Subgroups — #15686808

Order 2944.

1160 conjugacy classes of subgroups.

The subgroup lattice has 604 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	#13093010	C₂	1	2	yes	maximal, complemented
3	#13093009	C₂	1	2	yes	maximal, complemented
4	#13093008	C₂	1	2	yes	maximal, complemented
5	#13093005	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093001	C₂	1	2	yes	maximal, complemented
7	#13092999	C₂	1	2	yes	maximal, complemented
8	#13092977	C₂	1	2	yes	maximal, complemented
9	#13092975	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092953	C₂	1	1	yes	maximal, characteristic, complemented
11	#13092950	C₂	1	2	yes	maximal, complemented
12	#13092948	C₂	1	1	yes	maximal, characteristic, complemented
13	#13092946	C₂	1	2	yes	maximal, complemented
14	#13092927	C₂	1	2	yes	maximal, complemented
15	#13092925	C₂	1	2	yes	maximal, complemented
16	#13092923	C₂	1	2	yes	maximal, complemented
17	C₂×(C₂²⋊D₂₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₂₃	C₂	1	2	yes	maximal, complemented
19	C₂₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
21	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×#67290	C₂²	1	2	yes	complemented
23	C₂×D₄×D₂₃	C₂²	1	2	yes	—
24	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
26	C₂₃×#126	C₂²	1	2	yes	complemented
27	C₂₃×#124	C₂²	1	2	yes	complemented
28	C₂₃×#123	C₂²	1	2	yes	complemented
29	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#121	C₂²	1	1	yes	characteristic
31	C₂₃×#121	C₂²	1	2	yes	complemented
32	C₂₃×#120	C₂²	1	2	yes	complemented
33	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
34	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
35	#10625124	C₂²	1	2	yes	complemented
36	#10625118	C₂²	1	1	yes	characteristic, complemented
37	#10625117	C₂²	1	2	yes	complemented
38	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
39	#10625110	C₂²	1	2	yes	—
40	#10625110	C₂²	1	2	yes	complemented
41	#10625109	C₂²	1	2	yes	—
42	#10625109	C₂²	1	2	yes	—
43	#10625108	C₂²	1	2	yes	complemented
44	#10625108	C₂²	1	2	yes	complemented
45	#10625108	C₂²	1	2	yes	complemented
46	#10625107	C₂²	1	1	yes	characteristic, complemented
47	#10625106	C₂²	1	2	yes	complemented
48	#10625106	C₂²	1	2	yes	complemented
49	D₄×Dic₂₃	C₂²	1	2	yes	complemented
50	D₄×Dic₂₃	C₂²	1	2	yes	complemented
51	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
52	#10625101	C₂²	1	1	yes	characteristic
53	#10625100	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
56	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
57	#10625095	C₂²	1	2	yes	complemented
58	#10625095	C₂²	1	1	yes	characteristic, complemented
59	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
61	#10625069	C₂²	1	2	yes	complemented
62	#10625068	C₂²	1	2	yes	complemented
63	#10625067	C₂²	1	2	yes	complemented
