Subgroups — C₆₁×#61209 #29564642

Order 15616.

2078 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3330	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3329	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3320	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3307	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3303	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3298	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3097	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3057	C₂	1	2	yes	maximal, complemented
13	C₂×C₆₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3010	C₂	1	2	yes	maximal, complemented
15	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2898	C₂	1	2	yes	maximal, complemented
18	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
21	C₂×#131×C₆₁	C₂²	1	2	yes	—
22	C₆₁×#559	—	2	2	no	—
23	C₆₁×#556	—	2	1	no	—
24	C₆₁×#555	C₂²	1	2	yes	—
25	C₆₁×#553	C₂²	1	4	yes	—
26	C₆₁×#550	—	2	1	no	—
27	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
28	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
29	C₆₁×#547	—	2	2	no	—
30	C₆₁×#547	—	2	2	no	—
31	C₆₁×#547	C₂²	1	2	yes	—
32	C₆₁×#547	C₂²	1	2	yes	complemented
33	C₆₁×#547	C₂²	1	2	yes	complemented
34	C₆₁×#538	—	2	2	no	—
35	C₆₁×#536	—	2	2	no	—
36	C₆₁×#536	C₂²	1	2	yes	—
37	C₆₁×#535	C₂²	1	2	yes	—
38	C₆₁×#533	C₂²	1	1	yes	characteristic
39	C₆₁×#532	—	2	1	no	—
40	C₆₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
42	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#525	—	2	2	no	—
44	C₆₁×#520	C₂²	1	2	yes	—
45	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
47	C₆₁×#491	C₂²	1	4	yes	complemented
48	C₆₁×#487	C₂²	1	2	yes	complemented
49	C₆₁×#487	C₂²	1	2	yes	complemented
50	C₆₁×#485	C₂²	1	4	yes	complemented
51	C₆₁×#485	C₂²	1	4	yes	complemented
52	C₆₁×#484	C₂²	1	4	yes	complemented
53	C₆₁×#483	C₂²	1	4	yes	complemented
54	C₆₁×#479	C₂²	1	2	yes	complemented
55	C₆₁×#478	C₂²	1	2	yes	complemented
56	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
57	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
58	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
59	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#468	C₂²	1	4	yes	—
61	C₆₁×#468	C₂²	1	4	yes	—
62	C₆₁×#465	C₂²	1	4	yes	—
63	C₆₁×#465	C₂²	1	4	yes	—
64	C₆₁×#461	C₂²	1	2	yes	—
65	C₆₁×#461	C₂²	1	4	yes	—
66	C₆₁×#461	C₂²	1	2	yes	—
67	C₆₁×#449	C₂²	1	4	yes	—
68	C₆₁×#449	C₂²	1	4	yes	—
69	C₆₁×#448	C₂²	1	4	yes	—
70	C₆₁×#448	C₂²	1	4	yes	—
71	C₆₁×#442	C₂²	1	2	yes	—
72	C₆₁×#440	C₂²	1	2	yes	—
73	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
74	C₄×D₈×C₆₁	C₂²	1	2	yes	—
75	C₆₁×#436	C₂²	1	2	yes	complemented
76	C₆₁×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
78	C₆₁×#428	C₂²	1	1	yes	characteristic
79	C₆₁×#427	C₂²	1	2	yes	—
80	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
81	C₆₁×#419	C₂²	1	2	yes	—
82	C₆₁×#419	C₂²	1	2	yes	—
83	C₆₁×#419	C₂²	1	4	yes	complemented
84	C₆₁×#418	C₂²	1	1	yes	characteristic
85	C₆₁×#417	C₂²	1	1	yes	characteristic
86	C₆₁×#417	C₂²	1	4	yes	complemented
87	C₆₁×#416	C₂²	1	2	yes	—
88	C₆₁×#416	C₂²	1	4	yes	complemented
89	C₂×#103×C₆₁	C₂²	1	2	yes	—
90	C₂×#103×C₆₁	C₂²	1	4	yes	complemented
91	C₆₁×#408	C₂²	1	2	yes	—
92	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
93	2₋¹⁺⁴×C₆₁	—	2	8	no	—
94	2₋¹⁺⁴×C₆₁	—	4	4	no	—
