Subgroups — C₂₃×#11129 #19158755

Order 5888.

1022 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#418	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#418	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2309	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1740	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
15	C₂₃×#428	—	2	2	no	—
16	C₂₃×#428	—	2	2	no	—
17	C₂₃×#427	—	2	2	no	—
18	C₂₃×#418	—	2	2	no	—
19	C₂₃×#418	—	2	2	no	—
20	C₂₃×#418	—	2	2	no	—
21	C₂₃×#418	C₄	1	4	yes	complemented
22	C₂×C₂₃×#102	—	2	2	no	—
23	C₂×C₂₃×#102	—	2	2	no	—
24	C₂₃×#390	—	2	2	no	—
25	C₂₃×#390	—	2	2	no	—
26	C₂₃×#379	—	2	2	no	—
27	C₂₃×#344	—	2	2	no	—
28	C₂₃×#342	—	2	2	no	—
29	C₂₃×#339	—	2	2	no	—
30	C₂⁵×C₂₃	—	2	1	no	—
31	C₂²×D₄×C₂₃	—	2	1	no	—
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	—	2	1	no	—
36	C₂²×D₄×C₂₃	—	2	1	no	—
37	C₂²×D₄×C₂₃	—	2	1	no	—
38	C₂²×D₄×C₂₃	—	2	1	no	—
39	C₂²×D₄×C₂₃	—	2	1	no	—
40	C₂²×D₄×C₂₃	—	2	1	no	—
41	C₂²×D₄×C₂₃	—	2	1	no	—
42	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₂₃	D₄	1	2	yes	—
44	C₂²×D₄×C₂₃	Q₈	1	2	yes	—
45	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₂₃	—	2	1	no	—
47	C₂×M₁₆×C₂₃	—	2	1	no	—
48	C₂×M₁₆×C₂₃	—	2	1	no	—
49	C₂×M₁₆×C₂₃	—	2	1	no	—
50	C₂×M₁₆×C₂₃	—	2	1	no	—
51	C₂×M₁₆×C₂₃	—	2	1	no	—
52	C₂×M₁₆×C₂₃	—	2	1	no	—
53	C₂×M₁₆×C₂₃	—	2	1	no	—
54	C₂×M₁₆×C₂₃	—	2	1	no	—
55	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
56	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
57	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
58	C₂²×C₈×C₂₃	—	2	1	no	—
59	C₂²×C₈×C₂₃	D₄	1	2	yes	—
60	C₂₃×#117	—	2	1	no	—
61	C₂₃×#117	—	2	1	no	—
62	C₂₃×#117	—	2	1	no	—
63	C₂₃×#117	—	2	1	no	—
64	C₂₃×#117	—	2	1	no	—
65	C₂₃×#117	—	2	1	no	—
66	C₂₃×#117	—	2	1	no	—
67	C₂₃×#117	—	2	1	no	—
68	C₂₃×#117	—	2	1	no	—
69	C₂₃×#117	—	2	1	no	—
70	C₂₃×#117	—	2	1	no	—
71	C₂₃×#117	—	2	1	no	—
72	C₂₃×#117	—	2	1	no	—
73	C₂₃×#117	—	2	1	no	—
74	C₂₃×#117	—	2	1	no	—
75	C₂₃×#117	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
84	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
85	C₂×C₄²×C₂₃	—	2	1	no	—
86	C₂×C₄²×C₂₃	—	2	1	no	—
87	C₂×C₄²×C₂₃	—	2	1	no	—
88	C₂×C₄²×C₂₃	—	2	1	no	—
89	C₂₃×#107	—	2	4	no	—
90	C₂₃×#106	—	2	4	no	—
91	C₂₃×#102	—	2	8	no	—
92	C₂₃×#102	—	2	8	no	—
93	C₂⁴×C₂₃	—	2	2	no	—
94	C₂⁴×C₂₃	—	2	2	no	—
95	C₂⁴×C₂₃	—	2	2	no	—
96	C₂⁴×C₂₃	—	4	1	no	—
97	C₂⁴×C₂₃	—	4	1	no	—
98	C₂⁴×C₂₃	—	4	1	no	—
99	C₂⁴×C₂₃	—	4	1	no	—
100	C₂⁴×C₂₃	—	8	4	no	—
101	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₂₃	—	2	2	no	—
103	C₂×D₄×C₂₃	—	2	2	no	—
104	C₂×D₄×C₂₃	—	2	2	no	—
105	C₂×D₄×C₂₃	—	2	2	no	—
106	C₂×D₄×C₂₃	—	2	2	no	—
107	C₂×D₄×C₂₃	—	2	2	no	—
108	C₂×D₄×C₂₃	—	2	2	no	—
109	C₂×D₄×C₂₃	—	2	2	no	—
110	C₂×D₄×C₂₃	—	2	2	no	—
111	C₂×D₄×C₂₃	—	2	2	no	—
112	C₂×D₄×C₂₃	—	2	2	no	—
113	C₂×D₄×C₂₃	—	2	2	no	—
114	C₂×D₄×C₂₃	—	2	2	no	—
115	C₂×D₄×C₂₃	—	2	2	no	—
116	C₂×D₄×C₂₃	—	2	2	no	—
117	C₂×D₄×C₂₃	—	4	1	no	—
118	C₂×D₄×C₂₃	—	4	1	no	—
119	C₂×D₄×C₂₃	—	4	1	no	—
120	C₂×D₄×C₂₃	—	4	1	no	—
121	C₂×D₄×C₂₃	—	4	1	no	—
122	C₂×D₄×C₂₃	—	4	1	no	—
123	C₂×D₄×C₂₃	—	4	1	no	—
124	C₂×D₄×C₂₃	—	4	1	no	—
