Subgroups — C₂₃×#23331 #19170957

Order 5888.

854 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#121	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#390	C₄	1	1	yes	characteristic
40	C₂₃×#389	C₄	1	1	yes	characteristic
41	C₂₃×#388	C₄	1	1	yes	characteristic
42	C₂₃×#388	C₄	1	1	yes	characteristic
43	C₂₃×#386	C₄	1	1	yes	characteristic
44	C₂₃×#386	C₄	1	1	yes	characteristic
45	C₂₃×#380	C₄	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂₃×#336	C₂²	1	1	yes	characteristic
50	C₂₃×#336	C₂²	1	1	yes	characteristic
51	C₂₃×#336	C₂²	1	1	yes	characteristic
52	C₂₃×#336	C₂²	1	1	yes	characteristic
53	C₂₃×#336	C₂²	1	1	yes	characteristic
54	C₂₃×#336	C₂²	1	1	yes	characteristic
55	C₂₃×#336	C₂²	1	1	yes	characteristic
56	C₂₃×#336	C₂²	1	1	yes	characteristic
57	C₂₃×#336	C₂²	1	1	yes	characteristic
58	C₂₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₂₃	—	4	1	no	—
68	C₂×M₁₆×C₂₃	—	4	1	no	—
69	C₂×M₁₆×C₂₃	—	4	1	no	—
70	C₂²×C₈×C₂₃	—	4	1	no	—
71	C₂²×C₈×C₂₃	—	4	1	no	—
72	C₂²×C₈×C₂₃	—	4	1	no	—
73	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂₃×#121	—	2	4	no	—
82	C₄×D₄×C₂₃	—	4	1	no	—
83	C₄×D₄×C₂₃	—	4	1	no	—
84	C₄×D₄×C₂₃	—	4	1	no	—
85	C₄×D₄×C₂₃	—	4	1	no	—
86	C₄×D₄×C₂₃	—	4	1	no	—
87	C₄×D₄×C₂₃	—	4	1	no	—
88	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₂₃	—	4	1	no	—
104	C₂×C₄²×C₂₃	—	4	1	no	—
105	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
111	C₂₃×C₄⋊C₈	—	4	1	no	—
112	C₂₃×C₄⋊C₈	—	4	1	no	—
113	C₂₃×C₄⋊C₈	—	4	1	no	—
114	C₂₃×C₄⋊C₈	—	4	1	no	—
115	C₂₃×C₂²⋊C₈	—	4	1	no	—
116	C₂₃×C₂²⋊C₈	—	4	1	no	—
117	C₂₃×C₂²⋊C₈	—	4	1	no	—
118	C₂₃×C₂²⋊C₈	—	4	1	no	—
119	C₂₃×C₂²⋊C₈	—	4	1	no	—
120	C₂₃×C₂²⋊C₈	—	4	1	no	—
121	C₂₃×C₂²⋊C₈	—	4	1	no	—
122	C₂₃×C₂²⋊C₈	—	4	1	no	—
123	C₂₃×C₂²⋊C₈	—	4	1	no	—
124	C₂₃×C₂²⋊C₈	—	4	1	no	—
125	C₂₃×#97	—	4	1	no	—
126	C₄×C₈×C₂₃	—	4	1	no	—
127	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
128	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
129	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
130	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
131	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
132	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
133	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
134	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
135	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×D₄×C₂₃	—	2	2	no	—
137	C₂×D₄×C₂₃	—	2	2	no	—
138	C₂×D₄×C₂₃	—	2	2	no	—
139	C₂×D₄×C₂₃	—	4	1	no	—
140	C₂×D₄×C₂₃	—	4	1	no	—
141	C₂×D₄×C₂₃	—	4	1	no	—
142	C₂×D₄×C₂₃	—	4	1	no	—
143	C₂×D₄×C₂₃	—	4	1	no	—
144	C₂×D₄×C₂₃	M₁₆	1	4	yes	complemented
145	C₂²×C₄×C₂₃	—	2	2	no	—
146	C₂²×C₄×C₂₃	—	2	2	no	—
147	C₂²×C₄×C₂₃	—	2	2	no	—
148	C₂²×C₄×C₂₃	—	2	1	no	—
149	C₂²×C₄×C₂₃	—	2	1	no	—
150	C₂²×C₄×C₂₃	—	2	1	no	—
151	C₂²×C₄×C₂₃	—	2	1	no	—
