Subgroups — C₆₁×#34391 #29537824

Order 15616.

2458 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#525	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2375	C₂	1	4	yes	maximal, complemented
3	C₆₁×#2363	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2362	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2357	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2353	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2347	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2339	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2335	C₂	1	4	yes	maximal, complemented
12	C₆₁×#2324	C₂	1	2	yes	maximal, complemented
13	C₆₁×#2323	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2319	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2318	C₂	1	2	yes	maximal, complemented
16	C₆₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#525	C₄	1	16	yes	complemented
21	C₂×#123×C₆₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#120×C₆₁	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
28	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
31	C₂×#117×C₆₁	C₂²	1	2	yes	—
32	C₂×#117×C₆₁	C₂²	1	2	yes	—
33	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#391	C₂²	1	2	yes	complemented
35	C₆₁×#390	C₂²	1	4	yes	—
36	C₆₁×#390	C₂²	1	4	yes	—
37	C₆₁×#390	C₂²	1	4	yes	—
38	C₆₁×#390	C₂²	1	2	yes	complemented
39	C₆₁×#389	C₂²	1	4	yes	complemented
40	C₆₁×#389	C₂²	1	2	yes	complemented
41	C₆₁×#389	C₂²	1	2	yes	complemented
42	C₆₁×#388	C₂²	1	4	yes	—
43	C₆₁×#388	C₂²	1	4	yes	—
44	C₆₁×#388	C₂²	1	4	yes	—
45	C₆₁×#388	C₂²	1	4	yes	—
46	C₆₁×#388	C₂²	1	4	yes	—
47	C₆₁×#388	C₂²	1	4	yes	—
48	C₆₁×#388	C₂²	1	4	yes	complemented
49	C₆₁×#388	C₂²	1	4	yes	complemented
50	C₆₁×#387	C₂²	1	4	yes	complemented
51	C₆₁×#387	C₂²	1	4	yes	complemented
52	C₆₁×#386	C₂²	1	4	yes	—
53	C₆₁×#386	C₂²	1	4	yes	—
54	C₆₁×#386	C₂²	1	4	yes	—
55	C₆₁×#385	C₂²	1	4	yes	complemented
56	C₆₁×#383	C₂²	1	2	yes	complemented
57	C₆₁×#382	C₂²	1	2	yes	complemented
58	C₆₁×#381	C₂²	1	2	yes	—
59	C₆₁×#381	C₂²	1	1	yes	characteristic
60	C₆₁×#381	C₂²	1	1	yes	characteristic
61	C₆₁×#381	C₂²	1	2	yes	complemented
62	C₆₁×#380	C₂²	1	1	yes	characteristic
63	C₆₁×#380	C₂²	1	1	yes	characteristic
64	C₆₁×#380	C₂²	1	2	yes	—
65	C₆₁×#380	C₂²	1	2	yes	—
66	C₆₁×#380	C₂²	1	1	yes	characteristic
67	C₆₁×#380	C₂²	1	1	yes	characteristic
68	C₆₁×#380	C₂²	1	2	yes	complemented
69	C₆₁×#379	C₂²	1	2	yes	—
70	C₆₁×#379	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
72	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
73	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
74	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
78	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	complemented
82	C₆₁×#376	C₂²	1	2	yes	complemented
83	C₂×#95×C₆₁	C₂²	1	2	yes	complemented
84	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
85	C₂×#41×C₆₁	—	4	4	no	—
86	C₂×#41×C₆₁	C₂×C₄	1	8	yes	—
87	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
91	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₆₁	—	4	4	no	—
93	C₂³×C₄×C₆₁	C₂×C₄	1	8	yes	complemented
94	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
98	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
102	#123×C₆₁	C₂×C₄	1	16	yes	complemented
103	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
104	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
105	#121×C₆₁	C₂×C₄	1	8	yes	—
106	#121×C₆₁	C₂×C₄	1	8	yes	—
107	#120×C₆₁	C₂×C₄	1	16	yes	complemented
108	C₄×Q₈×C₆₁	—	4	4	no	—
109	C₄×D₄×C₆₁	—	4	4	no	—
110	C₄×D₄×C₆₁	C₂×C₄	1	16	yes	complemented
