Subgroups — C₆₁×#61788 #29565221

Order 15616.

1846 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3357	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3354	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3341	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3340	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3325	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3324	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3295	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3294	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3198	C₂	1	4	yes	maximal, complemented
14	C₆₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3096	C₂	1	4	yes	maximal, complemented
17	C₆₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×H(3,𝔽₄)	—	2	2	no	—
19	C₆₁×#556	C₂²	1	2	yes	complemented
20	C₆₁×#555	—	2	1	no	—
21	C₆₁×#555	C₂²	1	2	yes	—
22	C₆₁×#555	C₂²	1	2	yes	—
23	C₆₁×#555	C₂²	1	2	yes	complemented
24	C₆₁×#554	C₂²	1	2	yes	complemented
25	C₆₁×#553	—	2	2	no	—
26	C₆₁×#548	—	2	2	no	—
27	C₆₁×#547	C₂²	1	2	yes	complemented
28	D₄²×C₆₁	—	2	1	no	—
29	D₄²×C₆₁	C₂²	1	2	yes	—
30	D₄²×C₆₁	C₂²	1	2	yes	—
31	C₆₁×#542	—	2	2	no	—
32	C₆₁×#537	C₂²	1	2	yes	complemented
33	C₆₁×#535	—	2	2	no	—
34	C₆₁×#535	—	2	2	no	—
35	C₆₁×#535	C₂²	1	4	yes	—
36	C₆₁×#533	—	2	1	no	—
37	C₆₁×#532	—	2	1	no	—
38	C₆₁×#532	C₂²	1	1	yes	characteristic
39	C₆₁×#532	C₂²	1	1	yes	characteristic
40	C₆₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
42	C₆₁×#520	C₂²	1	2	yes	complemented
43	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#500	C₂²	1	2	yes	complemented
45	C₆₁×#498	C₂²	1	2	yes	complemented
46	C₆₁×#486	C₂²	1	2	yes	—
47	C₆₁×#486	C₂²	1	2	yes	—
48	C₆₁×#485	C₂²	1	4	yes	complemented
49	C₆₁×#482	C₂²	1	4	yes	complemented
50	C₆₁×#482	C₂²	1	4	yes	complemented
51	C₆₁×#482	C₂²	1	4	yes	complemented
52	C₆₁×#482	C₂²	1	2	yes	complemented
53	C₆₁×#482	C₂²	1	2	yes	complemented
54	C₆₁×#481	C₂²	1	4	yes	complemented
55	C₆₁×#481	C₂²	1	4	yes	complemented
56	C₆₁×#480	C₂²	1	4	yes	complemented
57	C₆₁×#480	C₂²	1	4	yes	complemented
58	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
59	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#476	C₂²	1	2	yes	complemented
61	C₆₁×#476	C₂²	1	2	yes	complemented
62	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#474	C₂²	1	2	yes	complemented
65	C₆₁×#474	C₂²	1	2	yes	complemented
66	C₆₁×#469	C₂²	1	4	yes	complemented
67	C₆₁×#468	C₂²	1	4	yes	complemented
68	C₆₁×#466	C₂²	1	4	yes	complemented
69	C₆₁×#465	C₂²	1	4	yes	complemented
70	C₆₁×#460	C₂²	1	1	yes	characteristic
71	C₆₁×#460	C₂²	1	1	yes	characteristic
72	C₆₁×#459	C₂²	1	1	yes	characteristic
73	C₆₁×#459	C₂²	1	1	yes	characteristic
74	C₆₁×#450	C₂²	1	4	yes	complemented
75	C₆₁×#449	C₂²	1	2	yes	complemented
76	C₆₁×#449	C₂²	1	2	yes	complemented
77	C₆₁×#447	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
79	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
80	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
81	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
82	C₆₁×#436	C₂²	1	2	yes	complemented
83	C₆₁×#436	C₂²	1	2	yes	complemented
84	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
85	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
86	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
87	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
88	C₆₁×#428	C₂²	1	4	yes	complemented