152	C₂²×C₄×C₂₃	—	2	1	no	—
153	C₂²×C₄×C₂₃	—	2	1	no	—
154	C₂²×C₄×C₂₃	—	2	1	no	—
155	C₂²×C₄×C₂₃	—	2	1	no	—
156	C₂²×C₄×C₂₃	—	2	1	no	—
157	C₂²×C₄×C₂₃	—	2	1	no	—
158	C₂²×C₄×C₂₃	—	2	1	no	—
159	C₂²×C₄×C₂₃	—	2	1	no	—
160	C₂²×C₄×C₂₃	—	2	1	no	—
161	C₂²×C₄×C₂₃	—	2	1	no	—
162	C₂²×C₄×C₂₃	—	2	1	no	—
163	C₂²×C₄×C₂₃	—	2	1	no	—
164	C₂²×C₄×C₂₃	—	2	1	no	—
165	C₂²×C₄×C₂₃	—	2	1	no	—
166	C₂²×C₄×C₂₃	—	4	1	no	—
167	C₂²×C₄×C₂₃	—	4	1	no	—
168	C₂²×C₄×C₂₃	—	4	1	no	—
169	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
181	M₁₆×C₂₃	—	4	4	no	—
182	C₂×C₈×C₂₃	—	2	1	no	—
183	C₂×C₈×C₂₃	—	2	1	no	—
184	C₂×C₈×C₂₃	—	2	1	no	—
185	C₂×C₈×C₂₃	—	2	1	no	—
186	C₂×C₈×C₂₃	—	2	1	no	—
187	C₂×C₈×C₂₃	—	2	1	no	—
188	C₂×C₈×C₂₃	—	2	1	no	—
189	C₂×C₈×C₂₃	—	2	1	no	—
190	C₂×C₈×C₂₃	—	2	1	no	—
191	C₂×C₈×C₂₃	—	2	1	no	—
192	C₂×C₈×C₂₃	—	2	1	no	—
193	C₂×C₈×C₂₃	—	2	1	no	—
194	C₂×C₈×C₂₃	—	2	1	no	—
195	C₂×C₈×C₂₃	—	2	1	no	—
196	C₂×C₈×C₂₃	—	2	1	no	—
197	C₂×C₈×C₂₃	—	2	1	no	—
198	C₂×C₈×C₂₃	—	2	1	no	—
199	C₂×C₈×C₂₃	—	2	1	no	—
200	C₂×C₈×C₂₃	—	2	1	no	—
201	C₂×C₈×C₂₃	—	2	1	no	—
202	C₂×C₈×C₂₃	—	2	1	no	—
203	C₂×C₈×C₂₃	—	2	1	no	—
204	C₂×C₈×C₂₃	—	2	1	no	—
205	C₂×C₈×C₂₃	—	2	1	no	—
206	C₂×C₈×C₂₃	—	4	4	no	—
207	C₄⋊C₄×C₂₃	—	2	2	no	—
208	C₄⋊C₄×C₂₃	—	2	2	no	—
209	C₄⋊C₄×C₂₃	—	4	1	no	—
210	C₄⋊C₄×C₂₃	—	4	1	no	—
211	C₄⋊C₄×C₂₃	—	4	1	no	—
212	C₂²⋊C₄×C₂₃	—	2	2	no	—
213	C₂²⋊C₄×C₂₃	—	2	2	no	—
214	C₂²⋊C₄×C₂₃	—	2	2	no	—
215	C₂²⋊C₄×C₂₃	—	2	2	no	—
216	C₂²⋊C₄×C₂₃	—	4	1	no	—
217	C₂²⋊C₄×C₂₃	—	4	1	no	—
218	C₂²⋊C₄×C₂₃	—	4	1	no	—
219	C₂²⋊C₄×C₂₃	—	4	1	no	—
220	C₂²⋊C₄×C₂₃	—	4	1	no	—
221	C₂²⋊C₄×C₂₃	—	4	1	no	—
222	C₄²×C₂₃	—	2	1	no	—
223	C₄²×C₂₃	—	2	1	no	—
224	C₄²×C₂₃	—	2	1	no	—
225	C₄²×C₂₃	—	2	1	no	—
226	C₄²×C₂₃	—	2	1	no	—
227	C₄²×C₂₃	—	2	1	no	—
228	C₄²×C₂₃	—	2	1	no	—
229	C₄²×C₂₃	—	2	1	no	—
230	C₄²×C₂₃	—	4	1	no	—
231	C₄²×C₂₃	—	4	1	no	—
232	#23331	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂³×C₂₃	—	2	1	no	—
234	C₂³×C₂₃	—	2	1	no	—
235	C₂³×C₂₃	—	2	1	no	—
236	C₂³×C₂₃	—	2	1	no	—
237	C₂³×C₂₃	—	2	1	no	—
238	C₂³×C₂₃	—	2	1	no	—
239	C₂³×C₂₃	—	2	1	no	—
240	C₂³×C₂₃	—	2	1	no	—
241	C₂³×C₂₃	—	2	1	no	—
242	C₂³×C₂₃	—	2	1	no	—
243	C₂³×C₂₃	—	2	1	no	—
244	C₂³×C₂₃	—	2	1	no	—
245	C₂³×C₂₃	—	2	1	no	—
246	C₂³×C₂₃	—	2	1	no	—
247	C₂³×C₂₃	—	2	1	no	—
248	C₂³×C₂₃	—	2	1	no	—
249	C₂³×C₂₃	—	2	1	no	—
250	C₂³×C₂₃	—	2	1	no	—
251	C₂³×C₂₃	—	2	1	no	—
252	C₂³×C₂₃	C₂×M₁₆	1	2	yes	—
253	C₂³×C₂₃	C₂×M₁₆	1	2	yes	—
254	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
255	D₄×C₂₃	—	4	4	no	—
256	D₄×C₂₃	—	4	4	no	—
257	D₄×C₂₃	—	4	4	no	—
258	C₂×C₄×C₂₃	—	2	1	no	—
259	C₂×C₄×C₂₃	—	2	1	no	—
260	C₂×C₄×C₂₃	—	2	1	no	—
261	C₂×C₄×C₂₃	—	2	1	no	—
262	C₂×C₄×C₂₃	—	2	1	no	—
263	C₂×C₄×C₂₃	—	2	1	no	—
264	C₂×C₄×C₂₃	—	2	1	no	—
265	C₂×C₄×C₂₃	—	2	1	no	—
266	C₂×C₄×C₂₃	—	2	1	no	—
267	C₂×C₄×C₂₃	—	2	1	no	—
268	C₂×C₄×C₂₃	—	2	1	no	—
