Subgroups — C₂×C₆₁×#1521 #29520999

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1521	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₆₁×#328	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#327	C₂	1	2	yes	maximal
7	C₆₁×#529	—	2	2	no	—
8	C₆₁×#529	—	2	2	no	—
9	C₆₁×#529	C₄	1	4	yes	complemented
10	C₆₁×#529	C₂²	1	4	yes	—
11	C₂×#126×C₆₁	—	2	1	no	—
12	C₂×#125×C₆₁	C₄	1	1	yes	characteristic, complemented
13	C₂×#124×C₆₁	C₄	1	1	yes	characteristic, complemented
14	C₂×#123×C₆₁	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₆₁	C₄	1	1	yes	characteristic, complemented
18	C₂×C₄×D₄×C₆₁	—	2	1	no	—
19	C₂×C₄×D₄×C₆₁	C₄	1	1	yes	characteristic, complemented
20	C₂×#117×C₆₁	—	2	1	no	—
21	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#431	—	2	2	no	—
23	C₆₁×#431	C₂²	1	4	yes	complemented
24	C₂×C₄⋊C₈×C₆₁	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₆₁	—	2	1	no	—
27	C₆₁×#383	—	2	2	no	—
28	C₆₁×#383	C₂²	1	4	yes	complemented
29	C₂×#95×C₆₁	—	2	1	no	—
30	C₂×#95×C₆₁	—	2	1	no	—
31	C₂×#95×C₆₁	C₂²	1	2	yes	—
32	C₆₁×#328	C₂²	1	8	yes	complemented
33	C₆₁×#327	C₂²	1	8	yes	—
34	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₆₁	—	2	1	no	—
36	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₆₁	—	2	1	no	—
38	C₂³×C₄×C₆₁	—	2	2	no	—
39	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₆₁	—	2	2	no	—
43	#126×C₆₁	—	2	4	no	—
44	#126×C₆₁	—	2	4	no	—
45	#125×C₆₁	—	2	2	no	—
46	#125×C₆₁	C₂×C₄	1	4	yes	complemented
47	#124×C₆₁	—	2	2	no	—
48	#124×C₆₁	C₂×C₄	1	4	yes	complemented
49	#123×C₆₁	—	2	4	no	—
50	#123×C₆₁	—	2	4	no	—
51	C₂²⋊Q₈×C₆₁	—	2	1	no	—
52	C₂²⋊Q₈×C₆₁	—	2	1	no	—
53	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
54	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
55	#121×C₆₁	—	2	1	no	—
56	#121×C₆₁	—	2	1	no	—
57	#121×C₆₁	C₂×C₄	1	2	yes	—
58	#121×C₆₁	C₂³	1	2	yes	—
59	C₄×Q₈×C₆₁	—	2	2	no	—
60	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	complemented
61	C₄×D₄×C₆₁	—	2	4	no	—
62	C₄×D₄×C₆₁	—	2	4	no	—
63	C₄×D₄×C₆₁	—	2	2	no	—
64	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	complemented
65	#117×C₆₁	—	2	4	no	—
66	#117×C₆₁	—	2	4	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₄²×C₆₁	—	2	1	no	—
79	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₆₁	D₄	1	2	yes	—
83	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₆₁	D₄	1	2	yes	—
86	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
87	C₄⋊C₈×C₆₁	—	2	4	no	—
88	C₂²⋊C₈×C₆₁	—	2	2	no	—
89	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
90	C₄×C₈×C₆₁	—	2	4	no	—
91	#95×C₆₁	—	2	4	no	—
92	#95×C₆₁	—	2	4	no	—
93	#95×C₆₁	—	2	2	no	—
94	#95×C₆₁	C₂³	1	4	yes	—
95	C₂⁴×C₆₁	—	2	1	no	—
96	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₆₁	—	2	1	no	—
98	C₂×Q₈×C₆₁	—	4	2	no	—
99	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	2	1	no	—
103	C₂×D₄×C₆₁	—	4	2	no	—
104	C₂×D₄×C₆₁	—	4	4	no	—
105	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₆₁	—	2	4	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	4	no	—
111	C₂²×C₄×C₆₁	—	2	4	no	—
112	C₂²×C₄×C₆₁	—	4	2	no	—
113	C₂²×C₄×C₆₁	—	4	2	no	—
114	C₂²×C₄×C₆₁	—	4	4	no	—
115	C₂²×C₄×C₆₁	—	4	4	no	—
116	C₂²×C₄×C₆₁	—	4	4	no	—
117	C₂²×C₄×C₆₁	—	4	4	no	—
