Subgroups — C₆₁×#3513 #21443554

Order 7808.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#553	C₂	1	2	yes	maximal, complemented
5	C₆₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#551	C₂	1	2	yes	maximal, complemented
7	C₆₁×#551	C₂	1	2	yes	maximal, complemented
8	C₆₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#546	C₂	1	2	yes	maximal, complemented
12	D₄²×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#539	C₂	1	2	yes	maximal, complemented
16	C₆₁×#538	C₂	1	2	yes	maximal, complemented
17	C₆₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#525	C₂	1	2	yes	maximal, complemented
20	C₂×#123×C₆₁	C₂	1	2	yes	maximal, complemented
21	C₆₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#41×C₆₁	C₂²	1	2	yes	complemented
26	C₂²×D₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×D₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×D₄×C₆₁	C₂²	1	2	yes	—
29	C₂³×C₄×C₆₁	C₂²	1	2	yes	complemented
30	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
31	#127×C₆₁	C₂²	1	1	yes	characteristic
32	#126×C₆₁	C₂²	1	2	yes	complemented
33	#126×C₆₁	C₂²	1	2	yes	complemented
34	#126×C₆₁	C₂²	1	2	yes	complemented
35	#126×C₆₁	C₂²	1	2	yes	complemented
36	#126×C₆₁	C₂²	1	1	yes	characteristic, complemented
37	#126×C₆₁	C₂²	1	1	yes	characteristic, complemented
38	#125×C₆₁	C₂²	1	1	yes	characteristic, complemented
39	#125×C₆₁	C₂²	1	2	yes	complemented
40	#125×C₆₁	C₂²	1	1	yes	characteristic, complemented
41	#125×C₆₁	C₂²	1	1	yes	characteristic, complemented
42	#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
43	#124×C₆₁	C₂²	1	2	yes	complemented
44	#124×C₆₁	C₂²	1	2	yes	complemented
45	#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
46	#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
47	#123×C₆₁	C₂²	1	2	yes	—
48	#123×C₆₁	C₂²	1	1	yes	characteristic
49	#123×C₆₁	C₂²	1	2	yes	complemented
50	#123×C₆₁	C₂²	1	2	yes	complemented
51	#123×C₆₁	C₂²	1	2	yes	complemented
52	#123×C₆₁	C₂²	1	2	yes	complemented
53	#123×C₆₁	C₂²	1	2	yes	complemented
54	#123×C₆₁	C₂²	1	2	yes	complemented
55	#123×C₆₁	C₂²	1	2	yes	complemented
56	#123×C₆₁	C₂²	1	2	yes	complemented
57	#123×C₆₁	C₂²	1	2	yes	complemented
58	#123×C₆₁	C₂²	1	2	yes	complemented
59	#123×C₆₁	C₂²	1	2	yes	complemented
60	#123×C₆₁	C₂²	1	1	yes	characteristic, complemented
61	C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
62	C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
63	C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
64	C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
65	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
66	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
67	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
68	C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
69	#121×C₆₁	C₂²	1	2	yes	—
70	#121×C₆₁	C₂²	1	1	yes	characteristic
71	#121×C₆₁	C₂²	1	1	yes	characteristic
72	#121×C₆₁	C₂²	1	1	yes	characteristic
73	#121×C₆₁	C₂²	1	2	yes	complemented
74	#121×C₆₁	C₂²	1	2	yes	complemented
75	#121×C₆₁	C₂²	1	2	yes	complemented
76	#121×C₆₁	C₂²	1	1	yes	characteristic, complemented
77	#121×C₆₁	C₂²	1	2	yes	complemented
78	#121×C₆₁	C₂²	1	1	yes	characteristic, complemented
79	#121×C₆₁	C₂²	1	2	yes	complemented
80	#120×C₆₁	C₂²	1	2	yes	—
81	#120×C₆₁	C₂²	1	2	yes	—
82	#120×C₆₁	C₂²	1	2	yes	complemented
83	#120×C₆₁	C₂²	1	2	yes	complemented
84	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
85	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
86	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
88	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
89	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
90	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
91	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
92	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
93	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
94	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
