Subgroups — C₆₁×#62815 #29566248

Order 15616.

7210 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3512	C₂	1	4	yes	maximal, complemented
2	C₆₁×#3511	C₂	1	4	yes	maximal, complemented
3	C₆₁×#3510	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3509	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3508	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3507	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3506	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3505	C₂	1	8	yes	maximal, complemented
9	C₆₁×#3480	C₂	1	8	yes	maximal, complemented
10	C₆₁×#3475	C₂	1	8	yes	maximal, complemented
11	C₆₁×#3455	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3449	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3444	C₂	1	4	yes	maximal, complemented
14	C₂×C₆₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₆₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3428	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₆₁	C₂²	1	2	yes	—
20	C₆₁×#559	C₂²	1	16	yes	complemented
21	C₆₁×#559	C₂²	1	8	yes	complemented
22	C₆₁×#557	C₂²	1	8	yes	complemented
23	C₆₁×#556	C₂²	1	8	yes	complemented
24	C₆₁×#556	C₂²	1	8	yes	complemented
25	C₆₁×#556	C₂²	1	16	yes	complemented
26	C₆₁×#555	C₂²	1	8	yes	complemented
27	C₆₁×#554	C₂²	1	8	yes	complemented
28	C₆₁×#553	C₂²	1	16	yes	complemented
29	C₆₁×#553	C₂²	1	16	yes	complemented
30	C₆₁×#553	C₂²	1	32	yes	complemented
31	C₆₁×#552	C₂²	1	16	yes	complemented
32	C₆₁×#552	C₂²	1	16	yes	complemented
33	C₆₁×#551	C₂²	1	32	yes	complemented
34	C₆₁×#550	C₂²	1	8	yes	complemented
35	C₆₁×#548	C₂²	1	16	yes	complemented
36	C₆₁×#547	C₂²	1	8	yes	complemented
37	C₆₁×#546	C₂²	1	16	yes	complemented
38	C₆₁×#542	C₂²	1	16	yes	complemented
39	C₆₁×#541	C₂²	1	8	yes	complemented
40	C₆₁×#540	C₂²	1	8	yes	complemented
41	C₆₁×#539	C₂²	1	16	yes	complemented
42	C₆₁×#538	C₂²	1	16	yes	complemented
43	C₆₁×#537	C₂²	1	8	yes	complemented
44	C₆₁×#536	C₂²	1	4	yes	—
45	C₆₁×#536	C₂²	1	4	yes	complemented
46	C₆₁×#535	C₂²	1	4	yes	—
47	C₆₁×#535	C₂²	1	4	yes	complemented
48	C₆₁×#534	C₂²	1	8	yes	—
49	C₆₁×#533	C₂²	1	2	yes	complemented
50	C₆₁×#533	C₂²	1	2	yes	complemented
51	C₆₁×#533	C₂²	1	4	yes	complemented
52	C₆₁×#533	C₂²	1	4	yes	complemented
53	C₆₁×#533	C₂²	1	2	yes	complemented
54	C₆₁×#533	C₂²	1	2	yes	complemented
55	C₆₁×#533	C₂²	1	8	yes	complemented
56	C₆₁×#532	C₂²	1	2	yes	—
57	C₆₁×#532	C₂²	1	2	yes	—
58	C₆₁×#532	C₂²	1	4	yes	—
59	C₆₁×#532	C₂²	1	4	yes	complemented
60	C₆₁×#532	C₂²	1	2	yes	complemented
61	C₆₁×#532	C₂²	1	2	yes	complemented
62	C₆₁×#532	C₂²	1	8	yes	complemented
63	C₆₁×#532	C₂²	1	8	yes	complemented
64	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
66	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#529	C₂²	1	16	yes	complemented
68	C₆₁×#529	C₂²	1	16	yes	complemented
69	C₆₁×#529	C₂²	1	16	yes	complemented
70	C₆₁×#529	C₂²	1	32	yes	complemented
71	C₂×#125×C₆₁	C₂²	1	2	yes	complemented
72	C₂×#124×C₆₁	C₂²	1	2	yes	complemented
73	C₆₁×#525	C₂²	1	8	yes	—
74	C₆₁×#525	C₂²	1	8	yes	complemented
75	C₆₁×#525	C₂²	1	16	yes	complemented
76	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	—
77	C₂×#121×C₆₁	C₂²	1	4	yes	—
78	C₆₁×#520	C₂²	1	8	yes	complemented
79	C₆₁×#520	C₂²	1	8	yes	complemented
80	C₆₁×#519	C₂²	1	4	yes	complemented
81	C₆₁×#518	C₂²	1	8	yes	—
82	C₆₁×#518	C₂²	1	4	yes	complemented
83	C₄×#41×C₆₁	C₂²	1	4	yes	—
84	C₄×#41×C₆₁	C₂²	1	2	yes	—
85	C₄×#41×C₆₁	C₂²	1	2	yes	—
86	C₄×#41×C₆₁	C₂²	1	4	yes	complemented
87	C₄×#41×C₆₁	C₂²	1	2	yes	complemented
88	C₄×#41×C₆₁	C₂²	1	2	yes	complemented
89	C₄×#41×C₆₁	C₂²	1	8	yes	complemented
90	C₄×#41×C₆₁	C₂²	1	8	yes	complemented
91	C₄×#41×C₆₁	C₂²	1	16	yes	complemented
92	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
93	C₂×C₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
94	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
95	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
96	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	complemented
97	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
98	C₂×#117×C₆₁	C₂²	1	2	yes	—
99	C₂×#117×C₆₁	C₂²	1	2	yes	complemented
100	C₂×#117×C₆₁	C₂²	1	8	yes	complemented
101	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
102	C₂²×C₄²×C₆₁	C₂²	1	2	yes	complemented
103	C₂×#41×C₆₁	—	2	8	no	—
104	C₂×#41×C₆₁	—	2	16	no	—
105	C₂×#41×C₆₁	C₂³	1	4	yes	—
106	C₂×#41×C₆₁	C₂³	1	4	yes	—
107	C₂×#41×C₆₁	C₂³	1	4	yes	—
108	C₂×#41×C₆₁	C₂³	1	2	yes	—
109	C₂×#41×C₆₁	C₂³	1	4	yes	—
110	C₂×#41×C₆₁	C₂³	1	2	yes	—
111	C₂×#41×C₆₁	C₂³	1	2	yes	—
112	C₂×#41×C₆₁	C₂³	1	2	yes	—
113	C₂×#41×C₆₁	C₂³	1	16	yes	—
114	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
115	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
116	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
117	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
119	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
120	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
