Subgroups — C₆₁×#62087 #29565520

Order 15616.

1842 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×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3401	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3367	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3329	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3319	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3313	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3273	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3266	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3265	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3262	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3225	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3118	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3042	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×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
23	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
24	C₆₁×#563	—	2	1	no	—
25	C₆₁×#562	—	2	1	no	—
26	C₆₁×#559	C₂²	1	1	yes	characteristic, complemented
27	C₆₁×#556	C₂²	1	2	yes	complemented
28	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#555	C₂²	1	2	yes	—
30	C₆₁×#551	—	2	2	no	—
31	C₆₁×#551	—	2	2	no	—
32	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
33	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
34	C₆₁×#548	—	2	1	no	—
35	C₆₁×#548	C₂²	1	2	yes	—
36	C₆₁×#546	—	2	1	no	—
37	C₆₁×#546	C₂²	1	2	yes	—
38	C₆₁×#546	C₂²	1	2	yes	complemented
39	D₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#543	—	2	1	no	—
41	C₆₁×#542	—	2	2	no	—
42	C₆₁×#542	C₂²	1	2	yes	complemented
43	C₆₁×#542	C₂²	1	2	yes	complemented
44	C₆₁×#538	—	2	2	no	—
45	C₆₁×#538	—	2	1	no	—
46	C₆₁×#536	C₂²	1	2	yes	complemented
47	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
48	C₆₁×#532	C₂²	1	1	yes	characteristic
49	C₆₁×#529	—	2	1	no	—
50	C₆₁×#529	C₂²	1	1	yes	characteristic
51	C₂×#124×C₆₁	—	2	1	no	—
52	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
53	C₆₁×#518	C₂²	1	2	yes	complemented
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×#497	C₂²	1	2	yes	complemented
56	C₆₁×#496	C₂²	1	2	yes	—
57	C₆₁×#495	C₂²	1	2	yes	complemented
58	C₆₁×#489	C₂²	1	2	yes	complemented
59	C₆₁×#489	C₂²	1	2	yes	complemented
60	C₆₁×#487	C₂²	1	2	yes	complemented
61	C₆₁×#485	C₂²	1	2	yes	complemented
62	C₆₁×#485	C₂²	1	2	yes	complemented
63	C₆₁×#482	C₂²	1	2	yes	complemented
64	C₆₁×#477	C₂²	1	2	yes	complemented
65	C₆₁×#477	C₂²	1	2	yes	complemented
66	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
68	C₆₁×#474	C₂²	1	2	yes	complemented
69	C₆₁×#474	C₂²	1	2	yes	complemented
70	C₆₁×#468	C₂²	1	2	yes	complemented
71	C₆₁×#468	C₂²	1	2	yes	complemented
72	C₆₁×#468	C₂²	1	2	yes	complemented
73	C₆₁×#468	C₂²	1	2	yes	complemented
74	C₆₁×#467	C₂²	1	2	yes	complemented
75	C₆₁×#466	C₂²	1	2	yes	—
76	C₆₁×#464	C₂²	1	2	yes	complemented
77	C₆₁×#464	C₂²	1	2	yes	complemented
