Subgroups — C₆₁×#60823 #29564256

Order 15616.

2054 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×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3223	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3222	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3221	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3220	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3212	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3211	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3153	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₆₁×#488	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3046	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3045	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3013	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3012	C₂	1	2	yes	maximal, complemented
17	C₆₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#137×C₆₁	C₂²	1	2	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
22	C₂×#135×C₆₁	C₂²	1	2	yes	—
23	C₂×#135×C₆₁	C₂²	1	2	yes	complemented
24	C₆₁×#553	—	2	4	no	—
25	C₆₁×#553	—	2	2	no	—
26	C₆₁×#552	—	2	2	no	—
27	C₆₁×#548	—	2	2	no	—
28	C₆₁×#546	—	2	4	no	—
29	C₆₁×#546	—	2	2	no	—
30	C₆₁×#541	C₂²	1	2	yes	complemented
31	C₆₁×#540	C₂²	1	2	yes	complemented
32	C₆₁×#537	C₂²	1	2	yes	—
33	C₆₁×#536	C₂²	1	1	yes	characteristic
34	C₆₁×#536	C₂²	1	2	yes	—
35	C₆₁×#535	C₂²	1	1	yes	characteristic
36	C₆₁×#535	C₂²	1	2	yes	—
37	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₆₁×#532	C₂²	1	2	yes	—
39	C₆₁×#532	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#529	C₂²	1	4	yes	complemented
41	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic, complemented
42	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#124×C₆₁	C₂²	1	2	yes	—
44	C₆₁×#520	C₂²	1	2	yes	complemented
45	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
46	C₆₁×#497	C₂²	1	2	yes	complemented
47	C₆₁×#496	C₂²	1	2	yes	complemented
48	C₆₁×#495	C₂²	1	2	yes	complemented
49	C₆₁×#495	C₂²	1	2	yes	complemented
50	C₆₁×#495	C₂²	1	4	yes	complemented
51	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
52	C₆₁×#493	C₂²	1	1	yes	characteristic, complemented
53	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
54	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
55	C₆₁×#491	C₂²	1	2	yes	complemented
56	C₆₁×#490	C₂²	1	2	yes	complemented
57	C₆₁×#488	C₂²	1	4	yes	complemented
58	C₆₁×#488	C₂²	1	2	yes	complemented
59	C₆₁×#488	C₂²	1	2	yes	complemented
60	C₆₁×#488	C₂²	1	2	yes	complemented
61	C₆₁×#488	C₂²	1	2	yes	complemented
62	C₆₁×#464	C₂²	1	4	yes	complemented
63	C₆₁×#464	C₂²	1	4	yes	complemented
64	C₆₁×#463	C₂²	1	4	yes	complemented
65	C₆₁×#463	C₂²	1	4	yes	complemented
66	C₆₁×#462	C₂²	1	4	yes	complemented
67	C₆₁×#461	C₂²	1	4	yes	complemented
68	C₆₁×#460	C₂²	1	4	yes	complemented
69	C₆₁×#459	C₂²	1	4	yes	complemented
70	C₆₁×#452	C₂²	1	4	yes	—
71	C₆₁×#452	C₂²	1	4	yes	complemented
72	C₆₁×#451	C₂²	1	4	yes	complemented
73	C₆₁×#450	C₂²	1	4	yes	—
74	C₆₁×#449	C₂²	1	4	yes	—
75	C₆₁×#449	C₂²	1	4	yes	complemented
76	C₆₁×#448	C₂²	1	4	yes	complemented
77	C₆₁×#447	C₂²	1	4	yes	—
78	C₆₁×#433	C₂²	1	2	yes	complemented
79	C₆₁×#433	C₂²	1	2	yes	complemented
80	C₆₁×#431	C₂²	1	4	yes	complemented
81	C₆₁×#424	C₂²	1	2	yes	complemented
82	C₆₁×#417	C₂²	1	2	yes	—
83	C₆₁×#417	C₂²	1	2	yes	complemented
84	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
85	C₂×#102×C₆₁	C₂²	1	2	yes	—
86	C₆₁×#408	C₂²	1	2	yes	—
87	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