89	C₆₁×#427	C₂²	1	4	yes	complemented
90	C₆₁×#418	C₂²	1	4	yes	complemented
91	C₂×#102×C₆₁	C₂²	1	4	yes	complemented
92	C₆₁×#408	C₂²	1	4	yes	complemented
93	C₂×#41×C₆₁	—	2	2	no	—
94	C₂×#41×C₆₁	—	2	1	no	—
95	C₂×#41×C₆₁	—	2	1	no	—
96	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×#41×C₆₁	C₂³	1	2	yes	—
98	C₂²×Q₈×C₆₁	—	2	1	no	—
99	C₂²×D₄×C₆₁	—	2	2	no	—
100	C₂²×D₄×C₆₁	—	2	2	no	—
101	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
104	C₂×D₈×C₆₁	C₂³	1	2	yes	—
105	C₂×D₈×C₆₁	C₂³	1	2	yes	—
106	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
107	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₆₁	—	2	1	no	—
109	C₄⋊Q₈×C₆₁	—	2	1	no	—
110	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
115	#127×C₆₁	—	2	4	no	—
116	#127×C₆₁	D₄	1	1	yes	characteristic
117	#127×C₆₁	C₂³	1	1	yes	characteristic
118	#127×C₆₁	C₂³	1	1	yes	characteristic
119	#126×C₆₁	—	2	4	no	—
120	#125×C₆₁	—	2	2	no	—
121	#124×C₆₁	—	2	4	no	—
122	#124×C₆₁	—	2	2	no	—
123	#124×C₆₁	—	2	4	no	—
124	#124×C₆₁	—	2	4	no	—
125	#124×C₆₁	—	2	4	no	—
126	#124×C₆₁	—	2	1	no	—
127	#124×C₆₁	—	2	1	no	—
128	#124×C₆₁	D₄	1	2	yes	—
129	#123×C₆₁	—	2	4	no	—
130	C₂²⋊Q₈×C₆₁	—	2	2	no	—
131	C₂²⋊Q₈×C₆₁	—	2	2	no	—
132	C₂²⋊Q₈×C₆₁	—	2	4	no	—
133	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
134	#121×C₆₁	—	2	2	no	—
135	#121×C₆₁	—	2	2	no	—
136	#121×C₆₁	—	2	2	no	—
137	#121×C₆₁	—	2	2	no	—
138	#121×C₆₁	—	2	4	no	—
139	#121×C₆₁	—	2	1	no	—
140	#121×C₆₁	—	2	1	no	—
141	#121×C₆₁	—	2	2	no	—
142	#121×C₆₁	—	2	2	no	—
143	#121×C₆₁	D₄	1	2	yes	—
144	#121×C₆₁	D₄	1	2	yes	—
145	#121×C₆₁	C₂³	1	2	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	4	yes	—
150	#120×C₆₁	—	2	4	no	—
151	#120×C₆₁	—	2	4	no	—
152	#120×C₆₁	—	2	4	no	—
153	#120×C₆₁	—	2	4	no	—
154	C₄×Q₈×C₆₁	—	2	2	no	—
155	C₄×Q₈×C₆₁	—	2	2	no	—
156	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
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	1	no	—
162	C₄×D₄×C₆₁	—	2	1	no	—
163	C₄×D₄×C₆₁	—	2	1	no	—
164	C₄×D₄×C₆₁	—	2	1	no	—
165	C₄×D₄×C₆₁	C₂³	1	2	yes	—
166	C₄×D₄×C₆₁	C₂³	1	2	yes	—
167	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₆₁	C₂³	1	2	yes	—
170	C₄×D₄×C₆₁	C₂³	1	2	yes	—
171	#117×C₆₁	—	2	2	no	—
172	#117×C₆₁	—	2	2	no	—
173	#117×C₆₁	—	2	2	no	—
174	#117×C₆₁	—	2	1	no	—
175	#117×C₆₁	C₂³	1	4	yes	—
176	#117×C₆₁	C₂³	1	4	yes	—
177	#117×C₆₁	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
181	C₂×C₄²×C₆₁	—	2	1	no	—
182	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
183	#107×C₆₁	C₂³	1	2	yes	—
184	#107×C₆₁	C₂³	1	4	yes	—
185	#107×C₆₁	C₂³	1	2	yes	—
186	#107×C₆₁	C₂³	1	4	yes	—
187	#106×C₆₁	C₂³	1	2	yes	—
188	#106×C₆₁	C₂³	1	4	yes	—
189	#106×C₆₁	C₂³	1	2	yes	—
190	#106×C₆₁	C₂³	1	4	yes	—
191	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
192	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
195	#103×C₆₁	C₂³	1	2	yes	—
196	#103×C₆₁	C₂³	1	2	yes	—
197	#102×C₆₁	C₂³	1	2	yes	—
198	#102×C₆₁	C₂³	1	2	yes	—
199	#102×C₆₁	C₂³	1	4	yes	—
200	#102×C₆₁	C₂³	1	4	yes	—
201	#102×C₆₁	C₂³	1	2	yes	—
202	#102×C₆₁	C₂³	1	2	yes	—
203	#102×C₆₁	C₂³	1	4	yes	—
204	#102×C₆₁	C₂³	1	4	yes	—
205	#102×C₆₁	C₂³	1	2	yes	—
206	#102×C₆₁	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
209	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
210	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
211	C₄×C₈×C₆₁	C₂³	1	2	yes	—
212	C₄×C₈×C₆₁	C₂³	1	2	yes	—
213	C₂⁴×C₆₁	—	2	4	no	—
214	#41×C₆₁	—	4	2	no	—
