Subgroups — C₆₁×#62102 #29565535

Order 15616.

1784 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3381	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3361	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3340	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3339	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3305	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3301	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3247	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3233	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3106	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3076	C₂	1	2	yes	maximal, complemented
16	C₂×C₆₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#559	—	2	1	no	—
19	C₆₁×#559	C₂²	1	1	yes	characteristic
20	C₆₁×#557	C₂²	1	1	yes	characteristic
21	C₆₁×#556	—	2	1	no	—
22	C₆₁×#556	—	2	1	no	—
23	C₆₁×#556	C₂²	1	1	yes	characteristic
24	C₆₁×#555	C₂²	1	2	yes	—
25	C₆₁×#554	C₂²	1	2	yes	—
26	C₆₁×#553	—	2	2	no	—
27	C₆₁×#553	C₂²	1	4	yes	—
28	C₆₁×#553	C₂²	1	2	yes	—
29	C₆₁×#550	C₂²	1	1	yes	characteristic
30	C₆₁×#548	—	2	2	no	—
31	C₆₁×#548	C₂²	1	2	yes	—
32	C₆₁×#547	—	2	1	no	—
33	C₆₁×#542	—	2	2	no	—
34	C₆₁×#537	—	2	1	no	—
35	C₆₁×#533	C₂²	1	2	yes	—
36	C₆₁×#532	—	2	1	no	—
37	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₆₁×#532	C₂²	1	2	yes	—
39	C₆₁×#532	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#529	—	2	2	no	—
42	C₆₁×#529	C₂²	1	2	yes	—
43	C₆₁×#520	—	2	1	no	—
44	C₄×#41×C₆₁	—	2	1	no	—
45	C₄×#41×C₆₁	C₂²	1	2	yes	—
46	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#499	C₂²	1	4	yes	—
49	C₆₁×#498	C₂²	1	2	yes	—
50	C₆₁×#488	C₂²	1	4	yes	—
51	C₆₁×#486	C₂²	1	2	yes	—
52	C₆₁×#485	C₂²	1	4	yes	—
53	C₆₁×#482	C₂²	1	4	yes	—
54	C₆₁×#482	C₂²	1	4	yes	—
55	C₆₁×#481	C₂²	1	4	yes	—
56	C₆₁×#481	C₂²	1	2	yes	—
57	C₆₁×#479	C₂²	1	4	yes	—
58	C₆₁×#478	C₂²	1	4	yes	—
59	C₆₁×#478	C₂²	1	4	yes	—
60	C₆₁×#477	C₂²	1	2	yes	—
61	C₆₁×#477	C₂²	1	2	yes	—
62	C₆₁×#477	C₂²	1	2	yes	—
63	C₆₁×#477	C₂²	1	2	yes	—
64	C₆₁×#476	C₂²	1	2	yes	—
65	C₆₁×#476	C₂²	1	2	yes	—
66	C₆₁×#475	C₂²	1	1	yes	characteristic
67	C₆₁×#475	C₂²	1	1	yes	characteristic
68	C₆₁×#474	C₂²	1	2	yes	—
69	C₆₁×#474	C₂²	1	2	yes	—
70	C₆₁×#466	C₂²	1	4	yes	—
71	C₆₁×#466	C₂²	1	4	yes	—
72	C₆₁×#465	C₂²	1	4	yes	—
73	C₆₁×#463	C₂²	1	4	yes	—
74	C₆₁×#460	C₂²	1	1	yes	characteristic
75	C₆₁×#460	C₂²	1	1	yes	characteristic
76	C₆₁×#459	C₂²	1	2	yes	—
77	C₆₁×#459	C₂²	1	2	yes	—
78	C₆₁×#449	C₂²	1	4	yes	—
79	C₆₁×#448	C₂²	1	2	yes	—
80	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
82	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
83	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
84	C₄×D₈×C₆₁	C₂²	1	4	yes	—
85	C₈×D₄×C₆₁	C₂²	1	4	yes	—
86	C₈×D₄×C₆₁	C₂²	1	2	yes	—
87	C₆₁×#431	C₂²	1	1	yes	characteristic
