Subgroups — C₂₃×#8095 #19155721

Order 5888.

674 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2285	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1303	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₂₃	—	2	1	no	—
6	C₂×C₂₃×#117	—	2	1	no	—
7	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#431	—	2	1	no	—
9	C₂₃×#431	—	2	1	no	—
10	C₂₃×#431	C₄	1	2	yes	complemented
11	C₂₃×#431	C₂²	1	2	yes	—
12	C₂₃×#423	—	2	1	no	—
13	C₂₃×#423	—	2	1	no	—
14	C₂₃×#423	C₄	1	2	yes	complemented
15	C₂₃×#423	C₂²	1	2	yes	—
16	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
17	C₂×C₂₃×C₄⋊C₈	C₄	1	2	yes	complemented
18	C₂×C₂₃×C₄⋊C₈	C₄	1	2	yes	complemented
19	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
20	C₂×C₄×C₈×C₂₃	—	2	1	no	—
21	C₂₃×#384	—	2	1	no	—
22	C₂₃×#382	C₄	1	2	yes	—
23	C₂₃×#380	—	2	1	no	—
24	C₂₃×#380	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
26	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
27	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₂₃	—	2	2	no	—
31	C₂×M₁₆×C₂₃	—	2	2	no	—
32	C₂×M₁₆×C₂₃	—	4	2	no	—
33	C₂×M₁₆×C₂₃	—	4	2	no	—
34	C₂²×C₈×C₂₃	—	2	2	no	—
35	C₂²×C₈×C₂₃	—	2	2	no	—
36	C₂₃×#117	—	4	2	no	—
37	C₂₃×#117	—	4	2	no	—
38	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
42	C₂×C₄²×C₂₃	—	2	2	no	—
43	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
53	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
54	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
55	C₂₃×C₄⋊C₈	—	2	2	no	—
56	C₂₃×C₄⋊C₈	—	2	2	no	—
57	C₂₃×C₄⋊C₈	—	2	2	no	—
58	C₂₃×C₄⋊C₈	—	2	2	no	—
59	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
60	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
61	C₂₃×C₂²⋊C₈	—	2	2	no	—
62	C₂₃×C₂²⋊C₈	—	2	2	no	—
63	C₄×C₈×C₂₃	—	2	2	no	—
64	C₄×C₈×C₂₃	—	2	2	no	—
65	C₂₃×#95	—	2	2	no	—
66	C₂₃×#95	C₂×C₄	1	4	yes	—
67	C₂⁴×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₂₃	—	2	4	no	—
69	C₂²×C₄×C₂₃	—	4	2	no	—
70	C₂²×C₄×C₂₃	—	4	2	no	—
71	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	D₈	1	2	yes	—
87	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
89	C₂²×C₄×C₂₃	Q₁₆	1	2	yes	—
90	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
93	M₁₆×C₂₃	—	4	4	no	—
94	M₁₆×C₂₃	—	4	2	no	—
95	M₁₆×C₂₃	—	4	2	no	—
96	C₂×C₈×C₂₃	—	2	4	no	—
97	C₂×C₈×C₂₃	—	2	4	no	—
98	C₂×C₈×C₂₃	—	4	4	no	—
99	C₂×C₈×C₂₃	—	4	4	no	—
100	C₄⋊C₄×C₂₃	—	4	4	no	—
101	C₄⋊C₄×C₂₃	—	4	4	no	—
102	C₄⋊C₄×C₂₃	—	4	4	no	—
103	C₂²⋊C₄×C₂₃	—	4	4	no	—
104	C₄²×C₂₃	—	4	2	no	—
105	C₄²×C₂₃	—	4	2	no	—
106	C₄²×C₂₃	C₄²	1	1	yes	characteristic
107	C₄²×C₂₃	C₄²	1	1	yes	characteristic
108	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₂₃	C₂×Q₈	1	1	yes	characteristic
122	#8095	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₂₃	—	4	1	no	—
124	C₂³×C₂₃	—	4	1	no	—
125	C₂³×C₂₃	#95	1	1	yes	characteristic
126	C₂³×C₂₃	#95	1	1	yes	characteristic
127	C₂³×C₂₃	#102	1	2	yes	—
128	C₂³×C₂₃	#103	1	2	yes	—
129	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₂₃	—	2	2	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	2	no	—
135	C₂×C₄×C₂₃	—	2	2	no	—
136	C₂×C₄×C₂₃	—	4	1	no	—
137	C₂×C₄×C₂₃	—	4	1	no	—
138	C₂×C₄×C₂₃	—	4	1	no	—
139	C₂×C₄×C₂₃	—	4	1	no	—
140	C₂×C₄×C₂₃	—	4	1	no	—
141	C₂×C₄×C₂₃	—	4	1	no	—
142	C₂×C₄×C₂₃	—	4	4	no	—
143	C₂×C₄×C₂₃	—	4	4	no	—
144	C₂×C₄×C₂₃	—	4	4	no	—
145	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
146	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
147	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
148	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
149	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
150	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
151	C₂×C₄×C₂₃	#102	1	2	yes	—
152	C₂×C₄×C₂₃	#102	1	2	yes	—
153	C₂×C₄×C₂₃	#102	1	2	yes	—
154	C₂×C₄×C₂₃	#103	1	2	yes	—
155	C₂×C₄×C₂₃	#103	1	2	yes	—
