Subgroups — C₆₁×#24538 #29527971

Order 15616.

1156 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#418	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2499	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2073	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2071	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₆₁	—	2	1	no	—
25	C₆₁×#450	—	2	4	no	—
26	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#418	—	2	4	no	—
29	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#102×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×#102×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#397	—	2	1	no	—
39	C₆₁×#397	—	2	1	no	—
40	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
41	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
42	C₆₁×#390	C₂²	1	1	yes	characteristic
43	C₆₁×#390	C₂²	1	1	yes	characteristic
44	C₆₁×#387	—	2	1	no	—
45	C₆₁×#387	—	2	1	no	—
46	C₆₁×#386	—	2	1	no	—
47	C₆₁×#386	—	2	1	no	—
48	C₆₁×#384	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#382	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#380	C₂²	1	1	yes	characteristic
51	C₆₁×#379	—	2	1	no	—
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
53	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
54	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
55	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
56	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
57	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
58	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
59	C₆₁×#336	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#336	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₆₁	—	2	1	no	—
62	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₆₁	—	2	2	no	—
64	C₂²×D₄×C₆₁	—	2	2	no	—
65	C₂²×D₄×C₆₁	—	2	1	no	—
66	C₂²×D₄×C₆₁	—	2	2	no	—
67	C₂²×D₄×C₆₁	—	4	1	no	—
68	C₂²×D₄×C₆₁	—	4	1	no	—
69	C₂²×D₄×C₆₁	D₄	1	4	yes	—
70	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₆₁	—	2	1	no	—
73	C₂³×C₄×C₆₁	—	2	1	no	—
74	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×SD₁₆×C₆₁	—	2	2	no	—
76	C₂×SD₁₆×C₆₁	—	2	2	no	—
77	C₂×SD₁₆×C₆₁	—	2	2	no	—
78	C₂×SD₁₆×C₆₁	—	2	2	no	—
79	C₂×SD₁₆×C₆₁	—	4	1	no	—
80	C₂×SD₁₆×C₆₁	—	4	1	no	—
81	C₂×M₁₆×C₆₁	—	2	2	no	—
82	C₂×M₁₆×C₆₁	—	4	1	no	—
83	C₂×M₁₆×C₆₁	—	4	1	no	—
84	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₂²⋊Q₈×C₆₁	—	2	2	no	—
89	C₂²⋊Q₈×C₆₁	—	2	2	no	—
90	C₄×D₄×C₆₁	—	2	2	no	—
91	C₄×D₄×C₆₁	—	2	2	no	—
92	C₄×D₄×C₆₁	—	4	1	no	—
93	C₄×D₄×C₆₁	—	4	1	no	—
94	#117×C₆₁	—	2	2	no	—
95	#117×C₆₁	—	2	2	no	—
96	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
97	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
99	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₆₁	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₆₁	—	4	4	no	—
