Subgroups — C₂₃×#21415 #19169041

Order 5888.

1430 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄³×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1994	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1962	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1896	C₂	1	4	yes	maximal, complemented
7	C₄×C₂₃×#104	C₂	1	4	yes	maximal, complemented
8	C₂₃×#533	C₄	1	2	yes	complemented
9	C₂₃×#533	C₂²	1	1	yes	characteristic
10	C₂₃×#532	C₄	1	2	yes	complemented
11	C₂₃×#532	C₂²	1	1	yes	characteristic
12	C₂₃×#529	—	2	2	no	—
13	C₂₃×#529	—	2	2	no	—
14	C₂₃×#529	C₄	1	4	yes	complemented
15	C₂₃×#525	—	2	2	no	—
16	C₂₃×#525	C₂²	1	2	yes	—
17	C₄×#41×C₂₃	—	2	2	no	—
18	C₄×#41×C₂₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₂₃	—	2	2	no	—
20	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#432	—	2	2	no	—
23	C₂₃×#431	—	2	2	no	—
24	C₂₃×#423	C₂²	1	2	yes	—
25	C₂×C₂₃×#104	C₂²	1	8	yes	—
26	C₂₃×#407	C₂²	1	2	yes	—
27	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
28	C₄³×C₂₃	—	2	2	no	—
29	C₄³×C₂₃	C₂²	1	2	yes	—
30	C₄³×C₂₃	C₂²	1	2	yes	—
31	C₂₃×#339	C₂²	1	8	yes	—
32	C₂×#41×C₂₃	—	2	2	no	—
33	C₂×#41×C₂₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₂₃	—	2	2	no	—
35	C₂³×C₄×C₂₃	D₄	1	2	yes	—
36	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
38	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
39	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
40	C₂₃×#127	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂₃×#126	—	2	4	no	—
42	C₂₃×#125	—	2	2	no	—
43	C₂₃×#125	C₂×C₄	1	2	yes	complemented
44	C₂₃×#124	—	2	2	no	—
45	C₂₃×#124	C₂×C₄	1	2	yes	complemented
46	C₂₃×#123	—	2	4	no	—
47	C₂₃×#123	—	2	2	no	—
48	C₂₃×C₂²⋊Q₈	—	2	2	no	—
49	C₂₃×C₂²⋊Q₈	—	2	2	no	—
50	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
51	C₂₃×#121	—	2	2	no	—
52	C₂₃×#121	—	2	2	no	—
53	C₂₃×#121	C₂×C₄	1	4	yes	—
54	C₂₃×#120	—	2	2	no	—
55	C₄×Q₈×C₂₃	—	2	2	no	—
56	C₄×Q₈×C₂₃	—	2	2	no	—
57	C₄×Q₈×C₂₃	C₂×C₄	1	4	yes	complemented
58	C₄×D₄×C₂₃	—	2	4	no	—
59	C₄×D₄×C₂₃	—	2	4	no	—
60	C₄×D₄×C₂₃	—	2	4	no	—
61	C₄×D₄×C₂₃	—	2	2	no	—
62	C₄×D₄×C₂₃	—	2	2	no	—
63	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	complemented
64	C₂₃×#117	—	2	2	no	—
65	C₂₃×#117	—	2	4	no	—
66	C₂₃×#117	—	2	2	no	—
67	C₂₃×#117	C₂³	1	2	yes	—
68	C₂×C₄²×C₂₃	—	2	16	no	—
69	C₂×C₄²×C₂₃	—	2	2	no	—
70	C₂×C₄²×C₂₃	—	2	4	no	—
71	C₂×C₄²×C₂₃	—	2	4	no	—
72	C₂×C₄²×C₂₃	—	2	2	no	—
73	C₂×C₄²×C₂₃	—	2	8	no	—
74	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₂₃	D₄	1	2	yes	—
77	C₂×C₄²×C₂₃	D₄	1	2	yes	—
78	C₂×C₄²×C₂₃	D₄	1	2	yes	—
79	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
80	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
82	C₂₃×C₄⋊C₈	—	2	4	no	—
83	C₂₃×#104	—	2	16	no	—
84	C₂₃×C₂²⋊C₈	—	2	4	no	—
85	C₂₃×#97	—	2	2	no	—
86	C₄×C₈×C₂₃	—	2	2	no	—
87	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
88	#41×C₂₃	—	2	8	no	—
89	#41×C₂₃	—	4	8	no	—
90	C₂×Q₈×C₂₃	—	2	2	no	—
91	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
92	C₂×D₄×C₂₃	—	2	4	no	—
93	C₂×D₄×C₂₃	—	2	2	no	—
94	C₂×D₄×C₂₃	—	2	2	no	—
95	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₂₃	—	2	16	no	—
97	C₂²×C₄×C₂₃	—	2	8	no	—
