Subgroups — C₂₃×#21525 #19169151

Order 5888.

954 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2323	C₂	1	2	yes	maximal
5	C₂₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1935	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1894	C₂	1	2	yes	maximal
9	C₂₃×#1808	C₂	1	1	yes	maximal, characteristic
10	C₄×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×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×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
17	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
18	C₂₃×#467	C₄	1	8	yes	complemented
19	C₄×Q₁₆×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×#103	C₂²	1	2	yes	—
24	C₂×C₂₃×#103	C₂²	1	2	yes	—
25	C₂×C₂₃×#103	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×#391	C₂²	1	2	yes	—
32	C₂₃×#389	—	2	2	no	—
33	C₂₃×#389	C₂²	1	2	yes	—
34	C₂₃×#388	—	2	2	no	—
35	C₂₃×#388	—	2	2	no	—
36	C₂₃×#387	—	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×Q₈×C₂₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₂₃	—	2	2	no	—
45	C₂×Q₁₆×C₂₃	—	2	2	no	—
46	C₂×Q₁₆×C₂₃	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₂₃	—	2	2	no	—
48	C₂×M₁₆×C₂₃	—	2	2	no	—
49	C₂×M₁₆×C₂₃	—	2	2	no	—
50	C₂²×C₈×C₂₃	—	2	2	no	—
51	C₂²×C₈×C₂₃	—	2	2	no	—
52	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
57	C₂₃×C₂²⋊Q₈	—	2	4	no	—
58	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
59	C₄×Q₈×C₂₃	—	2	4	no	—
60	C₄×Q₈×C₂₃	—	2	4	no	—
61	C₂₃×#117	—	2	2	no	—
62	C₂₃×#117	—	2	2	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₂₃	—	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	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₂₃	—	2	2	no	—
76	C₂×C₄²×C₂₃	—	2	2	no	—
77	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
79	C₂₃×#107	—	2	2	no	—
80	C₂₃×#107	—	2	2	no	—
81	C₂₃×#107	C₂×C₄	1	4	yes	—
82	C₂₃×#103	—	2	4	no	—
83	C₂₃×#103	—	2	4	no	—
84	C₂₃×#103	C₂×C₄	1	8	yes	—
85	C₂₃×#97	—	2	2	no	—
86	C₂₃×#97	—	2	2	no	—
87	C₄×C₈×C₂₃	—	2	2	no	—
88	C₄×C₈×C₂₃	D₄	1	4	yes	—
89	C₂₃×#95	—	2	2	no	—
90	C₂₃×#95	—	2	2	no	—
91	C₂₃×#95	—	2	2	no	—
92	C₂₃×#95	—	2	2	no	—
93	C₂₃×#95	—	2	2	no	—
94	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₂₃	—	2	2	no	—
96	C₂×Q₈×C₂₃	—	2	2	no	—
97	C₂×Q₈×C₂₃	—	2	2	no	—
98	C₂×Q₈×C₂₃	—	2	2	no	—
99	C₂×Q₈×C₂₃	—	2	2	no	—
100	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₂₃	—	2	1	no	—
102	C₂²×C₄×C₂₃	—	2	1	no	—
103	C₂²×C₄×C₂₃	—	2	1	no	—
104	C₂²×C₄×C₂₃	—	2	1	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	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₂₃	#41	1	2	yes	—
116	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₂₃	—	2	8	no	—
118	M₁₆×C₂₃	—	2	8	no	—
119	C₂×C₈×C₂₃	—	2	1	no	—
120	C₂×C₈×C₂₃	—	2	1	no	—
121	C₂×C₈×C₂₃	—	2	1	no	—
122	C₂×C₈×C₂₃	—	2	1	no	—
123	C₂×C₈×C₂₃	—	2	1	no	—
124	C₂×C₈×C₂₃	—	2	1	no	—
