Subgroups — C₆₁×#61800 #29565233

Order 15616.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3512	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3346	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3345	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3344	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3317	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3315	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3309	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3307	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3204	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3203	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3099	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3098	C₂	1	2	yes	maximal, complemented
19	C₆₁×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#562	—	2	1	no	—
21	C₆₁×#562	—	2	1	no	—
22	C₆₁×#554	—	2	1	no	—
23	C₆₁×#554	C₂²	1	2	yes	—
24	C₆₁×#553	—	2	2	no	—
25	C₆₁×#553	—	2	2	no	—
26	C₆₁×#553	C₂²	1	2	yes	—
27	C₆₁×#553	C₂²	1	2	yes	—
28	C₆₁×#552	C₂²	1	2	yes	—
29	C₆₁×#552	C₂²	1	2	yes	—
30	C₆₁×#550	—	2	1	no	—
31	C₆₁×#550	C₂²	1	2	yes	—
32	C₆₁×#547	C₂²	1	2	yes	—
33	C₆₁×#547	C₂²	1	2	yes	—
34	C₆₁×#541	—	2	1	no	—
35	C₆₁×#540	—	2	1	no	—
36	C₆₁×#540	—	2	2	no	—
37	C₆₁×#537	—	2	2	no	—
38	C₆₁×#537	C₂²	1	2	yes	—
39	C₆₁×#537	C₂²	1	2	yes	—
40	C₆₁×#537	C₂²	1	1	yes	characteristic
41	C₆₁×#537	C₂²	1	1	yes	characteristic
42	C₆₁×#533	C₂²	1	1	yes	characteristic
43	C₆₁×#532	C₂²	1	1	yes	characteristic
44	C₆₁×#532	C₂²	1	1	yes	characteristic
45	C₆₁×#529	—	2	1	no	—
46	C₆₁×#529	—	2	1	no	—
47	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#520	C₂²	1	1	yes	characteristic
49	C₆₁×#520	C₂²	1	1	yes	characteristic
50	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
51	C₆₁×#501	C₂²	1	2	yes	—
52	C₆₁×#501	C₂²	1	2	yes	—
53	C₆₁×#491	C₂²	1	2	yes	—
54	C₆₁×#490	C₂²	1	2	yes	—
55	C₆₁×#485	C₂²	1	2	yes	—
56	C₆₁×#485	C₂²	1	2	yes	—
57	C₆₁×#485	C₂²	1	2	yes	—
58	C₆₁×#484	C₂²	1	2	yes	—
59	C₆₁×#484	C₂²	1	2	yes	—
60	C₆₁×#484	C₂²	1	2	yes	—
61	C₆₁×#483	C₂²	1	2	yes	—
62	C₆₁×#483	C₂²	1	2	yes	—
63	C₆₁×#483	C₂²	1	2	yes	—
64	C₆₁×#482	C₂²	1	2	yes	—
65	C₆₁×#482	C₂²	1	2	yes	—
66	C₆₁×#482	C₂²	1	2	yes	—
67	C₆₁×#481	C₂²	1	2	yes	—
68	C₆₁×#481	C₂²	1	2	yes	—
69	C₆₁×#481	C₂²	1	2	yes	—
70	C₆₁×#480	C₂²	1	2	yes	—
71	C₆₁×#480	C₂²	1	2	yes	—
72	C₆₁×#480	C₂²	1	2	yes	—
73	C₆₁×#479	C₂²	1	2	yes	—
74	C₆₁×#479	C₂²	1	2	yes	—
75	C₆₁×#478	C₂²	1	2	yes	—
76	C₆₁×#478	C₂²	1	2	yes	—
77	C₆₁×#477	C₂²	1	1	yes	characteristic
78	C₆₁×#476	C₂²	1	1	yes	characteristic
79	C₆₁×#475	C₂²	1	1	yes	characteristic
80	C₆₁×#474	C₂²	1	1	yes	characteristic
81	C₆₁×#470	C₂²	1	2	yes	—
82	C₆₁×#469	C₂²	1	2	yes	—
83	C₆₁×#468	C₂²	1	2	yes	—
84	C₆₁×#468	C₂²	1	2	yes	—
85	C₆₁×#467	C₂²	1	2	yes	—
86	C₆₁×#466	C₂²	1	2	yes	—
87	C₆₁×#465	C₂²	1	2	yes	—
88	C₆₁×#465	C₂²	1	2	yes	—
89	C₆₁×#462	C₂²	1	1	yes	characteristic
90	C₆₁×#461	C₂²	1	1	yes	characteristic
91	C₆₁×#460	C₂²	1	1	yes	characteristic
92	C₆₁×#459	C₂²	1	1	yes	characteristic
93	C₆₁×#452	C₂²	1	2	yes	—
94	C₆₁×#452	C₂²	1	2	yes	—
95	C₆₁×#452	C₂²	1	2	yes	—
96	C₆₁×#449	C₂²	1	2	yes	—
97	C₆₁×#449	C₂²	1	2	yes	—
98	C₆₁×#449	C₂²	1	2	yes	—
99	C₆₁×#442	C₂²	1	2	yes	—
100	C₆₁×#441	C₂²	1	2	yes	—
101	C₆₁×#440	C₂²	1	2	yes	—
102	C₆₁×#440	C₂²	1	2	yes	—
103	C₆₁×#435	C₂²	1	2	yes	—
104	C₆₁×#435	C₂²	1	2	yes	—
105	C₆₁×#435	C₂²	1	2	yes	—
106	C₆₁×#435	C₂²	1	2	yes	—
107	C₆₁×#432	C₂²	1	1	yes	characteristic
108	C₆₁×#432	C₂²	1	1	yes	characteristic
109	C₆₁×#428	C₂²	1	2	yes	—
110	C₆₁×#428	C₂²	1	2	yes	—
111	C₂×#107×C₆₁	C₂²	1	2	yes	—
112	C₂×#106×C₆₁	C₂²	1	2	yes	—
113	C₆₁×#417	C₂²	1	2	yes	—
