Subgroups — C₆₁×#35109 #29538542

Order 15616.

2044 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2856	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2651	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2635	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2540	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2516	C₂	1	2	yes	maximal, complemented
12	C₆₁×#2476	C₂	1	2	yes	maximal, complemented
13	C₆₁×#2471	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2464	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2426	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2423	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#2420	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#2333	C₂	1	2	yes	maximal, complemented
20	C₆₁×#2333	C₂	1	2	yes	maximal, complemented
21	C₄×#124×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#123×C₆₁	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₁	C₂²	1	2	yes	—
31	C₂×#121×C₆₁	C₂²	1	2	yes	—
32	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#121×C₆₁	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#117×C₆₁	C₂²	1	2	yes	—
44	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
46	C₆₁×#400	C₂²	1	2	yes	—
47	C₆₁×#399	C₂²	1	2	yes	—
48	C₆₁×#399	C₂²	1	2	yes	—
49	C₆₁×#398	C₂²	1	2	yes	—
50	C₆₁×#398	C₂²	1	2	yes	—
51	C₆₁×#397	C₂²	1	2	yes	—
52	C₆₁×#397	C₂²	1	2	yes	—
53	C₆₁×#396	C₂²	1	2	yes	—
54	C₆₁×#394	C₂²	1	2	yes	—
55	C₆₁×#394	C₂²	1	2	yes	—
56	C₆₁×#394	C₂²	1	2	yes	—
57	C₆₁×#394	C₂²	1	2	yes	—
58	C₆₁×#394	C₂²	1	2	yes	—
59	C₆₁×#392	C₂²	1	2	yes	—
60	C₆₁×#392	C₂²	1	2	yes	—
61	C₆₁×#392	C₂²	1	2	yes	—
62	C₆₁×#391	C₂²	1	1	yes	characteristic
63	C₆₁×#391	C₂²	1	1	yes	characteristic
64	C₆₁×#390	C₂²	1	2	yes	—
65	C₆₁×#390	C₂²	1	2	yes	—
66	C₆₁×#390	C₂²	1	1	yes	characteristic
67	C₆₁×#390	C₂²	1	1	yes	characteristic
68	C₆₁×#390	C₂²	1	1	yes	characteristic
69	C₆₁×#390	C₂²	1	1	yes	characteristic
70	C₆₁×#390	C₂²	1	2	yes	—
71	C₆₁×#390	C₂²	1	2	yes	—
72	C₆₁×#390	C₂²	1	2	yes	—
73	C₆₁×#389	C₂²	1	1	yes	characteristic
74	C₆₁×#389	C₂²	1	1	yes	characteristic
75	C₆₁×#389	C₂²	1	1	yes	characteristic
76	C₆₁×#389	C₂²	1	1	yes	characteristic
77	C₆₁×#388	C₂²	1	2	yes	—
78	C₆₁×#388	C₂²	1	2	yes	—
79	C₆₁×#388	C₂²	1	2	yes	—
80	C₆₁×#388	C₂²	1	2	yes	—
81	C₆₁×#388	C₂²	1	2	yes	—
82	C₆₁×#388	C₂²	1	2	yes	—
83	C₆₁×#388	C₂²	1	2	yes	—
84	C₆₁×#388	C₂²	1	2	yes	—
85	C₆₁×#388	C₂²	1	2	yes	—
86	C₆₁×#388	C₂²	1	2	yes	—
87	C₆₁×#387	C₂²	1	2	yes	—
88	C₆₁×#387	C₂²	1	2	yes	—
89	C₆₁×#387	C₂²	1	2	yes	—
90	C₆₁×#387	C₂²	1	2	yes	—
91	C₆₁×#387	C₂²	1	2	yes	—
92	C₆₁×#386	C₂²	1	2	yes	—
93	C₆₁×#386	C₂²	1	2	yes	—
94	C₆₁×#386	C₂²	1	2	yes	—
95	C₆₁×#386	C₂²	1	2	yes	—
96	C₆₁×#386	C₂²	1	2	yes	—
97	C₆₁×#386	C₂²	1	2	yes	—
98	C₆₁×#386	C₂²	1	2	yes	—
99	C₆₁×#386	C₂²	1	2	yes	—
100	C₆₁×#386	C₂²	1	2	yes	—
101	C₆₁×#385	C₂²	1	2	yes	—
102	C₆₁×#384	C₂²	1	1	yes	characteristic
103	C₆₁×#382	C₂²	1	1	yes	characteristic
104	C₆₁×#382	C₂²	1	1	yes	characteristic
105	C₆₁×#381	C₂²	1	2	yes	—
106	C₆₁×#381	C₂²	1	2	yes	—
107	C₆₁×#380	C₂²	1	1	yes	characteristic
108	C₆₁×#380	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
122	C₄³×C₆₁	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
