Subgroups — #15686804

Order 2944.

1160 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093042	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093016	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093013	C₂	1	2	yes	maximal, complemented
4	#13093012	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093010	C₂	1	2	yes	maximal, complemented
6	#13093003	C₂	1	2	yes	maximal, complemented
7	#13093002	C₂	1	2	yes	maximal, complemented
8	#13092999	C₂	1	2	yes	maximal, complemented
9	#13092977	C₂	1	2	yes	maximal, complemented
10	#13092975	C₂	1	1	yes	maximal, characteristic, complemented
11	#13092949	C₂	1	2	yes	maximal, complemented
12	#13092947	C₂	1	2	yes	maximal, complemented
13	#13092945	C₂	1	2	yes	maximal, complemented
14	#13092928	C₂	1	1	yes	maximal, characteristic, complemented
15	#13092926	C₂	1	2	yes	maximal, complemented
16	#13092924	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₂₃	C₂	1	2	yes	maximal, complemented
19	C₂₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₂₃	C₂²	1	2	yes	—
24	C₂×#67288	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
27	C₂₃×#123	C₂²	1	2	yes	complemented
28	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#121	C₂²	1	1	yes	characteristic
31	C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#120	C₂²	1	2	yes	complemented
33	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
34	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
35	C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
36	#10625124	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
38	#10625117	C₂²	1	2	yes	complemented
39	#10625117	C₂²	1	2	yes	complemented
40	#10625110	C₂²	1	2	yes	—
41	#10625110	C₂²	1	2	yes	complemented
42	#10625109	C₂²	1	2	yes	—
43	#10625109	C₂²	1	2	yes	—
44	#10625109	C₂²	1	2	yes	complemented
45	#10625108	C₂²	1	2	yes	complemented
46	#10625108	C₂²	1	2	yes	complemented
47	#10625108	C₂²	1	2	yes	complemented
48	#10625107	C₂²	1	2	yes	complemented
49	#10625106	C₂²	1	2	yes	complemented
50	#10625106	C₂²	1	2	yes	complemented
51	#10625106	C₂²	1	2	yes	complemented
52	D₄×Dic₂₃	C₂²	1	2	yes	complemented
53	#10625101	C₂²	1	1	yes	characteristic
54	#10625101	C₂²	1	1	yes	characteristic, complemented
55	#10625100	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
64	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
65	#10625097	C₂²	1	2	yes	complemented
66	#10625097	C₂²	1	1	yes	characteristic, complemented
67	#10625095	C₂²	1	1	yes	characteristic, complemented