215	#41×C₆₁	—	4	2	no	—
216	#41×C₆₁	—	4	1	no	—
217	#41×C₆₁	—	4	1	no	—
218	#41×C₆₁	—	8	2	no	—
219	#41×C₆₁	—	8	2	no	—
220	#41×C₆₁	—	8	4	no	—
221	C₂×Q₈×C₆₁	—	2	2	no	—
222	C₂×Q₈×C₆₁	—	2	2	no	—
223	C₂×Q₈×C₆₁	—	2	1	no	—
224	C₂×Q₈×C₆₁	—	2	1	no	—
225	C₂×Q₈×C₆₁	—	8	2	no	—
226	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
228	C₂×D₄×C₆₁	—	2	1	no	—
229	C₂×D₄×C₆₁	—	2	4	no	—
230	C₂×D₄×C₆₁	—	2	4	no	—
231	C₂×D₄×C₆₁	—	2	2	no	—
232	C₂×D₄×C₆₁	—	2	2	no	—
233	C₂×D₄×C₆₁	—	2	4	no	—
234	C₂×D₄×C₆₁	—	2	1	no	—
235	C₂×D₄×C₆₁	—	2	1	no	—
236	C₂×D₄×C₆₁	—	2	1	no	—
237	C₂×D₄×C₆₁	—	2	1	no	—
238	C₂×D₄×C₆₁	—	2	4	no	—
239	C₂×D₄×C₆₁	—	4	4	no	—
240	C₂×D₄×C₆₁	—	4	4	no	—
241	C₂×D₄×C₆₁	—	8	4	no	—
242	C₂×D₄×C₆₁	—	8	4	no	—
243	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
244	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
245	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
246	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
247	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
248	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
249	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₆₁	—	2	2	no	—
251	C₂²×C₄×C₆₁	—	2	4	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	2	no	—
256	C₂²×C₄×C₆₁	—	2	2	no	—
257	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
261	SD₁₆×C₆₁	—	4	2	no	—
262	SD₁₆×C₆₁	—	4	2	no	—
263	D₈×C₆₁	—	4	2	no	—
264	D₈×C₆₁	—	4	2	no	—
265	M₁₆×C₆₁	—	4	4	no	—
266	C₂×C₈×C₆₁	—	4	4	no	—
267	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
268	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
269	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
270	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₆₁	—	2	2	no	—
272	C₄⋊C₄×C₆₁	—	2	2	no	—
273	C₄⋊C₄×C₆₁	—	2	2	no	—
274	C₄⋊C₄×C₆₁	—	2	4	no	—
275	C₄⋊C₄×C₆₁	—	2	1	no	—
276	C₄⋊C₄×C₆₁	—	2	1	no	—
277	C₄⋊C₄×C₆₁	—	2	1	no	—
278	C₄⋊C₄×C₆₁	—	2	1	no	—
279	C₄⋊C₄×C₆₁	—	2	4	no	—
280	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
284	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
287	C₂²⋊C₄×C₆₁	—	2	1	no	—
288	C₂²⋊C₄×C₆₁	—	2	4	no	—
289	C₂²⋊C₄×C₆₁	—	2	4	no	—
290	C₂²⋊C₄×C₆₁	—	2	4	no	—
291	C₂²⋊C₄×C₆₁	—	2	1	no	—
292	C₂²⋊C₄×C₆₁	—	2	1	no	—
293	C₂²⋊C₄×C₆₁	—	2	4	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	—	2	2	no	—
299	C₂²⋊C₄×C₆₁	—	2	2	no	—
300	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
301	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
302	C₄²×C₆₁	—	2	1	no	—
303	C₄²×C₆₁	—	2	1	no	—
304	C₄²×C₆₁	—	2	1	no	—
305	C₄²×C₆₁	—	2	4	no	—
306	C₄²×C₆₁	—	2	4	no	—
307	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
310	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
311	C₂³×C₆₁	—	2	1	no	—
312	C₂³×C₆₁	—	2	2	no	—
313	C₂³×C₆₁	—	2	2	no	—
314	C₂³×C₆₁	—	8	4	no	—
315	C₂³×C₆₁	—	8	4	no	—
316	C₂³×C₆₁	—	8	4	no	—
317	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
318	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₆₁	—	2	1	no	—
320	Q₈×C₆₁	—	2	1	no	—
321	Q₈×C₆₁	—	4	2	no	—
322	Q₈×C₆₁	—	4	4	no	—
323	Q₈×C₆₁	—	8	2	no	—
324	Q₈×C₆₁	—	8	1	no	—
325	Q₈×C₆₁	—	8	1	no	—
326	D₄×C₆₁	—	2	4	no	—
327	D₄×C₆₁	—	2	4	no	—
328	D₄×C₆₁	—	2	1	no	—
329	D₄×C₆₁	—	2	1	no	—
330	D₄×C₆₁	—	2	2	no	—
331	D₄×C₆₁	—	2	2	no	—
332	D₄×C₆₁	—	2	2	no	—
333	D₄×C₆₁	—	2	2	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	—	4	2	no	—
339	D₄×C₆₁	—	8	4	no	—
340	D₄×C₆₁	—	8	1	no	—
341	D₄×C₆₁	—	8	1	no	—
342	D₄×C₆₁	—	8	4	no	—
343	D₄×C₆₁	—	8	4	no	—