95	C₂×#41×C₆₁	—	2	2	no	—
96	C₂×#41×C₆₁	—	2	4	no	—
97	C₂×#41×C₆₁	—	2	2	no	—
98	C₂×#41×C₆₁	C₂³	1	4	yes	—
99	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×#41×C₆₁	C₂³	1	2	yes	—
101	C₂²×Q₈×C₆₁	—	2	2	no	—
102	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
103	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
104	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₆₁	—	2	1	no	—
106	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
107	C₂×SD₁₆×C₆₁	—	4	4	no	—
108	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
111	C₂×D₈×C₆₁	C₂³	1	2	yes	—
112	#131×C₆₁	—	4	4	no	—
113	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
114	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
116	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
117	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
118	C₄⋊Q₈×C₆₁	—	2	2	no	—
119	C₄⋊Q₈×C₆₁	—	2	2	no	—
120	C₄⋊Q₈×C₆₁	—	2	2	no	—
121	C₄⋊Q₈×C₆₁	—	2	1	no	—
122	C₄⋊Q₈×C₆₁	—	2	1	no	—
123	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
124	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
125	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
126	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
127	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
128	#127×C₆₁	—	2	2	no	—
129	#127×C₆₁	D₄	1	1	yes	characteristic
130	#126×C₆₁	—	2	4	no	—
131	#125×C₆₁	C₂³	1	2	yes	—
132	#124×C₆₁	—	2	2	no	—
133	#124×C₆₁	—	2	2	no	—
134	#124×C₆₁	—	2	4	no	—
135	#124×C₆₁	D₄	1	2	yes	—
136	#123×C₆₁	—	2	4	no	—
137	#123×C₆₁	—	2	4	no	—
138	#123×C₆₁	—	2	4	no	—
139	#123×C₆₁	—	2	4	no	—
140	#123×C₆₁	—	2	4	no	—
141	C₂²⋊Q₈×C₆₁	—	2	1	no	—
142	C₂²⋊Q₈×C₆₁	—	2	1	no	—
143	C₂²⋊Q₈×C₆₁	—	2	2	no	—
144	C₂²⋊Q₈×C₆₁	—	2	4	no	—
145	C₂²⋊Q₈×C₆₁	—	2	4	no	—
146	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
147	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
148	#121×C₆₁	—	2	2	no	—
149	#121×C₆₁	—	2	2	no	—
150	#121×C₆₁	—	2	4	no	—
151	#121×C₆₁	—	2	2	no	—
152	#121×C₆₁	D₄	1	2	yes	—
153	#121×C₆₁	D₄	1	2	yes	—
154	#121×C₆₁	C₂³	1	4	yes	—
155	#121×C₆₁	C₂³	1	4	yes	—
156	#120×C₆₁	—	2	4	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	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
162	C₄×D₄×C₆₁	—	2	2	no	—
163	C₄×D₄×C₆₁	—	2	2	no	—
164	C₄×D₄×C₆₁	—	2	4	no	—
165	C₄×D₄×C₆₁	—	2	2	no	—
166	C₄×D₄×C₆₁	—	2	1	no	—
167	C₄×D₄×C₆₁	—	2	1	no	—
168	C₄×D₄×C₆₁	—	2	4	no	—
169	C₄×D₄×C₆₁	—	2	1	no	—
170	C₄×D₄×C₆₁	—	2	1	no	—
171	C₄×D₄×C₆₁	C₂³	1	2	yes	—
172	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₆₁	C₂³	1	2	yes	—
175	C₄×D₄×C₆₁	C₂³	1	2	yes	—
176	C₄×D₄×C₆₁	C₂³	1	2	yes	—
177	#117×C₆₁	—	2	2	no	—
178	#117×C₆₁	—	2	1	no	—
179	#117×C₆₁	C₂³	1	2	yes	—
180	#117×C₆₁	C₂³	1	1	yes	characteristic
181	#117×C₆₁	C₂³	1	4	yes	—
182	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
183	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
184	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
185	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
186	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
189	C₂×C₄²×C₆₁	—	2	1	no	—
190	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
191	#107×C₆₁	C₂³	1	2	yes	—
192	#107×C₆₁	C₂³	1	2	yes	—
193	#107×C₆₁	C₂³	1	2	yes	—
194	#106×C₆₁	C₂³	1	2	yes	—
195	#106×C₆₁	C₂³	1	2	yes	—
196	#106×C₆₁	C₂³	1	2	yes	—
197	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
