Subgroups — #15687551

Order 2944.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093159	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093155	C₂	1	2	yes	maximal, complemented
3	#13093154	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093097	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093091	C₂	1	2	yes	maximal, complemented
6	#13093056	C₂	1	2	yes	maximal, complemented
7	#13093055	C₂	1	2	yes	maximal, complemented
8	#13093054	C₂	1	2	yes	maximal, complemented
9	#13093052	C₂	1	1	yes	maximal, characteristic, complemented
10	#13093049	C₂	1	2	yes	maximal, complemented
11	#13093002	C₂	1	2	yes	maximal, complemented
12	#13093001	C₂	1	2	yes	maximal, complemented
13	#13092999	C₂	1	2	yes	maximal, complemented
14	#13092980	C₂	1	2	yes	maximal, complemented
15	#13092976	C₂	1	1	yes	maximal, characteristic, complemented
16	#13092975	C₂	1	2	yes	maximal, complemented
17	C₂×#10625108	C₂	1	1	yes	maximal, characteristic, complemented
18	#120×D₂₃	C₂	1	2	yes	maximal, complemented
19	C₂₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×#67290	C₂²	1	2	yes	complemented
26	C₂×D₄×D₂₃	C₂²	1	2	yes	complemented
27	C₂×D₄×D₂₃	C₂²	1	2	yes	complemented
28	C₂×D₄×D₂₃	C₂²	1	2	yes	complemented
29	C₂×D₄×D₂₃	C₂²	1	2	yes	complemented
30	C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#121	C₂²	1	2	yes	complemented
35	C₂₃×#121	C₂²	1	2	yes	complemented
36	C₂₃×#120	C₂²	1	2	yes	complemented
37	C₂₃×#120	C₂²	1	2	yes	complemented
38	C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
39	#10625124	C₂²	1	2	yes	complemented
40	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
42	#10625118	C₂²	1	2	yes	complemented
43	#10625117	C₂²	1	2	yes	complemented
44	#10625111	C₂²	1	2	yes	complemented
45	#10625110	C₂²	1	2	yes	complemented
46	#10625110	C₂²	1	2	yes	complemented
47	#10625110	C₂²	1	2	yes	complemented
48	#10625110	C₂²	1	2	yes	complemented
49	#10625110	C₂²	1	2	yes	complemented
50	#10625110	C₂²	1	2	yes	complemented
51	#10625110	C₂²	1	2	yes	complemented
52	#10625110	C₂²	1	2	yes	complemented
53	#10625109	C₂²	1	2	yes	complemented
54	#10625109	C₂²	1	2	yes	complemented
55	#10625108	C₂²	1	1	yes	characteristic
56	#10625108	C₂²	1	2	yes	complemented
57	#10625108	C₂²	1	1	yes	characteristic, complemented
58	#10625108	C₂²	1	1	yes	characteristic, complemented
59	#10625108	C₂²	1	2	yes	complemented
60	#10625108	C₂²	1	2	yes	complemented
61	#10625108	C₂²	1	2	yes	complemented
62	#10625108	C₂²	1	2	yes	complemented
63	#10625108	C₂²	1	1	yes	characteristic, complemented
64	#10625108	C₂²	1	2	yes	complemented
65	#10625108	C₂²	1	2	yes	complemented
66	#10625108	C₂²	1	1	yes	characteristic, complemented
67	#10625108	C₂²	1	1	yes	characteristic, complemented
68	#10625107	C₂²	1	2	yes	complemented
69	#10625106	C₂²	1	1	yes	characteristic, complemented
70	#10625106	C₂²	1	2	yes	complemented
71	#10625106	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₂₃	C₂²	1	2	yes	complemented
