Subgroups — C₆₁×#25686 #29529119

Order 15616.

968 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#541	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2628	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2036	C₂	1	2	yes	maximal
6	C₆₁×#2035	C₂	1	2	yes	maximal
7	C₆₁×#1991	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1865	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1863	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1750	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#541	—	2	4	no	—
13	C₆₁×#541	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#126×C₆₁	—	2	1	no	—
17	C₂×#126×C₆₁	—	2	1	no	—
18	C₂×#125×C₆₁	—	2	1	no	—
19	C₂×#125×C₆₁	—	2	1	no	—
20	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#501	—	2	4	no	—
27	C₆₁×#487	—	2	4	no	—
28	C₂×#107×C₆₁	C₂²	1	2	yes	—
29	C₂×#106×C₆₁	C₂²	1	2	yes	—
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₂×#103×C₆₁	C₂²	1	2	yes	—
32	C₂×#103×C₆₁	C₂²	1	2	yes	—
33	C₂×#103×C₆₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
35	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#400	—	2	1	no	—
38	C₆₁×#399	—	2	1	no	—
39	C₆₁×#395	—	2	1	no	—
40	C₆₁×#393	—	2	1	no	—
41	C₆₁×#389	C₂²	1	2	yes	—
42	C₆₁×#382	C₂²	1	1	yes	characteristic
43	C₆₁×#380	C₂²	1	2	yes	—
44	C₆₁×#340	C₂²	1	2	yes	—
45	C₆₁×#340	C₂²	1	2	yes	—
46	C₆₁×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₆₁	—	2	1	no	—
48	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₆₁	—	2	2	no	—
54	C₄⋊Q₈×C₆₁	—	2	2	no	—
55	C₄⋊Q₈×C₆₁	—	2	2	no	—
56	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
57	#126×C₆₁	—	2	8	no	—
58	#126×C₆₁	—	2	8	no	—
59	#125×C₆₁	—	2	8	no	—
60	#125×C₆₁	—	2	8	no	—
61	#125×C₆₁	—	2	2	no	—
62	#125×C₆₁	D₄	1	4	yes	—
63	C₂²⋊Q₈×C₆₁	—	2	2	no	—
64	C₂²⋊Q₈×C₆₁	—	2	2	no	—
65	C₂²⋊Q₈×C₆₁	—	2	2	no	—
66	C₂²⋊Q₈×C₆₁	—	2	2	no	—
67	C₄×Q₈×C₆₁	—	2	2	no	—
68	C₄×Q₈×C₆₁	—	2	2	no	—
69	C₄×Q₈×C₆₁	—	2	2	no	—
70	C₄×Q₈×C₆₁	—	2	2	no	—
71	#117×C₆₁	—	2	2	no	—
72	#117×C₆₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₆₁	—	2	1	no	—
95	C₂×C₄²×C₆₁	—	2	1	no	—
96	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
98	#107×C₆₁	—	2	4	no	—
99	#106×C₆₁	—	2	4	no	—
100	#103×C₆₁	—	2	4	no	—
101	#103×C₆₁	—	2	4	no	—
102	#103×C₆₁	—	2	4	no	—
103	#103×C₆₁	—	2	4	no	—
104	C₂²⋊C₈×C₆₁	—	2	4	no	—
105	#97×C₆₁	—	2	2	no	—
106	C₄×C₈×C₆₁	—	2	2	no	—
107	#95×C₆₁	—	2	2	no	—
108	#95×C₆₁	—	2	1	no	—
109	#95×C₆₁	—	2	1	no	—
110	#95×C₆₁	—	2	2	no	—
111	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₆₁	—	2	1	no	—
113	C₂×Q₈×C₆₁	—	2	1	no	—
114	C₂×Q₈×C₆₁	—	2	2	no	—
115	C₂×Q₈×C₆₁	—	2	2	no	—
116	C₂×Q₈×C₆₁	—	2	2	no	—
117	C₂×Q₈×C₆₁	—	2	2	no	—
118	C₂×Q₈×C₆₁	—	4	2	no	—
119	C₂×Q₈×C₆₁	—	8	2	no	—
