Subgroups — C₂₃×#29464 #19177090

Order 5888.

850 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2034	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#2000	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₂₃	—	2	1	no	—
20	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#102	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×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#391	C₂²	1	1	yes	characteristic
36	C₂₃×#391	C₂²	1	1	yes	characteristic
37	C₂₃×#390	C₂²	1	1	yes	characteristic
38	C₂₃×#389	C₂²	1	1	yes	characteristic
39	C₂₃×#389	C₂²	1	1	yes	characteristic
40	C₂₃×#389	C₂²	1	1	yes	characteristic
41	C₂₃×#388	—	2	1	no	—
42	C₂₃×#387	—	2	1	no	—
43	C₂₃×#387	—	2	1	no	—
44	C₂₃×#386	—	2	1	no	—
45	C₂₃×#385	—	2	1	no	—
46	C₂₃×#381	—	2	1	no	—
47	C₂₃×#380	C₂²	1	1	yes	characteristic
48	C₂₃×#380	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
51	C₂₃×#340	C₂²	1	1	yes	characteristic
52	C₂₃×#340	C₂²	1	1	yes	characteristic
53	C₂₃×#340	C₂²	1	1	yes	characteristic
54	C₂₃×#340	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#336	C₂²	1	1	yes	characteristic
58	C₂₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₂₃	—	2	1	no	—
61	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₂₃	—	2	1	no	—
63	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₂₃	—	2	2	no	—
67	C₂×SD₁₆×C₂₃	—	2	2	no	—
68	C₂×SD₁₆×C₂₃	—	4	1	no	—
69	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
73	C₂₃×C₂²⋊Q₈	—	4	1	no	—
74	C₂₃×C₂²⋊Q₈	—	4	1	no	—
75	C₂₃×#121	—	2	2	no	—
76	C₂₃×#121	—	2	2	no	—
77	C₄×D₄×C₂₃	—	4	1	no	—
78	C₄×D₄×C₂₃	—	4	1	no	—
79	C₄×D₄×C₂₃	—	4	4	no	—
80	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
97	C₂×C₄²×C₂₃	—	2	1	no	—
98	C₂×C₄²×C₂₃	—	4	1	no	—
99	C₂×C₄²×C₂₃	—	4	1	no	—
100	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
104	C₂₃×#106	—	2	2	no	—
105	C₂₃×#106	—	2	2	no	—
106	C₂₃×#106	—	4	1	no	—
107	C₂₃×#103	—	2	2	no	—
108	C₂₃×#103	—	2	2	no	—
109	C₂₃×#103	—	4	1	no	—
110	C₂₃×#102	—	2	2	no	—
111	C₂₃×#102	—	2	2	no	—
112	C₂₃×#102	—	4	1	no	—
113	C₂₃×C₂²⋊C₈	—	2	2	no	—
114	C₂₃×C₂²⋊C₈	—	2	2	no	—
115	C₄×C₈×C₂₃	—	4	1	no	—
116	C₄×C₈×C₂₃	—	4	1	no	—
117	C₂₃×#95	—	2	1	no	—
118	C₂₃×#95	—	2	1	no	—
119	C₂₃×#95	—	2	1	no	—
120	C₂₃×#95	—	2	1	no	—
121	C₂₃×#95	—	2	1	no	—
122	C₂₃×#95	—	2	1	no	—
123	C₂₃×#95	—	2	1	no	—
124	C₂₃×#95	—	2	1	no	—
125	C₂₃×#95	—	2	1	no	—
126	C₂₃×#95	—	2	1	no	—
127	C₂⁴×C₂₃	—	2	1	no	—
128	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
129	C₂×Q₈×C₂₃	—	2	1	no	—
130	C₂×Q₈×C₂₃	—	2	1	no	—
131	C₂×Q₈×C₂₃	—	2	1	no	—
132	C₂×Q₈×C₂₃	—	2	1	no	—
