	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
98	#10625059	C₂²	1	2	yes	complemented
99	#10625058	C₂²	1	1	yes	characteristic, complemented
100	#10625058	C₂²	1	1	yes	characteristic, complemented
101	#10625057	C₂²	1	2	yes	complemented
102	#10625056	C₂²	1	2	yes	complemented
103	#10625056	C₂²	1	2	yes	complemented
104	#10625055	C₂²	1	2	yes	complemented
105	#10625055	C₂²	1	2	yes	complemented
106	#10625055	C₂²	1	2	yes	complemented
107	#10625055	C₂²	1	2	yes	complemented
108	#10625054	C₂²	1	2	yes	complemented
109	#10625054	C₂²	1	2	yes	complemented
110	#10625053	C₂²	1	2	yes	complemented
111	#10625053	C₂²	1	2	yes	complemented
112	#10625053	C₂²	1	2	yes	complemented
113	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
114	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
115	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
116	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
117	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
118	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
119	#10625049	C₂²	1	2	yes	complemented
120	#10625049	C₂²	1	2	yes	complemented
121	C₄×D₉₂	C₂²	1	2	yes	complemented
122	C₄×D₉₂	C₂²	1	2	yes	complemented
123	#10625043	C₂²	1	2	yes	complemented
124	C₄²×D₂₃	C₂²	1	2	yes	complemented
125	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
126	C₂³×D₂₃	C₂³	1	2	yes	—
127	C₂³×D₂₃	C₂³	1	2	yes	—
128	C₂³×D₂₃	C₂³	1	1	yes	characteristic
129	#41×C₂₃	—	2	4	no	—
130	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₂₃	C₂³	1	2	yes	—
132	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₂₃	C₂³	1	2	yes	—
134	C₂×D₄×C₂₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₂₃	—	2	4	no	—
136	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
140	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₂₃	—	2	8	no	—
144	C₂×C₂²⋊D₂₃	—	2	4	no	—
145	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
157	C₂²×Dic₂₃	C₂³	1	2	yes	—
158	C₂²×Dic₂₃	C₂³	1	2	yes	—
159	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
160	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
161	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
162	#67292	—	2	4	no	—
163	Q₈×D₂₃	—	2	4	no	—
164	#67290	—	2	8	no	—
165	#67290	—	2	4	no	—
166	D₄×D₂₃	—	2	8	no	—
167	D₄×D₂₃	—	2	8	no	—
168	D₄×D₂₃	—	2	4	no	—
169	#67288	—	2	4	no	—
170	#67288	—	2	8	no	—
171	#67288	—	2	4	no	—
172	#67288	—	2	8	no	—
173	#67288	—	2	8	no	—
174	#67288	—	2	4	no	—
175	#67288	D₄	1	8	yes	complemented
176	C₂×D₉₂	—	2	4	no	—
177	C₂×D₉₂	C₂³	1	2	yes	—
178	C₂×D₉₂	C₂³	1	2	yes	—
179	C₂×D₉₂	C₂³	1	2	yes	—
180	C₂×D₉₂	C₂³	1	1	yes	characteristic
181	C₂×D₉₂	C₂³	1	2	yes	—
182	C₂×D₉₂	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₂₃	—	2	4	no	—
184	C₂×C₄×D₂₃	—	2	8	no	—
185	C₂×C₄×D₂₃	—	2	8	no	—
186	C₂×C₄×D₂₃	C₂³	1	2	yes	—
187	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₂₃	C₂³	1	2	yes	—
189	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄×D₂₃	C₂³	1	2	yes	—
191	C₂×C₄×D₂₃	C₂³	1	2	yes	—