114	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₆₁	—	2	1	no	—
117	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
119	C₄⋊C₈×C₆₁	—	4	1	no	—
120	C₄⋊C₈×C₆₁	—	4	1	no	—
121	#103×C₆₁	—	4	1	no	—
122	#103×C₆₁	—	4	1	no	—
123	#102×C₆₁	—	2	2	no	—
124	#102×C₆₁	—	2	2	no	—
125	#102×C₆₁	—	2	2	no	—
126	#102×C₆₁	—	2	2	no	—
127	#102×C₆₁	—	2	2	no	—
128	#102×C₆₁	—	2	2	no	—
129	C₂²⋊C₈×C₆₁	—	2	2	no	—
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	D₄	1	1	yes	characteristic
138	#95×C₆₁	D₄	1	1	yes	characteristic
139	C₂⁴×C₆₁	—	2	1	no	—
140	C₂⁴×C₆₁	—	2	1	no	—
141	C₂⁴×C₆₁	—	2	4	no	—
142	C₂⁴×C₆₁	—	4	2	no	—
143	C₂⁴×C₆₁	—	4	2	no	—
144	C₂⁴×C₆₁	—	4	2	no	—
145	C₂⁴×C₆₁	—	4	2	no	—
146	C₂⁴×C₆₁	—	8	1	no	—
147	C₂⁴×C₆₁	—	8	1	no	—
148	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₆₁	—	2	1	no	—
150	C₂×Q₈×C₆₁	—	2	1	no	—
151	C₂×Q₈×C₆₁	—	2	1	no	—
152	C₂×Q₈×C₆₁	—	2	1	no	—
153	C₂×Q₈×C₆₁	—	2	1	no	—
154	C₂×Q₈×C₆₁	—	2	1	no	—
155	C₂×D₄×C₆₁	—	2	8	no	—
156	C₂×D₄×C₆₁	—	2	4	no	—
157	C₂×D₄×C₆₁	—	2	1	no	—
158	C₂×D₄×C₆₁	—	2	1	no	—
159	C₂×D₄×C₆₁	—	2	1	no	—
160	C₂×D₄×C₆₁	—	2	1	no	—
161	C₂×D₄×C₆₁	—	2	1	no	—
162	C₂×D₄×C₆₁	—	2	1	no	—
163	C₂×D₄×C₆₁	—	2	1	no	—
164	C₂×D₄×C₆₁	—	2	1	no	—
165	C₂×D₄×C₆₁	—	4	4	no	—
166	C₂×D₄×C₆₁	—	4	4	no	—
167	C₂×D₄×C₆₁	—	4	4	no	—
168	C₂×D₄×C₆₁	—	4	2	no	—
169	C₂×D₄×C₆₁	—	4	2	no	—
170	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
171	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
172	C₂×D₄×C₆₁	#41	1	2	yes	—
173	C₂×D₄×C₆₁	#41	1	2	yes	—
174	C₂²×C₄×C₆₁	—	2	1	no	—
175	C₂²×C₄×C₆₁	—	2	1	no	—
176	C₂²×C₄×C₆₁	—	2	1	no	—
177	C₂²×C₄×C₆₁	—	2	1	no	—
178	C₂²×C₄×C₆₁	—	2	1	no	—
179	C₂²×C₄×C₆₁	—	2	1	no	—
180	C₂²×C₄×C₆₁	—	2	1	no	—
181	C₂²×C₄×C₆₁	—	2	1	no	—
182	C₂²×C₄×C₆₁	—	2	1	no	—
183	C₂²×C₄×C₆₁	—	2	1	no	—
184	C₂²×C₄×C₆₁	—	4	2	no	—
185	C₂²×C₄×C₆₁	—	4	2	no	—
186	C₂²×C₄×C₆₁	—	4	2	no	—
187	C₂²×C₄×C₆₁	—	4	2	no	—
188	C₂²×C₄×C₆₁	—	8	1	no	—
189	C₂²×C₄×C₆₁	—	8	1	no	—
190	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₁	#41	1	2	yes	—
197	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
198	SD₁₆×C₆₁	—	4	4	no	—
199	SD₁₆×C₆₁	—	4	4	no	—
200	M₁₆×C₆₁	—	4	4	no	—
201	C₂×C₈×C₆₁	—	2	1	no	—
202	C₂×C₈×C₆₁	—	2	1	no	—
203	C₂×C₈×C₆₁	—	2	1	no	—
204	C₂×C₈×C₆₁	—	2	1	no	—
205	C₂×C₈×C₆₁	—	2	1	no	—
206	C₂×C₈×C₆₁	—	2	1	no	—
207	C₂×C₈×C₆₁	—	2	1	no	—
208	C₂×C₈×C₆₁	—	2	1	no	—
209	C₂×C₈×C₆₁	—	2	1	no	—
210	C₂×C₈×C₆₁	—	2	1	no	—
211	C₂×C₈×C₆₁	—	2	1	no	—
212	C₂×C₈×C₆₁	—	2	1	no	—
213	C₄⋊C₄×C₆₁	—	2	1	no	—
214	C₄⋊C₄×C₆₁	—	2	1	no	—
215	C₄⋊C₄×C₆₁	—	2	1	no	—
216	C₄⋊C₄×C₆₁	—	2	1	no	—
217	C₄⋊C₄×C₆₁	—	2	1	no	—
218	C₄⋊C₄×C₆₁	—	2	1	no	—
219	C₄⋊C₄×C₆₁	—	2	1	no	—
220	C₄⋊C₄×C₆₁	—	2	1	no	—
221	C₄⋊C₄×C₆₁	—	2	1	no	—
222	C₄⋊C₄×C₆₁	—	2	1	no	—
223	C₄⋊C₄×C₆₁	—	4	2	no	—
224	C₄⋊C₄×C₆₁	—	4	2	no	—
225	C₄⋊C₄×C₆₁	—	4	2	no	—