269	C₂×C₄×C₂₃	—	2	1	no	—
270	C₂×C₄×C₂₃	—	2	1	no	—
271	C₂×C₄×C₂₃	—	2	1	no	—
272	C₂×C₄×C₂₃	—	2	1	no	—
273	C₂×C₄×C₂₃	—	2	1	no	—
274	C₂×C₄×C₂₃	—	2	1	no	—
275	C₂×C₄×C₂₃	—	2	1	no	—
276	C₂×C₄×C₂₃	—	2	1	no	—
277	C₂×C₄×C₂₃	—	2	1	no	—
278	C₂×C₄×C₂₃	—	2	1	no	—
279	C₂×C₄×C₂₃	—	2	1	no	—
280	C₂×C₄×C₂₃	—	2	1	no	—
281	C₂×C₄×C₂₃	—	2	1	no	—
282	C₂×C₄×C₂₃	—	2	1	no	—
283	C₂×C₄×C₂₃	—	2	1	no	—
284	C₂×C₄×C₂₃	—	2	1	no	—
285	C₂×C₄×C₂₃	—	2	1	no	—
286	C₂×C₄×C₂₃	—	2	1	no	—
287	C₂×C₄×C₂₃	—	2	1	no	—
288	C₂×C₄×C₂₃	—	4	4	no	—
289	C₂×C₄×C₂₃	—	4	4	no	—
290	C₂×C₄×C₂₃	—	4	1	no	—
291	C₂×C₄×C₂₃	—	4	1	no	—
292	C₂×C₄×C₂₃	—	4	1	no	—
293	C₂×C₄×C₂₃	—	4	1	no	—
294	C₂×C₄×C₂₃	—	4	1	no	—
295	C₂×C₄×C₂₃	—	4	1	no	—
296	C₂×C₄×C₂₃	—	4	1	no	—
297	C₂×C₄×C₂₃	—	4	1	no	—
298	C₂×C₄×C₂₃	—	4	1	no	—
299	C₂×C₄×C₂₃	—	4	1	no	—
300	C₂×C₄×C₂₃	—	4	1	no	—
301	C₂×C₄×C₂₃	—	4	1	no	—
302	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
303	C₂×C₄×C₂₃	#131	1	2	yes	—
304	C₂×C₄×C₂₃	#131	1	2	yes	—
305	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
307	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
311	C₈×C₂₃	—	4	1	no	—
312	C₈×C₂₃	—	4	1	no	—
313	C₈×C₂₃	—	4	1	no	—
314	C₈×C₂₃	—	4	1	no	—
315	C₈×C₂₃	—	4	1	no	—
316	C₈×C₂₃	—	4	1	no	—
317	C₈×C₂₃	—	4	1	no	—
318	C₈×C₂₃	—	4	1	no	—
319	C₄×#121	C₂×C₂₃	1	1	yes	characteristic
320	#1955	C₂×C₂₃	1	1	yes	characteristic, complemented
321	#1954	C₂×C₂₃	1	1	yes	characteristic, complemented
322	#1924	C₂×C₂₃	1	1	yes	characteristic, complemented
323	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
324	#1917	C₂×C₂₃	1	1	yes	characteristic, complemented
325	#1916	C₂×C₂₃	1	1	yes	characteristic, complemented
326	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
327	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
328	#1869	C₂×C₂₃	1	1	yes	characteristic, complemented
329	#1869	C₂×C₂₃	1	1	yes	characteristic, complemented
330	#1851	C₂×C₂₃	1	1	yes	characteristic, complemented
331	#1850	C₂×C₂₃	1	1	yes	characteristic, complemented
332	#1817	C₂×C₂₃	1	1	yes	characteristic, complemented
333	#1797	C₂×C₂₃	1	1	yes	characteristic, complemented
334	C₂²×C₂₃	—	2	2	no	—
335	C₂²×C₂₃	—	2	2	no	—
336	C₂²×C₂₃	—	2	2	no	—
337	C₂²×C₂₃	—	2	2	no	—
338	C₂²×C₂₃	—	2	2	no	—
339	C₂²×C₂₃	—	2	2	no	—
340	C₂²×C₂₃	—	4	1	no	—
341	C₂²×C₂₃	—	4	1	no	—
342	C₂²×C₂₃	—	4	1	no	—
343	C₂²×C₂₃	—	4	1	no	—
344	C₂²×C₂₃	—	4	1	no	—
345	C₂²×C₂₃	—	4	1	no	—
346	C₂²×C₂₃	—	4	1	no	—
347	C₂²×C₂₃	—	4	1	no	—
348	C₂²×C₂₃	—	4	1	no	—
349	C₂²×C₂₃	—	4	1	no	—
350	C₂²×C₂₃	—	4	1	no	—
351	C₂²×C₂₃	—	4	1	no	—
352	C₂²×C₂₃	—	4	1	no	—
353	C₂²×C₂₃	—	4	1	no	—
354	C₂²×C₂₃	—	4	1	no	—
355	C₂²×C₂₃	#518	1	1	yes	characteristic
356	C₂²×C₂₃	#518	1	1	yes	characteristic
357	C₂²×C₂₃	#520	1	1	yes	characteristic
358	C₂²×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