98	C₂²×C₄×C₂₃	—	2	4	no	—
99	C₂²×C₄×C₂₃	—	2	8	no	—
100	C₂²×C₄×C₂₃	—	2	4	no	—
101	C₂²×C₄×C₂₃	—	2	4	no	—
102	C₂²×C₄×C₂₃	—	2	2	no	—
103	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
105	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
106	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
113	M₁₆×C₂₃	—	2	8	no	—
114	C₂×C₈×C₂₃	—	2	4	no	—
115	C₄⋊C₄×C₂₃	—	2	2	no	—
116	C₄⋊C₄×C₂₃	—	2	2	no	—
117	C₄⋊C₄×C₂₃	—	2	4	no	—
118	C₄⋊C₄×C₂₃	—	2	4	no	—
119	C₄⋊C₄×C₂₃	—	2	4	no	—
120	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₂₃	—	2	4	no	—
122	C₂²⋊C₄×C₂₃	—	2	2	no	—
123	C₂²⋊C₄×C₂₃	—	2	4	no	—
124	C₂²⋊C₄×C₂₃	—	2	4	no	—
125	C₂²⋊C₄×C₂₃	—	2	4	no	—
126	C₄²×C₂₃	—	2	16	no	—
127	C₄²×C₂₃	—	2	16	no	—
128	C₄²×C₂₃	—	2	8	no	—
129	C₄²×C₂₃	—	2	4	no	—
130	C₄²×C₂₃	—	2	2	no	—
131	C₄²×C₂₃	—	2	4	no	—
132	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
135	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
136	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₂₃	C₂×D₄	1	2	yes	—
140	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₂₃	#41	1	8	yes	complemented
143	#21415	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₂₃	—	2	2	no	—
145	C₂³×C₂₃	—	2	4	no	—
146	C₂³×C₂₃	—	2	2	no	—
147	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₂₃	—	2	4	no	—
150	Q₈×C₂₃	—	4	4	no	—
151	D₄×C₂₃	—	2	4	no	—
152	D₄×C₂₃	—	4	4	no	—
153	D₄×C₂₃	—	4	8	no	—
154	D₄×C₂₃	—	4	4	no	—
155	C₂×C₄×C₂₃	—	2	16	no	—
156	C₂×C₄×C₂₃	—	2	32	no	—
157	C₂×C₄×C₂₃	—	2	2	no	—
158	C₂×C₄×C₂₃	—	2	8	no	—
159	C₂×C₄×C₂₃	—	2	4	no	—
160	C₂×C₄×C₂₃	—	2	4	no	—
161	C₂×C₄×C₂₃	—	2	4	no	—
162	C₂×C₄×C₂₃	—	2	4	no	—
163	C₂×C₄×C₂₃	—	2	4	no	—
164	C₂×C₄×C₂₃	—	2	4	no	—
165	C₂×C₄×C₂₃	—	2	4	no	—
166	C₂×C₄×C₂₃	—	2	2	no	—
167	C₂×C₄×C₂₃	—	2	4	no	—
168	C₂×C₄×C₂₃	—	4	4	no	—
169	C₂×C₄×C₂₃	—	4	8	no	—
170	C₂×C₄×C₂₃	#104	1	8	yes	complemented
171	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
179	C₈×C₂₃	—	4	4	no	—
180	#3444	C₂×C₂₃	1	1	yes	characteristic
181	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
182	C₂×C₄³	C₂×C₂₃	1	1	yes	characteristic, complemented
183	#1994	C₂×C₂₃	1	2	yes	complemented
184	#1962	C₂×C₂₃	1	2	yes	complemented
185	#1896	C₂×C₂₃	1	4	yes	complemented
186	C₄×#104	C₂×C₂₃	1	4	yes	complemented
187	C₂²×C₂₃	—	2	8	no	—
188	C₂²×C₂₃	—	2	2	no	—
189	C₂²×C₂₃	—	2	2	no	—
190	C₂²×C₂₃	—	2	2	no	—
191	C₂²×C₂₃	—	4	4	no	—
192	C₂²×C₂₃	—	4	2	no	—
193	C₂²×C₂₃	C₂×#104	1	4	yes	—
194	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₂₃	#525	1	2	yes	—
196	C₄×C₂₃	—	2	16	no	—
197	C₄×C₂₃	—	2	2	no	—
198	C₄×C₂₃	—	2	2	no	—
199	C₄×C₂₃	—	2	2	no	—
200	C₄×C₂₃	—	4	4	no	—
201	C₄×C₂₃	—	4	2	no	—
202	C₄×C₂₃	C₂×#104	1	4	yes	—
203	C₄×C₂₃	C₂×#104	1	4	yes	—
204	C₄×C₂₃	C₄×#41	1	2	yes	—
205	C₄×C₂₃	#532	1	2	yes	—
206	#533	C₄×C₂₃	1	2	yes	complemented
207	#533	C₂²×C₂₃	1	1	yes	characteristic
208	#532	C₄×C₂₃	1	2	yes	complemented
209	#532	C₂²×C₂₃	1	1	yes	characteristic
210	#529	—	2	2	no	—
211	#529	—	2	2	no	—
212	#529	C₄×C₂₃	1	4	yes	complemented
213	#525	—	2	2	no	—
214	#525	C₂²×C₂₃	1	2	yes	—
215	C₄×#41	—	2	2	no	—
216	C₄×#41	C₂²×C₂₃	1	2	yes	—
217	C₂²×C₄²	—	2	2	no	—
218	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
