Subgroups — C₆₁×#63054 #29566487

Order 15616.

6624 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3565	C₂	1	4	yes	maximal, complemented
2	C₆₁×#3561	C₂	1	4	yes	maximal, complemented
3	C₆₁×#3559	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3554	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3553	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3547	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3541	C₂	1	8	yes	maximal, complemented
9	C₆₁×#3536	C₂	1	8	yes	maximal, complemented
10	C₆₁×#3535	C₂	1	8	yes	maximal, complemented
11	C₆₁×#3531	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₆₁×#562	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3519	C₂	1	4	yes	maximal, complemented
14	C₆₁×#3514	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3513	C₂	1	4	yes	maximal, complemented
16	C₆₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3501	C₂	1	4	yes	maximal, complemented
18	C₆₁×#564	C₂²	1	1	yes	characteristic, complemented
19	C₆₁×#563	C₂²	1	4	yes	complemented
20	C₆₁×#563	C₂²	1	2	yes	complemented
21	C₆₁×#563	C₂²	1	8	yes	complemented
22	C₆₁×#563	C₂²	1	4	yes	complemented
23	C₆₁×#563	C₂²	1	4	yes	complemented
24	C₆₁×#562	C₂²	1	1	yes	characteristic
25	C₆₁×#562	C₂²	1	8	yes	complemented
26	C₆₁×#562	C₂²	1	8	yes	complemented
27	C₆₁×#562	C₂²	1	2	yes	complemented
28	C₆₁×#562	C₂²	1	2	yes	complemented
29	C₆₁×#562	C₂²	1	8	yes	complemented
30	C₆₁×#562	C₂²	1	8	yes	complemented
31	C₆₁×#562	C₂²	1	4	yes	complemented
32	C₆₁×#562	C₂²	1	8	yes	complemented
33	C₆₁×#562	C₂²	1	4	yes	complemented
34	C₆₁×#559	C₂²	1	4	yes	complemented
35	C₆₁×#559	C₂²	1	2	yes	complemented
36	C₆₁×#557	C₂²	1	4	yes	complemented
37	C₆₁×#556	C₂²	1	8	yes	complemented
38	C₆₁×#556	C₂²	1	2	yes	complemented
39	C₆₁×#555	C₂²	1	4	yes	complemented
40	C₆₁×#555	C₂²	1	4	yes	complemented
41	C₆₁×#554	C₂²	1	4	yes	—
42	C₆₁×#554	C₂²	1	4	yes	—
43	C₆₁×#554	C₂²	1	4	yes	complemented
44	C₆₁×#554	C₂²	1	4	yes	complemented
45	C₆₁×#554	C₂²	1	8	yes	complemented
46	C₆₁×#554	C₂²	1	4	yes	complemented
47	C₆₁×#554	C₂²	1	8	yes	complemented
48	C₆₁×#554	C₂²	1	8	yes	complemented
49	C₆₁×#554	C₂²	1	8	yes	complemented
50	C₆₁×#553	C₂²	1	4	yes	complemented
51	C₆₁×#553	C₂²	1	4	yes	complemented
52	C₆₁×#553	C₂²	1	8	yes	complemented
53	C₆₁×#553	C₂²	1	4	yes	complemented
54	C₆₁×#553	C₂²	1	8	yes	complemented
55	C₆₁×#552	C₂²	1	8	yes	complemented
56	C₆₁×#552	C₂²	1	4	yes	complemented
57	C₆₁×#552	C₂²	1	8	yes	complemented
58	C₆₁×#551	C₂²	1	8	yes	complemented
59	C₆₁×#551	C₂²	1	8	yes	complemented
60	C₆₁×#551	C₂²	1	8	yes	complemented
61	C₆₁×#550	C₂²	1	4	yes	complemented
62	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
63	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
64	D₄×Q₈×C₆₁	C₂²	1	8	yes	complemented
65	C₆₁×#548	C₂²	1	8	yes	complemented
66	C₆₁×#548	C₂²	1	8	yes	complemented
67	C₆₁×#548	C₂²	1	4	yes	complemented
68	C₆₁×#547	C₂²	1	4	yes	complemented
69	C₆₁×#547	C₂²	1	4	yes	complemented
70	C₆₁×#547	C₂²	1	8	yes	complemented
71	C₆₁×#547	C₂²	1	8	yes	complemented
72	C₆₁×#546	C₂²	1	4	yes	—
73	C₆₁×#546	C₂²	1	8	yes	complemented
74	C₆₁×#546	C₂²	1	8	yes	complemented
75	C₆₁×#546	C₂²	1	4	yes	complemented
76	C₆₁×#546	C₂²	1	8	yes	complemented
77	C₆₁×#546	C₂²	1	8	yes	complemented
78	D₄²×C₆₁	C₂²	1	4	yes	—
79	D₄²×C₆₁	C₂²	1	2	yes	—
80	C₆₁×#544	C₂²	1	2	yes	complemented
81	C₆₁×#544	C₂²	1	4	yes	complemented
82	C₆₁×#544	C₂²	1	4	yes	complemented
83	C₆₁×#544	C₂²	1	4	yes	complemented
84	C₆₁×#543	C₂²	1	8	yes	complemented
85	C₆₁×#543	C₂²	1	8	yes	complemented
86	C₆₁×#542	C₂²	1	8	yes	complemented
87	C₆₁×#542	C₂²	1	8	yes	complemented
88	C₆₁×#542	C₂²	1	8	yes	complemented
89	C₆₁×#542	C₂²	1	4	yes	complemented
90	C₆₁×#542	C₂²	1	4	yes	complemented
91	C₆₁×#542	C₂²	1	8	yes	complemented
92	C₆₁×#542	C₂²	1	8	yes	complemented
93	C₆₁×#541	C₂²	1	8	yes	complemented
94	C₆₁×#540	C₂²	1	4	yes	complemented
95	C₆₁×#540	C₂²	1	4	yes	complemented
96	C₆₁×#540	C₂²	1	4	yes	complemented
97	C₆₁×#539	C₂²	1	8	yes	complemented
98	C₆₁×#539	C₂²	1	8	yes	complemented
99	C₆₁×#539	C₂²	1	8	yes	complemented
100	C₆₁×#539	C₂²	1	8	yes	complemented
101	C₆₁×#539	C₂²	1	4	yes	complemented
102	C₆₁×#539	C₂²	1	8	yes	complemented
103	C₆₁×#538	C₂²	1	8	yes	complemented
104	C₆₁×#538	C₂²	1	8	yes	complemented
105	C₆₁×#538	C₂²	1	8	yes	complemented
106	C₆₁×#538	C₂²	1	8	yes	complemented
107	C₆₁×#537	C₂²	1	8	yes	complemented
108	C₆₁×#537	C₂²	1	8	yes	complemented
109	C₆₁×#537	C₂²	1	4	yes	complemented
110	C₆₁×#536	C₂²	1	8	yes	complemented
111	C₆₁×#536	C₂²	1	8	yes	complemented
112	C₆₁×#533	C₂²	1	4	yes	complemented
113	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
114	C₆₁×#533	C₂²	1	4	yes	complemented
115	C₆₁×#533	C₂²	1	2	yes	complemented
116	C₆₁×#532	C₂²	1	4	yes	complemented
117	C₆₁×#532	C₂²	1	2	yes	complemented
118	C₆₁×#529	C₂²	1	4	yes	complemented
119	C₆₁×#529	C₂²	1	4	yes	complemented
120	C₆₁×#529	C₂²	1	4	yes	complemented
121	C₆₁×#529	C₂²	1	2	yes	complemented
122	C₆₁×#529	C₂²	1	4	yes	complemented
123	C₂×#125×C₆₁	C₂²	1	2	yes	complemented
124	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic, complemented
125	C₂×#124×C₆₁	C₂²	1	4	yes	complemented
126	C₆₁×#525	C₂²	1	8	yes	complemented
127	C₆₁×#525	C₂²	1	8	yes	complemented
128	C₂×#123×C₆₁	C₂²	1	8	yes	complemented
129	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	8	yes	complemented
130	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	8	yes	complemented
131	C₂×#121×C₆₁	C₂²	1	8	yes	complemented
132	C₆₁×#520	C₂²	1	2	yes	—
133	C₆₁×#518	C₂²	1	4	yes	—
134	C₆₁×#518	C₂²	1	4	yes	—
135	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
136	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
137	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₁	C₂³	1	8	yes	—
139	C₂×#41×C₆₁	C₂³	1	4	yes	—
140	C₂×#41×C₆₁	C₂³	1	8	yes	—
141	C₂×#41×C₆₁	C₂³	1	8	yes	—
142	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
143	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
144	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
145	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
146	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
147	C₂³×C₄×C₆₁	C₂³	1	8	yes	—
148	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
150	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
151	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
152	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
153	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
154	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
155	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
157	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
158	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
159	#127×C₆₁	C₂³	1	2	yes	—
160	#127×C₆₁	C₂³	1	4	yes	—
161	#126×C₆₁	C₂³	1	4	yes	—
162	#126×C₆₁	C₂³	1	4	yes	—
163	#126×C₆₁	C₂³	1	8	yes	—
164	#126×C₆₁	C₂³	1	8	yes	—
165	#126×C₆₁	C₂³	1	8	yes	—
166	#126×C₆₁	C₂³	1	8	yes	—
167	#126×C₆₁	C₂³	1	8	yes	—
168	#126×C₆₁	C₂³	1	8	yes	—
169	#126×C₆₁	C₂³	1	8	yes	—
170	#126×C₆₁	C₂³	1	4	yes	—
171	#126×C₆₁	C₂³	1	8	yes	—
172	#126×C₆₁	C₂³	1	4	yes	—