156	C₂×C₄×C₂₃	#103	1	2	yes	—
157	C₂×C₄×C₂₃	#106	1	2	yes	—
158	C₂×C₄×C₂₃	#106	1	2	yes	—
159	C₂×C₄×C₂₃	#107	1	2	yes	—
160	C₂×C₄×C₂₃	#107	1	2	yes	—
161	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
169	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
171	C₈×C₂₃	—	4	4	no	—
172	C₈×C₂₃	—	4	4	no	—
173	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
174	C₂×#423	C₂×C₂₃	1	1	yes	characteristic
175	#2285	C₂×C₂₃	1	1	yes	characteristic
176	#1303	C₂×C₂₃	1	4	yes	complemented
177	C₂²×C₂₃	—	2	1	no	—
178	C₂²×C₂₃	—	2	1	no	—
179	C₂²×C₂₃	—	2	1	no	—
180	C₂²×C₂₃	—	2	1	no	—
181	C₂²×C₂₃	—	2	1	no	—
182	C₂²×C₂₃	—	2	1	no	—
183	C₂²×C₂₃	—	4	2	no	—
184	C₂²×C₂₃	—	4	2	no	—
185	C₂²×C₂₃	#340	1	2	yes	—
186	C₂²×C₂₃	#340	1	2	yes	—
187	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
188	C₂²×C₂₃	C₂×#102	1	1	yes	characteristic
189	C₂²×C₂₃	C₂×#103	1	1	yes	characteristic
190	C₄×C₂₃	—	2	1	no	—
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	—	2	1	no	—
196	C₄×C₂₃	—	8	4	no	—
197	C₄×C₂₃	#340	1	2	yes	—
198	C₄×C₂₃	#340	1	2	yes	—
199	C₄×C₂₃	#344	1	2	yes	—
200	C₄×C₂₃	C₂×#102	1	1	yes	characteristic
201	C₄×C₂₃	C₂×#103	1	1	yes	characteristic
202	C₄×C₂₃	#421	1	2	yes	—
203	C₄×C₂₃	C₂×#106	1	1	yes	characteristic
204	C₄×C₂₃	C₂×#107	1	1	yes	characteristic
205	C₂²×M₁₆	—	2	1	no	—
206	C₂×#117	—	2	1	no	—
207	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
208	#431	—	2	1	no	—
209	#431	—	2	1	no	—
210	#431	C₄×C₂₃	1	2	yes	complemented
211	#431	C₂²×C₂₃	1	2	yes	—
212	#423	—	2	1	no	—
213	#423	—	2	1	no	—
214	#423	C₄×C₂₃	1	2	yes	complemented
215	#423	C₂²×C₂₃	1	2	yes	—
216	C₂×C₄⋊C₈	—	2	1	no	—
217	C₂×C₄⋊C₈	C₄×C₂₃	1	2	yes	complemented
218	C₂×C₄⋊C₈	C₄×C₂₃	1	2	yes	complemented
219	C₂×C₂²⋊C₈	—	2	1	no	—
220	C₂×C₄×C₈	—	2	1	no	—
221	#384	—	2	1	no	—
222	#382	C₄×C₂₃	1	2	yes	—
223	#380	—	2	1	no	—
224	#380	C₄×C₂₃	1	2	yes	—
225	C₄×C₄⋊C₄	—	2	1	no	—
226	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
227	C₂×C₂₃	—	2	1	no	—
228	C₂×C₂₃	—	2	2	no	—
229	C₂×C₂₃	—	2	2	no	—
230	C₂×C₂₃	—	2	1	no	—
231	C₂×C₂₃	#1733	1	1	yes	characteristic
232	C₂×C₂₃	C₂×#340	1	1	yes	characteristic
233	C₂×C₂₃	C₂×#344	1	1	yes	characteristic
234	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
235	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	4	2	no	—
240	C₂×M₁₆	—	4	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	#117	—	4	2	no	—
244	#117	—	4	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
252	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
253	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
254	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
255	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
259	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
260	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
267	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	C₂×C₄×C₂₃	1	4	yes	—
274	C₂₃	#8095	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁴	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
280	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
282	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
283	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
288	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
289	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
290	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
291	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
292	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
294	C₂²×C₄	D₈×C₂₃	1	2	yes	—
295	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
296	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
297	C₂²×C₄	Q₁₆×C₂₃	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
301	M₁₆	—	4	4	no	—
302	M₁₆	—	4	2	no	—
303	M₁₆	—	4	2	no	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	4	4	no	—