68	#10625095	C₂²	1	1	yes	characteristic, complemented
69	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
71	#10625069	C₂²	1	2	yes	complemented
72	#10625069	C₂²	1	2	yes	complemented
73	#10625068	C₂²	1	2	yes	complemented
74	#10625067	C₂²	1	2	yes	complemented
75	#10625067	C₂²	1	2	yes	complemented
76	#10625065	C₂²	1	2	yes	complemented
77	#10625065	C₂²	1	2	yes	complemented
78	#10625064	C₂²	1	2	yes	complemented
79	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
80	#10625061	C₂²	1	2	yes	complemented
81	#10625060	C₂²	1	2	yes	complemented
82	#10625060	C₂²	1	2	yes	complemented
83	#10625057	C₂²	1	2	yes	complemented
84	#10625056	C₂²	1	2	yes	complemented
85	#10625056	C₂²	1	2	yes	complemented
86	#10625055	C₂²	1	2	yes	—
87	#10625055	C₂²	1	2	yes	—
88	#10625054	C₂²	1	2	yes	complemented
89	#10625054	C₂²	1	2	yes	complemented
90	#10625054	C₂²	1	2	yes	complemented
91	#10625054	C₂²	1	2	yes	complemented
92	#10625053	C₂²	1	2	yes	complemented
93	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
94	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
97	#10625050	C₂²	1	2	yes	complemented
98	#10625050	C₂²	1	2	yes	complemented
99	#10625050	C₂²	1	2	yes	complemented
100	#10625050	C₂²	1	2	yes	complemented
101	#10625049	C₂²	1	2	yes	complemented
102	#10625049	C₂²	1	2	yes	complemented
103	C₄×D₉₂	C₂²	1	2	yes	complemented
104	#10625043	C₂²	1	2	yes	complemented
105	C₄²×D₂₃	C₂²	1	2	yes	complemented
106	C₄×Dic₄₆	C₂²	1	2	yes	complemented
107	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
108	C₂³×D₂₃	C₂³	1	2	yes	—
109	C₂³×D₂₃	C₂³	1	1	yes	characteristic
110	#41×C₂₃	—	4	2	no	—
111	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₂₃	C₂³	1	2	yes	—
113	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₂₃	C₂³	1	2	yes	—
115	C₂×D₄×C₂₃	C₂³	1	2	yes	—
116	C₂²×C₄×C₂₃	—	4	2	no	—
117	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
119	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊D₂₃	—	2	4	no	—
125	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
132	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
133	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
134	C₂²×Dic₂₃	C₂³	1	2	yes	—
135	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
136	D₄×D₂₃	—	2	8	no	—
137	#67288	—	4	2	no	—
138	C₂×D₉₂	C₂³	1	2	yes	—
139	C₂×D₉₂	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₂₃	—	4	2	no	—
141	C₂×C₄×D₂₃	—	4	4	no	—
142	C₂×C₄×D₂₃	C₂³	1	2	yes	—
143	C₂×C₄×D₂₃	C₂³	1	2	yes	—
144	C₂×C₄×D₂₃	C₂³	1	2	yes	—