359	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
360	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
361	C₂²×C₂₃	#568	1	1	yes	characteristic
362	C₄×C₂₃	—	2	2	no	—
363	C₄×C₂₃	—	2	2	no	—
364	C₄×C₂₃	—	2	2	no	—
365	C₄×C₂₃	—	4	1	no	—
366	C₄×C₂₃	—	4	1	no	—
367	C₄×C₂₃	—	4	1	no	—
368	C₄×C₂₃	—	4	1	no	—
369	C₄×C₂₃	—	4	1	no	—
370	C₄×C₂₃	—	4	1	no	—
371	C₄×C₂₃	—	4	1	no	—
372	C₄×C₂₃	—	4	1	no	—
373	C₄×C₂₃	#560	1	1	yes	characteristic
374	C₄×C₂₃	#560	1	1	yes	characteristic
375	C₄×C₂₃	#562	1	1	yes	characteristic
376	C₄×C₂₃	#562	1	1	yes	characteristic
377	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
378	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
379	C₂×#121	C₄×C₂₃	1	1	yes	characteristic
380	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
383	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
384	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
385	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
386	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
387	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
388	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
389	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
390	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
391	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
392	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
393	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
394	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
395	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
400	#390	C₄×C₂₃	1	1	yes	characteristic
401	#389	C₄×C₂₃	1	1	yes	characteristic
402	#388	C₄×C₂₃	1	1	yes	characteristic
403	#388	C₄×C₂₃	1	1	yes	characteristic
404	#386	C₄×C₂₃	1	1	yes	characteristic
405	#386	C₄×C₂₃	1	1	yes	characteristic
406	#380	C₄×C₂₃	1	1	yes	characteristic
407	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
408	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
409	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
410	#336	C₂²×C₂₃	1	1	yes	characteristic
411	#336	C₂²×C₂₃	1	1	yes	characteristic
412	#336	C₂²×C₂₃	1	1	yes	characteristic
413	#336	C₂²×C₂₃	1	1	yes	characteristic
414	#336	C₂²×C₂₃	1	1	yes	characteristic
415	#336	C₂²×C₂₃	1	1	yes	characteristic
416	#336	C₂²×C₂₃	1	1	yes	characteristic
417	#336	C₂²×C₂₃	1	1	yes	characteristic
418	#336	C₂²×C₂₃	1	1	yes	characteristic
419	#336	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×C₂₃	—	4	2	no	—
421	C₂×C₂₃	—	4	2	no	—
422	C₂×C₂₃	—	8	1	no	—
423	C₂×C₂₃	#2377	1	1	yes	characteristic
424	C₂×C₂₃	#2973	1	1	yes	characteristic
425	C₂×C₂₃	#2974	1	1	yes	characteristic
426	C₂×C₂₃	#2976	1	1	yes	characteristic
427	C₂×C₂₃	#2979	1	1	yes	characteristic
428	C₂×C₂₃	#2990	1	1	yes	characteristic
429	C₂×C₂₃	#2993	1	1	yes	characteristic