111	C₄×D₄×C₆₁	C₂×C₄	1	16	yes	complemented
112	#117×C₆₁	—	4	4	no	—
113	#117×C₆₁	—	4	4	no	—
114	#117×C₆₁	C₂×C₄	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
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	2	yes	—
129	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	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	2	yes	—
133	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
144	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
145	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
146	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
147	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
148	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
149	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
150	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
151	#95×C₆₁	C₂³	1	1	yes	characteristic
152	#95×C₆₁	C₂³	1	2	yes	—
153	#95×C₆₁	C₂³	1	4	yes	—
154	#95×C₆₁	C₂³	1	1	yes	characteristic
155	#95×C₆₁	C₂³	1	4	yes	—
156	#95×C₆₁	C₂³	1	1	yes	characteristic
157	#95×C₆₁	C₂³	1	2	yes	—
158	#95×C₆₁	C₂³	1	2	yes	—
159	#95×C₆₁	C₂³	1	1	yes	characteristic
160	#95×C₆₁	C₂³	1	2	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	4	yes	—
165	#95×C₆₁	C₂³	1	4	yes	—
166	C₂⁴×C₆₁	—	4	2	no	—
167	C₂⁴×C₆₁	—	4	1	no	—
168	C₂⁴×C₆₁	—	4	2	no	—
169	C₂⁴×C₆₁	—	4	1	no	—
170	C₂⁴×C₆₁	C₂²×C₄	1	4	yes	—
171	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
172	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
173	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
174	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
175	#41×C₆₁	—	4	16	no	—
176	C₂×Q₈×C₆₁	—	2	4	no	—
177	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
178	C₂×D₄×C₆₁	—	2	4	no	—
179	C₂×D₄×C₆₁	—	4	2	no	—
180	C₂×D₄×C₆₁	—	4	4	no	—
181	C₂×D₄×C₆₁	—	4	2	no	—
182	C₂×D₄×C₆₁	—	4	4	no	—
183	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
184	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
185	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
186	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
187	C₂²×C₄×C₆₁	—	2	4	no	—
188	C₂²×C₄×C₆₁	—	2	4	no	—
189	C₂²×C₄×C₆₁	—	2	4	no	—
190	C₂²×C₄×C₆₁	—	4	16	no	—
191	C₂²×C₄×C₆₁	—	4	2	no	—
192	C₂²×C₄×C₆₁	—	4	2	no	—
193	C₂²×C₄×C₆₁	—	4	2	no	—
194	C₂²×C₄×C₆₁	—	4	4	no	—
195	C₂²×C₄×C₆₁	—	4	4	no	—
196	C₂²×C₄×C₆₁	—	4	4	no	—
197	C₂²×C₄×C₆₁	—	4	4	no	—
198	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
199	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
200	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
202	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
203	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
204	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
205	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
218	C₄⋊C₄×C₆₁	—	2	4	no	—
219	C₄⋊C₄×C₆₁	—	2	4	no	—
220	C₄⋊C₄×C₆₁	—	4	4	no	—
221	C₄⋊C₄×C₆₁	—	4	4	no	—
222	C₄⋊C₄×C₆₁	—	4	2	no	—
223	C₄⋊C₄×C₆₁	—	4	2	no	—
224	C₄⋊C₄×C₆₁	—	4	4	no	—
225	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
226	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
227	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
228	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
229	C₂²⋊C₄×C₆₁	—	4	2	no	—
230	C₂²⋊C₄×C₆₁	—	4	2	no	—
231	C₂²⋊C₄×C₆₁	—	4	2	no	—
232	C₂²⋊C₄×C₆₁	—	4	4	no	—
233	C₂²⋊C₄×C₆₁	—	4	4	no	—
234	C₂²⋊C₄×C₆₁	—	4	4	no	—
235	C₂²⋊C₄×C₆₁	—	4	2	no	—
236	C₂²⋊C₄×C₆₁	—	4	2	no	—
237	C₂²⋊C₄×C₆₁	—	4	2	no	—
238	C₂²⋊C₄×C₆₁	—	4	2	no	—
239	C₂²⋊C₄×C₆₁	—	4	2	no	—
240	C₂²⋊C₄×C₆₁	—	4	4	no	—
