Subgroups — C₆₁×#25845 #29529278

Order 15616.

1040 conjugacy classes of subgroups.

The subgroup lattice has 460 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
2	C₂×C₆₁×#501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#478	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2584	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2059	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2059	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1864	C₂	1	2	yes	maximal
10	C₆₁×#1862	C₂	1	2	yes	maximal
11	C₆₁×#1762	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#554	—	2	4	no	—
13	C₆₁×#554	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#125×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	2	yes	—
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
23	C₆₁×#501	—	2	4	no	—
24	C₆₁×#478	—	2	4	no	—
25	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#107×C₆₁	C₂²	1	2	yes	—
27	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₆₁	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#102×C₆₁	C₂²	1	2	yes	—
33	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#398	—	2	1	no	—
35	C₆₁×#395	—	2	1	no	—
36	C₆₁×#389	—	2	2	no	—
37	C₆₁×#389	C₂²	1	2	yes	—
38	C₆₁×#389	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₆₁	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	C₂³×C₄×C₆₁	—	2	1	no	—
49	C₂³×C₄×C₆₁	—	2	2	no	—
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₆₁	—	2	2	no	—
54	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
55	#125×C₆₁	—	2	4	no	—
56	#125×C₆₁	—	2	4	no	—
57	#125×C₆₁	—	2	2	no	—
58	#125×C₆₁	—	2	2	no	—
59	C₂²⋊Q₈×C₆₁	—	2	8	no	—
60	C₂²⋊Q₈×C₆₁	—	2	16	no	—
61	C₄×Q₈×C₆₁	—	2	2	no	—
62	C₄×Q₈×C₆₁	—	2	2	no	—
63	C₄×D₄×C₆₁	—	2	4	no	—
64	C₄×D₄×C₆₁	—	2	4	no	—
65	C₄×D₄×C₆₁	—	2	2	no	—
66	C₄×D₄×C₆₁	D₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₆₁	C₂³	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×C₂²⋊C₄×C₆₁	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₄²×C₆₁	—	2	1	no	—
85	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
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	#102×C₆₁	—	2	2	no	—
93	#102×C₆₁	—	2	2	no	—
94	#102×C₆₁	Q₈	1	8	yes	complemented
95	#97×C₆₁	—	2	2	no	—
96	#95×C₆₁	—	2	1	no	—
97	#95×C₆₁	—	2	2	no	—
98	#95×C₆₁	—	2	2	no	—
99	C₂⁴×C₆₁	—	2	1	no	—
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	—	2	4	no	—
102	C₂×Q₈×C₆₁	—	4	2	no	—
103	C₂×Q₈×C₆₁	—	8	1	no	—
104	C₂×Q₈×C₆₁	—	8	1	no	—
105	C₂×D₄×C₆₁	—	2	1	no	—
106	C₂×D₄×C₆₁	—	2	2	no	—
107	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₆₁	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	—	2	8	no	—
113	C₂²×C₄×C₆₁	—	2	4	no	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	4	4	no	—
117	C₂²×C₄×C₆₁	—	8	2	no	—
118	C₂²×C₄×C₆₁	—	8	2	no	—
119	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₆₁	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
124	C₂×C₈×C₆₁	—	2	2	no	—
125	C₂×C₈×C₆₁	—	2	2	no	—
126	C₂×C₈×C₆₁	—	2	1	no	—
127	C₂×C₈×C₆₁	—	2	1	no	—
128	C₂×C₈×C₆₁	—	2	2	no	—
129	C₂×C₈×C₆₁	—	2	2	no	—
130	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	—
131	C₄⋊C₄×C₆₁	—	2	8	no	—
132	C₄⋊C₄×C₆₁	—	2	8	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	4	no	—
135	C₄⋊C₄×C₆₁	—	2	4	no	—
136	C₄⋊C₄×C₆₁	—	2	1	no	—
137	C₄⋊C₄×C₆₁	—	2	2	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	—	4	4	no	—
144	C₄⋊C₄×C₆₁	—	4	2	no	—
145	C₄⋊C₄×C₆₁	—	4	2	no	—
146	C₄⋊C₄×C₆₁	—	8	2	no	—
147	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
148	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₆₁	C₂×Q₈	1	4	yes	—
150	C₂²⋊C₄×C₆₁	—	2	8	no	—
151	C₂²⋊C₄×C₆₁	—	2	4	no	—