344	D₄×C₆₁	—	8	2	no	—
345	D₄×C₆₁	—	8	4	no	—
346	D₄×C₆₁	—	8	2	no	—
347	C₂×C₄×C₆₁	—	2	2	no	—
348	C₂×C₄×C₆₁	—	2	2	no	—
349	C₂×C₄×C₆₁	—	2	4	no	—
350	C₂×C₄×C₆₁	—	2	4	no	—
351	C₂×C₄×C₆₁	—	2	1	no	—
352	C₂×C₄×C₆₁	—	2	1	no	—
353	C₂×C₄×C₆₁	—	2	1	no	—
354	C₂×C₄×C₆₁	—	2	2	no	—
355	C₂×C₄×C₆₁	—	2	2	no	—
356	C₂×C₄×C₆₁	—	2	1	no	—
357	C₂×C₄×C₆₁	—	2	1	no	—
358	C₂×C₄×C₆₁	—	2	4	no	—
359	C₂×C₄×C₆₁	—	4	2	no	—
360	C₂×C₄×C₆₁	—	4	4	no	—
361	C₂×C₄×C₆₁	—	4	2	no	—
362	C₂×C₄×C₆₁	—	4	2	no	—
363	C₂×C₄×C₆₁	—	4	4	no	—
364	C₂×C₄×C₆₁	—	8	2	no	—
365	C₂×C₄×C₆₁	—	8	4	no	—
366	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
367	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
373	C₈×C₆₁	—	2	2	no	—
374	C₈×C₆₁	—	2	2	no	—
375	C₈×C₆₁	—	2	2	no	—
376	C₈×C₆₁	—	2	2	no	—
377	#61788	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₂²×C₆₁	—	2	1	no	—
379	C₂²×C₆₁	—	2	4	no	—
380	C₂²×C₆₁	—	2	1	no	—
381	C₂²×C₆₁	—	2	4	no	—
382	C₂²×C₆₁	—	2	1	no	—
383	C₂²×C₆₁	—	2	4	no	—
384	C₂²×C₆₁	—	4	1	no	—
385	C₂²×C₆₁	—	4	2	no	—
386	C₂²×C₆₁	—	4	2	no	—
387	C₂²×C₆₁	—	4	1	no	—
388	C₂²×C₆₁	—	4	2	no	—
389	C₂²×C₆₁	—	4	2	no	—
390	C₂²×C₆₁	—	4	2	no	—
391	C₂²×C₆₁	—	4	1	no	—
392	C₂²×C₆₁	—	4	2	no	—
393	C₂²×C₆₁	—	16	8	no	—
394	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
395	C₄×C₆₁	—	2	1	no	—
396	C₄×C₆₁	—	2	4	no	—
397	C₄×C₆₁	—	2	1	no	—
398	C₄×C₆₁	—	2	1	no	—
399	C₄×C₆₁	—	4	1	no	—
400	C₄×C₆₁	—	4	1	no	—
401	C₄×C₆₁	—	4	2	no	—
402	C₄×C₆₁	—	4	4	no	—
403	C₄×C₆₁	—	4	1	no	—
404	C₄×C₆₁	—	4	2	no	—
405	C₄×C₆₁	#576	1	2	yes	—
406	C₄×C₆₁	#577	1	2	yes	—
407	C₄×C₆₁	#585	1	1	yes	characteristic
408	C₄×C₆₁	#585	1	1	yes	characteristic
409	#3549	C₂×C₆₁	1	1	yes	characteristic, complemented
410	#3511	C₂×C₆₁	1	1	yes	characteristic, complemented
411	#3357	C₂×C₆₁	1	2	yes	complemented
412	#3354	C₂×C₆₁	1	2	yes	complemented
413	#3341	C₂×C₆₁	1	2	yes	complemented
414	#3340	C₂×C₆₁	1	2	yes	complemented
415	#3325	C₂×C₆₁	1	2	yes	complemented
416	#3324	C₂×C₆₁	1	2	yes	complemented
417	#3295	C₂×C₆₁	1	2	yes	complemented
418	#3294	C₂×C₆₁	1	2	yes	complemented
419	#3227	C₂×C₆₁	1	1	yes	characteristic, complemented
420	#3226	C₂×C₆₁	1	1	yes	characteristic, complemented
421	#3198	C₂×C₆₁	1	4	yes	complemented
422	#3106	C₂×C₆₁	1	1	yes	characteristic, complemented
423	#3106	C₂×C₆₁	1	1	yes	characteristic, complemented
424	#3096	C₂×C₆₁	1	4	yes	complemented
425	#2979	C₂×C₆₁	1	1	yes	characteristic, complemented
426	C₂×C₆₁	—	4	1	no	—
427	C₂×C₆₁	—	4	4	no	—
428	C₂×C₆₁	—	8	1	no	—
429	C₂×C₆₁	—	8	2	no	—
430	C₂×C₆₁	—	8	2	no	—
431	C₂×C₆₁	#3485	1	1	yes	characteristic
432	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
433	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
434	H(3,𝔽₄)	—	2	2	no	—
435	#556	C₂²×C₆₁	1	2	yes	complemented
436	#555	—	2	1	no	—
437	#555	C₂²×C₆₁	1	2	yes	—
438	#555	C₂²×C₆₁	1	2	yes	—
439	#555	C₂²×C₆₁	1	2	yes	complemented
440	#554	C₂²×C₆₁	1	2	yes	complemented
441	#553	—	2	2	no	—
442	#548	—	2	2	no	—
443	#547	C₂²×C₆₁	1	2	yes	complemented
444	D₄²	—	2	1	no	—
445	D₄²	C₂²×C₆₁	1	2	yes	—
446	D₄²	C₂²×C₆₁	1	2	yes	—
447	#542	—	2	2	no	—
448	#537	C₂²×C₆₁	1	2	yes	complemented
449	#535	—	2	2	no	—
450	#535	—	2	2	no	—
451	#535	C₂²×C₆₁	1	4	yes	—
452	#533	—	2	1	no	—
453	#532	—	2	1	no	—
454	#532	C₂²×C₆₁	1	1	yes	characteristic
455	#532	C₂²×C₆₁	1	1	yes	characteristic
456	#532	C₂²×C₆₁	1	1	yes	characteristic
457	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
