Subgroups — C₂₃×#10229 #19157855

Order 5888.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#459	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₂₃	—	2	1	no	—
9	C₂²×D₈×C₂₃	—	2	1	no	—
10	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂₃×#460	—	2	2	no	—
15	C₂₃×#460	—	2	2	no	—
16	C₂₃×#459	—	2	2	no	—
17	C₂₃×#459	—	2	2	no	—
18	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#102	—	2	1	no	—
21	C₂×C₂₃×#102	—	2	1	no	—
22	C₂×C₂₃×#102	—	2	2	no	—
23	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#396	—	2	2	no	—
25	C₂₃×#390	—	2	1	no	—
26	C₂₃×#389	—	2	1	no	—
27	C₂₃×#384	C₂²	1	1	yes	characteristic
28	C₂₃×#380	—	2	1	no	—
29	C₂₃×Q₈⋊C₈	—	2	2	no	—
30	C₂₃×D₄⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₂₃	—	2	1	no	—
33	C₂²×D₄×C₂₃	—	2	1	no	—
34	C₂²×D₄×C₂₃	—	2	1	no	—
35	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₂₃	—	2	1	no	—
37	C₂×SD₁₆×C₂₃	—	2	4	no	—
38	C₂×SD₁₆×C₂₃	—	4	2	no	—
39	C₂×SD₁₆×C₂₃	—	4	2	no	—
40	C₂×D₈×C₂₃	—	2	4	no	—
41	C₂×D₈×C₂₃	—	4	2	no	—
42	C₂×D₈×C₂₃	—	4	2	no	—
43	C₂²×C₈×C₂₃	—	2	1	no	—
44	C₂²×C₈×C₂₃	—	2	1	no	—
45	C₂²×C₈×C₂₃	—	2	1	no	—
46	C₂₃×#127	—	2	1	no	—
47	C₂₃×#127	—	2	1	no	—
48	C₂₃×#127	—	2	1	no	—
49	C₂₃×#127	D₄	1	2	yes	—
50	C₂₃×C₂²⋊Q₈	—	4	2	no	—
51	C₂₃×C₂²⋊Q₈	—	4	2	no	—
52	C₄×Q₈×C₂₃	—	2	1	no	—
53	C₄×Q₈×C₂₃	—	2	1	no	—
54	C₄×Q₈×C₂₃	—	2	1	no	—
55	C₄×Q₈×C₂₃	—	2	1	no	—
56	C₄×D₄×C₂₃	—	2	1	no	—
57	C₄×D₄×C₂₃	—	2	1	no	—
58	C₄×D₄×C₂₃	—	2	1	no	—
59	C₄×D₄×C₂₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
70	C₂×C₄²×C₂₃	—	2	1	no	—
71	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
72	C₂₃×C₄⋊C₈	—	2	1	no	—
73	C₂₃×C₄⋊C₈	—	2	1	no	—
74	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
75	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
76	C₂₃×#102	—	2	4	no	—
77	C₂₃×#102	—	2	4	no	—
78	C₂₃×#102	—	4	4	no	—
79	C₄×C₈×C₂₃	—	2	1	no	—
80	C₄×C₈×C₂₃	—	2	1	no	—
81	C₂₃×#95	—	2	2	no	—
82	C₂⁴×C₂₃	—	2	1	no	—
83	C₂⁴×C₂₃	—	4	1	no	—
84	C₂×Q₈×C₂₃	—	2	1	no	—
85	C₂×Q₈×C₂₃	—	2	1	no	—
86	C₂×Q₈×C₂₃	—	2	1	no	—
87	C₂×Q₈×C₂₃	—	2	1	no	—
88	C₂×Q₈×C₂₃	—	2	1	no	—
89	C₂×Q₈×C₂₃	D₈	1	2	yes	complemented
90	C₂×D₄×C₂₃	—	2	1	no	—
91	C₂×D₄×C₂₃	—	2	2	no	—
92	C₂×D₄×C₂₃	—	2	2	no	—
93	C₂×D₄×C₂₃	—	2	1	no	—
94	C₂×D₄×C₂₃	—	2	2	no	—
95	C₂×D₄×C₂₃	—	2	1	no	—
96	C₂×D₄×C₂₃	—	2	1	no	—
97	C₂×D₄×C₂₃	—	2	1	no	—
98	C₂×D₄×C₂₃	—	4	2	no	—
99	C₂×D₄×C₂₃	—	4	2	no	—
100	C₂×D₄×C₂₃	—	4	1	no	—
101	C₂×D₄×C₂₃	—	4	1	no	—
102	C₂×D₄×C₂₃	—	4	1	no	—
103	C₂×D₄×C₂₃	—	4	1	no	—
104	C₂×D₄×C₂₃	—	4	1	no	—
105	C₂×D₄×C₂₃	—	4	1	no	—
106	C₂×D₄×C₂₃	—	4	1	no	—
107	C₂×D₄×C₂₃	—	4	1	no	—
108	C₂×D₄×C₂₃	—	4	1	no	—
109	C₂×D₄×C₂₃	—	4	1	no	—
110	C₂×D₄×C₂₃	—	4	1	no	—
111	C₂×D₄×C₂₃	SD₁₆	1	2	yes	complemented
