Subgroups — D₂₃×#529 #15686655

Order 2944.

1232 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092954	C₂	1	1	yes	maximal, characteristic, complemented
2	#13092953	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092952	C₂	1	1	yes	maximal, characteristic, complemented
4	#13092951	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092950	C₂	1	2	yes	maximal, complemented
6	#13092949	C₂	1	1	yes	maximal, characteristic, complemented
7	#13092948	C₂	1	1	yes	maximal, characteristic, complemented
8	#13092947	C₂	1	2	yes	maximal, complemented
9	#13092946	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092945	C₂	1	2	yes	maximal, complemented
11	#13092944	C₂	1	2	yes	maximal, complemented
12	#126×D₂₃	C₂	1	2	yes	maximal, complemented
13	#125×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#124×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#123×D₂₃	C₂	1	2	yes	maximal, complemented
16	C₂²⋊Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#121×D₂₃	C₂	1	1	yes	maximal, characteristic
18	C₄×Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₄×D₂₃	C₂	1	2	yes	maximal, complemented
20	C₄×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#117×D₂₃	C₂	1	2	yes	maximal, complemented
22	C₂×C₄²×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₂₃	C₂²	1	2	yes	—
26	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
28	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#126	C₂²	1	2	yes	complemented
32	C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#123	C₂²	1	2	yes	complemented
35	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#121	C₂²	1	1	yes	characteristic
37	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
39	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#117	C₂²	1	2	yes	complemented
41	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
42	#10625118	C₂²	1	1	yes	characteristic, complemented
43	#10625117	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
45	#10625110	C₂²	1	2	yes	—
46	#10625109	C₂²	1	1	yes	characteristic
47	#10625107	C₂²	1	1	yes	characteristic, complemented
48	#10625106	C₂²	1	2	yes	complemented
49	D₄×Dic₂₃	C₂²	1	2	yes	complemented
50	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
51	#10625101	C₂²	1	1	yes	characteristic
52	#10625100	C₂²	1	2	yes	complemented
53	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
56	#10625097	C₂²	1	2	yes	complemented
57	#10625095	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
61	#10625069	C₂²	1	2	yes	complemented
62	#10625069	C₂²	1	2	yes	complemented
63	#10625069	C₂²	1	2	yes	complemented
64	#10625068	C₂²	1	1	yes	characteristic, complemented
