Subgroups — C₂₃×#21652 #19169278

Order 5888.

882 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#490	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2328	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1957	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1936	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1934	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1762	C₂	1	2	yes	maximal, complemented
10	C₄×C₂₃×#102	C₂	1	2	yes	maximal, complemented
11	C₂₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
15	C₂₃×#490	C₄	1	8	yes	complemented
16	C₂×C₂₃×#102	C₂²	1	2	yes	—
17	C₂×C₂₃×#102	C₂²	1	2	yes	—
18	C₂×C₂₃×#102	C₂²	1	2	yes	—
19	C₂×C₂₃×#102	C₂²	1	2	yes	—
20	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#390	C₂²	1	2	yes	—
27	C₂₃×#389	—	2	2	no	—
28	C₂₃×#389	C₂²	1	2	yes	—
29	C₂₃×#387	—	2	2	no	—
30	C₂₃×#386	—	2	2	no	—
31	C₂₃×#386	—	2	2	no	—
32	C₂₃×#384	C₂²	1	1	yes	characteristic
33	C₂₃×#382	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
35	C₂₃×#376	C₂²	1	1	yes	characteristic
36	C₂₃×#340	C₂²	1	2	yes	—
37	C₂₃×#340	C₂²	1	2	yes	—
38	C₂₃×#340	C₂²	1	2	yes	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂²×D₄×C₂₃	—	2	2	no	—
41	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₂₃	—	2	2	no	—
43	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
47	C₂₃×#127	—	2	2	no	—
48	C₂₃×#127	C₂×C₄	1	4	yes	—
49	C₂₃×#125	—	2	2	no	—
50	C₂₃×#125	C₂×C₄	1	4	yes	complemented
51	C₄×D₄×C₂₃	—	2	4	no	—
52	C₄×D₄×C₂₃	—	2	4	no	—
53	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
62	C₂×C₄²×C₂₃	—	2	2	no	—
63	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
66	C₂₃×#102	—	2	4	no	—
67	C₂₃×#102	—	2	4	no	—
68	C₂₃×#102	C₂×C₄	1	8	yes	complemented
69	C₂₃×#102	C₂×C₄	1	8	yes	complemented
70	C₂₃×#97	—	2	2	no	—
71	C₂₃×#97	—	2	2	no	—
72	C₂₃×#97	C₂×C₄	1	4	yes	complemented
73	C₄×C₈×C₂₃	—	2	2	no	—
74	C₄×C₈×C₂₃	—	2	2	no	—
75	C₄×C₈×C₂₃	—	2	2	no	—
76	C₂₃×#95	—	2	2	no	—
77	C₂₃×#95	—	2	2	no	—
78	C₂₃×#95	—	2	2	no	—
79	C₂₃×#95	D₄	1	2	yes	—
80	C₂₃×#95	D₄	1	2	yes	—
81	C₂⁴×C₂₃	—	2	2	no	—
82	C₂×D₄×C₂₃	—	2	8	no	—
83	C₂×D₄×C₂₃	—	2	2	no	—
84	C₂×D₄×C₂₃	—	2	2	no	—
85	C₂×D₄×C₂₃	—	2	2	no	—
86	C₂×D₄×C₂₃	—	2	2	no	—
87	C₂×D₄×C₂₃	—	2	2	no	—
88	C₂×D₄×C₂₃	—	8	2	no	—
89	C₂×D₄×C₂₃	—	8	2	no	—
90	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₂₃	—	2	2	no	—
92	C₂²×C₄×C₂₃	—	2	2	no	—
93	C₂²×C₄×C₂₃	—	2	2	no	—
94	C₂²×C₄×C₂₃	—	4	4	no	—
95	C₂²×C₄×C₂₃	—	8	2	no	—
96	C₂²×C₄×C₂₃	—	8	2	no	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
102	C₂×C₈×C₂₃	—	2	1	no	—
103	C₂×C₈×C₂₃	—	2	1	no	—