458	#520	C₂²×C₆₁	1	2	yes	complemented
459	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
460	#500	C₂²×C₆₁	1	2	yes	complemented
461	#498	C₂²×C₆₁	1	2	yes	complemented
462	#486	C₂²×C₆₁	1	2	yes	—
463	#486	C₂²×C₆₁	1	2	yes	—
464	#485	C₂²×C₆₁	1	4	yes	complemented
465	#482	C₂²×C₆₁	1	4	yes	complemented
466	#482	C₂²×C₆₁	1	4	yes	complemented
467	#482	C₂²×C₆₁	1	4	yes	complemented
468	#482	C₂²×C₆₁	1	2	yes	complemented
469	#482	C₂²×C₆₁	1	2	yes	complemented
470	#481	C₂²×C₆₁	1	4	yes	complemented
471	#481	C₂²×C₆₁	1	4	yes	complemented
472	#480	C₂²×C₆₁	1	4	yes	complemented
473	#480	C₂²×C₆₁	1	4	yes	complemented
474	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
475	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
476	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
477	#476	C₂²×C₆₁	1	2	yes	complemented
478	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
479	#476	C₂²×C₆₁	1	2	yes	complemented
480	#474	C₂²×C₆₁	1	2	yes	complemented
481	#474	C₂²×C₆₁	1	2	yes	complemented
482	#469	C₂²×C₆₁	1	4	yes	complemented
483	#468	C₂²×C₆₁	1	4	yes	complemented
484	#466	C₂²×C₆₁	1	4	yes	complemented
485	#465	C₂²×C₆₁	1	4	yes	complemented
486	#460	C₂²×C₆₁	1	1	yes	characteristic
487	#460	C₂²×C₆₁	1	1	yes	characteristic
488	#459	C₂²×C₆₁	1	1	yes	characteristic
489	#459	C₂²×C₆₁	1	1	yes	characteristic
490	#450	C₂²×C₆₁	1	4	yes	complemented
491	#449	C₂²×C₆₁	1	2	yes	complemented
492	#449	C₂²×C₆₁	1	2	yes	complemented
493	#447	C₂²×C₆₁	1	4	yes	complemented
494	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
495	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
496	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
497	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
498	#436	C₂²×C₆₁	1	2	yes	complemented
499	#436	C₂²×C₆₁	1	2	yes	complemented
500	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
501	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
502	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
503	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
504	#428	C₂²×C₆₁	1	4	yes	complemented
505	#427	C₂²×C₆₁	1	4	yes	complemented
506	#418	C₂²×C₆₁	1	4	yes	complemented
507	C₂×#102	C₂²×C₆₁	1	4	yes	complemented
508	#408	C₂²×C₆₁	1	4	yes	complemented
509	C₆₁	#61788	1	1	yes	characteristic, direct product factor, Sylow
510	C₂×#41	—	2	2	no	—
511	C₂×#41	—	2	1	no	—
512	C₂×#41	—	2	1	no	—
513	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
514	C₂×#41	C₂³×C₆₁	1	2	yes	—
515	C₂²×Q₈	—	2	1	no	—
516	C₂²×D₄	—	2	2	no	—
517	C₂²×D₄	—	2	2	no	—
518	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
519	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
520	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
521	C₂×D₈	C₂³×C₆₁	1	2	yes	—
522	C₂×D₈	C₂³×C₆₁	1	2	yes	—
523	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
524	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
532	#127	—	2	4	no	—
533	#127	D₄×C₆₁	1	1	yes	characteristic
534	#127	C₂³×C₆₁	1	1	yes	characteristic
535	#127	C₂³×C₆₁	1	1	yes	characteristic
536	#126	—	2	4	no	—
537	#125	—	2	2	no	—
538	#124	—	2	4	no	—
539	#124	—	2	2	no	—
540	#124	—	2	4	no	—
541	#124	—	2	4	no	—
542	#124	—	2	4	no	—
543	#124	—	2	1	no	—
544	#124	—	2	1	no	—
545	#124	D₄×C₆₁	1	2	yes	—
546	#123	—	2	4	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	4	no	—
550	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	2	no	—
554	#121	—	2	2	no	—