122	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
124	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
125	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
126	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
128	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
130	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
131	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
132	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
133	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
134	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
135	#127×C₆₁	C₂³	1	2	yes	—
136	#127×C₆₁	C₂³	1	2	yes	—
137	#127×C₆₁	C₂³	1	4	yes	—
138	#127×C₆₁	C₂³	1	8	yes	—
139	#126×C₆₁	C₂³	1	32	yes	—
140	#126×C₆₁	C₂³	1	32	yes	—
141	#126×C₆₁	C₂³	1	32	yes	—
142	#125×C₆₁	C₂³	1	4	yes	—
143	#125×C₆₁	C₂³	1	8	yes	—
144	#125×C₆₁	C₂³	1	4	yes	—
145	#125×C₆₁	C₂³	1	16	yes	—
146	#125×C₆₁	C₂³	1	32	yes	—
147	#124×C₆₁	C₂³	1	4	yes	—
148	#124×C₆₁	C₂³	1	8	yes	—
149	#124×C₆₁	C₂³	1	4	yes	—
150	#124×C₆₁	C₂³	1	8	yes	—
151	#124×C₆₁	C₂³	1	8	yes	—
152	#124×C₆₁	C₂³	1	16	yes	—
153	#124×C₆₁	C₂³	1	32	yes	—
154	#123×C₆₁	C₂³	1	16	yes	—
155	#123×C₆₁	C₂³	1	16	yes	—
156	#123×C₆₁	C₂³	1	32	yes	—
157	#123×C₆₁	C₂³	1	32	yes	—
158	#123×C₆₁	C₂³	1	32	yes	—
159	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
160	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
161	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
162	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
163	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
164	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
165	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
166	C₂²⋊Q₈×C₆₁	C₂³	1	32	yes	—
167	#121×C₆₁	C₂³	1	8	yes	—
168	#121×C₆₁	C₂³	1	8	yes	—
169	#121×C₆₁	C₂³	1	8	yes	—
170	#121×C₆₁	C₂³	1	8	yes	—
171	#121×C₆₁	C₂³	1	32	yes	—
172	#121×C₆₁	C₂³	1	16	yes	—
173	#121×C₆₁	C₂³	1	16	yes	—
174	#121×C₆₁	C₂³	1	16	yes	—
175	#121×C₆₁	C₂³	1	32	yes	—
176	#120×C₆₁	C₂³	1	16	yes	—
177	#120×C₆₁	C₂³	1	16	yes	—
178	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
179	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
180	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
181	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
182	C₄×Q₈×C₆₁	C₂³	1	16	yes	—
183	C₄×Q₈×C₆₁	C₂³	1	16	yes	—
184	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
185	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
186	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
187	C₄×Q₈×C₆₁	C₂³	1	16	yes	—
188	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
189	C₄×D₄×C₆₁	C₂³	1	8	yes	—
190	C₄×D₄×C₆₁	C₂³	1	8	yes	—
191	C₄×D₄×C₆₁	C₂³	1	8	yes	—
192	C₄×D₄×C₆₁	C₂³	1	8	yes	—
193	C₄×D₄×C₆₁	C₂³	1	16	yes	—
194	C₄×D₄×C₆₁	C₂³	1	16	yes	—
195	C₄×D₄×C₆₁	C₂³	1	32	yes	—
196	C₄×D₄×C₆₁	C₂³	1	32	yes	—
197	C₄×D₄×C₆₁	C₂³	1	8	yes	—
198	C₄×D₄×C₆₁	C₂³	1	4	yes	—
199	C₄×D₄×C₆₁	C₂³	1	8	yes	—
200	C₄×D₄×C₆₁	C₂³	1	32	yes	—
201	C₄×D₄×C₆₁	C₂³	1	4	yes	—
202	C₄×D₄×C₆₁	C₂³	1	16	yes	—
203	C₄×D₄×C₆₁	C₂³	1	8	yes	—
204	C₄×D₄×C₆₁	C₂³	1	32	yes	—
205	C₄×D₄×C₆₁	C₂³	1	8	yes	—
206	C₄×D₄×C₆₁	C₂³	1	4	yes	—
207	C₄×D₄×C₆₁	C₂³	1	4	yes	—
208	#117×C₆₁	C₂³	1	4	yes	—
209	#117×C₆₁	C₂³	1	4	yes	—
210	#117×C₆₁	C₂³	1	4	yes	—
211	#117×C₆₁	C₂³	1	4	yes	—
212	#117×C₆₁	C₂³	1	16	yes	—
213	#117×C₆₁	C₂³	1	4	yes	—
214	#117×C₆₁	C₂³	1	4	yes	—
215	#117×C₆₁	C₂³	1	16	yes	—
216	#117×C₆₁	C₂³	1	32	yes	—
217	#117×C₆₁	C₂³	1	16	yes	—
218	#117×C₆₁	C₂³	1	2	yes	—
219	#117×C₆₁	C₂³	1	2	yes	—
220	#117×C₆₁	C₂³	1	2	yes	—
221	#117×C₆₁	C₂³	1	2	yes	—
222	#117×C₆₁	C₂³	1	8	yes	—
223	#117×C₆₁	C₂³	1	16	yes	—
224	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
225	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
226	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
227	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
228	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
229	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
230	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
232	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
233	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
234	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
235	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
236	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
241	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
242	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
243	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
245	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
246	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
248	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
249	C₂×C₄²×C₆₁	C₂³	1	8	yes	—
250	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
251	C₂×C₄²×C₆₁	C₂³	1	16	yes	—
252	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
253	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