88	C₆₁×#431	C₂²	1	2	yes	—
89	C₆₁×#427	C₂²	1	4	yes	—
90	C₂×#107×C₆₁	C₂²	1	2	yes	—
91	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
93	C₆₁×#416	C₂²	1	4	yes	—
94	C₂×#103×C₆₁	C₂²	1	2	yes	—
95	C₂×#41×C₆₁	—	2	1	no	—
96	C₂×#41×C₆₁	—	2	1	no	—
97	C₂×#41×C₆₁	—	2	2	no	—
98	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
99	C₂×#41×C₆₁	C₂³	1	2	yes	—
100	C₂²×Q₈×C₆₁	—	2	1	no	—
101	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
104	C₂×D₈×C₆₁	C₂³	1	4	yes	—
105	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₆₁	—	2	1	no	—
108	C₄⋊Q₈×C₆₁	—	2	1	no	—
109	C₄⋊Q₈×C₆₁	—	2	1	no	—
110	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
114	#127×C₆₁	—	2	1	no	—
115	#127×C₆₁	C₂³	1	1	yes	characteristic
116	#127×C₆₁	C₂³	1	1	yes	characteristic
117	#126×C₆₁	—	2	4	no	—
118	#126×C₆₁	—	2	2	no	—
119	#126×C₆₁	—	2	2	no	—
120	#126×C₆₁	—	2	2	no	—
121	#125×C₆₁	—	2	2	no	—
122	#125×C₆₁	C₂³	1	4	yes	—
123	#125×C₆₁	C₂³	1	2	yes	—
124	#124×C₆₁	—	2	1	no	—
125	#124×C₆₁	—	2	1	no	—
126	#124×C₆₁	—	2	4	no	—
127	#124×C₆₁	—	2	2	no	—
128	#124×C₆₁	—	2	1	no	—
129	#124×C₆₁	—	2	2	no	—
130	#124×C₆₁	—	2	1	no	—
131	#124×C₆₁	C₂³	1	2	yes	—
132	#123×C₆₁	—	2	2	no	—
133	#123×C₆₁	—	2	2	no	—
134	#123×C₆₁	—	2	4	no	—
135	#123×C₆₁	—	2	2	no	—
136	C₂²⋊Q₈×C₆₁	—	2	2	no	—
137	C₂²⋊Q₈×C₆₁	—	2	2	no	—
138	C₂²⋊Q₈×C₆₁	—	2	2	no	—
139	C₂²⋊Q₈×C₆₁	—	2	4	no	—
140	C₂²⋊Q₈×C₆₁	—	2	2	no	—
141	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
142	#121×C₆₁	—	2	2	no	—
143	#121×C₆₁	—	2	2	no	—
144	#121×C₆₁	—	2	2	no	—
145	#121×C₆₁	—	2	4	no	—
146	#121×C₆₁	—	2	2	no	—
147	#121×C₆₁	—	2	1	no	—
148	#121×C₆₁	—	2	1	no	—
149	#121×C₆₁	—	2	2	no	—
150	#121×C₆₁	C₂³	1	2	yes	—
151	#121×C₆₁	C₂³	1	2	yes	—
152	#121×C₆₁	C₂³	1	4	yes	—
153	#121×C₆₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₆₁	—	2	1	no	—
155	C₄×Q₈×C₆₁	—	2	1	no	—
156	C₄×Q₈×C₆₁	—	2	2	no	—
157	C₄×Q₈×C₆₁	—	2	2	no	—
158	C₄×Q₈×C₆₁	—	2	1	no	—
159	C₄×Q₈×C₆₁	—	2	1	no	—
160	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
162	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₆₁	—	2	2	no	—
168	C₄×D₄×C₆₁	—	2	2	no	—
169	C₄×D₄×C₆₁	—	2	2	no	—
170	C₄×D₄×C₆₁	—	2	1	no	—
171	C₄×D₄×C₆₁	—	2	1	no	—
172	C₄×D₄×C₆₁	—	2	4	no	—
173	C₄×D₄×C₆₁	—	2	2	no	—
174	C₄×D₄×C₆₁	—	2	2	no	—
175	C₄×D₄×C₆₁	—	2	2	no	—
176	C₄×D₄×C₆₁	—	2	1	no	—
177	C₄×D₄×C₆₁	—	2	1	no	—
178	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
179	C₄×D₄×C₆₁	D₄	1	2	yes	—
180	C₄×D₄×C₆₁	C₂³	1	4	yes	—
181	C₄×D₄×C₆₁	C₂³	1	2	yes	—
182	C₄×D₄×C₆₁	C₂³	1	2	yes	—
183	C₄×D₄×C₆₁	C₂³	1	2	yes	—
184	C₄×D₄×C₆₁	C₂³	1	2	yes	—
185	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
186	#117×C₆₁	—	2	2	no	—
187	#117×C₆₁	—	2	2	no	—
188	#117×C₆₁	—	2	2	no	—
189	#117×C₆₁	D₄	1	2	yes	—
190	#117×C₆₁	D₄	1	1	yes	characteristic
191	#117×C₆₁	C₂³	1	4	yes	—
192	#117×C₆₁	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
