Subgroups — C₆₁×#34893 #29538326

Order 15616.

1900 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2589	C₂	1	2	yes	maximal, complemented
2	C₆₁×#2587	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2584	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2580	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2566	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#2550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2522	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2507	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2465	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2454	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#2452	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#2396	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2396	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#125×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#125×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂²⋊Q₈×C₆₁	C₂	1	2	yes	maximal, complemented
19	C₆₁×#2296	C₂	1	2	yes	maximal, complemented
20	C₆₁×#2293	C₂	1	1	yes	maximal, characteristic
21	C₆₁×#2293	C₂	1	1	yes	maximal, characteristic
22	C₄²×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#117×C₆₁	C₂²	1	2	yes	—
36	C₂×#117×C₆₁	C₂²	1	2	yes	—
37	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
38	C₆₁×#400	C₂²	1	2	yes	—
39	C₆₁×#400	C₂²	1	2	yes	—
40	C₆₁×#399	C₂²	1	2	yes	—
41	C₆₁×#399	C₂²	1	2	yes	—
42	C₆₁×#398	C₂²	1	2	yes	—
43	C₆₁×#398	C₂²	1	2	yes	—
44	C₆₁×#398	C₂²	1	2	yes	—
45	C₆₁×#398	C₂²	1	2	yes	—
46	C₆₁×#396	C₂²	1	2	yes	—
47	C₆₁×#396	C₂²	1	2	yes	—
48	C₆₁×#396	C₂²	1	2	yes	—
49	C₆₁×#396	C₂²	1	2	yes	—
50	C₆₁×#395	C₂²	1	2	yes	—
51	C₆₁×#395	C₂²	1	2	yes	—
52	C₆₁×#393	C₂²	1	2	yes	—
53	C₆₁×#393	C₂²	1	2	yes	—
54	C₆₁×#391	C₂²	1	2	yes	—
55	C₆₁×#391	C₂²	1	2	yes	—
56	C₆₁×#390	C₂²	1	1	yes	characteristic
57	C₆₁×#390	C₂²	1	1	yes	characteristic
58	C₆₁×#390	C₂²	1	1	yes	characteristic
59	C₆₁×#390	C₂²	1	1	yes	characteristic
60	C₆₁×#389	C₂²	1	2	yes	—
61	C₆₁×#389	C₂²	1	2	yes	—
62	C₆₁×#389	C₂²	1	1	yes	characteristic
63	C₆₁×#389	C₂²	1	1	yes	characteristic
64	C₆₁×#389	C₂²	1	1	yes	characteristic
65	C₆₁×#389	C₂²	1	1	yes	characteristic
66	C₆₁×#389	C₂²	1	2	yes	—
67	C₆₁×#389	C₂²	1	2	yes	—
68	C₆₁×#389	C₂²	1	2	yes	—
69	C₆₁×#389	C₂²	1	2	yes	—
70	C₆₁×#389	C₂²	1	1	yes	characteristic
71	C₆₁×#389	C₂²	1	1	yes	characteristic
72	C₆₁×#389	C₂²	1	1	yes	characteristic
73	C₆₁×#389	C₂²	1	1	yes	characteristic
74	C₆₁×#389	C₂²	1	1	yes	characteristic
75	C₆₁×#389	C₂²	1	1	yes	characteristic
76	C₆₁×#388	C₂²	1	2	yes	—
77	C₆₁×#388	C₂²	1	2	yes	—
78	C₆₁×#388	C₂²	1	2	yes	—
79	C₆₁×#388	C₂²	1	2	yes	—
80	C₆₁×#387	C₂²	1	2	yes	—
81	C₆₁×#387	C₂²	1	2	yes	—
82	C₆₁×#387	C₂²	1	2	yes	—