120	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₆₁	—	2	1	no	—
123	C₂²×C₄×C₆₁	—	2	1	no	—
124	C₂²×C₄×C₆₁	—	2	1	no	—
125	C₂²×C₄×C₆₁	—	2	1	no	—
126	C₂²×C₄×C₆₁	—	2	1	no	—
127	C₂²×C₄×C₆₁	—	2	1	no	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₆₁	—	2	2	no	—
139	C₂×C₈×C₆₁	—	2	2	no	—
140	C₂×C₈×C₆₁	—	2	2	no	—
141	C₂×C₈×C₆₁	—	2	2	no	—
142	C₂×C₈×C₆₁	—	2	2	no	—
143	C₂×C₈×C₆₁	#41	1	4	yes	—
144	C₄⋊C₄×C₆₁	—	2	4	no	—
145	C₄⋊C₄×C₆₁	—	2	4	no	—
146	C₄⋊C₄×C₆₁	—	2	4	no	—
147	C₄⋊C₄×C₆₁	—	2	4	no	—
148	C₄⋊C₄×C₆₁	—	2	4	no	—
149	C₄⋊C₄×C₆₁	—	2	4	no	—
150	C₄⋊C₄×C₆₁	—	2	4	no	—
151	C₄⋊C₄×C₆₁	—	2	4	no	—
152	C₄⋊C₄×C₆₁	—	2	2	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	1	no	—
155	C₄⋊C₄×C₆₁	—	2	1	no	—
156	C₄⋊C₄×C₆₁	—	2	2	no	—
157	C₄⋊C₄×C₆₁	—	2	2	no	—
158	C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	—	4	2	no	—
161	C₄⋊C₄×C₆₁	—	8	2	no	—
162	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₆₁	—	2	4	no	—
165	C₂²⋊C₄×C₆₁	—	2	4	no	—
166	C₂²⋊C₄×C₆₁	—	2	2	no	—
167	C₂²⋊C₄×C₆₁	—	2	2	no	—
168	C₂²⋊C₄×C₆₁	—	8	2	no	—
169	C₄²×C₆₁	—	2	4	no	—
170	C₄²×C₆₁	—	2	4	no	—
171	C₄²×C₆₁	—	2	1	no	—
172	C₄²×C₆₁	—	2	1	no	—
173	C₄²×C₆₁	C₂×D₄	1	2	yes	—
174	C₄²×C₆₁	C₂×D₄	1	2	yes	—
175	C₂³×C₆₁	—	2	1	no	—
176	C₂³×C₆₁	—	2	1	no	—
177	C₂³×C₆₁	—	2	1	no	—
178	C₂³×C₆₁	—	2	2	no	—
179	C₂³×C₆₁	—	2	2	no	—
180	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₆₁	—	2	4	no	—
182	Q₈×C₆₁	—	2	4	no	—
183	Q₈×C₆₁	—	4	2	no	—
184	Q₈×C₆₁	—	4	2	no	—
185	Q₈×C₆₁	—	8	4	no	—
186	C₂×C₄×C₆₁	—	2	2	no	—
187	C₂×C₄×C₆₁	—	2	2	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	—	2	2	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	1	no	—
195	C₂×C₄×C₆₁	—	2	1	no	—
196	C₂×C₄×C₆₁	—	2	1	no	—
197	C₂×C₄×C₆₁	—	2	2	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	4	1	no	—
200	C₂×C₄×C₆₁	—	4	1	no	—
201	C₂×C₄×C₆₁	—	4	1	no	—
202	C₂×C₄×C₆₁	—	4	1	no	—
203	C₂×C₄×C₆₁	—	4	2	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	—	4	2	no	—
209	C₂×C₄×C₆₁	—	4	2	no	—
210	C₂×C₄×C₆₁	—	4	2	no	—
211	C₂×C₄×C₆₁	—	4	2	no	—
212	C₂×C₄×C₆₁	—	4	2	no	—
213	C₂×C₄×C₆₁	#120	1	2	yes	—
214	C₂×C₄×C₆₁	#120	1	2	yes	—
215	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
218	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
219	C₈×C₆₁	—	2	4	no	—
220	C₈×C₆₁	—	4	2	no	—
221	#25686	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₆₁	—	4	2	no	—
223	C₂²×C₆₁	—	4	1	no	—
224	C₂²×C₆₁	—	4	2	no	—
225	C₂²×C₆₁	—	4	1	no	—
226	C₂²×C₆₁	—	4	1	no	—
227	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
228	C₂²×C₆₁	#532	1	1	yes	characteristic
229	C₂²×C₆₁	#536	1	1	yes	characteristic
230	C₂²×C₆₁	#577	1	2	yes	—
231	C₂²×C₆₁	#578	1	2	yes	—
232	C₄×C₆₁	—	2	2	no	—
233	C₄×C₆₁	—	2	2	no	—
234	C₄×C₆₁	—	4	1	no	—
235	C₄×C₆₁	—	4	2	no	—
