Subgroups — C₆₁×#60771 #29564204

Order 15616.

2254 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3488	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3204	C₂	1	2	yes	maximal, complemented
3	C₆₁×#3199	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3198	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3197	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3194	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3192	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3099	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3096	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3055	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₆₁×#469	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3012	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3008	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2879	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	2	yes	complemented
17	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	complemented
19	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
21	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
22	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
23	C₆₁×#550	—	2	2	no	—
24	C₆₁×#548	—	2	2	no	—
25	C₆₁×#546	—	2	4	no	—
26	C₆₁×#546	—	2	2	no	—
27	D₄²×C₆₁	—	2	4	no	—
28	D₄²×C₆₁	—	2	2	no	—
29	C₆₁×#537	C₂²	1	2	yes	—
30	C₆₁×#537	C₂²	1	4	yes	complemented
31	C₆₁×#535	C₂²	1	2	yes	—
32	C₆₁×#535	C₂²	1	4	yes	complemented
33	C₆₁×#525	C₂²	1	2	yes	complemented
34	C₆₁×#525	C₂²	1	4	yes	complemented
35	C₂×#121×C₆₁	C₂²	1	2	yes	complemented
36	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
37	C₆₁×#520	C₂²	1	2	yes	complemented
38	C₆₁×#485	C₂²	1	4	yes	complemented
39	C₆₁×#483	C₂²	1	4	yes	complemented
40	C₆₁×#482	C₂²	1	4	yes	complemented
41	C₆₁×#482	C₂²	1	4	yes	complemented
42	C₆₁×#482	C₂²	1	4	yes	complemented
43	C₆₁×#481	C₂²	1	4	yes	complemented
44	C₆₁×#481	C₂²	1	4	yes	complemented
45	C₆₁×#480	C₂²	1	4	yes	complemented
46	C₆₁×#470	C₂²	1	1	yes	characteristic, complemented
47	C₆₁×#470	C₂²	1	1	yes	characteristic, complemented
48	C₆₁×#469	C₂²	1	2	yes	complemented
49	C₆₁×#469	C₂²	1	2	yes	complemented
50	C₆₁×#469	C₂²	1	2	yes	complemented
51	C₆₁×#469	C₂²	1	2	yes	complemented
52	C₆₁×#469	C₂²	1	1	yes	characteristic, complemented
53	C₆₁×#469	C₂²	1	1	yes	characteristic, complemented
54	C₆₁×#469	C₂²	1	4	yes	complemented
55	C₆₁×#468	C₂²	1	2	yes	complemented
56	C₆₁×#468	C₂²	1	2	yes	complemented
57	C₆₁×#468	C₂²	1	4	yes	complemented
58	C₆₁×#466	C₂²	1	4	yes	complemented
59	C₆₁×#465	C₂²	1	4	yes	complemented
60	C₆₁×#452	C₂²	1	4	yes	complemented
61	C₆₁×#450	C₂²	1	4	yes	complemented
62	C₆₁×#449	C₂²	1	4	yes	complemented
63	C₆₁×#449	C₂²	1	4	yes	complemented
64	C₆₁×#449	C₂²	1	4	yes	complemented
65	C₆₁×#447	C₂²	1	4	yes	complemented
66	C₆₁×#447	C₂²	1	4	yes	complemented
67	C₆₁×#447	C₂²	1	4	yes	complemented
68	C₆₁×#428	C₂²	1	2	yes	complemented
69	C₆₁×#427	C₂²	1	1	yes	characteristic, complemented
70	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
71	C₆₁×#418	C₂²	1	2	yes	complemented
72	C₆₁×#417	C₂²	1	2	yes	complemented
73	C₆₁×#416	C₂²	1	2	yes	complemented
74	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
75	C₆₁×#408	C₂²	1	2	yes	complemented
76	C₆₁×#408	C₂²	1	2	yes	complemented
77	C₆₁×#408	C₂²	1	2	yes	complemented
78	C₆₁×#408	C₂²	1	2	yes	complemented
79	C₆₁×#407	C₂²	1	2	yes	complemented
80	C₆₁×#407	C₂²	1	2	yes	complemented
81	H(5,𝔽₂)×C₆₁	—	4	4	no	—
82	H(5,𝔽₂)×C₆₁	—	4	4	no	—
