Subgroups — C₄×C₆₁×#465 #29524953

Order 15616.

1138 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#465	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂²⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#121×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1934	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1893	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1892	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1807	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#106×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	—	2	1	no	—
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#465	C₄	1	8	yes	direct product factor
26	C₄×SD₁₆×C₆₁	—	2	4	no	—
27	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₆₁	—	2	4	no	—
37	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#391	C₂²	1	1	yes	characteristic
42	C₆₁×#390	C₂²	1	1	yes	characteristic
43	C₆₁×#389	C₂²	1	1	yes	characteristic
44	C₆₁×#389	C₂²	1	1	yes	characteristic
45	C₆₁×#388	—	2	1	no	—
46	C₆₁×#387	—	2	1	no	—
47	C₆₁×#386	—	2	1	no	—
48	C₆₁×#385	—	2	1	no	—
49	C₆₁×#380	C₂²	1	1	yes	characteristic
50	C₆₁×#380	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
52	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
55	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
56	C₆₁×#340	C₂²	1	1	yes	characteristic
57	C₆₁×#340	C₂²	1	1	yes	characteristic
58	C₆₁×#340	C₂²	1	1	yes	characteristic
59	C₆₁×#340	C₂²	1	1	yes	characteristic
60	C₆₁×#340	C₂²	1	1	yes	characteristic
61	C₆₁×#340	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₆₁	—	2	1	no	—
64	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₆₁	—	2	1	no	—
66	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
69	C₂×SD₁₆×C₆₁	—	2	2	no	—
70	C₂×SD₁₆×C₆₁	—	2	2	no	—
71	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
72	C₂²×C₈×C₆₁	—	2	2	no	—
73	C₂²×C₈×C₆₁	—	2	2	no	—
74	C₂²×C₈×C₆₁	—	2	2	no	—
75	C₂²×C₈×C₆₁	—	2	2	no	—
76	C₂²×C₈×C₆₁	—	2	2	no	—
77	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	complemented
78	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₂²⋊Q₈×C₆₁	—	2	2	no	—
83	C₂²⋊Q₈×C₆₁	C₂×C₄	1	4	yes	complemented
84	#121×C₆₁	—	2	2	no	—
85	#121×C₆₁	C₂×C₄	1	4	yes	—
86	C₄×Q₈×C₆₁	—	2	2	no	—
87	C₄×Q₈×C₆₁	—	2	2	no	—
88	C₄×D₄×C₆₁	—	2	2	no	—
89	C₄×D₄×C₆₁	—	2	2	no	—
90	C₄×D₄×C₆₁	—	4	4	no	—
91	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
108	C₂×C₄²×C₆₁	—	2	2	no	—
109	C₂×C₄²×C₆₁	—	2	2	no	—
110	C₂×C₄²×C₆₁	—	2	1	no	—
111	C₂×C₄²×C₆₁	—	2	1	no	—
112	C₂×C₄²×C₆₁	—	2	1	no	—
113	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
117	#106×C₆₁	—	2	2	no	—
118	#106×C₆₁	—	2	2	no	—
119	#106×C₆₁	C₂×C₄	1	4	yes	complemented
120	#103×C₆₁	—	2	2	no	—
121	#103×C₆₁	—	2	2	no	—
122	#103×C₆₁	C₂×C₄	1	4	yes	complemented
123	#102×C₆₁	—	2	2	no	—
124	#102×C₆₁	—	2	2	no	—