173	#126×C₆₁	C₂³	1	4	yes	—
174	#125×C₆₁	C₂³	1	1	yes	characteristic
175	#125×C₆₁	C₂³	1	4	yes	—
176	#125×C₆₁	C₂³	1	4	yes	—
177	#125×C₆₁	C₂³	1	4	yes	—
178	#125×C₆₁	C₂³	1	4	yes	—
179	#125×C₆₁	C₂³	1	1	yes	characteristic
180	#125×C₆₁	C₂³	1	2	yes	—
181	#125×C₆₁	C₂³	1	2	yes	—
182	#125×C₆₁	C₂³	1	8	yes	—
183	#125×C₆₁	C₂³	1	8	yes	—
184	#125×C₆₁	C₂³	1	4	yes	—
185	#125×C₆₁	C₂³	1	8	yes	—
186	#125×C₆₁	C₂³	1	8	yes	—
187	#125×C₆₁	C₂³	1	8	yes	—
188	#125×C₆₁	C₂³	1	4	yes	—
189	#125×C₆₁	C₂³	1	4	yes	—
190	#125×C₆₁	C₂³	1	4	yes	—
191	#125×C₆₁	C₂³	1	4	yes	—
192	#125×C₆₁	C₂³	1	2	yes	—
193	#124×C₆₁	C₂³	1	8	yes	—
194	#124×C₆₁	C₂³	1	4	yes	—
195	#124×C₆₁	C₂³	1	8	yes	—
196	#124×C₆₁	C₂³	1	8	yes	—
197	#124×C₆₁	C₂³	1	8	yes	—
198	#124×C₆₁	C₂³	1	4	yes	—
199	#124×C₆₁	C₂³	1	8	yes	—
200	#124×C₆₁	C₂³	1	8	yes	—
201	#124×C₆₁	C₂³	1	8	yes	—
202	#124×C₆₁	C₂³	1	8	yes	—
203	#124×C₆₁	C₂³	1	4	yes	—
204	#124×C₆₁	C₂³	1	4	yes	—
205	#124×C₆₁	C₂³	1	4	yes	—
206	#124×C₆₁	C₂³	1	4	yes	—
207	#124×C₆₁	C₂³	1	2	yes	—
208	#123×C₆₁	C₂³	1	8	yes	—
209	#123×C₆₁	C₂³	1	8	yes	—
210	#123×C₆₁	C₂³	1	8	yes	—
211	#123×C₆₁	C₂³	1	8	yes	—
212	#123×C₆₁	C₂³	1	8	yes	—
213	#123×C₆₁	C₂³	1	8	yes	—
214	#123×C₆₁	C₂³	1	8	yes	—
215	#123×C₆₁	C₂³	1	8	yes	—
216	#123×C₆₁	C₂³	1	4	yes	—
217	#123×C₆₁	C₂³	1	8	yes	—
218	#123×C₆₁	C₂³	1	8	yes	—
219	#123×C₆₁	C₂³	1	8	yes	—
220	#123×C₆₁	C₂³	1	8	yes	—
221	#123×C₆₁	C₂³	1	8	yes	—
222	#123×C₆₁	C₂³	1	4	yes	—
223	#123×C₆₁	C₂³	1	8	yes	—
224	#123×C₆₁	C₂³	1	8	yes	—
225	#123×C₆₁	C₂³	1	8	yes	—
226	#123×C₆₁	C₂³	1	8	yes	—
227	#123×C₆₁	C₂³	1	8	yes	—
228	#123×C₆₁	C₂³	1	4	yes	—
229	#123×C₆₁	C₂³	1	4	yes	—
230	#123×C₆₁	C₂³	1	8	yes	—
231	#123×C₆₁	C₂³	1	4	yes	—
232	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
233	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
234	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
235	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
236	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
237	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
238	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
239	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
240	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
241	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
242	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
243	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
244	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
245	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
246	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
247	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
248	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
249	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
250	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
251	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
252	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
253	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
254	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
255	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
256	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
257	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
258	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
259	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
260	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
261	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
262	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
263	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
264	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
265	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
266	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
267	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
268	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
269	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
270	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
271	#121×C₆₁	C₂³	1	4	yes	—
272	#121×C₆₁	C₂³	1	4	yes	—
273	#121×C₆₁	C₂³	1	4	yes	—
274	#121×C₆₁	C₂³	1	4	yes	—
275	#121×C₆₁	C₂³	1	8	yes	—
276	#121×C₆₁	C₂³	1	8	yes	—
277	#121×C₆₁	C₂³	1	8	yes	—
278	#121×C₆₁	C₂³	1	8	yes	—
279	#121×C₆₁	C₂³	1	8	yes	—
280	#121×C₆₁	C₂³	1	2	yes	—
281	#121×C₆₁	C₂³	1	4	yes	—
282	#121×C₆₁	C₂³	1	8	yes	—
283	#121×C₆₁	C₂³	1	8	yes	—
284	#121×C₆₁	C₂³	1	8	yes	—
285	#121×C₆₁	C₂³	1	8	yes	—
286	#121×C₆₁	C₂³	1	8	yes	—
287	#121×C₆₁	C₂³	1	8	yes	—
288	#121×C₆₁	C₂³	1	8	yes	—
289	#121×C₆₁	C₂³	1	8	yes	—
290	#121×C₆₁	C₂³	1	4	yes	—
291	#121×C₆₁	C₂³	1	8	yes	—
292	#121×C₆₁	C₂³	1	8	yes	—
293	#121×C₆₁	C₂³	1	8	yes	—
294	#121×C₆₁	C₂³	1	8	yes	—
295	#121×C₆₁	C₂³	1	4	yes	—
296	#121×C₆₁	C₂³	1	4	yes	—
297	#120×C₆₁	C₂³	1	8	yes	—
298	#120×C₆₁	C₂³	1	8	yes	—
299	#120×C₆₁	C₂³	1	8	yes	—
300	#120×C₆₁	C₂³	1	8	yes	—
301	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
302	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
303	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
304	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
305	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
306	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
307	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
308	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
309	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
310	C₄×D₄×C₆₁	C₂³	1	8	yes	—
311	C₄×D₄×C₆₁	C₂³	1	4	yes	—
312	C₄×D₄×C₆₁	C₂³	1	4	yes	—
313	C₄×D₄×C₆₁	C₂³	1	4	yes	—
314	C₄×D₄×C₆₁	C₂³	1	4	yes	—
315	C₄×D₄×C₆₁	C₂³	1	4	yes	—
316	C₄×D₄×C₆₁	C₂³	1	8	yes	—
317	C₄×D₄×C₆₁	C₂³	1	8	yes	—
318	C₄×D₄×C₆₁	C₂³	1	8	yes	—
319	C₄×D₄×C₆₁	C₂³	1	8	yes	—
320	C₄×D₄×C₆₁	C₂³	1	8	yes	—
321	C₄×D₄×C₆₁	C₂³	1	8	yes	—
322	C₄×D₄×C₆₁	C₂³	1	4	yes	—
323	C₄×D₄×C₆₁	C₂³	1	8	yes	—
324	C₄×D₄×C₆₁	C₂³	1	8	yes	—
325	C₄×D₄×C₆₁	C₂³	1	8	yes	—
326	C₄×D₄×C₆₁	C₂³	1	8	yes	—
327	C₄×D₄×C₆₁	C₂³	1	8	yes	—
328	C₄×D₄×C₆₁	C₂³	1	8	yes	—
329	C₄×D₄×C₆₁	C₂³	1	4	yes	—
330	C₄×D₄×C₆₁	C₂³	1	4	yes	—
331	C₄×D₄×C₆₁	C₂³	1	4	yes	—
332	C₄×D₄×C₆₁	C₂³	1	2	yes	—
333	C₄×D₄×C₆₁	C₂³	1	4	yes	—
334	C₄×D₄×C₆₁	C₂³	1	2	yes	—
335	C₄×D₄×C₆₁	C₂³	1	4	yes	—
336	C₄×D₄×C₆₁	C₂³	1	4	yes	—
337	C₄×D₄×C₆₁	C₂³	1	4	yes	—
338	#117×C₆₁	C₂³	1	2	yes	—
339	#117×C₆₁	C₂³	1	4	yes	—
340	#117×C₆₁	C₂³	1	4	yes	—
341	#117×C₆₁	C₂³	1	4	yes	—
342	#117×C₆₁	C₂³	1	4	yes	—
343	#117×C₆₁	C₂³	1	4	yes	—
344	#117×C₆₁	C₂³	1	8	yes	—
345	#117×C₆₁	C₂³	1	8	yes	—
346	#117×C₆₁	C₂³	1	8	yes	—
347	#117×C₆₁	C₂³	1	8	yes	—
348	#117×C₆₁	C₂³	1	2	yes	—
349	#117×C₆₁	C₂³	1	1	yes	characteristic
350	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
351	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
352	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
353	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
354	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
355	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
356	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
357	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
358	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
359	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