118	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
119	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
124	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₆₁	—	2	4	no	—
133	C₂×C₈×C₆₁	—	4	4	no	—
134	C₄⋊C₄×C₆₁	—	2	2	no	—
135	C₄⋊C₄×C₆₁	—	2	4	no	—
136	C₄⋊C₄×C₆₁	—	2	4	no	—
137	C₄⋊C₄×C₆₁	—	2	4	no	—
138	C₄⋊C₄×C₆₁	—	2	1	no	—
139	C₄⋊C₄×C₆₁	—	2	1	no	—
140	C₄⋊C₄×C₆₁	—	2	2	no	—
141	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
142	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
143	C₂²⋊C₄×C₆₁	—	2	2	no	—
144	C₂²⋊C₄×C₆₁	—	2	2	no	—
145	C₂²⋊C₄×C₆₁	—	2	2	no	—
146	C₂²⋊C₄×C₆₁	—	2	4	no	—
147	C₂²⋊C₄×C₆₁	—	2	4	no	—
148	C₂²⋊C₄×C₆₁	—	2	4	no	—
149	C₂²⋊C₄×C₆₁	—	2	2	no	—
150	C₄²×C₆₁	—	2	4	no	—
151	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
152	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
153	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
154	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
155	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
156	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
157	C₄²×C₆₁	C₂×D₄	1	2	yes	—
158	C₄²×C₆₁	C₂×D₄	1	2	yes	—
159	C₂³×C₆₁	—	2	2	no	—
160	C₂³×C₆₁	—	2	2	no	—
161	C₂³×C₆₁	—	2	2	no	—
162	C₂³×C₆₁	—	4	2	no	—
163	C₂³×C₆₁	—	4	2	no	—
164	C₂³×C₆₁	—	4	2	no	—
165	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂³×C₆₁	#135	1	4	yes	—
168	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₆₁	—	4	2	no	—
170	Q₈×C₆₁	—	4	2	no	—
171	D₄×C₆₁	—	4	2	no	—
172	D₄×C₆₁	—	4	2	no	—
173	D₄×C₆₁	—	4	4	no	—
174	D₄×C₆₁	—	4	4	no	—
175	C₂×C₄×C₆₁	—	2	4	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	4	no	—
179	C₂×C₄×C₆₁	—	2	2	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	2	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	—	4	2	no	—
187	C₂×C₄×C₆₁	—	4	1	no	—
188	C₂×C₄×C₆₁	—	4	1	no	—
189	C₂×C₄×C₆₁	—	4	1	no	—
190	C₂×C₄×C₆₁	—	4	2	no	—
191	C₂×C₄×C₆₁	—	4	1	no	—
192	C₂×C₄×C₆₁	—	4	8	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	4	no	—
197	C₂×C₄×C₆₁	—	4	4	no	—
198	C₂×C₄×C₆₁	—	4	4	no	—
199	C₂×C₄×C₆₁	—	8	8	no	—
200	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
205	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
208	C₈×C₆₁	—	4	4	no	—
209	C₂×#1521	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₆₁	—	2	1	no	—
211	C₂²×C₆₁	—	2	1	no	—
212	C₂²×C₆₁	—	2	1	no	—
213	C₂²×C₆₁	—	2	1	no	—
214	C₂²×C₆₁	—	2	8	no	—
215	C₂²×C₆₁	—	4	2	no	—
216	C₂²×C₆₁	—	4	2	no	—
217	C₂²×C₆₁	—	4	2	no	—
218	C₂²×C₆₁	—	8	4	no	—
219	C₂²×C₆₁	#410	1	2	yes	—
220	C₂²×C₆₁	#416	1	2	yes	—
221	C₂²×C₆₁	#416	1	2	yes	—
222	C₂²×C₆₁	#421	1	2	yes	—
223	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
224	C₂²×C₆₁	C₂×#135	1	2	yes	—
225	C₄×C₆₁	—	2	1	no	—
226	C₄×C₆₁	—	2	1	no	—
227	C₄×C₆₁	—	2	1	no	—
228	C₄×C₆₁	—	2	1	no	—
229	C₄×C₆₁	—	2	2	no	—
230	C₄×C₆₁	—	2	2	no	—
231	C₄×C₆₁	—	2	2	no	—
232	C₄×C₆₁	—	2	2	no	—
233	C₄×C₆₁	—	4	2	no	—
234	C₄×C₆₁	—	4	2	no	—
235	C₄×C₆₁	—	4	2	no	—
236	C₄×C₆₁	—	8	4	no	—
237	C₂×#529	C₂×C₆₁	1	1	yes	characteristic
238	C₂×#431	C₂×C₆₁	1	1	yes	characteristic, complemented
239	C₂×#383	C₂×C₆₁	1	1	yes	characteristic, complemented
240	#1521	C₂×C₆₁	1	8	yes	direct product factor
241	C₂×#328	C₂×C₆₁	1	2	yes	complemented
