Subgroups — C₆₁×#62880 #29566313

Order 15616.

7362 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3562	C₂	1	8	yes	maximal, complemented
2	C₆₁×#3543	C₂	1	8	yes	maximal, complemented
3	C₆₁×#3542	C₂	1	8	yes	maximal, complemented
4	C₆₁×#3539	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3537	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3537	C₂	1	8	yes	maximal, complemented
7	C₆₁×#3534	C₂	1	8	yes	maximal, complemented
8	C₆₁×#3512	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3506	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3498	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3496	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3488	C₂	1	4	yes	maximal, complemented
13	C₆₁×#3455	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	4	yes	complemented
17	C₂²×#41×C₆₁	C₂²	1	2	yes	complemented
18	C₆₁×#562	C₂²	1	16	yes	complemented
19	C₆₁×#560	C₂²	1	16	yes	complemented
20	C₆₁×#560	C₂²	1	16	yes	complemented
21	C₆₁×#560	C₂²	1	16	yes	complemented
22	C₆₁×#559	C₂²	1	8	yes	complemented
23	C₆₁×#556	C₂²	1	4	yes	complemented
24	C₆₁×#555	C₂²	1	4	yes	complemented
25	C₆₁×#553	C₂²	1	16	yes	complemented
26	C₆₁×#553	C₂²	1	8	yes	complemented
27	C₆₁×#553	C₂²	1	16	yes	complemented
28	C₆₁×#553	C₂²	1	8	yes	complemented
29	C₆₁×#552	C₂²	1	8	yes	complemented
30	C₆₁×#551	C₂²	1	16	yes	complemented
31	C₆₁×#550	C₂²	1	4	yes	complemented
32	C₆₁×#550	C₂²	1	8	yes	complemented
33	C₆₁×#550	C₂²	1	8	yes	complemented
34	C₆₁×#548	C₂²	1	8	yes	complemented
35	C₆₁×#547	C₂²	1	4	yes	complemented
36	C₆₁×#547	C₂²	1	4	yes	complemented
37	C₆₁×#547	C₂²	1	4	yes	complemented
38	C₆₁×#546	C₂²	1	8	yes	complemented
39	C₆₁×#546	C₂²	1	8	yes	complemented
40	C₆₁×#546	C₂²	1	16	yes	complemented
41	C₆₁×#546	C₂²	1	16	yes	complemented
42	C₆₁×#546	C₂²	1	8	yes	complemented
43	D₄²×C₆₁	C₂²	1	8	yes	complemented
44	D₄²×C₆₁	C₂²	1	4	yes	complemented
45	D₄²×C₆₁	C₂²	1	16	yes	complemented
46	D₄²×C₆₁	C₂²	1	16	yes	complemented
47	D₄²×C₆₁	C₂²	1	4	yes	complemented
48	D₄²×C₆₁	C₂²	1	16	yes	complemented
49	D₄²×C₆₁	C₂²	1	8	yes	complemented
50	C₆₁×#542	C₂²	1	4	yes	complemented
51	C₆₁×#541	C₂²	1	4	yes	complemented
52	C₆₁×#541	C₂²	1	2	yes	complemented
53	C₆₁×#540	C₂²	1	4	yes	complemented
54	C₆₁×#540	C₂²	1	8	yes	complemented
55	C₆₁×#540	C₂²	1	16	yes	complemented
56	C₆₁×#540	C₂²	1	16	yes	complemented
57	C₆₁×#540	C₂²	1	4	yes	complemented
58	C₆₁×#540	C₂²	1	4	yes	complemented
59	C₆₁×#540	C₂²	1	2	yes	complemented
60	C₆₁×#539	C₂²	1	16	yes	complemented
61	C₆₁×#539	C₂²	1	4	yes	complemented
62	C₆₁×#538	C₂²	1	16	yes	complemented
63	C₆₁×#538	C₂²	1	16	yes	complemented
64	C₆₁×#538	C₂²	1	4	yes	complemented
65	C₆₁×#538	C₂²	1	8	yes	complemented
66	C₆₁×#537	C₂²	1	4	yes	complemented
67	C₆₁×#537	C₂²	1	4	yes	complemented
68	C₆₁×#537	C₂²	1	8	yes	complemented
69	C₆₁×#536	C₂²	1	4	yes	complemented
70	C₆₁×#535	C₂²	1	4	yes	complemented
71	C₆₁×#535	C₂²	1	8	yes	complemented
72	C₆₁×#535	C₂²	1	16	yes	complemented
73	C₆₁×#535	C₂²	1	4	yes	complemented
74	C₆₁×#535	C₂²	1	8	yes	complemented
75	C₆₁×#534	C₂²	1	16	yes	complemented
76	C₆₁×#534	C₂²	1	16	yes	complemented
77	C₆₁×#534	C₂²	1	4	yes	complemented
78	C₆₁×#534	C₂²	1	8	yes	complemented
79	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
80	C₆₁×#532	C₂²	1	4	yes	complemented
81	C₆₁×#532	C₂²	1	2	yes	complemented
82	C₆₁×#532	C₂²	1	2	yes	complemented
83	C₆₁×#532	C₂²	1	1	yes	characteristic, complemented
84	C₂×#127×C₆₁	C₂²	1	4	yes	complemented
85	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic, complemented
86	C₆₁×#529	C₂²	1	8	yes	complemented
87	C₆₁×#529	C₂²	1	8	yes	complemented
88	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic, complemented
89	C₆₁×#525	C₂²	1	4	yes	complemented
90	C₆₁×#525	C₂²	1	4	yes	complemented
91	C₆₁×#525	C₂²	1	2	yes	complemented
92	C₆₁×#525	C₂²	1	8	yes	complemented
93	C₆₁×#525	C₂²	1	8	yes	complemented
94	C₂×#123×C₆₁	C₂²	1	4	yes	complemented
95	C₂×#121×C₆₁	C₂²	1	2	yes	complemented
96	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
97	C₂×#121×C₆₁	C₂²	1	8	yes	complemented
98	C₂×#121×C₆₁	C₂²	1	8	yes	complemented
99	C₆₁×#520	C₂²	1	4	yes	complemented
100	C₄×#41×C₆₁	C₂²	1	2	yes	complemented
101	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
102	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic, complemented
103	H(5,𝔽₂)×C₆₁	—	4	16	no	—
104	C₂×#41×C₆₁	—	4	8	no	—
105	C₂×#41×C₆₁	C₂³	1	4	yes	—
106	C₂×#41×C₆₁	C₂³	1	2	yes	—
107	C₂×#41×C₆₁	C₂³	1	8	yes	—
108	C₂×#41×C₆₁	C₂³	1	4	yes	—
109	C₂×#41×C₆₁	C₂³	1	4	yes	—
110	C₂×#41×C₆₁	C₂³	1	4	yes	—
111	C₂×#41×C₆₁	C₂³	1	8	yes	—
112	C₂×#41×C₆₁	C₂³	1	8	yes	—
113	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
116	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
117	C₂²×D₄×C₆₁	C₂³	1	16	yes	—
118	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
119	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
120	C₂²×D₄×C₆₁	C₂³	1	16	yes	—
121	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
122	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
123	C₂²×D₄×C₆₁	C₂³	1	16	yes	—
124	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
125	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
127	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