194	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
196	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₆₁	—	2	1	no	—
199	C₂×C₄²×C₆₁	—	2	2	no	—
200	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
202	#107×C₆₁	C₂³	1	4	yes	—
203	#107×C₆₁	C₂³	1	4	yes	—
204	#107×C₆₁	C₂³	1	4	yes	—
205	#106×C₆₁	C₂³	1	2	yes	—
206	#106×C₆₁	C₂³	1	4	yes	—
207	#106×C₆₁	C₂³	1	2	yes	—
208	#106×C₆₁	C₂³	1	4	yes	—
209	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
210	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
211	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
212	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
213	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
214	#103×C₆₁	C₂³	1	4	yes	—
215	#103×C₆₁	C₂³	1	4	yes	—
216	#103×C₆₁	C₂³	1	2	yes	—
217	#103×C₆₁	C₂³	1	2	yes	—
218	#102×C₆₁	C₂³	1	4	yes	—
219	#102×C₆₁	C₂³	1	4	yes	—
220	#102×C₆₁	C₂³	1	2	yes	—
221	#102×C₆₁	C₂³	1	4	yes	—
222	#102×C₆₁	C₂³	1	4	yes	—
223	#102×C₆₁	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
226	C₄×C₈×C₆₁	C₂³	1	4	yes	—
227	C₄×C₈×C₆₁	C₂³	1	2	yes	—
228	#41×C₆₁	—	2	4	no	—
229	#41×C₆₁	—	2	4	no	—
230	#41×C₆₁	—	4	2	no	—
231	#41×C₆₁	—	4	4	no	—
232	#41×C₆₁	—	4	4	no	—
233	#41×C₆₁	—	8	4	no	—
234	C₂×Q₈×C₆₁	—	2	1	no	—
235	C₂×Q₈×C₆₁	—	2	1	no	—
236	C₂×Q₈×C₆₁	—	2	1	no	—
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	—	4	1	no	—
241	C₂×Q₈×C₆₁	—	8	2	no	—
242	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
244	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₆₁	—	2	2	no	—
246	C₂×D₄×C₆₁	—	2	2	no	—
247	C₂×D₄×C₆₁	—	2	2	no	—
248	C₂×D₄×C₆₁	—	2	2	no	—
249	C₂×D₄×C₆₁	—	2	4	no	—
250	C₂×D₄×C₆₁	—	2	1	no	—
251	C₂×D₄×C₆₁	—	2	1	no	—
252	C₂×D₄×C₆₁	—	2	1	no	—
253	C₂×D₄×C₆₁	—	2	1	no	—
254	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
257	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₁	—	2	1	no	—
259	C₂²×C₄×C₆₁	—	2	1	no	—
260	C₂²×C₄×C₆₁	—	2	2	no	—
261	C₂²×C₄×C₆₁	—	2	2	no	—
262	C₂²×C₄×C₆₁	—	2	2	no	—
263	C₂²×C₄×C₆₁	—	2	2	no	—
264	C₂²×C₄×C₆₁	—	2	2	no	—
265	C₂²×C₄×C₆₁	—	2	4	no	—
266	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
272	SD₁₆×C₆₁	—	2	4	no	—
273	SD₁₆×C₆₁	—	4	2	no	—
274	D₈×C₆₁	—	4	4	no	—
275	C₂×C₈×C₆₁	—	4	2	no	—
276	C₂×C₈×C₆₁	—	4	4	no	—
277	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
278	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
279	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
280	C₄⋊C₄×C₆₁	—	2	2	no	—
281	C₄⋊C₄×C₆₁	—	2	1	no	—
282	C₄⋊C₄×C₆₁	—	2	2	no	—
283	C₄⋊C₄×C₆₁	—	2	4	no	—
284	C₄⋊C₄×C₆₁	—	2	1	no	—
285	C₄⋊C₄×C₆₁	—	2	1	no	—
286	C₄⋊C₄×C₆₁	—	2	1	no	—
287	C₄⋊C₄×C₆₁	—	2	1	no	—
288	C₄⋊C₄×C₆₁	—	2	2	no	—
289	C₄⋊C₄×C₆₁	—	2	2	no	—
290	C₄⋊C₄×C₆₁	—	2	2	no	—
291	C₄⋊C₄×C₆₁	—	2	2	no	—
292	C₄⋊C₄×C₆₁	—	2	1	no	—
293	C₄⋊C₄×C₆₁	—	2	1	no	—
