Subgroups — C₆₁×#62913 #29566346

Order 15616.

6974 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3554	C₂	1	6	yes	maximal, complemented
2	C₆₁×#3552	C₂	1	6	yes	maximal, complemented
3	C₆₁×#3550	C₂	1	6	yes	maximal, complemented
4	C₆₁×#3547	C₂	1	6	yes	maximal, complemented
5	C₆₁×#3541	C₂	1	12	yes	maximal, complemented
6	C₆₁×#3523	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3518	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3511	C₂	1	3	yes	maximal, complemented
9	C₆₁×#3506	C₂	1	3	yes	maximal, complemented
10	C₆₁×#3503	C₂	1	3	yes	maximal, complemented
11	C₆₁×#3499	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3497	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3486	C₂	1	4	yes	maximal, complemented
14	C₆₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3460	C₂	1	3	yes	maximal, complemented
18	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	4	yes	complemented
19	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
20	C₆₁×#563	C₂²	1	24	yes	complemented
21	C₆₁×#562	C₂²	1	24	yes	complemented
22	C₆₁×#559	C₂²	1	12	yes	—
23	C₆₁×#559	C₂²	1	3	yes	complemented
24	Q₈²×C₆₁	C₂²	1	6	yes	complemented
25	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
26	C₆₁×#557	C₂²	1	3	yes	complemented
27	C₆₁×#557	C₂²	1	6	yes	complemented
28	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#556	C₂²	1	6	yes	—
30	C₆₁×#556	C₂²	1	3	yes	complemented
31	C₆₁×#556	C₂²	1	12	yes	complemented
32	C₆₁×#556	C₂²	1	6	yes	complemented
33	C₆₁×#555	C₂²	1	6	yes	—
34	C₆₁×#555	C₂²	1	6	yes	complemented
35	C₆₁×#554	C₂²	1	6	yes	—
36	C₆₁×#554	C₂²	1	12	yes	—
37	C₆₁×#554	C₂²	1	3	yes	complemented
38	C₆₁×#554	C₂²	1	6	yes	complemented
39	C₆₁×#554	C₂²	1	6	yes	complemented
40	C₆₁×#553	C₂²	1	12	yes	—
41	C₆₁×#553	C₂²	1	6	yes	—
42	C₆₁×#553	C₂²	1	12	yes	—
43	C₆₁×#552	C₂²	1	12	yes	complemented
44	C₆₁×#550	C₂²	1	6	yes	—
45	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
46	D₄×Q₈×C₆₁	C₂²	1	6	yes	—
47	D₄×Q₈×C₆₁	C₂²	1	6	yes	—
48	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
49	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
50	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
51	D₄×Q₈×C₆₁	C₂²	1	12	yes	—
52	D₄×Q₈×C₆₁	C₂²	1	12	yes	complemented
53	D₄×Q₈×C₆₁	C₂²	1	6	yes	complemented
54	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
55	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
56	C₆₁×#548	C₂²	1	2	yes	—
57	C₆₁×#548	C₂²	1	12	yes	—
58	C₆₁×#548	C₂²	1	12	yes	complemented
59	C₆₁×#548	C₂²	1	12	yes	complemented
60	C₆₁×#548	C₂²	1	4	yes	complemented
61	C₆₁×#547	C₂²	1	6	yes	—
62	C₆₁×#547	C₂²	1	6	yes	complemented
63	C₆₁×#547	C₂²	1	12	yes	complemented
64	C₆₁×#544	C₂²	1	3	yes	—
65	C₆₁×#544	C₂²	1	12	yes	complemented
66	C₆₁×#542	C₂²	1	6	yes	—
67	C₆₁×#542	C₂²	1	6	yes	—
68	C₆₁×#542	C₂²	1	24	yes	complemented
69	C₆₁×#542	C₂²	1	12	yes	complemented
70	C₆₁×#542	C₂²	1	12	yes	complemented
71	C₆₁×#541	C₂²	1	12	yes	complemented
72	C₆₁×#540	C₂²	1	6	yes	—
73	C₆₁×#540	C₂²	1	6	yes	—
74	C₆₁×#539	C₂²	1	24	yes	complemented
75	C₆₁×#538	C₂²	1	12	yes	—
76	C₆₁×#538	C₂²	1	12	yes	—
77	C₆₁×#537	C₂²	1	3	yes	—
78	C₆₁×#537	C₂²	1	12	yes	complemented
79	C₆₁×#536	C₂²	1	12	yes	complemented
80	C₆₁×#536	C₂²	1	12	yes	complemented
81	C₆₁×#536	C₂²	1	12	yes	complemented
82	C₆₁×#535	C₂²	1	1	yes	characteristic
83	C₆₁×#535	C₂²	1	3	yes	—
84	C₆₁×#533	C₂²	1	3	yes	—
85	C₆₁×#533	C₂²	1	6	yes	complemented
86	C₆₁×#533	C₂²	1	6	yes	complemented
87	C₆₁×#533	C₂²	1	6	yes	complemented
88	C₆₁×#532	C₂²	1	6	yes	—
89	C₆₁×#532	C₂²	1	6	yes	—
90	C₆₁×#532	C₂²	1	3	yes	—
91	C₆₁×#532	C₂²	1	6	yes	complemented
92	C₂×C₄⋊Q₈×C₆₁	C₂²	1	3	yes	—
93	C₂×C₄⋊Q₈×C₆₁	C₂²	1	6	yes	complemented
94	C₆₁×#529	C₂²	1	6	yes	—
95	C₆₁×#529	C₂²	1	6	yes	—
96	C₆₁×#529	C₂²	1	6	yes	complemented
97	C₆₁×#525	C₂²	1	12	yes	—
98	C₆₁×#525	C₂²	1	12	yes	—
99	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	6	yes	—
100	C₆₁×#520	C₂²	1	6	yes	—
101	C₆₁×#519	C₂²	1	4	yes	complemented
102	C₄×#41×C₆₁	C₂²	1	3	yes	—
103	C₄×#41×C₆₁	C₂²	1	3	yes	—
104	C₄×#41×C₆₁	C₂²	1	2	yes	complemented
105	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
106	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
107	C₂×C₄×D₄×C₆₁	C₂²	1	3	yes	—
108	2₋¹⁺⁴×C₆₁	—	4	16	no	—
109	C₂×#41×C₆₁	C₂³	1	3	yes	—
110	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
111	C₂×#41×C₆₁	C₂³	1	2	yes	—
112	C₂×#41×C₆₁	C₂³	1	12	yes	—
113	C₂×#41×C₆₁	C₂³	1	12	yes	—
114	C₂×#41×C₆₁	C₂³	1	12	yes	—
115	C₂²×Q₈×C₆₁	—	4	8	no	—
116	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
118	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
119	C₂²×Q₈×C₆₁	C₂³	1	6	yes	—
120	C₂²×Q₈×C₆₁	C₂³	1	12	yes	—
121	C₂²×Q₈×C₆₁	C₂³	1	12	yes	—
122	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
123	C₂³×C₄×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	6	yes	—
128	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
129	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
130	C₄⋊Q₈×C₆₁	C₂³	1	12	yes	—
