Subgroups — C₆₁×#62094 #29565527

Order 15616.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3397	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3377	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3322	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3320	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3308	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3278	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3271	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3268	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3257	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3221	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3124	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3046	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#137×C₆₁	C₂²	1	2	yes	complemented
22	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#135×C₆₁	C₂²	1	2	yes	—
24	C₆₁×#563	—	2	1	no	—
25	C₆₁×#562	—	2	1	no	—
26	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
27	C₆₁×#556	C₂²	1	2	yes	—
28	C₆₁×#553	—	2	2	no	—
29	C₆₁×#553	C₂²	1	2	yes	—
30	C₆₁×#551	—	2	2	no	—
31	C₆₁×#550	—	2	1	no	—
32	C₆₁×#550	C₂²	1	2	yes	—
33	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
34	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
36	C₆₁×#548	C₂²	1	2	yes	—
37	C₆₁×#547	—	2	1	no	—
38	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
39	C₆₁×#546	C₂²	1	2	yes	—
40	C₆₁×#543	—	2	1	no	—
41	C₆₁×#542	—	2	2	no	—
42	C₆₁×#542	C₂²	1	2	yes	—
43	C₆₁×#540	—	2	2	no	—
44	C₆₁×#540	C₂²	1	2	yes	complemented
45	C₆₁×#538	—	2	1	no	—
46	C₆₁×#536	C₂²	1	2	yes	—
47	C₆₁×#533	C₂²	1	1	yes	characteristic
48	C₆₁×#532	—	2	1	no	—
49	C₆₁×#532	C₂²	1	1	yes	characteristic
50	C₆₁×#529	—	2	1	no	—
51	C₆₁×#529	C₂²	1	1	yes	characteristic
52	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
53	C₆₁×#520	C₂²	1	2	yes	complemented
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×#496	C₂²	1	2	yes	—
56	C₆₁×#496	C₂²	1	2	yes	—
57	C₆₁×#492	C₂²	1	2	yes	complemented
58	C₆₁×#491	C₂²	1	2	yes	complemented
59	C₆₁×#489	C₂²	1	2	yes	—
60	C₆₁×#488	C₂²	1	2	yes	—
61	C₆₁×#485	C₂²	1	2	yes	—
62	C₆₁×#484	C₂²	1	2	yes	complemented
63	C₆₁×#480	C₂²	1	2	yes	—
64	C₆₁×#479	C₂²	1	2	yes	complemented
65	C₆₁×#478	C₂²	1	2	yes	—
66	C₆₁×#477	C₂²	1	2	yes	complemented
67	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
68	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
69	C₆₁×#474	C₂²	1	2	yes	complemented
70	C₆₁×#469	C₂²	1	2	yes	—
71	C₆₁×#468	C₂²	1	2	yes	—
72	C₆₁×#468	C₂²	1	2	yes	—
73	C₆₁×#468	C₂²	1	2	yes	complemented
74	C₆₁×#466	C₂²	1	2	yes	—
75	C₆₁×#465	C₂²	1	2	yes	complemented
76	C₆₁×#464	C₂²	1	2	yes	—
77	C₆₁×#464	C₂²	1	2	yes	—
78	C₆₁×#464	C₂²	1	2	yes	—
79	C₆₁×#463	C₂²	1	2	yes	—
80	C₆₁×#463	C₂²	1	2	yes	—
81	C₆₁×#463	C₂²	1	2	yes	—
82	C₆₁×#463	C₂²	1	2	yes	—
83	C₆₁×#463	C₂²	1	2	yes	—
84	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
85	C₆₁×#462	C₂²	1	2	yes	complemented
86	C₆₁×#461	C₂²	1	2	yes	complemented
87	C₆₁×#461	C₂²	1	2	yes	complemented
88	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
89	C₆₁×#460	C₂²	1	2	yes	complemented
90	C₆₁×#460	C₂²	1	2	yes	complemented
91	C₆₁×#459	C₂²	1	2	yes	—
92	C₆₁×#452	C₂²	1	2	yes	—
93	C₆₁×#452	C₂²	1	2	yes	complemented
94	C₆₁×#449	C₂²	1	2	yes	—
95	C₆₁×#449	C₂²	1	2	yes	—
96	C₆₁×#449	C₂²	1	2	yes	—
97	C₆₁×#448	C₂²	1	2	yes	—
98	C₆₁×#448	C₂²	1	2	yes	complemented
99	C₆₁×#448	C₂²	1	2	yes	complemented
100	C₆₁×#447	C₂²	1	2	yes	—
101	C₆₁×#446	C₂²	1	2	yes	complemented
102	C₆₁×#441	C₂²	1	2	yes	complemented
103	C₆₁×#440	C₂²	1	2	yes	—
104	C₆₁×#440	C₂²	1	2	yes	complemented
105	C₆₁×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₆₁	C₂²	1	2	yes	—
108	C₆₁×#436	C₂²	1	2	yes	—
109	C₆₁×#435	C₂²	1	2	yes	—
110	C₆₁×#435	C₂²	1	2	yes	complemented
111	C₆₁×#433	C₂²	1	2	yes	complemented
112	C₆₁×#432	C₂²	1	1	yes	characteristic
113	C₆₁×#424	C₂²	1	2	yes	complemented
114	C₆₁×#423	C₂²	1	1	yes	characteristic
115	C₆₁×#419	C₂²	1	1	yes	characteristic
116	C₆₁×#418	C₂²	1	1	yes	characteristic