104	C₂×C₈×C₂₃	—	2	1	no	—
105	C₂×C₈×C₂₃	—	2	1	no	—
106	C₂×C₈×C₂₃	—	2	1	no	—
107	C₂×C₈×C₂₃	—	2	1	no	—
108	C₂×C₈×C₂₃	—	2	1	no	—
109	C₂×C₈×C₂₃	—	2	1	no	—
110	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₂₃	#41	1	2	yes	—
113	C₂×C₈×C₂₃	#41	1	2	yes	—
114	C₄⋊C₄×C₂₃	—	2	8	no	—
115	C₄⋊C₄×C₂₃	—	2	2	no	—
116	C₄⋊C₄×C₂₃	—	2	2	no	—
117	C₄⋊C₄×C₂₃	—	2	2	no	—
118	C₄⋊C₄×C₂₃	—	2	2	no	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	—	8	2	no	—
121	C₄⋊C₄×C₂₃	—	8	2	no	—
122	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
123	C₂²⋊C₄×C₂₃	—	4	4	no	—
124	C₂²⋊C₄×C₂₃	—	8	2	no	—
125	C₂²⋊C₄×C₂₃	—	8	2	no	—
126	C₄²×C₂₃	—	2	1	no	—
127	C₄²×C₂₃	—	2	1	no	—
128	C₄²×C₂₃	—	8	2	no	—
129	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
130	C₄²×C₂₃	#41	1	2	yes	—
131	C₄²×C₂₃	#41	1	2	yes	—
132	C₄²×C₂₃	#41	1	2	yes	—
133	#21652	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₂₃	—	2	4	no	—
135	C₂³×C₂₃	—	4	2	no	—
136	C₂³×C₂₃	—	4	2	no	—
137	C₂³×C₂₃	—	4	2	no	—
138	C₂³×C₂₃	—	4	2	no	—
139	C₂³×C₂₃	—	4	2	no	—
140	C₂³×C₂₃	—	4	2	no	—
141	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
142	D₄×C₂₃	—	2	4	no	—
143	D₄×C₂₃	—	2	4	no	—
144	D₄×C₂₃	—	4	2	no	—
145	D₄×C₂₃	—	4	2	no	—
146	D₄×C₂₃	—	8	8	no	—
147	C₂×C₄×C₂₃	—	2	2	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	4	no	—
152	C₂×C₄×C₂₃	—	2	1	no	—
153	C₂×C₄×C₂₃	—	2	1	no	—
154	C₂×C₄×C₂₃	—	2	2	no	—
155	C₂×C₄×C₂₃	—	2	2	no	—
156	C₂×C₄×C₂₃	—	4	2	no	—
157	C₂×C₄×C₂₃	—	4	2	no	—
158	C₂×C₄×C₂₃	—	4	2	no	—
159	C₂×C₄×C₂₃	—	4	2	no	—
160	C₂×C₄×C₂₃	—	4	2	no	—
161	C₂×C₄×C₂₃	—	4	2	no	—
162	C₂×C₄×C₂₃	—	4	2	no	—
163	C₂×C₄×C₂₃	—	4	2	no	—
164	C₂×C₄×C₂₃	—	8	8	no	—
165	C₂×C₄×C₂₃	C₄×D₄	1	4	yes	—
166	C₂×C₄×C₂₃	#124	1	4	yes	—
167	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
173	C₈×C₂₃	—	2	2	no	—
174	C₈×C₂₃	—	2	2	no	—
175	C₈×C₂₃	—	2	2	no	—
176	C₈×C₂₃	—	2	2	no	—
177	C₂×#490	C₂×C₂₃	1	1	yes	characteristic
178	#2330	C₂×C₂₃	1	1	yes	characteristic, complemented
179	#2328	C₂×C₂₃	1	1	yes	characteristic
180	#1991	C₂×C₂₃	1	1	yes	characteristic, complemented
181	#1957	C₂×C₂₃	1	1	yes	characteristic
182	#1936	C₂×C₂₃	1	2	yes	complemented
183	#1934	C₂×C₂₃	1	2	yes	complemented
184	#1836	C₂×C₂₃	1	1	yes	characteristic, complemented
185	#1762	C₂×C₂₃	1	2	yes	complemented
186	C₄×#102	C₂×C₂₃	1	2	yes	complemented
187	#1726	C₂×C₂₃	1	1	yes	characteristic, complemented
188	C₂²×C₂₃	—	4	4	no	—
189	C₂²×C₂₃	—	4	4	no	—
190	C₂²×C₂₃	—	4	4	no	—
191	C₂²×C₂₃	—	8	2	no	—
192	C₂²×C₂₃	—	8	2	no	—
193	C₂²×C₂₃	—	8	2	no	—
194	C₂²×C₂₃	—	8	2	no	—
195	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₂₃	C₂×#124	1	1	yes	characteristic
