Subgroups — C₆₁×#24339 #29527772

Order 15616.

1112 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#442	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2580	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2059	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2025	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1879	C₂	1	2	yes	maximal
10	C₆₁×#1862	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₆₁×#554	—	2	4	no	—
14	C₆₁×#554	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#125×C₆₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
24	C₆₁×#474	—	2	4	no	—
25	C₆₁×#442	—	2	4	no	—
26	C₂×#107×C₆₁	C₂²	1	2	yes	—
27	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#102×C₆₁	C₂²	1	2	yes	—
31	C₂×#102×C₆₁	C₂²	1	2	yes	—
32	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#399	—	2	1	no	—
35	C₆₁×#393	—	2	1	no	—
36	C₆₁×#390	C₂²	1	2	yes	—
37	C₆₁×#389	C₂²	1	2	yes	—
38	C₆₁×#385	—	2	2	no	—
39	C₆₁×#382	C₂²	1	1	yes	characteristic
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₆₁×#336	C₂²	1	2	yes	—
44	C₆₁×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₆₁	—	2	1	no	—
46	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	—	2	1	no	—
50	C₂³×C₄×C₆₁	—	2	2	no	—
51	C₂³×C₄×C₆₁	—	2	1	no	—
52	C₂×D₈×C₆₁	—	2	2	no	—
53	C₂×D₈×C₆₁	—	2	2	no	—
54	C₂×D₈×C₆₁	Q₈	1	4	yes	complemented
55	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₆₁	—	2	2	no	—
59	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
60	#125×C₆₁	—	2	4	no	—
61	#125×C₆₁	—	2	4	no	—
62	C₂²⋊Q₈×C₆₁	—	2	8	no	—
63	C₂²⋊Q₈×C₆₁	—	2	16	no	—
64	C₄×Q₈×C₆₁	—	2	2	no	—
65	C₄×Q₈×C₆₁	—	2	2	no	—
66	C₄×D₄×C₆₁	—	2	4	no	—
67	C₄×D₄×C₆₁	—	2	4	no	—
68	C₄×D₄×C₆₁	—	2	2	no	—
69	C₄×D₄×C₆₁	—	2	2	no	—
70	C₄×D₄×C₆₁	—	2	2	no	—
71	C₄×D₄×C₆₁	D₄	1	4	yes	—
72	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
88	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
89	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
90	#107×C₆₁	—	2	4	no	—
91	#106×C₆₁	—	2	2	no	—
92	C₄⋊C₈×C₆₁	—	2	2	no	—
93	#102×C₆₁	—	2	2	no	—
94	#102×C₆₁	—	2	4	no	—
95	#102×C₆₁	—	2	2	no	—
96	#102×C₆₁	—	2	4	no	—
97	#97×C₆₁	—	2	2	no	—
98	#95×C₆₁	—	2	1	no	—
99	#95×C₆₁	—	2	1	no	—
100	#95×C₆₁	—	2	2	no	—
101	C₂⁴×C₆₁	—	2	1	no	—
102	C₂⁴×C₆₁	—	2	1	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	—	2	4	no	—
105	C₂×Q₈×C₆₁	—	4	2	no	—
106	C₂×Q₈×C₆₁	—	8	2	no	—
107	C₂×D₄×C₆₁	—	2	1	no	—
108	C₂×D₄×C₆₁	—	2	1	no	—
109	C₂×D₄×C₆₁	—	2	1	no	—
110	C₂×D₄×C₆₁	—	2	1	no	—
111	C₂×D₄×C₆₁	—	2	1	no	—
112	C₂×D₄×C₆₁	—	2	1	no	—
113	C₂×D₄×C₆₁	—	2	1	no	—
114	C₂×D₄×C₆₁	—	2	1	no	—
115	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
116	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
117	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
118	C₂×D₄×C₆₁	#41	1	2	yes	—
119	C₂²×C₄×C₆₁	—	2	1	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	8	no	—
122	C₂²×C₄×C₆₁	—	2	4	no	—
123	C₂²×C₄×C₆₁	—	2	2	no	—
124	C₂²×C₄×C₆₁	—	2	1	no	—
125	C₂²×C₄×C₆₁	—	4	4	no	—
126	C₂²×C₄×C₆₁	—	4	2	no	—
127	C₂²×C₄×C₆₁	—	8	2	no	—