198	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
199	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
200	#103×C₆₁	C₂³	1	4	yes	—
201	#103×C₆₁	C₂³	1	4	yes	—
202	#103×C₆₁	C₂³	1	2	yes	—
203	#103×C₆₁	C₂³	1	2	yes	—
204	#103×C₆₁	C₂³	1	4	yes	—
205	#103×C₆₁	C₂³	1	2	yes	—
206	#103×C₆₁	C₂³	1	4	yes	—
207	#103×C₆₁	C₂³	1	4	yes	—
208	#103×C₆₁	C₂³	1	4	yes	—
209	#102×C₆₁	C₂³	1	2	yes	—
210	#102×C₆₁	C₂³	1	2	yes	—
211	#102×C₆₁	C₂³	1	2	yes	—
212	#102×C₆₁	C₂³	1	2	yes	—
213	#102×C₆₁	C₂³	1	2	yes	—
214	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
215	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
216	#97×C₆₁	C₂³	1	2	yes	—
217	C₄×C₈×C₆₁	C₂³	1	2	yes	—
218	C₂⁴×C₆₁	—	2	1	no	—
219	#41×C₆₁	—	2	4	no	—
220	#41×C₆₁	—	2	4	no	—
221	#41×C₆₁	—	2	2	no	—
222	#41×C₆₁	—	2	8	no	—
223	#41×C₆₁	—	4	4	no	—
224	#41×C₆₁	—	4	8	no	—
225	#41×C₆₁	—	4	16	no	—
226	#41×C₆₁	—	8	4	no	—
227	#41×C₆₁	#41	1	4	yes	complemented
228	C₂×Q₈×C₆₁	—	2	1	no	—
229	C₂×Q₈×C₆₁	—	2	4	no	—
230	C₂×Q₈×C₆₁	—	2	2	no	—
231	C₂×Q₈×C₆₁	—	2	1	no	—
232	C₂×Q₈×C₆₁	—	2	8	no	—
233	C₂×Q₈×C₆₁	—	2	4	no	—
234	C₂×Q₈×C₆₁	—	2	4	no	—
235	C₂×Q₈×C₆₁	—	4	4	no	—
236	C₂×Q₈×C₆₁	—	4	8	no	—
237	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
238	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
239	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
240	C₂×D₄×C₆₁	—	2	1	no	—
241	C₂×D₄×C₆₁	—	2	4	no	—
242	C₂×D₄×C₆₁	—	2	4	no	—
243	C₂×D₄×C₆₁	—	2	4	no	—
244	C₂×D₄×C₆₁	—	2	1	no	—
245	C₂×D₄×C₆₁	—	2	2	no	—
246	C₂×D₄×C₆₁	—	2	2	no	—
247	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
249	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
252	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₁	—	2	1	no	—
254	C₂²×C₄×C₆₁	—	2	2	no	—
255	C₂²×C₄×C₆₁	—	2	4	no	—
256	C₂²×C₄×C₆₁	—	2	1	no	—
257	C₂²×C₄×C₆₁	—	2	4	no	—
258	C₂²×C₄×C₆₁	—	2	1	no	—
259	C₂²×C₄×C₆₁	—	2	1	no	—
260	C₂²×C₄×C₆₁	—	2	4	no	—
261	C₂²×C₄×C₆₁	—	2	2	no	—
262	C₂²×C₄×C₆₁	—	2	2	no	—
263	C₂²×C₄×C₆₁	—	8	2	no	—
264	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
268	SD₁₆×C₆₁	—	2	4	no	—
269	SD₁₆×C₆₁	—	4	4	no	—
270	SD₁₆×C₆₁	—	4	4	no	—
271	D₈×C₆₁	—	2	4	no	—
272	M₁₆×C₆₁	—	2	2	no	—
273	M₁₆×C₆₁	—	2	2	no	—
274	M₁₆×C₆₁	—	4	4	no	—
275	C₂×C₈×C₆₁	—	2	4	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	2	yes	—
280	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₁	—	2	2	no	—
282	C₄⋊C₄×C₆₁	—	2	2	no	—
283	C₄⋊C₄×C₆₁	—	2	2	no	—
284	C₄⋊C₄×C₆₁	—	2	2	no	—
285	C₄⋊C₄×C₆₁	—	2	4	no	—
286	C₄⋊C₄×C₆₁	—	2	4	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	1	no	—
292	C₄⋊C₄×C₆₁	—	2	2	no	—
293	C₄⋊C₄×C₆₁	—	2	2	no	—
294	C₄⋊C₄×C₆₁	—	2	1	no	—
295	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
299	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
302	C₂²⋊C₄×C₆₁	—	2	2	no	—
303	C₂²⋊C₄×C₆₁	—	2	4	no	—
304	C₂²⋊C₄×C₆₁	—	2	1	no	—
305	C₂²⋊C₄×C₆₁	—	2	4	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	1	no	—
310	C₂²⋊C₄×C₆₁	—	2	1	no	—
311	C₂²⋊C₄×C₆₁	—	2	4	no	—
312	C₂²⋊C₄×C₆₁	—	2	4	no	—
313	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
314	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
315	C₄²×C₆₁	—	2	1	no	—
316	C₄²×C₆₁	—	2	1	no	—
317	C₄²×C₆₁	—	2	1	no	—
318	C₄²×C₆₁	—	2	4	no	—
319	C₄²×C₆₁	—	2	2	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	1	yes	characteristic
