Subgroups — C₆₁×#62858 #29566291

Order 15616.

7310 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3524	C₂	1	4	yes	maximal, complemented
2	C₆₁×#3519	C₂	1	12	yes	maximal, complemented
3	C₆₁×#3517	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3513	C₂	1	12	yes	maximal, complemented
5	C₆₁×#3512	C₂	1	3	yes	maximal, complemented
6	C₆₁×#3508	C₂	1	3	yes	maximal, complemented
7	C₆₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3494	C₂	1	6	yes	maximal, complemented
10	C₆₁×#3488	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3460	C₂	1	6	yes	maximal, complemented
12	C₆₁×#3455	C₂	1	3	yes	maximal, complemented
13	C₂×C₆₁×#540	C₂	1	3	yes	maximal, complemented
14	C₄×H(5,𝔽₂)×C₆₁	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	2	yes	—
17	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#559	C₂²	1	12	yes	complemented
19	C₆₁×#557	C₂²	1	4	yes	complemented
20	C₆₁×#555	C₂²	1	12	yes	complemented
21	C₆₁×#554	C₂²	1	12	yes	complemented
22	C₆₁×#553	C₂²	1	12	yes	complemented
23	C₆₁×#553	C₂²	1	12	yes	complemented
24	C₆₁×#553	C₂²	1	24	yes	complemented
25	C₆₁×#553	C₂²	1	12	yes	complemented
26	C₆₁×#552	C₂²	1	12	yes	complemented
27	C₆₁×#551	C₂²	1	24	yes	complemented
28	C₆₁×#550	C₂²	1	4	yes	complemented
29	C₆₁×#550	C₂²	1	4	yes	complemented
30	C₆₁×#550	C₂²	1	12	yes	complemented
31	C₆₁×#548	C₂²	1	4	yes	complemented
32	C₆₁×#547	C₂²	1	12	yes	complemented
33	C₆₁×#546	C₂²	1	12	yes	complemented
34	C₆₁×#546	C₂²	1	24	yes	complemented
35	C₆₁×#546	C₂²	1	24	yes	complemented
36	D₄²×C₆₁	C₂²	1	12	yes	complemented
37	D₄²×C₆₁	C₂²	1	12	yes	complemented
38	C₆₁×#544	C₂²	1	6	yes	complemented
39	C₆₁×#542	C₂²	1	6	yes	complemented
40	C₆₁×#542	C₂²	1	6	yes	complemented
41	C₆₁×#542	C₂²	1	12	yes	complemented
42	C₆₁×#541	C₂²	1	1	yes	characteristic, complemented
43	C₆₁×#541	C₂²	1	3	yes	complemented
44	C₆₁×#540	C₂²	1	3	yes	complemented
45	C₆₁×#540	C₂²	1	6	yes	complemented
46	C₆₁×#540	C₂²	1	6	yes	complemented
47	C₆₁×#540	C₂²	1	6	yes	complemented
48	C₆₁×#540	C₂²	1	12	yes	complemented
49	C₆₁×#540	C₂²	1	12	yes	complemented
50	C₆₁×#540	C₂²	1	3	yes	complemented
51	C₆₁×#540	C₂²	1	12	yes	complemented
52	C₆₁×#539	C₂²	1	12	yes	complemented
53	C₆₁×#538	C₂²	1	12	yes	complemented
54	C₆₁×#538	C₂²	1	24	yes	complemented
55	C₆₁×#537	C₂²	1	6	yes	complemented
56	C₆₁×#535	C₂²	1	6	yes	complemented
57	C₆₁×#535	C₂²	1	6	yes	complemented
58	C₆₁×#533	C₂²	1	3	yes	complemented
59	C₆₁×#532	C₂²	1	3	yes	complemented
60	C₆₁×#532	C₂²	1	12	yes	complemented
61	C₆₁×#532	C₂²	1	12	yes	complemented
62	C₂×#127×C₆₁	C₂²	1	3	yes	complemented
63	C₆₁×#529	C₂²	1	12	yes	complemented
64	C₆₁×#529	C₂²	1	12	yes	complemented
65	C₆₁×#529	C₂²	1	12	yes	complemented
66	C₆₁×#529	C₂²	1	12	yes	complemented
67	C₂×#125×C₆₁	C₂²	1	3	yes	complemented
68	C₆₁×#525	C₂²	1	6	yes	complemented
69	C₆₁×#525	C₂²	1	24	yes	complemented
70	C₂×#123×C₆₁	C₂²	1	12	yes	complemented
71	C₂×#121×C₆₁	C₂²	1	6	yes	complemented
72	C₂×#121×C₆₁	C₂²	1	12	yes	complemented
73	C₆₁×#520	C₂²	1	2	yes	—
74	C₆₁×#520	C₂²	1	6	yes	complemented
75	C₆₁×#520	C₂²	1	2	yes	complemented
76	C₆₁×#520	C₂²	1	6	yes	complemented
77	C₆₁×#520	C₂²	1	4	yes	complemented
78	C₆₁×#519	C₂²	1	2	yes	complemented
79	C₆₁×#518	C₂²	1	6	yes	complemented
80	C₆₁×#518	C₂²	1	6	yes	complemented
81	C₆₁×#518	C₂²	1	12	yes	complemented
82	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
83	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
84	C₄×#41×C₆₁	C₂²	1	3	yes	complemented
85	C₄×#41×C₆₁	C₂²	1	3	yes	complemented
86	C₄×#41×C₆₁	C₂²	1	6	yes	complemented
87	C₄×#41×C₆₁	C₂²	1	4	yes	complemented
88	C₂×C₄×D₄×C₆₁	C₂²	1	6	yes	complemented
89	C₂×C₄×D₄×C₆₁	C₂²	1	12	yes	complemented
90	C₂×#117×C₆₁	C₂²	1	3	yes	complemented
91	C₂×#117×C₆₁	C₂²	1	3	yes	complemented
92	H(5,𝔽₂)×C₆₁	—	2	16	no	—
93	C₂×#41×C₆₁	—	2	8	no	—
94	C₂×#41×C₆₁	C₂³	1	6	yes	—
95	C₂×#41×C₆₁	C₂³	1	3	yes	—
96	C₂×#41×C₆₁	C₂³	1	3	yes	—
97	C₂×#41×C₆₁	C₂³	1	4	yes	—
98	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₆₁	C₂³	1	24	yes	—
100	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
103	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
104	C₂²×D₄×C₆₁	C₂³	1	12	yes	—
105	C₂²×D₄×C₆₁	C₂³	1	12	yes	—
106	C₂²×D₄×C₆₁	C₂³	1	12	yes	—
107	C₂³×C₄×C₆₁	C₂³	1	3	yes	—
108	C₂³×C₄×C₆₁	C₂³	1	12	yes	—
109	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
111	C₄⋊Q₈×C₆₁	C₂³	1	12	yes	—
112	#127×C₆₁	C₂³	1	3	yes	—
113	#127×C₆₁	C₂³	1	6	yes	—
114	#127×C₆₁	C₂³	1	12	yes	—
