Subgroups — C₆₁×#25711 #29529144

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2562	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2036	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2035	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1955	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1854	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1854	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#556	—	2	4	no	—
13	C₆₁×#556	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#126×C₆₁	—	2	2	no	—
16	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#124×C₆₁	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#117×C₆₁	C₂²	1	2	yes	—
23	C₆₁×#501	—	2	4	no	—
24	C₆₁×#479	—	2	4	no	—
25	C₂×#107×C₆₁	C₂²	1	2	yes	—
26	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#106×C₆₁	C₂²	1	2	yes	—
28	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
35	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#400	—	2	1	no	—
37	C₆₁×#394	—	2	1	no	—
38	C₆₁×#388	—	2	2	no	—
39	C₆₁×#380	C₂²	1	2	yes	—
40	C₆₁×#380	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₆₁×#340	C₂²	1	2	yes	—
44	C₆₁×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₆₁	—	2	1	no	—
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₆₁	—	2	2	no	—
53	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
54	#126×C₆₁	—	2	16	no	—
55	#125×C₆₁	—	2	2	no	—
56	#125×C₆₁	—	2	2	no	—
57	#124×C₆₁	—	2	8	no	—
58	C₂²⋊Q₈×C₆₁	—	2	4	no	—
59	C₂²⋊Q₈×C₆₁	—	2	4	no	—
60	C₄×Q₈×C₆₁	—	2	8	no	—
61	C₄×Q₈×C₆₁	—	2	2	no	—
62	C₄×Q₈×C₆₁	D₄	1	4	yes	—
63	C₄×D₄×C₆₁	—	2	2	no	—
64	C₄×D₄×C₆₁	—	2	2	no	—
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	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
83	C₂×C₄²×C₆₁	—	2	2	no	—
84	C₂×C₄²×C₆₁	—	2	1	no	—
85	C₂×C₄²×C₆₁	—	2	1	no	—
86	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
87	#107×C₆₁	—	2	2	no	—
88	#107×C₆₁	—	2	4	no	—
89	#106×C₆₁	—	2	2	no	—
90	#106×C₆₁	—	2	4	no	—
91	C₄⋊C₈×C₆₁	—	2	2	no	—
92	#103×C₆₁	—	2	2	no	—
93	#103×C₆₁	—	2	2	no	—
94	#103×C₆₁	—	2	4	no	—
95	C₂²⋊C₈×C₆₁	—	2	4	no	—
96	C₂²⋊C₈×C₆₁	—	2	4	no	—
97	#97×C₆₁	—	2	2	no	—
98	#95×C₆₁	—	2	1	no	—
99	#95×C₆₁	—	2	2	no	—
100	#95×C₆₁	—	2	2	no	—
101	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
102	C₂×Q₈×C₆₁	—	2	4	no	—
103	C₂×Q₈×C₆₁	—	2	1	no	—
104	C₂×Q₈×C₆₁	—	2	2	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	4	4	no	—
107	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₆₁	—	2	2	no	—
109	C₂×D₄×C₆₁	—	4	2	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	2	2	no	—
113	C₂²×C₄×C₆₁	—	2	2	no	—
114	C₂²×C₄×C₆₁	—	2	2	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	1	no	—
121	C₂²×C₄×C₆₁	—	2	1	no	—
122	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
126	C₂×C₈×C₆₁	—	2	2	no	—
127	C₂×C₈×C₆₁	—	2	2	no	—
128	C₂×C₈×C₆₁	—	2	1	no	—
129	C₂×C₈×C₆₁	—	2	1	no	—
130	C₂×C₈×C₆₁	—	2	2	no	—
131	C₂×C₈×C₆₁	—	2	2	no	—
132	C₂×C₈×C₆₁	#41	1	4	yes	—
133	C₄⋊C₄×C₆₁	—	2	8	no	—
134	C₄⋊C₄×C₆₁	—	2	4	no	—
135	C₄⋊C₄×C₆₁	—	2	4	no	—
136	C₄⋊C₄×C₆₁	—	2	2	no	—
137	C₄⋊C₄×C₆₁	—	2	1	no	—
138	C₄⋊C₄×C₆₁	—	2	2	no	—
139	C₄⋊C₄×C₆₁	—	2	1	no	—
140	C₄⋊C₄×C₆₁	—	2	1	no	—
141	C₄⋊C₄×C₆₁	—	2	1	no	—
142	C₄⋊C₄×C₆₁	—	2	1	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	2	2	no	—
145	C₄⋊C₄×C₆₁	—	4	2	no	—
146	C₄⋊C₄×C₆₁	—	4	2	no	—
147	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
149	C₂²⋊C₄×C₆₁	—	2	8	no	—
150	C₂²⋊C₄×C₆₁	—	2	8	no	—
151	C₂²⋊C₄×C₆₁	—	2	4	no	—
