Subgroups — C₆₁×#62104 #29565537

Order 15616.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3337	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3336	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3301	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3300	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3250	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3232	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3108	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₆₁×#479	C₂	1	2	yes	maximal, complemented
23	C₆₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#557	C₂²	1	1	yes	characteristic
25	C₆₁×#557	C₂²	1	1	yes	characteristic
26	C₆₁×#556	—	2	1	no	—
27	C₆₁×#556	C₂²	1	1	yes	characteristic
28	C₆₁×#554	C₂²	1	1	yes	characteristic
29	C₆₁×#554	C₂²	1	1	yes	characteristic
30	C₆₁×#553	C₂²	1	2	yes	—
31	C₆₁×#552	—	2	2	no	—
32	C₆₁×#552	—	2	2	no	—
33	C₆₁×#552	—	2	1	no	—
34	C₆₁×#552	C₂²	1	2	yes	—
35	C₆₁×#552	C₂²	1	2	yes	—
36	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#548	C₂²	1	2	yes	—
38	C₆₁×#547	—	2	1	no	—
39	C₆₁×#547	—	2	1	no	—
40	C₆₁×#547	C₂²	1	1	yes	characteristic
41	C₆₁×#547	C₂²	1	1	yes	characteristic
42	C₆₁×#541	—	2	1	no	—
43	C₆₁×#539	—	2	2	no	—
44	C₆₁×#533	—	2	1	no	—
45	C₆₁×#533	C₂²	1	1	yes	characteristic
46	C₆₁×#533	C₂²	1	1	yes	characteristic
47	C₆₁×#529	—	2	2	no	—
48	C₆₁×#529	C₂²	1	1	yes	characteristic
49	C₆₁×#529	C₂²	1	2	yes	—
50	C₆₁×#529	C₂²	1	2	yes	—
51	C₂×#125×C₆₁	C₂²	1	2	yes	—
52	C₆₁×#520	—	2	1	no	—
53	C₄×#41×C₆₁	—	2	1	no	—
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
57	C₆₁×#500	C₂²	1	1	yes	characteristic
58	C₆₁×#499	C₂²	1	2	yes	—
59	C₆₁×#499	C₂²	1	2	yes	—
60	C₆₁×#498	C₂²	1	1	yes	characteristic
61	C₆₁×#488	C₂²	1	2	yes	—
62	C₆₁×#488	C₂²	1	2	yes	—
63	C₆₁×#487	C₂²	1	1	yes	characteristic
64	C₆₁×#487	C₂²	1	1	yes	characteristic
65	C₆₁×#485	C₂²	1	2	yes	—
66	C₆₁×#485	C₂²	1	2	yes	—
67	C₆₁×#485	C₂²	1	1	yes	characteristic
68	C₆₁×#484	C₂²	1	2	yes	—
69	C₆₁×#483	C₂²	1	2	yes	—
70	C₆₁×#483	C₂²	1	2	yes	—
71	C₆₁×#482	C₂²	1	1	yes	characteristic
72	C₆₁×#481	C₂²	1	2	yes	—
73	C₆₁×#480	C₂²	1	2	yes	—
74	C₆₁×#480	C₂²	1	2	yes	—
75	C₆₁×#479	C₂²	1	2	yes	—
76	C₆₁×#479	C₂²	1	2	yes	—
77	C₆₁×#479	C₂²	1	1	yes	characteristic
78	C₆₁×#479	C₂²	1	2	yes	—
79	C₆₁×#479	C₂²	1	2	yes	—
80	C₆₁×#479	C₂²	1	2	yes	—
81	C₆₁×#479	C₂²	1	2	yes	—
82	C₆₁×#479	C₂²	1	2	yes	—
83	C₆₁×#479	C₂²	1	2	yes	—
84	C₆₁×#479	C₂²	1	2	yes	—
85	C₆₁×#478	C₂²	1	2	yes	—
86	C₆₁×#478	C₂²	1	2	yes	—
87	C₆₁×#478	C₂²	1	1	yes	characteristic
88	C₆₁×#477	C₂²	1	1	yes	characteristic
89	C₆₁×#476	C₂²	1	1	yes	characteristic
90	C₆₁×#475	C₂²	1	1	yes	characteristic
91	C₆₁×#475	C₂²	1	1	yes	characteristic
92	C₆₁×#474	C₂²	1	1	yes	characteristic
93	C₆₁×#474	C₂²	1	1	yes	characteristic
94	C₆₁×#467	C₂²	1	2	yes	—
95	C₆₁×#467	C₂²	1	2	yes	—
96	C₆₁×#466	C₂²	1	2	yes	—
97	C₆₁×#465	C₂²	1	2	yes	—
98	C₆₁×#465	C₂²	1	2	yes	—
99	C₆₁×#465	C₂²	1	2	yes	—
100	C₆₁×#464	C₂²	1	2	yes	—
101	C₆₁×#464	C₂²	1	1	yes	characteristic
102	C₆₁×#464	C₂²	1	2	yes	—
103	C₆₁×#463	C₂²	1	2	yes	—
104	C₆₁×#463	C₂²	1	1	yes	characteristic
105	C₆₁×#462	C₂²	1	1	yes	characteristic
106	C₆₁×#461	C₂²	1	1	yes	characteristic
107	C₆₁×#452	C₂²	1	1	yes	characteristic
108	C₆₁×#451	C₂²	1	2	yes	—
109	C₆₁×#449	C₂²	1	1	yes	characteristic
110	C₆₁×#448	C₂²	1	2	yes	—
111	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
113	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
114	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
120	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
121	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₆₁	C₂²	1	2	yes	—