114	C₆₁×#417	C₂²	1	2	yes	—
115	C₆₁×#416	C₂²	1	2	yes	—
116	C₆₁×#416	C₂²	1	2	yes	—
117	C₆₁×#408	C₂²	1	2	yes	—
118	C₆₁×#408	C₂²	1	2	yes	—
119	C₂×#41×C₆₁	—	2	2	no	—
120	C₂×#41×C₆₁	—	2	1	no	—
121	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
122	C₂×#41×C₆₁	C₂³	1	2	yes	—
123	C₂×#41×C₆₁	C₂³	1	2	yes	—
124	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
125	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
126	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
129	C₂×D₈×C₆₁	C₂³	1	2	yes	—
130	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
131	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
132	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
133	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
135	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
138	#127×C₆₁	—	2	2	no	—
139	#127×C₆₁	D₄	1	1	yes	characteristic
140	#127×C₆₁	C₂³	1	1	yes	characteristic
141	#126×C₆₁	—	2	2	no	—
142	#126×C₆₁	—	2	2	no	—
143	#126×C₆₁	—	2	2	no	—
144	#126×C₆₁	—	2	2	no	—
145	#125×C₆₁	—	2	2	no	—
146	#125×C₆₁	—	2	2	no	—
147	#125×C₆₁	—	2	2	no	—
148	#125×C₆₁	—	2	1	no	—
149	#125×C₆₁	—	2	1	no	—
150	#125×C₆₁	—	2	1	no	—
151	#125×C₆₁	C₂³	1	2	yes	—
152	#125×C₆₁	C₂³	1	2	yes	—
153	#124×C₆₁	—	2	1	no	—
154	#124×C₆₁	D₄	1	1	yes	characteristic
155	#124×C₆₁	D₄	1	1	yes	characteristic
156	#123×C₆₁	—	2	2	no	—
157	#123×C₆₁	—	2	2	no	—
158	#123×C₆₁	—	2	2	no	—
159	#123×C₆₁	—	2	2	no	—
160	#123×C₆₁	—	2	2	no	—
161	#123×C₆₁	—	2	2	no	—
162	#123×C₆₁	—	2	2	no	—
163	#123×C₆₁	—	2	2	no	—
164	C₂²⋊Q₈×C₆₁	—	2	1	no	—
165	C₂²⋊Q₈×C₆₁	—	2	1	no	—
166	C₂²⋊Q₈×C₆₁	—	2	2	no	—
167	C₂²⋊Q₈×C₆₁	—	2	2	no	—
168	C₂²⋊Q₈×C₆₁	—	2	1	no	—
169	C₂²⋊Q₈×C₆₁	—	2	2	no	—
170	C₂²⋊Q₈×C₆₁	—	2	2	no	—
171	C₂²⋊Q₈×C₆₁	—	2	2	no	—
172	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
173	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
174	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
175	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
176	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
177	#121×C₆₁	—	2	2	no	—
178	#121×C₆₁	—	2	2	no	—
179	#121×C₆₁	—	2	2	no	—
180	#121×C₆₁	—	2	2	no	—
181	#121×C₆₁	—	2	2	no	—
182	#121×C₆₁	—	2	1	no	—
183	#121×C₆₁	—	2	1	no	—
184	#121×C₆₁	—	2	2	no	—
185	#121×C₆₁	—	2	2	no	—
186	#121×C₆₁	—	2	2	no	—
187	#121×C₆₁	—	2	2	no	—
188	#121×C₆₁	—	2	2	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	D₄	1	2	yes	—
194	#121×C₆₁	D₄	1	2	yes	—
195	#121×C₆₁	C₂³	1	2	yes	—
196	#121×C₆₁	C₂³	1	2	yes	—
197	#121×C₆₁	C₂³	1	2	yes	—
198	#121×C₆₁	C₂³	1	2	yes	—
199	#121×C₆₁	C₂³	1	2	yes	—
200	C₄×Q₈×C₆₁	—	2	1	no	—
201	C₄×Q₈×C₆₁	—	2	1	no	—
202	C₄×Q₈×C₆₁	—	2	1	no	—
203	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
205	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
206	C₄×D₄×C₆₁	—	2	2	no	—
207	C₄×D₄×C₆₁	—	2	1	no	—
208	C₄×D₄×C₆₁	—	2	1	no	—
209	C₄×D₄×C₆₁	—	2	2	no	—
210	C₄×D₄×C₆₁	—	2	2	no	—
211	C₄×D₄×C₆₁	—	2	1	no	—
212	C₄×D₄×C₆₁	—	2	1	no	—
213	C₄×D₄×C₆₁	—	2	2	no	—
214	C₄×D₄×C₆₁	—	2	2	no	—
215	C₄×D₄×C₆₁	—	2	2	no	—
216	C₄×D₄×C₆₁	—	2	1	no	—
217	C₄×D₄×C₆₁	C₂³	1	2	yes	—
218	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₆₁	C₂³	1	2	yes	—
221	C₄×D₄×C₆₁	C₂³	1	2	yes	—
222	#117×C₆₁	—	2	1	no	—
223	#117×C₆₁	—	2	2	no	—
224	#117×C₆₁	—	2	2	no	—
225	#117×C₆₁	—	2	1	no	—
226	#117×C₆₁	C₂³	1	2	yes	—
227	#117×C₆₁	C₂³	1	2	yes	—
228	#117×C₆₁	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
230	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
231	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
232	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
238	C₂×C₄²×C₆₁	—	2	1	no	—