89	2₋¹⁺⁴×C₆₁	—	4	4	no	—
90	H(5,𝔽₂)×C₆₁	—	4	4	no	—
91	C₂×#41×C₆₁	—	2	1	no	—
92	C₂×#41×C₆₁	—	2	1	no	—
93	C₂×#41×C₆₁	—	2	2	no	—
94	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
95	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×#41×C₆₁	C₂³	1	2	yes	—
97	C₂×#41×C₆₁	C₂³	1	2	yes	—
98	C₂×#41×C₆₁	C₂³	1	2	yes	—
99	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₆₁	—	2	1	no	—
101	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
103	C₂²×D₄×C₆₁	—	2	2	no	—
104	C₂²×D₄×C₆₁	—	2	1	no	—
105	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
107	#137×C₆₁	—	4	4	no	—
108	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
109	#135×C₆₁	—	4	4	no	—
110	#135×C₆₁	—	4	4	no	—
111	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
112	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
113	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
115	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
118	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
120	C₂×D₈×C₆₁	C₂³	1	2	yes	—
121	C₂×D₈×C₆₁	C₂³	1	2	yes	—
122	C₂×D₈×C₆₁	C₂³	1	4	yes	—
123	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
124	C₂²×C₈×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	C₂³	1	2	yes	—
129	#127×C₆₁	C₂³	1	1	yes	characteristic
130	#127×C₆₁	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
136	#125×C₆₁	C₂³	1	2	yes	—
137	#124×C₆₁	—	2	4	no	—
138	#124×C₆₁	—	2	2	no	—
139	#124×C₆₁	C₂³	1	1	yes	characteristic
140	#124×C₆₁	C₂³	1	1	yes	characteristic
141	#124×C₆₁	C₂³	1	2	yes	—
142	#124×C₆₁	C₂³	1	2	yes	—
143	#124×C₆₁	C₂³	1	2	yes	—
144	#124×C₆₁	C₂³	1	2	yes	—
145	#124×C₆₁	C₂³	1	2	yes	—
146	#123×C₆₁	—	2	4	no	—
147	#123×C₆₁	—	2	4	no	—
148	#123×C₆₁	—	2	2	no	—
149	#123×C₆₁	—	2	4	no	—
150	C₂²⋊Q₈×C₆₁	—	2	2	no	—
151	C₂²⋊Q₈×C₆₁	—	2	2	no	—
152	C₂²⋊Q₈×C₆₁	—	2	4	no	—
153	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
154	#121×C₆₁	—	2	2	no	—
155	#121×C₆₁	—	2	4	no	—
156	#121×C₆₁	—	2	2	no	—
157	#121×C₆₁	—	2	4	no	—
158	#121×C₆₁	—	2	2	no	—
159	#121×C₆₁	—	2	2	no	—
160	#121×C₆₁	—	2	4	no	—
161	#121×C₆₁	—	2	4	no	—
162	#121×C₆₁	C₂³	1	4	yes	—
163	#120×C₆₁	—	2	2	no	—
164	#120×C₆₁	—	2	4	no	—
165	C₄×Q₈×C₆₁	D₄	1	2	yes	—
166	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
167	C₄×D₄×C₆₁	—	2	4	no	—
168	C₄×D₄×C₆₁	—	2	4	no	—
169	C₄×D₄×C₆₁	—	2	4	no	—
170	C₄×D₄×C₆₁	—	2	2	no	—
171	C₄×D₄×C₆₁	—	2	2	no	—
172	C₄×D₄×C₆₁	D₄	1	4	yes	—
173	C₄×D₄×C₆₁	D₄	1	2	yes	—
174	C₄×D₄×C₆₁	C₂³	1	4	yes	—
175	#117×C₆₁	—	2	2	no	—
176	#117×C₆₁	—	2	4	no	—
177	#117×C₆₁	C₂³	1	2	yes	—
178	#117×C₆₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
180	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
181	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
183	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
184	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
186	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
187	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
188	#103×C₆₁	C₂³	1	4	yes	—
189	#103×C₆₁	C₂³	1	4	yes	—
190	#103×C₆₁	C₂³	1	4	yes	—
191	#103×C₆₁	C₂³	1	4	yes	—
192	#102×C₆₁	C₂³	1	4	yes	—
193	#102×C₆₁	C₂³	1	4	yes	—
194	#102×C₆₁	C₂³	1	4	yes	—
195	#102×C₆₁	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
197	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
198	#97×C₆₁	C₂³	1	2	yes	—
199	C₄×C₈×C₆₁	C₂³	1	2	yes	—
200	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
202	C₄×C₈×C₆₁	C₂³	1	2	yes	—
203	C₂⁴×C₆₁	—	2	2	no	—
204	C₂⁴×C₆₁	—	2	1	no	—
205	#41×C₆₁	—	2	4	no	—