236	C₄×C₆₁	—	4	2	no	—
237	C₄×C₆₁	—	4	1	no	—
238	C₄×C₆₁	—	4	2	no	—
239	C₄×C₆₁	—	4	1	no	—
240	C₄×C₆₁	—	4	2	no	—
241	C₄×C₆₁	—	8	2	no	—
242	C₄×C₆₁	—	8	2	no	—
243	C₄×C₆₁	#547	1	2	yes	—
244	C₄×C₆₁	#548	1	2	yes	—
245	C₂×#541	C₂×C₆₁	1	1	yes	characteristic
246	C₂×#501	C₂×C₆₁	1	1	yes	characteristic, complemented
247	C₂×#487	C₂×C₆₁	1	1	yes	characteristic, complemented
248	#2628	C₂×C₆₁	1	1	yes	characteristic
249	#2036	C₂×C₆₁	1	2	yes	—
250	#2035	C₂×C₆₁	1	2	yes	—
251	#1991	C₂×C₆₁	1	1	yes	characteristic, complemented
252	#1960	C₂×C₆₁	1	1	yes	characteristic, complemented
253	#1865	C₂×C₆₁	1	2	yes	complemented
254	#1863	C₂×C₆₁	1	2	yes	complemented
255	#1750	C₂×C₆₁	1	1	yes	characteristic
256	C₂×C₆₁	—	8	1	no	—
257	C₂×C₆₁	#2432	1	1	yes	characteristic
258	C₂×C₆₁	#3010	1	1	yes	characteristic
259	C₂×C₆₁	#3011	1	1	yes	characteristic
260	C₂×C₆₁	#3178	1	2	yes	—
261	C₂×C₆₁	#3242	1	2	yes	—
262	#541	—	2	4	no	—
263	#541	—	2	4	no	—
264	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
266	C₂×#126	—	2	1	no	—
267	C₂×#126	—	2	1	no	—
268	C₂×#125	—	2	1	no	—
269	C₂×#125	—	2	1	no	—
270	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
271	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
272	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
274	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
275	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
276	#501	—	2	4	no	—
277	#487	—	2	4	no	—
278	C₂×#107	C₂²×C₆₁	1	2	yes	—
279	C₂×#106	C₂²×C₆₁	1	2	yes	—
280	C₂×#103	C₂²×C₆₁	1	2	yes	—
281	C₂×#103	C₂²×C₆₁	1	2	yes	—
282	C₂×#103	C₂²×C₆₁	1	2	yes	—
283	C₂×#103	C₂²×C₆₁	1	2	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
285	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
287	#400	—	2	1	no	—
288	#399	—	2	1	no	—
289	#395	—	2	1	no	—
290	#393	—	2	1	no	—
291	#389	C₂²×C₆₁	1	2	yes	—
292	#382	C₂²×C₆₁	1	1	yes	characteristic
293	#380	C₂²×C₆₁	1	2	yes	—
294	#340	C₂²×C₆₁	1	2	yes	—
295	#340	C₂²×C₆₁	1	2	yes	—
296	#336	C₂²×C₆₁	1	2	yes	—
297	C₆₁	#25686	1	1	yes	characteristic, direct product factor, Sylow
298	C₂²×Q₈	—	2	1	no	—
299	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
300	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
303	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
308	#126	—	2	8	no	—
309	#126	—	2	8	no	—
310	#125	—	2	8	no	—
311	#125	—	2	8	no	—
312	#125	—	2	2	no	—
313	#125	D₄×C₆₁	1	4	yes	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	#117	—	2	2	no	—
323	#117	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
335	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
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	D₄×C₆₁	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
349	#107	—	2	4	no	—
350	#106	—	2	4	no	—