555	#121	—	2	4	no	—
556	#121	—	2	1	no	—
557	#121	—	2	1	no	—
558	#121	—	2	2	no	—
559	#121	—	2	2	no	—
560	#121	D₄×C₆₁	1	2	yes	—
561	#121	D₄×C₆₁	1	2	yes	—
562	#121	C₂³×C₆₁	1	2	yes	—
563	#121	C₂³×C₆₁	1	2	yes	—
564	#121	C₂³×C₆₁	1	4	yes	—
565	#121	C₂³×C₆₁	1	4	yes	—
566	#121	C₂³×C₆₁	1	4	yes	—
567	#120	—	2	4	no	—
568	#120	—	2	4	no	—
569	#120	—	2	4	no	—
570	#120	—	2	4	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
574	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	4	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
583	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
584	C₄×D₄	C₂³×C₆₁	1	2	yes	—
585	C₄×D₄	C₂³×C₆₁	1	2	yes	—
586	C₄×D₄	C₂³×C₆₁	1	2	yes	—
587	C₄×D₄	C₂³×C₆₁	1	2	yes	—
588	#117	—	2	2	no	—
589	#117	—	2	2	no	—
590	#117	—	2	2	no	—
591	#117	—	2	1	no	—
592	#117	C₂³×C₆₁	1	1	yes	characteristic
593	#117	C₂³×C₆₁	1	4	yes	—
594	#117	C₂³×C₆₁	1	4	yes	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
598	C₂×C₄²	—	2	1	no	—
599	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
600	#107	C₂³×C₆₁	1	2	yes	—
601	#107	C₂³×C₆₁	1	4	yes	—
602	#107	C₂³×C₆₁	1	2	yes	—
603	#107	C₂³×C₆₁	1	4	yes	—
604	#106	C₂³×C₆₁	1	2	yes	—
605	#106	C₂³×C₆₁	1	4	yes	—
606	#106	C₂³×C₆₁	1	2	yes	—
607	#106	C₂³×C₆₁	1	4	yes	—
608	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
609	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
610	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
611	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
612	#103	C₂³×C₆₁	1	2	yes	—
613	#103	C₂³×C₆₁	1	2	yes	—
614	#102	C₂³×C₆₁	1	2	yes	—
615	#102	C₂³×C₆₁	1	2	yes	—
616	#102	C₂³×C₆₁	1	4	yes	—
617	#102	C₂³×C₆₁	1	4	yes	—
618	#102	C₂³×C₆₁	1	2	yes	—
619	#102	C₂³×C₆₁	1	2	yes	—
620	#102	C₂³×C₆₁	1	4	yes	—
621	#102	C₂³×C₆₁	1	4	yes	—
622	#102	C₂³×C₆₁	1	2	yes	—
623	#102	C₂³×C₆₁	1	2	yes	—
624	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
625	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
626	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
627	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
628	C₄×C₈	C₂³×C₆₁	1	2	yes	—
629	C₄×C₈	C₂³×C₆₁	1	2	yes	—
630	C₂⁴	—	2	4	no	—
631	#41	—	4	2	no	—
632	#41	—	4	2	no	—
633	#41	—	4	1	no	—
634	#41	—	4	1	no	—
635	#41	—	8	2	no	—
636	#41	—	8	2	no	—
637	#41	—	8	4	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	8	2	no	—
643	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
644	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	8	4	no	—
659	C₂×D₄	—	8	4	no	—
660	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
661	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
662	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
663	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
664	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
665	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
666	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
678	SD₁₆	—	4	2	no	—
679	SD₁₆	—	4	2	no	—
680	D₈	—	4	2	no	—
681	D₈	—	4	2	no	—
682	M₁₆	—	4	4	no	—
683	C₂×C₈	—	4	4	no	—
684	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
685	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
686	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
687	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
698	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
700	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
701	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