192	C₂×C₄×D₂₃	C₂³	1	2	yes	—
193	C₂×C₄×D₂₃	C₂³	1	2	yes	—
194	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₄×D₂₃	C₂³	1	2	yes	—
197	C₂×C₄×D₂₃	C₂³	1	2	yes	—
198	C₂×Dic₄₆	—	2	4	no	—
199	C₂×Dic₄₆	C₂³	1	2	yes	—
200	C₂×Dic₄₆	C₂³	1	2	yes	—
201	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
202	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
203	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
204	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
206	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
207	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
208	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
209	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
210	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
211	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
212	C₄²×C₂₃	C₂³	1	2	yes	—
213	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
214	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
215	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
216	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
217	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
218	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
219	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
221	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
222	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
223	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
224	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
225	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
226	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
227	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
228	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
229	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
230	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₂₃	C₂³	1	2	yes	—
232	C₄⋊Dic₂₃	C₂³	1	2	yes	—
233	Dic₂₃⋊C₄	C₂³	1	2	yes	—
234	Dic₂₃⋊C₄	C₂³	1	2	yes	—
235	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₂₃⋊C₄	C₂³	1	2	yes	—
237	Dic₂₃⋊C₄	C₂³	1	2	yes	—
238	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
241	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
242	C₄×Dic₂₃	C₂³	1	2	yes	—
243	C₄×Dic₂₃	C₂³	1	2	yes	—
244	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
245	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
247	C₂³×C₂₃	—	2	2	no	—
248	C₂³×C₂₃	—	2	2	no	—
249	C₂³×C₂₃	—	4	1	no	—
250	C₂³×C₂₃	C₂⁴	1	2	yes	—
251	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
254	C₂²×D₂₃	—	2	2	no	—
255	C₂²×D₂₃	—	2	4	no	—
256	C₂²×D₂₃	—	2	4	no	—
257	C₂²×D₂₃	—	2	4	no	—
258	C₂²×D₂₃	—	2	4	no	—
259	C₂²×D₂₃	—	2	2	no	—
260	C₂²×D₂₃	—	4	2	no	—
261	C₂²×D₂₃	—	4	2	no	—
262	C₂²×D₂₃	—	4	1	no	—
263	C₂²×D₂₃	C₂⁴	1	2	yes	—
264	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
265	C₂²×D₂₃	C₂⁴	1	2	yes	—
266	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
267	Q₈×C₂₃	—	2	2	no	—