324	C₂³×C₆₁	—	2	1	no	—
325	C₂³×C₆₁	—	2	2	no	—
326	C₂³×C₆₁	—	4	2	no	—
327	C₂³×C₆₁	—	8	1	no	—
328	C₂³×C₆₁	—	8	1	no	—
329	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
330	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₆₁	—	2	4	no	—
332	Q₈×C₆₁	—	2	1	no	—
333	Q₈×C₆₁	—	2	4	no	—
334	Q₈×C₆₁	—	2	4	no	—
335	Q₈×C₆₁	—	4	8	no	—
336	Q₈×C₆₁	—	4	4	no	—
337	Q₈×C₆₁	—	4	2	no	—
338	Q₈×C₆₁	—	8	1	no	—
339	Q₈×C₆₁	C₂×#41	1	2	yes	—
340	D₄×C₆₁	—	2	4	no	—
341	D₄×C₆₁	—	2	8	no	—
342	D₄×C₆₁	—	2	4	no	—
343	D₄×C₆₁	—	2	4	no	—
344	D₄×C₆₁	—	2	2	no	—
345	D₄×C₆₁	—	2	1	no	—
346	D₄×C₆₁	—	2	2	no	—
347	D₄×C₆₁	—	4	2	no	—
348	D₄×C₆₁	—	4	8	no	—
349	D₄×C₆₁	—	4	2	no	—
350	D₄×C₆₁	—	8	4	no	—
351	D₄×C₆₁	—	8	4	no	—
352	D₄×C₆₁	C₂×#41	1	2	yes	—
353	C₂×C₄×C₆₁	—	2	1	no	—
354	C₂×C₄×C₆₁	—	2	4	no	—
355	C₂×C₄×C₆₁	—	2	2	no	—
356	C₂×C₄×C₆₁	—	2	4	no	—
357	C₂×C₄×C₆₁	—	2	4	no	—
358	C₂×C₄×C₆₁	—	2	2	no	—
359	C₂×C₄×C₆₁	—	2	1	no	—
360	C₂×C₄×C₆₁	—	2	1	no	—
361	C₂×C₄×C₆₁	—	2	2	no	—
362	C₂×C₄×C₆₁	—	2	2	no	—
363	C₂×C₄×C₆₁	—	2	4	no	—
364	C₂×C₄×C₆₁	—	4	1	no	—
365	C₂×C₄×C₆₁	—	4	8	no	—
366	C₂×C₄×C₆₁	—	4	8	no	—
367	C₂×C₄×C₆₁	—	4	2	no	—
368	C₂×C₄×C₆₁	—	4	4	no	—
369	C₂×C₄×C₆₁	—	4	2	no	—
370	C₂×C₄×C₆₁	—	4	4	no	—
371	C₂×C₄×C₆₁	—	8	2	no	—
372	C₂×C₄×C₆₁	—	8	1	no	—
373	C₂×C₄×C₆₁	—	8	4	no	—
374	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
376	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
381	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
382	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
383	C₈×C₆₁	—	2	2	no	—
384	C₈×C₆₁	—	2	2	no	—
385	C₈×C₆₁	—	2	2	no	—
386	C₈×C₆₁	—	2	2	no	—
387	#61209	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂²×C₆₁	—	2	1	no	—
389	C₂²×C₆₁	—	2	1	no	—
390	C₂²×C₆₁	—	2	4	no	—
391	C₂²×C₆₁	—	2	2	no	—
392	C₂²×C₆₁	—	2	4	no	—
393	C₂²×C₆₁	—	2	4	no	—
394	C₂²×C₆₁	—	4	1	no	—
395	C₂²×C₆₁	—	4	1	no	—
396	C₂²×C₆₁	—	4	2	no	—
397	C₂²×C₆₁	—	4	2	no	—
398	C₂²×C₆₁	—	4	2	no	—
399	C₂²×C₆₁	—	8	4	no	—
400	C₂²×C₆₁	#546	1	2	yes	—
401	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
402	C₄×C₆₁	—	2	1	no	—
403	C₄×C₆₁	—	2	1	no	—
404	C₄×C₆₁	—	2	2	no	—
405	C₄×C₆₁	—	2	4	no	—
406	C₄×C₆₁	—	2	1	no	—
407	C₄×C₆₁	—	4	1	no	—
408	C₄×C₆₁	—	4	2	no	—
409	C₄×C₆₁	—	4	4	no	—
410	C₄×C₆₁	—	4	1	no	—
411	C₄×C₆₁	—	4	2	no	—
412	C₄×C₆₁	—	4	2	no	—
413	C₄×C₆₁	#546	1	2	yes	—
414	C₄×C₆₁	#577	1	2	yes	—
415	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
416	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	#3506	C₂×C₆₁	1	1	yes	characteristic, complemented
418	#3499	C₂×C₆₁	1	1	yes	characteristic, complemented
419	#3330	C₂×C₆₁	1	2	yes	complemented
420	#3329	C₂×C₆₁	1	2	yes	complemented
421	#3320	C₂×C₆₁	1	4	yes	complemented
422	#3307	C₂×C₆₁	1	4	yes	complemented
423	#3303	C₂×C₆₁	1	2	yes	complemented
424	#3298	C₂×C₆₁	1	2	yes	complemented
425	#3139	C₂×C₆₁	1	1	yes	characteristic, complemented
426	#3097	C₂×C₆₁	1	2	yes	complemented
427	#3076	C₂×C₆₁	1	1	yes	characteristic, complemented
428	#3057	C₂×C₆₁	1	2	yes	complemented
429	C₂×#461	C₂×C₆₁	1	1	yes	characteristic, complemented
430	#3010	C₂×C₆₁	1	2	yes	complemented
431	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic, complemented
432	#2935	C₂×C₆₁	1	1	yes	characteristic, complemented
433	#2898	C₂×C₆₁	1	2	yes	complemented
434	C₂×C₆₁	—	2	2	no	—
435	C₂×C₆₁	—	4	4	no	—
436	C₂×C₆₁	—	4	2	no	—
