Subgroups — C₂₃×#27129 #19174755

Order 5888.

686 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2513	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2065	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2023	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1934	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1926	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#1926	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#1925	C₂	1	1	yes	maximal, characteristic
12	C₂₃×#1921	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
18	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#397	—	2	1	no	—
29	C₂₃×#397	—	2	1	no	—
30	C₂₃×#391	—	2	1	no	—
31	C₂₃×#390	C₂²	1	1	yes	characteristic
32	C₂₃×#390	C₂²	1	1	yes	characteristic
33	C₂₃×#390	C₂²	1	1	yes	characteristic
34	C₂₃×#389	C₂²	1	1	yes	characteristic
35	C₂₃×#389	C₂²	1	1	yes	characteristic
36	C₂₃×#389	C₂²	1	1	yes	characteristic
37	C₂₃×#388	—	2	1	no	—
38	C₂₃×#388	—	2	1	no	—
39	C₂₃×#387	—	2	1	no	—
40	C₂₃×#387	—	2	1	no	—
41	C₂₃×#382	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#340	C₂²	1	1	yes	characteristic
48	C₂₃×#340	C₂²	1	1	yes	characteristic
49	C₂₃×#340	C₂²	1	1	yes	characteristic
50	C₂₃×#340	C₂²	1	1	yes	characteristic
51	C₂₃×#340	C₂²	1	1	yes	characteristic
52	C₂₃×#340	C₂²	1	1	yes	characteristic
53	C₂₃×#340	C₂²	1	1	yes	characteristic
54	C₂₃×#340	C₂²	1	1	yes	characteristic
55	C₂₃×#336	C₂²	1	1	yes	characteristic
56	C₂₃×#336	C₂²	1	1	yes	characteristic
57	C₂₃×#336	C₂²	1	1	yes	characteristic
58	C₂₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₂₃	—	2	1	no	—
60	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
65	C₂₃×C₄⋊Q₈	—	2	2	no	—
66	C₂₃×C₄⋊Q₈	—	2	2	no	—
67	C₄×Q₈×C₂₃	—	4	4	no	—
68	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
87	C₂×C₄²×C₂₃	—	2	1	no	—
88	C₂×C₄²×C₂₃	—	2	1	no	—
89	C₂×C₄²×C₂₃	—	2	1	no	—
90	C₂×C₄²×C₂₃	—	2	1	no	—
91	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
94	C₂₃×#107	—	2	2	no	—
95	C₂₃×#106	—	2	2	no	—
96	C₂₃×#106	—	2	2	no	—
97	C₂₃×#106	—	2	2	no	—
98	C₂₃×C₄⋊C₈	—	2	2	no	—
99	C₂₃×#102	—	2	2	no	—
100	C₂₃×#102	—	2	2	no	—
101	C₂₃×#102	—	2	2	no	—
102	C₂₃×#102	—	2	2	no	—
103	C₄×C₈×C₂₃	—	2	2	no	—
104	C₂₃×#95	—	2	1	no	—
105	C₂₃×#95	—	2	1	no	—
106	C₂₃×#95	—	2	1	no	—
107	C₂₃×#95	—	2	1	no	—
108	C₂₃×#95	—	2	1	no	—
109	C₂₃×#95	—	2	1	no	—
110	C₂₃×#95	—	2	1	no	—
111	C₂₃×#95	—	2	1	no	—
112	C₂₃×#95	—	2	1	no	—
113	C₂₃×#95	D₄	1	1	yes	characteristic
114	C₂₃×#95	D₄	1	1	yes	characteristic
115	C₂⁴×C₂₃	—	2	1	no	—
116	C₂×Q₈×C₂₃	—	2	4	no	—
117	C₂×Q₈×C₂₃	—	4	2	no	—
118	C₂×Q₈×C₂₃	—	4	2	no	—
119	C₂×D₄×C₂₃	—	2	1	no	—
120	C₂×D₄×C₂₃	—	2	1	no	—
121	C₂×D₄×C₂₃	—	2	1	no	—