145	C₂×C₄×D₂₃	C₂³	1	2	yes	—
146	C₂×C₄×D₂₃	C₂³	1	2	yes	—
147	C₂×C₄×D₂₃	C₂³	1	2	yes	—
148	C₂×C₄×D₂₃	C₂³	1	2	yes	—
149	C₂×Dic₄₆	C₂³	1	2	yes	—
150	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₄²×C₂₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
162	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
164	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
166	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
167	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
169	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
170	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
180	C₄⋊Dic₂₃	C₂³	1	2	yes	—
181	C₄⋊Dic₂₃	C₂³	1	2	yes	—
182	C₄⋊Dic₂₃	C₂³	1	2	yes	—
183	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
184	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₂₃	C₂³	1	2	yes	—
186	Dic₂₃⋊C₄	C₂³	1	2	yes	—
187	Dic₂₃⋊C₄	C₂³	1	2	yes	—
188	Dic₂₃⋊C₄	C₂³	1	2	yes	—
189	Dic₂₃⋊C₄	C₂³	1	2	yes	—
190	Dic₂₃⋊C₄	C₂³	1	2	yes	—
191	Dic₂₃⋊C₄	C₂³	1	2	yes	—
192	Dic₂₃⋊C₄	C₂³	1	2	yes	—
193	Dic₂₃⋊C₄	C₂³	1	2	yes	—
194	Dic₂₃⋊C₄	C₂³	1	2	yes	—
195	Dic₂₃⋊C₄	C₂³	1	2	yes	—
196	C₄×Dic₂₃	C₂³	1	2	yes	—
197	C₄×Dic₂₃	C₂³	1	2	yes	—
198	C₄×Dic₂₃	C₂³	1	2	yes	—
199	C₄×Dic₂₃	C₂³	1	2	yes	—
200	C₄×Dic₂₃	C₂³	1	2	yes	—
201	C₂³×C₂₃	—	2	2	no	—
202	C₂³×C₂₃	—	4	1	no	—
203	C₂³×C₂₃	—	4	1	no	—
204	C₂³×C₂₃	C₂⁴	1	2	yes	—
205	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
206	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
207	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
208	C₂²×D₂₃	—	2	4	no	—
209	C₂²×D₂₃	—	4	1	no	—
210	C₂²×D₂₃	—	4	2	no	—
211	C₂²×D₂₃	—	4	1	no	—
212	C₂²×D₂₃	—	4	2	no	—
213	C₂²×D₂₃	#41	1	4	yes	complemented
214	C₂²×D₂₃	C₂⁴	1	2	yes	—
215	C₂²×D₂₃	C₂⁴	1	2	yes	—
216	Q₈×C₂₃	—	4	1	no	—
217	D₄×C₂₃	—	2	4	no	—
218	D₄×C₂₃	—	4	2	no	—
219	D₄×C₂₃	—	4	2	no	—
220	D₄×C₂₃	—	4	1	no	—
221	C₂×C₄×C₂₃	—	2	2	no	—
222	C₂×C₄×C₂₃	—	2	4	no	—
223	C₂×C₄×C₂₃	—	2	2	no	—
224	C₂×C₄×C₂₃	—	2	2	no	—
225	C₂×C₄×C₂₃	—	4	1	no	—
226	C₂×C₄×C₂₃	—	4	1	no	—
227	C₂×C₄×C₂₃	—	4	1	no	—
228	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
230	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
231	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
234	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
235	C₂²⋊D₂₃	—	2	4	no	—
236	C₂²⋊D₂₃	—	2	4	no	—
237	C₂²⋊D₂₃	—	2	4	no	—
238	C₂²⋊D₂₃	—	2	4	no	—
239	C₂²⋊D₂₃	—	4	2	no	—
240	C₂²⋊D₂₃	—	4	2	no	—
241	C₂²⋊D₂₃	—	4	2	no	—
242	C₂×Dic₂₃	—	2	2	no	—
243	C₂×Dic₂₃	—	4	2	no	—
244	C₂×Dic₂₃	—	4	1	no	—