197	C₂²×C₂₃	#532	1	1	yes	characteristic
198	C₂²×C₂₃	#576	1	2	yes	—
199	C₂²×C₂₃	#577	1	2	yes	—
200	C₄×C₂₃	—	2	4	no	—
201	C₄×C₂₃	—	2	4	no	—
202	C₄×C₂₃	—	4	1	no	—
203	C₄×C₂₃	—	4	1	no	—
204	C₄×C₂₃	—	4	4	no	—
205	C₄×C₂₃	—	8	2	no	—
206	C₄×C₂₃	—	8	2	no	—
207	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
208	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
209	C₄×C₂₃	#529	1	1	yes	characteristic
210	C₄×C₂₃	#529	1	1	yes	characteristic
211	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
212	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
213	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
214	#490	C₄×C₂₃	1	8	yes	complemented
215	C₂×#102	C₂²×C₂₃	1	2	yes	—
216	C₂×#102	C₂²×C₂₃	1	2	yes	—
217	C₂×#102	C₂²×C₂₃	1	2	yes	—
218	C₂×#102	C₂²×C₂₃	1	2	yes	—
219	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
220	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
221	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
225	#390	C₂²×C₂₃	1	2	yes	—
226	#389	—	2	2	no	—
227	#389	C₂²×C₂₃	1	2	yes	—
228	#387	—	2	2	no	—
229	#386	—	2	2	no	—
230	#386	—	2	2	no	—
231	#384	C₂²×C₂₃	1	1	yes	characteristic
232	#382	C₂²×C₂₃	1	1	yes	characteristic
233	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
234	#376	C₂²×C₂₃	1	1	yes	characteristic
235	#340	C₂²×C₂₃	1	2	yes	—
236	#340	C₂²×C₂₃	1	2	yes	—
237	#340	C₂²×C₂₃	1	2	yes	—
238	#340	C₂²×C₂₃	1	2	yes	—
239	C₂×C₂₃	—	8	4	no	—
240	C₂×C₂₃	C₄×#124	1	1	yes	characteristic
241	C₂×C₂₃	#2946	1	2	yes	—
242	C₂×C₂₃	#3136	1	2	yes	—
243	C₂×C₂₃	#3174	1	1	yes	characteristic
244	C₂×C₂₃	#3176	1	1	yes	characteristic
245	C₂²×D₄	—	2	2	no	—
246	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
247	C₂³×C₄	—	2	2	no	—
248	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
252	#127	—	2	2	no	—
253	#127	C₂×C₄×C₂₃	1	4	yes	—
254	#125	—	2	2	no	—
255	#125	C₂×C₄×C₂₃	1	4	yes	complemented
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
271	#102	—	2	4	no	—
272	#102	—	2	4	no	—
273	#102	C₂×C₄×C₂₃	1	8	yes	complemented
274	#102	C₂×C₄×C₂₃	1	8	yes	complemented
275	#97	—	2	2	no	—
276	#97	—	2	2	no	—
277	#97	C₂×C₄×C₂₃	1	4	yes	complemented
278	C₄×C₈	—	2	2	no	—
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	D₄×C₂₃	1	2	yes	—
285	#95	D₄×C₂₃	1	2	yes	—
286	C₂₃	#21652	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	—	2	2	no	—
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	8	2	no	—
295	C₂×D₄	—	8	2	no	—
296	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	—	8	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