117	C₆₁×#417	C₂²	1	2	yes	—
118	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
119	C₂×#41×C₆₁	—	2	1	no	—
120	C₂×#41×C₆₁	—	2	1	no	—
121	C₂×#41×C₆₁	—	2	1	no	—
122	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
123	C₂×#41×C₆₁	C₂³	1	2	yes	—
124	C₂×#41×C₆₁	C₂³	1	2	yes	—
125	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
126	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
128	#137×C₆₁	—	4	2	no	—
129	#137×C₆₁	—	4	4	no	—
130	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
131	#135×C₆₁	—	4	4	no	—
132	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
141	C₂×D₈×C₆₁	C₂³	1	2	yes	—
142	C₂×D₈×C₆₁	C₂³	1	2	yes	—
143	C₂×D₈×C₆₁	C₂³	1	2	yes	—
144	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
148	C₄⋊Q₈×C₆₁	—	2	1	no	—
149	C₄⋊Q₈×C₆₁	—	2	2	no	—
150	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
154	#127×C₆₁	—	2	1	no	—
155	#127×C₆₁	—	2	2	no	—
156	#127×C₆₁	C₂³	1	1	yes	characteristic
157	#127×C₆₁	C₂³	1	2	yes	—
158	#126×C₆₁	—	2	2	no	—
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	—	2	2	no	—
161	#126×C₆₁	—	2	2	no	—
162	#126×C₆₁	D₄	1	2	yes	—
163	#125×C₆₁	—	2	2	no	—
164	#125×C₆₁	—	2	1	no	—
165	#125×C₆₁	D₄	1	1	yes	characteristic
166	#125×C₆₁	C₂³	1	2	yes	—
167	#124×C₆₁	—	2	2	no	—
168	#124×C₆₁	—	2	2	no	—
169	#124×C₆₁	—	2	1	no	—
170	#124×C₆₁	—	2	1	no	—
171	#124×C₆₁	—	2	1	no	—
172	#124×C₆₁	D₄	1	1	yes	characteristic
173	#124×C₆₁	C₂³	1	2	yes	—
174	#124×C₆₁	C₂³	1	2	yes	—
175	#124×C₆₁	C₂³	1	2	yes	—
176	#123×C₆₁	—	2	2	no	—
177	#123×C₆₁	—	2	2	no	—
178	#123×C₆₁	—	2	2	no	—
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	#123×C₆₁	—	2	2	no	—
184	#123×C₆₁	D₄	1	2	yes	—
185	C₂²⋊Q₈×C₆₁	—	2	2	no	—
186	C₂²⋊Q₈×C₆₁	—	2	1	no	—
187	C₂²⋊Q₈×C₆₁	—	2	2	no	—
188	C₂²⋊Q₈×C₆₁	—	2	2	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	2	no	—
193	C₂²⋊Q₈×C₆₁	—	2	2	no	—
194	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
195	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
197	#121×C₆₁	—	2	2	no	—
198	#121×C₆₁	—	2	2	no	—
199	#121×C₆₁	—	2	1	no	—
200	#121×C₆₁	—	2	2	no	—
201	#121×C₆₁	—	2	1	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	—	2	2	no	—
204	#121×C₆₁	—	2	2	no	—
205	#121×C₆₁	—	2	2	no	—
206	#121×C₆₁	—	2	2	no	—
207	#121×C₆₁	—	2	2	no	—
208	#121×C₆₁	D₄	1	1	yes	characteristic
209	#121×C₆₁	C₂³	1	2	yes	—
210	#121×C₆₁	C₂³	1	2	yes	—
211	#121×C₆₁	C₂³	1	2	yes	—
212	#121×C₆₁	C₂³	1	2	yes	—
213	#120×C₆₁	—	2	2	no	—
214	C₄×Q₈×C₆₁	—	2	1	no	—
215	C₄×Q₈×C₆₁	—	2	1	no	—
216	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₆₁	—	2	2	no	—
223	C₄×D₄×C₆₁	—	2	1	no	—
224	C₄×D₄×C₆₁	—	2	1	no	—
225	C₄×D₄×C₆₁	—	2	1	no	—
226	C₄×D₄×C₆₁	—	2	2	no	—
227	C₄×D₄×C₆₁	—	2	2	no	—
228	C₄×D₄×C₆₁	—	2	2	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	—	2	2	no	—
231	C₄×D₄×C₆₁	—	2	1	no	—
232	C₄×D₄×C₆₁	C₂³	1	2	yes	—
233	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₆₁	C₂³	1	2	yes	—
235	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₆₁	C₂³	1	2	yes	—
237	C₄×D₄×C₆₁	C₂³	1	2	yes	—
238	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
239	#117×C₆₁	—	2	1	no	—
240	#117×C₆₁	—	2	2	no	—
241	#117×C₆₁	—	2	2	no	—
242	#117×C₆₁	—	2	1	no	—
243	#117×C₆₁	C₂³	1	1	yes	characteristic
244	#117×C₆₁	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
246	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
247	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
250	C₂×C₄²×C₆₁	—	2	1	no	—
251	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
252	#107×C₆₁	C₂³	1	2	yes	—
253	#107×C₆₁	C₂³	1	2	yes	—
254	#107×C₆₁	C₂³	1	2	yes	—
255	#106×C₆₁	C₂³	1	2	yes	—
256	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
257	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
258	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
259	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
260	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
261	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
262	#103×C₆₁	C₂³	1	2	yes	—
263	#103×C₆₁	C₂³	1	2	yes	—
264	#103×C₆₁	C₂³	1	2	yes	—
