Subgroups — C₆₁×#61874 #29565307

Order 15616.

1654 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3554	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3390	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3388	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3386	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3385	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3375	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3371	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3371	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3368	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3243	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3241	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3126	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3121	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#562	—	2	2	no	—
21	C₆₁×#559	C₂²	1	1	yes	characteristic
22	C₆₁×#559	C₂²	1	2	yes	—
23	Q₈²×C₆₁	—	2	1	no	—
24	Q₈²×C₆₁	C₂²	1	2	yes	—
25	C₆₁×#557	—	2	1	no	—
26	C₆₁×#557	—	2	2	no	—
27	C₆₁×#557	C₂²	1	1	yes	characteristic
28	C₆₁×#557	C₂²	1	2	yes	—
29	C₆₁×#557	C₂²	1	2	yes	—
30	C₆₁×#557	C₂²	1	2	yes	—
31	C₆₁×#554	C₂²	1	2	yes	—
32	C₆₁×#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#548	—	2	1	no	—
35	C₆₁×#547	—	2	1	no	—
36	C₆₁×#544	—	2	1	no	—
37	C₆₁×#544	—	2	1	no	—
38	C₆₁×#544	C₂²	1	2	yes	—
39	C₆₁×#542	—	2	1	no	—
40	C₆₁×#542	C₂²	1	2	yes	—
41	C₆₁×#540	C₂²	1	2	yes	—
42	C₆₁×#539	—	2	2	no	—
43	C₆₁×#536	—	2	1	no	—
44	C₆₁×#533	—	2	2	no	—
45	C₆₁×#533	C₂²	1	1	yes	characteristic
46	C₆₁×#533	C₂²	1	1	yes	characteristic
47	C₆₁×#532	C₂²	1	1	yes	characteristic
48	C₆₁×#529	C₂²	1	1	yes	characteristic
49	C₆₁×#519	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
51	C₆₁×#501	C₂²	1	1	yes	characteristic
52	C₆₁×#501	C₂²	1	2	yes	—
53	C₆₁×#501	C₂²	1	2	yes	—
54	C₆₁×#501	C₂²	1	2	yes	—
55	C₆₁×#501	C₂²	1	1	yes	characteristic
56	C₆₁×#500	C₂²	1	2	yes	—
57	C₆₁×#499	C₂²	1	2	yes	—
58	C₆₁×#490	C₂²	1	2	yes	—
59	C₆₁×#490	C₂²	1	2	yes	—
60	C₆₁×#489	C₂²	1	1	yes	characteristic
61	C₆₁×#489	C₂²	1	2	yes	—
62	C₆₁×#489	C₂²	1	1	yes	characteristic
63	C₆₁×#488	C₂²	1	2	yes	—
64	C₆₁×#486	C₂²	1	2	yes	—
65	C₆₁×#485	C₂²	1	2	yes	—
66	C₆₁×#484	C₂²	1	1	yes	characteristic
67	C₆₁×#482	C₂²	1	2	yes	—
68	C₆₁×#482	C₂²	1	2	yes	—
69	C₆₁×#482	C₂²	1	2	yes	—
70	C₆₁×#481	C₂²	1	1	yes	characteristic
71	C₆₁×#480	C₂²	1	2	yes	—
72	C₆₁×#479	C₂²	1	2	yes	—
73	C₆₁×#479	C₂²	1	2	yes	—
74	C₆₁×#479	C₂²	1	2	yes	—
75	C₆₁×#479	C₂²	1	2	yes	—
76	C₆₁×#479	C₂²	1	2	yes	—
77	C₆₁×#478	C₂²	1	2	yes	—
78	C₆₁×#478	C₂²	1	2	yes	—
79	C₆₁×#478	C₂²	1	2	yes	—
80	C₆₁×#478	C₂²	1	2	yes	—
81	C₆₁×#477	C₂²	1	2	yes	—
82	C₆₁×#477	C₂²	1	2	yes	—
83	C₆₁×#477	C₂²	1	2	yes	—
84	C₆₁×#476	C₂²	1	2	yes	—
85	C₆₁×#476	C₂²	1	2	yes	—
86	C₆₁×#475	C₂²	1	2	yes	—
87	C₆₁×#474	C₂²	1	2	yes	—
88	C₆₁×#474	C₂²	1	2	yes	—
89	C₆₁×#474	C₂²	1	2	yes	—
90	C₆₁×#464	C₂²	1	2	yes	—
91	C₆₁×#464	C₂²	1	2	yes	—
92	C₆₁×#464	C₂²	1	2	yes	—
93	C₆₁×#460	C₂²	1	2	yes	—
94	C₆₁×#460	C₂²	1	2	yes	—
95	C₆₁×#460	C₂²	1	2	yes	—
96	C₆₁×#451	C₂²	1	1	yes	characteristic
97	C₆₁×#448	C₂²	1	2	yes	—
98	C₆₁×#448	C₂²	1	1	yes	characteristic
99	C₆₁×#446	C₂²	1	2	yes	—
100	C₆₁×#446	C₂²	1	2	yes	—
101	C₆₁×#446	C₂²	1	2	yes	—
102	C₆₁×#446	C₂²	1	2	yes	—
103	C₆₁×#441	C₂²	1	2	yes	—
104	C₆₁×#441	C₂²	1	2	yes	—
105	C₆₁×#440	C₂²	1	2	yes	—
106	C₆₁×#440	C₂²	1	2	yes	—
107	C₆₁×#440	C₂²	1	2	yes	—
108	C₆₁×#440	C₂²	1	2	yes	—
109	C₆₁×#440	C₂²	1	2	yes	—
110	C₆₁×#440	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