124	C₈×D₄×C₆₁	C₂²	1	2	yes	—
125	C₆₁×#431	C₂²	1	1	yes	characteristic
126	C₆₁×#431	C₂²	1	2	yes	—
127	C₆₁×#427	C₂²	1	2	yes	—
128	C₂×#107×C₆₁	C₂²	1	2	yes	—
129	C₂×#106×C₆₁	C₂²	1	2	yes	—
130	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
132	C₆₁×#416	C₂²	1	2	yes	—
133	C₂×#103×C₆₁	C₂²	1	2	yes	—
134	C₂×#103×C₆₁	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
138	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
147	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
148	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₆₁	—	2	1	no	—
150	C₄⋊Q₈×C₆₁	—	2	1	no	—
151	C₄⋊Q₈×C₆₁	—	2	1	no	—
152	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
156	#126×C₆₁	—	2	2	no	—
157	#126×C₆₁	—	2	2	no	—
158	#126×C₆₁	—	2	2	no	—
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	—	2	2	no	—
161	#126×C₆₁	—	2	1	no	—
162	#126×C₆₁	—	2	2	no	—
163	#125×C₆₁	—	2	2	no	—
164	#125×C₆₁	—	2	2	no	—
165	#125×C₆₁	—	2	2	no	—
166	#125×C₆₁	—	2	1	no	—
167	#125×C₆₁	—	2	2	no	—
168	#125×C₆₁	—	2	1	no	—
169	#125×C₆₁	—	2	2	no	—
170	#125×C₆₁	—	2	2	no	—
171	#125×C₆₁	C₂³	1	2	yes	—
172	#125×C₆₁	C₂³	1	2	yes	—
173	#125×C₆₁	C₂³	1	2	yes	—
174	#125×C₆₁	C₂³	1	2	yes	—
175	#125×C₆₁	C₂³	1	1	yes	characteristic
176	#124×C₆₁	—	2	2	no	—
177	#124×C₆₁	C₂³	1	2	yes	—
178	#124×C₆₁	C₂³	1	1	yes	characteristic
179	#123×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	2	no	—
181	#123×C₆₁	—	2	1	no	—
182	#123×C₆₁	—	2	2	no	—
183	#123×C₆₁	—	2	2	no	—
184	#123×C₆₁	—	2	2	no	—
185	#123×C₆₁	—	2	2	no	—
186	#123×C₆₁	—	2	2	no	—
187	C₂²⋊Q₈×C₆₁	—	2	1	no	—
188	C₂²⋊Q₈×C₆₁	—	2	1	no	—
189	C₂²⋊Q₈×C₆₁	—	2	1	no	—
190	C₂²⋊Q₈×C₆₁	—	2	1	no	—
191	C₂²⋊Q₈×C₆₁	—	2	1	no	—
192	C₂²⋊Q₈×C₆₁	—	2	1	no	—
193	C₂²⋊Q₈×C₆₁	—	2	2	no	—
194	C₂²⋊Q₈×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	—	2	1	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	2	no	—
198	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
201	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	—	2	2	no	—
204	#121×C₆₁	C₂³	1	2	yes	—
205	#121×C₆₁	C₂³	1	2	yes	—
206	#121×C₆₁	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₆₁	—	2	1	no	—
208	C₄×Q₈×C₆₁	—	2	1	no	—
209	C₄×Q₈×C₆₁	—	2	1	no	—
210	C₄×Q₈×C₆₁	—	2	2	no	—
211	C₄×Q₈×C₆₁	—	2	1	no	—
212	C₄×Q₈×C₆₁	—	2	1	no	—
213	C₄×Q₈×C₆₁	—	2	2	no	—
214	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₆₁	—	2	1	no	—
224	C₄×D₄×C₆₁	—	2	1	no	—
225	C₄×D₄×C₆₁	—	2	2	no	—
226	C₄×D₄×C₆₁	—	2	1	no	—
227	C₄×D₄×C₆₁	—	2	1	no	—
228	C₄×D₄×C₆₁	—	2	2	no	—
229	C₄×D₄×C₆₁	—	2	1	no	—
230	C₄×D₄×C₆₁	—	2	2	no	—
231	C₄×D₄×C₆₁	—	2	2	no	—
232	C₄×D₄×C₆₁	D₄	1	2	yes	—
233	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
234	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₆₁	C₂³	1	2	yes	—
237	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₆₁	C₂³	1	2	yes	—
240	#117×C₆₁	—	2	1	no	—
241	#117×C₆₁	—	2	1	no	—
242	#117×C₆₁	—	2	2	no	—
243	#117×C₆₁	—	2	2	no	—
244	#117×C₆₁	—	2	2	no	—
245	#117×C₆₁	—	2	1	no	—
246	#117×C₆₁	—	2	1	no	—
247	#117×C₆₁	—	2	2	no	—
248	#117×C₆₁	D₄	1	2	yes	—
249	#117×C₆₁	D₄	1	1	yes	characteristic
250	#117×C₆₁	C₂³	1	2	yes	—
251	#117×C₆₁	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
254	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
259	C₂×C₄²×C₆₁	—	2	2	no	—
260	C₂×C₄²×C₆₁	—	2	1	no	—
261	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
263	#107×C₆₁	C₂³	1	1	yes	characteristic
264	#107×C₆₁	C₂³	1	2	yes	—
265	#107×C₆₁	C₂³	1	2	yes	—
266	#107×C₆₁	C₂³	1	2	yes	—
267	#107×C₆₁	C₂³	1	2	yes	—
268	#107×C₆₁	C₂³	1	1	yes	characteristic
269	#107×C₆₁	C₂³	1	2	yes	—
