Subgroups — D₂₃×#435 #15682072

Order 2944.

564 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic
4	#13092491	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092490	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092489	C₂	1	1	yes	maximal, characteristic, complemented
7	#13092488	C₂	1	1	yes	maximal, characteristic, complemented
8	#13092487	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092486	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₂₃	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	D₄×Dic₂₃	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
25	C₂×#67267	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	M₁₆×D₂₃	—	2	4	no	—
28	C₂×#67262	C₂²	1	1	yes	characteristic, complemented
29	C₂×#67262	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₂₃	—	2	4	no	—
31	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic, complemented
37	#10625064	C₄	1	1	yes	characteristic
38	C₄⋊C₄×D₂₃	C₄	1	1	yes	characteristic
39	(C₂²⋊D₂₃)⋊C₄	C₄	1	1	yes	characteristic
40	(C₂²⋊D₂₃)⋊C₄	C₄	1	1	yes	characteristic
41	C₂²⋊C₄×D₂₃	C₄	1	1	yes	characteristic
42	C₂²⋊C₄×D₂₃	C₄	1	1	yes	characteristic
43	C₄×D₉₂	C₂²	1	1	yes	characteristic
44	C₄²×D₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊(C₂₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊(C₂₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	#10624997	C₂²	1	1	yes	characteristic, complemented
56	#10624997	C₂²	1	1	yes	characteristic, complemented
57	Dic₂₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	Dic₂₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊(C₂₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
60	#10624985	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₂₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×D₂₃	C₂×C₄	1	1	yes	characteristic
63	C₂×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₂₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₂₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×Dic₂₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₂₃	C₂×C₄	1	1	yes	characteristic
70	D₄×D₂₃	—	2	4	no	—
71	C₂×D₉₂	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₂₃	—	2	2	no	—
73	C₂×C₄×D₂₃	—	2	2	no	—
74	C₂×C₄×D₂₃	—	2	2	no	—
75	C₂×C₄×D₂₃	—	2	2	no	—
76	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
83	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
85	M₁₆×C₂₃	—	2	2	no	—
86	C₂×C₈×C₂₃	—	2	2	no	—
87	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
89	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