64	#10625067	C₂²	1	2	yes	complemented
65	#10625067	C₂²	1	2	yes	complemented
66	#10625065	C₂²	1	2	yes	complemented
67	#10625064	C₂²	1	2	yes	complemented
68	#10625064	C₂²	1	1	yes	characteristic, complemented
69	#10625063	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
71	#10625061	C₂²	1	1	yes	characteristic, complemented
72	#10625061	C₂²	1	1	yes	characteristic, complemented
73	#10625060	C₂²	1	2	yes	complemented
74	#10625058	C₂²	1	1	yes	characteristic, complemented
75	#10625057	C₂²	1	2	yes	complemented
76	#10625057	C₂²	1	2	yes	complemented
77	#10625056	C₂²	1	2	yes	complemented
78	#10625055	C₂²	1	2	yes	—
79	#10625055	C₂²	1	2	yes	—
80	#10625055	C₂²	1	2	yes	complemented
81	#10625054	C₂²	1	2	yes	complemented
82	#10625054	C₂²	1	2	yes	complemented
83	#10625054	C₂²	1	2	yes	complemented
84	#10625054	C₂²	1	2	yes	complemented
85	#10625054	C₂²	1	2	yes	complemented
86	#10625053	C₂²	1	2	yes	complemented
87	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
88	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
89	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
90	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
91	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
92	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
93	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
96	#10625050	C₂²	1	2	yes	complemented
97	#10625050	C₂²	1	2	yes	complemented
98	#10625050	C₂²	1	2	yes	complemented
99	#10625049	C₂²	1	2	yes	complemented
100	#10625049	C₂²	1	2	yes	complemented
101	#10625048	C₂²	1	2	yes	complemented
102	#10625048	C₂²	1	2	yes	complemented
103	#10625047	C₂²	1	2	yes	complemented
104	C₄×D₉₂	C₂²	1	2	yes	complemented
105	C₄²×D₂₃	C₂²	1	2	yes	complemented
106	#10625041	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	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₂₃	C₂³	1	2	yes	—
112	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₂₃	C₂³	1	2	yes	—
114	C₂×D₄×C₂₃	C₂³	1	2	yes	—
115	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₂₃	—	2	4	no	—
119	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
126	C₂²×Dic₂₃	—	4	2	no	—
127	C₂²×Dic₂₃	C₂³	1	2	yes	—
128	C₂²×Dic₂₃	C₂³	1	2	yes	—
129	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
130	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
131	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
132	C₂²×Dic₂₃	C₂³	1	2	yes	—
133	#67290	—	4	4	no	—
134	D₄×D₂₃	—	2	8	no	—
135	C₂×D₉₂	C₂³	1	2	yes	—
136	C₂×D₉₂	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₂₃	—	4	2	no	—
138	C₂×C₄×D₂₃	—	4	4	no	—
139	C₂×C₄×D₂₃	C₂³	1	2	yes	—
140	C₂×C₄×D₂₃	C₂³	1	2	yes	—
141	C₂×C₄×D₂₃	C₂³	1	2	yes	—
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×Dic₄₆	C₂³	1	2	yes	—