73	#10625101	C₂²	1	2	yes	complemented
74	#10625100	C₂²	1	2	yes	complemented
75	#10625100	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
77	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	complemented
78	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	complemented
79	#10625069	C₂²	1	2	yes	complemented
80	#10625067	C₂²	1	2	yes	complemented
81	#10625065	C₂²	1	2	yes	complemented
82	#10625065	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	complemented
87	#10625055	C₂²	1	2	yes	complemented
88	#10625054	C₂²	1	2	yes	complemented
89	#10625054	C₂²	1	2	yes	complemented
90	#10625053	C₂²	1	2	yes	—
91	#10625053	C₂²	1	2	yes	complemented
92	#10625053	C₂²	1	2	yes	complemented
93	#10625053	C₂²	1	2	yes	complemented
94	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
95	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
96	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
98	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
99	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
100	#10625050	C₂²	1	2	yes	complemented
101	#10625050	C₂²	1	2	yes	complemented
102	#10625049	C₂²	1	2	yes	complemented
103	#10625047	C₂²	1	2	yes	complemented
104	#10625046	C₂²	1	2	yes	complemented
105	C₄×D₉₂	C₂²	1	2	yes	complemented
106	#10625043	C₂²	1	2	yes	complemented
107	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
108	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
109	C₂³×D₂₃	—	4	4	no	—
110	C₂³×D₂₃	—	4	2	no	—
111	C₂³×D₂₃	C₂³	1	1	yes	characteristic
112	C₂³×D₂₃	C₂³	1	2	yes	—
113	C₂³×D₂₃	C₂³	1	2	yes	—
114	C₂³×D₂₃	C₂³	1	2	yes	—
115	C₂³×D₂₃	C₂³	1	1	yes	characteristic
116	C₂³×D₂₃	C₂³	1	1	yes	characteristic, complemented
117	#41×C₂₃	—	4	2	no	—
118	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
119	C₂×D₄×C₂₃	—	4	2	no	—
120	C₂×D₄×C₂₃	C₂³	1	2	yes	—
121	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
123	C₂×D₄×C₂₃	C₂³	1	2	yes	—
124	C₂×D₄×C₂₃	C₂³	1	2	yes	—
125	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
128	C₂×D₄×C₂₃	C₂³	1	2	yes	complemented
129	C₂×D₄×C₂₃	C₂³	1	2	yes	complemented
130	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₂₃	C₂³	1	2	yes	complemented
132	C₂×C₂²⋊D₂₃	—	4	4	no	—
133	C₂×C₂²⋊D₂₃	—	4	2	no	—
134	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	complemented
145	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	complemented
146	C₂²×Dic₂₃	C₂³	1	2	yes	—
147	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic, complemented
148	C₂²×Dic₂₃	C₂³	1	2	yes	complemented
149	C₂²×Dic₂₃	C₂³	1	2	yes	complemented
150	#67290	—	4	4	no	—
151	D₄×D₂₃	—	4	4	no	—
152	D₄×D₂₃	—	4	4	no	—
153	D₄×D₂₃	—	4	4	no	—
154	D₄×D₂₃	—	4	4	no	—
155	C₂×D₉₂	C₂³	1	2	yes	—
156	C₂×D₉₂	C₂³	1	2	yes	—
157	C₂×D₉₂	C₂³	1	2	yes	—
158	C₂×C₄×D₂₃	C₂³	1	2	yes	—
159	C₂×C₄×D₂₃	C₂³	1	2	yes	—
160	C₂×C₄×D₂₃	C₂³	1	2	yes	—
161	C₂×C₄×D₂₃	C₂³	1	2	yes	complemented
162	C₂×Dic₄₆	C₂³	1	2	yes	complemented
163	C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