115	#127×C₆₁	C₂³	1	12	yes	—
116	#126×C₆₁	C₂³	1	4	yes	—
117	#126×C₆₁	C₂³	1	12	yes	—
118	#126×C₆₁	C₂³	1	12	yes	—
119	#126×C₆₁	C₂³	1	24	yes	—
120	#126×C₆₁	C₂³	1	12	yes	—
121	#125×C₆₁	C₂³	1	1	yes	characteristic
122	#125×C₆₁	C₂³	1	3	yes	—
123	#125×C₆₁	C₂³	1	4	yes	—
124	#125×C₆₁	C₂³	1	12	yes	—
125	#125×C₆₁	C₂³	1	6	yes	—
126	#125×C₆₁	C₂³	1	12	yes	—
127	#125×C₆₁	C₂³	1	12	yes	—
128	#124×C₆₁	C₂³	1	12	yes	—
129	#124×C₆₁	C₂³	1	6	yes	—
130	#124×C₆₁	C₂³	1	24	yes	—
131	#124×C₆₁	C₂³	1	12	yes	—
132	#124×C₆₁	C₂³	1	12	yes	—
133	#123×C₆₁	C₂³	1	24	yes	—
134	#123×C₆₁	C₂³	1	12	yes	—
135	#123×C₆₁	C₂³	1	24	yes	—
136	#123×C₆₁	C₂³	1	12	yes	—
137	#123×C₆₁	C₂³	1	12	yes	—
138	#123×C₆₁	C₂³	1	12	yes	—
139	#123×C₆₁	C₂³	1	12	yes	—
140	#123×C₆₁	C₂³	1	24	yes	—
141	#123×C₆₁	C₂³	1	24	yes	—
142	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
143	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
144	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
145	C₂²⋊Q₈×C₆₁	C₂³	1	24	yes	—
146	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
147	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
148	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
149	#121×C₆₁	C₂³	1	6	yes	—
150	#121×C₆₁	C₂³	1	12	yes	—
151	#121×C₆₁	C₂³	1	12	yes	—
152	#121×C₆₁	C₂³	1	12	yes	—
153	#121×C₆₁	C₂³	1	12	yes	—
154	#121×C₆₁	C₂³	1	24	yes	—
155	#121×C₆₁	C₂³	1	24	yes	—
156	#121×C₆₁	C₂³	1	12	yes	—
157	#121×C₆₁	C₂³	1	24	yes	—
158	#121×C₆₁	C₂³	1	12	yes	—
159	#121×C₆₁	C₂³	1	12	yes	—
160	#121×C₆₁	C₂³	1	6	yes	—
161	#121×C₆₁	C₂³	1	12	yes	—
162	#121×C₆₁	C₂³	1	24	yes	—
163	#121×C₆₁	C₂³	1	12	yes	—
164	#121×C₆₁	C₂³	1	24	yes	—
165	#120×C₆₁	C₂³	1	24	yes	—
166	#120×C₆₁	C₂³	1	24	yes	—
167	#120×C₆₁	C₂³	1	12	yes	—
168	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
169	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
170	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
171	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
172	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
173	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
174	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
175	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
176	C₄×D₄×C₆₁	C₂³	1	6	yes	—
177	C₄×D₄×C₆₁	C₂³	1	6	yes	—
178	C₄×D₄×C₆₁	C₂³	1	12	yes	—
179	C₄×D₄×C₆₁	C₂³	1	12	yes	—
180	C₄×D₄×C₆₁	C₂³	1	12	yes	—
181	C₄×D₄×C₆₁	C₂³	1	24	yes	—
182	C₄×D₄×C₆₁	C₂³	1	24	yes	—
183	C₄×D₄×C₆₁	C₂³	1	12	yes	—
184	C₄×D₄×C₆₁	C₂³	1	12	yes	—
185	C₄×D₄×C₆₁	C₂³	1	12	yes	—
186	C₄×D₄×C₆₁	C₂³	1	6	yes	—
187	C₄×D₄×C₆₁	C₂³	1	12	yes	—
188	C₄×D₄×C₆₁	C₂³	1	6	yes	—
189	C₄×D₄×C₆₁	C₂³	1	12	yes	—
190	C₄×D₄×C₆₁	C₂³	1	12	yes	—
191	C₄×D₄×C₆₁	C₂³	1	12	yes	—
192	C₄×D₄×C₆₁	C₂³	1	12	yes	—
193	C₄×D₄×C₆₁	C₂³	1	24	yes	—
194	C₄×D₄×C₆₁	C₂³	1	12	yes	—
195	C₄×D₄×C₆₁	C₂³	1	6	yes	—
196	C₄×D₄×C₆₁	C₂³	1	12	yes	—
197	C₄×D₄×C₆₁	C₂³	1	6	yes	—
198	#117×C₆₁	C₂³	1	6	yes	—
199	#117×C₆₁	C₂³	1	3	yes	—
200	#117×C₆₁	C₂³	1	1	yes	characteristic
201	#117×C₆₁	C₂³	1	3	yes	—
202	#117×C₆₁	C₂³	1	3	yes	—
203	#117×C₆₁	C₂³	1	3	yes	—
204	#117×C₆₁	C₂³	1	6	yes	—
205	#117×C₆₁	C₂³	1	6	yes	—
206	#117×C₆₁	C₂³	1	12	yes	—
207	#117×C₆₁	C₂³	1	6	yes	—
208	#117×C₆₁	C₂³	1	24	yes	—
209	#117×C₆₁	C₂³	1	12	yes	—
210	#117×C₆₁	C₂³	1	6	yes	—
211	#117×C₆₁	C₂³	1	3	yes	—
212	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
213	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
214	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
215	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
216	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
217	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
218	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
219	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
220	C₂×C₂²⋊C₄×C₆₁	C₂³	1	24	yes	—
221	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
222	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
223	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
224	C₂×C₄²×C₆₁	C₂³	1	12	yes	—
225	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
226	C₂⁴×C₆₁	C₂⁴	1	3	yes	—
227	C₂⁴×C₆₁	C₂⁴	1	12	yes	—
228	#41×C₆₁	—	2	4	no	—
229	#41×C₆₁	—	2	16	no	—
230	#41×C₆₁	—	2	12	no	—
231	#41×C₆₁	—	2	12	no	—
232	#41×C₆₁	—	2	24	no	—
233	#41×C₆₁	—	8	24	no	—
234	#41×C₆₁	#41	1	8	yes	complemented
235	C₂×Q₈×C₆₁	—	2	4	no	—
236	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
237	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