128	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
130	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
131	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
132	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
140	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
141	#127×C₆₁	—	4	2	no	—
142	#124×C₆₁	—	2	4	no	—
143	#124×C₆₁	—	4	2	no	—
144	#123×C₆₁	—	4	4	no	—
145	C₂²⋊Q₈×C₆₁	—	4	2	no	—
146	C₂²⋊Q₈×C₆₁	—	4	2	no	—
147	#121×C₆₁	—	2	8	no	—
148	#121×C₆₁	—	2	8	no	—
149	#121×C₆₁	—	4	4	no	—
150	#121×C₆₁	—	4	2	no	—
151	#121×C₆₁	—	4	2	no	—
152	#121×C₆₁	—	4	2	no	—
153	#121×C₆₁	—	4	2	no	—
154	C₄×Q₈×C₆₁	—	4	2	no	—
155	C₄×D₄×C₆₁	—	2	4	no	—
156	C₄×D₄×C₆₁	—	2	4	no	—
157	C₄×D₄×C₆₁	—	2	4	no	—
158	C₄×D₄×C₆₁	—	2	4	no	—
159	C₄×D₄×C₆₁	—	4	2	no	—
160	#117×C₆₁	—	4	4	no	—
161	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₆₁	—	4	2	no	—
207	C₂×C₄²×C₆₁	—	4	2	no	—
208	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
220	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
223	#95×C₆₁	C₂³	1	1	yes	characteristic
224	#95×C₆₁	C₂³	1	1	yes	characteristic
225	#95×C₆₁	C₂³	1	1	yes	characteristic
226	#95×C₆₁	C₂³	1	1	yes	characteristic
227	#95×C₆₁	C₂³	1	1	yes	characteristic
228	#95×C₆₁	C₂³	1	1	yes	characteristic
229	#95×C₆₁	C₂³	1	2	yes	—
230	#95×C₆₁	C₂³	1	2	yes	—
231	#95×C₆₁	C₂³	1	2	yes	—
232	#95×C₆₁	C₂³	1	2	yes	—
233	#95×C₆₁	C₂³	1	2	yes	—
234	#95×C₆₁	C₂³	1	2	yes	—
235	#95×C₆₁	C₂³	1	2	yes	—
236	#95×C₆₁	C₂³	1	2	yes	—
237	#95×C₆₁	C₂³	1	2	yes	—
238	#95×C₆₁	C₂³	1	2	yes	—
239	#95×C₆₁	C₂³	1	2	yes	—
240	#95×C₆₁	C₂³	1	2	yes	—
241	#95×C₆₁	C₂³	1	2	yes	—
242	#95×C₆₁	C₂³	1	2	yes	—
243	#95×C₆₁	C₂³	1	2	yes	—
244	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
245	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
246	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₆₁	—	2	2	no	—
249	C₂×Q₈×C₆₁	—	2	2	no	—
250	C₂×Q₈×C₆₁	—	2	2	no	—
251	C₂×D₄×C₆₁	—	2	2	no	—
252	C₂×D₄×C₆₁	—	2	2	no	—
253	C₂×D₄×C₆₁	—	2	4	no	—
254	C₂×D₄×C₆₁	—	2	4	no	—
255	C₂×D₄×C₆₁	—	2	4	no	—
256	C₂×D₄×C₆₁	—	2	4	no	—
257	C₂×D₄×C₆₁	—	2	2	no	—
258	C₂×D₄×C₆₁	—	2	2	no	—
259	C₂×D₄×C₆₁	—	2	2	no	—
260	C₂×D₄×C₆₁	—	2	4	no	—
261	C₂×D₄×C₆₁	—	2	4	no	—
262	C₂×D₄×C₆₁	—	2	2	no	—
263	C₂×D₄×C₆₁	—	2	2	no	—
264	C₂×D₄×C₆₁	—	2	2	no	—
265	C₂×D₄×C₆₁	—	2	2	no	—
266	C₂×D₄×C₆₁	—	4	2	no	—
267	C₂×D₄×C₆₁	—	4	2	no	—
268	C₂×D₄×C₆₁	—	4	2	no	—
269	C₂×D₄×C₆₁	—	4	2	no	—
270	C₂×D₄×C₆₁	—	4	2	no	—
271	C₂×D₄×C₆₁	—	4	2	no	—
272	C₂×D₄×C₆₁	—	4	2	no	—
273	C₂×D₄×C₆₁	—	4	2	no	—
274	C₂×D₄×C₆₁	—	4	2	no	—
275	C₂×D₄×C₆₁	—	4	2	no	—
276	C₂×D₄×C₆₁	—	4	2	no	—
277	C₂×D₄×C₆₁	—	4	2	no	—
278	C₂²×C₄×C₆₁	—	2	2	no	—
279	C₂²×C₄×C₆₁	—	2	2	no	—
280	C₂²×C₄×C₆₁	—	2	2	no	—
281	C₂²×C₄×C₆₁	—	2	4	no	—
282	C₂²×C₄×C₆₁	—	2	2	no	—
283	C₂²×C₄×C₆₁	—	2	2	no	—
284	C₂²×C₄×C₆₁	—	2	2	no	—
285	C₂²×C₄×C₆₁	—	2	2	no	—
286	C₂²×C₄×C₆₁	—	2	2	no	—
287	C₂²×C₄×C₆₁	—	2	2	no	—
288	C₂²×C₄×C₆₁	—	2	2	no	—
289	C₂²×C₄×C₆₁	—	2	2	no	—
290	C₂²×C₄×C₆₁	—	2	4	no	—
291	C₂²×C₄×C₆₁	—	4	1	no	—
292	C₂²×C₄×C₆₁	—	4	1	no	—
293	C₂²×C₄×C₆₁	—	4	1	no	—
294	C₂²×C₄×C₆₁	—	4	1	no	—
295	C₂²×C₄×C₆₁	—	4	2	no	—
296	C₂²×C₄×C₆₁	—	4	1	no	—
297	C₂²×C₄×C₆₁	—	4	1	no	—
298	C₂²×C₄×C₆₁	—	4	2	no	—
299	C₂²×C₄×C₆₁	—	4	2	no	—
300	C₂²×C₄×C₆₁	—	4	2	no	—
301	C₂²×C₄×C₆₁	#41	1	4	yes	—