265	#103×C₆₁	C₂³	1	2	yes	—
266	#103×C₆₁	C₂³	1	2	yes	—
267	#103×C₆₁	C₂³	1	2	yes	—
268	#103×C₆₁	C₂³	1	2	yes	—
269	#103×C₆₁	C₂³	1	2	yes	—
270	#103×C₆₁	C₂³	1	2	yes	—
271	#102×C₆₁	C₂³	1	2	yes	—
272	#102×C₆₁	C₂³	1	2	yes	—
273	#102×C₆₁	C₂³	1	2	yes	—
274	#102×C₆₁	C₂³	1	2	yes	—
275	#102×C₆₁	C₂³	1	2	yes	—
276	#102×C₆₁	C₂³	1	2	yes	—
277	#102×C₆₁	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
281	#97×C₆₁	C₂³	1	2	yes	—
282	#97×C₆₁	C₂³	1	2	yes	—
283	C₄×C₈×C₆₁	C₂³	1	2	yes	—
284	C₂⁴×C₆₁	—	2	1	no	—
285	#41×C₆₁	—	2	4	no	—
286	#41×C₆₁	—	2	2	no	—
287	#41×C₆₁	—	4	1	no	—
288	#41×C₆₁	—	4	2	no	—
289	#41×C₆₁	—	4	2	no	—
290	#41×C₆₁	—	4	2	no	—
291	#41×C₆₁	—	8	2	no	—
292	#41×C₆₁	—	8	2	no	—
293	#41×C₆₁	—	8	2	no	—
294	C₂×Q₈×C₆₁	—	2	1	no	—
295	C₂×Q₈×C₆₁	—	2	1	no	—
296	C₂×Q₈×C₆₁	—	2	2	no	—
297	C₂×Q₈×C₆₁	—	2	1	no	—
298	C₂×Q₈×C₆₁	—	4	2	no	—
299	C₂×Q₈×C₆₁	—	4	1	no	—
300	C₂×Q₈×C₆₁	—	4	1	no	—
301	C₂×Q₈×C₆₁	—	4	2	no	—
302	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
303	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₆₁	—	2	1	no	—
307	C₂×D₄×C₆₁	—	2	2	no	—
308	C₂×D₄×C₆₁	—	2	2	no	—
309	C₂×D₄×C₆₁	—	2	2	no	—
310	C₂×D₄×C₆₁	—	2	2	no	—
311	C₂×D₄×C₆₁	—	2	2	no	—
312	C₂×D₄×C₆₁	—	2	2	no	—
313	C₂×D₄×C₆₁	—	2	1	no	—
314	C₂×D₄×C₆₁	—	2	1	no	—
315	C₂×D₄×C₆₁	—	2	2	no	—
316	C₂×D₄×C₆₁	—	2	2	no	—
317	C₂×D₄×C₆₁	—	2	1	no	—
318	C₂×D₄×C₆₁	—	4	1	no	—
319	C₂×D₄×C₆₁	—	4	1	no	—
320	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
321	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
322	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
323	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₆₁	—	2	1	no	—
326	C₂²×C₄×C₆₁	—	2	2	no	—
327	C₂²×C₄×C₆₁	—	2	2	no	—
328	C₂²×C₄×C₆₁	—	2	1	no	—
329	C₂²×C₄×C₆₁	—	2	1	no	—
330	C₂²×C₄×C₆₁	—	2	2	no	—
331	C₂²×C₄×C₆₁	—	2	1	no	—
332	C₂²×C₄×C₆₁	—	2	2	no	—
333	C₂²×C₄×C₆₁	—	2	2	no	—
334	C₂²×C₄×C₆₁	—	2	2	no	—
335	C₂²×C₄×C₆₁	—	2	2	no	—
336	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
340	Q₁₆×C₆₁	—	2	4	no	—
341	Q₁₆×C₆₁	—	2	4	no	—
342	SD₁₆×C₆₁	—	2	4	no	—
343	SD₁₆×C₆₁	—	4	2	no	—
344	SD₁₆×C₆₁	—	4	2	no	—
345	SD₁₆×C₆₁	—	4	2	no	—
346	SD₁₆×C₆₁	—	4	2	no	—
347	SD₁₆×C₆₁	—	4	2	no	—
348	SD₁₆×C₆₁	—	4	2	no	—
349	D₈×C₆₁	—	4	2	no	—
350	D₈×C₆₁	—	4	2	no	—
351	D₈×C₆₁	—	4	2	no	—
352	M₁₆×C₆₁	—	4	1	no	—
353	M₁₆×C₆₁	—	4	2	no	—
354	M₁₆×C₆₁	—	4	1	no	—
355	C₂×C₈×C₆₁	—	4	2	no	—
356	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
357	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
358	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
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	1	no	—
364	C₄⋊C₄×C₆₁	—	2	2	no	—
365	C₄⋊C₄×C₆₁	—	2	1	no	—
366	C₄⋊C₄×C₆₁	—	2	1	no	—
367	C₄⋊C₄×C₆₁	—	2	1	no	—
368	C₄⋊C₄×C₆₁	—	2	2	no	—
369	C₄⋊C₄×C₆₁	—	2	2	no	—
370	C₄⋊C₄×C₆₁	—	2	2	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	2	no	—
375	C₄⋊C₄×C₆₁	—	2	2	no	—
376	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
383	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
385	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
386	C₂²⋊C₄×C₆₁	—	2	2	no	—
387	C₂²⋊C₄×C₆₁	—	2	1	no	—
388	C₂²⋊C₄×C₆₁	—	2	2	no	—
389	C₂²⋊C₄×C₆₁	—	2	2	no	—
390	C₂²⋊C₄×C₆₁	—	2	2	no	—
391	C₂²⋊C₄×C₆₁	—	2	2	no	—
392	C₂²⋊C₄×C₆₁	—	2	2	no	—
393	C₂²⋊C₄×C₆₁	—	2	2	no	—
394	C₂²⋊C₄×C₆₁	—	2	2	no	—
395	C₂²⋊C₄×C₆₁	—	2	2	no	—
396	C₂²⋊C₄×C₆₁	—	2	1	no	—
397	C₂²⋊C₄×C₆₁	—	2	1	no	—
398	C₂²⋊C₄×C₆₁	—	2	2	no	—
399	C₂²⋊C₄×C₆₁	—	2	2	no	—
400	C₂²⋊C₄×C₆₁	—	2	2	no	—
401	C₂²⋊C₄×C₆₁	—	2	2	no	—
402	C₂²⋊C₄×C₆₁	—	2	2	no	—
403	C₂²⋊C₄×C₆₁	—	2	2	no	—
404	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
405	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
406	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
407	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
408	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
409	C₄²×C₆₁	—	2	1	no	—
410	C₄²×C₆₁	—	2	1	no	—
411	C₄²×C₆₁	—	2	1	no	—
412	C₄²×C₆₁	—	2	2	no	—
413	C₄²×C₆₁	—	2	2	no	—
414	C₄²×C₆₁	—	2	2	no	—
415	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
