Subgroups — C₂₃×#22602 #19170228

Order 5888.

780 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#433	C₂	1	2	yes	maximal
2	C₂₃×#2285	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1940	C₂	1	2	yes	maximal, complemented
4	C₂₃×#1917	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1916	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1818	C₂	1	2	yes	maximal
7	C₂₃×#1797	C₂	1	1	yes	maximal, characteristic
8	C₂₃×#1771	C₂	1	2	yes	maximal, complemented
9	C₂₃×#1749	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₃×#117	C₂²	1	2	yes	—
11	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#433	—	2	8	no	—
13	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#97	C₂²	1	2	yes	—
20	C₂×C₂₃×#97	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
22	C₂₃×#384	C₄	1	1	yes	characteristic
23	C₂₃×#384	C₄	1	1	yes	characteristic
24	C₂₃×#382	C₄	1	2	yes	—
25	C₂₃×#380	C₄	1	2	yes	—
26	C₂₃×#380	C₄	1	1	yes	characteristic
27	C₂₃×#380	C₄	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#336	C₂²	1	1	yes	characteristic
32	C₂₃×#336	C₂²	1	2	yes	—
33	C₂₃×#336	C₂²	1	2	yes	—
34	C₂₃×#336	C₂²	1	2	yes	—
35	C₂₃×#336	C₂²	1	1	yes	characteristic
36	C₂₃×#336	C₂²	1	2	yes	—
37	C₂₃×#336	C₂²	1	2	yes	—
38	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
45	C₂₃×#117	—	2	4	no	—
46	C₂₃×#117	—	2	4	no	—
47	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₂₃	—	2	4	no	—
58	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
62	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
63	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
64	C₂₃×C₄⋊C₈	—	2	4	no	—
65	C₂₃×C₄⋊C₈	—	2	4	no	—
66	C₂₃×C₄⋊C₈	—	2	4	no	—
67	C₂₃×C₂²⋊C₈	—	2	4	no	—
68	C₂₃×C₂²⋊C₈	—	2	2	no	—
69	C₂₃×C₂²⋊C₈	D₄	1	4	yes	—
70	C₂₃×#97	—	2	4	no	—
71	C₂₃×#97	—	2	4	no	—
72	C₄×C₈×C₂₃	—	2	4	no	—
73	C₂₃×#95	C₂×C₄	1	2	yes	—
74	C₂₃×#95	C₂×C₄	1	2	yes	—
75	C₂₃×#95	C₂×C₄	1	2	yes	—
76	C₂₃×#95	C₂×C₄	1	2	yes	—
77	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	—	2	2	no	—
79	C₂²×C₄×C₂₃	—	2	2	no	—
80	C₂²×C₄×C₂₃	—	2	2	no	—
81	C₂²×C₄×C₂₃	—	2	2	no	—
82	C₂²×C₄×C₂₃	—	2	2	no	—
83	C₂²×C₄×C₂₃	—	4	1	no	—
84	C₂²×C₄×C₂₃	—	4	1	no	—
85	C₂²×C₄×C₂₃	—	4	1	no	—
86	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₂₃	#41	1	2	yes	—
97	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₂₃	—	2	2	no	—
99	C₂×C₈×C₂₃	—	2	2	no	—
100	C₂×C₈×C₂₃	—	2	2	no	—
101	C₂×C₈×C₂₃	—	2	2	no	—
102	C₂×C₈×C₂₃	—	2	2	no	—
103	C₂×C₈×C₂₃	—	2	2	no	—
104	C₂×C₈×C₂₃	—	2	2	no	—
105	C₂×C₈×C₂₃	—	2	2	no	—
106	C₂×C₈×C₂₃	—	2	2	no	—
107	C₂×C₈×C₂₃	—	2	2	no	—
108	C₂×C₈×C₂₃	—	2	2	no	—
109	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
110	C₄⋊C₄×C₂₃	—	2	4	no	—
111	C₄⋊C₄×C₂₃	—	2	4	no	—
112	C₄⋊C₄×C₂₃	—	2	4	no	—
113	C₄⋊C₄×C₂₃	—	4	1	no	—
114	C₄⋊C₄×C₂₃	—	4	1	no	—
115	C₄⋊C₄×C₂₃	—	4	1	no	—
116	C₄⋊C₄×C₂₃	—	4	1	no	—
117	C₄⋊C₄×C₂₃	—	4	2	no	—
118	C₂²⋊C₄×C₂₃	—	2	4	no	—
119	C₂²⋊C₄×C₂₃	—	2	4	no	—
120	C₄²×C₂₃	—	2	2	no	—
121	C₄²×C₂₃	—	2	2	no	—
122	C₄²×C₂₃	—	2	2	no	—
123	C₄²×C₂₃	—	2	2	no	—
124	C₄²×C₂₃	—	2	2	no	—
125	C₄²×C₂₃	—	2	2	no	—
126	C₄²×C₂₃	—	2	2	no	—
127	C₄²×C₂₃	#41	1	4	yes	—
128	#22602	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₂₃	—	2	1	no	—
130	C₂³×C₂₃	—	2	1	no	—
131	C₂³×C₂₃	—	2	1	no	—
132	C₂³×C₂₃	—	2	1	no	—
133	C₂³×C₂₃	—	2	1	no	—
134	C₂³×C₂₃	—	2	1	no	—
135	C₂³×C₂₃	C₄×D₄	1	2	yes	—