112	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
115	C₆₁×#433	C₂²	1	2	yes	—
116	C₆₁×#433	C₂²	1	2	yes	—
117	C₆₁×#432	C₂²	1	1	yes	characteristic
118	C₆₁×#432	C₂²	1	1	yes	characteristic
119	C₂×#41×C₆₁	—	2	1	no	—
120	C₂×#41×C₆₁	—	2	1	no	—
121	C₂²×Q₈×C₆₁	—	2	1	no	—
122	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
123	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₆₁	—	2	2	no	—
128	C₄⋊Q₈×C₆₁	—	2	1	no	—
129	C₄⋊Q₈×C₆₁	—	2	2	no	—
130	C₄⋊Q₈×C₆₁	—	2	2	no	—
131	C₄⋊Q₈×C₆₁	—	2	2	no	—
132	C₄⋊Q₈×C₆₁	—	2	2	no	—
133	C₄⋊Q₈×C₆₁	—	2	2	no	—
134	C₄⋊Q₈×C₆₁	—	2	2	no	—
135	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
136	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
137	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
140	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
141	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
142	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
143	#127×C₆₁	C₂³	1	1	yes	characteristic
144	#127×C₆₁	C₂³	1	2	yes	—
145	#126×C₆₁	—	2	2	no	—
146	#126×C₆₁	—	2	1	no	—
147	#125×C₆₁	—	2	2	no	—
148	#125×C₆₁	—	2	2	no	—
149	#125×C₆₁	—	2	2	no	—
150	#125×C₆₁	—	2	2	no	—
151	#125×C₆₁	—	2	2	no	—
152	#125×C₆₁	—	2	2	no	—
153	#125×C₆₁	—	2	2	no	—
154	#125×C₆₁	—	2	2	no	—
155	#125×C₆₁	D₄	1	2	yes	—
156	#125×C₆₁	C₂³	1	2	yes	—
157	#125×C₆₁	C₂³	1	2	yes	—
158	#125×C₆₁	C₂³	1	2	yes	—
159	#125×C₆₁	C₂³	1	2	yes	—
160	#125×C₆₁	C₂³	1	1	yes	characteristic
161	#124×C₆₁	—	2	1	no	—
162	#124×C₆₁	—	2	2	no	—
163	#124×C₆₁	—	2	2	no	—
164	#124×C₆₁	—	2	1	no	—
165	#124×C₆₁	C₂³	1	2	yes	—
166	#124×C₆₁	C₂³	1	1	yes	characteristic
167	#123×C₆₁	—	2	1	no	—
168	#123×C₆₁	—	2	2	no	—
169	#123×C₆₁	—	2	2	no	—
170	#123×C₆₁	—	2	2	no	—
171	#123×C₆₁	—	2	2	no	—
172	#123×C₆₁	—	2	2	no	—
173	#123×C₆₁	—	2	2	no	—
174	C₂²⋊Q₈×C₆₁	—	2	2	no	—
175	C₂²⋊Q₈×C₆₁	—	2	1	no	—
176	C₂²⋊Q₈×C₆₁	—	2	1	no	—
177	C₂²⋊Q₈×C₆₁	—	2	2	no	—
178	C₂²⋊Q₈×C₆₁	—	2	2	no	—
179	C₂²⋊Q₈×C₆₁	—	2	2	no	—
180	C₂²⋊Q₈×C₆₁	—	2	2	no	—
181	C₂²⋊Q₈×C₆₁	—	2	1	no	—
182	C₂²⋊Q₈×C₆₁	—	2	2	no	—
183	C₂²⋊Q₈×C₆₁	—	2	2	no	—
184	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
185	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
186	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
187	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
188	#121×C₆₁	—	2	1	no	—
189	#121×C₆₁	—	2	2	no	—
190	#121×C₆₁	—	2	1	no	—
191	#121×C₆₁	—	2	2	no	—
192	#121×C₆₁	—	2	2	no	—
193	#121×C₆₁	C₂³	1	2	yes	—
194	#121×C₆₁	C₂³	1	1	yes	characteristic
195	C₄×Q₈×C₆₁	—	2	2	no	—
196	C₄×Q₈×C₆₁	—	2	2	no	—
197	C₄×Q₈×C₆₁	—	2	2	no	—
198	C₄×Q₈×C₆₁	—	2	2	no	—
199	C₄×Q₈×C₆₁	—	2	1	no	—
200	C₄×Q₈×C₆₁	—	2	2	no	—
201	C₄×Q₈×C₆₁	—	2	2	no	—
202	C₄×Q₈×C₆₁	—	2	1	no	—
203	C₄×Q₈×C₆₁	—	2	1	no	—
204	C₄×Q₈×C₆₁	—	2	1	no	—
205	C₄×Q₈×C₆₁	—	2	1	no	—
206	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
207	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
208	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
217	C₄×D₄×C₆₁	—	2	1	no	—
218	C₄×D₄×C₆₁	—	2	2	no	—
219	C₄×D₄×C₆₁	—	2	1	no	—
220	C₄×D₄×C₆₁	—	2	1	no	—
221	C₄×D₄×C₆₁	C₂³	1	2	yes	—
222	C₄×D₄×C₆₁	C₂³	1	2	yes	—
223	C₄×D₄×C₆₁	C₂³	1	2	yes	—
224	C₄×D₄×C₆₁	C₂³	1	2	yes	—
225	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
226	#117×C₆₁	—	2	2	no	—
227	#117×C₆₁	—	2	2	no	—
228	#117×C₆₁	—	2	1	no	—
229	#117×C₆₁	C₂³	1	2	yes	—
230	#117×C₆₁	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
232	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
233	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₆₁	—	2	1	no	—