83	C₂×#41×C₆₁	—	2	2	no	—
84	C₂×#41×C₆₁	—	4	2	no	—
85	C₂×#41×C₆₁	—	4	2	no	—
86	C₂×#41×C₆₁	D₄	1	2	yes	—
87	C₂×#41×C₆₁	D₄	1	2	yes	—
88	C₂×#41×C₆₁	C₂³	1	2	yes	—
89	C₂×#41×C₆₁	C₂³	1	4	yes	—
90	C₂×#41×C₆₁	C₂³	1	2	yes	—
91	C₂×#41×C₆₁	C₂³	1	2	yes	—
92	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₆₁	—	2	2	no	—
94	C₂²×D₄×C₆₁	—	2	4	no	—
95	C₂²×D₄×C₆₁	—	2	4	no	—
96	C₂²×D₄×C₆₁	—	2	2	no	—
97	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
98	C₂²×D₄×C₆₁	D₄	1	2	yes	—
99	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
100	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
101	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
103	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
104	#135×C₆₁	—	4	2	no	—
105	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
106	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
108	C₂×D₈×C₆₁	—	4	2	no	—
109	C₂×D₈×C₆₁	C₂³	1	2	yes	—
110	C₂×D₈×C₆₁	C₂³	1	2	yes	—
111	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₂×D₈×C₆₁	C₂³	1	4	yes	—
113	C₂×M₁₆×C₆₁	—	4	2	no	—
114	C₂×M₁₆×C₆₁	—	4	2	no	—
115	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
116	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
118	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
124	#127×C₆₁	—	2	2	no	—
125	#127×C₆₁	—	2	4	no	—
126	#124×C₆₁	—	2	2	no	—
127	#124×C₆₁	—	2	4	no	—
128	#123×C₆₁	—	2	2	no	—
129	#123×C₆₁	—	2	4	no	—
130	C₂²⋊Q₈×C₆₁	—	2	2	no	—
131	C₂²⋊Q₈×C₆₁	—	2	4	no	—
132	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
133	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
134	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
135	#121×C₆₁	—	2	4	no	—
136	#121×C₆₁	—	2	2	no	—
137	#121×C₆₁	—	2	4	no	—
138	#121×C₆₁	—	2	4	no	—
139	#121×C₆₁	—	2	4	no	—
140	#121×C₆₁	—	2	2	no	—
141	#121×C₆₁	—	2	4	no	—
142	#121×C₆₁	—	2	2	no	—
143	#121×C₆₁	—	2	4	no	—
144	#121×C₆₁	C₂³	1	4	yes	—
145	#121×C₆₁	C₂³	1	4	yes	—
146	#121×C₆₁	C₂³	1	2	yes	—
147	#121×C₆₁	C₂³	1	4	yes	—
148	#121×C₆₁	C₂³	1	4	yes	—
149	#121×C₆₁	C₂³	1	2	yes	—
150	#121×C₆₁	C₂³	1	4	yes	—
151	#120×C₆₁	—	2	2	no	—
152	#120×C₆₁	—	2	4	no	—
153	#120×C₆₁	—	2	4	no	—
154	#120×C₆₁	—	2	4	no	—
155	#120×C₆₁	—	2	4	no	—
156	C₄×Q₈×C₆₁	—	2	2	no	—
157	C₄×D₄×C₆₁	—	2	4	no	—
158	C₄×D₄×C₆₁	—	2	2	no	—
159	C₄×D₄×C₆₁	—	2	2	no	—
160	C₄×D₄×C₆₁	—	2	4	no	—
161	C₄×D₄×C₆₁	—	2	2	no	—
162	C₄×D₄×C₆₁	—	2	4	no	—
163	#117×C₆₁	C₂³	1	2	yes	—
164	#117×C₆₁	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
168	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
169	#107×C₆₁	C₂³	1	2	yes	—
170	#107×C₆₁	C₂³	1	4	yes	—
171	#106×C₆₁	C₂³	1	2	yes	—
172	#106×C₆₁	C₂³	1	2	yes	—
173	#106×C₆₁	C₂³	1	1	yes	characteristic
174	#106×C₆₁	C₂³	1	1	yes	characteristic
175	#106×C₆₁	C₂³	1	4	yes	—
176	#103×C₆₁	C₂³	1	2	yes	—
177	#103×C₆₁	C₂³	1	2	yes	—
178	#103×C₆₁	C₂³	1	4	yes	—
179	#102×C₆₁	C₂³	1	4	yes	—
180	#102×C₆₁	C₂³	1	4	yes	—
181	#102×C₆₁	C₂³	1	2	yes	—
182	#102×C₆₁	C₂³	1	2	yes	—
183	#102×C₆₁	C₂³	1	4	yes	—
184	#102×C₆₁	C₂³	1	4	yes	—
185	#102×C₆₁	C₂³	1	4	yes	—
186	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
187	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
189	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
190	C₂⁴×C₆₁	—	2	4	no	—
191	C₂⁴×C₆₁	—	2	2	no	—
192	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
194	#41×C₆₁	—	2	4	no	—
195	#41×C₆₁	—	2	4	no	—
196	#41×C₆₁	—	2	4	no	—
197	#41×C₆₁	—	2	4	no	—
198	#41×C₆₁	—	4	2	no	—
199	#41×C₆₁	—	4	2	no	—
200	#41×C₆₁	—	4	4	no	—
201	#41×C₆₁	—	4	4	no	—
202	#41×C₆₁	—	4	4	no	—