131	C₄⋊Q₈×C₆₁	C₂³	1	12	yes	—
132	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
133	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
134	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
135	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
136	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
137	C₄⋊Q₈×C₆₁	C₂³	1	24	yes	—
138	#127×C₆₁	C₂³	1	2	yes	—
139	#127×C₆₁	C₂³	1	3	yes	—
140	#127×C₆₁	C₂³	1	6	yes	—
141	#126×C₆₁	C₂³	1	12	yes	—
142	#126×C₆₁	C₂³	1	24	yes	—
143	#126×C₆₁	C₂³	1	12	yes	—
144	#126×C₆₁	C₂³	1	24	yes	—
145	#126×C₆₁	C₂³	1	12	yes	—
146	#125×C₆₁	C₂³	1	6	yes	—
147	#125×C₆₁	C₂³	1	6	yes	—
148	#125×C₆₁	C₂³	1	12	yes	—
149	#125×C₆₁	C₂³	1	12	yes	—
150	#125×C₆₁	C₂³	1	24	yes	—
151	#125×C₆₁	C₂³	1	6	yes	—
152	#125×C₆₁	C₂³	1	6	yes	—
153	#124×C₆₁	C₂³	1	12	yes	—
154	#124×C₆₁	C₂³	1	12	yes	—
155	#124×C₆₁	C₂³	1	6	yes	—
156	#124×C₆₁	C₂³	1	12	yes	—
157	#124×C₆₁	C₂³	1	2	yes	—
158	#124×C₆₁	C₂³	1	6	yes	—
159	#124×C₆₁	C₂³	1	6	yes	—
160	#124×C₆₁	C₂³	1	24	yes	—
161	#124×C₆₁	C₂³	1	24	yes	—
162	#123×C₆₁	C₂³	1	12	yes	—
163	#123×C₆₁	C₂³	1	12	yes	—
164	#123×C₆₁	C₂³	1	24	yes	—
165	#123×C₆₁	C₂³	1	24	yes	—
166	#123×C₆₁	C₂³	1	24	yes	—
167	#123×C₆₁	C₂³	1	12	yes	—
168	#123×C₆₁	C₂³	1	12	yes	—
169	#123×C₆₁	C₂³	1	12	yes	—
170	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
171	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
172	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
173	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
174	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
175	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
176	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
177	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
178	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
179	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
180	C₂²⋊Q₈×C₆₁	C₂³	1	24	yes	—
181	C₂²⋊Q₈×C₆₁	C₂³	1	24	yes	—
182	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
183	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
184	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
185	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
186	C₂²⋊Q₈×C₆₁	C₂³	1	24	yes	—
187	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
188	C₂²⋊Q₈×C₆₁	C₂³	1	24	yes	—
189	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
190	#121×C₆₁	C₂³	1	2	yes	—
191	#121×C₆₁	C₂³	1	6	yes	—
192	#121×C₆₁	C₂³	1	6	yes	—
193	#121×C₆₁	C₂³	1	6	yes	—
194	#121×C₆₁	C₂³	1	12	yes	—
195	#121×C₆₁	C₂³	1	6	yes	—
196	#121×C₆₁	C₂³	1	12	yes	—
197	#121×C₆₁	C₂³	1	6	yes	—
198	#121×C₆₁	C₂³	1	12	yes	—
199	#121×C₆₁	C₂³	1	2	yes	—
200	#121×C₆₁	C₂³	1	6	yes	—
201	#121×C₆₁	C₂³	1	12	yes	—
202	#121×C₆₁	C₂³	1	6	yes	—
203	#121×C₆₁	C₂³	1	24	yes	—
204	#121×C₆₁	C₂³	1	12	yes	—
205	#121×C₆₁	C₂³	1	12	yes	—
206	#120×C₆₁	C₂³	1	4	yes	—
207	#120×C₆₁	C₂³	1	12	yes	—
208	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
209	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
210	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
211	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
212	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
213	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
214	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
215	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
216	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
217	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
218	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
223	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
224	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
225	C₄×D₄×C₆₁	C₂³	1	3	yes	—
226	C₄×D₄×C₆₁	C₂³	1	3	yes	—
227	C₄×D₄×C₆₁	C₂³	1	6	yes	—
228	C₄×D₄×C₆₁	C₂³	1	6	yes	—
229	C₄×D₄×C₆₁	C₂³	1	12	yes	—
230	C₄×D₄×C₆₁	C₂³	1	12	yes	—
231	C₄×D₄×C₆₁	C₂³	1	6	yes	—
232	C₄×D₄×C₆₁	C₂³	1	6	yes	—
233	C₄×D₄×C₆₁	C₂³	1	12	yes	—
234	C₄×D₄×C₆₁	C₂³	1	12	yes	—
235	C₄×D₄×C₆₁	C₂³	1	6	yes	—
236	C₄×D₄×C₆₁	C₂³	1	6	yes	—
237	C₄×D₄×C₆₁	C₂³	1	24	yes	—
238	C₄×D₄×C₆₁	C₂³	1	24	yes	—
239	C₄×D₄×C₆₁	C₂³	1	3	yes	—
240	C₄×D₄×C₆₁	C₂³	1	3	yes	—
241	C₄×D₄×C₆₁	C₂³	1	6	yes	—
242	C₄×D₄×C₆₁	C₂³	1	6	yes	—
243	C₄×D₄×C₆₁	C₂³	1	6	yes	—
244	C₄×D₄×C₆₁	C₂³	1	6	yes	—
245	C₄×D₄×C₆₁	C₂³	1	6	yes	—
246	#117×C₆₁	C₂³	1	3	yes	—
247	#117×C₆₁	C₂³	1	6	yes	—
248	#117×C₆₁	C₂³	1	12	yes	—
249	#117×C₆₁	C₂³	1	12	yes	—
250	#117×C₆₁	C₂³	1	1	yes	characteristic
251	#117×C₆₁	C₂³	1	6	yes	—
252	#117×C₆₁	C₂³	1	12	yes	—
253	#117×C₆₁	C₂³	1	12	yes	—
254	#117×C₆₁	C₂³	1	6	yes	—
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
259	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
260	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
261	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
262	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
263	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
264	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
265	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