128	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
131	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
132	#127×C₆₁	C₂³	1	2	yes	—
133	#127×C₆₁	C₂³	1	4	yes	—
134	#127×C₆₁	C₂³	1	8	yes	—
135	#127×C₆₁	C₂³	1	16	yes	—
136	#127×C₆₁	C₂³	1	4	yes	—
137	#127×C₆₁	C₂³	1	2	yes	—
138	#127×C₆₁	C₂³	1	1	yes	characteristic
139	#127×C₆₁	C₂³	1	16	yes	—
140	#126×C₆₁	C₂³	1	16	yes	—
141	#126×C₆₁	C₂³	1	16	yes	—
142	#126×C₆₁	C₂³	1	16	yes	—
143	#126×C₆₁	C₂³	1	8	yes	—
144	#126×C₆₁	C₂³	1	8	yes	—
145	#125×C₆₁	C₂³	1	2	yes	—
146	#125×C₆₁	C₂³	1	8	yes	—
147	#125×C₆₁	C₂³	1	16	yes	—
148	#125×C₆₁	C₂³	1	4	yes	—
149	#125×C₆₁	C₂³	1	4	yes	—
150	#124×C₆₁	C₂³	1	4	yes	—
151	#124×C₆₁	C₂³	1	8	yes	—
152	#124×C₆₁	C₂³	1	4	yes	—
153	#124×C₆₁	C₂³	1	2	yes	—
154	#124×C₆₁	C₂³	1	8	yes	—
155	#124×C₆₁	C₂³	1	16	yes	—
156	#124×C₆₁	C₂³	1	16	yes	—
157	#123×C₆₁	C₂³	1	8	yes	—
158	#123×C₆₁	C₂³	1	8	yes	—
159	#123×C₆₁	C₂³	1	16	yes	—
160	#123×C₆₁	C₂³	1	8	yes	—
161	#123×C₆₁	C₂³	1	8	yes	—
162	#123×C₆₁	C₂³	1	16	yes	—
163	#123×C₆₁	C₂³	1	16	yes	—
164	#123×C₆₁	C₂³	1	16	yes	—
165	#123×C₆₁	C₂³	1	16	yes	—
166	#123×C₆₁	C₂³	1	16	yes	—
167	#123×C₆₁	C₂³	1	16	yes	—
168	#123×C₆₁	C₂³	1	4	yes	—
169	#123×C₆₁	C₂³	1	16	yes	—
170	#123×C₆₁	C₂³	1	16	yes	—
171	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
172	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
173	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
174	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
175	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
176	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
177	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
178	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
179	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
180	#121×C₆₁	C₂³	1	4	yes	—
181	#121×C₆₁	C₂³	1	4	yes	—
182	#121×C₆₁	C₂³	1	4	yes	—
183	#121×C₆₁	C₂³	1	8	yes	—
184	#121×C₆₁	C₂³	1	16	yes	—
185	#121×C₆₁	C₂³	1	8	yes	—
186	#121×C₆₁	C₂³	1	8	yes	—
187	#121×C₆₁	C₂³	1	16	yes	—
188	#121×C₆₁	C₂³	1	16	yes	—
189	#121×C₆₁	C₂³	1	16	yes	—
190	#121×C₆₁	C₂³	1	16	yes	—
191	#121×C₆₁	C₂³	1	16	yes	—
192	#121×C₆₁	C₂³	1	16	yes	—
193	#121×C₆₁	C₂³	1	16	yes	—
194	#121×C₆₁	C₂³	1	4	yes	—
195	#121×C₆₁	C₂³	1	8	yes	—
196	#121×C₆₁	C₂³	1	8	yes	—
197	#121×C₆₁	C₂³	1	16	yes	—
198	#121×C₆₁	C₂³	1	8	yes	—
199	#121×C₆₁	C₂³	1	8	yes	—
200	#121×C₆₁	C₂³	1	8	yes	—
201	#121×C₆₁	C₂³	1	16	yes	—
202	#121×C₆₁	C₂³	1	16	yes	—
203	#121×C₆₁	C₂³	1	16	yes	—
204	#121×C₆₁	C₂³	1	8	yes	—
205	#121×C₆₁	C₂³	1	8	yes	—
206	#121×C₆₁	C₂³	1	8	yes	—
207	#121×C₆₁	C₂³	1	16	yes	—
208	#121×C₆₁	C₂³	1	8	yes	—
209	#121×C₆₁	C₂³	1	8	yes	—
210	#121×C₆₁	C₂³	1	16	yes	—
211	#120×C₆₁	C₂³	1	8	yes	—
212	#120×C₆₁	C₂³	1	16	yes	—
213	#120×C₆₁	C₂³	1	16	yes	—
214	#120×C₆₁	C₂³	1	16	yes	—
215	#120×C₆₁	C₂³	1	16	yes	—
216	#120×C₆₁	C₂³	1	16	yes	—
217	#120×C₆₁	C₂³	1	8	yes	—
218	#120×C₆₁	C₂³	1	16	yes	—
219	#120×C₆₁	C₂³	1	16	yes	—
220	#120×C₆₁	C₂³	1	16	yes	—
221	#120×C₆₁	C₂³	1	4	yes	—
222	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
223	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
224	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
225	C₄×D₄×C₆₁	C₂³	1	16	yes	—
226	C₄×D₄×C₆₁	C₂³	1	4	yes	—
227	C₄×D₄×C₆₁	C₂³	1	4	yes	—
228	C₄×D₄×C₆₁	C₂³	1	8	yes	—
229	C₄×D₄×C₆₁	C₂³	1	4	yes	—
230	C₄×D₄×C₆₁	C₂³	1	8	yes	—
231	C₄×D₄×C₆₁	C₂³	1	16	yes	—
232	C₄×D₄×C₆₁	C₂³	1	16	yes	—
233	C₄×D₄×C₆₁	C₂³	1	16	yes	—
234	C₄×D₄×C₆₁	C₂³	1	16	yes	—
235	C₄×D₄×C₆₁	C₂³	1	16	yes	—
236	C₄×D₄×C₆₁	C₂³	1	4	yes	—
237	C₄×D₄×C₆₁	C₂³	1	4	yes	—
238	C₄×D₄×C₆₁	C₂³	1	4	yes	—
239	C₄×D₄×C₆₁	C₂³	1	4	yes	—
240	C₄×D₄×C₆₁	C₂³	1	4	yes	—
241	C₄×D₄×C₆₁	C₂³	1	8	yes	—
242	C₄×D₄×C₆₁	C₂³	1	8	yes	—
243	#117×C₆₁	C₂³	1	2	yes	—
244	#117×C₆₁	C₂³	1	4	yes	—
245	#117×C₆₁	C₂³	1	4	yes	—
246	#117×C₆₁	C₂³	1	16	yes	—
247	#117×C₆₁	C₂³	1	8	yes	—
248	#117×C₆₁	C₂³	1	2	yes	—
249	#117×C₆₁	C₂³	1	2	yes	—
250	#117×C₆₁	C₂³	1	8	yes	—
251	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
254	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
256	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
257	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
258	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
259	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
260	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
261	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
263	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
264	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
266	C₂⁴×C₆₁	C₂⁴	1	16	yes	—
267	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
268	#41×C₆₁	—	2	16	no	—
269	#41×C₆₁	—	2	8	no	—
270	#41×C₆₁	—	4	8	no	—
271	#41×C₆₁	—	4	8	no	—
272	#41×C₆₁	—	4	8	no	—
273	#41×C₆₁	—	4	16	no	—
274	#41×C₆₁	—	4	16	no	—
275	#41×C₆₁	—	8	8	no	—
276	C₂×Q₈×C₆₁	—	4	4	no	—
277	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
278	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
279	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
280	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
281	C₂×D₄×C₆₁	—	2	8	no	—
282	C₂×D₄×C₆₁	—	4	4	no	—
283	C₂×D₄×C₆₁	—	4	16	no	—
284	C₂×D₄×C₆₁	—	4	16	no	—
285	C₂×D₄×C₆₁	—	4	8	no	—
286	C₂×D₄×C₆₁	—	4	32	no	—
287	C₂×D₄×C₆₁	—	8	4	no	—
288	C₂×D₄×C₆₁	—	8	8	no	—
289	C₂×D₄×C₆₁	—	8	4	no	—
