Subgroups — C₆₁×#61904 #29565337

Order 15616.

1788 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3401	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3400	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3394	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3373	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3371	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3365	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3217	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#3215	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3211	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3114	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3101	C₂	1	2	yes	maximal, complemented
17	C₆₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#559	—	2	1	no	—
19	C₆₁×#559	—	2	2	no	—
20	C₆₁×#559	—	2	1	no	—
21	C₆₁×#559	C₂²	1	2	yes	—
22	C₆₁×#559	C₂²	1	4	yes	—
23	C₆₁×#559	C₂²	1	2	yes	—
24	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
25	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
26	C₆₁×#557	C₂²	1	2	yes	complemented
27	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#556	C₂²	1	2	yes	complemented
29	C₆₁×#552	—	2	1	no	—
30	C₆₁×#552	—	2	2	no	—
31	D₄×Q₈×C₆₁	—	2	1	no	—
32	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
33	C₆₁×#541	—	2	2	no	—
34	C₆₁×#541	—	2	1	no	—
35	C₆₁×#533	C₂²	1	2	yes	—
36	C₆₁×#533	C₂²	1	1	yes	characteristic
37	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#529	C₂²	1	1	yes	characteristic
39	C₆₁×#529	C₂²	1	2	yes	—
40	C₂×#124×C₆₁	—	2	1	no	—
41	C₂×#124×C₆₁	C₂²	1	2	yes	—
42	C₂×#123×C₆₁	—	2	2	no	—
43	C₆₁×#519	—	2	1	no	—
44	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₁	—	2	1	no	—
47	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
48	C₆₁×#497	C₂²	1	4	yes	complemented
49	C₆₁×#496	C₂²	1	2	yes	—
50	C₆₁×#495	C₂²	1	4	yes	complemented
51	C₆₁×#492	C₂²	1	2	yes	—
52	C₆₁×#490	C₂²	1	2	yes	—
53	C₆₁×#489	C₂²	1	4	yes	complemented
54	C₆₁×#488	C₂²	1	4	yes	complemented
55	C₆₁×#486	C₂²	1	2	yes	—
56	C₆₁×#483	C₂²	1	1	yes	characteristic
57	C₆₁×#483	C₂²	1	2	yes	—
58	C₆₁×#480	C₂²	1	1	yes	characteristic
59	C₆₁×#479	C₂²	1	2	yes	complemented
60	C₆₁×#478	C₂²	1	4	yes	complemented
61	C₆₁×#476	C₂²	1	4	yes	complemented
62	C₆₁×#475	C₂²	1	2	yes	complemented
63	C₆₁×#464	C₂²	1	2	yes	complemented
64	C₆₁×#464	C₂²	1	4	yes	complemented
65	C₆₁×#464	C₂²	1	4	yes	complemented
66	C₆₁×#464	C₂²	1	4	yes	complemented
67	C₆₁×#463	C₂²	1	4	yes	complemented
68	C₆₁×#463	C₂²	1	4	yes	complemented
69	C₆₁×#462	C₂²	1	2	yes	complemented
70	C₆₁×#461	C₂²	1	4	yes	complemented
71	C₆₁×#460	C₂²	1	2	yes	—
72	C₆₁×#460	C₂²	1	4	yes	—
73	C₆₁×#459	C₂²	1	2	yes	—
74	C₆₁×#451	C₂²	1	1	yes	characteristic
75	C₆₁×#451	C₂²	1	2	yes	—
76	C₆₁×#450	C₂²	1	2	yes	—
77	C₆₁×#450	C₂²	1	2	yes	—
78	C₆₁×#450	C₂²	1	2	yes	—
79	C₆₁×#448	C₂²	1	1	yes	characteristic
80	C₆₁×#447	C₂²	1	2	yes	—
81	C₆₁×#446	C₂²	1	4	yes	complemented
82	C₆₁×#446	C₂²	1	2	yes	complemented
83	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
84	C₆₁×#442	C₂²	1	4	yes	complemented
85	C₆₁×#441	C₂²	1	4	yes	complemented
86	C₆₁×#440	C₂²	1	4	yes	complemented
87	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
88	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