242	C₂×#327	C₂×C₆₁	1	2	yes	—
243	C₂×C₆₁	—	2	2	no	—
244	C₂×C₆₁	—	2	2	no	—
245	C₂×C₆₁	—	8	2	no	—
246	C₂×C₆₁	#1521	1	4	yes	direct product factor
247	C₂×C₆₁	C₂×#410	1	1	yes	characteristic
248	C₂×C₆₁	C₂×#416	1	1	yes	characteristic
249	C₂×C₆₁	C₂×#421	1	1	yes	characteristic
250	#529	—	2	2	no	—
251	#529	—	2	2	no	—
252	#529	C₄×C₆₁	1	4	yes	complemented
253	#529	C₂²×C₆₁	1	4	yes	—
254	C₂×#126	—	2	1	no	—
255	C₂×#125	C₄×C₆₁	1	1	yes	characteristic, complemented
256	C₂×#124	C₄×C₆₁	1	1	yes	characteristic, complemented
257	C₂×#123	—	2	1	no	—
258	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₄×C₆₁	1	1	yes	characteristic, complemented
261	C₂×C₄×D₄	—	2	1	no	—
262	C₂×C₄×D₄	C₄×C₆₁	1	1	yes	characteristic, complemented
263	C₂×#117	—	2	1	no	—
264	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
265	#431	—	2	2	no	—
266	#431	C₂²×C₆₁	1	4	yes	complemented
267	C₂×C₄⋊C₈	—	2	1	no	—
268	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
269	C₂×C₄×C₈	—	2	1	no	—
270	#383	—	2	2	no	—
271	#383	C₂²×C₆₁	1	4	yes	complemented
272	C₂×#95	—	2	1	no	—
273	C₂×#95	—	2	1	no	—
274	C₂×#95	C₂²×C₆₁	1	2	yes	—
275	#328	C₂²×C₆₁	1	8	yes	complemented
276	#327	C₂²×C₆₁	1	8	yes	—
277	C₆₁	C₂×#1521	1	1	yes	characteristic, direct product factor, Sylow
278	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	—	2	2	no	—
283	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
284	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
286	C₂²×C₈	—	2	2	no	—
287	#126	—	2	4	no	—
288	#126	—	2	4	no	—
289	#125	—	2	2	no	—
290	#125	C₂×C₄×C₆₁	1	4	yes	complemented
291	#124	—	2	2	no	—
292	#124	C₂×C₄×C₆₁	1	4	yes	complemented
293	#123	—	2	4	no	—
294	#123	—	2	4	no	—
295	C₂²⋊Q₈	—	2	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	C₂²⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
298	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
299	#121	—	2	1	no	—
300	#121	—	2	1	no	—
301	#121	C₂×C₄×C₆₁	1	2	yes	—
302	#121	C₂³×C₆₁	1	2	yes	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	complemented
309	#117	—	2	4	no	—
310	#117	—	2	4	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
324	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
325	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
326	C₂×C₄²	D₄×C₆₁	1	2	yes	—
327	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
328	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
329	C₂×C₄²	D₄×C₆₁	1	2	yes	—
330	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
331	C₄⋊C₈	—	2	4	no	—
332	C₂²⋊C₈	—	2	2	no	—
333	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
334	C₄×C₈	—	2	4	no	—
335	#95	—	2	4	no	—
336	#95	—	2	4	no	—
337	#95	—	2	2	no	—
338	#95	C₂³×C₆₁	1	4	yes	—
339	C₂⁴	—	2	1	no	—
340	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	4	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
363	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
364	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
365	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
366	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
367	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
368	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
