Subgroups — C₂₃×#60862 #19208488

Order 5888.

1778 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3240	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3231	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3228	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3165	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3141	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3093	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3080	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#533	—	2	2	no	—
12	C₂₃×#533	—	2	2	no	—
13	C₂₃×#533	C₂²	1	2	yes	—
14	C₂₃×#533	C₂²	1	1	yes	characteristic
15	C₂₃×#533	C₂²	1	4	yes	—
16	C₂₃×#533	C₂²	1	4	yes	—
17	C₂₃×#532	C₂²	1	1	yes	characteristic
18	C₂₃×#532	C₂²	1	2	yes	—
19	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂₃×#529	—	2	2	no	—
21	C₂₃×#529	—	2	2	no	—
22	C₂₃×#529	C₂²	1	4	yes	—
23	C₂×C₂₃×#125	C₂²	1	2	yes	—
24	C₂₃×#525	—	2	2	no	—
25	C₂₃×#525	C₂²	1	2	yes	—
26	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
27	C₄×#41×C₂₃	—	2	2	no	—
28	C₄×#41×C₂₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
30	C₂×C₂₃×#117	C₂²	1	2	yes	—
31	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
32	C₂₃×#501	C₂²	1	8	yes	complemented
33	C₂₃×#500	C₂²	1	4	yes	complemented
34	C₂₃×#498	C₂²	1	4	yes	complemented
35	C₂₃×#489	C₂²	1	8	yes	complemented
36	C₂₃×#487	C₂²	1	4	yes	complemented
37	C₂₃×#486	C₂²	1	4	yes	complemented
38	C₂₃×#485	C₂²	1	16	yes	—
39	C₂₃×#482	C₂²	1	16	yes	—
40	C₂₃×#479	C₂²	1	16	yes	complemented
41	C₂₃×#478	C₂²	1	16	yes	complemented
42	C₂₃×#432	C₂²	1	4	yes	—
43	C₂₃×#431	C₂²	1	4	yes	—
44	C₂₃×#428	C₂²	1	8	yes	—
45	C₂₃×#423	C₂²	1	2	yes	—
46	C₂₃×#417	C₂²	1	8	yes	—
47	C₂₃×#407	C₂²	1	2	yes	—
48	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
49	C₂×#41×C₂₃	—	2	2	no	—
50	C₂×#41×C₂₃	C₂³	1	2	yes	—
51	C₂²×Q₈×C₂₃	—	2	2	no	—
52	C₂³×C₄×C₂₃	D₄	1	2	yes	—
53	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
55	C₂₃×C₄⋊Q₈	—	2	2	no	—
56	C₂₃×C₄⋊Q₈	—	2	2	no	—
57	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
59	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₂₃×#127	C₂³	1	1	yes	characteristic
62	C₂₃×#126	—	2	4	no	—
63	C₂₃×#125	—	2	2	no	—
64	C₂₃×#125	—	2	2	no	—
65	C₂₃×#125	—	2	2	no	—
66	C₂₃×#125	C₂³	1	8	yes	—
67	C₂₃×#125	C₂³	1	2	yes	—
68	C₂₃×#124	—	2	2	no	—
69	C₂₃×#124	C₂³	1	2	yes	—
70	C₂₃×#123	—	2	4	no	—
71	C₂₃×#123	—	2	2	no	—
72	C₂₃×C₂²⋊Q₈	—	2	4	no	—
73	C₂₃×C₂²⋊Q₈	—	2	4	no	—
74	C₂₃×C₂²⋊Q₈	—	2	4	no	—
75	C₂₃×C₂²⋊Q₈	—	2	4	no	—
76	C₂₃×C₂²⋊Q₈	—	2	2	no	—
77	C₂₃×C₂²⋊Q₈	—	2	2	no	—
78	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
79	C₂₃×#121	—	2	2	no	—
80	C₂₃×#121	—	2	2	no	—
81	C₂₃×#121	C₂³	1	4	yes	—
82	C₂₃×#120	—	2	2	no	—
83	C₄×Q₈×C₂₃	—	2	4	no	—
84	C₄×Q₈×C₂₃	—	2	4	no	—
85	C₄×Q₈×C₂₃	—	2	4	no	—