416	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
417	C₄²×C₆₁	C₂⁴	1	2	yes	—
418	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
419	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
420	C₂³×C₆₁	—	2	2	no	—
421	C₂³×C₆₁	—	2	1	no	—
422	C₂³×C₆₁	—	2	2	no	—
423	C₂³×C₆₁	—	4	2	no	—
424	C₂³×C₆₁	—	8	1	no	—
425	C₂³×C₆₁	—	8	1	no	—
426	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
427	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
428	Q₈×C₆₁	—	2	1	no	—
429	Q₈×C₆₁	—	2	2	no	—
430	Q₈×C₆₁	—	2	2	no	—
431	Q₈×C₆₁	—	2	2	no	—
432	Q₈×C₆₁	—	2	2	no	—
433	Q₈×C₆₁	—	4	1	no	—
434	Q₈×C₆₁	—	4	2	no	—
435	Q₈×C₆₁	—	8	1	no	—
436	Q₈×C₆₁	—	8	2	no	—
437	Q₈×C₆₁	—	8	1	no	—
438	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
439	D₄×C₆₁	—	2	2	no	—
440	D₄×C₆₁	—	2	1	no	—
441	D₄×C₆₁	—	2	2	no	—
442	D₄×C₆₁	—	2	2	no	—
443	D₄×C₆₁	—	2	2	no	—
444	D₄×C₆₁	—	2	1	no	—
445	D₄×C₆₁	—	4	2	no	—
446	D₄×C₆₁	—	4	1	no	—
447	D₄×C₆₁	—	4	4	no	—
448	D₄×C₆₁	—	4	2	no	—
449	D₄×C₆₁	—	4	2	no	—
450	D₄×C₆₁	—	8	1	no	—
451	D₄×C₆₁	—	8	2	no	—
452	D₄×C₆₁	—	8	1	no	—
453	D₄×C₆₁	—	8	2	no	—
454	D₄×C₆₁	—	8	2	no	—
455	D₄×C₆₁	—	8	2	no	—
456	D₄×C₆₁	—	8	2	no	—
457	D₄×C₆₁	—	8	2	no	—
458	D₄×C₆₁	—	8	2	no	—
459	C₂×C₄×C₆₁	—	2	1	no	—
460	C₂×C₄×C₆₁	—	2	2	no	—
461	C₂×C₄×C₆₁	—	2	1	no	—
462	C₂×C₄×C₆₁	—	2	1	no	—
463	C₂×C₄×C₆₁	—	2	2	no	—
464	C₂×C₄×C₆₁	—	2	1	no	—
465	C₂×C₄×C₆₁	—	2	2	no	—
466	C₂×C₄×C₆₁	—	2	1	no	—
467	C₂×C₄×C₆₁	—	2	2	no	—
468	C₂×C₄×C₆₁	—	2	2	no	—
469	C₂×C₄×C₆₁	—	2	2	no	—
470	C₂×C₄×C₆₁	—	4	1	no	—
471	C₂×C₄×C₆₁	—	4	1	no	—
472	C₂×C₄×C₆₁	—	4	4	no	—
473	C₂×C₄×C₆₁	—	4	2	no	—
474	C₂×C₄×C₆₁	—	4	2	no	—
475	C₂×C₄×C₆₁	—	8	2	no	—
476	C₂×C₄×C₆₁	—	8	1	no	—
477	C₂×C₄×C₆₁	—	8	2	no	—
478	C₂×C₄×C₆₁	—	8	2	no	—
479	C₂×C₄×C₆₁	—	8	2	no	—
480	C₂×C₄×C₆₁	—	8	2	no	—
481	C₂×C₄×C₆₁	—	8	1	no	—
482	C₂×C₄×C₆₁	—	8	2	no	—
483	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
492	C₈×C₆₁	—	2	2	no	—
493	C₈×C₆₁	—	2	2	no	—
494	C₈×C₆₁	—	2	2	no	—
495	C₈×C₆₁	—	2	2	no	—
496	#62094	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
497	C₂²×C₆₁	—	2	1	no	—
498	C₂²×C₆₁	—	2	2	no	—
499	C₂²×C₆₁	—	2	1	no	—
500	C₂²×C₆₁	—	2	2	no	—
501	C₂²×C₆₁	—	2	2	no	—
502	C₂²×C₆₁	—	2	1	no	—
503	C₂²×C₆₁	—	4	1	no	—
504	C₂²×C₆₁	—	4	2	no	—
505	C₂²×C₆₁	—	4	2	no	—
506	C₂²×C₆₁	—	4	1	no	—
507	C₂²×C₆₁	—	4	2	no	—
508	C₂²×C₆₁	—	4	2	no	—
509	C₂²×C₆₁	—	4	1	no	—
510	C₂²×C₆₁	—	4	2	no	—
511	C₂²×C₆₁	—	4	2	no	—
512	C₂²×C₆₁	—	16	2	no	—
513	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
514	C₄×C₆₁	—	2	1	no	—
515	C₄×C₆₁	—	2	1	no	—
516	C₄×C₆₁	—	2	2	no	—
517	C₄×C₆₁	—	2	1	no	—
518	C₄×C₆₁	—	2	1	no	—
519	C₄×C₆₁	—	2	2	no	—
520	C₄×C₆₁	—	2	2	no	—
521	C₄×C₆₁	—	2	1	no	—
522	C₄×C₆₁	—	2	2	no	—
523	C₄×C₆₁	—	4	1	no	—
524	C₄×C₆₁	—	4	2	no	—
525	C₄×C₆₁	—	4	2	no	—
526	C₄×C₆₁	—	4	1	no	—
527	C₄×C₆₁	—	4	2	no	—
528	C₄×C₆₁	—	4	2	no	—
529	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₄×C₆₁	#585	1	1	yes	characteristic
531	#3561	C₂×C₆₁	1	1	yes	characteristic, complemented
532	#3517	C₂×C₆₁	1	1	yes	characteristic, complemented
533	#3397	C₂×C₆₁	1	2	yes	complemented
534	#3377	C₂×C₆₁	1	2	yes	complemented
535	#3322	C₂×C₆₁	1	2	yes	complemented
536	#3320	C₂×C₆₁	1	2	yes	complemented
537	#3308	C₂×C₆₁	1	2	yes	complemented
538	#3278	C₂×C₆₁	1	2	yes	complemented
539	#3271	C₂×C₆₁	1	2	yes	complemented
540	#3268	C₂×C₆₁	1	2	yes	complemented
541	#3257	C₂×C₆₁	1	2	yes	complemented
542	#3254	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#3221	C₂×C₆₁	1	2	yes	complemented
544	#3213	C₂×C₆₁	1	1	yes	characteristic, complemented
545	#3124	C₂×C₆₁	1	2	yes	complemented
546	#3116	C₂×C₆₁	1	1	yes	characteristic, complemented
547	#3046	C₂×C₆₁	1	2	yes	complemented
548	#3040	C₂×C₆₁	1	1	yes	characteristic, complemented
549	#2995	C₂×C₆₁	1	1	yes	characteristic, complemented
550	C₂×C₆₁	—	4	2	no	—
551	C₂×C₆₁	—	4	1	no	—
552	C₂×C₆₁	—	8	1	no	—
553	C₂×C₆₁	—	8	2	no	—
554	C₂×C₆₁	—	8	2	no	—
555	C₂×C₆₁	#3488	1	1	yes	characteristic
556	C₂×C₆₁	#3585	1	1	yes	characteristic
557	C₂×C₆₁	#3586	1	1	yes	characteristic
558	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
