Subgroups — C₆₁×#61421 #29564854

Order 15616.

1964 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3401	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3400	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3399	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3397	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3396	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3392	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3154	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3045	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3042	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2946	C₂	1	2	yes	maximal, complemented
17	C₄×#137×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
21	C₂×#135×C₆₁	C₂²	1	2	yes	—
22	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
23	C₆₁×#559	C₂²	1	2	yes	—
24	C₆₁×#559	C₂²	1	2	yes	—
25	C₆₁×#559	C₂²	1	2	yes	complemented
26	C₆₁×#557	C₂²	1	2	yes	complemented
27	C₆₁×#556	—	2	1	no	—
28	C₆₁×#556	C₂²	1	4	yes	complemented
29	C₆₁×#554	—	2	1	no	—
30	C₆₁×#552	—	2	2	no	—
31	C₆₁×#550	C₂²	1	2	yes	—
32	C₆₁×#550	C₂²	1	2	yes	—
33	C₆₁×#546	—	2	2	no	—
34	C₆₁×#546	—	2	2	no	—
35	C₆₁×#540	—	2	2	no	—
36	C₆₁×#539	—	2	2	no	—
37	C₆₁×#536	C₂²	1	2	yes	—
38	C₆₁×#535	C₂²	1	2	yes	—
39	C₆₁×#533	C₂²	1	1	yes	characteristic
40	C₆₁×#532	—	2	1	no	—
41	C₆₁×#532	—	2	1	no	—
42	C₆₁×#532	C₂²	1	1	yes	characteristic
43	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#529	—	2	2	no	—
45	C₆₁×#520	C₂²	1	2	yes	—
46	C₆₁×#518	C₂²	1	2	yes	—
47	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
49	C₆₁×#497	C₂²	1	4	yes	complemented
50	C₆₁×#496	C₂²	1	4	yes	—
51	C₆₁×#496	C₂²	1	4	yes	complemented
52	C₆₁×#495	C₂²	1	4	yes	complemented
53	C₆₁×#493	C₂²	1	2	yes	—
54	C₆₁×#492	C₂²	1	2	yes	—
55	C₆₁×#492	C₂²	1	4	yes	complemented
56	C₆₁×#464	C₂²	1	2	yes	complemented
57	C₆₁×#464	C₂²	1	4	yes	complemented
58	C₆₁×#463	C₂²	1	2	yes	complemented
59	C₆₁×#463	C₂²	1	4	yes	complemented
60	C₆₁×#463	C₂²	1	4	yes	complemented
61	C₆₁×#463	C₂²	1	4	yes	complemented
62	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#461	C₂²	1	4	yes	complemented
65	C₆₁×#461	C₂²	1	4	yes	complemented
66	C₆₁×#460	C₂²	1	2	yes	—
67	C₆₁×#460	C₂²	1	4	yes	—
68	C₆₁×#460	C₂²	1	2	yes	—
69	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
70	C₆₁×#460	C₂²	1	4	yes	complemented
71	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
72	C₆₁×#459	C₂²	1	4	yes	complemented
73	C₆₁×#446	C₂²	1	4	yes	complemented
74	C₆₁×#446	C₂²	1	2	yes	complemented
75	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
76	C₆₁×#442	C₂²	1	4	yes	complemented
77	C₆₁×#441	C₂²	1	2	yes	complemented
78	C₆₁×#440	C₂²	1	2	yes	complemented
79	C₆₁×#440	C₂²	1	4	yes	complemented
80	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
83	C₄×D₈×C₆₁	C₂²	1	4	yes	complemented
84	C₆₁×#428	C₂²	1	1	yes	characteristic
85	C₆₁×#424	C₂²	1	2	yes	—
86	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
87	C₆₁×#419	C₂²	1	1	yes	characteristic
88	C₆₁×#417	C₂²	1	1	yes	characteristic
89	C₆₁×#416	C₂²	1	2	yes	—
90	C₂×#102×C₆₁	C₂²	1	2	yes	—
91	C₆₁×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₁	—	2	2	no	—
94	C₂×#41×C₆₁	—	2	2	no	—
95	C₂×#41×C₆₁	C₂³	1	2	yes	—
96	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₁	—	2	1	no	—
99	C₂²×D₄×C₆₁	—	2	1	no	—