219	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
220	#432	—	2	2	no	—
221	#431	—	2	2	no	—
222	#423	C₂²×C₂₃	1	2	yes	—
223	C₂×#104	C₂²×C₂₃	1	8	yes	—
224	#407	C₂²×C₂₃	1	2	yes	—
225	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
226	C₄³	—	2	2	no	—
227	C₄³	C₂²×C₂₃	1	2	yes	—
228	C₄³	C₂²×C₂₃	1	2	yes	—
229	#339	C₂²×C₂₃	1	8	yes	—
230	C₂×C₂₃	—	2	2	no	—
231	C₂×C₂₃	—	2	4	no	—
232	C₂×C₂₃	—	8	2	no	—
233	C₂×C₂₃	#2297	1	1	yes	characteristic
234	C₂×C₂₃	C₂²×#104	1	2	yes	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	C₂³×C₂₃	1	2	yes	—
237	C₂³×C₄	—	2	2	no	—
238	C₂³×C₄	D₄×C₂₃	1	2	yes	—
239	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
240	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
241	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
242	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	complemented
243	#127	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
244	#126	—	2	4	no	—
245	#125	—	2	2	no	—
246	#125	C₂×C₄×C₂₃	1	2	yes	complemented
247	#124	—	2	2	no	—
248	#124	C₂×C₄×C₂₃	1	2	yes	complemented
249	#123	—	2	4	no	—
250	#123	—	2	2	no	—
251	C₂²⋊Q₈	—	2	2	no	—
252	C₂²⋊Q₈	—	2	2	no	—
253	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
254	#121	—	2	2	no	—
255	#121	—	2	2	no	—
256	#121	C₂×C₄×C₂₃	1	4	yes	—
257	#120	—	2	2	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×Q₈	—	2	2	no	—
260	C₄×Q₈	C₂×C₄×C₂₃	1	4	yes	complemented
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	—	2	4	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	complemented
267	#117	—	2	2	no	—
268	#117	—	2	4	no	—
269	#117	—	2	2	no	—
270	#117	C₂³×C₂₃	1	2	yes	—
271	C₂×C₄²	—	2	16	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	4	no	—
274	C₂×C₄²	—	2	4	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	8	no	—
277	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
278	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
279	C₂×C₄²	D₄×C₂₃	1	2	yes	—
280	C₂×C₄²	D₄×C₂₃	1	2	yes	—
281	C₂×C₄²	D₄×C₂₃	1	2	yes	—
282	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
283	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
285	C₄⋊C₈	—	2	4	no	—
286	#104	—	2	16	no	—
287	C₂²⋊C₈	—	2	4	no	—
288	#97	—	2	2	no	—
289	C₄×C₈	—	2	2	no	—
290	C₂₃	#21415	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
292	#41	—	2	8	no	—
293	#41	—	4	8	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
300	C₂²×C₄	—	2	16	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
308	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
309	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
310	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
317	M₁₆	—	2	8	no	—
318	C₂×C₈	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₄²	—	2	16	no	—
331	C₄²	—	2	16	no	—
332	C₄²	—	2	8	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	4	no	—
336	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
337	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
338	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
339	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
340	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