83	C₆₁×#387	C₂²	1	2	yes	—
84	C₆₁×#387	C₂²	1	2	yes	—
85	C₆₁×#387	C₂²	1	2	yes	—
86	C₆₁×#385	C₂²	1	2	yes	—
87	C₆₁×#385	C₂²	1	2	yes	—
88	C₆₁×#385	C₂²	1	2	yes	—
89	C₆₁×#385	C₂²	1	2	yes	—
90	C₆₁×#385	C₂²	1	2	yes	—
91	C₆₁×#385	C₂²	1	2	yes	—
92	C₆₁×#384	C₂²	1	1	yes	characteristic
93	C₆₁×#382	C₂²	1	1	yes	characteristic
94	C₆₁×#382	C₂²	1	1	yes	characteristic
95	C₆₁×#380	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
120	C₄³×C₆₁	C₂²	1	1	yes	characteristic
121	C₄³×C₆₁	C₂²	1	1	yes	characteristic
122	C₄³×C₆₁	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₆₁	—	2	4	no	—
130	#125×C₆₁	—	2	4	no	—
131	#125×C₆₁	—	2	4	no	—
132	C₂²⋊Q₈×C₆₁	—	2	8	no	—
133	C₄×Q₈×C₆₁	—	2	4	no	—
134	C₄×Q₈×C₆₁	—	2	4	no	—
135	C₄×Q₈×C₆₁	—	2	4	no	—
136	C₄×Q₈×C₆₁	—	4	4	no	—
137	C₄×D₄×C₆₁	—	2	4	no	—
138	C₄×D₄×C₆₁	—	2	4	no	—
139	C₄×D₄×C₆₁	Q₈	1	8	yes	complemented
140	#117×C₆₁	—	2	8	no	—
141	#117×C₆₁	—	4	4	no	—
142	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₁	—	4	4	no	—
187	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
208	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
211	#95×C₆₁	C₂³	1	2	yes	—
212	#95×C₆₁	C₂³	1	2	yes	—
213	#95×C₆₁	C₂³	1	2	yes	—
214	#95×C₆₁	C₂³	1	2	yes	—
215	#95×C₆₁	C₂³	1	2	yes	—
216	#95×C₆₁	C₂³	1	2	yes	—
217	#95×C₆₁	C₂³	1	2	yes	—
218	#95×C₆₁	C₂³	1	1	yes	characteristic
219	#95×C₆₁	C₂³	1	1	yes	characteristic
220	#95×C₆₁	C₂³	1	1	yes	characteristic
221	#95×C₆₁	C₂³	1	1	yes	characteristic
222	#95×C₆₁	C₂³	1	1	yes	characteristic
223	#95×C₆₁	C₂³	1	1	yes	characteristic
224	#95×C₆₁	C₂³	1	2	yes	—
225	#95×C₆₁	C₂³	1	2	yes	—
226	#95×C₆₁	C₂³	1	2	yes	—
227	#95×C₆₁	C₂³	1	2	yes	—
228	#95×C₆₁	C₂³	1	2	yes	—
229	#95×C₆₁	C₂³	1	2	yes	—
230	#95×C₆₁	C₂³	1	2	yes	—
231	#95×C₆₁	C₂³	1	2	yes	—
232	#95×C₆₁	C₂³	1	2	yes	—
233	#95×C₆₁	C₂³	1	2	yes	—
234	#95×C₆₁	C₂³	1	2	yes	—
235	#95×C₆₁	C₂³	1	2	yes	—
236	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₆₁	—	2	2	no	—
238	C₂×Q₈×C₆₁	—	2	2	no	—
239	C₂×Q₈×C₆₁	—	2	2	no	—
240	C₂×Q₈×C₆₁	—	2	4	no	—
241	C₂×Q₈×C₆₁	—	2	4	no	—
242	C₂×Q₈×C₆₁	—	4	2	no	—
243	C₂×D₄×C₆₁	—	2	2	no	—
244	C₂×D₄×C₆₁	—	2	2	no	—
245	C₂×D₄×C₆₁	C₂×Q₈	1	4	yes	—
246	C₂²×C₄×C₆₁	—	2	4	no	—
247	C₂²×C₄×C₆₁	—	2	4	no	—
248	C₂²×C₄×C₆₁	—	2	4	no	—
249	C₂²×C₄×C₆₁	—	2	4	no	—
250	C₂²×C₄×C₆₁	—	2	4	no	—
251	C₂²×C₄×C₆₁	—	4	2	no	—
252	C₂²×C₄×C₆₁	—	4	2	no	—
253	C₂²×C₄×C₆₁	—	4	2	no	—
254	C₂²×C₄×C₆₁	C₂×Q₈	1	8	yes	—
255	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
277	C₄⋊C₄×C₆₁	—	2	4	no	—
278	C₄⋊C₄×C₆₁	—	2	4	no	—
279	C₄⋊C₄×C₆₁	—	2	2	no	—
280	C₄⋊C₄×C₆₁	—	2	2	no	—
281	C₄⋊C₄×C₆₁	—	2	2	no	—
282	C₄⋊C₄×C₆₁	—	2	2	no	—
283	C₄⋊C₄×C₆₁	—	2	2	no	—
284	C₄⋊C₄×C₆₁	—	2	2	no	—
285	C₄⋊C₄×C₆₁	—	2	2	no	—
286	C₄⋊C₄×C₆₁	—	2	2	no	—
287	C₄⋊C₄×C₆₁	—	2	2	no	—
288	C₄⋊C₄×C₆₁	—	2	4	no	—
