Subgroups — C₆₁×#34316 #29537749

Order 15616.

2548 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#547	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2374	C₂	1	4	yes	maximal, complemented
3	C₆₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2363	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2362	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2354	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2345	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2341	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2335	C₂	1	4	yes	maximal, complemented
11	C₆₁×#2324	C₂	1	2	yes	maximal, complemented
12	C₄×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂²⋊Q₈×C₆₁	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2297	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2274	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₁	C₂²	1	2	yes	—
19	C₆₁×#547	C₄	1	16	yes	complemented
20	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#123×C₆₁	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
23	C₂×#121×C₆₁	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#117×C₆₁	C₂²	1	2	yes	—
31	C₂×#117×C₆₁	C₂²	1	2	yes	—
32	C₂×#117×C₆₁	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
34	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
35	C₆₁×#391	C₂²	1	2	yes	—
36	C₆₁×#391	C₂²	1	2	yes	—
37	C₆₁×#390	C₂²	1	1	yes	characteristic
38	C₆₁×#390	C₂²	1	1	yes	characteristic
39	C₆₁×#390	C₂²	1	2	yes	—
40	C₆₁×#390	C₂²	1	4	yes	—
41	C₆₁×#390	C₂²	1	2	yes	—
42	C₆₁×#390	C₂²	1	4	yes	—
43	C₆₁×#389	C₂²	1	1	yes	characteristic
44	C₆₁×#389	C₂²	1	1	yes	characteristic
45	C₆₁×#389	C₂²	1	2	yes	—
46	C₆₁×#389	C₂²	1	2	yes	—
47	C₆₁×#389	C₂²	1	2	yes	—
48	C₆₁×#388	C₂²	1	2	yes	—
49	C₆₁×#388	C₂²	1	2	yes	—
50	C₆₁×#388	C₂²	1	4	yes	—
51	C₆₁×#388	C₂²	1	4	yes	—
52	C₆₁×#388	C₂²	1	4	yes	—
53	C₆₁×#388	C₂²	1	4	yes	—
54	C₆₁×#387	C₂²	1	4	yes	—
55	C₆₁×#387	C₂²	1	4	yes	—
56	C₆₁×#387	C₂²	1	4	yes	—
57	C₆₁×#386	C₂²	1	4	yes	—
58	C₆₁×#386	C₂²	1	4	yes	—
59	C₆₁×#385	C₂²	1	4	yes	—
60	C₆₁×#384	C₂²	1	1	yes	characteristic
61	C₆₁×#380	C₂²	1	2	yes	—
62	C₆₁×#380	C₂²	1	2	yes	—
63	C₆₁×#380	C₂²	1	4	yes	—
64	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
67	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
68	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
71	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
79	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
80	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
83	C₄³×C₆₁	C₂²	1	1	yes	characteristic
84	C₂×#41×C₆₁	—	4	4	no	—
85	C₂×#41×C₆₁	—	4	4	no	—
86	C₂×#41×C₆₁	C₂×C₄	1	16	yes	complemented
87	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
88	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
91	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
94	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
96	C₄⋊Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
97	#123×C₆₁	C₂×C₄	1	32	yes	complemented
98	C₂²⋊Q₈×C₆₁	C₂×C₄	1	16	yes	complemented
99	#121×C₆₁	C₂×C₄	1	16	yes	—
100	C₄×Q₈×C₆₁	—	4	4	no	—
101	C₄×Q₈×C₆₁	—	4	4	no	—
