Subgroups — C₆₁×#25812 #29529245

Order 15616.

1078 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2857	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2059	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1854	C₂	1	4	yes	maximal
9	C₄×C₂²⋊C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#533	—	2	4	no	—
11	C₆₁×#533	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#125×C₆₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
19	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
21	C₂×#117×C₆₁	C₂²	1	2	yes	—
22	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#500	—	2	4	no	—
24	C₆₁×#498	—	2	4	no	—
25	C₂×#107×C₆₁	C₂²	1	4	yes	—
26	C₂×#106×C₆₁	C₂²	1	4	yes	—
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#391	—	2	1	no	—
31	C₆₁×#389	—	2	1	no	—
32	C₆₁×#389	C₂²	1	2	yes	—
33	C₆₁×#384	C₂²	1	1	yes	characteristic
34	C₆₁×#380	—	2	1	no	—
35	C₆₁×#380	C₂²	1	2	yes	—
36	C₆₁×#340	C₂²	1	4	yes	—
37	C₆₁×#340	C₂²	1	4	yes	—
38	C₆₁×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₆₁	—	2	1	no	—
40	C₂²×Q₈×C₆₁	—	2	1	no	—
41	C₂²×Q₈×C₆₁	—	2	1	no	—
42	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₆₁	—	2	2	no	—
48	C₄⋊Q₈×C₆₁	—	2	2	no	—
49	C₄⋊Q₈×C₆₁	—	2	2	no	—
50	C₄⋊Q₈×C₆₁	—	2	2	no	—
51	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
52	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
53	#125×C₆₁	—	2	4	no	—
54	#125×C₆₁	—	2	4	no	—
55	C₂²⋊Q₈×C₆₁	—	2	8	no	—
56	C₂²⋊Q₈×C₆₁	—	2	8	no	—
57	C₂²⋊Q₈×C₆₁	—	4	4	no	—
58	C₄×Q₈×C₆₁	—	2	8	no	—
59	C₄×Q₈×C₆₁	—	2	8	no	—
60	#117×C₆₁	—	2	4	no	—
61	#117×C₆₁	—	2	4	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
76	C₂×C₄²×C₆₁	—	2	2	no	—
77	C₂×C₄²×C₆₁	—	2	2	no	—
78	C₂×C₄²×C₆₁	—	2	2	no	—
79	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
83	#107×C₆₁	—	2	8	no	—
84	#106×C₆₁	—	2	8	no	—
85	C₂²⋊C₈×C₆₁	Q₈	1	8	yes	complemented
86	C₄×C₈×C₆₁	—	2	2	no	—
87	C₄×C₈×C₆₁	—	2	2	no	—
88	#95×C₆₁	—	2	2	no	—
89	#95×C₆₁	—	2	2	no	—
90	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
91	C₂×Q₈×C₆₁	—	2	4	no	—
92	C₂×Q₈×C₆₁	—	2	4	no	—
93	C₂×Q₈×C₆₁	—	4	2	no	—
94	C₂×Q₈×C₆₁	—	4	2	no	—
95	C₂×Q₈×C₆₁	—	4	2	no	—
96	C₂×Q₈×C₆₁	—	4	2	no	—
97	C₂×Q₈×C₆₁	—	4	2	no	—
98	C₂×Q₈×C₆₁	—	4	2	no	—
99	C₂×Q₈×C₆₁	—	4	2	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	2	1	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	2	no	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	—	2	2	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	—	2	2	no	—
113	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
119	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₂×C₈×C₆₁	—	2	2	no	—
123	C₂×C₈×C₆₁	—	2	2	no	—
124	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	—
125	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	—
126	C₄⋊C₄×C₆₁	—	2	8	no	—
127	C₄⋊C₄×C₆₁	—	2	8	no	—
128	C₄⋊C₄×C₆₁	—	2	4	no	—
129	C₄⋊C₄×C₆₁	—	2	4	no	—
130	C₄⋊C₄×C₆₁	—	2	2	no	—
131	C₄⋊C₄×C₆₁	—	2	2	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	4	no	—
135	C₄⋊C₄×C₆₁	—	4	4	no	—
136	C₄⋊C₄×C₆₁	—	4	2	no	—
137	C₄⋊C₄×C₆₁	—	4	2	no	—
138	C₄⋊C₄×C₆₁	—	4	2	no	—
139	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
140	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
141	C₂²⋊C₄×C₆₁	—	2	8	no	—
142	C₂²⋊C₄×C₆₁	—	4	4	no	—
143	C₄²×C₆₁	—	2	8	no	—
144	C₄²×C₆₁	—	2	2	no	—
145	C₄²×C₆₁	—	2	2	no	—
146	C₄²×C₆₁	—	2	1	no	—
147	C₄²×C₆₁	—	2	1	no	—
148	C₄²×C₆₁	C₂×D₄	1	2	yes	—
149	C₄²×C₆₁	C₂×D₄	1	2	yes	—