95	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
99	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
100	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
103	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
104	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
105	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
106	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
107	#117×C₆₁	C₂²	1	1	yes	characteristic, complemented
108	#117×C₆₁	C₂²	1	1	yes	characteristic, complemented
109	#117×C₆₁	C₂²	1	2	yes	complemented
110	#117×C₆₁	C₂²	1	2	yes	complemented
111	#117×C₆₁	C₂²	1	2	yes	complemented
112	#117×C₆₁	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
114	C₂×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
117	C₂×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
118	C₂×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
119	C₂×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
120	C₂×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
121	C₂×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₆₁	C₂³	1	2	yes	—
124	C₂⁴×C₆₁	C₂³	1	2	yes	—
125	#41×C₆₁	—	2	4	no	—
126	#41×C₆₁	—	4	4	no	—
127	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₆₁	C₂³	1	2	yes	—
130	C₂×D₄×C₆₁	—	2	4	no	—
131	C₂×D₄×C₆₁	—	2	4	no	—
132	C₂×D₄×C₆₁	—	4	4	no	—
133	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₆₁	C₂³	1	2	yes	—
135	C₂×D₄×C₆₁	C₂³	1	2	yes	—
136	C₂×D₄×C₆₁	C₂³	1	2	yes	—
137	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₂×D₄×C₆₁	C₂³	1	2	yes	—
140	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₆₁	C₂³	1	2	yes	—
142	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×D₄×C₆₁	C₂³	1	2	yes	—
144	C₂×D₄×C₆₁	C₂³	1	2	yes	—
145	C₂×D₄×C₆₁	C₂³	1	2	yes	—
146	C₂×D₄×C₆₁	C₂³	1	2	yes	—
147	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
148	C₂²×C₄×C₆₁	—	4	4	no	—
149	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
152	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
153	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
155	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
156	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
157	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
158	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
159	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
160	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
161	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
162	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
163	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
164	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
165	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
167	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
170	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
173	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
174	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
175	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
176	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
177	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
180	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
182	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
183	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
184	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
185	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
186	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
187	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
189	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
190	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
192	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
194	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
195	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
196	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
202	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