360	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
361	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
362	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
363	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
364	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
365	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
366	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
367	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
368	C₂⁴×C₆₁	C₂⁴	1	8	yes	—
369	#41×C₆₁	—	2	4	no	—
370	#41×C₆₁	—	8	8	no	—
371	#41×C₆₁	—	8	8	no	—
372	#41×C₆₁	—	8	8	no	—
373	#41×C₆₁	—	8	4	no	—
374	C₂×Q₈×C₆₁	—	8	4	no	—
375	C₂×Q₈×C₆₁	—	8	8	no	—
376	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
377	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
378	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
379	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
380	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
381	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
382	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
383	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
384	C₂×D₄×C₆₁	—	2	16	no	—
385	C₂×D₄×C₆₁	—	8	8	no	—
386	C₂×D₄×C₆₁	—	8	4	no	—
387	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
388	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
389	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
390	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
391	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
392	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
393	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
394	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
395	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
396	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
397	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
398	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
399	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
400	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
401	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₆₁	—	8	8	no	—
403	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
404	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
406	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
407	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
408	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
409	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
410	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
411	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
412	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
413	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
414	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
415	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
416	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
417	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
418	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
419	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
420	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
421	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
422	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
424	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
425	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
426	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
427	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
428	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
429	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
430	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
431	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
432	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
433	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
434	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
435	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
436	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
437	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
438	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
439	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
440	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
441	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
442	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
443	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
444	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
445	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
446	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
447	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
448	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
449	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
450	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
451	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
452	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
453	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
454	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
455	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
456	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
457	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
458	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
459	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
460	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
461	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
462	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
463	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
464	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
465	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
466	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
467	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
468	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
469	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
470	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
471	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
472	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
473	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
474	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
475	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
476	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
477	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
478	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
479	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
480	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
481	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
482	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
483	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
484	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
485	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
486	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
487	C₄²×C₆₁	C₂⁴	1	2	yes	—
488	C₄²×C₆₁	C₂⁴	1	4	yes	—