152	C₂²⋊C₄×C₆₁	—	4	4	no	—
153	C₂²⋊C₄×C₆₁	—	8	2	no	—
154	C₄²×C₆₁	—	2	8	no	—
155	C₄²×C₆₁	—	2	4	no	—
156	C₄²×C₆₁	—	8	1	no	—
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	—	2	2	no	—
163	C₂³×C₆₁	—	2	2	no	—
164	C₂³×C₆₁	—	2	2	no	—
165	C₂³×C₆₁	—	2	2	no	—
166	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₆₁	—	2	2	no	—
168	Q₈×C₆₁	—	2	2	no	—
169	Q₈×C₆₁	—	4	8	no	—
170	Q₈×C₆₁	—	4	2	no	—
171	D₄×C₆₁	—	4	4	no	—
172	C₂×C₄×C₆₁	—	2	2	no	—
173	C₂×C₄×C₆₁	—	2	1	no	—
174	C₂×C₄×C₆₁	—	2	1	no	—
175	C₂×C₄×C₆₁	—	2	2	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	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	4	no	—
183	C₂×C₄×C₆₁	—	4	1	no	—
184	C₂×C₄×C₆₁	—	4	1	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	4	2	no	—
187	C₂×C₄×C₆₁	—	4	2	no	—
188	C₂×C₄×C₆₁	—	4	2	no	—
189	C₂×C₄×C₆₁	—	4	1	no	—
190	C₂×C₄×C₆₁	—	4	1	no	—
191	C₂×C₄×C₆₁	—	4	2	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	1	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	#120	1	2	yes	—
198	C₂×C₄×C₆₁	#120	1	2	yes	—
199	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
202	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
203	C₈×C₆₁	—	2	4	no	—
204	C₈×C₆₁	—	4	1	no	—
205	C₈×C₆₁	—	4	1	no	—
206	#25711	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₆₁	—	4	2	no	—
208	C₂²×C₆₁	—	4	2	no	—
209	C₂²×C₆₁	—	4	2	no	—
210	C₂²×C₆₁	—	4	2	no	—
211	C₂²×C₆₁	—	4	2	no	—
212	C₂²×C₆₁	—	4	2	no	—
213	C₂²×C₆₁	—	4	2	no	—
214	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
215	C₂²×C₆₁	#547	1	2	yes	—
216	C₂²×C₆₁	#575	1	2	yes	—
217	C₂²×C₆₁	#577	1	1	yes	characteristic
218	C₂²×C₆₁	#578	1	1	yes	characteristic
219	C₄×C₆₁	—	2	2	no	—
220	C₄×C₆₁	—	2	2	no	—
221	C₄×C₆₁	—	4	2	no	—
222	C₄×C₆₁	—	4	2	no	—
223	C₄×C₆₁	—	4	4	no	—
224	C₄×C₆₁	—	4	2	no	—
225	C₄×C₆₁	—	8	2	no	—
226	C₄×C₆₁	—	8	1	no	—
227	C₄×C₆₁	—	8	1	no	—
228	C₄×C₆₁	#532	1	1	yes	characteristic
229	C₄×C₆₁	#536	1	1	yes	characteristic
230	C₄×C₆₁	#548	1	2	yes	—
231	C₂×#556	C₂×C₆₁	1	1	yes	characteristic
232	C₂×#501	C₂×C₆₁	1	1	yes	characteristic, complemented
233	C₂×#479	C₂×C₆₁	1	1	yes	characteristic, complemented
234	#2562	C₂×C₆₁	1	1	yes	characteristic
235	#2036	C₂×C₆₁	1	2	yes	complemented
236	#2035	C₂×C₆₁	1	2	yes	complemented
237	#1987	C₂×C₆₁	1	1	yes	characteristic, complemented
238	#1955	C₂×C₆₁	1	1	yes	characteristic
239	#1854	C₂×C₆₁	1	2	yes	complemented
240	#1854	C₂×C₆₁	1	2	yes	complemented
241	#1763	C₂×C₆₁	1	1	yes	characteristic, complemented
242	C₂×C₆₁	—	8	2	no	—
243	C₂×C₆₁	#2432	1	1	yes	characteristic
244	C₂×C₆₁	#3005	1	1	yes	characteristic
245	C₂×C₆₁	#3013	1	1	yes	characteristic
246	C₂×C₆₁	#3349	1	2	yes	—
247	C₂×C₆₁	#3350	1	2	yes	—
248	#556	—	2	4	no	—
249	#556	—	2	4	no	—
250	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
251	C₂×#126	—	2	2	no	—
252	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
253	C₂×#124	—	2	1	no	—
254	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
255	C₂×C₄×Q₈	—	2	1	no	—
256	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×#117	C₂²×C₆₁	1	2	yes	—
259	#501	—	2	4	no	—
260	#479	—	2	4	no	—
261	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×#107	C₂²×C₆₁	1	2	yes	—
263	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
264	C₂×#106	C₂²×C₆₁	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
266	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
267	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