78	C₆₁×#464	C₂²	1	2	yes	complemented
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	complemented
83	C₆₁×#463	C₂²	1	2	yes	complemented
84	C₆₁×#463	C₂²	1	2	yes	complemented
85	C₆₁×#463	C₂²	1	2	yes	complemented
86	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
87	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
88	C₆₁×#461	C₂²	1	2	yes	complemented
89	C₆₁×#461	C₂²	1	2	yes	complemented
90	C₆₁×#461	C₂²	1	2	yes	complemented
91	C₆₁×#460	C₂²	1	2	yes	complemented
92	C₆₁×#452	C₂²	1	2	yes	—
93	C₆₁×#452	C₂²	1	2	yes	complemented
94	C₆₁×#451	C₂²	1	2	yes	complemented
95	C₆₁×#450	C₂²	1	2	yes	complemented
96	C₆₁×#449	C₂²	1	2	yes	—
97	C₆₁×#448	C₂²	1	2	yes	complemented
98	C₆₁×#448	C₂²	1	2	yes	complemented
99	C₆₁×#447	C₂²	1	2	yes	—
100	C₆₁×#447	C₂²	1	2	yes	complemented
101	C₆₁×#446	C₂²	1	2	yes	complemented
102	C₆₁×#442	C₂²	1	2	yes	complemented
103	C₆₁×#441	C₂²	1	2	yes	complemented
104	C₆₁×#440	C₂²	1	2	yes	complemented
105	C₆₁×#440	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₆₁	C₂²	1	2	yes	—
108	C₆₁×#436	C₂²	1	2	yes	complemented
109	C₆₁×#435	C₂²	1	2	yes	complemented
110	C₆₁×#435	C₂²	1	2	yes	complemented
111	C₆₁×#433	C₂²	1	2	yes	complemented
112	C₆₁×#432	C₂²	1	1	yes	characteristic, complemented
113	C₆₁×#424	C₂²	1	2	yes	complemented
114	C₆₁×#423	C₂²	1	1	yes	characteristic, complemented
115	C₆₁×#419	C₂²	1	1	yes	characteristic, complemented
116	C₆₁×#419	C₂²	1	2	yes	complemented
117	C₆₁×#418	C₂²	1	1	yes	characteristic, complemented
118	C₆₁×#416	C₂²	1	2	yes	complemented
119	C₂×#41×C₆₁	—	2	1	no	—
120	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
121	C₂×#41×C₆₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₆₁	—	2	1	no	—
123	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
124	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₁	—	2	1	no	—
126	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
128	#137×C₆₁	—	4	2	no	—
129	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
130	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
131	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
133	C₂×SD₁₆×C₆₁	—	4	4	no	—
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	2	yes	—
146	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
148	C₄⋊Q₈×C₆₁	—	2	2	no	—
149	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
150	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
154	#127×C₆₁	C₂³	1	1	yes	characteristic
155	#126×C₆₁	—	2	2	no	—
156	#126×C₆₁	—	2	2	no	—
157	#126×C₆₁	—	2	2	no	—
158	#126×C₆₁	—	2	2	no	—
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	D₄	1	2	yes	—
161	#125×C₆₁	—	2	1	no	—
162	#125×C₆₁	D₄	1	1	yes	characteristic
163	#124×C₆₁	—	2	1	no	—
164	#124×C₆₁	—	2	1	no	—
165	#124×C₆₁	—	2	2	no	—
166	#124×C₆₁	—	2	2	no	—
167	#124×C₆₁	—	2	2	no	—
168	#124×C₆₁	—	2	2	no	—
169	#124×C₆₁	—	2	2	no	—
170	#124×C₆₁	—	2	1	no	—
171	#124×C₆₁	—	2	1	no	—
172	#124×C₆₁	—	2	1	no	—
173	#124×C₆₁	D₄	1	1	yes	characteristic