65	#10625067	C₂²	1	2	yes	complemented
66	#10625066	C₂²	1	1	yes	characteristic
67	#10625065	C₂²	1	2	yes	complemented
68	#10625065	C₂²	1	2	yes	complemented
69	#10625064	C₂²	1	2	yes	complemented
70	#10625064	C₂²	1	1	yes	characteristic, complemented
71	#10625063	C₂²	1	2	yes	complemented
72	#10625063	C₂²	1	2	yes	complemented
73	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
74	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
75	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
76	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
77	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
79	#10625061	C₂²	1	1	yes	characteristic, complemented
80	#10625061	C₂²	1	1	yes	characteristic, complemented
81	#10625060	C₂²	1	2	yes	complemented
82	#10625060	C₂²	1	2	yes	complemented
83	#10625058	C₂²	1	2	yes	complemented
84	#10625058	C₂²	1	1	yes	characteristic, complemented
85	#10625057	C₂²	1	2	yes	complemented
86	#10625056	C₂²	1	2	yes	complemented
87	#10625056	C₂²	1	2	yes	complemented
88	#10625055	C₂²	1	2	yes	—
89	#10625054	C₂²	1	2	yes	complemented
90	#10625054	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	—
96	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
98	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
99	#10625050	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	#10625048	C₂²	1	2	yes	complemented
104	#10625048	C₂²	1	2	yes	complemented
105	#10625047	C₂²	1	2	yes	complemented
106	#10625046	C₂²	1	1	yes	characteristic, complemented
107	C₄×D₉₂	C₂²	1	2	yes	complemented
108	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
109	#10625043	C₂²	1	2	yes	complemented
110	#10625043	C₂²	1	2	yes	complemented
111	C₄²×D₂₃	C₂²	1	1	yes	characteristic
112	C₄²×D₂₃	C₂²	1	2	yes	—
113	C₄²×D₂₃	C₂²	1	1	yes	characteristic
114	C₄²×D₂₃	C₂²	1	1	yes	characteristic
115	C₄²×D₂₃	C₂²	1	1	yes	characteristic
116	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
120	#10625041	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₄₆	C₂²	1	2	yes	complemented
122	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₃	C₂³	1	2	yes	—
124	C₂³×D₂₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₂₃	C₂³	1	2	yes	—
127	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
135	C₂²×Dic₂₃	C₂³	1	2	yes	—
136	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
137	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
138	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
139	Q₈×D₂₃	—	2	4	no	—
140	D₄×D₂₃	—	2	8	no	—
141	D₄×D₂₃	—	2	4	no	—
142	C₂×D₉₂	C₂³	1	1	yes	characteristic
143	C₂×D₉₂	C₂³	1	2	yes	—
144	C₂×C₄×D₂₃	—	2	4	no	—