294	C₄⋊C₄×C₆₁	—	2	2	no	—
295	C₄⋊C₄×C₆₁	—	2	4	no	—
296	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
305	C₂²⋊C₄×C₆₁	—	2	2	no	—
306	C₂²⋊C₄×C₆₁	—	2	4	no	—
307	C₂²⋊C₄×C₆₁	—	2	2	no	—
308	C₂²⋊C₄×C₆₁	—	2	2	no	—
309	C₂²⋊C₄×C₆₁	—	2	4	no	—
310	C₂²⋊C₄×C₆₁	—	2	2	no	—
311	C₂²⋊C₄×C₆₁	—	2	2	no	—
312	C₂²⋊C₄×C₆₁	—	2	2	no	—
313	C₂²⋊C₄×C₆₁	—	2	2	no	—
314	C₂²⋊C₄×C₆₁	—	2	2	no	—
315	C₂²⋊C₄×C₆₁	—	2	2	no	—
316	C₂²⋊C₄×C₆₁	—	2	4	no	—
317	C₂²⋊C₄×C₆₁	—	2	2	no	—
318	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
321	C₄²×C₆₁	—	2	1	no	—
322	C₄²×C₆₁	—	2	1	no	—
323	C₄²×C₆₁	—	2	2	no	—
324	C₄²×C₆₁	—	2	2	no	—
325	C₄²×C₆₁	—	2	1	no	—
326	C₄²×C₆₁	—	2	1	no	—
327	C₄²×C₆₁	—	2	4	no	—
328	C₄²×C₆₁	C₂×D₄	1	2	yes	—
329	C₄²×C₆₁	C₂×D₄	1	2	yes	—
330	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₆₁	C₂⁴	1	2	yes	—
333	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂³×C₆₁	—	2	2	no	—
336	C₂³×C₆₁	—	2	2	no	—
337	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
338	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
339	Q₈×C₆₁	—	2	2	no	—
340	Q₈×C₆₁	—	2	1	no	—
341	Q₈×C₆₁	—	2	1	no	—
342	Q₈×C₆₁	—	2	1	no	—
343	Q₈×C₆₁	—	4	2	no	—
344	Q₈×C₆₁	—	4	4	no	—
345	Q₈×C₆₁	—	4	2	no	—
346	Q₈×C₆₁	—	4	2	no	—
347	Q₈×C₆₁	—	8	2	no	—
348	Q₈×C₆₁	2₋¹⁺⁴	1	2	yes	—
349	D₄×C₆₁	—	2	4	no	—
350	D₄×C₆₁	—	2	2	no	—
351	D₄×C₆₁	—	2	2	no	—
352	D₄×C₆₁	—	2	2	no	—
353	D₄×C₆₁	—	2	2	no	—
354	D₄×C₆₁	—	2	2	no	—
355	D₄×C₆₁	—	4	4	no	—
356	D₄×C₆₁	—	4	2	no	—
357	D₄×C₆₁	—	4	4	no	—
358	D₄×C₆₁	—	4	4	no	—
359	D₄×C₆₁	—	4	2	no	—
360	D₄×C₆₁	—	4	2	no	—
361	D₄×C₆₁	—	8	1	no	—
362	D₄×C₆₁	—	8	2	no	—
363	D₄×C₆₁	—	8	4	no	—
364	C₂×C₄×C₆₁	—	2	1	no	—
365	C₂×C₄×C₆₁	—	2	4	no	—
366	C₂×C₄×C₆₁	—	2	1	no	—
367	C₂×C₄×C₆₁	—	2	2	no	—
368	C₂×C₄×C₆₁	—	2	1	no	—
369	C₂×C₄×C₆₁	—	2	2	no	—
370	C₂×C₄×C₆₁	—	2	1	no	—
371	C₂×C₄×C₆₁	—	2	1	no	—
372	C₂×C₄×C₆₁	—	2	2	no	—
373	C₂×C₄×C₆₁	—	2	2	no	—
374	C₂×C₄×C₆₁	—	2	1	no	—
375	C₂×C₄×C₆₁	—	2	4	no	—
376	C₂×C₄×C₆₁	—	4	1	no	—
377	C₂×C₄×C₆₁	—	4	2	no	—
378	C₂×C₄×C₆₁	—	4	4	no	—
379	C₂×C₄×C₆₁	—	4	2	no	—
380	C₂×C₄×C₆₁	—	4	4	no	—
381	C₂×C₄×C₆₁	—	4	4	no	—
382	C₂×C₄×C₆₁	—	8	2	no	—
383	C₂×C₄×C₆₁	—	8	4	no	—
384	C₂×C₄×C₆₁	—	8	1	no	—
385	C₂×C₄×C₆₁	—	8	2	no	—
386	C₂×C₄×C₆₁	#135	1	4	yes	—
387	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
396	C₈×C₆₁	—	2	2	no	—
397	C₈×C₆₁	—	2	4	no	—
398	C₈×C₆₁	—	2	2	no	—
399	#62102	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
400	C₂²×C₆₁	—	2	1	no	—
401	C₂²×C₆₁	—	2	1	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	2	no	—
407	C₂²×C₆₁	—	4	2	no	—
408	C₂²×C₆₁	—	4	2	no	—
409	C₂²×C₆₁	—	4	2	no	—
410	C₂²×C₆₁	—	4	2	no	—
411	C₂²×C₆₁	C₂×#135	1	2	yes	—
412	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₆₁	—	2	1	no	—
414	C₄×C₆₁	—	2	2	no	—
415	C₄×C₆₁	—	2	1	no	—
416	C₄×C₆₁	—	2	2	no	—
417	C₄×C₆₁	—	2	1	no	—
418	C₄×C₆₁	—	2	2	no	—
419	C₄×C₆₁	—	2	2	no	—