235	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
236	#107×C₆₁	C₂³	1	2	yes	—
237	#107×C₆₁	C₂³	1	2	yes	—
238	#107×C₆₁	C₂³	1	2	yes	—
239	#107×C₆₁	C₂³	1	2	yes	—
240	#107×C₆₁	C₂³	1	2	yes	—
241	#107×C₆₁	C₂³	1	2	yes	—
242	#107×C₆₁	C₂³	1	2	yes	—
243	#106×C₆₁	C₂³	1	2	yes	—
244	#106×C₆₁	C₂³	1	2	yes	—
245	#106×C₆₁	C₂³	1	2	yes	—
246	#106×C₆₁	C₂³	1	2	yes	—
247	#106×C₆₁	C₂³	1	2	yes	—
248	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
249	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
250	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
251	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
252	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
253	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
254	#103×C₆₁	C₂³	1	2	yes	—
255	#103×C₆₁	C₂³	1	2	yes	—
256	#103×C₆₁	C₂³	1	2	yes	—
257	#103×C₆₁	C₂³	1	2	yes	—
258	#103×C₆₁	C₂³	1	2	yes	—
259	#103×C₆₁	C₂³	1	2	yes	—
260	#103×C₆₁	C₂³	1	2	yes	—
261	#102×C₆₁	C₂³	1	2	yes	—
262	#102×C₆₁	C₂³	1	2	yes	—
263	#102×C₆₁	C₂³	1	2	yes	—
264	#102×C₆₁	C₂³	1	2	yes	—
265	#102×C₆₁	C₂³	1	2	yes	—
266	#102×C₆₁	C₂³	1	2	yes	—
267	#102×C₆₁	C₂³	1	2	yes	—
268	#102×C₆₁	C₂³	1	2	yes	—
269	#102×C₆₁	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
271	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
273	#97×C₆₁	C₂³	1	1	yes	characteristic
274	#97×C₆₁	C₂³	1	1	yes	characteristic
275	#97×C₆₁	C₂³	1	2	yes	—
276	#97×C₆₁	C₂³	1	2	yes	—
277	#97×C₆₁	C₂³	1	2	yes	—
278	C₄×C₈×C₆₁	C₂³	1	2	yes	—
279	C₄×C₈×C₆₁	C₂³	1	2	yes	—
280	#41×C₆₁	—	8	2	no	—
281	#41×C₆₁	—	8	2	no	—
282	C₂×Q₈×C₆₁	—	2	4	no	—
283	C₂×Q₈×C₆₁	—	2	1	no	—
284	C₂×Q₈×C₆₁	—	2	1	no	—
285	C₂×Q₈×C₆₁	—	2	1	no	—
286	C₂×Q₈×C₆₁	—	2	1	no	—
287	C₂×Q₈×C₆₁	—	2	2	no	—
288	C₂×Q₈×C₆₁	—	2	2	no	—
289	C₂×Q₈×C₆₁	—	2	2	no	—
290	C₂×Q₈×C₆₁	—	8	2	no	—
291	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
292	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
296	C₂×D₄×C₆₁	—	2	1	no	—
297	C₂×D₄×C₆₁	—	2	2	no	—
298	C₂×D₄×C₆₁	—	2	1	no	—
299	C₂×D₄×C₆₁	—	2	1	no	—
300	C₂×D₄×C₆₁	—	2	2	no	—
301	C₂×D₄×C₆₁	—	2	2	no	—
302	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
303	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₁	—	2	1	no	—
305	C₂²×C₄×C₆₁	—	2	1	no	—
306	C₂²×C₄×C₆₁	—	2	1	no	—
307	C₂²×C₄×C₆₁	—	2	2	no	—
308	C₂²×C₄×C₆₁	—	2	2	no	—
309	C₂²×C₄×C₆₁	—	2	2	no	—
310	C₂²×C₄×C₆₁	—	2	2	no	—
311	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
314	Q₁₆×C₆₁	—	2	4	no	—
315	SD₁₆×C₆₁	—	2	4	no	—
316	SD₁₆×C₆₁	—	2	4	no	—
317	SD₁₆×C₆₁	—	2	4	no	—
318	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
319	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
320	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
321	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
322	C₄⋊C₄×C₆₁	—	2	1	no	—
323	C₄⋊C₄×C₆₁	—	2	2	no	—
324	C₄⋊C₄×C₆₁	—	2	2	no	—
325	C₄⋊C₄×C₆₁	—	2	2	no	—
326	C₄⋊C₄×C₆₁	—	2	2	no	—
327	C₄⋊C₄×C₆₁	—	2	1	no	—
328	C₄⋊C₄×C₆₁	—	2	2	no	—
329	C₄⋊C₄×C₆₁	—	2	2	no	—
330	C₄⋊C₄×C₆₁	—	2	2	no	—
331	C₄⋊C₄×C₆₁	—	2	2	no	—
332	C₄⋊C₄×C₆₁	—	2	1	no	—
333	C₄⋊C₄×C₆₁	—	2	1	no	—
334	C₄⋊C₄×C₆₁	—	2	1	no	—
335	C₄⋊C₄×C₆₁	—	2	2	no	—
336	C₄⋊C₄×C₆₁	—	2	1	no	—
337	C₄⋊C₄×C₆₁	—	2	2	no	—
338	C₄⋊C₄×C₆₁	—	2	1	no	—
339	C₄⋊C₄×C₆₁	—	2	2	no	—
340	C₄⋊C₄×C₆₁	—	2	2	no	—
341	C₄⋊C₄×C₆₁	—	2	2	no	—
342	C₄⋊C₄×C₆₁	—	2	2	no	—
343	C₄⋊C₄×C₆₁	—	2	2	no	—
344	C₄⋊C₄×C₆₁	—	2	2	no	—
345	C₄⋊C₄×C₆₁	—	2	2	no	—
346	C₄⋊C₄×C₆₁	—	2	2	no	—
347	C₄⋊C₄×C₆₁	—	2	1	no	—
348	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
349	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