145	C₂×C₄×D₂₃	—	2	4	no	—
146	C₂×C₄×D₂₃	—	2	8	no	—
147	C₂×C₄×D₂₃	—	2	4	no	—
148	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₂₃	C₂³	1	2	yes	—
153	C₂×C₄×D₂₃	C₂³	1	2	yes	—
154	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₂₃	C₂³	1	2	yes	—
161	C₂×C₄×D₂₃	C₂³	1	2	yes	—
162	C₂×C₄×D₂₃	C₂³	1	2	yes	—
163	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
165	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
166	C₂×Dic₄₆	C₂³	1	2	yes	—
167	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₄²×C₂₃	C₂³	1	1	yes	characteristic
179	C₄²×C₂₃	C₂³	1	2	yes	—
180	C₄²×C₂₃	C₂³	1	1	yes	characteristic
181	C₄²×C₂₃	C₂³	1	1	yes	characteristic
182	C₄²×C₂₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₂₃	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	—
192	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
198	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₂₃	C₂³	1	2	yes	—
200	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₂₃	C₂³	1	2	yes	—
202	C₄⋊Dic₂₃	C₂³	1	2	yes	—
203	C₄⋊Dic₂₃	C₂³	1	2	yes	—
204	Dic₂₃⋊C₄	C₂³	1	2	yes	—
205	Dic₂₃⋊C₄	C₂³	1	2	yes	—
206	Dic₂₃⋊C₄	C₂³	1	2	yes	—
207	Dic₂₃⋊C₄	C₂³	1	2	yes	—
208	Dic₂₃⋊C₄	C₂³	1	2	yes	—
209	Dic₂₃⋊C₄	C₂³	1	2	yes	—
210	Dic₂₃⋊C₄	C₂³	1	2	yes	—
211	Dic₂₃⋊C₄	C₂³	1	2	yes	—
212	Dic₂₃⋊C₄	C₂³	1	2	yes	—
213	Dic₂₃⋊C₄	C₂³	1	2	yes	—
214	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
215	C₄×Dic₂₃	C₂³	1	2	yes	—
216	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₂₃	C₂³	1	2	yes	—
228	C₄×Dic₂₃	C₂³	1	2	yes	—
229	C₂³×C₂₃	C₂⁴	1	2	yes	—
230	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₂₃	—	2	2	no	—
232	C₂²×D₂₃	—	2	2	no	—
233	C₂²×D₂₃	—	2	4	no	—
234	C₂²×D₂₃	—	2	4	no	—
235	C₂²×D₂₃	—	2	4	no	—
236	C₂²×D₂₃	#41	1	4	yes	—
237	C₂²×D₂₃	C₂⁴	1	2	yes	—
238	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
239	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
240	Q₈×C₂₃	—	2	2	no	—
241	D₄×C₂₃	—	2	4	no	—
242	D₄×C₂₃	—	2	2	no	—
243	C₂×C₄×C₂₃	—	2	2	no	—
244	C₂×C₄×C₂₃	—	2	2	no	—
245	C₂×C₄×C₂₃	—	2	2	no	—
246	C₂×C₄×C₂₃	—	2	4	no	—
247	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₂₃	—	2	4	no	—
257	C₂²⋊D₂₃	—	2	4	no	—
258	C₂²⋊D₂₃	—	2	4	no	—
259	C₂×Dic₂₃	—	2	2	no	—
260	C₂×Dic₂₃	—	2	2	no	—
261	C₂×Dic₂₃	—	2	2	no	—
262	C₂×Dic₂₃	—	2	4	no	—
263	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₂₃	C₂⁴	1	2	yes	—
268	C₂×Dic₂₃	C₂⁴	1	2	yes	—
269	C₂×Dic₂₃	C₂⁴	1	2	yes	—
270	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
272	D₉₂	—	2	4	no	—
273	D₉₂	—	2	2	no	—
274	C₄×D₂₃	—	2	2	no	—
275	C₄×D₂₃	—	2	2	no	—
276	C₄×D₂₃	—	2	2	no	—
277	C₄×D₂₃	—	2	2	no	—
278	C₄×D₂₃	—	2	2	no	—
279	C₄×D₂₃	—	2	2	no	—