133	C₂×Q₈×C₂₃	—	2	1	no	—
134	C₂×Q₈×C₂₃	—	2	1	no	—
135	C₂×D₄×C₂₃	—	2	4	no	—
136	C₂×D₄×C₂₃	—	2	1	no	—
137	C₂×D₄×C₂₃	—	2	1	no	—
138	C₂×D₄×C₂₃	—	2	1	no	—
139	C₂×D₄×C₂₃	—	2	1	no	—
140	C₂×D₄×C₂₃	—	2	1	no	—
141	C₂×D₄×C₂₃	—	4	2	no	—
142	C₂×D₄×C₂₃	—	4	2	no	—
143	C₂×D₄×C₂₃	#41	1	2	yes	—
144	C₂²×C₄×C₂₃	—	2	1	no	—
145	C₂²×C₄×C₂₃	—	2	2	no	—
146	C₂²×C₄×C₂₃	—	2	1	no	—
147	C₂²×C₄×C₂₃	—	2	1	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	—	4	1	no	—
159	C₂²×C₄×C₂₃	—	4	1	no	—
160	C₂²×C₄×C₂₃	—	4	1	no	—
161	C₂²×C₄×C₂₃	—	4	1	no	—
162	C₂²×C₄×C₂₃	—	4	2	no	—
163	C₂²×C₄×C₂₃	—	4	2	no	—
164	C₂²×C₄×C₂₃	—	4	2	no	—
165	C₂²×C₄×C₂₃	SD₁₆	1	4	yes	complemented
166	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
172	SD₁₆×C₂₃	—	4	4	no	—
173	C₂×C₈×C₂₃	—	2	1	no	—
174	C₂×C₈×C₂₃	—	2	1	no	—
175	C₂×C₈×C₂₃	—	2	1	no	—
176	C₂×C₈×C₂₃	—	2	1	no	—
177	C₂×C₈×C₂₃	—	2	1	no	—
178	C₂×C₈×C₂₃	—	2	1	no	—
179	C₂×C₈×C₂₃	—	2	1	no	—
180	C₂×C₈×C₂₃	—	2	1	no	—
181	C₂×C₈×C₂₃	—	2	1	no	—
182	C₂×C₈×C₂₃	—	2	1	no	—
183	C₂×C₈×C₂₃	#41	1	2	yes	—
184	C₂×C₈×C₂₃	#41	1	2	yes	—
185	C₄⋊C₄×C₂₃	—	2	1	no	—
186	C₄⋊C₄×C₂₃	—	2	1	no	—
187	C₄⋊C₄×C₂₃	—	2	1	no	—
188	C₄⋊C₄×C₂₃	—	2	1	no	—
189	C₄⋊C₄×C₂₃	—	2	1	no	—
190	C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₄⋊C₄×C₂₃	—	2	1	no	—
192	C₄⋊C₄×C₂₃	—	2	1	no	—
193	C₄⋊C₄×C₂₃	—	2	1	no	—
194	C₄⋊C₄×C₂₃	—	2	1	no	—
195	C₄⋊C₄×C₂₃	—	2	1	no	—
196	C₄⋊C₄×C₂₃	—	4	2	no	—
197	C₄⋊C₄×C₂₃	—	4	2	no	—
198	C₄⋊C₄×C₂₃	—	4	2	no	—
199	C₄⋊C₄×C₂₃	—	4	2	no	—
200	C₄⋊C₄×C₂₃	#41	1	2	yes	—
201	C₂²⋊C₄×C₂₃	—	2	4	no	—
202	C₂²⋊C₄×C₂₃	—	4	2	no	—
203	C₂²⋊C₄×C₂₃	—	4	2	no	—
204	C₂²⋊C₄×C₂₃	—	4	2	no	—
205	C₂²⋊C₄×C₂₃	—	4	2	no	—
206	C₂²⋊C₄×C₂₃	—	4	2	no	—
207	C₂²⋊C₄×C₂₃	—	4	2	no	—
208	C₄²×C₂₃	—	2	1	no	—
209	C₄²×C₂₃	—	2	1	no	—
210	C₄²×C₂₃	—	2	1	no	—
211	C₄²×C₂₃	—	2	1	no	—
212	C₄²×C₂₃	—	4	1	no	—
213	C₄²×C₂₃	—	4	1	no	—
214	C₄²×C₂₃	—	4	2	no	—
215	#29464	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₂₃	—	2	1	no	—
217	C₂³×C₂₃	—	2	1	no	—
218	C₂³×C₂₃	—	2	1	no	—
219	C₂³×C₂₃	—	2	1	no	—
220	C₂³×C₂₃	—	2	1	no	—
221	C₂³×C₂₃	—	2	1	no	—
222	C₂³×C₂₃	—	2	2	no	—
223	C₂³×C₂₃	—	4	1	no	—
224	C₂³×C₂₃	—	4	1	no	—
225	C₂³×C₂₃	—	4	1	no	—
226	C₂³×C₂₃	—	4	1	no	—
227	C₂³×C₂₃	—	4	1	no	—
228	C₂³×C₂₃	—	4	1	no	—
229	C₂³×C₂₃	C₂×SD₁₆	1	2	yes	—
230	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₂₃	—	4	1	no	—
232	Q₈×C₂₃	—	4	1	no	—
233	Q₈×C₂₃	—	4	1	no	—
234	Q₈×C₂₃	—	4	1	no	—
235	D₄×C₂₃	—	2	2	no	—
236	D₄×C₂₃	—	2	2	no	—
237	D₄×C₂₃	—	4	8	no	—
238	D₄×C₂₃	—	4	1	no	—
239	D₄×C₂₃	—	4	1	no	—
240	C₂×C₄×C₂₃	—	2	1	no	—
241	C₂×C₄×C₂₃	—	2	1	no	—
242	C₂×C₄×C₂₃	—	2	1	no	—
