Subgroups — C₆₁×#61845 #29565278

Order 15616.

1688 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3389	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3388	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3377	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3376	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3240	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3233	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3115	C₂	1	1	yes	maximal, characteristic
20	C₆₁×#3111	C₂	1	2	yes	maximal, complemented
21	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#3102	C₂	1	2	yes	maximal, complemented
23	C₆₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#559	C₂²	1	1	yes	characteristic
25	C₆₁×#559	C₂²	1	1	yes	characteristic
26	Q₈²×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#557	C₂²	1	1	yes	characteristic
28	C₆₁×#557	C₂²	1	2	yes	—
29	C₆₁×#557	C₂²	1	1	yes	characteristic
30	C₆₁×#557	C₂²	1	1	yes	characteristic
31	C₆₁×#556	—	2	1	no	—
32	C₆₁×#556	—	2	1	no	—
33	C₆₁×#556	C₂²	1	2	yes	—
34	C₆₁×#554	—	2	2	no	—
35	C₆₁×#554	—	2	1	no	—
36	C₆₁×#554	C₂²	1	1	yes	characteristic
37	C₆₁×#554	C₂²	1	2	yes	—
38	C₆₁×#554	C₂²	1	2	yes	—
39	C₆₁×#552	—	2	2	no	—
40	D₄×Q₈×C₆₁	—	2	1	no	—
41	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#539	—	2	2	no	—
43	C₆₁×#536	—	2	1	no	—
44	C₆₁×#533	—	2	2	no	—
45	C₆₁×#533	—	2	1	no	—
46	C₆₁×#533	C₂²	1	1	yes	characteristic
47	C₆₁×#533	C₂²	1	1	yes	characteristic
48	C₆₁×#533	C₂²	1	2	yes	—
49	C₆₁×#532	C₂²	1	1	yes	characteristic
50	C₆₁×#529	C₂²	1	2	yes	—
51	C₆₁×#529	C₂²	1	2	yes	—
52	C₆₁×#520	—	2	1	no	—
53	C₄×#41×C₆₁	C₂²	1	2	yes	—
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
56	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#501	C₂²	1	2	yes	—
58	C₆₁×#501	C₂²	1	2	yes	—
59	C₆₁×#501	C₂²	1	2	yes	—
60	C₆₁×#500	C₂²	1	1	yes	characteristic
61	C₆₁×#499	C₂²	1	2	yes	—
62	C₆₁×#499	C₂²	1	2	yes	—
63	C₆₁×#498	C₂²	1	1	yes	characteristic
64	C₆₁×#491	C₂²	1	2	yes	—
65	C₆₁×#489	C₂²	1	2	yes	—
66	C₆₁×#489	C₂²	1	2	yes	—
67	C₆₁×#488	C₂²	1	2	yes	—
68	C₆₁×#488	C₂²	1	2	yes	—
69	C₆₁×#486	C₂²	1	1	yes	characteristic
70	C₆₁×#486	C₂²	1	1	yes	characteristic
71	C₆₁×#485	C₂²	1	2	yes	—
72	C₆₁×#485	C₂²	1	1	yes	characteristic
73	C₆₁×#485	C₂²	1	1	yes	characteristic
74	C₆₁×#485	C₂²	1	2	yes	—
75	C₆₁×#482	C₂²	1	2	yes	—
76	C₆₁×#482	C₂²	1	2	yes	—
77	C₆₁×#482	C₂²	1	2	yes	—
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×#478	C₂²	1	2	yes	—
83	C₆₁×#478	C₂²	1	2	yes	—
84	C₆₁×#478	C₂²	1	2	yes	—
85	C₆₁×#478	C₂²	1	2	yes	—
86	C₆₁×#478	C₂²	1	2	yes	—
87	C₆₁×#478	C₂²	1	2	yes	—
88	C₆₁×#477	C₂²	1	1	yes	characteristic
89	C₆₁×#477	C₂²	1	1	yes	characteristic
90	C₆₁×#477	C₂²	1	2	yes	—
91	C₆₁×#476	C₂²	1	2	yes	—
92	C₆₁×#475	C₂²	1	1	yes	characteristic
93	C₆₁×#475	C₂²	1	1	yes	characteristic
94	C₆₁×#475	C₂²	1	1	yes	characteristic
95	C₆₁×#475	C₂²	1	1	yes	characteristic
96	C₆₁×#475	C₂²	1	2	yes	—
97	C₆₁×#474	C₂²	1	1	yes	characteristic
98	C₆₁×#474	C₂²	1	1	yes	characteristic
99	C₆₁×#474	C₂²	1	2	yes	—
100	C₆₁×#464	C₂²	1	2	yes	—
101	C₆₁×#464	C₂²	1	2	yes	—
102	C₆₁×#463	C₂²	1	2	yes	—
103	C₆₁×#463	C₂²	1	2	yes	—
104	C₆₁×#462	C₂²	1	1	yes	characteristic
105	C₆₁×#461	C₂²	1	1	yes	characteristic
106	C₆₁×#460	C₂²	1	1	yes	characteristic
107	C₆₁×#459	C₂²	1	1	yes	characteristic
108	C₆₁×#452	C₂²	1	1	yes	characteristic
109	C₆₁×#452	C₂²	1	1	yes	characteristic
110	C₆₁×#449	C₂²	1	2	yes	—
111	C₆₁×#446	C₂²	1	1	yes	characteristic
112	C₆₁×#446	C₂²	1	1	yes	characteristic
113	C₆₁×#446	C₂²	1	2	yes	—
114	C₆₁×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
117	C₆₁×#442	C₂²	1	2	yes	—
118	C₆₁×#442	C₂²	1	2	yes	—
