Subgroups — C₆₁×#62995 #29566428

Order 15616.

7030 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3521	C₂	1	12	yes	maximal, complemented
2	C₆₁×#3520	C₂	1	6	yes	maximal, complemented
3	C₆₁×#3518	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3516	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3510	C₂	1	6	yes	maximal, complemented
6	C₆₁×#3509	C₂	1	3	yes	maximal, complemented
7	C₆₁×#3507	C₂	1	6	yes	maximal, complemented
8	C₆₁×#3506	C₂	1	3	yes	maximal, complemented
9	C₆₁×#3500	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3482	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3480	C₂	1	3	yes	maximal, complemented
13	Q₈×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3475	C₂	1	6	yes	maximal, complemented
15	C₂×C₆₁×#556	C₂	1	3	yes	maximal, complemented
16	C₄×2₋¹⁺⁴×C₆₁	C₂	1	2	yes	maximal, complemented
17	C₄×H(5,𝔽₂)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	2	yes	—
19	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#559	C₂²	1	1	yes	characteristic, complemented
21	C₆₁×#559	C₂²	1	6	yes	complemented
22	C₆₁×#559	C₂²	1	12	yes	complemented
23	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
24	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
25	C₆₁×#557	C₂²	1	2	yes	complemented
26	C₆₁×#557	C₂²	1	3	yes	complemented
27	C₆₁×#557	C₂²	1	6	yes	complemented
28	C₆₁×#556	C₂²	1	3	yes	complemented
29	C₆₁×#556	C₂²	1	6	yes	complemented
30	C₆₁×#556	C₂²	1	6	yes	complemented
31	C₆₁×#556	C₂²	1	12	yes	complemented
32	C₆₁×#556	C₂²	1	12	yes	complemented
33	C₆₁×#556	C₂²	1	6	yes	complemented
34	C₆₁×#556	C₂²	1	6	yes	complemented
35	C₆₁×#556	C₂²	1	12	yes	complemented
36	C₆₁×#556	C₂²	1	6	yes	complemented
37	C₆₁×#555	C₂²	1	6	yes	complemented
38	C₆₁×#554	C₂²	1	3	yes	complemented
39	C₆₁×#554	C₂²	1	6	yes	complemented
40	C₆₁×#554	C₂²	1	12	yes	complemented
41	C₆₁×#553	C₂²	1	6	yes	complemented
42	C₆₁×#553	C₂²	1	12	yes	complemented
43	C₆₁×#553	C₂²	1	12	yes	complemented
44	C₆₁×#552	C₂²	1	12	yes	complemented
45	C₆₁×#552	C₂²	1	12	yes	complemented
46	C₆₁×#552	C₂²	1	12	yes	complemented
47	C₆₁×#552	C₂²	1	12	yes	complemented
48	C₆₁×#551	C₂²	1	24	yes	complemented
49	C₆₁×#551	C₂²	1	24	yes	complemented
50	C₆₁×#550	C₂²	1	3	yes	complemented
51	D₄×Q₈×C₆₁	C₂²	1	3	yes	complemented
52	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
53	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
54	C₆₁×#548	C₂²	1	4	yes	—
55	C₆₁×#548	C₂²	1	4	yes	—
56	C₆₁×#548	C₂²	1	6	yes	complemented
57	C₆₁×#547	C₂²	1	6	yes	complemented
58	C₆₁×#547	C₂²	1	6	yes	complemented
59	C₆₁×#547	C₂²	1	6	yes	complemented
60	C₆₁×#546	C₂²	1	12	yes	—
61	C₆₁×#546	C₂²	1	12	yes	—
62	C₆₁×#542	C₂²	1	12	yes	complemented
63	C₆₁×#542	C₂²	1	12	yes	complemented
64	C₆₁×#541	C₂²	1	12	yes	complemented
65	C₆₁×#539	C₂²	1	24	yes	complemented
66	C₆₁×#538	C₂²	1	12	yes	complemented
67	C₆₁×#536	C₂²	1	6	yes	—
68	C₆₁×#536	C₂²	1	6	yes	complemented
69	C₆₁×#535	C₂²	1	6	yes	—
70	C₆₁×#533	C₂²	1	6	yes	complemented
71	C₆₁×#533	C₂²	1	3	yes	complemented
72	C₆₁×#533	C₂²	1	6	yes	complemented
73	C₆₁×#533	C₂²	1	6	yes	complemented
74	C₆₁×#532	C₂²	1	6	yes	—
75	C₆₁×#532	C₂²	1	3	yes	complemented
76	C₂×C₄⋊Q₈×C₆₁	C₂²	1	3	yes	complemented
77	C₆₁×#529	C₂²	1	24	yes	complemented
78	C₆₁×#529	C₂²	1	12	yes	complemented
79	C₆₁×#529	C₂²	1	12	yes	complemented
80	C₆₁×#529	C₂²	1	6	yes	complemented
81	C₆₁×#529	C₂²	1	12	yes	complemented
82	C₂×#126×C₆₁	C₂²	1	12	yes	complemented
83	C₂×#124×C₆₁	C₂²	1	6	yes	—
84	C₆₁×#525	C₂²	1	12	yes	complemented
85	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	6	yes	complemented
86	C₆₁×#520	C₂²	1	1	yes	characteristic
87	C₆₁×#520	C₂²	1	3	yes	—
88	C₆₁×#520	C₂²	1	2	yes	—
89	C₆₁×#520	C₂²	1	6	yes	complemented
90	C₆₁×#520	C₂²	1	12	yes	complemented
91	C₆₁×#519	C₂²	1	6	yes	complemented
92	C₆₁×#519	C₂²	1	4	yes	complemented
93	C₆₁×#518	C₂²	1	3	yes	—
94	C₆₁×#518	C₂²	1	6	yes	—
95	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
96	C₄×#41×C₆₁	C₂²	1	3	yes	—
97	C₄×#41×C₆₁	C₂²	1	2	yes	—
98	C₄×#41×C₆₁	C₂²	1	2	yes	—
99	C₄×#41×C₆₁	C₂²	1	12	yes	complemented
100	C₄×#41×C₆₁	C₂²	1	6	yes	complemented
101	C₄×#41×C₆₁	C₂²	1	6	yes	complemented
102	C₂×C₄×Q₈×C₆₁	C₂²	1	6	yes	complemented
103	C₂×C₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
104	C₂×C₄×Q₈×C₆₁	C₂²	1	3	yes	complemented
105	C₂×C₄×D₄×C₆₁	C₂²	1	3	yes	—
106	C₂×C₄×D₄×C₆₁	C₂²	1	6	yes	—
107	C₂×#117×C₆₁	C₂²	1	6	yes	complemented
108	2₋¹⁺⁴×C₆₁	—	2	16	no	—
109	H(5,𝔽₂)×C₆₁	—	2	8	no	—
110	C₂×#41×C₆₁	C₂³	1	3	yes	—
111	C₂×#41×C₆₁	C₂³	1	6	yes	—
112	C₂×#41×C₆₁	C₂³	1	12	yes	—
113	C₂×#41×C₆₁	C₂³	1	2	yes	—
114	C₂×#41×C₆₁	C₂³	1	6	yes	—
115	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
116	C₂²×Q₈×C₆₁	C₂³	1	6	yes	—
117	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
118	C₂²×Q₈×C₆₁	C₂³	1	3	yes	—
119	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
120	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
121	C₂³×C₄×C₆₁	C₂³	1	6	yes	—
122	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
123	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
124	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
125	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
126	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
127	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