203	#41×C₆₁	—	4	4	no	—
204	#41×C₆₁	—	4	8	no	—
205	C₂×Q₈×C₆₁	—	4	2	no	—
206	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₆₁	—	2	2	no	—
210	C₂×D₄×C₆₁	—	2	4	no	—
211	C₂×D₄×C₆₁	—	2	4	no	—
212	C₂×D₄×C₆₁	—	2	2	no	—
213	C₂×D₄×C₆₁	—	2	4	no	—
214	C₂×D₄×C₆₁	—	2	2	no	—
215	C₂×D₄×C₆₁	—	2	4	no	—
216	C₂×D₄×C₆₁	—	2	4	no	—
217	C₂×D₄×C₆₁	—	2	4	no	—
218	C₂×D₄×C₆₁	—	2	4	no	—
219	C₂×D₄×C₆₁	—	2	2	no	—
220	C₂×D₄×C₆₁	—	2	4	no	—
221	C₂×D₄×C₆₁	—	2	4	no	—
222	C₂×D₄×C₆₁	—	4	2	no	—
223	C₂×D₄×C₆₁	—	4	4	no	—
224	C₂×D₄×C₆₁	—	4	4	no	—
225	C₂×D₄×C₆₁	—	4	4	no	—
226	C₂×D₄×C₆₁	—	4	16	no	—
227	C₂×D₄×C₆₁	—	4	8	no	—
228	C₂×D₄×C₆₁	—	8	4	no	—
229	C₂×D₄×C₆₁	—	8	8	no	—
230	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
231	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
232	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
234	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
235	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₆₁	—	2	2	no	—
237	C₂²×C₄×C₆₁	—	2	2	no	—
238	C₂²×C₄×C₆₁	—	2	4	no	—
239	C₂²×C₄×C₆₁	—	2	2	no	—
240	C₂²×C₄×C₆₁	—	2	4	no	—
241	C₂²×C₄×C₆₁	—	2	2	no	—
242	C₂²×C₄×C₆₁	—	4	2	no	—
243	C₂²×C₄×C₆₁	—	4	2	no	—
244	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
248	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
249	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
253	Q₁₆×C₆₁	—	4	1	no	—
254	SD₁₆×C₆₁	—	4	2	no	—
255	SD₁₆×C₆₁	—	4	4	no	—
256	D₈×C₆₁	—	4	2	no	—
257	D₈×C₆₁	—	4	2	no	—
258	D₈×C₆₁	—	4	1	no	—
259	D₈×C₆₁	—	4	4	no	—
260	M₁₆×C₆₁	—	2	4	no	—
261	M₁₆×C₆₁	—	4	1	no	—
262	M₁₆×C₆₁	—	4	1	no	—
263	M₁₆×C₆₁	—	4	1	no	—
264	M₁₆×C₆₁	—	4	1	no	—
265	M₁₆×C₆₁	—	4	2	no	—
266	C₂×C₈×C₆₁	—	2	2	no	—
267	C₂×C₈×C₆₁	—	2	2	no	—
268	C₂×C₈×C₆₁	—	4	2	no	—
269	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
270	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
271	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
272	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
273	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
274	C₄⋊C₄×C₆₁	—	2	4	no	—
275	C₄⋊C₄×C₆₁	—	2	2	no	—
276	C₄⋊C₄×C₆₁	—	2	2	no	—
277	C₄⋊C₄×C₆₁	—	2	4	no	—
278	C₄⋊C₄×C₆₁	—	2	2	no	—
279	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
280	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
282	C₂²⋊C₄×C₆₁	—	2	4	no	—
283	C₂²⋊C₄×C₆₁	—	2	2	no	—
284	C₂²⋊C₄×C₆₁	—	2	2	no	—
285	C₂²⋊C₄×C₆₁	—	2	4	no	—
286	C₂²⋊C₄×C₆₁	—	2	2	no	—
287	C₂²⋊C₄×C₆₁	—	2	4	no	—
288	C₂²⋊C₄×C₆₁	—	2	2	no	—
289	C₂²⋊C₄×C₆₁	—	2	4	no	—
290	C₂²⋊C₄×C₆₁	—	2	4	no	—
291	C₂²⋊C₄×C₆₁	—	2	4	no	—
292	C₂²⋊C₄×C₆₁	—	2	4	no	—
293	C₂²⋊C₄×C₆₁	—	2	2	no	—
294	C₄²×C₆₁	—	2	4	no	—
295	C₄²×C₆₁	—	2	2	no	—
296	C₂³×C₆₁	—	2	2	no	—
297	C₂³×C₆₁	—	2	4	no	—
298	C₂³×C₆₁	—	2	2	no	—
299	C₂³×C₆₁	—	4	2	no	—
300	C₂³×C₆₁	—	4	2	no	—
301	C₂³×C₆₁	—	4	4	no	—
302	C₂³×C₆₁	—	4	8	no	—
303	C₂³×C₆₁	—	4	4	no	—
304	C₂³×C₆₁	—	8	2	no	—
305	C₂³×C₆₁	—	8	4	no	—
306	C₂³×C₆₁	—	8	2	no	—
307	C₂³×C₆₁	—	8	4	no	—
308	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
309	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
310	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
311	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
312	Q₈×C₆₁	—	2	4	no	—
313	Q₈×C₆₁	—	2	2	no	—
314	Q₈×C₆₁	—	2	2	no	—
315	Q₈×C₆₁	—	4	2	no	—
316	D₄×C₆₁	—	2	8	no	—
317	D₄×C₆₁	—	2	4	no	—
318	D₄×C₆₁	—	2	4	no	—
319	D₄×C₆₁	—	2	2	no	—
320	D₄×C₆₁	—	2	4	no	—
321	D₄×C₆₁	—	2	2	no	—
322	D₄×C₆₁	—	4	2	no	—
323	D₄×C₆₁	—	4	4	no	—
324	D₄×C₆₁	—	4	8	no	—
325	D₄×C₆₁	—	4	8	no	—
326	D₄×C₆₁	—	4	8	no	—
327	D₄×C₆₁	—	4	4	no	—