254	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
255	#41×C₆₁	—	2	8	no	—
256	#41×C₆₁	—	2	16	no	—
257	#41×C₆₁	—	2	8	no	—
258	#41×C₆₁	—	2	16	no	—
259	#41×C₆₁	—	2	8	no	—
260	#41×C₆₁	—	2	16	no	—
261	#41×C₆₁	—	2	16	no	—
262	#41×C₆₁	—	2	8	no	—
263	#41×C₆₁	—	4	32	no	—
264	C₂×Q₈×C₆₁	—	2	8	no	—
265	C₂×Q₈×C₆₁	—	2	4	no	—
266	C₂×Q₈×C₆₁	—	4	8	no	—
267	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
268	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
269	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
270	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
271	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
272	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
273	C₂×D₄×C₆₁	—	2	8	no	—
274	C₂×D₄×C₆₁	—	2	16	no	—
275	C₂×D₄×C₆₁	—	2	8	no	—
276	C₂×D₄×C₆₁	—	2	4	no	—
277	C₂×D₄×C₆₁	—	4	8	no	—
278	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
279	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
280	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
281	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
282	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
283	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
284	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
285	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
286	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
287	C₂×D₄×C₆₁	C₂⁴	1	32	yes	—
288	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
289	C₂²×C₄×C₆₁	—	2	16	no	—
290	C₂²×C₄×C₆₁	—	2	8	no	—
291	C₂²×C₄×C₆₁	—	4	4	no	—
292	C₂²×C₄×C₆₁	—	4	8	no	—
293	C₂²×C₄×C₆₁	#41	1	8	yes	complemented
294	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
299	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
301	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
302	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
306	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
309	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
310	C₂²×C₄×C₆₁	C₂⁴	1	32	yes	—
311	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
318	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
319	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
320	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
321	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
322	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
323	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
324	C₄⋊C₄×C₆₁	C₂⁴	1	32	yes	—
325	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
326	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
327	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
328	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
329	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
330	C₄⋊C₄×C₆₁	C₂⁴	1	32	yes	—
331	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
332	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
334	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
335	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
336	C₂²⋊C₄×C₆₁	C₂⁴	1	32	yes	—
337	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
338	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
339	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
340	C₂²⋊C₄×C₆₁	C₂⁴	1	32	yes	—
341	C₂²⋊C₄×C₆₁	C₂⁴	1	32	yes	—
342	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
343	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
344	C₄²×C₆₁	C₂⁴	1	4	yes	—
345	C₄²×C₆₁	C₂⁴	1	8	yes	—
346	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
347	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
348	C₄²×C₆₁	C₂⁴	1	2	yes	—
349	C₄²×C₆₁	C₂⁴	1	2	yes	—
350	C₄²×C₆₁	C₂⁴	1	8	yes	—
351	C₄²×C₆₁	C₂⁴	1	2	yes	—
352	C₄²×C₆₁	C₂⁴	1	2	yes	—
353	C₄²×C₆₁	C₂⁴	1	32	yes	—
354	C₄²×C₆₁	C₂⁴	1	8	yes	—
355	C₄²×C₆₁	C₂⁴	1	4	yes	—
356	C₄²×C₆₁	C₂⁴	1	2	yes	—
357	C₄²×C₆₁	C₂⁴	1	2	yes	—
358	C₄²×C₆₁	C₂⁴	1	8	yes	—
359	C₂³×C₆₁	—	2	4	no	—
360	C₂³×C₆₁	—	2	8	no	—
361	C₂³×C₆₁	—	4	2	no	—
362	C₂³×C₆₁	—	4	4	no	—
363	C₂³×C₆₁	—	4	8	no	—
364	C₂³×C₆₁	C₂×#41	1	4	yes	—
365	C₂³×C₆₁	C₂⁵	1	4	yes	—
366	C₂³×C₆₁	C₂⁵	1	8	yes	—
367	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
368	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
369	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
370	Q₈×C₆₁	—	2	4	no	—
371	Q₈×C₆₁	—	2	8	no	—
372	Q₈×C₆₁	—	2	8	no	—
373	Q₈×C₆₁	—	2	4	no	—
374	Q₈×C₆₁	—	2	16	no	—
375	Q₈×C₆₁	—	4	8	no	—
376	D₄×C₆₁	—	2	8	no	—
377	D₄×C₆₁	—	2	16	no	—
378	D₄×C₆₁	—	2	8	no	—
379	D₄×C₆₁	—	2	16	no	—
380	D₄×C₆₁	—	2	4	no	—
381	D₄×C₆₁	—	2	8	no	—
382	D₄×C₆₁	—	2	4	no	—
383	D₄×C₆₁	—	2	8	no	—
384	D₄×C₆₁	—	2	16	no	—
385	D₄×C₆₁	—	4	8	no	—
386	D₄×C₆₁	—	4	32	no	—
387	C₂×C₄×C₆₁	—	2	8	no	—
388	C₂×C₄×C₆₁	—	2	4	no	—
389	C₂×C₄×C₆₁	—	2	8	no	—
390	C₂×C₄×C₆₁	—	2	16	no	—
391	C₂×C₄×C₆₁	—	2	16	no	—
392	C₂×C₄×C₆₁	—	2	8	no	—
393	C₂×C₄×C₆₁	—	2	4	no	—
394	C₂×C₄×C₆₁	—	2	4	no	—
395	C₂×C₄×C₆₁	—	2	4	no	—
396	C₂×C₄×C₆₁	—	2	16	no	—
397	C₂×C₄×C₆₁	—	4	4	no	—