128	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
129	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
130	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
131	#127×C₆₁	C₂³	1	6	yes	—
132	#127×C₆₁	C₂³	1	1	yes	characteristic
133	#126×C₆₁	C₂³	1	24	yes	—
134	#126×C₆₁	C₂³	1	12	yes	—
135	#126×C₆₁	C₂³	1	24	yes	—
136	#126×C₆₁	C₂³	1	24	yes	—
137	#126×C₆₁	C₂³	1	24	yes	—
138	#126×C₆₁	C₂³	1	12	yes	—
139	#126×C₆₁	C₂³	1	12	yes	—
140	#125×C₆₁	C₂³	1	6	yes	—
141	#125×C₆₁	C₂³	1	12	yes	—
142	#125×C₆₁	C₂³	1	6	yes	—
143	#125×C₆₁	C₂³	1	6	yes	—
144	#125×C₆₁	C₂³	1	6	yes	—
145	#125×C₆₁	C₂³	1	24	yes	—
146	#125×C₆₁	C₂³	1	12	yes	—
147	#124×C₆₁	C₂³	1	2	yes	—
148	#124×C₆₁	C₂³	1	6	yes	—
149	#124×C₆₁	C₂³	1	6	yes	—
150	#124×C₆₁	C₂³	1	12	yes	—
151	#124×C₆₁	C₂³	1	24	yes	—
152	#124×C₆₁	C₂³	1	12	yes	—
153	#124×C₆₁	C₂³	1	12	yes	—
154	#124×C₆₁	C₂³	1	12	yes	—
155	#124×C₆₁	C₂³	1	2	yes	—
156	#123×C₆₁	C₂³	1	24	yes	—
157	#123×C₆₁	C₂³	1	24	yes	—
158	#123×C₆₁	C₂³	1	24	yes	—
159	#123×C₆₁	C₂³	1	24	yes	—
160	#123×C₆₁	C₂³	1	12	yes	—
161	#123×C₆₁	C₂³	1	12	yes	—
162	#123×C₆₁	C₂³	1	4	yes	—
163	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
164	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
165	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
166	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
167	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
168	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
169	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
170	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
171	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
172	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
173	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
174	C₂²⋊Q₈×C₆₁	C₂³	1	24	yes	—
175	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
176	#121×C₆₁	C₂³	1	12	yes	—
177	#121×C₆₁	C₂³	1	12	yes	—
178	#121×C₆₁	C₂³	1	6	yes	—
179	#121×C₆₁	C₂³	1	6	yes	—
180	#121×C₆₁	C₂³	1	12	yes	—
181	#121×C₆₁	C₂³	1	12	yes	—
182	#121×C₆₁	C₂³	1	12	yes	—
183	#121×C₆₁	C₂³	1	6	yes	—
184	#120×C₆₁	C₂³	1	24	yes	—
185	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
186	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
187	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
188	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
189	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
190	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
191	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
192	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
193	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
194	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
195	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
196	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
197	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
198	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
199	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
200	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
201	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
202	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
204	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
205	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
206	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
208	C₄×D₄×C₆₁	C₂³	1	12	yes	—
209	C₄×D₄×C₆₁	C₂³	1	12	yes	—
210	C₄×D₄×C₆₁	C₂³	1	6	yes	—
211	C₄×D₄×C₆₁	C₂³	1	6	yes	—
212	C₄×D₄×C₆₁	C₂³	1	24	yes	—
213	C₄×D₄×C₆₁	C₂³	1	12	yes	—
214	C₄×D₄×C₆₁	C₂³	1	6	yes	—
215	C₄×D₄×C₆₁	C₂³	1	6	yes	—
216	C₄×D₄×C₆₁	C₂³	1	6	yes	—
217	C₄×D₄×C₆₁	C₂³	1	6	yes	—
218	C₄×D₄×C₆₁	C₂³	1	3	yes	—
219	C₄×D₄×C₆₁	C₂³	1	3	yes	—
220	C₄×D₄×C₆₁	C₂³	1	6	yes	—
221	C₄×D₄×C₆₁	C₂³	1	12	yes	—
222	C₄×D₄×C₆₁	C₂³	1	6	yes	—
223	C₄×D₄×C₆₁	C₂³	1	3	yes	—
224	C₄×D₄×C₆₁	C₂³	1	6	yes	—
225	C₄×D₄×C₆₁	C₂³	1	12	yes	—
226	C₄×D₄×C₆₁	C₂³	1	12	yes	—
227	C₄×D₄×C₆₁	C₂³	1	24	yes	—
228	C₄×D₄×C₆₁	C₂³	1	6	yes	—
229	C₄×D₄×C₆₁	C₂³	1	2	yes	—
230	C₄×D₄×C₆₁	C₂³	1	6	yes	—
231	C₄×D₄×C₆₁	C₂³	1	6	yes	—
232	C₄×D₄×C₆₁	C₂³	1	3	yes	—
233	C₄×D₄×C₆₁	C₂³	1	2	yes	—
234	C₄×D₄×C₆₁	C₂³	1	6	yes	—
235	#117×C₆₁	C₂³	1	6	yes	—
236	#117×C₆₁	C₂³	1	3	yes	—
237	#117×C₆₁	C₂³	1	12	yes	—
238	#117×C₆₁	C₂³	1	12	yes	—
239	#117×C₆₁	C₂³	1	6	yes	—
240	#117×C₆₁	C₂³	1	12	yes	—
241	#117×C₆₁	C₂³	1	24	yes	—
242	#117×C₆₁	C₂³	1	24	yes	—
243	#117×C₆₁	C₂³	1	12	yes	—
244	#117×C₆₁	C₂³	1	6	yes	—
245	#117×C₆₁	C₂³	1	12	yes	—
246	#117×C₆₁	C₂³	1	6	yes	—
247	#117×C₆₁	C₂³	1	3	yes	—
248	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
249	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
250	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
251	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
252	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
253	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
254	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
256	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
257	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
258	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
259	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
260	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
261	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