174	#124×C₆₁	C₂³	1	2	yes	—
175	#124×C₆₁	C₂³	1	2	yes	—
176	#124×C₆₁	C₂³	1	2	yes	—
177	#124×C₆₁	C₂³	1	2	yes	—
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	—	2	2	no	—
185	#123×C₆₁	D₄	1	2	yes	—
186	C₂²⋊Q₈×C₆₁	—	2	2	no	—
187	C₂²⋊Q₈×C₆₁	—	2	1	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	2	no	—
192	C₂²⋊Q₈×C₆₁	—	2	2	no	—
193	C₂²⋊Q₈×C₆₁	—	2	2	no	—
194	C₂²⋊Q₈×C₆₁	—	2	1	no	—
195	C₂²⋊Q₈×C₆₁	—	2	2	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
201	#121×C₆₁	—	2	2	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	—	2	1	no	—
204	#121×C₆₁	—	2	1	no	—
205	#121×C₆₁	—	2	2	no	—
206	#121×C₆₁	—	2	2	no	—
207	#121×C₆₁	D₄	1	1	yes	characteristic
208	#121×C₆₁	C₂³	1	2	yes	—
209	#121×C₆₁	C₂³	1	2	yes	—
210	#121×C₆₁	C₂³	1	2	yes	—
211	#120×C₆₁	—	2	2	no	—
212	#120×C₆₁	—	2	2	no	—
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	1	yes	characteristic
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×D₄×C₆₁	—	2	2	no	—
222	C₄×D₄×C₆₁	—	2	1	no	—
223	C₄×D₄×C₆₁	—	2	1	no	—
224	C₄×D₄×C₆₁	—	2	2	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	1	no	—
229	C₄×D₄×C₆₁	C₂³	1	2	yes	—
230	C₄×D₄×C₆₁	C₂³	1	2	yes	—
231	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₆₁	C₂³	1	2	yes	—
233	C₄×D₄×C₆₁	C₂³	1	2	yes	—
234	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₆₁	C₂³	1	2	yes	—
237	#117×C₆₁	—	2	1	no	—
238	#117×C₆₁	—	2	2	no	—
239	#117×C₆₁	—	2	2	no	—
240	#117×C₆₁	—	2	1	no	—
241	#117×C₆₁	C₂³	1	1	yes	characteristic
242	#117×C₆₁	C₂³	1	2	yes	—
243	#117×C₆₁	C₂³	1	2	yes	—
244	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
245	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
246	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
247	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
248	C₂×C₂²⋊C₄×C₆₁	—	2	2	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	C₂⁴×C₆₁	—	2	2	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	—	8	2	no	—
291	C₂×Q₈×C₆₁	—	2	1	no	—
292	C₂×Q₈×C₆₁	—	2	1	no	—
293	C₂×Q₈×C₆₁	—	2	2	no	—
294	C₂×Q₈×C₆₁	—	2	2	no	—
295	C₂×Q₈×C₆₁	—	2	1	no	—
296	C₂×Q₈×C₆₁	—	4	2	no	—
297	C₂×Q₈×C₆₁	—	4	1	no	—
298	C₂×Q₈×C₆₁	—	4	1	no	—
299	C₂×Q₈×C₆₁	—	4	2	no	—
300	C₂×Q₈×C₆₁	—	8	2	no	—
301	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
302	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
303	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
305	C₂×D₄×C₆₁	—	2	4	no	—
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	1	no	—
313	C₂×D₄×C₆₁	—	2	1	no	—
314	C₂×D₄×C₆₁	—	2	1	no	—
315	C₂×D₄×C₆₁	—	4	2	no	—
316	C₂×D₄×C₆₁	—	4	1	no	—
317	C₂×D₄×C₆₁	—	4	1	no	—
318	C₂×D₄×C₆₁	—	8	2	no	—
319	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
320	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
321	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
322	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
323	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₁	—	2	1	no	—
325	C₂²×C₄×C₆₁	—	2	2	no	—