350	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
351	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
353	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
359	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
363	C₂²⋊C₄×C₆₁	—	2	2	no	—
364	C₂²⋊C₄×C₆₁	—	2	1	no	—
365	C₂²⋊C₄×C₆₁	—	2	1	no	—
366	C₂²⋊C₄×C₆₁	—	2	1	no	—
367	C₂²⋊C₄×C₆₁	—	2	1	no	—
368	C₂²⋊C₄×C₆₁	—	2	2	no	—
369	C₂²⋊C₄×C₆₁	—	2	2	no	—
370	C₂²⋊C₄×C₆₁	—	2	2	no	—
371	C₂²⋊C₄×C₆₁	—	2	1	no	—
372	C₂²⋊C₄×C₆₁	—	2	2	no	—
373	C₂²⋊C₄×C₆₁	—	2	2	no	—
374	C₂²⋊C₄×C₆₁	—	2	2	no	—
375	C₂²⋊C₄×C₆₁	—	2	2	no	—
376	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
377	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
378	C₄²×C₆₁	—	2	2	no	—
379	C₄²×C₆₁	—	2	2	no	—
380	C₄²×C₆₁	—	2	1	no	—
381	C₄²×C₆₁	—	2	2	no	—
382	C₄²×C₆₁	—	2	2	no	—
383	C₄²×C₆₁	—	2	2	no	—
384	C₄²×C₆₁	—	2	2	no	—
385	C₄²×C₆₁	—	2	2	no	—
386	C₄²×C₆₁	—	2	2	no	—
387	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₆₁	C₂⁴	1	2	yes	—
390	C₄²×C₆₁	C₂⁴	1	2	yes	—
391	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
392	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
393	C₂³×C₆₁	—	2	1	no	—
394	C₂³×C₆₁	—	2	2	no	—
395	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
396	Q₈×C₆₁	—	2	4	no	—
397	Q₈×C₆₁	—	2	2	no	—
398	Q₈×C₆₁	—	2	2	no	—
399	Q₈×C₆₁	—	4	1	no	—
400	Q₈×C₆₁	—	4	2	no	—
401	Q₈×C₆₁	—	4	1	no	—
402	Q₈×C₆₁	—	4	2	no	—
403	Q₈×C₆₁	—	4	2	no	—
404	Q₈×C₆₁	—	8	1	no	—
405	Q₈×C₆₁	—	8	2	no	—
406	Q₈×C₆₁	—	8	2	no	—
407	Q₈×C₆₁	—	8	2	no	—
408	Q₈×C₆₁	2₋¹⁺⁴	1	4	yes	—
409	D₄×C₆₁	—	2	2	no	—
410	D₄×C₆₁	—	2	2	no	—
411	D₄×C₆₁	—	2	2	no	—
412	D₄×C₆₁	—	4	2	no	—
413	D₄×C₆₁	—	8	1	no	—
414	D₄×C₆₁	—	8	2	no	—
415	D₄×C₆₁	—	8	2	no	—
416	D₄×C₆₁	—	8	1	no	—
417	D₄×C₆₁	—	8	2	no	—
418	C₂×C₄×C₆₁	—	2	4	no	—
419	C₂×C₄×C₆₁	—	2	2	no	—
420	C₂×C₄×C₆₁	—	2	2	no	—
421	C₂×C₄×C₆₁	—	2	1	no	—
422	C₂×C₄×C₆₁	—	2	2	no	—
423	C₂×C₄×C₆₁	—	2	2	no	—
424	C₂×C₄×C₆₁	—	2	2	no	—
425	C₂×C₄×C₆₁	—	2	1	no	—
426	C₂×C₄×C₆₁	—	2	2	no	—
427	C₂×C₄×C₆₁	—	2	1	no	—
428	C₂×C₄×C₆₁	—	4	1	no	—
429	C₂×C₄×C₆₁	—	4	1	no	—
430	C₂×C₄×C₆₁	—	4	2	no	—
431	C₂×C₄×C₆₁	—	8	2	no	—
432	C₂×C₄×C₆₁	—	8	2	no	—
433	C₂×C₄×C₆₁	—	8	2	no	—
434	C₂×C₄×C₆₁	—	8	2	no	—
435	C₂×C₄×C₆₁	—	8	1	no	—
436	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
442	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
446	C₈×C₆₁	—	2	2	no	—
447	C₈×C₆₁	—	2	2	no	—
448	C₈×C₆₁	—	2	2	no	—
449	C₈×C₆₁	—	2	2	no	—
450	#61874	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂²×C₆₁	—	2	1	no	—
452	C₂²×C₆₁	—	2	1	no	—
453	C₂²×C₆₁	—	2	1	no	—
454	C₂²×C₆₁	—	4	1	no	—
455	C₂²×C₆₁	—	4	2	no	—
456	C₂²×C₆₁	—	4	2	no	—
457	C₂²×C₆₁	—	4	1	no	—
458	C₂²×C₆₁	—	4	1	no	—
459	C₂²×C₆₁	—	4	2	no	—
460	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
461	C₄×C₆₁	—	2	1	no	—
462	C₄×C₆₁	—	2	1	no	—
463	C₄×C₆₁	—	2	2	no	—
464	C₄×C₆₁	—	2	2	no	—
465	C₄×C₆₁	—	2	1	no	—
466	C₄×C₆₁	—	2	1	no	—
467	C₄×C₆₁	—	2	2	no	—
468	C₄×C₆₁	—	2	2	no	—
469	C₄×C₆₁	—	2	4	no	—
470	C₄×C₆₁	—	2	1	no	—
471	C₄×C₆₁	—	4	1	no	—
472	C₄×C₆₁	—	4	2	no	—
473	C₄×C₆₁	—	4	2	no	—
474	C₄×C₆₁	—	4	2	no	—
475	C₄×C₆₁	—	4	1	no	—
476	C₄×C₆₁	—	4	2	no	—
477	C₄×C₆₁	—	4	1	no	—
478	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
479	#3554	C₂×C₆₁	1	1	yes	characteristic
480	#3502	C₂×C₆₁	1	1	yes	characteristic, complemented
481	#3390	C₂×C₆₁	1	2	yes	complemented
482	#3388	C₂×C₆₁	1	2	yes	complemented
483	#3386	C₂×C₆₁	1	2	yes	complemented
484	#3385	C₂×C₆₁	1	2	yes	complemented
485	#3375	C₂×C₆₁	1	2	yes	complemented
486	#3371	C₂×C₆₁	1	2	yes	complemented