122	C₂×D₄×C₂₃	—	2	1	no	—
123	C₂×D₄×C₂₃	—	2	1	no	—
124	C₂×D₄×C₂₃	—	2	1	no	—
125	C₂²×C₄×C₂₃	—	2	1	no	—
126	C₂²×C₄×C₂₃	—	2	1	no	—
127	C₂²×C₄×C₂₃	—	2	1	no	—
128	C₂²×C₄×C₂₃	—	2	1	no	—
129	C₂²×C₄×C₂₃	—	2	1	no	—
130	C₂²×C₄×C₂₃	—	2	1	no	—
131	C₂²×C₄×C₂₃	—	2	1	no	—
132	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₂₃	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
139	C₂×C₈×C₂₃	—	2	1	no	—
140	C₂×C₈×C₂₃	—	2	1	no	—
141	C₂×C₈×C₂₃	—	2	1	no	—
142	C₂×C₈×C₂₃	—	2	1	no	—
143	C₂×C₈×C₂₃	—	2	1	no	—
144	C₂×C₈×C₂₃	—	2	1	no	—
145	C₂×C₈×C₂₃	—	2	1	no	—
146	C₂×C₈×C₂₃	—	2	1	no	—
147	C₂×C₈×C₂₃	—	2	1	no	—
148	C₂×C₈×C₂₃	—	2	1	no	—
149	C₂×C₈×C₂₃	—	2	1	no	—
150	C₂×C₈×C₂₃	#41	1	2	yes	—
151	C₄⋊C₄×C₂₃	—	2	4	no	—
152	C₄⋊C₄×C₂₃	—	2	2	no	—
153	C₄⋊C₄×C₂₃	—	2	2	no	—
154	C₄⋊C₄×C₂₃	—	2	1	no	—
155	C₄⋊C₄×C₂₃	—	2	1	no	—
156	C₄⋊C₄×C₂₃	—	2	1	no	—
157	C₄⋊C₄×C₂₃	—	2	1	no	—
158	C₄⋊C₄×C₂₃	—	2	1	no	—
159	C₄⋊C₄×C₂₃	—	2	1	no	—
160	C₄⋊C₄×C₂₃	—	2	1	no	—
161	C₄⋊C₄×C₂₃	—	2	1	no	—
162	C₄⋊C₄×C₂₃	—	2	1	no	—
163	C₄⋊C₄×C₂₃	—	2	1	no	—
164	C₄⋊C₄×C₂₃	—	2	1	no	—
165	C₄⋊C₄×C₂₃	—	4	2	no	—
166	C₄⋊C₄×C₂₃	—	4	2	no	—
167	C₄⋊C₄×C₂₃	—	8	1	no	—
168	C₄⋊C₄×C₂₃	#41	1	2	yes	—
169	C₄⋊C₄×C₂₃	#41	1	2	yes	—
170	C₄⋊C₄×C₂₃	#41	1	2	yes	—
171	C₂²⋊C₄×C₂₃	—	4	2	no	—
172	C₂²⋊C₄×C₂₃	—	4	2	no	—
173	C₂²⋊C₄×C₂₃	—	8	1	no	—
174	C₂²⋊C₄×C₂₃	—	8	1	no	—
175	C₂²⋊C₄×C₂₃	—	8	1	no	—
176	C₂²⋊C₄×C₂₃	—	8	1	no	—
177	C₄²×C₂₃	—	2	1	no	—
178	C₄²×C₂₃	—	2	1	no	—
179	C₄²×C₂₃	—	2	1	no	—
180	C₄²×C₂₃	—	2	1	no	—
181	C₄²×C₂₃	—	2	1	no	—
182	C₄²×C₂₃	—	2	1	no	—
183	C₄²×C₂₃	—	4	2	no	—
184	C₄²×C₂₃	—	4	2	no	—
185	C₄²×C₂₃	—	4	2	no	—
186	C₄²×C₂₃	—	8	1	no	—
187	#27129	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₂₃	—	4	1	no	—
189	C₂³×C₂₃	—	4	1	no	—
190	C₂³×C₂₃	—	4	1	no	—
191	C₂³×C₂₃	—	4	1	no	—
192	C₂³×C₂₃	—	4	1	no	—
193	C₂³×C₂₃	—	4	1	no	—
194	C₂³×C₂₃	—	4	1	no	—
195	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₂₃	—	4	8	no	—
197	D₄×C₂₃	—	4	1	no	—
198	D₄×C₂₃	—	4	1	no	—
199	D₄×C₂₃	—	4	1	no	—
200	D₄×C₂₃	—	4	1	no	—
201	C₂×C₄×C₂₃	—	2	1	no	—
202	C₂×C₄×C₂₃	—	2	1	no	—
203	C₂×C₄×C₂₃	—	2	1	no	—
204	C₂×C₄×C₂₃	—	2	1	no	—
205	C₂×C₄×C₂₃	—	2	1	no	—
206	C₂×C₄×C₂₃	—	2	2	no	—
207	C₂×C₄×C₂₃	—	2	2	no	—
208	C₂×C₄×C₂₃	—	2	1	no	—
209	C₂×C₄×C₂₃	—	2	1	no	—
210	C₂×C₄×C₂₃	—	2	1	no	—
211	C₂×C₄×C₂₃	—	2	2	no	—
212	C₂×C₄×C₂₃	—	2	1	no	—
213	C₂×C₄×C₂₃	—	2	1	no	—
214	C₂×C₄×C₂₃	—	2	1	no	—
215	C₂×C₄×C₂₃	—	2	1	no	—
216	C₂×C₄×C₂₃	—	2	1	no	—
217	C₂×C₄×C₂₃	—	2	1	no	—
218	C₂×C₄×C₂₃	—	2	1	no	—
219	C₂×C₄×C₂₃	—	2	1	no	—
220	C₂×C₄×C₂₃	—	4	1	no	—
221	C₂×C₄×C₂₃	—	4	1	no	—
222	C₂×C₄×C₂₃	—	4	1	no	—
223	C₂×C₄×C₂₃	—	4	1	no	—
224	C₂×C₄×C₂₃	—	4	1	no	—
225	C₂×C₄×C₂₃	—	4	1	no	—
226	C₂×C₄×C₂₃	—	4	1	no	—
227	C₂×C₄×C₂₃	—	4	1	no	—