266	#41×C₆₁	—	2	8	no	—
267	#41×C₆₁	—	2	12	no	—
268	#41×C₆₁	—	2	4	no	—
269	#41×C₆₁	—	4	24	no	—
270	#41×C₆₁	—	4	24	no	—
271	#41×C₆₁	—	4	24	no	—
272	C₂×Q₈×C₆₁	—	2	4	no	—
273	C₂×Q₈×C₆₁	—	2	16	no	—
274	C₂×Q₈×C₆₁	—	2	8	no	—
275	C₂×Q₈×C₆₁	—	4	12	no	—
276	C₂×Q₈×C₆₁	—	4	24	no	—
277	C₂×Q₈×C₆₁	—	4	24	no	—
278	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
279	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
280	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
281	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
282	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
283	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
284	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
285	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
286	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
287	C₂×D₄×C₆₁	—	2	4	no	—
288	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
289	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
290	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
291	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
292	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
293	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
294	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
295	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
296	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
297	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
298	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
299	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
300	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
301	C₂²×C₄×C₆₁	—	4	12	no	—
302	C₂²×C₄×C₆₁	C₂⁴	1	2	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	3	yes	—
309	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
310	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
311	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
312	C₂²×C₄×C₆₁	C₂⁴	1	24	yes	—
313	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
314	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
316	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
317	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
318	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
319	C₄⋊C₄×C₆₁	C₂⁴	1	12	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	12	yes	—
324	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
325	C₄⋊C₄×C₆₁	C₂⁴	1	24	yes	—
326	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
327	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
328	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
329	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
330	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
331	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
332	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
334	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
335	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
336	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
337	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
338	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
339	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
340	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
341	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
342	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
343	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
344	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
345	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
346	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
347	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
348	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
349	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
350	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
351	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
352	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
353	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
354	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
355	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
356	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
357	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
358	C₄²×C₆₁	C₂⁴	1	2	yes	—
359	C₄²×C₆₁	C₂⁴	1	3	yes	—
360	C₄²×C₆₁	C₂⁴	1	3	yes	—
361	C₄²×C₆₁	C₂⁴	1	3	yes	—
362	C₄²×C₆₁	C₂⁴	1	6	yes	—
363	C₄²×C₆₁	C₂⁴	1	6	yes	—
364	C₄²×C₆₁	C₂⁴	1	3	yes	—
365	C₄²×C₆₁	C₂⁴	1	6	yes	—
366	C₄²×C₆₁	C₂⁴	1	6	yes	—
367	C₄²×C₆₁	C₂⁴	1	6	yes	—
368	C₄²×C₆₁	C₂⁴	1	24	yes	—
369	C₂³×C₆₁	—	2	4	no	—
370	C₂³×C₆₁	—	4	2	no	—
371	C₂³×C₆₁	—	4	2	no	—
372	C₂³×C₆₁	C₂⁵	1	4	yes	—
373	C₂³×C₆₁	C₂⁵	1	2	yes	—
374	C₂³×C₆₁	C₂⁵	1	6	yes	—
375	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
376	Q₈×C₆₁	—	2	6	no	—
377	Q₈×C₆₁	—	2	24	no	—
378	Q₈×C₆₁	—	2	12	no	—
379	Q₈×C₆₁	—	2	2	no	—
380	Q₈×C₆₁	—	2	6	no	—
381	Q₈×C₆₁	—	4	12	no	—
382	Q₈×C₆₁	—	4	12	no	—
383	Q₈×C₆₁	—	4	6	no	—