239	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
240	C₂×D₄×C₆₁	—	2	12	no	—
241	C₂×D₄×C₆₁	—	2	48	no	—
242	C₂×D₄×C₆₁	—	2	24	no	—
243	C₂×D₄×C₆₁	—	8	12	no	—
244	C₂×D₄×C₆₁	—	8	12	no	—
245	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
246	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
247	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
248	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
249	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
250	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
251	C₂×D₄×C₆₁	C₂⁴	1	24	yes	—
252	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
253	C₂×D₄×C₆₁	C₂⁴	1	24	yes	—
254	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
255	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
256	C₂²×C₄×C₆₁	—	2	12	no	—
257	C₂²×C₄×C₆₁	—	8	12	no	—
258	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
259	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
260	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
261	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
262	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
263	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
265	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
266	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
267	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
268	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
269	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
270	C₂²×C₄×C₆₁	C₂⁴	1	24	yes	—
271	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
272	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
273	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
274	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
275	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
276	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
277	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
278	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
279	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
280	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
281	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
282	C₄⋊C₄×C₆₁	C₂⁴	1	24	yes	—
283	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
286	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
287	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
289	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
290	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
291	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
292	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
293	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
294	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
295	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
296	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
297	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
298	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
299	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
300	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
301	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
302	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
303	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
304	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
305	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
306	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
307	C₄²×C₆₁	C₂⁴	1	3	yes	—
308	C₄²×C₆₁	C₂⁴	1	6	yes	—
309	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
310	C₄²×C₆₁	C₂⁴	1	3	yes	—
311	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
312	C₄²×C₆₁	C₂⁴	1	4	yes	—
313	C₄²×C₆₁	C₂⁴	1	12	yes	—
314	C₄²×C₆₁	C₂⁴	1	12	yes	—
315	C₄²×C₆₁	C₂⁴	1	12	yes	—
316	C₄²×C₆₁	C₂⁴	1	6	yes	—
317	C₂³×C₆₁	—	2	6	no	—
318	C₂³×C₆₁	—	2	24	no	—
319	C₂³×C₆₁	—	4	12	no	—
320	C₂³×C₆₁	—	4	6	no	—
321	C₂³×C₆₁	—	4	12	no	—
322	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
323	C₂³×C₆₁	C₂⁵	1	12	yes	—
324	C₂³×C₆₁	C₂⁵	1	3	yes	—
325	C₂³×C₆₁	C₂⁵	1	3	yes	—
326	Q₈×C₆₁	—	2	6	no	—
327	Q₈×C₆₁	—	2	4	no	—
328	Q₈×C₆₁	—	4	12	no	—
329	Q₈×C₆₁	C₂×#41	1	4	yes	—
330	D₄×C₆₁	—	2	24	no	—
331	D₄×C₆₁	—	2	12	no	—
332	D₄×C₆₁	—	2	24	no	—
333	D₄×C₆₁	—	2	12	no	—
334	D₄×C₆₁	—	2	6	no	—
335	D₄×C₆₁	—	4	12	no	—
336	D₄×C₆₁	—	4	12	no	—
337	D₄×C₆₁	—	4	24	no	—
338	D₄×C₆₁	—	4	24	no	—
339	D₄×C₆₁	—	4	12	no	—
340	D₄×C₆₁	C₂×#41	1	12	yes	—
341	C₂×C₄×C₆₁	—	2	6	no	—