420	C₄×C₆₁	—	4	1	no	—
421	C₄×C₆₁	—	4	4	no	—
422	C₄×C₆₁	—	4	1	no	—
423	C₄×C₆₁	—	4	1	no	—
424	C₄×C₆₁	—	4	2	no	—
425	C₄×C₆₁	—	4	2	no	—
426	C₄×C₆₁	C₂×#135	1	2	yes	—
427	C₄×C₆₁	C₂×#135	1	2	yes	—
428	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
429	C₄×C₆₁	#585	1	1	yes	characteristic
430	#3511	C₂×C₆₁	1	1	yes	characteristic, complemented
431	#3480	C₂×C₆₁	1	1	yes	characteristic, complemented
432	#3381	C₂×C₆₁	1	2	yes	complemented
433	#3361	C₂×C₆₁	1	2	yes	complemented
434	#3340	C₂×C₆₁	1	2	yes	complemented
435	#3339	C₂×C₆₁	1	4	yes	complemented
436	#3305	C₂×C₆₁	1	2	yes	complemented
437	#3301	C₂×C₆₁	1	4	yes	complemented
438	#3247	C₂×C₆₁	1	2	yes	complemented
439	#3245	C₂×C₆₁	1	1	yes	characteristic, complemented
440	#3233	C₂×C₆₁	1	2	yes	complemented
441	#3227	C₂×C₆₁	1	1	yes	characteristic, complemented
442	#3106	C₂×C₆₁	1	2	yes	complemented
443	#3103	C₂×C₆₁	1	1	yes	characteristic, complemented
444	#3076	C₂×C₆₁	1	2	yes	complemented
445	C₂×#477	C₂×C₆₁	1	1	yes	characteristic, complemented
446	#2988	C₂×C₆₁	1	1	yes	characteristic, complemented
447	C₂×C₆₁	—	2	2	no	—
448	C₂×C₆₁	—	4	2	no	—
449	C₂×C₆₁	—	8	2	no	—
450	C₂×C₆₁	—	8	2	no	—
451	C₂×C₆₁	#3489	1	1	yes	characteristic
452	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
453	C₂×C₆₁	#3585	1	1	yes	characteristic
454	#559	—	2	1	no	—
455	#559	C₂²×C₆₁	1	1	yes	characteristic
456	#557	C₂²×C₆₁	1	1	yes	characteristic
457	#556	—	2	1	no	—
458	#556	—	2	1	no	—
459	#556	C₂²×C₆₁	1	1	yes	characteristic
460	#555	C₂²×C₆₁	1	2	yes	—
461	#554	C₂²×C₆₁	1	2	yes	—
462	#553	—	2	2	no	—
463	#553	C₂²×C₆₁	1	2	yes	—
464	#553	C₂²×C₆₁	1	4	yes	—
465	#550	C₂²×C₆₁	1	1	yes	characteristic
466	#548	—	2	2	no	—
467	#548	C₂²×C₆₁	1	2	yes	—
468	#547	—	2	1	no	—
469	#542	—	2	2	no	—
470	#537	—	2	1	no	—
471	#533	C₂²×C₆₁	1	2	yes	—
472	#532	—	2	1	no	—
473	#532	C₂²×C₆₁	1	1	yes	characteristic
474	#532	C₂²×C₆₁	1	2	yes	—
475	#532	C₂²×C₆₁	1	1	yes	characteristic
476	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
477	#529	—	2	2	no	—
478	#529	C₂²×C₆₁	1	2	yes	—
479	#520	—	2	1	no	—
480	C₄×#41	—	2	1	no	—
481	C₄×#41	C₂²×C₆₁	1	2	yes	—
482	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
483	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
484	#499	C₂²×C₆₁	1	4	yes	—
485	#498	C₂²×C₆₁	1	2	yes	—
486	#488	C₂²×C₆₁	1	4	yes	—
487	#486	C₂²×C₆₁	1	2	yes	—
488	#485	C₂²×C₆₁	1	4	yes	—
489	#482	C₂²×C₆₁	1	4	yes	—
490	#482	C₂²×C₆₁	1	4	yes	—
491	#481	C₂²×C₆₁	1	2	yes	—
492	#481	C₂²×C₆₁	1	4	yes	—
493	#479	C₂²×C₆₁	1	4	yes	—
494	#478	C₂²×C₆₁	1	4	yes	—
495	#478	C₂²×C₆₁	1	4	yes	—
496	#477	C₂²×C₆₁	1	2	yes	—
497	#477	C₂²×C₆₁	1	2	yes	—
498	#477	C₂²×C₆₁	1	2	yes	—
499	#477	C₂²×C₆₁	1	2	yes	—
500	#476	C₂²×C₆₁	1	2	yes	—
501	#476	C₂²×C₆₁	1	2	yes	—
502	#475	C₂²×C₆₁	1	1	yes	characteristic
503	#475	C₂²×C₆₁	1	1	yes	characteristic