203	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
204	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
205	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
206	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
207	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
208	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
209	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
210	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
211	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
212	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
213	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
214	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
219	C₄²×C₆₁	C₂³	1	1	yes	characteristic
220	C₄²×C₆₁	C₂³	1	1	yes	characteristic
221	C₄²×C₆₁	C₂³	1	1	yes	characteristic
222	C₄²×C₆₁	C₂³	1	1	yes	characteristic
223	C₄²×C₆₁	C₂³	1	2	yes	—
224	C₄²×C₆₁	C₂³	1	2	yes	—
225	C₄²×C₆₁	C₂³	1	2	yes	—
226	C₄²×C₆₁	C₂³	1	1	yes	characteristic
227	C₄²×C₆₁	C₂³	1	1	yes	characteristic
228	C₂³×C₆₁	—	2	4	no	—
229	C₂³×C₆₁	—	2	4	no	—
230	C₂³×C₆₁	—	2	4	no	—
231	C₂³×C₆₁	—	4	2	no	—
232	C₂³×C₆₁	—	4	2	no	—
233	C₂³×C₆₁	—	4	2	no	—
234	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
235	C₂³×C₆₁	C₂⁴	1	2	yes	—
236	C₂³×C₆₁	C₂⁴	1	2	yes	—
237	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
238	C₂³×C₆₁	C₂⁴	1	2	yes	—
239	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
240	Q₈×C₆₁	—	2	2	no	—
241	Q₈×C₆₁	—	4	1	no	—
242	Q₈×C₆₁	—	4	2	no	—
243	D₄×C₆₁	—	2	4	no	—
244	D₄×C₆₁	—	2	4	no	—
245	D₄×C₆₁	—	2	4	no	—
246	D₄×C₆₁	—	2	2	no	—
247	D₄×C₆₁	—	2	4	no	—
248	D₄×C₆₁	—	2	2	no	—
249	D₄×C₆₁	—	2	2	no	—
250	D₄×C₆₁	—	2	2	no	—
251	D₄×C₆₁	—	4	2	no	—
252	D₄×C₆₁	—	4	2	no	—
253	D₄×C₆₁	—	4	2	no	—
254	D₄×C₆₁	—	4	1	no	—
255	D₄×C₆₁	—	4	2	no	—
256	D₄×C₆₁	—	4	2	no	—
257	D₄×C₆₁	#41	1	4	yes	complemented
258	C₂×C₄×C₆₁	—	2	4	no	—
259	C₂×C₄×C₆₁	—	2	2	no	—
260	C₂×C₄×C₆₁	—	2	4	no	—
261	C₂×C₄×C₆₁	—	2	2	no	—
262	C₂×C₄×C₆₁	—	2	2	no	—
263	C₂×C₄×C₆₁	—	2	2	no	—
264	C₂×C₄×C₆₁	—	4	2	no	—
265	C₂×C₄×C₆₁	—	4	2	no	—
266	C₂×C₄×C₆₁	—	4	2	no	—
267	C₂×C₄×C₆₁	—	4	2	no	—
268	C₂×C₄×C₆₁	—	4	2	no	—
269	C₂×C₄×C₆₁	—	4	1	no	—
270	C₂×C₄×C₆₁	—	4	2	no	—
271	C₂×C₄×C₆₁	—	4	2	no	—
272	C₂×C₄×C₆₁	—	4	2	no	—
273	C₂×C₄×C₆₁	—	4	2	no	—
274	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
277	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
283	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
285	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
287	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
290	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₆₁	—	2	1	no	—
292	C₂²×C₆₁	—	2	2	no	—
293	C₂²×C₆₁	—	2	1	no	—
294	C₂²×C₆₁	—	2	2	no	—
295	C₂²×C₆₁	—	2	1	no	—
296	C₂²×C₆₁	—	2	1	no	—
297	C₂²×C₆₁	—	2	2	no	—
298	C₂²×C₆₁	—	2	2	no	—
299	C₂²×C₆₁	—	2	1	no	—
300	C₂²×C₆₁	—	2	2	no	—
301	C₂²×C₆₁	—	2	2	no	—
302	C₂²×C₆₁	—	2	1	no	—
303	C₂²×C₆₁	—	2	2	no	—
304	C₂²×C₆₁	—	2	1	no	—
305	C₂²×C₆₁	—	2	2	no	—
306	C₂²×C₆₁	—	2	1	no	—
307	C₂²×C₆₁	—	4	8	no	—
308	C₂²×C₆₁	—	8	4	no	—
309	C₂²×C₆₁	C₂×#41	1	4	yes	—
310	C₂²×C₆₁	H(5,𝔽₂)	1	2	yes	—
311	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
312	C₄×C₆₁	—	2	1	no	—
313	C₄×C₆₁	—	2	1	no	—
314	C₄×C₆₁	—	2	1	no	—
315	C₄×C₆₁	—	2	2	no	—
316	C₄×C₆₁	—	2	1	no	—
317	C₄×C₆₁	—	2	1	no	—
318	C₄×C₆₁	—	2	2	no	—
319	C₄×C₆₁	—	2	2	no	—
320	C₄×C₆₁	—	2	1	no	—
321	C₄×C₆₁	—	2	2	no	—
322	C₄×C₆₁	—	2	1	no	—
323	C₄×C₆₁	—	2	1	no	—
324	C₄×C₆₁	—	2	2	no	—
325	C₄×C₆₁	—	2	1	no	—
326	C₄×C₆₁	—	2	1	no	—
327	C₄×C₆₁	—	2	1	no	—
328	C₄×C₆₁	C₂×#41	1	2	yes	—
329	#3513	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂×C₆₁	—	2	2	no	—
331	C₂×C₆₁	—	2	4	no	—
332	C₂×C₆₁	—	4	1	no	—
333	C₂×C₆₁	—	4	2	no	—
334	C₂×C₆₁	—	4	2	no	—
335	C₂×C₆₁	—	4	1	no	—
336	C₂×C₆₁	C₂²×#41	1	1	yes	characteristic
337	C₂×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₆₁	#585	1	1	yes	characteristic
339	#559	C₂×C₆₁	1	1	yes	characteristic, complemented