280	C₄×D₂₃	—	2	4	no	—
281	C₄×D₂₃	—	2	4	no	—
282	C₄×D₂₃	—	2	4	no	—
283	C₄×D₂₃	—	2	2	no	—
284	C₄×D₂₃	—	2	2	no	—
285	C₄×D₂₃	—	2	4	no	—
286	C₄×D₂₃	—	2	2	no	—
287	C₄×D₂₃	—	2	2	no	—
288	C₄×D₂₃	—	2	4	no	—
289	C₄×D₂₃	#41	1	4	yes	—
290	C₄×D₂₃	#41	1	4	yes	—
291	Dic₄₆	—	2	2	no	—
292	Dic₄₆	—	2	4	no	—
293	C₂×#529	—	23	1	no	maximal, Sylow
294	C₂²×C₂₃	—	2	1	no	—
295	C₂²×C₂₃	—	2	1	no	—
296	C₂²×C₂₃	—	2	2	no	—
297	C₂²×C₂₃	—	2	2	no	—
298	C₂²×C₂₃	—	2	2	no	—
299	C₂²×C₂₃	C₂×#41	1	2	yes	—
300	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
301	C₂×D₂₃	—	2	1	no	—
302	C₂×D₂₃	—	2	1	no	—
303	C₂×D₂₃	—	2	8	no	—
304	C₂×D₂₃	—	2	2	no	—
305	C₂×D₂₃	—	2	2	no	—
306	C₂×D₂₃	—	2	2	no	—
307	C₂×D₂₃	—	4	8	no	—
308	C₂×D₂₃	C₂×#41	1	2	yes	—
309	C₂×D₂₃	C₂×#41	1	2	yes	—
310	C₂×D₂₃	C₂×#41	1	2	yes	—
311	C₂×D₂₃	C₂×#41	1	2	yes	—
312	C₄×C₂₃	—	2	2	no	—
313	C₄×C₂₃	—	2	1	no	—
314	C₄×C₂₃	—	2	1	no	—
315	C₄×C₂₃	—	2	1	no	—
316	C₄×C₂₃	—	2	1	no	—
317	C₄×C₂₃	—	2	2	no	—
318	C₄×C₂₃	—	2	2	no	—
319	C₄×C₂₃	C₂×#41	1	2	yes	—
320	C₄×C₂₃	C₂×#41	1	2	yes	—
321	Dic₂₃	—	2	2	no	—
322	Dic₂₃	—	2	1	no	—
323	Dic₂₃	—	2	1	no	—
324	Dic₂₃	—	2	1	no	—
325	Dic₂₃	—	2	1	no	—
326	Dic₂₃	—	2	2	no	—
327	Dic₂₃	—	2	2	no	—
328	Dic₂₃	C₂×#41	1	2	yes	—
329	Dic₂₃	C₂×#41	1	2	yes	—
330	#529	—	23	2	no	—
331	#529	—	23	1	no	—
332	#529	—	23	1	no	—
333	#529	—	23	2	no	—
334	#529	—	23	1	no	—
335	#529	—	23	1	no	—
336	#529	—	23	1	no	—
337	#529	—	23	2	no	—
338	#529	—	23	1	no	—
339	#529	—	23	2	no	—
340	#529	—	23	1	no	—
341	#529	D₂₃	1	1	yes	characteristic, direct product factor
342	C₂×#126	—	23	2	no	—
343	C₂×#125	—	23	1	no	—
344	C₂×#124	—	23	1	no	—
345	C₂×#123	—	23	2	no	—
346	C₂×C₂²⋊Q₈	—	23	1	no	—
347	C₂×#121	—	23	1	no	—
348	C₂×C₄×Q₈	—	23	1	no	—
349	C₂×C₄×D₄	—	23	2	no	—
350	C₂×C₄×D₄	—	23	1	no	—
351	C₂×#117	—	23	2	no	—
352	C₂²×C₄²	—	23	1	no	—
353	C₂×C₂₃	—	2	2	no	—
354	C₂×C₂₃	—	4	2	no	—
355	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
356	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
357	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
358	D₂₃	—	2	2	no	—
359	D₂₃	—	4	2	no	—
360	D₂₃	#529	1	4	yes	direct product factor
361	C₂²×Q₈	—	23	1	no	—
362	C₂²×D₄	—	23	2	no	—
363	C₂²×D₄	—	23	1	no	—
364	C₂³×C₄	—	23	2	no	—
365	C₂³×C₄	—	23	1	no	—
366	C₂³×C₄	—	23	1	no	—
367	C₂³×C₄	—	23	1	no	—
368	#126	—	23	2	no	—
369	#126	—	23	2	no	—
370	#126	—	23	2	no	—
371	#126	—	23	2	no	—
372	#126	—	23	2	no	—
373	#126	—	23	2	no	—
374	#126	—	23	2	no	—
375	#126	C₂×D₂₃	1	2	yes	complemented
376	#125	—	23	2	no	—
377	#125	—	23	2	no	—
378	#125	—	23	1	no	—
379	#125	—	23	1	no	—
380	#125	—	23	1	no	—
381	#125	C₂×D₂₃	1	1	yes	characteristic, complemented