241	C₂²⋊C₄×C₆₁	—	4	4	no	—
242	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
243	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
244	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
245	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
246	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
247	C₄²×C₆₁	—	2	4	no	—
248	C₄²×C₆₁	—	2	4	no	—
249	C₄²×C₆₁	—	4	4	no	—
250	C₄²×C₆₁	—	4	4	no	—
251	C₄²×C₆₁	—	4	4	no	—
252	C₄²×C₆₁	—	4	4	no	—
253	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
254	C₂³×C₆₁	—	2	2	no	—
255	C₂³×C₆₁	—	2	2	no	—
256	C₂³×C₆₁	—	2	4	no	—
257	C₂³×C₆₁	—	2	2	no	—
258	C₂³×C₆₁	—	2	2	no	—
259	C₂³×C₆₁	—	2	1	no	—
260	C₂³×C₆₁	—	2	1	no	—
261	C₂³×C₆₁	—	2	2	no	—
262	C₂³×C₆₁	—	2	2	no	—
263	C₂³×C₆₁	—	2	1	no	—
264	C₂³×C₆₁	—	2	1	no	—
265	C₂³×C₆₁	—	2	4	no	—
266	C₂³×C₆₁	—	2	2	no	—
267	C₂³×C₆₁	—	2	1	no	—
268	C₂³×C₆₁	—	2	2	no	—
269	C₂³×C₆₁	—	2	1	no	—
270	C₂³×C₆₁	—	4	4	no	—
271	C₂³×C₆₁	—	4	4	no	—
272	C₂³×C₆₁	—	4	4	no	—
273	C₂³×C₆₁	—	4	8	no	—
274	C₂³×C₆₁	—	4	8	no	—
275	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
276	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
277	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
278	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
279	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
280	Q₈×C₆₁	—	2	8	no	—
281	D₄×C₆₁	—	2	8	no	—
282	D₄×C₆₁	—	4	8	no	—
283	D₄×C₆₁	—	4	8	no	—
284	D₄×C₆₁	—	4	8	no	—
285	C₂×C₄×C₆₁	—	2	2	no	—
286	C₂×C₄×C₆₁	—	2	4	no	—
287	C₂×C₄×C₆₁	—	2	2	no	—
288	C₂×C₄×C₆₁	—	2	2	no	—
289	C₂×C₄×C₆₁	—	2	2	no	—
290	C₂×C₄×C₆₁	—	2	4	no	—
291	C₂×C₄×C₆₁	—	2	2	no	—
292	C₂×C₄×C₆₁	—	2	8	no	—
293	C₂×C₄×C₆₁	—	2	8	no	—
294	C₂×C₄×C₆₁	—	2	8	no	—
295	C₂×C₄×C₆₁	—	2	2	no	—
296	C₂×C₄×C₆₁	—	2	2	no	—
297	C₂×C₄×C₆₁	—	2	2	no	—
298	C₂×C₄×C₆₁	—	2	2	no	—
299	C₂×C₄×C₆₁	—	2	4	no	—
300	C₂×C₄×C₆₁	—	2	4	no	—
301	C₂×C₄×C₆₁	—	2	2	no	—
302	C₂×C₄×C₆₁	—	2	2	no	—
303	C₂×C₄×C₆₁	—	2	4	no	—
304	C₂×C₄×C₆₁	—	2	4	no	—
305	C₂×C₄×C₆₁	—	2	2	no	—
306	C₂×C₄×C₆₁	—	2	2	no	—
307	C₂×C₄×C₆₁	—	2	4	no	—
308	C₂×C₄×C₆₁	—	2	2	no	—
309	C₂×C₄×C₆₁	—	2	2	no	—
310	C₂×C₄×C₆₁	—	2	4	no	—
311	C₂×C₄×C₆₁	—	2	2	no	—
312	C₂×C₄×C₆₁	—	2	2	no	—
313	C₂×C₄×C₆₁	—	4	4	no	—
314	C₂×C₄×C₆₁	—	4	4	no	—
315	C₂×C₄×C₆₁	—	4	4	no	—
316	C₂×C₄×C₆₁	—	4	8	no	—
317	C₂×C₄×C₆₁	—	8	8	no	—
318	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
319	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
320	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
321	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
322	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
323	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
324	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
325	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
326	#34391	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
327	C₂²×C₆₁	—	2	2	no	—
328	C₂²×C₆₁	—	2	2	no	—
329	C₂²×C₆₁	—	2	2	no	—
330	C₂²×C₆₁	—	2	4	no	—
331	C₂²×C₆₁	—	2	2	no	—
332	C₂²×C₆₁	—	2	2	no	—
333	C₂²×C₆₁	—	2	4	no	—
334	C₂²×C₆₁	—	2	4	no	—
335	C₂²×C₆₁	—	2	2	no	—
336	C₂²×C₆₁	—	2	2	no	—
337	C₂²×C₆₁	—	2	2	no	—
338	C₂²×C₆₁	—	2	2	no	—
339	C₂²×C₆₁	—	4	16	no	—
340	C₂²×C₆₁	—	4	4	no	—
341	C₂²×C₆₁	—	4	2	no	—
342	C₂²×C₆₁	—	4	2	no	—
343	C₂²×C₆₁	—	4	2	no	—
344	C₂²×C₆₁	—	4	4	no	—
345	C₂²×C₆₁	—	4	2	no	—
346	C₂²×C₆₁	—	4	2	no	—
347	C₂²×C₆₁	—	4	2	no	—
348	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
349	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
350	C₂²×C₆₁	#585	1	1	yes	characteristic
351	C₂²×C₆₁	#585	1	2	yes	—
352	C₂²×C₆₁	#585	1	1	yes	characteristic
353	C₄×C₆₁	—	2	2	no	—