289	C₄⋊C₄×C₆₁	—	2	4	no	—
290	C₄⋊C₄×C₆₁	—	2	4	no	—
291	C₄⋊C₄×C₆₁	—	2	4	no	—
292	C₄⋊C₄×C₆₁	—	2	4	no	—
293	C₄⋊C₄×C₆₁	—	2	4	no	—
294	C₄⋊C₄×C₆₁	—	2	2	no	—
295	C₄⋊C₄×C₆₁	—	2	2	no	—
296	C₄⋊C₄×C₆₁	—	2	2	no	—
297	C₄⋊C₄×C₆₁	—	2	4	no	—
298	C₄⋊C₄×C₆₁	—	2	2	no	—
299	C₄⋊C₄×C₆₁	—	4	2	no	—
300	C₄⋊C₄×C₆₁	—	4	2	no	—
301	C₄⋊C₄×C₆₁	—	4	2	no	—
302	C₄⋊C₄×C₆₁	—	4	2	no	—
303	C₄⋊C₄×C₆₁	—	4	2	no	—
304	C₄⋊C₄×C₆₁	—	4	2	no	—
305	C₄⋊C₄×C₆₁	—	4	2	no	—
306	C₄⋊C₄×C₆₁	—	4	2	no	—
307	C₄⋊C₄×C₆₁	C₂×Q₈	1	4	yes	—
308	C₄⋊C₄×C₆₁	#41	1	4	yes	—
309	C₄⋊C₄×C₆₁	#41	1	4	yes	—
310	C₂²⋊C₄×C₆₁	—	2	4	no	—
311	C₂²⋊C₄×C₆₁	—	2	4	no	—
312	C₂²⋊C₄×C₆₁	—	2	4	no	—
313	C₂²⋊C₄×C₆₁	—	2	4	no	—
314	C₂²⋊C₄×C₆₁	—	2	4	no	—
315	C₂²⋊C₄×C₆₁	—	2	4	no	—
316	C₂²⋊C₄×C₆₁	—	4	2	no	—
317	C₂²⋊C₄×C₆₁	—	4	2	no	—
318	C₂²⋊C₄×C₆₁	—	4	2	no	—
319	C₂²⋊C₄×C₆₁	—	4	2	no	—
320	C₂²⋊C₄×C₆₁	C₂×Q₈	1	8	yes	—
321	C₄²×C₆₁	—	2	4	no	—
322	C₄²×C₆₁	—	2	2	no	—
323	C₄²×C₆₁	—	2	2	no	—
324	C₄²×C₆₁	—	2	2	no	—
325	C₄²×C₆₁	—	2	2	no	—
326	C₄²×C₆₁	—	2	2	no	—
327	C₄²×C₆₁	—	2	2	no	—
328	C₄²×C₆₁	—	2	2	no	—
329	C₄²×C₆₁	—	2	2	no	—
330	C₄²×C₆₁	—	2	2	no	—
331	C₄²×C₆₁	—	2	2	no	—
332	C₄²×C₆₁	—	2	2	no	—
333	C₄²×C₆₁	—	2	4	no	—
334	C₄²×C₆₁	—	2	2	no	—
335	C₄²×C₆₁	—	2	4	no	—
336	C₄²×C₆₁	—	2	2	no	—
337	C₄²×C₆₁	—	4	2	no	—
338	C₄²×C₆₁	—	4	2	no	—
339	C₄²×C₆₁	—	4	1	no	—
340	C₄²×C₆₁	—	4	1	no	—
341	C₄²×C₆₁	—	4	1	no	—
342	C₄²×C₆₁	C₂×Q₈	1	4	yes	—
343	C₄²×C₆₁	#41	1	4	yes	—
344	C₄²×C₆₁	#41	1	4	yes	—
345	C₂³×C₆₁	—	2	2	no	—
346	C₂³×C₆₁	—	2	2	no	—
347	C₂³×C₆₁	—	2	2	no	—
348	C₂³×C₆₁	—	2	2	no	—
349	C₂³×C₆₁	—	2	2	no	—
350	C₂³×C₆₁	—	2	2	no	—
351	C₂³×C₆₁	C₂²×Q₈	1	4	yes	—
352	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
353	Q₈×C₆₁	—	2	8	no	—
354	Q₈×C₆₁	—	4	8	no	—
355	D₄×C₆₁	—	2	8	no	—
356	C₂×C₄×C₆₁	—	2	1	no	—
357	C₂×C₄×C₆₁	—	2	1	no	—
358	C₂×C₄×C₆₁	—	2	1	no	—
359	C₂×C₄×C₆₁	—	2	1	no	—
360	C₂×C₄×C₆₁	—	2	1	no	—
361	C₂×C₄×C₆₁	—	2	1	no	—
362	C₂×C₄×C₆₁	—	2	1	no	—
363	C₂×C₄×C₆₁	—	2	1	no	—
364	C₂×C₄×C₆₁	—	2	1	no	—
365	C₂×C₄×C₆₁	—	2	1	no	—
366	C₂×C₄×C₆₁	—	2	2	no	—
367	C₂×C₄×C₆₁	—	2	2	no	—
368	C₂×C₄×C₆₁	—	2	1	no	—
369	C₂×C₄×C₆₁	—	2	1	no	—
370	C₂×C₄×C₆₁	—	2	2	no	—
371	C₂×C₄×C₆₁	—	2	1	no	—
372	C₂×C₄×C₆₁	—	2	2	no	—
373	C₂×C₄×C₆₁	—	2	1	no	—
374	C₂×C₄×C₆₁	—	2	1	no	—
375	C₂×C₄×C₆₁	—	2	1	no	—
376	C₂×C₄×C₆₁	—	2	16	no	—
377	C₂×C₄×C₆₁	—	2	1	no	—
378	C₂×C₄×C₆₁	—	2	2	no	—
379	C₂×C₄×C₆₁	—	2	2	no	—
380	C₂×C₄×C₆₁	—	2	1	no	—
381	C₂×C₄×C₆₁	—	2	1	no	—
382	C₂×C₄×C₆₁	—	2	1	no	—
383	C₂×C₄×C₆₁	—	2	1	no	—
384	C₂×C₄×C₆₁	—	2	1	no	—
385	C₂×C₄×C₆₁	—	2	1	no	—
386	C₂×C₄×C₆₁	—	2	1	no	—
387	C₂×C₄×C₆₁	—	2	2	no	—
388	C₂×C₄×C₆₁	—	2	2	no	—
389	C₂×C₄×C₆₁	—	2	2	no	—
390	C₂×C₄×C₆₁	—	2	2	no	—
391	C₂×C₄×C₆₁	—	2	2	no	—
392	C₂×C₄×C₆₁	—	2	2	no	—
393	C₂×C₄×C₆₁	—	2	2	no	—
394	C₂×C₄×C₆₁	—	2	2	no	—
395	C₂×C₄×C₆₁	—	2	1	no	—