86	C₄×Q₈×C₂₃	—	2	4	no	—
87	C₄×Q₈×C₂₃	—	2	2	no	—
88	C₄×Q₈×C₂₃	—	2	2	no	—
89	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
90	C₄×D₄×C₂₃	—	2	4	no	—
91	C₄×D₄×C₂₃	—	2	4	no	—
92	C₄×D₄×C₂₃	—	2	4	no	—
93	C₄×D₄×C₂₃	—	2	2	no	—
94	C₄×D₄×C₂₃	—	2	2	no	—
95	C₄×D₄×C₂₃	C₂³	1	4	yes	—
96	C₂₃×#117	—	2	4	no	—
97	C₂₃×#117	—	2	2	no	—
98	C₂₃×#117	—	2	4	no	—
99	C₂₃×#117	—	2	2	no	—
100	C₂₃×#117	C₂³	1	2	yes	—
101	C₂₃×#117	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
103	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
104	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
106	C₂×C₄²×C₂₃	—	2	2	no	—
107	C₂×C₄²×C₂₃	—	2	2	no	—
108	C₂×C₄²×C₂₃	D₄	1	2	yes	—
109	C₂×C₄²×C₂₃	D₄	1	2	yes	—
110	C₂×C₄²×C₂₃	D₄	1	2	yes	—
111	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
114	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
115	C₂₃×#107	C₂³	1	16	yes	—
116	C₂₃×#106	C₂³	1	16	yes	—
117	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
118	C₂₃×#103	C₂³	1	16	yes	—
119	C₂₃×#102	C₂³	1	16	yes	—
120	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
121	C₂₃×#97	C₂³	1	4	yes	—
122	C₄×C₈×C₂₃	C₂³	1	4	yes	—
123	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
124	#41×C₂₃	—	2	8	no	—
125	#41×C₂₃	—	4	8	no	—
126	C₂×Q₈×C₂₃	—	2	2	no	—
127	C₂×Q₈×C₂₃	—	2	4	no	—
128	C₂×Q₈×C₂₃	—	2	4	no	—
129	C₂×Q₈×C₂₃	—	4	8	no	—
130	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
131	C₂×D₄×C₂₃	—	2	2	no	—
132	C₂×D₄×C₂₃	—	2	4	no	—
133	C₂×D₄×C₂₃	—	2	2	no	—
134	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₂₃	—	2	4	no	—
136	C₂²×C₄×C₂₃	—	2	4	no	—
137	C₂²×C₄×C₂₃	—	2	2	no	—
138	C₂²×C₄×C₂₃	—	2	4	no	—
139	C₂²×C₄×C₂₃	—	4	4	no	—
140	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
150	M₁₆×C₂₃	—	2	8	no	—
151	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
152	C₄⋊C₄×C₂₃	—	2	8	no	—
153	C₄⋊C₄×C₂₃	—	2	8	no	—
154	C₄⋊C₄×C₂₃	—	2	4	no	—
155	C₄⋊C₄×C₂₃	—	2	4	no	—
156	C₄⋊C₄×C₂₃	—	2	4	no	—
157	C₄⋊C₄×C₂₃	—	2	2	no	—
158	C₄⋊C₄×C₂₃	—	2	2	no	—
159	C₄⋊C₄×C₂₃	—	2	4	no	—
160	C₄⋊C₄×C₂₃	—	2	4	no	—
161	C₄⋊C₄×C₂₃	—	2	4	no	—
162	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
163	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
164	C₂²⋊C₄×C₂₃	—	2	8	no	—
165	C₂²⋊C₄×C₂₃	—	2	4	no	—
166	C₂²⋊C₄×C₂₃	—	2	2	no	—
167	C₂²⋊C₄×C₂₃	—	2	4	no	—
168	C₂²⋊C₄×C₂₃	—	2	4	no	—
169	C₂²⋊C₄×C₂₃	—	2	4	no	—
170	C₄²×C₂₃	—	2	4	no	—
171	C₄²×C₂₃	—	2	2	no	—
172	C₄²×C₂₃	—	2	8	no	—
173	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₂₃	C₂×D₄	1	2	yes	—
175	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₂₃	C₂×D₄	1	2	yes	—
177	C₄²×C₂₃	C₂×D₄	1	2	yes	—
178	C₄²×C₂₃	C₂×D₄	1	2	yes	—
179	C₄²×C₂₃	C₂×D₄	1	2	yes	—
180	C₄²×C₂₃	C₂⁴	1	2	yes	—
181	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
