Subgroups — C₆₁×#61443 #29564876

Order 15616.

1848 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3480	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3403	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3371	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3355	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3350	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3326	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3313	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3309	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3277	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3271	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3171	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3108	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3106	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3102	C₂	1	2	yes	maximal, complemented
17	C₆₁×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#137×C₆₁	C₂	1	2	yes	maximal, complemented
19	C₄×#135×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₆₁	C₂²	1	2	yes	—
21	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#559	—	2	2	no	—
23	C₆₁×#559	C₂²	1	2	yes	—
24	C₆₁×#557	C₂²	1	2	yes	—
25	C₆₁×#556	—	2	2	no	—
26	C₆₁×#556	C₂²	1	2	yes	—
27	C₆₁×#553	—	2	2	no	—
28	C₆₁×#553	—	2	2	no	—
29	C₆₁×#553	C₂²	1	2	yes	—
30	C₆₁×#553	C₂²	1	2	yes	—
31	C₆₁×#550	C₂²	1	2	yes	—
32	C₆₁×#548	C₂²	1	2	yes	—
33	C₆₁×#548	C₂²	1	2	yes	—
34	C₆₁×#532	—	2	2	no	—
35	C₆₁×#532	C₂²	1	2	yes	—
36	C₆₁×#529	—	2	2	no	—
37	C₆₁×#529	—	2	2	no	—
38	C₆₁×#529	C₂²	1	2	yes	—
39	C₆₁×#529	C₂²	1	2	yes	—
40	C₄×#41×C₆₁	—	2	2	no	—
41	C₄×#41×C₆₁	C₂²	1	2	yes	—
42	C₄×#41×C₆₁	C₂²	1	2	yes	—
43	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
45	C₆₁×#501	C₂²	1	2	yes	—
46	C₆₁×#499	C₂²	1	1	yes	characteristic
47	C₆₁×#496	C₂²	1	2	yes	—
48	C₆₁×#495	C₂²	1	1	yes	characteristic
49	C₆₁×#490	C₂²	1	2	yes	—
50	C₆₁×#489	C₂²	1	2	yes	—
51	C₆₁×#488	C₂²	1	2	yes	—
52	C₆₁×#485	C₂²	1	2	yes	—
53	C₆₁×#483	C₂²	1	2	yes	—
54	C₆₁×#482	C₂²	1	2	yes	—
55	C₆₁×#482	C₂²	1	2	yes	—
56	C₆₁×#482	C₂²	1	2	yes	—
57	C₆₁×#480	C₂²	1	2	yes	—
58	C₆₁×#479	C₂²	1	2	yes	—
59	C₆₁×#479	C₂²	1	2	yes	—
60	C₆₁×#479	C₂²	1	2	yes	—
61	C₆₁×#478	C₂²	1	2	yes	—
62	C₆₁×#477	C₂²	1	2	yes	—
63	C₆₁×#476	C₂²	1	2	yes	—
64	C₆₁×#469	C₂²	1	2	yes	—
65	C₆₁×#469	C₂²	1	2	yes	—
66	C₆₁×#468	C₂²	1	2	yes	—
67	C₆₁×#468	C₂²	1	2	yes	—
68	C₆₁×#467	C₂²	1	1	yes	characteristic
69	C₆₁×#466	C₂²	1	1	yes	characteristic
70	C₆₁×#465	C₂²	1	2	yes	—
71	C₆₁×#464	C₂²	1	2	yes	—
72	C₆₁×#464	C₂²	1	2	yes	—
73	C₆₁×#464	C₂²	1	2	yes	—
74	C₆₁×#463	C₂²	1	2	yes	—
75	C₆₁×#460	C₂²	1	2	yes	—
76	C₆₁×#459	C₂²	1	2	yes	—
77	C₆₁×#452	C₂²	1	2	yes	—
78	C₆₁×#451	C₂²	1	2	yes	—
79	C₆₁×#449	C₂²	1	2	yes	—
80	C₆₁×#449	C₂²	1	2	yes	—
81	C₆₁×#449	C₂²	1	2	yes	—
82	C₆₁×#448	C₂²	1	2	yes	—
83	C₆₁×#446	C₂²	1	1	yes	characteristic
84	C₆₁×#446	C₂²	1	1	yes	characteristic
85	C₆₁×#441	C₂²	1	2	yes	—
86	C₆₁×#441	C₂²	1	2	yes	—
87	C₆₁×#440	C₂²	1	2	yes	—
88	C₆₁×#440	C₂²	1	2	yes	—
89	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
90	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
91	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
92	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
93	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
94	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
95	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
96	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
97	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
98	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