302	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₆₁	—	2	2	no	—
322	C₄⋊C₄×C₆₁	—	2	2	no	—
323	C₄⋊C₄×C₆₁	—	2	2	no	—
324	C₄⋊C₄×C₆₁	—	2	2	no	—
325	C₄⋊C₄×C₆₁	—	2	4	no	—
326	C₄⋊C₄×C₆₁	—	2	4	no	—
327	C₄⋊C₄×C₆₁	—	2	4	no	—
328	C₄⋊C₄×C₆₁	—	2	2	no	—
329	C₄⋊C₄×C₆₁	—	2	2	no	—
330	C₄⋊C₄×C₆₁	—	2	2	no	—
331	C₄⋊C₄×C₆₁	—	2	2	no	—
332	C₄⋊C₄×C₆₁	—	4	2	no	—
333	C₄⋊C₄×C₆₁	—	4	2	no	—
334	C₄⋊C₄×C₆₁	—	4	2	no	—
335	C₄⋊C₄×C₆₁	—	4	2	no	—
336	C₄⋊C₄×C₆₁	—	4	2	no	—
337	C₄⋊C₄×C₆₁	—	4	2	no	—
338	C₂²⋊C₄×C₆₁	—	2	2	no	—
339	C₂²⋊C₄×C₆₁	—	2	2	no	—
340	C₂²⋊C₄×C₆₁	—	2	2	no	—
341	C₂²⋊C₄×C₆₁	—	2	4	no	—
342	C₂²⋊C₄×C₆₁	—	2	2	no	—
343	C₂²⋊C₄×C₆₁	—	2	2	no	—
344	C₂²⋊C₄×C₆₁	—	2	4	no	—
345	C₂²⋊C₄×C₆₁	—	2	4	no	—
346	C₂²⋊C₄×C₆₁	—	2	4	no	—
347	C₂²⋊C₄×C₆₁	—	2	4	no	—
348	C₂²⋊C₄×C₆₁	—	2	4	no	—
349	C₂²⋊C₄×C₆₁	—	2	4	no	—
350	C₂²⋊C₄×C₆₁	—	2	4	no	—
351	C₂²⋊C₄×C₆₁	—	4	2	no	—
352	C₂²⋊C₄×C₆₁	—	4	2	no	—
353	C₂²⋊C₄×C₆₁	—	4	2	no	—
354	C₂²⋊C₄×C₆₁	—	4	2	no	—
355	C₂²⋊C₄×C₆₁	—	4	2	no	—
356	C₂²⋊C₄×C₆₁	—	4	2	no	—
357	C₂²⋊C₄×C₆₁	—	4	2	no	—
358	C₂²⋊C₄×C₆₁	—	4	2	no	—
359	C₂²⋊C₄×C₆₁	—	4	2	no	—
360	C₂²⋊C₄×C₆₁	—	4	2	no	—
361	C₂²⋊C₄×C₆₁	—	4	2	no	—
362	C₂²⋊C₄×C₆₁	—	4	2	no	—
363	C₂²⋊C₄×C₆₁	—	4	2	no	—
364	C₂²⋊C₄×C₆₁	—	4	2	no	—
365	C₂²⋊C₄×C₆₁	#41	1	4	yes	—
366	C₄²×C₆₁	—	2	2	no	—
367	C₄²×C₆₁	—	2	2	no	—
368	C₄²×C₆₁	—	2	2	no	—
369	C₄²×C₆₁	—	2	2	no	—
370	C₄²×C₆₁	—	2	2	no	—
371	C₄²×C₆₁	—	2	2	no	—
372	C₄²×C₆₁	—	2	2	no	—
373	C₄²×C₆₁	—	4	1	no	—
374	C₄²×C₆₁	—	4	1	no	—
375	C₄²×C₆₁	—	4	1	no	—
376	C₄²×C₆₁	—	4	1	no	—
377	C₄²×C₆₁	—	4	1	no	—
378	C₄²×C₆₁	—	4	2	no	—
379	C₄²×C₆₁	—	4	2	no	—
380	C₄²×C₆₁	#41	1	4	yes	—
381	C₂³×C₆₁	—	2	1	no	—
382	C₂³×C₆₁	—	2	1	no	—
383	C₂³×C₆₁	—	2	1	no	—
384	C₂³×C₆₁	—	2	1	no	—
385	C₂³×C₆₁	—	2	1	no	—
386	C₂³×C₆₁	—	2	1	no	—
387	C₂³×C₆₁	—	2	1	no	—
388	C₂³×C₆₁	—	2	1	no	—
389	C₂³×C₆₁	—	2	1	no	—
390	C₂³×C₆₁	—	2	1	no	—
391	C₂³×C₆₁	—	2	1	no	—
392	C₂³×C₆₁	—	2	1	no	—
393	C₂³×C₆₁	—	2	2	no	—
394	C₂³×C₆₁	—	2	2	no	—
395	C₂³×C₆₁	—	2	2	no	—
396	C₂³×C₆₁	—	2	2	no	—
397	C₂³×C₆₁	—	2	2	no	—
398	C₂³×C₆₁	—	2	2	no	—
399	C₂³×C₆₁	—	2	2	no	—
400	C₂³×C₆₁	—	2	2	no	—
401	C₂³×C₆₁	—	2	2	no	—
402	C₂³×C₆₁	—	2	2	no	—
403	C₂³×C₆₁	—	2	2	no	—
404	C₂³×C₆₁	—	2	2	no	—
405	C₂³×C₆₁	—	2	2	no	—
406	C₂³×C₆₁	—	2	2	no	—
407	C₂³×C₆₁	C₂×#41	1	2	yes	—
408	C₂³×C₆₁	C₂×#41	1	2	yes	—
409	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
410	Q₈×C₆₁	—	4	4	no	—
411	D₄×C₆₁	—	2	8	no	—
412	D₄×C₆₁	—	4	4	no	—
413	D₄×C₆₁	—	4	4	no	—
414	D₄×C₆₁	—	8	4	no	—
415	D₄×C₆₁	—	8	4	no	—
416	D₄×C₆₁	—	8	4	no	—
417	D₄×C₆₁	—	8	4	no	—
418	D₄×C₆₁	—	8	4	no	—
419	D₄×C₆₁	—	8	4	no	—
420	C₂×C₄×C₆₁	—	2	1	no	—
421	C₂×C₄×C₆₁	—	2	1	no	—
422	C₂×C₄×C₆₁	—	2	1	no	—
423	C₂×C₄×C₆₁	—	2	1	no	—
424	C₂×C₄×C₆₁	—	2	1	no	—
425	C₂×C₄×C₆₁	—	2	1	no	—
426	C₂×C₄×C₆₁	—	2	1	no	—
427	C₂×C₄×C₆₁	—	2	1	no	—
428	C₂×C₄×C₆₁	—	2	1	no	—
429	C₂×C₄×C₆₁	—	2	1	no	—
430	C₂×C₄×C₆₁	—	2	1	no	—
431	C₂×C₄×C₆₁	—	2	1	no	—
432	C₂×C₄×C₆₁	—	2	1	no	—
433	C₂×C₄×C₆₁	—	2	1	no	—
434	C₂×C₄×C₆₁	—	2	1	no	—
435	C₂×C₄×C₆₁	—	2	2	no	—
436	C₂×C₄×C₆₁	—	2	1	no	—
437	C₂×C₄×C₆₁	—	2	1	no	—
438	C₂×C₄×C₆₁	—	2	2	no	—
439	C₂×C₄×C₆₁	—	2	1	no	—
440	C₂×C₄×C₆₁	—	2	1	no	—
441	C₂×C₄×C₆₁	—	2	2	no	—
442	C₂×C₄×C₆₁	—	2	2	no	—
443	C₂×C₄×C₆₁	—	2	2	no	—
444	C₂×C₄×C₆₁	—	2	2	no	—
445	C₂×C₄×C₆₁	—	2	1	no	—
446	C₂×C₄×C₆₁	—	2	1	no	—
