Subgroups — D₂₃×#525 #15686633

Order 2944.

1880 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092930	C₂	1	2	yes	maximal, complemented
4	#13092929	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092928	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092927	C₂	1	2	yes	maximal, complemented
7	#13092926	C₂	1	4	yes	maximal, complemented
8	#13092925	C₂	1	2	yes	maximal, complemented
9	#13092924	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092923	C₂	1	2	yes	maximal, complemented
11	#123×D₂₃	C₂	1	2	yes	maximal, complemented
12	C₂²⋊Q₈×D₂₃	C₂	1	2	yes	maximal, complemented
13	#121×D₂₃	C₂	1	2	yes	maximal, complemented
14	#120×D₂₃	C₂	1	2	yes	maximal, complemented
15	C₄×D₄×D₂₃	C₂	1	4	yes	maximal, complemented
16	#117×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×D₂₃	C₂²	1	1	yes	characteristic
19	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
22	#41×D₂₃	—	2	8	no	—
23	C₂×#67292	C₂²	1	1	yes	characteristic, complemented
24	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×#67290	C₂²	1	1	yes	characteristic, complemented
26	C₂×#67290	C₂²	1	2	yes	complemented
27	C₂×D₄×D₂₃	C₂²	1	4	yes	—
28	C₂×D₄×D₂₃	C₂²	1	2	yes	—
29	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×#67288	C₂²	1	2	yes	complemented
31	C₂×#67288	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₂₃	—	2	8	no	—
33	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
34	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
35	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
40	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
41	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
42	C₂₃×#123	C₂²	1	2	yes	complemented
43	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
44	C₂₃×#121	C₂²	1	2	yes	complemented
45	C₂₃×#120	C₂²	1	2	yes	complemented
46	C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
47	C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
48	#10625124	C₂²	1	2	yes	complemented
49	#10625117	C₂²	1	2	yes	complemented
50	#10625110	C₂²	1	4	yes	complemented
51	#10625109	C₂²	1	2	yes	complemented
52	#10625108	C₂²	1	2	yes	complemented
53	#10625108	C₂²	1	4	yes	complemented
54	#10625106	C₂²	1	2	yes	complemented
55	D₄×Dic₂₃	C₂²	1	4	yes	complemented
56	#10625101	C₂²	1	2	yes	complemented
57	#10625100	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
59	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
60	#10625097	C₂²	1	1	yes	characteristic, complemented
61	#10625095	C₂²	1	2	yes	complemented
62	#10625068	C₂²	1	2	yes	complemented
63	#10625067	C₂²	1	4	yes	complemented
64	#10625066	C₂²	1	2	yes	complemented
65	#10625065	C₂²	1	4	yes	complemented