340	#554	C₂×C₆₁	1	1	yes	characteristic, complemented
341	#553	C₂×C₆₁	1	1	yes	characteristic, complemented
342	#553	C₂×C₆₁	1	2	yes	complemented
343	#552	C₂×C₆₁	1	1	yes	characteristic, complemented
344	#551	C₂×C₆₁	1	2	yes	complemented
345	#551	C₂×C₆₁	1	2	yes	complemented
346	#547	C₂×C₆₁	1	1	yes	characteristic, complemented
347	#546	C₂×C₆₁	1	1	yes	characteristic, complemented
348	#546	C₂×C₆₁	1	1	yes	characteristic, complemented
349	#546	C₂×C₆₁	1	2	yes	complemented
350	D₄²	C₂×C₆₁	1	1	yes	characteristic, complemented
351	#542	C₂×C₆₁	1	1	yes	characteristic, complemented
352	#540	C₂×C₆₁	1	1	yes	characteristic, complemented
353	#539	C₂×C₆₁	1	2	yes	complemented
354	#538	C₂×C₆₁	1	2	yes	complemented
355	#529	C₂×C₆₁	1	1	yes	characteristic, complemented
356	#529	C₂×C₆₁	1	1	yes	characteristic, complemented
357	#525	C₂×C₆₁	1	2	yes	complemented
358	C₂×#123	C₂×C₆₁	1	2	yes	complemented
359	#520	C₂×C₆₁	1	1	yes	characteristic, complemented
360	#518	C₂×C₆₁	1	1	yes	characteristic, complemented
361	C₂×C₄×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
362	C₆₁	#3513	1	1	yes	characteristic, direct product factor, Sylow
363	C₂×#41	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×#41	C₂²×C₆₁	1	2	yes	complemented
365	C₂²×D₄	C₂²×C₆₁	1	1	yes	characteristic
366	C₂²×D₄	C₂²×C₆₁	1	1	yes	characteristic
367	C₂²×D₄	C₂²×C₆₁	1	2	yes	—
368	C₂³×C₄	C₂²×C₆₁	1	2	yes	complemented
369	C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
370	#127	C₂²×C₆₁	1	1	yes	characteristic
371	#126	C₂²×C₆₁	1	2	yes	complemented
372	#126	C₂²×C₆₁	1	1	yes	characteristic, complemented
373	#126	C₂²×C₆₁	1	1	yes	characteristic, complemented
374	#126	C₂²×C₆₁	1	2	yes	complemented
375	#126	C₂²×C₆₁	1	2	yes	complemented
376	#126	C₂²×C₆₁	1	2	yes	complemented
377	#125	C₂²×C₆₁	1	1	yes	characteristic, complemented
378	#125	C₂²×C₆₁	1	1	yes	characteristic, complemented
379	#125	C₂²×C₆₁	1	2	yes	complemented
380	#125	C₂²×C₆₁	1	1	yes	characteristic, complemented
381	#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
382	#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
383	#124	C₂²×C₆₁	1	2	yes	complemented
384	#124	C₂²×C₆₁	1	2	yes	complemented
385	#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
386	#123	C₂²×C₆₁	1	1	yes	characteristic
387	#123	C₂²×C₆₁	1	2	yes	—
388	#123	C₂²×C₆₁	1	2	yes	complemented
389	#123	C₂²×C₆₁	1	2	yes	complemented
390	#123	C₂²×C₆₁	1	2	yes	complemented
391	#123	C₂²×C₆₁	1	2	yes	complemented
392	#123	C₂²×C₆₁	1	2	yes	complemented
393	#123	C₂²×C₆₁	1	2	yes	complemented
394	#123	C₂²×C₆₁	1	1	yes	characteristic, complemented
395	#123	C₂²×C₆₁	1	2	yes	complemented
396	#123	C₂²×C₆₁	1	2	yes	complemented
397	#123	C₂²×C₆₁	1	2	yes	complemented
398	#123	C₂²×C₆₁	1	2	yes	complemented
399	#123	C₂²×C₆₁	1	2	yes	complemented
400	C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
401	C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
402	C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
403	C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
404	C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
405	C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
406	C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
407	C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
408	#121	C₂²×C₆₁	1	1	yes	characteristic
409	#121	C₂²×C₆₁	1	1	yes	characteristic
410	#121	C₂²×C₆₁	1	2	yes	—
411	#121	C₂²×C₆₁	1	1	yes	characteristic
412	#121	C₂²×C₆₁	1	2	yes	complemented
413	#121	C₂²×C₆₁	1	2	yes	complemented
414	#121	C₂²×C₆₁	1	2	yes	complemented
415	#121	C₂²×C₆₁	1	2	yes	complemented
416	#121	C₂²×C₆₁	1	1	yes	characteristic, complemented
417	#121	C₂²×C₆₁	1	2	yes	complemented
418	#121	C₂²×C₆₁	1	1	yes	characteristic, complemented
419	#120	C₂²×C₆₁	1	2	yes	—
420	#120	C₂²×C₆₁	1	2	yes	—
421	#120	C₂²×C₆₁	1	2	yes	complemented
422	#120	C₂²×C₆₁	1	2	yes	complemented
423	C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
424	C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