384	Q₈×C₆₁	H(5,𝔽₂)	1	4	yes	—
385	D₄×C₆₁	—	2	4	no	—
386	D₄×C₆₁	—	2	12	no	—
387	D₄×C₆₁	—	2	12	no	—
388	D₄×C₆₁	—	2	4	no	—
389	D₄×C₆₁	—	2	4	no	—
390	D₄×C₆₁	—	2	2	no	—
391	D₄×C₆₁	—	2	6	no	—
392	D₄×C₆₁	—	4	4	no	—
393	D₄×C₆₁	—	4	6	no	—
394	D₄×C₆₁	—	4	12	no	—
395	D₄×C₆₁	—	4	4	no	—
396	D₄×C₆₁	—	4	12	no	—
397	D₄×C₆₁	—	4	12	no	—
398	C₂×C₄×C₆₁	—	2	6	no	—
399	C₂×C₄×C₆₁	—	2	24	no	—
400	C₂×C₄×C₆₁	—	2	12	no	—
401	C₂×C₄×C₆₁	—	2	12	no	—
402	C₂×C₄×C₆₁	—	2	12	no	—
403	C₂×C₄×C₆₁	—	2	4	no	—
404	C₂×C₄×C₆₁	—	4	6	no	—
405	C₂×C₄×C₆₁	—	4	12	no	—
406	C₂×C₄×C₆₁	—	4	3	no	—
407	C₂×C₄×C₆₁	—	4	6	no	—
408	C₂×C₄×C₆₁	—	4	6	no	—
409	C₂×C₄×C₆₁	—	4	24	no	—
410	C₂×C₄×C₆₁	2₋¹⁺⁴	1	4	yes	complemented
411	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
412	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
413	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
414	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
415	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
416	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
417	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
418	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
419	C₂×C₄×C₆₁	C₂⁵	1	12	yes	—
420	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
421	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
422	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
423	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
424	#62913	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
425	C₂²×C₆₁	—	2	1	no	—
426	C₂²×C₆₁	—	2	1	no	—
427	C₂²×C₆₁	—	2	4	no	—
428	C₂²×C₆₁	—	2	2	no	—
429	C₂²×C₆₁	—	2	6	no	—
430	C₂²×C₆₁	—	2	2	no	—
431	C₂²×C₆₁	—	2	6	no	—
432	C₂²×C₆₁	—	2	4	no	—
433	C₂²×C₆₁	—	2	2	no	—
434	C₂²×C₆₁	—	2	6	no	—
435	C₂²×C₆₁	—	2	4	no	—
436	C₂²×C₆₁	—	4	8	no	—
437	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
438	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
439	C₄×C₆₁	—	2	2	no	—
440	C₄×C₆₁	—	2	6	no	—
441	C₄×C₆₁	—	2	12	no	—
442	C₄×C₆₁	—	2	3	no	—
443	C₄×C₆₁	—	2	6	no	—
444	C₄×C₆₁	—	2	2	no	—
445	C₄×C₆₁	—	2	3	no	—
446	C₄×C₆₁	—	2	2	no	—
447	C₄×C₆₁	—	2	3	no	—
448	C₄×C₆₁	—	2	6	no	—
449	C₄×C₆₁	C₂×H(5,𝔽₂)	1	6	yes	—
450	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
451	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
452	#3554	C₂×C₆₁	1	6	yes	complemented
453	#3552	C₂×C₆₁	1	6	yes	complemented
454	#3550	C₂×C₆₁	1	6	yes	complemented
455	#3547	C₂×C₆₁	1	6	yes	complemented
456	#3541	C₂×C₆₁	1	12	yes	complemented
457	#3523	C₂×C₆₁	1	2	yes	complemented
458	#3518	C₂×C₆₁	1	2	yes	complemented
459	#3511	C₂×C₆₁	1	3	yes	complemented
460	#3506	C₂×C₆₁	1	3	yes	complemented
461	#3503	C₂×C₆₁	1	3	yes	complemented
462	#3499	C₂×C₆₁	1	2	yes	complemented
463	#3497	C₂×C₆₁	1	2	yes	complemented
464	#3486	C₂×C₆₁	1	4	yes	complemented
465	#3480	C₂×C₆₁	1	1	yes	characteristic, complemented
466	Q₈×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
467	C₂×D₄×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
468	#3460	C₂×C₆₁	1	3	yes	complemented
469	C₂×C₆₁	—	2	2	no	—
470	C₂×C₆₁	—	4	2	no	—
471	C₂×C₆₁	—	4	6	no	—
472	C₂×C₆₁	—	4	4	no	—
473	C₂×C₆₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂×C₆₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
475	C₂×C₆₁	2₋¹⁺⁶	1	1	yes	characteristic
476	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	4	yes	complemented
477	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
478	#563	C₂²×C₆₁	1	24	yes	complemented
479	#562	C₂²×C₆₁	1	24	yes	complemented
480	#559	C₂²×C₆₁	1	12	yes	—
481	#559	C₂²×C₆₁	1	3	yes	complemented
482	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
483	Q₈²	C₂²×C₆₁	1	6	yes	complemented
484	#557	C₂²×C₆₁	1	3	yes	complemented
485	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
486	#557	C₂²×C₆₁	1	6	yes	complemented
487	#556	C₂²×C₆₁	1	6	yes	—
488	#556	C₂²×C₆₁	1	3	yes	complemented
489	#556	C₂²×C₆₁	1	6	yes	complemented
490	#556	C₂²×C₆₁	1	12	yes	complemented
491	#555	C₂²×C₆₁	1	6	yes	—
492	#555	C₂²×C₆₁	1	6	yes	complemented
493	#554	C₂²×C₆₁	1	6	yes	—
494	#554	C₂²×C₆₁	1	12	yes	—
495	#554	C₂²×C₆₁	1	3	yes	complemented
496	#554	C₂²×C₆₁	1	6	yes	complemented
497	#554	C₂²×C₆₁	1	6	yes	complemented
498	#553	C₂²×C₆₁	1	6	yes	—
499	#553	C₂²×C₆₁	1	12	yes	—
500	#553	C₂²×C₆₁	1	12	yes	—
501	#552	C₂²×C₆₁	1	12	yes	complemented
502	#550	C₂²×C₆₁	1	6	yes	—
503	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
504	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
505	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
506	D₄×Q₈	C₂²×C₆₁	1	6	yes	—
507	D₄×Q₈	C₂²×C₆₁	1	6	yes	—
508	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
509	D₄×Q₈	C₂²×C₆₁	1	12	yes	—
510	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
511	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
512	D₄×Q₈	C₂²×C₆₁	1	12	yes	complemented
513	D₄×Q₈	C₂²×C₆₁	1	6	yes	complemented
514	#548	C₂²×C₆₁	1	2	yes	—
515	#548	C₂²×C₆₁	1	12	yes	—
516	#548	C₂²×C₆₁	1	4	yes	complemented
517	#548	C₂²×C₆₁	1	12	yes	complemented