100	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
101	#137×C₆₁	—	2	4	no	—
102	AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
103	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
104	#135×C₆₁	—	4	4	no	—
105	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
106	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₆₁	—	4	4	no	—
108	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
115	C₂×D₈×C₆₁	C₂³	1	4	yes	—
116	C₂×D₈×C₆₁	C₂³	1	2	yes	—
117	C₂×D₈×C₆₁	C₂³	1	4	yes	—
118	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
122	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
123	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
125	#127×C₆₁	—	2	1	no	—
126	#127×C₆₁	—	2	1	no	—
127	#127×C₆₁	C₂³	1	2	yes	—
128	#127×C₆₁	C₂³	1	2	yes	—
129	#127×C₆₁	C₂³	1	1	yes	characteristic
130	#127×C₆₁	C₂³	1	4	yes	—
131	#126×C₆₁	—	2	4	no	—
132	#126×C₆₁	—	2	4	no	—
133	#125×C₆₁	—	2	4	no	—
134	#125×C₆₁	—	2	2	no	—
135	#125×C₆₁	D₄	1	2	yes	—
136	#124×C₆₁	—	2	2	no	—
137	#124×C₆₁	—	2	2	no	—
138	#124×C₆₁	—	2	2	no	—
139	#124×C₆₁	C₂³	1	2	yes	—
140	#124×C₆₁	C₂³	1	4	yes	—
141	#124×C₆₁	C₂³	1	4	yes	—
142	#123×C₆₁	—	2	4	no	—
143	#123×C₆₁	—	2	4	no	—
144	#123×C₆₁	—	2	4	no	—
145	#123×C₆₁	—	2	4	no	—
146	C₂²⋊Q₈×C₆₁	—	2	4	no	—
147	C₂²⋊Q₈×C₆₁	—	2	2	no	—
148	C₂²⋊Q₈×C₆₁	—	2	2	no	—
149	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
150	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
151	#121×C₆₁	—	2	1	no	—
152	#121×C₆₁	—	2	1	no	—
153	#121×C₆₁	—	2	2	no	—
154	#121×C₆₁	—	2	2	no	—
155	#121×C₆₁	—	2	2	no	—
156	#121×C₆₁	—	2	2	no	—
157	#121×C₆₁	—	2	4	no	—
158	#121×C₆₁	—	2	4	no	—
159	#120×C₆₁	—	2	4	no	—
160	C₄×Q₈×C₆₁	—	2	2	no	—
161	C₄×Q₈×C₆₁	—	2	1	no	—
162	C₄×Q₈×C₆₁	—	2	1	no	—
163	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
164	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
165	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
166	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
170	C₄×D₄×C₆₁	—	2	1	no	—
171	C₄×D₄×C₆₁	—	2	1	no	—
172	C₄×D₄×C₆₁	—	2	2	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	2	no	—
177	C₄×D₄×C₆₁	—	2	4	no	—
178	C₄×D₄×C₆₁	—	2	1	no	—
179	C₄×D₄×C₆₁	—	2	1	no	—
180	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₆₁	C₂³	1	4	yes	—
183	C₄×D₄×C₆₁	C₂³	1	4	yes	—
184	C₄×D₄×C₆₁	C₂³	1	4	yes	—
185	#117×C₆₁	—	2	2	no	—
186	#117×C₆₁	—	2	4	no	—
187	#117×C₆₁	—	2	1	no	—
188	#117×C₆₁	C₂³	1	1	yes	characteristic
189	#117×C₆₁	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
192	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
194	C₂×C₄²×C₆₁	—	2	1	no	—
195	C₂×C₄²×C₆₁	—	2	1	no	—
196	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
197	#107×C₆₁	C₂³	1	2	yes	—
198	#106×C₆₁	C₂³	1	2	yes	—
199	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
200	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
201	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
202	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
203	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
204	#103×C₆₁	C₂³	1	2	yes	—
205	#103×C₆₁	C₂³	1	2	yes	—
206	#103×C₆₁	C₂³	1	2	yes	—
207	#103×C₆₁	C₂³	1	2	yes	—
208	#103×C₆₁	C₂³	1	2	yes	—
209	#102×C₆₁	C₂³	1	4	yes	—
210	#102×C₆₁	C₂³	1	4	yes	—
211	#102×C₆₁	C₂³	1	2	yes	—
212	#102×C₆₁	C₂³	1	2	yes	—
213	#102×C₆₁	C₂³	1	2	yes	—
214	#97×C₆₁	C₂³	1	2	yes	—
215	#97×C₆₁	C₂³	1	4	yes	—