125	C₂×C₈×C₂₃	—	2	8	no	—
126	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₂₃	#41	1	2	yes	—
131	C₂×C₈×C₂₃	#41	1	2	yes	—
132	C₄⋊C₄×C₂₃	—	2	8	no	—
133	C₄⋊C₄×C₂₃	—	2	2	no	—
134	C₄⋊C₄×C₂₃	—	2	2	no	—
135	C₄⋊C₄×C₂₃	—	2	2	no	—
136	C₄⋊C₄×C₂₃	—	2	2	no	—
137	C₄⋊C₄×C₂₃	—	2	2	no	—
138	C₄⋊C₄×C₂₃	—	2	2	no	—
139	C₄⋊C₄×C₂₃	—	2	2	no	—
140	C₄⋊C₄×C₂₃	—	4	4	no	—
141	C₄⋊C₄×C₂₃	—	8	2	no	—
142	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
143	C₂²⋊C₄×C₂₃	—	2	8	no	—
144	C₂²⋊C₄×C₂₃	—	2	2	no	—
145	C₂²⋊C₄×C₂₃	—	2	2	no	—
146	C₂²⋊C₄×C₂₃	—	8	2	no	—
147	C₄²×C₂₃	—	2	1	no	—
148	C₄²×C₂₃	—	2	1	no	—
149	C₄²×C₂₃	—	4	4	no	—
150	C₄²×C₂₃	—	8	2	no	—
151	C₄²×C₂₃	C₂×D₄	1	2	yes	—
152	C₄²×C₂₃	#41	1	2	yes	—
153	#21525	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₂₃	—	2	1	no	—
155	C₂³×C₂₃	—	2	1	no	—
156	C₂³×C₂₃	—	2	1	no	—
157	C₂³×C₂₃	—	2	1	no	—
158	C₂³×C₂₃	—	2	1	no	—
159	C₂³×C₂₃	—	2	1	no	—
160	C₂³×C₂₃	C₄×D₄	1	2	yes	—
161	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₂₃	—	2	4	no	—
163	Q₈×C₂₃	—	2	4	no	—
164	Q₈×C₂₃	—	4	2	no	—
165	Q₈×C₂₃	—	4	2	no	—
166	C₂×C₄×C₂₃	—	2	1	no	—
167	C₂×C₄×C₂₃	—	2	1	no	—
168	C₂×C₄×C₂₃	—	2	1	no	—
169	C₂×C₄×C₂₃	—	2	1	no	—
170	C₂×C₄×C₂₃	—	2	1	no	—
171	C₂×C₄×C₂₃	—	2	1	no	—
172	C₂×C₄×C₂₃	—	2	2	no	—
173	C₂×C₄×C₂₃	—	2	2	no	—
174	C₂×C₄×C₂₃	—	2	2	no	—
175	C₂×C₄×C₂₃	—	2	2	no	—
176	C₂×C₄×C₂₃	—	2	4	no	—
177	C₂×C₄×C₂₃	—	2	4	no	—
178	C₂×C₄×C₂₃	—	2	1	no	—
179	C₂×C₄×C₂₃	—	2	1	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	—	4	2	no	—
185	C₂×C₄×C₂₃	—	4	2	no	—
186	C₂×C₄×C₂₃	—	4	2	no	—
187	C₂×C₄×C₂₃	—	4	2	no	—
188	C₂×C₄×C₂₃	—	4	2	no	—
189	C₂×C₄×C₂₃	—	4	2	no	—
190	C₂×C₄×C₂₃	—	4	2	no	—
191	C₂×C₄×C₂₃	—	4	2	no	—
192	C₂×C₄×C₂₃	—	4	2	no	—
193	C₂×C₄×C₂₃	—	4	2	no	—
194	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₂₃	#121	1	2	yes	—
196	C₂×C₄×C₂₃	#121	1	2	yes	—
197	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
203	C₈×C₂₃	—	2	2	no	—
204	C₈×C₂₃	—	2	2	no	—
205	C₈×C₂₃	—	2	2	no	—
206	C₈×C₂₃	C₄×D₄	1	4	yes	—
207	C₂×#467	C₂×C₂₃	1	1	yes	characteristic
208	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
209	C₂×#405	C₂×C₂₃	1	1	yes	characteristic
210	#2323	C₂×C₂₃	1	2	yes	—
211	#1969	C₂×C₂₃	1	1	yes	characteristic, complemented
212	#1942	C₂×C₂₃	1	1	yes	characteristic, complemented
213	#1935	C₂×C₂₃	1	2	yes	complemented
214	#1894	C₂×C₂₃	1	2	yes	—
215	#1808	C₂×C₂₃	1	1	yes	characteristic
216	C₄×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
217	#1763	C₂×C₂₃	1	2	yes	complemented
218	C₂²×C₂₃	—	2	2	no	—
219	C₂²×C₂₃	—	2	2	no	—
220	C₂²×C₂₃	—	2	2	no	—
221	C₂²×C₂₃	—	4	1	no	—
222	C₂²×C₂₃	—	4	1	no	—
223	C₂²×C₂₃	—	4	1	no	—
224	C₂²×C₂₃	—	4	1	no	—
225	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
227	C₂²×C₂₃	#532	1	1	yes	characteristic
228	C₂²×C₂₃	#576	1	1	yes	characteristic
229	C₂²×C₂₃	#578	1	1	yes	characteristic
