Subgroups — C₂₃×#21524 #19169150

Order 5888.

1066 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2324	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1936	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1895	C₂	1	2	yes	maximal, complemented
9	C₂₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1762	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
17	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
18	C₂₃×#466	C₄	1	8	yes	complemented
19	C₄×D₈×C₂₃	—	2	4	no	—
20	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#102	C₂²	1	2	yes	—
24	C₂×C₂₃×#102	C₂²	1	2	yes	—
25	C₂×C₂₃×#102	C₂²	1	2	yes	—
26	C₂₃×#405	—	2	4	no	—
27	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#390	—	2	2	no	—
32	C₂₃×#390	C₂²	1	2	yes	—
33	C₂₃×#389	C₂²	1	2	yes	—
34	C₂₃×#388	—	2	2	no	—
35	C₂₃×#386	—	2	2	no	—
36	C₂₃×#385	—	2	2	no	—
37	C₂₃×#380	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂₃×#340	C₂²	1	2	yes	—
41	C₂₃×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₂₃	—	2	2	no	—
43	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₂₃	—	2	2	no	—
45	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
46	C₂×D₈×C₂₃	—	2	2	no	—
47	C₂×D₈×C₂₃	—	2	2	no	—
48	C₂×D₈×C₂₃	C₂×C₄	1	4	yes	—
49	C₂×M₁₆×C₂₃	—	2	2	no	—
50	C₂×M₁₆×C₂₃	—	2	2	no	—
51	C₂×M₁₆×C₂₃	—	2	2	no	—
52	C₂²×C₈×C₂₃	—	2	2	no	—
53	C₂²×C₈×C₂₃	—	2	2	no	—
54	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	complemented
55	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
59	C₂₃×#121	—	2	4	no	—
60	C₂₃×#121	C₂×C₄	1	8	yes	complemented
61	C₄×D₄×C₂₃	—	2	4	no	—
62	C₄×D₄×C₂₃	—	2	4	no	—
63	C₂₃×#117	—	2	2	no	—
64	C₂₃×#117	—	2	2	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₂₃	—	2	2	no	—
79	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
81	C₂₃×#107	—	2	2	no	—
82	C₂₃×#107	—	2	2	no	—
83	C₂₃×#107	C₂×C₄	1	4	yes	complemented
84	C₂₃×#102	—	2	4	no	—
85	C₂₃×#102	—	2	4	no	—
86	C₂₃×#102	C₂×C₄	1	8	yes	complemented
87	C₂₃×#97	—	2	2	no	—
88	C₂₃×#97	—	2	2	no	—
89	C₄×C₈×C₂₃	—	2	2	no	—
90	C₄×C₈×C₂₃	D₄	1	4	yes	complemented
91	C₂₃×#95	—	2	2	no	—
92	C₂₃×#95	—	2	2	no	—
93	C₂₃×#95	—	2	2	no	—
94	C₂⁴×C₂₃	—	2	2	no	—
95	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
96	C₂×D₄×C₂₃	—	2	8	no	—
97	C₂×D₄×C₂₃	—	2	2	no	—
98	C₂×D₄×C₂₃	—	2	2	no	—
99	C₂×D₄×C₂₃	—	2	2	no	—
100	C₂×D₄×C₂₃	—	2	2	no	—
101	C₂×D₄×C₂₃	—	2	2	no	—
102	C₂×D₄×C₂₃	—	8	2	no	—
103	C₂×D₄×C₂₃	—	8	2	no	—
104	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₂₃	—	2	1	no	—
106	C₂²×C₄×C₂₃	—	2	1	no	—
107	C₂²×C₄×C₂₃	—	2	1	no	—
108	C₂²×C₄×C₂₃	—	2	1	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	—	4	4	no	—
113	C₂²×C₄×C₂₃	—	8	2	no	—
114	C₂²×C₄×C₂₃	—	8	2	no	—
115	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₃	#41	1	2	yes	—
122	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
123	D₈×C₂₃	—	2	8	no	—
124	M₁₆×C₂₃	—	2	8	no	—
125	C₂×C₈×C₂₃	—	2	1	no	—
126	C₂×C₈×C₂₃	—	2	1	no	—
127	C₂×C₈×C₂₃	—	2	1	no	—
128	C₂×C₈×C₂₃	—	2	1	no	—
129	C₂×C₈×C₂₃	—	2	1	no	—
130	C₂×C₈×C₂₃	—	2	1	no	—
131	C₂×C₈×C₂₃	—	2	8	no	—
132	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₂₃	#41	1	2	yes	—
137	C₂×C₈×C₂₃	#41	1	2	yes	—
138	C₄⋊C₄×C₂₃	—	2	2	no	—
139	C₄⋊C₄×C₂₃	—	2	2	no	—