112	C₂²×C₄×C₂₃	—	2	1	no	—
113	C₂²×C₄×C₂₃	—	2	1	no	—
114	C₂²×C₄×C₂₃	—	2	2	no	—
115	C₂²×C₄×C₂₃	—	2	1	no	—
116	C₂²×C₄×C₂₃	—	4	1	no	—
117	C₂²×C₄×C₂₃	—	4	1	no	—
118	C₂²×C₄×C₂₃	—	4	1	no	—
119	C₂²×C₄×C₂₃	—	4	1	no	—
120	C₂²×C₄×C₂₃	—	4	1	no	—
121	C₂²×C₄×C₂₃	—	4	1	no	—
122	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
125	SD₁₆×C₂₃	—	4	8	no	—
126	D₈×C₂₃	—	4	8	no	—
127	C₂×C₈×C₂₃	—	2	2	no	—
128	C₂×C₈×C₂₃	—	2	2	no	—
129	C₂×C₈×C₂₃	—	2	2	no	—
130	C₂×C₈×C₂₃	—	4	1	no	—
131	C₂×C₈×C₂₃	—	4	1	no	—
132	C₂×C₈×C₂₃	—	4	1	no	—
133	C₂×C₈×C₂₃	—	4	1	no	—
134	C₂×C₈×C₂₃	—	4	1	no	—
135	C₂×C₈×C₂₃	—	4	1	no	—
136	C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₄⋊C₄×C₂₃	—	2	1	no	—
138	C₄⋊C₄×C₂₃	—	2	1	no	—
139	C₄⋊C₄×C₂₃	—	2	1	no	—
140	C₄⋊C₄×C₂₃	—	4	2	no	—
141	C₄⋊C₄×C₂₃	—	4	4	no	—
142	C₄⋊C₄×C₂₃	—	4	1	no	—
143	C₄⋊C₄×C₂₃	—	4	1	no	—
144	C₄⋊C₄×C₂₃	—	4	1	no	—
145	C₄⋊C₄×C₂₃	—	4	1	no	—
146	C₄⋊C₄×C₂₃	—	4	1	no	—
147	C₄⋊C₄×C₂₃	—	4	1	no	—
148	C₂²⋊C₄×C₂₃	—	4	4	no	—
149	C₂²⋊C₄×C₂₃	—	4	1	no	—
150	C₂²⋊C₄×C₂₃	—	4	1	no	—
151	C₂²⋊C₄×C₂₃	—	8	2	no	—
152	C₄²×C₂₃	—	4	1	no	—
153	C₄²×C₂₃	—	4	1	no	—
154	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₂₃	#41	1	1	yes	characteristic
158	#10229	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₂₃	—	2	2	no	—
160	C₂³×C₂₃	—	4	1	no	—
161	C₂³×C₂₃	—	4	1	no	—
162	C₂³×C₂₃	—	4	1	no	—
163	C₂³×C₂₃	—	4	1	no	—
164	C₂³×C₂₃	—	4	1	no	—
165	C₂³×C₂₃	—	4	1	no	—
166	C₂³×C₂₃	—	4	2	no	—
167	C₂³×C₂₃	—	8	1	no	—
168	C₂³×C₂₃	—	8	1	no	—
169	C₂³×C₂₃	—	8	1	no	—
170	C₂³×C₂₃	—	8	1	no	—
171	C₂³×C₂₃	—	8	1	no	—
172	C₂³×C₂₃	—	8	1	no	—
173	C₂³×C₂₃	#120	1	1	yes	characteristic
174	Q₈×C₂₃	—	2	2	no	—
175	Q₈×C₂₃	—	2	2	no	—
176	Q₈×C₂₃	—	4	1	no	—
177	Q₈×C₂₃	—	4	1	no	—
178	D₄×C₂₃	—	2	2	no	—
179	D₄×C₂₃	—	2	2	no	—
180	D₄×C₂₃	—	4	4	no	—
181	D₄×C₂₃	—	4	2	no	—
182	D₄×C₂₃	—	4	2	no	—
183	D₄×C₂₃	—	4	2	no	—
184	D₄×C₂₃	—	4	1	no	—
185	D₄×C₂₃	—	4	2	no	—
186	D₄×C₂₃	—	4	1	no	—
187	D₄×C₂₃	—	8	2	no	—
188	D₄×C₂₃	—	8	1	no	—
189	D₄×C₂₃	—	8	1	no	—
190	D₄×C₂₃	—	8	1	no	—
191	D₄×C₂₃	—	8	1	no	—
192	C₂×C₄×C₂₃	—	2	1	no	—
193	C₂×C₄×C₂₃	—	2	1	no	—
194	C₂×C₄×C₂₃	—	2	2	no	—
195	C₂×C₄×C₂₃	—	4	1	no	—
196	C₂×C₄×C₂₃	—	4	1	no	—
197	C₂×C₄×C₂₃	—	4	1	no	—
198	C₂×C₄×C₂₃	—	4	1	no	—
199	C₂×C₄×C₂₃	—	4	2	no	—
200	C₂×C₄×C₂₃	—	4	1	no	—
201	C₂×C₄×C₂₃	—	4	2	no	—
202	C₂×C₄×C₂₃	—	4	1	no	—
203	C₂×C₄×C₂₃	—	4	1	no	—
204	C₂×C₄×C₂₃	—	4	2	no	—
205	C₂×C₄×C₂₃	—	4	1	no	—
206	C₂×C₄×C₂₃	—	8	1	no	—
207	C₂×C₄×C₂₃	—	8	1	no	—
208	C₂×C₄×C₂₃	—	8	1	no	—
209	C₂×C₄×C₂₃	—	8	1	no	—
210	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
211	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
212	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