228	C₂×C₄×C₂₃	—	4	1	no	—
229	C₂×C₄×C₂₃	—	4	1	no	—
230	C₂×C₄×C₂₃	—	4	1	no	—
231	C₂×C₄×C₂₃	—	4	1	no	—
232	C₂×C₄×C₂₃	—	4	1	no	—
233	C₂×C₄×C₂₃	—	4	1	no	—
234	C₂×C₄×C₂₃	—	4	1	no	—
235	C₂×C₄×C₂₃	—	4	1	no	—
236	C₂×C₄×C₂₃	—	4	1	no	—
237	C₂×C₄×C₂₃	—	4	1	no	—
238	C₂×C₄×C₂₃	#135	1	2	yes	—
239	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
240	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
245	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
246	C₈×C₂₃	—	2	2	no	—
247	C₈×C₂₃	—	4	1	no	—
248	C₈×C₂₃	—	4	1	no	—
249	C₈×C₂₃	—	4	1	no	—
250	#2513	C₂×C₂₃	1	1	yes	characteristic
251	#2365	C₂×C₂₃	1	1	yes	characteristic, complemented
252	#2101	C₂×C₂₃	1	1	yes	characteristic, complemented
253	#2065	C₂×C₂₃	1	1	yes	characteristic
254	#2058	C₂×C₂₃	1	1	yes	characteristic, complemented
255	#2023	C₂×C₂₃	1	1	yes	characteristic
256	#1949	C₂×C₂₃	1	1	yes	characteristic, complemented
257	#1934	C₂×C₂₃	1	1	yes	characteristic
258	#1926	C₂×C₂₃	1	1	yes	characteristic
259	#1926	C₂×C₂₃	1	1	yes	characteristic
260	#1925	C₂×C₂₃	1	1	yes	characteristic
261	#1921	C₂×C₂₃	1	1	yes	characteristic, complemented
262	#1919	C₂×C₂₃	1	1	yes	characteristic, complemented
263	#1916	C₂×C₂₃	1	1	yes	characteristic, complemented
264	C₄×#106	C₂×C₂₃	1	1	yes	characteristic, complemented
265	C₂²×C₂₃	—	8	1	no	—
266	C₂²×C₂₃	—	8	1	no	—
267	C₂²×C₂₃	—	8	1	no	—
268	C₂²×C₂₃	—	8	1	no	—
269	C₂²×C₂₃	—	8	1	no	—
270	C₂²×C₂₃	—	8	1	no	—
271	C₂²×C₂₃	—	8	1	no	—
272	C₂²×C₂₃	#525	1	1	yes	characteristic
273	C₂²×C₂₃	#547	1	1	yes	characteristic
274	C₂²×C₂₃	#548	1	1	yes	characteristic
275	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
276	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₂²×C₂₃	#577	1	1	yes	characteristic
278	C₂²×C₂₃	#577	1	1	yes	characteristic
279	C₄×C₂₃	—	2	2	no	—
280	C₄×C₂₃	—	2	2	no	—
281	C₄×C₂₃	—	4	1	no	—
282	C₄×C₂₃	—	4	1	no	—
283	C₄×C₂₃	—	4	1	no	—
284	C₄×C₂₃	—	4	2	no	—
285	C₄×C₂₃	—	4	2	no	—
286	C₄×C₂₃	—	4	2	no	—
287	C₄×C₂₃	—	4	1	no	—
288	C₄×C₂₃	—	8	1	no	—
289	C₄×C₂₃	—	8	1	no	—
290	C₄×C₂₃	—	8	1	no	—
291	C₄×C₂₃	—	8	1	no	—
292	C₄×C₂₃	#529	1	1	yes	characteristic
293	C₄×C₂₃	#541	1	1	yes	characteristic
294	C₄×C₂₃	#556	1	1	yes	characteristic
295	C₄×C₂₃	#556	1	1	yes	characteristic
296	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
297	C₂×C₄×Q₈	—	2	1	no	—
298	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
299	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
300	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
301	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
302	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
303	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