245	C₂×Dic₂₃	—	4	1	no	—
246	C₂×Dic₂₃	C₂⁴	1	2	yes	—
247	C₂×Dic₂₃	C₂⁴	1	2	yes	—
248	C₂×Dic₂₃	C₂⁴	1	2	yes	—
249	C₂×Dic₂₃	C₂⁴	1	2	yes	—
250	C₂×Dic₂₃	C₂⁴	1	2	yes	—
251	C₂×Dic₂₃	C₂⁴	1	2	yes	—
252	D₉₂	—	2	4	no	—
253	D₉₂	—	4	1	no	—
254	C₄×D₂₃	—	2	4	no	—
255	C₄×D₂₃	—	2	4	no	—
256	C₄×D₂₃	—	2	4	no	—
257	C₄×D₂₃	—	4	2	no	—
258	C₄×D₂₃	—	4	2	no	—
259	C₄×D₂₃	—	4	2	no	—
260	C₄×D₂₃	—	4	2	no	—
261	Dic₄₆	—	4	2	no	—
262	Dic₄₆	—	4	1	no	—
263	#3459	—	23	1	no	maximal, Sylow
264	C₂²×C₂₃	—	2	1	no	—
265	C₂²×C₂₃	—	2	1	no	—
266	C₂²×C₂₃	—	2	1	no	—
267	C₂²×C₂₃	—	2	1	no	—
268	C₂²×C₂₃	—	2	2	no	—
269	C₂²×C₂₃	—	2	2	no	—
270	C₂²×C₂₃	—	2	1	no	—
271	C₂²×C₂₃	—	2	1	no	—
272	C₂²×C₂₃	—	2	1	no	—
273	C₂²×C₂₃	—	2	2	no	—
274	C₂²×C₂₃	—	2	1	no	—
275	C₂²×C₂₃	—	4	4	no	—
276	C₂²×C₂₃	C₂×#41	1	2	yes	—
277	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
278	C₂×D₂₃	—	2	2	no	—
279	C₂×D₂₃	—	2	2	no	—
280	C₂×D₂₃	—	2	2	no	—
281	C₂×D₂₃	—	2	2	no	—
282	C₂×D₂₃	—	2	2	no	—
283	C₂×D₂₃	—	4	4	no	—
284	C₂×D₂₃	—	4	8	no	—
285	C₂×D₂₃	C₂×#41	1	4	yes	—
286	C₄×C₂₃	—	2	2	no	—
287	C₄×C₂₃	—	2	1	no	—
288	C₄×C₂₃	—	2	1	no	—
289	C₄×C₂₃	—	2	2	no	—
290	C₄×C₂₃	—	2	1	no	—
291	C₄×C₂₃	—	2	2	no	—
292	C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
293	Dic₂₃	—	2	2	no	—
294	Dic₂₃	—	2	2	no	—
295	Dic₂₃	—	2	2	no	—
296	Dic₂₃	—	2	2	no	—
297	Dic₂₃	—	2	2	no	—
298	Dic₂₃	—	2	2	no	—
299	#543	—	23	1	no	—
300	#539	—	23	2	no	—
301	#539	—	23	2	no	—
302	#539	—	23	1	no	—
303	#539	—	23	1	no	—
304	#538	—	23	2	no	—
305	#538	—	23	2	no	—
306	#538	—	23	2	no	—
307	#534	—	23	1	no	—
308	#534	—	23	2	no	—
309	#529	—	23	2	no	—
310	#529	—	23	2	no	—
311	#529	—	23	2	no	—
312	#525	—	23	2	no	—
313	#525	—	23	1	no	—
314	#525	—	23	2	no	—
315	#525	D₂₃	1	1	yes	characteristic, complemented
316	C₂×C₄×D₄	—	23	1	no	—
317	C₂×C₄×D₄	—	23	2	no	—
318	C₂×C₂₃	—	2	2	no	—
319	C₂×C₂₃	—	4	2	no	—
320	C₂×C₂₃	—	4	1	no	—
321	C₂×C₂₃	—	4	1	no	—
322	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
323	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₂₃	#585	1	1	yes	characteristic
325	D₂₃	—	2	4	no	—
326	D₂₃	—	4	2	no	—
327	C₂×#41	—	23	1	no	—
328	C₂×#41	C₂×D₂₃	1	1	yes	characteristic, complemented
329	C₂²×D₄	—	23	1	no	—
330	C₂²×D₄	—	23	2	no	—
331	C₂³×C₄	—	23	1	no	—
332	C₂³×C₄	—	23	2	no	—
333	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
334	#126	—	23	2	no	—
335	#126	—	23	2	no	—
336	#126	—	23	2	no	—
337	#126	—	23	2	no	—
338	#126	—	23	2	no	—
339	#126	—	23	2	no	—
340	#125	—	23	2	no	—
341	#125	—	23	2	no	—
342	#125	—	23	2	no	—