518	#548	C₂²×C₆₁	1	12	yes	complemented
519	#547	C₂²×C₆₁	1	6	yes	—
520	#547	C₂²×C₆₁	1	6	yes	complemented
521	#547	C₂²×C₆₁	1	12	yes	complemented
522	#544	C₂²×C₆₁	1	3	yes	—
523	#544	C₂²×C₆₁	1	12	yes	complemented
524	#542	C₂²×C₆₁	1	6	yes	—
525	#542	C₂²×C₆₁	1	6	yes	—
526	#542	C₂²×C₆₁	1	12	yes	complemented
527	#542	C₂²×C₆₁	1	12	yes	complemented
528	#542	C₂²×C₆₁	1	24	yes	complemented
529	#541	C₂²×C₆₁	1	12	yes	complemented
530	#540	C₂²×C₆₁	1	6	yes	—
531	#540	C₂²×C₆₁	1	6	yes	—
532	#539	C₂²×C₆₁	1	24	yes	complemented
533	#538	C₂²×C₆₁	1	12	yes	—
534	#538	C₂²×C₆₁	1	12	yes	—
535	#537	C₂²×C₆₁	1	3	yes	—
536	#537	C₂²×C₆₁	1	12	yes	complemented
537	#536	C₂²×C₆₁	1	12	yes	complemented
538	#536	C₂²×C₆₁	1	12	yes	complemented
539	#536	C₂²×C₆₁	1	12	yes	complemented
540	#535	C₂²×C₆₁	1	1	yes	characteristic
541	#535	C₂²×C₆₁	1	3	yes	—
542	#533	C₂²×C₆₁	1	3	yes	—
543	#533	C₂²×C₆₁	1	6	yes	complemented
544	#533	C₂²×C₆₁	1	6	yes	complemented
545	#533	C₂²×C₆₁	1	6	yes	complemented
546	#532	C₂²×C₆₁	1	6	yes	—
547	#532	C₂²×C₆₁	1	6	yes	—
548	#532	C₂²×C₆₁	1	3	yes	—
549	#532	C₂²×C₆₁	1	6	yes	complemented
550	C₂×C₄⋊Q₈	C₂²×C₆₁	1	3	yes	—
551	C₂×C₄⋊Q₈	C₂²×C₆₁	1	6	yes	complemented
552	#529	C₂²×C₆₁	1	6	yes	—
553	#529	C₂²×C₆₁	1	6	yes	—
554	#529	C₂²×C₆₁	1	6	yes	complemented
555	#525	C₂²×C₆₁	1	12	yes	—
556	#525	C₂²×C₆₁	1	12	yes	—
557	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	6	yes	—
558	#520	C₂²×C₆₁	1	6	yes	—
559	#519	C₂²×C₆₁	1	4	yes	complemented
560	C₄×#41	C₂²×C₆₁	1	3	yes	—
561	C₄×#41	C₂²×C₆₁	1	3	yes	—
562	C₄×#41	C₂²×C₆₁	1	2	yes	complemented
563	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
564	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
565	C₂×C₄×D₄	C₂²×C₆₁	1	3	yes	—
566	C₆₁	#62913	1	1	yes	characteristic, direct product factor, Sylow
567	2₋¹⁺⁴	—	4	16	no	—
568	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
569	C₂×#41	C₂³×C₆₁	1	3	yes	—
570	C₂×#41	C₂³×C₆₁	1	2	yes	—
571	C₂×#41	C₂³×C₆₁	1	12	yes	—
572	C₂×#41	C₂³×C₆₁	1	12	yes	—
573	C₂×#41	C₂³×C₆₁	1	12	yes	—
574	C₂²×Q₈	—	4	8	no	—
575	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
576	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
577	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
578	C₂²×Q₈	C₂³×C₆₁	1	6	yes	—
579	C₂²×Q₈	C₂³×C₆₁	1	12	yes	—
580	C₂²×Q₈	C₂³×C₆₁	1	12	yes	—
581	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₆₁	1	6	yes	—
583	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
584	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
585	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
586	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
587	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
588	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
589	C₄⋊Q₈	C₂³×C₆₁	1	12	yes	—
590	C₄⋊Q₈	C₂³×C₆₁	1	12	yes	—
591	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
592	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
593	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
594	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
595	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
596	C₄⋊Q₈	C₂³×C₆₁	1	24	yes	—
597	#127	C₂³×C₆₁	1	2	yes	—
598	#127	C₂³×C₆₁	1	3	yes	—
599	#127	C₂³×C₆₁	1	6	yes	—
600	#126	C₂³×C₆₁	1	12	yes	—
601	#126	C₂³×C₆₁	1	12	yes	—
602	#126	C₂³×C₆₁	1	12	yes	—
603	#126	C₂³×C₆₁	1	24	yes	—
604	#126	C₂³×C₆₁	1	24	yes	—
605	#125	C₂³×C₆₁	1	6	yes	—
606	#125	C₂³×C₆₁	1	6	yes	—
607	#125	C₂³×C₆₁	1	6	yes	—
608	#125	C₂³×C₆₁	1	6	yes	—
609	#125	C₂³×C₆₁	1	12	yes	—
610	#125	C₂³×C₆₁	1	12	yes	—
611	#125	C₂³×C₆₁	1	24	yes	—
612	#124	C₂³×C₆₁	1	2	yes	—
613	#124	C₂³×C₆₁	1	6	yes	—
614	#124	C₂³×C₆₁	1	6	yes	—
615	#124	C₂³×C₆₁	1	12	yes	—
616	#124	C₂³×C₆₁	1	12	yes	—
617	#124	C₂³×C₆₁	1	6	yes	—
618	#124	C₂³×C₆₁	1	12	yes	—
619	#124	C₂³×C₆₁	1	24	yes	—
620	#124	C₂³×C₆₁	1	24	yes	—
621	#123	C₂³×C₆₁	1	12	yes	—
622	#123	C₂³×C₆₁	1	12	yes	—
623	#123	C₂³×C₆₁	1	24	yes	—
624	#123	C₂³×C₆₁	1	12	yes	—
625	#123	C₂³×C₆₁	1	12	yes	—
626	#123	C₂³×C₆₁	1	12	yes	—
627	#123	C₂³×C₆₁	1	24	yes	—
628	#123	C₂³×C₆₁	1	24	yes	—
629	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
630	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
631	C₂²⋊Q₈	C₂³×C₆₁	1	24	yes	—
632	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
633	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
634	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
635	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
636	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
637	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
638	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
639	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
640	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
641	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
642	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
643	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
644	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