262	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
263	C₂×C₄²×C₆₁	C₂³	1	12	yes	—
264	C₂×C₄²×C₆₁	C₂³	1	12	yes	—
265	C₂⁴×C₆₁	C₂⁴	1	6	yes	—
266	#41×C₆₁	—	2	8	no	—
267	#41×C₆₁	—	2	48	no	—
268	#41×C₆₁	—	2	12	no	—
269	#41×C₆₁	—	2	24	no	—
270	#41×C₆₁	—	4	12	no	—
271	#41×C₆₁	#41	1	8	yes	complemented
272	C₂×Q₈×C₆₁	—	2	16	no	—
273	C₂×Q₈×C₆₁	—	2	24	no	—
274	C₂×Q₈×C₆₁	—	4	6	no	—
275	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
276	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
277	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
278	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
279	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
280	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
281	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
282	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₂×D₄×C₆₁	—	2	24	no	—
284	C₂×D₄×C₆₁	—	2	12	no	—
285	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
286	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
287	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
288	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
289	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
290	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
291	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
292	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
293	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
294	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
295	C₂²×C₄×C₆₁	—	4	12	no	—
296	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
297	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
298	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
299	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
300	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
301	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
302	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
304	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
305	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
306	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
307	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
308	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
309	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
310	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
311	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
314	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
315	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
316	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
317	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
318	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
319	C₄⋊C₄×C₆₁	C₂⁴	1	24	yes	—
320	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
321	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
322	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
323	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
324	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
325	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
326	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
327	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
328	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
329	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
330	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
331	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
332	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
333	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
334	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
335	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
336	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
337	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
338	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
339	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
340	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
341	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
342	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
343	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
344	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
345	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
346	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
347	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
348	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
349	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
350	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
351	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
352	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
353	C₄²×C₆₁	C₂⁴	1	6	yes	—
354	C₄²×C₆₁	C₂⁴	1	12	yes	—
355	C₄²×C₆₁	C₂⁴	1	3	yes	—
356	C₄²×C₆₁	C₂⁴	1	2	yes	—
357	C₄²×C₆₁	C₂⁴	1	6	yes	—
358	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
359	C₄²×C₆₁	C₂⁴	1	2	yes	—
360	C₄²×C₆₁	C₂⁴	1	6	yes	—
361	C₄²×C₆₁	C₂⁴	1	12	yes	—
362	C₄²×C₆₁	C₂⁴	1	24	yes	—
363	C₄²×C₆₁	C₂⁴	1	3	yes	—
364	C₄²×C₆₁	C₂⁴	1	6	yes	—
365	C₄²×C₆₁	C₂⁴	1	3	yes	—
366	C₄²×C₆₁	C₂⁴	1	6	yes	—
367	C₂³×C₆₁	—	2	12	no	—
368	C₂³×C₆₁	—	4	6	no	—
369	C₂³×C₆₁	—	4	6	no	—
370	C₂³×C₆₁	C₂⁵	1	6	yes	—
371	C₂³×C₆₁	C₂⁵	1	4	yes	—
372	C₂³×C₆₁	C₂⁵	1	3	yes	—
373	Q₈×C₆₁	—	2	24	no	—
374	Q₈×C₆₁	—	2	12	no	—