89	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
90	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
91	C₆₁×#432	C₂²	1	1	yes	characteristic
92	C₆₁×#432	C₂²	1	2	yes	—
93	C₆₁×#431	C₂²	1	2	yes	—
94	C₆₁×#431	C₂²	1	1	yes	characteristic
95	C₂²×Q₈×C₆₁	—	2	1	no	—
96	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
97	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₁	—	2	1	no	—
99	C₂²×D₄×C₆₁	—	2	1	no	—
100	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
101	C₂³×C₄×C₆₁	—	2	2	no	—
102	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
103	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
108	C₂×D₈×C₆₁	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₆₁	—	2	1	no	—
110	C₄⋊Q₈×C₆₁	—	2	2	no	—
111	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
115	#127×C₆₁	—	2	1	no	—
116	#127×C₆₁	—	2	1	no	—
117	#127×C₆₁	C₂³	1	2	yes	—
118	#127×C₆₁	C₂³	1	2	yes	—
119	#126×C₆₁	—	2	2	no	—
120	#126×C₆₁	—	2	2	no	—
121	#126×C₆₁	—	2	2	no	—
122	#126×C₆₁	—	2	2	no	—
123	#126×C₆₁	—	2	1	no	—
124	#125×C₆₁	—	2	2	no	—
125	#125×C₆₁	—	2	2	no	—
126	#125×C₆₁	—	2	2	no	—
127	#125×C₆₁	—	2	1	no	—
128	#125×C₆₁	—	2	2	no	—
129	#125×C₆₁	—	2	2	no	—
130	#125×C₆₁	—	2	1	no	—
131	#125×C₆₁	C₂³	1	2	yes	—
132	#125×C₆₁	C₂³	1	1	yes	characteristic
133	#124×C₆₁	—	2	2	no	—
134	#124×C₆₁	—	2	2	no	—
135	#124×C₆₁	—	2	4	no	—
136	#124×C₆₁	—	2	2	no	—
137	#124×C₆₁	—	2	2	no	—
138	#124×C₆₁	C₂³	1	2	yes	—
139	#124×C₆₁	C₂³	1	1	yes	characteristic
140	#124×C₆₁	C₂³	1	4	yes	—
141	#124×C₆₁	C₂³	1	4	yes	—
142	#123×C₆₁	—	2	2	no	—
143	#123×C₆₁	—	2	1	no	—
144	#123×C₆₁	—	2	4	no	—
145	#123×C₆₁	—	2	4	no	—
146	#123×C₆₁	—	2	4	no	—
147	#123×C₆₁	—	2	4	no	—
148	C₂²⋊Q₈×C₆₁	—	2	1	no	—
149	C₂²⋊Q₈×C₆₁	—	2	2	no	—
150	C₂²⋊Q₈×C₆₁	—	2	1	no	—
151	C₂²⋊Q₈×C₆₁	—	2	2	no	—
152	C₂²⋊Q₈×C₆₁	—	2	1	no	—
153	C₂²⋊Q₈×C₆₁	—	2	2	no	—
154	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
155	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
156	#121×C₆₁	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₆₁	—	2	1	no	—
158	C₄×Q₈×C₆₁	—	2	1	no	—
159	C₄×Q₈×C₆₁	—	2	2	no	—
160	C₄×Q₈×C₆₁	—	2	2	no	—
161	C₄×Q₈×C₆₁	—	2	1	no	—
162	C₄×Q₈×C₆₁	—	2	1	no	—
163	C₄×Q₈×C₆₁	—	2	1	no	—
164	C₄×Q₈×C₆₁	D₄	1	2	yes	—
165	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
168	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
170	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
172	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
173	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
174	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
177	C₄×D₄×C₆₁	—	2	1	no	—
178	C₄×D₄×C₆₁	—	2	2	no	—
179	C₄×D₄×C₆₁	—	2	2	no	—
180	C₄×D₄×C₆₁	—	2	2	no	—
181	C₄×D₄×C₆₁	—	2	4	no	—
182	C₄×D₄×C₆₁	—	2	2	no	—
183	C₄×D₄×C₆₁	—	2	2	no	—
184	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₆₁	C₂³	1	2	yes	—
186	C₄×D₄×C₆₁	C₂³	1	4	yes	—
187	C₄×D₄×C₆₁	C₂³	1	4	yes	—
188	#117×C₆₁	—	2	2	no	—
189	#117×C₆₁	—	2	1	no	—
190	#117×C₆₁	—	2	1	no	—
191	#117×C₆₁	—	2	2	no	—
192	#117×C₆₁	—	2	2	no	—
193	#117×C₆₁	—	2	1	no	—
194	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
201	C₂×C₄²×C₆₁	—	2	1	no	—
202	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
204	#107×C₆₁	C₂³	1	2	yes	—
205	#106×C₆₁	C₂³	1	2	yes	—
206	#106×C₆₁	C₂³	1	4	yes	—