125	C₂×D₄×C₂₃	—	4	1	no	—
126	C₂×D₄×C₂₃	—	4	1	no	—
127	C₂×D₄×C₂₃	—	4	1	no	—
128	C₂×D₄×C₂₃	—	4	1	no	—
129	C₂×D₄×C₂₃	C₄⋊C₄	1	4	yes	—
130	C₂²×C₄×C₂₃	—	2	2	no	—
131	C₂²×C₄×C₂₃	—	2	2	no	—
132	C₂²×C₄×C₂₃	—	2	2	no	—
133	C₂²×C₄×C₂₃	—	4	1	no	—
134	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
142	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
143	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
144	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
145	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
146	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
147	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
148	M₁₆×C₂₃	—	2	2	no	—
149	M₁₆×C₂₃	—	2	2	no	—
150	M₁₆×C₂₃	—	2	2	no	—
151	M₁₆×C₂₃	—	2	2	no	—
152	M₁₆×C₂₃	—	2	2	no	—
153	M₁₆×C₂₃	—	2	2	no	—
154	M₁₆×C₂₃	—	4	1	no	—
155	M₁₆×C₂₃	—	4	1	no	—
156	C₂×C₈×C₂₃	—	2	2	no	—
157	C₂×C₈×C₂₃	—	2	2	no	—
158	C₂×C₈×C₂₃	—	2	2	no	—
159	C₂×C₈×C₂₃	—	4	1	no	—
160	C₂×C₈×C₂₃	—	4	1	no	—
161	C₂×C₈×C₂₃	C₂²⋊C₄	1	4	yes	complemented
162	C₄⋊C₄×C₂₃	—	2	2	no	—
163	C₄⋊C₄×C₂₃	—	2	2	no	—
164	C₄⋊C₄×C₂₃	—	2	2	no	—
165	C₄⋊C₄×C₂₃	—	2	2	no	—
166	C₄⋊C₄×C₂₃	—	2	2	no	—
167	C₄⋊C₄×C₂₃	—	4	1	no	—
168	C₄⋊C₄×C₂₃	—	4	1	no	—
169	C₄⋊C₄×C₂₃	—	4	1	no	—
170	C₂²⋊C₄×C₂₃	—	2	2	no	—
171	C₂²⋊C₄×C₂₃	—	2	2	no	—
172	C₂²⋊C₄×C₂₃	—	2	2	no	—
173	C₂²⋊C₄×C₂₃	—	4	1	no	—
174	C₂²⋊C₄×C₂₃	—	4	1	no	—
175	C₂²⋊C₄×C₂₃	—	4	1	no	—
176	C₂²⋊C₄×C₂₃	—	4	1	no	—
177	C₂²⋊C₄×C₂₃	—	4	1	no	—
178	C₂²⋊C₄×C₂₃	—	8	8	no	—
179	C₄²×C₂₃	—	2	2	no	—
180	C₄²×C₂₃	—	4	1	no	—
181	C₄²×C₂₃	—	4	1	no	—
182	C₄²×C₂₃	—	4	1	no	—
183	C₄²×C₂₃	—	4	1	no	—
184	C₄²×C₂₃	—	4	1	no	—
185	C₄²×C₂₃	—	4	1	no	—
186	C₄²×C₂₃	—	4	1	no	—
187	#11129	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₂₃	—	2	4	no	—
189	C₂³×C₂₃	—	4	2	no	—
190	C₂³×C₂₃	—	4	8	no	—
191	C₂³×C₂₃	—	4	2	no	—
192	C₂³×C₂₃	—	4	2	no	—
193	C₂³×C₂₃	—	4	2	no	—
194	C₂³×C₂₃	—	4	2	no	—
195	C₂³×C₂₃	—	4	2	no	—
196	C₂³×C₂₃	—	4	2	no	—
197	C₂³×C₂₃	—	8	4	no	—
198	C₂³×C₂₃	—	8	4	no	—
199	C₂³×C₂₃	—	8	4	no	—
200	C₂³×C₂₃	—	8	4	no	—
201	C₂³×C₂₃	—	8	4	no	—
202	C₂³×C₂₃	—	8	4	no	—
203	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
204	C₂³×C₂₃	#120	1	1	yes	characteristic
205	C₂³×C₂₃	#121	1	1	yes	characteristic
206	C₂³×C₂₃	#121	1	1	yes	characteristic
207	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
208	C₂³×C₂₃	#123	1	1	yes	characteristic
209	C₂³×C₂₃	#127	1	1	yes	characteristic
210	D₄×C₂₃	—	2	4	no	—
211	D₄×C₂₃	—	2	4	no	—
212	D₄×C₂₃	—	4	2	no	—
213	D₄×C₂₃	—	4	2	no	—
214	D₄×C₂₃	—	4	2	no	—
215	D₄×C₂₃	—	4	2	no	—
216	D₄×C₂₃	—	4	2	no	—
217	D₄×C₂₃	—	4	2	no	—
218	C₂×C₄×C₂₃	—	4	4	no	—
219	C₂×C₄×C₂₃	—	4	4	no	—
220	C₂×C₄×C₂₃	—	4	2	no	—
221	C₂×C₄×C₂₃	—	4	2	no	—
222	C₂×C₄×C₂₃	—	4	2	no	—
223	C₂×C₄×C₂₃	—	4	2	no	—
224	C₂×C₄×C₂₃	—	8	2	no	—
225	C₂×C₄×C₂₃	—	8	2	no	—
226	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
229	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
233	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
234	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
235	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