447	C₂×C₄×C₆₁	—	2	1	no	—
448	C₂×C₄×C₆₁	—	2	1	no	—
449	C₂×C₄×C₆₁	—	2	1	no	—
450	C₂×C₄×C₆₁	—	2	1	no	—
451	C₂×C₄×C₆₁	—	2	2	no	—
452	C₂×C₄×C₆₁	—	2	2	no	—
453	C₂×C₄×C₆₁	—	2	2	no	—
454	C₂×C₄×C₆₁	—	2	2	no	—
455	C₂×C₄×C₆₁	—	2	2	no	—
456	C₂×C₄×C₆₁	—	2	1	no	—
457	C₂×C₄×C₆₁	—	2	2	no	—
458	C₂×C₄×C₆₁	—	2	2	no	—
459	C₂×C₄×C₆₁	—	2	2	no	—
460	C₂×C₄×C₆₁	—	2	2	no	—
461	C₂×C₄×C₆₁	—	2	2	no	—
462	C₂×C₄×C₆₁	—	2	1	no	—
463	C₂×C₄×C₆₁	—	2	1	no	—
464	C₂×C₄×C₆₁	—	2	2	no	—
465	C₂×C₄×C₆₁	—	2	1	no	—
466	C₂×C₄×C₆₁	—	2	2	no	—
467	C₂×C₄×C₆₁	—	4	4	no	—
468	C₂×C₄×C₆₁	—	4	4	no	—
469	C₂×C₄×C₆₁	—	4	4	no	—
470	C₂×C₄×C₆₁	—	4	8	no	—
471	C₂×C₄×C₆₁	—	4	4	no	—
472	C₂×C₄×C₆₁	—	4	4	no	—
473	C₂×C₄×C₆₁	—	4	4	no	—
474	C₂×C₄×C₆₁	—	8	4	no	—
475	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
476	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
477	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
478	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
479	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
480	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
481	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
482	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
483	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
484	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
485	#35109	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
486	C₂²×C₆₁	—	2	2	no	—
487	C₂²×C₆₁	—	2	2	no	—
488	C₂²×C₆₁	—	2	2	no	—
489	C₂²×C₆₁	—	2	2	no	—
490	C₂²×C₆₁	—	2	2	no	—
491	C₂²×C₆₁	—	2	2	no	—
492	C₂²×C₆₁	—	4	1	no	—
493	C₂²×C₆₁	—	4	1	no	—
494	C₂²×C₆₁	—	4	1	no	—
495	C₂²×C₆₁	—	4	1	no	—
496	C₂²×C₆₁	—	4	1	no	—
497	C₂²×C₆₁	—	4	1	no	—
498	C₂²×C₆₁	—	4	1	no	—
499	C₂²×C₆₁	—	4	1	no	—
500	C₂²×C₆₁	—	4	2	no	—
501	C₂²×C₆₁	—	4	2	no	—
502	C₂²×C₆₁	—	4	2	no	—
503	C₂²×C₆₁	—	4	2	no	—
504	C₂²×C₆₁	—	4	2	no	—
505	C₂²×C₆₁	—	4	2	no	—
506	C₂²×C₆₁	—	4	2	no	—
507	C₂²×C₆₁	—	4	2	no	—
508	C₂²×C₆₁	—	4	2	no	—
509	C₂²×C₆₁	—	4	2	no	—
510	C₂²×C₆₁	—	4	2	no	—
511	C₂²×C₆₁	—	4	2	no	—
512	C₂²×C₆₁	—	4	2	no	—
513	C₂²×C₆₁	—	4	2	no	—
514	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
515	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
516	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
517	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
520	C₂²×C₆₁	#585	1	1	yes	characteristic
521	C₄×C₆₁	—	2	2	no	—
522	C₄×C₆₁	—	2	2	no	—
523	C₄×C₆₁	—	2	2	no	—
524	C₄×C₆₁	—	2	2	no	—
525	C₄×C₆₁	—	2	2	no	—
526	C₄×C₆₁	—	2	2	no	—
527	C₄×C₆₁	—	2	2	no	—
528	C₄×C₆₁	—	4	1	no	—
529	C₄×C₆₁	—	4	1	no	—
530	C₄×C₆₁	—	4	2	no	—
531	C₄×C₆₁	—	4	2	no	—
532	C₄×C₆₁	—	4	1	no	—
533	C₄×C₆₁	—	4	1	no	—
534	C₄×C₆₁	—	4	2	no	—
535	C₄×C₆₁	—	4	2	no	—
536	C₄×C₆₁	—	4	2	no	—
537	C₄×C₆₁	—	4	1	no	—
538	C₄×C₆₁	—	4	2	no	—
539	C₄×C₆₁	#540	1	4	yes	—
540	#2856	C₂×C₆₁	1	1	yes	characteristic, complemented
541	#2855	C₂×C₆₁	1	1	yes	characteristic, complemented
542	#2854	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#2850	C₂×C₆₁	1	1	yes	characteristic, complemented
544	#2651	C₂×C₆₁	1	2	yes	complemented
545	#2635	C₂×C₆₁	1	2	yes	complemented
546	#2570	C₂×C₆₁	1	1	yes	characteristic, complemented
547	#2544	C₂×C₆₁	1	1	yes	characteristic, complemented
548	#2540	C₂×C₆₁	1	1	yes	characteristic, complemented
