Subgroups — C₄×C₆₁×#469 #29524966

Order 15616.

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×C₆₁×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#121×C₆₁	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1936	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1895	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1809	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#106×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₆₁	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#121×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₆₁	—	2	2	no	—
17	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
18	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#469	C₄	1	8	yes	direct product factor
20	C₄×D₈×C₆₁	—	2	4	no	—
21	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#102×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	2	yes	—
26	C₂×#102×C₆₁	C₂²	1	2	yes	—
27	C₄×M₁₆×C₆₁	—	2	4	no	—
28	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#390	C₂²	1	2	yes	—
33	C₆₁×#389	C₂²	1	2	yes	—
34	C₆₁×#388	—	2	2	no	—
35	C₆₁×#386	—	2	2	no	—
36	C₆₁×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₆₁	—	2	2	no	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₆₁	—	2	2	no	—
43	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₆₁	—	2	2	no	—
45	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₆₁	—	2	2	no	—
49	C₂×D₈×C₆₁	—	2	2	no	—
50	C₂×D₈×C₆₁	C₂×C₄	1	4	yes	complemented
51	C₂×M₁₆×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	—	2	2	no	—
53	C₂×M₁₆×C₆₁	—	2	2	no	—
54	C₂×M₁₆×C₆₁	—	2	2	no	—
55	C₂×M₁₆×C₆₁	—	2	2	no	—
56	C₂×M₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
61	#121×C₆₁	—	2	4	no	—
62	#121×C₆₁	C₂×C₄	1	8	yes	complemented
63	C₄×D₄×C₆₁	—	2	4	no	—
64	C₄×D₄×C₆₁	—	2	4	no	—
65	C₄×D₄×C₆₁	—	4	8	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₄²×C₆₁	—	2	2	no	—
76	C₂×C₄²×C₆₁	—	2	2	no	—
77	C₂×C₄²×C₆₁	—	2	2	no	—
78	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
82	#107×C₆₁	—	2	2	no	—
83	#106×C₆₁	—	2	2	no	—
84	#106×C₆₁	C₂×C₄	1	4	yes	complemented
85	#102×C₆₁	—	2	4	no	—
86	#102×C₆₁	—	2	4	no	—
87	#102×C₆₁	C₂×C₄	1	8	yes	complemented
88	#97×C₆₁	—	2	2	no	—
89	#97×C₆₁	—	2	2	no	—
90	C₄×C₈×C₆₁	—	2	2	no	—
91	C₄×C₈×C₆₁	D₄	1	4	yes	complemented
92	#95×C₆₁	—	2	2	no	—
93	#95×C₆₁	—	2	2	no	—
94	#95×C₆₁	—	2	2	no	—
95	C₂⁴×C₆₁	—	2	2	no	—
96	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₆₁	—	2	8	no	—
98	C₂×D₄×C₆₁	—	2	2	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	4	4	no	—
104	C₂×D₄×C₆₁	—	4	4	no	—
105	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	—	2	2	no	—
113	C₂²×C₄×C₆₁	—	2	4	no	—
114	C₂²×C₄×C₆₁	—	2	2	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	4	2	no	—
117	C₂²×C₄×C₆₁	—	4	4	no	—
118	C₂²×C₄×C₆₁	—	4	4	no	—
119	C₂²×C₄×C₆₁	—	4	4	no	—
120	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	#41	1	2	yes	—
127	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
128	D₈×C₆₁	—	2	8	no	—
129	M₁₆×C₆₁	—	2	8	no	—
130	M₁₆×C₆₁	—	2	8	no	—
131	C₂×C₈×C₆₁	—	2	1	no	—
132	C₂×C₈×C₆₁	—	2	1	no	—
133	C₂×C₈×C₆₁	—	2	1	no	—
134	C₂×C₈×C₆₁	—	2	1	no	—
135	C₂×C₈×C₆₁	—	2	1	no	—
136	C₂×C₈×C₆₁	—	2	1	no	—
137	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₆₁	#41	1	2	yes	—