290	C₂×D₄×C₆₁	—	8	16	no	—
291	C₂×D₄×C₆₁	—	8	16	no	—
292	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
293	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
294	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
295	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
296	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
297	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
298	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
299	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
300	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
301	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
302	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
303	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
304	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
305	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
306	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
307	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
308	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
309	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
310	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
311	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
312	C₂²×C₄×C₆₁	—	2	4	no	—
313	C₂²×C₄×C₆₁	—	4	8	no	—
314	C₂²×C₄×C₆₁	—	8	4	no	—
315	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
316	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
318	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
323	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
324	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
325	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
326	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
327	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
328	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
329	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
330	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
332	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
333	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
334	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
335	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
336	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
337	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
338	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
339	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
340	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
341	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
342	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
343	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
344	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
345	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
346	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
347	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
348	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
349	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
350	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
351	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
352	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
353	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
354	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
355	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
356	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
357	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
358	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
359	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
360	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
361	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
362	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
363	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
364	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
365	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
366	C₄²×C₆₁	C₂⁴	1	2	yes	—
367	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
368	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
369	C₄²×C₆₁	C₂⁴	1	2	yes	—
370	C₄²×C₆₁	C₂⁴	1	2	yes	—
371	C₄²×C₆₁	C₂⁴	1	4	yes	—
372	C₄²×C₆₁	C₂⁴	1	8	yes	—
373	C₄²×C₆₁	C₂⁴	1	16	yes	—
374	C₂³×C₆₁	—	2	2	no	—
375	C₂³×C₆₁	—	2	8	no	—
376	C₂³×C₆₁	—	4	4	no	—
377	C₂³×C₆₁	—	4	4	no	—
378	C₂³×C₆₁	—	4	2	no	—
379	C₂³×C₆₁	—	4	4	no	—
380	C₂³×C₆₁	—	4	8	no	—
381	C₂³×C₆₁	—	4	16	no	—
382	C₂³×C₆₁	—	4	16	no	—
383	C₂³×C₆₁	—	4	16	no	—
384	C₂³×C₆₁	C₂⁵	1	4	yes	—
385	C₂³×C₆₁	C₂⁵	1	2	yes	—
386	C₂³×C₆₁	C₂⁵	1	8	yes	—
387	C₂³×C₆₁	C₂⁵	1	8	yes	—
388	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
389	Q₈×C₆₁	—	2	8	no	—
390	Q₈×C₆₁	—	2	4	no	—
391	Q₈×C₆₁	—	4	4	no	—
392	Q₈×C₆₁	—	4	4	no	—
393	D₄×C₆₁	—	2	8	no	—
394	D₄×C₆₁	—	2	16	no	—
395	D₄×C₆₁	—	2	8	no	—
396	D₄×C₆₁	—	2	8	no	—
397	D₄×C₆₁	—	2	4	no	—
398	D₄×C₆₁	—	2	8	no	—
399	D₄×C₆₁	—	4	16	no	—
400	D₄×C₆₁	—	4	16	no	—
401	D₄×C₆₁	—	4	4	no	—
402	D₄×C₆₁	—	4	8	no	—
403	D₄×C₆₁	—	4	4	no	—
404	D₄×C₆₁	—	4	16	no	—
405	D₄×C₆₁	—	4	4	no	—
406	D₄×C₆₁	—	4	16	no	—
407	D₄×C₆₁	—	4	16	no	—
408	D₄×C₆₁	—	4	8	no	—
409	D₄×C₆₁	—	4	8	no	—
410	D₄×C₆₁	—	4	16	no	—
411	D₄×C₆₁	—	4	16	no	—
412	D₄×C₆₁	—	4	4	no	—