102	C₄×D₄×C₆₁	—	2	4	no	—
103	C₄×D₄×C₆₁	—	2	4	no	—
104	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	—
105	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	complemented
106	#117×C₆₁	—	2	8	no	—
107	#117×C₆₁	—	2	8	no	—
108	#117×C₆₁	—	4	4	no	—
109	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	16	yes	complemented
110	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₆₁	—	4	4	no	—
140	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
145	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
146	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
147	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
149	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
150	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
151	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
152	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
153	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
155	#95×C₆₁	C₂³	1	2	yes	—
156	#95×C₆₁	C₂³	1	2	yes	—
157	#95×C₆₁	C₂³	1	2	yes	—
158	#95×C₆₁	C₂³	1	4	yes	—
159	#95×C₆₁	C₂³	1	2	yes	—
160	#95×C₆₁	C₂³	1	4	yes	—
161	#95×C₆₁	C₂³	1	4	yes	—
162	#95×C₆₁	C₂³	1	4	yes	—
163	#95×C₆₁	C₂³	1	4	yes	—
164	#95×C₆₁	C₂³	1	2	yes	—
165	#95×C₆₁	C₂³	1	4	yes	—
166	#95×C₆₁	C₂³	1	2	yes	—
167	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
168	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
169	#41×C₆₁	—	4	32	no	—
170	C₂×Q₈×C₆₁	—	2	4	no	—
171	C₂×Q₈×C₆₁	—	2	4	no	—
172	C₂×Q₈×C₆₁	C₂²×C₄	1	8	yes	—
173	C₂×D₄×C₆₁	—	2	2	no	—
174	C₂×D₄×C₆₁	—	2	2	no	—
175	C₂×D₄×C₆₁	—	2	2	no	—
176	C₂×D₄×C₆₁	—	2	2	no	—
177	C₂×D₄×C₆₁	—	4	4	no	—
178	C₂×D₄×C₆₁	—	4	4	no	—
179	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
180	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
181	C₂×D₄×C₆₁	C₂²×C₄	1	16	yes	—
182	C₂²×C₄×C₆₁	—	2	4	no	—
183	C₂²×C₄×C₆₁	—	2	4	no	—
184	C₂²×C₄×C₆₁	—	2	4	no	—
185	C₂²×C₄×C₆₁	—	2	4	no	—
186	C₂²×C₄×C₆₁	—	2	4	no	—
187	C₂²×C₄×C₆₁	—	2	4	no	—
188	C₂²×C₄×C₆₁	—	2	4	no	—
189	C₂²×C₄×C₆₁	—	4	2	no	—
190	C₂²×C₄×C₆₁	—	4	2	no	—
191	C₂²×C₄×C₆₁	—	4	2	no	—
192	C₂²×C₄×C₆₁	—	4	4	no	—
193	C₂²×C₄×C₆₁	—	4	4	no	—
194	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
195	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
196	C₂²×C₄×C₆₁	C₂²×C₄	1	16	yes	—
197	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
212	C₄⋊C₄×C₆₁	—	2	4	no	—
213	C₄⋊C₄×C₆₁	—	2	4	no	—
214	C₄⋊C₄×C₆₁	—	2	4	no	—
215	C₄⋊C₄×C₆₁	—	2	2	no	—
216	C₄⋊C₄×C₆₁	—	2	2	no	—
217	C₄⋊C₄×C₆₁	—	2	4	no	—
218	C₄⋊C₄×C₆₁	—	2	2	no	—
219	C₄⋊C₄×C₆₁	—	4	2	no	—
220	C₄⋊C₄×C₆₁	—	4	4	no	—
221	C₄⋊C₄×C₆₁	—	4	4	no	—
222	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
223	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
224	C₄⋊C₄×C₆₁	C₂²×C₄	1	16	yes	—
225	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
226	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
227	C₄⋊C₄×C₆₁	#41	1	4	yes	complemented
228	C₂²⋊C₄×C₆₁	—	2	8	no	—
229	C₂²⋊C₄×C₆₁	—	2	4	no	—
230	C₂²⋊C₄×C₆₁	—	2	4	no	—
231	C₂²⋊C₄×C₆₁	—	2	4	no	—
232	C₂²⋊C₄×C₆₁	—	2	4	no	—
233	C₂²⋊C₄×C₆₁	—	2	4	no	—
234	C₂²⋊C₄×C₆₁	—	4	2	no	—
235	C₂²⋊C₄×C₆₁	—	4	4	no	—