243	C₂×C₄×C₂₃	—	2	1	no	—
244	C₂×C₄×C₂₃	—	2	1	no	—
245	C₂×C₄×C₂₃	—	2	1	no	—
246	C₂×C₄×C₂₃	—	2	1	no	—
247	C₂×C₄×C₂₃	—	2	2	no	—
248	C₂×C₄×C₂₃	—	2	1	no	—
249	C₂×C₄×C₂₃	—	2	1	no	—
250	C₂×C₄×C₂₃	—	2	1	no	—
251	C₂×C₄×C₂₃	—	2	1	no	—
252	C₂×C₄×C₂₃	—	2	1	no	—
253	C₂×C₄×C₂₃	—	4	4	no	—
254	C₂×C₄×C₂₃	—	4	4	no	—
255	C₂×C₄×C₂₃	—	4	1	no	—
256	C₂×C₄×C₂₃	—	4	1	no	—
257	C₂×C₄×C₂₃	—	4	1	no	—
258	C₂×C₄×C₂₃	—	4	1	no	—
259	C₂×C₄×C₂₃	—	4	1	no	—
260	C₂×C₄×C₂₃	—	4	1	no	—
261	C₂×C₄×C₂₃	—	4	1	no	—
262	C₂×C₄×C₂₃	—	4	1	no	—
263	C₂×C₄×C₂₃	—	4	1	no	—
264	C₂×C₄×C₂₃	—	4	1	no	—
265	C₂×C₄×C₂₃	—	4	1	no	—
266	C₂×C₄×C₂₃	—	4	1	no	—
267	C₂×C₄×C₂₃	—	4	1	no	—
268	C₂×C₄×C₂₃	—	4	1	no	—
269	C₂×C₄×C₂₃	—	4	1	no	—
270	C₂×C₄×C₂₃	—	4	1	no	—
271	C₂×C₄×C₂₃	—	4	1	no	—
272	C₂×C₄×C₂₃	—	4	1	no	—
273	C₂×C₄×C₂₃	—	4	1	no	—
274	C₂×C₄×C₂₃	—	4	1	no	—
275	C₂×C₄×C₂₃	—	4	1	no	—
276	C₂×C₄×C₂₃	—	4	1	no	—
277	C₂×C₄×C₂₃	—	4	1	no	—
278	C₂×C₄×C₂₃	—	4	1	no	—
279	C₂×C₄×C₂₃	—	8	4	no	—
280	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
281	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
282	C₂×C₄×C₂₃	#135	1	2	yes	—
283	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
289	C₈×C₂₃	—	2	2	no	—
290	C₈×C₂₃	—	2	2	no	—
291	C₈×C₂₃	—	4	1	no	—
292	C₈×C₂₃	—	4	1	no	—
293	#2855	C₂×C₂₃	1	1	yes	characteristic, complemented
294	C₄×#121	C₂×C₂₃	1	1	yes	characteristic
295	#2077	C₂×C₂₃	1	1	yes	characteristic, complemented
296	#2035	C₂×C₂₃	1	1	yes	characteristic, complemented
297	#2034	C₂×C₂₃	1	1	yes	characteristic
298	#2000	C₂×C₂₃	1	1	yes	characteristic
299	#1968	C₂×C₂₃	1	1	yes	characteristic, complemented
300	#1941	C₂×C₂₃	1	1	yes	characteristic, complemented
301	#1934	C₂×C₂₃	1	1	yes	characteristic, complemented
302	#1933	C₂×C₂₃	1	1	yes	characteristic, complemented
303	#1927	C₂×C₂₃	1	1	yes	characteristic, complemented
304	#1920	C₂×C₂₃	1	1	yes	characteristic, complemented
305	#1877	C₂×C₂₃	1	1	yes	characteristic, complemented
306	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
307	C₄×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
308	C₂²×C₂₃	—	2	2	no	—
309	C₂²×C₂₃	—	2	2	no	—
310	C₂²×C₂₃	—	2	2	no	—
311	C₂²×C₂₃	—	4	1	no	—
312	C₂²×C₂₃	—	4	1	no	—
313	C₂²×C₂₃	—	4	1	no	—
314	C₂²×C₂₃	—	4	1	no	—
315	C₂²×C₂₃	—	4	2	no	—
316	C₂²×C₂₃	—	4	2	no	—
317	C₂²×C₂₃	—	4	2	no	—
318	C₂²×C₂₃	—	8	1	no	—
319	C₂²×C₂₃	—	8	1	no	—
320	C₂²×C₂₃	—	8	1	no	—
321	C₂²×C₂₃	—	8	1	no	—
322	C₂²×C₂₃	#525	1	1	yes	characteristic
323	C₂²×C₂₃	#532	1	1	yes	characteristic
324	C₂²×C₂₃	#534	1	1	yes	characteristic
325	C₂²×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