147	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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	C₄²×C₂₃	C₂³	1	2	yes	—
160	C₂²⋊Dic₂₃	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	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₂₃)⋊C₄	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	C₄⋊Dic₂₃	C₂³	1	2	yes	—
178	C₄⋊Dic₂₃	C₂³	1	2	yes	—
179	C₄⋊Dic₂₃	C₂³	1	2	yes	—
180	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
181	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₂₃	C₂³	1	2	yes	—
183	Dic₂₃⋊C₄	C₂³	1	2	yes	—
184	Dic₂₃⋊C₄	C₂³	1	2	yes	—
185	Dic₂₃⋊C₄	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	C₄×Dic₂₃	C₂³	1	2	yes	—
194	C₄×Dic₂₃	C₂³	1	2	yes	—
195	C₄×Dic₂₃	C₂³	1	2	yes	—
196	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
197	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
200	C₂³×C₂₃	—	2	2	no	—
201	C₂³×C₂₃	—	4	1	no	—
202	C₂³×C₂₃	—	4	1	no	—
203	C₂³×C₂₃	C₂⁴	1	2	yes	—
204	C₂³×C₂₃	C₂⁴	1	2	yes	—
205	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
206	C₂²×D₂₃	—	2	4	no	—
207	C₂²×D₂₃	—	4	1	no	—
208	C₂²×D₂₃	—	4	2	no	—
209	C₂²×D₂₃	—	4	1	no	—
210	C₂²×D₂₃	—	4	2	no	—
211	C₂²×D₂₃	#41	1	4	yes	complemented
212	C₂²×D₂₃	C₂⁴	1	2	yes	—
213	C₂²×D₂₃	C₂⁴	1	2	yes	—
214	Q₈×C₂₃	—	4	1	no	—
215	D₄×C₂₃	—	2	4	no	—
216	D₄×C₂₃	—	4	2	no	—
217	D₄×C₂₃	—	4	1	no	—
218	D₄×C₂₃	—	4	2	no	—
219	C₂×C₄×C₂₃	—	4	2	no	—
220	C₂×C₄×C₂₃	—	4	1	no	—
221	C₂×C₄×C₂₃	—	4	1	no	—
222	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
223	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
224	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
225	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
226	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
227	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
228	C₂²⋊D₂₃	—	2	4	no	—
229	C₂²⋊D₂₃	—	2	4	no	—
230	C₂²⋊D₂₃	—	2	4	no	—
231	C₂²⋊D₂₃	—	2	4	no	—
232	C₂²⋊D₂₃	—	4	2	no	—
233	C₂²⋊D₂₃	—	4	2	no	—
234	C₂²⋊D₂₃	—	4	2	no	—
235	C₂×Dic₂₃	—	2	2	no	—
236	C₂×Dic₂₃	—	2	4	no	—
237	C₂×Dic₂₃	—	2	2	no	—
238	C₂×Dic₂₃	—	2	4	no	—
239	C₂×Dic₂₃	—	4	1	no	—
240	C₂×Dic₂₃	—	4	2	no	—
241	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₂₃	C₂⁴	1	2	yes	—
244	C₂×Dic₂₃	C₂⁴	1	2	yes	—
245	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₂₃	C₂⁴	1	2	yes	—
247	C₂×Dic₂₃	C₂⁴	1	2	yes	—
248	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
249	D₉₂	—	2	4	no	—
250	D₉₂	—	4	1	no	—
251	C₄×D₂₃	—	2	4	no	—
252	C₄×D₂₃	—	2	4	no	—
253	C₄×D₂₃	—	2	4	no	—
254	C₄×D₂₃	—	4	2	no	—
255	C₄×D₂₃	—	4	2	no	—
256	C₄×D₂₃	—	4	2	no	—
257	C₄×D₂₃	—	4	2	no	—
258	Dic₄₆	—	4	1	no	—
259	Dic₄₆	—	4	2	no	—
260	#3459	—	23	1	no	maximal, Sylow
261	C₂²×C₂₃	—	2	1	no	—
262	C₂²×C₂₃	—	2	1	no	—
263	C₂²×C₂₃	—	2	2	no	—
264	C₂²×C₂₃	—	2	2	no	—
265	C₂²×C₂₃	—	2	2	no	—
266	C₂²×C₂₃	—	2	2	no	—
267	C₂²×C₂₃	—	2	2	no	—
268	C₂²×C₂₃	—	2	2	no	—
269	C₂²×C₂₃	—	4	4	no	—