94	C₄²×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²⋊Dic₂₃	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊Dic₂₃	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
100	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₄⋊Dic₂₃	C₂×C₄	1	1	yes	characteristic
102	Dic₂₃⋊C₄	C₂×C₄	1	1	yes	characteristic
103	Dic₂₃⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₂₃	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₂₃	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
107	#67267	—	2	2	no	—
108	C₂×C₂₃⋊C₈	—	2	2	no	—
109	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
112	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
113	#67262	—	2	2	no	—
114	#67262	—	2	2	no	—
115	C₈×D₂₃	—	2	2	no	—
116	C₈×D₂₃	—	2	2	no	—
117	C₈×D₂₃	—	2	2	no	—
118	C₈×D₂₃	—	2	2	no	—
119	C₈×D₂₃	—	2	2	no	—
120	C₈×D₂₃	D₄	1	4	yes	complemented
121	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
122	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×D₂₃	—	2	2	no	—
124	C₂²×D₂₃	—	2	2	no	—
125	C₂²×D₂₃	—	2	2	no	—
126	C₂²×D₂₃	—	2	2	no	—
127	C₂²×D₂₃	—	2	2	no	—
128	C₂²×D₂₃	M₁₆	1	4	yes	complemented
129	C₂²×D₂₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×D₂₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×D₂₃	C₂²×C₄	1	1	yes	characteristic
132	D₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	—	2	1	no	—
134	C₂×C₄×C₂₃	—	2	1	no	—
135	C₂×C₄×C₂₃	—	2	1	no	—
136	C₂×C₄×C₂₃	—	2	1	no	—
137	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
142	C₂²⋊D₂₃	—	2	2	no	—
143	C₂²⋊D₂₃	—	2	2	no	—
144	C₂×Dic₂₃	—	2	2	no	—
145	C₂×Dic₂₃	—	2	2	no	—
146	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
151	D₉₂	—	2	2	no	—
152	C₄×D₂₃	—	2	2	no	—
153	C₄×D₂₃	—	2	2	no	—
154	C₄×D₂₃	—	2	2	no	—
155	C₄×D₂₃	—	2	2	no	—
156	C₄×D₂₃	—	2	1	no	—
157	C₄×D₂₃	—	2	1	no	—
158	C₄×D₂₃	—	2	1	no	—
159	C₄×D₂₃	—	2	1	no	—
160	C₄×D₂₃	—	2	2	no	—
161	C₄×D₂₃	—	2	2	no	—
162	C₄×D₂₃	C₂×D₄	1	2	yes	—
163	C₄×D₂₃	#41	1	2	yes	—
164	C₈×C₂₃	—	2	1	no	—
165	C₈×C₂₃	—	2	1	no	—
166	C₈×C₂₃	—	2	1	no	—
167	C₈×C₂₃	C₂×D₄	1	2	yes	complemented
168	C₂₃⋊C₈	—	2	1	no	—
169	C₂₃⋊C₈	—	2	1	no	—
170	C₂₃⋊C₈	—	2	1	no	—
171	C₂₃⋊C₈	C₂×D₄	1	2	yes	complemented
172	C₂×#435	—	23	1	no	maximal, Sylow
173	C₂²×C₂₃	—	2	1	no	—
174	C₂²×C₂₃	—	2	1	no	—
175	C₂²×C₂₃	—	2	1	no	—
176	C₂²×C₂₃	—	2	1	no	—
177	C₂²×C₂₃	—	2	1	no	—
178	C₂²×C₂₃	C₂×M₁₆	1	2	yes	complemented
179	C₂²×C₂₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×D₂₃	—	2	1	no	—
181	C₂×D₂₃	—	2	1	no	—
182	C₂×D₂₃	—	2	8	no	—
183	C₂×D₂₃	—	2	1	no	—
184	C₂×D₂₃	—	2	1	no	—
185	C₂×D₂₃	—	2	1	no	—
186	C₂×D₂₃	—	4	4	no	—
187	C₂×D₂₃	C₄×D₄	1	2	yes	—
188	C₂×D₂₃	C₂×M₁₆	1	2	yes	—
189	C₂×D₂₃	C₂×M₁₆	1	2	yes	complemented
190	C₂×D₂₃	#131	1	2	yes	—
