Subgroups — C₆₁×#24439 #29527872

Order 15616.

1534 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#448	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2416	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1874	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1869	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#548	—	2	4	no	—
23	C₆₁×#548	—	2	4	no	—
24	C₂×#124×C₆₁	—	2	1	no	—
25	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#121×C₆₁	—	2	1	no	—
29	C₂×#121×C₆₁	—	2	1	no	—
30	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₁	—	2	1	no	—
35	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#466	—	2	4	no	—
38	C₆₁×#449	—	2	4	no	—
39	C₆₁×#448	—	2	4	no	—
40	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×#103×C₆₁	—	2	4	no	—
42	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
50	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×#396	—	2	1	no	—
56	C₆₁×#394	—	2	1	no	—
57	C₆₁×#390	C₂²	1	1	yes	characteristic
58	C₆₁×#389	C₂²	1	1	yes	characteristic
59	C₆₁×#386	—	2	1	no	—
60	C₆₁×#380	C₂²	1	1	yes	characteristic
61	C₆₁×#340	C₂²	1	1	yes	characteristic
62	C₆₁×#340	C₂²	1	1	yes	characteristic
63	C₆₁×#336	C₂²	1	1	yes	characteristic
64	C₆₁×#336	C₂²	1	1	yes	characteristic
65	C₂×#41×C₆₁	—	2	2	no	—
66	C₂×#41×C₆₁	—	2	2	no	—
67	C₂×#41×C₆₁	—	2	2	no	—
68	C₂×#41×C₆₁	—	2	2	no	—
69	C₂×#41×C₆₁	—	4	1	no	—
70	C₂×#41×C₆₁	—	4	1	no	—
71	C₂²×Q₈×C₆₁	—	2	2	no	—
72	C₂²×Q₈×C₆₁	—	2	1	no	—
73	C₂²×Q₈×C₆₁	—	2	2	no	—
74	C₂²×Q₈×C₆₁	—	2	2	no	—
75	C₂²×Q₈×C₆₁	—	4	1	no	—
76	C₂²×Q₈×C₆₁	—	4	1	no	—
77	C₂²×Q₈×C₆₁	D₄	1	4	yes	complemented
78	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₆₁	—	2	1	no	—
81	C₂²×D₄×C₆₁	—	2	1	no	—
82	C₂²×D₄×C₆₁	—	2	1	no	—
83	C₂²×D₄×C₆₁	—	2	1	no	—
84	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₁	—	2	1	no	—
88	C₂³×C₄×C₆₁	—	2	1	no	—
89	C₂³×C₄×C₆₁	—	2	1	no	—
90	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
92	C₂×SD₁₆×C₆₁	—	2	2	no	—
93	C₂×SD₁₆×C₆₁	—	2	2	no	—
94	C₂×SD₁₆×C₆₁	—	2	2	no	—
95	C₂×SD₁₆×C₆₁	—	2	2	no	—
96	C₂×SD₁₆×C₆₁	—	4	1	no	—
97	C₂×SD₁₆×C₆₁	—	4	1	no	—
98	C₂×D₈×C₆₁	—	2	2	no	—
99	C₂×D₈×C₆₁	—	2	2	no	—
100	C₂×D₈×C₆₁	—	4	1	no	—
101	C₂²×C₈×C₆₁	—	2	2	no	—
102	C₂²×C₈×C₆₁	—	2	2	no	—
103	C₂²×C₈×C₆₁	—	4	1	no	—
104	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
108	#124×C₆₁	—	2	8	no	—
109	#124×C₆₁	—	2	2	no	—
110	#124×C₆₁	—	2	2	no	—
111	C₂²⋊Q₈×C₆₁	—	2	8	no	—
112	C₂²⋊Q₈×C₆₁	—	2	2	no	—
113	C₂²⋊Q₈×C₆₁	—	2	2	no	—
114	#121×C₆₁	—	2	8	no	—
115	#121×C₆₁	—	2	2	no	—
116	#121×C₆₁	—	2	2	no	—
117	#121×C₆₁	—	2	2	no	—
118	#121×C₆₁	—	2	2	no	—
119	#121×C₆₁	—	4	1	no	—
120	#121×C₆₁	—	4	4	no	—
121	#121×C₆₁	D₄	1	4	yes	complemented
122	C₄×Q₈×C₆₁	—	2	2	no	—
123	C₄×Q₈×C₆₁	—	2	2	no	—
124	C₄×D₄×C₆₁	—	2	8	no	—
125	C₄×D₄×C₆₁	—	2	2	no	—
126	C₄×D₄×C₆₁	—	2	2	no	—