99	C₄×D₈×C₆₁	C₂²	1	2	yes	—
100	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
101	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
102	C₆₁×#436	C₂²	1	1	yes	characteristic
103	C₆₁×#436	C₂²	1	1	yes	characteristic
104	C₆₁×#435	C₂²	1	2	yes	—
105	C₆₁×#435	C₂²	1	2	yes	—
106	C₆₁×#431	C₂²	1	1	yes	characteristic
107	C₆₁×#431	C₂²	1	2	yes	—
108	C₆₁×#428	C₂²	1	2	yes	—
109	C₆₁×#427	C₂²	1	1	yes	characteristic
110	C₆₁×#419	C₂²	1	2	yes	—
111	C₆₁×#417	C₂²	1	2	yes	—
112	C₆₁×#416	C₂²	1	2	yes	—
113	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
114	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
115	C₂×#41×C₆₁	—	2	2	no	—
116	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
117	C₂×#41×C₆₁	C₂³	1	2	yes	—
118	C₂×#41×C₆₁	C₂³	1	2	yes	—
119	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
120	#137×C₆₁	—	2	8	no	—
121	#135×C₆₁	—	2	4	no	—
122	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
124	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
125	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
129	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
130	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
131	C₂×D₈×C₆₁	C₂³	1	2	yes	—
132	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
133	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
134	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₆₁	—	2	2	no	—
137	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
138	#127×C₆₁	—	2	2	no	—
139	#127×C₆₁	C₂³	1	2	yes	—
140	#126×C₆₁	—	2	2	no	—
141	#126×C₆₁	—	2	2	no	—
142	#126×C₆₁	—	2	2	no	—
143	#126×C₆₁	—	2	2	no	—
144	#126×C₆₁	—	2	2	no	—
145	#126×C₆₁	—	2	2	no	—
146	#125×C₆₁	—	2	2	no	—
147	#125×C₆₁	—	2	2	no	—
148	#125×C₆₁	C₂³	1	2	yes	—
149	#125×C₆₁	C₂³	1	2	yes	—
150	#124×C₆₁	—	2	2	no	—
151	#124×C₆₁	—	2	2	no	—
152	#124×C₆₁	—	2	2	no	—
153	#124×C₆₁	—	2	2	no	—
154	#124×C₆₁	—	2	2	no	—
155	#124×C₆₁	C₂³	1	2	yes	—
156	#124×C₆₁	C₂³	1	2	yes	—
157	#123×C₆₁	—	2	2	no	—
158	#123×C₆₁	—	2	2	no	—
159	#123×C₆₁	—	2	2	no	—
160	#123×C₆₁	—	2	2	no	—
161	#123×C₆₁	—	2	2	no	—
162	#123×C₆₁	—	2	2	no	—
163	C₂²⋊Q₈×C₆₁	—	2	2	no	—
164	C₂²⋊Q₈×C₆₁	—	2	2	no	—
165	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
166	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
167	#121×C₆₁	—	2	2	no	—
168	#121×C₆₁	—	2	2	no	—
169	#121×C₆₁	—	2	2	no	—
170	#121×C₆₁	—	2	2	no	—
171	#121×C₆₁	—	2	2	no	—
172	#121×C₆₁	—	2	2	no	—
173	#121×C₆₁	—	2	2	no	—
174	#121×C₆₁	C₂³	1	2	yes	—
175	#121×C₆₁	C₂³	1	2	yes	—
176	#121×C₆₁	C₂³	1	2	yes	—
177	#121×C₆₁	C₂³	1	2	yes	—
178	C₄×Q₈×C₆₁	—	2	2	no	—
179	C₄×Q₈×C₆₁	—	2	2	no	—
180	C₄×Q₈×C₆₁	—	2	2	no	—
181	C₄×Q₈×C₆₁	—	2	2	no	—
182	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
183	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
184	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
185	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
186	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
187	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
188	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
189	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₆₁	—	2	2	no	—
191	C₄×D₄×C₆₁	—	2	2	no	—
192	C₄×D₄×C₆₁	—	2	2	no	—
193	C₄×D₄×C₆₁	—	2	2	no	—
194	C₄×D₄×C₆₁	—	2	2	no	—
195	C₄×D₄×C₆₁	—	2	2	no	—
196	C₄×D₄×C₆₁	—	2	2	no	—
197	C₄×D₄×C₆₁	—	2	2	no	—
198	C₄×D₄×C₆₁	—	2	2	no	—
199	C₄×D₄×C₆₁	—	2	2	no	—
200	C₄×D₄×C₆₁	—	2	2	no	—
201	C₄×D₄×C₆₁	—	2	2	no	—
202	C₄×D₄×C₆₁	—	2	2	no	—
203	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
204	C₄×D₄×C₆₁	D₄	1	2	yes	—
205	C₄×D₄×C₆₁	C₂³	1	2	yes	—