413	C₂×C₄×C₆₁	—	2	2	no	—
414	C₂×C₄×C₆₁	—	2	4	no	—
415	C₂×C₄×C₆₁	—	2	4	no	—
416	C₂×C₄×C₆₁	—	2	16	no	—
417	C₂×C₄×C₆₁	—	2	8	no	—
418	C₂×C₄×C₆₁	—	4	4	no	—
419	C₂×C₄×C₆₁	—	4	8	no	—
420	C₂×C₄×C₆₁	—	4	2	no	—
421	C₂×C₄×C₆₁	—	4	4	no	—
422	C₂×C₄×C₆₁	—	4	8	no	—
423	C₂×C₄×C₆₁	—	4	8	no	—
424	C₂×C₄×C₆₁	—	4	16	no	—
425	C₂×C₄×C₆₁	—	4	2	no	—
426	C₂×C₄×C₆₁	—	4	8	no	—
427	C₂×C₄×C₆₁	—	4	16	no	—
428	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
429	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
430	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
431	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
432	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
433	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
434	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
435	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
436	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
437	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
438	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
439	#62880	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
440	C₂²×C₆₁	—	2	2	no	—
441	C₂²×C₆₁	—	2	2	no	—
442	C₂²×C₆₁	—	2	8	no	—
443	C₂²×C₆₁	—	2	4	no	—
444	C₂²×C₆₁	—	2	8	no	—
445	C₂²×C₆₁	—	2	8	no	—
446	C₂²×C₆₁	—	2	8	no	—
447	C₂²×C₆₁	—	2	8	no	—
448	C₂²×C₆₁	—	2	4	no	—
449	C₂²×C₆₁	—	2	8	no	—
450	C₂²×C₆₁	—	2	8	no	—
451	C₂²×C₆₁	—	8	2	no	—
452	C₂²×C₆₁	—	8	8	no	—
453	C₂²×C₆₁	—	8	8	no	—
454	C₂²×C₆₁	—	16	16	no	—
455	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
456	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
457	C₄×C₆₁	—	2	2	no	—
458	C₄×C₆₁	—	2	4	no	—
459	C₄×C₆₁	—	2	8	no	—
460	C₄×C₆₁	—	2	2	no	—
461	C₄×C₆₁	—	2	8	no	—
462	C₄×C₆₁	—	2	2	no	—
463	C₄×C₆₁	—	2	4	no	—
464	C₄×C₆₁	—	2	8	no	—
465	C₄×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
466	C₄×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
467	#3562	C₂×C₆₁	1	8	yes	complemented
468	#3543	C₂×C₆₁	1	8	yes	complemented
469	#3542	C₂×C₆₁	1	8	yes	complemented
470	#3539	C₂×C₆₁	1	4	yes	complemented
471	#3537	C₂×C₆₁	1	8	yes	complemented
472	#3537	C₂×C₆₁	1	4	yes	complemented
473	#3534	C₂×C₆₁	1	8	yes	complemented
474	#3512	C₂×C₆₁	1	2	yes	complemented
475	#3506	C₂×C₆₁	1	2	yes	complemented
476	#3498	C₂×C₆₁	1	2	yes	complemented
477	#3496	C₂×C₆₁	1	2	yes	complemented
478	#3488	C₂×C₆₁	1	4	yes	complemented
479	#3455	C₂×C₆₁	1	1	yes	characteristic, complemented
480	C₂×#540	C₂×C₆₁	1	1	yes	characteristic, complemented
481	#3449	C₂×C₆₁	1	1	yes	characteristic, complemented
482	C₂×C₆₁	—	2	2	no	—
483	C₂×C₆₁	—	4	2	no	—
484	C₂×C₆₁	—	4	8	no	—
485	C₂×C₆₁	—	4	8	no	—
486	C₂×C₆₁	—	4	4	no	—
487	C₂×C₆₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂×C₆₁	H(7,𝔽₂)	1	2	yes	—
489	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	4	yes	complemented
490	C₂²×#41	C₂²×C₆₁	1	2	yes	complemented
491	#562	C₂²×C₆₁	1	16	yes	complemented
492	#560	C₂²×C₆₁	1	16	yes	complemented
493	#560	C₂²×C₆₁	1	16	yes	complemented
494	#560	C₂²×C₆₁	1	16	yes	complemented
495	#559	C₂²×C₆₁	1	8	yes	complemented
496	#556	C₂²×C₆₁	1	4	yes	complemented
497	#555	C₂²×C₆₁	1	4	yes	complemented
498	#553	C₂²×C₆₁	1	8	yes	complemented
499	#553	C₂²×C₆₁	1	16	yes	complemented
500	#553	C₂²×C₆₁	1	8	yes	complemented
501	#553	C₂²×C₆₁	1	16	yes	complemented
502	#552	C₂²×C₆₁	1	8	yes	complemented
503	#551	C₂²×C₆₁	1	16	yes	complemented
504	#550	C₂²×C₆₁	1	8	yes	complemented
505	#550	C₂²×C₆₁	1	8	yes	complemented
506	#550	C₂²×C₆₁	1	4	yes	complemented
507	#548	C₂²×C₆₁	1	8	yes	complemented
508	#547	C₂²×C₆₁	1	4	yes	complemented
509	#547	C₂²×C₆₁	1	4	yes	complemented
510	#547	C₂²×C₆₁	1	4	yes	complemented
511	#546	C₂²×C₆₁	1	16	yes	complemented
512	#546	C₂²×C₆₁	1	8	yes	complemented
513	#546	C₂²×C₆₁	1	8	yes	complemented
514	#546	C₂²×C₆₁	1	8	yes	complemented
515	#546	C₂²×C₆₁	1	16	yes	complemented
516	D₄²	C₂²×C₆₁	1	16	yes	complemented
517	D₄²	C₂²×C₆₁	1	8	yes	complemented
518	D₄²	C₂²×C₆₁	1	4	yes	complemented
519	D₄²	C₂²×C₆₁	1	4	yes	complemented
520	D₄²	C₂²×C₆₁	1	16	yes	complemented
521	D₄²	C₂²×C₆₁	1	8	yes	complemented
522	D₄²	C₂²×C₆₁	1	16	yes	complemented
523	#542	C₂²×C₆₁	1	4	yes	complemented
524	#541	C₂²×C₆₁	1	2	yes	complemented
525	#541	C₂²×C₆₁	1	4	yes	complemented
526	#540	C₂²×C₆₁	1	4	yes	complemented
527	#540	C₂²×C₆₁	1	4	yes	complemented
528	#540	C₂²×C₆₁	1	8	yes	complemented
529	#540	C₂²×C₆₁	1	2	yes	complemented
530	#540	C₂²×C₆₁	1	4	yes	complemented
531	#540	C₂²×C₆₁	1	16	yes	complemented
532	#540	C₂²×C₆₁	1	16	yes	complemented
533	#539	C₂²×C₆₁	1	4	yes	complemented
534	#539	C₂²×C₆₁	1	16	yes	complemented
535	#538	C₂²×C₆₁	1	4	yes	complemented
536	#538	C₂²×C₆₁	1	8	yes	complemented
537	#538	C₂²×C₆₁	1	16	yes	complemented
538	#538	C₂²×C₆₁	1	16	yes	complemented
539	#537	C₂²×C₆₁	1	4	yes	complemented
540	#537	C₂²×C₆₁	1	4	yes	complemented
541	#537	C₂²×C₆₁	1	8	yes	complemented
542	#536	C₂²×C₆₁	1	4	yes	complemented
543	#535	C₂²×C₆₁	1	4	yes	complemented
544	#535	C₂²×C₆₁	1	4	yes	complemented
545	#535	C₂²×C₆₁	1	8	yes	complemented
546	#535	C₂²×C₆₁	1	8	yes	complemented
547	#535	C₂²×C₆₁	1	16	yes	complemented
548	#534	C₂²×C₆₁	1	4	yes	complemented
549	#534	C₂²×C₆₁	1	8	yes	complemented
550	#534	C₂²×C₆₁	1	16	yes	complemented
551	#534	C₂²×C₆₁	1	16	yes	complemented