268	D₄×C₂₃	—	2	4	no	—
269	D₄×C₂₃	—	2	4	no	—
270	D₄×C₂₃	—	2	2	no	—
271	D₄×C₂₃	—	4	2	no	—
272	C₂×C₄×C₂₃	—	2	2	no	—
273	C₂×C₄×C₂₃	—	2	2	no	—
274	C₂×C₄×C₂₃	—	2	2	no	—
275	C₂×C₄×C₂₃	—	2	4	no	—
276	C₂×C₄×C₂₃	—	2	2	no	—
277	C₂×C₄×C₂₃	—	2	2	no	—
278	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	complemented
279	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
280	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
281	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
286	C₂²⋊D₂₃	—	2	4	no	—
287	C₂²⋊D₂₃	—	2	2	no	—
288	C₂²⋊D₂₃	—	2	4	no	—
289	C₂²⋊D₂₃	—	2	4	no	—
290	C₂²⋊D₂₃	—	2	2	no	—
291	C₂²⋊D₂₃	—	2	4	no	—
292	C₂²⋊D₂₃	—	2	4	no	—
293	C₂²⋊D₂₃	—	2	4	no	—
294	C₂²⋊D₂₃	—	2	2	no	—
295	C₂²⋊D₂₃	—	4	2	no	—
296	C₂²⋊D₂₃	C₂×D₄	1	8	yes	complemented
297	C₂²⋊D₂₃	#41	1	4	yes	complemented
298	C₂×Dic₂₃	—	2	2	no	—
299	C₂×Dic₂₃	—	2	4	no	—
300	C₂×Dic₂₃	—	2	4	no	—
301	C₂×Dic₂₃	—	2	2	no	—
302	C₂×Dic₂₃	—	4	1	no	—
303	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
304	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
305	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
306	C₂×Dic₂₃	C₂⁴	1	2	yes	—
307	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
308	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
309	C₂×Dic₂₃	C₂⁴	1	2	yes	—
310	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
311	D₉₂	—	2	4	no	—
312	D₉₂	—	2	4	no	—
313	D₉₂	—	2	4	no	—
314	D₉₂	—	2	2	no	—
315	D₉₂	—	4	2	no	—
316	D₉₂	C₂×D₄	1	4	yes	complemented
317	C₄×D₂₃	—	2	4	no	—
318	C₄×D₂₃	—	2	4	no	—
319	C₄×D₂₃	—	2	2	no	—
320	C₄×D₂₃	—	2	2	no	—
321	C₄×D₂₃	—	2	4	no	—
322	C₄×D₂₃	—	2	2	no	—
323	C₄×D₂₃	—	2	2	no	—
324	C₄×D₂₃	—	2	4	no	—
325	C₄×D₂₃	—	2	4	no	—
326	C₄×D₂₃	—	2	4	no	—
327	C₄×D₂₃	—	4	2	no	—
328	C₄×D₂₃	C₂×D₄	1	8	yes	complemented
329	Dic₄₆	—	2	2	no	—
330	Dic₄₆	—	2	4	no	—
331	Dic₄₆	—	2	4	no	—
332	Dic₄₆	C₂×D₄	1	4	yes	complemented
333	D₄×#41	—	23	1	no	maximal, Sylow
334	C₂²×C₂₃	—	2	1	no	—
335	C₂²×C₂₃	—	2	1	no	—
336	C₂²×C₂₃	—	2	1	no	—
337	C₂²×C₂₃	—	2	1	no	—
338	C₂²×C₂₃	—	2	2	no	—
339	C₂²×C₂₃	—	2	1	no	—
340	C₂²×C₂₃	—	2	1	no	—
341	C₂²×C₂₃	—	2	2	no	—
342	C₂²×C₂₃	—	2	2	no	—
343	C₂²×C₂₃	—	2	1	no	—
344	C₂²×C₂₃	—	4	4	no	—
345	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
346	C₂²×C₂₃	C₂×#41	1	2	yes	complemented
347	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
348	C₂×D₂₃	—	2	1	no	—
349	C₂×D₂₃	—	2	2	no	—
350	C₂×D₂₃	—	2	2	no	—
351	C₂×D₂₃	—	2	1	no	—
352	C₂×D₂₃	—	2	1	no	—
353	C₂×D₂₃	—	2	2	no	—
354	C₂×D₂₃	—	2	2	no	—
355	C₂×D₂₃	—	2	1	no	—
356	C₂×D₂₃	—	2	1	no	—
357	C₂×D₂₃	—	2	2	no	—
358	C₂×D₂₃	—	4	8	no	—
359	C₂×D₂₃	—	4	4	no	—
360	C₂×D₂₃	—	4	8	no	—
361	C₂×D₂₃	C₂²×D₄	1	4	yes	—
362	C₂×D₂₃	C₂×#41	1	2	yes	complemented
363	C₄×C₂₃	—	2	1	no	—
364	C₄×C₂₃	—	2	2	no	—
365	C₄×C₂₃	—	2	1	no	—
366	C₄×C₂₃	—	2	2	no	—
367	C₄×C₂₃	—	2	2	no	—
368	C₄×C₂₃	C₂²×D₄	1	2	yes	—
369	C₄×C₂₃	C₂²×D₄	1	2	yes	—
370	Dic₂₃	—	2	2	no	—
371	Dic₂₃	—	2	1	no	—
372	Dic₂₃	—	2	1	no	—
373	Dic₂₃	—	2	1	no	—
374	Dic₂₃	—	2	1	no	—