216	C₄×C₈×C₆₁	C₂³	1	2	yes	—
217	C₄×C₈×C₆₁	C₂³	1	4	yes	—
218	C₂⁴×C₆₁	—	2	2	no	—
219	#41×C₆₁	—	2	4	no	—
220	#41×C₆₁	—	2	2	no	—
221	#41×C₆₁	—	2	2	no	—
222	#41×C₆₁	—	2	4	no	—
223	#41×C₆₁	—	8	4	no	—
224	#41×C₆₁	—	8	4	no	—
225	C₂×Q₈×C₆₁	—	2	1	no	—
226	C₂×Q₈×C₆₁	—	2	2	no	—
227	C₂×Q₈×C₆₁	—	2	2	no	—
228	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
231	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
232	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
233	C₂×D₄×C₆₁	—	2	1	no	—
234	C₂×D₄×C₆₁	—	2	2	no	—
235	C₂×D₄×C₆₁	—	2	1	no	—
236	C₂×D₄×C₆₁	—	2	2	no	—
237	C₂×D₄×C₆₁	—	2	2	no	—
238	C₂×D₄×C₆₁	—	2	2	no	—
239	C₂×D₄×C₆₁	—	2	1	no	—
240	C₂×D₄×C₆₁	—	2	4	no	—
241	C₂×D₄×C₆₁	—	2	4	no	—
242	C₂×D₄×C₆₁	—	2	2	no	—
243	C₂×D₄×C₆₁	—	2	2	no	—
244	C₂×D₄×C₆₁	—	2	4	no	—
245	C₂×D₄×C₆₁	—	2	4	no	—
246	C₂×D₄×C₆₁	—	8	2	no	—
247	C₂×D₄×C₆₁	—	8	2	no	—
248	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
249	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
250	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₆₁	—	2	1	no	—
252	C₂²×C₄×C₆₁	—	2	1	no	—
253	C₂²×C₄×C₆₁	—	2	1	no	—
254	C₂²×C₄×C₆₁	—	2	1	no	—
255	C₂²×C₄×C₆₁	—	2	1	no	—
256	C₂²×C₄×C₆₁	—	2	2	no	—
257	C₂²×C₄×C₆₁	—	2	4	no	—
258	C₂²×C₄×C₆₁	—	2	4	no	—
259	C₂²×C₄×C₆₁	—	2	4	no	—
260	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
263	Q₁₆×C₆₁	—	2	4	no	—
264	Q₁₆×C₆₁	—	4	2	no	—
265	SD₁₆×C₆₁	—	2	8	no	—
266	SD₁₆×C₆₁	—	2	4	no	—
267	SD₁₆×C₆₁	—	4	4	no	—
268	SD₁₆×C₆₁	—	4	4	no	—
269	SD₁₆×C₆₁	—	4	2	no	—
270	SD₁₆×C₆₁	—	4	2	no	—
271	SD₁₆×C₆₁	—	4	4	no	—
272	D₈×C₆₁	—	2	8	no	—
273	D₈×C₆₁	—	4	2	no	—
274	D₈×C₆₁	—	4	4	no	—
275	M₁₆×C₆₁	—	2	2	no	—
276	M₁₆×C₆₁	#41	1	4	yes	complemented
277	C₂×C₈×C₆₁	—	2	4	no	—
278	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
279	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
280	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
281	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₁	—	2	1	no	—
283	C₄⋊C₄×C₆₁	—	2	4	no	—
284	C₄⋊C₄×C₆₁	—	2	2	no	—
285	C₄⋊C₄×C₆₁	—	2	2	no	—
286	C₄⋊C₄×C₆₁	—	2	1	no	—
287	C₄⋊C₄×C₆₁	—	2	1	no	—
288	C₄⋊C₄×C₆₁	—	2	4	no	—
289	C₄⋊C₄×C₆₁	—	2	1	no	—
290	C₄⋊C₄×C₆₁	—	2	1	no	—
291	C₄⋊C₄×C₆₁	—	2	4	no	—
292	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
295	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
298	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
301	C₂²⋊C₄×C₆₁	—	2	1	no	—
302	C₂²⋊C₄×C₆₁	—	2	4	no	—
303	C₂²⋊C₄×C₆₁	—	2	4	no	—
304	C₂²⋊C₄×C₆₁	—	2	2	no	—
305	C₂²⋊C₄×C₆₁	—	2	1	no	—
306	C₂²⋊C₄×C₆₁	—	2	1	no	—
307	C₂²⋊C₄×C₆₁	—	2	4	no	—
308	C₂²⋊C₄×C₆₁	—	2	4	no	—
309	C₂²⋊C₄×C₆₁	—	2	4	no	—
310	C₂²⋊C₄×C₆₁	—	2	4	no	—
311	C₂²⋊C₄×C₆₁	—	2	2	no	—
312	C₂²⋊C₄×C₆₁	—	2	4	no	—
313	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
314	C₄²×C₆₁	—	2	2	no	—
315	C₄²×C₆₁	—	2	1	no	—
316	C₄²×C₆₁	—	2	1	no	—
317	C₄²×C₆₁	—	2	1	no	—
318	C₄²×C₆₁	—	2	2	no	—
319	C₄²×C₆₁	—	2	4	no	—
320	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
323	C₄²×C₆₁	C₂⁴	1	4	yes	—
324	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
325	C₂³×C₆₁	—	2	2	no	—
326	C₂³×C₆₁	—	2	4	no	—
327	C₂³×C₆₁	—	2	1	no	—
328	C₂³×C₆₁	—	4	4	no	—
329	C₂³×C₆₁	—	8	2	no	—
330	C₂³×C₆₁	—	8	2	no	—
331	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
332	Q₈×C₆₁	—	2	4	no	—
333	Q₈×C₆₁	—	2	2	no	—
334	Q₈×C₆₁	—	2	2	no	—
335	Q₈×C₆₁	—	2	1	no	—