270	C₂²×C₂₃	C₂×#41	1	2	yes	—
271	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
272	C₂×D₂₃	—	2	2	no	—
273	C₂×D₂₃	—	2	2	no	—
274	C₂×D₂₃	—	2	2	no	—
275	C₂×D₂₃	—	2	2	no	—
276	C₂×D₂₃	—	2	2	no	—
277	C₂×D₂₃	—	4	4	no	—
278	C₂×D₂₃	—	4	8	no	—
279	C₂×D₂₃	C₂×#41	1	4	yes	—
280	C₄×C₂₃	—	2	2	no	—
281	C₄×C₂₃	—	2	2	no	—
282	C₄×C₂₃	—	2	2	no	—
283	C₄×C₂₃	—	2	1	no	—
284	C₄×C₂₃	—	2	2	no	—
285	C₄×C₂₃	—	2	1	no	—
286	Dic₂₃	—	2	2	no	—
287	Dic₂₃	—	2	1	no	—
288	Dic₂₃	—	2	1	no	—
289	Dic₂₃	—	2	2	no	—
290	Dic₂₃	—	2	2	no	—
291	Dic₂₃	—	2	1	no	—
292	Dic₂₃	—	2	2	no	—
293	Dic₂₃	H(5,𝔽₂)	1	2	yes	—
294	#543	—	23	1	no	—
295	#539	—	23	2	no	—
296	#539	—	23	2	no	—
297	#539	—	23	2	no	—
298	#538	—	23	2	no	—
299	#538	—	23	2	no	—
300	#538	—	23	1	no	—
301	#538	D₂₃	1	1	yes	characteristic, complemented
302	#534	—	23	1	no	—
303	#534	—	23	2	no	—
304	#529	—	23	2	no	—
305	#529	—	23	2	no	—
306	#529	—	23	1	no	—
307	#529	—	23	1	no	—
308	#525	—	23	2	no	—
309	#525	—	23	2	no	—
310	#525	—	23	2	no	—
311	C₂×C₄×D₄	—	23	2	no	—
312	C₂×C₄×D₄	—	23	1	no	—
313	C₂×C₂₃	—	2	2	no	—
314	C₂×C₂₃	—	4	2	no	—
315	C₂×C₂₃	—	4	2	no	—
316	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
317	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂×C₂₃	#585	1	1	yes	characteristic
319	D₂₃	—	2	4	no	—
320	D₂₃	—	4	2	no	—
321	C₂×#41	—	23	2	no	—
322	C₂²×D₄	—	23	1	no	—
323	C₂²×D₄	—	23	2	no	—
324	C₂³×C₄	—	23	1	no	—
325	C₂³×C₄	—	23	1	no	—
326	C₂³×C₄	—	23	2	no	—
327	#126	—	23	2	no	—
328	#126	—	23	2	no	—
329	#126	—	23	2	no	—
330	#126	—	23	2	no	—
331	#126	—	23	2	no	—
332	#126	C₂×D₂₃	1	2	yes	complemented
333	#125	—	23	2	no	—
334	#125	—	23	1	no	—
335	#125	—	23	1	no	—
336	#125	—	23	2	no	—
337	#124	—	23	1	no	—
338	#124	—	23	1	no	—
339	#124	—	23	2	no	—
340	#124	C₂×D₂₃	1	2	yes	complemented
341	#123	—	23	2	no	—
342	#123	—	23	2	no	—
343	#123	—	23	2	no	—
344	#123	—	23	2	no	—
345	#123	—	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	C₂×D₂₃	1	2	yes	complemented
353	C₂²⋊Q₈	—	23	2	no	—
354	C₂²⋊Q₈	—	23	2	no	—
355	C₂²⋊Q₈	—	23	1	no	—
356	C₂²⋊Q₈	—	23	2	no	—
357	C₂²⋊Q₈	—	23	2	no	—
358	C₂²⋊Q₈	—	23	2	no	—
359	C₂²⋊Q₈	—	23	2	no	—
360	C₂²⋊Q₈	—	23	2	no	—
361	C₂²⋊Q₈	—	23	2	no	—
362	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
363	#121	—	23	2	no	—
364	#121	—	23	2	no	—
365	#121	—	23	2	no	—
366	#121	—	23	2	no	—
367	#121	—	23	1	no	—
368	#121	—	23	2	no	—
369	#121	—	23	2	no	—
370	#121	—	23	2	no	—
371	#121	C₂×D₂₃	1	1	yes	characteristic
372	#121	C₂×D₂₃	1	2	yes	complemented
373	#120	—	23	2	no	—
374	#120	—	23	2	no	—
375	#120	—	23	2	no	—
376	#120	—	23	2	no	—
377	#120	—	23	2	no	—
378	#120	C₂×D₂₃	1	2	yes	complemented
379	C₄×Q₈	—	23	1	no	—
380	C₄×Q₈	—	23	1	no	—
381	C₄×D₄	—	23	2	no	—
382	C₄×D₄	—	23	1	no	—
383	C₄×D₄	—	23	2	no	—
384	C₄×D₄	—	23	2	no	—
385	C₄×D₄	—	23	2	no	—
386	C₄×D₄	—	23	2	no	—