375	Dic₂₃	—	2	1	no	—
376	Dic₂₃	C₂²×D₄	1	4	yes	—
377	Dic₂₃	C₂×#41	1	2	yes	complemented
378	C₂²×#41	—	23	1	no	—
379	C₂²×#41	—	23	1	no	—
380	#550	—	23	1	no	—
381	D₄×Q₈	—	23	1	no	—
382	#548	—	23	1	no	—
383	#548	—	23	1	no	—
384	#547	—	23	2	no	—
385	#547	—	23	1	no	—
386	#546	—	23	2	no	—
387	#546	—	23	1	no	—
388	#546	—	23	1	no	—
389	#546	—	23	2	no	—
390	D₄²	—	23	1	no	—
391	D₄²	—	23	2	no	—
392	#532	—	23	1	no	—
393	#532	—	23	2	no	—
394	#525	—	23	2	no	—
395	#525	—	23	2	no	—
396	#525	—	23	1	no	—
397	#525	D₂₃	1	1	yes	characteristic, complemented
398	C₄×#41	—	23	1	no	—
399	C₂×C₄×D₄	—	23	1	no	—
400	C₂×C₄×D₄	—	23	2	no	—
401	C₂×C₂₃	—	2	2	no	—
402	C₂×C₂₃	—	2	2	no	—
403	C₂×C₂₃	—	4	2	no	—
404	C₂×C₂₃	—	4	1	no	—
405	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
406	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
407	C₂×C₂₃	#585	1	1	yes	characteristic
408	D₂₃	—	2	2	no	—
409	D₂₃	—	2	4	no	—
410	D₂₃	—	4	2	no	—
411	D₂₃	—	4	1	no	—
412	C₂×#41	—	23	1	no	—
413	C₂×#41	—	23	2	no	—
414	C₂×#41	—	23	1	no	—
415	C₂×#41	—	23	1	no	—
416	C₂×#41	—	23	2	no	—
417	C₂×#41	—	23	2	no	—
418	C₂×#41	—	23	1	no	—
419	C₂×#41	—	23	1	no	—
420	C₂×#41	—	23	2	no	—
421	C₂×#41	—	23	1	no	—
422	C₂×#41	—	46	8	no	—
423	C₂×#41	—	46	8	no	—
424	C₂×#41	C₂×D₂₃	1	1	yes	characteristic, complemented
425	C₂²×Q₈	—	23	1	no	—
426	C₂²×Q₈	—	23	1	no	—
427	C₂²×D₄	—	23	1	no	—
428	C₂²×D₄	—	23	2	no	—
429	C₂²×D₄	—	23	2	no	—
430	C₂²×D₄	—	23	2	no	—
431	C₂²×D₄	—	23	1	no	—
432	C₂²×D₄	—	23	1	no	—
433	C₂³×C₄	—	23	2	no	—
434	C₂³×C₄	—	23	2	no	—
435	C₂³×C₄	—	23	1	no	—
436	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
437	C₄⋊Q₈	—	23	1	no	—
438	C₄⋊Q₈	—	23	2	no	—
439	#127	—	23	2	no	—
440	#127	—	23	1	no	—
441	#124	—	23	1	no	—
442	#124	—	23	1	no	—
443	#124	—	23	2	no	—
444	#124	—	23	2	no	—
445	#123	—	23	2	no	—
446	#123	—	23	2	no	—
447	#123	—	23	2	no	—
448	#123	—	23	2	no	—
449	#123	—	23	2	no	—
450	#123	C₂×D₂₃	1	2	yes	complemented
451	C₂²⋊Q₈	—	23	2	no	—
452	C₂²⋊Q₈	—	23	1	no	—
453	C₂²⋊Q₈	—	23	2	no	—
454	C₂²⋊Q₈	—	23	1	no	—
455	C₂²⋊Q₈	—	23	2	no	—
456	C₂²⋊Q₈	—	23	2	no	—
457	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
458	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
459	#121	—	23	2	no	—
460	#121	—	23	2	no	—
461	#121	—	23	2	no	—
462	#121	—	23	2	no	—
463	#121	—	23	2	no	—
464	#121	—	23	1	no	—
465	#121	—	23	1	no	—
466	#121	—	23	2	no	—
467	#121	—	23	2	no	—
468	#121	—	23	2	no	—
469	#121	—	23	2	no	—
470	#121	—	23	2	no	—
471	#121	C₂×D₂₃	1	1	yes	characteristic, complemented
472	#121	C₂×D₂₃	1	1	yes	characteristic, complemented
473	#120	—	23	2	no	—
474	#120	—	23	2	no	—
475	#120	—	23	2	no	—
476	#120	—	23	2	no	—
477	#120	—	23	2	no	—
478	#120	C₂×D₂₃	1	2	yes	complemented
479	C₄×Q₈	—	23	1	no	—
480	C₄×Q₈	—	23	1	no	—
481	C₄×D₄	—	23	2	no	—
482	C₄×D₄	—	23	1	no	—
483	C₄×D₄	—	23	1	no	—
484	C₄×D₄	—	23	1	no	—
485	C₄×D₄	—	23	2	no	—
486	C₄×D₄	—	23	1	no	—
487	C₄×D₄	—	23	1	no	—
488	C₄×D₄	—	23	1	no	—
489	C₄×D₄	—	23	1	no	—
490	C₄×D₄	—	23	1	no	—