125	#102×C₆₁	C₂×C₄	1	4	yes	complemented
126	C₄×C₈×C₆₁	—	2	2	no	—
127	C₄×C₈×C₆₁	—	2	2	no	—
128	C₄×C₈×C₆₁	—	2	2	no	—
129	C₄×C₈×C₆₁	D₄	1	4	yes	complemented
130	#95×C₆₁	—	2	1	no	—
131	#95×C₆₁	—	2	1	no	—
132	#95×C₆₁	—	2	1	no	—
133	#95×C₆₁	—	2	1	no	—
134	#95×C₆₁	—	2	1	no	—
135	#95×C₆₁	—	2	1	no	—
136	#95×C₆₁	—	2	1	no	—
137	#95×C₆₁	—	2	1	no	—
138	C₂⁴×C₆₁	—	2	1	no	—
139	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
140	C₂×Q₈×C₆₁	—	2	1	no	—
141	C₂×Q₈×C₆₁	—	2	1	no	—
142	C₂×Q₈×C₆₁	—	2	1	no	—
143	C₂×Q₈×C₆₁	—	2	1	no	—
144	C₂×Q₈×C₆₁	—	2	1	no	—
145	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
146	C₂×D₄×C₆₁	—	2	4	no	—
147	C₂×D₄×C₆₁	—	2	1	no	—
148	C₂×D₄×C₆₁	—	2	1	no	—
149	C₂×D₄×C₆₁	—	2	1	no	—
150	C₂×D₄×C₆₁	—	2	1	no	—
151	C₂×D₄×C₆₁	—	2	1	no	—
152	C₂×D₄×C₆₁	—	4	2	no	—
153	C₂×D₄×C₆₁	—	4	2	no	—
154	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₆₁	—	2	2	no	—
156	C₂²×C₄×C₆₁	—	2	2	no	—
157	C₂²×C₄×C₆₁	—	2	2	no	—
158	C₂²×C₄×C₆₁	—	2	2	no	—
159	C₂²×C₄×C₆₁	—	2	2	no	—
160	C₂²×C₄×C₆₁	—	2	1	no	—
161	C₂²×C₄×C₆₁	—	2	1	no	—
162	C₂²×C₄×C₆₁	—	2	1	no	—
163	C₂²×C₄×C₆₁	—	2	1	no	—
164	C₂²×C₄×C₆₁	—	2	1	no	—
165	C₂²×C₄×C₆₁	—	2	1	no	—
166	C₂²×C₄×C₆₁	—	2	1	no	—
167	C₂²×C₄×C₆₁	—	2	1	no	—
168	C₂²×C₄×C₆₁	—	2	1	no	—
169	C₂²×C₄×C₆₁	—	2	1	no	—
170	C₂²×C₄×C₆₁	—	2	1	no	—
171	C₂²×C₄×C₆₁	—	4	2	no	—
172	C₂²×C₄×C₆₁	—	4	2	no	—
173	C₂²×C₄×C₆₁	—	4	2	no	—
174	C₂²×C₄×C₆₁	SD₁₆	1	4	yes	complemented
175	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
176	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₆₁	#41	1	2	yes	—
182	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
183	SD₁₆×C₆₁	—	2	8	no	—
184	C₂×C₈×C₆₁	—	2	8	no	—
185	C₂×C₈×C₆₁	—	2	1	no	—
186	C₂×C₈×C₆₁	—	2	1	no	—
187	C₂×C₈×C₆₁	—	2	1	no	—
188	C₂×C₈×C₆₁	—	2	1	no	—
189	C₂×C₈×C₆₁	—	2	1	no	—
190	C₂×C₈×C₆₁	—	2	1	no	—
191	C₂×C₈×C₆₁	—	2	8	no	—
192	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
193	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
194	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
195	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
196	C₂×C₈×C₆₁	#41	1	2	yes	—
197	C₂×C₈×C₆₁	#41	1	2	yes	—
198	C₄⋊C₄×C₆₁	—	2	4	no	—
199	C₄⋊C₄×C₆₁	—	2	1	no	—
200	C₄⋊C₄×C₆₁	—	2	1	no	—
201	C₄⋊C₄×C₆₁	—	2	1	no	—
202	C₄⋊C₄×C₆₁	—	2	1	no	—
203	C₄⋊C₄×C₆₁	—	2	1	no	—
204	C₄⋊C₄×C₆₁	—	2	1	no	—
205	C₄⋊C₄×C₆₁	—	2	1	no	—
206	C₄⋊C₄×C₆₁	—	2	1	no	—
207	C₄⋊C₄×C₆₁	—	2	1	no	—
208	C₄⋊C₄×C₆₁	—	2	1	no	—
209	C₄⋊C₄×C₆₁	—	4	2	no	—
210	C₄⋊C₄×C₆₁	—	4	2	no	—
211	C₄⋊C₄×C₆₁	—	4	2	no	—
212	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
213	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
214	C₂²⋊C₄×C₆₁	—	2	4	no	—
215	C₂²⋊C₄×C₆₁	—	2	4	no	—
216	C₂²⋊C₄×C₆₁	—	4	2	no	—
217	C₂²⋊C₄×C₆₁	—	4	2	no	—
218	C₂²⋊C₄×C₆₁	—	4	2	no	—
219	C₂²⋊C₄×C₆₁	—	4	2	no	—
220	C₂²⋊C₄×C₆₁	—	4	2	no	—
221	C₄²×C₆₁	—	2	2	no	—