66	#10625064	C₂²	1	4	yes	complemented
67	#10625063	C₂²	1	2	yes	complemented
68	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₂₃	C₂²	1	4	yes	complemented
70	#10625057	C₂²	1	2	yes	complemented
71	#10625055	C₂²	1	4	yes	complemented
72	#10625054	C₂²	1	4	yes	complemented
73	#10625053	C₂²	1	2	yes	complemented
74	#10625053	C₂²	1	4	yes	complemented
75	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	complemented
76	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	complemented
77	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
78	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	—
79	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	complemented
80	#10625049	C₂²	1	4	yes	complemented
81	#10625048	C₂²	1	2	yes	complemented
82	C₄×D₉₂	C₂²	1	4	yes	complemented
83	#10625043	C₂²	1	2	yes	complemented
84	C₄²×D₂₃	C₂²	1	2	yes	complemented
85	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
86	C₂³×D₂₃	—	2	4	no	—
87	C₂³×D₂₃	—	2	8	no	—
88	C₂³×D₂₃	C₂³	1	2	yes	—
89	C₂³×D₂₃	C₂³	1	1	yes	characteristic
90	C₂³×D₂₃	C₂³	1	2	yes	—
91	C₂³×D₂₃	C₂³	1	1	yes	characteristic
92	C₂³×D₂₃	C₂³	1	2	yes	—
93	#41×C₂₃	—	2	4	no	—
94	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
95	C₂×D₄×C₂₃	C₂³	1	4	yes	—
96	C₂×D₄×C₂₃	C₂³	1	2	yes	—
97	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
98	C₂²×C₄×C₂₃	—	2	4	no	—
99	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
100	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
101	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₂₃	C₂³	1	2	yes	complemented
104	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
105	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
106	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
107	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
108	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	complemented
109	C₂²×Dic₂₃	—	2	4	no	—
110	C₂²×Dic₂₃	C₂³	1	2	yes	—
111	C₂²×Dic₂₃	C₂³	1	2	yes	—
112	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
113	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
114	C₂²×Dic₂₃	C₂³	1	2	yes	complemented
115	#67292	—	2	4	no	—
116	Q₈×D₂₃	—	2	4	no	—
117	#67290	—	2	8	no	—
118	#67290	—	2	4	no	—
119	D₄×D₂₃	—	2	8	no	—
120	D₄×D₂₃	—	2	16	no	—
121	D₄×D₂₃	—	2	4	no	—
122	#67288	—	2	4	no	—
123	#67288	—	2	8	no	—
124	C₂×D₉₂	C₂³	1	4	yes	—
125	C₂×D₉₂	C₂³	1	2	yes	—
126	C₂×D₉₂	C₂³	1	1	yes	characteristic, complemented
127	C₂×C₄×D₂₃	—	2	4	no	—
128	C₂×C₄×D₂₃	—	2	4	no	—
129	C₂×C₄×D₂₃	—	2	4	no	—
130	C₂×C₄×D₂₃	—	2	8	no	—
131	C₂×C₄×D₂₃	—	2	8	no	—
132	C₂×C₄×D₂₃	—	2	8	no	—
133	C₂×C₄×D₂₃	—	2	8	no	—
134	C₂×C₄×D₂₃	—	2	8	no	—
135	C₂×C₄×D₂₃	D₄	1	8	yes	complemented
136	C₂×C₄×D₂₃	C₂³	1	4	yes	—