375	Q₈×C₆₁	—	2	2	no	—
376	Q₈×C₆₁	—	2	2	no	—
377	Q₈×C₆₁	—	2	6	no	—
378	Q₈×C₆₁	—	4	6	no	—
379	Q₈×C₆₁	—	4	6	no	—
380	Q₈×C₆₁	C₂×#41	1	4	yes	—
381	D₄×C₆₁	—	2	12	no	—
382	D₄×C₆₁	—	2	24	no	—
383	D₄×C₆₁	—	2	12	no	—
384	D₄×C₆₁	—	2	6	no	—
385	D₄×C₆₁	—	2	4	no	—
386	D₄×C₆₁	—	2	4	no	—
387	D₄×C₆₁	—	4	2	no	—
388	D₄×C₆₁	—	4	12	no	—
389	D₄×C₆₁	—	4	12	no	—
390	D₄×C₆₁	C₂×#41	1	12	yes	—
391	C₂×C₄×C₆₁	—	2	24	no	—
392	C₂×C₄×C₆₁	—	2	12	no	—
393	C₂×C₄×C₆₁	—	2	24	no	—
394	C₂×C₄×C₆₁	—	2	6	no	—
395	C₂×C₄×C₆₁	—	2	12	no	—
396	C₂×C₄×C₆₁	—	4	6	no	—
397	C₂×C₄×C₆₁	—	4	12	no	—
398	C₂×C₄×C₆₁	—	4	4	no	—
399	C₂×C₄×C₆₁	—	4	6	no	—
400	C₂×C₄×C₆₁	—	4	6	no	—
401	C₂×C₄×C₆₁	—	4	3	no	—
402	C₂×C₄×C₆₁	—	4	6	no	—
403	C₂×C₄×C₆₁	—	4	12	no	—
404	C₂×C₄×C₆₁	C₂×#41	1	12	yes	—
405	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
406	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
407	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
408	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
409	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
410	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
411	C₂×C₄×C₆₁	C₂⁵	1	12	yes	—
412	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
413	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
414	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
415	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
416	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
417	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
418	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
419	#62995	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
420	C₂²×C₆₁	—	2	3	no	—
421	C₂²×C₆₁	—	2	3	no	—
422	C₂²×C₆₁	—	2	4	no	—
423	C₂²×C₆₁	—	2	6	no	—
424	C₂²×C₆₁	—	2	6	no	—
425	C₂²×C₆₁	—	2	4	no	—
426	C₂²×C₆₁	—	2	4	no	—
427	C₂²×C₆₁	—	2	6	no	—
428	C₂²×C₆₁	—	8	12	no	—
429	C₂²×C₆₁	C₂²×#41	1	6	yes	—
430	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
431	C₄×C₆₁	—	2	2	no	—
432	C₄×C₆₁	—	2	12	no	—
433	C₄×C₆₁	—	2	6	no	—
434	C₄×C₆₁	—	2	3	no	—
435	C₄×C₆₁	—	2	6	no	—
436	C₄×C₆₁	—	2	2	no	—
437	C₄×C₆₁	—	2	2	no	—
438	C₄×C₆₁	—	2	2	no	—
439	C₄×C₆₁	—	2	1	no	—
440	C₄×C₆₁	—	2	3	no	—
441	C₄×C₆₁	—	2	6	no	—
442	C₄×C₆₁	C₂²×#41	1	6	yes	—
443	C₄×C₆₁	C₂²×#41	1	2	yes	—
444	C₄×C₆₁	#585	1	2	yes	—
445	#3521	C₂×C₆₁	1	12	yes	complemented
446	#3520	C₂×C₆₁	1	6	yes	complemented
447	#3518	C₂×C₆₁	1	2	yes	complemented
448	#3516	C₂×C₆₁	1	4	yes	complemented
449	#3510	C₂×C₆₁	1	6	yes	complemented
450	#3509	C₂×C₆₁	1	3	yes	complemented
451	#3507	C₂×C₆₁	1	6	yes	complemented
452	#3506	C₂×C₆₁	1	3	yes	complemented
453	#3500	C₂×C₆₁	1	2	yes	complemented
454	#3499	C₂×C₆₁	1	1	yes	characteristic, complemented
455	#3482	C₂×C₆₁	1	2	yes	complemented
456	#3480	C₂×C₆₁	1	3	yes	complemented
457	Q₈×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
458	#3475	C₂×C₆₁	1	6	yes	complemented
459	C₂×#556	C₂×C₆₁	1	3	yes	complemented
460	C₄×2₋¹⁺⁴	C₂×C₆₁	1	2	yes	complemented
461	C₄×H(5,𝔽₂)	C₂×C₆₁	1	1	yes	characteristic, complemented
462	C₂×C₆₁	—	2	6	no	—
463	C₂×C₆₁	—	4	4	no	—
464	C₂×C₆₁	—	4	6	no	—
465	C₂×C₆₁	C₂³×#41	1	1	yes	characteristic
466	C₂×C₆₁	C₂×#585	1	1	yes	characteristic
467	C₂×C₆₁	2₋¹⁺⁶	1	1	yes	characteristic
468	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	2	yes	—
469	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	1	yes	characteristic
470	#559	C₂²×C₆₁	1	1	yes	characteristic, complemented
471	#559	C₂²×C₆₁	1	6	yes	complemented
472	#559	C₂²×C₆₁	1	12	yes	complemented
473	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
474	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
475	#557	C₂²×C₆₁	1	2	yes	complemented
476	#557	C₂²×C₆₁	1	3	yes	complemented
477	#557	C₂²×C₆₁	1	6	yes	complemented
478	#556	C₂²×C₆₁	1	3	yes	complemented
479	#556	C₂²×C₆₁	1	6	yes	complemented
480	#556	C₂²×C₆₁	1	6	yes	complemented
481	#556	C₂²×C₆₁	1	12	yes	complemented
482	#556	C₂²×C₆₁	1	12	yes	complemented
483	#556	C₂²×C₆₁	1	6	yes	complemented
484	#556	C₂²×C₆₁	1	6	yes	complemented
485	#556	C₂²×C₆₁	1	12	yes	complemented
486	#556	C₂²×C₆₁	1	6	yes	complemented
487	#555	C₂²×C₆₁	1	6	yes	complemented
488	#554	C₂²×C₆₁	1	3	yes	complemented
489	#554	C₂²×C₆₁	1	6	yes	complemented
490	#554	C₂²×C₆₁	1	12	yes	complemented
491	#553	C₂²×C₆₁	1	6	yes	complemented
492	#553	C₂²×C₆₁	1	12	yes	complemented
493	#553	C₂²×C₆₁	1	12	yes	complemented
494	#552	C₂²×C₆₁	1	12	yes	complemented
495	#552	C₂²×C₆₁	1	12	yes	complemented
496	#552	C₂²×C₆₁	1	12	yes	complemented
497	#552	C₂²×C₆₁	1	12	yes	complemented
498	#551	C₂²×C₆₁	1	24	yes	complemented
499	#551	C₂²×C₆₁	1	24	yes	complemented
500	#550	C₂²×C₆₁	1	3	yes	complemented
501	D₄×Q₈	C₂²×C₆₁	1	3	yes	complemented
502	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
503	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
504	#548	C₂²×C₆₁	1	4	yes	—
505	#548	C₂²×C₆₁	1	4	yes	—
506	#548	C₂²×C₆₁	1	6	yes	complemented
507	#547	C₂²×C₆₁	1	6	yes	complemented
508	#547	C₂²×C₆₁	1	6	yes	complemented
509	#547	C₂²×C₆₁	1	6	yes	complemented
510	#546	C₂²×C₆₁	1	12	yes	—
511	#546	C₂²×C₆₁	1	12	yes	—
512	#542	C₂²×C₆₁	1	12	yes	complemented
513	#542	C₂²×C₆₁	1	12	yes	complemented
514	#541	C₂²×C₆₁	1	12	yes	complemented
515	#539	C₂²×C₆₁	1	24	yes	complemented
516	#538	C₂²×C₆₁	1	12	yes	complemented
517	#536	C₂²×C₆₁	1	6	yes	—
518	#536	C₂²×C₆₁	1	6	yes	complemented