549	#2535	C₂×C₆₁	1	1	yes	characteristic, complemented
550	#2516	C₂×C₆₁	1	2	yes	complemented
551	#2476	C₂×C₆₁	1	2	yes	complemented
552	#2471	C₂×C₆₁	1	2	yes	complemented
553	#2464	C₂×C₆₁	1	2	yes	complemented
554	#2428	C₂×C₆₁	1	1	yes	characteristic, complemented
555	#2426	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#2423	C₂×C₆₁	1	1	yes	characteristic, complemented
557	#2420	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#2333	C₂×C₆₁	1	2	yes	complemented
559	#2333	C₂×C₆₁	1	2	yes	complemented
560	C₄×#124	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#2293	C₂×C₆₁	1	1	yes	characteristic, complemented
562	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
563	C₂×C₆₁	—	4	2	no	—
564	C₂×C₆₁	—	4	2	no	—
565	C₂×C₆₁	—	8	2	no	—
566	C₂×C₆₁	—	8	2	no	—
567	C₂×C₆₁	#3444	1	1	yes	characteristic
568	C₂×C₆₁	C₂×#540	1	1	yes	characteristic
569	C₂×C₆₁	#3460	1	1	yes	characteristic
570	C₂×C₆₁	#3505	1	1	yes	characteristic
571	C₂×C₆₁	#3508	1	1	yes	characteristic
572	C₂×C₆₁	#3514	1	1	yes	characteristic
573	C₂×C₆₁	#3519	1	1	yes	characteristic
574	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
575	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
576	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
577	C₂×#123	C₂²×C₆₁	1	2	yes	—
578	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
579	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
580	C₂×#121	C₂²×C₆₁	1	2	yes	—
581	C₂×#121	C₂²×C₆₁	1	2	yes	—
582	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
583	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
584	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
585	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
586	C₂×#121	C₂²×C₆₁	1	2	yes	—
587	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
588	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
589	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
590	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
591	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
592	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
593	C₂×#117	C₂²×C₆₁	1	2	yes	—
594	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
595	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
596	#400	C₂²×C₆₁	1	2	yes	—
597	#399	C₂²×C₆₁	1	2	yes	—
598	#399	C₂²×C₆₁	1	2	yes	—
599	#398	C₂²×C₆₁	1	2	yes	—
600	#398	C₂²×C₆₁	1	2	yes	—
601	#397	C₂²×C₆₁	1	2	yes	—
602	#397	C₂²×C₆₁	1	2	yes	—
603	#396	C₂²×C₆₁	1	2	yes	—
604	#394	C₂²×C₆₁	1	2	yes	—
605	#394	C₂²×C₆₁	1	2	yes	—
606	#394	C₂²×C₆₁	1	2	yes	—
607	#394	C₂²×C₆₁	1	2	yes	—
608	#394	C₂²×C₆₁	1	2	yes	—
609	#392	C₂²×C₆₁	1	2	yes	—
610	#392	C₂²×C₆₁	1	2	yes	—
611	#392	C₂²×C₆₁	1	2	yes	—
612	#391	C₂²×C₆₁	1	1	yes	characteristic
613	#391	C₂²×C₆₁	1	1	yes	characteristic
614	#390	C₂²×C₆₁	1	2	yes	—
615	#390	C₂²×C₆₁	1	2	yes	—
616	#390	C₂²×C₆₁	1	2	yes	—
617	#390	C₂²×C₆₁	1	2	yes	—
618	#390	C₂²×C₆₁	1	1	yes	characteristic
619	#390	C₂²×C₆₁	1	1	yes	characteristic
620	#390	C₂²×C₆₁	1	1	yes	characteristic
621	#390	C₂²×C₆₁	1	2	yes	—
622	#390	C₂²×C₆₁	1	1	yes	characteristic
623	#389	C₂²×C₆₁	1	1	yes	characteristic
624	#389	C₂²×C₆₁	1	1	yes	characteristic
625	#389	C₂²×C₆₁	1	1	yes	characteristic