137	C₂×C₄×D₂₃	C₂³	1	2	yes	—
138	C₂×C₄×D₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
145	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₂₃	C₂³	1	2	yes	complemented
149	C₂×C₄×D₂₃	C₂³	1	2	yes	complemented
150	C₂×Dic₄₆	C₂³	1	2	yes	complemented
151	C₂×Dic₄₆	C₂³	1	1	yes	characteristic, complemented
152	C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
153	C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
154	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
156	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
157	C₄²×C₂₃	C₂³	1	2	yes	complemented
158	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
160	C₂²⋊Dic₂₃	C₂³	1	4	yes	complemented
161	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
162	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
163	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
164	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	complemented
165	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	complemented
166	C₄⋊Dic₂₃	C₂³	1	4	yes	complemented
167	C₄⋊Dic₂₃	C₂³	1	2	yes	complemented
168	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
169	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
170	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
171	C₄×Dic₂₃	C₂³	1	2	yes	complemented
172	C₄×Dic₂₃	C₂³	1	4	yes	complemented
173	C₂³×C₂₃	—	2	2	no	—
174	C₂³×C₂₃	—	2	4	no	—
175	C₂³×C₂₃	C₂⁴	1	2	yes	—
176	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
177	C₂³×C₂₃	C₂⁴	1	2	yes	—
178	C₂²×D₂₃	—	2	32	no	—
179	C₂²×D₂₃	—	2	2	no	—
180	C₂²×D₂₃	—	2	4	no	—
181	C₂²×D₂₃	—	2	4	no	—
182	C₂²×D₂₃	—	2	4	no	—
183	C₂²×D₂₃	—	2	4	no	—
184	C₂²×D₂₃	—	2	4	no	—
185	C₂²×D₂₃	—	2	4	no	—
186	C₂²×D₂₃	—	2	4	no	—
187	C₂²×D₂₃	—	2	4	no	—
188	C₂²×D₂₃	—	2	8	no	—
189	C₂²×D₂₃	C₂×D₄	1	4	yes	—
190	C₂²×D₂₃	#41	1	8	yes	complemented
191	C₂²×D₂₃	C₂⁴	1	2	yes	—
192	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
193	C₂²×D₂₃	C₂⁴	1	2	yes	—
194	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
195	Q₈×C₂₃	—	2	2	no	—
196	D₄×C₂₃	—	2	4	no	—
197	D₄×C₂₃	—	2	8	no	—
198	D₄×C₂₃	—	2	2	no	—
199	C₂×C₄×C₂₃	—	2	2	no	—
200	C₂×C₄×C₂₃	—	2	4	no	—
201	C₂×C₄×C₂₃	—	2	4	no	—
202	C₂×C₄×C₂₃	—	2	4	no	—
203	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	complemented
204	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
205	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
206	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
207	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
208	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
209	C₂²⋊D₂₃	—	2	4	no	—
210	C₂²⋊D₂₃	—	2	8	no	—
211	C₂²⋊D₂₃	—	2	4	no	—
212	C₂²⋊D₂₃	—	2	8	no	—