140	C₄⋊C₄×C₂₃	—	2	2	no	—
141	C₄⋊C₄×C₂₃	—	2	2	no	—
142	C₄⋊C₄×C₂₃	—	2	2	no	—
143	C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₄⋊C₄×C₂₃	—	2	2	no	—
145	C₄⋊C₄×C₂₃	—	8	2	no	—
146	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
147	C₂²⋊C₄×C₂₃	—	2	8	no	—
148	C₂²⋊C₄×C₂₃	—	2	2	no	—
149	C₂²⋊C₄×C₂₃	—	2	2	no	—
150	C₂²⋊C₄×C₂₃	—	4	4	no	—
151	C₂²⋊C₄×C₂₃	—	8	2	no	—
152	C₂²⋊C₄×C₂₃	—	8	2	no	—
153	C₂²⋊C₄×C₂₃	—	8	2	no	—
154	C₄²×C₂₃	—	2	1	no	—
155	C₄²×C₂₃	—	2	1	no	—
156	C₄²×C₂₃	—	8	2	no	—
157	C₄²×C₂₃	C₂×D₄	1	2	yes	—
158	C₄²×C₂₃	#41	1	2	yes	—
159	#21524	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₂₃	—	2	1	no	—
161	C₂³×C₂₃	—	2	1	no	—
162	C₂³×C₂₃	—	2	1	no	—
163	C₂³×C₂₃	—	2	1	no	—
164	C₂³×C₂₃	—	2	1	no	—
165	C₂³×C₂₃	—	2	1	no	—
166	C₂³×C₂₃	—	2	4	no	—
167	C₂³×C₂₃	—	4	2	no	—
168	C₂³×C₂₃	—	4	2	no	—
169	C₂³×C₂₃	—	4	2	no	—
170	C₂³×C₂₃	—	4	2	no	—
171	C₂³×C₂₃	—	4	2	no	—
172	C₂³×C₂₃	—	4	2	no	—
173	C₂³×C₂₃	C₄×D₄	1	2	yes	—
174	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
175	D₄×C₂₃	—	2	4	no	—
176	D₄×C₂₃	—	2	4	no	—
177	D₄×C₂₃	—	4	2	no	—
178	D₄×C₂₃	—	4	2	no	—
179	D₄×C₂₃	—	8	8	no	—
180	C₂×C₄×C₂₃	—	2	1	no	—
181	C₂×C₄×C₂₃	—	2	1	no	—
182	C₂×C₄×C₂₃	—	2	1	no	—
183	C₂×C₄×C₂₃	—	2	1	no	—
184	C₂×C₄×C₂₃	—	2	1	no	—
185	C₂×C₄×C₂₃	—	2	1	no	—
186	C₂×C₄×C₂₃	—	2	2	no	—
187	C₂×C₄×C₂₃	—	2	2	no	—
188	C₂×C₄×C₂₃	—	2	2	no	—
189	C₂×C₄×C₂₃	—	2	2	no	—
190	C₂×C₄×C₂₃	—	2	4	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	—	4	2	no	—
198	C₂×C₄×C₂₃	—	4	2	no	—
199	C₂×C₄×C₂₃	—	4	2	no	—
200	C₂×C₄×C₂₃	—	4	2	no	—
201	C₂×C₄×C₂₃	—	4	2	no	—
202	C₂×C₄×C₂₃	—	4	2	no	—
203	C₂×C₄×C₂₃	—	4	2	no	—
204	C₂×C₄×C₂₃	—	4	2	no	—
205	C₂×C₄×C₂₃	—	8	8	no	—
206	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₂₃	#121	1	2	yes	—
208	C₂×C₄×C₂₃	#121	1	2	yes	—
209	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
215	C₈×C₂₃	—	2	2	no	—
216	C₈×C₂₃	—	2	2	no	—
217	C₈×C₂₃	—	2	2	no	—
218	C₈×C₂₃	C₄×D₄	1	4	yes	—
219	C₂×#466	C₂×C₂₃	1	1	yes	characteristic
220	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
221	C₂×#405	C₂×C₂₃	1	1	yes	characteristic, complemented
222	#2324	C₂×C₂₃	1	2	yes	complemented
223	#1970	C₂×C₂₃	1	1	yes	characteristic, complemented
224	#1942	C₂×C₂₃	1	1	yes	characteristic, complemented
225	#1936	C₂×C₂₃	1	2	yes	complemented
226	#1895	C₂×C₂₃	1	2	yes	complemented
227	#1808	C₂×C₂₃	1	1	yes	characteristic, complemented
228	C₄×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
229	#1762	C₂×C₂₃	1	2	yes	complemented
230	C₂²×C₂₃	—	2	2	no	—
231	C₂²×C₂₃	—	2	2	no	—
232	C₂²×C₂₃	—	2	2	no	—
233	C₂²×C₂₃	—	4	1	no	—
234	C₂²×C₂₃	—	4	1	no	—
235	C₂²×C₂₃	—	4	1	no	—
236	C₂²×C₂₃	—	4	1	no	—
237	C₂²×C₂₃	—	4	4	no	—
238	C₂²×C₂₃	—	4	4	no	—
239	C₂²×C₂₃	—	4	4	no	—
240	C₂²×C₂₃	—	8	2	no	—
241	C₂²×C₂₃	—	8	2	no	—
242	C₂²×C₂₃	—	8	2	no	—
243	C₂²×C₂₃	—	8	2	no	—
244	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
246	C₂²×C₂₃	#532	1	1	yes	characteristic
247	C₂²×C₂₃	#576	1	1	yes	characteristic
248	C₂²×C₂₃	#576	1	1	yes	characteristic
249	C₂²×C₂₃	#576	1	1	yes	characteristic
250	C₂²×C₂₃	#578	1	1	yes	characteristic
251	C₄×C₂₃	—	2	2	no	—
252	C₄×C₂₃	—	2	2	no	—
253	C₄×C₂₃	—	2	2	no	—
254	C₄×C₂₃	—	4	4	no	—
255	C₄×C₂₃	—	4	1	no	—