230	C₂²×C₂₃	#578	1	1	yes	characteristic
231	C₂²×C₂₃	#578	1	1	yes	characteristic
232	C₄×C₂₃	—	2	2	no	—
233	C₄×C₂₃	—	2	2	no	—
234	C₄×C₂₃	—	2	2	no	—
235	C₄×C₂₃	—	4	4	no	—
236	C₄×C₂₃	—	4	1	no	—
237	C₄×C₂₃	—	4	1	no	—
238	C₄×C₂₃	—	4	4	no	—
239	C₄×C₂₃	—	8	2	no	—
240	C₄×C₂₃	—	8	2	no	—
241	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
242	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
243	C₄×C₂₃	#525	1	1	yes	characteristic
244	C₄×C₂₃	#529	1	1	yes	characteristic
245	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
247	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
249	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
250	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
251	#467	C₄×C₂₃	1	8	yes	complemented
252	C₄×Q₁₆	—	2	4	no	—
253	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
254	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
255	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
256	C₂×#103	C₂²×C₂₃	1	2	yes	—
257	C₂×#103	C₂²×C₂₃	1	2	yes	—
258	C₂×#103	C₂²×C₂₃	1	2	yes	—
259	#405	—	2	4	no	—
260	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
261	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
262	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
264	#391	C₂²×C₂₃	1	2	yes	—
265	#389	—	2	2	no	—
266	#389	C₂²×C₂₃	1	2	yes	—
267	#388	—	2	2	no	—
268	#388	—	2	2	no	—
269	#387	—	2	2	no	—
270	#380	C₂²×C₂₃	1	2	yes	—
271	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
272	#340	C₂²×C₂₃	1	2	yes	—
273	#340	C₂²×C₂₃	1	2	yes	—
274	#340	C₂²×C₂₃	1	2	yes	—
275	C₂×C₂₃	—	4	2	no	—
276	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
277	C₂×C₂₃	#2950	1	1	yes	characteristic
278	C₂×C₂₃	#2951	1	1	yes	characteristic
279	C₂×C₂₃	#3059	1	1	yes	characteristic
280	C₂×C₂₃	#3061	1	1	yes	characteristic
281	C₂×C₂₃	#3175	1	1	yes	characteristic
282	C₂×C₂₃	#3177	1	1	yes	characteristic
283	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
284	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
285	C₂×Q₁₆	—	2	2	no	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	C₂×C₄×C₂₃	1	4	yes	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	—
294	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
300	C₄×Q₈	—	2	4	no	—
301	C₄×Q₈	—	2	4	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
308	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
320	#107	—	2	2	no	—
321	#107	—	2	2	no	—
322	#107	C₂×C₄×C₂₃	1	4	yes	—
323	#103	—	2	4	no	—
324	#103	—	2	4	no	—
325	#103	C₂×C₄×C₂₃	1	8	yes	—
326	#97	—	2	2	no	—
327	#97	—	2	2	no	—
328	C₄×C₈	—	2	2	no	—
329	C₄×C₈	D₄×C₂₃	1	4	yes	—
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	C₂₃	#21525	1	1	yes	characteristic, direct product factor, Sylow
336	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