142	C₂×C₈×C₆₁	#41	1	2	yes	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	2	2	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	2	2	no	—
147	C₄⋊C₄×C₆₁	—	2	2	no	—
148	C₄⋊C₄×C₆₁	—	4	4	no	—
149	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
150	C₂²⋊C₄×C₆₁	—	2	8	no	—
151	C₂²⋊C₄×C₆₁	—	4	4	no	—
152	C₂²⋊C₄×C₆₁	—	4	4	no	—
153	C₂²⋊C₄×C₆₁	—	4	4	no	—
154	C₂²⋊C₄×C₆₁	—	4	4	no	—
155	C₄²×C₆₁	—	2	2	no	—
156	C₄²×C₆₁	—	2	2	no	—
157	C₄²×C₆₁	—	2	1	no	—
158	C₄²×C₆₁	—	2	1	no	—
159	C₄²×C₆₁	—	4	4	no	—
160	C₄²×C₆₁	C₂×D₄	1	2	yes	—
161	C₄²×C₆₁	#41	1	2	yes	—
162	C₂³×C₆₁	—	2	1	no	—
163	C₂³×C₆₁	—	2	1	no	—
164	C₂³×C₆₁	—	2	2	no	—
165	C₂³×C₆₁	—	2	2	no	—
166	C₂³×C₆₁	—	2	4	no	—
167	C₂³×C₆₁	—	4	2	no	—
168	C₂³×C₆₁	—	4	2	no	—
169	C₂³×C₆₁	—	4	2	no	—
170	C₂³×C₆₁	—	4	2	no	—
171	C₂³×C₆₁	—	4	2	no	—
172	C₂³×C₆₁	—	4	2	no	—
173	C₂³×C₆₁	C₄×D₄	1	2	yes	—
174	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
175	D₄×C₆₁	—	2	4	no	—
176	D₄×C₆₁	—	2	4	no	—
177	D₄×C₆₁	—	4	16	no	—
178	D₄×C₆₁	—	4	2	no	—
179	D₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	2	1	no	—
181	C₂×C₄×C₆₁	—	2	1	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	2	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	2	no	—
186	C₂×C₄×C₆₁	—	2	2	no	—
187	C₂×C₄×C₆₁	—	2	4	no	—
188	C₂×C₄×C₆₁	—	2	1	no	—
189	C₂×C₄×C₆₁	—	2	1	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	4	4	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	4	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	4	2	no	—
199	C₂×C₄×C₆₁	—	4	2	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	—	8	8	no	—
203	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₆₁	#121	1	2	yes	—
205	C₂×C₄×C₆₁	#121	1	2	yes	—
206	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
207	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
213	C₈×C₆₁	—	2	2	no	—
214	C₈×C₆₁	—	2	2	no	—
215	C₈×C₆₁	—	2	2	no	—
216	C₈×C₆₁	C₄×D₄	1	4	yes	complemented
217	C₄×#469	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₆₁	—	2	4	no	—
219	C₂²×C₆₁	—	2	2	no	—
220	C₂²×C₆₁	—	4	2	no	—
221	C₂²×C₆₁	—	4	1	no	—
222	C₂²×C₆₁	—	4	1	no	—
223	C₂²×C₆₁	—	4	4	no	—
224	C₂²×C₆₁	—	4	4	no	—
225	C₂²×C₆₁	—	4	4	no	—
226	C₂²×C₆₁	—	8	2	no	—
227	C₂²×C₆₁	—	8	2	no	—
228	C₂²×C₆₁	—	8	2	no	—
229	C₂²×C₆₁	—	8	2	no	—
230	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
231	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
232	C₂²×C₆₁	#532	1	1	yes	characteristic
233	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
234	C₂²×C₆₁	#575	1	2	yes	—
235	C₄×C₆₁	—	2	2	no	—
236	C₄×C₆₁	—	2	2	no	—
237	C₄×C₆₁	—	4	4	no	—
238	C₄×C₆₁	—	4	1	no	—
239	C₄×C₆₁	—	4	1	no	—
240	C₄×C₆₁	—	8	2	no	—
241	C₄×C₆₁	—	8	2	no	—
242	C₄×C₆₁	#469	1	4	yes	direct product factor
243	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
245	C₄×C₆₁	#525	1	1	yes	characteristic
246	C₄×C₆₁	#529	1	1	yes	characteristic
247	C₂×#469	C₂×C₆₁	1	1	yes	characteristic
248	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
249	C₂×C₄×M₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
250	C₄×#121	C₂×C₆₁	1	2	yes	complemented
251	#1972	C₂×C₆₁	1	1	yes	characteristic, complemented
252	#1944	C₂×C₆₁	1	1	yes	characteristic, complemented
253	#1936	C₂×C₆₁	1	2	yes	complemented
254	#1895	C₂×C₆₁	1	2	yes	complemented
255	#1809	C₂×C₆₁	1	1	yes	characteristic, complemented