487	#3371	C₂×C₆₁	1	2	yes	complemented
488	#3368	C₂×C₆₁	1	2	yes	complemented
489	#3243	C₂×C₆₁	1	2	yes	complemented
490	#3241	C₂×C₆₁	1	2	yes	complemented
491	#3240	C₂×C₆₁	1	1	yes	characteristic, complemented
492	#3235	C₂×C₆₁	1	1	yes	characteristic, complemented
493	#3126	C₂×C₆₁	1	2	yes	complemented
494	#3121	C₂×C₆₁	1	2	yes	complemented
495	#3117	C₂×C₆₁	1	1	yes	characteristic, complemented
496	#3112	C₂×C₆₁	1	1	yes	characteristic, complemented
497	#2987	C₂×C₆₁	1	1	yes	characteristic, complemented
498	C₂×C₆₁	—	4	1	no	—
499	C₂×C₆₁	—	8	1	no	—
500	C₂×C₆₁	—	8	2	no	—
501	C₂×C₆₁	#3486	1	1	yes	characteristic
502	C₂×C₆₁	#3585	1	1	yes	characteristic
503	C₂×C₆₁	#3586	1	1	yes	characteristic
504	#562	—	2	2	no	—
505	#559	C₂²×C₆₁	1	1	yes	characteristic
506	#559	C₂²×C₆₁	1	2	yes	—
507	Q₈²	—	2	1	no	—
508	Q₈²	C₂²×C₆₁	1	2	yes	—
509	#557	—	2	1	no	—
510	#557	—	2	2	no	—
511	#557	C₂²×C₆₁	1	2	yes	—
512	#557	C₂²×C₆₁	1	2	yes	—
513	#557	C₂²×C₆₁	1	2	yes	—
514	#557	C₂²×C₆₁	1	1	yes	characteristic
515	#554	C₂²×C₆₁	1	2	yes	—
516	#550	C₂²×C₆₁	1	1	yes	characteristic
517	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
518	#548	—	2	1	no	—
519	#547	—	2	1	no	—
520	#544	—	2	1	no	—
521	#544	—	2	1	no	—
522	#544	C₂²×C₆₁	1	2	yes	—
523	#542	—	2	1	no	—
524	#542	C₂²×C₆₁	1	2	yes	—
525	#540	C₂²×C₆₁	1	2	yes	—
526	#539	—	2	2	no	—
527	#536	—	2	1	no	—
528	#533	—	2	2	no	—
529	#533	C₂²×C₆₁	1	1	yes	characteristic
530	#533	C₂²×C₆₁	1	1	yes	characteristic
531	#532	C₂²×C₆₁	1	1	yes	characteristic
532	#529	C₂²×C₆₁	1	1	yes	characteristic
533	#519	C₂²×C₆₁	1	2	yes	—
534	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
535	#501	C₂²×C₆₁	1	1	yes	characteristic
536	#501	C₂²×C₆₁	1	2	yes	—
537	#501	C₂²×C₆₁	1	2	yes	—
538	#501	C₂²×C₆₁	1	2	yes	—
539	#501	C₂²×C₆₁	1	1	yes	characteristic
540	#500	C₂²×C₆₁	1	2	yes	—
541	#499	C₂²×C₆₁	1	2	yes	—
542	#490	C₂²×C₆₁	1	2	yes	—
543	#490	C₂²×C₆₁	1	2	yes	—
544	#489	C₂²×C₆₁	1	1	yes	characteristic
545	#489	C₂²×C₆₁	1	2	yes	—
546	#489	C₂²×C₆₁	1	1	yes	characteristic
547	#488	C₂²×C₆₁	1	2	yes	—
548	#486	C₂²×C₆₁	1	2	yes	—
549	#485	C₂²×C₆₁	1	2	yes	—
550	#484	C₂²×C₆₁	1	1	yes	characteristic
551	#482	C₂²×C₆₁	1	2	yes	—
552	#482	C₂²×C₆₁	1	2	yes	—
553	#482	C₂²×C₆₁	1	2	yes	—
554	#481	C₂²×C₆₁	1	1	yes	characteristic
555	#480	C₂²×C₆₁	1	2	yes	—
556	#479	C₂²×C₆₁	1	2	yes	—
557	#479	C₂²×C₆₁	1	2	yes	—
558	#479	C₂²×C₆₁	1	2	yes	—
559	#479	C₂²×C₆₁	1	2	yes	—
560	#479	C₂²×C₆₁	1	2	yes	—
561	#478	C₂²×C₆₁	1	2	yes	—
562	#478	C₂²×C₆₁	1	2	yes	—
563	#478	C₂²×C₆₁	1	2	yes	—
564	#478	C₂²×C₆₁	1	2	yes	—
565	#477	C₂²×C₆₁	1	2	yes	—
566	#477	C₂²×C₆₁	1	2	yes	—
567	#477	C₂²×C₆₁	1	2	yes	—
568	#476	C₂²×C₆₁	1	2	yes	—
569	#476	C₂²×C₆₁	1	2	yes	—
570	#475	C₂²×C₆₁	1	2	yes	—
571	#474	C₂²×C₆₁	1	2	yes	—
572	#474	C₂²×C₆₁	1	2	yes	—
573	#474	C₂²×C₆₁	1	2	yes	—
574	#464	C₂²×C₆₁	1	2	yes	—
575	#464	C₂²×C₆₁	1	2	yes	—
576	#464	C₂²×C₆₁	1	2	yes	—
577	#460	C₂²×C₆₁	1	2	yes	—
578	#460	C₂²×C₆₁	1	2	yes	—
579	#460	C₂²×C₆₁	1	2	yes	—
580	#451	C₂²×C₆₁	1	1	yes	characteristic
581	#448	C₂²×C₆₁	1	2	yes	—
582	#448	C₂²×C₆₁	1	1	yes	characteristic
583	#446	C₂²×C₆₁	1	2	yes	—
584	#446	C₂²×C₆₁	1	2	yes	—
585	#446	C₂²×C₆₁	1	2	yes	—
586	#446	C₂²×C₆₁	1	2	yes	—
587	#441	C₂²×C₆₁	1	2	yes	—
588	#441	C₂²×C₆₁	1	2	yes	—
589	#440	C₂²×C₆₁	1	2	yes	—
590	#440	C₂²×C₆₁	1	2	yes	—
591	#440	C₂²×C₆₁	1	2	yes	—
592	#440	C₂²×C₆₁	1	2	yes	—
593	#440	C₂²×C₆₁	1	2	yes	—
594	#440	C₂²×C₆₁	1	2	yes	—
595	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
596	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