559	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
560	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
561	C₂×#135	C₂²×C₆₁	1	2	yes	—
562	#563	—	2	1	no	—
563	#562	—	2	1	no	—
564	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
565	#556	C₂²×C₆₁	1	2	yes	—
566	#553	—	2	2	no	—
567	#553	C₂²×C₆₁	1	2	yes	—
568	#551	—	2	2	no	—
569	#550	—	2	1	no	—
570	#550	C₂²×C₆₁	1	2	yes	—
571	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
572	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
573	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
574	#548	C₂²×C₆₁	1	2	yes	—
575	#547	—	2	1	no	—
576	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
577	#546	C₂²×C₆₁	1	2	yes	—
578	#543	—	2	1	no	—
579	#542	—	2	2	no	—
580	#542	C₂²×C₆₁	1	2	yes	—
581	#540	—	2	2	no	—
582	#540	C₂²×C₆₁	1	2	yes	complemented
583	#538	—	2	1	no	—
584	#536	C₂²×C₆₁	1	2	yes	—
585	#533	C₂²×C₆₁	1	1	yes	characteristic
586	#532	—	2	1	no	—
587	#532	C₂²×C₆₁	1	1	yes	characteristic
588	#529	—	2	1	no	—
589	#529	C₂²×C₆₁	1	1	yes	characteristic
590	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
591	#520	C₂²×C₆₁	1	2	yes	complemented
592	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
593	#496	C₂²×C₆₁	1	2	yes	—
594	#496	C₂²×C₆₁	1	2	yes	—
595	#492	C₂²×C₆₁	1	2	yes	complemented
596	#491	C₂²×C₆₁	1	2	yes	complemented
597	#489	C₂²×C₆₁	1	2	yes	—
598	#488	C₂²×C₆₁	1	2	yes	—
599	#485	C₂²×C₆₁	1	2	yes	—
600	#484	C₂²×C₆₁	1	2	yes	complemented
601	#480	C₂²×C₆₁	1	2	yes	—
602	#479	C₂²×C₆₁	1	2	yes	complemented
603	#478	C₂²×C₆₁	1	2	yes	—
604	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
605	#477	C₂²×C₆₁	1	2	yes	complemented
606	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
607	#474	C₂²×C₆₁	1	2	yes	complemented
608	#469	C₂²×C₆₁	1	2	yes	—
609	#468	C₂²×C₆₁	1	2	yes	—
610	#468	C₂²×C₆₁	1	2	yes	—
611	#468	C₂²×C₆₁	1	2	yes	complemented
612	#466	C₂²×C₆₁	1	2	yes	—
613	#465	C₂²×C₆₁	1	2	yes	complemented
614	#464	C₂²×C₆₁	1	2	yes	—
615	#464	C₂²×C₆₁	1	2	yes	—
616	#464	C₂²×C₆₁	1	2	yes	—
617	#463	C₂²×C₆₁	1	2	yes	—
618	#463	C₂²×C₆₁	1	2	yes	—
619	#463	C₂²×C₆₁	1	2	yes	—
620	#463	C₂²×C₆₁	1	2	yes	—
621	#463	C₂²×C₆₁	1	2	yes	—
622	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
623	#462	C₂²×C₆₁	1	2	yes	complemented
624	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
625	#461	C₂²×C₆₁	1	2	yes	complemented
626	#461	C₂²×C₆₁	1	2	yes	complemented
627	#460	C₂²×C₆₁	1	2	yes	complemented
628	#460	C₂²×C₆₁	1	2	yes	complemented
629	#459	C₂²×C₆₁	1	2	yes	—
630	#452	C₂²×C₆₁	1	2	yes	—
631	#452	C₂²×C₆₁	1	2	yes	complemented
632	#449	C₂²×C₆₁	1	2	yes	—
633	#449	C₂²×C₆₁	1	2	yes	—
634	#449	C₂²×C₆₁	1	2	yes	—
635	#448	C₂²×C₆₁	1	2	yes	—
636	#448	C₂²×C₆₁	1	2	yes	complemented
637	#448	C₂²×C₆₁	1	2	yes	complemented
638	#447	C₂²×C₆₁	1	2	yes	—
639	#446	C₂²×C₆₁	1	2	yes	complemented
640	#441	C₂²×C₆₁	1	2	yes	complemented
641	#440	C₂²×C₆₁	1	2	yes	—
642	#440	C₂²×C₆₁	1	2	yes	complemented
643	#440	C₂²×C₆₁	1	2	yes	complemented
644	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
645	C₄×D₈	C₂²×C₆₁	1	2	yes	—
646	#436	C₂²×C₆₁	1	2	yes	—
647	#435	C₂²×C₆₁	1	2	yes	—
648	#435	C₂²×C₆₁	1	2	yes	complemented
649	#433	C₂²×C₆₁	1	2	yes	complemented
650	#432	C₂²×C₆₁	1	1	yes	characteristic
651	#424	C₂²×C₆₁	1	2	yes	complemented
652	#423	C₂²×C₆₁	1	1	yes	characteristic
653	#419	C₂²×C₆₁	1	1	yes	characteristic
654	#418	C₂²×C₆₁	1	1	yes	characteristic
655	#417	C₂²×C₆₁	1	2	yes	—
656	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
657	C₆₁	#62094	1	1	yes	characteristic, direct product factor, Sylow
658	C₂×#41	—	2	1	no	—
659	C₂×#41	—	2	1	no	—
660	C₂×#41	—	2	1	no	—
661	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
662	C₂×#41	C₂³×C₆₁	1	2	yes	—
663	C₂×#41	C₂³×C₆₁	1	2	yes	—
664	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
665	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
666	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
667	#137	—	4	2	no	—
668	#137	—	4	4	no	—
669	AGL(1,ℤ/8)	—	4	2	no	—
670	#135	—	4	4	no	—