437	C₂×C₆₁	—	8	2	no	—
438	C₂×C₆₁	C₂×#546	1	1	yes	characteristic
439	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
440	C₂×C₆₁	#3586	1	1	yes	characteristic
441	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	2	yes	—
442	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
443	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
444	C₂×#131	C₂²×C₆₁	1	2	yes	—
445	#559	—	2	2	no	—
446	#556	—	2	1	no	—
447	#555	C₂²×C₆₁	1	2	yes	—
448	#553	C₂²×C₆₁	1	4	yes	—
449	#550	—	2	1	no	—
450	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
451	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
452	#547	—	2	2	no	—
453	#547	—	2	2	no	—
454	#547	C₂²×C₆₁	1	2	yes	—
455	#547	C₂²×C₆₁	1	2	yes	complemented
456	#547	C₂²×C₆₁	1	2	yes	complemented
457	#538	—	2	2	no	—
458	#536	—	2	2	no	—
459	#536	C₂²×C₆₁	1	2	yes	—
460	#535	C₂²×C₆₁	1	2	yes	—
461	#533	C₂²×C₆₁	1	1	yes	characteristic
462	#532	—	2	1	no	—
463	#532	C₂²×C₆₁	1	1	yes	characteristic
464	C₂×C₄⋊Q₈	—	2	1	no	—
465	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
466	#525	—	2	2	no	—
467	#520	C₂²×C₆₁	1	2	yes	—
468	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
470	#491	C₂²×C₆₁	1	4	yes	complemented
471	#487	C₂²×C₆₁	1	2	yes	complemented
472	#487	C₂²×C₆₁	1	2	yes	complemented
473	#485	C₂²×C₆₁	1	4	yes	complemented
474	#485	C₂²×C₆₁	1	4	yes	complemented
475	#484	C₂²×C₆₁	1	4	yes	complemented
476	#483	C₂²×C₆₁	1	4	yes	complemented
477	#479	C₂²×C₆₁	1	2	yes	complemented
478	#478	C₂²×C₆₁	1	2	yes	complemented
479	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
480	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
481	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
482	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
483	#468	C₂²×C₆₁	1	4	yes	—
484	#468	C₂²×C₆₁	1	4	yes	—
485	#465	C₂²×C₆₁	1	4	yes	—
486	#465	C₂²×C₆₁	1	4	yes	—
487	#461	C₂²×C₆₁	1	2	yes	—
488	#461	C₂²×C₆₁	1	2	yes	—
489	#461	C₂²×C₆₁	1	4	yes	—
490	#449	C₂²×C₆₁	1	4	yes	—
491	#449	C₂²×C₆₁	1	4	yes	—
492	#448	C₂²×C₆₁	1	4	yes	—
493	#448	C₂²×C₆₁	1	4	yes	—
494	#442	C₂²×C₆₁	1	2	yes	—
495	#440	C₂²×C₆₁	1	2	yes	—
496	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
497	C₄×D₈	C₂²×C₆₁	1	2	yes	—
498	#436	C₂²×C₆₁	1	2	yes	complemented
499	#435	C₂²×C₆₁	1	4	yes	complemented
500	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
501	#428	C₂²×C₆₁	1	1	yes	characteristic
502	#427	C₂²×C₆₁	1	2	yes	—
503	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
504	#419	C₂²×C₆₁	1	2	yes	—
505	#419	C₂²×C₆₁	1	2	yes	—
506	#419	C₂²×C₆₁	1	4	yes	complemented
507	#418	C₂²×C₆₁	1	1	yes	characteristic
508	#417	C₂²×C₆₁	1	1	yes	characteristic
509	#417	C₂²×C₆₁	1	4	yes	complemented
510	#416	C₂²×C₆₁	1	2	yes	—
511	#416	C₂²×C₆₁	1	4	yes	complemented
512	C₂×#103	C₂²×C₆₁	1	2	yes	—
513	C₂×#103	C₂²×C₆₁	1	4	yes	complemented
514	#408	C₂²×C₆₁	1	2	yes	—
515	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
516	C₆₁	#61209	1	1	yes	characteristic, direct product factor, Sylow
517	2₋¹⁺⁴	—	2	8	no	—
518	2₋¹⁺⁴	—	4	4	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	2	4	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	C₂³×C₆₁	1	4	yes	—
523	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
524	C₂×#41	C₂³×C₆₁	1	2	yes	—
525	C₂²×Q₈	—	2	2	no	—
526	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