645	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
646	C₂²⋊Q₈	C₂³×C₆₁	1	24	yes	—
647	C₂²⋊Q₈	C₂³×C₆₁	1	24	yes	—
648	C₂²⋊Q₈	C₂³×C₆₁	1	24	yes	—
649	#121	C₂³×C₆₁	1	6	yes	—
650	#121	C₂³×C₆₁	1	12	yes	—
651	#121	C₂³×C₆₁	1	12	yes	—
652	#121	C₂³×C₆₁	1	12	yes	—
653	#121	C₂³×C₆₁	1	2	yes	—
654	#121	C₂³×C₆₁	1	6	yes	—
655	#121	C₂³×C₆₁	1	6	yes	—
656	#121	C₂³×C₆₁	1	2	yes	—
657	#121	C₂³×C₆₁	1	6	yes	—
658	#121	C₂³×C₆₁	1	6	yes	—
659	#121	C₂³×C₆₁	1	6	yes	—
660	#121	C₂³×C₆₁	1	12	yes	—
661	#121	C₂³×C₆₁	1	6	yes	—
662	#121	C₂³×C₆₁	1	12	yes	—
663	#121	C₂³×C₆₁	1	12	yes	—
664	#121	C₂³×C₆₁	1	24	yes	—
665	#120	C₂³×C₆₁	1	4	yes	—
666	#120	C₂³×C₆₁	1	12	yes	—
667	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
668	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
669	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
670	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
671	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
672	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
673	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
674	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
675	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
676	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
677	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
678	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
679	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
680	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
681	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
682	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
683	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
684	C₄×D₄	C₂³×C₆₁	1	6	yes	—
685	C₄×D₄	C₂³×C₆₁	1	6	yes	—
686	C₄×D₄	C₂³×C₆₁	1	6	yes	—
687	C₄×D₄	C₂³×C₆₁	1	6	yes	—
688	C₄×D₄	C₂³×C₆₁	1	6	yes	—
689	C₄×D₄	C₂³×C₆₁	1	6	yes	—
690	C₄×D₄	C₂³×C₆₁	1	3	yes	—
691	C₄×D₄	C₂³×C₆₁	1	3	yes	—
692	C₄×D₄	C₂³×C₆₁	1	6	yes	—
693	C₄×D₄	C₂³×C₆₁	1	6	yes	—
694	C₄×D₄	C₂³×C₆₁	1	3	yes	—
695	C₄×D₄	C₂³×C₆₁	1	3	yes	—
696	C₄×D₄	C₂³×C₆₁	1	6	yes	—
697	C₄×D₄	C₂³×C₆₁	1	6	yes	—
698	C₄×D₄	C₂³×C₆₁	1	24	yes	—
699	C₄×D₄	C₂³×C₆₁	1	12	yes	—
700	C₄×D₄	C₂³×C₆₁	1	12	yes	—
701	C₄×D₄	C₂³×C₆₁	1	12	yes	—
702	C₄×D₄	C₂³×C₆₁	1	24	yes	—
703	C₄×D₄	C₂³×C₆₁	1	6	yes	—
704	C₄×D₄	C₂³×C₆₁	1	12	yes	—
705	#117	C₂³×C₆₁	1	1	yes	characteristic
706	#117	C₂³×C₆₁	1	3	yes	—
707	#117	C₂³×C₆₁	1	6	yes	—
708	#117	C₂³×C₆₁	1	6	yes	—
709	#117	C₂³×C₆₁	1	6	yes	—
710	#117	C₂³×C₆₁	1	12	yes	—
711	#117	C₂³×C₆₁	1	12	yes	—
712	#117	C₂³×C₆₁	1	12	yes	—
713	#117	C₂³×C₆₁	1	12	yes	—
714	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
715	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
716	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
717	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
718	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
719	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
721	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
722	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
723	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
724	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
725	#41	—	2	8	no	—
726	#41	—	2	4	no	—
727	#41	—	2	12	no	—
728	#41	—	4	24	no	—
729	#41	—	4	24	no	—
730	#41	—	4	24	no	—
731	C₂×Q₈	—	2	4	no	—
732	C₂×Q₈	—	2	16	no	—
733	C₂×Q₈	—	2	8	no	—
734	C₂×Q₈	—	4	12	no	—
735	C₂×Q₈	—	4	24	no	—
736	C₂×Q₈	—	4	24	no	—
737	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
738	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
739	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
740	C₂×Q₈	C₂⁴×C₆₁	1	12	yes	—
741	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
742	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
743	C₂×Q₈	C₂⁴×C₆₁	1	12	yes	—
744	C₂×Q₈	C₂⁴×C₆₁	1	12	yes	—
745	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
748	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
749	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
750	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
751	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
752	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
753	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
754	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
755	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
756	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
757	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
758	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
759	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
760	C₂²×C₄	—	4	12	no	—
761	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
763	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
764	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
765	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
766	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
767	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
768	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