382	#124	—	23	1	no	—
383	#124	—	23	1	no	—
384	#124	—	23	2	no	—
385	#124	—	23	2	no	—
386	#124	—	23	1	no	—
387	#124	C₂×D₂₃	1	1	yes	characteristic, complemented
388	#123	—	23	2	no	—
389	#123	—	23	2	no	—
390	#123	—	23	2	no	—
391	#123	—	23	2	no	—
392	#123	—	23	2	no	—
393	#123	—	23	2	no	—
394	#123	—	23	2	no	—
395	#123	C₂×D₂₃	1	2	yes	complemented
396	C₂²⋊Q₈	—	23	1	no	—
397	C₂²⋊Q₈	—	23	1	no	—
398	C₂²⋊Q₈	—	23	2	no	—
399	C₂²⋊Q₈	—	23	1	no	—
400	C₂²⋊Q₈	—	23	2	no	—
401	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
402	#121	—	23	1	no	—
403	#121	—	23	2	no	—
404	#121	—	23	1	no	—
405	#121	—	23	1	no	—
406	#121	—	23	2	no	—
407	#121	C₂×D₂₃	1	1	yes	characteristic
408	C₄×Q₈	—	23	1	no	—
409	C₄×Q₈	—	23	2	no	—
410	C₄×Q₈	—	23	1	no	—
411	C₄×Q₈	—	23	2	no	—
412	C₄×Q₈	—	23	1	no	—
413	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
414	C₄×D₄	—	23	1	no	—
415	C₄×D₄	—	23	2	no	—
416	C₄×D₄	—	23	2	no	—
417	C₄×D₄	—	23	2	no	—
418	C₄×D₄	—	23	2	no	—
419	C₄×D₄	—	23	1	no	—
420	C₄×D₄	—	23	2	no	—
421	C₄×D₄	—	23	2	no	—
422	C₄×D₄	—	23	2	no	—
423	C₄×D₄	—	23	2	no	—
424	C₄×D₄	—	23	1	no	—
425	C₄×D₄	—	23	2	no	—
426	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
427	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
428	#117	—	23	2	no	—
429	#117	—	23	2	no	—
430	#117	—	23	2	no	—
431	#117	—	23	2	no	—
432	#117	—	23	2	no	—
433	#117	—	23	2	no	—
434	#117	—	23	2	no	—
435	#117	C₂×D₂₃	1	2	yes	complemented
436	C₂×C₄⋊C₄	—	23	2	no	—
437	C₂×C₄⋊C₄	—	23	2	no	—
438	C₂×C₄⋊C₄	—	23	1	no	—
439	C₂×C₄⋊C₄	—	23	2	no	—
440	C₂×C₄⋊C₄	—	23	1	no	—
441	C₂×C₄⋊C₄	—	23	2	no	—
442	C₂×C₂²⋊C₄	—	23	2	no	—
443	C₂×C₂²⋊C₄	—	23	2	no	—
444	C₂×C₂²⋊C₄	—	23	2	no	—
445	C₂×C₂²⋊C₄	—	23	2	no	—
446	C₂×C₂²⋊C₄	—	23	2	no	—
447	C₂×C₄²	—	23	1	no	—
448	C₂×C₄²	—	23	1	no	—
449	C₂×C₄²	—	23	1	no	—
450	C₂×C₄²	—	23	1	no	—
451	C₂×C₄²	—	23	2	no	—
452	C₂×C₄²	—	23	1	no	—
453	C₂×C₄²	—	23	1	no	—
454	C₂×C₄²	—	23	1	no	—
455	C₂×C₄²	—	23	1	no	—
456	C₂×C₄²	—	23	1	no	—
457	C₂×C₄²	—	23	1	no	—
458	C₂×C₄²	—	23	1	no	—
459	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic, complemented
460	C₂₃	C₂×#529	1	1	yes	characteristic, complemented, Sylow
461	C₂⁴	—	23	1	no	—
462	C₂⁴	—	23	2	no	—
463	C₂×Q₈	—	23	2	no	—
464	C₂×Q₈	—	23	1	no	—
465	C₂×Q₈	—	46	4	no	—
466	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
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	—	23	1	no	—
472	C₂×D₄	—	46	4	no	—
473	C₂×D₄	—	46	8	no	—
474	C₂×D₄	C₂²×D₂₃	1	2	yes	—
475	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
476	C₂²×C₄	—	23	1	no	—
477	C₂²×C₄	—	23	1	no	—
478	C₂²×C₄	—	23	1	no	—
479	C₂²×C₄	—	23	1	no	—
480	C₂²×C₄	—	23	1	no	—
481	C₂²×C₄	—	23	2	no	—