239	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
240	#107×C₆₁	C₂³	1	2	yes	—
241	#107×C₆₁	C₂³	1	2	yes	—
242	#107×C₆₁	C₂³	1	2	yes	—
243	#107×C₆₁	C₂³	1	2	yes	—
244	#107×C₆₁	C₂³	1	2	yes	—
245	#107×C₆₁	C₂³	1	2	yes	—
246	#106×C₆₁	C₂³	1	2	yes	—
247	#106×C₆₁	C₂³	1	2	yes	—
248	#106×C₆₁	C₂³	1	2	yes	—
249	#106×C₆₁	C₂³	1	2	yes	—
250	#106×C₆₁	C₂³	1	2	yes	—
251	#106×C₆₁	C₂³	1	2	yes	—
252	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
253	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
254	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
255	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
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	#103×C₆₁	C₂³	1	2	yes	—
262	#103×C₆₁	C₂³	1	2	yes	—
263	#103×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	#102×C₆₁	C₂³	1	2	yes	—
271	#102×C₆₁	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
278	#97×C₆₁	C₂³	1	2	yes	—
279	#97×C₆₁	C₂³	1	2	yes	—
280	#41×C₆₁	—	4	1	no	—
281	#41×C₆₁	—	4	1	no	—
282	#41×C₆₁	—	4	1	no	—
283	#41×C₆₁	—	4	1	no	—
284	#41×C₆₁	—	4	1	no	—
285	#41×C₆₁	—	4	1	no	—
286	#41×C₆₁	—	4	2	no	—
287	#41×C₆₁	—	4	2	no	—
288	#41×C₆₁	—	4	2	no	—
289	#41×C₆₁	—	4	2	no	—
290	#41×C₆₁	—	8	2	no	—
291	#41×C₆₁	—	8	4	no	—
292	C₂×Q₈×C₆₁	—	2	1	no	—
293	C₂×Q₈×C₆₁	—	2	1	no	—
294	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
295	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
296	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
297	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
298	C₂×D₄×C₆₁	—	2	1	no	—
299	C₂×D₄×C₆₁	—	2	2	no	—
300	C₂×D₄×C₆₁	—	2	2	no	—
301	C₂×D₄×C₆₁	—	2	2	no	—
302	C₂×D₄×C₆₁	—	2	2	no	—
303	C₂×D₄×C₆₁	—	2	2	no	—
304	C₂×D₄×C₆₁	—	2	2	no	—
305	C₂×D₄×C₆₁	—	2	2	no	—
306	C₂×D₄×C₆₁	—	2	1	no	—
307	C₂×D₄×C₆₁	—	2	1	no	—
308	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
309	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
310	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
311	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
312	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
313	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
315	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₆₁	—	2	1	no	—
317	C₂²×C₄×C₆₁	—	2	1	no	—
318	C₂²×C₄×C₆₁	—	2	2	no	—
319	C₂²×C₄×C₆₁	—	2	2	no	—
320	C₂²×C₄×C₆₁	—	2	2	no	—
321	C₂²×C₄×C₆₁	—	2	2	no	—
322	C₂²×C₄×C₆₁	—	2	1	no	—
323	C₂²×C₄×C₆₁	—	2	2	no	—
324	C₂²×C₄×C₆₁	—	2	1	no	—
325	C₂²×C₄×C₆₁	—	2	1	no	—
326	C₂²×C₄×C₆₁	—	2	2	no	—
327	C₂²×C₄×C₆₁	—	2	2	no	—
328	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
333	Q₁₆×C₆₁	—	4	2	no	—
334	SD₁₆×C₆₁	—	4	2	no	—
335	SD₁₆×C₆₁	—	4	2	no	—
336	D₈×C₆₁	—	4	2	no	—
337	M₁₆×C₆₁	—	4	2	no	—
338	M₁₆×C₆₁	—	4	2	no	—
339	C₂×C₈×C₆₁	—	4	2	no	—
340	C₂×C₈×C₆₁	—	4	2	no	—
341	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
342	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
343	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
344	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₆₁	—	2	1	no	—
346	C₄⋊C₄×C₆₁	—	2	2	no	—
347	C₄⋊C₄×C₆₁	—	2	2	no	—
348	C₄⋊C₄×C₆₁	—	2	2	no	—
349	C₄⋊C₄×C₆₁	—	2	2	no	—
350	C₄⋊C₄×C₆₁	—	2	2	no	—
351	C₄⋊C₄×C₆₁	—	2	2	no	—
352	C₄⋊C₄×C₆₁	—	2	1	no	—
353	C₄⋊C₄×C₆₁	—	2	1	no	—
354	C₄⋊C₄×C₆₁	—	2	2	no	—
355	C₄⋊C₄×C₆₁	—	2	2	no	—
356	C₄⋊C₄×C₆₁	—	2	2	no	—
357	C₄⋊C₄×C₆₁	—	2	2	no	—
358	C₄⋊C₄×C₆₁	—	2	1	no	—
359	C₄⋊C₄×C₆₁	—	2	1	no	—
360	C₄⋊C₄×C₆₁	—	2	2	no	—
361	C₄⋊C₄×C₆₁	—	2	2	no	—
362	C₄⋊C₄×C₆₁	—	2	1	no	—
363	C₄⋊C₄×C₆₁	—	2	1	no	—
364	C₄⋊C₄×C₆₁	—	2	1	no	—
365	C₄⋊C₄×C₆₁	—	2	2	no	—
366	C₄⋊C₄×C₆₁	—	2	2	no	—
367	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
372	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