769	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
770	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
771	C₂²×C₄	C₂⁴×C₆₁	1	24	yes	—
772	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
773	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
774	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
775	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
776	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
777	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
778	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
779	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
780	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
781	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
782	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
783	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
784	C₄⋊C₄	C₂⁴×C₆₁	1	24	yes	—
785	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
786	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
787	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
788	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
789	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
790	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
791	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
792	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
793	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
794	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
795	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
796	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
797	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
798	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
799	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
800	C₂²⋊C₄	C₂⁴×C₆₁	1	12	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	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
805	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
806	C₂²⋊C₄	C₂⁴×C₆₁	1	2	yes	—
807	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
808	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
809	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
810	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
811	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
812	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
813	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
814	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
815	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
816	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
817	C₄²	C₂⁴×C₆₁	1	2	yes	—
818	C₄²	C₂⁴×C₆₁	1	3	yes	—
819	C₄²	C₂⁴×C₆₁	1	3	yes	—
820	C₄²	C₂⁴×C₆₁	1	3	yes	—
821	C₄²	C₂⁴×C₆₁	1	6	yes	—
822	C₄²	C₂⁴×C₆₁	1	6	yes	—
823	C₄²	C₂⁴×C₆₁	1	3	yes	—
824	C₄²	C₂⁴×C₆₁	1	6	yes	—
825	C₄²	C₂⁴×C₆₁	1	6	yes	—
826	C₄²	C₂⁴×C₆₁	1	6	yes	—
827	C₄²	C₂⁴×C₆₁	1	24	yes	—
828	C₂³	—	2	4	no	—
829	C₂³	—	4	2	no	—
830	C₂³	—	4	2	no	—
831	C₂³	C₂⁵×C₆₁	1	4	yes	—
832	C₂³	C₂⁵×C₆₁	1	2	yes	—
833	C₂³	C₂⁵×C₆₁	1	6	yes	—
834	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
835	Q₈	—	2	6	no	—
836	Q₈	—	2	24	no	—
837	Q₈	—	2	12	no	—
838	Q₈	—	2	2	no	—
839	Q₈	—	2	6	no	—
840	Q₈	—	4	12	no	—
841	Q₈	—	4	12	no	—
842	Q₈	—	4	6	no	—
843	Q₈	H(5,𝔽₂)×C₆₁	1	4	yes	—
844	D₄	—	2	4	no	—
845	D₄	—	2	12	no	—
846	D₄	—	2	12	no	—
847	D₄	—	2	4	no	—
848	D₄	—	2	4	no	—
849	D₄	—	2	2	no	—
850	D₄	—	2	6	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	6	no	—
853	D₄	—	4	12	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	12	no	—
856	D₄	—	4	12	no	—
857	C₂×C₄	—	2	6	no	—
858	C₂×C₄	—	2	24	no	—
859	C₂×C₄	—	2	12	no	—
860	C₂×C₄	—	2	12	no	—
861	C₂×C₄	—	2	12	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	4	6	no	—
864	C₂×C₄	—	4	12	no	—
865	C₂×C₄	—	4	3	no	—
866	C₂×C₄	—	4	6	no	—
867	C₂×C₄	—	4	6	no	—
868	C₂×C₄	—	4	24	no	—
869	C₂×C₄	2₋¹⁺⁴×C₆₁	1	4	yes	complemented
870	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
871	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
872	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
873	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
874	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
875	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
876	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
877	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
878	C₂×C₄	C₂⁵×C₆₁	1	12	yes	—
879	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
880	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
881	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
882	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	6	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	6	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	6	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	4	8	no	—
895	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
896	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