226	C₂²⋊C₄×C₆₁	—	2	2	no	—
227	C₂²⋊C₄×C₆₁	—	4	1	no	—
228	C₂²⋊C₄×C₆₁	—	4	2	no	—
229	C₂²⋊C₄×C₆₁	—	4	2	no	—
230	C₂²⋊C₄×C₆₁	—	4	2	no	—
231	C₂²⋊C₄×C₆₁	—	4	2	no	—
232	C₂²⋊C₄×C₆₁	—	4	2	no	—
233	C₂²⋊C₄×C₆₁	—	4	2	no	—
234	C₂²⋊C₄×C₆₁	—	4	2	no	—
235	C₂²⋊C₄×C₆₁	—	8	1	no	—
236	C₂²⋊C₄×C₆₁	—	8	1	no	—
237	C₄²×C₆₁	—	2	1	no	—
238	C₄²×C₆₁	—	2	1	no	—
239	C₄²×C₆₁	—	2	1	no	—
240	C₄²×C₆₁	—	2	1	no	—
241	C₄²×C₆₁	—	4	2	no	—
242	C₂³×C₆₁	—	2	2	no	—
243	C₂³×C₆₁	—	2	2	no	—
244	C₂³×C₆₁	—	2	2	no	—
245	C₂³×C₆₁	—	2	1	no	—
246	C₂³×C₆₁	—	2	1	no	—
247	C₂³×C₆₁	—	2	1	no	—
248	C₂³×C₆₁	—	2	1	no	—
249	C₂³×C₆₁	—	2	1	no	—
250	C₂³×C₆₁	—	2	1	no	—
251	C₂³×C₆₁	—	2	2	no	—
252	C₂³×C₆₁	—	4	8	no	—
253	C₂³×C₆₁	—	4	8	no	—
254	C₂³×C₆₁	—	4	1	no	—
255	C₂³×C₆₁	—	4	1	no	—
256	C₂³×C₆₁	—	4	1	no	—
257	C₂³×C₆₁	—	4	1	no	—
258	C₂³×C₆₁	—	4	1	no	—
259	C₂³×C₆₁	—	4	1	no	—
260	C₂³×C₆₁	—	4	1	no	—
261	C₂³×C₆₁	—	4	1	no	—
262	C₂³×C₆₁	—	4	1	no	—
263	C₂³×C₆₁	—	4	1	no	—
264	C₂³×C₆₁	—	8	4	no	—
265	C₂³×C₆₁	—	8	4	no	—
266	C₂³×C₆₁	—	8	4	no	—
267	C₂³×C₆₁	—	8	4	no	—
268	C₂³×C₆₁	—	8	4	no	—
269	C₂³×C₆₁	#121	1	2	yes	—
270	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₆₁	—	4	1	no	—
272	Q₈×C₆₁	—	4	1	no	—
273	Q₈×C₆₁	—	4	1	no	—
274	Q₈×C₆₁	—	4	1	no	—
275	D₄×C₆₁	—	2	2	no	—
276	D₄×C₆₁	—	2	2	no	—
277	D₄×C₆₁	—	2	2	no	—
278	D₄×C₆₁	—	2	2	no	—
279	D₄×C₆₁	—	2	2	no	—
280	D₄×C₆₁	—	4	8	no	—
281	D₄×C₆₁	—	4	1	no	—
282	D₄×C₆₁	—	4	1	no	—
283	D₄×C₆₁	#123	1	4	yes	—
284	C₂×C₄×C₆₁	—	2	1	no	—
285	C₂×C₄×C₆₁	—	2	1	no	—
286	C₂×C₄×C₆₁	—	2	1	no	—
287	C₂×C₄×C₆₁	—	2	1	no	—
288	C₂×C₄×C₆₁	—	2	2	no	—
289	C₂×C₄×C₆₁	—	2	2	no	—
290	C₂×C₄×C₆₁	—	2	2	no	—
291	C₂×C₄×C₆₁	—	2	2	no	—
292	C₂×C₄×C₆₁	—	2	1	no	—
293	C₂×C₄×C₆₁	—	2	1	no	—
294	C₂×C₄×C₆₁	—	2	1	no	—
295	C₂×C₄×C₆₁	—	2	1	no	—
296	C₂×C₄×C₆₁	—	2	1	no	—
297	C₂×C₄×C₆₁	—	2	1	no	—
298	C₂×C₄×C₆₁	—	2	1	no	—
299	C₂×C₄×C₆₁	—	2	1	no	—
300	C₂×C₄×C₆₁	—	2	1	no	—
301	C₂×C₄×C₆₁	—	4	1	no	—
302	C₂×C₄×C₆₁	—	4	1	no	—
303	C₂×C₄×C₆₁	—	4	1	no	—
304	C₂×C₄×C₆₁	—	4	1	no	—
305	C₂×C₄×C₆₁	—	4	1	no	—
306	C₂×C₄×C₆₁	—	4	1	no	—
307	C₂×C₄×C₆₁	—	4	1	no	—
308	C₂×C₄×C₆₁	—	4	1	no	—
309	C₂×C₄×C₆₁	—	4	1	no	—
310	C₂×C₄×C₆₁	—	4	1	no	—
311	C₂×C₄×C₆₁	—	4	1	no	—
312	C₂×C₄×C₆₁	—	4	1	no	—
313	C₂×C₄×C₆₁	—	4	1	no	—
314	C₂×C₄×C₆₁	—	4	1	no	—
315	C₂×C₄×C₆₁	—	4	1	no	—
316	C₂×C₄×C₆₁	—	4	1	no	—
317	C₂×C₄×C₆₁	—	4	1	no	—
318	C₂×C₄×C₆₁	—	4	1	no	—
319	C₂×C₄×C₆₁	—	8	4	no	—
320	C₂×C₄×C₆₁	—	8	4	no	—
321	C₂×C₄×C₆₁	#121	1	2	yes	—
322	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
323	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
328	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
329	C₈×C₆₁	—	4	1	no	—
330	C₈×C₆₁	—	4	1	no	—
331	C₈×C₆₁	—	4	1	no	—
332	C₈×C₆₁	—	4	1	no	—
333	#24538	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂²×C₆₁	—	2	2	no	—
335	C₂²×C₆₁	—	2	4	no	—
336	C₂²×C₆₁	—	2	2	no	—