375	C₂²⋊C₄×C₆₁	—	2	2	no	—
376	C₂²⋊C₄×C₆₁	—	2	2	no	—
377	C₂²⋊C₄×C₆₁	—	2	2	no	—
378	C₂²⋊C₄×C₆₁	—	2	1	no	—
379	C₂²⋊C₄×C₆₁	—	2	2	no	—
380	C₂²⋊C₄×C₆₁	—	2	2	no	—
381	C₂²⋊C₄×C₆₁	—	2	2	no	—
382	C₂²⋊C₄×C₆₁	—	2	2	no	—
383	C₂²⋊C₄×C₆₁	—	2	1	no	—
384	C₂²⋊C₄×C₆₁	—	2	1	no	—
385	C₂²⋊C₄×C₆₁	—	2	2	no	—
386	C₂²⋊C₄×C₆₁	—	2	2	no	—
387	C₂²⋊C₄×C₆₁	—	2	2	no	—
388	C₂²⋊C₄×C₆₁	—	2	2	no	—
389	C₂²⋊C₄×C₆₁	—	2	2	no	—
390	C₂²⋊C₄×C₆₁	—	2	2	no	—
391	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
395	C₄²×C₆₁	—	2	1	no	—
396	C₄²×C₆₁	—	2	1	no	—
397	C₄²×C₆₁	—	2	1	no	—
398	C₄²×C₆₁	—	2	2	no	—
399	C₄²×C₆₁	—	2	2	no	—
400	C₄²×C₆₁	—	2	2	no	—
401	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
403	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
404	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
405	C₂³×C₆₁	—	2	1	no	—
406	C₂³×C₆₁	—	2	2	no	—
407	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
408	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
409	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
410	Q₈×C₆₁	—	2	1	no	—
411	Q₈×C₆₁	—	2	2	no	—
412	Q₈×C₆₁	—	2	1	no	—
413	Q₈×C₆₁	—	2	2	no	—
414	Q₈×C₆₁	—	4	1	no	—
415	Q₈×C₆₁	—	4	1	no	—
416	Q₈×C₆₁	—	4	2	no	—
417	Q₈×C₆₁	—	8	1	no	—
418	D₄×C₆₁	—	2	1	no	—
419	D₄×C₆₁	—	2	2	no	—
420	D₄×C₆₁	—	2	1	no	—
421	D₄×C₆₁	—	2	2	no	—
422	D₄×C₆₁	—	4	2	no	—
423	D₄×C₆₁	—	4	1	no	—
424	D₄×C₆₁	—	4	1	no	—
425	D₄×C₆₁	—	4	2	no	—
426	D₄×C₆₁	—	4	2	no	—
427	D₄×C₆₁	—	4	2	no	—
428	D₄×C₆₁	—	4	2	no	—
429	D₄×C₆₁	—	4	2	no	—
430	D₄×C₆₁	—	8	1	no	—
431	D₄×C₆₁	—	8	2	no	—
432	D₄×C₆₁	—	8	2	no	—
433	D₄×C₆₁	—	8	2	no	—
434	D₄×C₆₁	—	8	2	no	—
435	D₄×C₆₁	—	8	2	no	—
436	D₄×C₆₁	—	8	2	no	—
437	D₄×C₆₁	—	8	2	no	—
438	C₂×C₄×C₆₁	—	2	2	no	—
439	C₂×C₄×C₆₁	—	2	2	no	—
440	C₂×C₄×C₆₁	—	2	2	no	—
441	C₂×C₄×C₆₁	—	2	2	no	—
442	C₂×C₄×C₆₁	—	2	1	no	—
443	C₂×C₄×C₆₁	—	2	1	no	—
444	C₂×C₄×C₆₁	—	2	1	no	—
445	C₂×C₄×C₆₁	—	2	1	no	—
446	C₂×C₄×C₆₁	—	2	1	no	—
447	C₂×C₄×C₆₁	—	2	2	no	—
448	C₂×C₄×C₆₁	—	2	2	no	—
449	C₂×C₄×C₆₁	—	2	2	no	—
450	C₂×C₄×C₆₁	—	2	2	no	—
451	C₂×C₄×C₆₁	—	2	2	no	—
452	C₂×C₄×C₆₁	—	4	1	no	—
453	C₂×C₄×C₆₁	—	4	1	no	—
454	C₂×C₄×C₆₁	—	4	2	no	—
455	C₂×C₄×C₆₁	—	4	4	no	—
456	C₂×C₄×C₆₁	—	8	1	no	—
457	C₂×C₄×C₆₁	—	8	1	no	—
458	C₂×C₄×C₆₁	—	8	2	no	—
459	C₂×C₄×C₆₁	—	8	2	no	—
460	C₂×C₄×C₆₁	—	8	2	no	—
461	C₂×C₄×C₆₁	—	8	1	no	—
462	C₂×C₄×C₆₁	—	8	2	no	—
463	C₂×C₄×C₆₁	—	8	1	no	—
464	C₂×C₄×C₆₁	—	8	2	no	—
465	C₂×C₄×C₆₁	—	8	2	no	—
466	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
474	C₈×C₆₁	—	2	2	no	—
475	C₈×C₆₁	—	2	2	no	—
476	C₈×C₆₁	—	2	2	no	—
477	C₈×C₆₁	—	2	2	no	—
478	#61800	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
479	C₂²×C₆₁	—	2	1	no	—
480	C₂²×C₆₁	—	2	2	no	—
481	C₂²×C₆₁	—	2	2	no	—
482	C₂²×C₆₁	—	2	1	no	—
483	C₂²×C₆₁	—	2	2	no	—
484	C₂²×C₆₁	—	2	2	no	—
485	C₂²×C₆₁	—	2	1	no	—
486	C₂²×C₆₁	—	2	2	no	—
487	C₂²×C₆₁	—	2	2	no	—
488	C₂²×C₆₁	—	4	2	no	—
489	C₂²×C₆₁	—	4	1	no	—
490	C₂²×C₆₁	—	4	1	no	—
491	C₂²×C₆₁	—	4	2	no	—
492	C₂²×C₆₁	—	4	1	no	—
493	C₂²×C₆₁	—	4	2	no	—
494	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
495	C₄×C₆₁	—	2	1	no	—
496	C₄×C₆₁	—	2	1	no	—
497	C₄×C₆₁	—	2	1	no	—
498	C₄×C₆₁	—	2	1	no	—
499	C₄×C₆₁	—	2	1	no	—
500	C₄×C₆₁	—	2	2	no	—
501	C₄×C₆₁	—	2	2	no	—
502	C₄×C₆₁	—	4	2	no	—
503	C₄×C₆₁	—	4	1	no	—
504	C₄×C₆₁	—	4	2	no	—
505	C₄×C₆₁	—	4	2	no	—
506	C₄×C₆₁	—	4	1	no	—
507	C₄×C₆₁	—	4	2	no	—
508	C₄×C₆₁	—	4	1	no	—
509	C₄×C₆₁	—	4	2	no	—
510	C₄×C₆₁	#585	1	1	yes	characteristic
511	C₄×C₆₁	#585	1	1	yes	characteristic
512	#3548	C₂×C₆₁	1	1	yes	characteristic, complemented
513	#3512	C₂×C₆₁	1	1	yes	characteristic, complemented
514	#3346	C₂×C₆₁	1	2	yes	complemented
515	#3345	C₂×C₆₁	1	2	yes	complemented