504	#474	C₂²×C₆₁	1	2	yes	—
505	#474	C₂²×C₆₁	1	2	yes	—
506	#466	C₂²×C₆₁	1	4	yes	—
507	#466	C₂²×C₆₁	1	4	yes	—
508	#465	C₂²×C₆₁	1	4	yes	—
509	#463	C₂²×C₆₁	1	4	yes	—
510	#460	C₂²×C₆₁	1	1	yes	characteristic
511	#460	C₂²×C₆₁	1	1	yes	characteristic
512	#459	C₂²×C₆₁	1	2	yes	—
513	#459	C₂²×C₆₁	1	2	yes	—
514	#449	C₂²×C₆₁	1	4	yes	—
515	#448	C₂²×C₆₁	1	2	yes	—
516	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
517	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
518	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
519	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
520	C₄×D₈	C₂²×C₆₁	1	4	yes	—
521	C₈×D₄	C₂²×C₆₁	1	4	yes	—
522	C₈×D₄	C₂²×C₆₁	1	2	yes	—
523	#431	C₂²×C₆₁	1	1	yes	characteristic
524	#431	C₂²×C₆₁	1	2	yes	—
525	#427	C₂²×C₆₁	1	4	yes	—
526	C₂×#107	C₂²×C₆₁	1	2	yes	—
527	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
528	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
529	#416	C₂²×C₆₁	1	4	yes	—
530	C₂×#103	C₂²×C₆₁	1	2	yes	—
531	C₆₁	#62102	1	1	yes	characteristic, direct product factor, Sylow
532	C₂×#41	—	2	1	no	—
533	C₂×#41	—	2	1	no	—
534	C₂×#41	—	2	2	no	—
535	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
536	C₂×#41	C₂³×C₆₁	1	2	yes	—
537	C₂²×Q₈	—	2	1	no	—
538	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
539	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
540	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
541	C₂×D₈	C₂³×C₆₁	1	4	yes	—
542	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
543	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
551	#127	—	2	1	no	—
552	#127	C₂³×C₆₁	1	1	yes	characteristic
553	#127	C₂³×C₆₁	1	1	yes	characteristic
554	#126	—	2	2	no	—
555	#126	—	2	4	no	—
556	#126	—	2	2	no	—
557	#126	—	2	2	no	—
558	#125	—	2	2	no	—
559	#125	C₂³×C₆₁	1	2	yes	—
560	#125	C₂³×C₆₁	1	4	yes	—
561	#124	—	2	1	no	—
562	#124	—	2	1	no	—
563	#124	—	2	2	no	—
564	#124	—	2	4	no	—
565	#124	—	2	1	no	—
566	#124	—	2	2	no	—
567	#124	—	2	1	no	—
568	#124	C₂³×C₆₁	1	2	yes	—
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	#123	—	2	4	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	4	no	—
578	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	4	no	—
583	#121	—	2	2	no	—
584	#121	—	2	1	no	—
585	#121	—	2	1	no	—
586	#121	—	2	2	no	—
587	#121	C₂³×C₆₁	1	2	yes	—
588	#121	C₂³×C₆₁	1	2	yes	—
589	#121	C₂³×C₆₁	1	2	yes	—
590	#121	C₂³×C₆₁	1	4	yes	—
591	C₄×Q₈	—	2	1	no	—
592	C₄×Q₈	—	2	1	no	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
603	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	4	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
616	C₄×D₄	D₄×C₆₁	1	2	yes	—
617	C₄×D₄	C₂³×C₆₁	1	2	yes	—
618	C₄×D₄	C₂³×C₆₁	1	2	yes	—
619	C₄×D₄	C₂³×C₆₁	1	4	yes	—
620	C₄×D₄	C₂³×C₆₁	1	2	yes	—
621	C₄×D₄	C₂³×C₆₁	1	2	yes	—