552	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
553	#532	C₂²×C₆₁	1	2	yes	complemented
554	#532	C₂²×C₆₁	1	2	yes	complemented
555	#532	C₂²×C₆₁	1	1	yes	characteristic, complemented
556	#532	C₂²×C₆₁	1	4	yes	complemented
557	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic, complemented
558	C₂×#127	C₂²×C₆₁	1	4	yes	complemented
559	#529	C₂²×C₆₁	1	8	yes	complemented
560	#529	C₂²×C₆₁	1	8	yes	complemented
561	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic, complemented
562	#525	C₂²×C₆₁	1	4	yes	complemented
563	#525	C₂²×C₆₁	1	4	yes	complemented
564	#525	C₂²×C₆₁	1	2	yes	complemented
565	#525	C₂²×C₆₁	1	8	yes	complemented
566	#525	C₂²×C₆₁	1	8	yes	complemented
567	C₂×#123	C₂²×C₆₁	1	4	yes	complemented
568	C₂×#121	C₂²×C₆₁	1	2	yes	complemented
569	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
570	C₂×#121	C₂²×C₆₁	1	8	yes	complemented
571	C₂×#121	C₂²×C₆₁	1	8	yes	complemented
572	#520	C₂²×C₆₁	1	4	yes	complemented
573	C₄×#41	C₂²×C₆₁	1	2	yes	complemented
574	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
575	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic, complemented
576	C₆₁	#62880	1	1	yes	characteristic, direct product factor, Sylow
577	H(5,𝔽₂)	—	4	16	no	—
578	C₂×#41	—	4	8	no	—
579	C₂×#41	C₂³×C₆₁	1	2	yes	—
580	C₂×#41	C₂³×C₆₁	1	4	yes	—
581	C₂×#41	C₂³×C₆₁	1	4	yes	—
582	C₂×#41	C₂³×C₆₁	1	8	yes	—
583	C₂×#41	C₂³×C₆₁	1	8	yes	—
584	C₂×#41	C₂³×C₆₁	1	4	yes	—
585	C₂×#41	C₂³×C₆₁	1	4	yes	—
586	C₂×#41	C₂³×C₆₁	1	8	yes	—
587	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
588	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
589	C₂²×D₄	C₂³×C₆₁	1	16	yes	—
590	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
591	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
592	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
593	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
594	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
595	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
596	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
597	C₂²×D₄	C₂³×C₆₁	1	16	yes	—
598	C₂²×D₄	C₂³×C₆₁	1	16	yes	—
599	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
601	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
602	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
603	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
604	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
605	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
606	#127	C₂³×C₆₁	1	4	yes	—
607	#127	C₂³×C₆₁	1	2	yes	—
608	#127	C₂³×C₆₁	1	8	yes	—
609	#127	C₂³×C₆₁	1	16	yes	—
610	#127	C₂³×C₆₁	1	4	yes	—
611	#127	C₂³×C₆₁	1	2	yes	—
612	#127	C₂³×C₆₁	1	1	yes	characteristic
613	#127	C₂³×C₆₁	1	16	yes	—
614	#126	C₂³×C₆₁	1	16	yes	—
615	#126	C₂³×C₆₁	1	8	yes	—
616	#126	C₂³×C₆₁	1	8	yes	—
617	#126	C₂³×C₆₁	1	16	yes	—
618	#126	C₂³×C₆₁	1	16	yes	—
619	#125	C₂³×C₆₁	1	4	yes	—
620	#125	C₂³×C₆₁	1	4	yes	—
621	#125	C₂³×C₆₁	1	8	yes	—
622	#125	C₂³×C₆₁	1	2	yes	—
623	#125	C₂³×C₆₁	1	16	yes	—
624	#124	C₂³×C₆₁	1	4	yes	—
625	#124	C₂³×C₆₁	1	8	yes	—
626	#124	C₂³×C₆₁	1	8	yes	—
627	#124	C₂³×C₆₁	1	4	yes	—
628	#124	C₂³×C₆₁	1	2	yes	—
629	#124	C₂³×C₆₁	1	16	yes	—
630	#124	C₂³×C₆₁	1	16	yes	—
631	#123	C₂³×C₆₁	1	16	yes	—
632	#123	C₂³×C₆₁	1	16	yes	—
633	#123	C₂³×C₆₁	1	8	yes	—
634	#123	C₂³×C₆₁	1	8	yes	—
635	#123	C₂³×C₆₁	1	16	yes	—
636	#123	C₂³×C₆₁	1	4	yes	—
637	#123	C₂³×C₆₁	1	16	yes	—
638	#123	C₂³×C₆₁	1	8	yes	—
639	#123	C₂³×C₆₁	1	8	yes	—
640	#123	C₂³×C₆₁	1	16	yes	—
641	#123	C₂³×C₆₁	1	16	yes	—
642	#123	C₂³×C₆₁	1	16	yes	—
643	#123	C₂³×C₆₁	1	16	yes	—
644	#123	C₂³×C₆₁	1	16	yes	—
645	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
646	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
647	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
648	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
649	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
650	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
651	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
652	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
653	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
654	#121	C₂³×C₆₁	1	4	yes	—
655	#121	C₂³×C₆₁	1	8	yes	—
656	#121	C₂³×C₆₁	1	4	yes	—
657	#121	C₂³×C₆₁	1	4	yes	—
658	#121	C₂³×C₆₁	1	16	yes	—
659	#121	C₂³×C₆₁	1	16	yes	—
660	#121	C₂³×C₆₁	1	16	yes	—
661	#121	C₂³×C₆₁	1	8	yes	—
662	#121	C₂³×C₆₁	1	8	yes	—
663	#121	C₂³×C₆₁	1	16	yes	—
664	#121	C₂³×C₆₁	1	8	yes	—
665	#121	C₂³×C₆₁	1	16	yes	—
666	#121	C₂³×C₆₁	1	8	yes	—
667	#121	C₂³×C₆₁	1	8	yes	—
668	#121	C₂³×C₆₁	1	16	yes	—
669	#121	C₂³×C₆₁	1	4	yes	—
670	#121	C₂³×C₆₁	1	8	yes	—
671	#121	C₂³×C₆₁	1	8	yes	—
672	#121	C₂³×C₆₁	1	8	yes	—
673	#121	C₂³×C₆₁	1	8	yes	—
674	#121	C₂³×C₆₁	1	8	yes	—
675	#121	C₂³×C₆₁	1	8	yes	—
676	#121	C₂³×C₆₁	1	8	yes	—
677	#121	C₂³×C₆₁	1	16	yes	—
678	#121	C₂³×C₆₁	1	16	yes	—
679	#121	C₂³×C₆₁	1	16	yes	—
680	#121	C₂³×C₆₁	1	16	yes	—
681	#121	C₂³×C₆₁	1	16	yes	—
682	#121	C₂³×C₆₁	1	16	yes	—
683	#121	C₂³×C₆₁	1	16	yes	—
684	#121	C₂³×C₆₁	1	16	yes	—
685	#120	C₂³×C₆₁	1	8	yes	—
686	#120	C₂³×C₆₁	1	8	yes	—
687	#120	C₂³×C₆₁	1	16	yes	—
688	#120	C₂³×C₆₁	1	16	yes	—
689	#120	C₂³×C₆₁	1	4	yes	—
690	#120	C₂³×C₆₁	1	16	yes	—
691	#120	C₂³×C₆₁	1	16	yes	—
692	#120	C₂³×C₆₁	1	16	yes	—
693	#120	C₂³×C₆₁	1	16	yes	—