270	#106×C₆₁	C₂³	1	1	yes	characteristic
271	#106×C₆₁	C₂³	1	2	yes	—
272	#106×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	2	yes	—
275	#106×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	2	yes	—
277	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
279	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
282	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	#103×C₆₁	C₂³	1	1	yes	characteristic
285	#103×C₆₁	C₂³	1	1	yes	characteristic
286	#103×C₆₁	C₂³	1	2	yes	—
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	1	yes	characteristic
293	#103×C₆₁	C₂³	1	2	yes	—
294	#103×C₆₁	C₂³	1	2	yes	—
295	#103×C₆₁	C₂³	1	1	yes	characteristic
296	#103×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	1	yes	characteristic
302	#102×C₆₁	C₂³	1	1	yes	characteristic
303	#102×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₁	C₂³	1	2	yes	—
311	C₄×C₈×C₆₁	C₂³	1	2	yes	—
312	#41×C₆₁	—	2	4	no	—
313	#41×C₆₁	—	2	2	no	—
314	#41×C₆₁	—	4	1	no	—
315	#41×C₆₁	—	4	4	no	—
316	#41×C₆₁	—	4	4	no	—
317	C₂×Q₈×C₆₁	—	2	2	no	—
318	C₂×Q₈×C₆₁	—	2	1	no	—
319	C₂×Q₈×C₆₁	—	2	1	no	—
320	C₂×Q₈×C₆₁	—	2	1	no	—
321	C₂×Q₈×C₆₁	—	2	4	no	—
322	C₂×Q₈×C₆₁	—	4	2	no	—
323	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₆₁	—	2	1	no	—
328	C₂×D₄×C₆₁	—	2	2	no	—
329	C₂×D₄×C₆₁	—	2	2	no	—
330	C₂×D₄×C₆₁	—	2	1	no	—
331	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
332	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₆₁	—	2	2	no	—
336	C₂²×C₄×C₆₁	—	2	2	no	—
337	C₂²×C₄×C₆₁	—	2	2	no	—
338	C₂²×C₄×C₆₁	—	2	2	no	—
339	C₂²×C₄×C₆₁	—	2	1	no	—
340	C₂²×C₄×C₆₁	—	2	1	no	—
341	C₂²×C₄×C₆₁	—	2	1	no	—
342	C₂²×C₄×C₆₁	—	2	1	no	—
343	C₂²×C₄×C₆₁	—	2	2	no	—
344	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
345	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
347	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
350	Q₁₆×C₆₁	—	2	2	no	—
351	Q₁₆×C₆₁	—	4	2	no	—
352	SD₁₆×C₆₁	—	2	2	no	—
353	SD₁₆×C₆₁	—	4	2	no	—
354	SD₁₆×C₆₁	—	4	1	no	—
355	D₈×C₆₁	—	4	1	no	—
356	C₂×C₈×C₆₁	—	4	2	no	—
357	C₂×C₈×C₆₁	—	4	2	no	—
358	C₂×C₈×C₆₁	—	4	2	no	—
359	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
362	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
364	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₆₁	—	2	1	no	—
366	C₄⋊C₄×C₆₁	—	2	2	no	—
367	C₄⋊C₄×C₆₁	—	2	1	no	—
368	C₄⋊C₄×C₆₁	—	2	1	no	—
369	C₄⋊C₄×C₆₁	—	2	2	no	—
370	C₄⋊C₄×C₆₁	—	2	1	no	—
371	C₄⋊C₄×C₆₁	—	2	2	no	—
372	C₄⋊C₄×C₆₁	—	2	2	no	—
373	C₄⋊C₄×C₆₁	—	2	2	no	—
374	C₄⋊C₄×C₆₁	—	2	2	no	—
375	C₄⋊C₄×C₆₁	—	2	2	no	—
376	C₄⋊C₄×C₆₁	—	2	2	no	—
377	C₄⋊C₄×C₆₁	—	2	2	no	—
378	C₄⋊C₄×C₆₁	—	2	2	no	—
379	C₄⋊C₄×C₆₁	—	2	2	no	—
380	C₄⋊C₄×C₆₁	—	2	2	no	—
381	C₄⋊C₄×C₆₁	—	2	1	no	—
382	C₄⋊C₄×C₆₁	—	2	1	no	—
383	C₄⋊C₄×C₆₁	—	2	2	no	—
384	C₄⋊C₄×C₆₁	—	2	2	no	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	—	2	2	no	—
389	C₄⋊C₄×C₆₁	—	2	1	no	—
390	C₄⋊C₄×C₆₁	—	2	2	no	—
391	C₄⋊C₄×C₆₁	—	2	1	no	—
392	C₄⋊C₄×C₆₁	—	2	1	no	—
393	C₄⋊C₄×C₆₁	—	2	2	no	—
394	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄×C₆₁	—	2	2	no	—
406	C₂²⋊C₄×C₆₁	—	2	2	no	—
407	C₂²⋊C₄×C₆₁	—	2	2	no	—
408	C₂²⋊C₄×C₆₁	—	2	1	no	—
409	C₂²⋊C₄×C₆₁	—	2	2	no	—
410	C₂²⋊C₄×C₆₁	—	2	1	no	—
411	C₂²⋊C₄×C₆₁	—	2	1	no	—
412	C₂²⋊C₄×C₆₁	—	2	1	no	—
413	C₂²⋊C₄×C₆₁	—	2	1	no	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	—	2	1	no	—
416	C₂²⋊C₄×C₆₁	—	2	1	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₂²⋊C₄×C₆₁	—	2	2	no	—
420	C₂²⋊C₄×C₆₁	—	2	2	no	—
421	C₂²⋊C₄×C₆₁	—	2	1	no	—
422	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
425	C₄²×C₆₁	—	2	1	no	—
426	C₄²×C₆₁	—	2	1	no	—
427	C₄²×C₆₁	—	2	2	no	—
428	C₄²×C₆₁	—	2	2	no	—