626	#389	C₂²×C₆₁	1	1	yes	characteristic
627	#388	C₂²×C₆₁	1	2	yes	—
628	#388	C₂²×C₆₁	1	2	yes	—
629	#388	C₂²×C₆₁	1	2	yes	—
630	#388	C₂²×C₆₁	1	2	yes	—
631	#388	C₂²×C₆₁	1	2	yes	—
632	#388	C₂²×C₆₁	1	2	yes	—
633	#388	C₂²×C₆₁	1	2	yes	—
634	#388	C₂²×C₆₁	1	2	yes	—
635	#388	C₂²×C₆₁	1	2	yes	—
636	#388	C₂²×C₆₁	1	2	yes	—
637	#387	C₂²×C₆₁	1	2	yes	—
638	#387	C₂²×C₆₁	1	2	yes	—
639	#387	C₂²×C₆₁	1	2	yes	—
640	#387	C₂²×C₆₁	1	2	yes	—
641	#387	C₂²×C₆₁	1	2	yes	—
642	#386	C₂²×C₆₁	1	2	yes	—
643	#386	C₂²×C₆₁	1	2	yes	—
644	#386	C₂²×C₆₁	1	2	yes	—
645	#386	C₂²×C₆₁	1	2	yes	—
646	#386	C₂²×C₆₁	1	2	yes	—
647	#386	C₂²×C₆₁	1	2	yes	—
648	#386	C₂²×C₆₁	1	2	yes	—
649	#386	C₂²×C₆₁	1	2	yes	—
650	#386	C₂²×C₆₁	1	2	yes	—
651	#385	C₂²×C₆₁	1	2	yes	—
652	#384	C₂²×C₆₁	1	1	yes	characteristic
653	#382	C₂²×C₆₁	1	1	yes	characteristic
654	#382	C₂²×C₆₁	1	1	yes	characteristic
655	#381	C₂²×C₆₁	1	2	yes	—
656	#381	C₂²×C₆₁	1	2	yes	—
657	#380	C₂²×C₆₁	1	1	yes	characteristic
658	#380	C₂²×C₆₁	1	1	yes	characteristic
659	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
660	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
661	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
662	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
663	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
664	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
665	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
666	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
667	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
668	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
669	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
670	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
671	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
672	C₄³	C₂²×C₆₁	1	1	yes	characteristic
673	C₆₁	#35109	1	1	yes	characteristic, direct product factor, Sylow
674	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
676	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
677	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
678	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
679	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
680	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
681	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
682	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
683	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
684	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
688	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
689	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
690	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
691	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
692	#127	—	4	2	no	—
693	#124	—	2	4	no	—
694	#124	—	4	2	no	—
695	#123	—	4	4	no	—
696	C₂²⋊Q₈	—	4	2	no	—
697	C₂²⋊Q₈	—	4	2	no	—
698	#121	—	2	8	no	—
699	#121	—	2	8	no	—
700	#121	—	4	4	no	—
701	#121	—	4	2	no	—
702	#121	—	4	2	no	—
703	#121	—	4	2	no	—
704	#121	—	4	2	no	—
705	C₄×Q₈	—	4	2	no	—
706	C₄×D₄	—	2	4	no	—
707	C₄×D₄	—	2	4	no	—
708	C₄×D₄	—	2	4	no	—
709	C₄×D₄	—	2	4	no	—
710	C₄×D₄	—	4	2	no	—
711	#117	—	4	4	no	—
712	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	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	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
