Subgroups — C₄×C₂₃×#469 #19169159

Order 5888.

1170 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂₃×#121	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1936	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1895	C₂	1	2	yes	maximal, complemented
9	C₂₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₂₃	—	2	2	no	—
17	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#469	C₄	1	8	yes	direct product factor
20	C₄×D₈×C₂₃	—	2	4	no	—
21	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#102	C₂²	1	2	yes	—
25	C₂×C₂₃×#102	C₂²	1	2	yes	—
26	C₂×C₂₃×#102	C₂²	1	2	yes	—
27	C₄×M₁₆×C₂₃	—	2	4	no	—
28	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂₃×#390	C₂²	1	2	yes	—
33	C₂₃×#389	C₂²	1	2	yes	—
34	C₂₃×#388	—	2	2	no	—
35	C₂₃×#386	—	2	2	no	—
36	C₂₃×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₂₃	—	2	2	no	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂₃×#340	C₂²	1	2	yes	—
41	C₂₃×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₂₃	—	2	2	no	—
43	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₂₃	—	2	2	no	—
45	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₂₃	—	2	2	no	—
49	C₂×D₈×C₂₃	—	2	2	no	—
50	C₂×D₈×C₂₃	C₂×C₄	1	4	yes	complemented
51	C₂×M₁₆×C₂₃	—	2	2	no	—
52	C₂×M₁₆×C₂₃	—	2	2	no	—
53	C₂×M₁₆×C₂₃	—	2	2	no	—
54	C₂×M₁₆×C₂₃	—	2	2	no	—
55	C₂×M₁₆×C₂₃	—	2	2	no	—
56	C₂×M₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
57	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
61	C₂₃×#121	—	2	4	no	—
62	C₂₃×#121	C₂×C₄	1	8	yes	complemented
63	C₄×D₄×C₂₃	—	2	4	no	—
64	C₄×D₄×C₂₃	—	2	4	no	—
65	C₄×D₄×C₂₃	—	4	8	no	—
66	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
75	C₂×C₄²×C₂₃	—	2	2	no	—
76	C₂×C₄²×C₂₃	—	2	2	no	—
77	C₂×C₄²×C₂₃	—	2	2	no	—
78	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
82	C₂₃×#107	—	2	2	no	—
83	C₂₃×#106	—	2	2	no	—
84	C₂₃×#106	C₂×C₄	1	4	yes	complemented
85	C₂₃×#102	—	2	4	no	—
86	C₂₃×#102	—	2	4	no	—
87	C₂₃×#102	C₂×C₄	1	8	yes	complemented
88	C₂₃×#97	—	2	2	no	—
89	C₂₃×#97	—	2	2	no	—
90	C₄×C₈×C₂₃	—	2	2	no	—
91	C₄×C₈×C₂₃	D₄	1	4	yes	complemented
92	C₂₃×#95	—	2	2	no	—
93	C₂₃×#95	—	2	2	no	—
94	C₂₃×#95	—	2	2	no	—
95	C₂⁴×C₂₃	—	2	2	no	—
96	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₂₃	—	2	8	no	—
98	C₂×D₄×C₂₃	—	2	2	no	—
99	C₂×D₄×C₂₃	—	2	2	no	—
100	C₂×D₄×C₂₃	—	2	2	no	—
101	C₂×D₄×C₂₃	—	2	2	no	—
102	C₂×D₄×C₂₃	—	2	2	no	—
103	C₂×D₄×C₂₃	—	4	4	no	—
104	C₂×D₄×C₂₃	—	4	4	no	—
105	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₂₃	—	2	1	no	—
107	C₂²×C₄×C₂₃	—	2	1	no	—
108	C₂²×C₄×C₂₃	—	2	1	no	—
109	C₂²×C₄×C₂₃	—	2	1	no	—
110	C₂²×C₄×C₂₃	—	2	2	no	—
111	C₂²×C₄×C₂₃	—	2	2	no	—
112	C₂²×C₄×C₂₃	—	2	2	no	—
113	C₂²×C₄×C₂₃	—	2	4	no	—
114	C₂²×C₄×C₂₃	—	2	2	no	—
115	C₂²×C₄×C₂₃	—	2	2	no	—
116	C₂²×C₄×C₂₃	—	4	2	no	—
117	C₂²×C₄×C₂₃	—	4	4	no	—
118	C₂²×C₄×C₂₃	—	4	4	no	—
119	C₂²×C₄×C₂₃	—	4	4	no	—
120	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₃	#41	1	2	yes	—
127	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
128	D₈×C₂₃	—	2	8	no	—
129	M₁₆×C₂₃	—	2	8	no	—
130	M₁₆×C₂₃	—	2	8	no	—
131	C₂×C₈×C₂₃	—	2	1	no	—
132	C₂×C₈×C₂₃	—	2	1	no	—
133	C₂×C₈×C₂₃	—	2	1	no	—
134	C₂×C₈×C₂₃	—	2	1	no	—
135	C₂×C₈×C₂₃	—	2	1	no	—
136	C₂×C₈×C₂₃	—	2	1	no	—