213	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
214	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
215	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
216	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
217	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
218	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
219	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
220	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
224	C₈×C₂₃	—	4	2	no	—
225	C₈×C₂₃	—	4	2	no	—
226	C₈×C₂₃	—	4	2	no	—
227	C₂×#460	C₂×C₂₃	1	1	yes	characteristic, complemented
228	C₂×#459	C₂×C₂₃	1	1	yes	characteristic
229	#2538	C₂×C₂₃	1	1	yes	characteristic, complemented
230	#1957	C₂×C₂₃	1	1	yes	characteristic, complemented
231	C₂×Q₈⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
232	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
233	#1296	C₂×C₂₃	1	1	yes	characteristic, complemented
234	C₂²×C₂₃	—	4	2	no	—
235	C₂²×C₂₃	—	4	2	no	—
236	C₂²×C₂₃	—	4	2	no	—
237	C₂²×C₂₃	—	8	1	no	—
238	C₂²×C₂₃	—	8	1	no	—
239	C₂²×C₂₃	—	8	1	no	—
240	C₂²×C₂₃	—	8	1	no	—
241	C₂²×C₂₃	—	8	2	no	—
242	C₂²×C₂₃	—	8	2	no	—
243	C₂²×C₂₃	—	8	2	no	—
244	C₂²×C₂₃	—	16	1	no	—
245	C₂²×C₂₃	—	16	1	no	—
246	C₂²×C₂₃	—	16	1	no	—
247	C₂²×C₂₃	—	16	1	no	—
248	C₂²×C₂₃	#392	1	1	yes	characteristic
249	C₂²×C₂₃	#447	1	1	yes	characteristic
250	C₂²×C₂₃	#448	1	1	yes	characteristic
251	C₂²×C₂₃	#449	1	1	yes	characteristic
252	C₂²×C₂₃	#449	1	1	yes	characteristic
253	C₂²×C₂₃	#453	1	1	yes	characteristic
254	C₂²×C₂₃	#454	1	1	yes	characteristic
255	C₄×C₂₃	—	2	1	no	—
256	C₄×C₂₃	—	2	1	no	—
257	C₄×C₂₃	—	4	2	no	—
258	C₄×C₂₃	—	8	2	no	—
259	C₄×C₂₃	—	8	1	no	—
260	C₄×C₂₃	—	8	1	no	—
261	C₄×C₂₃	#447	1	1	yes	characteristic
262	C₄×C₂₃	#449	1	1	yes	characteristic
263	C₄×C₂₃	#450	1	1	yes	characteristic
264	C₄×C₂₃	#452	1	1	yes	characteristic
265	C₄×C₂₃	#465	1	1	yes	characteristic
266	C₄×C₂₃	#466	1	1	yes	characteristic
267	C₄×C₂₃	#468	1	1	yes	characteristic
268	C₄×C₂₃	#469	1	1	yes	characteristic
269	C₂²×SD₁₆	—	2	1	no	—
270	C₂²×D₈	—	2	1	no	—
271	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
272	C₂×C₂²⋊Q₈	—	2	1	no	—
273	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
275	#460	—	2	2	no	—
276	#460	—	2	2	no	—
277	#459	—	2	2	no	—
278	#459	—	2	2	no	—
279	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
281	C₂×#102	—	2	1	no	—
282	C₂×#102	—	2	1	no	—
283	C₂×#102	—	2	2	no	—
284	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
285	#396	—	2	2	no	—
286	#390	—	2	1	no	—
287	#389	—	2	1	no	—
288	#384	C₂²×C₂₃	1	1	yes	characteristic
289	#380	—	2	1	no	—
290	Q₈⋊C₈	—	2	2	no	—
291	D₄⋊C₈	—	2	2	no	—
292	C₂×C₂₃	—	8	2	no	—