343	#124	—	23	2	no	—
344	#124	—	23	2	no	—
345	#124	—	23	2	no	—
346	#123	—	23	2	no	—
347	#123	—	23	2	no	—
348	#123	—	23	2	no	—
349	#123	—	23	2	no	—
350	#123	—	23	2	no	—
351	#123	—	23	2	no	—
352	#123	—	23	2	no	—
353	#123	—	23	2	no	—
354	#123	—	23	2	no	—
355	#123	—	23	2	no	—
356	#123	—	23	2	no	—
357	#123	C₂×D₂₃	1	2	yes	complemented
358	C₂²⋊Q₈	—	23	2	no	—
359	C₂²⋊Q₈	—	23	2	no	—
360	C₂²⋊Q₈	—	23	1	no	—
361	C₂²⋊Q₈	—	23	1	no	—
362	C₂²⋊Q₈	—	23	2	no	—
363	C₂²⋊Q₈	—	23	2	no	—
364	C₂²⋊Q₈	—	23	2	no	—
365	C₂²⋊Q₈	—	23	2	no	—
366	C₂²⋊Q₈	—	23	2	no	—
367	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
368	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
369	#121	—	23	2	no	—
370	#121	—	23	2	no	—
371	#121	—	23	2	no	—
372	#121	—	23	2	no	—
373	#121	—	23	2	no	—
374	#121	—	23	1	no	—
375	#121	—	23	1	no	—
376	#121	—	23	2	no	—
377	#121	—	23	2	no	—
378	#121	C₂×D₂₃	1	1	yes	characteristic
379	#121	C₂×D₂₃	1	1	yes	characteristic, complemented
380	#120	—	23	2	no	—
381	#120	—	23	2	no	—
382	#120	—	23	2	no	—
383	#120	—	23	2	no	—
384	#120	—	23	2	no	—
385	#120	C₂×D₂₃	1	2	yes	complemented
386	C₄×Q₈	—	23	2	no	—
387	C₄×D₄	—	23	2	no	—
388	C₄×D₄	—	23	2	no	—
389	C₄×D₄	—	23	2	no	—
390	C₄×D₄	—	23	2	no	—
391	C₄×D₄	—	23	2	no	—
392	C₄×D₄	—	23	2	no	—
393	C₄×D₄	—	23	2	no	—
394	C₄×D₄	—	23	2	no	—
395	C₄×D₄	—	23	2	no	—
396	C₄×D₄	—	23	2	no	—
397	C₄×D₄	—	23	2	no	—
398	C₄×D₄	—	23	2	no	—
399	C₄×D₄	—	23	2	no	—
400	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
401	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
402	#117	—	23	2	no	—
403	#117	—	23	1	no	—
404	#117	—	23	2	no	—
405	#117	C₂×D₂₃	1	1	yes	characteristic, complemented
406	C₂×C₄⋊C₄	—	23	1	no	—
407	C₂×C₄⋊C₄	—	23	2	no	—
408	C₂×C₂²⋊C₄	—	23	1	no	—
409	C₂×C₂²⋊C₄	—	23	1	no	—
410	C₂×C₂²⋊C₄	—	23	2	no	—
411	C₂×C₂²⋊C₄	—	23	2	no	—
412	C₂×C₄²	—	23	1	no	—
413	C₂×C₄²	—	23	2	no	—
414	C₂₃	#3459	1	1	yes	characteristic, complemented, Sylow
415	C₂⁴	—	23	1	no	—
416	C₂⁴	—	23	2	no	—
417	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
418	#41	—	4	2	no	—
419	#41	—	92	2	no	—
420	C₂×Q₈	—	23	2	no	—
421	C₂×Q₈	—	23	1	no	—
422	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
423	C₂×D₄	—	23	2	no	—
424	C₂×D₄	—	23	2	no	—
425	C₂×D₄	—	23	2	no	—
426	C₂×D₄	—	23	2	no	—
427	C₂×D₄	—	23	2	no	—
428	C₂×D₄	—	23	2	no	—
429	C₂×D₄	—	23	2	no	—
430	C₂×D₄	—	23	2	no	—
431	C₂×D₄	—	23	1	no	—
432	C₂×D₄	—	46	8	no	—
433	C₂×D₄	—	46	4	no	—
434	C₂×D₄	C₂²×D₂₃	1	2	yes	—
435	C₂×D₄	C₂²×D₂₃	1	2	yes	—
436	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