702	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
703	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
718	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
719	C₄²	—	2	1	no	—
720	C₄²	—	2	1	no	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	4	no	—
723	C₄²	—	2	4	no	—
724	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
725	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
726	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
727	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
728	C₂³	—	2	1	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	8	4	no	—
732	C₂³	—	8	4	no	—
733	C₂³	—	8	4	no	—
734	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
735	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
736	Q₈	—	2	1	no	—
737	Q₈	—	2	1	no	—
738	Q₈	—	4	2	no	—
739	Q₈	—	4	4	no	—
740	Q₈	—	8	2	no	—
741	Q₈	—	8	1	no	—
742	Q₈	—	8	1	no	—
743	D₄	—	2	4	no	—
744	D₄	—	2	4	no	—
745	D₄	—	2	1	no	—
746	D₄	—	2	1	no	—
747	D₄	—	2	2	no	—
748	D₄	—	2	2	no	—
749	D₄	—	2	2	no	—
750	D₄	—	2	2	no	—
751	D₄	—	4	2	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	2	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	1	no	—
758	D₄	—	8	1	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	—	8	2	no	—
762	D₄	—	8	4	no	—
763	D₄	—	8	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	8	2	no	—
782	C₂×C₄	—	8	4	no	—
783	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
784	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
787	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
789	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
790	C₈	—	2	2	no	—
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₈	—	2	2	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	16	8	no	—
810	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	4	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	4	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	1	no	—
821	C₄	C₆₁×#576	1	2	yes	—
822	C₄	C₆₁×#577	1	2	yes	—
823	C₄	C₆₁×#585	1	1	yes	characteristic
824	C₄	C₆₁×#585	1	1	yes	characteristic
825	C₂	—	4	4	no	—
826	C₂	—	4	1	no	—
827	C₂	—	8	2	no	—
828	C₂	—	8	2	no	—
829	C₂	—	8	1	no	—
830	C₂	C₆₁×#3485	1	1	yes	characteristic
831	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
832	C₂	C₂×C₆₁×#577	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×#3549	C₂	semidirect
2. C₆₁×#3511	C₂	semidirect
3. C₆₁×#3357	C₂	semidirect
4. C₆₁×#3354	C₂	semidirect
5. C₆₁×#3341	C₂	semidirect
6. C₆₁×#3340	C₂	semidirect
7. C₆₁×#3325	C₂	semidirect
8. C₆₁×#3324	C₂	semidirect
9. C₆₁×#3295	C₂	semidirect
10. C₆₁×#3294	C₂	semidirect
11. C₆₁×#3227	C₂	semidirect
12. C₆₁×#3226	C₂	semidirect
13. C₆₁×#3198	C₂	semidirect
14. C₆₁×#3106	C₂	semidirect
15. C₆₁×#3106	C₂	semidirect
16. C₆₁×#3096	C₂	semidirect
17. C₆₁×#2979	C₂	semidirect
19. C₆₁×#556	C₂²	semidirect
23. C₆₁×#555	C₂²	semidirect
24. C₆₁×#554	C₂²	semidirect
27. C₆₁×#547	C₂²	semidirect
32. C₆₁×#537	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
42. C₆₁×#520	C₂²	semidirect
43. C₄×#41×C₆₁	C₂²	semidirect
44. C₆₁×#500	C₂²	semidirect
45. C₆₁×#498	C₂²	semidirect
48. C₆₁×#485	C₂²	semidirect
49. C₆₁×#482	C₂²	semidirect
50. C₆₁×#482	C₂²	semidirect
51. C₆₁×#482	C₂²	semidirect
52. C₆₁×#482	C₂²	semidirect
53. C₆₁×#482	C₂²	semidirect
54. C₆₁×#481	C₂²	semidirect
55. C₆₁×#481	C₂²	semidirect
56. C₆₁×#480	C₂²	semidirect