128	C₂²×C₄×C₆₁	—	8	2	no	—
129	C₂²×C₄×C₆₁	—	8	2	no	—
130	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
135	D₈×C₆₁	—	2	8	no	—
136	C₂×C₈×C₆₁	—	2	1	no	—
137	C₂×C₈×C₆₁	—	2	1	no	—
138	C₂×C₈×C₆₁	—	2	1	no	—
139	C₂×C₈×C₆₁	—	2	2	no	—
140	C₂×C₈×C₆₁	—	2	2	no	—
141	C₂×C₈×C₆₁	—	2	1	no	—
142	C₂×C₈×C₆₁	—	2	1	no	—
143	C₂×C₈×C₆₁	—	2	2	no	—
144	C₂×C₈×C₆₁	C₂×Q₈	1	2	yes	—
145	C₄⋊C₄×C₆₁	—	2	8	no	—
146	C₄⋊C₄×C₆₁	—	2	8	no	—
147	C₄⋊C₄×C₆₁	—	2	2	no	—
148	C₄⋊C₄×C₆₁	—	2	4	no	—
149	C₄⋊C₄×C₆₁	—	2	4	no	—
150	C₄⋊C₄×C₆₁	—	2	1	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	1	no	—
153	C₄⋊C₄×C₆₁	—	2	1	no	—
154	C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₄⋊C₄×C₆₁	—	2	2	no	—
156	C₄⋊C₄×C₆₁	—	8	2	no	—
157	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
159	C₂²⋊C₄×C₆₁	—	2	8	no	—
160	C₂²⋊C₄×C₆₁	—	2	4	no	—
161	C₂²⋊C₄×C₆₁	—	4	4	no	—
162	C₂²⋊C₄×C₆₁	—	4	2	no	—
163	C₂²⋊C₄×C₆₁	—	8	2	no	—
164	C₄²×C₆₁	—	2	2	no	—
165	C₄²×C₆₁	—	2	2	no	—
166	C₄²×C₆₁	C₂×D₄	1	2	yes	—
167	C₄²×C₆₁	C₂×D₄	1	2	yes	—
168	C₂³×C₆₁	—	2	2	no	—
169	C₂³×C₆₁	—	2	2	no	—
170	C₂³×C₆₁	—	2	2	no	—
171	C₂³×C₆₁	—	2	2	no	—
172	C₂³×C₆₁	—	4	2	no	—
173	C₂³×C₆₁	—	4	2	no	—
174	C₂³×C₆₁	—	4	1	no	—
175	C₂³×C₆₁	—	4	1	no	—
176	C₂³×C₆₁	—	4	2	no	—
177	C₂³×C₆₁	—	4	2	no	—
178	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₆₁	—	4	4	no	—
180	Q₈×C₆₁	—	8	4	no	—
181	D₄×C₆₁	—	2	2	no	—
182	D₄×C₆₁	—	2	2	no	—
183	D₄×C₆₁	—	2	2	no	—
184	D₄×C₆₁	—	2	2	no	—
185	D₄×C₆₁	—	2	2	no	—
186	D₄×C₆₁	—	4	1	no	—
187	D₄×C₆₁	—	4	1	no	—
188	D₄×C₆₁	C₂²⋊Q₈	1	4	yes	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	4	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	2	2	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	4	8	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	1	no	—
204	C₂×C₄×C₆₁	—	4	2	no	—
205	C₂×C₄×C₆₁	—	4	2	no	—
206	C₂×C₄×C₆₁	—	4	2	no	—
207	C₂×C₄×C₆₁	—	4	2	no	—
208	C₂×C₄×C₆₁	—	8	4	no	—
209	C₂×C₄×C₆₁	—	8	8	no	—
210	C₂×C₄×C₆₁	#120	1	2	yes	—
211	C₂×C₄×C₆₁	#120	1	2	yes	—
212	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
218	C₈×C₆₁	—	2	2	no	—
219	C₈×C₆₁	—	4	1	no	—
220	C₈×C₆₁	—	4	2	no	—
221	#24339	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₆₁	—	2	4	no	—
223	C₂²×C₆₁	—	4	4	no	—
224	C₂²×C₆₁	—	4	4	no	—
225	C₂²×C₆₁	—	4	2	no	—
226	C₂²×C₆₁	—	4	2	no	—
227	C₂²×C₆₁	—	4	4	no	—
228	C₂²×C₆₁	—	4	2	no	—
229	C₂²×C₆₁	—	8	2	no	—
230	C₂²×C₆₁	—	8	1	no	—
231	C₂²×C₆₁	—	8	1	no	—
232	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
233	C₂²×C₆₁	#548	1	1	yes	characteristic
234	C₂²×C₆₁	D₄×Q₈	1	1	yes	characteristic
235	C₂²×C₆₁	#575	1	2	yes	—
236	C₂²×C₆₁	#576	1	2	yes	—
237	C₄×C₆₁	—	2	2	no	—
238	C₄×C₆₁	—	2	2	no	—
239	C₄×C₆₁	—	4	2	no	—
240	C₄×C₆₁	—	4	2	no	—
241	C₄×C₆₁	—	4	2	no	—
242	C₄×C₆₁	—	4	4	no	—
243	C₄×C₆₁	—	8	2	no	—
244	C₄×C₆₁	—	8	1	no	—
245	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
246	C₄×C₆₁	#536	1	1	yes	characteristic
247	C₄×C₆₁	#548	1	1	yes	characteristic
248	C₄×C₆₁	D₄×Q₈	1	1	yes	characteristic
249	C₂×#554	C₂×C₆₁	1	1	yes	characteristic, complemented