213	C₂²⋊D₂₃	—	2	4	no	—
214	C₂×Dic₂₃	—	2	2	no	—
215	C₂×Dic₂₃	—	2	4	no	—
216	C₂×Dic₂₃	—	2	4	no	—
217	C₂×Dic₂₃	—	2	4	no	—
218	C₂×Dic₂₃	C₂×D₄	1	4	yes	complemented
219	C₂×Dic₂₃	C₂⁴	1	4	yes	—
220	C₂×Dic₂₃	C₂⁴	1	2	yes	—
221	C₂×Dic₂₃	C₂⁴	1	2	yes	—
222	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
223	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
224	D₉₂	—	2	4	no	—
225	D₉₂	—	2	8	no	—
226	D₉₂	—	2	2	no	—
227	C₄×D₂₃	—	2	4	no	—
228	C₄×D₂₃	—	2	4	no	—
229	C₄×D₂₃	—	2	4	no	—
230	C₄×D₂₃	—	2	8	no	—
231	C₄×D₂₃	—	2	4	no	—
232	C₄×D₂₃	—	2	4	no	—
233	C₄×D₂₃	—	2	4	no	—
234	C₄×D₂₃	—	2	4	no	—
235	C₄×D₂₃	—	2	4	no	—
236	C₄×D₂₃	—	2	4	no	—
237	C₄×D₂₃	C₂×D₄	1	4	yes	—
238	C₄×D₂₃	C₂×D₄	1	4	yes	—
239	C₄×D₂₃	C₂×D₄	1	4	yes	complemented
240	C₄×D₂₃	C₂×D₄	1	4	yes	complemented
241	Dic₄₆	—	2	2	no	—
242	Dic₄₆	—	2	4	no	—
243	C₂×#525	—	23	1	no	maximal, Sylow
244	C₂²×C₂₃	—	2	8	no	—
245	C₂²×C₂₃	—	2	2	no	—
246	C₂²×C₂₃	—	2	2	no	—
247	C₂²×C₂₃	—	2	2	no	—
248	C₂²×C₂₃	—	2	2	no	—
249	C₂²×C₂₃	—	2	4	no	—
250	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
251	C₂²×C₂₃	C₂×#41	1	4	yes	complemented
252	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
253	C₂×D₂₃	—	2	16	no	—
254	C₂×D₂₃	—	2	8	no	—
255	C₂×D₂₃	—	2	2	no	—
256	C₂×D₂₃	—	2	2	no	—
257	C₂×D₂₃	—	2	2	no	—
258	C₂×D₂₃	—	2	8	no	—
259	C₂×D₂₃	—	2	16	no	—
260	C₂×D₂₃	—	2	2	no	—
261	C₂×D₂₃	—	2	4	no	—
262	C₂×D₂₃	—	4	8	no	—
263	C₂×D₂₃	C₂²×D₄	1	2	yes	—
264	C₂×D₂₃	C₂²×D₄	1	2	yes	—
265	C₂×D₂₃	C₂×#41	1	4	yes	—
266	C₂×D₂₃	C₂×#41	1	4	yes	complemented
267	C₄×C₂₃	—	2	2	no	—
268	C₄×C₂₃	—	2	2	no	—
269	C₄×C₂₃	—	2	4	no	—
270	C₄×C₂₃	C₂²×D₄	1	2	yes	—
271	C₄×C₂₃	C₂²×D₄	1	2	yes	—
272	Dic₂₃	—	2	2	no	—
273	Dic₂₃	—	2	2	no	—
274	Dic₂₃	—	2	4	no	—
275	Dic₂₃	C₂²×D₄	1	2	yes	—
276	Dic₂₃	C₂²×D₄	1	2	yes	—
277	C₂²×#41	—	23	1	no	—
278	C₂⁴×C₄	—	23	1	no	—
279	#525	—	23	1	no	—
280	#525	—	23	1	no	—
281	#525	—	23	2	no	—
282	#525	—	23	2	no	—
283	#525	—	23	2	no	—
284	#525	—	23	2	no	—
285	#525	—	23	4	no	—
286	#525	—	23	1	no	—
287	#525	D₂₃	1	1	yes	characteristic, direct product factor
288	C₂×#123	—	23	2	no	—
289	C₂×C₂²⋊Q₈	—	23	2	no	—
290	C₂×#121	—	23	2	no	—
291	C₂×#120	—	23	2	no	—
292	C₂×C₄×D₄	—	23	4	no	—
293	C₂×#117	—	23	1	no	—
294	C₂×C₂₃	—	2	2	no	—
295	C₂×C₂₃	—	2	4	no	—
296	C₂×C₂₃	—	4	2	no	—
297	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
298	C₂×C₂₃	C₂²×#41	1	2	yes	—
299	D₂₃	—	2	2	no	—
300	D₂₃	—	2	4	no	—
301	D₂₃	—	4	2	no	—
302	D₂₃	#525	1	4	yes	direct product factor
303	C₂⁵	—	23	1	no	—
304	C₂×#41	—	23	1	no	—
305	C₂×#41	—	23	2	no	—
306	C₂×#41	—	23	1	no	—
307	C₂×#41	—	23	1	no	—
308	C₂×#41	—	23	2	no	—
309	C₂×#41	—	46	8	no	—
310	C₂×#41	C₂×D₂₃	1	1	yes	characteristic, complemented
311	C₂²×Q₈	—	23	1	no	—