396	C₂×C₄×C₆₁	—	2	1	no	—
397	C₂×C₄×C₆₁	—	2	2	no	—
398	C₂×C₄×C₆₁	—	2	2	no	—
399	C₂×C₄×C₆₁	—	2	1	no	—
400	C₂×C₄×C₆₁	—	2	1	no	—
401	C₂×C₄×C₆₁	—	2	1	no	—
402	C₂×C₄×C₆₁	—	2	1	no	—
403	C₂×C₄×C₆₁	—	2	1	no	—
404	C₂×C₄×C₆₁	—	2	2	no	—
405	C₂×C₄×C₆₁	—	2	2	no	—
406	C₂×C₄×C₆₁	—	2	2	no	—
407	C₂×C₄×C₆₁	—	4	8	no	—
408	C₂×C₄×C₆₁	—	4	8	no	—
409	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
410	C₂×C₄×C₆₁	C₂²×Q₈	1	4	yes	—
411	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
412	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
413	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
414	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
415	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
416	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
417	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
418	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
419	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
420	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
421	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
422	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
423	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
424	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
425	#34893	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
426	C₂²×C₆₁	—	2	4	no	—
427	C₂²×C₆₁	—	2	4	no	—
428	C₂²×C₆₁	—	2	4	no	—
429	C₂²×C₆₁	—	4	2	no	—
430	C₂²×C₆₁	—	4	2	no	—
431	C₂²×C₆₁	—	4	2	no	—
432	C₂²×C₆₁	—	4	2	no	—
433	C₂²×C₆₁	C₂³×Q₈	1	1	yes	characteristic
434	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
435	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
436	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
438	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₆₁	#585	1	1	yes	characteristic
440	C₄×C₆₁	—	2	2	no	—
441	C₄×C₆₁	—	2	2	no	—
442	C₄×C₆₁	—	2	2	no	—
443	C₄×C₆₁	—	2	2	no	—
444	C₄×C₆₁	—	2	4	no	—
445	C₄×C₆₁	—	2	2	no	—
446	C₄×C₆₁	—	2	2	no	—
447	C₄×C₆₁	—	2	2	no	—
448	C₄×C₆₁	—	2	4	no	—
449	C₄×C₆₁	—	2	2	no	—
450	C₄×C₆₁	—	4	2	no	—
451	C₄×C₆₁	—	4	1	no	—
452	C₄×C₆₁	—	4	1	no	—
453	C₄×C₆₁	—	4	2	no	—
454	C₄×C₆₁	—	4	2	no	—
455	C₄×C₆₁	—	4	1	no	—
456	C₄×C₆₁	—	4	2	no	—
457	C₄×C₆₁	—	4	1	no	—
458	C₄×C₆₁	—	4	1	no	—
459	C₄×C₆₁	—	4	2	no	—
460	C₄×C₆₁	#533	1	4	yes	—
461	C₄×C₆₁	#554	1	4	yes	—
462	#2589	C₂×C₆₁	1	2	yes	complemented
463	#2587	C₂×C₆₁	1	2	yes	complemented
464	#2584	C₂×C₆₁	1	1	yes	characteristic, complemented
465	#2580	C₂×C₆₁	1	1	yes	characteristic
466	#2566	C₂×C₆₁	1	1	yes	characteristic
467	#2550	C₂×C₆₁	1	1	yes	characteristic, complemented
468	#2522	C₂×C₆₁	1	2	yes	complemented
469	#2509	C₂×C₆₁	1	1	yes	characteristic, complemented
470	#2507	C₂×C₆₁	1	1	yes	characteristic, complemented