437	C₂×D₄	C₂²×D₂₃	1	2	yes	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	23	1	no	—
440	C₂²×C₄	—	23	1	no	—
441	C₂²×C₄	—	23	1	no	—
442	C₂²×C₄	—	23	2	no	—
443	C₂²×C₄	—	23	2	no	—
444	C₂²×C₄	—	23	2	no	—
445	C₂²×C₄	—	23	2	no	—
446	C₂²×C₄	—	23	2	no	—
447	C₂²×C₄	—	23	2	no	—
448	C₂²×C₄	—	23	2	no	—
449	C₂²×C₄	—	23	2	no	—
450	C₂²×C₄	—	92	2	no	—
451	C₂²×C₄	—	92	4	no	—
452	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
454	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
456	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
457	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
458	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
459	C₄⋊C₄	—	23	2	no	—
460	C₄⋊C₄	—	23	2	no	—
461	C₄⋊C₄	—	23	2	no	—
462	C₄⋊C₄	—	23	2	no	—
463	C₄⋊C₄	—	23	2	no	—
464	C₄⋊C₄	—	23	2	no	—
465	C₄⋊C₄	—	23	2	no	—
466	C₄⋊C₄	—	23	1	no	—
467	C₄⋊C₄	—	23	2	no	—
468	C₄⋊C₄	—	23	2	no	—
469	C₄⋊C₄	—	23	1	no	—
470	C₄⋊C₄	—	23	2	no	—
471	C₄⋊C₄	—	23	2	no	—
472	C₄⋊C₄	—	23	2	no	—
473	C₄⋊C₄	—	23	2	no	—
474	C₄⋊C₄	—	23	2	no	—
475	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
476	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
479	C₂²⋊C₄	—	23	2	no	—
480	C₂²⋊C₄	—	23	2	no	—
481	C₂²⋊C₄	—	23	2	no	—
482	C₂²⋊C₄	—	23	2	no	—
483	C₂²⋊C₄	—	23	2	no	—
484	C₂²⋊C₄	—	23	2	no	—
485	C₂²⋊C₄	—	23	2	no	—
486	C₂²⋊C₄	—	23	2	no	—
487	C₂²⋊C₄	—	23	2	no	—
488	C₂²⋊C₄	—	23	2	no	—
489	C₂²⋊C₄	—	23	2	no	—
490	C₂²⋊C₄	—	23	2	no	—
491	C₂²⋊C₄	—	23	2	no	—
492	C₂²⋊C₄	—	23	2	no	—
493	C₂²⋊C₄	—	23	2	no	—
494	C₂²⋊C₄	—	23	2	no	—
495	C₂²⋊C₄	—	23	2	no	—
496	C₂²⋊C₄	—	23	2	no	—
497	C₂²⋊C₄	—	23	2	no	—
498	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
503	C₄²	—	23	2	no	—
504	C₄²	—	23	2	no	—
505	C₄²	—	23	2	no	—
506	C₄²	—	23	2	no	—
507	C₄²	—	23	2	no	—
508	C₄²	C₂²×D₂₃	1	2	yes	—
509	C₂³	—	2	2	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	23	2	no	—
513	C₂³	—	23	4	no	—
514	C₂³	—	23	2	no	—
515	C₂³	—	46	4	no	—
516	C₂³	—	92	1	no	—
517	C₂³	—	92	2	no	—
518	C₂³	—	92	1	no	—
519	C₂³	—	92	2	no	—
520	C₂³	C₂³×D₂₃	1	2	yes	—
521	C₂³	C₂³×D₂₃	1	1	yes	characteristic
522	C₂³	C₂³×D₂₃	1	1	yes	characteristic
523	C₂³	C₂³×D₂₃	1	1	yes	characteristic
524	Q₈	—	4	1	no	—
525	Q₈	—	92	1	no	—
526	Q₈	—	92	2	no	—
527	D₄	—	2	4	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	46	4	no	—
532	D₄	—	46	4	no	—
533	D₄	—	46	4	no	—
534	D₄	—	46	4	no	—
535	D₄	—	46	4	no	—
536	D₄	—	92	1	no	—
537	D₄	—	92	2	no	—
538	D₄	—	92	2	no	—
539	D₄	—	92	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	23	2	no	—