671	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
672	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
673	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
674	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
680	C₂×D₈	C₂³×C₆₁	1	2	yes	—
681	C₂×D₈	C₂³×C₆₁	1	2	yes	—
682	C₂×D₈	C₂³×C₆₁	1	2	yes	—
683	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
684	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
685	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
686	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
687	C₄⋊Q₈	—	2	1	no	—
688	C₄⋊Q₈	—	2	2	no	—
689	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
691	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
693	#127	—	2	1	no	—
694	#127	—	2	2	no	—
695	#127	C₂³×C₆₁	1	1	yes	characteristic
696	#127	C₂³×C₆₁	1	2	yes	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	D₄×C₆₁	1	2	yes	—
702	#125	—	2	2	no	—
703	#125	—	2	1	no	—
704	#125	D₄×C₆₁	1	1	yes	characteristic
705	#125	C₂³×C₆₁	1	2	yes	—
706	#124	—	2	2	no	—
707	#124	—	2	2	no	—
708	#124	—	2	1	no	—
709	#124	—	2	1	no	—
710	#124	—	2	1	no	—
711	#124	D₄×C₆₁	1	1	yes	characteristic
712	#124	C₂³×C₆₁	1	2	yes	—
713	#124	C₂³×C₆₁	1	2	yes	—
714	#124	C₂³×C₆₁	1	2	yes	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	#123	D₄×C₆₁	1	2	yes	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
734	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
735	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	—	2	1	no	—
739	#121	—	2	1	no	—
740	#121	—	2	2	no	—
741	#121	—	2	2	no	—
742	#121	—	2	2	no	—
743	#121	—	2	2	no	—
744	#121	—	2	2	no	—
745	#121	—	2	2	no	—
746	#121	—	2	2	no	—
747	#121	D₄×C₆₁	1	1	yes	characteristic
748	#121	C₂³×C₆₁	1	2	yes	—
749	#121	C₂³×C₆₁	1	2	yes	—
750	#121	C₂³×C₆₁	1	2	yes	—
751	#121	C₂³×C₆₁	1	2	yes	—
752	#120	—	2	2	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
758	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
759	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	1	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₆₁	1	2	yes	—
774	C₄×D₄	C₂³×C₆₁	1	2	yes	—
775	C₄×D₄	C₂³×C₆₁	1	2	yes	—
776	C₄×D₄	C₂³×C₆₁	1	2	yes	—
777	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
778	#117	—	2	1	no	—
779	#117	—	2	2	no	—
780	#117	—	2	2	no	—
781	#117	—	2	1	no	—
782	#117	C₂³×C₆₁	1	1	yes	characteristic
783	#117	C₂³×C₆₁	1	2	yes	—
784	C₂×C₄⋊C₄	—	2	2	no	—
785	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
786	C₂×C₂²⋊C₄	—	2	1	no	—
787	C₂×C₂²⋊C₄	—	2	1	no	—
788	C₂×C₂²⋊C₄	—	2	2	no	—
789	C₂×C₄²	—	2	1	no	—
790	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
791	#107	C₂³×C₆₁	1	2	yes	—
792	#107	C₂³×C₆₁	1	2	yes	—
793	#107	C₂³×C₆₁	1	2	yes	—
794	#106	C₂³×C₆₁	1	2	yes	—
795	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
796	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
797	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
798	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
799	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
800	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
801	#103	C₂³×C₆₁	1	2	yes	—
802	#103	C₂³×C₆₁	1	2	yes	—
803	#103	C₂³×C₆₁	1	2	yes	—
804	#103	C₂³×C₆₁	1	2	yes	—
805	#103	C₂³×C₆₁	1	2	yes	—
806	#103	C₂³×C₆₁	1	2	yes	—
807	#103	C₂³×C₆₁	1	2	yes	—
808	#103	C₂³×C₆₁	1	2	yes	—
809	#103	C₂³×C₆₁	1	2	yes	—
810	#102	C₂³×C₆₁	1	2	yes	—
811	#102	C₂³×C₆₁	1	2	yes	—
812	#102	C₂³×C₆₁	1	2	yes	—
813	#102	C₂³×C₆₁	1	2	yes	—
814	#102	C₂³×C₆₁	1	2	yes	—
815	#102	C₂³×C₆₁	1	2	yes	—
816	#102	C₂³×C₆₁	1	2	yes	—
817	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
818	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
819	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
820	#97	C₂³×C₆₁	1	2	yes	—
821	#97	C₂³×C₆₁	1	2	yes	—
822	C₄×C₈	C₂³×C₆₁	1	2	yes	—
823	C₂⁴	—	2	1	no	—
824	#41	—	2	4	no	—
825	#41	—	2	2	no	—
826	#41	—	4	1	no	—
827	#41	—	4	2	no	—
828	#41	—	4	2	no	—
829	#41	—	4	2	no	—
830	#41	—	8	2	no	—
831	#41	—	8	2	no	—
832	#41	—	8	2	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	2	no	—