336	Q₈×C₆₁	—	2	2	no	—
337	Q₈×C₆₁	—	2	2	no	—
338	Q₈×C₆₁	—	2	1	no	—
339	Q₈×C₆₁	—	4	2	no	—
340	Q₈×C₆₁	—	4	2	no	—
341	D₄×C₆₁	—	2	2	no	—
342	D₄×C₆₁	—	2	4	no	—
343	D₄×C₆₁	—	2	1	no	—
344	D₄×C₆₁	—	2	2	no	—
345	D₄×C₆₁	—	2	1	no	—
346	D₄×C₆₁	—	2	4	no	—
347	D₄×C₆₁	—	4	4	no	—
348	D₄×C₆₁	—	4	2	no	—
349	D₄×C₆₁	—	4	4	no	—
350	D₄×C₆₁	—	4	4	no	—
351	D₄×C₆₁	—	4	2	no	—
352	D₄×C₆₁	—	4	4	no	—
353	D₄×C₆₁	—	8	1	no	—
354	D₄×C₆₁	—	8	2	no	—
355	D₄×C₆₁	—	8	2	no	—
356	D₄×C₆₁	—	8	4	no	—
357	D₄×C₆₁	—	8	4	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	1	no	—
363	C₂×C₄×C₆₁	—	2	2	no	—
364	C₂×C₄×C₆₁	—	2	2	no	—
365	C₂×C₄×C₆₁	—	4	1	no	—
366	C₂×C₄×C₆₁	—	4	2	no	—
367	C₂×C₄×C₆₁	—	4	2	no	—
368	C₂×C₄×C₆₁	—	4	2	no	—
369	C₂×C₄×C₆₁	—	4	4	no	—
370	C₂×C₄×C₆₁	—	4	2	no	—
371	C₂×C₄×C₆₁	—	8	4	no	—
372	C₂×C₄×C₆₁	—	8	4	no	—
373	C₂×C₄×C₆₁	—	8	4	no	—
374	C₂×C₄×C₆₁	—	8	1	no	—
375	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
378	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
380	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
383	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
384	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
385	C₈×C₆₁	—	2	2	no	—
386	C₈×C₆₁	—	2	2	no	—
387	C₈×C₆₁	—	2	2	no	—
388	C₈×C₆₁	C₂×#41	1	4	yes	—
389	#61421	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂²×C₆₁	—	2	1	no	—
391	C₂²×C₆₁	—	2	1	no	—
392	C₂²×C₆₁	—	4	1	no	—
393	C₂²×C₆₁	—	4	2	no	—
394	C₂²×C₆₁	—	4	4	no	—
395	C₂²×C₆₁	—	4	2	no	—
396	C₂²×C₆₁	—	4	1	no	—
397	C₂²×C₆₁	—	4	4	no	—
398	C₂²×C₆₁	—	4	1	no	—
399	C₂²×C₆₁	—	4	4	no	—
400	C₂²×C₆₁	—	4	2	no	—
401	C₂²×C₆₁	—	16	4	no	—
402	C₂²×C₆₁	#550	1	2	yes	—
403	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
404	C₄×C₆₁	—	2	1	no	—
405	C₄×C₆₁	—	2	1	no	—
406	C₄×C₆₁	—	2	4	no	—
407	C₄×C₆₁	—	2	1	no	—
408	C₄×C₆₁	—	2	4	no	—
409	C₄×C₆₁	—	4	1	no	—
410	C₄×C₆₁	—	4	2	no	—
411	C₄×C₆₁	—	4	1	no	—
412	C₄×C₆₁	—	4	2	no	—
413	C₄×C₆₁	—	4	2	no	—
414	C₄×C₆₁	—	4	1	no	—
415	C₄×C₆₁	#550	1	2	yes	—
416	C₄×C₆₁	#577	1	2	yes	—
417	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
418	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
419	#3508	C₂×C₆₁	1	1	yes	characteristic, complemented
420	#3507	C₂×C₆₁	1	1	yes	characteristic, complemented
421	#3401	C₂×C₆₁	1	4	yes	complemented
422	#3400	C₂×C₆₁	1	2	yes	complemented
423	#3399	C₂×C₆₁	1	2	yes	complemented
424	#3397	C₂×C₆₁	1	4	yes	complemented
425	#3396	C₂×C₆₁	1	2	yes	complemented
426	#3392	C₂×C₆₁	1	2	yes	complemented
427	#3154	C₂×C₆₁	1	2	yes	complemented
428	#3151	C₂×C₆₁	1	1	yes	characteristic, complemented
429	#3045	C₂×C₆₁	1	2	yes	complemented
430	#3042	C₂×C₆₁	1	2	yes	complemented
431	#3035	C₂×C₆₁	1	1	yes	characteristic, complemented
432	C₂×#460	C₂×C₆₁	1	1	yes	characteristic, complemented
433	#2962	C₂×C₆₁	1	1	yes	characteristic, complemented
434	#2946	C₂×C₆₁	1	2	yes	complemented
435	C₄×#137	C₂×C₆₁	1	1	yes	characteristic, complemented
436	C₂×C₆₁	—	2	2	no	—
437	C₂×C₆₁	—	8	1	no	—
438	C₂×C₆₁	—	8	2	no	—
439	C₂×C₆₁	—	8	4	no	—
440	C₂×C₆₁	C₂×#550	1	1	yes	characteristic
441	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
442	C₂×C₆₁	#3585	1	1	yes	characteristic
443	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
444	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
445	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
446	C₂×#135	C₂²×C₆₁	1	2	yes	—