207	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
208	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
209	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
210	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
211	#103×C₆₁	C₂³	1	2	yes	—
212	#103×C₆₁	C₂³	1	4	yes	—
213	#103×C₆₁	C₂³	1	2	yes	—
214	#103×C₆₁	C₂³	1	2	yes	—
215	#103×C₆₁	C₂³	1	4	yes	—
216	#102×C₆₁	C₂³	1	2	yes	—
217	#102×C₆₁	C₂³	1	4	yes	—
218	#102×C₆₁	C₂³	1	4	yes	—
219	#102×C₆₁	C₂³	1	4	yes	—
220	#102×C₆₁	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
223	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
224	#97×C₆₁	C₂³	1	4	yes	—
225	#97×C₆₁	C₂³	1	2	yes	—
226	C₄×C₈×C₆₁	C₂³	1	4	yes	—
227	C₄×C₈×C₆₁	C₂³	1	2	yes	—
228	C₂⁴×C₆₁	—	2	2	no	—
229	C₂×Q₈×C₆₁	—	2	2	no	—
230	C₂×Q₈×C₆₁	—	2	1	no	—
231	C₂×Q₈×C₆₁	—	2	1	no	—
232	C₂×Q₈×C₆₁	—	4	2	no	—
233	C₂×Q₈×C₆₁	—	4	2	no	—
234	C₂×Q₈×C₆₁	—	4	4	no	—
235	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
236	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
237	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
238	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
241	C₂×D₄×C₆₁	—	2	1	no	—
242	C₂×D₄×C₆₁	—	2	2	no	—
243	C₂×D₄×C₆₁	—	2	2	no	—
244	C₂×D₄×C₆₁	—	2	2	no	—
245	C₂×D₄×C₆₁	—	2	2	no	—
246	C₂×D₄×C₆₁	—	2	2	no	—
247	C₂×D₄×C₆₁	—	4	4	no	—
248	C₂×D₄×C₆₁	—	4	4	no	—
249	C₂×D₄×C₆₁	—	8	2	no	—
250	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
251	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₆₁	—	2	1	no	—
253	C₂²×C₄×C₆₁	—	2	1	no	—
254	C₂²×C₄×C₆₁	—	2	2	no	—
255	C₂²×C₄×C₆₁	—	2	1	no	—
256	C₂²×C₄×C₆₁	—	2	4	no	—
257	C₂²×C₄×C₆₁	—	2	4	no	—
258	C₂²×C₄×C₆₁	—	8	4	no	—
259	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
264	Q₁₆×C₆₁	—	4	4	no	—
265	Q₁₆×C₆₁	—	4	2	no	—
266	SD₁₆×C₆₁	—	4	4	no	—
267	SD₁₆×C₆₁	—	4	2	no	—
268	SD₁₆×C₆₁	—	4	4	no	—
269	SD₁₆×C₆₁	—	4	4	no	—
270	D₈×C₆₁	—	4	4	no	—
271	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
272	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
273	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
274	C₄⋊C₄×C₆₁	—	2	2	no	—
275	C₄⋊C₄×C₆₁	—	2	2	no	—
276	C₄⋊C₄×C₆₁	—	2	1	no	—
277	C₄⋊C₄×C₆₁	—	2	2	no	—
278	C₄⋊C₄×C₆₁	—	2	1	no	—
279	C₄⋊C₄×C₆₁	—	2	2	no	—
280	C₄⋊C₄×C₆₁	—	2	1	no	—
281	C₄⋊C₄×C₆₁	—	2	2	no	—
282	C₄⋊C₄×C₆₁	—	2	1	no	—
283	C₄⋊C₄×C₆₁	—	2	2	no	—
284	C₄⋊C₄×C₆₁	—	2	1	no	—
285	C₄⋊C₄×C₆₁	—	2	2	no	—
286	C₄⋊C₄×C₆₁	—	2	1	no	—
287	C₄⋊C₄×C₆₁	—	2	1	no	—
288	C₄⋊C₄×C₆₁	—	2	2	no	—
289	C₄⋊C₄×C₆₁	—	2	2	no	—
290	C₄⋊C₄×C₆₁	—	2	2	no	—
291	C₄⋊C₄×C₆₁	—	2	2	no	—
292	C₄⋊C₄×C₆₁	—	2	2	no	—
293	C₄⋊C₄×C₆₁	—	2	1	no	—
294	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
305	C₂²⋊C₄×C₆₁	—	2	1	no	—
306	C₂²⋊C₄×C₆₁	—	2	2	no	—
307	C₂²⋊C₄×C₆₁	—	2	4	no	—
308	C₂²⋊C₄×C₆₁	—	2	4	no	—
309	C₂²⋊C₄×C₆₁	—	2	4	no	—
310	C₂²⋊C₄×C₆₁	—	2	4	no	—
311	C₂²⋊C₄×C₆₁	—	2	4	no	—
312	C₂²⋊C₄×C₆₁	—	2	4	no	—
313	C₂²⋊C₄×C₆₁	—	2	1	no	—
314	C₂²⋊C₄×C₆₁	—	2	2	no	—
315	C₂²⋊C₄×C₆₁	—	2	1	no	—
316	C₂²⋊C₄×C₆₁	—	2	1	no	—
317	C₂²⋊C₄×C₆₁	—	2	2	no	—
318	C₂²⋊C₄×C₆₁	—	2	2	no	—
319	C₂²⋊C₄×C₆₁	—	2	1	no	—
320	C₄²×C₆₁	—	2	2	no	—
321	C₄²×C₆₁	—	2	2	no	—
322	C₄²×C₆₁	—	2	2	no	—
323	C₄²×C₆₁	—	2	2	no	—
324	C₄²×C₆₁	—	2	2	no	—
325	C₄²×C₆₁	—	2	2	no	—
326	C₄²×C₆₁	—	2	1	no	—
327	C₄²×C₆₁	C₂×D₄	1	2	yes	—
328	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₆₁	C₂×D₄	1	2	yes	—