136	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₂₃	—	2	1	no	—
138	C₂×C₄×C₂₃	—	2	1	no	—
139	C₂×C₄×C₂₃	—	2	1	no	—
140	C₂×C₄×C₂₃	—	2	1	no	—
141	C₂×C₄×C₂₃	—	2	1	no	—
142	C₂×C₄×C₂₃	—	2	1	no	—
143	C₂×C₄×C₂₃	—	2	1	no	—
144	C₂×C₄×C₂₃	—	2	1	no	—
145	C₂×C₄×C₂₃	—	2	4	no	—
146	C₂×C₄×C₂₃	—	2	4	no	—
147	C₂×C₄×C₂₃	—	2	1	no	—
148	C₂×C₄×C₂₃	—	2	2	no	—
149	C₂×C₄×C₂₃	—	2	2	no	—
150	C₂×C₄×C₂₃	—	2	2	no	—
151	C₂×C₄×C₂₃	—	2	2	no	—
152	C₂×C₄×C₂₃	—	2	2	no	—
153	C₂×C₄×C₂₃	—	2	2	no	—
154	C₂×C₄×C₂₃	—	2	2	no	—
155	C₂×C₄×C₂₃	—	2	2	no	—
156	C₂×C₄×C₂₃	—	2	2	no	—
157	C₂×C₄×C₂₃	—	2	2	no	—
158	C₂×C₄×C₂₃	—	2	2	no	—
159	C₂×C₄×C₂₃	—	2	2	no	—
160	C₂×C₄×C₂₃	—	2	1	no	—
161	C₂×C₄×C₂₃	—	2	1	no	—
162	C₂×C₄×C₂₃	—	4	4	no	—
163	C₂×C₄×C₂₃	—	4	4	no	—
164	C₂×C₄×C₂₃	#117	1	2	yes	—
165	C₂×C₄×C₂₃	#117	1	2	yes	—
166	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₂₃	#131	1	2	yes	—
168	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
170	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
172	C₈×C₂₃	—	2	4	no	—
173	C₈×C₂₃	—	4	2	no	—
174	C₈×C₂₃	—	4	2	no	—
175	C₈×C₂₃	—	4	2	no	—
176	C₂×#433	C₂×C₂₃	1	2	yes	—
177	#2285	C₂×C₂₃	1	1	yes	characteristic
178	#1940	C₂×C₂₃	1	2	yes	complemented
179	#1917	C₂×C₂₃	1	2	yes	complemented
180	#1916	C₂×C₂₃	1	2	yes	complemented
181	#1818	C₂×C₂₃	1	2	yes	—
182	#1797	C₂×C₂₃	1	1	yes	characteristic
183	#1771	C₂×C₂₃	1	2	yes	complemented
184	#1749	C₂×C₂₃	1	1	yes	characteristic
185	C₂²×C₂₃	—	2	2	no	—
186	C₂²×C₂₃	—	2	2	no	—
187	C₂²×C₂₃	—	2	2	no	—
188	C₂²×C₂₃	—	4	1	no	—
189	C₂²×C₂₃	—	4	1	no	—
190	C₂²×C₂₃	—	4	1	no	—
191	C₂²×C₂₃	—	4	1	no	—
192	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
193	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂²×C₂₃	#519	1	1	yes	characteristic
195	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
196	C₂²×C₂₃	#568	1	1	yes	characteristic
197	C₂²×C₂₃	#568	1	1	yes	characteristic
198	C₂²×C₂₃	#568	1	1	yes	characteristic
199	C₄×C₂₃	—	2	2	no	—
200	C₄×C₂₃	—	2	2	no	—
201	C₄×C₂₃	—	2	2	no	—
202	C₄×C₂₃	—	2	2	no	—
203	C₄×C₂₃	—	4	1	no	—
204	C₄×C₂₃	—	4	2	no	—
205	C₄×C₂₃	—	4	2	no	—
206	C₄×C₂₃	—	4	2	no	—
207	C₄×C₂₃	—	4	2	no	—
208	C₄×C₂₃	#547	1	2	yes	—
209	C₄×C₂₃	#552	1	2	yes	—
210	C₂×#117	C₂²×C₂₃	1	2	yes	—
211	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
212	#433	—	2	8	no	—
213	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
214	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
215	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
216	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
218	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
219	C₂×#97	C₂²×C₂₃	1	2	yes	—
220	C₂×#97	C₂²×C₂₃	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
222	#384	C₄×C₂₃	1	1	yes	characteristic
223	#384	C₄×C₂₃	1	1	yes	characteristic
224	#382	C₄×C₂₃	1	2	yes	—
225	#380	C₄×C₂₃	1	2	yes	—
226	#380	C₄×C₂₃	1	1	yes	characteristic
227	#380	C₄×C₂₃	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
229	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
230	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
231	#336	C₂²×C₂₃	1	1	yes	characteristic
232	#336	C₂²×C₂₃	1	1	yes	characteristic
233	#336	C₂²×C₂₃	1	2	yes	—
234	#336	C₂²×C₂₃	1	2	yes	—
235	#336	C₂²×C₂₃	1	2	yes	—
236	#336	C₂²×C₂₃	1	2	yes	—
237	#336	C₂²×C₂₃	1	2	yes	—
238	C₂×C₂₃	—	4	2	no	—
239	C₂×C₂₃	#2344	1	1	yes	characteristic