489	C₄²×C₆₁	C₂⁴	1	4	yes	—
490	C₄²×C₆₁	C₂⁴	1	2	yes	—
491	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
492	C₄²×C₆₁	C₂⁴	1	4	yes	—
493	C₄²×C₆₁	C₂⁴	1	4	yes	—
494	C₄²×C₆₁	C₂⁴	1	4	yes	—
495	C₄²×C₆₁	C₂⁴	1	8	yes	—
496	C₄²×C₆₁	C₂⁴	1	8	yes	—
497	C₄²×C₆₁	C₂⁴	1	8	yes	—
498	C₂³×C₆₁	—	2	16	no	—
499	C₂³×C₆₁	—	4	8	no	—
500	C₂³×C₆₁	—	4	8	no	—
501	C₂³×C₆₁	C₂⁵	1	4	yes	—
502	C₂³×C₆₁	C₂⁵	1	8	yes	—
503	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
504	C₂³×C₆₁	C₂⁵	1	2	yes	—
505	Q₈×C₆₁	—	2	2	no	—
506	Q₈×C₆₁	—	4	8	no	—
507	Q₈×C₆₁	—	4	4	no	—
508	Q₈×C₆₁	—	4	2	no	—
509	Q₈×C₆₁	—	4	8	no	—
510	Q₈×C₆₁	—	4	8	no	—
511	Q₈×C₆₁	—	4	4	no	—
512	Q₈×C₆₁	—	4	4	no	—
513	D₄×C₆₁	—	2	16	no	—
514	D₄×C₆₁	—	2	4	no	—
515	D₄×C₆₁	—	2	8	no	—
516	D₄×C₆₁	—	4	4	no	—
517	D₄×C₆₁	—	4	2	no	—
518	D₄×C₆₁	—	4	8	no	—
519	D₄×C₆₁	—	4	8	no	—
520	D₄×C₆₁	—	4	8	no	—
521	D₄×C₆₁	—	4	4	no	—
522	D₄×C₆₁	—	4	8	no	—
523	D₄×C₆₁	—	4	4	no	—
524	D₄×C₆₁	—	4	4	no	—
525	D₄×C₆₁	—	4	8	no	—
526	D₄×C₆₁	—	4	8	no	—
527	D₄×C₆₁	2₋¹⁺⁴	1	4	yes	—
528	C₂×C₄×C₆₁	—	2	4	no	—
529	C₂×C₄×C₆₁	—	2	8	no	—
530	C₂×C₄×C₆₁	—	2	2	no	—
531	C₂×C₄×C₆₁	—	4	4	no	—
532	C₂×C₄×C₆₁	—	4	8	no	—
533	C₂×C₄×C₆₁	—	4	8	no	—
534	C₂×C₄×C₆₁	—	4	8	no	—
535	C₂×C₄×C₆₁	—	4	8	no	—
536	C₂×C₄×C₆₁	—	4	8	no	—
537	C₂×C₄×C₆₁	—	4	4	no	—
538	C₂×C₄×C₆₁	—	4	8	no	—
539	C₂×C₄×C₆₁	—	4	8	no	—
540	C₂×C₄×C₆₁	—	4	4	no	—
541	C₂×C₄×C₆₁	—	4	8	no	—
542	C₂×C₄×C₆₁	—	4	8	no	—
543	C₂×C₄×C₆₁	—	4	2	no	—
544	C₂×C₄×C₆₁	—	4	4	no	—
545	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
546	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
547	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
548	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
549	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
550	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
551	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
552	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
553	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
554	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
555	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
556	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
557	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
558	#63054	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
559	C₂²×C₆₁	—	2	4	no	—
560	C₂²×C₆₁	—	2	1	no	—
561	C₂²×C₆₁	—	2	4	no	—
562	C₂²×C₆₁	—	2	8	no	—
563	C₂²×C₆₁	—	2	8	no	—
564	C₂²×C₆₁	—	2	2	no	—
565	C₂²×C₆₁	—	2	4	no	—
566	C₂²×C₆₁	—	2	8	no	—
567	C₂²×C₆₁	—	2	4	no	—
568	C₂²×C₆₁	—	8	16	no	—
569	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	4	yes	—
570	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
571	C₄×C₆₁	—	2	1	no	—
572	C₄×C₆₁	—	2	4	no	—
573	C₄×C₆₁	—	2	2	no	—
574	C₄×C₆₁	—	2	4	no	—
575	C₄×C₆₁	—	2	8	no	—
576	C₄×C₆₁	—	2	2	no	—
577	C₄×C₆₁	—	2	8	no	—
578	C₄×C₆₁	—	2	4	no	—
579	C₄×C₆₁	—	2	4	no	—
580	C₄×C₆₁	—	2	2	no	—
581	C₄×C₆₁	—	2	4	no	—
582	C₄×C₆₁	—	2	4	no	—
583	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
584	#3565	C₂×C₆₁	1	4	yes	complemented
585	#3561	C₂×C₆₁	1	4	yes	complemented
586	#3559	C₂×C₆₁	1	2	yes	complemented
587	#3554	C₂×C₆₁	1	4	yes	complemented
588	#3553	C₂×C₆₁	1	2	yes	complemented
589	#3548	C₂×C₆₁	1	1	yes	characteristic, complemented
590	#3547	C₂×C₆₁	1	4	yes	complemented
591	#3541	C₂×C₆₁	1	8	yes	complemented
592	#3536	C₂×C₆₁	1	8	yes	complemented
593	#3535	C₂×C₆₁	1	8	yes	complemented
594	#3531	C₂×C₆₁	1	1	yes	characteristic, complemented
595	C₂×#562	C₂×C₆₁	1	2	yes	complemented
596	#3519	C₂×C₆₁	1	4	yes	complemented
597	#3514	C₂×C₆₁	1	2	yes	complemented
598	#3513	C₂×C₆₁	1	4	yes	complemented
599	#3504	C₂×C₆₁	1	1	yes	characteristic, complemented
600	#3501	C₂×C₆₁	1	4	yes	complemented
601	C₂×C₆₁	—	2	4	no	—
602	C₂×C₆₁	—	4	1	no	—
603	C₂×C₆₁	—	4	8	no	—
604	C₂×C₆₁	—	4	4	no	—
605	C₂×C₆₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
606	C₂×C₆₁	H(7,𝔽₂)	1	2	yes	—
607	#564	C₂²×C₆₁	1	1	yes	characteristic, complemented
608	#563	C₂²×C₆₁	1	4	yes	complemented
609	#563	C₂²×C₆₁	1	4	yes	complemented
610	#563	C₂²×C₆₁	1	2	yes	complemented
611	#563	C₂²×C₆₁	1	8	yes	complemented
612	#563	C₂²×C₆₁	1	4	yes	complemented
613	#562	C₂²×C₆₁	1	1	yes	characteristic
614	#562	C₂²×C₆₁	1	8	yes	complemented
615	#562	C₂²×C₆₁	1	8	yes	complemented
616	#562	C₂²×C₆₁	1	8	yes	complemented
617	#562	C₂²×C₆₁	1	2	yes	complemented
618	#562	C₂²×C₆₁	1	4	yes	complemented
619	#562	C₂²×C₆₁	1	4	yes	complemented
620	#562	C₂²×C₆₁	1	8	yes	complemented
621	#562	C₂²×C₆₁	1	8	yes	complemented
622	#562	C₂²×C₆₁	1	2	yes	complemented
623	#559	C₂²×C₆₁	1	4	yes	complemented
624	#559	C₂²×C₆₁	1	2	yes	complemented
625	#557	C₂²×C₆₁	1	4	yes	complemented
626	#556	C₂²×C₆₁	1	2	yes	complemented
627	#556	C₂²×C₆₁	1	8	yes	complemented
628	#555	C₂²×C₆₁	1	4	yes	complemented
629	#555	C₂²×C₆₁	1	4	yes	complemented
630	#554	C₂²×C₆₁	1	4	yes	—
631	#554	C₂²×C₆₁	1	4	yes	—
632	#554	C₂²×C₆₁	1	8	yes	complemented
633	#554	C₂²×C₆₁	1	8	yes	complemented
634	#554	C₂²×C₆₁	1	8	yes	complemented
635	#554	C₂²×C₆₁	1	4	yes	complemented
636	#554	C₂²×C₆₁	1	4	yes	complemented
637	#554	C₂²×C₆₁	1	4	yes	complemented
638	#554	C₂²×C₆₁	1	8	yes	complemented
639	#553	C₂²×C₆₁	1	8	yes	complemented
640	#553	C₂²×C₆₁	1	4	yes	complemented
641	#553	C₂²×C₆₁	1	8	yes	complemented
642	#553	C₂²×C₆₁	1	4	yes	complemented
643	#553	C₂²×C₆₁	1	4	yes	complemented
644	#552	C₂²×C₆₁	1	4	yes	complemented
645	#552	C₂²×C₆₁	1	8	yes	complemented
646	#552	C₂²×C₆₁	1	8	yes	complemented
647	#551	C₂²×C₆₁	1	8	yes	complemented
648	#551	C₂²×C₆₁	1	8	yes	complemented
649	#551	C₂²×C₆₁	1	8	yes	complemented
650	#550	C₂²×C₆₁	1	4	yes	complemented
651	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
652	D₄×Q₈	C₂²×C₆₁	1	8	yes	complemented
653	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
654	#548	C₂²×C₆₁	1	4	yes	complemented
655	#548	C₂²×C₆₁	1	8	yes	complemented
656	#548	C₂²×C₆₁	1	8	yes	complemented
657	#547	C₂²×C₆₁	1	4	yes	complemented
658	#547	C₂²×C₆₁	1	4	yes	complemented
659	#547	C₂²×C₆₁	1	8	yes	complemented
660	#547	C₂²×C₆₁	1	8	yes	complemented
661	#546	C₂²×C₆₁	1	4	yes	—
662	#546	C₂²×C₆₁	1	8	yes	complemented
663	#546	C₂²×C₆₁	1	4	yes	complemented
664	#546	C₂²×C₆₁	1	8	yes	complemented
665	#546	C₂²×C₆₁	1	8	yes	complemented
666	#546	C₂²×C₆₁	1	8	yes	complemented
667	D₄²	C₂²×C₆₁	1	4	yes	—
668	D₄²	C₂²×C₆₁	1	2	yes	—
669	#544	C₂²×C₆₁	1	4	yes	complemented
670	#544	C₂²×C₆₁	1	4	yes	complemented
671	#544	C₂²×C₆₁	1	4	yes	complemented
672	#544	C₂²×C₆₁	1	2	yes	complemented
673	#543	C₂²×C₆₁	1	8	yes	complemented
674	#543	C₂²×C₆₁	1	8	yes	complemented
675	#542	C₂²×C₆₁	1	4	yes	complemented
676	#542	C₂²×C₆₁	1	4	yes	complemented
677	#542	C₂²×C₆₁	1	8	yes	complemented
678	#542	C₂²×C₆₁	1	8	yes	complemented
679	#542	C₂²×C₆₁	1	8	yes	complemented
680	#542	C₂²×C₆₁	1	8	yes	complemented
681	#542	C₂²×C₆₁	1	8	yes	complemented
682	#541	C₂²×C₆₁	1	8	yes	complemented
683	#540	C₂²×C₆₁	1	4	yes	complemented
684	#540	C₂²×C₆₁	1	4	yes	complemented
685	#540	C₂²×C₆₁	1	4	yes	complemented
686	#539	C₂²×C₆₁	1	8	yes	complemented
687	#539	C₂²×C₆₁	1	8	yes	complemented
688	#539	C₂²×C₆₁	1	8	yes	complemented