164	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	complemented
168	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	complemented
169	C₄²×C₂₃	C₂³	1	1	yes	characteristic, complemented
170	C₄²×C₂₃	C₂³	1	1	yes	characteristic, complemented
171	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic, complemented
178	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic, complemented
179	C₂²⋊Dic₂₃	C₂³	1	2	yes	complemented
180	C₂²⋊Dic₂₃	C₂³	1	2	yes	complemented
181	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	complemented
192	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	complemented
193	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	complemented
194	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	complemented
195	C₄⋊Dic₂₃	C₂³	1	2	yes	complemented
196	C₄⋊Dic₂₃	C₂³	1	2	yes	complemented
197	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
198	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
199	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
200	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
201	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
202	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
203	C₄×Dic₂₃	C₂³	1	2	yes	complemented
204	C₄×Dic₂₃	C₂³	1	2	yes	complemented
205	C₂³×C₂₃	—	2	2	no	—
206	C₂³×C₂₃	—	2	2	no	—
207	C₂³×C₂₃	—	4	2	no	—
208	C₂³×C₂₃	—	4	2	no	—
209	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
210	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
211	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
212	C₂³×C₂₃	C₂⁴	1	2	yes	—
213	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
214	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
215	C₂²×D₂₃	—	2	4	no	—
216	C₂²×D₂₃	—	2	4	no	—
217	C₂²×D₂₃	—	2	4	no	—
218	C₂²×D₂₃	—	2	4	no	—
219	C₂²×D₂₃	—	2	4	no	—
220	C₂²×D₂₃	—	4	1	no	—
221	C₂²×D₂₃	—	4	2	no	—
222	C₂²×D₂₃	—	4	2	no	—
223	C₂²×D₂₃	—	4	2	no	—
224	C₂²×D₂₃	—	4	1	no	—
225	C₂²×D₂₃	—	4	2	no	—
226	C₂²×D₂₃	—	4	2	no	—
227	C₂²×D₂₃	—	4	2	no	—
228	C₂²×D₂₃	—	4	2	no	—
229	C₂²×D₂₃	—	4	1	no	—
230	C₂²×D₂₃	—	4	16	no	—
231	C₂²×D₂₃	C₂⁴	1	2	yes	—
232	C₂²×D₂₃	C₂⁴	1	2	yes	—
233	C₂²×D₂₃	C₂⁴	1	2	yes	—
234	Q₈×C₂₃	—	4	1	no	—
235	D₄×C₂₃	—	2	4	no	—
236	D₄×C₂₃	—	4	2	no	—
237	D₄×C₂₃	—	4	2	no	—
238	D₄×C₂₃	—	4	2	no	—
239	D₄×C₂₃	—	4	2	no	—
240	D₄×C₂₃	—	4	1	no	—
241	D₄×C₂₃	—	4	1	no	—
242	D₄×C₂₃	—	4	1	no	—
243	D₄×C₂₃	—	4	1	no	—
244	D₄×C₂₃	—	4	1	no	—
245	C₂×C₄×C₂₃	—	2	2	no	—
246	C₂×C₄×C₂₃	—	4	2	no	—
247	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₂₃	—	2	4	no	—
253	C₂²⋊D₂₃	—	2	4	no	—
254	C₂²⋊D₂₃	—	2	4	no	—
255	C₂²⋊D₂₃	—	2	4	no	—
256	C₂²⋊D₂₃	—	4	2	no	—
257	C₂²⋊D₂₃	—	4	2	no	—
258	C₂²⋊D₂₃	—	4	2	no	—
259	C₂²⋊D₂₃	—	4	2	no	—
260	C₂²⋊D₂₃	—	4	2	no	—
261	C₂²⋊D₂₃	—	4	2	no	—
262	C₂²⋊D₂₃	—	4	2	no	—
263	C₂²⋊D₂₃	—	4	2	no	—
264	C₂×Dic₂₃	—	4	2	no	—
265	C₂×Dic₂₃	—	4	2	no	—
266	C₂×Dic₂₃	—	4	2	no	—
267	C₂×Dic₂₃	—	4	1	no	—
268	C₂×Dic₂₃	C₂⁴	1	2	yes	—
269	C₂×Dic₂₃	C₂⁴	1	2	yes	—
270	C₂×Dic₂₃	C₂⁴	1	2	yes	—