304	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
305	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
306	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
307	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
308	#397	—	2	1	no	—
309	#397	—	2	1	no	—
310	#391	—	2	1	no	—
311	#390	C₂²×C₂₃	1	1	yes	characteristic
312	#390	C₂²×C₂₃	1	1	yes	characteristic
313	#390	C₂²×C₂₃	1	1	yes	characteristic
314	#389	C₂²×C₂₃	1	1	yes	characteristic
315	#389	C₂²×C₂₃	1	1	yes	characteristic
316	#389	C₂²×C₂₃	1	1	yes	characteristic
317	#388	—	2	1	no	—
318	#388	—	2	1	no	—
319	#387	—	2	1	no	—
320	#387	—	2	1	no	—
321	#382	C₂²×C₂₃	1	1	yes	characteristic
322	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
323	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
324	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
325	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
326	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
327	#340	C₂²×C₂₃	1	1	yes	characteristic
328	#340	C₂²×C₂₃	1	1	yes	characteristic
329	#340	C₂²×C₂₃	1	1	yes	characteristic
330	#340	C₂²×C₂₃	1	1	yes	characteristic
331	#340	C₂²×C₂₃	1	1	yes	characteristic
332	#340	C₂²×C₂₃	1	1	yes	characteristic
333	#340	C₂²×C₂₃	1	1	yes	characteristic
334	#340	C₂²×C₂₃	1	1	yes	characteristic
335	#336	C₂²×C₂₃	1	1	yes	characteristic
336	#336	C₂²×C₂₃	1	1	yes	characteristic
337	#336	C₂²×C₂₃	1	1	yes	characteristic
338	#336	C₂²×C₂₃	1	1	yes	characteristic
339	C₂×C₂₃	—	16	1	no	—
340	C₂×C₂₃	#2469	1	1	yes	characteristic
341	C₂×C₂₃	#3105	1	1	yes	characteristic
342	C₂×C₂₃	#3126	1	1	yes	characteristic
343	C₂×C₂₃	#3340	1	1	yes	characteristic
344	C₂×C₂₃	#3345	1	1	yes	characteristic
345	C₂×C₂₃	#3365	1	1	yes	characteristic
346	C₂×C₂₃	#3373	1	1	yes	characteristic
347	C₂²×Q₈	—	2	1	no	—
348	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
353	C₄⋊Q₈	—	2	2	no	—
354	C₄⋊Q₈	—	2	2	no	—
355	C₄×Q₈	—	4	4	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
382	#107	—	2	2	no	—
383	#106	—	2	2	no	—
384	#106	—	2	2	no	—
385	#106	—	2	2	no	—
386	C₄⋊C₈	—	2	2	no	—
387	#102	—	2	2	no	—
388	#102	—	2	2	no	—
389	#102	—	2	2	no	—
390	#102	—	2	2	no	—
391	C₄×C₈	—	2	2	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	D₄×C₂₃	1	1	yes	characteristic
402	#95	D₄×C₂₃	1	1	yes	characteristic
403	C₂₃	#27129	1	1	yes	characteristic, direct product factor, Sylow
404	C₂⁴	—	2	1	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	—	4	2	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	#41×C₂₃	1	2	yes	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₄⋊C₄	—	8	1	no	—
457	C₄⋊C₄	#41×C₂₃	1	2	yes	—
458	C₄⋊C₄	#41×C₂₃	1	2	yes	—
459	C₄⋊C₄	#41×C₂₃	1	2	yes	—