398	C₂×C₄×C₆₁	—	4	8	no	—
399	C₂×C₄×C₆₁	—	4	2	no	—
400	C₂×C₄×C₆₁	—	4	2	no	—
401	C₂×C₄×C₆₁	—	4	2	no	—
402	C₂×C₄×C₆₁	—	4	8	no	—
403	C₂×C₄×C₆₁	—	4	32	no	—
404	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
405	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
406	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
407	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
408	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
409	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
410	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
411	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
412	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
413	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
414	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
415	C₂×C₄×C₆₁	C₂⁵	1	16	yes	—
416	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
417	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
418	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
419	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
420	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
421	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
422	#62815	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
423	C₂²×C₆₁	—	2	2	no	—
424	C₂²×C₆₁	—	2	2	no	—
425	C₂²×C₆₁	—	2	2	no	—
426	C₂²×C₆₁	—	2	4	no	—
427	C₂²×C₆₁	—	2	8	no	—
428	C₂²×C₆₁	—	2	8	no	—
429	C₂²×C₆₁	—	2	16	no	—
430	C₂²×C₆₁	—	4	4	no	—
431	C₂²×C₆₁	—	4	8	no	—
432	C₂²×C₆₁	—	8	8	no	—
433	C₂²×C₆₁	C₂²×#41	1	2	yes	—
434	C₂²×C₆₁	C₂²×#41	1	2	yes	—
435	C₂²×C₆₁	C₂²×#41	1	2	yes	—
436	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
437	C₄×C₆₁	—	2	8	no	—
438	C₄×C₆₁	—	2	4	no	—
439	C₄×C₆₁	—	2	2	no	—
440	C₄×C₆₁	—	2	8	no	—
441	C₄×C₆₁	—	2	2	no	—
442	C₄×C₆₁	—	2	2	no	—
443	C₄×C₆₁	—	2	16	no	—
444	C₄×C₆₁	C₂²×#41	1	2	yes	—
445	C₄×C₆₁	C₂²×#41	1	2	yes	—
446	C₄×C₆₁	C₂²×#41	1	2	yes	—
447	C₄×C₆₁	C₂²×#41	1	2	yes	—
448	C₄×C₆₁	#585	1	4	yes	—
449	#3512	C₂×C₆₁	1	4	yes	complemented
450	#3511	C₂×C₆₁	1	4	yes	complemented
451	#3510	C₂×C₆₁	1	4	yes	complemented
452	#3509	C₂×C₆₁	1	2	yes	complemented
453	#3508	C₂×C₆₁	1	2	yes	complemented
454	#3507	C₂×C₆₁	1	4	yes	complemented
455	#3506	C₂×C₆₁	1	4	yes	complemented
456	#3505	C₂×C₆₁	1	8	yes	complemented
457	#3480	C₂×C₆₁	1	8	yes	complemented
458	#3475	C₂×C₆₁	1	8	yes	complemented
459	#3455	C₂×C₆₁	1	4	yes	complemented
460	#3449	C₂×C₆₁	1	2	yes	complemented
461	#3444	C₂×C₆₁	1	4	yes	complemented
462	C₂×#533	C₂×C₆₁	1	1	yes	characteristic, complemented
463	C₂×#532	C₂×C₆₁	1	1	yes	characteristic, complemented
464	#3428	C₂×C₆₁	1	2	yes	complemented
465	C₂×C₄×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
466	C₂×C₆₁	—	2	2	no	—
467	C₂×C₆₁	—	2	2	no	—
468	C₂×C₆₁	—	2	2	no	—
469	C₂×C₆₁	—	4	4	no	—
470	C₂×C₆₁	—	4	8	no	—
471	C₂×C₆₁	C₂³×#41	1	1	yes	characteristic
472	C₂×C₆₁	C₂×#585	1	2	yes	—
473	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
474	C₂²×#41	C₂²×C₆₁	1	2	yes	—
475	#559	C₂²×C₆₁	1	16	yes	complemented
476	#559	C₂²×C₆₁	1	8	yes	complemented
477	#557	C₂²×C₆₁	1	8	yes	complemented
478	#556	C₂²×C₆₁	1	8	yes	complemented
479	#556	C₂²×C₆₁	1	8	yes	complemented
480	#556	C₂²×C₆₁	1	16	yes	complemented
481	#555	C₂²×C₆₁	1	8	yes	complemented
482	#554	C₂²×C₆₁	1	8	yes	complemented
483	#553	C₂²×C₆₁	1	16	yes	complemented
484	#553	C₂²×C₆₁	1	16	yes	complemented
485	#553	C₂²×C₆₁	1	32	yes	complemented
486	#552	C₂²×C₆₁	1	16	yes	complemented
487	#552	C₂²×C₆₁	1	16	yes	complemented
488	#551	C₂²×C₆₁	1	32	yes	complemented
489	#550	C₂²×C₆₁	1	8	yes	complemented
490	#548	C₂²×C₆₁	1	16	yes	complemented
491	#547	C₂²×C₆₁	1	8	yes	complemented
492	#546	C₂²×C₆₁	1	16	yes	complemented
493	#542	C₂²×C₆₁	1	16	yes	complemented
494	#541	C₂²×C₆₁	1	8	yes	complemented
495	#540	C₂²×C₆₁	1	8	yes	complemented
496	#539	C₂²×C₆₁	1	16	yes	complemented
497	#538	C₂²×C₆₁	1	16	yes	complemented
498	#537	C₂²×C₆₁	1	8	yes	complemented
499	#536	C₂²×C₆₁	1	4	yes	—
500	#536	C₂²×C₆₁	1	4	yes	complemented
501	#535	C₂²×C₆₁	1	4	yes	—
502	#535	C₂²×C₆₁	1	4	yes	complemented
503	#534	C₂²×C₆₁	1	8	yes	—
504	#533	C₂²×C₆₁	1	2	yes	complemented
505	#533	C₂²×C₆₁	1	2	yes	complemented
506	#533	C₂²×C₆₁	1	4	yes	complemented
507	#533	C₂²×C₆₁	1	4	yes	complemented
508	#533	C₂²×C₆₁	1	2	yes	complemented
509	#533	C₂²×C₆₁	1	2	yes	complemented
510	#533	C₂²×C₆₁	1	8	yes	complemented
511	#532	C₂²×C₆₁	1	2	yes	—
512	#532	C₂²×C₆₁	1	2	yes	—
513	#532	C₂²×C₆₁	1	4	yes	—
514	#532	C₂²×C₆₁	1	4	yes	complemented
515	#532	C₂²×C₆₁	1	2	yes	complemented
516	#532	C₂²×C₆₁	1	2	yes	complemented
517	#532	C₂²×C₆₁	1	8	yes	complemented
518	#532	C₂²×C₆₁	1	8	yes	complemented
519	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
520	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
521	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic, complemented
522	#529	C₂²×C₆₁	1	16	yes	complemented
523	#529	C₂²×C₆₁	1	16	yes	complemented
524	#529	C₂²×C₆₁	1	16	yes	complemented