351	#103	—	2	4	no	—
352	#103	—	2	4	no	—
353	#103	—	2	4	no	—
354	#103	—	2	4	no	—
355	C₂²⋊C₈	—	2	4	no	—
356	#97	—	2	2	no	—
357	C₄×C₈	—	2	2	no	—
358	#95	—	2	2	no	—
359	#95	—	2	1	no	—
360	#95	—	2	1	no	—
361	#95	—	2	2	no	—
362	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	—	8	2	no	—
371	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
372	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	#41×C₆₁	1	4	yes	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	8	2	no	—
413	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
414	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	8	2	no	—
420	C₄²	—	2	4	no	—
421	C₄²	—	2	4	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	C₂×D₄×C₆₁	1	2	yes	—
425	C₄²	C₂×D₄×C₆₁	1	2	yes	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	1	no	—
431	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
432	Q₈	—	2	4	no	—
433	Q₈	—	2	4	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	8	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
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	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	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	2	no	—
464	C₂×C₄	#120×C₆₁	1	2	yes	—
465	C₂×C₄	#120×C₆₁	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
468	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
469	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
470	C₈	—	2	4	no	—
471	C₈	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
478	C₂²	C₆₁×#532	1	1	yes	characteristic
479	C₂²	C₆₁×#536	1	1	yes	characteristic
480	C₂²	C₆₁×#577	1	2	yes	—
481	C₂²	C₆₁×#578	1	2	yes	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	8	2	no	—
492	C₄	—	8	2	no	—
493	C₄	C₆₁×#547	1	2	yes	—
494	C₄	C₆₁×#548	1	2	yes	—
495	C₂	—	8	1	no	—
496	C₂	C₆₁×#2432	1	1	yes	characteristic
497	C₂	C₆₁×#3010	1	1	yes	characteristic
498	C₂	C₆₁×#3011	1	1	yes	characteristic
499	C₂	C₆₁×#3178	1	2	yes	—
500	C₂	C₆₁×#3242	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#501	C₂	semidirect
3. C₂×C₆₁×#487	C₂	semidirect
7. C₆₁×#1991	C₂	semidirect
8. C₆₁×#1960	C₂	semidirect
9. C₆₁×#1865	C₂	semidirect
10. C₆₁×#1863	C₂	semidirect
221. #25686	C₆₁	direct (N × H)
246. C₂×#501	C₂×C₆₁	semidirect
247. C₂×#487	C₂×C₆₁	semidirect
251. #1991	C₂×C₆₁	semidirect
252. #1960	C₂×C₆₁	semidirect
253. #1865	C₂×C₆₁	semidirect
254. #1863	C₂×C₆₁	semidirect
297. C₆₁	#25686	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×#541	2
C₂×C₆₁×#501	2
C₂×C₆₁×#487	2
C₆₁×#2628	2
C₆₁×#2036	2
C₆₁×#2035	2
C₆₁×#1991	2
C₆₁×#1960	2
C₆₁×#1865	2
C₆₁×#1863	2
C₆₁×#1750	2
#25686	61

Subgroups — C61×#25686 #29529119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25686 #29529119