Subgroups — C₂₃×#22601 #19170227

Order 5888.

932 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1940	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1917	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1916	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1817	C₂	1	1	yes	maximal, characteristic
8	C₂₃×#1817	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1797	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#1771	C₂	1	2	yes	maximal, complemented
11	C₂₃×#1749	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄⋊C₄×C₂₃	C₄	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₂₃	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
17	C₂₃×#432	—	2	4	no	—
18	C₂₃×#431	—	2	4	no	—
19	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#97	C₂²	1	2	yes	—
27	C₂×C₂₃×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₂₃	C₄	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₂₃	C₄	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₂₃	C₄	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₂₃	C₄	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#95	C₄	1	1	yes	characteristic
38	C₂×C₂₃×#95	C₄	1	1	yes	characteristic
39	C₂₃×#336	C₂²	1	2	yes	—
40	C₂₃×#336	C₂²	1	2	yes	—
41	C₂₃×#336	C₂²	1	2	yes	—
42	C₂₃×#336	C₂²	1	2	yes	—
43	C₂₃×#336	C₂²	1	2	yes	—
44	C₂₃×#336	C₂²	1	2	yes	—
45	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
58	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₂₃	—	2	2	no	—
67	C₂×C₄²×C₂₃	—	2	2	no	—
68	C₂×C₄²×C₂₃	—	2	2	no	—
69	C₂×C₄²×C₂₃	—	2	2	no	—
70	C₂×C₄²×C₂₃	—	2	4	no	—
71	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
83	C₂₃×C₄⋊C₈	—	2	4	no	—
84	C₂₃×C₄⋊C₈	—	2	4	no	—
85	C₂₃×C₄⋊C₈	—	2	4	no	—
86	C₂₃×C₂²⋊C₈	—	2	2	no	—
87	C₂₃×C₂²⋊C₈	—	2	2	no	—
88	C₂₃×C₂²⋊C₈	—	2	2	no	—
89	C₂₃×C₂²⋊C₈	D₄	1	4	yes	—
90	C₂₃×#97	—	2	4	no	—
91	C₂₃×#97	—	2	4	no	—
92	C₄×C₈×C₂₃	—	2	4	no	—
93	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
94	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
95	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
96	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
97	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
98	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
99	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
100	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
101	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	—	2	2	no	—
103	C₂²×C₄×C₂₃	—	2	2	no	—
104	C₂²×C₄×C₂₃	—	2	2	no	—
105	C₂²×C₄×C₂₃	—	2	2	no	—
106	C₂²×C₄×C₂₃	—	2	2	no	—
107	C₂²×C₄×C₂₃	—	2	2	no	—
108	C₂²×C₄×C₂₃	—	2	2	no	—
109	C₂²×C₄×C₂₃	—	2	2	no	—
110	C₂²×C₄×C₂₃	—	2	2	no	—
111	C₂²×C₄×C₂₃	—	2	2	no	—
112	C₂²×C₄×C₂₃	—	2	2	no	—
113	C₂²×C₄×C₂₃	—	2	2	no	—
114	C₂²×C₄×C₂₃	—	2	2	no	—
115	C₂²×C₄×C₂₃	—	2	2	no	—
116	C₂²×C₄×C₂₃	—	2	2	no	—
117	C₂²×C₄×C₂₃	—	2	2	no	—
118	C₂²×C₄×C₂₃	—	4	1	no	—
119	C₂²×C₄×C₂₃	—	4	1	no	—
120	C₂²×C₄×C₂₃	—	4	1	no	—
121	C₂²×C₄×C₂₃	M₁₆	1	4	yes	—
122	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₂₃	#41	1	2	yes	—
137	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₂₃	—	2	2	no	—
139	C₂×C₈×C₂₃	—	2	2	no	—
140	C₂×C₈×C₂₃	—	2	2	no	—
141	C₂×C₈×C₂₃	—	2	2	no	—
142	C₂×C₈×C₂₃	—	2	2	no	—
143	C₂×C₈×C₂₃	—	2	2	no	—
144	C₂×C₈×C₂₃	—	2	2	no	—
145	C₂×C₈×C₂₃	—	2	2	no	—
146	C₂×C₈×C₂₃	—	2	2	no	—
147	C₂×C₈×C₂₃	—	2	2	no	—
148	C₂×C₈×C₂₃	—	2	2	no	—
149	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₂₃	—	2	2	no	—
151	C₄⋊C₄×C₂₃	—	2	2	no	—