527	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
528	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
529	C₂³×C₄	—	2	1	no	—
530	AGL(1,ℤ/8)	—	2	4	no	—
531	C₂×SD₁₆	—	4	4	no	—
532	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
533	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
534	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
535	C₂×D₈	C₂³×C₆₁	1	2	yes	—
536	#131	—	4	4	no	—
537	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
538	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
539	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
540	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
541	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
542	C₄⋊Q₈	—	2	2	no	—
543	C₄⋊Q₈	—	2	2	no	—
544	C₄⋊Q₈	—	2	2	no	—
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
548	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
551	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
552	#127	—	2	2	no	—
553	#127	D₄×C₆₁	1	1	yes	characteristic
554	#126	—	2	4	no	—
555	#125	C₂³×C₆₁	1	2	yes	—
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	—	2	4	no	—
559	#124	D₄×C₆₁	1	2	yes	—
560	#123	—	2	4	no	—
561	#123	—	2	4	no	—
562	#123	—	2	4	no	—
563	#123	—	2	4	no	—
564	#123	—	2	4	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
571	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	#121	—	2	4	no	—
576	#121	D₄×C₆₁	1	2	yes	—
577	#121	D₄×C₆₁	1	2	yes	—
578	#121	C₂³×C₆₁	1	4	yes	—
579	#121	C₂³×C₆₁	1	4	yes	—
580	#120	—	2	4	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
585	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
586	C₄×D₄	—	2	4	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	4	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	C₂³×C₆₁	1	2	yes	—
596	C₄×D₄	C₂³×C₆₁	1	2	yes	—
597	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
598	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
599	C₄×D₄	C₂³×C₆₁	1	2	yes	—
600	C₄×D₄	C₂³×C₆₁	1	2	yes	—
601	#117	—	2	2	no	—
602	#117	—	2	1	no	—
603	#117	C₂³×C₆₁	1	1	yes	characteristic
604	#117	C₂³×C₆₁	1	2	yes	—
605	#117	C₂³×C₆₁	1	4	yes	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	—	2	2	no	—
610	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₄²	—	2	1	no	—
614	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
615	#107	C₂³×C₆₁	1	2	yes	—
616	#107	C₂³×C₆₁	1	2	yes	—
617	#107	C₂³×C₆₁	1	2	yes	—
618	#106	C₂³×C₆₁	1	2	yes	—
619	#106	C₂³×C₆₁	1	2	yes	—
620	#106	C₂³×C₆₁	1	2	yes	—
621	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
622	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
623	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
624	#103	C₂³×C₆₁	1	4	yes	—
625	#103	C₂³×C₆₁	1	4	yes	—
626	#103	C₂³×C₆₁	1	2	yes	—
627	#103	C₂³×C₆₁	1	2	yes	—
628	#103	C₂³×C₆₁	1	4	yes	—
629	#103	C₂³×C₆₁	1	2	yes	—
630	#103	C₂³×C₆₁	1	4	yes	—
631	#103	C₂³×C₆₁	1	4	yes	—
632	#103	C₂³×C₆₁	1	4	yes	—
633	#102	C₂³×C₆₁	1	2	yes	—
634	#102	C₂³×C₆₁	1	2	yes	—
635	#102	C₂³×C₆₁	1	2	yes	—
636	#102	C₂³×C₆₁	1	2	yes	—
637	#102	C₂³×C₆₁	1	2	yes	—
638	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
639	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
640	#97	C₂³×C₆₁	1	2	yes	—
641	C₄×C₈	C₂³×C₆₁	1	2	yes	—
642	C₂⁴	—	2	1	no	—
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	#41	—	2	2	no	—
646	#41	—	2	8	no	—
647	#41	—	4	4	no	—