354	C₄×C₆₁	—	2	2	no	—
355	C₄×C₆₁	—	2	2	no	—
356	C₄×C₆₁	—	2	4	no	—
357	C₄×C₆₁	—	2	4	no	—
358	C₄×C₆₁	—	2	4	no	—
359	C₄×C₆₁	—	4	2	no	—
360	C₄×C₆₁	—	4	2	no	—
361	C₄×C₆₁	—	4	4	no	—
362	C₄×C₆₁	—	4	2	no	—
363	C₄×C₆₁	—	4	4	no	—
364	C₄×C₆₁	—	4	2	no	—
365	C₄×C₆₁	#518	1	4	yes	—
366	C₂×#525	C₂×C₆₁	1	1	yes	characteristic
367	#2375	C₂×C₆₁	1	4	yes	complemented
368	#2363	C₂×C₆₁	1	2	yes	complemented
369	#2362	C₂×C₆₁	1	2	yes	complemented
370	#2357	C₂×C₆₁	1	2	yes	complemented
371	#2353	C₂×C₆₁	1	2	yes	complemented
372	#2347	C₂×C₆₁	1	1	yes	characteristic, complemented
373	#2346	C₂×C₆₁	1	1	yes	characteristic, complemented
374	#2341	C₂×C₆₁	1	1	yes	characteristic, complemented
375	#2339	C₂×C₆₁	1	1	yes	characteristic, complemented
376	#2335	C₂×C₆₁	1	4	yes	complemented
377	#2324	C₂×C₆₁	1	2	yes	complemented
378	#2323	C₂×C₆₁	1	2	yes	complemented
379	#2319	C₂×C₆₁	1	2	yes	complemented
380	#2318	C₂×C₆₁	1	2	yes	complemented
381	#2280	C₂×C₆₁	1	1	yes	characteristic, complemented
382	#2280	C₂×C₆₁	1	1	yes	characteristic, complemented
383	C₂×C₆₁	—	4	4	no	—
384	C₂×C₆₁	—	4	2	no	—
385	C₂×C₆₁	—	4	2	no	—
386	C₂×C₆₁	—	4	2	no	—
387	C₂×C₆₁	C₂×#518	1	1	yes	characteristic
388	C₂×C₆₁	#3428	1	1	yes	characteristic
389	C₂×C₆₁	#3428	1	1	yes	characteristic
390	C₂×C₆₁	#3539	1	2	yes	—
391	C₂×C₆₁	#3540	1	2	yes	—
392	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
393	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
394	#525	C₄×C₆₁	1	16	yes	complemented
395	C₂×#123	C₂²×C₆₁	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
397	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
398	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
399	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
400	C₂×#120	C₂²×C₆₁	1	2	yes	—
401	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
402	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
403	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
404	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
405	C₂×#117	C₂²×C₆₁	1	2	yes	—
406	C₂×#117	C₂²×C₆₁	1	2	yes	—
407	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
408	#391	C₂²×C₆₁	1	2	yes	complemented
409	#390	C₂²×C₆₁	1	4	yes	—
410	#390	C₂²×C₆₁	1	4	yes	—
411	#390	C₂²×C₆₁	1	4	yes	—
412	#390	C₂²×C₆₁	1	2	yes	complemented
413	#389	C₂²×C₆₁	1	4	yes	complemented
414	#389	C₂²×C₆₁	1	2	yes	complemented
415	#389	C₂²×C₆₁	1	2	yes	complemented
416	#388	C₂²×C₆₁	1	4	yes	—
417	#388	C₂²×C₆₁	1	4	yes	—
418	#388	C₂²×C₆₁	1	4	yes	—
419	#388	C₂²×C₆₁	1	4	yes	—
420	#388	C₂²×C₆₁	1	4	yes	—
421	#388	C₂²×C₆₁	1	4	yes	—
422	#388	C₂²×C₆₁	1	4	yes	complemented
423	#388	C₂²×C₆₁	1	4	yes	complemented
424	#387	C₂²×C₆₁	1	4	yes	complemented
425	#387	C₂²×C₆₁	1	4	yes	complemented
426	#386	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	complemented
430	#383	C₂²×C₆₁	1	2	yes	complemented
431	#382	C₂²×C₆₁	1	2	yes	complemented
432	#381	C₂²×C₆₁	1	2	yes	—
433	#381	C₂²×C₆₁	1	1	yes	characteristic
434	#381	C₂²×C₆₁	1	1	yes	characteristic
435	#381	C₂²×C₆₁	1	2	yes	complemented
436	#380	C₂²×C₆₁	1	1	yes	characteristic
437	#380	C₂²×C₆₁	1	1	yes	characteristic
438	#380	C₂²×C₆₁	1	2	yes	—
439	#380	C₂²×C₆₁	1	2	yes	—
440	#380	C₂²×C₆₁	1	1	yes	characteristic
441	#380	C₂²×C₆₁	1	1	yes	characteristic
442	#380	C₂²×C₆₁	1	2	yes	complemented
443	#379	C₂²×C₆₁	1	2	yes	—
444	#379	C₂²×C₆₁	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
446	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
447	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
448	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	complemented