222	C₄²×C₆₁	—	2	2	no	—
223	C₄²×C₆₁	—	2	1	no	—
224	C₄²×C₆₁	—	2	1	no	—
225	C₄²×C₆₁	—	4	2	no	—
226	C₄²×C₆₁	—	4	2	no	—
227	C₄²×C₆₁	—	4	2	no	—
228	C₄²×C₆₁	C₂×D₄	1	2	yes	—
229	C₄²×C₆₁	#41	1	2	yes	—
230	C₂³×C₆₁	—	2	1	no	—
231	C₂³×C₆₁	—	2	1	no	—
232	C₂³×C₆₁	—	2	1	no	—
233	C₂³×C₆₁	—	2	1	no	—
234	C₂³×C₆₁	—	2	2	no	—
235	C₂³×C₆₁	—	4	1	no	—
236	C₂³×C₆₁	—	4	1	no	—
237	C₂³×C₆₁	—	4	1	no	—
238	C₂³×C₆₁	—	4	1	no	—
239	C₂³×C₆₁	—	4	1	no	—
240	C₂³×C₆₁	—	4	1	no	—
241	C₂³×C₆₁	C₄×D₄	1	2	yes	—
242	C₂³×C₆₁	C₂×SD₁₆	1	2	yes	—
243	C₂³×C₆₁	#135	1	2	yes	—
244	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
245	Q₈×C₆₁	—	2	2	no	—
246	Q₈×C₆₁	—	2	2	no	—
247	Q₈×C₆₁	—	4	1	no	—
248	Q₈×C₆₁	—	4	1	no	—
249	D₄×C₆₁	—	2	2	no	—
250	D₄×C₆₁	—	2	2	no	—
251	D₄×C₆₁	—	4	8	no	—
252	D₄×C₆₁	—	4	1	no	—
253	D₄×C₆₁	—	4	1	no	—
254	C₂×C₄×C₆₁	—	2	8	no	—
255	C₂×C₄×C₆₁	—	2	1	no	—
256	C₂×C₄×C₆₁	—	2	1	no	—
257	C₂×C₄×C₆₁	—	2	1	no	—
258	C₂×C₄×C₆₁	—	2	1	no	—
259	C₂×C₄×C₆₁	—	2	1	no	—
260	C₂×C₄×C₆₁	—	2	1	no	—
261	C₂×C₄×C₆₁	—	2	1	no	—
262	C₂×C₄×C₆₁	—	2	1	no	—
263	C₂×C₄×C₆₁	—	2	2	no	—
264	C₂×C₄×C₆₁	—	2	2	no	—
265	C₂×C₄×C₆₁	—	2	2	no	—
266	C₂×C₄×C₆₁	—	2	2	no	—
267	C₂×C₄×C₆₁	—	2	8	no	—
268	C₂×C₄×C₆₁	—	2	2	no	—
269	C₂×C₄×C₆₁	—	2	2	no	—
270	C₂×C₄×C₆₁	—	2	2	no	—
271	C₂×C₄×C₆₁	—	4	1	no	—
272	C₂×C₄×C₆₁	—	4	1	no	—
273	C₂×C₄×C₆₁	—	4	1	no	—
274	C₂×C₄×C₆₁	—	4	1	no	—
275	C₂×C₄×C₆₁	—	4	1	no	—
276	C₂×C₄×C₆₁	—	4	1	no	—
277	C₂×C₄×C₆₁	—	4	1	no	—
278	C₂×C₄×C₆₁	—	4	1	no	—
279	C₂×C₄×C₆₁	—	4	1	no	—
280	C₂×C₄×C₆₁	—	4	1	no	—
281	C₂×C₄×C₆₁	—	4	1	no	—
282	C₂×C₄×C₆₁	—	4	1	no	—
283	C₂×C₄×C₆₁	—	4	1	no	—
284	C₂×C₄×C₆₁	—	4	1	no	—
285	C₂×C₄×C₆₁	—	4	1	no	—
286	C₂×C₄×C₆₁	—	4	1	no	—
287	C₂×C₄×C₆₁	—	4	1	no	—
288	C₂×C₄×C₆₁	—	4	1	no	—
289	C₂×C₄×C₆₁	—	8	4	no	—
290	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
291	C₂×C₄×C₆₁	#121	1	2	yes	—
292	C₂×C₄×C₆₁	#121	1	2	yes	—
293	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
294	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
295	C₂×C₄×C₆₁	#135	1	2	yes	—
296	C₂×C₄×C₆₁	#135	1	2	yes	—
297	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
303	C₈×C₆₁	—	2	2	no	—
304	C₈×C₆₁	—	2	2	no	—
305	C₈×C₆₁	—	2	2	no	—
306	C₈×C₆₁	C₄×D₄	1	4	yes	complemented
307	C₄×#465	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
308	C₂²×C₆₁	—	2	2	no	—
309	C₂²×C₆₁	—	2	2	no	—
310	C₂²×C₆₁	—	2	2	no	—
311	C₂²×C₆₁	—	2	2	no	—
312	C₂²×C₆₁	—	2	2	no	—
313	C₂²×C₆₁	—	2	2	no	—
314	C₂²×C₆₁	—	4	2	no	—
315	C₂²×C₆₁	—	4	2	no	—
316	C₂²×C₆₁	—	4	2	no	—
317	C₂²×C₆₁	—	8	1	no	—
318	C₂²×C₆₁	—	8	1	no	—
319	C₂²×C₆₁	—	8	1	no	—
320	C₂²×C₆₁	—	8	1	no	—
321	C₂²×C₆₁	C₄×SD₁₆	1	4	yes	complemented
322	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
323	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
324	C₂²×C₆₁	#532	1	1	yes	characteristic
325	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