236	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
237	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
238	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
239	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
240	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
242	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
246	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
247	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
248	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
249	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
250	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
251	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
252	C₂×C₄×C₂₃	#126	1	1	yes	characteristic
253	C₂×C₄×C₂₃	#126	1	1	yes	characteristic
254	C₈×C₂₃	—	2	4	no	—
255	C₈×C₂₃	—	4	2	no	—
256	#2911	C₂×C₂₃	1	1	yes	characteristic, complemented
257	C₂×#418	C₂×C₂₃	1	1	yes	characteristic
258	C₂×#418	C₂×C₂₃	1	1	yes	characteristic
259	#2309	C₂×C₂₃	1	1	yes	characteristic
260	C₂×#344	C₂×C₂₃	1	1	yes	characteristic, complemented
261	#1740	C₂×C₂₃	1	1	yes	characteristic, complemented
262	#1733	C₂×C₂₃	1	1	yes	characteristic, complemented
263	C₂²×C₂₃	—	2	2	no	—
264	C₂²×C₂₃	—	2	2	no	—
265	C₂²×C₂₃	—	2	2	no	—
266	C₂²×C₂₃	—	4	1	no	—
267	C₂²×C₂₃	—	4	1	no	—
268	C₂²×C₂₃	—	4	1	no	—
269	C₂²×C₂₃	—	4	1	no	—
270	C₂²×C₂₃	—	4	8	no	—
271	C₂²×C₂₃	—	4	4	no	—
272	C₂²×C₂₃	—	8	4	no	—
273	C₂²×C₂₃	—	8	4	no	—
274	C₂²×C₂₃	—	8	4	no	—
275	C₂²×C₂₃	—	8	4	no	—
276	C₂²×C₂₃	—	8	4	no	—
277	C₂²×C₂₃	—	8	4	no	—
278	C₂²×C₂₃	#385	1	1	yes	characteristic
279	C₂²×C₂₃	#388	1	1	yes	characteristic
280	C₂²×C₂₃	#390	1	1	yes	characteristic
281	C₂²×C₂₃	#392	1	1	yes	characteristic
282	C₂²×C₂₃	#394	1	1	yes	characteristic
283	C₂²×C₂₃	#396	1	1	yes	characteristic
284	C₂²×C₂₃	#399	1	1	yes	characteristic
285	C₄×C₂₃	—	8	2	no	—
286	C₄×C₂₃	—	8	2	no	—
287	C₄×C₂₃	—	8	2	no	—
288	C₄×C₂₃	—	8	2	no	—
289	C₄×C₂₃	#380	1	1	yes	characteristic
290	C₄×C₂₃	#385	1	1	yes	characteristic
291	C₄×C₂₃	#386	1	1	yes	characteristic
292	C₄×C₂₃	#388	1	1	yes	characteristic
293	C₄×C₂₃	#393	1	1	yes	characteristic
294	C₄×C₂₃	#394	1	1	yes	characteristic
295	C₄×C₂₃	#396	1	1	yes	characteristic
296	C₄×C₂₃	#397	1	1	yes	characteristic
297	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
298	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
299	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
300	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
301	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
302	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
303	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
304	#428	—	2	2	no	—
305	#428	—	2	2	no	—
306	#427	—	2	2	no	—
307	#418	—	2	2	no	—
308	#418	—	2	2	no	—
309	#418	—	2	2	no	—
310	#418	C₄×C₂₃	1	4	yes	complemented
311	C₂×#102	—	2	2	no	—
312	C₂×#102	—	2	2	no	—
313	#390	—	2	2	no	—
314	#390	—	2	2	no	—
315	#379	—	2	2	no	—
316	#344	—	2	2	no	—
317	#342	—	2	2	no	—
318	#339	—	2	2	no	—
319	C₂×C₂₃	—	2	1	no	—
320	C₂×C₂₃	—	2	1	no	—
321	C₂×C₂₃	—	2	1	no	—
322	C₂×C₂₃	—	2	1	no	—
323	C₂×C₂₃	—	2	1	no	—