689	#539	C₂²×C₆₁	1	8	yes	complemented
690	#539	C₂²×C₆₁	1	8	yes	complemented
691	#539	C₂²×C₆₁	1	4	yes	complemented
692	#538	C₂²×C₆₁	1	8	yes	complemented
693	#538	C₂²×C₆₁	1	8	yes	complemented
694	#538	C₂²×C₆₁	1	8	yes	complemented
695	#538	C₂²×C₆₁	1	8	yes	complemented
696	#537	C₂²×C₆₁	1	8	yes	complemented
697	#537	C₂²×C₆₁	1	4	yes	complemented
698	#537	C₂²×C₆₁	1	8	yes	complemented
699	#536	C₂²×C₆₁	1	8	yes	complemented
700	#536	C₂²×C₆₁	1	8	yes	complemented
701	#533	C₂²×C₆₁	1	4	yes	complemented
702	#533	C₂²×C₆₁	1	4	yes	complemented
703	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
704	#533	C₂²×C₆₁	1	2	yes	complemented
705	#532	C₂²×C₆₁	1	2	yes	complemented
706	#532	C₂²×C₆₁	1	4	yes	complemented
707	#529	C₂²×C₆₁	1	4	yes	complemented
708	#529	C₂²×C₆₁	1	4	yes	complemented
709	#529	C₂²×C₆₁	1	2	yes	complemented
710	#529	C₂²×C₆₁	1	4	yes	complemented
711	#529	C₂²×C₆₁	1	4	yes	complemented
712	C₂×#125	C₂²×C₆₁	1	2	yes	complemented
713	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic, complemented
714	C₂×#124	C₂²×C₆₁	1	4	yes	complemented
715	#525	C₂²×C₆₁	1	8	yes	complemented
716	#525	C₂²×C₆₁	1	8	yes	complemented
717	C₂×#123	C₂²×C₆₁	1	8	yes	complemented
718	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	8	yes	complemented
719	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	8	yes	complemented
720	C₂×#121	C₂²×C₆₁	1	8	yes	complemented
721	#520	C₂²×C₆₁	1	2	yes	—
722	#518	C₂²×C₆₁	1	4	yes	—
723	#518	C₂²×C₆₁	1	4	yes	—
724	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
725	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
726	C₆₁	#63054	1	1	yes	characteristic, direct product factor, Sylow
727	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
728	C₂×#41	C₂³×C₆₁	1	8	yes	—
729	C₂×#41	C₂³×C₆₁	1	8	yes	—
730	C₂×#41	C₂³×C₆₁	1	8	yes	—
731	C₂×#41	C₂³×C₆₁	1	4	yes	—
732	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
733	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
734	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
735	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
736	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
737	C₂³×C₄	C₂³×C₆₁	1	8	yes	—
738	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
739	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
740	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
741	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
742	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
743	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
744	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
745	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
746	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
747	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
748	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
749	#127	C₂³×C₆₁	1	2	yes	—
750	#127	C₂³×C₆₁	1	4	yes	—
751	#126	C₂³×C₆₁	1	4	yes	—
752	#126	C₂³×C₆₁	1	4	yes	—
753	#126	C₂³×C₆₁	1	8	yes	—
754	#126	C₂³×C₆₁	1	8	yes	—
755	#126	C₂³×C₆₁	1	4	yes	—
756	#126	C₂³×C₆₁	1	4	yes	—
757	#126	C₂³×C₆₁	1	4	yes	—
758	#126	C₂³×C₆₁	1	8	yes	—
759	#126	C₂³×C₆₁	1	8	yes	—
760	#126	C₂³×C₆₁	1	8	yes	—
761	#126	C₂³×C₆₁	1	8	yes	—
762	#126	C₂³×C₆₁	1	8	yes	—
763	#126	C₂³×C₆₁	1	8	yes	—
764	#125	C₂³×C₆₁	1	1	yes	characteristic
765	#125	C₂³×C₆₁	1	2	yes	—
766	#125	C₂³×C₆₁	1	2	yes	—
767	#125	C₂³×C₆₁	1	8	yes	—
768	#125	C₂³×C₆₁	1	4	yes	—
769	#125	C₂³×C₆₁	1	4	yes	—
770	#125	C₂³×C₆₁	1	2	yes	—
771	#125	C₂³×C₆₁	1	4	yes	—
772	#125	C₂³×C₆₁	1	4	yes	—
773	#125	C₂³×C₆₁	1	4	yes	—
774	#125	C₂³×C₆₁	1	1	yes	characteristic
775	#125	C₂³×C₆₁	1	4	yes	—
776	#125	C₂³×C₆₁	1	4	yes	—
777	#125	C₂³×C₆₁	1	4	yes	—
778	#125	C₂³×C₆₁	1	4	yes	—
779	#125	C₂³×C₆₁	1	8	yes	—
780	#125	C₂³×C₆₁	1	8	yes	—
781	#125	C₂³×C₆₁	1	8	yes	—
782	#125	C₂³×C₆₁	1	8	yes	—
783	#124	C₂³×C₆₁	1	2	yes	—
784	#124	C₂³×C₆₁	1	4	yes	—
785	#124	C₂³×C₆₁	1	8	yes	—
786	#124	C₂³×C₆₁	1	8	yes	—
787	#124	C₂³×C₆₁	1	4	yes	—
788	#124	C₂³×C₆₁	1	4	yes	—
789	#124	C₂³×C₆₁	1	4	yes	—
790	#124	C₂³×C₆₁	1	4	yes	—
791	#124	C₂³×C₆₁	1	4	yes	—
792	#124	C₂³×C₆₁	1	8	yes	—
793	#124	C₂³×C₆₁	1	8	yes	—
794	#124	C₂³×C₆₁	1	8	yes	—
795	#124	C₂³×C₆₁	1	8	yes	—
796	#124	C₂³×C₆₁	1	8	yes	—
797	#124	C₂³×C₆₁	1	8	yes	—
798	#123	C₂³×C₆₁	1	4	yes	—
799	#123	C₂³×C₆₁	1	8	yes	—
800	#123	C₂³×C₆₁	1	8	yes	—
801	#123	C₂³×C₆₁	1	8	yes	—
802	#123	C₂³×C₆₁	1	8	yes	—
803	#123	C₂³×C₆₁	1	8	yes	—
804	#123	C₂³×C₆₁	1	8	yes	—
805	#123	C₂³×C₆₁	1	8	yes	—
806	#123	C₂³×C₆₁	1	4	yes	—
807	#123	C₂³×C₆₁	1	8	yes	—
808	#123	C₂³×C₆₁	1	8	yes	—
809	#123	C₂³×C₆₁	1	4	yes	—
810	#123	C₂³×C₆₁	1	8	yes	—
811	#123	C₂³×C₆₁	1	4	yes	—
812	#123	C₂³×C₆₁	1	4	yes	—
813	#123	C₂³×C₆₁	1	8	yes	—
814	#123	C₂³×C₆₁	1	8	yes	—
815	#123	C₂³×C₆₁	1	8	yes	—
816	#123	C₂³×C₆₁	1	8	yes	—
817	#123	C₂³×C₆₁	1	8	yes	—
818	#123	C₂³×C₆₁	1	8	yes	—
819	#123	C₂³×C₆₁	1	8	yes	—
820	#123	C₂³×C₆₁	1	8	yes	—
821	#123	C₂³×C₆₁	1	8	yes	—
822	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
823	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
824	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
825	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
826	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
827	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
828	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
829	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
830	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
831	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
832	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
833	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
834	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
835	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
836	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
837	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
838	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
839	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
840	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
841	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
842	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
843	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
844	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
845	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
846	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
847	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
848	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
849	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
850	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
851	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
852	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
853	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
854	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
855	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
856	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
857	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
858	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