449	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
450	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
451	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
455	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	complemented
456	#376	C₂²×C₆₁	1	2	yes	complemented
457	C₂×#95	C₂²×C₆₁	1	2	yes	complemented
458	C₆₁	#34391	1	1	yes	characteristic, direct product factor, Sylow
459	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
460	C₂×#41	—	4	4	no	—
461	C₂×#41	C₂×C₄×C₆₁	1	8	yes	—
462	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
465	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
466	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
467	C₂³×C₄	—	4	4	no	—
468	C₂³×C₄	C₂×C₄×C₆₁	1	8	yes	complemented
469	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
473	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
476	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
477	#123	C₂×C₄×C₆₁	1	16	yes	complemented
478	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
479	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
480	#121	C₂×C₄×C₆₁	1	8	yes	—
481	#121	C₂×C₄×C₆₁	1	8	yes	—
482	#120	C₂×C₄×C₆₁	1	16	yes	complemented
483	C₄×Q₈	—	4	4	no	—
484	C₄×D₄	—	4	4	no	—
485	C₄×D₄	C₂×C₄×C₆₁	1	16	yes	complemented
486	C₄×D₄	C₂×C₄×C₆₁	1	16	yes	complemented
487	#117	—	4	4	no	—
488	#117	—	4	4	no	—
489	#117	C₂×C₄×C₆₁	1	8	yes	complemented
490	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	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	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
519	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
520	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
521	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
522	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
523	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
524	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
525	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
526	#95	C₂³×C₆₁	1	1	yes	characteristic
527	#95	C₂³×C₆₁	1	2	yes	—
528	#95	C₂³×C₆₁	1	4	yes	—
529	#95	C₂³×C₆₁	1	1	yes	characteristic
530	#95	C₂³×C₆₁	1	4	yes	—
531	#95	C₂³×C₆₁	1	1	yes	characteristic
532	#95	C₂³×C₆₁	1	2	yes	—
533	#95	C₂³×C₆₁	1	2	yes	—
534	#95	C₂³×C₆₁	1	1	yes	characteristic
535	#95	C₂³×C₆₁	1	2	yes	—
536	#95	C₂³×C₆₁	1	4	yes	—
537	#95	C₂³×C₆₁	1	4	yes	—
538	#95	C₂³×C₆₁	1	4	yes	—
539	#95	C₂³×C₆₁	1	4	yes	—
540	#95	C₂³×C₆₁	1	4	yes	—
541	C₂⁴	—	4	2	no	—
542	C₂⁴	—	4	1	no	—
543	C₂⁴	—	4	2	no	—
544	C₂⁴	—	4	1	no	—
545	C₂⁴	C₂²×C₄×C₆₁	1	4	yes	—
546	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
547	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
548	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
549	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
550	#41	—	4	16	no	—
551	C₂×Q₈	—	2	4	no	—
552	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	2	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
559	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
560	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
561	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	4	16	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	4	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
574	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
575	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
576	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
577	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
578	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