271	C₂×Dic₂₃	C₂⁴	1	2	yes	—
272	C₂×Dic₂₃	C₂⁴	1	2	yes	—
273	D₉₂	—	2	4	no	—
274	D₉₂	—	4	2	no	—
275	D₉₂	—	4	2	no	—
276	C₄×D₂₃	—	2	4	no	—
277	C₄×D₂₃	—	4	2	no	—
278	C₄×D₂₃	—	4	2	no	—
279	C₄×D₂₃	—	4	2	no	—
280	Dic₄₆	—	4	2	no	—
281	#3532	—	23	1	no	maximal, Sylow
282	C₂²×C₂₃	—	2	2	no	—
283	C₂²×C₂₃	—	2	2	no	—
284	C₂²×C₂₃	—	2	2	no	—
285	C₂²×C₂₃	—	2	1	no	—
286	C₂²×C₂₃	—	2	2	no	—
287	C₂²×C₂₃	—	2	2	no	—
288	C₂²×C₂₃	—	2	1	no	—
289	C₂²×C₂₃	—	2	2	no	—
290	C₂²×C₂₃	—	2	2	no	—
291	C₂²×C₂₃	—	2	2	no	—
292	C₂²×C₂₃	—	2	1	no	—
293	C₂²×C₂₃	—	2	1	no	—
294	C₂²×C₂₃	—	4	4	no	—
295	C₂²×C₂₃	—	8	2	no	—
296	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
297	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
298	C₂×D₂₃	—	2	2	no	—
299	C₂×D₂₃	—	2	2	no	—
300	C₂×D₂₃	—	2	2	no	—
301	C₂×D₂₃	—	2	2	no	—
302	C₂×D₂₃	—	2	2	no	—
303	C₂×D₂₃	—	2	2	no	—
304	C₂×D₂₃	—	2	2	no	—
305	C₂×D₂₃	—	2	2	no	—
306	C₂×D₂₃	—	4	4	no	—
307	C₂×D₂₃	—	4	8	no	—
308	C₂×D₂₃	—	4	8	no	—
309	C₂×D₂₃	—	4	4	no	—
310	C₂×D₂₃	—	8	4	no	—
311	C₂×D₂₃	—	8	2	no	—
312	C₂×D₂₃	H(5,𝔽₂)	1	4	yes	—
313	C₄×C₂₃	—	2	2	no	—
314	C₄×C₂₃	—	2	2	no	—
315	C₄×C₂₃	—	2	2	no	—
316	C₄×C₂₃	—	2	1	no	—
317	C₄×C₂₃	—	2	1	no	—
318	Dic₂₃	—	2	2	no	—
319	Dic₂₃	—	2	2	no	—
320	Dic₂₃	—	2	2	no	—
321	Dic₂₃	—	2	2	no	—
322	Dic₂₃	—	2	2	no	—
323	H(3,𝔽₄)	—	23	1	no	—
324	#560	—	23	1	no	—
325	#560	—	23	2	no	—
326	#551	—	23	1	no	—
327	#551	—	23	2	no	—
328	#546	—	23	2	no	—
329	#546	—	23	2	no	—
330	#546	—	23	2	no	—
331	D₄²	—	23	1	no	—
332	D₄²	—	23	2	no	—
333	#538	—	23	2	no	—
334	#538	—	23	2	no	—
335	#538	—	23	2	no	—
336	#535	—	23	2	no	—
337	#535	D₂₃	1	1	yes	characteristic, complemented
338	#534	—	23	1	no	—
339	#534	—	23	2	no	—
340	C₂×#120	—	23	1	no	—
341	C₂×#120	—	23	2	no	—
342	C₂×C₂₃	—	2	2	no	—
343	C₂×C₂₃	—	4	1	no	—
344	C₂×C₂₃	—	4	1	no	—
345	C₂×C₂₃	—	4	2	no	—
346	C₂×C₂₃	—	4	1	no	—
347	C₂×C₂₃	—	4	1	no	—
348	C₂×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
349	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	D₂₃	—	2	4	no	—
351	D₂₃	—	4	2	no	—
352	D₂₃	—	4	2	no	—
353	C₂⁵	—	23	1	no	—
354	C₂×#41	—	23	2	no	—
355	C₂×#41	C₂×D₂₃	1	1	yes	characteristic, complemented
356	C₂²×D₄	—	23	2	no	—
357	C₂²×D₄	—	23	1	no	—
358	C₂²×D₄	—	23	2	no	—
359	C₂²×D₄	—	23	2	no	—
360	C₂²×D₄	—	23	2	no	—
361	C₂²×D₄	—	23	2	no	—
362	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
363	#127	—	23	2	no	—
364	#127	C₂×D₂₃	1	1	yes	characteristic, complemented
365	#127	C₂×D₂₃	1	1	yes	characteristic, complemented
366	#126	—	23	2	no	—
367	#126	—	23	2	no	—
368	#126	—	23	2	no	—
369	#126	—	23	2	no	—
370	#124	—	23	2	no	—
371	#124	—	23	2	no	—
372	#124	—	23	2	no	—
373	#124	—	23	2	no	—
374	#124	—	23	2	no	—
375	#124	C₂×D₂₃	1	1	yes	characteristic, complemented
376	#124	C₂×D₂₃	1	1	yes	characteristic, complemented
377	#123	—	23	1	no	—
378	#123	—	23	1	no	—
379	#123	—	23	2	no	—
380	#123	—	23	2	no	—
381	#123	—	23	2	no	—
382	#123	—	23	2	no	—
383	#123	—	23	2	no	—
384	#123	—	23	2	no	—
385	#123	—	23	2	no	—