57. C₆₁×#480	C₂²	semidirect
58. C₆₁×#477	C₂²	semidirect
59. C₆₁×#477	C₂²	semidirect
60. C₆₁×#476	C₂²	semidirect
61. C₆₁×#476	C₂²	semidirect
62. C₆₁×#476	C₂²	semidirect
63. C₆₁×#476	C₂²	semidirect
64. C₆₁×#474	C₂²	semidirect
65. C₆₁×#474	C₂²	semidirect
66. C₆₁×#469	C₂²	semidirect
67. C₆₁×#468	C₂²	semidirect
68. C₆₁×#466	C₂²	semidirect
69. C₆₁×#465	C₂²	semidirect
74. C₆₁×#450	C₂²	semidirect
75. C₆₁×#449	C₂²	semidirect
76. C₆₁×#449	C₂²	semidirect
77. C₆₁×#447	C₂²	semidirect
78. C₄×SD₁₆×C₆₁	C₂²	semidirect
79. C₄×SD₁₆×C₆₁	C₂²	semidirect
80. C₄×D₈×C₆₁	C₂²	semidirect
81. C₄×D₈×C₆₁	C₂²	semidirect
82. C₆₁×#436	C₂²	semidirect
83. C₆₁×#436	C₂²	semidirect
84. C₈×D₄×C₆₁	C₂²	semidirect
85. C₈×D₄×C₆₁	C₂²	semidirect
86. C₆₁×#431	C₂²	semidirect
87. C₆₁×#431	C₂²	semidirect
88. C₆₁×#428	C₂²	semidirect
89. C₆₁×#427	C₂²	semidirect
90. C₆₁×#418	C₂²	semidirect
91. C₂×#102×C₆₁	C₂²	semidirect
92. C₆₁×#408	C₂²	semidirect
377. #61788	C₆₁	direct (N × H)
409. #3549	C₂×C₆₁	semidirect
410. #3511	C₂×C₆₁	semidirect
411. #3357	C₂×C₆₁	semidirect
412. #3354	C₂×C₆₁	semidirect
413. #3341	C₂×C₆₁	semidirect
414. #3340	C₂×C₆₁	semidirect
415. #3325	C₂×C₆₁	semidirect
416. #3324	C₂×C₆₁	semidirect
417. #3295	C₂×C₆₁	semidirect
418. #3294	C₂×C₆₁	semidirect
419. #3227	C₂×C₆₁	semidirect
420. #3226	C₂×C₆₁	semidirect
421. #3198	C₂×C₆₁	semidirect
422. #3106	C₂×C₆₁	semidirect
423. #3106	C₂×C₆₁	semidirect
424. #3096	C₂×C₆₁	semidirect
425. #2979	C₂×C₆₁	semidirect
435. #556	C₂²×C₆₁	semidirect
439. #555	C₂²×C₆₁	semidirect
440. #554	C₂²×C₆₁	semidirect
443. #547	C₂²×C₆₁	semidirect
448. #537	C₂²×C₆₁	semidirect
457. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
458. #520	C₂²×C₆₁	semidirect
459. C₄×#41	C₂²×C₆₁	semidirect
460. #500	C₂²×C₆₁	semidirect
461. #498	C₂²×C₆₁	semidirect
464. #485	C₂²×C₆₁	semidirect
465. #482	C₂²×C₆₁	semidirect
466. #482	C₂²×C₆₁	semidirect
467. #482	C₂²×C₆₁	semidirect
468. #482	C₂²×C₆₁	semidirect
469. #482	C₂²×C₆₁	semidirect
470. #481	C₂²×C₆₁	semidirect
471. #481	C₂²×C₆₁	semidirect
472. #480	C₂²×C₆₁	semidirect
473. #480	C₂²×C₆₁	semidirect
474. #477	C₂²×C₆₁	semidirect
475. #477	C₂²×C₆₁	semidirect
476. #476	C₂²×C₆₁	semidirect
477. #476	C₂²×C₆₁	semidirect
478. #476	C₂²×C₆₁	semidirect
479. #476	C₂²×C₆₁	semidirect
480. #474	C₂²×C₆₁	semidirect
481. #474	C₂²×C₆₁	semidirect
482. #469	C₂²×C₆₁	semidirect
483. #468	C₂²×C₆₁	semidirect
484. #466	C₂²×C₆₁	semidirect
485. #465	C₂²×C₆₁	semidirect
490. #450	C₂²×C₆₁	semidirect
491. #449	C₂²×C₆₁	semidirect
492. #449	C₂²×C₆₁	semidirect
493. #447	C₂²×C₆₁	semidirect
494. C₄×SD₁₆	C₂²×C₆₁	semidirect
495. C₄×SD₁₆	C₂²×C₆₁	semidirect
496. C₄×D₈	C₂²×C₆₁	semidirect
497. C₄×D₈	C₂²×C₆₁	semidirect
498. #436	C₂²×C₆₁	semidirect
499. #436	C₂²×C₆₁	semidirect
500. C₈×D₄	C₂²×C₆₁	semidirect
501. C₈×D₄	C₂²×C₆₁	semidirect
502. #431	C₂²×C₆₁	semidirect
503. #431	C₂²×C₆₁	semidirect
504. #428	C₂²×C₆₁	semidirect
505. #427	C₂²×C₆₁	semidirect
506. #418	C₂²×C₆₁	semidirect
507. C₂×#102	C₂²×C₆₁	semidirect
508. #408	C₂²×C₆₁	semidirect
509. C₆₁	#61788	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×#3549	2
C₆₁×#3511	2
C₆₁×#3357	2
C₆₁×#3354	2
C₆₁×#3341	2
C₆₁×#3340	2
C₆₁×#3325	2
C₆₁×#3324	2
C₆₁×#3295	2
C₆₁×#3294	2
C₆₁×#3227	2
C₆₁×#3226	2
C₆₁×#3198	2
C₆₁×#3106	2
C₆₁×#3096	2
C₆₁×#2979	2
#61788	61

Subgroups — C61×#61788 #29565221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61788 #29565221