579	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
582	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
586	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	4	2	no	—
596	C₄⋊C₄	—	4	2	no	—
597	C₄⋊C₄	—	4	4	no	—
598	C₄⋊C₄	—	4	4	no	—
599	C₄⋊C₄	—	4	4	no	—
600	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
601	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
602	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
603	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
604	C₂²⋊C₄	—	4	2	no	—
605	C₂²⋊C₄	—	4	2	no	—
606	C₂²⋊C₄	—	4	4	no	—
607	C₂²⋊C₄	—	4	4	no	—
608	C₂²⋊C₄	—	4	2	no	—
609	C₂²⋊C₄	—	4	2	no	—
610	C₂²⋊C₄	—	4	2	no	—
611	C₂²⋊C₄	—	4	4	no	—
612	C₂²⋊C₄	—	4	4	no	—
613	C₂²⋊C₄	—	4	4	no	—
614	C₂²⋊C₄	—	4	2	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
618	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
619	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
620	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
621	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	4	4	no	—
625	C₄²	—	4	4	no	—
626	C₄²	—	4	4	no	—
627	C₄²	—	4	4	no	—
628	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	4	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	4	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	4	no	—
648	C₂³	—	4	8	no	—
649	C₂³	—	4	8	no	—
650	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
651	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
652	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
653	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
654	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
655	Q₈	—	2	8	no	—
656	D₄	—	2	8	no	—
657	D₄	—	4	8	no	—
658	D₄	—	4	8	no	—
659	D₄	—	4	8	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	8	no	—
668	C₂×C₄	—	2	8	no	—
669	C₂×C₄	—	2	8	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	4	no	—
691	C₂×C₄	—	4	8	no	—
692	C₂×C₄	—	8	8	no	—
693	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
694	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
695	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
696	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
697	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
698	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
699	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
700	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	4	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	4	16	no	—
714	C₂²	—	4	4	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
723	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
724	C₂²	C₆₁×#585	1	1	yes	characteristic
725	C₂²	C₆₁×#585	1	2	yes	—
726	C₂²	C₆₁×#585	1	1	yes	characteristic
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	4	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	4	no	—
738	C₄	—	4	2	no	—
739	C₄	C₆₁×#518	1	4	yes	—
740	C₂	—	4	2	no	—
741	C₂	—	4	2	no	—
742	C₂	—	4	2	no	—
743	C₂	—	4	4	no	—
744	C₂	C₂×C₆₁×#518	1	1	yes	characteristic
745	C₂	C₆₁×#3428	1	1	yes	characteristic
746	C₂	C₆₁×#3428	1	1	yes	characteristic
747	C₂	C₆₁×#3539	1	2	yes	—
748	C₂	C₆₁×#3540	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#525	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×#2375	C₂	semidirect
3. C₆₁×#2363	C₂	semidirect
4. C₆₁×#2362	C₂	semidirect
5. C₆₁×#2357	C₂	semidirect
6. C₆₁×#2353	C₂	semidirect
7. C₆₁×#2347	C₂	semidirect
8. C₆₁×#2346	C₂	semidirect
9. C₆₁×#2341	C₂	semidirect
10. C₆₁×#2339	C₂	semidirect
11. C₆₁×#2335	C₂	semidirect
12. C₆₁×#2324	C₂	semidirect