425	C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
426	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
427	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
428	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
429	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
430	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
431	C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
432	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
433	C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
434	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
435	C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
436	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
437	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
438	C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
439	C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
440	C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
441	C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
442	C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
443	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
444	C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
445	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
446	#117	C₂²×C₆₁	1	1	yes	characteristic, complemented
447	#117	C₂²×C₆₁	1	1	yes	characteristic, complemented
448	#117	C₂²×C₆₁	1	1	yes	characteristic, complemented
449	#117	C₂²×C₆₁	1	2	yes	complemented
450	#117	C₂²×C₆₁	1	2	yes	complemented
451	#117	C₂²×C₆₁	1	2	yes	complemented
452	C₂×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
453	C₂×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
454	C₂×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
456	C₂×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
457	C₂×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
458	C₂×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
459	C₂×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
460	C₂×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
461	C₂×C₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
462	C₂⁴	C₂³×C₆₁	1	2	yes	—
463	C₂⁴	C₂³×C₆₁	1	2	yes	—
464	#41	—	2	4	no	—
465	#41	—	4	4	no	—
466	C₂×Q₈	C₂³×C₆₁	1	1	yes	characteristic
467	C₂×Q₈	C₂³×C₆₁	1	1	yes	characteristic
468	C₂×Q₈	C₂³×C₆₁	1	2	yes	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	4	4	no	—
472	C₂×D₄	C₂³×C₆₁	1	1	yes	characteristic
473	C₂×D₄	C₂³×C₆₁	1	2	yes	—
474	C₂×D₄	C₂³×C₆₁	1	2	yes	—
475	C₂×D₄	C₂³×C₆₁	1	2	yes	—
476	C₂×D₄	C₂³×C₆₁	1	1	yes	characteristic
477	C₂×D₄	C₂³×C₆₁	1	1	yes	characteristic
478	C₂×D₄	C₂³×C₆₁	1	2	yes	—
479	C₂×D₄	C₂³×C₆₁	1	1	yes	characteristic
480	C₂×D₄	C₂³×C₆₁	1	2	yes	—
481	C₂×D₄	C₂³×C₆₁	1	1	yes	characteristic
482	C₂×D₄	C₂³×C₆₁	1	2	yes	—
483	C₂×D₄	C₂³×C₆₁	1	2	yes	—
484	C₂×D₄	C₂³×C₆₁	1	2	yes	—
485	C₂×D₄	C₂³×C₆₁	1	2	yes	—
486	C₂×D₄	C₂³×C₆₁	1	1	yes	characteristic
487	C₂²×C₄	—	4	4	no	—
488	C₂²×C₄	C₂³×C₆₁	1	1	yes	characteristic
489	C₂²×C₄	C₂³×C₆₁	1	1	yes	characteristic
490	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
491	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
492	C₂²×C₄	C₂³×C₆₁	1	1	yes	characteristic
493	C₂²×C₄	C₂³×C₆₁	1	1	yes	characteristic
494	C₂²×C₄	C₂³×C₆₁	1	1	yes	characteristic
495	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
496	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
497	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
498	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
499	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
500	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
501	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
502	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
503	C₂²×C₄	C₂³×C₆₁	1	2	yes	—
504	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
506	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
507	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