236	C₂²⋊C₄×C₆₁	—	4	4	no	—
237	C₂²⋊C₄×C₆₁	—	4	4	no	—
238	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
239	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
240	C₂²⋊C₄×C₆₁	C₂²×C₄	1	16	yes	—
241	C₄²×C₆₁	—	2	8	no	—
242	C₄²×C₆₁	—	2	4	no	—
243	C₄²×C₆₁	—	2	2	no	—
244	C₄²×C₆₁	—	2	2	no	—
245	C₄²×C₆₁	—	2	4	no	—
246	C₄²×C₆₁	—	2	2	no	—
247	C₄²×C₆₁	—	2	2	no	—
248	C₄²×C₆₁	—	4	2	no	—
249	C₄²×C₆₁	—	4	2	no	—
250	C₄²×C₆₁	—	4	1	no	—
251	C₄²×C₆₁	—	4	4	no	—
252	C₄²×C₆₁	—	4	4	no	—
253	C₄²×C₆₁	—	4	4	no	—
254	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
255	C₄²×C₆₁	#41	1	4	yes	complemented
256	C₂³×C₆₁	—	2	2	no	—
257	C₂³×C₆₁	—	2	2	no	—
258	C₂³×C₆₁	—	2	2	no	—
259	C₂³×C₆₁	—	2	2	no	—
260	C₂³×C₆₁	—	2	2	no	—
261	C₂³×C₆₁	—	2	2	no	—
262	C₂³×C₆₁	—	2	2	no	—
263	C₂³×C₆₁	—	2	2	no	—
264	C₂³×C₆₁	—	2	2	no	—
265	C₂³×C₆₁	—	2	2	no	—
266	C₂³×C₆₁	—	2	2	no	—
267	C₂³×C₆₁	—	2	2	no	—
268	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
269	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
270	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
271	Q₈×C₆₁	—	2	16	no	—
272	D₄×C₆₁	—	2	8	no	—
273	D₄×C₆₁	—	2	8	no	—
274	D₄×C₆₁	—	4	16	no	—
275	C₂×C₄×C₆₁	—	2	2	no	—
276	C₂×C₄×C₆₁	—	2	1	no	—
277	C₂×C₄×C₆₁	—	2	2	no	—
278	C₂×C₄×C₆₁	—	2	1	no	—
279	C₂×C₄×C₆₁	—	2	2	no	—
280	C₂×C₄×C₆₁	—	2	1	no	—
281	C₂×C₄×C₆₁	—	2	1	no	—
282	C₂×C₄×C₆₁	—	2	2	no	—
283	C₂×C₄×C₆₁	—	2	2	no	—
284	C₂×C₄×C₆₁	—	2	4	no	—
285	C₂×C₄×C₆₁	—	2	4	no	—
286	C₂×C₄×C₆₁	—	2	1	no	—
287	C₂×C₄×C₆₁	—	2	1	no	—
288	C₂×C₄×C₆₁	—	2	2	no	—
289	C₂×C₄×C₆₁	—	2	1	no	—
290	C₂×C₄×C₆₁	—	2	1	no	—
291	C₂×C₄×C₆₁	—	2	16	no	—
292	C₂×C₄×C₆₁	—	2	16	no	—
293	C₂×C₄×C₆₁	—	2	1	no	—
294	C₂×C₄×C₆₁	—	2	2	no	—
295	C₂×C₄×C₆₁	—	2	2	no	—
296	C₂×C₄×C₆₁	—	2	4	no	—
297	C₂×C₄×C₆₁	—	2	2	no	—
298	C₂×C₄×C₆₁	—	2	2	no	—
299	C₂×C₄×C₆₁	—	2	1	no	—
300	C₂×C₄×C₆₁	—	2	2	no	—
301	C₂×C₄×C₆₁	—	2	4	no	—
302	C₂×C₄×C₆₁	—	2	2	no	—
303	C₂×C₄×C₆₁	—	2	2	no	—
304	C₂×C₄×C₆₁	—	2	1	no	—
305	C₂×C₄×C₆₁	—	2	2	no	—
306	C₂×C₄×C₆₁	—	2	4	no	—
307	C₂×C₄×C₆₁	—	2	2	no	—
308	C₂×C₄×C₆₁	—	4	16	no	—
309	C₂×C₄×C₆₁	—	4	8	no	—
310	C₂×C₄×C₆₁	—	4	8	no	—
311	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
313	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
314	C₂×C₄×C₆₁	C₂³×C₄	1	8	yes	—
315	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
316	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
317	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
318	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
319	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
320	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
321	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
322	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
323	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
324	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
325	#34316	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
326	C₂²×C₆₁	—	2	4	no	—
327	C₂²×C₆₁	—	2	4	no	—
328	C₂²×C₆₁	—	2	4	no	—
329	C₂²×C₆₁	—	2	4	no	—
330	C₂²×C₆₁	—	2	4	no	—
331	C₂²×C₆₁	—	2	4	no	—
332	C₂²×C₆₁	—	4	2	no	—
333	C₂²×C₆₁	—	4	2	no	—
334	C₂²×C₆₁	—	4	2	no	—