525	#529	C₂²×C₆₁	1	32	yes	complemented
526	C₂×#125	C₂²×C₆₁	1	2	yes	complemented
527	C₂×#124	C₂²×C₆₁	1	2	yes	complemented
528	#525	C₂²×C₆₁	1	8	yes	—
529	#525	C₂²×C₆₁	1	8	yes	complemented
530	#525	C₂²×C₆₁	1	16	yes	complemented
531	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	—
532	C₂×#121	C₂²×C₆₁	1	4	yes	—
533	#520	C₂²×C₆₁	1	8	yes	complemented
534	#520	C₂²×C₆₁	1	8	yes	complemented
535	#519	C₂²×C₆₁	1	4	yes	complemented
536	#518	C₂²×C₆₁	1	8	yes	—
537	#518	C₂²×C₆₁	1	4	yes	complemented
538	C₄×#41	C₂²×C₆₁	1	4	yes	—
539	C₄×#41	C₂²×C₆₁	1	2	yes	—
540	C₄×#41	C₂²×C₆₁	1	2	yes	—
541	C₄×#41	C₂²×C₆₁	1	4	yes	complemented
542	C₄×#41	C₂²×C₆₁	1	2	yes	complemented
543	C₄×#41	C₂²×C₆₁	1	2	yes	complemented
544	C₄×#41	C₂²×C₆₁	1	8	yes	complemented
545	C₄×#41	C₂²×C₆₁	1	8	yes	complemented
546	C₄×#41	C₂²×C₆₁	1	16	yes	complemented
547	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
548	C₂×C₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
549	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
550	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
551	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	complemented
552	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
553	C₂×#117	C₂²×C₆₁	1	2	yes	—
554	C₂×#117	C₂²×C₆₁	1	2	yes	complemented
555	C₂×#117	C₂²×C₆₁	1	8	yes	complemented
556	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
557	C₂²×C₄²	C₂²×C₆₁	1	2	yes	complemented
558	C₆₁	#62815	1	1	yes	characteristic, direct product factor, Sylow
559	C₂×#41	—	2	8	no	—
560	C₂×#41	—	2	16	no	—
561	C₂×#41	C₂³×C₆₁	1	2	yes	—
562	C₂×#41	C₂³×C₆₁	1	2	yes	—
563	C₂×#41	C₂³×C₆₁	1	4	yes	—
564	C₂×#41	C₂³×C₆₁	1	2	yes	—
565	C₂×#41	C₂³×C₆₁	1	4	yes	—
566	C₂×#41	C₂³×C₆₁	1	2	yes	—
567	C₂×#41	C₂³×C₆₁	1	4	yes	—
568	C₂×#41	C₂³×C₆₁	1	4	yes	—
569	C₂×#41	C₂³×C₆₁	1	16	yes	—
570	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
572	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
573	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
574	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
575	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
576	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
577	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
578	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
579	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
580	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
581	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
582	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
584	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
585	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
586	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
587	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
588	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
589	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
590	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
591	#127	C₂³×C₆₁	1	2	yes	—
592	#127	C₂³×C₆₁	1	2	yes	—
593	#127	C₂³×C₆₁	1	4	yes	—
594	#127	C₂³×C₆₁	1	8	yes	—
595	#126	C₂³×C₆₁	1	32	yes	—
596	#126	C₂³×C₆₁	1	32	yes	—
597	#126	C₂³×C₆₁	1	32	yes	—
598	#125	C₂³×C₆₁	1	4	yes	—
599	#125	C₂³×C₆₁	1	4	yes	—
600	#125	C₂³×C₆₁	1	8	yes	—
601	#125	C₂³×C₆₁	1	16	yes	—
602	#125	C₂³×C₆₁	1	32	yes	—
603	#124	C₂³×C₆₁	1	4	yes	—
604	#124	C₂³×C₆₁	1	4	yes	—
605	#124	C₂³×C₆₁	1	8	yes	—
606	#124	C₂³×C₆₁	1	16	yes	—
607	#124	C₂³×C₆₁	1	32	yes	—
608	#124	C₂³×C₆₁	1	8	yes	—
609	#124	C₂³×C₆₁	1	8	yes	—
610	#123	C₂³×C₆₁	1	16	yes	—
611	#123	C₂³×C₆₁	1	16	yes	—
612	#123	C₂³×C₆₁	1	32	yes	—
613	#123	C₂³×C₆₁	1	32	yes	—
614	#123	C₂³×C₆₁	1	32	yes	—
615	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
616	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
617	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
618	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
619	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
620	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
621	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
622	C₂²⋊Q₈	C₂³×C₆₁	1	32	yes	—
623	#121	C₂³×C₆₁	1	8	yes	—
624	#121	C₂³×C₆₁	1	8	yes	—
625	#121	C₂³×C₆₁	1	8	yes	—
626	#121	C₂³×C₆₁	1	8	yes	—
627	#121	C₂³×C₆₁	1	16	yes	—
628	#121	C₂³×C₆₁	1	16	yes	—
629	#121	C₂³×C₆₁	1	16	yes	—
630	#121	C₂³×C₆₁	1	32	yes	—
631	#121	C₂³×C₆₁	1	32	yes	—
632	#120	C₂³×C₆₁	1	16	yes	—
633	#120	C₂³×C₆₁	1	16	yes	—
634	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
635	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
636	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
637	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
638	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
639	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
640	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
641	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
642	C₄×Q₈	C₂³×C₆₁	1	16	yes	—