460	C₂²⋊C₄	—	4	2	no	—
461	C₂²⋊C₄	—	4	2	no	—
462	C₂²⋊C₄	—	8	1	no	—
463	C₂²⋊C₄	—	8	1	no	—
464	C₂²⋊C₄	—	8	1	no	—
465	C₂²⋊C₄	—	8	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	4	2	no	—
473	C₄²	—	4	2	no	—
474	C₄²	—	4	2	no	—
475	C₄²	—	8	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
484	Q₈	—	4	8	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	1	no	—
487	D₄	—	4	1	no	—
488	D₄	—	4	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	C₂₃×#135	1	2	yes	—
527	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
528	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
529	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
530	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
531	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
532	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
533	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
534	C₈	—	2	2	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	C₂₃×#525	1	1	yes	characteristic
546	C₂²	C₂₃×#547	1	1	yes	characteristic
547	C₂²	C₂₃×#548	1	1	yes	characteristic
548	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
549	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
550	C₂²	C₂₃×#577	1	1	yes	characteristic
551	C₂²	C₂₃×#577	1	1	yes	characteristic
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	C₂₃×#529	1	1	yes	characteristic
566	C₄	C₂₃×#541	1	1	yes	characteristic
567	C₄	C₂₃×#556	1	1	yes	characteristic
568	C₄	C₂₃×#556	1	1	yes	characteristic
569	C₂	—	16	1	no	—
570	C₂	C₂₃×#2469	1	1	yes	characteristic
571	C₂	C₂₃×#3105	1	1	yes	characteristic
572	C₂	C₂₃×#3126	1	1	yes	characteristic
573	C₂	C₂₃×#3340	1	1	yes	characteristic
574	C₂	C₂₃×#3345	1	1	yes	characteristic
575	C₂	C₂₃×#3365	1	1	yes	characteristic
576	C₂	C₂₃×#3373	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2365	C₂	semidirect
3. C₂₃×#2101	C₂	semidirect
5. C₂₃×#2058	C₂	semidirect
7. C₂₃×#1949	C₂	semidirect
12. C₂₃×#1921	C₂	semidirect
13. C₂₃×#1919	C₂	semidirect
14. C₂₃×#1916	C₂	semidirect
15. C₄×C₂₃×#106	C₂	semidirect
187. #27129	C₂₃	direct (N × H)
251. #2365	C₂×C₂₃	semidirect
252. #2101	C₂×C₂₃	semidirect
254. #2058	C₂×C₂₃	semidirect
256. #1949	C₂×C₂₃	semidirect
261. #1921	C₂×C₂₃	semidirect
262. #1919	C₂×C₂₃	semidirect
263. #1916	C₂×C₂₃	semidirect
264. C₄×#106	C₂×C₂₃	semidirect
403. C₂₃	#27129	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×#2513	2
C₂₃×#2365	2
C₂₃×#2101	2
C₂₃×#2065	2
C₂₃×#2058	2
C₂₃×#2023	2
C₂₃×#1949	2
C₂₃×#1934	2
C₂₃×#1926	2
C₂₃×#1925	2
C₂₃×#1921	2
C₂₃×#1919	2
C₂₃×#1916	2
C₄×C₂₃×#106	2
#27129	23

Subgroups — C23×#27129 #19174755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#27129 #19174755