342	C₂×C₄×C₆₁	—	2	2	no	—
343	C₂×C₄×C₆₁	—	2	6	no	—
344	C₂×C₄×C₆₁	—	2	6	no	—
345	C₂×C₄×C₆₁	—	2	6	no	—
346	C₂×C₄×C₆₁	—	2	24	no	—
347	C₂×C₄×C₆₁	—	4	6	no	—
348	C₂×C₄×C₆₁	—	4	12	no	—
349	C₂×C₄×C₆₁	—	4	12	no	—
350	C₂×C₄×C₆₁	—	4	24	no	—
351	C₂×C₄×C₆₁	—	4	6	no	—
352	C₂×C₄×C₆₁	—	4	12	no	—
353	C₂×C₄×C₆₁	—	4	12	no	—
354	C₂×C₄×C₆₁	C₂×#41	1	12	yes	—
355	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
356	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
357	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
358	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
359	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
360	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
361	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
362	C₂×C₄×C₆₁	C₂⁵	1	12	yes	—
363	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
364	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
365	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
366	#62858	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₂²×C₆₁	—	2	6	no	—
368	C₂²×C₆₁	—	2	1	no	—
369	C₂²×C₆₁	—	2	3	no	—
370	C₂²×C₆₁	—	2	12	no	—
371	C₂²×C₆₁	—	2	12	no	—
372	C₂²×C₆₁	—	2	6	no	—
373	C₂²×C₆₁	—	2	12	no	—
374	C₂²×C₆₁	—	2	2	no	—
375	C₂²×C₆₁	—	8	6	no	—
376	C₂²×C₆₁	—	8	24	no	—
377	C₂²×C₆₁	C₂²×#41	1	6	yes	—
378	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
379	C₄×C₆₁	—	2	1	no	—
380	C₄×C₆₁	—	2	4	no	—
381	C₄×C₆₁	—	2	3	no	—
382	C₄×C₆₁	—	2	2	no	—
383	C₄×C₆₁	—	2	6	no	—
384	C₄×C₆₁	—	2	12	no	—
385	C₄×C₆₁	—	2	2	no	—
386	C₄×C₆₁	—	2	6	no	—
387	C₄×C₆₁	—	2	4	no	—
388	C₄×C₆₁	C₂²×#41	1	6	yes	—
389	C₄×C₆₁	C₂²×#41	1	2	yes	—
390	#3524	C₂×C₆₁	1	4	yes	complemented
391	#3519	C₂×C₆₁	1	12	yes	complemented
392	#3517	C₂×C₆₁	1	4	yes	complemented
393	#3513	C₂×C₆₁	1	12	yes	complemented
394	#3512	C₂×C₆₁	1	3	yes	complemented
395	#3508	C₂×C₆₁	1	3	yes	complemented
396	#3504	C₂×C₆₁	1	1	yes	characteristic, complemented
397	#3498	C₂×C₆₁	1	1	yes	characteristic, complemented
398	#3494	C₂×C₆₁	1	6	yes	complemented
399	#3488	C₂×C₆₁	1	2	yes	complemented
400	#3460	C₂×C₆₁	1	6	yes	complemented
401	#3455	C₂×C₆₁	1	3	yes	complemented
402	C₂×#540	C₂×C₆₁	1	3	yes	complemented
403	C₄×H(5,𝔽₂)	C₂×C₆₁	1	2	yes	complemented
404	#3428	C₂×C₆₁	1	1	yes	characteristic, complemented
405	C₂×C₆₁	—	2	6	no	—
406	C₂×C₆₁	—	4	3	no	—
407	C₂×C₆₁	—	4	12	no	—
408	C₂×C₆₁	—	4	1	no	—
409	C₂×C₆₁	C₂³×#41	1	1	yes	characteristic
410	C₂×C₆₁	H(7,𝔽₂)	1	2	yes	—
411	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	2	yes	—
412	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
413	#559	C₂²×C₆₁	1	12	yes	complemented
414	#557	C₂²×C₆₁	1	4	yes	complemented
415	#555	C₂²×C₆₁	1	12	yes	complemented
416	#554	C₂²×C₆₁	1	12	yes	complemented
417	#553	C₂²×C₆₁	1	12	yes	complemented
418	#553	C₂²×C₆₁	1	12	yes	complemented
419	#553	C₂²×C₆₁	1	24	yes	complemented
420	#553	C₂²×C₆₁	1	12	yes	complemented
421	#552	C₂²×C₆₁	1	12	yes	complemented
422	#551	C₂²×C₆₁	1	24	yes	complemented
423	#550	C₂²×C₆₁	1	4	yes	complemented
424	#550	C₂²×C₆₁	1	4	yes	complemented
425	#550	C₂²×C₆₁	1	12	yes	complemented
426	#548	C₂²×C₆₁	1	4	yes	complemented
427	#547	C₂²×C₆₁	1	12	yes	complemented
428	#546	C₂²×C₆₁	1	12	yes	complemented
429	#546	C₂²×C₆₁	1	24	yes	complemented
430	#546	C₂²×C₆₁	1	24	yes	complemented
431	D₄²	C₂²×C₆₁	1	12	yes	complemented
432	D₄²	C₂²×C₆₁	1	12	yes	complemented
433	#544	C₂²×C₆₁	1	6	yes	complemented
434	#542	C₂²×C₆₁	1	6	yes	complemented
435	#542	C₂²×C₆₁	1	6	yes	complemented
436	#542	C₂²×C₆₁	1	12	yes	complemented
437	#541	C₂²×C₆₁	1	1	yes	characteristic, complemented
438	#541	C₂²×C₆₁	1	3	yes	complemented
439	#540	C₂²×C₆₁	1	3	yes	complemented
440	#540	C₂²×C₆₁	1	6	yes	complemented
441	#540	C₂²×C₆₁	1	6	yes	complemented
442	#540	C₂²×C₆₁	1	6	yes	complemented
443	#540	C₂²×C₆₁	1	12	yes	complemented
444	#540	C₂²×C₆₁	1	12	yes	complemented
445	#540	C₂²×C₆₁	1	3	yes	complemented
446	#540	C₂²×C₆₁	1	12	yes	complemented
447	#539	C₂²×C₆₁	1	12	yes	complemented
448	#538	C₂²×C₆₁	1	12	yes	complemented
449	#538	C₂²×C₆₁	1	24	yes	complemented
450	#537	C₂²×C₆₁	1	6	yes	complemented
451	#535	C₂²×C₆₁	1	6	yes	complemented
452	#535	C₂²×C₆₁	1	6	yes	complemented
453	#533	C₂²×C₆₁	1	3	yes	complemented
454	#532	C₂²×C₆₁	1	3	yes	complemented
455	#532	C₂²×C₆₁	1	12	yes	complemented
456	#532	C₂²×C₆₁	1	12	yes	complemented
457	C₂×#127	C₂²×C₆₁	1	3	yes	complemented
458	#529	C₂²×C₆₁	1	12	yes	complemented
459	#529	C₂²×C₆₁	1	12	yes	complemented