127	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
128	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
129	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
131	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
132	C₂×C₄⋊C₄×C₆₁	—	4	1	no	—
133	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
149	C₂×C₄²×C₆₁	—	2	1	no	—
150	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
151	#107×C₆₁	—	2	2	no	—
152	#103×C₆₁	—	2	2	no	—
153	#103×C₆₁	—	2	2	no	—
154	#103×C₆₁	—	2	2	no	—
155	#103×C₆₁	—	2	2	no	—
156	#103×C₆₁	—	2	2	no	—
157	#103×C₆₁	D₄	1	4	yes	complemented
158	#102×C₆₁	—	2	2	no	—
159	#102×C₆₁	—	2	2	no	—
160	#102×C₆₁	—	2	2	no	—
161	#102×C₆₁	—	4	1	no	—
162	C₂²⋊C₈×C₆₁	—	2	2	no	—
163	C₂²⋊C₈×C₆₁	—	2	2	no	—
164	C₂²⋊C₈×C₆₁	—	4	1	no	—
165	#95×C₆₁	—	2	1	no	—
166	#95×C₆₁	—	2	1	no	—
167	C₂⁴×C₆₁	—	2	1	no	—
168	C₂⁴×C₆₁	—	2	1	no	—
169	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
170	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
171	#41×C₆₁	—	4	4	no	—
172	#41×C₆₁	—	4	4	no	—
173	#41×C₆₁	—	4	4	no	—
174	#41×C₆₁	—	4	4	no	—
175	C₂×Q₈×C₆₁	—	2	4	no	—
176	C₂×Q₈×C₆₁	—	2	1	no	—
177	C₂×Q₈×C₆₁	—	2	1	no	—
178	C₂×Q₈×C₆₁	—	2	1	no	—
179	C₂×Q₈×C₆₁	—	2	1	no	—
180	C₂×Q₈×C₆₁	—	2	8	no	—
181	C₂×Q₈×C₆₁	—	2	1	no	—
182	C₂×Q₈×C₆₁	—	2	1	no	—
183	C₂×Q₈×C₆₁	—	2	1	no	—
184	C₂×Q₈×C₆₁	—	2	1	no	—
185	C₂×Q₈×C₆₁	—	4	2	no	—
186	C₂×Q₈×C₆₁	—	4	2	no	—
187	C₂×Q₈×C₆₁	—	4	4	no	—
188	C₂×Q₈×C₆₁	—	4	4	no	—
189	C₂×Q₈×C₆₁	—	4	4	no	—
190	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
191	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
192	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
193	C₂×Q₈×C₆₁	#41	1	2	yes	—
194	C₂×D₄×C₆₁	—	2	4	no	—
195	C₂×D₄×C₆₁	—	2	2	no	—
196	C₂×D₄×C₆₁	—	2	4	no	—
197	C₂×D₄×C₆₁	—	2	2	no	—
198	C₂×D₄×C₆₁	—	2	2	no	—
199	C₂×D₄×C₆₁	—	2	1	no	—
200	C₂×D₄×C₆₁	—	2	1	no	—
201	C₂×D₄×C₆₁	—	2	1	no	—
202	C₂×D₄×C₆₁	—	2	1	no	—
203	C₂×D₄×C₆₁	—	2	1	no	—
204	C₂×D₄×C₆₁	—	2	1	no	—
205	C₂×D₄×C₆₁	—	2	1	no	—
206	C₂×D₄×C₆₁	—	2	1	no	—
207	C₂×D₄×C₆₁	—	2	1	no	—
208	C₂×D₄×C₆₁	—	2	1	no	—
209	C₂×D₄×C₆₁	—	2	1	no	—
210	C₂×D₄×C₆₁	—	4	2	no	—
211	C₂×D₄×C₆₁	—	4	2	no	—
212	C₂×D₄×C₆₁	—	4	2	no	—
213	C₂×D₄×C₆₁	—	4	2	no	—
214	C₂×D₄×C₆₁	—	4	2	no	—
215	C₂×D₄×C₆₁	—	4	2	no	—
216	C₂×D₄×C₆₁	—	4	2	no	—
217	C₂×D₄×C₆₁	—	4	2	no	—
218	C₂×D₄×C₆₁	—	4	2	no	—
219	C₂×D₄×C₆₁	—	8	1	no	—
220	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₆₁	—	2	1	no	—
222	C₂²×C₄×C₆₁	—	2	1	no	—
223	C₂²×C₄×C₆₁	—	2	1	no	—
224	C₂²×C₄×C₆₁	—	2	1	no	—
225	C₂²×C₄×C₆₁	—	2	1	no	—
226	C₂²×C₄×C₆₁	—	2	4	no	—
227	C₂²×C₄×C₆₁	—	2	4	no	—
228	C₂²×C₄×C₆₁	—	2	1	no	—
229	C₂²×C₄×C₆₁	—	2	1	no	—
230	C₂²×C₄×C₆₁	—	2	1	no	—
231	C₂²×C₄×C₆₁	—	2	1	no	—
232	C₂²×C₄×C₆₁	—	2	1	no	—
233	C₂²×C₄×C₆₁	—	2	1	no	—
234	C₂²×C₄×C₆₁	—	2	1	no	—
235	C₂²×C₄×C₆₁	—	2	1	no	—
236	C₂²×C₄×C₆₁	—	2	1	no	—
237	C₂²×C₄×C₆₁	—	2	1	no	—