119	C₆₁×#441	C₂²	1	2	yes	—
120	C₆₁×#440	C₂²	1	2	yes	—
121	C₆₁×#440	C₂²	1	2	yes	—
122	C₆₁×#440	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
124	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
125	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₆₁	C₂²	1	2	yes	—
131	C₆₁×#432	C₂²	1	2	yes	—
132	C₆₁×#432	C₂²	1	1	yes	characteristic
133	C₆₁×#431	C₂²	1	2	yes	—
134	C₆₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₆₁	—	2	1	no	—
138	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
139	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×D₈×C₆₁	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₆₁	—	2	1	no	—
146	C₄⋊Q₈×C₆₁	—	2	2	no	—
147	C₄⋊Q₈×C₆₁	—	2	1	no	—
148	C₄⋊Q₈×C₆₁	—	2	1	no	—
149	C₄⋊Q₈×C₆₁	—	2	1	no	—
150	C₄⋊Q₈×C₆₁	—	2	2	no	—
151	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
158	#127×C₆₁	C₂³	1	1	yes	characteristic
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	—	2	2	no	—
161	#126×C₆₁	—	2	2	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	2	no	—
167	#125×C₆₁	—	2	2	no	—
168	#125×C₆₁	—	2	1	no	—
169	#125×C₆₁	C₂³	1	2	yes	—
170	#125×C₆₁	C₂³	1	2	yes	—
171	#125×C₆₁	C₂³	1	2	yes	—
172	#125×C₆₁	C₂³	1	2	yes	—
173	#125×C₆₁	C₂³	1	2	yes	—
174	#124×C₆₁	—	2	1	no	—
175	#124×C₆₁	—	2	1	no	—
176	#124×C₆₁	—	2	1	no	—
177	#124×C₆₁	C₂³	1	2	yes	—
178	#124×C₆₁	C₂³	1	2	yes	—
179	#123×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	2	no	—
181	#123×C₆₁	—	2	2	no	—
182	#123×C₆₁	—	2	2	no	—
183	C₂²⋊Q₈×C₆₁	—	2	1	no	—
184	C₂²⋊Q₈×C₆₁	—	2	2	no	—
185	C₂²⋊Q₈×C₆₁	—	2	2	no	—
186	C₂²⋊Q₈×C₆₁	—	2	2	no	—
187	C₂²⋊Q₈×C₆₁	—	2	1	no	—
188	C₂²⋊Q₈×C₆₁	—	2	1	no	—
189	C₂²⋊Q₈×C₆₁	—	2	2	no	—
190	C₂²⋊Q₈×C₆₁	—	2	2	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	2	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	2	no	—
198	C₂²⋊Q₈×C₆₁	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
200	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
201	#121×C₆₁	—	2	1	no	—
202	#121×C₆₁	C₂³	1	2	yes	—
203	C₄×Q₈×C₆₁	—	2	1	no	—
204	C₄×Q₈×C₆₁	—	2	1	no	—
205	C₄×Q₈×C₆₁	—	2	2	no	—
206	C₄×Q₈×C₆₁	—	2	1	no	—
207	C₄×Q₈×C₆₁	—	2	1	no	—
208	C₄×Q₈×C₆₁	—	2	2	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	D₄	1	2	yes	—
214	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
221	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₆₁	—	2	2	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	—	2	1	no	—
233	C₄×D₄×C₆₁	—	2	1	no	—
234	C₄×D₄×C₆₁	—	2	1	no	—
235	C₄×D₄×C₆₁	—	2	1	no	—
236	C₄×D₄×C₆₁	C₂³	1	2	yes	—
237	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₆₁	C₂³	1	2	yes	—
239	C₄×D₄×C₆₁	C₂³	1	2	yes	—
240	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₁	C₂³	1	2	yes	—
242	C₄×D₄×C₆₁	C₂³	1	2	yes	—
243	#117×C₆₁	—	2	1	no	—
244	#117×C₆₁	—	2	2	no	—
245	#117×C₆₁	—	2	2	no	—
246	#117×C₆₁	—	2	1	no	—
247	#117×C₆₁	—	2	2	no	—
248	#117×C₆₁	—	2	2	no	—
249	#117×C₆₁	C₂³	1	2	yes	—
250	#117×C₆₁	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
252	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
254	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
255	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
256	C₂×C₄²×C₆₁	—	2	2	no	—
257	C₂×C₄²×C₆₁	—	2	1	no	—
258	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
260	#107×C₆₁	C₂³	1	2	yes	—
261	#107×C₆₁	C₂³	1	1	yes	characteristic
262	#107×C₆₁	C₂³	1	1	yes	characteristic
263	#107×C₆₁	C₂³	1	2	yes	—
264	#107×C₆₁	C₂³	1	2	yes	—
265	#107×C₆₁	C₂³	1	2	yes	—
266	#107×C₆₁	C₂³	1	2	yes	—
267	#106×C₆₁	C₂³	1	1	yes	characteristic
268	#106×C₆₁	C₂³	1	2	yes	—
269	#106×C₆₁	C₂³	1	1	yes	characteristic
270	#106×C₆₁	C₂³	1	2	yes	—
271	#106×C₆₁	C₂³	1	2	yes	—