337	C₂²×C₆₁	—	2	2	no	—
338	C₂²×C₆₁	—	4	2	no	—
339	C₂²×C₆₁	—	4	2	no	—
340	C₂²×C₆₁	—	4	2	no	—
341	C₂²×C₆₁	—	4	1	no	—
342	C₂²×C₆₁	—	4	1	no	—
343	C₂²×C₆₁	—	4	2	no	—
344	C₂²×C₆₁	—	4	1	no	—
345	C₂²×C₆₁	—	4	2	no	—
346	C₂²×C₆₁	—	4	2	no	—
347	C₂²×C₆₁	—	4	1	no	—
348	C₂²×C₆₁	—	4	2	no	—
349	C₂²×C₆₁	—	4	2	no	—
350	C₂²×C₆₁	—	4	2	no	—
351	C₂²×C₆₁	—	8	16	no	—
352	C₂²×C₆₁	—	8	1	no	—
353	C₂²×C₆₁	—	8	1	no	—
354	C₂²×C₆₁	—	8	1	no	—
355	C₂²×C₆₁	—	8	1	no	—
356	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
357	C₂²×C₆₁	#546	1	1	yes	characteristic
358	C₂²×C₆₁	#546	1	1	yes	characteristic
359	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
360	C₂²×C₆₁	#575	1	1	yes	characteristic
361	C₂²×C₆₁	#577	1	1	yes	characteristic
362	C₂²×C₆₁	#577	1	1	yes	characteristic
363	C₄×C₆₁	—	2	2	no	—
364	C₄×C₆₁	—	2	2	no	—
365	C₄×C₆₁	—	4	1	no	—
366	C₄×C₆₁	—	4	1	no	—
367	C₄×C₆₁	—	4	1	no	—
368	C₄×C₆₁	—	8	1	no	—
369	C₄×C₆₁	—	8	1	no	—
370	C₄×C₆₁	—	8	1	no	—
371	C₄×C₆₁	—	8	1	no	—
372	C₄×C₆₁	—	8	1	no	—
373	C₄×C₆₁	—	8	1	no	—
374	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
375	C₄×C₆₁	#534	1	1	yes	characteristic
376	C₄×C₆₁	#551	1	1	yes	characteristic
377	C₄×C₆₁	#551	1	1	yes	characteristic
378	C₂×#450	C₂×C₆₁	1	1	yes	characteristic
379	C₂×#418	C₂×C₆₁	1	1	yes	characteristic
380	#2499	C₂×C₆₁	1	1	yes	characteristic, complemented
381	D₄×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic
382	#2073	C₂×C₆₁	1	1	yes	characteristic, complemented
383	#2071	C₂×C₆₁	1	1	yes	characteristic, complemented
384	#2055	C₂×C₆₁	1	1	yes	characteristic, complemented
385	#2055	C₂×C₆₁	1	1	yes	characteristic, complemented
386	#1894	C₂×C₆₁	1	1	yes	characteristic, complemented
387	#1877	C₂×C₆₁	1	1	yes	characteristic, complemented
388	#1877	C₂×C₆₁	1	1	yes	characteristic, complemented
389	#1851	C₂×C₆₁	1	1	yes	characteristic, complemented
390	#1825	C₂×C₆₁	1	1	yes	characteristic, complemented
391	#1804	C₂×C₆₁	1	1	yes	characteristic, complemented
392	#1802	C₂×C₆₁	1	1	yes	characteristic, complemented
393	C₂×C₆₁	—	4	2	no	—
394	C₂×C₆₁	—	4	4	no	—
395	C₂×C₆₁	—	8	2	no	—
396	C₂×C₆₁	#2412	1	1	yes	characteristic
397	C₂×C₆₁	#3036	1	1	yes	characteristic
398	C₂×C₆₁	#3042	1	1	yes	characteristic
399	C₂×C₆₁	#3310	1	1	yes	characteristic
400	C₂×C₆₁	#3311	1	1	yes	characteristic
401	C₂×C₆₁	#3323	1	1	yes	characteristic
402	C₂×C₆₁	#3324	1	1	yes	characteristic
403	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
404	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
405	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
406	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
407	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
410	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	—	2	1	no	—
412	#450	—	2	4	no	—