238	C₂²×C₄×C₆₁	—	2	1	no	—
239	C₂²×C₄×C₆₁	—	4	2	no	—
240	C₂²×C₄×C₆₁	—	4	2	no	—
241	C₂²×C₄×C₆₁	—	4	2	no	—
242	C₂²×C₄×C₆₁	—	4	2	no	—
243	C₂²×C₄×C₆₁	—	4	2	no	—
244	C₂²×C₄×C₆₁	—	4	2	no	—
245	C₂²×C₄×C₆₁	—	8	1	no	—
246	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
252	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
253	SD₁₆×C₆₁	—	4	4	no	—
254	SD₁₆×C₆₁	—	4	4	no	—
255	D₈×C₆₁	—	4	4	no	—
256	C₂×C₈×C₆₁	—	2	1	no	—
257	C₂×C₈×C₆₁	—	2	1	no	—
258	C₂×C₈×C₆₁	—	2	1	no	—
259	C₂×C₈×C₆₁	—	2	1	no	—
260	C₂×C₈×C₆₁	—	2	1	no	—
261	C₂×C₈×C₆₁	—	2	1	no	—
262	C₂×C₈×C₆₁	—	2	1	no	—
263	C₂×C₈×C₆₁	—	2	1	no	—
264	C₂×C₈×C₆₁	—	2	1	no	—
265	C₂×C₈×C₆₁	—	2	1	no	—
266	C₂×C₈×C₆₁	—	2	1	no	—
267	C₂×C₈×C₆₁	—	4	4	no	—
268	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
269	C₄⋊C₄×C₆₁	—	2	4	no	—
270	C₄⋊C₄×C₆₁	—	2	4	no	—
271	C₄⋊C₄×C₆₁	—	2	2	no	—
272	C₄⋊C₄×C₆₁	—	2	1	no	—
273	C₄⋊C₄×C₆₁	—	2	1	no	—
274	C₄⋊C₄×C₆₁	—	2	1	no	—
275	C₄⋊C₄×C₆₁	—	2	1	no	—
276	C₄⋊C₄×C₆₁	—	2	1	no	—
277	C₄⋊C₄×C₆₁	—	2	1	no	—
278	C₄⋊C₄×C₆₁	—	4	2	no	—
279	C₄⋊C₄×C₆₁	—	4	2	no	—
280	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₆₁	—	2	4	no	—
283	C₂²⋊C₄×C₆₁	—	2	4	no	—
284	C₂²⋊C₄×C₆₁	—	2	4	no	—
285	C₂²⋊C₄×C₆₁	—	2	2	no	—
286	C₂²⋊C₄×C₆₁	—	2	4	no	—
287	C₂²⋊C₄×C₆₁	—	2	2	no	—
288	C₂²⋊C₄×C₆₁	—	4	2	no	—
289	C₂²⋊C₄×C₆₁	—	4	2	no	—
290	C₂²⋊C₄×C₆₁	—	4	2	no	—
291	C₂²⋊C₄×C₆₁	—	4	2	no	—
292	C₂²⋊C₄×C₆₁	—	8	1	no	—
293	C₄²×C₆₁	—	2	4	no	—
294	C₄²×C₆₁	—	2	1	no	—
295	C₄²×C₆₁	—	2	1	no	—
296	C₂³×C₆₁	—	2	1	no	—
297	C₂³×C₆₁	—	2	1	no	—
298	C₂³×C₆₁	—	2	1	no	—
299	C₂³×C₆₁	—	2	1	no	—
300	C₂³×C₆₁	—	2	1	no	—
301	C₂³×C₆₁	—	2	2	no	—
302	C₂³×C₆₁	—	2	1	no	—
303	C₂³×C₆₁	—	2	1	no	—
304	C₂³×C₆₁	—	2	1	no	—
305	C₂³×C₆₁	—	2	1	no	—
306	C₂³×C₆₁	—	2	1	no	—
307	C₂³×C₆₁	—	2	1	no	—
308	C₂³×C₆₁	—	4	1	no	—
309	C₂³×C₆₁	—	4	1	no	—
310	C₂³×C₆₁	—	4	1	no	—
311	C₂³×C₆₁	—	4	1	no	—
312	C₂³×C₆₁	—	4	1	no	—
313	C₂³×C₆₁	—	4	1	no	—
314	C₂³×C₆₁	—	4	1	no	—
315	C₂³×C₆₁	—	4	1	no	—
316	C₂³×C₆₁	—	4	1	no	—
317	C₂³×C₆₁	—	4	1	no	—
318	C₂³×C₆₁	—	4	1	no	—
319	C₂³×C₆₁	—	4	1	no	—
320	C₂³×C₆₁	—	4	1	no	—
321	C₂³×C₆₁	#120	1	2	yes	—
322	C₂³×C₆₁	#135	1	2	yes	—
323	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
324	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₆₁	—	2	2	no	—
326	Q₈×C₆₁	—	2	2	no	—
327	Q₈×C₆₁	—	2	2	no	—
328	Q₈×C₆₁	—	2	2	no	—
329	Q₈×C₆₁	—	2	2	no	—
330	Q₈×C₆₁	—	4	8	no	—
331	Q₈×C₆₁	—	4	1	no	—
332	Q₈×C₆₁	—	4	1	no	—
333	Q₈×C₆₁	#121	1	4	yes	complemented
334	D₄×C₆₁	—	2	2	no	—
335	D₄×C₆₁	—	2	2	no	—
336	D₄×C₆₁	—	4	8	no	—
337	D₄×C₆₁	—	4	4	no	—
338	D₄×C₆₁	—	4	8	no	—
339	D₄×C₆₁	—	4	1	no	—
340	D₄×C₆₁	—	4	1	no	—
341	D₄×C₆₁	—	4	1	no	—
342	D₄×C₆₁	—	4	1	no	—
343	D₄×C₆₁	—	4	1	no	—
344	D₄×C₆₁	—	4	1	no	—
345	D₄×C₆₁	—	8	4	no	—
346	D₄×C₆₁	—	8	4	no	—
347	C₂×C₄×C₆₁	—	2	2	no	—
348	C₂×C₄×C₆₁	—	2	1	no	—
349	C₂×C₄×C₆₁	—	2	2	no	—