272	#106×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	2	yes	—
274	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
277	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
282	#103×C₆₁	C₂³	1	1	yes	characteristic
283	#103×C₆₁	C₂³	1	1	yes	characteristic
284	#103×C₆₁	C₂³	1	1	yes	characteristic
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	1	yes	characteristic
289	#103×C₆₁	C₂³	1	1	yes	characteristic
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	2	yes	—
293	#102×C₆₁	C₂³	1	1	yes	characteristic
294	#102×C₆₁	C₂³	1	2	yes	—
295	#102×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	1	yes	characteristic
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
305	#97×C₆₁	C₂³	1	2	yes	—
306	#97×C₆₁	C₂³	1	2	yes	—
307	#97×C₆₁	C₂³	1	2	yes	—
308	C₄×C₈×C₆₁	C₂³	1	2	yes	—
309	C₄×C₈×C₆₁	C₂³	1	2	yes	—
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
312	#41×C₆₁	—	2	2	no	—
313	#41×C₆₁	—	2	2	no	—
314	#41×C₆₁	—	4	4	no	—
315	C₂×Q₈×C₆₁	—	2	2	no	—
316	C₂×Q₈×C₆₁	—	2	1	no	—
317	C₂×Q₈×C₆₁	—	2	1	no	—
318	C₂×Q₈×C₆₁	—	2	1	no	—
319	C₂×Q₈×C₆₁	—	2	2	no	—
320	C₂×Q₈×C₆₁	—	2	1	no	—
321	C₂×Q₈×C₆₁	—	4	2	no	—
322	C₂×Q₈×C₆₁	—	4	4	no	—
323	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₆₁	—	2	1	no	—
330	C₂×D₄×C₆₁	—	2	2	no	—
331	C₂×D₄×C₆₁	—	2	1	no	—
332	C₂×D₄×C₆₁	—	2	1	no	—
333	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
334	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₆₁	—	2	1	no	—
336	C₂²×C₄×C₆₁	—	2	2	no	—
337	C₂²×C₄×C₆₁	—	2	1	no	—
338	C₂²×C₄×C₆₁	—	2	2	no	—
339	C₂²×C₄×C₆₁	—	2	2	no	—
340	C₂²×C₄×C₆₁	—	2	1	no	—
341	C₂²×C₄×C₆₁	—	2	2	no	—
342	C₂²×C₄×C₆₁	—	2	2	no	—
343	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
348	Q₁₆×C₆₁	—	2	2	no	—
349	Q₁₆×C₆₁	—	2	2	no	—
350	SD₁₆×C₆₁	—	2	4	no	—
351	SD₁₆×C₆₁	—	2	2	no	—
352	SD₁₆×C₆₁	—	2	2	no	—
353	D₈×C₆₁	—	2	4	no	—
354	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
358	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₆₁	—	2	1	no	—
361	C₄⋊C₄×C₆₁	—	2	2	no	—
362	C₄⋊C₄×C₆₁	—	2	2	no	—
363	C₄⋊C₄×C₆₁	—	2	2	no	—
364	C₄⋊C₄×C₆₁	—	2	2	no	—
365	C₄⋊C₄×C₆₁	—	2	2	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	1	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	1	no	—
374	C₄⋊C₄×C₆₁	—	2	1	no	—
375	C₄⋊C₄×C₆₁	—	2	2	no	—
376	C₄⋊C₄×C₆₁	—	2	2	no	—
377	C₄⋊C₄×C₆₁	—	2	1	no	—
378	C₄⋊C₄×C₆₁	—	2	2	no	—
379	C₄⋊C₄×C₆₁	—	2	1	no	—
380	C₄⋊C₄×C₆₁	—	2	2	no	—
381	C₄⋊C₄×C₆₁	—	2	2	no	—
382	C₄⋊C₄×C₆₁	—	2	2	no	—
383	C₄⋊C₄×C₆₁	—	2	1	no	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	2	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
389	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
402	C₂²⋊C₄×C₆₁	—	2	1	no	—
403	C₂²⋊C₄×C₆₁	—	2	1	no	—
404	C₂²⋊C₄×C₆₁	—	2	2	no	—
405	C₂²⋊C₄×C₆₁	—	2	1	no	—
406	C₂²⋊C₄×C₆₁	—	2	2	no	—
407	C₂²⋊C₄×C₆₁	—	2	2	no	—
408	C₂²⋊C₄×C₆₁	—	2	2	no	—
409	C₂²⋊C₄×C₆₁	—	2	2	no	—
410	C₂²⋊C₄×C₆₁	—	2	2	no	—
411	C₂²⋊C₄×C₆₁	—	2	1	no	—
412	C₂²⋊C₄×C₆₁	—	2	1	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	—	2	2	no	—
416	C₂²⋊C₄×C₆₁	—	2	2	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₄²×C₆₁	—	2	2	no	—
419	C₄²×C₆₁	—	2	1	no	—
420	C₄²×C₆₁	—	2	2	no	—
421	C₄²×C₆₁	—	2	1	no	—
422	C₄²×C₆₁	—	2	2	no	—
423	C₄²×C₆₁	—	2	1	no	—
424	C₄²×C₆₁	—	2	2	no	—
425	C₄²×C₆₁	—	2	2	no	—
426	C₄²×C₆₁	—	2	1	no	—
427	C₄²×C₆₁	—	2	1	no	—
428	C₄²×C₆₁	C₂×D₄	1	2	yes	—
429	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
430	C₄²×C₆₁	C₂×D₄	1	2	yes	—
431	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₆₁	C₂⁴	1	2	yes	—
433	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
434	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
435	C₄²×C₆₁	C₂⁴	1	2	yes	—
436	C₂³×C₆₁	—	2	1	no	—