471	#2465	C₂×C₆₁	1	2	yes	complemented
472	#2454	C₂×C₆₁	1	1	yes	characteristic
473	#2452	C₂×C₆₁	1	1	yes	characteristic
474	#2396	C₂×C₆₁	1	2	yes	complemented
475	#2396	C₂×C₆₁	1	2	yes	complemented
476	C₄×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
477	C₄×#125	C₂×C₆₁	1	1	yes	characteristic, complemented
478	C₄×#125	C₂×C₆₁	1	1	yes	characteristic, complemented
479	C₄×C₂²⋊Q₈	C₂×C₆₁	1	2	yes	complemented
480	#2296	C₂×C₆₁	1	2	yes	complemented
481	#2293	C₂×C₆₁	1	1	yes	characteristic
482	#2293	C₂×C₆₁	1	1	yes	characteristic
483	C₄²×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
484	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic
485	C₂×C₆₁	—	4	4	no	—
486	C₂×C₆₁	C₂×#533	1	1	yes	characteristic
487	C₂×C₆₁	#3444	1	1	yes	characteristic
488	C₂×C₆₁	#3460	1	1	yes	characteristic
489	C₂×C₆₁	C₂×#554	1	1	yes	characteristic
490	C₂×C₆₁	Q₈×#41	1	1	yes	characteristic
491	C₂×C₆₁	#3480	1	1	yes	characteristic
492	C₂×C₆₁	#3481	1	1	yes	characteristic
493	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
494	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
495	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
496	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
497	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
498	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
499	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
500	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
501	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
502	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
503	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
504	C₂×#117	C₂²×C₆₁	1	2	yes	—
505	C₂×#117	C₂²×C₆₁	1	2	yes	—
506	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
507	#400	C₂²×C₆₁	1	2	yes	—
508	#400	C₂²×C₆₁	1	2	yes	—
509	#399	C₂²×C₆₁	1	2	yes	—
510	#399	C₂²×C₆₁	1	2	yes	—
511	#398	C₂²×C₆₁	1	2	yes	—
512	#398	C₂²×C₆₁	1	2	yes	—
513	#398	C₂²×C₆₁	1	2	yes	—
514	#398	C₂²×C₆₁	1	2	yes	—
515	#396	C₂²×C₆₁	1	2	yes	—
516	#396	C₂²×C₆₁	1	2	yes	—
517	#396	C₂²×C₆₁	1	2	yes	—
518	#396	C₂²×C₆₁	1	2	yes	—
519	#395	C₂²×C₆₁	1	2	yes	—
520	#395	C₂²×C₆₁	1	2	yes	—
521	#393	C₂²×C₆₁	1	2	yes	—
522	#393	C₂²×C₆₁	1	2	yes	—
523	#391	C₂²×C₆₁	1	2	yes	—
524	#391	C₂²×C₆₁	1	2	yes	—
525	#390	C₂²×C₆₁	1	1	yes	characteristic
526	#390	C₂²×C₆₁	1	1	yes	characteristic
527	#390	C₂²×C₆₁	1	1	yes	characteristic
528	#390	C₂²×C₆₁	1	1	yes	characteristic
529	#389	C₂²×C₆₁	1	1	yes	characteristic
530	#389	C₂²×C₆₁	1	1	yes	characteristic
531	#389	C₂²×C₆₁	1	1	yes	characteristic
532	#389	C₂²×C₆₁	1	1	yes	characteristic
533	#389	C₂²×C₆₁	1	1	yes	characteristic
534	#389	C₂²×C₆₁	1	1	yes	characteristic
535	#389	C₂²×C₆₁	1	2	yes	—
536	#389	C₂²×C₆₁	1	2	yes	—
537	#389	C₂²×C₆₁	1	2	yes	—