350	C₂×C₄×C₆₁	—	2	1	no	—
351	C₂×C₄×C₆₁	—	2	2	no	—
352	C₂×C₄×C₆₁	—	2	2	no	—
353	C₂×C₄×C₆₁	—	2	2	no	—
354	C₂×C₄×C₆₁	—	2	2	no	—
355	C₂×C₄×C₆₁	—	2	2	no	—
356	C₂×C₄×C₆₁	—	2	1	no	—
357	C₂×C₄×C₆₁	—	2	1	no	—
358	C₂×C₄×C₆₁	—	2	2	no	—
359	C₂×C₄×C₆₁	—	2	2	no	—
360	C₂×C₄×C₆₁	—	2	1	no	—
361	C₂×C₄×C₆₁	—	2	1	no	—
362	C₂×C₄×C₆₁	—	2	2	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	1	no	—
367	C₂×C₄×C₆₁	—	2	1	no	—
368	C₂×C₄×C₆₁	—	4	8	no	—
369	C₂×C₄×C₆₁	—	4	8	no	—
370	C₂×C₄×C₆₁	—	4	1	no	—
371	C₂×C₄×C₆₁	—	4	1	no	—
372	C₂×C₄×C₆₁	—	4	1	no	—
373	C₂×C₄×C₆₁	—	4	1	no	—
374	C₂×C₄×C₆₁	—	4	1	no	—
375	C₂×C₄×C₆₁	—	4	1	no	—
376	C₂×C₄×C₆₁	—	4	1	no	—
377	C₂×C₄×C₆₁	—	4	1	no	—
378	C₂×C₄×C₆₁	—	4	1	no	—
379	C₂×C₄×C₆₁	—	4	1	no	—
380	C₂×C₄×C₆₁	—	4	1	no	—
381	C₂×C₄×C₆₁	—	4	1	no	—
382	C₂×C₄×C₆₁	—	4	1	no	—
383	C₂×C₄×C₆₁	—	4	1	no	—
384	C₂×C₄×C₆₁	—	4	1	no	—
385	C₂×C₄×C₆₁	—	4	1	no	—
386	C₂×C₄×C₆₁	—	8	4	no	—
387	C₂×C₄×C₆₁	#120	1	2	yes	—
388	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
392	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
393	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
394	C₈×C₆₁	—	2	2	no	—
395	C₈×C₆₁	—	4	1	no	—
396	C₈×C₆₁	—	4	1	no	—
397	C₈×C₆₁	—	4	1	no	—
398	#24439	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂²×C₆₁	—	2	2	no	—
400	C₂²×C₆₁	—	2	2	no	—
401	C₂²×C₆₁	—	2	2	no	—
402	C₂²×C₆₁	—	2	2	no	—
403	C₂²×C₆₁	—	2	2	no	—
404	C₂²×C₆₁	—	2	2	no	—
405	C₂²×C₆₁	—	4	2	no	—
406	C₂²×C₆₁	—	4	1	no	—
407	C₂²×C₆₁	—	4	1	no	—
408	C₂²×C₆₁	—	4	2	no	—
409	C₂²×C₆₁	—	4	1	no	—
410	C₂²×C₆₁	—	4	1	no	—
411	C₂²×C₆₁	—	4	2	no	—
412	C₂²×C₆₁	—	4	1	no	—
413	C₂²×C₆₁	—	4	1	no	—
414	C₂²×C₆₁	—	4	1	no	—
415	C₂²×C₆₁	—	8	1	no	—
416	C₂²×C₆₁	—	8	1	no	—
417	C₂²×C₆₁	—	8	1	no	—
418	C₂²×C₆₁	—	8	1	no	—
419	C₂²×C₆₁	—	8	1	no	—
420	C₂²×C₆₁	—	8	1	no	—
421	C₂²×C₆₁	—	8	1	no	—
422	C₂²×C₆₁	—	8	1	no	—
423	C₂²×C₆₁	—	8	1	no	—
424	C₂²×C₆₁	—	8	1	no	—
425	C₂²×C₆₁	—	8	1	no	—
426	C₂²×C₆₁	#449	1	4	yes	complemented
427	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
428	C₂²×C₆₁	D₄²	1	1	yes	characteristic
429	C₂²×C₆₁	#546	1	1	yes	characteristic
430	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
431	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₂²×C₆₁	#577	1	1	yes	characteristic
433	C₂²×C₆₁	#578	1	1	yes	characteristic
434	C₄×C₆₁	—	2	2	no	—
435	C₄×C₆₁	—	2	4	no	—
436	C₄×C₆₁	—	4	1	no	—
437	C₄×C₆₁	—	4	2	no	—
438	C₄×C₆₁	—	4	1	no	—
439	C₄×C₆₁	—	4	2	no	—
440	C₄×C₆₁	—	4	2	no	—
441	C₄×C₆₁	—	4	1	no	—
442	C₄×C₆₁	—	8	1	no	—
443	C₄×C₆₁	—	8	1	no	—
444	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
445	C₄×C₆₁	#534	1	1	yes	characteristic
446	C₄×C₆₁	D₄²	1	1	yes	characteristic
447	C₄×C₆₁	#546	1	1	yes	characteristic
448	C₂×#548	C₂×C₆₁	1	1	yes	characteristic, complemented
449	C₂×#466	C₂×C₆₁	1	1	yes	characteristic, complemented