341	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
342	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
343	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
344	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₂₃	1	2	yes	—
346	C₄²	#41×C₂₃	1	8	yes	complemented
347	C₂³	—	2	4	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
351	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
352	Q₈	—	2	4	no	—
353	Q₈	—	4	4	no	—
354	D₄	—	2	4	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	4	no	—
358	C₂×C₄	—	2	16	no	—
359	C₂×C₄	—	2	32	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	C₂₃×#104	1	8	yes	complemented
374	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
377	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
378	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
379	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
380	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
382	C₈	—	4	4	no	—
383	C₂²	—	2	8	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	C₂×C₂₃×#104	1	4	yes	—
390	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
391	C₂²	C₂₃×#525	1	2	yes	—
392	C₄	—	2	16	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	4	no	—
398	C₄	C₂×C₂₃×#104	1	4	yes	—
399	C₄	C₂×C₂₃×#104	1	4	yes	—
400	C₄	C₄×#41×C₂₃	1	2	yes	—
401	C₄	C₂₃×#532	1	2	yes	—
402	C₂	—	2	2	no	—
403	C₂	—	2	4	no	—
404	C₂	—	8	2	no	—
405	C₂	C₂₃×#2297	1	1	yes	characteristic
406	C₂	C₂²×C₂₃×#104	1	2	yes	—

	subgroup	G/H
center	C₄²×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂²×C₂²⋊C₄
prime radical	C₂₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2920	C₂	semidirect
3. C₂×C₄³×C₂₃	C₂	semidirect
4. C₂₃×#1994	C₂	semidirect
5. C₂₃×#1962	C₂	semidirect
6. C₂₃×#1896	C₂	semidirect
7. C₄×C₂₃×#104	C₂	semidirect
8. C₂₃×#533	C₄	semidirect
10. C₂₃×#532	C₄	semidirect
14. C₂₃×#529	C₄	semidirect
38. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
39. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
40. C₂₃×#127	C₂×C₄	semidirect
43. C₂₃×#125	C₂×C₄	semidirect
45. C₂₃×#124	C₂×C₄	semidirect
57. C₄×Q₈×C₂₃	C₂×C₄	semidirect
63. C₄×D₄×C₂₃	C₂×C₄	semidirect
142. C₄²×C₂₃	#41	semidirect
143. #21415	C₂₃	direct (N × H)
170. C₂×C₄×C₂₃	#104	semidirect
181. #2920	C₂×C₂₃	semidirect
182. C₂×C₄³	C₂×C₂₃	semidirect
183. #1994	C₂×C₂₃	semidirect
184. #1962	C₂×C₂₃	semidirect
185. #1896	C₂×C₂₃	semidirect
186. C₄×#104	C₂×C₂₃	semidirect
206. #533	C₄×C₂₃	semidirect
208. #532	C₄×C₂₃	semidirect
212. #529	C₄×C₂₃	semidirect
241. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
242. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
243. #127	C₂×C₄×C₂₃	semidirect
246. #125	C₂×C₄×C₂₃	semidirect
248. #124	C₂×C₄×C₂₃	semidirect
260. C₄×Q₈	C₂×C₄×C₂₃	semidirect
266. C₄×D₄	C₂×C₄×C₂₃	semidirect
290. C₂₃	#21415	direct (N × H)
346. C₄²	#41×C₂₃	semidirect
373. C₂×C₄	C₂₃×#104	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3444	2
C₂₃×#2920	2
C₂×C₄³×C₂₃	2
C₂₃×#1994	2
C₂₃×#1962	2
C₂₃×#1896	2
C₄×C₂₃×#104	2
#21415	23

Subgroups — C23×#21415 #19169041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21415 #19169041