516	#3344	C₂×C₆₁	1	2	yes	complemented
517	#3343	C₂×C₆₁	1	2	yes	complemented
518	#3317	C₂×C₆₁	1	2	yes	complemented
519	#3315	C₂×C₆₁	1	2	yes	complemented
520	#3309	C₂×C₆₁	1	2	yes	complemented
521	#3307	C₂×C₆₁	1	2	yes	complemented
522	#3236	C₂×C₆₁	1	1	yes	characteristic, complemented
523	#3234	C₂×C₆₁	1	1	yes	characteristic, complemented
524	#3204	C₂×C₆₁	1	2	yes	complemented
525	#3203	C₂×C₆₁	1	2	yes	complemented
526	#3116	C₂×C₆₁	1	1	yes	characteristic, complemented
527	#3115	C₂×C₆₁	1	1	yes	characteristic, complemented
528	#3099	C₂×C₆₁	1	2	yes	complemented
529	#3098	C₂×C₆₁	1	2	yes	complemented
530	#2980	C₂×C₆₁	1	1	yes	characteristic, complemented
531	C₂×C₆₁	—	4	1	no	—
532	C₂×C₆₁	—	4	2	no	—
533	C₂×C₆₁	—	4	2	no	—
534	C₂×C₆₁	—	8	2	no	—
535	C₂×C₆₁	—	8	1	no	—
536	C₂×C₆₁	#3485	1	1	yes	characteristic
537	C₂×C₆₁	#3585	1	1	yes	characteristic
538	C₂×C₆₁	#3586	1	1	yes	characteristic
539	#562	—	2	1	no	—
540	#562	—	2	1	no	—
541	#554	—	2	1	no	—
542	#554	C₂²×C₆₁	1	2	yes	—
543	#553	—	2	2	no	—
544	#553	—	2	2	no	—
545	#553	C₂²×C₆₁	1	2	yes	—
546	#553	C₂²×C₆₁	1	2	yes	—
547	#552	C₂²×C₆₁	1	2	yes	—
548	#552	C₂²×C₆₁	1	2	yes	—
549	#550	—	2	1	no	—
550	#550	C₂²×C₆₁	1	2	yes	—
551	#547	C₂²×C₆₁	1	2	yes	—
552	#547	C₂²×C₆₁	1	2	yes	—
553	#541	—	2	1	no	—
554	#540	—	2	1	no	—
555	#540	—	2	2	no	—
556	#537	—	2	2	no	—
557	#537	C₂²×C₆₁	1	2	yes	—
558	#537	C₂²×C₆₁	1	2	yes	—
559	#537	C₂²×C₆₁	1	1	yes	characteristic
560	#537	C₂²×C₆₁	1	1	yes	characteristic
561	#533	C₂²×C₆₁	1	1	yes	characteristic
562	#532	C₂²×C₆₁	1	1	yes	characteristic
563	#532	C₂²×C₆₁	1	1	yes	characteristic
564	#529	—	2	1	no	—
565	#529	—	2	1	no	—
566	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
567	#520	C₂²×C₆₁	1	1	yes	characteristic
568	#520	C₂²×C₆₁	1	1	yes	characteristic
569	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
570	#501	C₂²×C₆₁	1	2	yes	—
571	#501	C₂²×C₆₁	1	2	yes	—
572	#491	C₂²×C₆₁	1	2	yes	—
573	#490	C₂²×C₆₁	1	2	yes	—
574	#485	C₂²×C₆₁	1	2	yes	—
575	#485	C₂²×C₆₁	1	2	yes	—
576	#485	C₂²×C₆₁	1	2	yes	—
577	#484	C₂²×C₆₁	1	2	yes	—
578	#484	C₂²×C₆₁	1	2	yes	—
579	#484	C₂²×C₆₁	1	2	yes	—
580	#483	C₂²×C₆₁	1	2	yes	—
581	#483	C₂²×C₆₁	1	2	yes	—
582	#483	C₂²×C₆₁	1	2	yes	—
583	#482	C₂²×C₆₁	1	2	yes	—
584	#482	C₂²×C₆₁	1	2	yes	—
585	#482	C₂²×C₆₁	1	2	yes	—
586	#481	C₂²×C₆₁	1	2	yes	—
587	#481	C₂²×C₆₁	1	2	yes	—
588	#481	C₂²×C₆₁	1	2	yes	—
589	#480	C₂²×C₆₁	1	2	yes	—
590	#480	C₂²×C₆₁	1	2	yes	—
591	#480	C₂²×C₆₁	1	2	yes	—
592	#479	C₂²×C₆₁	1	2	yes	—
593	#479	C₂²×C₆₁	1	2	yes	—
594	#478	C₂²×C₆₁	1	2	yes	—
595	#478	C₂²×C₆₁	1	2	yes	—
596	#477	C₂²×C₆₁	1	1	yes	characteristic
597	#476	C₂²×C₆₁	1	1	yes	characteristic
598	#475	C₂²×C₆₁	1	1	yes	characteristic
599	#474	C₂²×C₆₁	1	1	yes	characteristic
600	#470	C₂²×C₆₁	1	2	yes	—
601	#469	C₂²×C₆₁	1	2	yes	—
602	#468	C₂²×C₆₁	1	2	yes	—
603	#468	C₂²×C₆₁	1	2	yes	—
604	#467	C₂²×C₆₁	1	2	yes	—
605	#466	C₂²×C₆₁	1	2	yes	—
606	#465	C₂²×C₆₁	1	2	yes	—
607	#465	C₂²×C₆₁	1	2	yes	—
608	#462	C₂²×C₆₁	1	1	yes	characteristic
609	#461	C₂²×C₆₁	1	1	yes	characteristic
610	#460	C₂²×C₆₁	1	1	yes	characteristic
611	#459	C₂²×C₆₁	1	1	yes	characteristic
612	#452	C₂²×C₆₁	1	2	yes	—
613	#452	C₂²×C₆₁	1	2	yes	—
614	#452	C₂²×C₆₁	1	2	yes	—
615	#449	C₂²×C₆₁	1	2	yes	—
616	#449	C₂²×C₆₁	1	2	yes	—
617	#449	C₂²×C₆₁	1	2	yes	—
618	#442	C₂²×C₆₁	1	2	yes	—
619	#441	C₂²×C₆₁	1	2	yes	—
620	#440	C₂²×C₆₁	1	2	yes	—
621	#440	C₂²×C₆₁	1	2	yes	—
622	#435	C₂²×C₆₁	1	2	yes	—
623	#435	C₂²×C₆₁	1	2	yes	—
624	#435	C₂²×C₆₁	1	2	yes	—
625	#435	C₂²×C₆₁	1	2	yes	—
626	#432	C₂²×C₆₁	1	1	yes	characteristic
627	#432	C₂²×C₆₁	1	1	yes	characteristic
628	#428	C₂²×C₆₁	1	2	yes	—
629	#428	C₂²×C₆₁	1	2	yes	—