256	C₄×C₂₃	—	4	1	no	—
257	C₄×C₂₃	—	8	2	no	—
258	C₄×C₂₃	—	8	2	no	—
259	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
260	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
261	C₄×C₂₃	#525	1	1	yes	characteristic
262	C₄×C₂₃	#529	1	1	yes	characteristic
263	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
264	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
265	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
266	C₂×#121	C₂²×C₂₃	1	2	yes	—
267	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
268	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
269	#466	C₄×C₂₃	1	8	yes	complemented
270	C₄×D₈	—	2	4	no	—
271	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
272	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
273	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
274	C₂×#102	C₂²×C₂₃	1	2	yes	—
275	C₂×#102	C₂²×C₂₃	1	2	yes	—
276	C₂×#102	C₂²×C₂₃	1	2	yes	—
277	#405	—	2	4	no	—
278	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
279	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
281	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
282	#390	—	2	2	no	—
283	#390	C₂²×C₂₃	1	2	yes	—
284	#389	C₂²×C₂₃	1	2	yes	—
285	#388	—	2	2	no	—
286	#386	—	2	2	no	—
287	#385	—	2	2	no	—
288	#380	C₂²×C₂₃	1	2	yes	—
289	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
290	#340	C₂²×C₂₃	1	2	yes	—
291	#340	C₂²×C₂₃	1	2	yes	—
292	#340	C₂²×C₂₃	1	2	yes	—
293	C₂×C₂₃	—	4	2	no	—
294	C₂×C₂₃	—	8	4	no	—
295	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
296	C₂×C₂₃	#2948	1	1	yes	characteristic
297	C₂×C₂₃	#2951	1	1	yes	characteristic
298	C₂×C₂₃	#3058	1	1	yes	characteristic
299	C₂×C₂₃	#3061	1	1	yes	characteristic
300	C₂×C₂₃	#3175	1	1	yes	characteristic
301	C₂×C₂₃	#3176	1	1	yes	characteristic
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
306	C₂×D₈	—	2	2	no	—
307	C₂×D₈	—	2	2	no	—
308	C₂×D₈	C₂×C₄×C₂₃	1	4	yes	—
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	complemented
315	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
319	#121	—	2	4	no	—
320	#121	C₂×C₄×C₂₃	1	8	yes	complemented
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	—	2	4	no	—
323	#117	—	2	2	no	—
324	#117	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
341	#107	—	2	2	no	—
342	#107	—	2	2	no	—
343	#107	C₂×C₄×C₂₃	1	4	yes	complemented
344	#102	—	2	4	no	—
345	#102	—	2	4	no	—
346	#102	C₂×C₄×C₂₃	1	8	yes	complemented
347	#97	—	2	2	no	—
348	#97	—	2	2	no	—
349	C₄×C₈	—	2	2	no	—
350	C₄×C₈	D₄×C₂₃	1	4	yes	complemented
351	#95	—	2	2	no	—
352	#95	—	2	2	no	—
353	#95	—	2	2	no	—
354	C₂₃	#21524	1	1	yes	characteristic, direct product factor, Sylow
355	C₂⁴	—	2	2	no	—
356	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂×D₄	—	8	2	no	—
365	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	8	2	no	—
375	C₂²×C₄	—	8	2	no	—
376	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
382	C₂²×C₄	#41×C₂₃	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
384	D₈	—	2	8	no	—
385	M₁₆	—	2	8	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	8	no	—
393	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
394	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