330	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₆₁	C₂⁴	1	2	yes	—
332	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₄²×C₆₁	C₂⁴	1	2	yes	—
334	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂³×C₆₁	—	2	1	no	—
336	C₂³×C₆₁	—	2	4	no	—
337	C₂³×C₆₁	—	4	4	no	—
338	C₂³×C₆₁	—	4	4	no	—
339	C₂³×C₆₁	—	4	4	no	—
340	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₆₁	—	2	2	no	—
342	Q₈×C₆₁	—	2	2	no	—
343	Q₈×C₆₁	—	2	2	no	—
344	Q₈×C₆₁	—	2	4	no	—
345	Q₈×C₆₁	—	2	2	no	—
346	Q₈×C₆₁	—	2	2	no	—
347	Q₈×C₆₁	—	4	2	no	—
348	Q₈×C₆₁	—	4	2	no	—
349	Q₈×C₆₁	—	4	4	no	—
350	Q₈×C₆₁	—	4	2	no	—
351	D₄×C₆₁	—	2	2	no	—
352	D₄×C₆₁	—	2	4	no	—
353	D₄×C₆₁	—	2	4	no	—
354	D₄×C₆₁	—	4	4	no	—
355	D₄×C₆₁	—	4	4	no	—
356	D₄×C₆₁	—	4	2	no	—
357	D₄×C₆₁	—	4	4	no	—
358	D₄×C₆₁	—	8	2	no	—
359	D₄×C₆₁	—	8	2	no	—
360	C₂×C₄×C₆₁	—	2	4	no	—
361	C₂×C₄×C₆₁	—	2	2	no	—
362	C₂×C₄×C₆₁	—	2	2	no	—
363	C₂×C₄×C₆₁	—	2	2	no	—
364	C₂×C₄×C₆₁	—	2	1	no	—
365	C₂×C₄×C₆₁	—	2	2	no	—
366	C₂×C₄×C₆₁	—	2	1	no	—
367	C₂×C₄×C₆₁	—	2	2	no	—
368	C₂×C₄×C₆₁	—	2	2	no	—
369	C₂×C₄×C₆₁	—	2	2	no	—
370	C₂×C₄×C₆₁	—	2	1	no	—
371	C₂×C₄×C₆₁	—	4	2	no	—
372	C₂×C₄×C₆₁	—	4	4	no	—
373	C₂×C₄×C₆₁	—	4	2	no	—
374	C₂×C₄×C₆₁	—	4	2	no	—
375	C₂×C₄×C₆₁	—	4	2	no	—
376	C₂×C₄×C₆₁	—	8	4	no	—
377	C₂×C₄×C₆₁	—	8	4	no	—
378	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
388	C₈×C₆₁	—	2	4	no	—
389	C₈×C₆₁	—	2	2	no	—
390	C₈×C₆₁	—	2	2	no	—
391	#61904	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₂²×C₆₁	—	2	1	no	—
393	C₂²×C₆₁	—	2	1	no	—
394	C₂²×C₆₁	—	4	4	no	—
395	C₂²×C₆₁	—	4	1	no	—
396	C₂²×C₆₁	—	4	1	no	—
397	C₂²×C₆₁	—	4	4	no	—
398	C₂²×C₆₁	—	4	4	no	—
399	C₂²×C₆₁	—	4	1	no	—
400	C₂²×C₆₁	—	8	8	no	—
401	C₂²×C₆₁	#577	1	2	yes	—
402	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
403	C₄×C₆₁	—	2	1	no	—
404	C₄×C₆₁	—	2	1	no	—
405	C₄×C₆₁	—	2	2	no	—
406	C₄×C₆₁	—	2	2	no	—
407	C₄×C₆₁	—	2	2	no	—
408	C₄×C₆₁	—	2	2	no	—
409	C₄×C₆₁	—	2	1	no	—
410	C₄×C₆₁	—	2	1	no	—
411	C₄×C₆₁	—	4	2	no	—
412	C₄×C₆₁	—	4	1	no	—
413	C₄×C₆₁	—	4	2	no	—
414	C₄×C₆₁	—	4	2	no	—
415	C₄×C₆₁	—	4	1	no	—
416	C₄×C₆₁	—	4	2	no	—
417	C₄×C₆₁	—	4	1	no	—
418	C₄×C₆₁	#575	1	2	yes	—
419	C₄×C₆₁	#585	1	2	yes	—
420	#3523	C₂×C₆₁	1	1	yes	characteristic, complemented
421	C₂×#559	C₂×C₆₁	1	1	yes	characteristic, complemented
422	#3401	C₂×C₆₁	1	4	yes	complemented
423	#3400	C₂×C₆₁	1	2	yes	complemented
424	#3394	C₂×C₆₁	1	2	yes	complemented
425	#3373	C₂×C₆₁	1	2	yes	complemented
426	#3371	C₂×C₆₁	1	4	yes	complemented
427	#3365	C₂×C₆₁	1	2	yes	complemented
428	#3217	C₂×C₆₁	1	1	yes	characteristic
429	#3215	C₂×C₆₁	1	2	yes	complemented
430	#3211	C₂×C₆₁	1	2	yes	complemented
431	#3208	C₂×C₆₁	1	1	yes	characteristic, complemented
432	#3114	C₂×C₆₁	1	2	yes	complemented
433	#3113	C₂×C₆₁	1	1	yes	characteristic, complemented
434	#3108	C₂×C₆₁	1	1	yes	characteristic, complemented
435	#3101	C₂×C₆₁	1	2	yes	complemented
436	#2984	C₂×C₆₁	1	1	yes	characteristic, complemented
437	C₂×C₆₁	—	2	2	no	—
438	C₂×C₆₁	—	8	1	no	—
439	C₂×C₆₁	—	8	4	no	—
440	C₂×C₆₁	#3487	1	1	yes	characteristic
441	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
442	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
443	#559	—	2	1	no	—
444	#559	—	2	1	no	—
445	#559	—	2	2	no	—
446	#559	C₂²×C₆₁	1	2	yes	—
447	#559	C₂²×C₆₁	1	4	yes	—