191	C₄×C₂₃	—	2	1	no	—
192	C₄×C₂₃	—	2	1	no	—
193	C₄×C₂₃	—	2	1	no	—
194	C₄×C₂₃	—	2	1	no	—
195	C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
196	C₄×C₂₃	C₂×#41	1	1	yes	characteristic
197	Dic₂₃	—	2	1	no	—
198	Dic₂₃	—	2	1	no	—
199	Dic₂₃	—	2	1	no	—
200	Dic₂₃	—	2	1	no	—
201	Dic₂₃	C₄×D₄	1	2	yes	—
202	C₂²×M₁₆	—	23	1	no	—
203	C₂³×C₈	—	23	1	no	—
204	C₂×C₄×D₄	—	23	1	no	—
205	#435	—	23	1	no	—
206	#435	—	23	1	no	—
207	#435	—	23	1	no	—
208	#435	—	23	1	no	—
209	#435	—	23	1	no	—
210	#435	—	23	1	no	—
211	#435	—	23	1	no	—
212	#435	D₂₃	1	1	yes	characteristic, direct product factor
213	C₂×C₄⋊C₈	—	23	1	no	—
214	C₂×C₂²⋊C₈	—	23	1	no	—
215	C₂×C₂²⋊C₈	—	23	1	no	—
216	C₂×#97	—	23	1	no	—
217	C₂×C₂₃	—	2	2	no	—
218	C₂×C₂₃	—	4	1	no	—
219	C₂×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
221	C₂×C₂₃	C₂×#131	1	1	yes	characteristic
222	D₂₃	—	2	2	no	—
223	D₂₃	—	4	1	no	—
224	D₂₃	#435	1	4	yes	direct product factor
225	C₂²×D₄	—	23	1	no	—
226	C₂³×C₄	—	23	1	no	—
227	C₂³×C₄	—	23	1	no	—
228	C₂×M₁₆	—	23	1	no	—
229	C₂×M₁₆	—	23	1	no	—
230	C₂×M₁₆	—	23	1	no	—
231	C₂×M₁₆	—	46	4	no	—
232	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic, complemented
233	C₂²×C₈	—	23	1	no	—
234	C₂²×C₈	—	23	1	no	—
235	C₂²×C₈	—	23	1	no	—
236	C₂²×C₈	—	23	1	no	—
237	C₂²×C₈	—	23	1	no	—
238	C₂²×C₈	—	23	1	no	—
239	C₂²×C₈	—	23	1	no	—
240	C₂²×C₈	—	46	4	no	—
241	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic, complemented
242	C₄×D₄	—	23	1	no	—
243	C₄×D₄	—	23	1	no	—
244	C₄×D₄	—	23	1	no	—
245	C₄×D₄	—	23	1	no	—
246	C₄×D₄	—	23	1	no	—
247	C₄×D₄	—	23	1	no	—
248	C₄×D₄	—	23	1	no	—
249	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
250	C₂×C₄⋊C₄	—	23	1	no	—
251	C₂×C₂²⋊C₄	—	23	1	no	—
252	C₂×C₂²⋊C₄	—	23	1	no	—
253	C₂×C₄²	—	23	1	no	—
254	C₄⋊C₈	—	23	1	no	—
255	C₄⋊C₈	—	23	1	no	—
256	C₄⋊C₈	—	23	1	no	—
257	C₄⋊C₈	C₂×D₂₃	1	1	yes	characteristic, complemented
258	C₂²⋊C₈	—	23	1	no	—
259	C₂²⋊C₈	—	23	1	no	—
260	C₂²⋊C₈	—	23	1	no	—
261	C₂²⋊C₈	—	23	1	no	—
262	C₂²⋊C₈	—	23	1	no	—
263	C₂²⋊C₈	—	23	1	no	—
264	C₂²⋊C₈	C₂×D₂₃	1	1	yes	characteristic, complemented
265	C₂²⋊C₈	C₂×D₂₃	1	1	yes	characteristic, complemented
266	#97	—	23	1	no	—
267	#97	—	23	1	no	—
268	#97	—	23	1	no	—
269	#97	C₂×D₂₃	1	1	yes	characteristic, complemented
270	C₂₃	C₂×#435	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	—	23	1	no	—
272	C₂⁴	—	23	1	no	—
273	C₂×D₄	—	23	1	no	—
274	C₂×D₄	—	23	1	no	—
275	C₂×D₄	—	23	1	no	—
276	C₂×D₄	—	46	4	no	—
277	C₂×D₄	C₄×D₂₃	1	1	yes	characteristic
278	C₂²×C₄	—	23	1	no	—
279	C₂²×C₄	—	23	1	no	—
280	C₂²×C₄	—	23	1	no	—
281	C₂²×C₄	—	23	1	no	—
282	C₂²×C₄	—	23	1	no	—
283	C₂²×C₄	—	23	1	no	—