413	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
414	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
415	#418	—	2	4	no	—
416	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
417	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
418	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
419	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
420	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
421	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
422	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
423	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
424	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
425	#397	—	2	1	no	—
426	#397	—	2	1	no	—
427	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
428	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
429	#390	C₂²×C₆₁	1	1	yes	characteristic
430	#390	C₂²×C₆₁	1	1	yes	characteristic
431	#387	—	2	1	no	—
432	#387	—	2	1	no	—
433	#386	—	2	1	no	—
434	#386	—	2	1	no	—
435	#384	C₂²×C₆₁	1	1	yes	characteristic, complemented
436	#382	C₂²×C₆₁	1	1	yes	characteristic, complemented
437	#380	C₂²×C₆₁	1	1	yes	characteristic
438	#379	—	2	1	no	—
439	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
440	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
441	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
442	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
443	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
444	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
445	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
446	#336	C₂²×C₆₁	1	1	yes	characteristic, complemented
447	#336	C₂²×C₆₁	1	1	yes	characteristic, complemented
448	C₆₁	#24538	1	1	yes	characteristic, direct product factor, Sylow
449	C₂⁵	—	2	1	no	—
450	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
451	C₂²×D₄	—	2	2	no	—
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	—	2	2	no	—
455	C₂²×D₄	—	4	1	no	—
456	C₂²×D₄	—	4	1	no	—
457	C₂²×D₄	D₄×C₆₁	1	4	yes	—
458	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
459	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
463	C₂×SD₁₆	—	2	2	no	—
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×SD₁₆	—	2	2	no	—
466	C₂×SD₁₆	—	2	2	no	—
467	C₂×SD₁₆	—	4	1	no	—
468	C₂×SD₁₆	—	4	1	no	—
469	C₂×M₁₆	—	2	2	no	—
470	C₂×M₁₆	—	4	1	no	—
471	C₂×M₁₆	—	4	1	no	—
472	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	4	1	no	—
481	C₄×D₄	—	4	1	no	—
482	#117	—	2	2	no	—
483	#117	—	2	2	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	4	4	no	—
502	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
504	C₂×C₄²	—	2	1	no	—
505	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
507	C₄⋊C₈	—	4	1	no	—
508	C₄⋊C₈	—	4	1	no	—
509	#103	—	4	1	no	—
510	#103	—	4	1	no	—
511	#102	—	2	2	no	—
512	#102	—	2	2	no	—