335	C₂²×C₆₁	—	4	2	no	—
336	C₂²×C₆₁	—	4	2	no	—
337	C₂²×C₆₁	—	4	2	no	—
338	C₂²×C₆₁	—	4	2	no	—
339	C₂²×C₆₁	—	4	2	no	—
340	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
341	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
343	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
346	C₂²×C₆₁	#585	1	1	yes	characteristic
347	C₄×C₆₁	—	2	4	no	—
348	C₄×C₆₁	—	2	4	no	—
349	C₄×C₆₁	—	2	8	no	—
350	C₄×C₆₁	—	2	2	no	—
351	C₄×C₆₁	—	2	2	no	—
352	C₄×C₆₁	—	2	2	no	—
353	C₄×C₆₁	—	2	2	no	—
354	C₄×C₆₁	—	2	4	no	—
355	C₄×C₆₁	—	4	2	no	—
356	C₄×C₆₁	—	4	2	no	—
357	C₄×C₆₁	—	4	2	no	—
358	C₄×C₆₁	—	4	1	no	—
359	C₄×C₆₁	—	4	4	no	—
360	C₄×C₆₁	C₄×#41	1	4	yes	—
361	C₄×C₆₁	#518	1	4	yes	—
362	C₂×#547	C₂×C₆₁	1	1	yes	characteristic
363	#2374	C₂×C₆₁	1	4	yes	complemented
364	#2365	C₂×C₆₁	1	1	yes	characteristic, complemented
365	#2363	C₂×C₆₁	1	2	yes	complemented
366	#2362	C₂×C₆₁	1	2	yes	complemented
367	#2354	C₂×C₆₁	1	1	yes	characteristic, complemented
368	#2354	C₂×C₆₁	1	1	yes	characteristic, complemented
369	#2345	C₂×C₆₁	1	2	yes	complemented
370	#2341	C₂×C₆₁	1	2	yes	complemented
371	#2335	C₂×C₆₁	1	4	yes	complemented
372	#2324	C₂×C₆₁	1	2	yes	complemented
373	C₄×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
374	C₄×C₂²⋊Q₈	C₂×C₆₁	1	2	yes	complemented
375	#2297	C₂×C₆₁	1	2	yes	complemented
376	#2293	C₂×C₆₁	1	1	yes	characteristic, complemented
377	#2274	C₂×C₆₁	1	2	yes	complemented
378	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
379	C₂×C₆₁	—	4	4	no	—
380	C₂×C₆₁	—	4	4	no	—
381	C₂×C₆₁	C₂×C₄×#41	1	1	yes	characteristic
382	C₂×C₆₁	C₂×#518	1	1	yes	characteristic
383	C₂×C₆₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
384	C₂×C₆₁	#3506	1	1	yes	characteristic
385	C₂×C₆₁	#3511	1	1	yes	characteristic
386	C₂×C₆₁	#3517	1	1	yes	characteristic
387	C₂×C₆₁	#3520	1	1	yes	characteristic
388	C₂²×#41	C₂²×C₆₁	1	2	yes	—
389	#547	C₄×C₆₁	1	16	yes	complemented
390	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
391	C₂×#123	C₂²×C₆₁	1	4	yes	—
392	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
393	C₂×#121	C₂²×C₆₁	1	2	yes	—
394	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
395	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
396	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
400	C₂×#117	C₂²×C₆₁	1	2	yes	—
401	C₂×#117	C₂²×C₆₁	1	2	yes	—
402	C₂×#117	C₂²×C₆₁	1	2	yes	—
403	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
404	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
405	#391	C₂²×C₆₁	1	2	yes	—
406	#391	C₂²×C₆₁	1	2	yes	—
407	#390	C₂²×C₆₁	1	4	yes	—
408	#390	C₂²×C₆₁	1	2	yes	—
409	#390	C₂²×C₆₁	1	4	yes	—
410	#390	C₂²×C₆₁	1	1	yes	characteristic
411	#390	C₂²×C₆₁	1	2	yes	—
412	#390	C₂²×C₆₁	1	1	yes	characteristic
413	#389	C₂²×C₆₁	1	2	yes	—
414	#389	C₂²×C₆₁	1	2	yes	—
415	#389	C₂²×C₆₁	1	2	yes	—
416	#389	C₂²×C₆₁	1	1	yes	characteristic
417	#389	C₂²×C₆₁	1	1	yes	characteristic
418	#388	C₂²×C₆₁	1	4	yes	—
419	#388	C₂²×C₆₁	1	2	yes	—
420	#388	C₂²×C₆₁	1	4	yes	—
421	#388	C₂²×C₆₁	1	4	yes	—
422	#388	C₂²×C₆₁	1	4	yes	—
423	#388	C₂²×C₆₁	1	2	yes	—
424	#387	C₂²×C₆₁	1	4	yes	—
425	#387	C₂²×C₆₁	1	4	yes	—