630	C₂×#107	C₂²×C₆₁	1	2	yes	—
631	C₂×#106	C₂²×C₆₁	1	2	yes	—
632	#417	C₂²×C₆₁	1	2	yes	—
633	#417	C₂²×C₆₁	1	2	yes	—
634	#416	C₂²×C₆₁	1	2	yes	—
635	#416	C₂²×C₆₁	1	2	yes	—
636	#408	C₂²×C₆₁	1	2	yes	—
637	#408	C₂²×C₆₁	1	2	yes	—
638	C₆₁	#61800	1	1	yes	characteristic, direct product factor, Sylow
639	C₂×#41	—	2	2	no	—
640	C₂×#41	—	2	1	no	—
641	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
642	C₂×#41	C₂³×C₆₁	1	2	yes	—
643	C₂×#41	C₂³×C₆₁	1	2	yes	—
644	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
645	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
646	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
647	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
648	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
649	C₂×D₈	C₂³×C₆₁	1	2	yes	—
650	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
651	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
652	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
653	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
654	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
655	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
656	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
657	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
658	#127	—	2	2	no	—
659	#127	D₄×C₆₁	1	1	yes	characteristic
660	#127	C₂³×C₆₁	1	1	yes	characteristic
661	#126	—	2	2	no	—
662	#126	—	2	2	no	—
663	#126	—	2	2	no	—
664	#126	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	—	2	2	no	—
668	#125	—	2	1	no	—
669	#125	—	2	1	no	—
670	#125	—	2	1	no	—
671	#125	C₂³×C₆₁	1	2	yes	—
672	#125	C₂³×C₆₁	1	2	yes	—
673	#124	—	2	1	no	—
674	#124	D₄×C₆₁	1	1	yes	characteristic
675	#124	D₄×C₆₁	1	1	yes	characteristic
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
696	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
697	#121	—	2	1	no	—
698	#121	—	2	1	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	—	2	2	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	—	2	2	no	—
710	#121	—	2	1	no	—
711	#121	—	2	2	no	—
712	#121	—	2	2	no	—
713	#121	D₄×C₆₁	1	2	yes	—
714	#121	D₄×C₆₁	1	2	yes	—
715	#121	C₂³×C₆₁	1	2	yes	—
716	#121	C₂³×C₆₁	1	2	yes	—
717	#121	C₂³×C₆₁	1	2	yes	—
718	#121	C₂³×C₆₁	1	2	yes	—
719	#121	C₂³×C₆₁	1	2	yes	—
720	C₄×Q₈	—	2	1	no	—
721	C₄×Q₈	—	2	1	no	—
722	C₄×Q₈	—	2	1	no	—
723	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
724	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
725	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	—	2	2	no	—
730	C₄×D₄	—	2	2	no	—
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	2	no	—
735	C₄×D₄	—	2	2	no	—
736	C₄×D₄	—	2	1	no	—
737	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
738	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
739	C₄×D₄	C₂³×C₆₁	1	2	yes	—
740	C₄×D₄	C₂³×C₆₁	1	2	yes	—
741	C₄×D₄	C₂³×C₆₁	1	2	yes	—
742	#117	—	2	1	no	—
743	#117	—	2	2	no	—
744	#117	—	2	2	no	—
745	#117	—	2	1	no	—
746	#117	C₂³×C₆₁	1	1	yes	characteristic
747	#117	C₂³×C₆₁	1	2	yes	—
748	#117	C₂³×C₆₁	1	2	yes	—
749	C₂×C₄⋊C₄	—	2	1	no	—
750	C₂×C₄⋊C₄	—	2	1	no	—
751	C₂×C₄⋊C₄	—	2	2	no	—
752	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
753	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
756	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
757	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
758	C₂×C₄²	—	2	1	no	—
759	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
760	#107	C₂³×C₆₁	1	2	yes	—
761	#107	C₂³×C₆₁	1	2	yes	—
762	#107	C₂³×C₆₁	1	2	yes	—
763	#107	C₂³×C₆₁	1	2	yes	—
764	#107	C₂³×C₆₁	1	2	yes	—
765	#107	C₂³×C₆₁	1	2	yes	—
766	#106	C₂³×C₆₁	1	2	yes	—