206	C₄×D₄×C₆₁	C₂³	1	2	yes	—
207	C₄×D₄×C₆₁	C₂³	1	2	yes	—
208	C₄×D₄×C₆₁	C₂³	1	2	yes	—
209	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
210	C₄×D₄×C₆₁	C₂³	1	2	yes	—
211	#117×C₆₁	—	2	2	no	—
212	#117×C₆₁	—	2	2	no	—
213	#117×C₆₁	—	2	2	no	—
214	#117×C₆₁	—	2	2	no	—
215	#117×C₆₁	D₄	1	2	yes	—
216	#117×C₆₁	D₄	1	1	yes	characteristic
217	#117×C₆₁	C₂³	1	2	yes	—
218	#117×C₆₁	C₂³	1	2	yes	—
219	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
220	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
221	C₂×C₄²×C₆₁	—	2	2	no	—
222	C₂×C₄²×C₆₁	—	2	2	no	—
223	C₂×C₄²×C₆₁	—	2	2	no	—
224	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
225	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
226	#107×C₆₁	C₂³	1	1	yes	characteristic
227	#107×C₆₁	C₂³	1	1	yes	characteristic
228	#107×C₆₁	C₂³	1	2	yes	—
229	#107×C₆₁	C₂³	1	1	yes	characteristic
230	#107×C₆₁	C₂³	1	2	yes	—
231	#107×C₆₁	C₂³	1	1	yes	characteristic
232	#106×C₆₁	C₂³	1	2	yes	—
233	#106×C₆₁	C₂³	1	2	yes	—
234	#106×C₆₁	C₂³	1	2	yes	—
235	#106×C₆₁	C₂³	1	2	yes	—
236	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
238	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
239	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
240	#103×C₆₁	C₂³	1	2	yes	—
241	#103×C₆₁	C₂³	1	2	yes	—
242	#103×C₆₁	C₂³	1	2	yes	—
243	#103×C₆₁	C₂³	1	2	yes	—
244	#103×C₆₁	C₂³	1	2	yes	—
245	#103×C₆₁	C₂³	1	2	yes	—
246	#103×C₆₁	C₂³	1	2	yes	—
247	#103×C₆₁	C₂³	1	2	yes	—
248	#102×C₆₁	C₂³	1	2	yes	—
249	#102×C₆₁	C₂³	1	2	yes	—
250	#102×C₆₁	C₂³	1	2	yes	—
251	#102×C₆₁	C₂³	1	2	yes	—
252	#102×C₆₁	C₂³	1	2	yes	—
253	#102×C₆₁	C₂³	1	2	yes	—
254	#102×C₆₁	C₂³	1	2	yes	—
255	#102×C₆₁	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
258	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
259	#97×C₆₁	C₂³	1	2	yes	—
260	#97×C₆₁	C₂³	1	2	yes	—
261	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₆₁	C₂³	1	2	yes	—
266	#41×C₆₁	—	2	4	no	—
267	#41×C₆₁	—	2	4	no	—
268	#41×C₆₁	—	4	2	no	—
269	#41×C₆₁	—	4	2	no	—
270	#41×C₆₁	—	4	2	no	—
271	#41×C₆₁	—	4	8	no	—
272	C₂×Q₈×C₆₁	—	2	2	no	—
273	C₂×Q₈×C₆₁	—	2	2	no	—
274	C₂×Q₈×C₆₁	—	2	4	no	—
275	C₂×Q₈×C₆₁	—	4	2	no	—
276	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
277	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
278	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
279	C₂×D₄×C₆₁	—	2	2	no	—
280	C₂×D₄×C₆₁	—	2	2	no	—
281	C₂×D₄×C₆₁	—	2	2	no	—
282	C₂×D₄×C₆₁	—	2	2	no	—
283	C₂×D₄×C₆₁	—	2	2	no	—
284	C₂×D₄×C₆₁	—	2	2	no	—
285	C₂×D₄×C₆₁	—	2	2	no	—
286	C₂×D₄×C₆₁	—	2	2	no	—
287	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
288	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
289	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
290	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₆₁	—	2	2	no	—
292	C₂²×C₄×C₆₁	—	2	2	no	—
293	C₂²×C₄×C₆₁	—	2	2	no	—
294	C₂²×C₄×C₆₁	—	2	2	no	—
295	C₂²×C₄×C₆₁	—	2	2	no	—
296	C₂²×C₄×C₆₁	—	2	2	no	—
297	C₂²×C₄×C₆₁	—	2	2	no	—
298	C₂²×C₄×C₆₁	—	2	2	no	—
299	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
305	Q₁₆×C₆₁	—	2	4	no	—
306	Q₁₆×C₆₁	—	4	1	no	—
307	Q₁₆×C₆₁	#41	1	4	yes	complemented
308	SD₁₆×C₆₁	—	2	4	no	—
309	SD₁₆×C₆₁	—	2	4	no	—
310	SD₁₆×C₆₁	—	2	4	no	—
311	SD₁₆×C₆₁	—	4	2	no	—
312	D₈×C₆₁	—	2	2	no	—
313	D₈×C₆₁	—	4	1	no	—
314	D₈×C₆₁	—	4	2	no	—
315	M₁₆×C₆₁	—	2	4	no	—
316	M₁₆×C₆₁	—	4	2	no	—
317	C₂×C₈×C₆₁	—	2	2	no	—
318	C₂×C₈×C₆₁	—	4	1	no	—
319	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
320	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
321	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
322	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