206	#41×C₆₁	—	2	4	no	—
207	#41×C₆₁	—	2	4	no	—
208	#41×C₆₁	—	2	4	no	—
209	#41×C₆₁	—	2	4	no	—
210	#41×C₆₁	—	4	4	no	—
211	#41×C₆₁	—	4	4	no	—
212	#41×C₆₁	—	4	8	no	—
213	#41×C₆₁	—	4	4	no	—
214	#41×C₆₁	—	4	4	no	—
215	C₂×Q₈×C₆₁	—	2	2	no	—
216	C₂×Q₈×C₆₁	—	2	1	no	—
217	C₂×Q₈×C₆₁	—	2	4	no	—
218	C₂×Q₈×C₆₁	—	4	4	no	—
219	C₂×Q₈×C₆₁	—	4	4	no	—
220	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
221	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
222	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
223	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
224	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
225	C₂×D₄×C₆₁	—	2	2	no	—
226	C₂×D₄×C₆₁	—	2	2	no	—
227	C₂×D₄×C₆₁	—	2	1	no	—
228	C₂×D₄×C₆₁	—	2	2	no	—
229	C₂×D₄×C₆₁	—	2	1	no	—
230	C₂×D₄×C₆₁	—	2	4	no	—
231	C₂×D₄×C₆₁	—	2	2	no	—
232	C₂×D₄×C₆₁	—	2	1	no	—
233	C₂×D₄×C₆₁	—	2	4	no	—
234	C₂×D₄×C₆₁	—	2	2	no	—
235	C₂×D₄×C₆₁	—	2	2	no	—
236	C₂×D₄×C₆₁	—	2	4	no	—
237	C₂×D₄×C₆₁	—	4	4	no	—
238	C₂×D₄×C₆₁	—	4	8	no	—
239	C₂×D₄×C₆₁	—	4	4	no	—
240	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
242	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
243	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₆₁	—	2	2	no	—
247	C₂²×C₄×C₆₁	—	2	1	no	—
248	C₂²×C₄×C₆₁	—	2	2	no	—
249	C₂²×C₄×C₆₁	—	2	2	no	—
250	C₂²×C₄×C₆₁	—	2	2	no	—
251	C₂²×C₄×C₆₁	—	2	1	no	—
252	C₂²×C₄×C₆₁	—	2	2	no	—
253	C₂²×C₄×C₆₁	—	2	1	no	—
254	C₂²×C₄×C₆₁	—	2	4	no	—
255	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
257	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
259	Q₁₆×C₆₁	—	4	2	no	—
260	Q₁₆×C₆₁	—	4	2	no	—
261	Q₁₆×C₆₁	—	4	4	no	—
262	SD₁₆×C₆₁	—	4	2	no	—
263	SD₁₆×C₆₁	—	4	2	no	—
264	SD₁₆×C₆₁	—	4	2	no	—
265	SD₁₆×C₆₁	—	4	2	no	—
266	SD₁₆×C₆₁	—	4	4	no	—
267	SD₁₆×C₆₁	—	4	4	no	—
268	D₈×C₆₁	—	4	2	no	—
269	D₈×C₆₁	—	4	2	no	—
270	D₈×C₆₁	—	4	4	no	—
271	M₁₆×C₆₁	—	2	4	no	—
272	C₂×C₈×C₆₁	—	2	4	no	—
273	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
274	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
275	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
276	C₄⋊C₄×C₆₁	—	2	2	no	—
277	C₄⋊C₄×C₆₁	—	2	4	no	—
278	C₄⋊C₄×C₆₁	—	2	4	no	—
279	C₄⋊C₄×C₆₁	—	2	4	no	—
280	C₄⋊C₄×C₆₁	—	2	4	no	—
281	C₄⋊C₄×C₆₁	—	2	4	no	—
282	C₄⋊C₄×C₆₁	—	2	2	no	—
283	C₄⋊C₄×C₆₁	—	2	2	no	—
284	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
286	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
287	C₂²⋊C₄×C₆₁	—	2	4	no	—
288	C₂²⋊C₄×C₆₁	—	2	4	no	—
289	C₂²⋊C₄×C₆₁	—	2	2	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	C₂²⋊C₄×C₆₁	—	2	4	no	—
295	C₂²⋊C₄×C₆₁	—	2	4	no	—
296	C₂²⋊C₄×C₆₁	—	2	2	no	—
297	C₂²⋊C₄×C₆₁	—	2	2	no	—
298	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
299	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
300	C₄²×C₆₁	—	2	4	no	—
301	C₄²×C₆₁	C₂×D₄	1	4	yes	—
302	C₄²×C₆₁	C₂×D₄	1	2	yes	—
303	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
304	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
305	C₄²×C₆₁	C₂⁴	1	2	yes	—
306	C₂³×C₆₁	—	2	2	no	—
307	C₂³×C₆₁	—	2	2	no	—
308	C₂³×C₆₁	—	2	1	no	—
309	C₂³×C₆₁	—	2	1	no	—
310	C₂³×C₆₁	—	4	4	no	—
311	C₂³×C₆₁	—	4	2	no	—
312	C₂³×C₆₁	—	8	2	no	—
313	C₂³×C₆₁	—	8	4	no	—
314	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
315	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
316	Q₈×C₆₁	—	2	2	no	—
317	Q₈×C₆₁	—	2	2	no	—
318	Q₈×C₆₁	—	2	2	no	—
319	Q₈×C₆₁	—	2	4	no	—
320	Q₈×C₆₁	—	2	2	no	—
321	Q₈×C₆₁	—	2	2	no	—
322	Q₈×C₆₁	—	4	4	no	—
323	Q₈×C₆₁	—	4	2	no	—
324	D₄×C₆₁	—	2	4	no	—