326	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
327	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
328	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
329	C₄×C₆₁	—	2	2	no	—
330	C₄×C₆₁	—	2	2	no	—
331	C₄×C₆₁	—	2	2	no	—
332	C₄×C₆₁	—	2	2	no	—
333	C₄×C₆₁	—	4	2	no	—
334	C₄×C₆₁	—	4	2	no	—
335	C₄×C₆₁	—	4	2	no	—
336	C₄×C₆₁	—	8	1	no	—
337	C₄×C₆₁	—	8	1	no	—
338	C₄×C₆₁	—	8	1	no	—
339	C₄×C₆₁	—	8	1	no	—
340	C₄×C₆₁	#465	1	4	yes	direct product factor
341	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
342	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
343	C₄×C₆₁	#525	1	1	yes	characteristic
344	C₄×C₆₁	#529	1	1	yes	characteristic
345	C₂×#465	C₂×C₆₁	1	1	yes	characteristic
346	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
347	C₂²×C₄×C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
348	C₄×C₂²⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
349	C₄×#121	C₂×C₆₁	1	1	yes	characteristic
350	#1968	C₂×C₆₁	1	1	yes	characteristic, complemented
351	#1941	C₂×C₆₁	1	1	yes	characteristic, complemented
352	#1934	C₂×C₆₁	1	1	yes	characteristic, complemented
353	#1933	C₂×C₆₁	1	1	yes	characteristic, complemented
354	#1893	C₂×C₆₁	1	1	yes	characteristic
355	#1892	C₂×C₆₁	1	1	yes	characteristic, complemented
356	#1807	C₂×C₆₁	1	1	yes	characteristic, complemented
357	C₄×#106	C₂×C₆₁	1	1	yes	characteristic, complemented
358	C₄×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
359	C₄×#102	C₂×C₆₁	1	1	yes	characteristic, complemented
360	C₂×C₆₁	—	2	4	no	—
361	C₂×C₆₁	—	8	2	no	—
362	C₂×C₆₁	C₄×#121	1	1	yes	characteristic
363	C₂×C₆₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
364	C₂×C₆₁	C₄×#135	1	1	yes	characteristic
365	C₂×C₆₁	C₂×#465	1	1	yes	characteristic
366	C₂×C₆₁	#3050	1	1	yes	characteristic
367	C₂×C₆₁	#3167	1	1	yes	characteristic
368	C₂×C₆₁	#3168	1	1	yes	characteristic
369	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
370	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
371	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
372	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
373	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
374	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
375	C₂×C₄×D₄	—	2	1	no	—
376	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
377	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
378	#465	C₄×C₆₁	1	8	yes	direct product factor
379	C₄×SD₁₆	—	2	4	no	—
380	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
381	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
382	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
383	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
384	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
385	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