328	D₄×C₆₁	—	4	4	no	—
329	D₄×C₆₁	—	4	4	no	—
330	D₄×C₆₁	—	8	4	no	—
331	D₄×C₆₁	—	8	2	no	—
332	D₄×C₆₁	—	8	4	no	—
333	D₄×C₆₁	—	8	4	no	—
334	D₄×C₆₁	—	8	4	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	2	2	no	—
337	C₂×C₄×C₆₁	—	2	2	no	—
338	C₂×C₄×C₆₁	—	2	1	no	—
339	C₂×C₄×C₆₁	—	2	1	no	—
340	C₂×C₄×C₆₁	—	2	1	no	—
341	C₂×C₄×C₆₁	—	2	1	no	—
342	C₂×C₄×C₆₁	—	2	4	no	—
343	C₂×C₄×C₆₁	—	2	4	no	—
344	C₂×C₄×C₆₁	—	2	2	no	—
345	C₂×C₄×C₆₁	—	2	4	no	—
346	C₂×C₄×C₆₁	—	2	2	no	—
347	C₂×C₄×C₆₁	—	2	2	no	—
348	C₂×C₄×C₆₁	—	4	2	no	—
349	C₂×C₄×C₆₁	—	4	4	no	—
350	C₂×C₄×C₆₁	—	4	8	no	—
351	C₂×C₄×C₆₁	—	4	4	no	—
352	C₂×C₄×C₆₁	—	8	2	no	—
353	C₂×C₄×C₆₁	—	8	4	no	—
354	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
355	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
359	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
360	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
361	C₈×C₆₁	—	2	1	no	—
362	C₈×C₆₁	—	2	1	no	—
363	C₈×C₆₁	—	2	1	no	—
364	C₈×C₆₁	—	2	1	no	—
365	C₈×C₆₁	—	2	4	no	—
366	#60771	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₂²×C₆₁	—	2	2	no	—
368	C₂²×C₆₁	—	2	4	no	—
369	C₂²×C₆₁	—	2	2	no	—
370	C₂²×C₆₁	—	2	2	no	—
371	C₂²×C₆₁	—	2	4	no	—
372	C₂²×C₆₁	—	2	1	no	—
373	C₂²×C₆₁	—	2	1	no	—
374	C₂²×C₆₁	—	2	4	no	—
375	C₂²×C₆₁	—	4	4	no	—
376	C₂²×C₆₁	—	4	2	no	—
377	C₂²×C₆₁	—	4	4	no	—
378	C₂²×C₆₁	—	4	2	no	—
379	C₂²×C₆₁	—	4	4	no	—
380	C₂²×C₆₁	—	4	2	no	—
381	C₂²×C₆₁	—	8	2	no	—
382	C₂²×C₆₁	—	8	4	no	—
383	C₂²×C₆₁	—	16	4	no	—
384	C₂²×C₆₁	—	16	8	no	—
385	C₂²×C₆₁	#534	1	2	yes	—
386	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
387	C₄×C₆₁	—	2	1	no	—
388	C₄×C₆₁	—	2	1	no	—
389	C₄×C₆₁	—	2	4	no	—
390	C₄×C₆₁	—	4	4	no	—
391	C₄×C₆₁	—	4	2	no	—
392	C₄×C₆₁	—	4	2	no	—
393	C₄×C₆₁	—	4	2	no	—
394	C₄×C₆₁	#534	1	2	yes	—
395	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
397	#3488	C₂×C₆₁	1	2	yes	complemented
398	#3204	C₂×C₆₁	1	2	yes	complemented
399	#3199	C₂×C₆₁	1	2	yes	complemented
400	#3198	C₂×C₆₁	1	4	yes	complemented
401	#3197	C₂×C₆₁	1	2	yes	complemented
402	#3194	C₂×C₆₁	1	4	yes	complemented
403	#3192	C₂×C₆₁	1	2	yes	complemented
404	#3099	C₂×C₆₁	1	2	yes	complemented
405	#3096	C₂×C₆₁	1	2	yes	complemented
406	#3055	C₂×C₆₁	1	2	yes	complemented
407	#3054	C₂×C₆₁	1	1	yes	characteristic, complemented
408	C₂×#469	C₂×C₆₁	1	1	yes	characteristic, complemented
409	#3012	C₂×C₆₁	1	2	yes	complemented
410	#3008	C₂×C₆₁	1	2	yes	complemented
411	#2879	C₂×C₆₁	1	1	yes	characteristic, complemented
412	C₂×C₆₁	—	2	2	no	—
413	C₂×C₆₁	—	4	1	no	—
414	C₂×C₆₁	—	4	1	no	—
415	C₂×C₆₁	—	4	4	no	—
416	C₂×C₆₁	—	8	4	no	—
417	C₂×C₆₁	—	8	2	no	—
418	C₂×C₆₁	C₂×#534	1	1	yes	characteristic
419	C₂×C₆₁	#3585	1	2	yes	—
420	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	2	yes	complemented
421	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
422	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	complemented
423	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic, complemented
424	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
425	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
426	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
427	#550	—	2	2	no	—
428	#548	—	2	2	no	—
429	#546	—	2	4	no	—
430	#546	—	2	2	no	—
431	D₄²	—	2	4	no	—
432	D₄²	—	2	2	no	—
433	#537	C₂²×C₆₁	1	2	yes	—
434	#537	C₂²×C₆₁	1	4	yes	complemented
435	#535	C₂²×C₆₁	1	2	yes	—
436	#535	C₂²×C₆₁	1	4	yes	complemented
437	#525	C₂²×C₆₁	1	4	yes	complemented
438	#525	C₂²×C₆₁	1	2	yes	complemented
439	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