513	#102	—	2	2	no	—
514	#102	—	2	2	no	—
515	#102	—	2	2	no	—
516	#102	—	2	2	no	—
517	C₂²⋊C₈	—	2	2	no	—
518	#95	—	2	1	no	—
519	#95	—	2	1	no	—
520	#95	—	2	1	no	—
521	#95	—	2	1	no	—
522	#95	—	2	1	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	D₄×C₆₁	1	1	yes	characteristic
526	#95	D₄×C₆₁	1	1	yes	characteristic
527	C₂⁴	—	2	1	no	—
528	C₂⁴	—	2	1	no	—
529	C₂⁴	—	2	4	no	—
530	C₂⁴	—	4	2	no	—
531	C₂⁴	—	4	2	no	—
532	C₂⁴	—	4	2	no	—
533	C₂⁴	—	4	2	no	—
534	C₂⁴	—	8	1	no	—
535	C₂⁴	—	8	1	no	—
536	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×D₄	—	2	8	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
559	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
560	C₂×D₄	#41×C₆₁	1	2	yes	—
561	C₂×D₄	#41×C₆₁	1	2	yes	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	8	1	no	—
577	C₂²×C₄	—	8	1	no	—
578	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
583	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
584	C₂²×C₄	#41×C₆₁	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
586	SD₁₆	—	4	4	no	—
587	SD₁₆	—	4	4	no	—
588	M₁₆	—	4	4	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	4	1	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	8	1	no	—
624	C₂²⋊C₄	—	8	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	4	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	4	8	no	—
641	C₂³	—	4	8	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	8	4	no	—
653	C₂³	—	8	4	no	—
654	C₂³	—	8	4	no	—
655	C₂³	—	8	4	no	—
656	C₂³	—	8	4	no	—
657	C₂³	#121×C₆₁	1	2	yes	—
658	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
659	Q₈	—	4	1	no	—
660	Q₈	—	4	1	no	—
661	Q₈	—	4	1	no	—
662	Q₈	—	4	1	no	—
663	D₄	—	2	2	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	4	8	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	#123×C₆₁	1	4	yes	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	4	no	—
709	C₂×C₄	#121×C₆₁	1	2	yes	—
710	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
711	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
712	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
713	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
714	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
715	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
716	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
717	C₈	—	4	1	no	—
718	C₈	—	4	1	no	—
719	C₈	—	4	1	no	—
720	C₈	—	4	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	8	16	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
744	C₂²	C₆₁×#546	1	1	yes	characteristic
745	C₂²	C₆₁×#546	1	1	yes	characteristic
746	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
747	C₂²	C₆₁×#575	1	1	yes	characteristic
748	C₂²	C₆₁×#577	1	1	yes	characteristic
749	C₂²	C₆₁×#577	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	8	1	no	—