429	C₄²×C₆₁	—	2	1	no	—
430	C₄²×C₆₁	—	2	2	no	—
431	C₄²×C₆₁	—	2	2	no	—
432	C₄²×C₆₁	—	2	2	no	—
433	C₄²×C₆₁	—	2	1	no	—
434	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₆₁	C₂×D₄	1	2	yes	—
437	C₄²×C₆₁	C₂×D₄	1	2	yes	—
438	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
439	C₄²×C₆₁	C₂⁴	1	2	yes	—
440	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
441	C₂³×C₆₁	—	2	1	no	—
442	C₂³×C₆₁	—	2	1	no	—
443	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
444	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
445	Q₈×C₆₁	—	2	2	no	—
446	Q₈×C₆₁	—	2	1	no	—
447	Q₈×C₆₁	—	2	1	no	—
448	Q₈×C₆₁	—	2	2	no	—
449	Q₈×C₆₁	—	2	1	no	—
450	Q₈×C₆₁	—	2	2	no	—
451	Q₈×C₆₁	—	4	4	no	—
452	Q₈×C₆₁	—	4	2	no	—
453	Q₈×C₆₁	—	4	2	no	—
454	Q₈×C₆₁	—	8	1	no	—
455	Q₈×C₆₁	2₋¹⁺⁴	1	2	yes	—
456	D₄×C₆₁	—	2	4	no	—
457	D₄×C₆₁	—	2	1	no	—
458	D₄×C₆₁	—	2	1	no	—
459	D₄×C₆₁	—	2	1	no	—
460	D₄×C₆₁	—	2	1	no	—
461	D₄×C₆₁	—	4	2	no	—
462	D₄×C₆₁	—	4	4	no	—
463	D₄×C₆₁	—	4	4	no	—
464	D₄×C₆₁	—	8	1	no	—
465	D₄×C₆₁	#135	1	4	yes	—
466	C₂×C₄×C₆₁	—	2	4	no	—
467	C₂×C₄×C₆₁	—	2	1	no	—
468	C₂×C₄×C₆₁	—	2	2	no	—
469	C₂×C₄×C₆₁	—	2	2	no	—
470	C₂×C₄×C₆₁	—	2	1	no	—
471	C₂×C₄×C₆₁	—	2	2	no	—
472	C₂×C₄×C₆₁	—	2	1	no	—
473	C₂×C₄×C₆₁	—	2	1	no	—
474	C₂×C₄×C₆₁	—	2	1	no	—
475	C₂×C₄×C₆₁	—	2	1	no	—
476	C₂×C₄×C₆₁	—	2	2	no	—
477	C₂×C₄×C₆₁	—	2	2	no	—
478	C₂×C₄×C₆₁	—	2	2	no	—
479	C₂×C₄×C₆₁	—	2	2	no	—
480	C₂×C₄×C₆₁	—	2	1	no	—
481	C₂×C₄×C₆₁	—	2	1	no	—
482	C₂×C₄×C₆₁	—	4	2	no	—
483	C₂×C₄×C₆₁	—	4	1	no	—
484	C₂×C₄×C₆₁	—	4	2	no	—
485	C₂×C₄×C₆₁	—	4	4	no	—
486	C₂×C₄×C₆₁	—	4	2	no	—
487	C₂×C₄×C₆₁	—	4	4	no	—
488	C₂×C₄×C₆₁	—	4	4	no	—
489	C₂×C₄×C₆₁	—	4	2	no	—
490	C₂×C₄×C₆₁	—	4	2	no	—
491	C₂×C₄×C₆₁	—	8	2	no	—
492	C₂×C₄×C₆₁	—	8	2	no	—
493	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
502	C₈×C₆₁	—	2	1	no	—
503	C₈×C₆₁	—	2	1	no	—
504	C₈×C₆₁	—	2	1	no	—
505	C₈×C₆₁	—	2	1	no	—
506	C₈×C₆₁	—	2	2	no	—
507	C₈×C₆₁	—	2	2	no	—
508	#62104	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
509	C₂²×C₆₁	—	2	2	no	—
510	C₂²×C₆₁	—	2	2	no	—
511	C₂²×C₆₁	—	2	1	no	—
512	C₂²×C₆₁	—	2	1	no	—
513	C₂²×C₆₁	—	2	1	no	—
514	C₂²×C₆₁	—	4	1	no	—
515	C₂²×C₆₁	—	4	1	no	—
516	C₂²×C₆₁	—	4	1	no	—
517	C₂²×C₆₁	—	4	1	no	—
518	C₂²×C₆₁	—	4	1	no	—
519	C₂²×C₆₁	—	4	1	no	—
520	C₂²×C₆₁	C₂×#135	1	4	yes	—
521	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
522	C₄×C₆₁	—	2	1	no	—
523	C₄×C₆₁	—	2	2	no	—
524	C₄×C₆₁	—	2	1	no	—
525	C₄×C₆₁	—	2	1	no	—
526	C₄×C₆₁	—	2	2	no	—
527	C₄×C₆₁	—	2	2	no	—
528	C₄×C₆₁	—	2	1	no	—
529	C₄×C₆₁	—	2	2	no	—
530	C₄×C₆₁	—	4	1	no	—
531	C₄×C₆₁	—	4	1	no	—
532	C₄×C₆₁	—	4	2	no	—
533	C₄×C₆₁	—	4	2	no	—
534	C₄×C₆₁	—	4	1	no	—
535	C₄×C₆₁	—	4	1	no	—
536	C₄×C₆₁	—	4	1	no	—
537	C₄×C₆₁	—	4	2	no	—
538	C₄×C₆₁	—	4	2	no	—
539	C₄×C₆₁	C₂×#135	1	2	yes	—
540	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
541	C₄×C₆₁	#585	1	1	yes	characteristic
542	#3515	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#3482	C₂×C₆₁	1	1	yes	characteristic, complemented
544	#3383	C₂×C₆₁	1	1	yes	characteristic, complemented
545	#3381	C₂×C₆₁	1	1	yes	characteristic, complemented
546	#3364	C₂×C₆₁	1	1	yes	characteristic, complemented
547	#3360	C₂×C₆₁	1	1	yes	characteristic, complemented
548	#3337	C₂×C₆₁	1	2	yes	complemented
549	#3336	C₂×C₆₁	1	2	yes	complemented
550	#3335	C₂×C₆₁	1	1	yes	characteristic, complemented
551	#3334	C₂×C₆₁	1	1	yes	characteristic, complemented
552	#3301	C₂×C₆₁	1	2	yes	complemented
553	#3300	C₂×C₆₁	1	2	yes	complemented
554	#3299	C₂×C₆₁	1	1	yes	characteristic, complemented
555	#3298	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#3250	C₂×C₆₁	1	2	yes	complemented