643	C₄×Q₈	C₂³×C₆₁	1	16	yes	—
644	C₄×Q₈	C₂³×C₆₁	1	16	yes	—
645	C₄×D₄	C₂³×C₆₁	1	8	yes	—
646	C₄×D₄	C₂³×C₆₁	1	8	yes	—
647	C₄×D₄	C₂³×C₆₁	1	8	yes	—
648	C₄×D₄	C₂³×C₆₁	1	8	yes	—
649	C₄×D₄	C₂³×C₆₁	1	4	yes	—
650	C₄×D₄	C₂³×C₆₁	1	4	yes	—
651	C₄×D₄	C₂³×C₆₁	1	4	yes	—
652	C₄×D₄	C₂³×C₆₁	1	4	yes	—
653	C₄×D₄	C₂³×C₆₁	1	8	yes	—
654	C₄×D₄	C₂³×C₆₁	1	8	yes	—
655	C₄×D₄	C₂³×C₆₁	1	8	yes	—
656	C₄×D₄	C₂³×C₆₁	1	8	yes	—
657	C₄×D₄	C₂³×C₆₁	1	32	yes	—
658	C₄×D₄	C₂³×C₆₁	1	32	yes	—
659	C₄×D₄	C₂³×C₆₁	1	16	yes	—
660	C₄×D₄	C₂³×C₆₁	1	16	yes	—
661	C₄×D₄	C₂³×C₆₁	1	32	yes	—
662	C₄×D₄	C₂³×C₆₁	1	32	yes	—
663	C₄×D₄	C₂³×C₆₁	1	16	yes	—
664	#117	C₂³×C₆₁	1	2	yes	—
665	#117	C₂³×C₆₁	1	4	yes	—
666	#117	C₂³×C₆₁	1	2	yes	—
667	#117	C₂³×C₆₁	1	2	yes	—
668	#117	C₂³×C₆₁	1	2	yes	—
669	#117	C₂³×C₆₁	1	4	yes	—
670	#117	C₂³×C₆₁	1	4	yes	—
671	#117	C₂³×C₆₁	1	4	yes	—
672	#117	C₂³×C₆₁	1	8	yes	—
673	#117	C₂³×C₆₁	1	4	yes	—
674	#117	C₂³×C₆₁	1	4	yes	—
675	#117	C₂³×C₆₁	1	16	yes	—
676	#117	C₂³×C₆₁	1	16	yes	—
677	#117	C₂³×C₆₁	1	16	yes	—
678	#117	C₂³×C₆₁	1	16	yes	—
679	#117	C₂³×C₆₁	1	32	yes	—
680	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
682	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
683	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
684	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
685	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
686	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
692	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
693	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
694	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₆₁	1	16	yes	—
696	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
697	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
698	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
699	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
700	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₆₁	1	8	yes	—
703	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
704	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
705	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
708	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
709	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
710	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
711	#41	—	2	8	no	—
712	#41	—	2	16	no	—
713	#41	—	2	8	no	—
714	#41	—	2	16	no	—
715	#41	—	2	8	no	—
716	#41	—	2	16	no	—
717	#41	—	2	8	no	—
718	#41	—	2	16	no	—
719	#41	—	4	32	no	—
720	C₂×Q₈	—	2	8	no	—
721	C₂×Q₈	—	2	4	no	—
722	C₂×Q₈	—	4	8	no	—
723	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
724	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
725	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
726	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
727	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
728	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
729	C₂×D₄	—	2	8	no	—
730	C₂×D₄	—	2	16	no	—
731	C₂×D₄	—	2	8	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	4	8	no	—
734	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
735	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
736	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
737	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
738	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
739	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
740	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
741	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
742	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
743	C₂×D₄	C₂⁴×C₆₁	1	32	yes	—
744	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
745	C₂²×C₄	—	2	16	no	—
746	C₂²×C₄	—	2	8	no	—
747	C₂²×C₄	—	4	4	no	—
748	C₂²×C₄	—	4	8	no	—
749	C₂²×C₄	#41×C₆₁	1	8	yes	complemented
750	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
755	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
756	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
757	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
758	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
759	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
760	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
762	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
765	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
766	C₂²×C₄	C₂⁴×C₆₁	1	32	yes	—
767	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
773	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
774	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
775	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
776	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
777	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
778	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
779	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
780	C₄⋊C₄	C₂⁴×C₆₁	1	32	yes	—
781	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
782	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