597	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
598	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
599	#433	C₂²×C₆₁	1	2	yes	—
600	#433	C₂²×C₆₁	1	2	yes	—
601	#432	C₂²×C₆₁	1	1	yes	characteristic
602	#432	C₂²×C₆₁	1	1	yes	characteristic
603	C₆₁	#61874	1	1	yes	characteristic, direct product factor, Sylow
604	C₂×#41	—	2	1	no	—
605	C₂×#41	—	2	1	no	—
606	C₂²×Q₈	—	2	1	no	—
607	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
608	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
609	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
610	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
612	C₄⋊Q₈	—	2	2	no	—
613	C₄⋊Q₈	—	2	1	no	—
614	C₄⋊Q₈	—	2	2	no	—
615	C₄⋊Q₈	—	2	2	no	—
616	C₄⋊Q₈	—	2	2	no	—
617	C₄⋊Q₈	—	2	2	no	—
618	C₄⋊Q₈	—	2	2	no	—
619	C₄⋊Q₈	—	2	2	no	—
620	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
621	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
622	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
625	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
626	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
627	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
628	#127	C₂³×C₆₁	1	1	yes	characteristic
629	#127	C₂³×C₆₁	1	2	yes	—
630	#126	—	2	2	no	—
631	#126	—	2	1	no	—
632	#125	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	2	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	D₄×C₆₁	1	2	yes	—
641	#125	C₂³×C₆₁	1	1	yes	characteristic
642	#125	C₂³×C₆₁	1	2	yes	—
643	#125	C₂³×C₆₁	1	2	yes	—
644	#125	C₂³×C₆₁	1	2	yes	—
645	#125	C₂³×C₆₁	1	2	yes	—
646	#124	—	2	1	no	—
647	#124	—	2	2	no	—
648	#124	—	2	2	no	—
649	#124	—	2	1	no	—
650	#124	C₂³×C₆₁	1	1	yes	characteristic
651	#124	C₂³×C₆₁	1	2	yes	—
652	#123	—	2	1	no	—
653	#123	—	2	2	no	—
654	#123	—	2	2	no	—
655	#123	—	2	2	no	—
656	#123	—	2	2	no	—
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	—	2	1	no	—
661	C₂²⋊Q₈	—	2	1	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	2	no	—
666	C₂²⋊Q₈	—	2	1	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
670	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
671	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
672	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
673	#121	—	2	1	no	—
674	#121	—	2	2	no	—
675	#121	—	2	1	no	—
676	#121	—	2	2	no	—
677	#121	—	2	2	no	—
678	#121	C₂³×C₆₁	1	1	yes	characteristic
679	#121	C₂³×C₆₁	1	2	yes	—
680	C₄×Q₈	—	2	2	no	—
681	C₄×Q₈	—	2	2	no	—
682	C₄×Q₈	—	2	2	no	—
683	C₄×Q₈	—	2	2	no	—
684	C₄×Q₈	—	2	2	no	—
685	C₄×Q₈	—	2	2	no	—
686	C₄×Q₈	—	2	1	no	—
687	C₄×Q₈	—	2	1	no	—
688	C₄×Q₈	—	2	1	no	—
689	C₄×Q₈	—	2	1	no	—
690	C₄×Q₈	—	2	1	no	—
691	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
692	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
693	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
694	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
695	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
696	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
697	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
698	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
699	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
700	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
701	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
702	C₄×D₄	—	2	1	no	—
703	C₄×D₄	—	2	2	no	—
704	C₄×D₄	—	2	1	no	—
705	C₄×D₄	—	2	1	no	—
706	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
707	C₄×D₄	C₂³×C₆₁	1	2	yes	—
708	C₄×D₄	C₂³×C₆₁	1	2	yes	—
709	C₄×D₄	C₂³×C₆₁	1	2	yes	—