450	C₂×#449	C₂×C₆₁	1	1	yes	characteristic, complemented
451	C₂×#448	C₂×C₆₁	1	1	yes	characteristic, complemented
452	C₂²×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
453	#2416	C₂×C₆₁	1	1	yes	characteristic, complemented
454	#2042	C₂×C₆₁	1	1	yes	characteristic, complemented
455	#2036	C₂×C₆₁	1	1	yes	characteristic, complemented
456	#2012	C₂×C₆₁	1	1	yes	characteristic, complemented
457	#2000	C₂×C₆₁	1	1	yes	characteristic, complemented
458	#1880	C₂×C₆₁	1	1	yes	characteristic, complemented
459	#1874	C₂×C₆₁	1	1	yes	characteristic, complemented
460	#1869	C₂×C₆₁	1	1	yes	characteristic, complemented
461	#1863	C₂×C₆₁	1	1	yes	characteristic, complemented
462	#1788	C₂×C₆₁	1	1	yes	characteristic, complemented
463	C₂×C₆₁	—	2	4	no	—
464	C₂×C₆₁	—	8	1	no	—
465	C₂×C₆₁	—	8	2	no	—
466	C₂×C₆₁	—	16	1	no	—
467	C₂×C₆₁	#2410	1	1	yes	characteristic
468	C₂×C₆₁	C₂×#449	1	1	yes	characteristic
469	C₂×C₆₁	#3013	1	1	yes	characteristic
470	C₂×C₆₁	#3265	1	1	yes	characteristic
471	C₂×C₆₁	#3285	1	1	yes	characteristic
472	C₂×C₆₁	#3301	1	1	yes	characteristic
473	C₂×C₆₁	#3308	1	1	yes	characteristic
474	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
475	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
476	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
477	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
478	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
479	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
480	#548	—	2	4	no	—
481	#548	—	2	4	no	—
482	C₂×#124	—	2	1	no	—
483	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
484	C₂×C₂²⋊Q₈	—	2	1	no	—
485	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
486	C₂×#121	—	2	1	no	—
487	C₂×#121	—	2	1	no	—
488	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
489	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
490	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
491	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
492	C₂×C₄×D₄	—	2	1	no	—
493	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
494	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
495	#466	—	2	4	no	—
496	#449	—	2	4	no	—
497	#448	—	2	4	no	—
498	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
499	C₂×#103	—	2	4	no	—
500	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
501	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
502	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
503	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
504	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
505	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
506	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
507	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
508	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
509	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