448	#559	C₂²×C₆₁	1	2	yes	—
449	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
450	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
451	#557	C₂²×C₆₁	1	2	yes	complemented
452	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
453	#556	C₂²×C₆₁	1	2	yes	complemented
454	#552	—	2	1	no	—
455	#552	—	2	2	no	—
456	D₄×Q₈	—	2	1	no	—
457	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
458	#541	—	2	2	no	—
459	#541	—	2	1	no	—
460	#533	C₂²×C₆₁	1	2	yes	—
461	#533	C₂²×C₆₁	1	1	yes	characteristic
462	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
463	#529	C₂²×C₆₁	1	1	yes	characteristic
464	#529	C₂²×C₆₁	1	2	yes	—
465	C₂×#124	—	2	1	no	—
466	C₂×#124	C₂²×C₆₁	1	2	yes	—
467	C₂×#123	—	2	2	no	—
468	#519	—	2	1	no	—
469	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
470	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
471	C₂×C₄×D₄	—	2	1	no	—
472	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
473	#497	C₂²×C₆₁	1	4	yes	complemented
474	#496	C₂²×C₆₁	1	2	yes	—
475	#495	C₂²×C₆₁	1	4	yes	complemented
476	#492	C₂²×C₆₁	1	2	yes	—
477	#490	C₂²×C₆₁	1	2	yes	—
478	#489	C₂²×C₆₁	1	4	yes	complemented
479	#488	C₂²×C₆₁	1	4	yes	complemented
480	#486	C₂²×C₆₁	1	2	yes	—
481	#483	C₂²×C₆₁	1	1	yes	characteristic
482	#483	C₂²×C₆₁	1	2	yes	—
483	#480	C₂²×C₆₁	1	1	yes	characteristic
484	#479	C₂²×C₆₁	1	2	yes	complemented
485	#478	C₂²×C₆₁	1	4	yes	complemented
486	#476	C₂²×C₆₁	1	4	yes	complemented
487	#475	C₂²×C₆₁	1	2	yes	complemented
488	#464	C₂²×C₆₁	1	2	yes	complemented
489	#464	C₂²×C₆₁	1	4	yes	complemented
490	#464	C₂²×C₆₁	1	4	yes	complemented
491	#464	C₂²×C₆₁	1	4	yes	complemented
492	#463	C₂²×C₆₁	1	4	yes	complemented
493	#463	C₂²×C₆₁	1	4	yes	complemented
494	#462	C₂²×C₆₁	1	2	yes	complemented
495	#461	C₂²×C₆₁	1	4	yes	complemented
496	#460	C₂²×C₆₁	1	2	yes	—
497	#460	C₂²×C₆₁	1	4	yes	—
498	#459	C₂²×C₆₁	1	2	yes	—
499	#451	C₂²×C₆₁	1	1	yes	characteristic
500	#451	C₂²×C₆₁	1	2	yes	—
501	#450	C₂²×C₆₁	1	2	yes	—
502	#450	C₂²×C₆₁	1	2	yes	—
503	#450	C₂²×C₆₁	1	2	yes	—
504	#448	C₂²×C₆₁	1	1	yes	characteristic
505	#447	C₂²×C₆₁	1	2	yes	—
506	#446	C₂²×C₆₁	1	4	yes	complemented
507	#446	C₂²×C₆₁	1	2	yes	complemented
508	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
509	#442	C₂²×C₆₁	1	4	yes	complemented
510	#441	C₂²×C₆₁	1	4	yes	complemented
511	#440	C₂²×C₆₁	1	4	yes	complemented
512	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
513	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
514	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
515	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
516	#432	C₂²×C₆₁	1	1	yes	characteristic
517	#432	C₂²×C₆₁	1	2	yes	—
518	#431	C₂²×C₆₁	1	2	yes	—
519	#431	C₂²×C₆₁	1	1	yes	characteristic
520	C₆₁	#61904	1	1	yes	characteristic, direct product factor, Sylow
521	C₂²×Q₈	—	2	1	no	—
522	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
523	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	—	2	1	no	—
526	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
527	C₂³×C₄	—	2	2	no	—
528	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
529	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
530	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
531	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