859	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
860	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
861	#121	C₂³×C₆₁	1	4	yes	—
862	#121	C₂³×C₆₁	1	8	yes	—
863	#121	C₂³×C₆₁	1	8	yes	—
864	#121	C₂³×C₆₁	1	8	yes	—
865	#121	C₂³×C₆₁	1	8	yes	—
866	#121	C₂³×C₆₁	1	8	yes	—
867	#121	C₂³×C₆₁	1	8	yes	—
868	#121	C₂³×C₆₁	1	8	yes	—
869	#121	C₂³×C₆₁	1	8	yes	—
870	#121	C₂³×C₆₁	1	8	yes	—
871	#121	C₂³×C₆₁	1	8	yes	—
872	#121	C₂³×C₆₁	1	2	yes	—
873	#121	C₂³×C₆₁	1	4	yes	—
874	#121	C₂³×C₆₁	1	4	yes	—
875	#121	C₂³×C₆₁	1	4	yes	—
876	#121	C₂³×C₆₁	1	4	yes	—
877	#121	C₂³×C₆₁	1	4	yes	—
878	#121	C₂³×C₆₁	1	4	yes	—
879	#121	C₂³×C₆₁	1	4	yes	—
880	#121	C₂³×C₆₁	1	8	yes	—
881	#121	C₂³×C₆₁	1	8	yes	—
882	#121	C₂³×C₆₁	1	8	yes	—
883	#121	C₂³×C₆₁	1	8	yes	—
884	#121	C₂³×C₆₁	1	8	yes	—
885	#121	C₂³×C₆₁	1	8	yes	—
886	#121	C₂³×C₆₁	1	8	yes	—
887	#120	C₂³×C₆₁	1	8	yes	—
888	#120	C₂³×C₆₁	1	8	yes	—
889	#120	C₂³×C₆₁	1	8	yes	—
890	#120	C₂³×C₆₁	1	8	yes	—
891	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
892	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
893	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
894	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
895	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
896	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
897	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
898	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
899	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
900	C₄×D₄	C₂³×C₆₁	1	4	yes	—
901	C₄×D₄	C₂³×C₆₁	1	4	yes	—
902	C₄×D₄	C₂³×C₆₁	1	8	yes	—
903	C₄×D₄	C₂³×C₆₁	1	8	yes	—
904	C₄×D₄	C₂³×C₆₁	1	4	yes	—
905	C₄×D₄	C₂³×C₆₁	1	4	yes	—
906	C₄×D₄	C₂³×C₆₁	1	2	yes	—
907	C₄×D₄	C₂³×C₆₁	1	4	yes	—
908	C₄×D₄	C₂³×C₆₁	1	8	yes	—
909	C₄×D₄	C₂³×C₆₁	1	8	yes	—
910	C₄×D₄	C₂³×C₆₁	1	8	yes	—
911	C₄×D₄	C₂³×C₆₁	1	8	yes	—
912	C₄×D₄	C₂³×C₆₁	1	4	yes	—
913	C₄×D₄	C₂³×C₆₁	1	4	yes	—
914	C₄×D₄	C₂³×C₆₁	1	4	yes	—
915	C₄×D₄	C₂³×C₆₁	1	4	yes	—
916	C₄×D₄	C₂³×C₆₁	1	8	yes	—
917	C₄×D₄	C₂³×C₆₁	1	8	yes	—
918	C₄×D₄	C₂³×C₆₁	1	8	yes	—
919	C₄×D₄	C₂³×C₆₁	1	8	yes	—
920	C₄×D₄	C₂³×C₆₁	1	8	yes	—
921	C₄×D₄	C₂³×C₆₁	1	4	yes	—
922	C₄×D₄	C₂³×C₆₁	1	2	yes	—
923	C₄×D₄	C₂³×C₆₁	1	4	yes	—
924	C₄×D₄	C₂³×C₆₁	1	4	yes	—
925	C₄×D₄	C₂³×C₆₁	1	8	yes	—
926	C₄×D₄	C₂³×C₆₁	1	8	yes	—
927	C₄×D₄	C₂³×C₆₁	1	4	yes	—
928	#117	C₂³×C₆₁	1	2	yes	—
929	#117	C₂³×C₆₁	1	1	yes	characteristic
930	#117	C₂³×C₆₁	1	4	yes	—
931	#117	C₂³×C₆₁	1	4	yes	—
932	#117	C₂³×C₆₁	1	4	yes	—
933	#117	C₂³×C₆₁	1	4	yes	—
934	#117	C₂³×C₆₁	1	2	yes	—
935	#117	C₂³×C₆₁	1	4	yes	—
936	#117	C₂³×C₆₁	1	8	yes	—
937	#117	C₂³×C₆₁	1	8	yes	—
938	#117	C₂³×C₆₁	1	8	yes	—
939	#117	C₂³×C₆₁	1	8	yes	—
940	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
941	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
942	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
943	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
944	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
945	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
946	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
947	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
948	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
949	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
950	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
951	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
952	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
953	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
954	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
955	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
956	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
957	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
958	C₂⁴	C₂⁴×C₆₁	1	8	yes	—
959	#41	—	2	4	no	—
960	#41	—	8	8	no	—
961	#41	—	8	8	no	—
962	#41	—	8	8	no	—
963	#41	—	8	4	no	—
964	C₂×Q₈	—	8	4	no	—
965	C₂×Q₈	—	8	8	no	—
966	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
967	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
968	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
969	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
970	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
971	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
972	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
973	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
974	C₂×D₄	—	2	16	no	—
975	C₂×D₄	—	8	8	no	—
976	C₂×D₄	—	8	4	no	—
977	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
978	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
979	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
980	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
981	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
982	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
983	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
984	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
985	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
986	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
987	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
988	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
989	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
990	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
991	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
992	C₂²×C₄	—	8	8	no	—
993	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
994	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
995	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
996	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
997	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
998	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
999	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
1000	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
1001	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
1002	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
1003	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
1004	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
1005	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
1006	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
1007	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
1008	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
1009	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