510	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
511	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
512	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
513	#396	—	2	1	no	—
514	#394	—	2	1	no	—
515	#390	C₂²×C₆₁	1	1	yes	characteristic
516	#389	C₂²×C₆₁	1	1	yes	characteristic
517	#386	—	2	1	no	—
518	#380	C₂²×C₆₁	1	1	yes	characteristic
519	#340	C₂²×C₆₁	1	1	yes	characteristic
520	#340	C₂²×C₆₁	1	1	yes	characteristic
521	#336	C₂²×C₆₁	1	1	yes	characteristic
522	#336	C₂²×C₆₁	1	1	yes	characteristic
523	C₆₁	#24439	1	1	yes	characteristic, direct product factor, Sylow
524	C₂×#41	—	2	2	no	—
525	C₂×#41	—	2	2	no	—
526	C₂×#41	—	2	2	no	—
527	C₂×#41	—	2	2	no	—
528	C₂×#41	—	4	1	no	—
529	C₂×#41	—	4	1	no	—
530	C₂²×Q₈	—	2	1	no	—
531	C₂²×Q₈	—	2	2	no	—
532	C₂²×Q₈	—	2	2	no	—
533	C₂²×Q₈	—	2	2	no	—
534	C₂²×Q₈	—	4	1	no	—
535	C₂²×Q₈	—	4	1	no	—
536	C₂²×Q₈	D₄×C₆₁	1	4	yes	complemented
537	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	2	1	no	—
542	C₂²×D₄	—	2	1	no	—
543	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
546	C₂³×C₄	—	2	1	no	—
547	C₂³×C₄	—	2	1	no	—
548	C₂³×C₄	—	2	1	no	—
549	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
551	C₂×SD₁₆	—	2	2	no	—
552	C₂×SD₁₆	—	2	2	no	—
553	C₂×SD₁₆	—	2	2	no	—
554	C₂×SD₁₆	—	2	2	no	—
555	C₂×SD₁₆	—	4	1	no	—
556	C₂×SD₁₆	—	4	1	no	—
557	C₂×D₈	—	2	2	no	—
558	C₂×D₈	—	2	2	no	—
559	C₂×D₈	—	4	1	no	—
560	C₂²×C₈	—	2	2	no	—
561	C₂²×C₈	—	2	2	no	—
562	C₂²×C₈	—	4	1	no	—
563	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
564	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
565	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
566	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
567	#124	—	2	8	no	—
568	#124	—	2	2	no	—
569	#124	—	2	2	no	—
570	C₂²⋊Q₈	—	2	8	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	#121	—	2	8	no	—
574	#121	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#121	—	2	2	no	—
578	#121	—	4	1	no	—
579	#121	—	4	4	no	—
580	#121	D₄×C₆₁	1	4	yes	complemented
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×D₄	—	2	8	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	2	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	4	1	no	—
592	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
608	C₂×C₄²	—	2	1	no	—
609	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
610	#107	—	2	2	no	—
611	#103	—	2	2	no	—
612	#103	—	2	2	no	—
613	#103	—	2	2	no	—
614	#103	—	2	2	no	—
615	#103	—	2	2	no	—
616	#103	D₄×C₆₁	1	4	yes	complemented
617	#102	—	2	2	no	—
618	#102	—	2	2	no	—
619	#102	—	2	2	no	—
620	#102	—	4	1	no	—
621	C₂²⋊C₈	—	2	2	no	—
622	C₂²⋊C₈	—	2	2	no	—
623	C₂²⋊C₈	—	4	1	no	—
624	#95	—	2	1	no	—
625	#95	—	2	1	no	—
626	C₂⁴	—	2	1	no	—
627	C₂⁴	—	2	1	no	—
628	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