447	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
448	#559	C₂²×C₆₁	1	2	yes	—
449	#559	C₂²×C₆₁	1	2	yes	—
450	#559	C₂²×C₆₁	1	2	yes	complemented
451	#557	C₂²×C₆₁	1	2	yes	complemented
452	#556	—	2	1	no	—
453	#556	C₂²×C₆₁	1	4	yes	complemented
454	#554	—	2	1	no	—
455	#552	—	2	2	no	—
456	#550	C₂²×C₆₁	1	2	yes	—
457	#550	C₂²×C₆₁	1	2	yes	—
458	#546	—	2	2	no	—
459	#546	—	2	2	no	—
460	#540	—	2	2	no	—
461	#539	—	2	2	no	—
462	#536	C₂²×C₆₁	1	2	yes	—
463	#535	C₂²×C₆₁	1	2	yes	—
464	#533	C₂²×C₆₁	1	1	yes	characteristic
465	#532	—	2	1	no	—
466	#532	—	2	1	no	—
467	#532	C₂²×C₆₁	1	1	yes	characteristic
468	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
469	#529	—	2	2	no	—
470	#520	C₂²×C₆₁	1	2	yes	—
471	#518	C₂²×C₆₁	1	2	yes	—
472	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
473	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
474	#497	C₂²×C₆₁	1	4	yes	complemented
475	#496	C₂²×C₆₁	1	4	yes	—
476	#496	C₂²×C₆₁	1	4	yes	complemented
477	#495	C₂²×C₆₁	1	4	yes	complemented
478	#493	C₂²×C₆₁	1	2	yes	—
479	#492	C₂²×C₆₁	1	2	yes	—
480	#492	C₂²×C₆₁	1	4	yes	complemented
481	#464	C₂²×C₆₁	1	4	yes	complemented
482	#464	C₂²×C₆₁	1	2	yes	complemented
483	#463	C₂²×C₆₁	1	4	yes	complemented
484	#463	C₂²×C₆₁	1	4	yes	complemented
485	#463	C₂²×C₆₁	1	2	yes	complemented
486	#463	C₂²×C₆₁	1	4	yes	complemented
487	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
488	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
489	#461	C₂²×C₆₁	1	4	yes	complemented
490	#461	C₂²×C₆₁	1	4	yes	complemented
491	#460	C₂²×C₆₁	1	2	yes	—
492	#460	C₂²×C₆₁	1	4	yes	—
493	#460	C₂²×C₆₁	1	2	yes	—
494	#460	C₂²×C₆₁	1	4	yes	complemented
495	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
496	#459	C₂²×C₆₁	1	4	yes	complemented
497	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
498	#446	C₂²×C₆₁	1	4	yes	complemented
499	#446	C₂²×C₆₁	1	2	yes	complemented
500	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
501	#442	C₂²×C₆₁	1	4	yes	complemented
502	#441	C₂²×C₆₁	1	2	yes	complemented
503	#440	C₂²×C₆₁	1	2	yes	complemented
504	#440	C₂²×C₆₁	1	4	yes	complemented
505	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
506	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
507	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
508	C₄×D₈	C₂²×C₆₁	1	4	yes	complemented
509	#428	C₂²×C₆₁	1	1	yes	characteristic
510	#424	C₂²×C₆₁	1	2	yes	—
511	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
512	#419	C₂²×C₆₁	1	1	yes	characteristic
513	#417	C₂²×C₆₁	1	1	yes	characteristic
514	#416	C₂²×C₆₁	1	2	yes	—
515	C₂×#102	C₂²×C₆₁	1	2	yes	—
516	#405	C₂²×C₆₁	1	2	yes	—
517	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
518	C₆₁	#61421	1	1	yes	characteristic, direct product factor, Sylow
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
522	C₂×#41	C₂³×C₆₁	1	2	yes	—
523	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	—	2	1	no	—
526	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
527	#137	—	2	4	no	—
528	AGL(1,ℤ/8)	—	2	8	no	—
529	AGL(1,ℤ/8)	—	4	4	no	—
530	#135	—	4	4	no	—
531	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
532	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
533	C₂×SD₁₆	—	4	4	no	—
534	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
535	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