325	D₄×C₆₁	—	2	2	no	—
326	D₄×C₆₁	—	2	2	no	—
327	D₄×C₆₁	—	2	2	no	—
328	D₄×C₆₁	—	2	4	no	—
329	D₄×C₆₁	—	2	2	no	—
330	D₄×C₆₁	—	2	2	no	—
331	D₄×C₆₁	—	4	4	no	—
332	D₄×C₆₁	—	4	4	no	—
333	D₄×C₆₁	—	4	4	no	—
334	D₄×C₆₁	—	4	2	no	—
335	D₄×C₆₁	—	4	4	no	—
336	D₄×C₆₁	—	4	2	no	—
337	D₄×C₆₁	—	4	2	no	—
338	D₄×C₆₁	—	8	4	no	—
339	D₄×C₆₁	—	8	2	no	—
340	D₄×C₆₁	—	8	2	no	—
341	D₄×C₆₁	—	8	4	no	—
342	C₂×C₄×C₆₁	—	2	4	no	—
343	C₂×C₄×C₆₁	—	2	2	no	—
344	C₂×C₄×C₆₁	—	2	4	no	—
345	C₂×C₄×C₆₁	—	2	2	no	—
346	C₂×C₄×C₆₁	—	2	1	no	—
347	C₂×C₄×C₆₁	—	2	1	no	—
348	C₂×C₄×C₆₁	—	4	4	no	—
349	C₂×C₄×C₆₁	—	4	2	no	—
350	C₂×C₄×C₆₁	—	4	4	no	—
351	C₂×C₄×C₆₁	—	4	4	no	—
352	C₂×C₄×C₆₁	—	4	4	no	—
353	C₂×C₄×C₆₁	—	4	2	no	—
354	C₂×C₄×C₆₁	—	4	2	no	—
355	C₂×C₄×C₆₁	—	4	2	no	—
356	C₂×C₄×C₆₁	—	4	4	no	—
357	C₂×C₄×C₆₁	—	8	4	no	—
358	C₂×C₄×C₆₁	—	8	2	no	—
359	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
365	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
366	C₈×C₆₁	—	2	2	no	—
367	C₈×C₆₁	—	2	2	no	—
368	C₈×C₆₁	—	2	4	no	—
369	#60823	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
370	C₂²×C₆₁	—	2	2	no	—
371	C₂²×C₆₁	—	2	4	no	—
372	C₂²×C₆₁	—	2	2	no	—
373	C₂²×C₆₁	—	4	2	no	—
374	C₂²×C₆₁	—	4	2	no	—
375	C₂²×C₆₁	—	4	2	no	—
376	C₂²×C₆₁	—	4	4	no	—
377	C₂²×C₆₁	—	4	2	no	—
378	C₂²×C₆₁	—	4	1	no	—
379	C₂²×C₆₁	—	4	2	no	—
380	C₂²×C₆₁	—	4	1	no	—
381	C₂²×C₆₁	—	4	2	no	—
382	C₂²×C₆₁	—	16	2	no	—
383	C₂²×C₆₁	—	16	4	no	—
384	C₂²×C₆₁	#535	1	2	yes	—
385	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
386	C₄×C₆₁	—	2	2	no	—
387	C₄×C₆₁	—	2	4	no	—
388	C₄×C₆₁	—	2	2	no	—
389	C₄×C₆₁	—	2	2	no	—
390	C₄×C₆₁	—	4	4	no	—
391	C₄×C₆₁	—	4	1	no	—
392	C₄×C₆₁	—	4	2	no	—
393	C₄×C₆₁	—	4	1	no	—
394	C₄×C₆₁	—	4	2	no	—
395	C₄×C₆₁	#535	1	2	yes	—
396	C₄×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
397	#3512	C₂×C₆₁	1	1	yes	characteristic, complemented
398	#3500	C₂×C₆₁	1	1	yes	characteristic, complemented
399	#3223	C₂×C₆₁	1	2	yes	complemented
400	#3222	C₂×C₆₁	1	2	yes	complemented
401	#3221	C₂×C₆₁	1	2	yes	complemented
402	#3220	C₂×C₆₁	1	2	yes	complemented
403	#3212	C₂×C₆₁	1	4	yes	complemented
404	#3211	C₂×C₆₁	1	4	yes	complemented
405	#3153	C₂×C₆₁	1	1	yes	characteristic, complemented
406	#3147	C₂×C₆₁	1	1	yes	characteristic, complemented
407	#3142	C₂×C₆₁	1	1	yes	characteristic, complemented
408	C₂×#488	C₂×C₆₁	1	1	yes	characteristic, complemented
409	#3046	C₂×C₆₁	1	2	yes	complemented
410	#3045	C₂×C₆₁	1	2	yes	complemented
411	#3013	C₂×C₆₁	1	2	yes	complemented
412	#3012	C₂×C₆₁	1	2	yes	complemented
413	#2922	C₂×C₆₁	1	1	yes	characteristic, complemented
414	C₂×C₆₁	—	2	2	no	—
415	C₂×C₆₁	—	4	2	no	—
416	C₂×C₆₁	—	8	2	no	—
417	C₂×C₆₁	—	8	1	no	—
418	C₂×C₆₁	—	8	2	no	—
419	C₂×C₆₁	—	8	1	no	—
420	C₂×C₆₁	C₂×#535	1	1	yes	characteristic
421	C₂×C₆₁	#3584	1	2	yes	—
422	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
423	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	1	yes	characteristic
424	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
425	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
426	C₂×#135	C₂²×C₆₁	1	2	yes	—
427	C₂×#135	C₂²×C₆₁	1	2	yes	complemented
428	#553	—	2	4	no	—
429	#553	—	2	2	no	—
430	#552	—	2	2	no	—
431	#548	—	2	2	no	—
432	#546	—	2	4	no	—
433	#546	—	2	2	no	—
434	#541	C₂²×C₆₁	1	2	yes	complemented
435	#540	C₂²×C₆₁	1	2	yes	complemented
436	#537	C₂²×C₆₁	1	2	yes	—
437	#536	C₂²×C₆₁	1	2	yes	—
438	#536	C₂²×C₆₁	1	1	yes	characteristic
439	#535	C₂²×C₆₁	1	2	yes	—
440	#535	C₂²×C₆₁	1	1	yes	characteristic
441	#532	C₂²×C₆₁	1	1	yes	characteristic