440	C₂×#121	C₂²×C₆₁	1	2	yes	complemented
441	#520	C₂²×C₆₁	1	2	yes	complemented
442	#485	C₂²×C₆₁	1	4	yes	complemented
443	#483	C₂²×C₆₁	1	4	yes	complemented
444	#482	C₂²×C₆₁	1	4	yes	complemented
445	#482	C₂²×C₆₁	1	4	yes	complemented
446	#482	C₂²×C₆₁	1	4	yes	complemented
447	#481	C₂²×C₆₁	1	4	yes	complemented
448	#481	C₂²×C₆₁	1	4	yes	complemented
449	#480	C₂²×C₆₁	1	4	yes	complemented
450	#470	C₂²×C₆₁	1	1	yes	characteristic, complemented
451	#470	C₂²×C₆₁	1	1	yes	characteristic, complemented
452	#469	C₂²×C₆₁	1	1	yes	characteristic, complemented
453	#469	C₂²×C₆₁	1	4	yes	complemented
454	#469	C₂²×C₆₁	1	2	yes	complemented
455	#469	C₂²×C₆₁	1	2	yes	complemented
456	#469	C₂²×C₆₁	1	2	yes	complemented
457	#469	C₂²×C₆₁	1	1	yes	characteristic, complemented
458	#469	C₂²×C₆₁	1	2	yes	complemented
459	#468	C₂²×C₆₁	1	2	yes	complemented
460	#468	C₂²×C₆₁	1	4	yes	complemented
461	#468	C₂²×C₆₁	1	2	yes	complemented
462	#466	C₂²×C₆₁	1	4	yes	complemented
463	#465	C₂²×C₆₁	1	4	yes	complemented
464	#452	C₂²×C₆₁	1	4	yes	complemented
465	#450	C₂²×C₆₁	1	4	yes	complemented
466	#449	C₂²×C₆₁	1	4	yes	complemented
467	#449	C₂²×C₆₁	1	4	yes	complemented
468	#449	C₂²×C₆₁	1	4	yes	complemented
469	#447	C₂²×C₆₁	1	4	yes	complemented
470	#447	C₂²×C₆₁	1	4	yes	complemented
471	#447	C₂²×C₆₁	1	4	yes	complemented
472	#428	C₂²×C₆₁	1	2	yes	complemented
473	#427	C₂²×C₆₁	1	1	yes	characteristic, complemented
474	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
475	#418	C₂²×C₆₁	1	2	yes	complemented
476	#417	C₂²×C₆₁	1	2	yes	complemented
477	#416	C₂²×C₆₁	1	2	yes	complemented
478	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
479	#408	C₂²×C₆₁	1	2	yes	complemented
480	#408	C₂²×C₆₁	1	2	yes	complemented
481	#408	C₂²×C₆₁	1	2	yes	complemented
482	#408	C₂²×C₆₁	1	2	yes	complemented
483	#407	C₂²×C₆₁	1	2	yes	complemented
484	#407	C₂²×C₆₁	1	2	yes	complemented
485	C₆₁	#60771	1	1	yes	characteristic, direct product factor, Sylow
486	H(5,𝔽₂)	—	4	4	no	—
487	H(5,𝔽₂)	—	4	4	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	—	4	2	no	—
490	C₂×#41	—	4	2	no	—
491	C₂×#41	D₄×C₆₁	1	2	yes	—
492	C₂×#41	D₄×C₆₁	1	2	yes	—
493	C₂×#41	C₂³×C₆₁	1	2	yes	—
494	C₂×#41	C₂³×C₆₁	1	4	yes	—
495	C₂×#41	C₂³×C₆₁	1	2	yes	—
496	C₂×#41	C₂³×C₆₁	1	2	yes	—
497	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	4	no	—
500	C₂²×D₄	—	2	4	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
503	C₂²×D₄	D₄×C₆₁	1	2	yes	—
504	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
505	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
506	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
508	AGL(1,ℤ/8)	—	4	4	no	—
509	#135	—	4	2	no	—
510	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
511	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
512	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
513	C₂×D₈	—	4	2	no	—
514	C₂×D₈	C₂³×C₆₁	1	2	yes	—
515	C₂×D₈	C₂³×C₆₁	1	2	yes	—
516	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
517	C₂×D₈	C₂³×C₆₁	1	4	yes	—
518	C₂×M₁₆	—	4	2	no	—
519	C₂×M₁₆	—	4	2	no	—
520	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
521	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
522	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
523	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
524	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
525	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
526	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