629	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
630	#41	—	4	4	no	—
631	#41	—	4	4	no	—
632	#41	—	4	4	no	—
633	#41	—	4	4	no	—
634	C₂×Q₈	—	2	4	no	—
635	C₂×Q₈	—	2	1	no	—
636	C₂×Q₈	—	2	1	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	8	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	1	no	—
644	C₂×Q₈	—	4	2	no	—
645	C₂×Q₈	—	4	2	no	—
646	C₂×Q₈	—	4	4	no	—
647	C₂×Q₈	—	4	4	no	—
648	C₂×Q₈	—	4	4	no	—
649	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
650	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
651	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
652	C₂×Q₈	#41×C₆₁	1	2	yes	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	—	4	2	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	2	no	—
678	C₂×D₄	—	8	1	no	—
679	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	8	1	no	—
705	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
712	SD₁₆	—	4	4	no	—
713	SD₁₆	—	4	4	no	—
714	D₈	—	4	4	no	—
715	C₂×C₈	—	2	1	no	—
716	C₂×C₈	—	2	1	no	—
717	C₂×C₈	—	2	1	no	—
718	C₂×C₈	—	2	1	no	—
719	C₂×C₈	—	2	1	no	—
720	C₂×C₈	—	2	1	no	—
721	C₂×C₈	—	2	1	no	—
722	C₂×C₈	—	2	1	no	—
723	C₂×C₈	—	2	1	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	2	1	no	—
726	C₂×C₈	—	4	4	no	—
727	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
740	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	8	1	no	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	1	no	—
754	C₄²	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	4	1	no	—
770	C₂³	—	4	1	no	—
771	C₂³	—	4	1	no	—
772	C₂³	—	4	1	no	—
773	C₂³	—	4	1	no	—
774	C₂³	—	4	1	no	—
775	C₂³	—	4	1	no	—
776	C₂³	—	4	1	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	4	1	no	—
780	C₂³	#120×C₆₁	1	2	yes	—
781	C₂³	#135×C₆₁	1	2	yes	—
782	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
783	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
784	Q₈	—	2	2	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	4	8	no	—
790	Q₈	—	4	1	no	—
791	Q₈	—	4	1	no	—
792	Q₈	#121×C₆₁	1	4	yes	complemented
793	D₄	—	2	2	no	—
794	D₄	—	2	2	no	—
795	D₄	—	4	8	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	8	no	—
798	D₄	—	4	1	no	—
799	D₄	—	4	1	no	—
800	D₄	—	4	1	no	—
801	D₄	—	4	1	no	—
802	D₄	—	4	1	no	—
803	D₄	—	4	1	no	—
804	D₄	—	8	4	no	—
805	D₄	—	8	4	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	4	8	no	—
828	C₂×C₄	—	4	8	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	8	4	no	—
846	C₂×C₄	#120×C₆₁	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
850	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
851	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
852	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
853	C₈	—	2	2	no	—
854	C₈	—	4	1	no	—
855	C₈	—	4	1	no	—
856	C₈	—	4	1	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	8	1	no	—
874	C₂²	—	8	1	no	—
875	C₂²	—	8	1	no	—