442	#532	C₂²×C₆₁	1	2	yes	—
443	#532	C₂²×C₆₁	1	1	yes	characteristic, complemented
444	#529	C₂²×C₆₁	1	4	yes	complemented
445	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic, complemented
446	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
447	C₂×#124	C₂²×C₆₁	1	2	yes	—
448	#520	C₂²×C₆₁	1	2	yes	complemented
449	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
450	#497	C₂²×C₆₁	1	2	yes	complemented
451	#496	C₂²×C₆₁	1	2	yes	complemented
452	#495	C₂²×C₆₁	1	2	yes	complemented
453	#495	C₂²×C₆₁	1	2	yes	complemented
454	#495	C₂²×C₆₁	1	4	yes	complemented
455	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
456	#493	C₂²×C₆₁	1	1	yes	characteristic, complemented
457	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
458	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
459	#491	C₂²×C₆₁	1	2	yes	complemented
460	#490	C₂²×C₆₁	1	2	yes	complemented
461	#488	C₂²×C₆₁	1	4	yes	complemented
462	#488	C₂²×C₆₁	1	2	yes	complemented
463	#488	C₂²×C₆₁	1	2	yes	complemented
464	#488	C₂²×C₆₁	1	2	yes	complemented
465	#488	C₂²×C₆₁	1	2	yes	complemented
466	#464	C₂²×C₆₁	1	4	yes	complemented
467	#464	C₂²×C₆₁	1	4	yes	complemented
468	#463	C₂²×C₆₁	1	4	yes	complemented
469	#463	C₂²×C₆₁	1	4	yes	complemented
470	#462	C₂²×C₆₁	1	4	yes	complemented
471	#461	C₂²×C₆₁	1	4	yes	complemented
472	#460	C₂²×C₆₁	1	4	yes	complemented
473	#459	C₂²×C₆₁	1	4	yes	complemented
474	#452	C₂²×C₆₁	1	4	yes	—
475	#452	C₂²×C₆₁	1	4	yes	complemented
476	#451	C₂²×C₆₁	1	4	yes	complemented
477	#450	C₂²×C₆₁	1	4	yes	—
478	#449	C₂²×C₆₁	1	4	yes	—
479	#449	C₂²×C₆₁	1	4	yes	complemented
480	#448	C₂²×C₆₁	1	4	yes	complemented
481	#447	C₂²×C₆₁	1	4	yes	—
482	#433	C₂²×C₆₁	1	2	yes	complemented
483	#433	C₂²×C₆₁	1	2	yes	complemented
484	#431	C₂²×C₆₁	1	4	yes	complemented
485	#424	C₂²×C₆₁	1	2	yes	complemented
486	#417	C₂²×C₆₁	1	2	yes	—
487	#417	C₂²×C₆₁	1	2	yes	complemented
488	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
489	C₂×#102	C₂²×C₆₁	1	2	yes	—
490	#408	C₂²×C₆₁	1	2	yes	—
491	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
492	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
493	C₆₁	#60823	1	1	yes	characteristic, direct product factor, Sylow
494	2₋¹⁺⁴	—	4	4	no	—
495	H(5,𝔽₂)	—	4	4	no	—
496	C₂×#41	—	2	1	no	—
497	C₂×#41	—	2	1	no	—
498	C₂×#41	—	2	2	no	—
499	C₂×#41	C₂³×C₆₁	1	2	yes	—
500	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
501	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
502	C₂×#41	C₂³×C₆₁	1	2	yes	—
503	C₂×#41	C₂³×C₆₁	1	2	yes	—
504	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
505	C₂²×Q₈	—	2	1	no	—
506	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
507	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
508	C₂²×D₄	—	2	2	no	—
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
512	#137	—	4	4	no	—
513	AGL(1,ℤ/8)	—	4	4	no	—
514	#135	—	4	4	no	—
515	#135	—	4	4	no	—
516	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
517	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
518	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
519	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
520	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
521	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
522	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
523	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
524	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
525	C₂×D₈	C₂³×C₆₁	1	2	yes	—
526	C₂×D₈	C₂³×C₆₁	1	2	yes	—