386	#123	—	23	2	no	—
387	C₂²⋊Q₈	—	23	2	no	—
388	C₂²⋊Q₈	—	23	2	no	—
389	C₂²⋊Q₈	—	23	2	no	—
390	#121	—	23	2	no	—
391	#121	—	23	2	no	—
392	#121	—	23	2	no	—
393	#121	—	23	2	no	—
394	#121	—	23	2	no	—
395	#121	—	23	2	no	—
396	#121	—	23	2	no	—
397	#121	—	23	2	no	—
398	#121	—	23	2	no	—
399	#121	—	23	2	no	—
400	#121	—	23	2	no	—
401	#121	—	23	2	no	—
402	#121	—	23	2	no	—
403	#121	C₂×D₂₃	1	2	yes	complemented
404	#121	C₂×D₂₃	1	2	yes	complemented
405	#120	—	23	2	no	—
406	#120	—	23	2	no	—
407	#120	—	23	2	no	—
408	#120	—	23	2	no	—
409	#120	—	23	1	no	—
410	#120	—	23	2	no	—
411	#120	—	23	1	no	—
412	#120	—	23	1	no	—
413	#120	—	23	2	no	—
414	#120	—	23	1	no	—
415	#120	—	23	1	no	—
416	#120	—	23	1	no	—
417	#120	—	23	2	no	—
418	#120	—	23	2	no	—
419	#120	—	23	2	no	—
420	#120	—	23	2	no	—
421	#120	—	23	2	no	—
422	#120	—	23	2	no	—
423	#120	C₂×D₂₃	1	2	yes	complemented
424	#120	C₂×D₂₃	1	2	yes	complemented
425	C₄×D₄	—	23	2	no	—
426	C₄×D₄	—	23	2	no	—
427	C₄×D₄	—	23	2	no	—
428	C₄×D₄	—	23	2	no	—
429	C₄×D₄	—	23	2	no	—
430	C₄×D₄	—	23	2	no	—
431	#117	—	23	2	no	—
432	#117	C₂×D₂₃	1	1	yes	characteristic, complemented
433	C₂×C₂²⋊C₄	—	23	1	no	—
434	C₂×C₂²⋊C₄	—	23	1	no	—
435	C₂×C₂²⋊C₄	—	23	2	no	—
436	C₂×C₂²⋊C₄	—	23	2	no	—
437	C₂×C₂²⋊C₄	—	23	2	no	—
438	C₂×C₂²⋊C₄	—	23	2	no	—
439	C₂×C₂²⋊C₄	—	23	2	no	—
440	C₂₃	#3532	1	1	yes	characteristic, complemented, Sylow
441	C₂⁴	—	23	1	no	—
442	C₂⁴	—	23	2	no	—
443	C₂⁴	—	23	2	no	—
444	C₂⁴	—	23	2	no	—
445	C₂⁴	—	23	1	no	—
446	C₂⁴	—	23	1	no	—
447	C₂⁴	—	92	2	no	—
448	C₂⁴	—	92	4	no	—
449	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
450	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
451	#41	—	4	2	no	—
452	#41	—	92	4	no	—
453	C₂×Q₈	—	23	2	no	—
454	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic, complemented
455	C₂×D₄	—	4	2	no	—
456	C₂×D₄	—	23	2	no	—
457	C₂×D₄	—	23	2	no	—
458	C₂×D₄	—	23	2	no	—
459	C₂×D₄	—	23	2	no	—
460	C₂×D₄	—	23	2	no	—
461	C₂×D₄	—	23	2	no	—
462	C₂×D₄	—	23	2	no	—
463	C₂×D₄	—	23	2	no	—
464	C₂×D₄	—	23	2	no	—
465	C₂×D₄	—	23	2	no	—
466	C₂×D₄	—	23	2	no	—
467	C₂×D₄	—	23	2	no	—
468	C₂×D₄	—	23	2	no	—
469	C₂×D₄	—	23	2	no	—
470	C₂×D₄	—	23	2	no	—
471	C₂×D₄	—	92	4	no	—
472	C₂×D₄	—	92	4	no	—
473	C₂×D₄	—	92	4	no	—
474	C₂×D₄	—	92	4	no	—
475	C₂×D₄	—	92	2	no	—
476	C₂×D₄	—	92	4	no	—
477	C₂×D₄	C₂²×D₂₃	1	2	yes	—
478	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
480	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
481	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₂₃	1	2	yes	—
483	C₂×D₄	C₂²×D₂₃	1	2	yes	—
484	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic, complemented
485	C₂×D₄	C₂²×D₂₃	1	2	yes	complemented
486	C₂×D₄	C₂²×D₂₃	1	2	yes	complemented
487	C₂²×C₄	—	23	2	no	—
488	C₂²×C₄	—	23	2	no	—
489	C₂²×C₄	—	23	2	no	—
490	C₂²×C₄	—	23	1	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	C₂²×D₂₃	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₂₃	1	2	yes	complemented
497	C₄⋊C₄	—	23	2	no	—
498	C₄⋊C₄	—	23	2	no	—