836	C₂×Q₈	—	2	1	no	—
837	C₂×Q₈	—	4	2	no	—
838	C₂×Q₈	—	4	1	no	—
839	C₂×Q₈	—	4	1	no	—
840	C₂×Q₈	—	4	2	no	—
841	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
842	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
843	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
844	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
845	C₂×D₄	—	2	1	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	1	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	—	4	1	no	—
858	C₂×D₄	—	4	1	no	—
859	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
860	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
861	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
862	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
863	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
876	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
879	Q₁₆	—	2	4	no	—
880	Q₁₆	—	2	4	no	—
881	SD₁₆	—	2	4	no	—
882	SD₁₆	—	4	2	no	—
883	SD₁₆	—	4	2	no	—
884	SD₁₆	—	4	2	no	—
885	SD₁₆	—	4	2	no	—
886	SD₁₆	—	4	2	no	—
887	SD₁₆	—	4	2	no	—
888	D₈	—	4	2	no	—
889	D₈	—	4	2	no	—
890	D₈	—	4	2	no	—
891	M₁₆	—	4	1	no	—
892	M₁₆	—	4	2	no	—
893	M₁₆	—	4	1	no	—
894	C₂×C₈	—	4	2	no	—
895	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
896	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
897	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
898	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
916	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
917	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
918	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
920	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
921	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
922	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
923	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
924	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	1	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	1	no	—
936	C₂²⋊C₄	—	2	1	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
944	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
945	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
946	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
947	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
948	C₄²	—	2	1	no	—
949	C₄²	—	2	1	no	—
950	C₄²	—	2	1	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
955	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
956	C₄²	C₂⁴×C₆₁	1	2	yes	—
957	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
958	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
959	C₂³	—	2	2	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	4	2	no	—
963	C₂³	—	8	1	no	—
964	C₂³	—	8	1	no	—
965	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
966	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
967	Q₈	—	2	1	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	2	2	no	—
970	Q₈	—	2	2	no	—
971	Q₈	—	2	2	no	—
972	Q₈	—	4	1	no	—
973	Q₈	—	4	2	no	—
974	Q₈	—	8	1	no	—
975	Q₈	—	8	2	no	—
976	Q₈	—	8	1	no	—
977	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
978	D₄	—	2	2	no	—
979	D₄	—	2	1	no	—
980	D₄	—	2	2	no	—
981	D₄	—	2	2	no	—
982	D₄	—	2	2	no	—
983	D₄	—	2	1	no	—
984	D₄	—	4	2	no	—
985	D₄	—	4	1	no	—
986	D₄	—	4	4	no	—
987	D₄	—	4	2	no	—
988	D₄	—	4	2	no	—
989	D₄	—	8	1	no	—
990	D₄	—	8	2	no	—
991	D₄	—	8	1	no	—
992	D₄	—	8	2	no	—
993	D₄	—	8	2	no	—
994	D₄	—	8	2	no	—
995	D₄	—	8	2	no	—
996	D₄	—	8	2	no	—
997	D₄	—	8	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	4	1	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	8	2	no	—
1015	C₂×C₄	—	8	1	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	—	8	1	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1026	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1029	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1030	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1031	C₈	—	2	2	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₈	—	2	2	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	16	2	no	—