387	C₄×D₄	—	23	1	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	C₂×D₂₃	1	2	yes	complemented
397	#117	—	23	2	no	—
398	#117	—	23	2	no	—
399	#117	—	23	2	no	—
400	C₂×C₄⋊C₄	—	23	1	no	—
401	C₂×C₄⋊C₄	—	23	2	no	—
402	C₂×C₂²⋊C₄	—	23	1	no	—
403	C₂×C₂²⋊C₄	—	23	2	no	—
404	C₂×C₂²⋊C₄	—	23	2	no	—
405	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
406	C₂×C₄²	—	23	1	no	—
407	C₂×C₄²	—	23	2	no	—
408	C₂₃	#3459	1	1	yes	characteristic, complemented, Sylow
409	C₂⁴	—	23	1	no	—
410	C₂⁴	—	23	2	no	—
411	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
412	#41	—	92	4	no	—
413	C₂×Q₈	—	23	1	no	—
414	C₂×Q₈	—	23	2	no	—
415	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
416	C₂×D₄	—	23	2	no	—
417	C₂×D₄	—	23	2	no	—
418	C₂×D₄	—	23	2	no	—
419	C₂×D₄	—	23	2	no	—
420	C₂×D₄	—	23	2	no	—
421	C₂×D₄	—	23	2	no	—
422	C₂×D₄	—	23	2	no	—
423	C₂×D₄	—	23	2	no	—
424	C₂×D₄	—	23	1	no	—
425	C₂×D₄	—	46	8	no	—
426	C₂×D₄	—	46	4	no	—
427	C₂×D₄	C₂²×D₂₃	1	2	yes	—
428	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₂₃	1	2	yes	—
430	C₂×D₄	C₂²×D₂₃	1	2	yes	—
431	C₂²×C₄	—	23	1	no	—
432	C₂²×C₄	—	23	1	no	—
433	C₂²×C₄	—	23	2	no	—
434	C₂²×C₄	—	23	2	no	—
435	C₂²×C₄	—	23	1	no	—
436	C₂²×C₄	—	23	2	no	—
437	C₂²×C₄	—	23	2	no	—
438	C₂²×C₄	—	23	2	no	—
439	C₂²×C₄	—	23	2	no	—
440	C₂²×C₄	—	23	2	no	—
441	C₂²×C₄	—	23	2	no	—
442	C₂²×C₄	—	23	2	no	—
443	C₂²×C₄	—	23	2	no	—
444	C₂²×C₄	—	92	2	no	—
445	C₂²×C₄	—	92	4	no	—
446	C₂²×C₄	—	92	2	no	—
447	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
448	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
450	C₄⋊C₄	—	23	2	no	—
451	C₄⋊C₄	—	23	2	no	—
452	C₄⋊C₄	—	23	2	no	—
453	C₄⋊C₄	—	23	2	no	—
454	C₄⋊C₄	—	23	2	no	—
455	C₄⋊C₄	—	23	2	no	—
456	C₄⋊C₄	—	23	2	no	—
457	C₄⋊C₄	—	23	2	no	—
458	C₄⋊C₄	—	23	2	no	—
459	C₄⋊C₄	—	23	2	no	—
460	C₄⋊C₄	—	23	2	no	—
461	C₄⋊C₄	—	23	1	no	—
462	C₄⋊C₄	—	23	2	no	—
463	C₄⋊C₄	—	23	2	no	—
464	C₄⋊C₄	—	23	1	no	—
465	C₄⋊C₄	—	23	2	no	—
466	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
467	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
468	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
470	C₂²⋊C₄	—	23	2	no	—
471	C₂²⋊C₄	—	23	2	no	—
472	C₂²⋊C₄	—	23	2	no	—
473	C₂²⋊C₄	—	23	2	no	—
474	C₂²⋊C₄	—	23	2	no	—
475	C₂²⋊C₄	—	23	2	no	—
476	C₂²⋊C₄	—	23	2	no	—
477	C₂²⋊C₄	—	23	2	no	—
478	C₂²⋊C₄	—	23	2	no	—
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	C₂²×D₂₃	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
489	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
490	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
491	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
494	C₄²	—	23	2	no	—
495	C₄²	—	23	1	no	—
496	C₄²	—	23	1	no	—
497	C₄²	—	23	2	no	—
498	C₄²	—	23	2	no	—
499	C₄²	—	23	1	no	—
500	C₄²	—	23	1	no	—
501	C₄²	C₂²×D₂₃	1	2	yes	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	23	2	no	—