460	#529	C₂²×C₆₁	1	12	yes	complemented
461	#529	C₂²×C₆₁	1	12	yes	complemented
462	C₂×#125	C₂²×C₆₁	1	3	yes	complemented
463	#525	C₂²×C₆₁	1	6	yes	complemented
464	#525	C₂²×C₆₁	1	24	yes	complemented
465	C₂×#123	C₂²×C₆₁	1	12	yes	complemented
466	C₂×#121	C₂²×C₆₁	1	6	yes	complemented
467	C₂×#121	C₂²×C₆₁	1	12	yes	complemented
468	#520	C₂²×C₆₁	1	2	yes	—
469	#520	C₂²×C₆₁	1	6	yes	complemented
470	#520	C₂²×C₆₁	1	2	yes	complemented
471	#520	C₂²×C₆₁	1	6	yes	complemented
472	#520	C₂²×C₆₁	1	4	yes	complemented
473	#519	C₂²×C₆₁	1	2	yes	complemented
474	#518	C₂²×C₆₁	1	6	yes	complemented
475	#518	C₂²×C₆₁	1	6	yes	complemented
476	#518	C₂²×C₆₁	1	12	yes	complemented
477	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
478	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
479	C₄×#41	C₂²×C₆₁	1	3	yes	complemented
480	C₄×#41	C₂²×C₆₁	1	3	yes	complemented
481	C₄×#41	C₂²×C₆₁	1	6	yes	complemented
482	C₄×#41	C₂²×C₆₁	1	4	yes	complemented
483	C₂×C₄×D₄	C₂²×C₆₁	1	6	yes	complemented
484	C₂×C₄×D₄	C₂²×C₆₁	1	12	yes	complemented
485	C₂×#117	C₂²×C₆₁	1	3	yes	complemented
486	C₂×#117	C₂²×C₆₁	1	3	yes	complemented
487	C₆₁	#62858	1	1	yes	characteristic, direct product factor, Sylow
488	H(5,𝔽₂)	—	2	16	no	—
489	C₂×#41	—	2	8	no	—
490	C₂×#41	C₂³×C₆₁	1	3	yes	—
491	C₂×#41	C₂³×C₆₁	1	6	yes	—
492	C₂×#41	C₂³×C₆₁	1	4	yes	—
493	C₂×#41	C₂³×C₆₁	1	3	yes	—
494	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
495	C₂×#41	C₂³×C₆₁	1	24	yes	—
496	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
499	C₂²×D₄	C₂³×C₆₁	1	12	yes	—
500	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
501	C₂²×D₄	C₂³×C₆₁	1	12	yes	—
502	C₂²×D₄	C₂³×C₆₁	1	12	yes	—
503	C₂³×C₄	C₂³×C₆₁	1	3	yes	—
504	C₂³×C₄	C₂³×C₆₁	1	12	yes	—
505	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
507	C₄⋊Q₈	C₂³×C₆₁	1	12	yes	—
508	#127	C₂³×C₆₁	1	3	yes	—
509	#127	C₂³×C₆₁	1	6	yes	—
510	#127	C₂³×C₆₁	1	12	yes	—
511	#127	C₂³×C₆₁	1	12	yes	—
512	#126	C₂³×C₆₁	1	4	yes	—
513	#126	C₂³×C₆₁	1	12	yes	—
514	#126	C₂³×C₆₁	1	12	yes	—
515	#126	C₂³×C₆₁	1	24	yes	—
516	#126	C₂³×C₆₁	1	12	yes	—
517	#125	C₂³×C₆₁	1	3	yes	—
518	#125	C₂³×C₆₁	1	6	yes	—
519	#125	C₂³×C₆₁	1	12	yes	—
520	#125	C₂³×C₆₁	1	4	yes	—
521	#125	C₂³×C₆₁	1	12	yes	—
522	#125	C₂³×C₆₁	1	12	yes	—
523	#125	C₂³×C₆₁	1	1	yes	characteristic
524	#124	C₂³×C₆₁	1	6	yes	—
525	#124	C₂³×C₆₁	1	12	yes	—
526	#124	C₂³×C₆₁	1	12	yes	—
527	#124	C₂³×C₆₁	1	12	yes	—
528	#124	C₂³×C₆₁	1	24	yes	—
529	#123	C₂³×C₆₁	1	12	yes	—
530	#123	C₂³×C₆₁	1	24	yes	—
531	#123	C₂³×C₆₁	1	24	yes	—
532	#123	C₂³×C₆₁	1	24	yes	—
533	#123	C₂³×C₆₁	1	12	yes	—
534	#123	C₂³×C₆₁	1	12	yes	—
535	#123	C₂³×C₆₁	1	24	yes	—
536	#123	C₂³×C₆₁	1	12	yes	—
537	#123	C₂³×C₆₁	1	12	yes	—
538	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
539	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
540	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
541	C₂²⋊Q₈	C₂³×C₆₁	1	24	yes	—
542	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
543	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
544	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
545	#121	C₂³×C₆₁	1	6	yes	—
546	#121	C₂³×C₆₁	1	12	yes	—
547	#121	C₂³×C₆₁	1	24	yes	—
548	#121	C₂³×C₆₁	1	12	yes	—
549	#121	C₂³×C₆₁	1	12	yes	—
550	#121	C₂³×C₆₁	1	24	yes	—
551	#121	C₂³×C₆₁	1	12	yes	—
552	#121	C₂³×C₆₁	1	24	yes	—
553	#121	C₂³×C₆₁	1	6	yes	—
554	#121	C₂³×C₆₁	1	24	yes	—
555	#121	C₂³×C₆₁	1	12	yes	—
556	#121	C₂³×C₆₁	1	12	yes	—
557	#121	C₂³×C₆₁	1	12	yes	—
558	#121	C₂³×C₆₁	1	12	yes	—
559	#121	C₂³×C₆₁	1	12	yes	—
560	#121	C₂³×C₆₁	1	24	yes	—
561	#120	C₂³×C₆₁	1	24	yes	—
562	#120	C₂³×C₆₁	1	24	yes	—
563	#120	C₂³×C₆₁	1	12	yes	—
564	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
565	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
566	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
567	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
568	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
569	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
570	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
571	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
572	C₄×D₄	C₂³×C₆₁	1	6	yes	—
573	C₄×D₄	C₂³×C₆₁	1	12	yes	—
574	C₄×D₄	C₂³×C₆₁	1	6	yes	—
575	C₄×D₄	C₂³×C₆₁	1	12	yes	—
576	C₄×D₄	C₂³×C₆₁	1	12	yes	—
577	C₄×D₄	C₂³×C₆₁	1	12	yes	—
578	C₄×D₄	C₂³×C₆₁	1	12	yes	—
579	C₄×D₄	C₂³×C₆₁	1	24	yes	—
580	C₄×D₄	C₂³×C₆₁	1	12	yes	—
581	C₄×D₄	C₂³×C₆₁	1	6	yes	—
582	C₄×D₄	C₂³×C₆₁	1	12	yes	—
583	C₄×D₄	C₂³×C₆₁	1	6	yes	—