508	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
509	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
510	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
511	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
512	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
513	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
514	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
515	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
516	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
517	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
518	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
519	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
520	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
521	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
522	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
523	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
526	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
527	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
529	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
530	C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
531	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
532	C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
533	C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
534	C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
535	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
536	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
537	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
538	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
539	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
540	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
541	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
542	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
543	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
544	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
545	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
546	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
547	C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
548	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
549	C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
550	C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
551	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
552	C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
553	C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
554	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
555	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
556	C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
557	C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
558	C₄²	C₂³×C₆₁	1	1	yes	characteristic
559	C₄²	C₂³×C₆₁	1	1	yes	characteristic
560	C₄²	C₂³×C₆₁	1	1	yes	characteristic
561	C₄²	C₂³×C₆₁	1	1	yes	characteristic
562	C₄²	C₂³×C₆₁	1	2	yes	—
563	C₄²	C₂³×C₆₁	1	2	yes	—
564	C₄²	C₂³×C₆₁	1	2	yes	—
565	C₄²	C₂³×C₆₁	1	1	yes	characteristic
566	C₄²	C₂³×C₆₁	1	1	yes	characteristic
567	C₂³	—	2	4	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	4	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	C₂⁴×C₆₁	1	1	yes	characteristic
574	C₂³	C₂⁴×C₆₁	1	2	yes	—
575	C₂³	C₂⁴×C₆₁	1	2	yes	—
576	C₂³	C₂⁴×C₆₁	1	1	yes	characteristic
577	C₂³	C₂⁴×C₆₁	1	2	yes	—
578	C₂³	C₂⁴×C₆₁	1	1	yes	characteristic
579	Q₈	—	2	2	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	4	2	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	4	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	2	no	—
586	D₄	—	2	4	no	—
587	D₄	—	2	2	no	—
588	D₄	—	2	2	no	—
589	D₄	—	2	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	#41×C₆₁	1	4	yes	complemented
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
614	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
615	C₂×C₄	C₂⁴×C₆₁	1	2	yes	—