426	#387	C₂²×C₆₁	1	4	yes	—
427	#386	C₂²×C₆₁	1	4	yes	—
428	#386	C₂²×C₆₁	1	4	yes	—
429	#385	C₂²×C₆₁	1	4	yes	—
430	#384	C₂²×C₆₁	1	1	yes	characteristic
431	#380	C₂²×C₆₁	1	2	yes	—
432	#380	C₂²×C₆₁	1	4	yes	—
433	#380	C₂²×C₆₁	1	2	yes	—
434	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
435	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
437	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
440	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
443	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
444	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
445	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
446	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
447	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
448	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
450	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
451	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
452	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
453	C₄³	C₂²×C₆₁	1	1	yes	characteristic
454	C₆₁	#34316	1	1	yes	characteristic, direct product factor, Sylow
455	C₂×#41	—	4	4	no	—
456	C₂×#41	—	4	4	no	—
457	C₂×#41	C₂×C₄×C₆₁	1	16	yes	complemented
458	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
459	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
460	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
462	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
463	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
464	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
465	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
466	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
467	C₄⋊Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
468	#123	C₂×C₄×C₆₁	1	32	yes	complemented
469	C₂²⋊Q₈	C₂×C₄×C₆₁	1	16	yes	complemented
470	#121	C₂×C₄×C₆₁	1	16	yes	—
471	C₄×Q₈	—	4	4	no	—
472	C₄×Q₈	—	4	4	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	2	4	no	—
475	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	—
476	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	complemented
477	#117	—	2	8	no	—
478	#117	—	2	8	no	—
479	#117	—	4	4	no	—
480	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	16	yes	complemented
481	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
510	C₂×C₄²	—	4	4	no	—
511	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
512	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
513	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
515	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
516	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
519	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
520	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
521	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
523	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
524	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
526	#95	C₂³×C₆₁	1	2	yes	—
527	#95	C₂³×C₆₁	1	2	yes	—
528	#95	C₂³×C₆₁	1	2	yes	—
529	#95	C₂³×C₆₁	1	4	yes	—
530	#95	C₂³×C₆₁	1	2	yes	—
531	#95	C₂³×C₆₁	1	4	yes	—
532	#95	C₂³×C₆₁	1	4	yes	—