317	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
318	C₂×C₈	#41×C₂₃	1	2	yes	—
319	C₂×C₈	#41×C₂₃	1	2	yes	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	—	8	2	no	—
328	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₂²⋊C₄	—	8	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	8	2	no	—
335	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
336	C₄²	#41×C₂₃	1	2	yes	—
337	C₄²	#41×C₂₃	1	2	yes	—
338	C₄²	#41×C₂₃	1	2	yes	—
339	C₂³	—	2	4	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
347	D₄	—	2	4	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	8	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	8	no	—
370	C₂×C₄	C₄×D₄×C₂₃	1	4	yes	—
371	C₂×C₄	C₂₃×#124	1	4	yes	—
372	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	2	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
390	C₂²	C₂×C₂₃×#124	1	1	yes	characteristic
391	C₂²	C₂₃×#532	1	1	yes	characteristic
392	C₂²	C₂₃×#576	1	2	yes	—
393	C₂²	C₂₃×#577	1	2	yes	—
394	C₄	—	2	4	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	2	no	—
401	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
402	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
403	C₄	C₂₃×#529	1	1	yes	characteristic
404	C₄	C₂₃×#529	1	1	yes	characteristic
405	C₂	—	8	4	no	—
406	C₂	C₄×C₂₃×#124	1	1	yes	characteristic
407	C₂	C₂₃×#2946	1	2	yes	—
408	C₂	C₂₃×#3136	1	2	yes	—
409	C₂	C₂₃×#3174	1	1	yes	characteristic
410	C₂	C₂₃×#3176	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2330	C₂	semidirect
4. C₂₃×#1991	C₂	semidirect
6. C₂₃×#1936	C₂	semidirect
7. C₂₃×#1934	C₂	semidirect
8. C₂₃×#1836	C₂	semidirect
9. C₂₃×#1762	C₂	semidirect
10. C₄×C₂₃×#102	C₂	semidirect
11. C₂₃×#1726	C₂	semidirect
15. C₂₃×#490	C₄	semidirect
50. C₂₃×#125	C₂×C₄	semidirect
68. C₂₃×#102	C₂×C₄	semidirect
69. C₂₃×#102	C₂×C₄	semidirect
72. C₂₃×#97	C₂×C₄	semidirect
133. #21652	C₂₃	direct (N × H)
178. #2330	C₂×C₂₃	semidirect
180. #1991	C₂×C₂₃	semidirect
182. #1936	C₂×C₂₃	semidirect
183. #1934	C₂×C₂₃	semidirect
184. #1836	C₂×C₂₃	semidirect
185. #1762	C₂×C₂₃	semidirect
186. C₄×#102	C₂×C₂₃	semidirect
187. #1726	C₂×C₂₃	semidirect
214. #490	C₄×C₂₃	semidirect
255. #125	C₂×C₄×C₂₃	semidirect
273. #102	C₂×C₄×C₂₃	semidirect
274. #102	C₂×C₄×C₂₃	semidirect
277. #97	C₂×C₄×C₂₃	semidirect
286. C₂₃	#21652	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×#490	2
C₂₃×#2330	2
C₂₃×#2328	2
C₂₃×#1991	2
C₂₃×#1957	2
C₂₃×#1936	2
C₂₃×#1934	2
C₂₃×#1836	2
C₂₃×#1762	2
C₄×C₂₃×#102	2
C₂₃×#1726	2
#21652	23

Subgroups — C23×#21652 #19169278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21652 #19169278