323	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
324	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₆₁	—	2	2	no	—
326	C₄⋊C₄×C₆₁	—	2	2	no	—
327	C₄⋊C₄×C₆₁	—	2	2	no	—
328	C₄⋊C₄×C₆₁	—	2	2	no	—
329	C₄⋊C₄×C₆₁	—	2	2	no	—
330	C₄⋊C₄×C₆₁	—	2	2	no	—
331	C₄⋊C₄×C₆₁	—	2	2	no	—
332	C₄⋊C₄×C₆₁	—	2	2	no	—
333	C₄⋊C₄×C₆₁	—	2	2	no	—
334	C₄⋊C₄×C₆₁	—	2	2	no	—
335	C₄⋊C₄×C₆₁	—	2	2	no	—
336	C₄⋊C₄×C₆₁	—	2	2	no	—
337	C₄⋊C₄×C₆₁	—	2	2	no	—
338	C₄⋊C₄×C₆₁	—	2	2	no	—
339	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
340	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
342	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
347	C₂²⋊C₄×C₆₁	—	2	2	no	—
348	C₂²⋊C₄×C₆₁	—	2	2	no	—
349	C₂²⋊C₄×C₆₁	—	2	2	no	—
350	C₂²⋊C₄×C₆₁	—	2	2	no	—
351	C₂²⋊C₄×C₆₁	—	2	2	no	—
352	C₂²⋊C₄×C₆₁	—	2	2	no	—
353	C₂²⋊C₄×C₆₁	—	2	2	no	—
354	C₂²⋊C₄×C₆₁	—	2	2	no	—
355	C₂²⋊C₄×C₆₁	—	2	2	no	—
356	C₂²⋊C₄×C₆₁	—	2	2	no	—
357	C₂²⋊C₄×C₆₁	—	2	2	no	—
358	C₂²⋊C₄×C₆₁	—	2	2	no	—
359	C₂²⋊C₄×C₆₁	—	2	2	no	—
360	C₂²⋊C₄×C₆₁	—	2	2	no	—
361	C₂²⋊C₄×C₆₁	—	2	2	no	—
362	C₂²⋊C₄×C₆₁	—	2	2	no	—
363	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
365	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
366	C₄²×C₆₁	—	2	2	no	—
367	C₄²×C₆₁	—	2	2	no	—
368	C₄²×C₆₁	—	2	2	no	—
369	C₄²×C₆₁	—	2	2	no	—
370	C₄²×C₆₁	—	2	2	no	—
371	C₄²×C₆₁	—	2	2	no	—
372	C₄²×C₆₁	—	2	2	no	—
373	C₄²×C₆₁	—	2	2	no	—
374	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₆₁	C₂×D₄	1	2	yes	—
376	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₆₁	C₂×D₄	1	2	yes	—
378	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
379	C₄²×C₆₁	C₂⁴	1	2	yes	—
380	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
381	C₂³×C₆₁	—	2	2	no	—
382	C₂³×C₆₁	—	2	2	no	—
383	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
384	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
385	Q₈×C₆₁	—	2	2	no	—
386	Q₈×C₆₁	—	2	2	no	—
387	Q₈×C₆₁	—	2	2	no	—
388	Q₈×C₆₁	—	4	1	no	—
389	Q₈×C₆₁	—	4	4	no	—
390	Q₈×C₆₁	—	4	4	no	—
391	Q₈×C₆₁	C₂×#41	1	4	yes	—
392	D₄×C₆₁	—	2	2	no	—
393	D₄×C₆₁	—	2	2	no	—
394	D₄×C₆₁	—	2	2	no	—
395	D₄×C₆₁	—	2	2	no	—
396	D₄×C₆₁	—	4	2	no	—
397	D₄×C₆₁	—	4	1	no	—
398	D₄×C₆₁	—	4	4	no	—
399	D₄×C₆₁	—	4	4	no	—
400	D₄×C₆₁	—	4	4	no	—
401	D₄×C₆₁	—	4	4	no	—
402	D₄×C₆₁	—	4	4	no	—
403	D₄×C₆₁	—	8	2	no	—
404	D₄×C₆₁	—	8	2	no	—
405	D₄×C₆₁	—	8	2	no	—
406	C₂×C₄×C₆₁	—	2	2	no	—
407	C₂×C₄×C₆₁	—	2	2	no	—
408	C₂×C₄×C₆₁	—	2	4	no	—
409	C₂×C₄×C₆₁	—	2	1	no	—
410	C₂×C₄×C₆₁	—	2	2	no	—
411	C₂×C₄×C₆₁	—	2	1	no	—
412	C₂×C₄×C₆₁	—	2	2	no	—
413	C₂×C₄×C₆₁	—	2	2	no	—
414	C₂×C₄×C₆₁	—	2	2	no	—
415	C₂×C₄×C₆₁	—	2	2	no	—
416	C₂×C₄×C₆₁	—	2	2	no	—
417	C₂×C₄×C₆₁	—	2	2	no	—
418	C₂×C₄×C₆₁	—	4	1	no	—
419	C₂×C₄×C₆₁	—	4	2	no	—
420	C₂×C₄×C₆₁	—	4	4	no	—
421	C₂×C₄×C₆₁	—	4	4	no	—
422	C₂×C₄×C₆₁	—	4	4	no	—
423	C₂×C₄×C₆₁	—	4	4	no	—
424	C₂×C₄×C₆₁	—	4	4	no	—
425	C₂×C₄×C₆₁	—	8	2	no	—
426	C₂×C₄×C₆₁	—	8	2	no	—
427	C₂×C₄×C₆₁	—	8	2	no	—
428	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
437	C₈×C₆₁	—	2	1	no	—
438	C₈×C₆₁	—	2	2	no	—
439	C₈×C₆₁	—	2	1	no	—
440	C₈×C₆₁	—	2	1	no	—
441	C₈×C₆₁	—	2	2	no	—
442	C₈×C₆₁	C₂×#41	1	2	yes	—
443	#61443	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂²×C₆₁	—	2	2	no	—
445	C₂²×C₆₁	—	2	1	no	—
446	C₂²×C₆₁	—	2	2	no	—
447	C₂²×C₆₁	—	2	1	no	—
448	C₂²×C₆₁	—	2	2	no	—
449	C₂²×C₆₁	—	2	1	no	—
450	C₂²×C₆₁	—	4	2	no	—
451	C₂²×C₆₁	—	4	2	no	—
452	C₂²×C₆₁	—	4	2	no	—
453	C₂²×C₆₁	—	4	2	no	—
454	C₂²×C₆₁	—	4	2	no	—
455	C₂²×C₆₁	—	4	2	no	—
456	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
457	C₄×C₆₁	—	2	1	no	—
458	C₄×C₆₁	—	2	1	no	—