386	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
387	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
388	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
389	C₂×C₄×C₈	—	2	4	no	—
390	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
391	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
392	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
393	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
394	#391	C₂²×C₆₁	1	1	yes	characteristic
395	#390	C₂²×C₆₁	1	1	yes	characteristic
396	#389	C₂²×C₆₁	1	1	yes	characteristic
397	#389	C₂²×C₆₁	1	1	yes	characteristic
398	#388	—	2	1	no	—
399	#387	—	2	1	no	—
400	#386	—	2	1	no	—
401	#385	—	2	1	no	—
402	#380	C₂²×C₆₁	1	1	yes	characteristic
403	#380	C₂²×C₆₁	1	1	yes	characteristic
404	C₄×C₄⋊C₄	—	2	1	no	—
405	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
406	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
407	C₄×C₂²⋊C₄	—	2	1	no	—
408	C₄×C₂²⋊C₄	—	2	1	no	—
409	#340	C₂²×C₆₁	1	1	yes	characteristic
410	#340	C₂²×C₆₁	1	1	yes	characteristic
411	#340	C₂²×C₆₁	1	1	yes	characteristic
412	#340	C₂²×C₆₁	1	1	yes	characteristic
413	#340	C₂²×C₆₁	1	1	yes	characteristic
414	#340	C₂²×C₆₁	1	1	yes	characteristic
415	C₆₁	C₄×#465	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
419	C₂³×C₄	—	2	1	no	—
420	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
421	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
423	C₂×SD₁₆	—	2	2	no	—
424	C₂×SD₁₆	—	2	2	no	—
425	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
426	C₂²×C₈	—	2	2	no	—
427	C₂²×C₈	—	2	2	no	—
428	C₂²×C₈	—	2	2	no	—
429	C₂²×C₈	—	2	2	no	—
430	C₂²×C₈	—	2	2	no	—
431	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	complemented
432	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
434	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
436	C₂²⋊Q₈	—	2	2	no	—
437	C₂²⋊Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
438	#121	—	2	2	no	—
439	#121	C₂×C₄×C₆₁	1	4	yes	—
440	C₄×Q₈	—	2	2	no	—
441	C₄×Q₈	—	2	2	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	4	4	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₄²	—	2	2	no	—
463	C₂×C₄²	—	2	2	no	—
464	C₂×C₄²	—	2	1	no	—
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	—	2	1	no	—
467	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
468	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
471	#106	—	2	2	no	—
472	#106	—	2	2	no	—
473	#106	C₂×C₄×C₆₁	1	4	yes	complemented
474	#103	—	2	2	no	—
475	#103	—	2	2	no	—
476	#103	C₂×C₄×C₆₁	1	4	yes	complemented
477	#102	—	2	2	no	—
478	#102	—	2	2	no	—
479	#102	C₂×C₄×C₆₁	1	4	yes	complemented
480	C₄×C₈	—	2	2	no	—
481	C₄×C₈	—	2	2	no	—
482	C₄×C₈	—	2	2	no	—
483	C₄×C₈	D₄×C₆₁	1	4	yes	complemented
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	C₂⁴	—	2	1	no	—
493	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	4	2	no	—