538	#389	C₂²×C₆₁	1	1	yes	characteristic
539	#389	C₂²×C₆₁	1	1	yes	characteristic
540	#389	C₂²×C₆₁	1	2	yes	—
541	#389	C₂²×C₆₁	1	2	yes	—
542	#389	C₂²×C₆₁	1	2	yes	—
543	#389	C₂²×C₆₁	1	1	yes	characteristic
544	#389	C₂²×C₆₁	1	1	yes	characteristic
545	#388	C₂²×C₆₁	1	2	yes	—
546	#388	C₂²×C₆₁	1	2	yes	—
547	#388	C₂²×C₆₁	1	2	yes	—
548	#388	C₂²×C₆₁	1	2	yes	—
549	#387	C₂²×C₆₁	1	2	yes	—
550	#387	C₂²×C₆₁	1	2	yes	—
551	#387	C₂²×C₆₁	1	2	yes	—
552	#387	C₂²×C₆₁	1	2	yes	—
553	#387	C₂²×C₆₁	1	2	yes	—
554	#387	C₂²×C₆₁	1	2	yes	—
555	#385	C₂²×C₆₁	1	2	yes	—
556	#385	C₂²×C₆₁	1	2	yes	—
557	#385	C₂²×C₆₁	1	2	yes	—
558	#385	C₂²×C₆₁	1	2	yes	—
559	#385	C₂²×C₆₁	1	2	yes	—
560	#385	C₂²×C₆₁	1	2	yes	—
561	#384	C₂²×C₆₁	1	1	yes	characteristic
562	#382	C₂²×C₆₁	1	1	yes	characteristic
563	#382	C₂²×C₆₁	1	1	yes	characteristic
564	#380	C₂²×C₆₁	1	2	yes	—
565	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
567	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
569	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
570	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
571	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
572	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
573	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
583	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
584	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
585	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
586	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
587	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
588	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
589	C₄³	C₂²×C₆₁	1	1	yes	characteristic
590	C₄³	C₂²×C₆₁	1	1	yes	characteristic
591	C₄³	C₂²×C₆₁	1	1	yes	characteristic
592	C₆₁	#34893	1	1	yes	characteristic, direct product factor, Sylow
593	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
594	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
595	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
597	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
598	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
599	C₄⋊Q₈	—	2	4	no	—
600	#125	—	2	4	no	—
601	#125	—	2	4	no	—
602	C₂²⋊Q₈	—	2	8	no	—
603	C₄×Q₈	—	2	4	no	—
604	C₄×Q₈	—	2	4	no	—
605	C₄×Q₈	—	2	4	no	—
606	C₄×Q₈	—	4	4	no	—
607	C₄×D₄	—	2	4	no	—
608	C₄×D₄	—	2	4	no	—
609	C₄×D₄	Q₈×C₆₁	1	8	yes	complemented
610	#117	—	2	8	no	—
611	#117	—	4	4	no	—
612	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
656	C₂×C₄²	—	4	4	no	—
657	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
659	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
660	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
670	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
677	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