756	C₄	—	8	1	no	—
757	C₄	—	8	1	no	—
758	C₄	—	8	1	no	—
759	C₄	—	8	1	no	—
760	C₄	—	8	1	no	—
761	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
762	C₄	C₆₁×#534	1	1	yes	characteristic
763	C₄	C₆₁×#551	1	1	yes	characteristic
764	C₄	C₆₁×#551	1	1	yes	characteristic
765	C₂	—	4	2	no	—
766	C₂	—	4	4	no	—
767	C₂	—	8	2	no	—
768	C₂	C₆₁×#2412	1	1	yes	characteristic
769	C₂	C₆₁×#3036	1	1	yes	characteristic
770	C₂	C₆₁×#3042	1	1	yes	characteristic
771	C₂	C₆₁×#3310	1	1	yes	characteristic
772	C₂	C₆₁×#3311	1	1	yes	characteristic
773	C₂	C₆₁×#3323	1	1	yes	characteristic
774	C₂	C₆₁×#3324	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₆₁×#2499	C₂	semidirect
5. C₆₁×#2073	C₂	semidirect
6. C₆₁×#2071	C₂	semidirect
7. C₆₁×#2055	C₂	semidirect
8. C₆₁×#2055	C₂	semidirect
9. C₆₁×#1894	C₂	semidirect
10. C₆₁×#1877	C₂	semidirect
11. C₆₁×#1877	C₂	semidirect
12. C₆₁×#1851	C₂	semidirect
13. C₆₁×#1825	C₂	semidirect
14. C₆₁×#1804	C₂	semidirect
15. C₆₁×#1802	C₂	semidirect
26. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
27. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
29. C₂×#103×C₆₁	C₂²	semidirect
30. C₂×#103×C₆₁	C₂²	semidirect
40. C₆₁×#391	C₂²	semidirect
41. C₆₁×#391	C₂²	semidirect
48. C₆₁×#384	C₂²	semidirect
49. C₆₁×#382	C₂²	semidirect
53. C₆₁×#340	C₂²	semidirect
54. C₆₁×#340	C₂²	semidirect
55. C₆₁×#340	C₂²	semidirect
56. C₆₁×#340	C₂²	semidirect
57. C₆₁×#340	C₂²	semidirect
58. C₆₁×#340	C₂²	semidirect
59. C₆₁×#336	C₂²	semidirect
60. C₆₁×#336	C₂²	semidirect
333. #24538	C₆₁	direct (N × H)
380. #2499	C₂×C₆₁	semidirect
382. #2073	C₂×C₆₁	semidirect
383. #2071	C₂×C₆₁	semidirect
384. #2055	C₂×C₆₁	semidirect
385. #2055	C₂×C₆₁	semidirect
386. #1894	C₂×C₆₁	semidirect
387. #1877	C₂×C₆₁	semidirect
388. #1877	C₂×C₆₁	semidirect
389. #1851	C₂×C₆₁	semidirect
390. #1825	C₂×C₆₁	semidirect
391. #1804	C₂×C₆₁	semidirect
392. #1802	C₂×C₆₁	semidirect
413. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
414. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
416. C₂×#103	C₂²×C₆₁	semidirect
417. C₂×#103	C₂²×C₆₁	semidirect
427. #391	C₂²×C₆₁	semidirect
428. #391	C₂²×C₆₁	semidirect
435. #384	C₂²×C₆₁	semidirect
436. #382	C₂²×C₆₁	semidirect
440. #340	C₂²×C₆₁	semidirect
441. #340	C₂²×C₆₁	semidirect
442. #340	C₂²×C₆₁	semidirect
443. #340	C₂²×C₆₁	semidirect
444. #340	C₂²×C₆₁	semidirect
445. #340	C₂²×C₆₁	semidirect
446. #336	C₂²×C₆₁	semidirect
447. #336	C₂²×C₆₁	semidirect
448. C₆₁	#24538	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×#450	2
C₂×C₆₁×#418	2
C₆₁×#2499	2
D₄×C₂²⋊C₄×C₆₁	2
C₆₁×#2073	2
C₆₁×#2071	2
C₆₁×#2055	2
C₆₁×#1894	2
C₆₁×#1877	2
C₆₁×#1851	2
C₆₁×#1825	2
C₆₁×#1804	2
C₆₁×#1802	2
#24538	61

Subgroups — C61×#24538 #29527971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24538 #29527971