137	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₂₃	#41	1	2	yes	—
142	C₂×C₈×C₂₃	#41	1	2	yes	—
143	C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₄⋊C₄×C₂₃	—	2	2	no	—
145	C₄⋊C₄×C₂₃	—	2	2	no	—
146	C₄⋊C₄×C₂₃	—	2	2	no	—
147	C₄⋊C₄×C₂₃	—	2	2	no	—
148	C₄⋊C₄×C₂₃	—	4	4	no	—
149	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
150	C₂²⋊C₄×C₂₃	—	2	8	no	—
151	C₂²⋊C₄×C₂₃	—	4	4	no	—
152	C₂²⋊C₄×C₂₃	—	4	4	no	—
153	C₂²⋊C₄×C₂₃	—	4	4	no	—
154	C₂²⋊C₄×C₂₃	—	4	4	no	—
155	C₄²×C₂₃	—	2	2	no	—
156	C₄²×C₂₃	—	2	2	no	—
157	C₄²×C₂₃	—	2	1	no	—
158	C₄²×C₂₃	—	2	1	no	—
159	C₄²×C₂₃	—	4	4	no	—
160	C₄²×C₂₃	C₂×D₄	1	2	yes	—
161	C₄²×C₂₃	#41	1	2	yes	—
162	C₄×#469	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₂₃	—	2	1	no	—
164	C₂³×C₂₃	—	2	1	no	—
165	C₂³×C₂₃	—	2	2	no	—
166	C₂³×C₂₃	—	2	2	no	—
167	C₂³×C₂₃	—	2	4	no	—
168	C₂³×C₂₃	—	4	2	no	—
169	C₂³×C₂₃	—	4	2	no	—
170	C₂³×C₂₃	—	4	2	no	—
171	C₂³×C₂₃	—	4	2	no	—
172	C₂³×C₂₃	—	4	2	no	—
173	C₂³×C₂₃	—	4	2	no	—
174	C₂³×C₂₃	C₄×D₄	1	2	yes	—
175	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
176	D₄×C₂₃	—	2	4	no	—
177	D₄×C₂₃	—	2	4	no	—
178	D₄×C₂₃	—	4	16	no	—
179	D₄×C₂₃	—	4	2	no	—
180	D₄×C₂₃	—	4	2	no	—
181	C₂×C₄×C₂₃	—	2	1	no	—
182	C₂×C₄×C₂₃	—	2	1	no	—
183	C₂×C₄×C₂₃	—	2	2	no	—
184	C₂×C₄×C₂₃	—	2	2	no	—
185	C₂×C₄×C₂₃	—	2	2	no	—
186	C₂×C₄×C₂₃	—	2	2	no	—
187	C₂×C₄×C₂₃	—	2	2	no	—
188	C₂×C₄×C₂₃	—	2	4	no	—
189	C₂×C₄×C₂₃	—	2	1	no	—
190	C₂×C₄×C₂₃	—	2	1	no	—
191	C₂×C₄×C₂₃	—	2	2	no	—
192	C₂×C₄×C₂₃	—	2	2	no	—
193	C₂×C₄×C₂₃	—	4	4	no	—
194	C₂×C₄×C₂₃	—	4	2	no	—
195	C₂×C₄×C₂₃	—	4	2	no	—
196	C₂×C₄×C₂₃	—	4	4	no	—
197	C₂×C₄×C₂₃	—	4	2	no	—
198	C₂×C₄×C₂₃	—	4	2	no	—
199	C₂×C₄×C₂₃	—	4	2	no	—
200	C₂×C₄×C₂₃	—	4	2	no	—
201	C₂×C₄×C₂₃	—	4	2	no	—
202	C₂×C₄×C₂₃	—	4	2	no	—
203	C₂×C₄×C₂₃	—	8	8	no	—
204	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₂₃	#121	1	2	yes	—
206	C₂×C₄×C₂₃	#121	1	2	yes	—
207	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
208	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
214	C₈×C₂₃	—	2	2	no	—
215	C₈×C₂₃	—	2	2	no	—
216	C₈×C₂₃	—	2	2	no	—
217	C₈×C₂₃	C₄×D₄	1	4	yes	complemented
218	C₂×#469	C₂×C₂₃	1	1	yes	characteristic
219	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
220	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
221	C₄×#121	C₂×C₂₃	1	2	yes	complemented
222	#1972	C₂×C₂₃	1	1	yes	characteristic, complemented
223	#1944	C₂×C₂₃	1	1	yes	characteristic, complemented
224	#1936	C₂×C₂₃	1	2	yes	complemented
225	#1895	C₂×C₂₃	1	2	yes	complemented
226	#1809	C₂×C₂₃	1	1	yes	characteristic, complemented
227	C₄×#106	C₂×C₂₃	1	1	yes	characteristic, complemented
228	C₄×#102	C₂×C₂₃	1	2	yes	complemented
229	C₂²×C₂₃	—	2	4	no	—
230	C₂²×C₂₃	—	2	2	no	—
231	C₂²×C₂₃	—	4	2	no	—
232	C₂²×C₂₃	—	4	1	no	—
233	C₂²×C₂₃	—	4	1	no	—
234	C₂²×C₂₃	—	4	4	no	—
235	C₂²×C₂₃	—	4	4	no	—
236	C₂²×C₂₃	—	4	4	no	—
237	C₂²×C₂₃	—	8	2	no	—
238	C₂²×C₂₃	—	8	2	no	—
239	C₂²×C₂₃	—	8	2	no	—
240	C₂²×C₂₃	—	8	2	no	—
241	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
242	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
243	C₂²×C₂₃	#532	1	1	yes	characteristic
244	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
245	C₂²×C₂₃	#575	1	2	yes	—
246	C₄×C₂₃	—	2	2	no	—
247	C₄×C₂₃	—	2	2	no	—
248	C₄×C₂₃	—	4	4	no	—
249	C₄×C₂₃	—	4	1	no	—