783	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
784	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
785	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
786	C₄⋊C₄	C₂⁴×C₆₁	1	32	yes	—
787	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
788	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
789	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
790	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
791	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
792	C₂²⋊C₄	C₂⁴×C₆₁	1	32	yes	—
793	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
794	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
795	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
796	C₂²⋊C₄	C₂⁴×C₆₁	1	32	yes	—
797	C₂²⋊C₄	C₂⁴×C₆₁	1	32	yes	—
798	C₄²	C₂⁴×C₆₁	1	4	yes	—
799	C₄²	C₂⁴×C₆₁	1	2	yes	—
800	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
801	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
802	C₄²	C₂⁴×C₆₁	1	4	yes	—
803	C₄²	C₂⁴×C₆₁	1	2	yes	—
804	C₄²	C₂⁴×C₆₁	1	8	yes	—
805	C₄²	C₂⁴×C₆₁	1	8	yes	—
806	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
807	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
808	C₄²	C₂⁴×C₆₁	1	2	yes	—
809	C₄²	C₂⁴×C₆₁	1	2	yes	—
810	C₄²	C₂⁴×C₆₁	1	8	yes	—
811	C₄²	C₂⁴×C₆₁	1	2	yes	—
812	C₄²	C₂⁴×C₆₁	1	2	yes	—
813	C₄²	C₂⁴×C₆₁	1	32	yes	—
814	C₄²	C₂⁴×C₆₁	1	8	yes	—
815	C₂³	—	2	4	no	—
816	C₂³	—	2	8	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	4	4	no	—
819	C₂³	—	4	8	no	—
820	C₂³	C₂×#41×C₆₁	1	4	yes	—
821	C₂³	C₂⁵×C₆₁	1	4	yes	—
822	C₂³	C₂⁵×C₆₁	1	8	yes	—
823	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
824	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
825	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
826	Q₈	—	2	4	no	—
827	Q₈	—	2	8	no	—
828	Q₈	—	2	8	no	—
829	Q₈	—	2	4	no	—
830	Q₈	—	2	16	no	—
831	Q₈	—	4	8	no	—
832	D₄	—	2	8	no	—
833	D₄	—	2	16	no	—
834	D₄	—	2	8	no	—
835	D₄	—	2	16	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	8	no	—
838	D₄	—	2	4	no	—
839	D₄	—	2	8	no	—
840	D₄	—	2	16	no	—
841	D₄	—	4	8	no	—
842	D₄	—	4	32	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	16	no	—
847	C₂×C₄	—	2	16	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	16	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	4	32	no	—
860	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
861	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
862	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
863	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
864	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
865	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
866	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
867	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
868	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
869	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
870	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
871	C₂×C₄	C₂⁵×C₆₁	1	16	yes	—
872	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
873	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
874	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
875	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
876	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
877	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	8	no	—
883	C₂²	—	2	8	no	—
884	C₂²	—	2	16	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	8	no	—
887	C₂²	—	8	8	no	—
888	C₂²	C₂²×#41×C₆₁	1	2	yes	—
889	C₂²	C₂²×#41×C₆₁	1	2	yes	—
890	C₂²	C₂²×#41×C₆₁	1	2	yes	—
891	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
892	C₄	—	2	8	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	8	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	16	no	—
899	C₄	C₂²×#41×C₆₁	1	2	yes	—
900	C₄	C₂²×#41×C₆₁	1	2	yes	—
901	C₄	C₂²×#41×C₆₁	1	2	yes	—
902	C₄	C₂²×#41×C₆₁	1	2	yes	—
903	C₄	C₆₁×#585	1	4	yes	—
904	C₂	—	2	2	no	—
905	C₂	—	2	2	no	—
906	C₂	—	2	2	no	—
907	C₂	—	4	4	no	—
908	C₂	—	4	8	no	—
909	C₂	C₂³×#41×C₆₁	1	1	yes	characteristic
910	C₂	C₂×C₆₁×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₁
socle	C₂²×C₆₁	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3512	C₂	semidirect
2. C₆₁×#3511	C₂	semidirect
3. C₆₁×#3510	C₂	semidirect
4. C₆₁×#3509	C₂	semidirect
5. C₆₁×#3508	C₂	semidirect
6. C₆₁×#3507	C₂	semidirect
7. C₆₁×#3506	C₂	semidirect
8. C₆₁×#3505	C₂	semidirect
9. C₆₁×#3480	C₂	semidirect
10. C₆₁×#3475	C₂	semidirect
11. C₆₁×#3455	C₂	semidirect
12. C₆₁×#3449	C₂	semidirect
13. C₆₁×#3444	C₂	semidirect
14. C₂×C₆₁×#533	C₂	semidirect
15. C₂×C₆₁×#532	C₂	semidirect
16. C₆₁×#3428	C₂	semidirect
17. C₂×C₄×#41×C₆₁	C₂	semidirect
20. C₆₁×#559	C₂²	semidirect
21. C₆₁×#559	C₂²	semidirect
22. C₆₁×#557	C₂²	semidirect
23. C₆₁×#556	C₂²	semidirect
24. C₆₁×#556	C₂²	semidirect
25. C₆₁×#556	C₂²	semidirect
26. C₆₁×#555	C₂²	semidirect
27. C₆₁×#554	C₂²	semidirect
28. C₆₁×#553	C₂²	semidirect