312	C₂²×D₄	—	23	4	no	—
313	C₂²×D₄	—	23	2	no	—
314	C₂²×D₄	—	23	1	no	—
315	C₂³×C₄	—	23	1	no	—
316	C₂³×C₄	—	23	1	no	—
317	C₂³×C₄	—	23	2	no	—
318	C₂³×C₄	—	23	2	no	—
319	C₂³×C₄	—	23	1	no	—
320	C₂³×C₄	—	23	1	no	—
321	C₂³×C₄	—	23	2	no	—
322	C₂³×C₄	—	23	2	no	—
323	C₂³×C₄	—	23	1	no	—
324	C₂³×C₄	—	23	2	no	—
325	C₂³×C₄	—	46	8	no	—
326	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
327	#123	—	23	2	no	—
328	#123	—	23	2	no	—
329	#123	—	23	4	no	—
330	#123	—	23	2	no	—
331	#123	—	23	4	no	—
332	#123	C₂×D₂₃	1	2	yes	complemented
333	C₂²⋊Q₈	—	23	2	no	—
334	C₂²⋊Q₈	—	23	2	no	—
335	C₂²⋊Q₈	—	23	4	no	—
336	C₂²⋊Q₈	—	23	2	no	—
337	C₂²⋊Q₈	—	23	4	no	—
338	C₂²⋊Q₈	C₂×D₂₃	1	2	yes	complemented
339	#121	—	23	4	no	—
340	#121	—	23	2	no	—
341	#121	—	23	2	no	—
342	#121	—	23	2	no	—
343	#121	—	23	4	no	—
344	#121	C₂×D₂₃	1	2	yes	complemented
345	#120	—	23	2	no	—
346	#120	—	23	2	no	—
347	#120	—	23	4	no	—
348	#120	—	23	4	no	—
349	#120	—	23	2	no	—
350	#120	C₂×D₂₃	1	2	yes	complemented
351	C₄×D₄	—	23	4	no	—
352	C₄×D₄	—	23	4	no	—
353	C₄×D₄	—	23	4	no	—
354	C₄×D₄	—	23	4	no	—
355	C₄×D₄	—	23	4	no	—
356	C₄×D₄	—	23	4	no	—
357	C₄×D₄	—	23	4	no	—
358	C₄×D₄	C₂×D₂₃	1	4	yes	complemented
359	#117	—	23	1	no	—
360	#117	—	23	2	no	—
361	#117	—	23	2	no	—
362	#117	—	23	2	no	—
363	#117	C₂×D₂₃	1	1	yes	characteristic, complemented
364	C₂×C₄⋊C₄	—	23	2	no	—
365	C₂×C₄⋊C₄	—	23	4	no	—
366	C₂×C₂²⋊C₄	—	23	2	no	—
367	C₂×C₂²⋊C₄	—	23	4	no	—
368	C₂×C₂²⋊C₄	—	23	4	no	—
369	C₂×C₄²	—	23	2	no	—
370	C₂₃	C₂×#525	1	1	yes	characteristic, complemented, Sylow
371	C₂⁴	—	23	1	no	—
372	C₂⁴	—	23	2	no	—
373	C₂⁴	—	23	2	no	—
374	C₂⁴	—	23	2	no	—
375	C₂⁴	—	23	1	no	—
376	C₂⁴	—	46	4	no	—
377	C₂⁴	—	46	8	no	—
378	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
379	#41	—	2	4	no	—
380	#41	—	46	8	no	—
381	#41	—	46	8	no	—
382	#41	—	46	4	no	—
383	#41	—	46	4	no	—
384	#41	—	46	4	no	—
385	C₂×Q₈	—	23	2	no	—
386	C₂×Q₈	—	23	1	no	—
387	C₂×Q₈	—	46	4	no	—
388	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic, complemented
389	C₂×D₄	—	23	4	no	—
390	C₂×D₄	—	23	4	no	—
391	C₂×D₄	—	23	2	no	—
392	C₂×D₄	—	23	2	no	—
393	C₂×D₄	—	23	2	no	—
394	C₂×D₄	—	23	4	no	—
395	C₂×D₄	—	23	2	no	—
396	C₂×D₄	—	23	1	no	—
397	C₂×D₄	—	46	4	no	—
398	C₂×D₄	—	46	8	no	—
399	C₂×D₄	—	46	16	no	—
400	C₂×D₄	C₂²×D₂₃	1	4	yes	—
401	C₂×D₄	C₂²×D₂₃	1	2	yes	—
402	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic, complemented
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	23	1	no	—
405	C₂²×C₄	—	23	8	no	—
406	C₂²×C₄	—	23	1	no	—
407	C₂²×C₄	—	23	1	no	—
408	C₂²×C₄	—	23	1	no	—
409	C₂²×C₄	—	23	1	no	—
410	C₂²×C₄	—	23	2	no	—
411	C₂²×C₄	—	23	2	no	—
412	C₂²×C₄	—	23	2	no	—
413	C₂²×C₄	—	23	1	no	—