533	#95	C₂³×C₆₁	1	4	yes	—
534	#95	C₂³×C₆₁	1	4	yes	—
535	#95	C₂³×C₆₁	1	2	yes	—
536	#95	C₂³×C₆₁	1	4	yes	—
537	#95	C₂³×C₆₁	1	2	yes	—
538	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
539	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
540	#41	—	4	32	no	—
541	C₂×Q₈	—	2	4	no	—
542	C₂×Q₈	—	2	4	no	—
543	C₂×Q₈	C₂²×C₄×C₆₁	1	8	yes	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	4	4	no	—
549	C₂×D₄	—	4	4	no	—
550	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
551	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
552	C₂×D₄	C₂²×C₄×C₆₁	1	16	yes	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	4	no	—
563	C₂²×C₄	—	4	4	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
566	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
567	C₂²×C₄	C₂²×C₄×C₆₁	1	16	yes	—
568	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	4	4	no	—
591	C₄⋊C₄	—	4	4	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
594	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
595	C₄⋊C₄	C₂²×C₄×C₆₁	1	16	yes	—
596	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
597	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
598	C₄⋊C₄	#41×C₆₁	1	4	yes	complemented
599	C₂²⋊C₄	—	2	8	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	4	4	no	—
606	C₂²⋊C₄	—	4	2	no	—
607	C₂²⋊C₄	—	4	4	no	—
608	C₂²⋊C₄	—	4	4	no	—
609	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
610	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
611	C₂²⋊C₄	C₂²×C₄×C₆₁	1	16	yes	—
612	C₄²	—	2	8	no	—
613	C₄²	—	2	4	no	—
614	C₄²	—	2	2	no	—
615	C₄²	—	2	2	no	—
616	C₄²	—	2	4	no	—
617	C₄²	—	2	2	no	—
618	C₄²	—	2	2	no	—
619	C₄²	—	4	2	no	—
620	C₄²	—	4	2	no	—
621	C₄²	—	4	4	no	—
622	C₄²	—	4	4	no	—
623	C₄²	—	4	4	no	—
624	C₄²	—	4	1	no	—
625	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
626	C₄²	#41×C₆₁	1	4	yes	complemented
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
640	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
641	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
642	Q₈	—	2	16	no	—
643	D₄	—	2	8	no	—
644	D₄	—	2	8	no	—
645	D₄	—	4	16	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	16	no	—
663	C₂×C₄	—	2	16	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	4	16	no	—
680	C₂×C₄	—	4	8	no	—
681	C₂×C₄	—	4	8	no	—
682	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
683	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
684	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
685	C₂×C₄	C₂³×C₄×C₆₁	1	8	yes	—
686	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
687	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
688	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
689	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
690	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
691	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
692	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
693	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
694	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
695	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