532	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
533	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
534	C₂×D₈	C₂³×C₆₁	1	4	yes	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
538	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
539	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
540	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
541	#127	—	2	1	no	—
542	#127	—	2	1	no	—
543	#127	C₂³×C₆₁	1	2	yes	—
544	#127	C₂³×C₆₁	1	2	yes	—
545	#126	—	2	2	no	—
546	#126	—	2	2	no	—
547	#126	—	2	2	no	—
548	#126	—	2	2	no	—
549	#126	—	2	1	no	—
550	#125	—	2	2	no	—
551	#125	—	2	2	no	—
552	#125	—	2	2	no	—
553	#125	—	2	1	no	—
554	#125	—	2	2	no	—
555	#125	—	2	2	no	—
556	#125	—	2	1	no	—
557	#125	C₂³×C₆₁	1	2	yes	—
558	#125	C₂³×C₆₁	1	1	yes	characteristic
559	#124	—	2	2	no	—
560	#124	—	2	2	no	—
561	#124	—	2	4	no	—
562	#124	—	2	2	no	—
563	#124	—	2	2	no	—
564	#124	C₂³×C₆₁	1	4	yes	—
565	#124	C₂³×C₆₁	1	4	yes	—
566	#124	C₂³×C₆₁	1	2	yes	—
567	#124	C₂³×C₆₁	1	1	yes	characteristic
568	#123	—	2	2	no	—
569	#123	—	2	1	no	—
570	#123	—	2	4	no	—
571	#123	—	2	4	no	—
572	#123	—	2	4	no	—
573	#123	—	2	4	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
581	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
582	#121	C₂³×C₆₁	1	1	yes	characteristic
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
591	C₄×Q₈	D₄×C₆₁	1	2	yes	—
592	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
594	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
595	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
596	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
597	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
598	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
599	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
600	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	4	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	C₂³×C₆₁	1	4	yes	—
611	C₄×D₄	C₂³×C₆₁	1	4	yes	—
612	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
613	C₄×D₄	C₂³×C₆₁	1	2	yes	—
614	#117	—	2	2	no	—
615	#117	—	2	1	no	—
616	#117	—	2	1	no	—
617	#117	—	2	2	no	—
618	#117	—	2	2	no	—
619	#117	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
622	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	—	2	2	no	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₂²⋊C₄	—	2	2	no	—
627	C₂×C₄²	—	2	1	no	—
628	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
629	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
630	#107	C₂³×C₆₁	1	2	yes	—
631	#106	C₂³×C₆₁	1	2	yes	—
632	#106	C₂³×C₆₁	1	4	yes	—
633	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
634	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
635	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
636	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
637	#103	C₂³×C₆₁	1	2	yes	—
638	#103	C₂³×C₆₁	1	4	yes	—
639	#103	C₂³×C₆₁	1	2	yes	—
640	#103	C₂³×C₆₁	1	2	yes	—
641	#103	C₂³×C₆₁	1	4	yes	—
642	#102	C₂³×C₆₁	1	2	yes	—
643	#102	C₂³×C₆₁	1	4	yes	—
644	#102	C₂³×C₆₁	1	4	yes	—
645	#102	C₂³×C₆₁	1	4	yes	—
646	#102	C₂³×C₆₁	1	4	yes	—
647	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
648	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
649	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