256	C₄×#106	C₂×C₆₁	1	1	yes	characteristic, complemented
257	C₄×#102	C₂×C₆₁	1	2	yes	complemented
258	C₂×C₆₁	—	4	2	no	—
259	C₂×C₆₁	—	8	4	no	—
260	C₂×C₆₁	C₄×#121	1	1	yes	characteristic
261	C₂×C₆₁	C₄×AGL(1,ℤ/8)	1	2	yes	—
262	C₂×C₆₁	C₂×#469	1	1	yes	characteristic
263	C₂×C₆₁	#3054	1	1	yes	characteristic
264	C₂×C₆₁	#3171	1	2	yes	—
265	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
266	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
267	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
268	C₂×#121	C₂²×C₆₁	1	2	yes	—
269	C₂×C₄×D₄	—	2	2	no	—
270	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
271	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
272	#469	C₄×C₆₁	1	8	yes	direct product factor
273	C₄×D₈	—	2	4	no	—
274	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
275	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
276	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
277	C₂×#102	C₂²×C₆₁	1	2	yes	—
278	C₂×#102	C₂²×C₆₁	1	2	yes	—
279	C₂×#102	C₂²×C₆₁	1	2	yes	—
280	C₄×M₁₆	—	2	4	no	—
281	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
282	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
284	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
285	#390	C₂²×C₆₁	1	2	yes	—
286	#389	C₂²×C₆₁	1	2	yes	—
287	#388	—	2	2	no	—
288	#386	—	2	2	no	—
289	#380	C₂²×C₆₁	1	2	yes	—
290	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
291	C₄×C₂²⋊C₄	—	2	2	no	—
292	#340	C₂²×C₆₁	1	2	yes	—
293	#340	C₂²×C₆₁	1	2	yes	—
294	#340	C₂²×C₆₁	1	2	yes	—
295	C₆₁	C₄×#469	1	1	yes	characteristic, direct product factor, Sylow
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
300	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
302	C₂×D₈	—	2	2	no	—
303	C₂×D₈	—	2	2	no	—
304	C₂×D₈	C₂×C₄×C₆₁	1	4	yes	complemented
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	—	2	2	no	—
310	C₂×M₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
311	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
315	#121	—	2	4	no	—
316	#121	C₂×C₄×C₆₁	1	8	yes	complemented
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	4	8	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
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×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	2	no	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
333	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
336	#107	—	2	2	no	—
337	#106	—	2	2	no	—
338	#106	C₂×C₄×C₆₁	1	4	yes	complemented
339	#102	—	2	4	no	—
340	#102	—	2	4	no	—
341	#102	C₂×C₄×C₆₁	1	8	yes	complemented
342	#97	—	2	2	no	—
343	#97	—	2	2	no	—
344	C₄×C₈	—	2	2	no	—
345	C₄×C₈	D₄×C₆₁	1	4	yes	complemented
346	#95	—	2	2	no	—
347	#95	—	2	2	no	—
348	#95	—	2	2	no	—
349	C₂⁴	—	2	2	no	—
350	C₂⁴	C₂×D₄×C₆₁	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×C₆₁	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×C₆₁	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
380	C₂²×C₄	#41×C₆₁	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₆₁	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×C₆₁	1	2	yes	—
392	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
393	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
394	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
395	C₂×C₈	#41×C₆₁	1	2	yes	—