537	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
538	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
539	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
540	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
541	C₂×D₈	C₂³×C₆₁	1	4	yes	—
542	C₂×D₈	C₂³×C₆₁	1	2	yes	—
543	C₂×D₈	C₂³×C₆₁	1	4	yes	—
544	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
545	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
546	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
547	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
548	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
551	#127	—	2	1	no	—
552	#127	—	2	1	no	—
553	#127	C₂³×C₆₁	1	2	yes	—
554	#127	C₂³×C₆₁	1	2	yes	—
555	#127	C₂³×C₆₁	1	1	yes	characteristic
556	#127	C₂³×C₆₁	1	4	yes	—
557	#126	—	2	4	no	—
558	#126	—	2	4	no	—
559	#125	—	2	2	no	—
560	#125	—	2	4	no	—
561	#125	D₄×C₆₁	1	2	yes	—
562	#124	—	2	2	no	—
563	#124	—	2	2	no	—
564	#124	—	2	2	no	—
565	#124	C₂³×C₆₁	1	2	yes	—
566	#124	C₂³×C₆₁	1	4	yes	—
567	#124	C₂³×C₆₁	1	4	yes	—
568	#123	—	2	4	no	—
569	#123	—	2	4	no	—
570	#123	—	2	4	no	—
571	#123	—	2	4	no	—
572	C₂²⋊Q₈	—	2	4	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
576	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
577	#121	—	2	1	no	—
578	#121	—	2	1	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	2	no	—
583	#121	—	2	4	no	—
584	#121	—	2	4	no	—
585	#120	—	2	4	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
590	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
591	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
594	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
595	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	4	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
607	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₆₁	1	4	yes	—
609	C₄×D₄	C₂³×C₆₁	1	4	yes	—
610	C₄×D₄	C₂³×C₆₁	1	4	yes	—
611	#117	—	2	2	no	—
612	#117	—	2	4	no	—
613	#117	—	2	1	no	—
614	#117	C₂³×C₆₁	1	1	yes	characteristic
615	#117	C₂³×C₆₁	1	2	yes	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	2	no	—
618	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	—	2	4	no	—
620	C₂×C₄²	—	2	1	no	—
621	C₂×C₄²	—	2	1	no	—
622	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
623	#107	C₂³×C₆₁	1	2	yes	—
624	#106	C₂³×C₆₁	1	2	yes	—
625	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
626	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
627	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
628	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
629	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
630	#103	C₂³×C₆₁	1	2	yes	—
631	#103	C₂³×C₆₁	1	2	yes	—
632	#103	C₂³×C₆₁	1	2	yes	—
633	#103	C₂³×C₆₁	1	2	yes	—
634	#103	C₂³×C₆₁	1	2	yes	—
635	#102	C₂³×C₆₁	1	4	yes	—
636	#102	C₂³×C₆₁	1	4	yes	—
637	#102	C₂³×C₆₁	1	2	yes	—
638	#102	C₂³×C₆₁	1	2	yes	—
639	#102	C₂³×C₆₁	1	2	yes	—
640	#97	C₂³×C₆₁	1	2	yes	—
641	#97	C₂³×C₆₁	1	4	yes	—
642	C₄×C₈	C₂³×C₆₁	1	2	yes	—
643	C₄×C₈	C₂³×C₆₁	1	4	yes	—
644	C₂⁴	—	2	2	no	—
645	#41	—	2	4	no	—
646	#41	—	2	2	no	—
647	#41	—	2	2	no	—
648	#41	—	2	4	no	—
649	#41	—	8	4	no	—
650	#41	—	8	4	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
655	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
656	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
657	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