437	C₂³×C₆₁	—	2	2	no	—
438	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
439	Q₈×C₆₁	—	2	2	no	—
440	Q₈×C₆₁	—	2	2	no	—
441	Q₈×C₆₁	—	2	1	no	—
442	Q₈×C₆₁	—	2	1	no	—
443	Q₈×C₆₁	—	2	1	no	—
444	Q₈×C₆₁	—	2	1	no	—
445	Q₈×C₆₁	—	2	1	no	—
446	Q₈×C₆₁	—	4	2	no	—
447	Q₈×C₆₁	—	4	4	no	—
448	Q₈×C₆₁	—	4	2	no	—
449	Q₈×C₆₁	—	4	2	no	—
450	Q₈×C₆₁	—	8	1	no	—
451	Q₈×C₆₁	—	8	2	no	—
452	Q₈×C₆₁	—	8	1	no	—
453	Q₈×C₆₁	2₋¹⁺⁴	1	2	yes	—
454	D₄×C₆₁	—	2	4	no	—
455	D₄×C₆₁	—	2	1	no	—
456	D₄×C₆₁	—	2	2	no	—
457	D₄×C₆₁	—	2	2	no	—
458	D₄×C₆₁	—	4	4	no	—
459	D₄×C₆₁	—	4	2	no	—
460	D₄×C₆₁	—	8	1	no	—
461	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
462	C₂×C₄×C₆₁	—	2	4	no	—
463	C₂×C₄×C₆₁	—	2	1	no	—
464	C₂×C₄×C₆₁	—	2	2	no	—
465	C₂×C₄×C₆₁	—	2	1	no	—
466	C₂×C₄×C₆₁	—	2	1	no	—
467	C₂×C₄×C₆₁	—	2	1	no	—
468	C₂×C₄×C₆₁	—	2	1	no	—
469	C₂×C₄×C₆₁	—	2	2	no	—
470	C₂×C₄×C₆₁	—	2	2	no	—
471	C₂×C₄×C₆₁	—	2	1	no	—
472	C₂×C₄×C₆₁	—	2	2	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	—	4	2	no	—
477	C₂×C₄×C₆₁	—	4	1	no	—
478	C₂×C₄×C₆₁	—	4	2	no	—
479	C₂×C₄×C₆₁	—	4	4	no	—
480	C₂×C₄×C₆₁	—	4	4	no	—
481	C₂×C₄×C₆₁	—	4	2	no	—
482	C₂×C₄×C₆₁	—	8	2	no	—
483	C₂×C₄×C₆₁	—	8	2	no	—
484	C₂×C₄×C₆₁	—	8	2	no	—
485	C₂×C₄×C₆₁	—	8	1	no	—
486	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
496	C₈×C₆₁	—	2	2	no	—
497	C₈×C₆₁	—	2	2	no	—
498	C₈×C₆₁	—	2	1	no	—
499	C₈×C₆₁	—	2	1	no	—
500	C₈×C₆₁	—	2	1	no	—
501	C₈×C₆₁	—	2	1	no	—
502	#61845	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
503	C₂²×C₆₁	—	2	1	no	—
504	C₂²×C₆₁	—	2	1	no	—
505	C₂²×C₆₁	—	2	2	no	—
506	C₂²×C₆₁	—	2	1	no	—
507	C₂²×C₆₁	—	4	1	no	—
508	C₂²×C₆₁	—	4	1	no	—
509	C₂²×C₆₁	—	4	2	no	—
510	C₂²×C₆₁	—	4	2	no	—
511	C₂²×C₆₁	—	4	2	no	—
512	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
513	C₄×C₆₁	—	2	2	no	—
514	C₄×C₆₁	—	2	2	no	—
515	C₄×C₆₁	—	2	1	no	—
516	C₄×C₆₁	—	2	1	no	—
517	C₄×C₆₁	—	2	1	no	—
518	C₄×C₆₁	—	2	2	no	—
519	C₄×C₆₁	—	2	1	no	—
520	C₄×C₆₁	—	2	2	no	—
521	C₄×C₆₁	—	2	2	no	—
522	C₄×C₆₁	—	4	1	no	—
523	C₄×C₆₁	—	4	1	no	—
524	C₄×C₆₁	—	4	2	no	—
525	C₄×C₆₁	—	4	1	no	—
526	C₄×C₆₁	—	4	1	no	—
527	C₄×C₆₁	—	4	1	no	—
528	C₄×C₆₁	—	4	2	no	—
529	C₄×C₆₁	—	4	2	no	—
530	C₄×C₆₁	—	4	1	no	—
531	C₄×C₆₁	#575	1	2	yes	—
532	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
533	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
534	#3507	C₂×C₆₁	1	1	yes	characteristic, complemented
535	Q₈×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
536	#3389	C₂×C₆₁	1	2	yes	complemented
537	#3388	C₂×C₆₁	1	2	yes	complemented
538	#3387	C₂×C₆₁	1	1	yes	characteristic, complemented
539	#3386	C₂×C₆₁	1	1	yes	characteristic, complemented
540	#3383	C₂×C₆₁	1	1	yes	characteristic, complemented
541	#3381	C₂×C₆₁	1	1	yes	characteristic, complemented
542	#3377	C₂×C₆₁	1	2	yes	complemented
543	#3376	C₂×C₆₁	1	2	yes	complemented
544	#3375	C₂×C₆₁	1	1	yes	characteristic, complemented
545	#3373	C₂×C₆₁	1	1	yes	characteristic, complemented
546	#3365	C₂×C₆₁	1	1	yes	characteristic, complemented
547	#3361	C₂×C₆₁	1	1	yes	characteristic, complemented
548	#3240	C₂×C₆₁	1	2	yes	complemented
549	#3237	C₂×C₆₁	1	1	yes	characteristic, complemented
550	#3233	C₂×C₆₁	1	2	yes	complemented
551	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
552	#3115	C₂×C₆₁	1	1	yes	characteristic
553	#3111	C₂×C₆₁	1	2	yes	complemented
554	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
555	#3102	C₂×C₆₁	1	2	yes	complemented
556	#2984	C₂×C₆₁	1	1	yes	characteristic, complemented
557	C₂×C₆₁	—	4	1	no	—
558	C₂×C₆₁	—	4	2	no	—
559	C₂×C₆₁	—	8	2	no	—
560	C₂×C₆₁	#3486	1	1	yes	characteristic
561	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
562	C₂×C₆₁	#3584	1	1	yes	characteristic