395	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
396	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
397	C₂×C₈	#41×C₂₃	1	2	yes	—
398	C₂×C₈	#41×C₂₃	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	8	2	no	—
407	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	8	2	no	—
413	C₂²⋊C₄	—	8	2	no	—
414	C₂²⋊C₄	—	8	2	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	8	2	no	—
418	C₄²	C₂×D₄×C₂₃	1	2	yes	—
419	C₄²	#41×C₂₃	1	2	yes	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	C₄×D₄×C₂₃	1	2	yes	—
434	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
435	D₄	—	2	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	8	8	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	8	8	no	—
466	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
467	C₂×C₄	C₂₃×#121	1	2	yes	—
468	C₂×C₄	C₂₃×#121	1	2	yes	—
469	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	C₄×D₄×C₂₃	1	4	yes	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
494	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
495	C₂²	C₂₃×#532	1	1	yes	characteristic
496	C₂²	C₂₃×#576	1	1	yes	characteristic
497	C₂²	C₂₃×#576	1	1	yes	characteristic
498	C₂²	C₂₃×#576	1	1	yes	characteristic
499	C₂²	C₂₃×#578	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	1	no	—
506	C₄	—	8	2	no	—
507	C₄	—	8	2	no	—
508	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
509	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
510	C₄	C₂₃×#525	1	1	yes	characteristic
511	C₄	C₂₃×#529	1	1	yes	characteristic
512	C₂	—	4	2	no	—
513	C₂	—	8	4	no	—
514	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
515	C₂	C₂₃×#2948	1	1	yes	characteristic
516	C₂	C₂₃×#2951	1	1	yes	characteristic
517	C₂	C₂₃×#3058	1	1	yes	characteristic
518	C₂	C₂₃×#3061	1	1	yes	characteristic
519	C₂	C₂₃×#3175	1	1	yes	characteristic
520	C₂	C₂₃×#3176	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₂₃	C₂	semidirect
3. C₂×C₂₃×#405	C₂	semidirect
4. C₂₃×#2324	C₂	semidirect
5. C₂₃×#1970	C₂	semidirect
6. C₂₃×#1942	C₂	semidirect
7. C₂₃×#1936	C₂	semidirect
8. C₂₃×#1895	C₂	semidirect
9. C₂₃×#1808	C₂	semidirect
10. C₄×C₂₃×#107	C₂	semidirect
11. C₂₃×#1762	C₂	semidirect
18. C₂₃×#466	C₄	semidirect
54. C₂²×C₈×C₂₃	C₂×C₄	semidirect
60. C₂₃×#121	C₂×C₄	semidirect
83. C₂₃×#107	C₂×C₄	semidirect
86. C₂₃×#102	C₂×C₄	semidirect
90. C₄×C₈×C₂₃	D₄	semidirect
159. #21524	C₂₃	direct (N × H)
220. C₂×C₄×D₈	C₂×C₂₃	semidirect
221. C₂×#405	C₂×C₂₃	semidirect
222. #2324	C₂×C₂₃	semidirect
223. #1970	C₂×C₂₃	semidirect
224. #1942	C₂×C₂₃	semidirect
225. #1936	C₂×C₂₃	semidirect
226. #1895	C₂×C₂₃	semidirect
227. #1808	C₂×C₂₃	semidirect
228. C₄×#107	C₂×C₂₃	semidirect
229. #1762	C₂×C₂₃	semidirect
269. #466	C₄×C₂₃	semidirect
314. C₂²×C₈	C₂×C₄×C₂₃	semidirect
320. #121	C₂×C₄×C₂₃	semidirect
343. #107	C₂×C₄×C₂₃	semidirect
346. #102	C₂×C₄×C₂₃	semidirect
350. C₄×C₈	D₄×C₂₃	semidirect
354. C₂₃	#21524	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×#466	2
C₂×C₄×D₈×C₂₃	2
C₂×C₂₃×#405	2
C₂₃×#2324	2
C₂₃×#1970	2
C₂₃×#1942	2
C₂₃×#1936	2
C₂₃×#1895	2
C₂₃×#1808	2
C₄×C₂₃×#107	2
C₂₃×#1762	2
#21524	23

Subgroups — C23×#21524 #19169150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21524 #19169150