324	C₂×C₂₃	—	2	1	no	—
325	C₂×C₂₃	—	8	4	no	—
326	C₂×C₂₃	#1439	1	1	yes	characteristic
327	C₂×C₂₃	#2008	1	2	yes	—
328	C₂⁵	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
341	C₂²×D₄	D₄×C₂₃	1	2	yes	—
342	C₂²×D₄	Q₈×C₂₃	1	2	yes	—
343	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
354	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
355	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	D₄×C₂₃	1	2	yes	—
358	#117	—	2	1	no	—
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	#117	—	2	1	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	#117	—	2	1	no	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	C₂×C₄×C₂₃	1	2	yes	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
377	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	8	no	—
382	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	#107	—	2	4	no	—
388	#106	—	2	4	no	—
389	#102	—	2	8	no	—
390	#102	—	2	8	no	—
391	C₂₃	#11129	1	1	yes	characteristic, direct product factor, Sylow
392	C₂⁴	—	2	2	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	4	1	no	—
396	C₂⁴	—	4	1	no	—
397	C₂⁴	—	4	1	no	—
398	C₂⁴	—	4	1	no	—
399	C₂⁴	—	8	4	no	—
400	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	C₄⋊C₄×C₂₃	1	4	yes	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
441	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
442	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
443	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
444	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
445	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
446	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	4	1	no	—
454	M₁₆	—	4	1	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	4	1	no	—
459	C₂×C₈	—	4	1	no	—
460	C₂×C₈	C₂²⋊C₄×C₂₃	1	4	yes	complemented
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	8	8	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	4	1	no	—
480	C₄²	—	4	1	no	—
481	C₄²	—	4	1	no	—
482	C₄²	—	4	1	no	—
483	C₄²	—	4	1	no	—
484	C₄²	—	4	1	no	—
485	C₄²	—	4	1	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	8	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	8	4	no	—
496	C₂³	—	8	4	no	—
497	C₂³	—	8	4	no	—
498	C₂³	—	8	4	no	—
499	C₂³	—	8	4	no	—
500	C₂³	—	8	4	no	—
501	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
502	C₂³	C₂₃×#120	1	1	yes	characteristic
503	C₂³	C₂₃×#121	1	1	yes	characteristic
504	C₂³	C₂₃×#121	1	1	yes	characteristic
505	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
506	C₂³	C₂₃×#123	1	1	yes	characteristic
507	C₂³	C₂₃×#127	1	1	yes	characteristic
508	D₄	—	2	4	no	—
509	D₄	—	2	4	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
525	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
526	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
527	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
528	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
529	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
530	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
531	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