507	C₂×D₄	—	4	2	no	—
508	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	SD₁₆×C₆₁	1	4	yes	complemented
529	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
530	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
535	C₂²×C₄	#41×C₆₁	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
537	SD₁₆	—	2	8	no	—
538	C₂×C₈	—	2	8	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	8	no	—
546	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
547	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
548	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
549	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
550	C₂×C₈	#41×C₆₁	1	2	yes	—
551	C₂×C₈	#41×C₆₁	1	2	yes	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	4	2	no	—
564	C₄⋊C₄	—	4	2	no	—
565	C₄⋊C₄	—	4	2	no	—
566	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
567	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	2	2	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	4	2	no	—
580	C₄²	—	4	2	no	—
581	C₄²	—	4	2	no	—
582	C₄²	C₂×D₄×C₆₁	1	2	yes	—
583	C₄²	#41×C₆₁	1	2	yes	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	C₄×D₄×C₆₁	1	2	yes	—
596	C₂³	C₂×SD₁₆×C₆₁	1	2	yes	—
597	C₂³	#135×C₆₁	1	2	yes	—
598	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
599	Q₈	—	2	2	no	—
600	Q₈	—	2	2	no	—
601	Q₈	—	4	1	no	—
602	Q₈	—	4	1	no	—
603	D₄	—	2	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	4	8	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	C₂×C₄	—	2	8	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	8	4	no	—
644	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
645	C₂×C₄	#121×C₆₁	1	2	yes	—
646	C₂×C₄	#121×C₆₁	1	2	yes	—
647	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
648	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
649	C₂×C₄	#135×C₆₁	1	2	yes	—
650	C₂×C₄	#135×C₆₁	1	2	yes	—
651	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
652	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
653	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
654	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
655	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
656	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
657	C₈	—	2	2	no	—
658	C₈	—	2	2	no	—
659	C₈	—	2	2	no	—
660	C₈	C₄×D₄×C₆₁	1	4	yes	complemented
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	8	1	no	—
671	C₂²	—	8	1	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	C₄×SD₁₆×C₆₁	1	4	yes	complemented
675	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
676	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
677	C₂²	C₆₁×#532	1	1	yes	characteristic
678	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
679	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
680	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