519	#535	C₂²×C₆₁	1	6	yes	—
520	#533	C₂²×C₆₁	1	6	yes	complemented
521	#533	C₂²×C₆₁	1	3	yes	complemented
522	#533	C₂²×C₆₁	1	6	yes	complemented
523	#533	C₂²×C₆₁	1	6	yes	complemented
524	#532	C₂²×C₆₁	1	6	yes	—
525	#532	C₂²×C₆₁	1	3	yes	complemented
526	C₂×C₄⋊Q₈	C₂²×C₆₁	1	3	yes	complemented
527	#529	C₂²×C₆₁	1	24	yes	complemented
528	#529	C₂²×C₆₁	1	12	yes	complemented
529	#529	C₂²×C₆₁	1	12	yes	complemented
530	#529	C₂²×C₆₁	1	6	yes	complemented
531	#529	C₂²×C₆₁	1	12	yes	complemented
532	C₂×#126	C₂²×C₆₁	1	12	yes	complemented
533	C₂×#124	C₂²×C₆₁	1	6	yes	—
534	#525	C₂²×C₆₁	1	12	yes	complemented
535	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	6	yes	complemented
536	#520	C₂²×C₆₁	1	1	yes	characteristic
537	#520	C₂²×C₆₁	1	3	yes	—
538	#520	C₂²×C₆₁	1	2	yes	—
539	#520	C₂²×C₆₁	1	6	yes	complemented
540	#520	C₂²×C₆₁	1	12	yes	complemented
541	#519	C₂²×C₆₁	1	6	yes	complemented
542	#519	C₂²×C₆₁	1	4	yes	complemented
543	#518	C₂²×C₆₁	1	3	yes	—
544	#518	C₂²×C₆₁	1	6	yes	—
545	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
546	C₄×#41	C₂²×C₆₁	1	3	yes	—
547	C₄×#41	C₂²×C₆₁	1	2	yes	—
548	C₄×#41	C₂²×C₆₁	1	2	yes	—
549	C₄×#41	C₂²×C₆₁	1	12	yes	complemented
550	C₄×#41	C₂²×C₆₁	1	6	yes	complemented
551	C₄×#41	C₂²×C₆₁	1	6	yes	complemented
552	C₂×C₄×Q₈	C₂²×C₆₁	1	6	yes	complemented
553	C₂×C₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
554	C₂×C₄×Q₈	C₂²×C₆₁	1	3	yes	complemented
555	C₂×C₄×D₄	C₂²×C₆₁	1	3	yes	—
556	C₂×C₄×D₄	C₂²×C₆₁	1	6	yes	—
557	C₂×#117	C₂²×C₆₁	1	6	yes	complemented
558	C₆₁	#62995	1	1	yes	characteristic, direct product factor, Sylow
559	2₋¹⁺⁴	—	2	16	no	—
560	H(5,𝔽₂)	—	2	8	no	—
561	C₂×#41	C₂³×C₆₁	1	3	yes	—
562	C₂×#41	C₂³×C₆₁	1	2	yes	—
563	C₂×#41	C₂³×C₆₁	1	6	yes	—
564	C₂×#41	C₂³×C₆₁	1	12	yes	—
565	C₂×#41	C₂³×C₆₁	1	6	yes	—
566	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
567	C₂²×Q₈	C₂³×C₆₁	1	6	yes	—
568	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
569	C₂²×Q₈	C₂³×C₆₁	1	3	yes	—
570	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
571	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
572	C₂³×C₄	C₂³×C₆₁	1	6	yes	—
573	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
574	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
575	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
576	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
577	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
578	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
579	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
580	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
581	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
582	#127	C₂³×C₆₁	1	6	yes	—
583	#127	C₂³×C₆₁	1	1	yes	characteristic
584	#126	C₂³×C₆₁	1	12	yes	—
585	#126	C₂³×C₆₁	1	24	yes	—
586	#126	C₂³×C₆₁	1	24	yes	—
587	#126	C₂³×C₆₁	1	24	yes	—
588	#126	C₂³×C₆₁	1	12	yes	—
589	#126	C₂³×C₆₁	1	12	yes	—
590	#126	C₂³×C₆₁	1	24	yes	—
591	#125	C₂³×C₆₁	1	6	yes	—
592	#125	C₂³×C₆₁	1	6	yes	—
593	#125	C₂³×C₆₁	1	6	yes	—
594	#125	C₂³×C₆₁	1	24	yes	—
595	#125	C₂³×C₆₁	1	12	yes	—
596	#125	C₂³×C₆₁	1	12	yes	—
597	#125	C₂³×C₆₁	1	6	yes	—
598	#124	C₂³×C₆₁	1	6	yes	—
599	#124	C₂³×C₆₁	1	12	yes	—
600	#124	C₂³×C₆₁	1	12	yes	—
601	#124	C₂³×C₆₁	1	12	yes	—
602	#124	C₂³×C₆₁	1	2	yes	—
603	#124	C₂³×C₆₁	1	24	yes	—
604	#124	C₂³×C₆₁	1	12	yes	—
605	#124	C₂³×C₆₁	1	2	yes	—
606	#124	C₂³×C₆₁	1	6	yes	—
607	#123	C₂³×C₆₁	1	24	yes	—
608	#123	C₂³×C₆₁	1	12	yes	—
609	#123	C₂³×C₆₁	1	4	yes	—
610	#123	C₂³×C₆₁	1	24	yes	—
611	#123	C₂³×C₆₁	1	24	yes	—
612	#123	C₂³×C₆₁	1	24	yes	—
613	#123	C₂³×C₆₁	1	12	yes	—
614	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
615	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
616	C₂²⋊Q₈	C₂³×C₆₁	1	24	yes	—
617	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
618	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
619	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
620	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
621	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
622	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
623	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
624	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
625	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
626	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
627	#121	C₂³×C₆₁	1	6	yes	—
628	#121	C₂³×C₆₁	1	6	yes	—
629	#121	C₂³×C₆₁	1	12	yes	—
630	#121	C₂³×C₆₁	1	12	yes	—
631	#121	C₂³×C₆₁	1	12	yes	—
632	#121	C₂³×C₆₁	1	12	yes	—
633	#121	C₂³×C₆₁	1	12	yes	—
634	#121	C₂³×C₆₁	1	6	yes	—
635	#120	C₂³×C₆₁	1	24	yes	—
636	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
637	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
638	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
639	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
640	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
641	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
642	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
643	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
644	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
645	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
646	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
647	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