414	C₂²×C₄	—	23	4	no	—
415	C₂²×C₄	—	23	2	no	—
416	C₂²×C₄	—	23	2	no	—
417	C₂²×C₄	—	23	2	no	—
418	C₂²×C₄	—	23	2	no	—
419	C₂²×C₄	—	23	2	no	—
420	C₂²×C₄	—	23	2	no	—
421	C₂²×C₄	—	23	2	no	—
422	C₂²×C₄	—	23	2	no	—
423	C₂²×C₄	—	23	2	no	—
424	C₂²×C₄	—	46	4	no	—
425	C₂²×C₄	—	46	8	no	—
426	C₂²×C₄	—	46	8	no	—
427	C₂²×C₄	—	46	8	no	—
428	C₂²×C₄	—	46	8	no	—
429	C₂²×C₄	—	46	8	no	—
430	C₂²×C₄	—	46	4	no	—
431	C₂²×C₄	—	46	4	no	—
432	C₂²×C₄	—	46	4	no	—
433	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
434	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
435	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
436	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₂₃	1	2	yes	complemented
438	C₄⋊C₄	—	23	4	no	—
439	C₄⋊C₄	—	23	2	no	—
440	C₄⋊C₄	—	23	4	no	—
441	C₄⋊C₄	—	23	4	no	—
442	C₄⋊C₄	—	23	4	no	—
443	C₄⋊C₄	C₂²×D₂₃	1	2	yes	complemented
444	C₄⋊C₄	C₂²×D₂₃	1	4	yes	complemented
445	C₂²⋊C₄	—	23	2	no	—
446	C₂²⋊C₄	—	23	4	no	—
447	C₂²⋊C₄	—	23	4	no	—
448	C₂²⋊C₄	—	23	4	no	—
449	C₂²⋊C₄	—	23	4	no	—
450	C₂²⋊C₄	—	23	4	no	—
451	C₂²⋊C₄	—	23	4	no	—
452	C₂²⋊C₄	—	23	4	no	—
453	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
454	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
455	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	complemented
456	C₄²	—	23	4	no	—
457	C₄²	—	23	2	no	—
458	C₄²	C₂²×D₂₃	1	2	yes	complemented
459	C₂³	—	2	2	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	23	1	no	—
462	C₂³	—	23	4	no	—
463	C₂³	—	23	8	no	—
464	C₂³	—	23	1	no	—
465	C₂³	—	23	2	no	—
466	C₂³	—	23	2	no	—
467	C₂³	—	46	4	no	—
468	C₂³	—	46	4	no	—
469	C₂³	—	46	4	no	—
470	C₂³	—	46	4	no	—
471	C₂³	—	46	4	no	—
472	C₂³	—	46	4	no	—
473	C₂³	—	46	4	no	—
474	C₂³	—	46	8	no	—
475	C₂³	—	46	32	no	—
476	C₂³	—	46	2	no	—
477	C₂³	—	46	4	no	—
478	C₂³	C₂³×D₂₃	1	2	yes	—
479	C₂³	C₂³×D₂₃	1	1	yes	characteristic
480	C₂³	C₂³×D₂₃	1	2	yes	—
481	Q₈	—	2	2	no	—
482	Q₈	—	46	4	no	—
483	Q₈	—	46	2	no	—
484	D₄	—	2	4	no	—
485	D₄	—	2	8	no	—
486	D₄	—	2	2	no	—
487	D₄	—	46	4	no	—
488	D₄	—	46	8	no	—
489	D₄	—	46	4	no	—
490	D₄	—	46	4	no	—
491	D₄	—	46	8	no	—
492	D₄	—	46	4	no	—
493	D₄	—	46	8	no	—
494	D₄	—	46	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	23	4	no	—
500	C₂×C₄	—	23	1	no	—
501	C₂×C₄	—	23	1	no	—
502	C₂×C₄	—	23	4	no	—
503	C₂×C₄	—	23	4	no	—
504	C₂×C₄	—	23	4	no	—
505	C₂×C₄	—	23	4	no	—
506	C₂×C₄	—	23	4	no	—
507	C₂×C₄	—	23	2	no	—
508	C₂×C₄	—	23	2	no	—
509	C₂×C₄	—	46	4	no	—
510	C₂×C₄	—	46	4	no	—
511	C₂×C₄	—	46	4	no	—
512	C₂×C₄	—	46	4	no	—
513	C₂×C₄	—	46	4	no	—
514	C₂×C₄	—	46	4	no	—
515	C₂×C₄	—	46	8	no	—
516	C₂×C₄	—	46	4	no	—
517	C₂×C₄	—	46	4	no	—
518	C₂×C₄	—	46	4	no	—
519	C₂×C₄	—	46	2	no	—
520	C₂×C₄	—	46	4	no	—
521	C₂×C₄	—	46	4	no	—