182	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
183	#60862	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₂₃	—	2	2	no	—
185	C₂³×C₂₃	—	2	2	no	—
186	C₂³×C₂₃	—	4	2	no	—
187	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
188	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₂₃	—	2	4	no	—
190	Q₈×C₂₃	—	4	8	no	—
191	Q₈×C₂₃	—	4	8	no	—
192	Q₈×C₂₃	—	4	4	no	—
193	D₄×C₂₃	—	2	4	no	—
194	D₄×C₂₃	—	4	8	no	—
195	D₄×C₂₃	—	4	4	no	—
196	D₄×C₂₃	—	4	4	no	—
197	C₂×C₄×C₂₃	—	2	2	no	—
198	C₂×C₄×C₂₃	—	2	4	no	—
199	C₂×C₄×C₂₃	—	2	4	no	—
200	C₂×C₄×C₂₃	—	2	4	no	—
201	C₂×C₄×C₂₃	—	2	4	no	—
202	C₂×C₄×C₂₃	—	2	4	no	—
203	C₂×C₄×C₂₃	—	2	2	no	—
204	C₂×C₄×C₂₃	—	2	4	no	—
205	C₂×C₄×C₂₃	—	2	8	no	—
206	C₂×C₄×C₂₃	—	4	2	no	—
207	C₂×C₄×C₂₃	—	4	2	no	—
208	C₂×C₄×C₂₃	—	4	2	no	—
209	C₂×C₄×C₂₃	—	4	8	no	—
210	C₂×C₄×C₂₃	—	4	8	no	—
211	C₂×C₄×C₂₃	—	4	4	no	—
212	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
219	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
220	C₈×C₂₃	—	2	8	no	—
221	#3444	C₂×C₂₃	1	1	yes	characteristic
222	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
223	#3240	C₂×C₂₃	1	8	yes	complemented
224	#3231	C₂×C₂₃	1	4	yes	complemented
225	#3228	C₂×C₂₃	1	4	yes	complemented
226	#3165	C₂×C₂₃	1	2	yes	complemented
227	#3141	C₂×C₂₃	1	2	yes	complemented
228	#3093	C₂×C₂₃	1	4	yes	complemented
229	#3080	C₂×C₂₃	1	4	yes	complemented
230	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
231	C₂²×C₂₃	—	2	2	no	—
232	C₂²×C₂₃	—	2	2	no	—
233	C₂²×C₂₃	—	2	2	no	—
234	C₂²×C₂₃	—	2	2	no	—
235	C₂²×C₂₃	—	4	4	no	—
236	C₂²×C₂₃	—	4	2	no	—
237	C₂²×C₂₃	—	4	4	no	—
238	C₂²×C₂₃	#536	1	2	yes	—
239	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
240	C₄×C₂₃	—	2	2	no	—
241	C₄×C₂₃	—	2	2	no	—
242	C₄×C₂₃	—	2	2	no	—
243	C₄×C₂₃	—	2	2	no	—
244	C₄×C₂₃	—	4	2	no	—
245	C₄×C₂₃	—	4	4	no	—
246	C₄×C₂₃	—	4	8	no	—
247	C₄×C₂₃	#536	1	2	yes	—
248	C₄×C₂₃	#575	1	4	yes	—
249	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
250	#533	—	2	2	no	—
251	#533	—	2	2	no	—
252	#533	C₂²×C₂₃	1	2	yes	—
253	#533	C₂²×C₂₃	1	1	yes	characteristic
254	#533	C₂²×C₂₃	1	4	yes	—
255	#533	C₂²×C₂₃	1	4	yes	—
256	#532	C₂²×C₂₃	1	1	yes	characteristic
257	#532	C₂²×C₂₃	1	2	yes	—
258	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
259	#529	—	2	2	no	—
260	#529	—	2	2	no	—
261	#529	C₂²×C₂₃	1	4	yes	—
262	C₂×#125	C₂²×C₂₃	1	2	yes	—
263	#525	—	2	2	no	—
264	#525	C₂²×C₂₃	1	2	yes	—
265	C₂×C₂²⋊Q₈	—	2	2	no	—
266	C₄×#41	—	2	2	no	—
267	C₄×#41	C₂²×C₂₃	1	2	yes	—
268	C₂×C₄×Q₈	—	2	2	no	—
269	C₂×#117	C₂²×C₂₃	1	2	yes	—
270	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
271	#501	C₂²×C₂₃	1	8	yes	complemented
272	#500	C₂²×C₂₃	1	4	yes	complemented
273	#498	C₂²×C₂₃	1	4	yes	complemented
274	#489	C₂²×C₂₃	1	8	yes	complemented
275	#487	C₂²×C₂₃	1	4	yes	complemented