284	C₂²×C₄	—	23	1	no	—
285	C₂²×C₄	—	23	1	no	—
286	C₂²×C₄	—	23	1	no	—
287	C₂²×C₄	—	23	1	no	—
288	C₂²×C₄	—	23	1	no	—
289	C₂²×C₄	—	46	2	no	—
290	C₂²×C₄	—	46	2	no	—
291	C₂²×C₄	—	46	2	no	—
292	C₂²×C₄	—	46	2	no	—
293	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
294	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
295	M₁₆	—	2	2	no	—
296	M₁₆	—	46	2	no	—
297	M₁₆	—	46	2	no	—
298	M₁₆	—	46	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	23	1	no	—
301	C₂×C₈	—	23	4	no	—
302	C₂×C₈	—	23	1	no	—
303	C₂×C₈	—	23	1	no	—
304	C₂×C₈	—	23	1	no	—
305	C₂×C₈	—	46	2	no	—
306	C₂×C₈	—	46	2	no	—
307	C₂×C₈	—	46	2	no	—
308	C₂×C₈	—	46	2	no	—
309	C₂×C₈	—	46	2	no	—
310	C₂×C₈	—	46	2	no	—
311	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
313	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
314	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
315	C₄⋊C₄	—	23	1	no	—
316	C₄⋊C₄	—	23	1	no	—
317	C₄⋊C₄	—	23	1	no	—
318	C₄⋊C₄	C₄×D₂₃	1	1	yes	characteristic
319	C₂²⋊C₄	—	23	1	no	—
320	C₂²⋊C₄	—	23	1	no	—
321	C₂²⋊C₄	—	23	1	no	—
322	C₂²⋊C₄	—	23	1	no	—
323	C₂²⋊C₄	—	23	1	no	—
324	C₂²⋊C₄	—	23	1	no	—
325	C₂²⋊C₄	C₄×D₂₃	1	1	yes	characteristic
326	C₂²⋊C₄	C₄×D₂₃	1	1	yes	characteristic
327	C₄²	—	23	1	no	—
328	C₄²	—	23	1	no	—
329	C₄²	—	23	1	no	—
330	C₄²	C₂²×D₂₃	1	1	yes	characteristic
331	C₂³	—	23	1	no	—
332	C₂³	—	23	4	no	—
333	C₂³	—	23	1	no	—
334	C₂³	—	23	1	no	—
335	C₂³	—	46	2	no	—
336	C₂³	—	46	2	no	—
337	C₂³	—	46	2	no	—
338	C₂³	—	46	2	no	—
339	C₂³	—	46	2	no	—
340	C₂³	C₂×C₄×D₂₃	1	1	yes	characteristic
341	C₂³	C₂×C₄×D₂₃	1	1	yes	characteristic
342	D₄	—	2	2	no	—
343	D₄	—	46	2	no	—
344	D₄	—	46	2	no	—
345	D₄	—	46	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	23	1	no	—
351	C₂×C₄	—	23	2	no	—
352	C₂×C₄	—	23	2	no	—
353	C₂×C₄	—	23	1	no	—
354	C₂×C₄	—	23	1	no	—
355	C₂×C₄	—	23	1	no	—
356	C₂×C₄	—	23	1	no	—
357	C₂×C₄	—	46	2	no	—
358	C₂×C₄	—	46	2	no	—
359	C₂×C₄	—	46	2	no	—
360	C₂×C₄	—	46	2	no	—
361	C₂×C₄	—	46	2	no	—
362	C₂×C₄	—	46	2	no	—
363	C₂×C₄	—	46	2	no	—
364	C₂×C₄	—	46	2	no	—
365	C₂×C₄	—	46	1	no	—
366	C₂×C₄	—	46	1	no	—
367	C₂×C₄	—	46	1	no	—
368	C₂×C₄	—	46	1	no	—
369	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
373	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	23	2	no	—
378	C₈	—	46	1	no	—
379	C₈	—	46	1	no	—
380	C₈	—	46	1	no	—
381	C₈	D₄×D₂₃	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	23	2	no	—
388	C₂²	—	23	2	no	—
389	C₂²	—	23	2	no	—
390	C₂²	—	23	2	no	—
391	C₂²	—	46	8	no	—
392	C₂²	—	46	1	no	—
393	C₂²	—	46	1	no	—
394	C₂²	—	46	1	no	—
395	C₂²	—	46	1	no	—
396	C₂²	—	46	1	no	—
397	C₂²	—	92	4	no	—
398	C₂²	M₁₆×D₂₃	1	2	yes	complemented