522	C₂×C₄	—	46	4	no	—
523	C₂×C₄	D₄×D₂₃	1	4	yes	complemented
524	C₂×C₄	C₂³×D₂₃	1	4	yes	—
525	C₂×C₄	C₂³×D₂₃	1	2	yes	—
526	C₂×C₄	C₂³×D₂₃	1	2	yes	—
527	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
528	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
529	C₂²	—	2	8	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	23	2	no	—
536	C₂²	—	23	4	no	—
537	C₂²	—	23	2	no	—
538	C₂²	—	23	4	no	—
539	C₂²	—	46	8	no	—
540	C₂²	—	46	16	no	—
541	C₂²	—	46	8	no	—
542	C₂²	—	46	16	no	—
543	C₂²	—	46	2	no	—
544	C₂²	—	46	2	no	—
545	C₂²	—	46	2	no	—
546	C₂²	—	46	2	no	—
547	C₂²	—	46	4	no	—
548	C₂²	—	92	8	no	—
549	C₂²	C₂×D₄×D₂₃	1	2	yes	—
550	C₂²	#41×D₂₃	1	4	yes	complemented
551	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	4	no	—
555	C₄	—	23	2	no	—
556	C₄	—	23	2	no	—
557	C₄	—	46	2	no	—
558	C₄	—	46	2	no	—
559	C₄	—	46	4	no	—
560	C₄	C₂×D₄×D₂₃	1	2	yes	—
561	C₄	C₂×D₄×D₂₃	1	2	yes	—
562	C₂	—	2	2	no	—
563	C₂	—	2	4	no	—
564	C₂	—	4	2	no	—
565	C₂	—	23	4	no	—
566	C₂	—	46	2	no	—
567	C₂	—	46	4	no	—
568	C₂	—	92	2	no	—
569	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
570	C₂	C₂×#41×D₂₃	1	2	yes	—

	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	C₂×#525
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. C₂×#41×D₂₃	C₂	semidirect
2. C₂³×C₄×D₂₃	C₂	semidirect
3. #13092930	C₂	semidirect
4. #13092929	C₂	semidirect
5. #13092928	C₂	semidirect
6. #13092927	C₂	semidirect
7. #13092926	C₂	semidirect
8. #13092925	C₂	semidirect
9. #13092924	C₂	semidirect
10. #13092923	C₂	semidirect
11. #123×D₂₃	C₂	semidirect
12. C₂²⋊Q₈×D₂₃	C₂	semidirect
13. #121×D₂₃	C₂	semidirect
14. #120×D₂₃	C₂	semidirect
15. C₄×D₄×D₂₃	C₂	semidirect
16. #117×D₂₃	C₂	semidirect
17. C₂₃×#525	C₂	semidirect
19. C₂×#41×C₂₃	C₂²	semidirect
20. C₂³×C₄×C₂₃	C₂²	semidirect
21. C₂³×Dic₂₃	C₂²	semidirect
23. C₂×#67292	C₂²	semidirect
24. C₂×Q₈×D₂₃	C₂²	semidirect
25. C₂×#67290	C₂²	semidirect
26. C₂×#67290	C₂²	semidirect
29. C₂×D₄×D₂₃	C₂²	semidirect
30. C₂×#67288	C₂²	semidirect
31. C₂×#67288	C₂²	semidirect
37. C₂²×C₄×D₂₃	C₂²	semidirect
38. C₂²×C₄×D₂₃	C₂²	semidirect
39. C₂²×C₄×D₂₃	C₂²	semidirect
40. C₂²×C₄×D₂₃	C₂²	semidirect
41. C₂²×C₄×D₂₃	C₂²	semidirect
42. C₂₃×#123	C₂²	semidirect
43. C₂₃×C₂²⋊Q₈	C₂²	semidirect
44. C₂₃×#121	C₂²	semidirect
45. C₂₃×#120	C₂²	semidirect
46. C₄×D₄×C₂₃	C₂²	semidirect
47. C₂₃×#117	C₂²	semidirect
48. #10625124	C₂²	semidirect
49. #10625117	C₂²	semidirect
50. #10625110	C₂²	semidirect
51. #10625109	C₂²	semidirect
52. #10625108	C₂²	semidirect
53. #10625108	C₂²	semidirect
54. #10625106	C₂²	semidirect
55. D₄×Dic₂₃	C₂²	semidirect
56. #10625101	C₂²	semidirect
57. #10625100	C₂²	semidirect
58. C₄×C₂²⋊D₂₃	C₂²	semidirect