1010	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1011	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1012	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1013	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1014	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1015	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1016	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1017	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1018	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1019	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1020	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1021	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1022	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1023	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1024	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1025	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1026	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1027	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1028	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1029	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1030	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1031	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1032	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1033	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1034	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1035	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1036	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1037	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1038	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1039	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1040	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1041	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1042	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1043	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1044	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1045	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1046	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1047	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1048	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1049	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1050	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1051	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1052	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1053	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1054	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1055	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1056	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1057	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1058	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1059	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1060	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1061	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1062	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1063	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1064	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1065	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1066	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1067	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1068	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1069	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1070	C₂²⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1071	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1072	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1073	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1074	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
1075	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
1076	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1077	C₄²	C₂⁴×C₆₁	1	2	yes	—
1078	C₄²	C₂⁴×C₆₁	1	4	yes	—
1079	C₄²	C₂⁴×C₆₁	1	4	yes	—
1080	C₄²	C₂⁴×C₆₁	1	2	yes	—
1081	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1082	C₄²	C₂⁴×C₆₁	1	4	yes	—
1083	C₄²	C₂⁴×C₆₁	1	4	yes	—
1084	C₄²	C₂⁴×C₆₁	1	4	yes	—
1085	C₄²	C₂⁴×C₆₁	1	8	yes	—
1086	C₄²	C₂⁴×C₆₁	1	8	yes	—
1087	C₄²	C₂⁴×C₆₁	1	8	yes	—
1088	C₂³	—	2	16	no	—
1089	C₂³	—	4	8	no	—
1090	C₂³	—	4	8	no	—
1091	C₂³	C₂⁵×C₆₁	1	4	yes	—
1092	C₂³	C₂⁵×C₆₁	1	8	yes	—
1093	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
1094	C₂³	C₂⁵×C₆₁	1	2	yes	—
1095	Q₈	—	2	2	no	—
1096	Q₈	—	4	8	no	—
1097	Q₈	—	4	4	no	—
1098	Q₈	—	4	2	no	—
1099	Q₈	—	4	8	no	—
1100	Q₈	—	4	8	no	—
1101	Q₈	—	4	4	no	—
1102	Q₈	—	4	4	no	—
1103	D₄	—	2	16	no	—
1104	D₄	—	2	4	no	—
1105	D₄	—	2	8	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	8	no	—
1109	D₄	—	4	8	no	—
1110	D₄	—	4	8	no	—
1111	D₄	—	4	4	no	—
1112	D₄	—	4	8	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	8	no	—
1116	D₄	—	4	8	no	—
1117	D₄	2₋¹⁺⁴×C₆₁	1	4	yes	—
1118	C₂×C₄	—	2	4	no	—
1119	C₂×C₄	—	2	8	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	4	4	no	—
1122	C₂×C₄	—	4	8	no	—
1123	C₂×C₄	—	4	8	no	—
1124	C₂×C₄	—	4	8	no	—
1125	C₂×C₄	—	4	8	no	—
1126	C₂×C₄	—	4	8	no	—
1127	C₂×C₄	—	4	4	no	—
1128	C₂×C₄	—	4	8	no	—
1129	C₂×C₄	—	4	8	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	8	no	—
1132	C₂×C₄	—	4	8	no	—
1133	C₂×C₄	—	4	2	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1136	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1137	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1138	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1139	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1140	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1141	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1142	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1143	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
1144	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1145	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
1146	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1147	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1148	C₂²	—	2	4	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	4	no	—
1151	C₂²	—	2	8	no	—
1152	C₂²	—	2	8	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	4	no	—
1155	C₂²	—	2	8	no	—
1156	C₂²	—	2	4	no	—
1157	C₂²	—	8	16	no	—
1158	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	4	yes	—
1159	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
1160	C₄	—	2	1	no	—
1161	C₄	—	2	4	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	4	no	—
1164	C₄	—	2	8	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	8	no	—
1167	C₄	—	2	4	no	—
1168	C₄	—	2	4	no	—
1169	C₄	—	2	2	no	—
1170	C₄	—	2	4	no	—
1171	C₄	—	2	4	no	—
1172	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
1173	C₂	—	2	4	no	—
1174	C₂	—	4	4	no	—
1175	C₂	—	4	8	no	—
1176	C₂	—	4	1	no	—
1177	C₂	C₂²×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1178	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×#3565	C₂	semidirect
2. C₆₁×#3561	C₂	semidirect
3. C₆₁×#3559	C₂	semidirect
4. C₆₁×#3554	C₂	semidirect
5. C₆₁×#3553	C₂	semidirect
6. C₆₁×#3548	C₂	semidirect
7. C₆₁×#3547	C₂	semidirect
8. C₆₁×#3541	C₂	semidirect
9. C₆₁×#3536	C₂	semidirect
10. C₆₁×#3535	C₂	semidirect
11. C₆₁×#3531	C₂	semidirect
12. C₂×C₆₁×#562	C₂	semidirect
13. C₆₁×#3519	C₂	semidirect
14. C₆₁×#3514	C₂	semidirect
15. C₆₁×#3513	C₂	semidirect
16. C₆₁×#3504	C₂	semidirect
17. C₆₁×#3501	C₂	semidirect
18. C₆₁×#564	C₂²	semidirect
19. C₆₁×#563	C₂²	semidirect
20. C₆₁×#563	C₂²	semidirect
21. C₆₁×#563	C₂²	semidirect
22. C₆₁×#563	C₂²	semidirect
23. C₆₁×#563	C₂²	semidirect
25. C₆₁×#562	C₂²	semidirect
26. C₆₁×#562	C₂²	semidirect
27. C₆₁×#562	C₂²	semidirect
28. C₆₁×#562	C₂²	semidirect