293	C₂×C₂₃	—	16	2	no	—
294	C₂×C₂₃	#1621	1	1	yes	characteristic
295	C₂×C₂₃	#1622	1	1	yes	characteristic
296	C₂×C₂₃	#1627	1	1	yes	characteristic
297	C₂×C₂₃	#1628	1	1	yes	characteristic
298	C₂×C₂₃	#1999	1	1	yes	characteristic
299	C₂×C₂₃	#2000	1	1	yes	characteristic
300	C₂×C₂₃	#2006	1	1	yes	characteristic
301	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
306	C₂³×C₄	—	2	1	no	—
307	C₂×SD₁₆	—	2	4	no	—
308	C₂×SD₁₆	—	4	2	no	—
309	C₂×SD₁₆	—	4	2	no	—
310	C₂×D₈	—	2	4	no	—
311	C₂×D₈	—	4	2	no	—
312	C₂×D₈	—	4	2	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	1	no	—
316	#127	—	2	1	no	—
317	#127	—	2	1	no	—
318	#127	—	2	1	no	—
319	#127	D₄×C₂₃	1	2	yes	—
320	C₂²⋊Q₈	—	4	2	no	—
321	C₂²⋊Q₈	—	4	2	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
345	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
346	#102	—	2	4	no	—
347	#102	—	2	4	no	—
348	#102	—	4	4	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	#95	—	2	2	no	—
352	C₂₃	#10229	1	1	yes	characteristic, direct product factor, Sylow
353	C₂⁴	—	2	1	no	—
354	C₂⁴	—	4	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	D₈×C₂₃	1	2	yes	complemented
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂×D₄	—	4	1	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂×D₄	—	4	1	no	—
375	C₂×D₄	—	4	1	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	SD₁₆×C₂₃	1	2	yes	complemented
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
396	SD₁₆	—	4	8	no	—
397	D₈	—	4	8	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	—	4	1	no	—
404	C₂×C₈	—	4	1	no	—
405	C₂×C₈	—	4	1	no	—
406	C₂×C₈	—	4	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₂²⋊C₄	—	4	1	no	—
422	C₂²⋊C₄	—	8	2	no	—
423	C₄²	—	4	1	no	—
424	C₄²	—	4	1	no	—
425	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
428	C₄²	#41×C₂₃	1	1	yes	characteristic
429	C₂³	—	2	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	8	1	no	—
438	C₂³	—	8	1	no	—
439	C₂³	—	8	1	no	—
440	C₂³	—	8	1	no	—
441	C₂³	—	8	1	no	—
442	C₂³	—	8	1	no	—
443	C₂³	C₂₃×#120	1	1	yes	characteristic
444	Q₈	—	2	2	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	4	1	no	—
447	Q₈	—	4	1	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	1	no	—
457	D₄	—	8	2	no	—
458	D₄	—	8	1	no	—
459	D₄	—	8	1	no	—
460	D₄	—	8	1	no	—
461	D₄	—	8	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	8	1	no	—
477	C₂×C₄	—	8	1	no	—
478	C₂×C₄	—	8	1	no	—
479	C₂×C₄	—	8	1	no	—
480	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
481	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
482	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
483	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