491	C₄×D₄	—	23	2	no	—
492	C₄×D₄	—	23	2	no	—
493	C₄×D₄	—	23	1	no	—
494	C₄×D₄	—	23	1	no	—
495	C₄×D₄	—	23	2	no	—
496	C₄×D₄	—	23	2	no	—
497	C₄×D₄	—	23	2	no	—
498	C₄×D₄	—	23	2	no	—
499	C₄×D₄	—	23	2	no	—
500	C₄×D₄	—	23	2	no	—
501	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
502	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
503	#117	—	23	2	no	—
504	#117	C₂×D₂₃	1	1	yes	characteristic, complemented
505	C₂×C₄⋊C₄	—	23	1	no	—
506	C₂×C₄⋊C₄	—	23	2	no	—
507	C₂×C₂²⋊C₄	—	23	1	no	—
508	C₂×C₂²⋊C₄	—	23	1	no	—
509	C₂×C₂²⋊C₄	—	23	2	no	—
510	C₂×C₂²⋊C₄	—	23	2	no	—
511	C₂×C₄²	—	23	1	no	—
512	C₂×C₄²	—	23	2	no	—
513	C₂₃	D₄×#41	1	1	yes	characteristic, complemented, Sylow
514	C₂⁴	—	23	2	no	—
515	C₂⁴	—	23	1	no	—
516	C₂⁴	—	23	2	no	—
517	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
518	#41	—	2	4	no	—
519	#41	—	23	8	no	—
520	#41	—	46	8	no	—
521	#41	—	46	8	no	—
522	#41	—	46	8	no	—
523	#41	—	46	4	no	—
524	#41	—	46	4	no	—
525	#41	—	46	8	no	—
526	#41	—	46	4	no	—
527	#41	—	46	4	no	—
528	#41	—	46	4	no	—
529	C₂×Q₈	—	23	1	no	—
530	C₂×Q₈	—	23	2	no	—
531	C₂×Q₈	—	23	2	no	—
532	C₂×Q₈	—	23	1	no	—
533	C₂×Q₈	—	46	4	no	—
534	C₂×Q₈	—	46	4	no	—
535	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
536	C₂×D₄	—	23	1	no	—
537	C₂×D₄	—	23	2	no	—
538	C₂×D₄	—	23	1	no	—
539	C₂×D₄	—	23	1	no	—
540	C₂×D₄	—	23	2	no	—
541	C₂×D₄	—	23	1	no	—
542	C₂×D₄	—	23	2	no	—
543	C₂×D₄	—	23	2	no	—
544	C₂×D₄	—	23	2	no	—
545	C₂×D₄	—	23	2	no	—
546	C₂×D₄	—	23	2	no	—
547	C₂×D₄	—	23	2	no	—
548	C₂×D₄	—	23	1	no	—
549	C₂×D₄	—	23	2	no	—
550	C₂×D₄	—	23	2	no	—
551	C₂×D₄	—	23	2	no	—
552	C₂×D₄	—	23	1	no	—
553	C₂×D₄	—	23	2	no	—
554	C₂×D₄	—	46	4	no	—
555	C₂×D₄	—	46	8	no	—
556	C₂×D₄	—	46	4	no	—
557	C₂×D₄	—	46	8	no	—
558	C₂×D₄	—	46	8	no	—
559	C₂×D₄	—	46	4	no	—
560	C₂×D₄	C₂²×D₂₃	1	2	yes	—
561	C₂×D₄	C₂²×D₂₃	1	2	yes	—
562	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
563	C₂×D₄	C₂²×D₂₃	1	2	yes	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	23	2	no	—
566	C₂²×C₄	—	23	1	no	—
567	C₂²×C₄	—	23	1	no	—
568	C₂²×C₄	—	23	2	no	—
569	C₂²×C₄	—	23	2	no	—
570	C₂²×C₄	—	23	1	no	—
571	C₂²×C₄	—	23	2	no	—
572	C₂²×C₄	—	23	2	no	—
573	C₂²×C₄	—	23	2	no	—
574	C₂²×C₄	—	23	2	no	—
575	C₂²×C₄	—	23	1	no	—
576	C₂²×C₄	—	23	2	no	—
577	C₂²×C₄	—	23	1	no	—
578	C₂²×C₄	—	23	1	no	—
579	C₂²×C₄	—	23	1	no	—
580	C₂²×C₄	—	23	2	no	—
581	C₂²×C₄	—	23	2	no	—
582	C₂²×C₄	—	46	8	no	—
583	C₂²×C₄	—	46	8	no	—
584	C₂²×C₄	—	46	4	no	—
585	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
586	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
587	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
588	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
589	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
590	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
591	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
592	C₄⋊C₄	—	23	1	no	—
593	C₄⋊C₄	—	23	2	no	—
594	C₄⋊C₄	—	23	1	no	—
595	C₄⋊C₄	—	23	1	no	—
596	C₄⋊C₄	—	23	1	no	—