563	#559	C₂²×C₆₁	1	1	yes	characteristic
564	#559	C₂²×C₆₁	1	1	yes	characteristic
565	Q₈²	C₂²×C₆₁	1	1	yes	characteristic
566	#557	C₂²×C₆₁	1	1	yes	characteristic
567	#557	C₂²×C₆₁	1	2	yes	—
568	#557	C₂²×C₆₁	1	1	yes	characteristic
569	#557	C₂²×C₆₁	1	1	yes	characteristic
570	#556	—	2	1	no	—
571	#556	—	2	1	no	—
572	#556	C₂²×C₆₁	1	2	yes	—
573	#554	—	2	1	no	—
574	#554	—	2	2	no	—
575	#554	C₂²×C₆₁	1	1	yes	characteristic
576	#554	C₂²×C₆₁	1	2	yes	—
577	#554	C₂²×C₆₁	1	2	yes	—
578	#552	—	2	2	no	—
579	D₄×Q₈	—	2	1	no	—
580	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
581	#539	—	2	2	no	—
582	#536	—	2	1	no	—
583	#533	—	2	2	no	—
584	#533	—	2	1	no	—
585	#533	C₂²×C₆₁	1	1	yes	characteristic
586	#533	C₂²×C₆₁	1	1	yes	characteristic
587	#533	C₂²×C₆₁	1	2	yes	—
588	#532	C₂²×C₆₁	1	1	yes	characteristic
589	#529	C₂²×C₆₁	1	2	yes	—
590	#529	C₂²×C₆₁	1	2	yes	—
591	#520	—	2	1	no	—
592	C₄×#41	C₂²×C₆₁	1	2	yes	—
593	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
594	C₂×C₄×Q₈	—	2	1	no	—
595	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
596	#501	C₂²×C₆₁	1	2	yes	—
597	#501	C₂²×C₆₁	1	2	yes	—
598	#501	C₂²×C₆₁	1	2	yes	—
599	#500	C₂²×C₆₁	1	1	yes	characteristic
600	#499	C₂²×C₆₁	1	2	yes	—
601	#499	C₂²×C₆₁	1	2	yes	—
602	#498	C₂²×C₆₁	1	1	yes	characteristic
603	#491	C₂²×C₆₁	1	2	yes	—
604	#489	C₂²×C₆₁	1	2	yes	—
605	#489	C₂²×C₆₁	1	2	yes	—
606	#488	C₂²×C₆₁	1	2	yes	—
607	#488	C₂²×C₆₁	1	2	yes	—
608	#486	C₂²×C₆₁	1	1	yes	characteristic
609	#486	C₂²×C₆₁	1	1	yes	characteristic
610	#485	C₂²×C₆₁	1	2	yes	—
611	#485	C₂²×C₆₁	1	1	yes	characteristic
612	#485	C₂²×C₆₁	1	1	yes	characteristic
613	#485	C₂²×C₆₁	1	2	yes	—
614	#482	C₂²×C₆₁	1	2	yes	—
615	#482	C₂²×C₆₁	1	2	yes	—
616	#482	C₂²×C₆₁	1	2	yes	—
617	#479	C₂²×C₆₁	1	2	yes	—
618	#479	C₂²×C₆₁	1	2	yes	—
619	#479	C₂²×C₆₁	1	2	yes	—
620	#479	C₂²×C₆₁	1	2	yes	—
621	#478	C₂²×C₆₁	1	2	yes	—
622	#478	C₂²×C₆₁	1	2	yes	—
623	#478	C₂²×C₆₁	1	2	yes	—
624	#478	C₂²×C₆₁	1	2	yes	—
625	#478	C₂²×C₆₁	1	2	yes	—
626	#478	C₂²×C₆₁	1	2	yes	—
627	#477	C₂²×C₆₁	1	1	yes	characteristic
628	#477	C₂²×C₆₁	1	1	yes	characteristic
629	#477	C₂²×C₆₁	1	2	yes	—
630	#476	C₂²×C₆₁	1	2	yes	—
631	#475	C₂²×C₆₁	1	1	yes	characteristic
632	#475	C₂²×C₆₁	1	1	yes	characteristic
633	#475	C₂²×C₆₁	1	1	yes	characteristic
634	#475	C₂²×C₆₁	1	1	yes	characteristic
635	#475	C₂²×C₆₁	1	2	yes	—
636	#474	C₂²×C₆₁	1	1	yes	characteristic
637	#474	C₂²×C₆₁	1	1	yes	characteristic
638	#474	C₂²×C₆₁	1	2	yes	—
639	#464	C₂²×C₆₁	1	2	yes	—
640	#464	C₂²×C₆₁	1	2	yes	—
641	#463	C₂²×C₆₁	1	2	yes	—
642	#463	C₂²×C₆₁	1	2	yes	—
643	#462	C₂²×C₆₁	1	1	yes	characteristic
644	#461	C₂²×C₆₁	1	1	yes	characteristic
645	#460	C₂²×C₆₁	1	1	yes	characteristic
646	#459	C₂²×C₆₁	1	1	yes	characteristic
647	#452	C₂²×C₆₁	1	1	yes	characteristic
648	#452	C₂²×C₆₁	1	1	yes	characteristic
649	#449	C₂²×C₆₁	1	2	yes	—
650	#446	C₂²×C₆₁	1	1	yes	characteristic
651	#446	C₂²×C₆₁	1	1	yes	characteristic
652	#446	C₂²×C₆₁	1	2	yes	—
653	#446	C₂²×C₆₁	1	2	yes	—
654	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
655	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
656	#442	C₂²×C₆₁	1	2	yes	—
657	#442	C₂²×C₆₁	1	2	yes	—
658	#441	C₂²×C₆₁	1	2	yes	—
659	#440	C₂²×C₆₁	1	2	yes	—
660	#440	C₂²×C₆₁	1	2	yes	—
661	#440	C₂²×C₆₁	1	2	yes	—
662	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
663	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
664	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
665	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
666	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
667	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
668	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