459	C₄×C₆₁	—	2	2	no	—
460	C₄×C₆₁	—	2	1	no	—
461	C₄×C₆₁	—	2	2	no	—
462	C₄×C₆₁	—	2	4	no	—
463	C₄×C₆₁	—	2	2	no	—
464	C₄×C₆₁	—	2	1	no	—
465	C₄×C₆₁	—	4	2	no	—
466	C₄×C₆₁	—	4	2	no	—
467	C₄×C₆₁	—	4	2	no	—
468	C₄×C₆₁	—	4	2	no	—
469	C₄×C₆₁	—	4	2	no	—
470	C₄×C₆₁	#575	1	2	yes	—
471	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
472	C₄×C₆₁	#585	1	1	yes	characteristic
473	#3480	C₂×C₆₁	1	2	yes	complemented
474	#3403	C₂×C₆₁	1	1	yes	characteristic, complemented
475	#3390	C₂×C₆₁	1	1	yes	characteristic, complemented
476	#3371	C₂×C₆₁	1	2	yes	complemented
477	#3355	C₂×C₆₁	1	1	yes	characteristic, complemented
478	#3350	C₂×C₆₁	1	2	yes	complemented
479	#3326	C₂×C₆₁	1	2	yes	complemented
480	#3313	C₂×C₆₁	1	2	yes	complemented
481	#3309	C₂×C₆₁	1	2	yes	complemented
482	#3277	C₂×C₆₁	1	1	yes	characteristic, complemented
483	#3271	C₂×C₆₁	1	2	yes	complemented
484	#3171	C₂×C₆₁	1	2	yes	complemented
485	#3168	C₂×C₆₁	1	1	yes	characteristic, complemented
486	#3108	C₂×C₆₁	1	2	yes	complemented
487	#3106	C₂×C₆₁	1	2	yes	complemented
488	#3102	C₂×C₆₁	1	2	yes	complemented
489	#2965	C₂×C₆₁	1	1	yes	characteristic, complemented
490	C₄×#137	C₂×C₆₁	1	2	yes	complemented
491	C₄×#135	C₂×C₆₁	1	1	yes	characteristic, complemented
492	C₂×C₆₁	—	4	2	no	—
493	C₂×C₆₁	—	4	1	no	—
494	C₂×C₆₁	—	8	2	no	—
495	C₂×C₆₁	—	8	2	no	—
496	C₂×C₆₁	D₄×#41	1	1	yes	characteristic
497	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
498	C₂×C₆₁	#3584	1	1	yes	characteristic
499	C₂×#137	C₂²×C₆₁	1	2	yes	—
500	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
501	#559	—	2	2	no	—
502	#559	C₂²×C₆₁	1	2	yes	—
503	#557	C₂²×C₆₁	1	2	yes	—
504	#556	—	2	2	no	—
505	#556	C₂²×C₆₁	1	2	yes	—
506	#553	—	2	2	no	—
507	#553	—	2	2	no	—
508	#553	C₂²×C₆₁	1	2	yes	—
509	#553	C₂²×C₆₁	1	2	yes	—
510	#550	C₂²×C₆₁	1	2	yes	—
511	#548	C₂²×C₆₁	1	2	yes	—
512	#548	C₂²×C₆₁	1	2	yes	—
513	#532	—	2	2	no	—
514	#532	C₂²×C₆₁	1	2	yes	—
515	#529	—	2	2	no	—
516	#529	—	2	2	no	—
517	#529	C₂²×C₆₁	1	2	yes	—
518	#529	C₂²×C₆₁	1	2	yes	—
519	C₄×#41	—	2	2	no	—
520	C₄×#41	C₂²×C₆₁	1	2	yes	—
521	C₄×#41	C₂²×C₆₁	1	2	yes	—
522	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
523	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
524	#501	C₂²×C₆₁	1	2	yes	—
525	#499	C₂²×C₆₁	1	1	yes	characteristic
526	#496	C₂²×C₆₁	1	2	yes	—
527	#495	C₂²×C₆₁	1	1	yes	characteristic
528	#490	C₂²×C₆₁	1	2	yes	—
529	#489	C₂²×C₆₁	1	2	yes	—
530	#488	C₂²×C₆₁	1	2	yes	—
531	#485	C₂²×C₆₁	1	2	yes	—
532	#483	C₂²×C₆₁	1	2	yes	—
533	#482	C₂²×C₆₁	1	2	yes	—
534	#482	C₂²×C₆₁	1	2	yes	—
535	#482	C₂²×C₆₁	1	2	yes	—
536	#480	C₂²×C₆₁	1	2	yes	—
537	#479	C₂²×C₆₁	1	2	yes	—
538	#479	C₂²×C₆₁	1	2	yes	—
539	#479	C₂²×C₆₁	1	2	yes	—
540	#478	C₂²×C₆₁	1	2	yes	—
541	#477	C₂²×C₆₁	1	2	yes	—
542	#476	C₂²×C₆₁	1	2	yes	—
543	#469	C₂²×C₆₁	1	2	yes	—
544	#469	C₂²×C₆₁	1	2	yes	—
545	#468	C₂²×C₆₁	1	2	yes	—
546	#468	C₂²×C₆₁	1	2	yes	—
547	#467	C₂²×C₆₁	1	1	yes	characteristic
548	#466	C₂²×C₆₁	1	1	yes	characteristic
549	#465	C₂²×C₆₁	1	2	yes	—
550	#464	C₂²×C₆₁	1	2	yes	—
551	#464	C₂²×C₆₁	1	2	yes	—
552	#464	C₂²×C₆₁	1	2	yes	—
553	#463	C₂²×C₆₁	1	2	yes	—
554	#460	C₂²×C₆₁	1	2	yes	—
555	#459	C₂²×C₆₁	1	2	yes	—
556	#452	C₂²×C₆₁	1	2	yes	—
557	#451	C₂²×C₆₁	1	2	yes	—
558	#449	C₂²×C₆₁	1	2	yes	—
559	#449	C₂²×C₆₁	1	2	yes	—
560	#449	C₂²×C₆₁	1	2	yes	—
561	#448	C₂²×C₆₁	1	2	yes	—
562	#446	C₂²×C₆₁	1	1	yes	characteristic
563	#446	C₂²×C₆₁	1	1	yes	characteristic
564	#441	C₂²×C₆₁	1	2	yes	—
565	#441	C₂²×C₆₁	1	2	yes	—
566	#440	C₂²×C₆₁	1	2	yes	—
567	#440	C₂²×C₆₁	1	2	yes	—
568	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