648	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
649	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
650	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
651	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
652	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
653	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
654	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
655	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
656	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
657	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
658	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
659	C₄×D₄	C₂³×C₆₁	1	3	yes	—
660	C₄×D₄	C₂³×C₆₁	1	6	yes	—
661	C₄×D₄	C₂³×C₆₁	1	6	yes	—
662	C₄×D₄	C₂³×C₆₁	1	3	yes	—
663	C₄×D₄	C₂³×C₆₁	1	6	yes	—
664	C₄×D₄	C₂³×C₆₁	1	12	yes	—
665	C₄×D₄	C₂³×C₆₁	1	6	yes	—
666	C₄×D₄	C₂³×C₆₁	1	6	yes	—
667	C₄×D₄	C₂³×C₆₁	1	6	yes	—
668	C₄×D₄	C₂³×C₆₁	1	6	yes	—
669	C₄×D₄	C₂³×C₆₁	1	6	yes	—
670	C₄×D₄	C₂³×C₆₁	1	3	yes	—
671	C₄×D₄	C₂³×C₆₁	1	6	yes	—
672	C₄×D₄	C₂³×C₆₁	1	3	yes	—
673	C₄×D₄	C₂³×C₆₁	1	6	yes	—
674	C₄×D₄	C₂³×C₆₁	1	12	yes	—
675	C₄×D₄	C₂³×C₆₁	1	2	yes	—
676	C₄×D₄	C₂³×C₆₁	1	2	yes	—
677	C₄×D₄	C₂³×C₆₁	1	24	yes	—
678	C₄×D₄	C₂³×C₆₁	1	12	yes	—
679	C₄×D₄	C₂³×C₆₁	1	6	yes	—
680	C₄×D₄	C₂³×C₆₁	1	12	yes	—
681	C₄×D₄	C₂³×C₆₁	1	12	yes	—
682	C₄×D₄	C₂³×C₆₁	1	6	yes	—
683	C₄×D₄	C₂³×C₆₁	1	24	yes	—
684	C₄×D₄	C₂³×C₆₁	1	12	yes	—
685	C₄×D₄	C₂³×C₆₁	1	6	yes	—
686	#117	C₂³×C₆₁	1	6	yes	—
687	#117	C₂³×C₆₁	1	12	yes	—
688	#117	C₂³×C₆₁	1	24	yes	—
689	#117	C₂³×C₆₁	1	3	yes	—
690	#117	C₂³×C₆₁	1	6	yes	—
691	#117	C₂³×C₆₁	1	3	yes	—
692	#117	C₂³×C₆₁	1	6	yes	—
693	#117	C₂³×C₆₁	1	6	yes	—
694	#117	C₂³×C₆₁	1	12	yes	—
695	#117	C₂³×C₆₁	1	24	yes	—
696	#117	C₂³×C₆₁	1	12	yes	—
697	#117	C₂³×C₆₁	1	12	yes	—
698	#117	C₂³×C₆₁	1	12	yes	—
699	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
700	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
701	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
702	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
703	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
704	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
705	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
706	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
711	C₂×C₄²	C₂³×C₆₁	1	12	yes	—
712	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
713	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
714	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
715	C₂×C₄²	C₂³×C₆₁	1	12	yes	—
716	C₂⁴	C₂⁴×C₆₁	1	6	yes	—
717	#41	—	2	8	no	—
718	#41	—	2	48	no	—
719	#41	—	2	12	no	—
720	#41	—	2	24	no	—
721	#41	—	4	12	no	—
722	#41	#41×C₆₁	1	8	yes	complemented
723	C₂×Q₈	—	2	16	no	—
724	C₂×Q₈	—	2	24	no	—
725	C₂×Q₈	—	4	6	no	—
726	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
727	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
728	C₂×Q₈	C₂⁴×C₆₁	1	12	yes	—
729	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
730	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
731	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
732	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
733	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
734	C₂×D₄	—	2	24	no	—
735	C₂×D₄	—	2	12	no	—
736	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
737	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
738	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
739	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
740	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
741	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
742	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
743	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
744	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
745	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
746	C₂²×C₄	—	4	12	no	—
747	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
748	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
749	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
750	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
751	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
752	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
753	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
754	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
755	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
756	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
757	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
758	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
759	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
760	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
761	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
762	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
764	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
765	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
766	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
767	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
768	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
769	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
770	C₄⋊C₄	C₂⁴×C₆₁	1	24	yes	—
771	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
772	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