669	C₄×D₈	C₂²×C₆₁	1	2	yes	—
670	#432	C₂²×C₆₁	1	2	yes	—
671	#432	C₂²×C₆₁	1	1	yes	characteristic
672	#431	C₂²×C₆₁	1	2	yes	—
673	#431	C₂²×C₆₁	1	1	yes	characteristic
674	C₆₁	#61845	1	1	yes	characteristic, direct product factor, Sylow
675	C₂×#41	—	2	1	no	—
676	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
677	C₂²×Q₈	—	2	1	no	—
678	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
679	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
680	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
681	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
682	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
683	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
684	C₂×D₈	C₂³×C₆₁	1	2	yes	—
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	—	2	2	no	—
687	C₄⋊Q₈	—	2	1	no	—
688	C₄⋊Q₈	—	2	1	no	—
689	C₄⋊Q₈	—	2	1	no	—
690	C₄⋊Q₈	—	2	2	no	—
691	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
693	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
694	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
695	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
696	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
697	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
698	#127	C₂³×C₆₁	1	1	yes	characteristic
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	—	2	2	no	—
705	#125	—	2	2	no	—
706	#125	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	1	no	—
709	#125	C₂³×C₆₁	1	2	yes	—
710	#125	C₂³×C₆₁	1	2	yes	—
711	#125	C₂³×C₆₁	1	2	yes	—
712	#125	C₂³×C₆₁	1	2	yes	—
713	#125	C₂³×C₆₁	1	2	yes	—
714	#124	—	2	1	no	—
715	#124	—	2	1	no	—
716	#124	—	2	1	no	—
717	#124	C₂³×C₆₁	1	2	yes	—
718	#124	C₂³×C₆₁	1	2	yes	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	1	no	—
728	C₂²⋊Q₈	—	2	1	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
740	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
741	#121	—	2	1	no	—
742	#121	C₂³×C₆₁	1	2	yes	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	2	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	2	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	2	2	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
754	C₄×Q₈	D₄×C₆₁	1	2	yes	—
755	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
757	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
759	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
761	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
762	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
763	C₄×Q₈	C₂³×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	1	yes	characteristic
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
777	C₄×D₄	C₂³×C₆₁	1	2	yes	—
778	C₄×D₄	C₂³×C₆₁	1	2	yes	—
779	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
780	C₄×D₄	C₂³×C₆₁	1	2	yes	—
781	C₄×D₄	C₂³×C₆₁	1	2	yes	—
782	C₄×D₄	C₂³×C₆₁	1	2	yes	—
783	#117	—	2	1	no	—
784	#117	—	2	2	no	—
785	#117	—	2	2	no	—
786	#117	—	2	1	no	—
787	#117	—	2	2	no	—
788	#117	—	2	2	no	—
789	#117	C₂³×C₆₁	1	2	yes	—
790	#117	C₂³×C₆₁	1	1	yes	characteristic
791	C₂×C₄⋊C₄	—	2	1	no	—
792	C₂×C₄⋊C₄	—	2	2	no	—
793	C₂×C₄⋊C₄	—	2	2	no	—
794	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
795	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
796	C₂×C₄²	—	2	2	no	—
797	C₂×C₄²	—	2	1	no	—
798	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
799	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
800	#107	C₂³×C₆₁	1	2	yes	—
801	#107	C₂³×C₆₁	1	1	yes	characteristic
802	#107	C₂³×C₆₁	1	1	yes	characteristic
803	#107	C₂³×C₆₁	1	2	yes	—
804	#107	C₂³×C₆₁	1	2	yes	—
805	#107	C₂³×C₆₁	1	2	yes	—
806	#107	C₂³×C₆₁	1	2	yes	—
807	#106	C₂³×C₆₁	1	1	yes	characteristic