584	C₄×D₄	C₂³×C₆₁	1	12	yes	—
585	C₄×D₄	C₂³×C₆₁	1	12	yes	—
586	C₄×D₄	C₂³×C₆₁	1	6	yes	—
587	C₄×D₄	C₂³×C₆₁	1	12	yes	—
588	C₄×D₄	C₂³×C₆₁	1	6	yes	—
589	C₄×D₄	C₂³×C₆₁	1	12	yes	—
590	C₄×D₄	C₂³×C₆₁	1	12	yes	—
591	C₄×D₄	C₂³×C₆₁	1	24	yes	—
592	C₄×D₄	C₂³×C₆₁	1	24	yes	—
593	C₄×D₄	C₂³×C₆₁	1	12	yes	—
594	#117	C₂³×C₆₁	1	1	yes	characteristic
595	#117	C₂³×C₆₁	1	3	yes	—
596	#117	C₂³×C₆₁	1	3	yes	—
597	#117	C₂³×C₆₁	1	3	yes	—
598	#117	C₂³×C₆₁	1	3	yes	—
599	#117	C₂³×C₆₁	1	3	yes	—
600	#117	C₂³×C₆₁	1	6	yes	—
601	#117	C₂³×C₆₁	1	6	yes	—
602	#117	C₂³×C₆₁	1	6	yes	—
603	#117	C₂³×C₆₁	1	6	yes	—
604	#117	C₂³×C₆₁	1	6	yes	—
605	#117	C₂³×C₆₁	1	12	yes	—
606	#117	C₂³×C₆₁	1	12	yes	—
607	#117	C₂³×C₆₁	1	24	yes	—
608	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
609	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
610	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
611	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
612	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₁	1	24	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
618	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
619	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
620	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
621	C₂×C₄²	C₂³×C₆₁	1	12	yes	—
622	C₂⁴	C₂⁴×C₆₁	1	3	yes	—
623	C₂⁴	C₂⁴×C₆₁	1	12	yes	—
624	#41	—	2	4	no	—
625	#41	—	2	16	no	—
626	#41	—	2	12	no	—
627	#41	—	2	12	no	—
628	#41	—	2	24	no	—
629	#41	—	8	24	no	—
630	#41	#41×C₆₁	1	8	yes	complemented
631	C₂×Q₈	—	2	4	no	—
632	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
633	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
634	C₂×Q₈	C₂⁴×C₆₁	1	12	yes	—
635	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
636	C₂×D₄	—	2	12	no	—
637	C₂×D₄	—	2	48	no	—
638	C₂×D₄	—	2	24	no	—
639	C₂×D₄	—	8	12	no	—
640	C₂×D₄	—	8	12	no	—
641	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
642	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
643	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
644	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
645	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
646	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
647	C₂×D₄	C₂⁴×C₆₁	1	24	yes	—
648	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
649	C₂×D₄	C₂⁴×C₆₁	1	24	yes	—
650	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
651	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
652	C₂²×C₄	—	2	12	no	—
653	C₂²×C₄	—	8	12	no	—
654	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
655	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
656	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
657	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
658	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
659	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
661	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
662	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
663	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
664	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
665	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
666	C₂²×C₄	C₂⁴×C₆₁	1	24	yes	—
667	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
668	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
669	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
670	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
672	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
673	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
674	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
675	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
676	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
677	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
678	C₄⋊C₄	C₂⁴×C₆₁	1	24	yes	—
679	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
681	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
682	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
683	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
684	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
685	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
686	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
687	C₂²⋊C₄	C₂⁴×C₆₁	1	2	yes	—
688	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
689	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
690	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