694	#120	C₂³×C₆₁	1	16	yes	—
695	#120	C₂³×C₆₁	1	16	yes	—
696	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
697	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
698	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
699	C₄×D₄	C₂³×C₆₁	1	4	yes	—
700	C₄×D₄	C₂³×C₆₁	1	4	yes	—
701	C₄×D₄	C₂³×C₆₁	1	4	yes	—
702	C₄×D₄	C₂³×C₆₁	1	4	yes	—
703	C₄×D₄	C₂³×C₆₁	1	8	yes	—
704	C₄×D₄	C₂³×C₆₁	1	4	yes	—
705	C₄×D₄	C₂³×C₆₁	1	16	yes	—
706	C₄×D₄	C₂³×C₆₁	1	8	yes	—
707	C₄×D₄	C₂³×C₆₁	1	4	yes	—
708	C₄×D₄	C₂³×C₆₁	1	8	yes	—
709	C₄×D₄	C₂³×C₆₁	1	4	yes	—
710	C₄×D₄	C₂³×C₆₁	1	8	yes	—
711	C₄×D₄	C₂³×C₆₁	1	16	yes	—
712	C₄×D₄	C₂³×C₆₁	1	16	yes	—
713	C₄×D₄	C₂³×C₆₁	1	16	yes	—
714	C₄×D₄	C₂³×C₆₁	1	4	yes	—
715	C₄×D₄	C₂³×C₆₁	1	16	yes	—
716	C₄×D₄	C₂³×C₆₁	1	16	yes	—
717	#117	C₂³×C₆₁	1	2	yes	—
718	#117	C₂³×C₆₁	1	2	yes	—
719	#117	C₂³×C₆₁	1	4	yes	—
720	#117	C₂³×C₆₁	1	2	yes	—
721	#117	C₂³×C₆₁	1	4	yes	—
722	#117	C₂³×C₆₁	1	8	yes	—
723	#117	C₂³×C₆₁	1	8	yes	—
724	#117	C₂³×C₆₁	1	16	yes	—
725	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
728	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
729	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
735	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
738	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
739	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
740	C₂⁴	C₂⁴×C₆₁	1	16	yes	—
741	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
742	#41	—	2	16	no	—
743	#41	—	2	8	no	—
744	#41	—	4	8	no	—
745	#41	—	4	8	no	—
746	#41	—	4	8	no	—
747	#41	—	4	16	no	—
748	#41	—	4	16	no	—
749	#41	—	8	8	no	—
750	C₂×Q₈	—	4	4	no	—
751	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
752	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
753	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
754	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
755	C₂×D₄	—	2	8	no	—
756	C₂×D₄	—	4	4	no	—
757	C₂×D₄	—	4	16	no	—
758	C₂×D₄	—	4	16	no	—
759	C₂×D₄	—	4	8	no	—
760	C₂×D₄	—	4	32	no	—
761	C₂×D₄	—	8	4	no	—
762	C₂×D₄	—	8	8	no	—
763	C₂×D₄	—	8	4	no	—
764	C₂×D₄	—	8	16	no	—
765	C₂×D₄	—	8	16	no	—
766	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
767	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
768	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
769	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
770	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
771	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
772	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
773	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
774	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
775	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
776	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
777	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
778	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
779	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
780	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
781	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
782	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
783	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
784	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
785	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
786	C₂²×C₄	—	2	4	no	—
787	C₂²×C₄	—	4	8	no	—
788	C₂²×C₄	—	8	4	no	—
789	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
790	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
792	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
797	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
798	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
799	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
800	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
801	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
802	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
803	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
804	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
805	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
806	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
807	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
808	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
809	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
810	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
811	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
812	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
813	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
814	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
815	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
816	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
817	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
818	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
819	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
820	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
821	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
822	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
823	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
824	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
825	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