506	C₂³	—	23	4	no	—
507	C₂³	—	23	2	no	—
508	C₂³	—	46	4	no	—
509	C₂³	—	92	1	no	—
510	C₂³	—	92	2	no	—
511	C₂³	—	92	1	no	—
512	C₂³	—	92	2	no	—
513	C₂³	C₂³×D₂₃	1	2	yes	—
514	C₂³	C₂³×D₂₃	1	2	yes	—
515	C₂³	C₂³×D₂₃	1	1	yes	characteristic
516	Q₈	—	4	1	no	—
517	Q₈	—	92	2	no	—
518	Q₈	—	92	1	no	—
519	D₄	—	2	4	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	2	no	—
523	D₄	—	46	4	no	—
524	D₄	—	46	4	no	—
525	D₄	—	46	4	no	—
526	D₄	—	46	4	no	—
527	D₄	—	46	4	no	—
528	D₄	—	92	1	no	—
529	D₄	—	92	2	no	—
530	D₄	—	92	2	no	—
531	D₄	—	92	2	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	23	1	no	—
536	C₂×C₄	—	23	2	no	—
537	C₂×C₄	—	23	1	no	—
538	C₂×C₄	—	23	2	no	—
539	C₂×C₄	—	23	1	no	—
540	C₂×C₄	—	23	1	no	—
541	C₂×C₄	—	23	2	no	—
542	C₂×C₄	—	23	2	no	—
543	C₂×C₄	—	46	4	no	—
544	C₂×C₄	—	46	4	no	—
545	C₂×C₄	—	46	4	no	—
546	C₂×C₄	—	46	2	no	—
547	C₂×C₄	—	46	4	no	—
548	C₂×C₄	—	46	4	no	—
549	C₂×C₄	—	46	2	no	—
550	C₂×C₄	—	92	2	no	—
551	C₂×C₄	—	92	2	no	—
552	C₂×C₄	—	92	2	no	—
553	C₂×C₄	—	92	2	no	—
554	C₂×C₄	—	92	2	no	—
555	C₂×C₄	—	92	1	no	—
556	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₂₃	1	2	yes	—
559	C₂×C₄	C₂³×D₂₃	1	2	yes	—
560	C₂×C₄	C₂³×D₂₃	1	2	yes	—
561	C₂×C₄	C₂³×D₂₃	1	2	yes	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	23	4	no	—
572	C₂²	—	46	2	no	—
573	C₂²	—	46	2	no	—
574	C₂²	—	46	2	no	—
575	C₂²	—	46	2	no	—
576	C₂²	—	46	2	no	—
577	C₂²	—	92	4	no	—
578	C₂²	—	92	8	no	—
579	C₂²	#41×D₂₃	1	2	yes	—
580	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	23	2	no	—
588	C₄	—	46	2	no	—
589	C₄	—	46	1	no	—
590	C₄	—	46	1	no	—
591	C₄	—	46	1	no	—
592	C₄	—	46	2	no	—
593	C₄	—	46	2	no	—
594	C₄	—	46	2	no	—
595	C₂	—	2	2	no	—
596	C₂	—	4	2	no	—
597	C₂	—	4	2	no	—
598	C₂	—	46	4	no	—
599	C₂	—	92	2	no	—
600	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
601	C₂	H(5,𝔽₂)×D₂₃	1	1	yes	characteristic
602	C₂	#13093252	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#538	C₂
hypercenter	#538	D₂₃
hypocenter	C₂₃	#3459
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #13093042	C₂	semidirect
2. #13093010	C₂	semidirect
3. #13093009	C₂	semidirect
4. #13093008	C₂	semidirect
5. #13093005	C₂	semidirect
6. #13093001	C₂	semidirect
7. #13092999	C₂	semidirect
8. #13092977	C₂	semidirect
9. #13092975	C₂	semidirect
10. #13092953	C₂	semidirect
11. #13092950	C₂	semidirect
12. #13092948	C₂	semidirect
13. #13092946	C₂	semidirect
14. #13092927	C₂	semidirect
15. #13092925	C₂	semidirect
16. #13092923	C₂	semidirect
17. C₂×(C₂²⋊D₂₃)⋊C₄	C₂	semidirect
18. C₄×D₄×D₂₃	C₂	semidirect
19. C₂₃×#538	C₂	semidirect
21. C₂³×Dic₂₃	C₂²	semidirect
22. C₂×#67290	C₂²	semidirect
25. C₂²×C₄×D₂₃	C₂²	semidirect
26. C₂₃×#126	C₂²	semidirect
27. C₂₃×#124	C₂²	semidirect