152	C₄²×C₆₁	—	2	2	no	—
153	C₄²×C₆₁	—	2	2	no	—
154	C₄²×C₆₁	—	8	1	no	—
155	C₄²×C₆₁	C₂×D₄	1	2	yes	—
156	C₄²×C₆₁	C₂×D₄	1	2	yes	—
157	C₂³×C₆₁	—	2	2	no	—
158	C₂³×C₆₁	—	2	4	no	—
159	C₂³×C₆₁	—	4	2	no	—
160	C₂³×C₆₁	—	4	1	no	—
161	C₂³×C₆₁	—	4	1	no	—
162	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₆₁	—	4	4	no	—
164	Q₈×C₆₁	—	8	4	no	—
165	D₄×C₆₁	—	2	2	no	—
166	D₄×C₆₁	—	2	4	no	—
167	D₄×C₆₁	C₄⋊Q₈	1	4	yes	—
168	C₂×C₄×C₆₁	—	2	2	no	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	—	2	1	no	—
171	C₂×C₄×C₆₁	—	2	2	no	—
172	C₂×C₄×C₆₁	—	2	2	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	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	2	no	—
179	C₂×C₄×C₆₁	—	2	2	no	—
180	C₂×C₄×C₆₁	—	4	8	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	4	1	no	—
187	C₂×C₄×C₆₁	—	4	1	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	—	8	8	no	—
192	C₂×C₄×C₆₁	#120	1	2	yes	—
193	C₂×C₄×C₆₁	#120	1	2	yes	—
194	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
197	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
198	C₈×C₆₁	—	2	4	no	—
199	C₈×C₆₁	—	4	1	no	—
200	C₈×C₆₁	—	4	1	no	—
201	#25845	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₆₁	—	2	4	no	—
203	C₂²×C₆₁	—	4	4	no	—
204	C₂²×C₆₁	—	4	4	no	—
205	C₂²×C₆₁	—	4	2	no	—
206	C₂²×C₆₁	—	4	2	no	—
207	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
208	C₂²×C₆₁	D₄×Q₈	1	2	yes	—
209	C₂²×C₆₁	#575	1	2	yes	—
210	C₂²×C₆₁	#576	1	1	yes	characteristic
211	C₂²×C₆₁	#577	1	1	yes	characteristic
212	C₄×C₆₁	—	2	2	no	—
213	C₄×C₆₁	—	2	2	no	—
214	C₄×C₆₁	—	4	4	no	—
215	C₄×C₆₁	—	4	2	no	—
216	C₄×C₆₁	—	4	2	no	—
217	C₄×C₆₁	—	4	2	no	—
218	C₄×C₆₁	—	4	4	no	—
219	C₄×C₆₁	—	8	1	no	—
220	C₄×C₆₁	—	8	1	no	—
221	C₄×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
222	C₄×C₆₁	#536	1	1	yes	characteristic
223	C₄×C₆₁	D₄×Q₈	1	2	yes	—
224	C₂×#554	C₂×C₆₁	1	1	yes	characteristic
225	C₂×#501	C₂×C₆₁	1	1	yes	characteristic, complemented
226	C₂×#478	C₂×C₆₁	1	1	yes	characteristic
227	#2584	C₂×C₆₁	1	1	yes	characteristic, complemented
228	#2059	C₂×C₆₁	1	2	yes	complemented
229	#2059	C₂×C₆₁	1	2	yes	complemented
230	#1988	C₂×C₆₁	1	1	yes	characteristic, complemented
231	#1985	C₂×C₆₁	1	1	yes	characteristic, complemented
232	#1864	C₂×C₆₁	1	2	yes	—
233	#1862	C₂×C₆₁	1	2	yes	—
234	#1762	C₂×C₆₁	1	1	yes	characteristic
235	C₂×C₆₁	—	4	4	no	—
236	C₂×C₆₁	#2434	1	1	yes	characteristic
237	C₂×C₆₁	#3005	1	1	yes	characteristic
238	C₂×C₆₁	#3012	1	1	yes	characteristic
239	C₂×C₆₁	#3388	1	2	yes	—
240	C₂×C₆₁	#3389	1	2	yes	—
241	#554	—	2	4	no	—
242	#554	—	2	4	no	—
243	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
244	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
245	C₂×#125	C₂²×C₆₁	1	2	yes	—
246	C₂×C₂²⋊Q₈	—	2	1	no	—
247	C₂×C₂²⋊Q₈	—	2	2	no	—
248	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
250	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	—	2	1	no	—
252	#501	—	2	4	no	—
253	#478	—	2	4	no	—
254	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
255	C₂×#107	C₂²×C₆₁	1	2	yes	—
256	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
257	C₂×#106	C₂²×C₆₁	1	2	yes	—
258	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
260	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
261	C₂×#102	C₂²×C₆₁	1	2	yes	—
262	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
263	#398	—	2	1	no	—
264	#395	—	2	1	no	—
265	#389	—	2	2	no	—
266	#389	C₂²×C₆₁	1	2	yes	—
267	#389	C₂²×C₆₁	1	2	yes	—
268	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
269	#340	C₂²×C₆₁	1	2	yes	—
270	#340	C₂²×C₆₁	1	2	yes	—
271	#340	C₂²×C₆₁	1	2	yes	—
272	#336	C₂²×C₆₁	1	2	yes	—
273	#336	C₂²×C₆₁	1	2	yes	—