326	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
327	C₂²×C₂₃	#575	1	1	yes	characteristic
328	C₂²×C₂₃	#575	1	1	yes	characteristic
329	C₄×C₂₃	—	2	2	no	—
330	C₄×C₂₃	—	2	2	no	—
331	C₄×C₂₃	—	2	2	no	—
332	C₄×C₂₃	—	4	2	no	—
333	C₄×C₂₃	—	4	1	no	—
334	C₄×C₂₃	—	4	1	no	—
335	C₄×C₂₃	—	8	1	no	—
336	C₄×C₂₃	—	8	1	no	—
337	C₄×C₂₃	—	8	1	no	—
338	C₄×C₂₃	—	8	1	no	—
339	C₄×C₂₃	—	8	1	no	—
340	C₄×C₂₃	—	8	1	no	—
341	C₄×C₂₃	#551	1	1	yes	characteristic
342	C₄×C₂₃	#553	1	1	yes	characteristic
343	C₄×C₂₃	#553	1	1	yes	characteristic
344	C₄×C₂₃	#559	1	1	yes	characteristic
345	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
346	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
347	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
348	C₂×C₄×D₄	—	2	1	no	—
349	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
350	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
351	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
352	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
353	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
354	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
355	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
356	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
357	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
358	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
359	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
360	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
361	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
362	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
363	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
364	#391	C₂²×C₂₃	1	1	yes	characteristic
365	#391	C₂²×C₂₃	1	1	yes	characteristic
366	#390	C₂²×C₂₃	1	1	yes	characteristic
367	#389	C₂²×C₂₃	1	1	yes	characteristic
368	#389	C₂²×C₂₃	1	1	yes	characteristic
369	#389	C₂²×C₂₃	1	1	yes	characteristic
370	#388	—	2	1	no	—
371	#387	—	2	1	no	—
372	#387	—	2	1	no	—
373	#386	—	2	1	no	—
374	#385	—	2	1	no	—
375	#381	—	2	1	no	—
376	#380	C₂²×C₂₃	1	1	yes	characteristic
377	#380	C₂²×C₂₃	1	1	yes	characteristic
378	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
379	C₄×C₂²⋊C₄	—	2	1	no	—
380	#340	C₂²×C₂₃	1	1	yes	characteristic
381	#340	C₂²×C₂₃	1	1	yes	characteristic
382	#340	C₂²×C₂₃	1	1	yes	characteristic
383	#340	C₂²×C₂₃	1	1	yes	characteristic
384	#340	C₂²×C₂₃	1	1	yes	characteristic
385	#340	C₂²×C₂₃	1	1	yes	characteristic
386	#336	C₂²×C₂₃	1	1	yes	characteristic
387	#336	C₂²×C₂₃	1	1	yes	characteristic