826	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
827	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
828	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
829	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
830	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
831	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
832	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
833	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
834	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
835	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
836	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
837	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
838	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
839	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
840	C₄²	C₂⁴×C₆₁	1	2	yes	—
841	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
842	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
843	C₄²	C₂⁴×C₆₁	1	2	yes	—
844	C₄²	C₂⁴×C₆₁	1	2	yes	—
845	C₄²	C₂⁴×C₆₁	1	4	yes	—
846	C₄²	C₂⁴×C₆₁	1	8	yes	—
847	C₄²	C₂⁴×C₆₁	1	16	yes	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	8	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	4	no	—
852	C₂³	—	4	2	no	—
853	C₂³	—	4	4	no	—
854	C₂³	—	4	8	no	—
855	C₂³	—	4	16	no	—
856	C₂³	—	4	16	no	—
857	C₂³	—	4	16	no	—
858	C₂³	C₂⁵×C₆₁	1	4	yes	—
859	C₂³	C₂⁵×C₆₁	1	2	yes	—
860	C₂³	C₂⁵×C₆₁	1	8	yes	—
861	C₂³	C₂⁵×C₆₁	1	8	yes	—
862	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
863	Q₈	—	2	8	no	—
864	Q₈	—	2	4	no	—
865	Q₈	—	4	4	no	—
866	Q₈	—	4	4	no	—
867	D₄	—	2	8	no	—
868	D₄	—	2	16	no	—
869	D₄	—	2	8	no	—
870	D₄	—	2	8	no	—
871	D₄	—	2	4	no	—
872	D₄	—	2	8	no	—
873	D₄	—	4	16	no	—
874	D₄	—	4	16	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	8	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	16	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	16	no	—
881	D₄	—	4	16	no	—
882	D₄	—	4	8	no	—
883	D₄	—	4	8	no	—
884	D₄	—	4	16	no	—
885	D₄	—	4	16	no	—
886	D₄	—	4	4	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	4	no	—
889	C₂×C₄	—	2	4	no	—
890	C₂×C₄	—	2	16	no	—
891	C₂×C₄	—	2	8	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	4	2	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	8	no	—
897	C₂×C₄	—	4	8	no	—
898	C₂×C₄	—	4	16	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	8	no	—
901	C₂×C₄	—	4	16	no	—
902	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
903	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
904	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
905	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
906	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
907	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
908	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
909	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
910	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
911	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
912	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	8	no	—
916	C₂²	—	2	4	no	—
917	C₂²	—	2	8	no	—
918	C₂²	—	2	8	no	—
919	C₂²	—	2	8	no	—
920	C₂²	—	2	8	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	8	no	—
923	C₂²	—	2	8	no	—
924	C₂²	—	8	2	no	—
925	C₂²	—	8	8	no	—
926	C₂²	—	8	8	no	—
927	C₂²	—	16	16	no	—
928	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
929	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
930	C₄	—	2	2	no	—
931	C₄	—	2	4	no	—
932	C₄	—	2	8	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	8	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	4	no	—
937	C₄	—	2	8	no	—
938	C₄	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
939	C₄	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
940	C₂	—	2	2	no	—
941	C₂	—	4	2	no	—
942	C₂	—	4	8	no	—
943	C₂	—	4	8	no	—
944	C₂	—	4	4	no	—
945	C₂	C₂²×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
946	C₂	C₆₁×H(7,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×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×#3562	C₂	semidirect
2. C₆₁×#3543	C₂	semidirect
3. C₆₁×#3542	C₂	semidirect
4. C₆₁×#3539	C₂	semidirect
5. C₆₁×#3537	C₂	semidirect
6. C₆₁×#3537	C₂	semidirect
7. C₆₁×#3534	C₂	semidirect
8. C₆₁×#3512	C₂	semidirect
9. C₆₁×#3506	C₂	semidirect
10. C₆₁×#3498	C₂	semidirect
11. C₆₁×#3496	C₂	semidirect
12. C₆₁×#3488	C₂	semidirect
13. C₆₁×#3455	C₂	semidirect
14. C₂×C₆₁×#540	C₂	semidirect
15. C₆₁×#3449	C₂	semidirect
16. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
17. C₂²×#41×C₆₁	C₂²	semidirect
18. C₆₁×#562	C₂²	semidirect
19. C₆₁×#560	C₂²	semidirect
20. C₆₁×#560	C₂²	semidirect
21. C₆₁×#560	C₂²	semidirect
22. C₆₁×#559	C₂²	semidirect
23. C₆₁×#556	C₂²	semidirect
24. C₆₁×#555	C₂²	semidirect
25. C₆₁×#553	C₂²	semidirect
26. C₆₁×#553	C₂²	semidirect
27. C₆₁×#553	C₂²	semidirect
28. C₆₁×#553	C₂²	semidirect
29. C₆₁×#552	C₂²	semidirect
30. C₆₁×#551	C₂²	semidirect
31. C₆₁×#550	C₂²	semidirect
32. C₆₁×#550	C₂²	semidirect
33. C₆₁×#550	C₂²	semidirect
34. C₆₁×#548	C₂²	semidirect
35. C₆₁×#547	C₂²	semidirect
36. C₆₁×#547	C₂²	semidirect
37. C₆₁×#547	C₂²	semidirect
38. C₆₁×#546	C₂²	semidirect
39. C₆₁×#546	C₂²	semidirect
40. C₆₁×#546	C₂²	semidirect
41. C₆₁×#546	C₂²	semidirect