527	C₂×D₈	C₂³×C₆₁	1	4	yes	—
528	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
529	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
533	#127	C₂³×C₆₁	1	2	yes	—
534	#127	C₂³×C₆₁	1	1	yes	characteristic
535	#127	C₂³×C₆₁	1	1	yes	characteristic
536	#126	—	2	4	no	—
537	#126	—	2	4	no	—
538	#125	—	2	4	no	—
539	#125	—	2	2	no	—
540	#125	C₂³×C₆₁	1	2	yes	—
541	#125	C₂³×C₆₁	1	2	yes	—
542	#124	—	2	4	no	—
543	#124	—	2	2	no	—
544	#124	C₂³×C₆₁	1	2	yes	—
545	#124	C₂³×C₆₁	1	1	yes	characteristic
546	#124	C₂³×C₆₁	1	2	yes	—
547	#124	C₂³×C₆₁	1	2	yes	—
548	#124	C₂³×C₆₁	1	2	yes	—
549	#124	C₂³×C₆₁	1	2	yes	—
550	#124	C₂³×C₆₁	1	1	yes	characteristic
551	#123	—	2	4	no	—
552	#123	—	2	4	no	—
553	#123	—	2	2	no	—
554	#123	—	2	4	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	4	no	—
558	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
559	#121	—	2	2	no	—
560	#121	—	2	4	no	—
561	#121	—	2	2	no	—
562	#121	—	2	4	no	—
563	#121	—	2	2	no	—
564	#121	—	2	2	no	—
565	#121	—	2	4	no	—
566	#121	—	2	4	no	—
567	#121	C₂³×C₆₁	1	4	yes	—
568	#120	—	2	2	no	—
569	#120	—	2	4	no	—
570	C₄×Q₈	D₄×C₆₁	1	2	yes	—
571	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
572	C₄×D₄	—	2	4	no	—
573	C₄×D₄	—	2	4	no	—
574	C₄×D₄	—	2	4	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	D₄×C₆₁	1	4	yes	—
578	C₄×D₄	D₄×C₆₁	1	2	yes	—
579	C₄×D₄	C₂³×C₆₁	1	4	yes	—
580	#117	—	2	2	no	—
581	#117	—	2	4	no	—
582	#117	C₂³×C₆₁	1	1	yes	characteristic
583	#117	C₂³×C₆₁	1	2	yes	—
584	C₂×C₄⋊C₄	—	2	2	no	—
585	C₂×C₄⋊C₄	—	2	2	no	—
586	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
587	C₂×C₂²⋊C₄	—	2	2	no	—
588	C₂×C₂²⋊C₄	—	2	4	no	—
589	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
591	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
592	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
593	#103	C₂³×C₆₁	1	4	yes	—
594	#103	C₂³×C₆₁	1	4	yes	—
595	#103	C₂³×C₆₁	1	4	yes	—
596	#103	C₂³×C₆₁	1	4	yes	—
597	#102	C₂³×C₆₁	1	4	yes	—
598	#102	C₂³×C₆₁	1	4	yes	—
599	#102	C₂³×C₆₁	1	4	yes	—
600	#102	C₂³×C₆₁	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
602	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
603	#97	C₂³×C₆₁	1	2	yes	—
604	C₄×C₈	C₂³×C₆₁	1	2	yes	—
605	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
606	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
607	C₄×C₈	C₂³×C₆₁	1	2	yes	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	1	no	—
610	#41	—	2	4	no	—
611	#41	—	2	4	no	—
612	#41	—	2	4	no	—
613	#41	—	2	4	no	—
614	#41	—	2	4	no	—
615	#41	—	4	4	no	—
616	#41	—	4	4	no	—
617	#41	—	4	8	no	—
618	#41	—	4	4	no	—
619	#41	—	4	4	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	4	no	—
623	C₂×Q₈	—	4	4	no	—
624	C₂×Q₈	—	4	4	no	—
625	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
626	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
627	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
628	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
629	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	4	4	no	—
643	C₂×D₄	—	4	8	no	—
644	C₂×D₄	—	4	4	no	—
645	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
646	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
647	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
648	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
649	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
650	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
661	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
664	Q₁₆	—	4	2	no	—
665	Q₁₆	—	4	2	no	—