499	C₄⋊C₄	—	23	2	no	—
500	C₄⋊C₄	—	23	2	no	—
501	C₄⋊C₄	—	23	2	no	—
502	C₄⋊C₄	—	23	2	no	—
503	C₄⋊C₄	—	23	2	no	—
504	C₄⋊C₄	—	23	2	no	—
505	C₄⋊C₄	C₂²×D₂₃	1	2	yes	complemented
506	C₂²⋊C₄	—	23	2	no	—
507	C₂²⋊C₄	—	23	1	no	—
508	C₂²⋊C₄	—	23	2	no	—
509	C₂²⋊C₄	—	23	2	no	—
510	C₂²⋊C₄	—	23	2	no	—
511	C₂²⋊C₄	—	23	1	no	—
512	C₂²⋊C₄	—	23	1	no	—
513	C₂²⋊C₄	—	23	1	no	—
514	C₂²⋊C₄	—	23	2	no	—
515	C₂²⋊C₄	—	23	2	no	—
516	C₂²⋊C₄	—	23	2	no	—
517	C₂²⋊C₄	—	23	2	no	—
518	C₂²⋊C₄	—	23	2	no	—
519	C₂²⋊C₄	—	23	2	no	—
520	C₂²⋊C₄	—	23	2	no	—
521	C₂²⋊C₄	—	23	2	no	—
522	C₂²⋊C₄	—	23	2	no	—
523	C₂²⋊C₄	—	23	2	no	—
524	C₂²⋊C₄	—	23	2	no	—
525	C₂²⋊C₄	—	23	2	no	—
526	C₂²⋊C₄	—	23	2	no	—
527	C₂²⋊C₄	—	23	2	no	—
528	C₂²⋊C₄	—	23	2	no	—
529	C₂²⋊C₄	—	23	2	no	—
530	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	complemented
534	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	complemented
535	C₄²	—	23	2	no	—
536	C₄²	—	23	2	no	—
537	C₄²	C₂²×D₂₃	1	1	yes	characteristic, complemented
538	C₄²	C₂²×D₂₃	1	1	yes	characteristic, complemented
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	23	2	no	—
544	C₂³	—	23	2	no	—
545	C₂³	—	23	2	no	—
546	C₂³	—	46	4	no	—
547	C₂³	—	46	4	no	—
548	C₂³	—	46	4	no	—
549	C₂³	—	46	4	no	—
550	C₂³	—	46	4	no	—
551	C₂³	—	92	2	no	—
552	C₂³	—	92	2	no	—
553	C₂³	—	92	2	no	—
554	C₂³	—	92	1	no	—
555	C₂³	—	92	2	no	—
556	C₂³	—	92	1	no	—
557	C₂³	—	92	2	no	—
558	C₂³	—	92	2	no	—
559	C₂³	—	92	2	no	—
560	C₂³	—	92	1	no	—
561	C₂³	—	92	16	no	—
562	C₂³	C₂³×D₂₃	1	1	yes	characteristic
563	C₂³	C₂³×D₂₃	1	1	yes	characteristic
564	C₂³	C₂³×D₂₃	1	1	yes	characteristic
565	C₂³	C₂³×D₂₃	1	2	yes	—
566	C₂³	C₂³×D₂₃	1	1	yes	characteristic
567	C₂³	C₂³×D₂₃	1	1	yes	characteristic
568	Q₈	—	4	1	no	—
569	Q₈	—	92	2	no	—
570	D₄	—	2	4	no	—
571	D₄	—	4	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	1	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	2	no	—
580	D₄	—	46	4	no	—
581	D₄	—	46	4	no	—
582	D₄	—	46	4	no	—
583	D₄	—	46	4	no	—
584	D₄	—	46	4	no	—
585	D₄	—	92	2	no	—
586	D₄	—	92	2	no	—
587	D₄	—	92	2	no	—
588	D₄	—	92	2	no	—
589	D₄	—	92	2	no	—
590	D₄	—	92	2	no	—
591	D₄	—	92	2	no	—
592	D₄	—	92	2	no	—
593	D₄	—	92	2	no	—
594	D₄	—	92	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	23	2	no	—
598	C₂×C₄	—	23	2	no	—
599	C₂×C₄	—	23	2	no	—
600	C₂×C₄	—	23	2	no	—
601	C₂×C₄	—	23	2	no	—
602	C₂×C₄	—	46	4	no	—
603	C₂×C₄	—	92	2	no	—
604	C₂×C₄	—	92	2	no	—
605	C₂×C₄	—	92	2	no	—
606	C₂×C₄	—	92	2	no	—
607	C₂×C₄	—	92	1	no	—
608	C₂×C₄	—	92	2	no	—
609	C₂×C₄	—	92	2	no	—
610	C₂×C₄	C₂³×D₂₃	1	2	yes	—
611	C₂×C₄	C₂³×D₂₃	1	2	yes	—
612	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₂₃	1	2	yes	—
614	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	8	2	no	—
629	C₂²	—	23	4	no	—
630	C₂²	—	46	2	no	—
631	C₂²	—	46	2	no	—
632	C₂²	—	46	2	no	—
633	C₂²	—	46	2	no	—
634	C₂²	—	46	2	no	—
635	C₂²	—	46	2	no	—
636	C₂²	—	46	2	no	—
637	C₂²	—	46	2	no	—
638	C₂²	—	92	8	no	—
639	C₂²	—	92	4	no	—
640	C₂²	—	92	8	no	—
641	C₂²	—	92	4	no	—