152	C₄⋊C₄×C₂₃	—	2	2	no	—
153	C₄⋊C₄×C₂₃	—	2	2	no	—
154	C₄⋊C₄×C₂₃	—	2	2	no	—
155	C₄⋊C₄×C₂₃	—	2	2	no	—
156	C₄⋊C₄×C₂₃	—	2	2	no	—
157	C₄⋊C₄×C₂₃	M₁₆	1	4	yes	—
158	C₄²×C₂₃	—	2	2	no	—
159	C₄²×C₂₃	—	2	2	no	—
160	C₄²×C₂₃	—	2	2	no	—
161	C₄²×C₂₃	—	2	2	no	—
162	C₄²×C₂₃	—	2	2	no	—
163	C₄²×C₂₃	—	2	2	no	—
164	C₄²×C₂₃	—	2	1	no	—
165	C₄²×C₂₃	—	2	1	no	—
166	C₄²×C₂₃	—	2	1	no	—
167	C₄²×C₂₃	—	2	1	no	—
168	C₄²×C₂₃	—	2	2	no	—
169	C₄²×C₂₃	—	2	1	no	—
170	C₄²×C₂₃	—	2	1	no	—
171	C₄²×C₂₃	—	2	1	no	—
172	C₄²×C₂₃	—	2	1	no	—
173	C₄²×C₂₃	#41	1	4	yes	—
174	#22601	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₂₃	—	2	1	no	—
176	C₂³×C₂₃	—	2	1	no	—
177	C₂³×C₂₃	—	2	1	no	—
178	C₂³×C₂₃	—	2	1	no	—
179	C₂³×C₂₃	C₄×D₄	1	2	yes	—
180	C₂³×C₂₃	C₂×M₁₆	1	2	yes	—
181	C₂³×C₂₃	#131	1	2	yes	—
182	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₂₃	—	2	8	no	—
184	C₂×C₄×C₂₃	—	2	1	no	—
185	C₂×C₄×C₂₃	—	2	1	no	—
186	C₂×C₄×C₂₃	—	2	1	no	—
187	C₂×C₄×C₂₃	—	2	1	no	—
188	C₂×C₄×C₂₃	—	2	1	no	—
189	C₂×C₄×C₂₃	—	2	1	no	—
190	C₂×C₄×C₂₃	—	2	1	no	—
191	C₂×C₄×C₂₃	—	2	1	no	—
192	C₂×C₄×C₂₃	—	2	1	no	—
193	C₂×C₄×C₂₃	—	2	1	no	—
194	C₂×C₄×C₂₃	—	2	1	no	—
195	C₂×C₄×C₂₃	—	2	1	no	—
196	C₂×C₄×C₂₃	—	2	1	no	—
197	C₂×C₄×C₂₃	—	2	1	no	—
198	C₂×C₄×C₂₃	—	2	1	no	—
199	C₂×C₄×C₂₃	—	2	1	no	—
200	C₂×C₄×C₂₃	—	2	8	no	—
201	C₂×C₄×C₂₃	—	2	4	no	—
202	C₂×C₄×C₂₃	—	2	4	no	—
203	C₂×C₄×C₂₃	—	2	1	no	—
204	C₂×C₄×C₂₃	—	2	1	no	—
205	C₂×C₄×C₂₃	—	2	1	no	—
206	C₂×C₄×C₂₃	—	2	1	no	—
207	C₂×C₄×C₂₃	—	2	1	no	—
208	C₂×C₄×C₂₃	—	2	1	no	—
209	C₂×C₄×C₂₃	—	2	1	no	—
210	C₂×C₄×C₂₃	—	2	1	no	—
211	C₂×C₄×C₂₃	—	2	1	no	—
212	C₂×C₄×C₂₃	—	2	1	no	—
213	C₂×C₄×C₂₃	—	2	1	no	—
214	C₂×C₄×C₂₃	—	2	1	no	—
215	C₂×C₄×C₂₃	—	2	1	no	—
216	C₂×C₄×C₂₃	—	2	1	no	—
217	C₂×C₄×C₂₃	—	2	1	no	—
218	C₂×C₄×C₂₃	—	4	4	no	—
219	C₂×C₄×C₂₃	—	4	4	no	—
220	C₂×C₄×C₂₃	—	4	4	no	—
221	C₂×C₄×C₂₃	—	4	4	no	—
222	C₂×C₄×C₂₃	#117	1	2	yes	—
223	C₂×C₄×C₂₃	#117	1	2	yes	—
224	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
226	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
227	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
228	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
229	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
230	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
232	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
234	C₈×C₂₃	—	2	4	no	—
235	C₈×C₂₃	—	4	2	no	—
236	C₈×C₂₃	—	4	2	no	—
237	C₈×C₂₃	—	4	2	no	—
238	C₂×#432	C₂×C₂₃	1	1	yes	characteristic
239	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
240	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic
241	#1940	C₂×C₂₃	1	2	yes	complemented
242	#1917	C₂×C₂₃	1	2	yes	complemented
243	#1916	C₂×C₂₃	1	2	yes	complemented
244	#1817	C₂×C₂₃	1	1	yes	characteristic
245	#1817	C₂×C₂₃	1	1	yes	characteristic
246	#1797	C₂×C₂₃	1	1	yes	characteristic
247	#1771	C₂×C₂₃	1	2	yes	complemented
248	#1749	C₂×C₂₃	1	1	yes	characteristic
249	C₂²×C₂₃	—	2	2	no	—
250	C₂²×C₂₃	—	2	2	no	—
251	C₂²×C₂₃	—	2	2	no	—
252	C₂²×C₂₃	—	2	2	no	—
253	C₂²×C₂₃	—	2	2	no	—
254	C₂²×C₂₃	—	2	2	no	—
255	C₂²×C₂₃	#435	1	4	yes	—
256	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
257	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₂₃	#519	1	1	yes	characteristic
259	C₂²×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
260	C₂²×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
261	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
262	C₂²×C₂₃	#568	1	1	yes	characteristic