250	C₂×#474	C₂×C₆₁	1	1	yes	characteristic, complemented
251	C₂×#442	C₂×C₆₁	1	1	yes	characteristic
252	#2580	C₂×C₆₁	1	1	yes	characteristic, complemented
253	#2059	C₂×C₆₁	1	2	yes	complemented
254	#2025	C₂×C₆₁	1	2	yes	complemented
255	#1993	C₂×C₆₁	1	1	yes	characteristic, complemented
256	#1985	C₂×C₆₁	1	1	yes	characteristic, complemented
257	#1879	C₂×C₆₁	1	2	yes	—
258	#1862	C₂×C₆₁	1	2	yes	complemented
259	#1804	C₂×C₆₁	1	1	yes	characteristic, complemented
260	C₂×C₆₁	—	4	4	no	—
261	C₂×C₆₁	—	8	2	no	—
262	C₂×C₆₁	#2409	1	1	yes	characteristic
263	C₂×C₆₁	#3005	1	1	yes	characteristic
264	C₂×C₆₁	#3008	1	1	yes	characteristic
265	C₂×C₆₁	#3370	1	2	yes	—
266	C₂×C₆₁	#3389	1	2	yes	—
267	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
268	#554	—	2	4	no	—
269	#554	—	2	4	no	—
270	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
271	C₂×#125	C₂²×C₆₁	1	2	yes	—
272	C₂×C₂²⋊Q₈	—	2	1	no	—
273	C₂×C₂²⋊Q₈	—	2	2	no	—
274	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
277	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
278	C₂²×C₄⋊C₄	—	2	1	no	—
279	#474	—	2	4	no	—
280	#442	—	2	4	no	—
281	C₂×#107	C₂²×C₆₁	1	2	yes	—
282	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
284	C₂×#102	C₂²×C₆₁	1	2	yes	—
285	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×#102	C₂²×C₆₁	1	2	yes	—
287	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
288	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
289	#399	—	2	1	no	—
290	#393	—	2	1	no	—
291	#390	C₂²×C₆₁	1	2	yes	—
292	#389	C₂²×C₆₁	1	2	yes	—
293	#385	—	2	2	no	—
294	#382	C₂²×C₆₁	1	1	yes	characteristic
295	#340	C₂²×C₆₁	1	2	yes	—
296	#340	C₂²×C₆₁	1	2	yes	—
297	#340	C₂²×C₆₁	1	2	yes	—
298	#336	C₂²×C₆₁	1	2	yes	—
299	#336	C₂²×C₆₁	1	2	yes	—
300	C₆₁	#24339	1	1	yes	characteristic, direct product factor, Sylow
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
303	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
304	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	2	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂×D₈	—	2	2	no	—
309	C₂×D₈	—	2	2	no	—
310	C₂×D₈	Q₈×C₆₁	1	4	yes	complemented
311	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
313	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
316	#125	—	2	4	no	—
317	#125	—	2	4	no	—
318	C₂²⋊Q₈	—	2	8	no	—
319	C₂²⋊Q₈	—	2	16	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	4	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	D₄×C₆₁	1	4	yes	—
328	C₂×C₄⋊C₄	—	2	8	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
334	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
345	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
346	#107	—	2	4	no	—
347	#106	—	2	2	no	—
348	C₄⋊C₈	—	2	2	no	—
349	#102	—	2	2	no	—
350	#102	—	2	4	no	—
351	#102	—	2	2	no	—
352	#102	—	2	4	no	—
353	#97	—	2	2	no	—
354	#95	—	2	1	no	—
355	#95	—	2	1	no	—
356	#95	—	2	2	no	—
357	C₂⁴	—	2	1	no	—
358	C₂⁴	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×Q₈	—	8	2	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