773	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
774	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
775	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
776	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
777	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
778	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
779	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
780	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
781	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
782	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
783	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
784	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
785	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
786	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
787	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
788	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
789	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
790	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
791	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
792	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
793	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
794	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
795	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
796	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
797	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
798	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
799	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
800	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
801	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
802	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
803	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
804	C₄²	C₂⁴×C₆₁	1	6	yes	—
805	C₄²	C₂⁴×C₆₁	1	12	yes	—
806	C₄²	C₂⁴×C₆₁	1	3	yes	—
807	C₄²	C₂⁴×C₆₁	1	2	yes	—
808	C₄²	C₂⁴×C₆₁	1	6	yes	—
809	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
810	C₄²	C₂⁴×C₆₁	1	2	yes	—
811	C₄²	C₂⁴×C₆₁	1	6	yes	—
812	C₄²	C₂⁴×C₆₁	1	12	yes	—
813	C₄²	C₂⁴×C₆₁	1	24	yes	—
814	C₄²	C₂⁴×C₆₁	1	3	yes	—
815	C₄²	C₂⁴×C₆₁	1	6	yes	—
816	C₄²	C₂⁴×C₆₁	1	3	yes	—
817	C₄²	C₂⁴×C₆₁	1	6	yes	—
818	C₂³	—	2	12	no	—
819	C₂³	—	4	6	no	—
820	C₂³	—	4	6	no	—
821	C₂³	C₂⁵×C₆₁	1	6	yes	—
822	C₂³	C₂⁵×C₆₁	1	4	yes	—
823	C₂³	C₂⁵×C₆₁	1	3	yes	—
824	Q₈	—	2	24	no	—
825	Q₈	—	2	12	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	2	6	no	—
829	Q₈	—	4	6	no	—
830	Q₈	—	4	6	no	—
831	Q₈	C₂×#41×C₆₁	1	4	yes	—
832	D₄	—	2	12	no	—
833	D₄	—	2	24	no	—
834	D₄	—	2	12	no	—
835	D₄	—	2	6	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	4	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	12	no	—
840	D₄	—	4	12	no	—
841	D₄	C₂×#41×C₆₁	1	12	yes	—
842	C₂×C₄	—	2	24	no	—
843	C₂×C₄	—	2	12	no	—
844	C₂×C₄	—	2	24	no	—
845	C₂×C₄	—	2	6	no	—
846	C₂×C₄	—	2	12	no	—
847	C₂×C₄	—	4	6	no	—
848	C₂×C₄	—	4	12	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	4	6	no	—
851	C₂×C₄	—	4	6	no	—
852	C₂×C₄	—	4	3	no	—
853	C₂×C₄	—	4	6	no	—
854	C₂×C₄	—	4	12	no	—
855	C₂×C₄	C₂×#41×C₆₁	1	12	yes	—
856	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
857	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
858	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
859	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
860	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
861	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
862	C₂×C₄	C₂⁵×C₆₁	1	12	yes	—
863	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
864	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
865	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
866	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
867	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
868	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
869	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
870	C₂²	—	2	3	no	—
871	C₂²	—	2	3	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	6	no	—
874	C₂²	—	2	6	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	6	no	—
878	C₂²	—	8	12	no	—
879	C₂²	C₂²×#41×C₆₁	1	6	yes	—
880	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
881	C₄	—	2	2	no	—
882	C₄	—	2	12	no	—
883	C₄	—	2	6	no	—
884	C₄	—	2	3	no	—
885	C₄	—	2	6	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	3	no	—
891	C₄	—	2	6	no	—
892	C₄	C₂²×#41×C₆₁	1	6	yes	—
893	C₄	C₂²×#41×C₆₁	1	2	yes	—
894	C₄	C₆₁×#585	1	2	yes	—
895	C₂	—	2	6	no	—
896	C₂	—	4	6	no	—
897	C₂	—	4	4	no	—
898	C₂	C₂³×#41×C₆₁	1	1	yes	characteristic
899	C₂	C₂×C₆₁×#585	1	1	yes	characteristic
900	C₂	C₆₁×2₋¹⁺⁶	1	1	yes	characteristic

	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×#3521	C₂	semidirect
2. C₆₁×#3520	C₂	semidirect
3. C₆₁×#3518	C₂	semidirect
4. C₆₁×#3516	C₂	semidirect
5. C₆₁×#3510	C₂	semidirect
6. C₆₁×#3509	C₂	semidirect
7. C₆₁×#3507	C₂	semidirect
8. C₆₁×#3506	C₂	semidirect
9. C₆₁×#3500	C₂	semidirect
10. C₆₁×#3499	C₂	semidirect
11. C₆₁×#3482	C₂	semidirect
12. C₆₁×#3480	C₂	semidirect
13. Q₈×#41×C₆₁	C₂	semidirect
14. C₆₁×#3475	C₂	semidirect
15. C₂×C₆₁×#556	C₂	semidirect
16. C₄×2₋¹⁺⁴×C₆₁	C₂	semidirect
17. C₄×H(5,𝔽₂)×C₆₁	C₂	semidirect
20. C₆₁×#559	C₂²	semidirect
21. C₆₁×#559	C₂²	semidirect