388	C₂×C₂₃	—	4	2	no	—
389	C₂×C₂₃	—	8	2	no	—
390	C₂×C₂₃	#2602	1	1	yes	characteristic
391	C₂×C₂₃	#3101	1	1	yes	characteristic
392	C₂×C₂₃	#3102	1	1	yes	characteristic
393	C₂×C₂₃	#3167	1	1	yes	characteristic
394	C₂×C₂₃	#3183	1	1	yes	characteristic
395	C₂×C₂₃	#3187	1	1	yes	characteristic
396	C₂×C₂₃	#3191	1	1	yes	characteristic
397	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
398	C₂²×D₄	—	2	1	no	—
399	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
402	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
404	C₂×SD₁₆	—	2	2	no	—
405	C₂×SD₁₆	—	2	2	no	—
406	C₂×SD₁₆	—	4	1	no	—
407	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
411	C₂²⋊Q₈	—	4	1	no	—
412	C₂²⋊Q₈	—	4	1	no	—
413	#121	—	2	2	no	—
414	#121	—	2	2	no	—
415	C₄×D₄	—	4	1	no	—
416	C₄×D₄	—	4	1	no	—
417	C₄×D₄	—	4	4	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	4	1	no	—
437	C₂×C₄²	—	4	1	no	—
438	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
439	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
442	#106	—	2	2	no	—
443	#106	—	2	2	no	—
444	#106	—	4	1	no	—
445	#103	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	4	1	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	#102	—	4	1	no	—
451	C₂²⋊C₈	—	2	2	no	—
452	C₂²⋊C₈	—	2	2	no	—
453	C₄×C₈	—	4	1	no	—
454	C₄×C₈	—	4	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	C₂₃	#29464	1	1	yes	characteristic, direct product factor, Sylow
466	C₂⁴	—	2	1	no	—
467	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	4	2	no	—
481	C₂×D₄	—	4	2	no	—
482	C₂×D₄	#41×C₂₃	1	2	yes	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	4	1	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	SD₁₆×C₂₃	1	4	yes	complemented
505	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
510	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
511	SD₁₆	—	4	4	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	#41×C₂₃	1	2	yes	—
523	C₂×C₈	#41×C₂₃	1	2	yes	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	#41×C₂₃	1	2	yes	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	4	2	no	—
542	C₂²⋊C₄	—	4	2	no	—
543	C₂²⋊C₄	—	4	2	no	—
544	C₂²⋊C₄	—	4	2	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	4	1	no	—
552	C₄²	—	4	1	no	—
553	C₄²	—	4	2	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	C₂×SD₁₆×C₂₃	1	2	yes	—
568	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	4	8	no	—
576	D₄	—	4	1	no	—
577	D₄	—	4	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	8	4	no	—
618	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
619	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