808	#106	C₂³×C₆₁	1	2	yes	—
809	#106	C₂³×C₆₁	1	1	yes	characteristic
810	#106	C₂³×C₆₁	1	2	yes	—
811	#106	C₂³×C₆₁	1	2	yes	—
812	#106	C₂³×C₆₁	1	2	yes	—
813	#106	C₂³×C₆₁	1	2	yes	—
814	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
817	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
818	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
821	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
822	#103	C₂³×C₆₁	1	1	yes	characteristic
823	#103	C₂³×C₆₁	1	1	yes	characteristic
824	#103	C₂³×C₆₁	1	1	yes	characteristic
825	#103	C₂³×C₆₁	1	2	yes	—
826	#103	C₂³×C₆₁	1	1	yes	characteristic
827	#103	C₂³×C₆₁	1	2	yes	—
828	#103	C₂³×C₆₁	1	1	yes	characteristic
829	#103	C₂³×C₆₁	1	1	yes	characteristic
830	#103	C₂³×C₆₁	1	2	yes	—
831	#103	C₂³×C₆₁	1	2	yes	—
832	#103	C₂³×C₆₁	1	2	yes	—
833	#102	C₂³×C₆₁	1	1	yes	characteristic
834	#102	C₂³×C₆₁	1	2	yes	—
835	#102	C₂³×C₆₁	1	2	yes	—
836	#102	C₂³×C₆₁	1	1	yes	characteristic
837	#102	C₂³×C₆₁	1	2	yes	—
838	#102	C₂³×C₆₁	1	2	yes	—
839	#102	C₂³×C₆₁	1	2	yes	—
840	#102	C₂³×C₆₁	1	2	yes	—
841	#102	C₂³×C₆₁	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
843	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
845	#97	C₂³×C₆₁	1	2	yes	—
846	#97	C₂³×C₆₁	1	2	yes	—
847	#97	C₂³×C₆₁	1	2	yes	—
848	C₄×C₈	C₂³×C₆₁	1	2	yes	—
849	C₄×C₈	C₂³×C₆₁	1	2	yes	—
850	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
851	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
852	#41	—	2	2	no	—
853	#41	—	2	2	no	—
854	#41	—	4	4	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	4	2	no	—
862	C₂×Q₈	—	4	4	no	—
863	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
864	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
865	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
866	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
867	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	1	no	—
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
874	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
884	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
885	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
886	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
888	Q₁₆	—	2	2	no	—
889	Q₁₆	—	2	2	no	—
890	SD₁₆	—	2	4	no	—
891	SD₁₆	—	2	2	no	—
892	SD₁₆	—	2	2	no	—
893	D₈	—	2	4	no	—
894	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
896	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
897	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
898	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
899	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	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	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
929	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
930	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
931	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
932	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
933	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
934	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
937	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
938	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
939	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
941	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	C₂×D₄×C₆₁	1	2	yes	—
969	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
970	C₄²	C₂×D₄×C₆₁	1	2	yes	—
971	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
972	C₄²	C₂⁴×C₆₁	1	2	yes	—
973	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
974	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