569	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
570	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
571	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
572	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
573	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
574	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
575	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
576	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
577	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
578	C₄×D₈	C₂²×C₆₁	1	2	yes	—
579	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
580	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
581	#436	C₂²×C₆₁	1	1	yes	characteristic
582	#436	C₂²×C₆₁	1	1	yes	characteristic
583	#435	C₂²×C₆₁	1	2	yes	—
584	#435	C₂²×C₆₁	1	2	yes	—
585	#431	C₂²×C₆₁	1	1	yes	characteristic
586	#431	C₂²×C₆₁	1	2	yes	—
587	#428	C₂²×C₆₁	1	2	yes	—
588	#427	C₂²×C₆₁	1	1	yes	characteristic
589	#419	C₂²×C₆₁	1	2	yes	—
590	#417	C₂²×C₆₁	1	2	yes	—
591	#416	C₂²×C₆₁	1	2	yes	—
592	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
593	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
594	C₆₁	#61443	1	1	yes	characteristic, direct product factor, Sylow
595	C₂×#41	—	2	2	no	—
596	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
597	C₂×#41	C₂³×C₆₁	1	2	yes	—
598	C₂×#41	C₂³×C₆₁	1	2	yes	—
599	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
600	#137	—	2	8	no	—
601	#135	—	2	4	no	—
602	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
603	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
604	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
605	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
606	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
607	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
608	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
609	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
610	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
611	C₂×D₈	C₂³×C₆₁	1	2	yes	—
612	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
613	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
614	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
615	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
616	C₄⋊Q₈	—	2	2	no	—
617	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
618	#127	—	2	2	no	—
619	#127	C₂³×C₆₁	1	2	yes	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#126	—	2	2	no	—
624	#126	—	2	2	no	—
625	#126	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	—	2	2	no	—
628	#125	C₂³×C₆₁	1	2	yes	—
629	#125	C₂³×C₆₁	1	2	yes	—
630	#124	—	2	2	no	—
631	#124	—	2	2	no	—
632	#124	—	2	2	no	—
633	#124	—	2	2	no	—
634	#124	—	2	2	no	—
635	#124	C₂³×C₆₁	1	2	yes	—
636	#124	C₂³×C₆₁	1	2	yes	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
646	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	C₂³×C₆₁	1	2	yes	—
655	#121	C₂³×C₆₁	1	2	yes	—
656	#121	C₂³×C₆₁	1	2	yes	—
657	#121	C₂³×C₆₁	1	2	yes	—
658	C₄×Q₈	—	2	2	no	—
659	C₄×Q₈	—	2	2	no	—
660	C₄×Q₈	—	2	2	no	—
661	C₄×Q₈	—	2	2	no	—
662	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
663	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
664	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
665	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
666	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
667	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
668	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
669	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
684	C₄×D₄	D₄×C₆₁	1	2	yes	—
685	C₄×D₄	C₂³×C₆₁	1	2	yes	—