597	C₄⋊C₄	—	23	2	no	—
598	C₄⋊C₄	—	23	2	no	—
599	C₄⋊C₄	—	23	2	no	—
600	C₄⋊C₄	—	23	2	no	—
601	C₄⋊C₄	—	23	2	no	—
602	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
603	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
604	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
605	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
606	C₂²⋊C₄	—	23	1	no	—
607	C₂²⋊C₄	—	23	1	no	—
608	C₂²⋊C₄	—	23	1	no	—
609	C₂²⋊C₄	—	23	2	no	—
610	C₂²⋊C₄	—	23	1	no	—
611	C₂²⋊C₄	—	23	2	no	—
612	C₂²⋊C₄	—	23	1	no	—
613	C₂²⋊C₄	—	23	1	no	—
614	C₂²⋊C₄	—	23	2	no	—
615	C₂²⋊C₄	—	23	1	no	—
616	C₂²⋊C₄	—	23	2	no	—
617	C₂²⋊C₄	—	23	2	no	—
618	C₂²⋊C₄	—	23	1	no	—
619	C₂²⋊C₄	—	23	2	no	—
620	C₂²⋊C₄	—	23	2	no	—
621	C₂²⋊C₄	—	23	2	no	—
622	C₂²⋊C₄	—	23	2	no	—
623	C₂²⋊C₄	—	23	2	no	—
624	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
625	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
626	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
627	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
628	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
629	C₄²	—	23	2	no	—
630	C₄²	—	23	1	no	—
631	C₄²	—	23	2	no	—
632	C₄²	—	23	1	no	—
633	C₄²	—	23	1	no	—
634	C₄²	—	23	1	no	—
635	C₄²	C₂²×D₂₃	1	2	yes	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	23	1	no	—
640	C₂³	—	23	2	no	—
641	C₂³	—	23	1	no	—
642	C₂³	—	23	2	no	—
643	C₂³	—	46	4	no	—
644	C₂³	—	46	4	no	—
645	C₂³	—	46	2	no	—
646	C₂³	—	46	4	no	—
647	C₂³	—	46	2	no	—
648	C₂³	—	46	4	no	—
649	C₂³	—	92	1	no	—
650	C₂³	—	92	2	no	—
651	C₂³	—	92	2	no	—
652	C₂³	C₂³×D₂₃	1	2	yes	—
653	C₂³	C₂³×D₂₃	1	1	yes	characteristic
654	C₂³	C₂³×D₂₃	1	1	yes	characteristic
655	C₂³	C₂³×D₂₃	1	1	yes	characteristic
656	Q₈	—	2	2	no	—
657	Q₈	—	23	4	no	—
658	Q₈	—	46	4	no	—
659	Q₈	—	46	4	no	—
660	Q₈	—	46	2	no	—
661	D₄	—	2	4	no	—
662	D₄	—	2	4	no	—
663	D₄	—	2	2	no	—
664	D₄	—	4	2	no	—
665	D₄	—	23	8	no	—
666	D₄	—	23	4	no	—
667	D₄	—	23	4	no	—
668	D₄	—	46	4	no	—
669	D₄	—	46	4	no	—
670	D₄	—	46	4	no	—
671	D₄	—	46	4	no	—
672	D₄	—	46	4	no	—
673	D₄	—	46	4	no	—
674	D₄	—	46	2	no	—
675	D₄	—	46	4	no	—
676	D₄	—	46	4	no	—
677	D₄	—	46	2	no	—
678	D₄	—	46	4	no	—
679	D₄	—	46	2	no	—
680	D₄	—	46	2	no	—
681	D₄	—	92	2	no	—
682	D₄	—	92	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	23	1	no	—
690	C₂×C₄	—	23	2	no	—
691	C₂×C₄	—	23	8	no	—
692	C₂×C₄	—	23	1	no	—
693	C₂×C₄	—	23	1	no	—
694	C₂×C₄	—	23	1	no	—
695	C₂×C₄	—	23	1	no	—
696	C₂×C₄	—	23	1	no	—
697	C₂×C₄	—	23	2	no	—
698	C₂×C₄	—	46	4	no	—
699	C₂×C₄	—	46	4	no	—
700	C₂×C₄	—	46	4	no	—
701	C₂×C₄	—	46	4	no	—
702	C₂×C₄	—	46	4	no	—
703	C₂×C₄	—	46	4	no	—
704	C₂×C₄	—	46	4	no	—
705	C₂×C₄	—	46	2	no	—
706	C₂×C₄	—	46	2	no	—
707	C₂×C₄	—	46	2	no	—
708	C₂×C₄	—	46	2	no	—
709	C₂×C₄	—	46	2	no	—
710	C₂×C₄	—	46	4	no	—
711	C₂×C₄	—	46	2	no	—
712	C₂×C₄	—	92	2	no	—
713	C₂×C₄	—	92	1	no	—
714	C₂×C₄	D₄×D₂₃	1	4	yes	complemented
715	C₂×C₄	C₂³×D₂₃	1	2	yes	—
716	C₂×C₄	C₂³×D₂₃	1	2	yes	—
717	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