250	C₄×C₂₃	—	4	1	no	—
251	C₄×C₂₃	—	8	2	no	—
252	C₄×C₂₃	—	8	2	no	—
253	C₄×C₂₃	#469	1	4	yes	direct product factor
254	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
256	C₄×C₂₃	#525	1	1	yes	characteristic
257	C₄×C₂₃	#529	1	1	yes	characteristic
258	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
259	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
260	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
261	C₂×#121	C₂²×C₂₃	1	2	yes	—
262	C₂×C₄×D₄	—	2	2	no	—
263	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
264	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
265	#469	C₄×C₂₃	1	8	yes	direct product factor
266	C₄×D₈	—	2	4	no	—
267	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
268	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
269	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
270	C₂×#102	C₂²×C₂₃	1	2	yes	—
271	C₂×#102	C₂²×C₂₃	1	2	yes	—
272	C₂×#102	C₂²×C₂₃	1	2	yes	—
273	C₄×M₁₆	—	2	4	no	—
274	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
275	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
277	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
278	#390	C₂²×C₂₃	1	2	yes	—
279	#389	C₂²×C₂₃	1	2	yes	—
280	#388	—	2	2	no	—
281	#386	—	2	2	no	—
282	#380	C₂²×C₂₃	1	2	yes	—
283	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
284	C₄×C₂²⋊C₄	—	2	2	no	—
285	#340	C₂²×C₂₃	1	2	yes	—
286	#340	C₂²×C₂₃	1	2	yes	—
287	#340	C₂²×C₂₃	1	2	yes	—
288	C₂×C₂₃	—	4	2	no	—
289	C₂×C₂₃	—	8	4	no	—
290	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
291	C₂×C₂₃	C₄×AGL(1,ℤ/8)	1	2	yes	—
292	C₂×C₂₃	C₂×#469	1	1	yes	characteristic
293	C₂×C₂₃	#3054	1	1	yes	characteristic
294	C₂×C₂₃	#3171	1	2	yes	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
299	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
301	C₂×D₈	—	2	2	no	—
302	C₂×D₈	—	2	2	no	—
303	C₂×D₈	C₂×C₄×C₂₃	1	4	yes	complemented
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	C₂×C₄×C₂₃	1	4	yes	complemented
310	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
314	#121	—	2	4	no	—
315	#121	C₂×C₄×C₂₃	1	8	yes	complemented
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	4	8	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	2	no	—
331	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
332	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
335	#107	—	2	2	no	—
336	#106	—	2	2	no	—
337	#106	C₂×C₄×C₂₃	1	4	yes	complemented
338	#102	—	2	4	no	—
339	#102	—	2	4	no	—
340	#102	C₂×C₄×C₂₃	1	8	yes	complemented
341	#97	—	2	2	no	—
342	#97	—	2	2	no	—
343	C₄×C₈	—	2	2	no	—
344	C₄×C₈	D₄×C₂₃	1	4	yes	complemented
345	#95	—	2	2	no	—
346	#95	—	2	2	no	—
347	#95	—	2	2	no	—
348	C₂₃	C₄×#469	1	1	yes	characteristic, direct product factor, Sylow
349	C₂⁴	—	2	2	no	—
350	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	4	4	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
380	C₂²×C₄	#41×C₂₃	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
382	D₈	—	2	8	no	—
383	M₁₆	—	2	8	no	—
384	M₁₆	—	2	8	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
392	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
393	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
394	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