681	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	8	1	no	—
690	C₄	—	8	1	no	—
691	C₄	—	8	1	no	—
692	C₄	—	8	1	no	—
693	C₄	C₆₁×#465	1	4	yes	direct product factor
694	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
695	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
696	C₄	C₆₁×#525	1	1	yes	characteristic
697	C₄	C₆₁×#529	1	1	yes	characteristic
698	C₂	—	2	4	no	—
699	C₂	—	8	2	no	—
700	C₂	C₄×#121×C₆₁	1	1	yes	characteristic
701	C₂	C₂×C₄×SD₁₆×C₆₁	1	1	yes	characteristic
702	C₂	C₄×#135×C₆₁	1	1	yes	characteristic
703	C₂	C₂×C₆₁×#465	1	1	yes	characteristic
704	C₂	C₆₁×#3050	1	1	yes	characteristic
705	C₂	C₆₁×#3167	1	1	yes	characteristic
706	C₂	C₆₁×#3168	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂³×C₆₁	C₂²×D₄
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
3. C₂²×C₄×C₈×C₆₁	C₂	semidirect
4. C₄×C₂²⋊Q₈×C₆₁	C₂	semidirect
6. C₆₁×#1968	C₂	semidirect
7. C₆₁×#1941	C₂	semidirect
8. C₆₁×#1934	C₂	semidirect
9. C₆₁×#1933	C₂	semidirect
11. C₆₁×#1892	C₂	semidirect
12. C₆₁×#1807	C₂	semidirect
13. C₄×#106×C₆₁	C₂	semidirect
14. C₄×#103×C₆₁	C₂	semidirect
15. C₄×#102×C₆₁	C₂	semidirect
25. C₆₁×#465	C₄	direct (N × H)
71. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
77. C₂²×C₈×C₆₁	C₂×C₄	semidirect
83. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
119. #106×C₆₁	C₂×C₄	semidirect
122. #103×C₆₁	C₂×C₄	semidirect
125. #102×C₆₁	C₂×C₄	semidirect
129. C₄×C₈×C₆₁	D₄	semidirect
174. C₂²×C₄×C₆₁	SD₁₆	semidirect
306. C₈×C₆₁	C₄×D₄	semidirect
307. C₄×#465	C₆₁	direct (N × H)
321. C₂²×C₆₁	C₄×SD₁₆	semidirect
340. C₄×C₆₁	#465	direct (N × H)
346. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
347. C₂²×C₄×C₈	C₂×C₆₁	semidirect
348. C₄×C₂²⋊Q₈	C₂×C₆₁	semidirect
350. #1968	C₂×C₆₁	semidirect
351. #1941	C₂×C₆₁	semidirect
352. #1934	C₂×C₆₁	semidirect
353. #1933	C₂×C₆₁	semidirect
355. #1892	C₂×C₆₁	semidirect
356. #1807	C₂×C₆₁	semidirect
357. C₄×#106	C₂×C₆₁	semidirect
358. C₄×#103	C₂×C₆₁	semidirect
359. C₄×#102	C₂×C₆₁	semidirect
378. #465	C₄×C₆₁	direct (N × H)
415. C₆₁	C₄×#465	direct (N × H)
425. C₂×SD₁₆	C₂×C₄×C₆₁	semidirect
431. C₂²×C₈	C₂×C₄×C₆₁	semidirect
437. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
473. #106	C₂×C₄×C₆₁	semidirect
476. #103	C₂×C₄×C₆₁	semidirect
479. #102	C₂×C₄×C₆₁	semidirect
483. C₄×C₈	D₄×C₆₁	semidirect
528. C₂²×C₄	SD₁₆×C₆₁	semidirect
660. C₈	C₄×D₄×C₆₁	semidirect
674. C₂²	C₄×SD₁₆×C₆₁	semidirect
693. C₄	C₆₁×#465	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×#465	2
C₂×C₄×SD₁₆×C₆₁	2
C₂²×C₄×C₈×C₆₁	2
C₄×C₂²⋊Q₈×C₆₁	2
C₄×#121×C₆₁	2
C₆₁×#1968	2
C₆₁×#1941	2
C₆₁×#1934	2
C₆₁×#1933	2
C₆₁×#1893	2
C₆₁×#1892	2
C₆₁×#1807	2
C₄×#106×C₆₁	2
C₄×#103×C₆₁	2
C₄×#102×C₆₁	2
C₄×#465	61

Subgroups — C4×C61×#465 #29524953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₆₁×#465 #29524953