718	C₂×C₄	C₂³×D₂₃	1	2	yes	—
719	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
720	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
721	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	23	4	no	—
734	C₂²	—	23	2	no	—
735	C₂²	—	46	1	no	—
736	C₂²	—	46	2	no	—
737	C₂²	—	46	2	no	—
738	C₂²	—	46	1	no	—
739	C₂²	—	46	2	no	—
740	C₂²	—	46	1	no	—
741	C₂²	—	46	2	no	—
742	C₂²	—	46	1	no	—
743	C₂²	—	46	1	no	—
744	C₂²	—	46	2	no	—
745	C₂²	—	92	8	no	—
746	C₂²	—	92	4	no	—
747	C₂²	—	92	8	no	—
748	C₂²	C₂×D₄×D₂₃	1	2	yes	—
749	C₂²	#41×D₂₃	1	2	yes	complemented
750	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	23	4	no	—
757	C₄	—	23	2	no	—
758	C₄	—	46	1	no	—
759	C₄	—	46	2	no	—
760	C₄	—	46	1	no	—
761	C₄	—	46	1	no	—
762	C₄	—	46	1	no	—
763	C₄	—	46	1	no	—
764	C₄	C₂×D₄×D₂₃	1	2	yes	—
765	C₄	C₂×D₄×D₂₃	1	2	yes	—
766	C₂	—	2	2	no	—
767	C₂	—	2	2	no	—
768	C₂	—	4	1	no	—
769	C₂	—	4	2	no	—
770	C₂	—	46	2	no	—
771	C₂	—	46	4	no	—
772	C₂	—	92	2	no	—
773	C₂	—	92	1	no	—
774	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
775	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
776	C₂	#13093253	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂₃×#525	C₂
hypercenter	#525	D₂₃
hypocenter	C₂₃	D₄×#41
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂²×#67288	C₂	semidirect
2. C₂×#41×D₂₃	C₂	semidirect
3. #13093085	C₂	semidirect
4. #13093080	C₂	semidirect
5. #13093077	C₂	semidirect
6. #13093073	C₂	semidirect
7. #13093069	C₂	semidirect
8. #13093065	C₂	semidirect
9. #13093064	C₂	semidirect
10. #13093059	C₂	semidirect
11. #13093058	C₂	semidirect
12. #13093054	C₂	semidirect
13. #13093051	C₂	semidirect
14. #13093049	C₂	semidirect
15. #13092964	C₂	semidirect
16. #13092963	C₂	semidirect
17. #13092929	C₂	semidirect
18. #13092926	C₂	semidirect
19. #13092926	C₂	semidirect
20. #13092885	C₂	semidirect
21. C₂×C₄×C₂²⋊D₂₃	C₂	semidirect
22. C₄×D₄×D₂₃	C₂	semidirect
23. C₂₃×#525	C₂	semidirect
24. C₂×#41×C₂₃	C₂²	semidirect
25. C₂³×C₄×C₂₃	C₂²	semidirect
27. C₂²×C₂²⋊D₂₃	C₂²	semidirect
29. C₂×#67292	C₂²	semidirect
30. C₂×Q₈×D₂₃	C₂²	semidirect
31. C₂×#67290	C₂²	semidirect
32. C₂×#67290	C₂²	semidirect
34. C₂×D₄×D₂₃	C₂²	semidirect
35. C₂×D₄×D₂₃	C₂²	semidirect
38. C₂×#67288	C₂²	semidirect
39. C₂×#67288	C₂²	semidirect
40. C₂×#67288	C₂²	semidirect
41. C₂×#67288	C₂²	semidirect
42. C₂×#67288	C₂²	semidirect
43. C₂×#67288	C₂²	semidirect
44. C₂²×D₉₂	C₂²	semidirect
45. C₂²×C₄×D₂₃	C₂²	semidirect
46. C₂²×C₄×D₂₃	C₂²	semidirect
47. C₂²×C₄×D₂₃	C₂²	semidirect
48. C₂²×Dic₄₆	C₂²	semidirect
49. C₂₃×#123	C₂²	semidirect
50. C₂₃×C₂²⋊Q₈	C₂²	semidirect
51. C₂₃×C₂²⋊Q₈	C₂²	semidirect
52. C₂₃×#121	C₂²	semidirect
53. C₂₃×#121	C₂²	semidirect
54. C₂₃×#120	C₂²	semidirect
55. C₄×D₄×C₂₃	C₂²	semidirect
56. C₄×D₄×C₂₃	C₂²	semidirect
57. C₂₃×#117	C₂²	semidirect
58. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
59. #10625118	C₂²	semidirect
60. #10625115	C₂²	semidirect
61. #10625111	C₂²	semidirect
62. #10625111	C₂²	semidirect