482	C₂²×C₄	—	23	1	no	—
483	C₂²×C₄	—	23	1	no	—
484	C₂²×C₄	—	23	1	no	—
485	C₂²×C₄	—	23	1	no	—
486	C₂²×C₄	—	23	1	no	—
487	C₂²×C₄	—	23	1	no	—
488	C₂²×C₄	—	23	1	no	—
489	C₂²×C₄	—	23	1	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	—	23	1	no	—
496	C₂²×C₄	—	23	2	no	—
497	C₂²×C₄	—	46	4	no	—
498	C₂²×C₄	—	46	8	no	—
499	C₂²×C₄	—	46	4	no	—
500	C₂²×C₄	—	46	4	no	—
501	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
504	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
505	C₄⋊C₄	—	23	2	no	—
506	C₄⋊C₄	—	23	2	no	—
507	C₄⋊C₄	—	23	2	no	—
508	C₄⋊C₄	—	23	2	no	—
509	C₄⋊C₄	—	23	2	no	—
510	C₄⋊C₄	—	23	2	no	—
511	C₄⋊C₄	—	23	2	no	—
512	C₄⋊C₄	—	23	1	no	—
513	C₄⋊C₄	—	23	2	no	—
514	C₄⋊C₄	—	23	2	no	—
515	C₄⋊C₄	—	23	2	no	—
516	C₄⋊C₄	—	23	2	no	—
517	C₄⋊C₄	—	23	1	no	—
518	C₄⋊C₄	—	23	2	no	—
519	C₄⋊C₄	—	23	2	no	—
520	C₄⋊C₄	—	23	2	no	—
521	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
522	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
523	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
525	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
527	C₂²⋊C₄	—	23	2	no	—
528	C₂²⋊C₄	—	23	2	no	—
529	C₂²⋊C₄	—	23	2	no	—
530	C₂²⋊C₄	—	23	2	no	—
531	C₂²⋊C₄	—	23	2	no	—
532	C₂²⋊C₄	—	23	2	no	—
533	C₂²⋊C₄	—	23	2	no	—
534	C₂²⋊C₄	—	23	2	no	—
535	C₂²⋊C₄	—	23	2	no	—
536	C₂²⋊C₄	—	23	2	no	—
537	C₂²⋊C₄	—	23	2	no	—
538	C₂²⋊C₄	—	23	2	no	—
539	C₂²⋊C₄	—	23	2	no	—
540	C₂²⋊C₄	—	23	2	no	—
541	C₂²⋊C₄	—	23	2	no	—
542	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
547	C₄²	—	23	1	no	—
548	C₄²	—	23	1	no	—
549	C₄²	—	23	1	no	—
550	C₄²	—	23	1	no	—
551	C₄²	—	23	1	no	—
552	C₄²	—	23	1	no	—
553	C₄²	—	23	1	no	—
554	C₄²	—	23	1	no	—
555	C₄²	—	23	1	no	—
556	C₄²	—	23	1	no	—
557	C₄²	—	23	2	no	—
558	C₄²	—	23	2	no	—
559	C₄²	—	23	1	no	—
560	C₄²	—	23	1	no	—
561	C₄²	—	23	2	no	—
562	C₄²	C₂²×D₂₃	1	1	yes	characteristic
563	C₄²	C₂²×D₂₃	1	1	yes	characteristic
564	C₄²	C₂²×D₂₃	1	1	yes	characteristic
565	C₄²	C₂²×D₂₃	1	1	yes	characteristic
566	C₄²	C₂²×D₂₃	1	2	yes	—
567	C₂³	—	23	1	no	—
568	C₂³	—	23	4	no	—
569	C₂³	—	23	1	no	—
570	C₂³	—	23	2	no	—
571	C₂³	—	46	2	no	—
572	C₂³	—	46	2	no	—
573	C₂³	—	46	4	no	—
574	C₂³	—	46	4	no	—
575	C₂³	—	46	4	no	—
576	C₂³	C₂³×D₂₃	1	2	yes	—
577	C₂³	C₂³×D₂₃	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	46	4	no	—
580	Q₈	—	46	2	no	—
581	D₄	—	2	4	no	—
582	D₄	—	2	2	no	—
583	D₄	—	46	4	no	—
584	D₄	—	46	4	no	—
585	D₄	—	46	4	no	—
586	D₄	—	46	4	no	—
587	D₄	—	46	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	23	1	no	—
593	C₂×C₄	—	23	1	no	—
594	C₂×C₄	—	23	4	no	—
595	C₂×C₄	—	23	4	no	—
596	C₂×C₄	—	23	1	no	—
597	C₂×C₄	—	23	1	no	—
598	C₂×C₄	—	23	1	no	—