150	C₂³×C₆₁	—	2	1	no	—
151	C₂³×C₆₁	—	2	1	no	—
152	C₂³×C₆₁	—	2	1	no	—
153	C₂³×C₆₁	—	2	1	no	—
154	C₂³×C₆₁	—	2	1	no	—
155	C₂³×C₆₁	—	2	1	no	—
156	C₂³×C₆₁	C₄⋊Q₈	1	2	yes	—
157	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₆₁	—	4	8	no	—
159	Q₈×C₆₁	—	4	8	no	—
160	Q₈×C₆₁	—	8	4	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	4	no	—
164	C₂×C₄×C₆₁	—	2	4	no	—
165	C₂×C₄×C₆₁	—	2	1	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	2	4	no	—
168	C₂×C₄×C₆₁	—	2	4	no	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	—	2	1	no	—
171	C₂×C₄×C₆₁	—	2	1	no	—
172	C₂×C₄×C₆₁	—	2	1	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	4	2	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	4	2	no	—
177	C₂×C₄×C₆₁	—	4	4	no	—
178	C₂×C₄×C₆₁	—	4	4	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	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	#120	1	2	yes	—
186	C₂×C₄×C₆₁	#120	1	2	yes	—
187	C₂×C₄×C₆₁	C₄⋊Q₈	1	2	yes	—
188	C₂×C₄×C₆₁	#135	1	2	yes	—
189	C₂×C₄×C₆₁	#135	1	2	yes	—
190	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
191	C₂×C₄×C₆₁	#137	1	2	yes	—
192	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
195	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
196	C₈×C₆₁	—	2	4	no	—
197	C₈×C₆₁	—	2	4	no	—
198	#25812	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₆₁	—	2	2	no	—
200	C₂²×C₆₁	—	2	2	no	—
201	C₂²×C₆₁	—	2	2	no	—
202	C₂²×C₆₁	—	4	1	no	—
203	C₂²×C₆₁	—	4	1	no	—
204	C₂²×C₆₁	—	4	1	no	—
205	C₂²×C₆₁	—	4	1	no	—
206	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
207	C₂²×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
208	C₂²×C₆₁	#536	1	1	yes	characteristic
209	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
210	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
211	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
213	C₄×C₆₁	—	2	2	no	—
214	C₄×C₆₁	—	4	1	no	—
215	C₄×C₆₁	—	4	4	no	—
216	C₄×C₆₁	—	4	1	no	—
217	C₄×C₆₁	—	4	4	no	—
218	C₄×C₆₁	—	8	2	no	—
219	C₄×C₆₁	—	8	2	no	—
220	C₄×C₆₁	#449	1	4	yes	—
221	C₄×C₆₁	#452	1	4	yes	—
222	C₄×C₆₁	D₄×Q₈	1	2	yes	—
223	C₄×C₆₁	D₄×Q₈	1	2	yes	—
224	C₂×#533	C₂×C₆₁	1	1	yes	characteristic
225	C₂×#500	C₂×C₆₁	1	1	yes	characteristic, complemented
226	C₂×#498	C₂×C₆₁	1	1	yes	characteristic, complemented
227	#2857	C₂×C₆₁	1	1	yes	characteristic
228	#2059	C₂×C₆₁	1	4	yes	complemented
229	#1990	C₂×C₆₁	1	1	yes	characteristic, complemented
230	#1990	C₂×C₆₁	1	1	yes	characteristic, complemented
231	#1854	C₂×C₆₁	1	4	yes	—
232	C₄×C₂²⋊C₈	C₂×C₆₁	1	1	yes	characteristic
233	C₂×C₆₁	—	4	2	no	—
234	C₂×C₆₁	#2434	1	1	yes	characteristic
235	C₂×C₆₁	C₂×#449	1	1	yes	characteristic
236	C₂×C₆₁	C₂×#452	1	1	yes	characteristic
237	C₂×C₆₁	#3160	1	1	yes	characteristic
238	C₂×C₆₁	#3165	1	1	yes	characteristic
239	C₂×C₆₁	#3228	1	1	yes	characteristic
240	C₂×C₆₁	#3231	1	1	yes	characteristic
241	#533	—	2	4	no	—
242	#533	—	2	4	no	—
243	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
244	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
246	C₂×#125	C₂²×C₆₁	1	2	yes	—
247	C₂×C₂²⋊Q₈	—	2	1	no	—
248	C₂×C₂²⋊Q₈	—	2	1	no	—
249	C₂×C₂²⋊Q₈	—	2	1	no	—
250	C₂×C₄×Q₈	—	2	1	no	—
251	C₂×C₄×Q₈	—	2	1	no	—
252	C₂×#117	C₂²×C₆₁	1	2	yes	—
253	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
254	#500	—	2	4	no	—
255	#498	—	2	4	no	—
256	C₂×#107	C₂²×C₆₁	1	4	yes	—
257	C₂×#106	C₂²×C₆₁	1	4	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