666	Q₁₆	—	4	4	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	2	no	—
669	SD₁₆	—	4	2	no	—
670	SD₁₆	—	4	2	no	—
671	SD₁₆	—	4	4	no	—
672	SD₁₆	—	4	4	no	—
673	D₈	—	4	2	no	—
674	D₈	—	4	2	no	—
675	D₈	—	4	4	no	—
676	M₁₆	—	2	4	no	—
677	C₂×C₈	—	2	4	no	—
678	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
679	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
680	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
690	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
691	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	2	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	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
704	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
705	C₄²	—	2	4	no	—
706	C₄²	C₂×D₄×C₆₁	1	4	yes	—
707	C₄²	C₂×D₄×C₆₁	1	2	yes	—
708	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
709	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
710	C₄²	C₂⁴×C₆₁	1	2	yes	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	8	2	no	—
718	C₂³	—	8	4	no	—
719	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
720	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
721	Q₈	—	2	2	no	—
722	Q₈	—	2	2	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	2	4	no	—
725	Q₈	—	2	2	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	4	4	no	—
728	Q₈	—	4	2	no	—
729	D₄	—	2	4	no	—
730	D₄	—	2	2	no	—
731	D₄	—	2	2	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	4	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	4	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	2	no	—
743	D₄	—	8	4	no	—
744	D₄	—	8	2	no	—
745	D₄	—	8	2	no	—
746	D₄	—	8	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	4	4	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	4	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	8	4	no	—
763	C₂×C₄	—	8	2	no	—
764	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
765	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
766	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
767	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
768	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
769	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
770	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₈	—	2	4	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	16	2	no	—
787	C₂²	—	16	4	no	—
788	C₂²	C₆₁×#535	1	2	yes	—
789	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
790	C₄	—	2	2	no	—
791	C₄	—	2	4	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	4	4	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	2	no	—
799	C₄	C₆₁×#535	1	2	yes	—
800	C₄	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
801	C₂	—	2	2	no	—
802	C₂	—	4	2	no	—
803	C₂	—	8	2	no	—
804	C₂	—	8	1	no	—
805	C₂	—	8	2	no	—
806	C₂	—	8	1	no	—
807	C₂	C₂×C₆₁×#535	1	1	yes	characteristic
808	C₂	C₆₁×#3584	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 ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3512	C₂	semidirect
2. C₆₁×#3500	C₂	semidirect
3. C₆₁×#3223	C₂	semidirect
4. C₆₁×#3222	C₂	semidirect
5. C₆₁×#3221	C₂	semidirect
6. C₆₁×#3220	C₂	semidirect
7. C₆₁×#3212	C₂	semidirect
8. C₆₁×#3211	C₂	semidirect
9. C₆₁×#3153	C₂	semidirect
10. C₆₁×#3147	C₂	semidirect
11. C₆₁×#3142	C₂	semidirect
12. C₂×C₆₁×#488	C₂	semidirect
13. C₆₁×#3046	C₂	semidirect
14. C₆₁×#3045	C₂	semidirect
15. C₆₁×#3013	C₂	semidirect
16. C₆₁×#3012	C₂	semidirect
17. C₆₁×#2922	C₂	semidirect
20. C₂×#137×C₆₁	C₂²	semidirect
23. C₂×#135×C₆₁	C₂²	semidirect