527	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
528	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
529	#127	—	2	2	no	—
530	#127	—	2	4	no	—
531	#124	—	2	2	no	—
532	#124	—	2	4	no	—
533	#123	—	2	2	no	—
534	#123	—	2	4	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
538	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
539	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
540	#121	—	2	4	no	—
541	#121	—	2	2	no	—
542	#121	—	2	4	no	—
543	#121	—	2	4	no	—
544	#121	—	2	4	no	—
545	#121	—	2	2	no	—
546	#121	—	2	4	no	—
547	#121	—	2	2	no	—
548	#121	—	2	4	no	—
549	#121	C₂³×C₆₁	1	2	yes	—
550	#121	C₂³×C₆₁	1	4	yes	—
551	#121	C₂³×C₆₁	1	4	yes	—
552	#121	C₂³×C₆₁	1	4	yes	—
553	#121	C₂³×C₆₁	1	4	yes	—
554	#121	C₂³×C₆₁	1	4	yes	—
555	#121	C₂³×C₆₁	1	2	yes	—
556	#120	—	2	2	no	—
557	#120	—	2	4	no	—
558	#120	—	2	4	no	—
559	#120	—	2	4	no	—
560	#120	—	2	4	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	4	no	—
568	#117	C₂³×C₆₁	1	2	yes	—
569	#117	C₂³×C₆₁	1	4	yes	—
570	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
572	C₂×C₂²⋊C₄	—	2	2	no	—
573	C₂×C₂²⋊C₄	—	2	4	no	—
574	#107	C₂³×C₆₁	1	2	yes	—
575	#107	C₂³×C₆₁	1	4	yes	—
576	#106	C₂³×C₆₁	1	2	yes	—
577	#106	C₂³×C₆₁	1	2	yes	—
578	#106	C₂³×C₆₁	1	1	yes	characteristic
579	#106	C₂³×C₆₁	1	1	yes	characteristic
580	#106	C₂³×C₆₁	1	4	yes	—
581	#103	C₂³×C₆₁	1	2	yes	—
582	#103	C₂³×C₆₁	1	2	yes	—
583	#103	C₂³×C₆₁	1	4	yes	—
584	#102	C₂³×C₆₁	1	4	yes	—
585	#102	C₂³×C₆₁	1	4	yes	—
586	#102	C₂³×C₆₁	1	2	yes	—
587	#102	C₂³×C₆₁	1	2	yes	—
588	#102	C₂³×C₆₁	1	4	yes	—
589	#102	C₂³×C₆₁	1	4	yes	—
590	#102	C₂³×C₆₁	1	4	yes	—
591	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
592	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
593	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
594	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
595	C₂⁴	—	2	4	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
598	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
599	#41	—	2	4	no	—
600	#41	—	2	4	no	—
601	#41	—	2	4	no	—
602	#41	—	2	4	no	—
603	#41	—	4	2	no	—
604	#41	—	4	2	no	—
605	#41	—	4	4	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	4	no	—
609	#41	—	4	8	no	—
610	C₂×Q₈	—	4	2	no	—
611	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
612	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
613	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	4	16	no	—
632	C₂×D₄	—	4	8	no	—
633	C₂×D₄	—	8	4	no	—
634	C₂×D₄	—	8	8	no	—
635	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
636	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
637	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
638	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
639	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
640	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
653	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
655	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
658	Q₁₆	—	4	1	no	—
659	SD₁₆	—	4	2	no	—
660	SD₁₆	—	4	4	no	—
661	D₈	—	4	2	no	—
662	D₈	—	4	2	no	—
663	D₈	—	4	1	no	—
664	D₈	—	4	4	no	—
665	M₁₆	—	2	4	no	—
666	M₁₆	—	4	1	no	—
667	M₁₆	—	4	1	no	—
668	M₁₆	—	4	1	no	—
669	M₁₆	—	4	1	no	—
670	M₁₆	—	4	2	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	2	2	no	—
673	C₂×C₈	—	4	2	no	—
674	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
675	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
676	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
677	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