396	C₂×C₈	#41×C₆₁	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×C₆₁	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×C₆₁	1	2	yes	—
415	C₄²	#41×C₆₁	1	2	yes	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	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×C₆₁	1	2	yes	—
428	C₂³	C₂²×D₄×C₆₁	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	1	no	—
435	C₂×C₄	—	2	2	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×C₆₁	1	2	yes	—
458	C₂×C₄	#121×C₆₁	1	2	yes	—
459	C₂×C₄	#121×C₆₁	1	2	yes	—
460	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
461	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	C₄×D₄×C₆₁	1	4	yes	complemented
471	C₂²	—	2	2	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	2	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×C₆₁	1	1	yes	characteristic
484	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
485	C₂²	C₆₁×#532	1	1	yes	characteristic
486	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
487	C₂²	C₆₁×#575	1	2	yes	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	4	no	—
493	C₄	—	8	2	no	—
494	C₄	—	8	2	no	—
495	C₄	C₆₁×#469	1	4	yes	direct product factor
496	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
497	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
498	C₄	C₆₁×#525	1	1	yes	characteristic
499	C₄	C₆₁×#529	1	1	yes	characteristic
500	C₂	—	4	2	no	—
501	C₂	—	8	4	no	—
502	C₂	C₄×#121×C₆₁	1	1	yes	characteristic
503	C₂	C₄×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
504	C₂	C₂×C₆₁×#469	1	1	yes	characteristic
505	C₂	C₆₁×#3054	1	1	yes	characteristic
506	C₂	C₆₁×#3171	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂³×C₆₁	C₂²×D₄
prime radical	C₂×C₆₁×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₆₁	C₂	semidirect
3. C₂×C₄×M₁₆×C₆₁	C₂	semidirect
4. C₄×#121×C₆₁	C₂	semidirect
5. C₆₁×#1972	C₂	semidirect
6. C₆₁×#1944	C₂	semidirect
7. C₆₁×#1936	C₂	semidirect
8. C₆₁×#1895	C₂	semidirect
9. C₆₁×#1809	C₂	semidirect
10. C₄×#106×C₆₁	C₂	semidirect
11. C₄×#102×C₆₁	C₂	semidirect
19. C₆₁×#469	C₄	direct (N × H)
50. C₂×D₈×C₆₁	C₂×C₄	semidirect
56. C₂×M₁₆×C₆₁	C₂×C₄	semidirect
62. #121×C₆₁	C₂×C₄	semidirect
84. #106×C₆₁	C₂×C₄	semidirect
87. #102×C₆₁	C₂×C₄	semidirect
91. C₄×C₈×C₆₁	D₄	semidirect
216. C₈×C₆₁	C₄×D₄	semidirect
217. C₄×#469	C₆₁	direct (N × H)
242. C₄×C₆₁	#469	direct (N × H)
248. C₂×C₄×D₈	C₂×C₆₁	semidirect
249. C₂×C₄×M₁₆	C₂×C₆₁	semidirect
250. C₄×#121	C₂×C₆₁	semidirect
251. #1972	C₂×C₆₁	semidirect
252. #1944	C₂×C₆₁	semidirect
253. #1936	C₂×C₆₁	semidirect
254. #1895	C₂×C₆₁	semidirect
255. #1809	C₂×C₆₁	semidirect
256. C₄×#106	C₂×C₆₁	semidirect
257. C₄×#102	C₂×C₆₁	semidirect
272. #469	C₄×C₆₁	direct (N × H)
295. C₆₁	C₄×#469	direct (N × H)
304. C₂×D₈	C₂×C₄×C₆₁	semidirect
310. C₂×M₁₆	C₂×C₄×C₆₁	semidirect
316. #121	C₂×C₄×C₆₁	semidirect
338. #106	C₂×C₄×C₆₁	semidirect
341. #102	C₂×C₄×C₆₁	semidirect
345. C₄×C₈	D₄×C₆₁	semidirect
470. C₈	C₄×D₄×C₆₁	semidirect
495. C₄	C₆₁×#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×C₆₁×#469	2
C₂×C₄×D₈×C₆₁	2
C₂×C₄×M₁₆×C₆₁	2
C₄×#121×C₆₁	2
C₆₁×#1972	2
C₆₁×#1944	2
C₆₁×#1936	2
C₆₁×#1895	2
C₆₁×#1809	2
C₄×#106×C₆₁	2
C₄×#102×C₆₁	2
C₄×#469	61

Subgroups — C4×C61×#469 #29524966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₆₁×#469 #29524966