263	C₄×C₂₃	—	2	2	no	—
264	C₄×C₂₃	—	2	2	no	—
265	C₄×C₂₃	—	2	2	no	—
266	C₄×C₂₃	—	2	2	no	—
267	C₄×C₂₃	—	2	2	no	—
268	C₄×C₂₃	—	2	2	no	—
269	C₄×C₂₃	—	2	2	no	—
270	C₄×C₂₃	—	2	2	no	—
271	C₄×C₂₃	—	4	1	no	—
272	C₄×C₂₃	—	4	1	no	—
273	C₄×C₂₃	—	4	1	no	—
274	C₄×C₂₃	—	4	1	no	—
275	C₄×C₂₃	—	4	1	no	—
276	C₄×C₂₃	#547	1	2	yes	—
277	C₄×C₂₃	#552	1	2	yes	—
278	C₂²×C₄⋊C₄	C₄×C₂₃	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₄×C₂₃	1	1	yes	characteristic
280	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
281	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
282	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
283	#432	—	2	4	no	—
284	#431	—	2	4	no	—
285	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
286	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
287	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
288	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
290	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
291	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
292	C₂×#97	C₂²×C₂₃	1	2	yes	—
293	C₂×#97	C₂²×C₂₃	1	2	yes	—
294	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
295	C₄×C₄⋊C₄	C₄×C₂₃	1	1	yes	characteristic
296	C₄×C₄⋊C₄	C₄×C₂₃	1	1	yes	characteristic
297	C₄×C₄⋊C₄	C₄×C₂₃	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₄×C₂₃	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
301	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
302	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
303	C₂×#95	C₄×C₂₃	1	1	yes	characteristic
304	C₂×#95	C₄×C₂₃	1	1	yes	characteristic
305	#336	C₂²×C₂₃	1	2	yes	—
306	#336	C₂²×C₂₃	1	2	yes	—
307	#336	C₂²×C₂₃	1	2	yes	—
308	#336	C₂²×C₂₃	1	2	yes	—
309	#336	C₂²×C₂₃	1	2	yes	—
310	#336	C₂²×C₂₃	1	2	yes	—
311	C₂×C₂₃	—	2	4	no	—
312	C₂×C₂₃	#2344	1	1	yes	characteristic
313	C₂×C₂₃	#2920	1	1	yes	characteristic
314	C₂×C₂₃	#2924	1	1	yes	characteristic
315	C₂×C₂₃	C₂×#435	1	1	yes	characteristic
316	C₂×C₂₃	D₄×M₁₆	1	1	yes	characteristic
317	C₂×C₂₃	#2983	1	1	yes	characteristic
318	C₂×C₂₃	#2984	1	1	yes	characteristic
319	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
320	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
321	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
322	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
323	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
324	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
327	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
328	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
329	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
330	C₂×C₄⋊C₄	—	2	4	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	4	no	—
345	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
346	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
347	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
348	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
349	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
350	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
357	C₄⋊C₈	—	2	4	no	—
358	C₄⋊C₈	—	2	4	no	—
359	C₄⋊C₈	—	2	4	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	C₂²⋊C₈	—	2	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	D₄×C₂₃	1	4	yes	—
364	#97	—	2	4	no	—
365	#97	—	2	4	no	—
366	C₄×C₈	—	2	4	no	—
367	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
368	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
