Subgroups — C₂₃×#36567 #19184193

Order 5888.

1574 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2864	C₂	1	2	yes	maximal
2	C₂₃×#2859	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2590	C₂	1	4	yes	maximal
4	C₂₃×#2585	C₂	1	4	yes	maximal
5	C₂₃×#2584	C₂	1	2	yes	maximal
6	C₂₃×#2507	C₂	1	2	yes	maximal
7	C₂₃×#2506	C₂	1	2	yes	maximal
8	C₂₃×#2462	C₂	1	4	yes	maximal
9	C₂₃×#2370	C₂	1	4	yes	maximal
10	C₂₃×#2370	C₂	1	2	yes	maximal
11	C₄×C₂₃×#125	C₂	1	1	yes	maximal, characteristic
12	C₄×C₂₃×#125	C₂	1	2	yes	maximal
13	C₄²×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic
14	C₂×C₂₃×#125	C₂²	1	4	yes	—
15	C₂×C₂₃×#125	C₂²	1	2	yes	—
16	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#400	C₂²	1	4	yes	—
20	C₂₃×#398	C₂²	1	4	yes	—
21	C₂₃×#398	C₂²	1	4	yes	—
22	C₂₃×#398	C₂²	1	4	yes	—
23	C₂₃×#398	C₂²	1	4	yes	—
24	C₂₃×#395	C₂²	1	4	yes	—
25	C₂₃×#389	C₂²	1	4	yes	—
26	C₂₃×#389	C₂²	1	4	yes	—
27	C₂₃×#389	C₂²	1	2	yes	—
28	C₂₃×#389	C₂²	1	2	yes	—
29	C₂₃×#389	C₂²	1	2	yes	—
30	C₂₃×#389	C₂²	1	2	yes	—
31	C₂₃×#389	C₂²	1	2	yes	—
32	C₂₃×#389	C₂²	1	2	yes	—
33	C₂₃×#389	C₂²	1	4	yes	—
34	C₂₃×#389	C₂²	1	2	yes	—
35	C₂₃×#389	C₂²	1	4	yes	—
36	C₂₃×#389	C₂²	1	4	yes	—
37	C₂₃×#389	C₂²	1	4	yes	—
38	C₂₃×#387	C₂²	1	4	yes	—
39	C₂₃×#387	C₂²	1	4	yes	—
40	C₂₃×#387	C₂²	1	4	yes	—
41	C₂₃×#387	C₂²	1	4	yes	—
42	C₂₃×#387	C₂²	1	4	yes	—
43	C₂₃×#387	C₂²	1	4	yes	—
44	C₂₃×#387	C₂²	1	4	yes	—
45	C₂₃×#387	C₂²	1	4	yes	—
46	C₂₃×#387	C₂²	1	4	yes	—
47	C₂₃×#387	C₂²	1	4	yes	—
48	C₂₃×#387	C₂²	1	4	yes	—
49	C₂₃×#384	C₂²	1	1	yes	characteristic
50	C₂₃×#384	C₂²	1	1	yes	characteristic
51	C₂₃×#382	C₂²	1	2	yes	—
52	C₂₃×#382	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
54	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
55	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
56	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
64	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
65	C₄³×C₂₃	C₂²	1	1	yes	characteristic
66	C₄³×C₂₃	C₂²	1	2	yes	—
67	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
68	C₂₃×#125	—	2	16	no	—
69	C₂₃×#125	—	2	8	no	—
70	C₂₃×#125	Q₈	1	8	yes	complemented
71	C₄×Q₈×C₂₃	—	2	8	no	—
72	C₄×Q₈×C₂₃	—	2	4	no	—
73	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
94	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
95	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
96	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
98	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
99	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
100	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
101	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
102	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
103	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
104	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
105	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
106	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
108	C₂₃×#95	C₂³	1	1	yes	characteristic
109	C₂₃×#95	C₂³	1	1	yes	characteristic
110	C₂₃×#95	C₂³	1	2	yes	—
111	C₂₃×#95	C₂³	1	2	yes	—
112	C₂₃×#95	C₂³	1	4	yes	—
113	C₂₃×#95	C₂³	1	4	yes	—
114	C₂₃×#95	C₂³	1	4	yes	—
115	C₂₃×#95	C₂³	1	4	yes	—
116	C₂₃×#95	C₂³	1	4	yes	—