484	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
485	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
486	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
487	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
488	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
489	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
490	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
491	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
492	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
493	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
494	C₈	—	4	2	no	—
495	C₈	—	4	2	no	—
496	C₈	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	16	1	no	—
508	C₂²	—	16	1	no	—
509	C₂²	—	16	1	no	—
510	C₂²	—	16	1	no	—
511	C₂²	C₂₃×#392	1	1	yes	characteristic
512	C₂²	C₂₃×#447	1	1	yes	characteristic
513	C₂²	C₂₃×#448	1	1	yes	characteristic
514	C₂²	C₂₃×#449	1	1	yes	characteristic
515	C₂²	C₂₃×#449	1	1	yes	characteristic
516	C₂²	C₂₃×#453	1	1	yes	characteristic
517	C₂²	C₂₃×#454	1	1	yes	characteristic
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	2	no	—
524	C₄	C₂₃×#447	1	1	yes	characteristic
525	C₄	C₂₃×#449	1	1	yes	characteristic
526	C₄	C₂₃×#450	1	1	yes	characteristic
527	C₄	C₂₃×#452	1	1	yes	characteristic
528	C₄	C₂₃×#465	1	1	yes	characteristic
529	C₄	C₂₃×#466	1	1	yes	characteristic
530	C₄	C₂₃×#468	1	1	yes	characteristic
531	C₄	C₂₃×#469	1	1	yes	characteristic
532	C₂	—	8	2	no	—
533	C₂	—	16	2	no	—
534	C₂	C₂₃×#1621	1	1	yes	characteristic
535	C₂	C₂₃×#1622	1	1	yes	characteristic
536	C₂	C₂₃×#1627	1	1	yes	characteristic
537	C₂	C₂₃×#1628	1	1	yes	characteristic
538	C₂	C₂₃×#1999	1	1	yes	characteristic
539	C₂	C₂₃×#2000	1	1	yes	characteristic
540	C₂	C₂₃×#2006	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂×C₂₃×#459	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#460	C₂	semidirect
3. C₂₃×#2538	C₂	semidirect
4. C₂₃×#1957	C₂	semidirect
5. C₂×C₂₃×Q₈⋊C₈	C₂	semidirect
6. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
7. C₂₃×#1296	C₂	semidirect
89. C₂×Q₈×C₂₃	D₈	semidirect
111. C₂×D₄×C₂₃	SD₁₆	semidirect
158. #10229	C₂₃	direct (N × H)
227. C₂×#460	C₂×C₂₃	semidirect
229. #2538	C₂×C₂₃	semidirect
230. #1957	C₂×C₂₃	semidirect
231. C₂×Q₈⋊C₈	C₂×C₂₃	semidirect
232. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
233. #1296	C₂×C₂₃	semidirect
352. C₂₃	#10229	direct (N × H)
360. C₂×Q₈	D₈×C₂₃	semidirect
382. C₂×D₄	SD₁₆×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#460	2
C₂×C₂₃×#459	2
C₂₃×#2538	2
C₂₃×#1957	2
C₂×C₂₃×Q₈⋊C₈	2
C₂×C₂₃×D₄⋊C₈	2
C₂₃×#1296	2
#10229	23

Subgroups — C23×#10229 #19157855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10229 #19157855