307	C₂×C₈	—	4	4	no	—
308	C₄⋊C₄	—	4	4	no	—
309	C₄⋊C₄	—	4	4	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₄²	—	4	2	no	—
313	C₄²	—	4	2	no	—
314	C₄²	C₄²×C₂₃	1	1	yes	characteristic
315	C₄²	C₄²×C₂₃	1	1	yes	characteristic
316	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
317	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
318	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
319	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
320	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
321	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
322	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
323	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
324	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
325	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
326	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
327	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
328	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
329	C₄²	C₂×Q₈×C₂₃	1	1	yes	characteristic
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	C₂₃×#95	1	1	yes	characteristic
333	C₂³	C₂₃×#95	1	1	yes	characteristic
334	C₂³	C₂₃×#102	1	2	yes	—
335	C₂³	C₂₃×#103	1	2	yes	—
336	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
353	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
354	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
355	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
356	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
357	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
358	C₂×C₄	C₂₃×#102	1	2	yes	—
359	C₂×C₄	C₂₃×#102	1	2	yes	—
360	C₂×C₄	C₂₃×#102	1	2	yes	—
361	C₂×C₄	C₂₃×#103	1	2	yes	—
362	C₂×C₄	C₂₃×#103	1	2	yes	—
363	C₂×C₄	C₂₃×#103	1	2	yes	—
364	C₂×C₄	C₂₃×#106	1	2	yes	—
365	C₂×C₄	C₂₃×#106	1	2	yes	—
366	C₂×C₄	C₂₃×#107	1	2	yes	—
367	C₂×C₄	C₂₃×#107	1	2	yes	—
368	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
369	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
370	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
374	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
375	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
376	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
377	C₂×C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
378	C₈	—	4	4	no	—
379	C₈	—	4	4	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	C₂₃×#340	1	2	yes	—
389	C₂²	C₂₃×#340	1	2	yes	—
390	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
391	C₂²	C₂×C₂₃×#102	1	1	yes	characteristic
392	C₂²	C₂×C₂₃×#103	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	8	4	no	—
400	C₄	C₂₃×#340	1	2	yes	—
401	C₄	C₂₃×#340	1	2	yes	—
402	C₄	C₂₃×#344	1	2	yes	—
403	C₄	C₂×C₂₃×#102	1	1	yes	characteristic
404	C₄	C₂×C₂₃×#103	1	1	yes	characteristic
405	C₄	C₂₃×#421	1	2	yes	—
406	C₄	C₂×C₂₃×#106	1	1	yes	characteristic
407	C₄	C₂×C₂₃×#107	1	1	yes	characteristic
408	C₂	—	2	1	no	—
409	C₂	—	2	2	no	—
410	C₂	—	2	2	no	—
411	C₂	—	2	1	no	—
412	C₂	C₂₃×#1733	1	1	yes	characteristic
413	C₂	C₂×C₂₃×#340	1	1	yes	characteristic
414	C₂	C₂×C₂₃×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×#95
prime radical	C₂⁴×C₂₃	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1303	C₂	semidirect
10. C₂₃×#431	C₄	semidirect
14. C₂₃×#423	C₄	semidirect
17. C₂×C₂₃×C₄⋊C₈	C₄	semidirect
18. C₂×C₂₃×C₄⋊C₈	C₄	semidirect
122. #8095	C₂₃	direct (N × H)
176. #1303	C₂×C₂₃	semidirect
210. #431	C₄×C₂₃	semidirect
214. #423	C₄×C₂₃	semidirect
217. C₂×C₄⋊C₈	C₄×C₂₃	semidirect
218. C₂×C₄⋊C₈	C₄×C₂₃	semidirect
274. C₂₃	#8095	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×#431	2
C₂×C₂₃×#423	2
C₂₃×#2285	2
C₂₃×#1303	2
#8095	23

Subgroups — C23×#8095 #19155721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8095 #19155721