1051	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1068	C₄	C₆₁×#585	1	1	yes	characteristic
1069	C₂	—	4	1	no	—
1070	C₂	—	4	2	no	—
1071	C₂	—	8	2	no	—
1072	C₂	—	8	1	no	—
1073	C₂	—	8	2	no	—
1074	C₂	C₆₁×#3488	1	1	yes	characteristic
1075	C₂	C₆₁×#3585	1	1	yes	characteristic
1076	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3561	C₂	semidirect
2. C₆₁×#3517	C₂	semidirect
3. C₆₁×#3397	C₂	semidirect
4. C₆₁×#3377	C₂	semidirect
5. C₆₁×#3322	C₂	semidirect
6. C₆₁×#3320	C₂	semidirect
7. C₆₁×#3308	C₂	semidirect
8. C₆₁×#3278	C₂	semidirect
9. C₆₁×#3271	C₂	semidirect
10. C₆₁×#3268	C₂	semidirect
11. C₆₁×#3257	C₂	semidirect
12. C₆₁×#3254	C₂	semidirect
13. C₆₁×#3221	C₂	semidirect
14. C₆₁×#3213	C₂	semidirect
15. C₆₁×#3124	C₂	semidirect
16. C₆₁×#3116	C₂	semidirect
17. C₆₁×#3046	C₂	semidirect
18. C₆₁×#3040	C₂	semidirect
19. C₆₁×#2995	C₂	semidirect
21. C₂×#137×C₆₁	C₂²	semidirect
26. C₆₁×#557	C₂²	semidirect
33. C₆₁×#550	C₂²	semidirect
34. C₆₁×#550	C₂²	semidirect
38. C₆₁×#547	C₂²	semidirect
44. C₆₁×#540	C₂²	semidirect
53. C₆₁×#520	C₂²	semidirect
57. C₆₁×#492	C₂²	semidirect
58. C₆₁×#491	C₂²	semidirect
62. C₆₁×#484	C₂²	semidirect
64. C₆₁×#479	C₂²	semidirect
66. C₆₁×#477	C₂²	semidirect
67. C₆₁×#477	C₂²	semidirect
68. C₆₁×#476	C₂²	semidirect
69. C₆₁×#474	C₂²	semidirect
73. C₆₁×#468	C₂²	semidirect
75. C₆₁×#465	C₂²	semidirect
84. C₆₁×#462	C₂²	semidirect
85. C₆₁×#462	C₂²	semidirect
86. C₆₁×#461	C₂²	semidirect
87. C₆₁×#461	C₂²	semidirect
88. C₆₁×#461	C₂²	semidirect
89. C₆₁×#460	C₂²	semidirect
90. C₆₁×#460	C₂²	semidirect
93. C₆₁×#452	C₂²	semidirect
98. C₆₁×#448	C₂²	semidirect
99. C₆₁×#448	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₆₁×#441	C₂²	semidirect
104. C₆₁×#440	C₂²	semidirect
105. C₆₁×#440	C₂²	semidirect
106. C₄×Q₁₆×C₆₁	C₂²	semidirect
110. C₆₁×#435	C₂²	semidirect
111. C₆₁×#433	C₂²	semidirect
113. C₆₁×#424	C₂²	semidirect
118. C₂×#103×C₆₁	C₂²	semidirect
496. #62094	C₆₁	direct (N × H)
531. #3561	C₂×C₆₁	semidirect
532. #3517	C₂×C₆₁	semidirect
533. #3397	C₂×C₆₁	semidirect
534. #3377	C₂×C₆₁	semidirect
535. #3322	C₂×C₆₁	semidirect
536. #3320	C₂×C₆₁	semidirect
537. #3308	C₂×C₆₁	semidirect
538. #3278	C₂×C₆₁	semidirect
539. #3271	C₂×C₆₁	semidirect
540. #3268	C₂×C₆₁	semidirect
541. #3257	C₂×C₆₁	semidirect
542. #3254	C₂×C₆₁	semidirect
543. #3221	C₂×C₆₁	semidirect
544. #3213	C₂×C₆₁	semidirect
545. #3124	C₂×C₆₁	semidirect
546. #3116	C₂×C₆₁	semidirect
547. #3046	C₂×C₆₁	semidirect
548. #3040	C₂×C₆₁	semidirect
549. #2995	C₂×C₆₁	semidirect
559. C₂×#137	C₂²×C₆₁	semidirect
564. #557	C₂²×C₆₁	semidirect
571. #550	C₂²×C₆₁	semidirect
572. #550	C₂²×C₆₁	semidirect
576. #547	C₂²×C₆₁	semidirect
582. #540	C₂²×C₆₁	semidirect
591. #520	C₂²×C₆₁	semidirect
595. #492	C₂²×C₆₁	semidirect
596. #491	C₂²×C₆₁	semidirect
600. #484	C₂²×C₆₁	semidirect
602. #479	C₂²×C₆₁	semidirect
604. #477	C₂²×C₆₁	semidirect
605. #477	C₂²×C₆₁	semidirect
606. #476	C₂²×C₆₁	semidirect
607. #474	C₂²×C₆₁	semidirect
611. #468	C₂²×C₆₁	semidirect
613. #465	C₂²×C₆₁	semidirect
622. #462	C₂²×C₆₁	semidirect
623. #462	C₂²×C₆₁	semidirect
624. #461	C₂²×C₆₁	semidirect
625. #461	C₂²×C₆₁	semidirect
626. #461	C₂²×C₆₁	semidirect
627. #460	C₂²×C₆₁	semidirect
628. #460	C₂²×C₆₁	semidirect
631. #452	C₂²×C₆₁	semidirect
636. #448	C₂²×C₆₁	semidirect
637. #448	C₂²×C₆₁	semidirect
639. #446	C₂²×C₆₁	semidirect
640. #441	C₂²×C₆₁	semidirect
642. #440	C₂²×C₆₁	semidirect
643. #440	C₂²×C₆₁	semidirect
644. C₄×Q₁₆	C₂²×C₆₁	semidirect
648. #435	C₂²×C₆₁	semidirect
649. #433	C₂²×C₆₁	semidirect
651. #424	C₂²×C₆₁	semidirect
656. C₂×#103	C₂²×C₆₁	semidirect
657. C₆₁	#62094	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×#3561	2
C₆₁×#3517	2
C₆₁×#3397	2
C₆₁×#3377	2
C₆₁×#3322	2
C₆₁×#3320	2
C₆₁×#3308	2
C₆₁×#3278	2
C₆₁×#3271	2
C₆₁×#3268	2
C₆₁×#3257	2
C₆₁×#3254	2
C₆₁×#3221	2
C₆₁×#3213	2
C₆₁×#3124	2
C₆₁×#3116	2
C₆₁×#3046	2
C₆₁×#3040	2
C₆₁×#2995	2
#62094	61

Subgroups — C61×#62094 #29565527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62094 #29565527