30. C₆₁×#541	C₂²	semidirect
31. C₆₁×#540	C₂²	semidirect
39. C₆₁×#532	C₂²	semidirect
40. C₆₁×#529	C₂²	semidirect
41. C₂×#125×C₆₁	C₂²	semidirect
44. C₆₁×#520	C₂²	semidirect
46. C₆₁×#497	C₂²	semidirect
47. C₆₁×#496	C₂²	semidirect
48. C₆₁×#495	C₂²	semidirect
49. C₆₁×#495	C₂²	semidirect
50. C₆₁×#495	C₂²	semidirect
51. C₆₁×#494	C₂²	semidirect
52. C₆₁×#493	C₂²	semidirect
53. C₆₁×#492	C₂²	semidirect
54. C₆₁×#492	C₂²	semidirect
55. C₆₁×#491	C₂²	semidirect
56. C₆₁×#490	C₂²	semidirect
57. C₆₁×#488	C₂²	semidirect
58. C₆₁×#488	C₂²	semidirect
59. C₆₁×#488	C₂²	semidirect
60. C₆₁×#488	C₂²	semidirect
61. C₆₁×#488	C₂²	semidirect
62. C₆₁×#464	C₂²	semidirect
63. C₆₁×#464	C₂²	semidirect
64. C₆₁×#463	C₂²	semidirect
65. C₆₁×#463	C₂²	semidirect
66. C₆₁×#462	C₂²	semidirect
67. C₆₁×#461	C₂²	semidirect
68. C₆₁×#460	C₂²	semidirect
69. C₆₁×#459	C₂²	semidirect
71. C₆₁×#452	C₂²	semidirect
72. C₆₁×#451	C₂²	semidirect
75. C₆₁×#449	C₂²	semidirect
76. C₆₁×#448	C₂²	semidirect
78. C₆₁×#433	C₂²	semidirect
79. C₆₁×#433	C₂²	semidirect
80. C₆₁×#431	C₂²	semidirect
81. C₆₁×#424	C₂²	semidirect
83. C₆₁×#417	C₂²	semidirect
84. C₂×#103×C₆₁	C₂²	semidirect
87. C₄×M₁₆×C₆₁	C₂²	semidirect
88. C₂×C₄×C₈×C₆₁	C₂²	semidirect
369. #60823	C₆₁	direct (N × H)
397. #3512	C₂×C₆₁	semidirect
398. #3500	C₂×C₆₁	semidirect
399. #3223	C₂×C₆₁	semidirect
400. #3222	C₂×C₆₁	semidirect
401. #3221	C₂×C₆₁	semidirect
402. #3220	C₂×C₆₁	semidirect
403. #3212	C₂×C₆₁	semidirect
404. #3211	C₂×C₆₁	semidirect
405. #3153	C₂×C₆₁	semidirect
406. #3147	C₂×C₆₁	semidirect
407. #3142	C₂×C₆₁	semidirect
408. C₂×#488	C₂×C₆₁	semidirect
409. #3046	C₂×C₆₁	semidirect
410. #3045	C₂×C₆₁	semidirect
411. #3013	C₂×C₆₁	semidirect
412. #3012	C₂×C₆₁	semidirect
413. #2922	C₂×C₆₁	semidirect
424. C₂×#137	C₂²×C₆₁	semidirect
427. C₂×#135	C₂²×C₆₁	semidirect
434. #541	C₂²×C₆₁	semidirect
435. #540	C₂²×C₆₁	semidirect
443. #532	C₂²×C₆₁	semidirect
444. #529	C₂²×C₆₁	semidirect
445. C₂×#125	C₂²×C₆₁	semidirect
448. #520	C₂²×C₆₁	semidirect
450. #497	C₂²×C₆₁	semidirect
451. #496	C₂²×C₆₁	semidirect
452. #495	C₂²×C₆₁	semidirect
453. #495	C₂²×C₆₁	semidirect
454. #495	C₂²×C₆₁	semidirect
455. #494	C₂²×C₆₁	semidirect
456. #493	C₂²×C₆₁	semidirect
457. #492	C₂²×C₆₁	semidirect
458. #492	C₂²×C₆₁	semidirect
459. #491	C₂²×C₆₁	semidirect
460. #490	C₂²×C₆₁	semidirect
461. #488	C₂²×C₆₁	semidirect
462. #488	C₂²×C₆₁	semidirect
463. #488	C₂²×C₆₁	semidirect
464. #488	C₂²×C₆₁	semidirect
465. #488	C₂²×C₆₁	semidirect
466. #464	C₂²×C₆₁	semidirect
467. #464	C₂²×C₆₁	semidirect
468. #463	C₂²×C₆₁	semidirect
469. #463	C₂²×C₆₁	semidirect
470. #462	C₂²×C₆₁	semidirect
471. #461	C₂²×C₆₁	semidirect
472. #460	C₂²×C₆₁	semidirect
473. #459	C₂²×C₆₁	semidirect
475. #452	C₂²×C₆₁	semidirect
476. #451	C₂²×C₆₁	semidirect
479. #449	C₂²×C₆₁	semidirect
480. #448	C₂²×C₆₁	semidirect
482. #433	C₂²×C₆₁	semidirect
483. #433	C₂²×C₆₁	semidirect
484. #431	C₂²×C₆₁	semidirect
485. #424	C₂²×C₆₁	semidirect
487. #417	C₂²×C₆₁	semidirect
488. C₂×#103	C₂²×C₆₁	semidirect
491. C₄×M₁₆	C₂²×C₆₁	semidirect
492. C₂×C₄×C₈	C₂²×C₆₁	semidirect
493. C₆₁	#60823	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×#3512	2
C₆₁×#3500	2
C₆₁×#3223	2
C₆₁×#3222	2
C₆₁×#3221	2
C₆₁×#3220	2
C₆₁×#3212	2
C₆₁×#3211	2
C₆₁×#3153	2
C₆₁×#3147	2
C₆₁×#3142	2
C₂×C₆₁×#488	2
C₆₁×#3046	2
C₆₁×#3045	2
C₆₁×#3013	2
C₆₁×#3012	2
C₆₁×#2922	2
#60823	61

Subgroups — C61×#60823 #29564256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60823 #29564256