650	#97	C₂³×C₆₁	1	4	yes	—
651	#97	C₂³×C₆₁	1	2	yes	—
652	C₄×C₈	C₂³×C₆₁	1	4	yes	—
653	C₄×C₈	C₂³×C₆₁	1	2	yes	—
654	C₂⁴	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×Q₈	—	4	4	no	—
661	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
662	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
663	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
664	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
665	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
666	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	—	8	2	no	—
676	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
677	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	8	4	no	—
685	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
687	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
690	Q₁₆	—	4	4	no	—
691	Q₁₆	—	4	2	no	—
692	SD₁₆	—	4	4	no	—
693	SD₁₆	—	4	2	no	—
694	SD₁₆	—	4	4	no	—
695	SD₁₆	—	4	4	no	—
696	D₈	—	4	4	no	—
697	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
698	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
699	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
721	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
723	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
724	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
726	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
728	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
730	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	1	no	—
753	C₄²	C₂×D₄×C₆₁	1	2	yes	—
754	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
755	C₄²	C₂×D₄×C₆₁	1	2	yes	—
756	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
757	C₄²	C₂⁴×C₆₁	1	2	yes	—
758	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
759	C₄²	C₂⁴×C₆₁	1	2	yes	—
760	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
761	C₂³	—	2	1	no	—
762	C₂³	—	2	4	no	—
763	C₂³	—	4	4	no	—
764	C₂³	—	4	4	no	—
765	C₂³	—	4	4	no	—
766	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	4	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	4	2	no	—
774	Q₈	—	4	4	no	—
775	Q₈	—	4	2	no	—
776	Q₈	—	4	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	2	no	—
783	D₄	—	4	4	no	—
784	D₄	—	8	2	no	—
785	D₄	—	8	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	4	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	8	4	no	—
803	C₂×C₄	—	8	4	no	—
804	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
810	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
813	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
814	C₈	—	2	4	no	—
815	C₈	—	2	2	no	—
816	C₈	—	2	2	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	4	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	4	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	8	8	no	—
826	C₂²	C₆₁×#577	1	2	yes	—
827	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
828	C₄	—	2	1	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	1	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	C₆₁×#575	1	2	yes	—
844	C₄	C₆₁×#585	1	2	yes	—
845	C₂	—	2	2	no	—
846	C₂	—	8	4	no	—
847	C₂	—	8	1	no	—
848	C₂	C₆₁×#3487	1	1	yes	characteristic
849	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
850	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3217	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×#3523	C₂	semidirect