22. C₆₁×#559	C₂²	semidirect
23. Q₈²×C₆₁	C₂²	semidirect
24. C₆₁×#557	C₂²	semidirect
25. C₆₁×#557	C₂²	semidirect
26. C₆₁×#557	C₂²	semidirect
27. C₆₁×#557	C₂²	semidirect
28. C₆₁×#556	C₂²	semidirect
29. C₆₁×#556	C₂²	semidirect
30. C₆₁×#556	C₂²	semidirect
31. C₆₁×#556	C₂²	semidirect
32. C₆₁×#556	C₂²	semidirect
33. C₆₁×#556	C₂²	semidirect
34. C₆₁×#556	C₂²	semidirect
35. C₆₁×#556	C₂²	semidirect
36. C₆₁×#556	C₂²	semidirect
37. C₆₁×#555	C₂²	semidirect
38. C₆₁×#554	C₂²	semidirect
39. C₆₁×#554	C₂²	semidirect
40. C₆₁×#554	C₂²	semidirect
41. C₆₁×#553	C₂²	semidirect
42. C₆₁×#553	C₂²	semidirect
43. C₆₁×#553	C₂²	semidirect
44. C₆₁×#552	C₂²	semidirect
45. C₆₁×#552	C₂²	semidirect
46. C₆₁×#552	C₂²	semidirect
47. C₆₁×#552	C₂²	semidirect
48. C₆₁×#551	C₂²	semidirect
49. C₆₁×#551	C₂²	semidirect
50. C₆₁×#550	C₂²	semidirect
51. D₄×Q₈×C₆₁	C₂²	semidirect
52. D₄×Q₈×C₆₁	C₂²	semidirect
53. D₄×Q₈×C₆₁	C₂²	semidirect
56. C₆₁×#548	C₂²	semidirect
57. C₆₁×#547	C₂²	semidirect
58. C₆₁×#547	C₂²	semidirect
59. C₆₁×#547	C₂²	semidirect
62. C₆₁×#542	C₂²	semidirect
63. C₆₁×#542	C₂²	semidirect
64. C₆₁×#541	C₂²	semidirect
65. C₆₁×#539	C₂²	semidirect
66. C₆₁×#538	C₂²	semidirect
68. C₆₁×#536	C₂²	semidirect
70. C₆₁×#533	C₂²	semidirect
71. C₆₁×#533	C₂²	semidirect
72. C₆₁×#533	C₂²	semidirect
73. C₆₁×#533	C₂²	semidirect
75. C₆₁×#532	C₂²	semidirect
76. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
77. C₆₁×#529	C₂²	semidirect
78. C₆₁×#529	C₂²	semidirect
79. C₆₁×#529	C₂²	semidirect
80. C₆₁×#529	C₂²	semidirect
81. C₆₁×#529	C₂²	semidirect
82. C₂×#126×C₆₁	C₂²	semidirect
84. C₆₁×#525	C₂²	semidirect
85. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
89. C₆₁×#520	C₂²	semidirect
90. C₆₁×#520	C₂²	semidirect
91. C₆₁×#519	C₂²	semidirect
92. C₆₁×#519	C₂²	semidirect
99. C₄×#41×C₆₁	C₂²	semidirect
100. C₄×#41×C₆₁	C₂²	semidirect
101. C₄×#41×C₆₁	C₂²	semidirect
102. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
103. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
104. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
107. C₂×#117×C₆₁	C₂²	semidirect
271. #41×C₆₁	#41	semidirect
419. #62995	C₆₁	direct (N × H)
445. #3521	C₂×C₆₁	semidirect
446. #3520	C₂×C₆₁	semidirect
447. #3518	C₂×C₆₁	semidirect
448. #3516	C₂×C₆₁	semidirect
449. #3510	C₂×C₆₁	semidirect
450. #3509	C₂×C₆₁	semidirect
451. #3507	C₂×C₆₁	semidirect
452. #3506	C₂×C₆₁	semidirect
453. #3500	C₂×C₆₁	semidirect
454. #3499	C₂×C₆₁	semidirect
455. #3482	C₂×C₆₁	semidirect
456. #3480	C₂×C₆₁	semidirect
457. Q₈×#41	C₂×C₆₁	semidirect
458. #3475	C₂×C₆₁	semidirect
459. C₂×#556	C₂×C₆₁	semidirect
460. C₄×2₋¹⁺⁴	C₂×C₆₁	semidirect
461. C₄×H(5,𝔽₂)	C₂×C₆₁	semidirect
470. #559	C₂²×C₆₁	semidirect
471. #559	C₂²×C₆₁	semidirect
472. #559	C₂²×C₆₁	semidirect
473. Q₈²	C₂²×C₆₁	semidirect
474. #557	C₂²×C₆₁	semidirect
475. #557	C₂²×C₆₁	semidirect
476. #557	C₂²×C₆₁	semidirect
477. #557	C₂²×C₆₁	semidirect
478. #556	C₂²×C₆₁	semidirect
479. #556	C₂²×C₆₁	semidirect
480. #556	C₂²×C₆₁	semidirect
481. #556	C₂²×C₆₁	semidirect
482. #556	C₂²×C₆₁	semidirect
483. #556	C₂²×C₆₁	semidirect
484. #556	C₂²×C₆₁	semidirect
485. #556	C₂²×C₆₁	semidirect
486. #556	C₂²×C₆₁	semidirect
487. #555	C₂²×C₆₁	semidirect
488. #554	C₂²×C₆₁	semidirect
489. #554	C₂²×C₆₁	semidirect
490. #554	C₂²×C₆₁	semidirect
491. #553	C₂²×C₆₁	semidirect
492. #553	C₂²×C₆₁	semidirect
493. #553	C₂²×C₆₁	semidirect
494. #552	C₂²×C₆₁	semidirect
495. #552	C₂²×C₆₁	semidirect
496. #552	C₂²×C₆₁	semidirect
497. #552	C₂²×C₆₁	semidirect
498. #551	C₂²×C₆₁	semidirect
499. #551	C₂²×C₆₁	semidirect
500. #550	C₂²×C₆₁	semidirect
501. D₄×Q₈	C₂²×C₆₁	semidirect
502. D₄×Q₈	C₂²×C₆₁	semidirect
503. D₄×Q₈	C₂²×C₆₁	semidirect
506. #548	C₂²×C₆₁	semidirect
507. #547	C₂²×C₆₁	semidirect
508. #547	C₂²×C₆₁	semidirect
509. #547	C₂²×C₆₁	semidirect
512. #542	C₂²×C₆₁	semidirect
513. #542	C₂²×C₆₁	semidirect
514. #541	C₂²×C₆₁	semidirect
515. #539	C₂²×C₆₁	semidirect
516. #538	C₂²×C₆₁	semidirect
518. #536	C₂²×C₆₁	semidirect
520. #533	C₂²×C₆₁	semidirect
521. #533	C₂²×C₆₁	semidirect
522. #533	C₂²×C₆₁	semidirect
523. #533	C₂²×C₆₁	semidirect
525. #532	C₂²×C₆₁	semidirect
526. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
527. #529	C₂²×C₆₁	semidirect
528. #529	C₂²×C₆₁	semidirect
529. #529	C₂²×C₆₁	semidirect
530. #529	C₂²×C₆₁	semidirect
531. #529	C₂²×C₆₁	semidirect
532. C₂×#126	C₂²×C₆₁	semidirect
534. #525	C₂²×C₆₁	semidirect
535. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
539. #520	C₂²×C₆₁	semidirect
540. #520	C₂²×C₆₁	semidirect
541. #519	C₂²×C₆₁	semidirect
542. #519	C₂²×C₆₁	semidirect
549. C₄×#41	C₂²×C₆₁	semidirect
550. C₄×#41	C₂²×C₆₁	semidirect
551. C₄×#41	C₂²×C₆₁	semidirect
552. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
553. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
554. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
557. C₂×#117	C₂²×C₆₁	semidirect
558. C₆₁	#62995	direct (N × H)
722. #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×#3521	2
C₆₁×#3520	2
C₆₁×#3518	2
C₆₁×#3516	2
C₆₁×#3510	2
C₆₁×#3509	2
C₆₁×#3507	2
C₆₁×#3506	2
C₆₁×#3500	2
C₆₁×#3499	2
C₆₁×#3482	2
C₆₁×#3480	2
Q₈×#41×C₆₁	2
C₆₁×#3475	2
C₂×C₆₁×#556	2
C₄×2₋¹⁺⁴×C₆₁	2
C₄×H(5,𝔽₂)×C₆₁	2
#62995	61

Subgroups — C61×#62995 #29566428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62995 #29566428