557	#3248	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#3232	C₂×C₆₁	1	2	yes	complemented
559	#3231	C₂×C₆₁	1	1	yes	characteristic, complemented
560	#3108	C₂×C₆₁	1	2	yes	complemented
561	#3102	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3076	C₂×C₆₁	1	1	yes	characteristic, complemented
563	C₂×#479	C₂×C₆₁	1	2	yes	complemented
564	#2988	C₂×C₆₁	1	1	yes	characteristic, complemented
565	C₂×C₆₁	—	2	4	no	—
566	C₂×C₆₁	—	4	1	no	—
567	C₂×C₆₁	—	8	1	no	—
568	C₂×C₆₁	—	8	1	no	—
569	C₂×C₆₁	#3489	1	1	yes	characteristic
570	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
571	C₂×C₆₁	#3586	1	1	yes	characteristic
572	#557	C₂²×C₆₁	1	1	yes	characteristic
573	#557	C₂²×C₆₁	1	1	yes	characteristic
574	#556	—	2	1	no	—
575	#556	C₂²×C₆₁	1	1	yes	characteristic
576	#554	C₂²×C₆₁	1	1	yes	characteristic
577	#554	C₂²×C₆₁	1	1	yes	characteristic
578	#553	C₂²×C₆₁	1	2	yes	—
579	#552	—	2	2	no	—
580	#552	—	2	2	no	—
581	#552	—	2	1	no	—
582	#552	C₂²×C₆₁	1	2	yes	—
583	#552	C₂²×C₆₁	1	2	yes	—
584	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
585	#548	C₂²×C₆₁	1	2	yes	—
586	#547	—	2	1	no	—
587	#547	—	2	1	no	—
588	#547	C₂²×C₆₁	1	1	yes	characteristic
589	#547	C₂²×C₆₁	1	1	yes	characteristic
590	#541	—	2	1	no	—
591	#539	—	2	2	no	—
592	#533	—	2	1	no	—
593	#533	C₂²×C₆₁	1	1	yes	characteristic
594	#533	C₂²×C₆₁	1	1	yes	characteristic
595	#529	—	2	2	no	—
596	#529	C₂²×C₆₁	1	1	yes	characteristic
597	#529	C₂²×C₆₁	1	2	yes	—
598	#529	C₂²×C₆₁	1	2	yes	—
599	C₂×#125	C₂²×C₆₁	1	2	yes	—
600	#520	—	2	1	no	—
601	C₄×#41	—	2	1	no	—
602	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
603	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
604	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
605	#500	C₂²×C₆₁	1	1	yes	characteristic
606	#499	C₂²×C₆₁	1	2	yes	—
607	#499	C₂²×C₆₁	1	2	yes	—
608	#498	C₂²×C₆₁	1	1	yes	characteristic
609	#488	C₂²×C₆₁	1	2	yes	—
610	#488	C₂²×C₆₁	1	2	yes	—
611	#487	C₂²×C₆₁	1	1	yes	characteristic
612	#487	C₂²×C₆₁	1	1	yes	characteristic
613	#485	C₂²×C₆₁	1	1	yes	characteristic
614	#485	C₂²×C₆₁	1	2	yes	—
615	#485	C₂²×C₆₁	1	2	yes	—
616	#484	C₂²×C₆₁	1	2	yes	—
617	#483	C₂²×C₆₁	1	2	yes	—
618	#483	C₂²×C₆₁	1	2	yes	—
619	#482	C₂²×C₆₁	1	1	yes	characteristic
620	#481	C₂²×C₆₁	1	2	yes	—
621	#480	C₂²×C₆₁	1	2	yes	—
622	#480	C₂²×C₆₁	1	2	yes	—
623	#479	C₂²×C₆₁	1	1	yes	characteristic
624	#479	C₂²×C₆₁	1	2	yes	—
625	#479	C₂²×C₆₁	1	2	yes	—
626	#479	C₂²×C₆₁	1	2	yes	—
627	#479	C₂²×C₆₁	1	2	yes	—
628	#479	C₂²×C₆₁	1	2	yes	—
629	#479	C₂²×C₆₁	1	2	yes	—
630	#479	C₂²×C₆₁	1	2	yes	—
631	#479	C₂²×C₆₁	1	2	yes	—
632	#479	C₂²×C₆₁	1	2	yes	—
633	#478	C₂²×C₆₁	1	2	yes	—
634	#478	C₂²×C₆₁	1	2	yes	—
635	#478	C₂²×C₆₁	1	1	yes	characteristic
636	#477	C₂²×C₆₁	1	1	yes	characteristic
637	#476	C₂²×C₆₁	1	1	yes	characteristic
638	#475	C₂²×C₆₁	1	1	yes	characteristic
639	#475	C₂²×C₆₁	1	1	yes	characteristic
640	#474	C₂²×C₆₁	1	1	yes	characteristic
641	#474	C₂²×C₆₁	1	1	yes	characteristic
642	#467	C₂²×C₆₁	1	2	yes	—
643	#467	C₂²×C₆₁	1	2	yes	—
644	#466	C₂²×C₆₁	1	2	yes	—
645	#465	C₂²×C₆₁	1	2	yes	—
646	#465	C₂²×C₆₁	1	2	yes	—
647	#465	C₂²×C₆₁	1	2	yes	—
648	#464	C₂²×C₆₁	1	1	yes	characteristic
649	#464	C₂²×C₆₁	1	2	yes	—
650	#464	C₂²×C₆₁	1	2	yes	—
651	#463	C₂²×C₆₁	1	1	yes	characteristic
652	#463	C₂²×C₆₁	1	2	yes	—
653	#462	C₂²×C₆₁	1	1	yes	characteristic
654	#461	C₂²×C₆₁	1	1	yes	characteristic
655	#452	C₂²×C₆₁	1	1	yes	characteristic
656	#451	C₂²×C₆₁	1	2	yes	—
657	#449	C₂²×C₆₁	1	1	yes	characteristic
658	#448	C₂²×C₆₁	1	2	yes	—
659	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
660	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