240	C₂×C₂₃	#2921	1	1	yes	characteristic
241	C₂×C₂₃	#2924	1	1	yes	characteristic
242	C₂×C₂₃	#2932	1	1	yes	characteristic
243	C₂×C₂₃	#2935	1	1	yes	characteristic
244	C₂×C₂₃	#2985	1	1	yes	characteristic
245	C₂×C₂₃	#2987	1	1	yes	characteristic
246	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
247	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
250	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
251	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
252	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
253	#117	—	2	4	no	—
254	#117	—	2	4	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
265	C₂×C₄²	—	2	4	no	—
266	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
267	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
269	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
270	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
272	C₄⋊C₈	—	2	4	no	—
273	C₄⋊C₈	—	2	4	no	—
274	C₄⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	C₂²⋊C₈	D₄×C₂₃	1	4	yes	—
278	#97	—	2	4	no	—
279	#97	—	2	4	no	—
280	C₄×C₈	—	2	4	no	—
281	#95	C₂×C₄×C₂₃	1	2	yes	—
282	#95	C₂×C₄×C₂₃	1	2	yes	—
283	#95	C₂×C₄×C₂₃	1	2	yes	—
284	#95	C₂×C₄×C₂₃	1	2	yes	—
285	C₂₃	#22602	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
305	C₂²×C₄	#41×C₂₃	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	#41×C₂₃	1	4	yes	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	C₄×D₄×C₂₃	1	2	yes	—
344	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
345	C₂×C₄	—	2	1	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	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	C₂₃×#117	1	2	yes	—
373	C₂×C₄	C₂₃×#117	1	2	yes	—
374	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
375	C₂×C₄	C₂₃×#131	1	2	yes	—
376	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
378	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
379	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
380	C₈	—	2	4	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
392	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
393	C₂²	C₂₃×#519	1	1	yes	characteristic
394	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
395	C₂²	C₂₃×#568	1	1	yes	characteristic
396	C₂²	C₂₃×#568	1	1	yes	characteristic
397	C₂²	C₂₃×#568	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	C₂₃×#547	1	2	yes	—
408	C₄	C₂₃×#552	1	2	yes	—
409	C₂	—	4	2	no	—
410	C₂	C₂₃×#2344	1	1	yes	characteristic
411	C₂	C₂₃×#2921	1	1	yes	characteristic
412	C₂	C₂₃×#2924	1	1	yes	characteristic
413	C₂	C₂₃×#2932	1	1	yes	characteristic
414	C₂	C₂₃×#2935	1	1	yes	characteristic
415	C₂	C₂₃×#2985	1	1	yes	characteristic
416	C₂	C₂₃×#2987	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂³×C₄
prime radical	C₂⁴×C₂₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×#1940	C₂	semidirect
4. C₂₃×#1917	C₂	semidirect
5. C₂₃×#1916	C₂	semidirect
8. C₂₃×#1771	C₂	semidirect
128. #22602	C₂₃	direct (N × H)
178. #1940	C₂×C₂₃	semidirect
179. #1917	C₂×C₂₃	semidirect
180. #1916	C₂×C₂₃	semidirect
183. #1771	C₂×C₂₃	semidirect
285. C₂₃	#22602	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#433	2
C₂₃×#2285	2
C₂₃×#1940	2
C₂₃×#1917	2
C₂₃×#1916	2
C₂₃×#1818	2
C₂₃×#1797	2
C₂₃×#1771	2
C₂₃×#1749	2
#22602	23

Subgroups — C23×#22602 #19170228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22602 #19170228