59. C₄×C₂²⋊D₂₃	C₂²	semidirect
60. #10625097	C₂²	semidirect
61. #10625095	C₂²	semidirect
62. #10625068	C₂²	semidirect
63. #10625067	C₂²	semidirect
64. #10625066	C₂²	semidirect
65. #10625065	C₂²	semidirect
66. #10625064	C₂²	semidirect
67. #10625063	C₂²	semidirect
68. C₄⋊C₄×D₂₃	C₂²	semidirect
69. C₄⋊C₄×D₂₃	C₂²	semidirect
70. #10625057	C₂²	semidirect
71. #10625055	C₂²	semidirect
72. #10625054	C₂²	semidirect
73. #10625053	C₂²	semidirect
74. #10625053	C₂²	semidirect
75. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
76. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
79. C₂²⋊C₄×D₂₃	C₂²	semidirect
80. #10625049	C₂²	semidirect
81. #10625048	C₂²	semidirect
82. C₄×D₉₂	C₂²	semidirect
83. #10625043	C₂²	semidirect
84. C₄²×D₂₃	C₂²	semidirect
94. C₂×Q₈×C₂₃	C₂³	semidirect
97. C₂×D₄×C₂₃	C₂³	semidirect
103. C₂²×C₄×C₂₃	C₂³	semidirect
108. C₂×C₂²⋊D₂₃	C₂³	semidirect
114. C₂²×Dic₂₃	C₂³	semidirect
126. C₂×D₉₂	C₂³	semidirect
135. C₂×C₄×D₂₃	D₄	semidirect
148. C₂×C₄×D₂₃	C₂³	semidirect
149. C₂×C₄×D₂₃	C₂³	semidirect
150. C₂×Dic₄₆	C₂³	semidirect
151. C₂×Dic₄₆	C₂³	semidirect
152. C₄⋊C₄×C₂₃	C₂³	semidirect
153. C₄⋊C₄×C₂₃	C₂³	semidirect
156. C₂²⋊C₄×C₂₃	C₂³	semidirect
157. C₄²×C₂₃	C₂³	semidirect
160. C₂²⋊Dic₂₃	C₂³	semidirect
164. (C₂×D₂₃)⋊C₄	C₂³	semidirect
165. (C₂×D₂₃)⋊C₄	C₂³	semidirect
166. C₄⋊Dic₂₃	C₂³	semidirect
167. C₄⋊Dic₂₃	C₂³	semidirect
168. Dic₂₃⋊C₄	C₂³	semidirect
169. Dic₂₃⋊C₄	C₂³	semidirect
170. Dic₂₃⋊C₄	C₂³	semidirect
171. C₄×Dic₂₃	C₂³	semidirect
172. C₄×Dic₂₃	C₂³	semidirect
190. C₂²×D₂₃	#41	semidirect
203. C₂×C₄×C₂₃	C₂×D₄	semidirect
218. C₂×Dic₂₃	C₂×D₄	semidirect
239. C₄×D₂₃	C₂×D₄	semidirect
240. C₄×D₂₃	C₂×D₄	semidirect
251. C₂²×C₂₃	C₂×#41	semidirect
266. C₂×D₂₃	C₂×#41	semidirect
287. #525	D₂₃	direct (N × H)
302. D₂₃	#525	direct (N × H)
310. C₂×#41	C₂×D₂₃	semidirect
326. C₂³×C₄	C₂×D₂₃	semidirect
332. #123	C₂×D₂₃	semidirect
338. C₂²⋊Q₈	C₂×D₂₃	semidirect
344. #121	C₂×D₂₃	semidirect
350. #120	C₂×D₂₃	semidirect
358. C₄×D₄	C₂×D₂₃	semidirect
363. #117	C₂×D₂₃	semidirect
370. C₂₃	C₂×#525	semidirect
388. C₂×Q₈	C₂²×D₂₃	semidirect
402. C₂×D₄	C₂²×D₂₃	semidirect
437. C₂²×C₄	C₂²×D₂₃	semidirect
443. C₄⋊C₄	C₂²×D₂₃	semidirect
444. C₄⋊C₄	C₂²×D₂₃	semidirect
455. C₂²⋊C₄	C₂²×D₂₃	semidirect
458. C₄²	C₂²×D₂₃	semidirect
523. C₂×C₄	D₄×D₂₃	semidirect
550. 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
C₂×#41×D₂₃	2
C₂³×C₄×D₂₃	2
#13092930	2
#13092929	2
#13092928	2
#13092927	2
#13092926	2
#13092925	2
#13092924	2
#13092923	2
#123×D₂₃	2
C₂²⋊Q₈×D₂₃	2
#121×D₂₃	2
#120×D₂₃	2
C₄×D₄×D₂₃	2
#117×D₂₃	2
C₂₃×#525	2
C₂×#525	23

Subgroups — D23×#525 #15686633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#525 #15686633