28. C₂₃×#123	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. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
35. #10625124	C₂²	semidirect
36. #10625118	C₂²	semidirect
37. #10625117	C₂²	semidirect
38. Q₈×Dic₂₃	C₂²	semidirect
40. #10625110	C₂²	semidirect
43. #10625108	C₂²	semidirect
44. #10625108	C₂²	semidirect
45. #10625108	C₂²	semidirect
46. #10625107	C₂²	semidirect
47. #10625106	C₂²	semidirect
48. #10625106	C₂²	semidirect
49. D₄×Dic₂₃	C₂²	semidirect
50. D₄×Dic₂₃	C₂²	semidirect
51. D₄×Dic₂₃	C₂²	semidirect
53. #10625100	C₂²	semidirect
54. C₄×C₂²⋊D₂₃	C₂²	semidirect
55. C₄×C₂²⋊D₂₃	C₂²	semidirect
57. #10625095	C₂²	semidirect
58. #10625095	C₂²	semidirect
59. C₂×Dic₂₃⋊C₄	C₂²	semidirect
60. C₂×C₄×Dic₂₃	C₂²	semidirect
61. #10625069	C₂²	semidirect
62. #10625068	C₂²	semidirect
63. #10625067	C₂²	semidirect
64. #10625067	C₂²	semidirect
65. #10625067	C₂²	semidirect
66. #10625065	C₂²	semidirect
67. #10625064	C₂²	semidirect
68. #10625064	C₂²	semidirect
69. #10625063	C₂²	semidirect
70. C₄⋊C₄×D₂₃	C₂²	semidirect
71. #10625061	C₂²	semidirect
72. #10625061	C₂²	semidirect
73. #10625060	C₂²	semidirect
74. #10625058	C₂²	semidirect
75. #10625057	C₂²	semidirect
76. #10625057	C₂²	semidirect
77. #10625056	C₂²	semidirect
80. #10625055	C₂²	semidirect
81. #10625054	C₂²	semidirect
82. #10625054	C₂²	semidirect
83. #10625054	C₂²	semidirect
84. #10625054	C₂²	semidirect
85. #10625054	C₂²	semidirect
86. #10625053	C₂²	semidirect
87. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
88. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
89. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
90. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
91. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
92. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
93. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
95. C₂²⋊C₄×D₂₃	C₂²	semidirect
96. #10625050	C₂²	semidirect
97. #10625050	C₂²	semidirect
98. #10625050	C₂²	semidirect
99. #10625049	C₂²	semidirect
100. #10625049	C₂²	semidirect
101. #10625048	C₂²	semidirect
102. #10625048	C₂²	semidirect
103. #10625047	C₂²	semidirect
104. C₄×D₉₂	C₂²	semidirect
105. C₄²×D₂₃	C₂²	semidirect
106. #10625041	C₂²	semidirect
211. C₂²×D₂₃	#41	semidirect
301. #538	D₂₃	semidirect
332. #126	C₂×D₂₃	semidirect
340. #124	C₂×D₂₃	semidirect
352. #123	C₂×D₂₃	semidirect
362. C₂²⋊Q₈	C₂×D₂₃	semidirect
372. #121	C₂×D₂₃	semidirect
378. #120	C₂×D₂₃	semidirect
396. C₄×D₄	C₂×D₂₃	semidirect
405. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
408. 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
#13093010	2
#13093009	2
#13093008	2
#13093005	2
#13093001	2
#13092999	2
#13092977	2
#13092975	2
#13092953	2
#13092950	2
#13092948	2
#13092946	2
#13092927	2
#13092925	2
#13092923	2
C₂×(C₂²⋊D₂₃)⋊C₄	2
C₄×D₄×D₂₃	2
C₂₃×#538	2
#3459	23