548	C₂×C₄	—	23	2	no	—
549	C₂×C₄	—	23	2	no	—
550	C₂×C₄	—	23	2	no	—
551	C₂×C₄	—	23	2	no	—
552	C₂×C₄	—	23	2	no	—
553	C₂×C₄	—	46	4	no	—
554	C₂×C₄	—	46	2	no	—
555	C₂×C₄	—	46	4	no	—
556	C₂×C₄	—	46	4	no	—
557	C₂×C₄	—	92	2	no	—
558	C₂×C₄	—	92	2	no	—
559	C₂×C₄	—	92	2	no	—
560	C₂×C₄	—	92	2	no	—
561	C₂×C₄	—	92	1	no	—
562	C₂×C₄	—	92	2	no	—
563	C₂×C₄	—	92	1	no	—
564	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₂₃	1	2	yes	—
566	C₂×C₄	C₂³×D₂₃	1	2	yes	—
567	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₂₃	1	2	yes	—
569	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	23	4	no	—
584	C₂²	—	46	2	no	—
585	C₂²	—	46	2	no	—
586	C₂²	—	46	2	no	—
587	C₂²	—	46	2	no	—
588	C₂²	—	46	2	no	—
589	C₂²	—	92	4	no	—
590	C₂²	—	92	8	no	—
591	C₂²	#41×D₂₃	1	2	yes	—
592	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
593	C₄	—	2	2	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	46	2	no	—
600	C₄	—	46	2	no	—
601	C₄	—	46	2	no	—
602	C₄	—	46	2	no	—
603	C₄	—	46	2	no	—
604	C₄	—	46	2	no	—
605	C₄	#10625155	1	2	yes	—
606	C₂	—	2	2	no	—
607	C₂	—	4	1	no	—
608	C₂	—	4	1	no	—
609	C₂	—	4	2	no	—
610	C₂	—	46	4	no	—
611	C₂	—	92	2	no	—
612	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
613	C₂	C₂×#10625155	1	1	yes	characteristic
614	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	#3459
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. #13093042	C₂	semidirect
2. #13093016	C₂	semidirect
3. #13093013	C₂	semidirect
4. #13093012	C₂	semidirect
5. #13093010	C₂	semidirect
6. #13093003	C₂	semidirect
7. #13093002	C₂	semidirect
8. #13092999	C₂	semidirect
9. #13092977	C₂	semidirect
10. #13092975	C₂	semidirect
11. #13092949	C₂	semidirect
12. #13092947	C₂	semidirect
13. #13092945	C₂	semidirect
14. #13092928	C₂	semidirect
15. #13092926	C₂	semidirect
16. #13092924	C₂	semidirect
17. C₂×C₄×C₂²⋊D₂₃	C₂	semidirect
18. C₄×D₄×D₂₃	C₂	semidirect
19. C₂₃×#525	C₂	semidirect
20. C₂×#41×C₂₃	C₂²	semidirect
21. C₂³×C₄×C₂₃	C₂²	semidirect
24. C₂×#67288	C₂²	semidirect
26. C₂²×C₄×D₂₃	C₂²	semidirect
27. C₂₃×#123	C₂²	semidirect
28. C₂₃×C₂²⋊Q₈	C₂²	semidirect
29. C₂₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂₃×#121	C₂²	semidirect
32. C₂₃×#120	C₂²	semidirect
33. C₄×D₄×C₂₃	C₂²	semidirect
34. C₄×D₄×C₂₃	C₂²	semidirect
35. C₂₃×#117	C₂²	semidirect
36. #10625124	C₂²	semidirect
37. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
38. #10625117	C₂²	semidirect
39. #10625117	C₂²	semidirect
41. #10625110	C₂²	semidirect