13. C₆₁×#2323	C₂	semidirect
14. C₆₁×#2319	C₂	semidirect
15. C₆₁×#2318	C₂	semidirect
16. C₆₁×#2280	C₂	semidirect
17. C₆₁×#2280	C₂	semidirect
20. C₆₁×#525	C₄	semidirect
27. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
30. C₂×C₄×D₄×C₆₁	C₂²	semidirect
34. C₆₁×#391	C₂²	semidirect
38. C₆₁×#390	C₂²	semidirect
39. C₆₁×#389	C₂²	semidirect
40. C₆₁×#389	C₂²	semidirect
41. C₆₁×#389	C₂²	semidirect
48. C₆₁×#388	C₂²	semidirect
49. C₆₁×#388	C₂²	semidirect
50. C₆₁×#387	C₂²	semidirect
51. C₆₁×#387	C₂²	semidirect
55. C₆₁×#385	C₂²	semidirect
56. C₆₁×#383	C₂²	semidirect
57. C₆₁×#382	C₂²	semidirect
61. C₆₁×#381	C₂²	semidirect
68. C₆₁×#380	C₂²	semidirect
71. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
72. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
73. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
74. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
80. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
81. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
82. C₆₁×#376	C₂²	semidirect
83. C₂×#95×C₆₁	C₂²	semidirect
93. C₂³×C₄×C₆₁	C₂×C₄	semidirect
102. #123×C₆₁	C₂×C₄	semidirect
103. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
104. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
107. #120×C₆₁	C₂×C₄	semidirect
110. C₄×D₄×C₆₁	C₂×C₄	semidirect
111. C₄×D₄×C₆₁	C₂×C₄	semidirect
114. #117×C₆₁	C₂×C₄	semidirect
326. #34391	C₆₁	direct (N × H)
367. #2375	C₂×C₆₁	semidirect
368. #2363	C₂×C₆₁	semidirect
369. #2362	C₂×C₆₁	semidirect
370. #2357	C₂×C₆₁	semidirect
371. #2353	C₂×C₆₁	semidirect
372. #2347	C₂×C₆₁	semidirect
373. #2346	C₂×C₆₁	semidirect
374. #2341	C₂×C₆₁	semidirect
375. #2339	C₂×C₆₁	semidirect
376. #2335	C₂×C₆₁	semidirect
377. #2324	C₂×C₆₁	semidirect
378. #2323	C₂×C₆₁	semidirect
379. #2319	C₂×C₆₁	semidirect
380. #2318	C₂×C₆₁	semidirect
381. #2280	C₂×C₆₁	semidirect
382. #2280	C₂×C₆₁	semidirect
394. #525	C₄×C₆₁	semidirect
401. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
404. C₂×C₄×D₄	C₂²×C₆₁	semidirect
408. #391	C₂²×C₆₁	semidirect
412. #390	C₂²×C₆₁	semidirect
413. #389	C₂²×C₆₁	semidirect
414. #389	C₂²×C₆₁	semidirect
415. #389	C₂²×C₆₁	semidirect
422. #388	C₂²×C₆₁	semidirect
423. #388	C₂²×C₆₁	semidirect
424. #387	C₂²×C₆₁	semidirect
425. #387	C₂²×C₆₁	semidirect
429. #385	C₂²×C₆₁	semidirect
430. #383	C₂²×C₆₁	semidirect
431. #382	C₂²×C₆₁	semidirect
435. #381	C₂²×C₆₁	semidirect
442. #380	C₂²×C₆₁	semidirect
445. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
446. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
447. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
448. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
454. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
455. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
456. #376	C₂²×C₆₁	semidirect
457. C₂×#95	C₂²×C₆₁	semidirect
458. C₆₁	#34391	direct (N × H)
468. C₂³×C₄	C₂×C₄×C₆₁	semidirect
477. #123	C₂×C₄×C₆₁	semidirect
478. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
479. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
482. #120	C₂×C₄×C₆₁	semidirect
485. C₄×D₄	C₂×C₄×C₆₁	semidirect
486. C₄×D₄	C₂×C₄×C₆₁	semidirect
489. #117	C₂×C₄×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×#525	2
C₆₁×#2375	2
C₆₁×#2363	2
C₆₁×#2362	2
C₆₁×#2357	2
C₆₁×#2353	2
C₆₁×#2347	2
C₆₁×#2346	2
C₆₁×#2341	2
C₆₁×#2339	2
C₆₁×#2335	2
C₆₁×#2324	2
C₆₁×#2323	2
C₆₁×#2319	2
C₆₁×#2318	2
C₆₁×#2280	2
#34391	61

Subgroups — C61×#34391 #29537824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34391 #29537824