767	#106	C₂³×C₆₁	1	2	yes	—
768	#106	C₂³×C₆₁	1	2	yes	—
769	#106	C₂³×C₆₁	1	2	yes	—
770	#106	C₂³×C₆₁	1	2	yes	—
771	#106	C₂³×C₆₁	1	2	yes	—
772	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
773	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
774	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
775	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
776	#103	C₂³×C₆₁	1	2	yes	—
777	#103	C₂³×C₆₁	1	2	yes	—
778	#103	C₂³×C₆₁	1	2	yes	—
779	#103	C₂³×C₆₁	1	2	yes	—
780	#103	C₂³×C₆₁	1	2	yes	—
781	#103	C₂³×C₆₁	1	2	yes	—
782	#103	C₂³×C₆₁	1	2	yes	—
783	#103	C₂³×C₆₁	1	2	yes	—
784	#102	C₂³×C₆₁	1	2	yes	—
785	#102	C₂³×C₆₁	1	2	yes	—
786	#102	C₂³×C₆₁	1	2	yes	—
787	#102	C₂³×C₆₁	1	2	yes	—
788	#102	C₂³×C₆₁	1	2	yes	—
789	#102	C₂³×C₆₁	1	2	yes	—
790	#102	C₂³×C₆₁	1	2	yes	—
791	#102	C₂³×C₆₁	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
793	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
794	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
795	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
796	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
797	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
798	#97	C₂³×C₆₁	1	2	yes	—
799	#97	C₂³×C₆₁	1	2	yes	—
800	#41	—	4	1	no	—
801	#41	—	4	1	no	—
802	#41	—	4	1	no	—
803	#41	—	4	1	no	—
804	#41	—	4	1	no	—
805	#41	—	4	1	no	—
806	#41	—	4	2	no	—
807	#41	—	4	2	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	8	2	no	—
811	#41	—	8	4	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
815	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
816	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
817	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	1	no	—
827	C₂×D₄	—	2	1	no	—
828	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
829	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
830	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
831	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
832	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
833	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
834	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
835	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
849	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
853	Q₁₆	—	4	2	no	—
854	SD₁₆	—	4	2	no	—
855	SD₁₆	—	4	2	no	—
856	D₈	—	4	2	no	—
857	M₁₆	—	4	2	no	—
858	M₁₆	—	4	2	no	—
859	C₂×C₈	—	4	2	no	—
860	C₂×C₈	—	4	2	no	—
861	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
862	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
863	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
864	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
888	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
889	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
890	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
891	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
892	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
893	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
894	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	1	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	1	no	—
904	C₂²⋊C₄	—	2	1	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
912	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
913	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
914	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
915	C₄²	—	2	1	no	—
916	C₄²	—	2	1	no	—
917	C₄²	—	2	1	no	—
918	C₄²	—	2	2	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	2	no	—
921	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
922	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