620	C₂×C₄	C₂₃×#135	1	2	yes	—
621	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
622	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
624	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
625	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
626	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
627	C₈	—	2	2	no	—
628	C₈	—	2	2	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	C₂₃×#525	1	1	yes	characteristic
646	C₂²	C₂₃×#532	1	1	yes	characteristic
647	C₂²	C₂₃×#534	1	1	yes	characteristic
648	C₂²	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
649	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
650	C₂²	C₂₃×#575	1	1	yes	characteristic
651	C₂²	C₂₃×#575	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	1	no	—
658	C₄	—	8	1	no	—
659	C₄	—	8	1	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	C₂₃×#551	1	1	yes	characteristic
665	C₄	C₂₃×#553	1	1	yes	characteristic
666	C₄	C₂₃×#553	1	1	yes	characteristic
667	C₄	C₂₃×#559	1	1	yes	characteristic
668	C₂	—	4	2	no	—
669	C₂	—	8	2	no	—
670	C₂	C₂₃×#2602	1	1	yes	characteristic
671	C₂	C₂₃×#3101	1	1	yes	characteristic
672	C₂	C₂₃×#3102	1	1	yes	characteristic
673	C₂	C₂₃×#3167	1	1	yes	characteristic
674	C₂	C₂₃×#3183	1	1	yes	characteristic
675	C₂	C₂₃×#3187	1	1	yes	characteristic
676	C₂	C₂₃×#3191	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2855	C₂	semidirect
3. C₂₃×#2077	C₂	semidirect
4. C₂₃×#2035	C₂	semidirect
7. C₂₃×#1968	C₂	semidirect
8. C₂₃×#1941	C₂	semidirect
9. C₂₃×#1934	C₂	semidirect
10. C₂₃×#1933	C₂	semidirect
11. C₂₃×#1927	C₂	semidirect
12. C₂₃×#1920	C₂	semidirect
13. C₂₃×#1877	C₂	semidirect
14. C₂₃×#1864	C₂	semidirect
15. C₄×C₂₃×C₂²⋊C₈	C₂	semidirect
165. C₂²×C₄×C₂₃	SD₁₆	semidirect
215. #29464	C₂₃	direct (N × H)
293. #2855	C₂×C₂₃	semidirect
295. #2077	C₂×C₂₃	semidirect
296. #2035	C₂×C₂₃	semidirect
299. #1968	C₂×C₂₃	semidirect
300. #1941	C₂×C₂₃	semidirect
301. #1934	C₂×C₂₃	semidirect
302. #1933	C₂×C₂₃	semidirect
303. #1927	C₂×C₂₃	semidirect
304. #1920	C₂×C₂₃	semidirect
305. #1877	C₂×C₂₃	semidirect
306. #1864	C₂×C₂₃	semidirect
307. C₄×C₂²⋊C₈	C₂×C₂₃	semidirect
465. C₂₃	#29464	direct (N × H)
504. C₂²×C₄	SD₁₆×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#2855	2
C₄×C₂₃×#121	2
C₂₃×#2077	2
C₂₃×#2035	2
C₂₃×#2034	2
C₂₃×#2000	2
C₂₃×#1968	2
C₂₃×#1941	2
C₂₃×#1934	2
C₂₃×#1933	2
C₂₃×#1927	2
C₂₃×#1920	2
C₂₃×#1877	2
C₂₃×#1864	2
C₄×C₂₃×C₂²⋊C₈	2
#29464	23

Subgroups — C23×#29464 #19177090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#29464 #19177090