259	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
261	#391	—	2	1	no	—
262	#389	—	2	1	no	—
263	#389	C₂²×C₆₁	1	2	yes	—
264	#384	C₂²×C₆₁	1	1	yes	characteristic
265	#380	—	2	1	no	—
266	#380	C₂²×C₆₁	1	2	yes	—
267	#340	C₂²×C₆₁	1	4	yes	—
268	#340	C₂²×C₆₁	1	4	yes	—
269	#336	C₂²×C₆₁	1	2	yes	—
270	C₆₁	#25812	1	1	yes	characteristic, direct product factor, Sylow
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
275	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
278	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
284	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
285	#125	—	2	4	no	—
286	#125	—	2	4	no	—
287	C₂²⋊Q₈	—	2	8	no	—
288	C₂²⋊Q₈	—	2	8	no	—
289	C₂²⋊Q₈	—	4	4	no	—
290	C₄×Q₈	—	2	8	no	—
291	C₄×Q₈	—	2	8	no	—
292	#117	—	2	4	no	—
293	#117	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
312	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
315	#107	—	2	8	no	—
316	#106	—	2	8	no	—
317	C₂²⋊C₈	Q₈×C₆₁	1	8	yes	complemented
318	C₄×C₈	—	2	2	no	—
319	C₄×C₈	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	—
357	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
372	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₄²	—	2	8	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	C₂×D₄×C₆₁	1	2	yes	—
381	C₄²	C₂×D₄×C₆₁	1	2	yes	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	C₄⋊Q₈×C₆₁	1	2	yes	—
389	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
390	Q₈	—	4	8	no	—
391	Q₈	—	4	8	no	—
392	Q₈	—	8	4	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	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	#120×C₆₁	1	2	yes	—
418	C₂×C₄	#120×C₆₁	1	2	yes	—
419	C₂×C₄	C₄⋊Q₈×C₆₁	1	2	yes	—
420	C₂×C₄	#135×C₆₁	1	2	yes	—
421	C₂×C₄	#135×C₆₁	1	2	yes	—
422	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
423	C₂×C₄	#137×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	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
438	C₂²	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
439	C₂²	C₆₁×#536	1	1	yes	characteristic
440	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
441	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
442	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
443	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	4	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₆₁×#449	1	4	yes	—
452	C₄	C₆₁×#452	1	4	yes	—
453	C₄	D₄×Q₈×C₆₁	1	2	yes	—
454	C₄	D₄×Q₈×C₆₁	1	2	yes	—
455	C₂	—	4	2	no	—
456	C₂	C₆₁×#2434	1	1	yes	characteristic
457	C₂	C₂×C₆₁×#449	1	1	yes	characteristic
458	C₂	C₂×C₆₁×#452	1	1	yes	characteristic
459	C₂	C₆₁×#3160	1	1	yes	characteristic
460	C₂	C₆₁×#3165	1	1	yes	characteristic
461	C₂	C₆₁×#3228	1	1	yes	characteristic
462	C₂	C₆₁×#3231	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#500	C₂	semidirect
3. C₂×C₆₁×#498	C₂	semidirect
5. C₆₁×#2059	C₂	semidirect
6. C₆₁×#1990	C₂	semidirect
7. C₆₁×#1990	C₂	semidirect
85. C₂²⋊C₈×C₆₁	Q₈	semidirect
198. #25812	C₆₁	direct (N × H)
225. C₂×#500	C₂×C₆₁	semidirect
226. C₂×#498	C₂×C₆₁	semidirect
228. #2059	C₂×C₆₁	semidirect
229. #1990	C₂×C₆₁	semidirect
230. #1990	C₂×C₆₁	semidirect
270. C₆₁	#25812	direct (N × H)
317. C₂²⋊C₈	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×#533	2
C₂×C₆₁×#500	2
C₂×C₆₁×#498	2
C₆₁×#2857	2
C₆₁×#2059	2
C₆₁×#1990	2
C₆₁×#1854	2
C₄×C₂²⋊C₈×C₆₁	2
#25812	61

Subgroups — C61×#25812 #29529245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25812 #29529245