642	C₂²	—	184	4	no	—
643	C₂²	—	184	2	no	—
644	C₂²	#10625155	1	2	yes	—
645	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	46	2	no	—
652	C₄	—	46	2	no	—
653	C₄	—	46	2	no	—
654	C₄	—	46	2	no	—
655	C₄	—	46	2	no	—
656	C₂	—	2	2	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	1	no	—
659	C₂	—	4	1	no	—
660	C₂	—	4	1	no	—
661	C₂	—	4	2	no	—
662	C₂	—	46	4	no	—
663	C₂	—	92	2	no	—
664	C₂	—	92	2	no	—
665	C₂	H(5,𝔽₂)×D₂₃	1	2	yes	—
666	C₂	C₂×#10625155	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#535	C₂
hypercenter	#535	D₂₃
hypocenter	C₂₃	#3532
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. #13093159	C₂	semidirect
2. #13093155	C₂	semidirect
3. #13093154	C₂	semidirect
4. #13093097	C₂	semidirect
5. #13093091	C₂	semidirect
6. #13093056	C₂	semidirect
7. #13093055	C₂	semidirect
8. #13093054	C₂	semidirect
9. #13093052	C₂	semidirect
10. #13093049	C₂	semidirect
11. #13093002	C₂	semidirect
12. #13093001	C₂	semidirect
13. #13092999	C₂	semidirect
14. #13092980	C₂	semidirect
15. #13092976	C₂	semidirect
16. #13092975	C₂	semidirect
17. C₂×#10625108	C₂	semidirect
18. #120×D₂₃	C₂	semidirect
19. C₂₃×#535	C₂	semidirect
20. C₂⁴×D₂₃	C₂²	semidirect
21. C₂×#41×C₂₃	C₂²	semidirect
22. C₂²×D₄×C₂₃	C₂²	semidirect
23. C₂²×C₂²⋊D₂₃	C₂²	semidirect
24. C₂²×C₂²⋊D₂₃	C₂²	semidirect
25. C₂×#67290	C₂²	semidirect
26. C₂×D₄×D₂₃	C₂²	semidirect
27. C₂×D₄×D₂₃	C₂²	semidirect
28. C₂×D₄×D₂₃	C₂²	semidirect
29. C₂×D₄×D₂₃	C₂²	semidirect
30. C₂₃×#127	C₂²	semidirect
31. C₂₃×#127	C₂²	semidirect
32. C₂₃×#124	C₂²	semidirect
33. C₂₃×#124	C₂²	semidirect
34. C₂₃×#121	C₂²	semidirect
35. C₂₃×#121	C₂²	semidirect
36. C₂₃×#120	C₂²	semidirect
37. C₂₃×#120	C₂²	semidirect
38. C₂₃×#117	C₂²	semidirect
39. #10625124	C₂²	semidirect
40. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
41. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
42. #10625118	C₂²	semidirect
43. #10625117	C₂²	semidirect
44. #10625111	C₂²	semidirect
45. #10625110	C₂²	semidirect
46. #10625110	C₂²	semidirect
47. #10625110	C₂²	semidirect
48. #10625110	C₂²	semidirect
49. #10625110	C₂²	semidirect
50. #10625110	C₂²	semidirect
51. #10625110	C₂²	semidirect
52. #10625110	C₂²	semidirect
53. #10625109	C₂²	semidirect
54. #10625109	C₂²	semidirect
56. #10625108	C₂²	semidirect
57. #10625108	C₂²	semidirect
58. #10625108	C₂²	semidirect
59. #10625108	C₂²	semidirect
60. #10625108	C₂²	semidirect
61. #10625108	C₂²	semidirect
62. #10625108	C₂²	semidirect
63. #10625108	C₂²	semidirect
64. #10625108	C₂²	semidirect
65. #10625108	C₂²	semidirect
66. #10625108	C₂²	semidirect
67. #10625108	C₂²	semidirect
68. #10625107	C₂²	semidirect
69. #10625106	C₂²	semidirect
70. #10625106	C₂²	semidirect
71. #10625106	C₂²	semidirect
72. D₄×Dic₂₃	C₂²	semidirect
73. #10625101	C₂²	semidirect
74. #10625100	C₂²	semidirect
75. #10625100	C₂²	semidirect
76. C₄×C₂²⋊D₂₃	C₂²	semidirect
77. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
78. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