376	C₂×C₈	—	2	4	no	—
377	C₂×C₈	—	4	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
386	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₄²	—	2	4	no	—
395	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
396	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
397	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
398	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
399	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
400	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
401	C₄²	C₂×D₄×C₆₁	1	2	yes	—
402	C₄²	C₂×D₄×C₆₁	1	2	yes	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
410	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
411	C₂³	#135×C₆₁	1	4	yes	—
412	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	8	8	no	—
444	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
445	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
446	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
447	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
448	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
449	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
450	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
452	C₈	—	4	4	no	—
453	C₂²	—	2	8	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	8	4	no	—
462	C₂²	C₆₁×#410	1	2	yes	—
463	C₂²	C₆₁×#416	1	2	yes	—
464	C₂²	C₆₁×#416	1	2	yes	—
465	C₂²	C₆₁×#421	1	2	yes	—
466	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
467	C₂²	C₂×#135×C₆₁	1	2	yes	—
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	4	no	—
480	C₂	—	2	2	no	—
481	C₂	—	2	2	no	—
482	C₂	—	8	2	no	—
483	C₂	C₆₁×#1521	1	4	yes	direct product factor
484	C₂	C₂×C₆₁×#410	1	1	yes	characteristic
485	C₂	C₂×C₆₁×#416	1	1	yes	characteristic
486	C₂	C₂×C₆₁×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#431	C₂	semidirect
3. C₂×C₆₁×#383	C₂	semidirect
4. C₆₁×#1521	C₂	direct (N × H)
5. C₂×C₆₁×#328	C₂	semidirect
9. C₆₁×#529	C₄	semidirect
12. C₂×#125×C₆₁	C₄	semidirect
13. C₂×#124×C₆₁	C₄	semidirect
17. C₂×C₄×Q₈×C₆₁	C₄	semidirect
19. C₂×C₄×D₄×C₆₁	C₄	semidirect
23. C₆₁×#431	C₂²	semidirect
28. C₆₁×#383	C₂²	semidirect
32. C₆₁×#328	C₂²	semidirect
46. #125×C₆₁	C₂×C₄	semidirect
48. #124×C₆₁	C₂×C₄	semidirect
60. C₄×Q₈×C₆₁	C₂×C₄	semidirect
64. C₄×D₄×C₆₁	C₂×C₄	semidirect
209. C₂×#1521	C₆₁	direct (N × H)
238. C₂×#431	C₂×C₆₁	semidirect
239. C₂×#383	C₂×C₆₁	semidirect
240. #1521	C₂×C₆₁	direct (N × H)
241. C₂×#328	C₂×C₆₁	semidirect
246. C₂×C₆₁	#1521	direct (N × H)
252. #529	C₄×C₆₁	semidirect
255. C₂×#125	C₄×C₆₁	semidirect
256. C₂×#124	C₄×C₆₁	semidirect
260. C₂×C₄×Q₈	C₄×C₆₁	semidirect
262. C₂×C₄×D₄	C₄×C₆₁	semidirect
266. #431	C₂²×C₆₁	semidirect
271. #383	C₂²×C₆₁	semidirect
275. #328	C₂²×C₆₁	semidirect
277. C₆₁	C₂×#1521	direct (N × H)
290. #125	C₂×C₄×C₆₁	semidirect
292. #124	C₂×C₄×C₆₁	semidirect
304. C₄×Q₈	C₂×C₄×C₆₁	semidirect
308. C₄×D₄	C₂×C₄×C₆₁	semidirect
483. C₂	C₆₁×#1521	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×#529	2
C₂×C₆₁×#431	2
C₂×C₆₁×#383	2
C₆₁×#1521	2
C₂×C₆₁×#328	2
C₂×C₆₁×#327	2
C₂×#1521	61

Subgroups — C2×C61×#1521 #29520999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1521 #29520999