975	C₄²	C₂⁴×C₆₁	1	2	yes	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	2	no	—
978	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
979	Q₈	—	2	2	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	2	1	no	—
983	Q₈	—	2	1	no	—
984	Q₈	—	2	1	no	—
985	Q₈	—	2	1	no	—
986	Q₈	—	4	2	no	—
987	Q₈	—	4	4	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	8	1	no	—
991	Q₈	—	8	2	no	—
992	Q₈	—	8	1	no	—
993	Q₈	2₋¹⁺⁴×C₆₁	1	2	yes	—
994	D₄	—	2	4	no	—
995	D₄	—	2	1	no	—
996	D₄	—	2	2	no	—
997	D₄	—	2	2	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	2	no	—
1000	D₄	—	8	1	no	—
1001	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1002	C₂×C₄	—	2	4	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	4	2	no	—
1017	C₂×C₄	—	4	1	no	—
1018	C₂×C₄	—	4	2	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	—	8	2	no	—
1024	C₂×C₄	—	8	2	no	—
1025	C₂×C₄	—	8	1	no	—
1026	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1028	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1029	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1030	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1031	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1033	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1034	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1035	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1036	C₈	—	2	2	no	—
1037	C₈	—	2	2	no	—
1038	C₈	—	2	1	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	1	no	—
1070	C₄	C₆₁×#575	1	2	yes	—
1071	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1072	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1073	C₂	—	4	1	no	—
1074	C₂	—	4	2	no	—
1075	C₂	—	8	2	no	—
1076	C₂	C₆₁×#3486	1	1	yes	characteristic
1077	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
1078	C₂	C₆₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3115	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3507	C₂	semidirect
2. Q₈×#41×C₆₁	C₂	semidirect
3. C₆₁×#3389	C₂	semidirect
4. C₆₁×#3388	C₂	semidirect
5. C₆₁×#3387	C₂	semidirect
6. C₆₁×#3386	C₂	semidirect
7. C₆₁×#3383	C₂	semidirect
8. C₆₁×#3381	C₂	semidirect
9. C₆₁×#3377	C₂	semidirect
10. C₆₁×#3376	C₂	semidirect
11. C₆₁×#3375	C₂	semidirect
12. C₆₁×#3373	C₂	semidirect
13. C₆₁×#3365	C₂	semidirect
14. C₆₁×#3361	C₂	semidirect
15. C₆₁×#3240	C₂	semidirect
16. C₆₁×#3237	C₂	semidirect
17. C₆₁×#3233	C₂	semidirect
18. C₆₁×#3228	C₂	semidirect
20. C₆₁×#3111	C₂	semidirect
21. C₆₁×#3107	C₂	semidirect
22. C₆₁×#3102	C₂	semidirect
23. C₆₁×#2984	C₂	semidirect
502. #61845	C₆₁	direct (N × H)
534. #3507	C₂×C₆₁	semidirect
535. Q₈×#41	C₂×C₆₁	semidirect
536. #3389	C₂×C₆₁	semidirect
537. #3388	C₂×C₆₁	semidirect
538. #3387	C₂×C₆₁	semidirect
539. #3386	C₂×C₆₁	semidirect
540. #3383	C₂×C₆₁	semidirect
541. #3381	C₂×C₆₁	semidirect
542. #3377	C₂×C₆₁	semidirect
543. #3376	C₂×C₆₁	semidirect
544. #3375	C₂×C₆₁	semidirect
545. #3373	C₂×C₆₁	semidirect
546. #3365	C₂×C₆₁	semidirect
547. #3361	C₂×C₆₁	semidirect
548. #3240	C₂×C₆₁	semidirect
549. #3237	C₂×C₆₁	semidirect
550. #3233	C₂×C₆₁	semidirect
551. #3228	C₂×C₆₁	semidirect
553. #3111	C₂×C₆₁	semidirect
554. #3107	C₂×C₆₁	semidirect
555. #3102	C₂×C₆₁	semidirect
556. #2984	C₂×C₆₁	semidirect
674. C₆₁	#61845	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×#3507	2
Q₈×#41×C₆₁	2
C₆₁×#3389	2
C₆₁×#3388	2
C₆₁×#3387	2
C₆₁×#3386	2
C₆₁×#3383	2
C₆₁×#3381	2
C₆₁×#3377	2
C₆₁×#3376	2
C₆₁×#3375	2
C₆₁×#3373	2
C₆₁×#3365	2
C₆₁×#3361	2
C₆₁×#3240	2
C₆₁×#3237	2
C₆₁×#3233	2
C₆₁×#3228	2
C₆₁×#3115	2
C₆₁×#3111	2
C₆₁×#3107	2
C₆₁×#3102	2
C₆₁×#2984	2
#61845	61

Subgroups — C61×#61845 #29565278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61845 #29565278