616	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
617	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
618	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
619	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
620	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
621	C₂×C₄	C₂⁴×C₆₁	1	2	yes	—
622	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
623	C₂×C₄	C₂⁴×C₆₁	1	2	yes	—
624	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
625	C₂×C₄	C₂⁴×C₆₁	1	2	yes	—
626	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
627	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
628	C₂×C₄	C₂⁴×C₆₁	1	2	yes	—
629	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	4	8	no	—
647	C₂²	—	8	4	no	—
648	C₂²	C₂×#41×C₆₁	1	4	yes	—
649	C₂²	H(5,𝔽₂)×C₆₁	1	2	yes	—
650	C₂²	C₂⁵×C₆₁	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	C₂×#41×C₆₁	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	4	1	no	—
674	C₂	C₂²×#41×C₆₁	1	1	yes	characteristic
675	C₂	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
676	C₂	C₆₁×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₆₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#559	C₂	semidirect
2. C₆₁×#554	C₂	semidirect
3. C₆₁×#553	C₂	semidirect
4. C₆₁×#553	C₂	semidirect
5. C₆₁×#552	C₂	semidirect
6. C₆₁×#551	C₂	semidirect
7. C₆₁×#551	C₂	semidirect
8. C₆₁×#547	C₂	semidirect
9. C₆₁×#546	C₂	semidirect
10. C₆₁×#546	C₂	semidirect
11. C₆₁×#546	C₂	semidirect
12. D₄²×C₆₁	C₂	semidirect
13. C₆₁×#542	C₂	semidirect
14. C₆₁×#540	C₂	semidirect
15. C₆₁×#539	C₂	semidirect
16. C₆₁×#538	C₂	semidirect
17. C₆₁×#529	C₂	semidirect
18. C₆₁×#529	C₂	semidirect
19. C₆₁×#525	C₂	semidirect
20. C₂×#123×C₆₁	C₂	semidirect
21. C₆₁×#520	C₂	semidirect
22. C₆₁×#518	C₂	semidirect
23. C₂×C₄×D₄×C₆₁	C₂	semidirect
25. C₂×#41×C₆₁	C₂²	semidirect
29. C₂³×C₄×C₆₁	C₂²	semidirect
30. C₄⋊Q₈×C₆₁	C₂²	semidirect
32. #126×C₆₁	C₂²	semidirect
33. #126×C₆₁	C₂²	semidirect
34. #126×C₆₁	C₂²	semidirect
35. #126×C₆₁	C₂²	semidirect
36. #126×C₆₁	C₂²	semidirect
37. #126×C₆₁	C₂²	semidirect
38. #125×C₆₁	C₂²	semidirect
39. #125×C₆₁	C₂²	semidirect
40. #125×C₆₁	C₂²	semidirect
41. #125×C₆₁	C₂²	semidirect
42. #124×C₆₁	C₂²	semidirect
43. #124×C₆₁	C₂²	semidirect
44. #124×C₆₁	C₂²	semidirect
45. #124×C₆₁	C₂²	semidirect
46. #124×C₆₁	C₂²	semidirect
49. #123×C₆₁	C₂²	semidirect
50. #123×C₆₁	C₂²	semidirect
51. #123×C₆₁	C₂²	semidirect
52. #123×C₆₁	C₂²	semidirect
53. #123×C₆₁	C₂²	semidirect
54. #123×C₆₁	C₂²	semidirect
55. #123×C₆₁	C₂²	semidirect
56. #123×C₆₁	C₂²	semidirect
57. #123×C₆₁	C₂²	semidirect
58. #123×C₆₁	C₂²	semidirect
59. #123×C₆₁	C₂²	semidirect
60. #123×C₆₁	C₂²	semidirect
61. C₂²⋊Q₈×C₆₁	C₂²	semidirect
62. C₂²⋊Q₈×C₆₁	C₂²	semidirect
63. C₂²⋊Q₈×C₆₁	C₂²	semidirect
64. C₂²⋊Q₈×C₆₁	C₂²	semidirect
65. C₂²⋊Q₈×C₆₁	C₂²	semidirect
66. C₂²⋊Q₈×C₆₁	C₂²	semidirect
67. C₂²⋊Q₈×C₆₁	C₂²	semidirect
68. C₂²⋊Q₈×C₆₁	C₂²	semidirect
73. #121×C₆₁	C₂²	semidirect
74. #121×C₆₁	C₂²	semidirect
75. #121×C₆₁	C₂²	semidirect
76. #121×C₆₁	C₂²	semidirect
77. #121×C₆₁	C₂²	semidirect
78. #121×C₆₁	C₂²	semidirect
79. #121×C₆₁	C₂²	semidirect
82. #120×C₆₁	C₂²	semidirect
83. #120×C₆₁	C₂²	semidirect
84. C₄×Q₈×C₆₁	C₂²	semidirect
85. C₄×Q₈×C₆₁	C₂²	semidirect
86. C₄×Q₈×C₆₁	C₂²	semidirect
92. C₄×D₄×C₆₁	C₂²	semidirect
93. C₄×D₄×C₆₁	C₂²	semidirect
94. C₄×D₄×C₆₁	C₂²	semidirect
95. C₄×D₄×C₆₁	C₂²	semidirect
96. C₄×D₄×C₆₁	C₂²	semidirect
97. C₄×D₄×C₆₁	C₂²	semidirect
98. C₄×D₄×C₆₁	C₂²	semidirect
99. C₄×D₄×C₆₁	C₂²	semidirect
100. C₄×D₄×C₆₁	C₂²	semidirect
101. C₄×D₄×C₆₁	C₂²	semidirect
102. C₄×D₄×C₆₁	C₂²	semidirect
103. C₄×D₄×C₆₁	C₂²	semidirect
104. C₄×D₄×C₆₁	C₂²	semidirect
105. C₄×D₄×C₆₁	C₂²	semidirect
106. C₄×D₄×C₆₁	C₂²	semidirect
107. #117×C₆₁	C₂²	semidirect
108. #117×C₆₁	C₂²	semidirect
109. #117×C₆₁	C₂²	semidirect
110. #117×C₆₁	C₂²	semidirect
111. #117×C₆₁	C₂²	semidirect
112. #117×C₆₁	C₂²	semidirect
113. C₂×C₄⋊C₄×C₆₁	C₂²	semidirect
114. C₂×C₄⋊C₄×C₆₁	C₂²	semidirect