44. #10625109	C₂²	semidirect
45. #10625108	C₂²	semidirect
46. #10625108	C₂²	semidirect
47. #10625108	C₂²	semidirect
48. #10625107	C₂²	semidirect
49. #10625106	C₂²	semidirect
50. #10625106	C₂²	semidirect
51. #10625106	C₂²	semidirect
52. D₄×Dic₂₃	C₂²	semidirect
54. #10625101	C₂²	semidirect
55. #10625100	C₂²	semidirect
56. C₄×C₂²⋊D₂₃	C₂²	semidirect
57. C₄×C₂²⋊D₂₃	C₂²	semidirect
58. C₄×C₂²⋊D₂₃	C₂²	semidirect
59. C₄×C₂²⋊D₂₃	C₂²	semidirect
60. C₄×C₂²⋊D₂₃	C₂²	semidirect
61. C₄×C₂²⋊D₂₃	C₂²	semidirect
62. C₄×C₂²⋊D₂₃	C₂²	semidirect
63. C₄×C₂²⋊D₂₃	C₂²	semidirect
65. #10625097	C₂²	semidirect
66. #10625097	C₂²	semidirect
67. #10625095	C₂²	semidirect
68. #10625095	C₂²	semidirect
69. C₂×Dic₂₃⋊C₄	C₂²	semidirect
70. C₂×C₄×Dic₂₃	C₂²	semidirect
71. #10625069	C₂²	semidirect
72. #10625069	C₂²	semidirect
73. #10625068	C₂²	semidirect
74. #10625067	C₂²	semidirect
75. #10625067	C₂²	semidirect
76. #10625065	C₂²	semidirect
77. #10625065	C₂²	semidirect
78. #10625064	C₂²	semidirect
79. C₄⋊C₄×D₂₃	C₂²	semidirect
80. #10625061	C₂²	semidirect
81. #10625060	C₂²	semidirect
82. #10625060	C₂²	semidirect
83. #10625057	C₂²	semidirect
84. #10625056	C₂²	semidirect
85. #10625056	C₂²	semidirect
88. #10625054	C₂²	semidirect
89. #10625054	C₂²	semidirect
90. #10625054	C₂²	semidirect
91. #10625054	C₂²	semidirect
92. #10625053	C₂²	semidirect
93. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
94. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
96. C₂²⋊C₄×D₂₃	C₂²	semidirect
97. #10625050	C₂²	semidirect
98. #10625050	C₂²	semidirect
99. #10625050	C₂²	semidirect
100. #10625050	C₂²	semidirect
101. #10625049	C₂²	semidirect
102. #10625049	C₂²	semidirect
103. C₄×D₉₂	C₂²	semidirect
104. #10625043	C₂²	semidirect
105. C₄²×D₂₃	C₂²	semidirect
106. C₄×Dic₄₆	C₂²	semidirect
213. C₂²×D₂₃	#41	semidirect
315. #525	D₂₃	semidirect
328. C₂×#41	C₂×D₂₃	semidirect
333. C₂³×C₄	C₂×D₂₃	semidirect
357. #123	C₂×D₂₃	semidirect
367. C₂²⋊Q₈	C₂×D₂₃	semidirect
368. C₂²⋊Q₈	C₂×D₂₃	semidirect
379. #121	C₂×D₂₃	semidirect
385. #120	C₂×D₂₃	semidirect
400. C₄×D₄	C₂×D₂₃	semidirect
401. C₄×D₄	C₂×D₂₃	semidirect
405. #117	C₂×D₂₃	semidirect
414. C₂₃	#3459	semidirect

Maximal subgroups

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

subgroup	index
#13093042	2
#13093016	2
#13093013	2
#13093012	2
#13093010	2
#13093003	2
#13093002	2
#13092999	2
#13092977	2
#13092975	2
#13092949	2
#13092947	2
#13092945	2
#13092928	2
#13092926	2
#13092924	2
C₂×C₄×C₂²⋊D₂₃	2
C₄×D₄×D₂₃	2
C₂₃×#525	2
#3459	23