276	#486	C₂²×C₂₃	1	4	yes	complemented
277	#485	C₂²×C₂₃	1	16	yes	—
278	#482	C₂²×C₂₃	1	16	yes	—
279	#479	C₂²×C₂₃	1	16	yes	complemented
280	#478	C₂²×C₂₃	1	16	yes	complemented
281	#432	C₂²×C₂₃	1	4	yes	—
282	#431	C₂²×C₂₃	1	4	yes	—
283	#428	C₂²×C₂₃	1	8	yes	—
284	#423	C₂²×C₂₃	1	2	yes	—
285	#417	C₂²×C₂₃	1	8	yes	—
286	#407	C₂²×C₂₃	1	2	yes	—
287	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
288	C₂×C₂₃	—	2	2	no	—
289	C₂×C₂₃	—	4	2	no	—
290	C₂×C₂₃	—	8	2	no	—
291	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
292	C₂×C₂₃	C₂×#575	1	2	yes	—
293	C₂×#41	—	2	2	no	—
294	C₂×#41	C₂³×C₂₃	1	2	yes	—
295	C₂²×Q₈	—	2	2	no	—
296	C₂³×C₄	D₄×C₂₃	1	2	yes	—
297	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
298	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
302	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
303	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
304	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
305	#127	C₂³×C₂₃	1	1	yes	characteristic
306	#126	—	2	4	no	—
307	#125	—	2	2	no	—
308	#125	—	2	2	no	—
309	#125	—	2	2	no	—
310	#125	C₂³×C₂₃	1	8	yes	—
311	#125	C₂³×C₂₃	1	2	yes	—
312	#124	—	2	2	no	—
313	#124	C₂³×C₂₃	1	2	yes	—
314	#123	—	2	4	no	—
315	#123	—	2	2	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
323	#121	—	2	2	no	—
324	#121	—	2	2	no	—
325	#121	C₂³×C₂₃	1	4	yes	—
326	#120	—	2	2	no	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	—	2	4	no	—
329	C₄×Q₈	—	2	4	no	—
330	C₄×Q₈	—	2	4	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	4	no	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	C₂³×C₂₃	1	4	yes	—
340	#117	—	2	4	no	—
341	#117	—	2	2	no	—
342	#117	—	2	4	no	—
343	#117	—	2	2	no	—
344	#117	C₂³×C₂₃	1	8	yes	—
345	#117	C₂³×C₂₃	1	2	yes	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₄²	—	2	2	no	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	D₄×C₂₃	1	2	yes	—
353	C₂×C₄²	D₄×C₂₃	1	2	yes	—
354	C₂×C₄²	D₄×C₂₃	1	2	yes	—
355	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
357	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
359	#107	C₂³×C₂₃	1	16	yes	—
360	#106	C₂³×C₂₃	1	16	yes	—
361	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
362	#103	C₂³×C₂₃	1	16	yes	—
363	#102	C₂³×C₂₃	1	16	yes	—
364	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
365	#97	C₂³×C₂₃	1	4	yes	—
366	C₄×C₈	C₂³×C₂₃	1	4	yes	—
367	C₂₃	#60862	1	1	yes	characteristic, direct product factor, Sylow
368	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
369	#41	—	2	8	no	—
370	#41	—	4	8	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	4	8	no	—
375	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
395	M₁₆	—	2	8	no	—
396	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