42. C₆₁×#546	C₂²	semidirect
43. D₄²×C₆₁	C₂²	semidirect
44. D₄²×C₆₁	C₂²	semidirect
45. D₄²×C₆₁	C₂²	semidirect
46. D₄²×C₆₁	C₂²	semidirect
47. D₄²×C₆₁	C₂²	semidirect
48. D₄²×C₆₁	C₂²	semidirect
49. D₄²×C₆₁	C₂²	semidirect
50. C₆₁×#542	C₂²	semidirect
51. C₆₁×#541	C₂²	semidirect
52. C₆₁×#541	C₂²	semidirect
53. C₆₁×#540	C₂²	semidirect
54. C₆₁×#540	C₂²	semidirect
55. C₆₁×#540	C₂²	semidirect
56. C₆₁×#540	C₂²	semidirect
57. C₆₁×#540	C₂²	semidirect
58. C₆₁×#540	C₂²	semidirect
59. C₆₁×#540	C₂²	semidirect
60. C₆₁×#539	C₂²	semidirect
61. C₆₁×#539	C₂²	semidirect
62. C₆₁×#538	C₂²	semidirect
63. C₆₁×#538	C₂²	semidirect
64. C₆₁×#538	C₂²	semidirect
65. C₆₁×#538	C₂²	semidirect
66. C₆₁×#537	C₂²	semidirect
67. C₆₁×#537	C₂²	semidirect
68. C₆₁×#537	C₂²	semidirect
69. C₆₁×#536	C₂²	semidirect
70. C₆₁×#535	C₂²	semidirect
71. C₆₁×#535	C₂²	semidirect
72. C₆₁×#535	C₂²	semidirect
73. C₆₁×#535	C₂²	semidirect
74. C₆₁×#535	C₂²	semidirect
75. C₆₁×#534	C₂²	semidirect
76. C₆₁×#534	C₂²	semidirect
77. C₆₁×#534	C₂²	semidirect
78. C₆₁×#534	C₂²	semidirect
79. C₆₁×#533	C₂²	semidirect
80. C₆₁×#532	C₂²	semidirect
81. C₆₁×#532	C₂²	semidirect
82. C₆₁×#532	C₂²	semidirect
83. C₆₁×#532	C₂²	semidirect
84. C₂×#127×C₆₁	C₂²	semidirect
85. C₂×#127×C₆₁	C₂²	semidirect
86. C₆₁×#529	C₂²	semidirect
87. C₆₁×#529	C₂²	semidirect
88. C₂×#125×C₆₁	C₂²	semidirect
89. C₆₁×#525	C₂²	semidirect
90. C₆₁×#525	C₂²	semidirect
91. C₆₁×#525	C₂²	semidirect
92. C₆₁×#525	C₂²	semidirect
93. C₆₁×#525	C₂²	semidirect
94. C₂×#123×C₆₁	C₂²	semidirect
95. C₂×#121×C₆₁	C₂²	semidirect
96. C₂×#121×C₆₁	C₂²	semidirect
97. C₂×#121×C₆₁	C₂²	semidirect
98. C₂×#121×C₆₁	C₂²	semidirect
99. C₆₁×#520	C₂²	semidirect
100. C₄×#41×C₆₁	C₂²	semidirect
101. C₂×C₄×D₄×C₆₁	C₂²	semidirect
102. C₂×#117×C₆₁	C₂²	semidirect
439. #62880	C₆₁	direct (N × H)
467. #3562	C₂×C₆₁	semidirect
468. #3543	C₂×C₆₁	semidirect
469. #3542	C₂×C₆₁	semidirect
470. #3539	C₂×C₆₁	semidirect
471. #3537	C₂×C₆₁	semidirect
472. #3537	C₂×C₆₁	semidirect
473. #3534	C₂×C₆₁	semidirect
474. #3512	C₂×C₆₁	semidirect
475. #3506	C₂×C₆₁	semidirect
476. #3498	C₂×C₆₁	semidirect
477. #3496	C₂×C₆₁	semidirect
478. #3488	C₂×C₆₁	semidirect
479. #3455	C₂×C₆₁	semidirect
480. C₂×#540	C₂×C₆₁	semidirect
481. #3449	C₂×C₆₁	semidirect
489. C₂×H(5,𝔽₂)	C₂²×C₆₁	semidirect
490. C₂²×#41	C₂²×C₆₁	semidirect
491. #562	C₂²×C₆₁	semidirect
492. #560	C₂²×C₆₁	semidirect
493. #560	C₂²×C₆₁	semidirect
494. #560	C₂²×C₆₁	semidirect
495. #559	C₂²×C₆₁	semidirect
496. #556	C₂²×C₆₁	semidirect
497. #555	C₂²×C₆₁	semidirect
498. #553	C₂²×C₆₁	semidirect
499. #553	C₂²×C₆₁	semidirect
500. #553	C₂²×C₆₁	semidirect
501. #553	C₂²×C₆₁	semidirect
502. #552	C₂²×C₆₁	semidirect
503. #551	C₂²×C₆₁	semidirect
504. #550	C₂²×C₆₁	semidirect
505. #550	C₂²×C₆₁	semidirect
506. #550	C₂²×C₆₁	semidirect
507. #548	C₂²×C₆₁	semidirect
508. #547	C₂²×C₆₁	semidirect
509. #547	C₂²×C₆₁	semidirect
510. #547	C₂²×C₆₁	semidirect
511. #546	C₂²×C₆₁	semidirect
512. #546	C₂²×C₆₁	semidirect
513. #546	C₂²×C₆₁	semidirect
514. #546	C₂²×C₆₁	semidirect
515. #546	C₂²×C₆₁	semidirect
516. D₄²	C₂²×C₆₁	semidirect
517. D₄²	C₂²×C₆₁	semidirect
518. D₄²	C₂²×C₆₁	semidirect
519. D₄²	C₂²×C₆₁	semidirect
520. D₄²	C₂²×C₆₁	semidirect
521. D₄²	C₂²×C₆₁	semidirect
522. D₄²	C₂²×C₆₁	semidirect
523. #542	C₂²×C₆₁	semidirect
524. #541	C₂²×C₆₁	semidirect
525. #541	C₂²×C₆₁	semidirect
526. #540	C₂²×C₆₁	semidirect
527. #540	C₂²×C₆₁	semidirect
528. #540	C₂²×C₆₁	semidirect
529. #540	C₂²×C₆₁	semidirect
530. #540	C₂²×C₆₁	semidirect
531. #540	C₂²×C₆₁	semidirect
532. #540	C₂²×C₆₁	semidirect
533. #539	C₂²×C₆₁	semidirect
534. #539	C₂²×C₆₁	semidirect
535. #538	C₂²×C₆₁	semidirect
536. #538	C₂²×C₆₁	semidirect
537. #538	C₂²×C₆₁	semidirect
538. #538	C₂²×C₆₁	semidirect
539. #537	C₂²×C₆₁	semidirect
540. #537	C₂²×C₆₁	semidirect
541. #537	C₂²×C₆₁	semidirect
542. #536	C₂²×C₆₁	semidirect
543. #535	C₂²×C₆₁	semidirect
544. #535	C₂²×C₆₁	semidirect
545. #535	C₂²×C₆₁	semidirect
546. #535	C₂²×C₆₁	semidirect
547. #535	C₂²×C₆₁	semidirect
548. #534	C₂²×C₆₁	semidirect
549. #534	C₂²×C₆₁	semidirect
550. #534	C₂²×C₆₁	semidirect
551. #534	C₂²×C₆₁	semidirect
552. #533	C₂²×C₆₁	semidirect
553. #532	C₂²×C₆₁	semidirect
554. #532	C₂²×C₆₁	semidirect
555. #532	C₂²×C₆₁	semidirect
556. #532	C₂²×C₆₁	semidirect
557. C₂×#127	C₂²×C₆₁	semidirect
558. C₂×#127	C₂²×C₆₁	semidirect
559. #529	C₂²×C₆₁	semidirect
560. #529	C₂²×C₆₁	semidirect
561. C₂×#125	C₂²×C₆₁	semidirect
562. #525	C₂²×C₆₁	semidirect
563. #525	C₂²×C₆₁	semidirect
564. #525	C₂²×C₆₁	semidirect
565. #525	C₂²×C₆₁	semidirect
566. #525	C₂²×C₆₁	semidirect
567. C₂×#123	C₂²×C₆₁	semidirect
568. C₂×#121	C₂²×C₆₁	semidirect
569. C₂×#121	C₂²×C₆₁	semidirect
570. C₂×#121	C₂²×C₆₁	semidirect
571. C₂×#121	C₂²×C₆₁	semidirect
572. #520	C₂²×C₆₁	semidirect
573. C₄×#41	C₂²×C₆₁	semidirect
574. C₂×C₄×D₄	C₂²×C₆₁	semidirect
575. C₂×#117	C₂²×C₆₁	semidirect
576. C₆₁	#62880	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3562	2
C₆₁×#3543	2
C₆₁×#3542	2
C₆₁×#3539	2
C₆₁×#3537	2
C₆₁×#3534	2
C₆₁×#3512	2
C₆₁×#3506	2
C₆₁×#3498	2
C₆₁×#3496	2
C₆₁×#3488	2
C₆₁×#3455	2
C₂×C₆₁×#540	2
C₆₁×#3449	2
#62880	61

Subgroups — C61×#62880 #29566313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62880 #29566313