622	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
623	#117	—	2	2	no	—
624	#117	—	2	2	no	—
625	#117	—	2	2	no	—
626	#117	D₄×C₆₁	1	1	yes	characteristic
627	#117	D₄×C₆₁	1	2	yes	—
628	#117	C₂³×C₆₁	1	2	yes	—
629	#117	C₂³×C₆₁	1	4	yes	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	2	no	—
633	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	2	no	—
637	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
639	#107	C₂³×C₆₁	1	4	yes	—
640	#107	C₂³×C₆₁	1	4	yes	—
641	#107	C₂³×C₆₁	1	4	yes	—
642	#106	C₂³×C₆₁	1	2	yes	—
643	#106	C₂³×C₆₁	1	4	yes	—
644	#106	C₂³×C₆₁	1	2	yes	—
645	#106	C₂³×C₆₁	1	4	yes	—
646	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
647	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
648	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
649	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
650	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
651	#103	C₂³×C₆₁	1	4	yes	—
652	#103	C₂³×C₆₁	1	4	yes	—
653	#103	C₂³×C₆₁	1	2	yes	—
654	#103	C₂³×C₆₁	1	2	yes	—
655	#102	C₂³×C₆₁	1	4	yes	—
656	#102	C₂³×C₆₁	1	4	yes	—
657	#102	C₂³×C₆₁	1	2	yes	—
658	#102	C₂³×C₆₁	1	4	yes	—
659	#102	C₂³×C₆₁	1	4	yes	—
660	#102	C₂³×C₆₁	1	2	yes	—
661	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
662	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
663	C₄×C₈	C₂³×C₆₁	1	4	yes	—
664	C₄×C₈	C₂³×C₆₁	1	2	yes	—
665	#41	—	2	4	no	—
666	#41	—	2	4	no	—
667	#41	—	4	2	no	—
668	#41	—	4	4	no	—
669	#41	—	4	4	no	—
670	#41	—	8	4	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	4	1	no	—
678	C₂×Q₈	—	8	2	no	—
679	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
680	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
681	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
692	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
693	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
694	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
704	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
706	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
709	SD₁₆	—	2	4	no	—
710	SD₁₆	—	4	2	no	—
711	D₈	—	4	4	no	—
712	C₂×C₈	—	4	2	no	—
713	C₂×C₈	—	4	4	no	—
714	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
715	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
716	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
741	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
756	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
757	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	4	no	—
765	C₄²	C₂×D₄×C₆₁	1	2	yes	—
766	C₄²	C₂×D₄×C₆₁	1	2	yes	—
767	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
769	C₄²	C₂⁴×C₆₁	1	2	yes	—
770	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
771	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
775	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