648	#41	—	4	8	no	—
649	#41	—	4	16	no	—
650	#41	—	8	4	no	—
651	#41	#41×C₆₁	1	4	yes	complemented
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	8	no	—
657	C₂×Q₈	—	2	4	no	—
658	C₂×Q₈	—	2	4	no	—
659	C₂×Q₈	—	4	4	no	—
660	C₂×Q₈	—	4	8	no	—
661	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
662	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
663	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
672	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
673	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
674	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
675	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
676	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	8	2	no	—
688	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
691	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
692	SD₁₆	—	2	4	no	—
693	SD₁₆	—	4	4	no	—
694	SD₁₆	—	4	4	no	—
695	D₈	—	2	4	no	—
696	M₁₆	—	2	2	no	—
697	M₁₆	—	2	2	no	—
698	M₁₆	—	4	4	no	—
699	C₂×C₈	—	2	4	no	—
700	C₂×C₈	—	4	4	no	—
701	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
702	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
703	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
704	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
720	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
722	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
723	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
738	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	4	no	—
743	C₄²	—	2	2	no	—
744	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
746	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
747	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
748	C₂³	—	2	1	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	8	1	no	—
752	C₂³	—	8	1	no	—
753	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
754	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
755	Q₈	—	2	4	no	—
756	Q₈	—	2	1	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	2	4	no	—
759	Q₈	—	4	8	no	—
760	Q₈	—	4	4	no	—
761	Q₈	—	4	2	no	—
762	Q₈	—	8	1	no	—
763	Q₈	C₂×#41×C₆₁	1	2	yes	—
764	D₄	—	2	4	no	—
765	D₄	—	2	8	no	—
766	D₄	—	2	4	no	—
767	D₄	—	2	4	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	1	no	—
770	D₄	—	2	2	no	—
771	D₄	—	4	2	no	—
772	D₄	—	4	8	no	—
773	D₄	—	4	2	no	—
774	D₄	—	8	4	no	—
775	D₄	—	8	4	no	—
776	D₄	C₂×#41×C₆₁	1	2	yes	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	8	no	—
790	C₂×C₄	—	4	8	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	8	2	no	—
796	C₂×C₄	—	8	1	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
800	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
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	1	yes	characteristic
804	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
805	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
806	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
807	C₈	—	2	2	no	—
808	C₈	—	2	2	no	—
809	C₈	—	2	2	no	—
810	C₈	—	2	2	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	4	no	—
823	C₂²	C₆₁×#546	1	2	yes	—
824	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
825	C₄	—	2	1	no	—
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	4	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	4	no	—
836	C₄	C₆₁×#546	1	2	yes	—