357	C₂²×C₄	#41×C₂₃	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
359	Q₁₆	—	2	8	no	—
360	M₁₆	—	2	8	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	8	no	—
368	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
369	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
371	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
372	C₂×C₈	#41×C₂₃	1	2	yes	—
373	C₂×C₈	#41×C₂₃	1	2	yes	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	8	2	no	—
384	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	8	2	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	4	4	no	—
392	C₄²	—	8	2	no	—
393	C₄²	C₂×D₄×C₂₃	1	2	yes	—
394	C₄²	#41×C₂₃	1	2	yes	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	C₄×D₄×C₂₃	1	2	yes	—
402	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
436	C₂×C₄	C₂₃×#121	1	2	yes	—
437	C₂×C₄	C₂₃×#121	1	2	yes	—
438	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
444	C₈	—	2	2	no	—
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	C₄×D₄×C₂₃	1	4	yes	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
456	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
457	C₂²	C₂₃×#532	1	1	yes	characteristic
458	C₂²	C₂₃×#576	1	1	yes	characteristic
459	C₂²	C₂₃×#578	1	1	yes	characteristic
460	C₂²	C₂₃×#578	1	1	yes	characteristic
461	C₂²	C₂₃×#578	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	4	no	—
469	C₄	—	8	2	no	—
470	C₄	—	8	2	no	—
471	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
472	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
473	C₄	C₂₃×#525	1	1	yes	characteristic
474	C₄	C₂₃×#529	1	1	yes	characteristic
475	C₂	—	4	2	no	—
476	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
477	C₂	C₂₃×#2950	1	1	yes	characteristic
478	C₂	C₂₃×#2951	1	1	yes	characteristic
479	C₂	C₂₃×#3059	1	1	yes	characteristic
480	C₂	C₂₃×#3061	1	1	yes	characteristic
481	C₂	C₂₃×#3175	1	1	yes	characteristic
482	C₂	C₂₃×#3177	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	C₂⁴×C₂₃	C₂×D₄
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×Q₁₆×C₂₃	C₂	semidirect
5. C₂₃×#1969	C₂	semidirect
6. C₂₃×#1942	C₂	semidirect
7. C₂₃×#1935	C₂	semidirect
10. C₄×C₂₃×#107	C₂	semidirect
11. C₂₃×#1763	C₂	semidirect
18. C₂₃×#467	C₄	semidirect
153. #21525	C₂₃	direct (N × H)
208. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
211. #1969	C₂×C₂₃	semidirect
212. #1942	C₂×C₂₃	semidirect
213. #1935	C₂×C₂₃	semidirect
216. C₄×#107	C₂×C₂₃	semidirect
217. #1763	C₂×C₂₃	semidirect
251. #467	C₄×C₂₃	semidirect
335. C₂₃	#21525	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×#467	2
C₂×C₄×Q₁₆×C₂₃	2
C₂×C₂₃×#405	2
C₂₃×#2323	2
C₂₃×#1969	2
C₂₃×#1942	2
C₂₃×#1935	2
C₂₃×#1894	2
C₂₃×#1808	2
C₄×C₂₃×#107	2
C₂₃×#1763	2
#21525	23

Subgroups — C23×#21525 #19169151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21525 #19169151