776	Q₈	—	2	2	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	1	no	—
779	Q₈	—	2	1	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	4	4	no	—
782	Q₈	—	4	2	no	—
783	Q₈	—	4	2	no	—
784	Q₈	—	8	2	no	—
785	Q₈	2₋¹⁺⁴×C₆₁	1	2	yes	—
786	D₄	—	2	4	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	2	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	2	no	—
798	D₄	—	8	1	no	—
799	D₄	—	8	2	no	—
800	D₄	—	8	4	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	4	no	—
821	C₂×C₄	—	8	1	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	#135×C₆₁	1	4	yes	—
824	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
832	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
833	C₈	—	2	2	no	—
834	C₈	—	2	4	no	—
835	C₈	—	2	2	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	C₂×#135×C₆₁	1	2	yes	—
848	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
849	C₄	—	2	2	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	4	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	C₂×#135×C₆₁	1	2	yes	—
863	C₄	C₂×#135×C₆₁	1	2	yes	—
864	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
865	C₄	C₆₁×#585	1	1	yes	characteristic
866	C₂	—	2	2	no	—
867	C₂	—	4	2	no	—
868	C₂	—	8	2	no	—
869	C₂	—	8	2	no	—
870	C₂	C₆₁×#3489	1	1	yes	characteristic
871	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
872	C₂	C₆₁×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3511	C₂	semidirect
2. C₆₁×#3480	C₂	semidirect
3. C₆₁×#3381	C₂	semidirect
4. C₆₁×#3361	C₂	semidirect
5. C₆₁×#3340	C₂	semidirect
6. C₆₁×#3339	C₂	semidirect
7. C₆₁×#3305	C₂	semidirect
8. C₆₁×#3301	C₂	semidirect
9. C₆₁×#3247	C₂	semidirect
10. C₆₁×#3245	C₂	semidirect
11. C₆₁×#3233	C₂	semidirect
12. C₆₁×#3227	C₂	semidirect
13. C₆₁×#3106	C₂	semidirect
14. C₆₁×#3103	C₂	semidirect
15. C₆₁×#3076	C₂	semidirect
16. C₂×C₆₁×#477	C₂	semidirect
17. C₆₁×#2988	C₂	semidirect
399. #62102	C₆₁	direct (N × H)
430. #3511	C₂×C₆₁	semidirect
431. #3480	C₂×C₆₁	semidirect
432. #3381	C₂×C₆₁	semidirect
433. #3361	C₂×C₆₁	semidirect
434. #3340	C₂×C₆₁	semidirect
435. #3339	C₂×C₆₁	semidirect
436. #3305	C₂×C₆₁	semidirect
437. #3301	C₂×C₆₁	semidirect
438. #3247	C₂×C₆₁	semidirect
439. #3245	C₂×C₆₁	semidirect
440. #3233	C₂×C₆₁	semidirect
441. #3227	C₂×C₆₁	semidirect
442. #3106	C₂×C₆₁	semidirect
443. #3103	C₂×C₆₁	semidirect
444. #3076	C₂×C₆₁	semidirect
445. C₂×#477	C₂×C₆₁	semidirect
446. #2988	C₂×C₆₁	semidirect
531. C₆₁	#62102	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3511	2
C₆₁×#3480	2
C₆₁×#3381	2
C₆₁×#3361	2
C₆₁×#3340	2
C₆₁×#3339	2
C₆₁×#3305	2
C₆₁×#3301	2
C₆₁×#3247	2
C₆₁×#3245	2
C₆₁×#3233	2
C₆₁×#3227	2
C₆₁×#3106	2
C₆₁×#3103	2
C₆₁×#3076	2
C₂×C₆₁×#477	2
C₆₁×#2988	2
#62102	61

Subgroups — C61×#62102 #29565535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62102 #29565535