837	C₄	C₆₁×#577	1	2	yes	—
838	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
839	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
840	C₂	—	2	2	no	—
841	C₂	—	4	4	no	—
842	C₂	—	4	2	no	—
843	C₂	—	8	2	no	—
844	C₂	C₂×C₆₁×#546	1	1	yes	characteristic
845	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
846	C₂	C₆₁×#3586	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3506	C₂	semidirect
2. C₆₁×#3499	C₂	semidirect
3. C₆₁×#3330	C₂	semidirect
4. C₆₁×#3329	C₂	semidirect
5. C₆₁×#3320	C₂	semidirect
6. C₆₁×#3307	C₂	semidirect
7. C₆₁×#3303	C₂	semidirect
8. C₆₁×#3298	C₂	semidirect
9. C₆₁×#3139	C₂	semidirect
10. C₆₁×#3097	C₂	semidirect
11. C₆₁×#3076	C₂	semidirect
12. C₆₁×#3057	C₂	semidirect
13. C₂×C₆₁×#461	C₂	semidirect
14. C₆₁×#3010	C₂	semidirect
15. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
16. C₆₁×#2935	C₂	semidirect
17. C₆₁×#2898	C₂	semidirect
27. D₄×Q₈×C₆₁	C₂²	semidirect
28. D₄×Q₈×C₆₁	C₂²	semidirect
32. C₆₁×#547	C₂²	semidirect
33. C₆₁×#547	C₂²	semidirect
47. C₆₁×#491	C₂²	semidirect
48. C₆₁×#487	C₂²	semidirect
49. C₆₁×#487	C₂²	semidirect
50. C₆₁×#485	C₂²	semidirect
51. C₆₁×#485	C₂²	semidirect
52. C₆₁×#484	C₂²	semidirect
53. C₆₁×#483	C₂²	semidirect
54. C₆₁×#479	C₂²	semidirect
55. C₆₁×#478	C₂²	semidirect
56. C₆₁×#477	C₂²	semidirect
57. C₆₁×#476	C₂²	semidirect
58. C₆₁×#475	C₂²	semidirect
59. C₆₁×#474	C₂²	semidirect
75. C₆₁×#436	C₂²	semidirect
76. C₆₁×#435	C₂²	semidirect
77. C₈×D₄×C₆₁	C₂²	semidirect
83. C₆₁×#419	C₂²	semidirect
86. C₆₁×#417	C₂²	semidirect
88. C₆₁×#416	C₂²	semidirect
90. C₂×#103×C₆₁	C₂²	semidirect
227. #41×C₆₁	#41	semidirect
387. #61209	C₆₁	direct (N × H)
417. #3506	C₂×C₆₁	semidirect
418. #3499	C₂×C₆₁	semidirect
419. #3330	C₂×C₆₁	semidirect
420. #3329	C₂×C₆₁	semidirect
421. #3320	C₂×C₆₁	semidirect
422. #3307	C₂×C₆₁	semidirect
423. #3303	C₂×C₆₁	semidirect
424. #3298	C₂×C₆₁	semidirect
425. #3139	C₂×C₆₁	semidirect
426. #3097	C₂×C₆₁	semidirect
427. #3076	C₂×C₆₁	semidirect
428. #3057	C₂×C₆₁	semidirect
429. C₂×#461	C₂×C₆₁	semidirect
430. #3010	C₂×C₆₁	semidirect
431. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
432. #2935	C₂×C₆₁	semidirect
433. #2898	C₂×C₆₁	semidirect
450. D₄×Q₈	C₂²×C₆₁	semidirect
451. D₄×Q₈	C₂²×C₆₁	semidirect
455. #547	C₂²×C₆₁	semidirect
456. #547	C₂²×C₆₁	semidirect
470. #491	C₂²×C₆₁	semidirect
471. #487	C₂²×C₆₁	semidirect
472. #487	C₂²×C₆₁	semidirect
473. #485	C₂²×C₆₁	semidirect
474. #485	C₂²×C₆₁	semidirect
475. #484	C₂²×C₆₁	semidirect
476. #483	C₂²×C₆₁	semidirect
477. #479	C₂²×C₆₁	semidirect
478. #478	C₂²×C₆₁	semidirect
479. #477	C₂²×C₆₁	semidirect
480. #476	C₂²×C₆₁	semidirect
481. #475	C₂²×C₆₁	semidirect
482. #474	C₂²×C₆₁	semidirect
498. #436	C₂²×C₆₁	semidirect
499. #435	C₂²×C₆₁	semidirect
500. C₈×D₄	C₂²×C₆₁	semidirect
506. #419	C₂²×C₆₁	semidirect
509. #417	C₂²×C₆₁	semidirect
511. #416	C₂²×C₆₁	semidirect
513. C₂×#103	C₂²×C₆₁	semidirect
516. C₆₁	#61209	direct (N × H)
651. #41	#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×#3506	2
C₆₁×#3499	2
C₆₁×#3330	2
C₆₁×#3329	2
C₆₁×#3320	2
C₆₁×#3307	2
C₆₁×#3303	2
C₆₁×#3298	2
C₆₁×#3139	2
C₆₁×#3097	2
C₆₁×#3076	2
C₆₁×#3057	2
C₂×C₆₁×#461	2
C₆₁×#3010	2
C₄×AGL(1,ℤ/8)×C₆₁	2
C₆₁×#2935	2
C₆₁×#2898	2
#61209	61

Subgroups — C61×#61209 #29564642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61209 #29564642