395	C₂×C₈	#41×C₂₃	1	2	yes	—
396	C₂×C₈	#41×C₂₃	1	2	yes	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	4	4	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	4	4	no	—
414	C₄²	C₂×D₄×C₂₃	1	2	yes	—
415	C₄²	#41×C₂₃	1	2	yes	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	C₄×D₄×C₂₃	1	2	yes	—
428	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	4	16	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	8	8	no	—
457	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
458	C₂×C₄	C₂₃×#121	1	2	yes	—
459	C₂×C₄	C₂₃×#121	1	2	yes	—
460	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
461	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	C₄×D₄×C₂₃	1	4	yes	complemented
471	C₂²	—	2	4	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
484	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
485	C₂²	C₂₃×#532	1	1	yes	characteristic
486	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
487	C₂²	C₂₃×#575	1	2	yes	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	8	2	no	—
494	C₄	—	8	2	no	—
495	C₄	C₂₃×#469	1	4	yes	direct product factor
496	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
497	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
498	C₄	C₂₃×#525	1	1	yes	characteristic
499	C₄	C₂₃×#529	1	1	yes	characteristic
500	C₂	—	4	2	no	—
501	C₂	—	8	4	no	—
502	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
503	C₂	C₄×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
504	C₂	C₂×C₂₃×#469	1	1	yes	characteristic
505	C₂	C₂₃×#3054	1	1	yes	characteristic
506	C₂	C₂₃×#3171	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂²×D₄
prime radical	C₂×C₂₃×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₂₃	C₂	semidirect
3. C₂×C₄×M₁₆×C₂₃	C₂	semidirect
4. C₄×C₂₃×#121	C₂	semidirect
5. C₂₃×#1972	C₂	semidirect
6. C₂₃×#1944	C₂	semidirect
7. C₂₃×#1936	C₂	semidirect
8. C₂₃×#1895	C₂	semidirect
9. C₂₃×#1809	C₂	semidirect
10. C₄×C₂₃×#106	C₂	semidirect
11. C₄×C₂₃×#102	C₂	semidirect
19. C₂₃×#469	C₄	direct (N × H)
50. C₂×D₈×C₂₃	C₂×C₄	semidirect
56. C₂×M₁₆×C₂₃	C₂×C₄	semidirect
62. C₂₃×#121	C₂×C₄	semidirect
84. C₂₃×#106	C₂×C₄	semidirect
87. C₂₃×#102	C₂×C₄	semidirect
91. C₄×C₈×C₂₃	D₄	semidirect
162. C₄×#469	C₂₃	direct (N × H)
217. C₈×C₂₃	C₄×D₄	semidirect
219. C₂×C₄×D₈	C₂×C₂₃	semidirect
220. C₂×C₄×M₁₆	C₂×C₂₃	semidirect
221. C₄×#121	C₂×C₂₃	semidirect
222. #1972	C₂×C₂₃	semidirect
223. #1944	C₂×C₂₃	semidirect
224. #1936	C₂×C₂₃	semidirect
225. #1895	C₂×C₂₃	semidirect
226. #1809	C₂×C₂₃	semidirect
227. C₄×#106	C₂×C₂₃	semidirect
228. C₄×#102	C₂×C₂₃	semidirect
253. C₄×C₂₃	#469	direct (N × H)
265. #469	C₄×C₂₃	direct (N × H)
303. C₂×D₈	C₂×C₄×C₂₃	semidirect
309. C₂×M₁₆	C₂×C₄×C₂₃	semidirect
315. #121	C₂×C₄×C₂₃	semidirect
337. #106	C₂×C₄×C₂₃	semidirect
340. #102	C₂×C₄×C₂₃	semidirect
344. C₄×C₈	D₄×C₂₃	semidirect
348. C₂₃	C₄×#469	direct (N × H)
470. C₈	C₄×D₄×C₂₃	semidirect
495. C₄	C₂₃×#469	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×#469	2
C₂×C₄×D₈×C₂₃	2
C₂×C₄×M₁₆×C₂₃	2
C₄×C₂₃×#121	2
C₂₃×#1972	2
C₂₃×#1944	2
C₂₃×#1936	2
C₂₃×#1895	2
C₂₃×#1809	2
C₄×C₂₃×#106	2
C₄×C₂₃×#102	2
C₄×#469	23

Subgroups — C4×C23×#469 #19169159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#469 #19169159