29. C₆₁×#562	C₂²	semidirect
30. C₆₁×#562	C₂²	semidirect
31. C₆₁×#562	C₂²	semidirect
32. C₆₁×#562	C₂²	semidirect
33. C₆₁×#562	C₂²	semidirect
34. C₆₁×#559	C₂²	semidirect
35. C₆₁×#559	C₂²	semidirect
36. C₆₁×#557	C₂²	semidirect
37. C₆₁×#556	C₂²	semidirect
38. C₆₁×#556	C₂²	semidirect
39. C₆₁×#555	C₂²	semidirect
40. C₆₁×#555	C₂²	semidirect
43. C₆₁×#554	C₂²	semidirect
44. C₆₁×#554	C₂²	semidirect
45. C₆₁×#554	C₂²	semidirect
46. C₆₁×#554	C₂²	semidirect
47. C₆₁×#554	C₂²	semidirect
48. C₆₁×#554	C₂²	semidirect
49. C₆₁×#554	C₂²	semidirect
50. C₆₁×#553	C₂²	semidirect
51. C₆₁×#553	C₂²	semidirect
52. C₆₁×#553	C₂²	semidirect
53. C₆₁×#553	C₂²	semidirect
54. C₆₁×#553	C₂²	semidirect
55. C₆₁×#552	C₂²	semidirect
56. C₆₁×#552	C₂²	semidirect
57. C₆₁×#552	C₂²	semidirect
58. C₆₁×#551	C₂²	semidirect
59. C₆₁×#551	C₂²	semidirect
60. C₆₁×#551	C₂²	semidirect
61. C₆₁×#550	C₂²	semidirect
63. D₄×Q₈×C₆₁	C₂²	semidirect
64. D₄×Q₈×C₆₁	C₂²	semidirect
65. C₆₁×#548	C₂²	semidirect
66. C₆₁×#548	C₂²	semidirect
67. C₆₁×#548	C₂²	semidirect
68. C₆₁×#547	C₂²	semidirect
69. C₆₁×#547	C₂²	semidirect
70. C₆₁×#547	C₂²	semidirect
71. C₆₁×#547	C₂²	semidirect
73. C₆₁×#546	C₂²	semidirect
74. C₆₁×#546	C₂²	semidirect
75. C₆₁×#546	C₂²	semidirect
76. C₆₁×#546	C₂²	semidirect
77. C₆₁×#546	C₂²	semidirect
80. C₆₁×#544	C₂²	semidirect
81. C₆₁×#544	C₂²	semidirect
82. C₆₁×#544	C₂²	semidirect
83. C₆₁×#544	C₂²	semidirect
84. C₆₁×#543	C₂²	semidirect
85. C₆₁×#543	C₂²	semidirect
86. C₆₁×#542	C₂²	semidirect
87. C₆₁×#542	C₂²	semidirect
88. C₆₁×#542	C₂²	semidirect
89. C₆₁×#542	C₂²	semidirect
90. C₆₁×#542	C₂²	semidirect
91. C₆₁×#542	C₂²	semidirect
92. C₆₁×#542	C₂²	semidirect
93. C₆₁×#541	C₂²	semidirect
94. C₆₁×#540	C₂²	semidirect
95. C₆₁×#540	C₂²	semidirect
96. C₆₁×#540	C₂²	semidirect
97. C₆₁×#539	C₂²	semidirect
98. C₆₁×#539	C₂²	semidirect
99. C₆₁×#539	C₂²	semidirect
100. C₆₁×#539	C₂²	semidirect
101. C₆₁×#539	C₂²	semidirect
102. C₆₁×#539	C₂²	semidirect
103. C₆₁×#538	C₂²	semidirect
104. C₆₁×#538	C₂²	semidirect
105. C₆₁×#538	C₂²	semidirect
106. C₆₁×#538	C₂²	semidirect
107. C₆₁×#537	C₂²	semidirect
108. C₆₁×#537	C₂²	semidirect
109. C₆₁×#537	C₂²	semidirect
110. C₆₁×#536	C₂²	semidirect
111. C₆₁×#536	C₂²	semidirect
112. C₆₁×#533	C₂²	semidirect
113. C₆₁×#533	C₂²	semidirect
114. C₆₁×#533	C₂²	semidirect
115. C₆₁×#533	C₂²	semidirect
116. C₆₁×#532	C₂²	semidirect
117. C₆₁×#532	C₂²	semidirect
118. C₆₁×#529	C₂²	semidirect
119. C₆₁×#529	C₂²	semidirect
120. C₆₁×#529	C₂²	semidirect
121. C₆₁×#529	C₂²	semidirect
122. C₆₁×#529	C₂²	semidirect
123. C₂×#125×C₆₁	C₂²	semidirect
124. C₂×#125×C₆₁	C₂²	semidirect
125. C₂×#124×C₆₁	C₂²	semidirect
126. C₆₁×#525	C₂²	semidirect
127. C₆₁×#525	C₂²	semidirect
128. C₂×#123×C₆₁	C₂²	semidirect
129. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
130. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
131. C₂×#121×C₆₁	C₂²	semidirect
558. #63054	C₆₁	direct (N × H)
584. #3565	C₂×C₆₁	semidirect
585. #3561	C₂×C₆₁	semidirect
586. #3559	C₂×C₆₁	semidirect
587. #3554	C₂×C₆₁	semidirect
588. #3553	C₂×C₆₁	semidirect
589. #3548	C₂×C₆₁	semidirect
590. #3547	C₂×C₆₁	semidirect
591. #3541	C₂×C₆₁	semidirect
592. #3536	C₂×C₆₁	semidirect
593. #3535	C₂×C₆₁	semidirect
594. #3531	C₂×C₆₁	semidirect
595. C₂×#562	C₂×C₆₁	semidirect
596. #3519	C₂×C₆₁	semidirect
597. #3514	C₂×C₆₁	semidirect
598. #3513	C₂×C₆₁	semidirect
599. #3504	C₂×C₆₁	semidirect
600. #3501	C₂×C₆₁	semidirect
607. #564	C₂²×C₆₁	semidirect
608. #563	C₂²×C₆₁	semidirect
609. #563	C₂²×C₆₁	semidirect
610. #563	C₂²×C₆₁	semidirect
611. #563	C₂²×C₆₁	semidirect
612. #563	C₂²×C₆₁	semidirect
614. #562	C₂²×C₆₁	semidirect
615. #562	C₂²×C₆₁	semidirect
616. #562	C₂²×C₆₁	semidirect
617. #562	C₂²×C₆₁	semidirect
618. #562	C₂²×C₆₁	semidirect
619. #562	C₂²×C₆₁	semidirect
620. #562	C₂²×C₆₁	semidirect
621. #562	C₂²×C₆₁	semidirect
622. #562	C₂²×C₆₁	semidirect
623. #559	C₂²×C₆₁	semidirect
624. #559	C₂²×C₆₁	semidirect
625. #557	C₂²×C₆₁	semidirect
626. #556	C₂²×C₆₁	semidirect
627. #556	C₂²×C₆₁	semidirect
628. #555	C₂²×C₆₁	semidirect
629. #555	C₂²×C₆₁	semidirect
632. #554	C₂²×C₆₁	semidirect
633. #554	C₂²×C₆₁	semidirect
634. #554	C₂²×C₆₁	semidirect
635. #554	C₂²×C₆₁	semidirect
636. #554	C₂²×C₆₁	semidirect
637. #554	C₂²×C₆₁	semidirect
638. #554	C₂²×C₆₁	semidirect
639. #553	C₂²×C₆₁	semidirect
640. #553	C₂²×C₆₁	semidirect
641. #553	C₂²×C₆₁	semidirect
642. #553	C₂²×C₆₁	semidirect
643. #553	C₂²×C₆₁	semidirect
644. #552	C₂²×C₆₁	semidirect
645. #552	C₂²×C₆₁	semidirect
646. #552	C₂²×C₆₁	semidirect
647. #551	C₂²×C₆₁	semidirect
648. #551	C₂²×C₆₁	semidirect
649. #551	C₂²×C₆₁	semidirect
650. #550	C₂²×C₆₁	semidirect
652. D₄×Q₈	C₂²×C₆₁	semidirect
653. D₄×Q₈	C₂²×C₆₁	semidirect
654. #548	C₂²×C₆₁	semidirect
655. #548	C₂²×C₆₁	semidirect
656. #548	C₂²×C₆₁	semidirect
657. #547	C₂²×C₆₁	semidirect
658. #547	C₂²×C₆₁	semidirect
659. #547	C₂²×C₆₁	semidirect
660. #547	C₂²×C₆₁	semidirect
662. #546	C₂²×C₆₁	semidirect
663. #546	C₂²×C₆₁	semidirect
664. #546	C₂²×C₆₁	semidirect
665. #546	C₂²×C₆₁	semidirect
666. #546	C₂²×C₆₁	semidirect
669. #544	C₂²×C₆₁	semidirect
670. #544	C₂²×C₆₁	semidirect
671. #544	C₂²×C₆₁	semidirect
672. #544	C₂²×C₆₁	semidirect
673. #543	C₂²×C₆₁	semidirect
674. #543	C₂²×C₆₁	semidirect
675. #542	C₂²×C₆₁	semidirect
676. #542	C₂²×C₆₁	semidirect
677. #542	C₂²×C₆₁	semidirect
678. #542	C₂²×C₆₁	semidirect
679. #542	C₂²×C₆₁	semidirect
680. #542	C₂²×C₆₁	semidirect
681. #542	C₂²×C₆₁	semidirect
682. #541	C₂²×C₆₁	semidirect
683. #540	C₂²×C₆₁	semidirect
684. #540	C₂²×C₆₁	semidirect
685. #540	C₂²×C₆₁	semidirect
686. #539	C₂²×C₆₁	semidirect
687. #539	C₂²×C₆₁	semidirect
688. #539	C₂²×C₆₁	semidirect
689. #539	C₂²×C₆₁	semidirect
690. #539	C₂²×C₆₁	semidirect
691. #539	C₂²×C₆₁	semidirect
692. #538	C₂²×C₆₁	semidirect
693. #538	C₂²×C₆₁	semidirect
694. #538	C₂²×C₆₁	semidirect
695. #538	C₂²×C₆₁	semidirect
696. #537	C₂²×C₆₁	semidirect
697. #537	C₂²×C₆₁	semidirect
698. #537	C₂²×C₆₁	semidirect
699. #536	C₂²×C₆₁	semidirect
700. #536	C₂²×C₆₁	semidirect
701. #533	C₂²×C₆₁	semidirect
702. #533	C₂²×C₆₁	semidirect
703. #533	C₂²×C₆₁	semidirect
704. #533	C₂²×C₆₁	semidirect
705. #532	C₂²×C₆₁	semidirect
706. #532	C₂²×C₆₁	semidirect
707. #529	C₂²×C₆₁	semidirect
708. #529	C₂²×C₆₁	semidirect
709. #529	C₂²×C₆₁	semidirect
710. #529	C₂²×C₆₁	semidirect
711. #529	C₂²×C₆₁	semidirect
712. C₂×#125	C₂²×C₆₁	semidirect
713. C₂×#125	C₂²×C₆₁	semidirect
714. C₂×#124	C₂²×C₆₁	semidirect
715. #525	C₂²×C₆₁	semidirect
716. #525	C₂²×C₆₁	semidirect
717. C₂×#123	C₂²×C₆₁	semidirect
718. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
719. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
720. C₂×#121	C₂²×C₆₁	semidirect
726. C₆₁	#63054	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×#3565	2
C₆₁×#3561	2
C₆₁×#3559	2
C₆₁×#3554	2
C₆₁×#3553	2
C₆₁×#3548	2
C₆₁×#3547	2
C₆₁×#3541	2
C₆₁×#3536	2
C₆₁×#3535	2
C₆₁×#3531	2
C₂×C₆₁×#562	2
C₆₁×#3519	2
C₆₁×#3514	2
C₆₁×#3513	2
C₆₁×#3504	2
C₆₁×#3501	2
#63054	61

Subgroups — C61×#63054 #29566487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#63054 #29566487