599	C₂×C₄	—	23	1	no	—
600	C₂×C₄	—	23	2	no	—
601	C₂×C₄	—	23	2	no	—
602	C₂×C₄	—	23	2	no	—
603	C₂×C₄	—	46	2	no	—
604	C₂×C₄	—	46	4	no	—
605	C₂×C₄	—	46	2	no	—
606	C₂×C₄	—	46	2	no	—
607	C₂×C₄	—	46	2	no	—
608	C₂×C₄	—	46	4	no	—
609	C₂×C₄	—	46	2	no	—
610	C₂×C₄	—	46	2	no	—
611	C₂×C₄	—	46	2	no	—
612	C₂×C₄	—	46	2	no	—
613	C₂×C₄	—	46	4	no	—
614	C₂×C₄	—	46	4	no	—
615	C₂×C₄	—	46	2	no	—
616	C₂×C₄	—	46	4	no	—
617	C₂×C₄	—	46	2	no	—
618	C₂×C₄	—	46	2	no	—
619	C₂×C₄	—	46	2	no	—
620	C₂×C₄	—	46	4	no	—
621	C₂×C₄	—	46	2	no	—
622	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₂₃	1	2	yes	—
627	C₂×C₄	C₂³×D₂₃	1	2	yes	—
628	C₂×C₄	C₂³×D₂₃	1	2	yes	—
629	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	23	2	no	—
637	C₂²	—	23	2	no	—
638	C₂²	—	23	2	no	—
639	C₂²	—	23	2	no	—
640	C₂²	—	46	8	no	—
641	C₂²	—	46	1	no	—
642	C₂²	—	46	1	no	—
643	C₂²	—	46	2	no	—
644	C₂²	—	46	2	no	—
645	C₂²	—	46	2	no	—
646	C₂²	—	92	8	no	—
647	C₂²	#41×D₂₃	1	2	yes	—
648	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	23	2	no	—
657	C₄	—	23	2	no	—
658	C₄	—	46	1	no	—
659	C₄	—	46	1	no	—
660	C₄	—	46	1	no	—
661	C₄	—	46	1	no	—
662	C₄	—	46	2	no	—
663	C₄	—	46	2	no	—
664	C₄	—	46	2	no	—
665	C₄	#41×D₂₃	1	2	yes	—
666	C₄	#41×D₂₃	1	2	yes	—
667	C₂	—	2	2	no	—
668	C₂	—	4	2	no	—
669	C₂	—	23	4	no	—
670	C₂	—	46	2	no	—
671	C₂	—	92	2	no	—
672	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
673	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
674	C₂	C₂×#41×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂₃×#529	C₂
prime radical	#121×D₂₃	C₂
hypercenter	#529	D₂₃
hypocenter	C₂₃	C₂×#529
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #13092954	C₂	semidirect
2. #13092953	C₂	semidirect
3. #13092952	C₂	semidirect
4. #13092951	C₂	semidirect
5. #13092950	C₂	semidirect
6. #13092949	C₂	semidirect
7. #13092948	C₂	semidirect
8. #13092947	C₂	semidirect
9. #13092946	C₂	semidirect
10. #13092945	C₂	semidirect
11. #13092944	C₂	semidirect
12. #126×D₂₃	C₂	semidirect
13. #125×D₂₃	C₂	semidirect
14. #124×D₂₃	C₂	semidirect
15. #123×D₂₃	C₂	semidirect
16. C₂²⋊Q₈×D₂₃	C₂	semidirect
18. C₄×Q₈×D₂₃	C₂	semidirect
19. C₄×D₄×D₂₃	C₂	semidirect
20. C₄×D₄×D₂₃	C₂	semidirect
21. #117×D₂₃	C₂	semidirect
22. C₂×C₄²×D₂₃	C₂	semidirect
23. C₂₃×#529	C₂	semidirect
31. C₂₃×#126	C₂²	semidirect
32. C₂₃×#125	C₂²	semidirect
33. C₂₃×#124	C₂²	semidirect
34. C₂₃×#123	C₂²	semidirect
35. C₂₃×C₂²⋊Q₈	C₂²	semidirect
37. C₄×Q₈×C₂₃	C₂²	semidirect
38. C₄×D₄×C₂₃	C₂²	semidirect
39. C₄×D₄×C₂₃	C₂²	semidirect
40. C₂₃×#117	C₂²	semidirect
41. C₂×C₄²×C₂₃	C₂²	semidirect
42. #10625118	C₂²	semidirect
43. #10625117	C₂²	semidirect
44. Q₈×Dic₂₃	C₂²	semidirect