661	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
662	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
663	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
664	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
665	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
666	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
668	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
669	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
670	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
671	C₈×D₄	C₂²×C₆₁	1	2	yes	—
672	C₈×D₄	C₂²×C₆₁	1	2	yes	—
673	#431	C₂²×C₆₁	1	1	yes	characteristic
674	#431	C₂²×C₆₁	1	2	yes	—
675	#427	C₂²×C₆₁	1	2	yes	—
676	C₂×#107	C₂²×C₆₁	1	2	yes	—
677	C₂×#106	C₂²×C₆₁	1	2	yes	—
678	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
679	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
680	#416	C₂²×C₆₁	1	2	yes	—
681	C₂×#103	C₂²×C₆₁	1	2	yes	—
682	C₂×#103	C₂²×C₆₁	1	2	yes	—
683	C₆₁	#62104	1	1	yes	characteristic, direct product factor, Sylow
684	C₂×#41	—	2	1	no	—
685	C₂×#41	—	2	1	no	—
686	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
687	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
688	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
689	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
690	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
692	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
693	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
694	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
695	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
696	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
697	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	—	2	1	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	1	no	—
711	#126	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	1	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	1	no	—
720	#125	C₂³×C₆₁	1	1	yes	characteristic
721	#125	C₂³×C₆₁	1	2	yes	—
722	#125	C₂³×C₆₁	1	2	yes	—
723	#125	C₂³×C₆₁	1	2	yes	—
724	#125	C₂³×C₆₁	1	2	yes	—
725	#124	—	2	2	no	—
726	#124	C₂³×C₆₁	1	1	yes	characteristic
727	#124	C₂³×C₆₁	1	2	yes	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	1	no	—
731	#123	—	2	2	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	1	no	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
749	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
750	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
751	#121	—	2	2	no	—
752	#121	—	2	2	no	—
753	#121	C₂³×C₆₁	1	2	yes	—
754	#121	C₂³×C₆₁	1	2	yes	—
755	#121	C₂³×C₆₁	1	1	yes	characteristic
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	2	no	—
759	C₄×Q₈	—	2	2	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
766	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
767	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
768	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
770	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
782	C₄×D₄	D₄×C₆₁	1	2	yes	—
783	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
785	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₆₁	1	2	yes	—
787	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₆₁	1	2	yes	—
789	#117	—	2	1	no	—
790	#117	—	2	1	no	—
791	#117	—	2	2	no	—
792	#117	—	2	2	no	—
793	#117	—	2	1	no	—
794	#117	—	2	1	no	—
795	#117	—	2	2	no	—
796	#117	—	2	2	no	—
797	#117	D₄×C₆₁	1	2	yes	—
798	#117	D₄×C₆₁	1	1	yes	characteristic
799	#117	C₂³×C₆₁	1	1	yes	characteristic
800	#117	C₂³×C₆₁	1	2	yes	—
801	C₂×C₄⋊C₄	—	2	2	no	—
802	C₂×C₄⋊C₄	—	2	2	no	—