29. C₆₁×#553	C₂²	semidirect
30. C₆₁×#553	C₂²	semidirect
31. C₆₁×#552	C₂²	semidirect
32. C₆₁×#552	C₂²	semidirect
33. C₆₁×#551	C₂²	semidirect
34. C₆₁×#550	C₂²	semidirect
35. C₆₁×#548	C₂²	semidirect
36. C₆₁×#547	C₂²	semidirect
37. C₆₁×#546	C₂²	semidirect
38. C₆₁×#542	C₂²	semidirect
39. C₆₁×#541	C₂²	semidirect
40. C₆₁×#540	C₂²	semidirect
41. C₆₁×#539	C₂²	semidirect
42. C₆₁×#538	C₂²	semidirect
43. C₆₁×#537	C₂²	semidirect
45. C₆₁×#536	C₂²	semidirect
47. C₆₁×#535	C₂²	semidirect
49. C₆₁×#533	C₂²	semidirect
50. C₆₁×#533	C₂²	semidirect
51. C₆₁×#533	C₂²	semidirect
52. C₆₁×#533	C₂²	semidirect
53. C₆₁×#533	C₂²	semidirect
54. C₆₁×#533	C₂²	semidirect
55. C₆₁×#533	C₂²	semidirect
59. C₆₁×#532	C₂²	semidirect
60. C₆₁×#532	C₂²	semidirect
61. C₆₁×#532	C₂²	semidirect
62. C₆₁×#532	C₂²	semidirect
63. C₆₁×#532	C₂²	semidirect
64. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
65. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
66. C₂×#127×C₆₁	C₂²	semidirect
67. C₆₁×#529	C₂²	semidirect
68. C₆₁×#529	C₂²	semidirect
69. C₆₁×#529	C₂²	semidirect
70. C₆₁×#529	C₂²	semidirect
71. C₂×#125×C₆₁	C₂²	semidirect
72. C₂×#124×C₆₁	C₂²	semidirect
74. C₆₁×#525	C₂²	semidirect
75. C₆₁×#525	C₂²	semidirect
78. C₆₁×#520	C₂²	semidirect
79. C₆₁×#520	C₂²	semidirect
80. C₆₁×#519	C₂²	semidirect
82. C₆₁×#518	C₂²	semidirect
86. C₄×#41×C₆₁	C₂²	semidirect
87. C₄×#41×C₆₁	C₂²	semidirect
88. C₄×#41×C₆₁	C₂²	semidirect
89. C₄×#41×C₆₁	C₂²	semidirect
90. C₄×#41×C₆₁	C₂²	semidirect
91. C₄×#41×C₆₁	C₂²	semidirect
92. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
93. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
95. C₂×C₄×D₄×C₆₁	C₂²	semidirect
96. C₂×C₄×D₄×C₆₁	C₂²	semidirect
99. C₂×#117×C₆₁	C₂²	semidirect
100. C₂×#117×C₆₁	C₂²	semidirect
102. C₂²×C₄²×C₆₁	C₂²	semidirect
293. C₂²×C₄×C₆₁	#41	semidirect
422. #62815	C₆₁	direct (N × H)
449. #3512	C₂×C₆₁	semidirect
450. #3511	C₂×C₆₁	semidirect
451. #3510	C₂×C₆₁	semidirect
452. #3509	C₂×C₆₁	semidirect
453. #3508	C₂×C₆₁	semidirect
454. #3507	C₂×C₆₁	semidirect
455. #3506	C₂×C₆₁	semidirect
456. #3505	C₂×C₆₁	semidirect
457. #3480	C₂×C₆₁	semidirect
458. #3475	C₂×C₆₁	semidirect
459. #3455	C₂×C₆₁	semidirect
460. #3449	C₂×C₆₁	semidirect
461. #3444	C₂×C₆₁	semidirect
462. C₂×#533	C₂×C₆₁	semidirect
463. C₂×#532	C₂×C₆₁	semidirect
464. #3428	C₂×C₆₁	semidirect
465. C₂×C₄×#41	C₂×C₆₁	semidirect
475. #559	C₂²×C₆₁	semidirect
476. #559	C₂²×C₆₁	semidirect
477. #557	C₂²×C₆₁	semidirect
478. #556	C₂²×C₆₁	semidirect
479. #556	C₂²×C₆₁	semidirect
480. #556	C₂²×C₆₁	semidirect
481. #555	C₂²×C₆₁	semidirect
482. #554	C₂²×C₆₁	semidirect
483. #553	C₂²×C₆₁	semidirect
484. #553	C₂²×C₆₁	semidirect
485. #553	C₂²×C₆₁	semidirect
486. #552	C₂²×C₆₁	semidirect
487. #552	C₂²×C₆₁	semidirect
488. #551	C₂²×C₆₁	semidirect
489. #550	C₂²×C₆₁	semidirect
490. #548	C₂²×C₆₁	semidirect
491. #547	C₂²×C₆₁	semidirect
492. #546	C₂²×C₆₁	semidirect
493. #542	C₂²×C₆₁	semidirect
494. #541	C₂²×C₆₁	semidirect
495. #540	C₂²×C₆₁	semidirect
496. #539	C₂²×C₆₁	semidirect
497. #538	C₂²×C₆₁	semidirect
498. #537	C₂²×C₆₁	semidirect
500. #536	C₂²×C₆₁	semidirect
502. #535	C₂²×C₆₁	semidirect
504. #533	C₂²×C₆₁	semidirect
505. #533	C₂²×C₆₁	semidirect
506. #533	C₂²×C₆₁	semidirect
507. #533	C₂²×C₆₁	semidirect
508. #533	C₂²×C₆₁	semidirect
509. #533	C₂²×C₆₁	semidirect
510. #533	C₂²×C₆₁	semidirect
514. #532	C₂²×C₆₁	semidirect
515. #532	C₂²×C₆₁	semidirect
516. #532	C₂²×C₆₁	semidirect
517. #532	C₂²×C₆₁	semidirect
518. #532	C₂²×C₆₁	semidirect
519. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
520. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
521. C₂×#127	C₂²×C₆₁	semidirect
522. #529	C₂²×C₆₁	semidirect
523. #529	C₂²×C₆₁	semidirect
524. #529	C₂²×C₆₁	semidirect
525. #529	C₂²×C₆₁	semidirect
526. C₂×#125	C₂²×C₆₁	semidirect
527. C₂×#124	C₂²×C₆₁	semidirect
529. #525	C₂²×C₆₁	semidirect
530. #525	C₂²×C₆₁	semidirect
533. #520	C₂²×C₆₁	semidirect
534. #520	C₂²×C₆₁	semidirect
535. #519	C₂²×C₆₁	semidirect
537. #518	C₂²×C₆₁	semidirect
541. C₄×#41	C₂²×C₆₁	semidirect
542. C₄×#41	C₂²×C₆₁	semidirect
543. C₄×#41	C₂²×C₆₁	semidirect
544. C₄×#41	C₂²×C₆₁	semidirect
545. C₄×#41	C₂²×C₆₁	semidirect
546. C₄×#41	C₂²×C₆₁	semidirect
547. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
548. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
550. C₂×C₄×D₄	C₂²×C₆₁	semidirect
551. C₂×C₄×D₄	C₂²×C₆₁	semidirect
554. C₂×#117	C₂²×C₆₁	semidirect
555. C₂×#117	C₂²×C₆₁	semidirect
557. C₂²×C₄²	C₂²×C₆₁	semidirect
558. C₆₁	#62815	direct (N × H)
749. C₂²×C₄	#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×#3512	2
C₆₁×#3511	2
C₆₁×#3510	2
C₆₁×#3509	2
C₆₁×#3508	2
C₆₁×#3507	2
C₆₁×#3506	2
C₆₁×#3505	2
C₆₁×#3480	2
C₆₁×#3475	2
C₆₁×#3455	2
C₆₁×#3449	2
C₆₁×#3444	2
C₂×C₆₁×#533	2
C₂×C₆₁×#532	2
C₆₁×#3428	2
C₂×C₄×#41×C₆₁	2
#62815	61

Subgroups — C61×#62815 #29566248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62815 #29566248