658	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	8	2	no	—
673	C₂×D₄	—	8	2	no	—
674	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
675	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
676	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
689	Q₁₆	—	2	4	no	—
690	Q₁₆	—	4	2	no	—
691	SD₁₆	—	2	8	no	—
692	SD₁₆	—	2	4	no	—
693	SD₁₆	—	4	4	no	—
694	SD₁₆	—	4	4	no	—
695	SD₁₆	—	4	2	no	—
696	SD₁₆	—	4	2	no	—
697	SD₁₆	—	4	4	no	—
698	D₈	—	2	8	no	—
699	D₈	—	4	2	no	—
700	D₈	—	4	4	no	—
701	M₁₆	—	2	2	no	—
702	M₁₆	#41×C₆₁	1	4	yes	complemented
703	C₂×C₈	—	2	4	no	—
704	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
705	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
706	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
707	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
720	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
721	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
723	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
724	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	4	no	—
746	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
748	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
749	C₄²	C₂⁴×C₆₁	1	4	yes	—
750	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	4	4	no	—
755	C₂³	—	8	2	no	—
756	C₂³	—	8	2	no	—
757	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
758	Q₈	—	2	4	no	—
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	1	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	1	no	—
765	Q₈	—	4	2	no	—
766	Q₈	—	4	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	1	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	1	no	—
772	D₄	—	2	4	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	4	no	—
776	D₄	—	4	4	no	—
777	D₄	—	4	2	no	—
778	D₄	—	4	4	no	—
779	D₄	—	8	1	no	—
780	D₄	—	8	2	no	—
781	D₄	—	8	2	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	4	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	—	8	4	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	—	8	1	no	—
801	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
804	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
806	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
808	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
809	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
810	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
811	C₈	—	2	2	no	—
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₈	C₂×#41×C₆₁	1	4	yes	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	4	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	16	4	no	—
827	C₂²	C₆₁×#550	1	2	yes	—
828	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
829	C₄	—	2	1	no	—
830	C₄	—	2	4	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	4	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	C₆₁×#550	1	2	yes	—
841	C₄	C₆₁×#577	1	2	yes	—
842	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
843	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	8	4	no	—
846	C₂	—	8	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₆₁×#550	1	1	yes	characteristic
849	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
850	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 ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3508	C₂	semidirect