2. C₂×C₆₁×#559	C₂	semidirect
3. C₆₁×#3401	C₂	semidirect
4. C₆₁×#3400	C₂	semidirect
5. C₆₁×#3394	C₂	semidirect
6. C₆₁×#3373	C₂	semidirect
7. C₆₁×#3371	C₂	semidirect
8. C₆₁×#3365	C₂	semidirect
10. C₆₁×#3215	C₂	semidirect
11. C₆₁×#3211	C₂	semidirect
12. C₆₁×#3208	C₂	semidirect
13. C₆₁×#3114	C₂	semidirect
14. C₆₁×#3113	C₂	semidirect
15. C₆₁×#3108	C₂	semidirect
16. C₆₁×#3101	C₂	semidirect
17. C₆₁×#2984	C₂	semidirect
24. C₆₁×#557	C₂²	semidirect
25. C₆₁×#557	C₂²	semidirect
26. C₆₁×#557	C₂²	semidirect
27. C₆₁×#556	C₂²	semidirect
28. C₆₁×#556	C₂²	semidirect
32. D₄×Q₈×C₆₁	C₂²	semidirect
48. C₆₁×#497	C₂²	semidirect
50. C₆₁×#495	C₂²	semidirect
53. C₆₁×#489	C₂²	semidirect
54. C₆₁×#488	C₂²	semidirect
59. C₆₁×#479	C₂²	semidirect
60. C₆₁×#478	C₂²	semidirect
61. C₆₁×#476	C₂²	semidirect
62. C₆₁×#475	C₂²	semidirect
63. C₆₁×#464	C₂²	semidirect
64. C₆₁×#464	C₂²	semidirect
65. C₆₁×#464	C₂²	semidirect
66. C₆₁×#464	C₂²	semidirect
67. C₆₁×#463	C₂²	semidirect
68. C₆₁×#463	C₂²	semidirect
69. C₆₁×#462	C₂²	semidirect
70. C₆₁×#461	C₂²	semidirect
81. C₆₁×#446	C₂²	semidirect
82. C₆₁×#446	C₂²	semidirect
83. C₈×Q₈×C₆₁	C₂²	semidirect
84. C₆₁×#442	C₂²	semidirect
85. C₆₁×#441	C₂²	semidirect
86. C₆₁×#440	C₂²	semidirect
87. C₄×Q₁₆×C₆₁	C₂²	semidirect
88. C₄×SD₁₆×C₆₁	C₂²	semidirect
89. C₄×SD₁₆×C₆₁	C₂²	semidirect
90. C₄×SD₁₆×C₆₁	C₂²	semidirect
391. #61904	C₆₁	direct (N × H)
420. #3523	C₂×C₆₁	semidirect
421. C₂×#559	C₂×C₆₁	semidirect
422. #3401	C₂×C₆₁	semidirect
423. #3400	C₂×C₆₁	semidirect
424. #3394	C₂×C₆₁	semidirect
425. #3373	C₂×C₆₁	semidirect
426. #3371	C₂×C₆₁	semidirect
427. #3365	C₂×C₆₁	semidirect
429. #3215	C₂×C₆₁	semidirect
430. #3211	C₂×C₆₁	semidirect
431. #3208	C₂×C₆₁	semidirect
432. #3114	C₂×C₆₁	semidirect
433. #3113	C₂×C₆₁	semidirect
434. #3108	C₂×C₆₁	semidirect
435. #3101	C₂×C₆₁	semidirect
436. #2984	C₂×C₆₁	semidirect
449. #557	C₂²×C₆₁	semidirect
450. #557	C₂²×C₆₁	semidirect
451. #557	C₂²×C₆₁	semidirect
452. #556	C₂²×C₆₁	semidirect
453. #556	C₂²×C₆₁	semidirect
457. D₄×Q₈	C₂²×C₆₁	semidirect
473. #497	C₂²×C₆₁	semidirect
475. #495	C₂²×C₆₁	semidirect
478. #489	C₂²×C₆₁	semidirect
479. #488	C₂²×C₆₁	semidirect
484. #479	C₂²×C₆₁	semidirect
485. #478	C₂²×C₆₁	semidirect
486. #476	C₂²×C₆₁	semidirect
487. #475	C₂²×C₆₁	semidirect
488. #464	C₂²×C₆₁	semidirect
489. #464	C₂²×C₆₁	semidirect
490. #464	C₂²×C₆₁	semidirect
491. #464	C₂²×C₆₁	semidirect
492. #463	C₂²×C₆₁	semidirect
493. #463	C₂²×C₆₁	semidirect
494. #462	C₂²×C₆₁	semidirect
495. #461	C₂²×C₆₁	semidirect
506. #446	C₂²×C₆₁	semidirect
507. #446	C₂²×C₆₁	semidirect
508. C₈×Q₈	C₂²×C₆₁	semidirect
509. #442	C₂²×C₆₁	semidirect
510. #441	C₂²×C₆₁	semidirect
511. #440	C₂²×C₆₁	semidirect
512. C₄×Q₁₆	C₂²×C₆₁	semidirect
513. C₄×SD₁₆	C₂²×C₆₁	semidirect
514. C₄×SD₁₆	C₂²×C₆₁	semidirect
515. C₄×SD₁₆	C₂²×C₆₁	semidirect
520. C₆₁	#61904	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×#3523	2
C₂×C₆₁×#559	2
C₆₁×#3401	2
C₆₁×#3400	2
C₆₁×#3394	2
C₆₁×#3373	2
C₆₁×#3371	2
C₆₁×#3365	2
C₆₁×#3217	2
C₆₁×#3215	2
C₆₁×#3211	2
C₆₁×#3208	2
C₆₁×#3114	2
C₆₁×#3113	2
C₆₁×#3108	2
C₆₁×#3101	2
C₆₁×#2984	2
#61904	61

Subgroups — C61×#61904 #29565337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61904 #29565337