369	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
370	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
371	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
372	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
373	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
374	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
375	C₂₃	#22601	1	1	yes	characteristic, direct product factor, Sylow
376	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	M₁₆×C₂₃	1	4	yes	—
397	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
402	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
404	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
405	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
406	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
407	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
408	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
409	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
411	C₂²×C₄	#41×C₂₃	1	2	yes	—
412	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	M₁₆×C₂₃	1	4	yes	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	#41×C₂₃	1	4	yes	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	C₄×D₄×C₂₃	1	2	yes	—
454	C₂³	C₂×M₁₆×C₂₃	1	2	yes	—
455	C₂³	C₂₃×#131	1	2	yes	—
456	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	C₂₃×#117	1	2	yes	—
497	C₂×C₄	C₂₃×#117	1	2	yes	—
498	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
499	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
500	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
501	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
502	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
503	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
506	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
507	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
508	C₈	—	2	4	no	—
509	C₈	—	4	2	no	—
510	C₈	—	4	2	no	—
511	C₈	—	4	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	C₂₃×#435	1	4	yes	—
519	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
520	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
521	C₂²	C₂₃×#519	1	1	yes	characteristic
522	C₂²	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
523	C₂²	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
524	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
525	C₂²	C₂₃×#568	1	1	yes	characteristic
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	C₂₃×#547	1	2	yes	—
540	C₄	C₂₃×#552	1	2	yes	—
541	C₂	—	2	4	no	—
542	C₂	C₂₃×#2344	1	1	yes	characteristic
543	C₂	C₂₃×#2920	1	1	yes	characteristic
544	C₂	C₂₃×#2924	1	1	yes	characteristic
545	C₂	C₂×C₂₃×#435	1	1	yes	characteristic
546	C₂	D₄×M₁₆×C₂₃	1	1	yes	characteristic
547	C₂	C₂₃×#2983	1	1	yes	characteristic
548	C₂	C₂₃×#2984	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
4. C₂₃×#1940	C₂	semidirect
5. C₂₃×#1917	C₂	semidirect
6. C₂₃×#1916	C₂	semidirect
10. C₂₃×#1771	C₂	semidirect
174. #22601	C₂₃	direct (N × H)
241. #1940	C₂×C₂₃	semidirect
242. #1917	C₂×C₂₃	semidirect
243. #1916	C₂×C₂₃	semidirect
247. #1771	C₂×C₂₃	semidirect
375. C₂₃	#22601	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×#432	2
C₂×C₂₃×#431	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂₃×#1940	2
C₂₃×#1917	2
C₂₃×#1916	2
C₂₃×#1817	2
C₂₃×#1797	2
C₂₃×#1771	2
C₂₃×#1749	2
#22601	23

Subgroups — C23×#22601 #19170227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22601 #19170227