274	C₆₁	#25845	1	1	yes	characteristic, direct product factor, Sylow
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
277	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	2	2	no	—
280	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
283	C₄⋊Q₈	—	2	2	no	—
284	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
285	#125	—	2	4	no	—
286	#125	—	2	4	no	—
287	#125	—	2	2	no	—
288	#125	—	2	2	no	—
289	C₂²⋊Q₈	—	2	8	no	—
290	C₂²⋊Q₈	—	2	16	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×D₄	—	2	4	no	—
294	C₄×D₄	—	2	4	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	D₄×C₆₁	1	4	yes	—
297	C₂×C₄⋊C₄	—	2	8	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
306	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
316	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
317	#107	—	2	2	no	—
318	#107	—	2	4	no	—
319	#106	—	2	2	no	—
320	#106	—	2	4	no	—
321	C₄⋊C₈	—	2	2	no	—
322	#102	—	2	2	no	—
323	#102	—	2	2	no	—
324	#102	Q₈×C₆₁	1	8	yes	complemented
325	#97	—	2	2	no	—
326	#95	—	2	1	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	C₂⁴	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	8	1	no	—
334	C₂×Q₈	—	8	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
338	C₂×D₄	C₂×Q₈×C₆₁	1	4	yes	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	8	2	no	—
348	C₂²×C₄	—	8	2	no	—
349	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	8	2	no	—
377	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
378	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
379	C₄⋊C₄	C₂×Q₈×C₆₁	1	4	yes	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	8	1	no	—
385	C₄²	C₂×D₄×C₆₁	1	2	yes	—
386	C₄²	C₂×D₄×C₆₁	1	2	yes	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
393	Q₈	—	4	4	no	—
394	Q₈	—	8	4	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	4	no	—
397	D₄	C₄⋊Q₈×C₆₁	1	4	yes	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	8	8	no	—
422	C₂×C₄	#120×C₆₁	1	2	yes	—
423	C₂×C₄	#120×C₆₁	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
426	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
427	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
428	C₈	—	2	4	no	—
429	C₈	—	4	1	no	—
430	C₈	—	4	1	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
437	C₂²	D₄×Q₈×C₆₁	1	2	yes	—
438	C₂²	C₆₁×#575	1	2	yes	—
439	C₂²	C₆₁×#576	1	1	yes	characteristic
440	C₂²	C₆₁×#577	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	4	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	1	no	—
450	C₄	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
451	C₄	C₆₁×#536	1	1	yes	characteristic
452	C₄	D₄×Q₈×C₆₁	1	2	yes	—
453	C₂	—	4	4	no	—
454	C₂	C₆₁×#2434	1	1	yes	characteristic
455	C₂	C₆₁×#3005	1	1	yes	characteristic
456	C₂	C₆₁×#3012	1	1	yes	characteristic
457	C₂	C₆₁×#3388	1	2	yes	—
458	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×D₄×C₆₁	C₂³
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
2. C₂×C₆₁×#501	C₂	semidirect
4. C₆₁×#2584	C₂	semidirect
5. C₆₁×#2059	C₂	semidirect
6. C₆₁×#2059	C₂	semidirect
7. C₆₁×#1988	C₂	semidirect
8. C₆₁×#1985	C₂	semidirect
94. #102×C₆₁	Q₈	semidirect
201. #25845	C₆₁	direct (N × H)
225. C₂×#501	C₂×C₆₁	semidirect
227. #2584	C₂×C₆₁	semidirect
228. #2059	C₂×C₆₁	semidirect
229. #2059	C₂×C₆₁	semidirect
230. #1988	C₂×C₆₁	semidirect
231. #1985	C₂×C₆₁	semidirect
274. C₆₁	#25845	direct (N × H)
324. #102	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×#501	2
C₂×C₆₁×#478	2
C₆₁×#2584	2
C₆₁×#2059	2
C₆₁×#1988	2
C₆₁×#1985	2
C₆₁×#1864	2
C₆₁×#1862	2
C₆₁×#1762	2
#25845	61

Subgroups — C61×#25845 #29529278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25845 #29529278