63. #10625110	C₂²	semidirect
64. #10625110	C₂²	semidirect
65. #10625110	C₂²	semidirect
66. #10625110	C₂²	semidirect
67. #10625109	C₂²	semidirect
68. #10625108	C₂²	semidirect
69. #10625108	C₂²	semidirect
70. #10625107	C₂²	semidirect
71. D₄×Dic₂₃	C₂²	semidirect
74. C₄×C₂²⋊D₂₃	C₂²	semidirect
75. C₄×C₂²⋊D₂₃	C₂²	semidirect
76. C₄×C₂²⋊D₂₃	C₂²	semidirect
77. C₄×C₂²⋊D₂₃	C₂²	semidirect
78. C₄×C₂²⋊D₂₃	C₂²	semidirect
79. C₄×C₂²⋊D₂₃	C₂²	semidirect
80. C₄×C₂²⋊D₂₃	C₂²	semidirect
81. C₄×C₂²⋊D₂₃	C₂²	semidirect
82. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
83. C₂×Dic₂₃⋊C₄	C₂²	semidirect
84. C₂×C₄×Dic₂₃	C₂²	semidirect
85. #10625068	C₂²	semidirect
86. #10625068	C₂²	semidirect
87. #10625067	C₂²	semidirect
88. #10625067	C₂²	semidirect
89. #10625066	C₂²	semidirect
90. #10625066	C₂²	semidirect
91. #10625066	C₂²	semidirect
92. #10625065	C₂²	semidirect
93. #10625065	C₂²	semidirect
94. #10625064	C₂²	semidirect
95. #10625064	C₂²	semidirect
96. #10625064	C₂²	semidirect
97. C₄⋊C₄×D₂₃	C₂²	semidirect
98. #10625059	C₂²	semidirect
99. #10625058	C₂²	semidirect
100. #10625058	C₂²	semidirect
101. #10625057	C₂²	semidirect
102. #10625056	C₂²	semidirect
103. #10625056	C₂²	semidirect
104. #10625055	C₂²	semidirect
105. #10625055	C₂²	semidirect
106. #10625055	C₂²	semidirect
107. #10625055	C₂²	semidirect
108. #10625054	C₂²	semidirect
109. #10625054	C₂²	semidirect
110. #10625053	C₂²	semidirect
111. #10625053	C₂²	semidirect
112. #10625053	C₂²	semidirect
114. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
115. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
116. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
117. C₂²⋊C₄×D₂₃	C₂²	semidirect
118. C₂²⋊C₄×D₂₃	C₂²	semidirect
119. #10625049	C₂²	semidirect
120. #10625049	C₂²	semidirect
121. C₄×D₉₂	C₂²	semidirect
122. C₄×D₉₂	C₂²	semidirect
123. #10625043	C₂²	semidirect
124. C₄²×D₂₃	C₂²	semidirect
175. #67288	D₄	semidirect
278. C₂×C₄×C₂₃	C₂×D₄	semidirect
296. C₂²⋊D₂₃	C₂×D₄	semidirect
297. C₂²⋊D₂₃	#41	semidirect
316. D₉₂	C₂×D₄	semidirect
328. C₄×D₂₃	C₂×D₄	semidirect
332. Dic₄₆	C₂×D₄	semidirect
346. C₂²×C₂₃	C₂×#41	semidirect
362. C₂×D₂₃	C₂×#41	semidirect
377. Dic₂₃	C₂×#41	semidirect
397. #525	D₂₃	semidirect
424. C₂×#41	C₂×D₂₃	semidirect
436. C₂³×C₄	C₂×D₂₃	semidirect
450. #123	C₂×D₂₃	semidirect
457. C₂²⋊Q₈	C₂×D₂₃	semidirect
458. C₂²⋊Q₈	C₂×D₂₃	semidirect
471. #121	C₂×D₂₃	semidirect
472. #121	C₂×D₂₃	semidirect
478. #120	C₂×D₂₃	semidirect
501. C₄×D₄	C₂×D₂₃	semidirect
502. C₄×D₄	C₂×D₂₃	semidirect
504. #117	C₂×D₂₃	semidirect
513. C₂₃	D₄×#41	semidirect
714. C₂×C₄	D₄×D₂₃	semidirect
749. C₂²	#41×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#67288	2
C₂×#41×D₂₃	2
#13093085	2
#13093080	2
#13093077	2
#13093073	2
#13093069	2
#13093065	2
#13093064	2
#13093059	2
#13093058	2
#13093054	2
#13093051	2
#13093049	2
#13092964	2
#13092963	2
#13092929	2
#13092926	2
#13092885	2
C₂×C₄×C₂²⋊D₂₃	2
C₄×D₄×D₂₃	2
C₂₃×#525	2
D₄×#41	23