2. C₆₁×#3507	C₂	semidirect
3. C₆₁×#3401	C₂	semidirect
4. C₆₁×#3400	C₂	semidirect
5. C₆₁×#3399	C₂	semidirect
6. C₆₁×#3397	C₂	semidirect
7. C₆₁×#3396	C₂	semidirect
8. C₆₁×#3392	C₂	semidirect
9. C₆₁×#3154	C₂	semidirect
10. C₆₁×#3151	C₂	semidirect
11. C₆₁×#3045	C₂	semidirect
12. C₆₁×#3042	C₂	semidirect
13. C₆₁×#3035	C₂	semidirect
14. C₂×C₆₁×#460	C₂	semidirect
15. C₆₁×#2962	C₂	semidirect
16. C₆₁×#2946	C₂	semidirect
17. C₄×#137×C₆₁	C₂	semidirect
25. C₆₁×#559	C₂²	semidirect
26. C₆₁×#557	C₂²	semidirect
28. C₆₁×#556	C₂²	semidirect
49. C₆₁×#497	C₂²	semidirect
51. C₆₁×#496	C₂²	semidirect
52. C₆₁×#495	C₂²	semidirect
55. C₆₁×#492	C₂²	semidirect
56. C₆₁×#464	C₂²	semidirect
57. C₆₁×#464	C₂²	semidirect
58. C₆₁×#463	C₂²	semidirect
59. C₆₁×#463	C₂²	semidirect
60. C₆₁×#463	C₂²	semidirect
61. C₆₁×#463	C₂²	semidirect
62. C₆₁×#462	C₂²	semidirect
63. C₆₁×#461	C₂²	semidirect
64. C₆₁×#461	C₂²	semidirect
65. C₆₁×#461	C₂²	semidirect
69. C₆₁×#460	C₂²	semidirect
70. C₆₁×#460	C₂²	semidirect
71. C₆₁×#459	C₂²	semidirect
72. C₆₁×#459	C₂²	semidirect
73. C₆₁×#446	C₂²	semidirect
74. C₆₁×#446	C₂²	semidirect
75. C₈×Q₈×C₆₁	C₂²	semidirect
76. C₆₁×#442	C₂²	semidirect
77. C₆₁×#441	C₂²	semidirect
78. C₆₁×#440	C₂²	semidirect
79. C₆₁×#440	C₂²	semidirect
80. C₄×Q₁₆×C₆₁	C₂²	semidirect
81. C₄×SD₁₆×C₆₁	C₂²	semidirect
82. C₄×SD₁₆×C₆₁	C₂²	semidirect
83. C₄×D₈×C₆₁	C₂²	semidirect
276. M₁₆×C₆₁	#41	semidirect
389. #61421	C₆₁	direct (N × H)
419. #3508	C₂×C₆₁	semidirect
420. #3507	C₂×C₆₁	semidirect
421. #3401	C₂×C₆₁	semidirect
422. #3400	C₂×C₆₁	semidirect
423. #3399	C₂×C₆₁	semidirect
424. #3397	C₂×C₆₁	semidirect
425. #3396	C₂×C₆₁	semidirect
426. #3392	C₂×C₆₁	semidirect
427. #3154	C₂×C₆₁	semidirect
428. #3151	C₂×C₆₁	semidirect
429. #3045	C₂×C₆₁	semidirect
430. #3042	C₂×C₆₁	semidirect
431. #3035	C₂×C₆₁	semidirect
432. C₂×#460	C₂×C₆₁	semidirect
433. #2962	C₂×C₆₁	semidirect
434. #2946	C₂×C₆₁	semidirect
435. C₄×#137	C₂×C₆₁	semidirect
450. #559	C₂²×C₆₁	semidirect
451. #557	C₂²×C₆₁	semidirect
453. #556	C₂²×C₆₁	semidirect
474. #497	C₂²×C₆₁	semidirect
476. #496	C₂²×C₆₁	semidirect
477. #495	C₂²×C₆₁	semidirect
480. #492	C₂²×C₆₁	semidirect
481. #464	C₂²×C₆₁	semidirect
482. #464	C₂²×C₆₁	semidirect
483. #463	C₂²×C₆₁	semidirect
484. #463	C₂²×C₆₁	semidirect
485. #463	C₂²×C₆₁	semidirect
486. #463	C₂²×C₆₁	semidirect
487. #462	C₂²×C₆₁	semidirect
488. #461	C₂²×C₆₁	semidirect
489. #461	C₂²×C₆₁	semidirect
490. #461	C₂²×C₆₁	semidirect
494. #460	C₂²×C₆₁	semidirect
495. #460	C₂²×C₆₁	semidirect
496. #459	C₂²×C₆₁	semidirect
497. #459	C₂²×C₆₁	semidirect
498. #446	C₂²×C₆₁	semidirect
499. #446	C₂²×C₆₁	semidirect
500. C₈×Q₈	C₂²×C₆₁	semidirect
501. #442	C₂²×C₆₁	semidirect
502. #441	C₂²×C₆₁	semidirect
503. #440	C₂²×C₆₁	semidirect
504. #440	C₂²×C₆₁	semidirect
505. C₄×Q₁₆	C₂²×C₆₁	semidirect
506. C₄×SD₁₆	C₂²×C₆₁	semidirect
507. C₄×SD₁₆	C₂²×C₆₁	semidirect
508. C₄×D₈	C₂²×C₆₁	semidirect
518. C₆₁	#61421	direct (N × H)
702. M₁₆	#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×#3508	2
C₆₁×#3507	2
C₆₁×#3401	2
C₆₁×#3400	2
C₆₁×#3399	2
C₆₁×#3397	2
C₆₁×#3396	2
C₆₁×#3392	2
C₆₁×#3154	2
C₆₁×#3151	2
C₆₁×#3045	2
C₆₁×#3042	2
C₆₁×#3035	2
C₂×C₆₁×#460	2
C₆₁×#2962	2
C₆₁×#2946	2
C₄×#137×C₆₁	2
#61421	61

Subgroups — C61×#61421 #29564854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61421 #29564854