408	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₄²	—	2	4	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	8	no	—
418	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₂₃	1	2	yes	—
420	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
421	C₄²	C₂×D₄×C₂₃	1	2	yes	—
422	C₄²	C₂×D₄×C₂₃	1	2	yes	—
423	C₄²	C₂×D₄×C₂₃	1	2	yes	—
424	C₄²	C₂×D₄×C₂₃	1	2	yes	—
425	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
426	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
427	C₄²	C₂⁴×C₂₃	1	2	yes	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
432	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
433	Q₈	—	2	4	no	—
434	Q₈	—	4	8	no	—
435	Q₈	—	4	8	no	—
436	Q₈	—	4	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	4	8	no	—
439	D₄	—	4	4	no	—
440	D₄	—	4	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
457	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
462	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
463	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
464	C₈	—	2	8	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	C₂₃×#536	1	2	yes	—
473	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	4	no	—
480	C₄	—	4	8	no	—
481	C₄	C₂₃×#536	1	2	yes	—
482	C₄	C₂₃×#575	1	4	yes	—
483	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
484	C₂	—	2	2	no	—
485	C₂	—	4	2	no	—
486	C₂	—	8	2	no	—
487	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
488	C₂	C₂×C₂₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#533	C₂	semidirect
3. C₂₃×#3240	C₂	semidirect
4. C₂₃×#3231	C₂	semidirect
5. C₂₃×#3228	C₂	semidirect
6. C₂₃×#3165	C₂	semidirect
7. C₂₃×#3141	C₂	semidirect
8. C₂₃×#3093	C₂	semidirect
9. C₂₃×#3080	C₂	semidirect
10. C₂₃×#2920	C₂	semidirect
32. C₂₃×#501	C₂²	semidirect
33. C₂₃×#500	C₂²	semidirect
34. C₂₃×#498	C₂²	semidirect
35. C₂₃×#489	C₂²	semidirect
36. C₂₃×#487	C₂²	semidirect
37. C₂₃×#486	C₂²	semidirect
40. C₂₃×#479	C₂²	semidirect
41. C₂₃×#478	C₂²	semidirect
183. #60862	C₂₃	direct (N × H)
222. C₂×#533	C₂×C₂₃	semidirect
223. #3240	C₂×C₂₃	semidirect
224. #3231	C₂×C₂₃	semidirect
225. #3228	C₂×C₂₃	semidirect
226. #3165	C₂×C₂₃	semidirect
227. #3141	C₂×C₂₃	semidirect
228. #3093	C₂×C₂₃	semidirect
229. #3080	C₂×C₂₃	semidirect
230. #2920	C₂×C₂₃	semidirect
271. #501	C₂²×C₂₃	semidirect
272. #500	C₂²×C₂₃	semidirect
273. #498	C₂²×C₂₃	semidirect
274. #489	C₂²×C₂₃	semidirect
275. #487	C₂²×C₂₃	semidirect
276. #486	C₂²×C₂₃	semidirect
279. #479	C₂²×C₂₃	semidirect
280. #478	C₂²×C₂₃	semidirect
367. C₂₃	#60862	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3444	2
C₂×C₂₃×#533	2
C₂₃×#3240	2
C₂₃×#3231	2
C₂₃×#3228	2
C₂₃×#3165	2
C₂₃×#3141	2
C₂₃×#3093	2
C₂₃×#3080	2
C₂₃×#2920	2
#60862	23

Subgroups — C23×#60862 #19208488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60862 #19208488