117	C₂₃×#95	C₂³	1	4	yes	—
118	C₂₃×#95	C₂³	1	4	yes	—
119	C₂₃×#95	C₂³	1	4	yes	—
120	C₂₃×#95	C₂³	1	4	yes	—
121	C₂₃×#95	C₂³	1	4	yes	—
122	C₂₃×#95	C₂³	1	4	yes	—
123	C₂₃×#95	C₂³	1	4	yes	—
124	C₂₃×#95	C₂³	1	4	yes	—
125	C₂×Q₈×C₂₃	—	2	4	no	—
126	C₂×Q₈×C₂₃	—	2	2	no	—
127	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
140	C₄⋊C₄×C₂₃	—	2	4	no	—
141	C₄⋊C₄×C₂₃	—	2	4	no	—
142	C₄⋊C₄×C₂₃	—	2	4	no	—
143	C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₄⋊C₄×C₂₃	—	2	8	no	—
145	C₄⋊C₄×C₂₃	—	2	8	no	—
146	C₄⋊C₄×C₂₃	—	2	8	no	—
147	C₄⋊C₄×C₂₃	—	2	8	no	—
148	C₄⋊C₄×C₂₃	—	2	8	no	—
149	C₄⋊C₄×C₂₃	—	2	8	no	—
150	C₄⋊C₄×C₂₃	—	2	8	no	—
151	C₄⋊C₄×C₂₃	—	2	4	no	—
152	C₄⋊C₄×C₂₃	—	2	4	no	—
153	C₄⋊C₄×C₂₃	—	2	4	no	—
154	C₄⋊C₄×C₂₃	—	4	4	no	—
155	C₄⋊C₄×C₂₃	—	4	4	no	—
156	C₄⋊C₄×C₂₃	—	4	4	no	—
157	C₄⋊C₄×C₂₃	—	4	4	no	—
158	C₄⋊C₄×C₂₃	C₂×Q₈	1	16	yes	—
159	C₄⋊C₄×C₂₃	C₂×Q₈	1	8	yes	—
160	C₄⋊C₄×C₂₃	#41	1	8	yes	—
161	C₄²×C₂₃	—	2	4	no	—
162	C₄²×C₂₃	—	2	4	no	—
163	C₄²×C₂₃	—	2	4	no	—
164	C₄²×C₂₃	—	2	4	no	—
165	C₄²×C₂₃	—	2	8	no	—
166	C₄²×C₂₃	—	2	2	no	—
167	C₄²×C₂₃	—	2	4	no	—
168	C₄²×C₂₃	—	4	2	no	—
169	C₄²×C₂₃	—	4	2	no	—
170	C₄²×C₂₃	—	4	4	no	—
171	C₄²×C₂₃	—	4	4	no	—
172	C₄²×C₂₃	—	4	2	no	—
173	C₄²×C₂₃	C₂×Q₈	1	4	yes	—
174	C₄²×C₂₃	#41	1	4	yes	—
175	#36567	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
177	Q₈×C₂₃	—	2	8	no	—
178	C₂×C₄×C₂₃	—	2	2	no	—
179	C₂×C₄×C₂₃	—	2	4	no	—
180	C₂×C₄×C₂₃	—	2	2	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	—	2	2	no	—
183	C₂×C₄×C₂₃	—	2	2	no	—
184	C₂×C₄×C₂₃	—	2	2	no	—
185	C₂×C₄×C₂₃	—	2	2	no	—
186	C₂×C₄×C₂₃	—	2	2	no	—
187	C₂×C₄×C₂₃	—	2	2	no	—
188	C₂×C₄×C₂₃	—	2	4	no	—
189	C₂×C₄×C₂₃	—	2	2	no	—
190	C₂×C₄×C₂₃	—	2	4	no	—
191	C₂×C₄×C₂₃	—	2	2	no	—
192	C₂×C₄×C₂₃	—	2	2	no	—
193	C₂×C₄×C₂₃	—	2	4	no	—
194	C₂×C₄×C₂₃	—	2	4	no	—
195	C₂×C₄×C₂₃	—	2	4	no	—
196	C₂×C₄×C₂₃	—	2	4	no	—
197	C₂×C₄×C₂₃	—	2	2	no	—
198	C₂×C₄×C₂₃	—	2	4	no	—
199	C₂×C₄×C₂₃	—	2	2	no	—
200	C₂×C₄×C₂₃	—	2	2	no	—
201	C₂×C₄×C₂₃	—	2	4	no	—
202	C₂×C₄×C₂₃	—	2	2	no	—
203	C₂×C₄×C₂₃	—	2	4	no	—
204	C₂×C₄×C₂₃	—	2	4	no	—
205	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
206	C₂×C₄×C₂₃	C₂²×Q₈	1	8	yes	—
207	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
208	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
209	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
210	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
211	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
212	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
213	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
214	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
215	#2864	C₂×C₂₃	1	2	yes	—
216	#2859	C₂×C₂₃	1	1	yes	characteristic
217	#2590	C₂×C₂₃	1	4	yes	—
218	#2585	C₂×C₂₃	1	4	yes	—
219	#2584	C₂×C₂₃	1	2	yes	—
220	#2507	C₂×C₂₃	1	2	yes	—
221	#2506	C₂×C₂₃	1	2	yes	—
222	#2462	C₂×C₂₃	1	4	yes	—
223	#2370	C₂×C₂₃	1	2	yes	—
224	#2370	C₂×C₂₃	1	4	yes	—
225	C₄×#125	C₂×C₂₃	1	1	yes	characteristic
226	C₄×#125	C₂×C₂₃	1	2	yes	—
227	C₄²×Q₈	C₂×C₂₃	1	1	yes	characteristic
228	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
229	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
230	C₂²×C₂₃	C₂²×#41	1	2	yes	—
231	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
232	C₂²×C₂₃	#585	1	2	yes	—