731	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
733	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
734	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
735	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
757	C₂×C₄²	—	4	2	no	—
758	C₂×C₄²	—	4	2	no	—
759	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
760	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
765	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
767	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
768	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
774	#95	C₂³×C₆₁	1	1	yes	characteristic
775	#95	C₂³×C₆₁	1	1	yes	characteristic
776	#95	C₂³×C₆₁	1	1	yes	characteristic
777	#95	C₂³×C₆₁	1	1	yes	characteristic
778	#95	C₂³×C₆₁	1	1	yes	characteristic
779	#95	C₂³×C₆₁	1	1	yes	characteristic
780	#95	C₂³×C₆₁	1	2	yes	—
781	#95	C₂³×C₆₁	1	2	yes	—
782	#95	C₂³×C₆₁	1	2	yes	—
783	#95	C₂³×C₆₁	1	2	yes	—
784	#95	C₂³×C₆₁	1	2	yes	—
785	#95	C₂³×C₆₁	1	2	yes	—
786	#95	C₂³×C₆₁	1	2	yes	—
787	#95	C₂³×C₆₁	1	2	yes	—
788	#95	C₂³×C₆₁	1	2	yes	—
789	#95	C₂³×C₆₁	1	2	yes	—
790	#95	C₂³×C₆₁	1	2	yes	—
791	#95	C₂³×C₆₁	1	2	yes	—
792	#95	C₂³×C₆₁	1	2	yes	—
793	#95	C₂³×C₆₁	1	2	yes	—
794	#95	C₂³×C₆₁	1	2	yes	—
795	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
796	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
797	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
798	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	4	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	4	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	4	1	no	—
843	C₂²×C₄	—	4	1	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	1	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	1	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	#41×C₆₁	1	4	yes	—
853	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
863	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	4	no	—
877	C₄⋊C₄	—	2	4	no	—
878	C₄⋊C₄	—	2	4	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	4	2	no	—
884	C₄⋊C₄	—	4	2	no	—
885	C₄⋊C₄	—	4	2	no	—
886	C₄⋊C₄	—	4	2	no	—
887	C₄⋊C₄	—	4	2	no	—
888	C₄⋊C₄	—	4	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	4	2	no	—
903	C₂²⋊C₄	—	4	2	no	—
904	C₂²⋊C₄	—	4	2	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	#41×C₆₁	1	4	yes	—
917	C₄²	—	2	2	no	—
918	C₄²	—	2	2	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	2	no	—
921	C₄²	—	2	2	no	—
922	C₄²	—	2	2	no	—
923	C₄²	—	2	2	no	—
924	C₄²	—	4	1	no	—
925	C₄²	—	4	1	no	—
926	C₄²	—	4	1	no	—
927	C₄²	—	4	1	no	—
928	C₄²	—	4	2	no	—
929	C₄²	—	4	2	no	—
930	C₄²	—	4	1	no	—
931	C₄²	#41×C₆₁	1	4	yes	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	C₂×#41×C₆₁	1	2	yes	—
959	C₂³	C₂×#41×C₆₁	1	2	yes	—
960	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
961	Q₈	—	4	4	no	—
962	D₄	—	2	8	no	—
963	D₄	—	4	4	no	—
964	D₄	—	4	4	no	—
965	D₄	—	8	4	no	—
966	D₄	—	8	4	no	—
967	D₄	—	8	4	no	—
968	D₄	—	8	4	no	—
969	D₄	—	8	4	no	—
970	D₄	—	8	4	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	8	no	—
1022	C₂×C₄	—	4	4	no	—
1023	C₂×C₄	—	4	4	no	—
1024	C₂×C₄	—	4	4	no	—
1025	C₂×C₄	—	8	4	no	—