115. C₂×C₄⋊C₄×C₆₁	C₂²	semidirect
116. C₂×C₄⋊C₄×C₆₁	C₂²	semidirect
117. C₂×C₂²⋊C₄×C₆₁	C₂²	semidirect
118. C₂×C₂²⋊C₄×C₆₁	C₂²	semidirect
119. C₂×C₂²⋊C₄×C₆₁	C₂²	semidirect
120. C₂×C₂²⋊C₄×C₆₁	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₆₁	C₂²	semidirect
122. C₂×C₄²×C₆₁	C₂²	semidirect
257. D₄×C₆₁	#41	semidirect
329. #3513	C₆₁	direct (N × H)
339. #559	C₂×C₆₁	semidirect
340. #554	C₂×C₆₁	semidirect
341. #553	C₂×C₆₁	semidirect
342. #553	C₂×C₆₁	semidirect
343. #552	C₂×C₆₁	semidirect
344. #551	C₂×C₆₁	semidirect
345. #551	C₂×C₆₁	semidirect
346. #547	C₂×C₆₁	semidirect
347. #546	C₂×C₆₁	semidirect
348. #546	C₂×C₆₁	semidirect
349. #546	C₂×C₆₁	semidirect
350. D₄²	C₂×C₆₁	semidirect
351. #542	C₂×C₆₁	semidirect
352. #540	C₂×C₆₁	semidirect
353. #539	C₂×C₆₁	semidirect
354. #538	C₂×C₆₁	semidirect
355. #529	C₂×C₆₁	semidirect
356. #529	C₂×C₆₁	semidirect
357. #525	C₂×C₆₁	semidirect
358. C₂×#123	C₂×C₆₁	semidirect
359. #520	C₂×C₆₁	semidirect
360. #518	C₂×C₆₁	semidirect
361. C₂×C₄×D₄	C₂×C₆₁	semidirect
362. C₆₁	#3513	direct (N × H)
364. C₂×#41	C₂²×C₆₁	semidirect
368. C₂³×C₄	C₂²×C₆₁	semidirect
369. C₄⋊Q₈	C₂²×C₆₁	semidirect
371. #126	C₂²×C₆₁	semidirect
372. #126	C₂²×C₆₁	semidirect
373. #126	C₂²×C₆₁	semidirect
374. #126	C₂²×C₆₁	semidirect
375. #126	C₂²×C₆₁	semidirect
376. #126	C₂²×C₆₁	semidirect
377. #125	C₂²×C₆₁	semidirect
378. #125	C₂²×C₆₁	semidirect
379. #125	C₂²×C₆₁	semidirect
380. #125	C₂²×C₆₁	semidirect
381. #124	C₂²×C₆₁	semidirect
382. #124	C₂²×C₆₁	semidirect
383. #124	C₂²×C₆₁	semidirect
384. #124	C₂²×C₆₁	semidirect
385. #124	C₂²×C₆₁	semidirect
388. #123	C₂²×C₆₁	semidirect
389. #123	C₂²×C₆₁	semidirect
390. #123	C₂²×C₆₁	semidirect
391. #123	C₂²×C₆₁	semidirect
392. #123	C₂²×C₆₁	semidirect
393. #123	C₂²×C₆₁	semidirect
394. #123	C₂²×C₆₁	semidirect
395. #123	C₂²×C₆₁	semidirect
396. #123	C₂²×C₆₁	semidirect
397. #123	C₂²×C₆₁	semidirect
398. #123	C₂²×C₆₁	semidirect
399. #123	C₂²×C₆₁	semidirect
400. C₂²⋊Q₈	C₂²×C₆₁	semidirect
401. C₂²⋊Q₈	C₂²×C₆₁	semidirect
402. C₂²⋊Q₈	C₂²×C₆₁	semidirect
403. C₂²⋊Q₈	C₂²×C₆₁	semidirect
404. C₂²⋊Q₈	C₂²×C₆₁	semidirect
405. C₂²⋊Q₈	C₂²×C₆₁	semidirect
406. C₂²⋊Q₈	C₂²×C₆₁	semidirect
407. C₂²⋊Q₈	C₂²×C₆₁	semidirect
412. #121	C₂²×C₆₁	semidirect
413. #121	C₂²×C₆₁	semidirect
414. #121	C₂²×C₆₁	semidirect
415. #121	C₂²×C₆₁	semidirect
416. #121	C₂²×C₆₁	semidirect
417. #121	C₂²×C₆₁	semidirect
418. #121	C₂²×C₆₁	semidirect
421. #120	C₂²×C₆₁	semidirect
422. #120	C₂²×C₆₁	semidirect
423. C₄×Q₈	C₂²×C₆₁	semidirect
424. C₄×Q₈	C₂²×C₆₁	semidirect
425. C₄×Q₈	C₂²×C₆₁	semidirect
431. C₄×D₄	C₂²×C₆₁	semidirect
432. C₄×D₄	C₂²×C₆₁	semidirect
433. C₄×D₄	C₂²×C₆₁	semidirect
434. C₄×D₄	C₂²×C₆₁	semidirect
435. C₄×D₄	C₂²×C₆₁	semidirect
436. C₄×D₄	C₂²×C₆₁	semidirect
437. C₄×D₄	C₂²×C₆₁	semidirect
438. C₄×D₄	C₂²×C₆₁	semidirect
439. C₄×D₄	C₂²×C₆₁	semidirect
440. C₄×D₄	C₂²×C₆₁	semidirect
441. C₄×D₄	C₂²×C₆₁	semidirect
442. C₄×D₄	C₂²×C₆₁	semidirect
443. C₄×D₄	C₂²×C₆₁	semidirect
444. C₄×D₄	C₂²×C₆₁	semidirect
445. C₄×D₄	C₂²×C₆₁	semidirect
446. #117	C₂²×C₆₁	semidirect
447. #117	C₂²×C₆₁	semidirect
448. #117	C₂²×C₆₁	semidirect
449. #117	C₂²×C₆₁	semidirect
450. #117	C₂²×C₆₁	semidirect
451. #117	C₂²×C₆₁	semidirect
452. C₂×C₄⋊C₄	C₂²×C₆₁	semidirect
453. C₂×C₄⋊C₄	C₂²×C₆₁	semidirect
454. C₂×C₄⋊C₄	C₂²×C₆₁	semidirect
455. C₂×C₄⋊C₄	C₂²×C₆₁	semidirect
456. C₂×C₂²⋊C₄	C₂²×C₆₁	semidirect
457. C₂×C₂²⋊C₄	C₂²×C₆₁	semidirect
458. C₂×C₂²⋊C₄	C₂²×C₆₁	semidirect
459. C₂×C₂²⋊C₄	C₂²×C₆₁	semidirect
460. C₂×C₂²⋊C₄	C₂²×C₆₁	semidirect
461. C₂×C₄²	C₂²×C₆₁	semidirect
596. D₄	#41×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#559	2
C₆₁×#554	2
C₆₁×#553	2
C₆₁×#552	2
C₆₁×#551	2
C₆₁×#547	2
C₆₁×#546	2
D₄²×C₆₁	2
C₆₁×#542	2
C₆₁×#540	2
C₆₁×#539	2
C₆₁×#538	2
C₆₁×#529	2
C₆₁×#525	2
C₂×#123×C₆₁	2
C₆₁×#520	2
C₆₁×#518	2
C₂×C₄×D₄×C₆₁	2
#3513	61

Subgroups — C61×#3513 #21443554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#3513 #21443554