268	C₂×#103	C₂²×C₆₁	1	2	yes	—
269	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
271	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
272	#400	—	2	1	no	—
273	#394	—	2	1	no	—
274	#388	—	2	2	no	—
275	#380	C₂²×C₆₁	1	2	yes	—
276	#380	C₂²×C₆₁	1	2	yes	—
277	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
278	#340	C₂²×C₆₁	1	2	yes	—
279	#340	C₂²×C₆₁	1	2	yes	—
280	#340	C₂²×C₆₁	1	2	yes	—
281	C₆₁	#25711	1	1	yes	characteristic, direct product factor, Sylow
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
286	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
291	#126	—	2	16	no	—
292	#125	—	2	2	no	—
293	#125	—	2	2	no	—
294	#124	—	2	8	no	—
295	C₂²⋊Q₈	—	2	4	no	—
296	C₂²⋊Q₈	—	2	4	no	—
297	C₄×Q₈	—	2	8	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	D₄×C₆₁	1	4	yes	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	#117	—	2	4	no	—
303	#117	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
324	#107	—	2	2	no	—
325	#107	—	2	4	no	—
326	#106	—	2	2	no	—
327	#106	—	2	4	no	—
328	C₄⋊C₈	—	2	2	no	—
329	#103	—	2	2	no	—
330	#103	—	2	2	no	—
331	#103	—	2	4	no	—
332	C₂²⋊C₈	—	2	4	no	—
333	C₂²⋊C₈	—	2	4	no	—
334	#97	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	4	4	no	—
344	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	#41×C₆₁	1	4	yes	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
385	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	8	2	no	—
391	C₄²	—	2	8	no	—
392	C₄²	—	2	4	no	—
393	C₄²	—	8	1	no	—
394	C₄²	C₂×D₄×C₆₁	1	2	yes	—
395	C₄²	C₂×D₄×C₆₁	1	2	yes	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	4	8	no	—
407	Q₈	—	4	2	no	—
408	D₄	—	4	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	#120×C₆₁	1	2	yes	—
435	C₂×C₄	#120×C₆₁	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
439	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
440	C₈	—	2	4	no	—
441	C₈	—	4	1	no	—
442	C₈	—	4	1	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
451	C₂²	C₆₁×#547	1	2	yes	—
452	C₂²	C₆₁×#575	1	2	yes	—
453	C₂²	C₆₁×#577	1	1	yes	characteristic
454	C₂²	C₆₁×#578	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	4	no	—
460	C₄	—	4	2	no	—
461	C₄	—	8	2	no	—
462	C₄	—	8	1	no	—
463	C₄	—	8	1	no	—
464	C₄	C₆₁×#532	1	1	yes	characteristic
465	C₄	C₆₁×#536	1	1	yes	characteristic
466	C₄	C₆₁×#548	1	2	yes	—
467	C₂	—	8	2	no	—
468	C₂	C₆₁×#2432	1	1	yes	characteristic
469	C₂	C₆₁×#3005	1	1	yes	characteristic
470	C₂	C₆₁×#3013	1	1	yes	characteristic
471	C₂	C₆₁×#3349	1	2	yes	—
472	C₂	C₆₁×#3350	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₄×C₆₁	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×D₄×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×#479	C₂	semidirect
5. C₆₁×#2036	C₂	semidirect
6. C₆₁×#2035	C₂	semidirect
7. C₆₁×#1987	C₂	semidirect
9. C₆₁×#1854	C₂	semidirect
10. C₆₁×#1854	C₂	semidirect
11. C₆₁×#1763	C₂	semidirect
206. #25711	C₆₁	direct (N × H)
232. C₂×#501	C₂×C₆₁	semidirect
233. C₂×#479	C₂×C₆₁	semidirect
235. #2036	C₂×C₆₁	semidirect
236. #2035	C₂×C₆₁	semidirect
237. #1987	C₂×C₆₁	semidirect
239. #1854	C₂×C₆₁	semidirect
240. #1854	C₂×C₆₁	semidirect
241. #1763	C₂×C₆₁	semidirect
281. C₆₁	#25711	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×#556	2
C₂×C₆₁×#501	2
C₂×C₆₁×#479	2
C₆₁×#2562	2
C₆₁×#2036	2
C₆₁×#2035	2
C₆₁×#1987	2
C₆₁×#1955	2
C₆₁×#1854	2
C₆₁×#1763	2
#25711	61

Subgroups — C61×#25711 #29529144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25711 #29529144