233	C₄×C₂₃	—	2	4	no	—
234	C₄×C₂₃	—	2	2	no	—
235	C₄×C₂₃	—	2	4	no	—
236	C₄×C₂₃	—	2	8	no	—
237	C₄×C₂₃	—	2	2	no	—
238	C₄×C₂₃	—	2	4	no	—
239	C₄×C₂₃	—	2	4	no	—
240	C₄×C₂₃	—	4	4	no	—
241	C₄×C₂₃	—	4	2	no	—
242	C₄×C₂₃	—	4	4	no	—
243	C₄×C₂₃	—	4	2	no	—
244	C₄×C₂₃	—	4	4	no	—
245	C₄×C₂₃	#557	1	4	yes	—
246	C₂×#125	C₂²×C₂₃	1	2	yes	—
247	C₂×#125	C₂²×C₂₃	1	4	yes	—
248	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
251	#400	C₂²×C₂₃	1	4	yes	—
252	#398	C₂²×C₂₃	1	4	yes	—
253	#398	C₂²×C₂₃	1	4	yes	—
254	#398	C₂²×C₂₃	1	4	yes	—
255	#398	C₂²×C₂₃	1	4	yes	—
256	#395	C₂²×C₂₃	1	4	yes	—
257	#389	C₂²×C₂₃	1	2	yes	—
258	#389	C₂²×C₂₃	1	2	yes	—
259	#389	C₂²×C₂₃	1	2	yes	—
260	#389	C₂²×C₂₃	1	4	yes	—
261	#389	C₂²×C₂₃	1	4	yes	—
262	#389	C₂²×C₂₃	1	2	yes	—
263	#389	C₂²×C₂₃	1	2	yes	—
264	#389	C₂²×C₂₃	1	4	yes	—
265	#389	C₂²×C₂₃	1	4	yes	—
266	#389	C₂²×C₂₃	1	4	yes	—
267	#389	C₂²×C₂₃	1	4	yes	—
268	#389	C₂²×C₂₃	1	2	yes	—
269	#389	C₂²×C₂₃	1	2	yes	—
270	#387	C₂²×C₂₃	1	4	yes	—
271	#387	C₂²×C₂₃	1	4	yes	—
272	#387	C₂²×C₂₃	1	4	yes	—
273	#387	C₂²×C₂₃	1	4	yes	—
274	#387	C₂²×C₂₃	1	4	yes	—
275	#387	C₂²×C₂₃	1	4	yes	—
276	#387	C₂²×C₂₃	1	4	yes	—
277	#387	C₂²×C₂₃	1	4	yes	—
278	#387	C₂²×C₂₃	1	4	yes	—
279	#387	C₂²×C₂₃	1	4	yes	—
280	#387	C₂²×C₂₃	1	4	yes	—
281	#384	C₂²×C₂₃	1	1	yes	characteristic
282	#384	C₂²×C₂₃	1	1	yes	characteristic
283	#382	C₂²×C₂₃	1	2	yes	—
284	#382	C₂²×C₂₃	1	1	yes	characteristic
285	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
286	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
287	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
288	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
289	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
290	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
291	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
292	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
293	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
294	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
296	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
297	C₄³	C₂²×C₂₃	1	1	yes	characteristic
298	C₄³	C₂²×C₂₃	1	2	yes	—
299	C₂×C₂₃	#3444	1	1	yes	characteristic
300	C₂×C₂₃	C₂×#557	1	1	yes	characteristic
301	C₂×C₂₃	Q₈×#41	1	2	yes	—
302	C₂×C₂₃	#3512	1	1	yes	characteristic
303	C₂×C₂₃	#3515	1	2	yes	—
304	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
305	#125	—	2	16	no	—
306	#125	—	2	8	no	—
307	#125	Q₈×C₂₃	1	8	yes	complemented
308	C₄×Q₈	—	2	8	no	—
309	C₄×Q₈	—	2	4	no	—
310	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
319	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
321	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
329	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
331	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
332	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
333	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
334	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
335	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
336	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
337	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
339	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