803	C₂×C₄⋊C₄	—	2	2	no	—
804	C₂×C₄⋊C₄	—	2	1	no	—
805	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
806	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
807	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
808	C₂×C₄²	—	2	2	no	—
809	C₂×C₄²	—	2	1	no	—
810	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
811	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
812	#107	C₂³×C₆₁	1	1	yes	characteristic
813	#107	C₂³×C₆₁	1	2	yes	—
814	#107	C₂³×C₆₁	1	2	yes	—
815	#107	C₂³×C₆₁	1	2	yes	—
816	#107	C₂³×C₆₁	1	2	yes	—
817	#107	C₂³×C₆₁	1	1	yes	characteristic
818	#107	C₂³×C₆₁	1	2	yes	—
819	#106	C₂³×C₆₁	1	1	yes	characteristic
820	#106	C₂³×C₆₁	1	2	yes	—
821	#106	C₂³×C₆₁	1	2	yes	—
822	#106	C₂³×C₆₁	1	2	yes	—
823	#106	C₂³×C₆₁	1	2	yes	—
824	#106	C₂³×C₆₁	1	1	yes	characteristic
825	#106	C₂³×C₆₁	1	2	yes	—
826	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
828	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
831	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
832	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
833	#103	C₂³×C₆₁	1	1	yes	characteristic
834	#103	C₂³×C₆₁	1	1	yes	characteristic
835	#103	C₂³×C₆₁	1	2	yes	—
836	#103	C₂³×C₆₁	1	2	yes	—
837	#103	C₂³×C₆₁	1	2	yes	—
838	#103	C₂³×C₆₁	1	2	yes	—
839	#103	C₂³×C₆₁	1	2	yes	—
840	#103	C₂³×C₆₁	1	2	yes	—
841	#103	C₂³×C₆₁	1	1	yes	characteristic
842	#103	C₂³×C₆₁	1	2	yes	—
843	#103	C₂³×C₆₁	1	2	yes	—
844	#103	C₂³×C₆₁	1	1	yes	characteristic
845	#103	C₂³×C₆₁	1	2	yes	—
846	#102	C₂³×C₆₁	1	2	yes	—
847	#102	C₂³×C₆₁	1	2	yes	—
848	#102	C₂³×C₆₁	1	1	yes	characteristic
849	#102	C₂³×C₆₁	1	1	yes	characteristic
850	#102	C₂³×C₆₁	1	1	yes	characteristic
851	#102	C₂³×C₆₁	1	1	yes	characteristic
852	#102	C₂³×C₆₁	1	2	yes	—
853	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
855	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
857	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
858	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
859	C₄×C₈	C₂³×C₆₁	1	2	yes	—
860	C₄×C₈	C₂³×C₆₁	1	2	yes	—
861	#41	—	2	4	no	—
862	#41	—	2	2	no	—
863	#41	—	4	1	no	—
864	#41	—	4	4	no	—
865	#41	—	4	4	no	—
866	C₂×Q₈	—	2	2	no	—
867	C₂×Q₈	—	2	1	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	4	no	—
871	C₂×Q₈	—	4	2	no	—
872	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
873	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
874	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
875	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
881	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
882	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
883	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
894	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
895	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
896	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
899	Q₁₆	—	2	2	no	—
900	Q₁₆	—	4	2	no	—
901	SD₁₆	—	2	2	no	—
902	SD₁₆	—	4	2	no	—
903	SD₁₆	—	4	1	no	—
904	D₈	—	4	1	no	—
905	C₂×C₈	—	4	2	no	—
906	C₂×C₈	—	4	2	no	—
907	C₂×C₈	—	4	2	no	—
908	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
911	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
912	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
913	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
944	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
946	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
973	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	1	no	—
983	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
984	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
985	C₄²	C₂×D₄×C₆₁	1	2	yes	—