399	C₂²	C₂²×C₄×D₂₃	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	23	2	no	—
405	C₄	—	46	1	no	—
406	C₄	—	46	1	no	—
407	C₄	—	46	1	no	—
408	C₄	—	46	1	no	—
409	C₄	C₂×D₄×D₂₃	1	1	yes	characteristic
410	C₄	#41×D₂₃	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	23	4	no	—
414	C₂	—	46	2	no	—
415	C₂	—	92	1	no	—
416	C₂	C₄×D₄×D₂₃	1	1	yes	characteristic
417	C₂	C₂×M₁₆×D₂₃	1	1	yes	characteristic
418	C₂	#131×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₃
commutator, socle	C₂²×C₂₃	C₂³×C₄
Fitting	C₂₃×#435	C₂
prime radical	C₂×D₄×D₂₃	C₄
cosocle	C₂×C₄×C₂₃	C₂⁴
hypercenter	#435	D₂₃
hypocenter	C₂₃	C₂×#435
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×M₁₆×D₂₃	C₂	semidirect
2. C₂²×C₈×D₂₃	C₂	semidirect
4. #13092491	C₂	semidirect
5. #13092490	C₂	semidirect
6. #13092489	C₂	semidirect
7. #13092488	C₂	semidirect
8. #13092487	C₂	semidirect
9. #13092486	C₂	semidirect
10. #13092485	C₂	semidirect
11. C₄⋊C₈×D₂₃	C₂	semidirect
12. C₂²⋊C₈×D₂₃	C₂	semidirect
13. C₂²⋊C₈×D₂₃	C₂	semidirect
14. #97×D₂₃	C₂	semidirect
15. C₂₃×#435	C₂	semidirect
19. C₂×M₁₆×C₂₃	C₂²	semidirect
20. C₂²×C₈×C₂₃	C₂²	semidirect
25. C₂×#67267	C₂²	semidirect
26. C₂²×C₂₃⋊C₈	C₂²	semidirect
28. C₂×#67262	C₂²	semidirect
29. C₂×#67262	C₂²	semidirect
35. C₂×C₈×D₂₃	C₂²	semidirect
36. C₂×C₈×D₂₃	C₂²	semidirect
45. C₂₃×C₄⋊C₈	C₂²	semidirect
46. C₂₃×C₂²⋊C₈	C₂²	semidirect
47. C₂₃×C₂²⋊C₈	C₂²	semidirect
48. C₂₃×#97	C₂²	semidirect
49. C₂²⋊(C₂₃⋊C₈)	C₂²	semidirect
50. C₂²⋊(C₂₃⋊C₈)	C₂²	semidirect
51. (C₂×D₂₃)⋊C₈	C₂²	semidirect
52. (C₂×D₂₃)⋊C₈	C₂²	semidirect
53. (C₂×D₂₃)⋊C₈	C₂²	semidirect
54. (C₂×D₂₃)⋊C₈	C₂²	semidirect
55. #10624997	C₂²	semidirect
56. #10624997	C₂²	semidirect
57. Dic₂₃⋊C₈	C₂²	semidirect
58. Dic₂₃⋊C₈	C₂²	semidirect
59. C₄⋊(C₂₃⋊C₈)	C₂²	semidirect
60. #10624985	C₂²	semidirect
120. C₈×D₂₃	D₄	semidirect
128. C₂²×D₂₃	M₁₆	semidirect
167. C₈×C₂₃	C₂×D₄	semidirect
171. C₂₃⋊C₈	C₂×D₄	semidirect
178. C₂²×C₂₃	C₂×M₁₆	semidirect
189. C₂×D₂₃	C₂×M₁₆	semidirect
212. #435	D₂₃	direct (N × H)
224. D₂₃	#435	direct (N × H)
232. C₂×M₁₆	C₂×D₂₃	semidirect
241. C₂²×C₈	C₂×D₂₃	semidirect
257. C₄⋊C₈	C₂×D₂₃	semidirect
264. C₂²⋊C₈	C₂×D₂₃	semidirect
265. C₂²⋊C₈	C₂×D₂₃	semidirect
269. #97	C₂×D₂₃	semidirect
270. C₂₃	C₂×#435	semidirect
381. C₈	D₄×D₂₃	semidirect
398. C₂²	M₁₆×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×D₂₃	2
C₂²×C₈×D₂₃	2
C₄×D₄×D₂₃	2
#13092491	2
#13092490	2
#13092489	2
#13092488	2
#13092487	2
#13092486	2
#13092485	2
C₄⋊C₈×D₂₃	2
C₂²⋊C₈×D₂₃	2
#97×D₂₃	2
C₂₃×#435	2
C₂×#435	23

Subgroups — D23×#435 #15682072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#435 #15682072