340	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
341	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
342	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
343	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
345	#95	C₂³×C₂₃	1	1	yes	characteristic
346	#95	C₂³×C₂₃	1	1	yes	characteristic
347	#95	C₂³×C₂₃	1	2	yes	—
348	#95	C₂³×C₂₃	1	2	yes	—
349	#95	C₂³×C₂₃	1	4	yes	—
350	#95	C₂³×C₂₃	1	4	yes	—
351	#95	C₂³×C₂₃	1	4	yes	—
352	#95	C₂³×C₂₃	1	4	yes	—
353	#95	C₂³×C₂₃	1	4	yes	—
354	#95	C₂³×C₂₃	1	4	yes	—
355	#95	C₂³×C₂₃	1	4	yes	—
356	#95	C₂³×C₂₃	1	4	yes	—
357	#95	C₂³×C₂₃	1	4	yes	—
358	#95	C₂³×C₂₃	1	4	yes	—
359	#95	C₂³×C₂₃	1	4	yes	—
360	#95	C₂³×C₂₃	1	4	yes	—
361	#95	C₂³×C₂₃	1	4	yes	—
362	C₂₃	#36567	1	1	yes	characteristic, direct product factor, Sylow
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
371	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
372	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	4	4	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	—	4	4	no	—
396	C₄⋊C₄	C₂×Q₈×C₂₃	1	16	yes	—
397	C₄⋊C₄	C₂×Q₈×C₂₃	1	8	yes	—
398	C₄⋊C₄	#41×C₂₃	1	8	yes	—
399	C₄²	—	2	4	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	2	4	no	—
402	C₄²	—	2	4	no	—
403	C₄²	—	2	8	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	4	no	—
406	C₄²	—	4	2	no	—
407	C₄²	—	4	2	no	—
408	C₄²	—	4	4	no	—
409	C₄²	—	4	4	no	—
410	C₄²	—	4	2	no	—
411	C₄²	C₂×Q₈×C₂₃	1	4	yes	—
412	C₄²	#41×C₂₃	1	4	yes	—
413	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
414	Q₈	—	2	8	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
443	C₂×C₄	C₂²×Q₈×C₂₃	1	8	yes	—
444	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
445	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
446	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
447	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
448	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
449	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
450	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
451	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
452	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
453	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
454	C₂²	C₂²×#41×C₂₃	1	2	yes	—
455	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
456	C₂²	C₂₃×#585	1	2	yes	—
457	C₄	—	2	4	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	4	no	—
460	C₄	—	2	8	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	4	no	—
463	C₄	—	2	4	no	—
464	C₄	—	4	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	4	no	—
469	C₄	C₂₃×#557	1	4	yes	—
470	C₂	C₂₃×#3444	1	1	yes	characteristic
471	C₂	C₂×C₂₃×#557	1	1	yes	characteristic
472	C₂	Q₈×#41×C₂₃	1	2	yes	—
473	C₂	C₂₃×#3512	1	1	yes	characteristic
474	C₂	C₂₃×#3515	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
70. C₂₃×#125	Q₈	semidirect
175. #36567	C₂₃	direct (N × H)
307. #125	Q₈×C₂₃	semidirect
362. C₂₃	#36567	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#2864	2
C₂₃×#2859	2
C₂₃×#2590	2
C₂₃×#2585	2
C₂₃×#2584	2
C₂₃×#2507	2
C₂₃×#2506	2
C₂₃×#2462	2
C₂₃×#2370	2
C₄×C₂₃×#125	2
C₄²×Q₈×C₂₃	2
#36567	23

Subgroups — C23×#36567 #19184193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36567 #19184193