532	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
533	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
534	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
535	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
536	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
537	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
538	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
539	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
540	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
541	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
542	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
543	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
544	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
545	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
546	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
547	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
548	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
549	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
550	C₂×C₄	C₂₃×#126	1	1	yes	characteristic
551	C₂×C₄	C₂₃×#126	1	1	yes	characteristic
552	C₈	—	2	4	no	—
553	C₈	—	4	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	8	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	8	4	no	—
564	C₂²	—	8	4	no	—
565	C₂²	—	8	4	no	—
566	C₂²	—	8	4	no	—
567	C₂²	—	8	4	no	—
568	C₂²	—	8	4	no	—
569	C₂²	C₂₃×#385	1	1	yes	characteristic
570	C₂²	C₂₃×#388	1	1	yes	characteristic
571	C₂²	C₂₃×#390	1	1	yes	characteristic
572	C₂²	C₂₃×#392	1	1	yes	characteristic
573	C₂²	C₂₃×#394	1	1	yes	characteristic
574	C₂²	C₂₃×#396	1	1	yes	characteristic
575	C₂²	C₂₃×#399	1	1	yes	characteristic
576	C₄	—	8	2	no	—
577	C₄	—	8	2	no	—
578	C₄	—	8	2	no	—
579	C₄	—	8	2	no	—
580	C₄	C₂₃×#380	1	1	yes	characteristic
581	C₄	C₂₃×#385	1	1	yes	characteristic
582	C₄	C₂₃×#386	1	1	yes	characteristic
583	C₄	C₂₃×#388	1	1	yes	characteristic
584	C₄	C₂₃×#393	1	1	yes	characteristic
585	C₄	C₂₃×#394	1	1	yes	characteristic
586	C₄	C₂₃×#396	1	1	yes	characteristic
587	C₄	C₂₃×#397	1	1	yes	characteristic
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	1	no	—
592	C₂	—	2	1	no	—
593	C₂	—	2	1	no	—
594	C₂	—	8	4	no	—
595	C₂	C₂₃×#1439	1	1	yes	characteristic
596	C₂	C₂₃×#2008	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	#392
commutator	C₂²×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂³×C₄	C₂³×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2911	C₂	semidirect
5. C₂×C₂₃×#344	C₂	semidirect
6. C₂₃×#1740	C₂	semidirect
7. C₂₃×#1733	C₂	semidirect
21. C₂₃×#418	C₄	semidirect
161. C₂×C₈×C₂₃	C₂²⋊C₄	semidirect
187. #11129	C₂₃	direct (N × H)
256. #2911	C₂×C₂₃	semidirect
260. C₂×#344	C₂×C₂₃	semidirect
261. #1740	C₂×C₂₃	semidirect
262. #1733	C₂×C₂₃	semidirect
310. #418	C₄×C₂₃	semidirect
391. C₂₃	#11129	direct (N × H)
460. C₂×C₈	C₂²⋊C₄×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#2911	2
C₂×C₂₃×#418	2
C₂₃×#2309	2
C₂×C₂₃×#344	2
C₂₃×#1740	2
C₂₃×#1733	2
#11129	23

Subgroups — C23×#11129 #19158755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#11129 #19158755