923	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
924	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
925	C₂³	—	2	1	no	—
926	C₂³	—	2	2	no	—
927	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
928	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
929	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
930	Q₈	—	2	1	no	—
931	Q₈	—	2	2	no	—
932	Q₈	—	2	1	no	—
933	Q₈	—	2	2	no	—
934	Q₈	—	4	1	no	—
935	Q₈	—	4	1	no	—
936	Q₈	—	4	2	no	—
937	Q₈	—	8	1	no	—
938	D₄	—	2	1	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	1	no	—
941	D₄	—	2	2	no	—
942	D₄	—	4	2	no	—
943	D₄	—	4	1	no	—
944	D₄	—	4	1	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	2	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	2	no	—
950	D₄	—	8	1	no	—
951	D₄	—	8	2	no	—
952	D₄	—	8	2	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	2	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	D₄	—	8	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	1	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	8	1	no	—
977	C₂×C₄	—	8	1	no	—
978	C₂×C₄	—	8	2	no	—
979	C₂×C₄	—	8	2	no	—
980	C₂×C₄	—	8	2	no	—
981	C₂×C₄	—	8	1	no	—
982	C₂×C₄	—	8	2	no	—
983	C₂×C₄	—	8	1	no	—
984	C₂×C₄	—	8	2	no	—
985	C₂×C₄	—	8	2	no	—
986	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
988	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
989	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
991	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
992	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
993	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
994	C₈	—	2	2	no	—
995	C₈	—	2	2	no	—
996	C₈	—	2	2	no	—
997	C₈	—	2	2	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	1	no	—
1028	C₄	—	4	2	no	—
1029	C₄	C₆₁×#585	1	1	yes	characteristic
1030	C₄	C₆₁×#585	1	1	yes	characteristic
1031	C₂	—	4	1	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	4	2	no	—
1034	C₂	—	8	2	no	—
1035	C₂	—	8	1	no	—
1036	C₂	C₆₁×#3485	1	1	yes	characteristic
1037	C₂	C₆₁×#3585	1	1	yes	characteristic
1038	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×#3548	C₂	semidirect
2. C₆₁×#3512	C₂	semidirect
3. C₆₁×#3346	C₂	semidirect
4. C₆₁×#3345	C₂	semidirect
5. C₆₁×#3344	C₂	semidirect
6. C₆₁×#3343	C₂	semidirect
7. C₆₁×#3317	C₂	semidirect
8. C₆₁×#3315	C₂	semidirect
9. C₆₁×#3309	C₂	semidirect
10. C₆₁×#3307	C₂	semidirect
11. C₆₁×#3236	C₂	semidirect
12. C₆₁×#3234	C₂	semidirect
13. C₆₁×#3204	C₂	semidirect
14. C₆₁×#3203	C₂	semidirect
15. C₆₁×#3116	C₂	semidirect
16. C₆₁×#3115	C₂	semidirect
17. C₆₁×#3099	C₂	semidirect
18. C₆₁×#3098	C₂	semidirect
19. C₆₁×#2980	C₂	semidirect
478. #61800	C₆₁	direct (N × H)
512. #3548	C₂×C₆₁	semidirect
513. #3512	C₂×C₆₁	semidirect
514. #3346	C₂×C₆₁	semidirect
515. #3345	C₂×C₆₁	semidirect
516. #3344	C₂×C₆₁	semidirect
517. #3343	C₂×C₆₁	semidirect
518. #3317	C₂×C₆₁	semidirect
519. #3315	C₂×C₆₁	semidirect
520. #3309	C₂×C₆₁	semidirect
521. #3307	C₂×C₆₁	semidirect
522. #3236	C₂×C₆₁	semidirect
523. #3234	C₂×C₆₁	semidirect
524. #3204	C₂×C₆₁	semidirect
525. #3203	C₂×C₆₁	semidirect
526. #3116	C₂×C₆₁	semidirect
527. #3115	C₂×C₆₁	semidirect
528. #3099	C₂×C₆₁	semidirect
529. #3098	C₂×C₆₁	semidirect
530. #2980	C₂×C₆₁	semidirect
638. C₆₁	#61800	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×#3548	2
C₆₁×#3512	2
C₆₁×#3346	2
C₆₁×#3345	2
C₆₁×#3344	2
C₆₁×#3343	2
C₆₁×#3317	2
C₆₁×#3315	2
C₆₁×#3309	2
C₆₁×#3307	2
C₆₁×#3236	2
C₆₁×#3234	2
C₆₁×#3204	2
C₆₁×#3203	2
C₆₁×#3116	2
C₆₁×#3115	2
C₆₁×#3099	2
C₆₁×#3098	2
C₆₁×#2980	2
#61800	61

Subgroups — C61×#61800 #29565233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61800 #29565233