710	C₄×D₄	C₂³×C₆₁	1	2	yes	—
711	#117	—	2	2	no	—
712	#117	—	2	2	no	—
713	#117	—	2	1	no	—
714	#117	C₂³×C₆₁	1	2	yes	—
715	#117	C₂³×C₆₁	1	2	yes	—
716	C₂×C₄⋊C₄	—	2	1	no	—
717	C₂×C₄⋊C₄	—	2	2	no	—
718	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
719	C₂×C₄²	—	2	1	no	—
720	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
721	#107	C₂³×C₆₁	1	2	yes	—
722	#107	C₂³×C₆₁	1	2	yes	—
723	#107	C₂³×C₆₁	1	2	yes	—
724	#107	C₂³×C₆₁	1	2	yes	—
725	#107	C₂³×C₆₁	1	2	yes	—
726	#107	C₂³×C₆₁	1	2	yes	—
727	#107	C₂³×C₆₁	1	2	yes	—
728	#106	C₂³×C₆₁	1	2	yes	—
729	#106	C₂³×C₆₁	1	2	yes	—
730	#106	C₂³×C₆₁	1	2	yes	—
731	#106	C₂³×C₆₁	1	2	yes	—
732	#106	C₂³×C₆₁	1	2	yes	—
733	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
734	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
735	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
736	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
737	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
738	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
739	#103	C₂³×C₆₁	1	2	yes	—
740	#103	C₂³×C₆₁	1	2	yes	—
741	#103	C₂³×C₆₁	1	2	yes	—
742	#103	C₂³×C₆₁	1	2	yes	—
743	#103	C₂³×C₆₁	1	2	yes	—
744	#103	C₂³×C₆₁	1	2	yes	—
745	#103	C₂³×C₆₁	1	2	yes	—
746	#102	C₂³×C₆₁	1	2	yes	—
747	#102	C₂³×C₆₁	1	2	yes	—
748	#102	C₂³×C₆₁	1	2	yes	—
749	#102	C₂³×C₆₁	1	2	yes	—
750	#102	C₂³×C₆₁	1	2	yes	—
751	#102	C₂³×C₆₁	1	2	yes	—
752	#102	C₂³×C₆₁	1	2	yes	—
753	#102	C₂³×C₆₁	1	2	yes	—
754	#102	C₂³×C₆₁	1	2	yes	—
755	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
756	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
757	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
758	#97	C₂³×C₆₁	1	1	yes	characteristic
759	#97	C₂³×C₆₁	1	1	yes	characteristic
760	#97	C₂³×C₆₁	1	2	yes	—
761	#97	C₂³×C₆₁	1	2	yes	—
762	#97	C₂³×C₆₁	1	2	yes	—
763	C₄×C₈	C₂³×C₆₁	1	2	yes	—
764	C₄×C₈	C₂³×C₆₁	1	2	yes	—
765	#41	—	8	2	no	—
766	#41	—	8	2	no	—
767	C₂×Q₈	—	2	4	no	—
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	—	2	1	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	8	2	no	—
776	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
777	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
778	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
779	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
780	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
788	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
799	Q₁₆	—	2	4	no	—
800	SD₁₆	—	2	4	no	—
801	SD₁₆	—	2	4	no	—
802	SD₁₆	—	2	4	no	—
803	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
804	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
805	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
806	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
834	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
835	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
836	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
837	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
838	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
839	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
840	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
841	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
844	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
846	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
847	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	1	no	—
850	C₂²⋊C₄	—	2	1	no	—
851	C₂²⋊C₄	—	2	1	no	—
852	C₂²⋊C₄	—	2	1	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	1	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