696	C₂²	—	2	4	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	2	4	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
711	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
712	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
713	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
714	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
715	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
716	C₂²	C₆₁×#585	1	1	yes	characteristic
717	C₄	—	2	4	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	8	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	4	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	4	no	—
730	C₄	C₄×#41×C₆₁	1	4	yes	—
731	C₄	C₆₁×#518	1	4	yes	—
732	C₂	—	4	4	no	—
733	C₂	—	4	4	no	—
734	C₂	C₂×C₄×#41×C₆₁	1	1	yes	characteristic
735	C₂	C₂×C₆₁×#518	1	1	yes	characteristic
736	C₂	C₄×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
737	C₂	C₆₁×#3506	1	1	yes	characteristic
738	C₂	C₆₁×#3511	1	1	yes	characteristic
739	C₂	C₆₁×#3517	1	1	yes	characteristic
740	C₂	C₆₁×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#547	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2374	C₂	semidirect
3. C₆₁×#2365	C₂	semidirect
4. C₆₁×#2363	C₂	semidirect
5. C₆₁×#2362	C₂	semidirect
6. C₆₁×#2354	C₂	semidirect
7. C₆₁×#2354	C₂	semidirect
8. C₆₁×#2345	C₂	semidirect
9. C₆₁×#2341	C₂	semidirect
10. C₆₁×#2335	C₂	semidirect
11. C₆₁×#2324	C₂	semidirect
12. C₄×C₄⋊Q₈×C₆₁	C₂	semidirect
13. C₄×C₂²⋊Q₈×C₆₁	C₂	semidirect
14. C₆₁×#2297	C₂	semidirect
15. C₆₁×#2293	C₂	semidirect
16. C₆₁×#2274	C₂	semidirect
17. C₄²×D₄×C₆₁	C₂	semidirect
19. C₆₁×#547	C₄	semidirect
86. C₂×#41×C₆₁	C₂×C₄	semidirect
96. C₄⋊Q₈×C₆₁	C₂×C₄	semidirect
97. #123×C₆₁	C₂×C₄	semidirect
98. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
105. C₄×D₄×C₆₁	C₂×C₄	semidirect
109. C₂×C₄⋊C₄×C₆₁	C₂×C₄	semidirect
227. C₄⋊C₄×C₆₁	#41	semidirect
255. C₄²×C₆₁	#41	semidirect
325. #34316	C₆₁	direct (N × H)
363. #2374	C₂×C₆₁	semidirect
364. #2365	C₂×C₆₁	semidirect
365. #2363	C₂×C₆₁	semidirect
366. #2362	C₂×C₆₁	semidirect
367. #2354	C₂×C₆₁	semidirect
368. #2354	C₂×C₆₁	semidirect
369. #2345	C₂×C₆₁	semidirect
370. #2341	C₂×C₆₁	semidirect
371. #2335	C₂×C₆₁	semidirect
372. #2324	C₂×C₆₁	semidirect
373. C₄×C₄⋊Q₈	C₂×C₆₁	semidirect
374. C₄×C₂²⋊Q₈	C₂×C₆₁	semidirect
375. #2297	C₂×C₆₁	semidirect
376. #2293	C₂×C₆₁	semidirect
377. #2274	C₂×C₆₁	semidirect
378. C₄²×D₄	C₂×C₆₁	semidirect
389. #547	C₄×C₆₁	semidirect
454. C₆₁	#34316	direct (N × H)
457. C₂×#41	C₂×C₄×C₆₁	semidirect
467. C₄⋊Q₈	C₂×C₄×C₆₁	semidirect
468. #123	C₂×C₄×C₆₁	semidirect
469. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
476. C₄×D₄	C₂×C₄×C₆₁	semidirect
480. C₂×C₄⋊C₄	C₂×C₄×C₆₁	semidirect
598. C₄⋊C₄	#41×C₆₁	semidirect
626. C₄²	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#547	2
C₆₁×#2374	2
C₆₁×#2365	2
C₆₁×#2363	2
C₆₁×#2362	2
C₆₁×#2354	2
C₆₁×#2345	2
C₆₁×#2341	2
C₆₁×#2335	2
C₆₁×#2324	2
C₄×C₄⋊Q₈×C₆₁	2
C₄×C₂²⋊Q₈×C₆₁	2
C₆₁×#2297	2
C₆₁×#2293	2
C₆₁×#2274	2
C₄²×D₄×C₆₁	2
#34316	61

Subgroups — C61×#34316 #29537749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34316 #29537749