430	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
431	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
432	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
433	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
434	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
438	C₂×M₁₆	—	4	1	no	—
439	C₂×M₁₆	—	4	1	no	—
440	C₂×M₁₆	—	4	1	no	—
441	C₂²×C₈	—	4	1	no	—
442	C₂²×C₈	—	4	1	no	—
443	C₂²×C₈	—	4	1	no	—
444	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
452	#121	—	2	4	no	—
453	C₄×D₄	—	4	1	no	—
454	C₄×D₄	—	4	1	no	—
455	C₄×D₄	—	4	1	no	—
456	C₄×D₄	—	4	1	no	—
457	C₄×D₄	—	4	1	no	—
458	C₄×D₄	—	4	1	no	—
459	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
474	C₂×C₄²	—	4	1	no	—
475	C₂×C₄²	—	4	1	no	—
476	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
477	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
482	C₄⋊C₈	—	4	1	no	—
483	C₄⋊C₈	—	4	1	no	—
484	C₄⋊C₈	—	4	1	no	—
485	C₄⋊C₈	—	4	1	no	—
486	C₂²⋊C₈	—	4	1	no	—
487	C₂²⋊C₈	—	4	1	no	—
488	C₂²⋊C₈	—	4	1	no	—
489	C₂²⋊C₈	—	4	1	no	—
490	C₂²⋊C₈	—	4	1	no	—
491	C₂²⋊C₈	—	4	1	no	—
492	C₂²⋊C₈	—	4	1	no	—
493	C₂²⋊C₈	—	4	1	no	—
494	C₂²⋊C₈	—	4	1	no	—
495	C₂²⋊C₈	—	4	1	no	—
496	#97	—	4	1	no	—
497	C₄×C₈	—	4	1	no	—
498	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
499	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
500	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
501	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
502	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
503	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
504	C₂₃	#23331	1	1	yes	characteristic, direct product factor, Sylow
505	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
506	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
507	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	4	1	no	—
512	C₂×D₄	—	4	1	no	—
513	C₂×D₄	—	4	1	no	—
514	C₂×D₄	—	4	1	no	—
515	C₂×D₄	—	4	1	no	—
516	C₂×D₄	M₁₆×C₂₃	1	4	yes	complemented
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	4	1	no	—
539	C₂²×C₄	—	4	1	no	—
540	C₂²×C₄	—	4	1	no	—
541	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
549	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
550	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
551	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
553	M₁₆	—	4	4	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	4	4	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	4	1	no	—
582	C₄⋊C₄	—	4	1	no	—
583	C₄⋊C₄	—	4	1	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	4	1	no	—
589	C₂²⋊C₄	—	4	1	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₂²⋊C₄	—	4	1	no	—
593	C₂²⋊C₄	—	4	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	4	1	no	—
603	C₄²	—	4	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	C₂×M₁₆×C₂₃	1	2	yes	—