876	C₂²	—	8	1	no	—
877	C₂²	—	8	1	no	—
878	C₂²	—	8	1	no	—
879	C₂²	—	8	1	no	—
880	C₂²	—	8	1	no	—
881	C₂²	—	8	1	no	—
882	C₂²	—	8	1	no	—
883	C₂²	—	8	1	no	—
884	C₂²	C₆₁×#449	1	4	yes	complemented
885	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
886	C₂²	D₄²×C₆₁	1	1	yes	characteristic
887	C₂²	C₆₁×#546	1	1	yes	characteristic
888	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
889	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
890	C₂²	C₆₁×#577	1	1	yes	characteristic
891	C₂²	C₆₁×#578	1	1	yes	characteristic
892	C₄	—	2	2	no	—
893	C₄	—	2	4	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	8	1	no	—
901	C₄	—	8	1	no	—
902	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
903	C₄	C₆₁×#534	1	1	yes	characteristic
904	C₄	D₄²×C₆₁	1	1	yes	characteristic
905	C₄	C₆₁×#546	1	1	yes	characteristic
906	C₂	—	2	4	no	—
907	C₂	—	8	1	no	—
908	C₂	—	8	2	no	—
909	C₂	—	16	1	no	—
910	C₂	C₆₁×#2410	1	1	yes	characteristic
911	C₂	C₂×C₆₁×#449	1	1	yes	characteristic
912	C₂	C₆₁×#3013	1	1	yes	characteristic
913	C₂	C₆₁×#3265	1	1	yes	characteristic
914	C₂	C₆₁×#3285	1	1	yes	characteristic
915	C₂	C₆₁×#3301	1	1	yes	characteristic
916	C₂	C₆₁×#3308	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#548	C₂	semidirect
2. C₂×C₆₁×#466	C₂	semidirect
3. C₂×C₆₁×#449	C₂	semidirect
4. C₂×C₆₁×#448	C₂	semidirect
5. C₂²×#103×C₆₁	C₂	semidirect
6. C₆₁×#2416	C₂	semidirect
7. C₆₁×#2042	C₂	semidirect
8. C₆₁×#2036	C₂	semidirect
9. C₆₁×#2012	C₂	semidirect
10. C₆₁×#2000	C₂	semidirect
11. C₆₁×#1880	C₂	semidirect
12. C₆₁×#1874	C₂	semidirect
13. C₆₁×#1869	C₂	semidirect
14. C₆₁×#1863	C₂	semidirect
15. C₆₁×#1788	C₂	semidirect
77. C₂²×Q₈×C₆₁	D₄	semidirect
121. #121×C₆₁	D₄	semidirect
157. #103×C₆₁	D₄	semidirect
333. Q₈×C₆₁	#121	semidirect
398. #24439	C₆₁	direct (N × H)
426. C₂²×C₆₁	#449	semidirect
448. C₂×#548	C₂×C₆₁	semidirect
449. C₂×#466	C₂×C₆₁	semidirect
450. C₂×#449	C₂×C₆₁	semidirect
451. C₂×#448	C₂×C₆₁	semidirect
452. C₂²×#103	C₂×C₆₁	semidirect
453. #2416	C₂×C₆₁	semidirect
454. #2042	C₂×C₆₁	semidirect
455. #2036	C₂×C₆₁	semidirect
456. #2012	C₂×C₆₁	semidirect
457. #2000	C₂×C₆₁	semidirect
458. #1880	C₂×C₆₁	semidirect
459. #1874	C₂×C₆₁	semidirect
460. #1869	C₂×C₆₁	semidirect
461. #1863	C₂×C₆₁	semidirect
462. #1788	C₂×C₆₁	semidirect
523. C₆₁	#24439	direct (N × H)
536. C₂²×Q₈	D₄×C₆₁	semidirect
580. #121	D₄×C₆₁	semidirect
616. #103	D₄×C₆₁	semidirect
792. Q₈	#121×C₆₁	semidirect
884. C₂²	C₆₁×#449	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#548	2
C₂×C₆₁×#466	2
C₂×C₆₁×#449	2
C₂×C₆₁×#448	2
C₂²×#103×C₆₁	2
C₆₁×#2416	2
C₆₁×#2042	2
C₆₁×#2036	2
C₆₁×#2012	2
C₆₁×#2000	2
C₆₁×#1880	2
C₆₁×#1874	2
C₆₁×#1869	2
C₆₁×#1863	2
C₆₁×#1788	2
#24439	61

Subgroups — C61×#24439 #29527872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24439 #29527872