686	C₄×D₄	C₂³×C₆₁	1	2	yes	—
687	C₄×D₄	C₂³×C₆₁	1	2	yes	—
688	C₄×D₄	C₂³×C₆₁	1	2	yes	—
689	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
690	C₄×D₄	C₂³×C₆₁	1	2	yes	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	—	2	2	no	—
695	#117	D₄×C₆₁	1	2	yes	—
696	#117	D₄×C₆₁	1	1	yes	characteristic
697	#117	C₂³×C₆₁	1	2	yes	—
698	#117	C₂³×C₆₁	1	2	yes	—
699	C₂×C₄⋊C₄	—	2	2	no	—
700	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
701	C₂×C₄²	—	2	2	no	—
702	C₂×C₄²	—	2	2	no	—
703	C₂×C₄²	—	2	2	no	—
704	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
705	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
706	#107	C₂³×C₆₁	1	1	yes	characteristic
707	#107	C₂³×C₆₁	1	1	yes	characteristic
708	#107	C₂³×C₆₁	1	2	yes	—
709	#107	C₂³×C₆₁	1	1	yes	characteristic
710	#107	C₂³×C₆₁	1	2	yes	—
711	#107	C₂³×C₆₁	1	1	yes	characteristic
712	#106	C₂³×C₆₁	1	2	yes	—
713	#106	C₂³×C₆₁	1	2	yes	—
714	#106	C₂³×C₆₁	1	2	yes	—
715	#106	C₂³×C₆₁	1	2	yes	—
716	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
717	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
718	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
719	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
720	#103	C₂³×C₆₁	1	2	yes	—
721	#103	C₂³×C₆₁	1	2	yes	—
722	#103	C₂³×C₆₁	1	2	yes	—
723	#103	C₂³×C₆₁	1	2	yes	—
724	#103	C₂³×C₆₁	1	2	yes	—
725	#103	C₂³×C₆₁	1	2	yes	—
726	#103	C₂³×C₆₁	1	2	yes	—
727	#103	C₂³×C₆₁	1	2	yes	—
728	#102	C₂³×C₆₁	1	2	yes	—
729	#102	C₂³×C₆₁	1	2	yes	—
730	#102	C₂³×C₆₁	1	2	yes	—
731	#102	C₂³×C₆₁	1	2	yes	—
732	#102	C₂³×C₆₁	1	2	yes	—
733	#102	C₂³×C₆₁	1	2	yes	—
734	#102	C₂³×C₆₁	1	2	yes	—
735	#102	C₂³×C₆₁	1	2	yes	—
736	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
737	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
738	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
739	#97	C₂³×C₆₁	1	2	yes	—
740	#97	C₂³×C₆₁	1	2	yes	—
741	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
742	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
743	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
744	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
745	C₄×C₈	C₂³×C₆₁	1	2	yes	—
746	#41	—	2	4	no	—
747	#41	—	2	4	no	—
748	#41	—	4	2	no	—
749	#41	—	4	2	no	—
750	#41	—	4	2	no	—
751	#41	—	4	8	no	—
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	—	2	4	no	—
755	C₂×Q₈	—	4	2	no	—
756	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
757	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
758	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
768	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
769	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
770	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
780	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
782	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
785	Q₁₆	—	2	4	no	—
786	Q₁₆	—	4	1	no	—
787	Q₁₆	#41×C₆₁	1	4	yes	complemented
788	SD₁₆	—	2	4	no	—
789	SD₁₆	—	2	4	no	—
790	SD₁₆	—	2	4	no	—
791	SD₁₆	—	4	2	no	—
792	D₈	—	2	2	no	—
793	D₈	—	4	1	no	—
794	D₈	—	4	2	no	—
795	M₁₆	—	2	4	no	—
796	M₁₆	—	4	2	no	—
797	C₂×C₈	—	2	2	no	—
798	C₂×C₈	—	4	1	no	—
799	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
800	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
801	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
802	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
803	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
804	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
820	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
821	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