678	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
681	#95	C₂³×C₆₁	1	2	yes	—
682	#95	C₂³×C₆₁	1	2	yes	—
683	#95	C₂³×C₆₁	1	2	yes	—
684	#95	C₂³×C₆₁	1	2	yes	—
685	#95	C₂³×C₆₁	1	2	yes	—
686	#95	C₂³×C₆₁	1	2	yes	—
687	#95	C₂³×C₆₁	1	2	yes	—
688	#95	C₂³×C₆₁	1	1	yes	characteristic
689	#95	C₂³×C₆₁	1	1	yes	characteristic
690	#95	C₂³×C₆₁	1	1	yes	characteristic
691	#95	C₂³×C₆₁	1	1	yes	characteristic
692	#95	C₂³×C₆₁	1	1	yes	characteristic
693	#95	C₂³×C₆₁	1	1	yes	characteristic
694	#95	C₂³×C₆₁	1	2	yes	—
695	#95	C₂³×C₆₁	1	2	yes	—
696	#95	C₂³×C₆₁	1	2	yes	—
697	#95	C₂³×C₆₁	1	2	yes	—
698	#95	C₂³×C₆₁	1	2	yes	—
699	#95	C₂³×C₆₁	1	2	yes	—
700	#95	C₂³×C₆₁	1	2	yes	—
701	#95	C₂³×C₆₁	1	2	yes	—
702	#95	C₂³×C₆₁	1	2	yes	—
703	#95	C₂³×C₆₁	1	2	yes	—
704	#95	C₂³×C₆₁	1	2	yes	—
705	#95	C₂³×C₆₁	1	2	yes	—
706	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	4	no	—
711	C₂×Q₈	—	2	4	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	C₂×Q₈×C₆₁	1	4	yes	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	C₂×Q₈×C₆₁	1	8	yes	—
725	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	C₂×Q₈×C₆₁	1	4	yes	—
778	C₄⋊C₄	#41×C₆₁	1	4	yes	—
779	C₄⋊C₄	#41×C₆₁	1	4	yes	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	C₂×Q₈×C₆₁	1	8	yes	—
791	C₄²	—	2	4	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	4	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	4	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	4	2	no	—
808	C₄²	—	4	2	no	—
809	C₄²	—	4	1	no	—
810	C₄²	—	4	1	no	—
811	C₄²	—	4	1	no	—
812	C₄²	C₂×Q₈×C₆₁	1	4	yes	—
813	C₄²	#41×C₆₁	1	4	yes	—
814	C₄²	#41×C₆₁	1	4	yes	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	C₂²×Q₈×C₆₁	1	4	yes	—
822	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
823	Q₈	—	2	8	no	—
824	Q₈	—	4	8	no	—
825	D₄	—	2	8	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	16	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	4	8	no	—
878	C₂×C₄	—	4	8	no	—
879	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
880	C₂×C₄	C₂²×Q₈×C₆₁	1	4	yes	—
881	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
882	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
883	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
884	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
885	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
886	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
887	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
888	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
889	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
890	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
891	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
892	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