47. #10625107	C₂²	semidirect
48. #10625106	C₂²	semidirect
49. D₄×Dic₂₃	C₂²	semidirect
50. D₄×Dic₂₃	C₂²	semidirect
52. #10625100	C₂²	semidirect
53. C₄×C₂²⋊D₂₃	C₂²	semidirect
54. C₄×C₂²⋊D₂₃	C₂²	semidirect
55. C₄×C₂²⋊D₂₃	C₂²	semidirect
56. #10625097	C₂²	semidirect
57. #10625095	C₂²	semidirect
58. C₂×C₄×Dic₂₃	C₂²	semidirect
59. C₂×C₄×Dic₂₃	C₂²	semidirect
60. C₂×C₄×Dic₂₃	C₂²	semidirect
61. #10625069	C₂²	semidirect
62. #10625069	C₂²	semidirect
63. #10625069	C₂²	semidirect
64. #10625068	C₂²	semidirect
65. #10625067	C₂²	semidirect
67. #10625065	C₂²	semidirect
68. #10625065	C₂²	semidirect
69. #10625064	C₂²	semidirect
70. #10625064	C₂²	semidirect
71. #10625063	C₂²	semidirect
72. #10625063	C₂²	semidirect
79. #10625061	C₂²	semidirect
80. #10625061	C₂²	semidirect
81. #10625060	C₂²	semidirect
82. #10625060	C₂²	semidirect
83. #10625058	C₂²	semidirect
84. #10625058	C₂²	semidirect
85. #10625057	C₂²	semidirect
86. #10625056	C₂²	semidirect
87. #10625056	C₂²	semidirect
89. #10625054	C₂²	semidirect
90. #10625054	C₂²	semidirect
91. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
92. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
93. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
99. #10625050	C₂²	semidirect
100. #10625050	C₂²	semidirect
101. #10625050	C₂²	semidirect
102. #10625049	C₂²	semidirect
103. #10625048	C₂²	semidirect
104. #10625048	C₂²	semidirect
105. #10625047	C₂²	semidirect
106. #10625046	C₂²	semidirect
107. C₄×D₉₂	C₂²	semidirect
108. C₄×D₉₂	C₂²	semidirect
109. #10625043	C₂²	semidirect
110. #10625043	C₂²	semidirect
116. C₄²×D₂₃	C₂²	semidirect
117. C₄²×D₂₃	C₂²	semidirect
118. C₄²×D₂₃	C₂²	semidirect
119. C₄²×D₂₃	C₂²	semidirect
120. #10625041	C₂²	semidirect
121. C₄×Dic₄₆	C₂²	semidirect
122. C₄×Dic₄₆	C₂²	semidirect
341. #529	D₂₃	direct (N × H)
360. D₂₃	#529	direct (N × H)
375. #126	C₂×D₂₃	semidirect
381. #125	C₂×D₂₃	semidirect
387. #124	C₂×D₂₃	semidirect
395. #123	C₂×D₂₃	semidirect
401. C₂²⋊Q₈	C₂×D₂₃	semidirect
413. C₄×Q₈	C₂×D₂₃	semidirect
426. C₄×D₄	C₂×D₂₃	semidirect
427. C₄×D₄	C₂×D₂₃	semidirect
435. #117	C₂×D₂₃	semidirect
459. C₂×C₄²	C₂×D₂₃	semidirect
460. C₂₃	C₂×#529	semidirect

Maximal subgroups

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

subgroup	index
#13092954	2
#13092953	2
#13092952	2
#13092951	2
#13092950	2
#13092949	2
#13092948	2
#13092947	2
#13092946	2
#13092945	2
#13092944	2
#126×D₂₃	2
#125×D₂₃	2
#124×D₂₃	2
#123×D₂₃	2
C₂²⋊Q₈×D₂₃	2
#121×D₂₃	2
C₄×Q₈×D₂₃	2
C₄×D₄×D₂₃	2
#117×D₂₃	2
C₂×C₄²×D₂₃	2
C₂₃×#529	2
C₂×#529	23

Subgroups — D23×#529 #15686655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#529 #15686655