678	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
685	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
686	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	4	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	4	2	no	—
705	C₂³	—	4	2	no	—
706	C₂³	—	4	4	no	—
707	C₂³	—	4	8	no	—
708	C₂³	—	4	4	no	—
709	C₂³	—	8	2	no	—
710	C₂³	—	8	4	no	—
711	C₂³	—	8	2	no	—
712	C₂³	—	8	4	no	—
713	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
714	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
715	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
716	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
717	Q₈	—	2	4	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	4	2	no	—
721	D₄	—	2	8	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	4	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	4	no	—
726	D₄	—	2	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	4	no	—
733	D₄	—	4	4	no	—
734	D₄	—	4	4	no	—
735	D₄	—	8	4	no	—
736	D₄	—	8	2	no	—
737	D₄	—	8	4	no	—
738	D₄	—	8	4	no	—
739	D₄	—	8	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	8	2	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
760	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
763	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
764	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
765	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
766	C₈	—	2	1	no	—
767	C₈	—	2	1	no	—
768	C₈	—	2	1	no	—
769	C₈	—	2	1	no	—
770	C₈	—	2	4	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	4	4	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	4	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	8	2	no	—
786	C₂²	—	8	4	no	—
787	C₂²	—	16	4	no	—
788	C₂²	—	16	8	no	—
789	C₂²	C₆₁×#534	1	2	yes	—
790	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	4	no	—
794	C₄	—	4	4	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	C₆₁×#534	1	2	yes	—
799	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
800	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
801	C₂	—	2	2	no	—
802	C₂	—	4	1	no	—
803	C₂	—	4	4	no	—
804	C₂	—	4	1	no	—
805	C₂	—	8	4	no	—
806	C₂	—	8	2	no	—
807	C₂	C₂×C₆₁×#534	1	1	yes	characteristic
808	C₂	C₆₁×#3585	1	2	yes	—

	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 ◁ C₂²×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3488	C₂	semidirect
2. C₆₁×#3204	C₂	semidirect
3. C₆₁×#3199	C₂	semidirect
4. C₆₁×#3198	C₂	semidirect
5. C₆₁×#3197	C₂	semidirect
6. C₆₁×#3194	C₂	semidirect
7. C₆₁×#3192	C₂	semidirect
8. C₆₁×#3099	C₂	semidirect
9. C₆₁×#3096	C₂	semidirect
10. C₆₁×#3055	C₂	semidirect
11. C₆₁×#3054	C₂	semidirect
12. C₂×C₆₁×#469	C₂	semidirect
13. C₆₁×#3012	C₂	semidirect
14. C₆₁×#3008	C₂	semidirect
15. C₆₁×#2879	C₂	semidirect
16. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
18. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
19. C₂×#135×C₆₁	C₂²	semidirect
20. C₂²×D₈×C₆₁	C₂²	semidirect
21. C₂²×M₁₆×C₆₁	C₂²	semidirect
22. C₂²×M₁₆×C₆₁	C₂²	semidirect
30. C₆₁×#537	C₂²	semidirect
32. C₆₁×#535	C₂²	semidirect
33. C₆₁×#525	C₂²	semidirect
34. C₆₁×#525	C₂²	semidirect
35. C₂×#121×C₆₁	C₂²	semidirect
36. C₂×#121×C₆₁	C₂²	semidirect
37. C₆₁×#520	C₂²	semidirect
38. C₆₁×#485	C₂²	semidirect
39. C₆₁×#483	C₂²	semidirect
40. C₆₁×#482	C₂²	semidirect
41. C₆₁×#482	C₂²	semidirect
42. C₆₁×#482	C₂²	semidirect
43. C₆₁×#481	C₂²	semidirect
44. C₆₁×#481	C₂²	semidirect
45. C₆₁×#480	C₂²	semidirect
46. C₆₁×#470	C₂²	semidirect
47. C₆₁×#470	C₂²	semidirect
48. C₆₁×#469	C₂²	semidirect