822	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
823	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
824	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
845	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
855	C₄²	C₂×D₄×C₆₁	1	2	yes	—
856	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
857	C₄²	C₂×D₄×C₆₁	1	2	yes	—
858	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
859	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
860	C₄²	C₂⁴×C₆₁	1	2	yes	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
864	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	2	2	no	—
868	Q₈	—	4	1	no	—
869	Q₈	—	4	4	no	—
870	Q₈	—	4	4	no	—
871	Q₈	C₂×#41×C₆₁	1	4	yes	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	4	2	no	—
877	D₄	—	4	1	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	4	no	—
881	D₄	—	4	4	no	—
882	D₄	—	4	4	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	4	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	1	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	8	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
909	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
915	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
916	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
917	C₈	—	2	1	no	—
918	C₈	—	2	2	no	—
919	C₈	—	2	1	no	—
920	C₈	—	2	1	no	—
921	C₈	—	2	2	no	—
922	C₈	C₂×#41×C₆₁	1	2	yes	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
936	C₄	—	2	2	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	C₆₁×#575	1	2	yes	—
950	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
951	C₄	C₆₁×#585	1	1	yes	characteristic
952	C₂	—	4	2	no	—
953	C₂	—	4	1	no	—
954	C₂	—	8	2	no	—
955	C₂	—	8	2	no	—
956	C₂	D₄×#41×C₆₁	1	1	yes	characteristic
957	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
958	C₂	C₆₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂²×C₆₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3480	C₂	semidirect
2. C₆₁×#3403	C₂	semidirect
3. C₆₁×#3390	C₂	semidirect
4. C₆₁×#3371	C₂	semidirect
5. C₆₁×#3355	C₂	semidirect
6. C₆₁×#3350	C₂	semidirect
7. C₆₁×#3326	C₂	semidirect
8. C₆₁×#3313	C₂	semidirect
9. C₆₁×#3309	C₂	semidirect
10. C₆₁×#3277	C₂	semidirect
11. C₆₁×#3271	C₂	semidirect
12. C₆₁×#3171	C₂	semidirect
13. C₆₁×#3168	C₂	semidirect
14. C₆₁×#3108	C₂	semidirect
15. C₆₁×#3106	C₂	semidirect
16. C₆₁×#3102	C₂	semidirect
17. C₆₁×#2965	C₂	semidirect
18. C₄×#137×C₆₁	C₂	semidirect
19. C₄×#135×C₆₁	C₂	semidirect
307. Q₁₆×C₆₁	#41	semidirect
443. #61443	C₆₁	direct (N × H)
473. #3480	C₂×C₆₁	semidirect
474. #3403	C₂×C₆₁	semidirect
475. #3390	C₂×C₆₁	semidirect
476. #3371	C₂×C₆₁	semidirect
477. #3355	C₂×C₆₁	semidirect
478. #3350	C₂×C₆₁	semidirect
479. #3326	C₂×C₆₁	semidirect
480. #3313	C₂×C₆₁	semidirect
481. #3309	C₂×C₆₁	semidirect
482. #3277	C₂×C₆₁	semidirect
483. #3271	C₂×C₆₁	semidirect
484. #3171	C₂×C₆₁	semidirect
485. #3168	C₂×C₆₁	semidirect
486. #3108	C₂×C₆₁	semidirect
487. #3106	C₂×C₆₁	semidirect
488. #3102	C₂×C₆₁	semidirect
489. #2965	C₂×C₆₁	semidirect
490. C₄×#137	C₂×C₆₁	semidirect
491. C₄×#135	C₂×C₆₁	semidirect
594. C₆₁	#61443	direct (N × H)
787. Q₁₆	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3480	2
C₆₁×#3403	2
C₆₁×#3390	2
C₆₁×#3371	2
C₆₁×#3355	2
C₆₁×#3350	2
C₆₁×#3326	2
C₆₁×#3313	2
C₆₁×#3309	2
C₆₁×#3277	2
C₆₁×#3271	2
C₆₁×#3171	2
C₆₁×#3168	2
C₆₁×#3108	2
C₆₁×#3106	2
C₆₁×#3102	2
C₆₁×#2965	2
C₄×#137×C₆₁	2
C₄×#135×C₆₁	2
#61443	61

Subgroups — C61×#61443 #29564876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61443 #29564876