862	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	1	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
873	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
874	C₄²	C₂⁴×C₆₁	1	2	yes	—
875	C₄²	C₂⁴×C₆₁	1	2	yes	—
876	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
877	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
878	C₂³	—	2	1	no	—
879	C₂³	—	2	2	no	—
880	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
881	Q₈	—	2	4	no	—
882	Q₈	—	2	2	no	—
883	Q₈	—	2	2	no	—
884	Q₈	—	4	1	no	—
885	Q₈	—	4	2	no	—
886	Q₈	—	4	1	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	4	2	no	—
889	Q₈	—	8	1	no	—
890	Q₈	—	8	2	no	—
891	Q₈	—	8	2	no	—
892	Q₈	—	8	2	no	—
893	Q₈	2₋¹⁺⁴×C₆₁	1	4	yes	—
894	D₄	—	2	2	no	—
895	D₄	—	2	2	no	—
896	D₄	—	2	2	no	—
897	D₄	—	4	2	no	—
898	D₄	—	8	1	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	1	no	—
902	D₄	—	8	2	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	2	no	—
916	C₂×C₄	—	8	2	no	—
917	C₂×C₄	—	8	2	no	—
918	C₂×C₄	—	8	2	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	1	no	—
921	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
922	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
923	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
926	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
928	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
929	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
930	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₈	—	2	2	no	—
934	C₈	—	2	2	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	2	no	—
944	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	1	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	1	no	—
962	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
963	C₂	—	4	1	no	—
964	C₂	—	8	1	no	—
965	C₂	—	8	2	no	—
966	C₂	C₆₁×#3486	1	1	yes	characteristic
967	C₂	C₆₁×#3585	1	1	yes	characteristic
968	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3554	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3502	C₂	semidirect
3. C₆₁×#3390	C₂	semidirect
4. C₆₁×#3388	C₂	semidirect
5. C₆₁×#3386	C₂	semidirect
6. C₆₁×#3385	C₂	semidirect
7. C₆₁×#3375	C₂	semidirect
8. C₆₁×#3371	C₂	semidirect
9. C₆₁×#3371	C₂	semidirect
10. C₆₁×#3368	C₂	semidirect
11. C₆₁×#3243	C₂	semidirect
12. C₆₁×#3241	C₂	semidirect
13. C₆₁×#3240	C₂	semidirect
14. C₆₁×#3235	C₂	semidirect
15. C₆₁×#3126	C₂	semidirect
16. C₆₁×#3121	C₂	semidirect
17. C₆₁×#3117	C₂	semidirect
18. C₆₁×#3112	C₂	semidirect
19. C₆₁×#2987	C₂	semidirect
450. #61874	C₆₁	direct (N × H)
480. #3502	C₂×C₆₁	semidirect
481. #3390	C₂×C₆₁	semidirect
482. #3388	C₂×C₆₁	semidirect
483. #3386	C₂×C₆₁	semidirect
484. #3385	C₂×C₆₁	semidirect
485. #3375	C₂×C₆₁	semidirect
486. #3371	C₂×C₆₁	semidirect
487. #3371	C₂×C₆₁	semidirect
488. #3368	C₂×C₆₁	semidirect
489. #3243	C₂×C₆₁	semidirect
490. #3241	C₂×C₆₁	semidirect
491. #3240	C₂×C₆₁	semidirect
492. #3235	C₂×C₆₁	semidirect
493. #3126	C₂×C₆₁	semidirect
494. #3121	C₂×C₆₁	semidirect
495. #3117	C₂×C₆₁	semidirect
496. #3112	C₂×C₆₁	semidirect
497. #2987	C₂×C₆₁	semidirect
603. C₆₁	#61874	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×#3554	2
C₆₁×#3502	2
C₆₁×#3390	2
C₆₁×#3388	2
C₆₁×#3386	2
C₆₁×#3385	2
C₆₁×#3375	2
C₆₁×#3371	2
C₆₁×#3368	2
C₆₁×#3243	2
C₆₁×#3241	2
C₆₁×#3240	2
C₆₁×#3235	2
C₆₁×#3126	2
C₆₁×#3121	2
C₆₁×#3117	2
C₆₁×#3112	2
C₆₁×#2987	2
#61874	61

Subgroups — C61×#61874 #29565307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61874 #29565307