986	C₄²	C₂×D₄×C₆₁	1	2	yes	—
987	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
988	C₄²	C₂⁴×C₆₁	1	2	yes	—
989	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
993	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
994	Q₈	—	2	2	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	2	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	2	no	—
1000	Q₈	—	4	4	no	—
1001	Q₈	—	4	2	no	—
1002	Q₈	—	4	2	no	—
1003	Q₈	—	8	1	no	—
1004	Q₈	2₋¹⁺⁴×C₆₁	1	2	yes	—
1005	D₄	—	2	4	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	4	2	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	4	no	—
1013	D₄	—	8	1	no	—
1014	D₄	#135×C₆₁	1	4	yes	—
1015	C₂×C₄	—	2	4	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	4	1	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	4	4	no	—
1037	C₂×C₄	—	4	4	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1045	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1047	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1049	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1050	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1051	C₈	—	2	1	no	—
1052	C₈	—	2	1	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	2	no	—
1056	C₈	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	C₂×#135×C₆₁	1	4	yes	—
1069	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	C₂×#135×C₆₁	1	2	yes	—
1088	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1089	C₄	C₆₁×#585	1	1	yes	characteristic
1090	C₂	—	2	4	no	—
1091	C₂	—	4	1	no	—
1092	C₂	—	8	1	no	—
1093	C₂	—	8	1	no	—
1094	C₂	C₆₁×#3489	1	1	yes	characteristic
1095	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
1096	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 ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3515	C₂	semidirect
2. C₆₁×#3482	C₂	semidirect
3. C₆₁×#3383	C₂	semidirect
4. C₆₁×#3381	C₂	semidirect
5. C₆₁×#3364	C₂	semidirect
6. C₆₁×#3360	C₂	semidirect
7. C₆₁×#3337	C₂	semidirect
8. C₆₁×#3336	C₂	semidirect
9. C₆₁×#3335	C₂	semidirect
10. C₆₁×#3334	C₂	semidirect
11. C₆₁×#3301	C₂	semidirect
12. C₆₁×#3300	C₂	semidirect
13. C₆₁×#3299	C₂	semidirect
14. C₆₁×#3298	C₂	semidirect
15. C₆₁×#3250	C₂	semidirect
16. C₆₁×#3248	C₂	semidirect
17. C₆₁×#3232	C₂	semidirect
18. C₆₁×#3231	C₂	semidirect
19. C₆₁×#3108	C₂	semidirect
20. C₆₁×#3102	C₂	semidirect
21. C₆₁×#3076	C₂	semidirect
22. C₂×C₆₁×#479	C₂	semidirect
23. C₆₁×#2988	C₂	semidirect
508. #62104	C₆₁	direct (N × H)
542. #3515	C₂×C₆₁	semidirect
543. #3482	C₂×C₆₁	semidirect
544. #3383	C₂×C₆₁	semidirect
545. #3381	C₂×C₆₁	semidirect
546. #3364	C₂×C₆₁	semidirect
547. #3360	C₂×C₆₁	semidirect
548. #3337	C₂×C₆₁	semidirect
549. #3336	C₂×C₆₁	semidirect
550. #3335	C₂×C₆₁	semidirect
551. #3334	C₂×C₆₁	semidirect
552. #3301	C₂×C₆₁	semidirect
553. #3300	C₂×C₆₁	semidirect
554. #3299	C₂×C₆₁	semidirect
555. #3298	C₂×C₆₁	semidirect
556. #3250	C₂×C₆₁	semidirect
557. #3248	C₂×C₆₁	semidirect
558. #3232	C₂×C₆₁	semidirect
559. #3231	C₂×C₆₁	semidirect
560. #3108	C₂×C₆₁	semidirect
561. #3102	C₂×C₆₁	semidirect
562. #3076	C₂×C₆₁	semidirect
563. C₂×#479	C₂×C₆₁	semidirect
564. #2988	C₂×C₆₁	semidirect
683. C₆₁	#62104	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×#3515	2
C₆₁×#3482	2
C₆₁×#3383	2
C₆₁×#3381	2
C₆₁×#3364	2
C₆₁×#3360	2
C₆₁×#3337	2
C₆₁×#3336	2
C₆₁×#3335	2
C₆₁×#3334	2
C₆₁×#3301	2
C₆₁×#3300	2
C₆₁×#3299	2
C₆₁×#3298	2
C₆₁×#3250	2
C₆₁×#3248	2
C₆₁×#3232	2
C₆₁×#3231	2
C₆₁×#3108	2
C₆₁×#3102	2
C₆₁×#3076	2
C₂×C₆₁×#479	2
C₆₁×#2988	2
#62104	61

Subgroups — C61×#62104 #29565537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62104 #29565537