372	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
373	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
374	C₂×D₄	#41×C₆₁	1	2	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	8	2	no	—
384	C₂²×C₄	—	8	2	no	—
385	C₂²×C₄	—	8	2	no	—
386	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
391	D₈	—	2	8	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	C₂×Q₈×C₆₁	1	2	yes	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	8	2	no	—
413	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
414	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	8	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	C₂×D₄×C₆₁	1	2	yes	—
423	C₄²	C₂×D₄×C₆₁	1	2	yes	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	1	no	—
434	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
435	Q₈	—	4	4	no	—
436	Q₈	—	8	4	no	—
437	D₄	—	2	2	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	D₄	C₂²⋊Q₈×C₆₁	1	4	yes	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	8	4	no	—
465	C₂×C₄	—	8	8	no	—
466	C₂×C₄	#120×C₆₁	1	2	yes	—
467	C₂×C₄	#120×C₆₁	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
470	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
472	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
473	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	4	1	no	—
476	C₈	—	4	2	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
488	C₂²	C₆₁×#548	1	1	yes	characteristic
489	C₂²	D₄×Q₈×C₆₁	1	1	yes	characteristic
490	C₂²	C₆₁×#575	1	2	yes	—
491	C₂²	C₆₁×#576	1	2	yes	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	4	no	—
498	C₄	—	8	2	no	—
499	C₄	—	8	1	no	—
500	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
501	C₄	C₆₁×#536	1	1	yes	characteristic
502	C₄	C₆₁×#548	1	1	yes	characteristic
503	C₄	D₄×Q₈×C₆₁	1	1	yes	characteristic
504	C₂	—	4	4	no	—
505	C₂	—	8	2	no	—
506	C₂	C₆₁×#2409	1	1	yes	characteristic
507	C₂	C₆₁×#3005	1	1	yes	characteristic
508	C₂	C₆₁×#3008	1	1	yes	characteristic
509	C₂	C₆₁×#3370	1	2	yes	—
510	C₂	C₆₁×#3389	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₈×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#554	C₂	semidirect
2. C₂×C₆₁×#474	C₂	semidirect
4. C₆₁×#2580	C₂	semidirect
5. C₆₁×#2059	C₂	semidirect
6. C₆₁×#2025	C₂	semidirect
7. C₆₁×#1993	C₂	semidirect
8. C₆₁×#1985	C₂	semidirect
10. C₆₁×#1862	C₂	semidirect
11. C₆₁×#1804	C₂	semidirect
54. C₂×D₈×C₆₁	Q₈	semidirect
221. #24339	C₆₁	direct (N × H)
249. C₂×#554	C₂×C₆₁	semidirect
250. C₂×#474	C₂×C₆₁	semidirect
252. #2580	C₂×C₆₁	semidirect
253. #2059	C₂×C₆₁	semidirect
254. #2025	C₂×C₆₁	semidirect
255. #1993	C₂×C₆₁	semidirect
256. #1985	C₂×C₆₁	semidirect
258. #1862	C₂×C₆₁	semidirect
259. #1804	C₂×C₆₁	semidirect
300. C₆₁	#24339	direct (N × H)
310. C₂×D₈	Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#554	2
C₂×C₆₁×#474	2
C₂×C₆₁×#442	2
C₆₁×#2580	2
C₆₁×#2059	2
C₆₁×#2025	2
C₆₁×#1993	2
C₆₁×#1985	2
C₆₁×#1879	2
C₆₁×#1862	2
C₆₁×#1804	2
#24339	61

Subgroups — C61×#24339 #29527772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24339 #29527772