897	C₄	—	2	2	no	—
898	C₄	—	2	6	no	—
899	C₄	—	2	12	no	—
900	C₄	—	2	3	no	—
901	C₄	—	2	6	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	3	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	3	no	—
906	C₄	—	2	6	no	—
907	C₄	C₂×H(5,𝔽₂)×C₆₁	1	6	yes	—
908	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
909	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
910	C₂	—	2	2	no	—
911	C₂	—	4	4	no	—
912	C₂	—	4	2	no	—
913	C₂	—	4	6	no	—
914	C₂	C₂²×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
915	C₂	C₂²×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
916	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×#3554	C₂	semidirect
2. C₆₁×#3552	C₂	semidirect
3. C₆₁×#3550	C₂	semidirect
4. C₆₁×#3547	C₂	semidirect
5. C₆₁×#3541	C₂	semidirect
6. C₆₁×#3523	C₂	semidirect
7. C₆₁×#3518	C₂	semidirect
8. C₆₁×#3511	C₂	semidirect
9. C₆₁×#3506	C₂	semidirect
10. C₆₁×#3503	C₂	semidirect
11. C₆₁×#3499	C₂	semidirect
12. C₆₁×#3497	C₂	semidirect
13. C₆₁×#3486	C₂	semidirect
14. C₆₁×#3480	C₂	semidirect
15. Q₈×#41×C₆₁	C₂	semidirect
16. C₂×D₄×Q₈×C₆₁	C₂	semidirect
17. C₆₁×#3460	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₆₁	C₂²	semidirect
20. C₆₁×#563	C₂²	semidirect
21. C₆₁×#562	C₂²	semidirect
23. C₆₁×#559	C₂²	semidirect
24. Q₈²×C₆₁	C₂²	semidirect
25. Q₈²×C₆₁	C₂²	semidirect
26. C₆₁×#557	C₂²	semidirect
27. C₆₁×#557	C₂²	semidirect
28. C₆₁×#557	C₂²	semidirect
30. C₆₁×#556	C₂²	semidirect
31. C₆₁×#556	C₂²	semidirect
32. C₆₁×#556	C₂²	semidirect
34. C₆₁×#555	C₂²	semidirect
37. C₆₁×#554	C₂²	semidirect
38. C₆₁×#554	C₂²	semidirect
39. C₆₁×#554	C₂²	semidirect
43. C₆₁×#552	C₂²	semidirect
45. C₆₁×#550	C₂²	semidirect
52. D₄×Q₈×C₆₁	C₂²	semidirect
53. D₄×Q₈×C₆₁	C₂²	semidirect
54. D₄×Q₈×C₆₁	C₂²	semidirect
55. D₄×Q₈×C₆₁	C₂²	semidirect
58. C₆₁×#548	C₂²	semidirect
59. C₆₁×#548	C₂²	semidirect
60. C₆₁×#548	C₂²	semidirect
62. C₆₁×#547	C₂²	semidirect
63. C₆₁×#547	C₂²	semidirect
65. C₆₁×#544	C₂²	semidirect
68. C₆₁×#542	C₂²	semidirect
69. C₆₁×#542	C₂²	semidirect
70. C₆₁×#542	C₂²	semidirect
71. C₆₁×#541	C₂²	semidirect
74. C₆₁×#539	C₂²	semidirect
78. C₆₁×#537	C₂²	semidirect
79. C₆₁×#536	C₂²	semidirect
80. C₆₁×#536	C₂²	semidirect
81. C₆₁×#536	C₂²	semidirect
85. C₆₁×#533	C₂²	semidirect
86. C₆₁×#533	C₂²	semidirect
87. C₆₁×#533	C₂²	semidirect
91. C₆₁×#532	C₂²	semidirect
93. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
96. C₆₁×#529	C₂²	semidirect
101. C₆₁×#519	C₂²	semidirect
104. C₄×#41×C₆₁	C₂²	semidirect
106. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
410. C₂×C₄×C₆₁	2₋¹⁺⁴	semidirect
424. #62913	C₆₁	direct (N × H)
452. #3554	C₂×C₆₁	semidirect
453. #3552	C₂×C₆₁	semidirect
454. #3550	C₂×C₆₁	semidirect
455. #3547	C₂×C₆₁	semidirect
456. #3541	C₂×C₆₁	semidirect
457. #3523	C₂×C₆₁	semidirect
458. #3518	C₂×C₆₁	semidirect
459. #3511	C₂×C₆₁	semidirect
460. #3506	C₂×C₆₁	semidirect
461. #3503	C₂×C₆₁	semidirect
462. #3499	C₂×C₆₁	semidirect
463. #3497	C₂×C₆₁	semidirect
464. #3486	C₂×C₆₁	semidirect
465. #3480	C₂×C₆₁	semidirect
466. Q₈×#41	C₂×C₆₁	semidirect
467. C₂×D₄×Q₈	C₂×C₆₁	semidirect
468. #3460	C₂×C₆₁	semidirect
476. C₂×2₋¹⁺⁴	C₂²×C₆₁	semidirect
478. #563	C₂²×C₆₁	semidirect
479. #562	C₂²×C₆₁	semidirect
481. #559	C₂²×C₆₁	semidirect
482. Q₈²	C₂²×C₆₁	semidirect
483. Q₈²	C₂²×C₆₁	semidirect
484. #557	C₂²×C₆₁	semidirect
485. #557	C₂²×C₆₁	semidirect
486. #557	C₂²×C₆₁	semidirect
488. #556	C₂²×C₆₁	semidirect
489. #556	C₂²×C₆₁	semidirect
490. #556	C₂²×C₆₁	semidirect
492. #555	C₂²×C₆₁	semidirect
495. #554	C₂²×C₆₁	semidirect
496. #554	C₂²×C₆₁	semidirect
497. #554	C₂²×C₆₁	semidirect
501. #552	C₂²×C₆₁	semidirect
503. #550	C₂²×C₆₁	semidirect
510. D₄×Q₈	C₂²×C₆₁	semidirect
511. D₄×Q₈	C₂²×C₆₁	semidirect
512. D₄×Q₈	C₂²×C₆₁	semidirect
513. D₄×Q₈	C₂²×C₆₁	semidirect
516. #548	C₂²×C₆₁	semidirect
517. #548	C₂²×C₆₁	semidirect
518. #548	C₂²×C₆₁	semidirect
520. #547	C₂²×C₆₁	semidirect
521. #547	C₂²×C₆₁	semidirect
523. #544	C₂²×C₆₁	semidirect
526. #542	C₂²×C₆₁	semidirect
527. #542	C₂²×C₆₁	semidirect
528. #542	C₂²×C₆₁	semidirect
529. #541	C₂²×C₆₁	semidirect
532. #539	C₂²×C₆₁	semidirect
536. #537	C₂²×C₆₁	semidirect
537. #536	C₂²×C₆₁	semidirect
538. #536	C₂²×C₆₁	semidirect
539. #536	C₂²×C₆₁	semidirect
543. #533	C₂²×C₆₁	semidirect
544. #533	C₂²×C₆₁	semidirect
545. #533	C₂²×C₆₁	semidirect
549. #532	C₂²×C₆₁	semidirect
551. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
554. #529	C₂²×C₆₁	semidirect
559. #519	C₂²×C₆₁	semidirect
562. C₄×#41	C₂²×C₆₁	semidirect
564. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
566. C₆₁	#62913	direct (N × H)
869. C₂×C₄	2₋¹⁺⁴×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3554	2
C₆₁×#3552	2
C₆₁×#3550	2
C₆₁×#3547	2
C₆₁×#3541	2
C₆₁×#3523	2
C₆₁×#3518	2
C₆₁×#3511	2
C₆₁×#3506	2
C₆₁×#3503	2
C₆₁×#3499	2
C₆₁×#3497	2
C₆₁×#3486	2
C₆₁×#3480	2
Q₈×#41×C₆₁	2
C₂×D₄×Q₈×C₆₁	2
C₆₁×#3460	2
#62913	61

Subgroups — C61×#62913 #29566346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62913 #29566346