49. C₆₁×#469	C₂²	semidirect
50. C₆₁×#469	C₂²	semidirect
51. C₆₁×#469	C₂²	semidirect
52. C₆₁×#469	C₂²	semidirect
53. C₆₁×#469	C₂²	semidirect
54. C₆₁×#469	C₂²	semidirect
55. C₆₁×#468	C₂²	semidirect
56. C₆₁×#468	C₂²	semidirect
57. C₆₁×#468	C₂²	semidirect
58. C₆₁×#466	C₂²	semidirect
59. C₆₁×#465	C₂²	semidirect
60. C₆₁×#452	C₂²	semidirect
61. C₆₁×#450	C₂²	semidirect
62. C₆₁×#449	C₂²	semidirect
63. C₆₁×#449	C₂²	semidirect
64. C₆₁×#449	C₂²	semidirect
65. C₆₁×#447	C₂²	semidirect
66. C₆₁×#447	C₂²	semidirect
67. C₆₁×#447	C₂²	semidirect
68. C₆₁×#428	C₂²	semidirect
69. C₆₁×#427	C₂²	semidirect
70. C₂×#106×C₆₁	C₂²	semidirect
71. C₆₁×#418	C₂²	semidirect
72. C₆₁×#417	C₂²	semidirect
73. C₆₁×#416	C₂²	semidirect
74. C₂×#102×C₆₁	C₂²	semidirect
75. C₆₁×#408	C₂²	semidirect
76. C₆₁×#408	C₂²	semidirect
77. C₆₁×#408	C₂²	semidirect
78. C₆₁×#408	C₂²	semidirect
79. C₆₁×#407	C₂²	semidirect
80. C₆₁×#407	C₂²	semidirect
366. #60771	C₆₁	direct (N × H)
397. #3488	C₂×C₆₁	semidirect
398. #3204	C₂×C₆₁	semidirect
399. #3199	C₂×C₆₁	semidirect
400. #3198	C₂×C₆₁	semidirect
401. #3197	C₂×C₆₁	semidirect
402. #3194	C₂×C₆₁	semidirect
403. #3192	C₂×C₆₁	semidirect
404. #3099	C₂×C₆₁	semidirect
405. #3096	C₂×C₆₁	semidirect
406. #3055	C₂×C₆₁	semidirect
407. #3054	C₂×C₆₁	semidirect
408. C₂×#469	C₂×C₆₁	semidirect
409. #3012	C₂×C₆₁	semidirect
410. #3008	C₂×C₆₁	semidirect
411. #2879	C₂×C₆₁	semidirect
420. C₂×H(5,𝔽₂)	C₂²×C₆₁	semidirect
422. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
423. C₂×#135	C₂²×C₆₁	semidirect
424. C₂²×D₈	C₂²×C₆₁	semidirect
425. C₂²×M₁₆	C₂²×C₆₁	semidirect
426. C₂²×M₁₆	C₂²×C₆₁	semidirect
434. #537	C₂²×C₆₁	semidirect
436. #535	C₂²×C₆₁	semidirect
437. #525	C₂²×C₆₁	semidirect
438. #525	C₂²×C₆₁	semidirect
439. C₂×#121	C₂²×C₆₁	semidirect
440. C₂×#121	C₂²×C₆₁	semidirect
441. #520	C₂²×C₆₁	semidirect
442. #485	C₂²×C₆₁	semidirect
443. #483	C₂²×C₆₁	semidirect
444. #482	C₂²×C₆₁	semidirect
445. #482	C₂²×C₆₁	semidirect
446. #482	C₂²×C₆₁	semidirect
447. #481	C₂²×C₆₁	semidirect
448. #481	C₂²×C₆₁	semidirect
449. #480	C₂²×C₆₁	semidirect
450. #470	C₂²×C₆₁	semidirect
451. #470	C₂²×C₆₁	semidirect
452. #469	C₂²×C₆₁	semidirect
453. #469	C₂²×C₆₁	semidirect
454. #469	C₂²×C₆₁	semidirect
455. #469	C₂²×C₆₁	semidirect
456. #469	C₂²×C₆₁	semidirect
457. #469	C₂²×C₆₁	semidirect
458. #469	C₂²×C₆₁	semidirect
459. #468	C₂²×C₆₁	semidirect
460. #468	C₂²×C₆₁	semidirect
461. #468	C₂²×C₆₁	semidirect
462. #466	C₂²×C₆₁	semidirect
463. #465	C₂²×C₆₁	semidirect
464. #452	C₂²×C₆₁	semidirect
465. #450	C₂²×C₆₁	semidirect
466. #449	C₂²×C₆₁	semidirect
467. #449	C₂²×C₆₁	semidirect
468. #449	C₂²×C₆₁	semidirect
469. #447	C₂²×C₆₁	semidirect
470. #447	C₂²×C₆₁	semidirect
471. #447	C₂²×C₆₁	semidirect
472. #428	C₂²×C₆₁	semidirect
473. #427	C₂²×C₆₁	semidirect
474. C₂×#106	C₂²×C₆₁	semidirect
475. #418	C₂²×C₆₁	semidirect
476. #417	C₂²×C₆₁	semidirect
477. #416	C₂²×C₆₁	semidirect
478. C₂×#102	C₂²×C₆₁	semidirect
479. #408	C₂²×C₆₁	semidirect
480. #408	C₂²×C₆₁	semidirect
481. #408	C₂²×C₆₁	semidirect
482. #408	C₂²×C₆₁	semidirect
483. #407	C₂²×C₆₁	semidirect
484. #407	C₂²×C₆₁	semidirect
485. C₆₁	#60771	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×#3488	2
C₆₁×#3204	2
C₆₁×#3199	2
C₆₁×#3198	2
C₆₁×#3197	2
C₆₁×#3194	2
C₆₁×#3192	2
C₆₁×#3099	2
C₆₁×#3096	2
C₆₁×#3055	2
C₆₁×#3054	2
C₂×C₆₁×#469	2
C₆₁×#3012	2
C₆₁×#3008	2
C₆₁×#2879	2
#60771	61

Subgroups — C61×#60771 #29564204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60771 #29564204