624	C₂³	C₂×M₁₆×C₂₃	1	2	yes	—
625	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
626	D₄	—	4	4	no	—
627	D₄	—	4	4	no	—
628	D₄	—	4	4	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
674	C₂×C₄	C₂₃×#131	1	2	yes	—
675	C₂×C₄	C₂₃×#131	1	2	yes	—
676	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
677	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
681	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
682	C₈	—	4	1	no	—
683	C₈	—	4	1	no	—
684	C₈	—	4	1	no	—
685	C₈	—	4	1	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	C₂₃×#518	1	1	yes	characteristic
712	C₂²	C₂₃×#518	1	1	yes	characteristic
713	C₂²	C₂₃×#520	1	1	yes	characteristic
714	C₂²	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
715	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
716	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
717	C₂²	C₂₃×#568	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	C₂₃×#560	1	1	yes	characteristic
730	C₄	C₂₃×#560	1	1	yes	characteristic
731	C₄	C₂₃×#562	1	1	yes	characteristic
732	C₄	C₂₃×#562	1	1	yes	characteristic
733	C₂	—	4	2	no	—
734	C₂	—	4	2	no	—
735	C₂	—	8	1	no	—
736	C₂	C₂₃×#2377	1	1	yes	characteristic
737	C₂	C₂₃×#2973	1	1	yes	characteristic
738	C₂	C₂₃×#2974	1	1	yes	characteristic
739	C₂	C₂₃×#2976	1	1	yes	characteristic
740	C₂	C₂₃×#2979	1	1	yes	characteristic
741	C₂	C₂₃×#2990	1	1	yes	characteristic
742	C₂	C₂₃×#2993	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	C₂×C₂₃×#121	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
2. C₂₃×#1955	C₂	semidirect
3. C₂₃×#1954	C₂	semidirect
4. C₂₃×#1924	C₂	semidirect
5. C₂₃×#1923	C₂	semidirect
6. C₂₃×#1917	C₂	semidirect
7. C₂₃×#1916	C₂	semidirect
8. C₂₃×#1870	C₂	semidirect
9. C₂₃×#1870	C₂	semidirect
10. C₂₃×#1869	C₂	semidirect
11. C₂₃×#1869	C₂	semidirect
12. C₂₃×#1851	C₂	semidirect
13. C₂₃×#1850	C₂	semidirect
14. C₂₃×#1817	C₂	semidirect
15. C₂₃×#1797	C₂	semidirect
144. C₂×D₄×C₂₃	M₁₆	semidirect
232. #23331	C₂₃	direct (N × H)
320. #1955	C₂×C₂₃	semidirect
321. #1954	C₂×C₂₃	semidirect
322. #1924	C₂×C₂₃	semidirect
323. #1923	C₂×C₂₃	semidirect
324. #1917	C₂×C₂₃	semidirect
325. #1916	C₂×C₂₃	semidirect
326. #1870	C₂×C₂₃	semidirect
327. #1870	C₂×C₂₃	semidirect
328. #1869	C₂×C₂₃	semidirect
329. #1869	C₂×C₂₃	semidirect
330. #1851	C₂×C₂₃	semidirect
331. #1850	C₂×C₂₃	semidirect
332. #1817	C₂×C₂₃	semidirect
333. #1797	C₂×C₂₃	semidirect
504. C₂₃	#23331	direct (N × H)
516. C₂×D₄	M₁₆×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₂₃×#121	2
C₂₃×#1955	2
C₂₃×#1954	2
C₂₃×#1924	2
C₂₃×#1923	2
C₂₃×#1917	2
C₂₃×#1916	2
C₂₃×#1870	2
C₂₃×#1869	2
C₂₃×#1851	2
C₂₃×#1850	2
C₂₃×#1817	2
C₂₃×#1797	2
#23331	23

Subgroups — C23×#23331 #19170957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#23331 #19170957