1026	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1027	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1028	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1029	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1030	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1031	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1032	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1033	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1034	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1035	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1065	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1066	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1067	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1068	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1069	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1070	C₂²	C₆₁×#585	1	1	yes	characteristic
1071	C₄	—	2	2	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	2	no	—
1089	C₄	C₆₁×#540	1	4	yes	—
1090	C₂	—	4	2	no	—
1091	C₂	—	4	2	no	—
1092	C₂	—	8	2	no	—
1093	C₂	—	8	2	no	—
1094	C₂	C₆₁×#3444	1	1	yes	characteristic
1095	C₂	C₂×C₆₁×#540	1	1	yes	characteristic
1096	C₂	C₆₁×#3460	1	1	yes	characteristic
1097	C₂	C₆₁×#3505	1	1	yes	characteristic
1098	C₂	C₆₁×#3508	1	1	yes	characteristic
1099	C₂	C₆₁×#3514	1	1	yes	characteristic
1100	C₂	C₆₁×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2856	C₂	semidirect
2. C₆₁×#2855	C₂	semidirect
3. C₆₁×#2854	C₂	semidirect
4. C₆₁×#2850	C₂	semidirect
5. C₆₁×#2651	C₂	semidirect
6. C₆₁×#2635	C₂	semidirect
7. C₆₁×#2570	C₂	semidirect
8. C₆₁×#2544	C₂	semidirect
9. C₆₁×#2540	C₂	semidirect
10. C₆₁×#2535	C₂	semidirect
11. C₆₁×#2516	C₂	semidirect
12. C₆₁×#2476	C₂	semidirect
13. C₆₁×#2471	C₂	semidirect
14. C₆₁×#2464	C₂	semidirect
15. C₆₁×#2428	C₂	semidirect
16. C₆₁×#2426	C₂	semidirect
17. C₆₁×#2423	C₂	semidirect
18. C₆₁×#2420	C₂	semidirect
19. C₆₁×#2333	C₂	semidirect
20. C₆₁×#2333	C₂	semidirect
21. C₄×#124×C₆₁	C₂	semidirect
22. C₆₁×#2293	C₂	semidirect
23. C₄²×D₄×C₆₁	C₂	semidirect
485. #35109	C₆₁	direct (N × H)
540. #2856	C₂×C₆₁	semidirect
541. #2855	C₂×C₆₁	semidirect
542. #2854	C₂×C₆₁	semidirect
543. #2850	C₂×C₆₁	semidirect
544. #2651	C₂×C₆₁	semidirect
545. #2635	C₂×C₆₁	semidirect
546. #2570	C₂×C₆₁	semidirect
547. #2544	C₂×C₆₁	semidirect
548. #2540	C₂×C₆₁	semidirect
549. #2535	C₂×C₆₁	semidirect
550. #2516	C₂×C₆₁	semidirect
551. #2476	C₂×C₆₁	semidirect
552. #2471	C₂×C₆₁	semidirect
553. #2464	C₂×C₆₁	semidirect
554. #2428	C₂×C₆₁	semidirect
555. #2426	C₂×C₆₁	semidirect
556. #2423	C₂×C₆₁	semidirect
557. #2420	C₂×C₆₁	semidirect
558. #2333	C₂×C₆₁	semidirect
559. #2333	C₂×C₆₁	semidirect
560. C₄×#124	C₂×C₆₁	semidirect
561. #2293	C₂×C₆₁	semidirect
562. C₄²×D₄	C₂×C₆₁	semidirect
673. C₆₁	#35109	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×#2856	2
C₆₁×#2855	2
C₆₁×#2854	2
C₆₁×#2850	2
C₆₁×#2651	2
C₆₁×#2635	2
C₆₁×#2570	2
C₆₁×#2544	2
C₆₁×#2540	2
C₆₁×#2535	2
C₆₁×#2516	2
C₆₁×#2476	2
C₆₁×#2471	2
C₆₁×#2464	2
C₆₁×#2428	2
C₆₁×#2426	2
C₆₁×#2423	2
C₆₁×#2420	2
C₆₁×#2333	2
C₄×#124×C₆₁	2
C₆₁×#2293	2
C₄²×D₄×C₆₁	2
#35109	61

Subgroups — C61×#35109 #29538542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#35109 #29538542