79. #10625069	C₂²	semidirect
80. #10625067	C₂²	semidirect
81. #10625065	C₂²	semidirect
82. #10625065	C₂²	semidirect
83. #10625057	C₂²	semidirect
84. #10625056	C₂²	semidirect
85. #10625056	C₂²	semidirect
86. #10625055	C₂²	semidirect
87. #10625055	C₂²	semidirect
88. #10625054	C₂²	semidirect
89. #10625054	C₂²	semidirect
91. #10625053	C₂²	semidirect
92. #10625053	C₂²	semidirect
93. #10625053	C₂²	semidirect
94. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
95. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
96. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
97. C₂²⋊C₄×D₂₃	C₂²	semidirect
98. C₂²⋊C₄×D₂₃	C₂²	semidirect
99. C₂²⋊C₄×D₂₃	C₂²	semidirect
100. #10625050	C₂²	semidirect
101. #10625050	C₂²	semidirect
102. #10625049	C₂²	semidirect
103. #10625047	C₂²	semidirect
104. #10625046	C₂²	semidirect
105. C₄×D₉₂	C₂²	semidirect
106. #10625043	C₂²	semidirect
116. C₂³×D₂₃	C₂³	semidirect
118. C₂×Q₈×C₂₃	C₂³	semidirect
127. C₂×D₄×C₂₃	C₂³	semidirect
128. C₂×D₄×C₂₃	C₂³	semidirect
129. C₂×D₄×C₂₃	C₂³	semidirect
131. C₂²×C₄×C₂₃	C₂³	semidirect
144. C₂×C₂²⋊D₂₃	C₂³	semidirect
145. C₂×C₂²⋊D₂₃	C₂³	semidirect
147. C₂²×Dic₂₃	C₂³	semidirect
148. C₂²×Dic₂₃	C₂³	semidirect
149. C₂²×Dic₂₃	C₂³	semidirect
161. C₂×C₄×D₂₃	C₂³	semidirect
162. C₂×Dic₄₆	C₂³	semidirect
163. C₄⋊C₄×C₂₃	C₂³	semidirect
167. C₂²⋊C₄×C₂₃	C₂³	semidirect
168. C₂²⋊C₄×C₂₃	C₂³	semidirect
169. C₄²×C₂₃	C₂³	semidirect
170. C₄²×C₂₃	C₂³	semidirect
177. C₂²⋊Dic₂₃	C₂³	semidirect
178. C₂²⋊Dic₂₃	C₂³	semidirect
179. C₂²⋊Dic₂₃	C₂³	semidirect
180. C₂²⋊Dic₂₃	C₂³	semidirect
191. (C₂×D₂₃)⋊C₄	C₂³	semidirect
192. (C₂×D₂₃)⋊C₄	C₂³	semidirect
193. (C₂×D₂₃)⋊C₄	C₂³	semidirect
194. (C₂×D₂₃)⋊C₄	C₂³	semidirect
195. C₄⋊Dic₂₃	C₂³	semidirect
196. C₄⋊Dic₂₃	C₂³	semidirect
197. Dic₂₃⋊C₄	C₂³	semidirect
198. Dic₂₃⋊C₄	C₂³	semidirect
199. Dic₂₃⋊C₄	C₂³	semidirect
200. Dic₂₃⋊C₄	C₂³	semidirect
201. Dic₂₃⋊C₄	C₂³	semidirect
202. Dic₂₃⋊C₄	C₂³	semidirect
203. C₄×Dic₂₃	C₂³	semidirect
204. C₄×Dic₂₃	C₂³	semidirect
337. #535	D₂₃	semidirect
355. C₂×#41	C₂×D₂₃	semidirect
362. C₂²×D₄	C₂×D₂₃	semidirect
364. #127	C₂×D₂₃	semidirect
365. #127	C₂×D₂₃	semidirect
375. #124	C₂×D₂₃	semidirect
376. #124	C₂×D₂₃	semidirect
403. #121	C₂×D₂₃	semidirect
404. #121	C₂×D₂₃	semidirect
423. #120	C₂×D₂₃	semidirect
424. #120	C₂×D₂₃	semidirect
432. #117	C₂×D₂₃	semidirect
440. C₂₃	#3532	semidirect
454. C₂×Q₈	C₂²×D₂₃	semidirect
484. C₂×D₄	C₂²×D₂₃	semidirect
485. C₂×D₄	C₂²×D₂₃	semidirect
486. C₂×D₄	C₂²×D₂₃	semidirect
496. C₂²×C₄	C₂²×D₂₃	semidirect
505. C₄⋊C₄	C₂²×D₂₃	semidirect
533. C₂²⋊C₄	C₂²×D₂₃	semidirect
534. C₂²⋊C₄	C₂²×D₂₃	semidirect
537. C₄²	C₂²×D₂₃	semidirect
538. C₄²	C₂²×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
#13093159	2
#13093155	2
#13093154	2
#13093097	2
#13093091	2
#13093056	2
#13093055	2
#13093054	2
#13093052	2
#13093049	2
#13093002	2
#13093001	2
#13092999	2
#13092980	2
#13092976	2
#13092975	2
C₂×#10625108	2
#120×D₂₃	2
C₂₃×#535	2
#3532	23