691	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
692	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
693	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
694	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
695	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
696	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
697	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
698	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
699	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
700	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
701	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
702	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
703	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
704	C₄²	C₂⁴×C₆₁	1	3	yes	—
705	C₄²	C₂⁴×C₆₁	1	6	yes	—
706	C₄²	C₂⁴×C₆₁	1	3	yes	—
707	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
708	C₄²	C₂⁴×C₆₁	1	4	yes	—
709	C₄²	C₂⁴×C₆₁	1	12	yes	—
710	C₄²	C₂⁴×C₆₁	1	12	yes	—
711	C₄²	C₂⁴×C₆₁	1	12	yes	—
712	C₄²	C₂⁴×C₆₁	1	6	yes	—
713	C₂³	—	2	6	no	—
714	C₂³	—	2	24	no	—
715	C₂³	—	4	12	no	—
716	C₂³	—	4	6	no	—
717	C₂³	—	4	12	no	—
718	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
719	C₂³	C₂⁵×C₆₁	1	12	yes	—
720	C₂³	C₂⁵×C₆₁	1	3	yes	—
721	C₂³	C₂⁵×C₆₁	1	3	yes	—
722	Q₈	—	2	6	no	—
723	Q₈	—	2	4	no	—
724	Q₈	—	4	12	no	—
725	Q₈	C₂×#41×C₆₁	1	4	yes	—
726	D₄	—	2	24	no	—
727	D₄	—	2	12	no	—
728	D₄	—	2	24	no	—
729	D₄	—	2	12	no	—
730	D₄	—	2	6	no	—
731	D₄	—	4	12	no	—
732	D₄	—	4	12	no	—
733	D₄	—	4	24	no	—
734	D₄	—	4	24	no	—
735	D₄	—	4	12	no	—
736	D₄	C₂×#41×C₆₁	1	12	yes	—
737	C₂×C₄	—	2	6	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	6	no	—
740	C₂×C₄	—	2	6	no	—
741	C₂×C₄	—	2	6	no	—
742	C₂×C₄	—	2	24	no	—
743	C₂×C₄	—	4	6	no	—
744	C₂×C₄	—	4	12	no	—
745	C₂×C₄	—	4	12	no	—
746	C₂×C₄	—	4	24	no	—
747	C₂×C₄	—	4	6	no	—
748	C₂×C₄	—	4	12	no	—
749	C₂×C₄	—	4	12	no	—
750	C₂×C₄	C₂×#41×C₆₁	1	12	yes	—
751	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
752	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
753	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
754	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
755	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
756	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
757	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
758	C₂×C₄	C₂⁵×C₆₁	1	12	yes	—
759	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
760	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
761	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
762	C₂²	—	2	6	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	3	no	—
765	C₂²	—	2	12	no	—
766	C₂²	—	2	12	no	—
767	C₂²	—	2	6	no	—
768	C₂²	—	2	12	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	8	6	no	—
771	C₂²	—	8	24	no	—
772	C₂²	C₂²×#41×C₆₁	1	6	yes	—
773	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
774	C₄	—	2	1	no	—
775	C₄	—	2	4	no	—
776	C₄	—	2	3	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	6	no	—
779	C₄	—	2	12	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	6	no	—
782	C₄	—	2	4	no	—
783	C₄	C₂²×#41×C₆₁	1	6	yes	—
784	C₄	C₂²×#41×C₆₁	1	2	yes	—
785	C₂	—	2	6	no	—
786	C₂	—	4	1	no	—
787	C₂	—	4	12	no	—
788	C₂	—	4	3	no	—
789	C₂	C₂³×#41×C₆₁	1	1	yes	characteristic
790	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×#3524	C₂	semidirect
2. C₆₁×#3519	C₂	semidirect
3. C₆₁×#3517	C₂	semidirect
4. C₆₁×#3513	C₂	semidirect
5. C₆₁×#3512	C₂	semidirect
6. C₆₁×#3508	C₂	semidirect
7. C₆₁×#3504	C₂	semidirect
8. C₆₁×#3498	C₂	semidirect
9. C₆₁×#3494	C₂	semidirect
10. C₆₁×#3488	C₂	semidirect
11. C₆₁×#3460	C₂	semidirect
12. C₆₁×#3455	C₂	semidirect
13. C₂×C₆₁×#540	C₂	semidirect
14. C₄×H(5,𝔽₂)×C₆₁	C₂	semidirect
15. C₆₁×#3428	C₂	semidirect
18. C₆₁×#559	C₂²	semidirect
19. C₆₁×#557	C₂²	semidirect
20. C₆₁×#555	C₂²	semidirect
21. C₆₁×#554	C₂²	semidirect
22. C₆₁×#553	C₂²	semidirect
23. C₆₁×#553	C₂²	semidirect
24. C₆₁×#553	C₂²	semidirect
25. C₆₁×#553	C₂²	semidirect
26. C₆₁×#552	C₂²	semidirect
27. C₆₁×#551	C₂²	semidirect
28. C₆₁×#550	C₂²	semidirect
29. C₆₁×#550	C₂²	semidirect
30. C₆₁×#550	C₂²	semidirect
31. C₆₁×#548	C₂²	semidirect
32. C₆₁×#547	C₂²	semidirect
33. C₆₁×#546	C₂²	semidirect
34. C₆₁×#546	C₂²	semidirect
35. C₆₁×#546	C₂²	semidirect
36. D₄²×C₆₁	C₂²	semidirect
37. D₄²×C₆₁	C₂²	semidirect
38. C₆₁×#544	C₂²	semidirect
39. C₆₁×#542	C₂²	semidirect
40. C₆₁×#542	C₂²	semidirect
41. C₆₁×#542	C₂²	semidirect
42. C₆₁×#541	C₂²	semidirect