893	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
894	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
895	C₂²	—	2	4	no	—
896	C₂²	—	2	4	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	C₂³×Q₈×C₆₁	1	1	yes	characteristic
903	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
904	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
905	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
906	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
907	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
908	C₂²	C₆₁×#585	1	1	yes	characteristic
909	C₄	—	2	2	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	4	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	4	no	—
918	C₄	—	2	2	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	C₆₁×#533	1	4	yes	—
930	C₄	C₆₁×#554	1	4	yes	—
931	C₂	—	4	4	no	—
932	C₂	C₂×C₆₁×#533	1	1	yes	characteristic
933	C₂	C₆₁×#3444	1	1	yes	characteristic
934	C₂	C₆₁×#3460	1	1	yes	characteristic
935	C₂	C₂×C₆₁×#554	1	1	yes	characteristic
936	C₂	Q₈×#41×C₆₁	1	1	yes	characteristic
937	C₂	C₆₁×#3480	1	1	yes	characteristic
938	C₂	C₆₁×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂⁵
prime radical	C₂²×D₄×C₆₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2589	C₂	semidirect
2. C₆₁×#2587	C₂	semidirect
3. C₆₁×#2584	C₂	semidirect
6. C₆₁×#2550	C₂	semidirect
7. C₆₁×#2522	C₂	semidirect
8. C₆₁×#2509	C₂	semidirect
9. C₆₁×#2507	C₂	semidirect
10. C₆₁×#2465	C₂	semidirect
13. C₆₁×#2396	C₂	semidirect
14. C₆₁×#2396	C₂	semidirect
15. C₄×C₄⋊Q₈×C₆₁	C₂	semidirect
16. C₄×#125×C₆₁	C₂	semidirect
17. C₄×#125×C₆₁	C₂	semidirect
18. C₄×C₂²⋊Q₈×C₆₁	C₂	semidirect
19. C₆₁×#2296	C₂	semidirect
22. C₄²×Q₈×C₆₁	C₂	semidirect
139. C₄×D₄×C₆₁	Q₈	semidirect
425. #34893	C₆₁	direct (N × H)
462. #2589	C₂×C₆₁	semidirect
463. #2587	C₂×C₆₁	semidirect
464. #2584	C₂×C₆₁	semidirect
467. #2550	C₂×C₆₁	semidirect
468. #2522	C₂×C₆₁	semidirect
469. #2509	C₂×C₆₁	semidirect
470. #2507	C₂×C₆₁	semidirect
471. #2465	C₂×C₆₁	semidirect
474. #2396	C₂×C₆₁	semidirect
475. #2396	C₂×C₆₁	semidirect
476. C₄×C₄⋊Q₈	C₂×C₆₁	semidirect
477. C₄×#125	C₂×C₆₁	semidirect
478. C₄×#125	C₂×C₆₁	semidirect
479. C₄×C₂²⋊Q₈	C₂×C₆₁	semidirect
480. #2296	C₂×C₆₁	semidirect
483. C₄²×Q₈	C₂×C₆₁	semidirect
592. C₆₁	#34893	direct (N × H)
609. C₄×D₄	Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#2589	2
C₆₁×#2587	2
C₆₁×#2584	2
C₆₁×#2580	2
C₆₁×#2566	2
C₆₁×#2550	2
C₆₁×#2522	2
C₆₁×#2509	2
C₆₁×#2507	2
C₆₁×#2465	2
C₆₁×#2454	2
C₆₁×#2452	2
C₆₁×#2396	2
C₄×C₄⋊Q₈×C₆₁	2
C₄×#125×C₆₁	2
C₄×C₂²⋊Q₈×C₆₁	2
C₆₁×#2296	2
C₆₁×#2293	2
C₄²×Q₈×C₆₁	2
C₄²×D₄×C₆₁	2
#34893	61

Subgroups — C61×#34893 #29538326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34893 #29538326