43. C₆₁×#541	C₂²	semidirect
44. C₆₁×#540	C₂²	semidirect
45. C₆₁×#540	C₂²	semidirect
46. C₆₁×#540	C₂²	semidirect
47. C₆₁×#540	C₂²	semidirect
48. C₆₁×#540	C₂²	semidirect
49. C₆₁×#540	C₂²	semidirect
50. C₆₁×#540	C₂²	semidirect
51. C₆₁×#540	C₂²	semidirect
52. C₆₁×#539	C₂²	semidirect
53. C₆₁×#538	C₂²	semidirect
54. C₆₁×#538	C₂²	semidirect
55. C₆₁×#537	C₂²	semidirect
56. C₆₁×#535	C₂²	semidirect
57. C₆₁×#535	C₂²	semidirect
58. C₆₁×#533	C₂²	semidirect
59. C₆₁×#532	C₂²	semidirect
60. C₆₁×#532	C₂²	semidirect
61. C₆₁×#532	C₂²	semidirect
62. C₂×#127×C₆₁	C₂²	semidirect
63. C₆₁×#529	C₂²	semidirect
64. C₆₁×#529	C₂²	semidirect
65. C₆₁×#529	C₂²	semidirect
66. C₆₁×#529	C₂²	semidirect
67. C₂×#125×C₆₁	C₂²	semidirect
68. C₆₁×#525	C₂²	semidirect
69. C₆₁×#525	C₂²	semidirect
70. C₂×#123×C₆₁	C₂²	semidirect
71. C₂×#121×C₆₁	C₂²	semidirect
72. C₂×#121×C₆₁	C₂²	semidirect
74. C₆₁×#520	C₂²	semidirect
75. C₆₁×#520	C₂²	semidirect
76. C₆₁×#520	C₂²	semidirect
77. C₆₁×#520	C₂²	semidirect
78. C₆₁×#519	C₂²	semidirect
79. C₆₁×#518	C₂²	semidirect
80. C₆₁×#518	C₂²	semidirect
81. C₆₁×#518	C₂²	semidirect
84. C₄×#41×C₆₁	C₂²	semidirect
85. C₄×#41×C₆₁	C₂²	semidirect
86. C₄×#41×C₆₁	C₂²	semidirect
87. C₄×#41×C₆₁	C₂²	semidirect
88. C₂×C₄×D₄×C₆₁	C₂²	semidirect
89. C₂×C₄×D₄×C₆₁	C₂²	semidirect
90. C₂×#117×C₆₁	C₂²	semidirect
91. C₂×#117×C₆₁	C₂²	semidirect
234. #41×C₆₁	#41	semidirect
366. #62858	C₆₁	direct (N × H)
390. #3524	C₂×C₆₁	semidirect
391. #3519	C₂×C₆₁	semidirect
392. #3517	C₂×C₆₁	semidirect
393. #3513	C₂×C₆₁	semidirect
394. #3512	C₂×C₆₁	semidirect
395. #3508	C₂×C₆₁	semidirect
396. #3504	C₂×C₆₁	semidirect
397. #3498	C₂×C₆₁	semidirect
398. #3494	C₂×C₆₁	semidirect
399. #3488	C₂×C₆₁	semidirect
400. #3460	C₂×C₆₁	semidirect
401. #3455	C₂×C₆₁	semidirect
402. C₂×#540	C₂×C₆₁	semidirect
403. C₄×H(5,𝔽₂)	C₂×C₆₁	semidirect
404. #3428	C₂×C₆₁	semidirect
413. #559	C₂²×C₆₁	semidirect
414. #557	C₂²×C₆₁	semidirect
415. #555	C₂²×C₆₁	semidirect
416. #554	C₂²×C₆₁	semidirect
417. #553	C₂²×C₆₁	semidirect
418. #553	C₂²×C₆₁	semidirect
419. #553	C₂²×C₆₁	semidirect
420. #553	C₂²×C₆₁	semidirect
421. #552	C₂²×C₆₁	semidirect
422. #551	C₂²×C₆₁	semidirect
423. #550	C₂²×C₆₁	semidirect
424. #550	C₂²×C₆₁	semidirect
425. #550	C₂²×C₆₁	semidirect
426. #548	C₂²×C₆₁	semidirect
427. #547	C₂²×C₆₁	semidirect
428. #546	C₂²×C₆₁	semidirect
429. #546	C₂²×C₆₁	semidirect
430. #546	C₂²×C₆₁	semidirect
431. D₄²	C₂²×C₆₁	semidirect
432. D₄²	C₂²×C₆₁	semidirect
433. #544	C₂²×C₆₁	semidirect
434. #542	C₂²×C₆₁	semidirect
435. #542	C₂²×C₆₁	semidirect
436. #542	C₂²×C₆₁	semidirect
437. #541	C₂²×C₆₁	semidirect
438. #541	C₂²×C₆₁	semidirect
439. #540	C₂²×C₆₁	semidirect
440. #540	C₂²×C₆₁	semidirect
441. #540	C₂²×C₆₁	semidirect
442. #540	C₂²×C₆₁	semidirect
443. #540	C₂²×C₆₁	semidirect
444. #540	C₂²×C₆₁	semidirect
445. #540	C₂²×C₆₁	semidirect
446. #540	C₂²×C₆₁	semidirect
447. #539	C₂²×C₆₁	semidirect
448. #538	C₂²×C₆₁	semidirect
449. #538	C₂²×C₆₁	semidirect
450. #537	C₂²×C₆₁	semidirect
451. #535	C₂²×C₆₁	semidirect
452. #535	C₂²×C₆₁	semidirect
453. #533	C₂²×C₆₁	semidirect
454. #532	C₂²×C₆₁	semidirect
455. #532	C₂²×C₆₁	semidirect
456. #532	C₂²×C₆₁	semidirect
457. C₂×#127	C₂²×C₆₁	semidirect
458. #529	C₂²×C₆₁	semidirect
459. #529	C₂²×C₆₁	semidirect
460. #529	C₂²×C₆₁	semidirect
461. #529	C₂²×C₆₁	semidirect
462. C₂×#125	C₂²×C₆₁	semidirect
463. #525	C₂²×C₆₁	semidirect
464. #525	C₂²×C₆₁	semidirect
465. C₂×#123	C₂²×C₆₁	semidirect
466. C₂×#121	C₂²×C₆₁	semidirect
467. C₂×#121	C₂²×C₆₁	semidirect
469. #520	C₂²×C₆₁	semidirect
470. #520	C₂²×C₆₁	semidirect
471. #520	C₂²×C₆₁	semidirect
472. #520	C₂²×C₆₁	semidirect
473. #519	C₂²×C₆₁	semidirect
474. #518	C₂²×C₆₁	semidirect
475. #518	C₂²×C₆₁	semidirect
476. #518	C₂²×C₆₁	semidirect
479. C₄×#41	C₂²×C₆₁	semidirect
480. C₄×#41	C₂²×C₆₁	semidirect
481. C₄×#41	C₂²×C₆₁	semidirect
482. C₄×#41	C₂²×C₆₁	semidirect
483. C₂×C₄×D₄	C₂²×C₆₁	semidirect
484. C₂×C₄×D₄	C₂²×C₆₁	semidirect
485. C₂×#117	C₂²×C₆₁	semidirect
486. C₂×#117	C₂²×C₆₁	semidirect
487. C₆₁	#62858	direct (N × H)
630. #41	#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×#3524	2
C₆₁×#3519	2
C₆₁×#3517	2
C₆₁×#3513	2
C₆₁×#3512	2
C₆₁×#3508	2
C₆₁×#3504	2
C₆₁×#3498	2
C₆₁×#3494	2
C₆₁×#3488	2
C₆₁×#3460	2
C₆₁×#3455	2
C₂×C₆₁×#540	2
C₄×H(5,𝔽₂)×C₆₁	2
C₆₁×#3428	2
#62858	61

Subgroups — C61×#62858 #29566291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62858 #29566291