326	C₂²×C₄×C₆₁	—	2	1	no	—
327	C₂²×C₄×C₆₁	—	2	1	no	—
328	C₂²×C₄×C₆₁	—	2	1	no	—
329	C₂²×C₄×C₆₁	—	2	2	no	—
330	C₂²×C₄×C₆₁	—	2	2	no	—
331	C₂²×C₄×C₆₁	—	2	2	no	—
332	C₂²×C₄×C₆₁	—	2	2	no	—
333	C₂²×C₄×C₆₁	—	2	2	no	—
334	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
338	Q₁₆×C₆₁	—	4	2	no	—
339	Q₁₆×C₆₁	—	4	2	no	—
340	SD₁₆×C₆₁	—	2	4	no	—
341	SD₁₆×C₆₁	—	2	4	no	—
342	SD₁₆×C₆₁	—	4	2	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	D₈×C₆₁	—	2	4	no	—
348	D₈×C₆₁	—	4	2	no	—
349	D₈×C₆₁	—	4	2	no	—
350	M₁₆×C₆₁	—	4	2	no	—
351	M₁₆×C₆₁	—	4	1	no	—
352	M₁₆×C₆₁	—	4	1	no	—
353	C₂×C₈×C₆₁	—	4	2	no	—
354	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
355	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
356	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
357	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₆₁	—	2	1	no	—
359	C₄⋊C₄×C₆₁	—	2	1	no	—
360	C₄⋊C₄×C₆₁	—	2	2	no	—
361	C₄⋊C₄×C₆₁	—	2	2	no	—
362	C₄⋊C₄×C₆₁	—	2	1	no	—
363	C₄⋊C₄×C₆₁	—	2	1	no	—
364	C₄⋊C₄×C₆₁	—	2	1	no	—
365	C₄⋊C₄×C₆₁	—	2	2	no	—
366	C₄⋊C₄×C₆₁	—	2	2	no	—
367	C₄⋊C₄×C₆₁	—	2	2	no	—
368	C₄⋊C₄×C₆₁	—	2	2	no	—
369	C₄⋊C₄×C₆₁	—	2	1	no	—
370	C₄⋊C₄×C₆₁	—	2	2	no	—
371	C₄⋊C₄×C₆₁	—	2	2	no	—
372	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
373	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
381	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
382	C₂²⋊C₄×C₆₁	—	2	2	no	—
383	C₂²⋊C₄×C₆₁	—	2	2	no	—
384	C₂²⋊C₄×C₆₁	—	2	2	no	—
385	C₂²⋊C₄×C₆₁	—	2	1	no	—
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	2	no	—
397	C₂²⋊C₄×C₆₁	—	2	2	no	—
398	C₂²⋊C₄×C₆₁	—	2	2	no	—
399	C₂²⋊C₄×C₆₁	—	2	1	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	1	no	—
421	C₂³×C₆₁	—	2	2	no	—
422	C₂³×C₆₁	—	2	2	no	—
423	C₂³×C₆₁	—	4	4	no	—
424	C₂³×C₆₁	—	4	2	no	—
425	C₂³×C₆₁	—	8	1	no	—
426	C₂³×C₆₁	—	8	2	no	—
427	C₂³×C₆₁	—	8	1	no	—
428	C₂³×C₆₁	—	8	2	no	—
429	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
430	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
431	Q₈×C₆₁	—	2	2	no	—
432	Q₈×C₆₁	—	2	2	no	—
433	Q₈×C₆₁	—	2	1	no	—
434	Q₈×C₆₁	—	2	2	no	—
435	Q₈×C₆₁	—	2	1	no	—
436	Q₈×C₆₁	—	2	2	no	—
437	Q₈×C₆₁	—	4	1	no	—
438	Q₈×C₆₁	—	4	2	no	—
439	Q₈×C₆₁	—	8	1	no	—
440	Q₈×C₆₁	—	8	1	no	—
441	Q₈×C₆₁	—	8	2	no	—
442	Q₈×C₆₁	—	8	2	no	—
443	D₄×C₆₁	—	2	2	no	—
444	D₄×C₆₁	—	2	2	no	—
445	D₄×C₆₁	—	2	1	no	—
446	D₄×C₆₁	—	2	2	no	—
447	D₄×C₆₁	—	2	2	no	—
448	D₄×C₆₁	—	4	1	no	—
449	D₄×C₆₁	—	4	2	no	—
450	D₄×C₆₁	—	4	4	no	—
451	D₄×C₆₁	—	4	2	no	—
452	D₄×C₆₁	—	4	2	no	—
453	D₄×C₆₁	—	8	1	no	—
454	D₄×C₆₁	—	8	1	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	D₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
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	1	no	—
466	C₂×C₄×C₆₁	—	2	2	no	—
467	C₂×C₄×C₆₁	—	2	1	no	—
468	C₂×C₄×C₆₁	—	2	2	no	—
469	C₂×C₄×C₆₁	—	2	2	no	—
470	C₂×C₄×C₆₁	—	2	2	no	—
471	C₂×C₄×C₆₁	—	4	1	no	—
472	C₂×C₄×C₆₁	—	4	1	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	2	no	—
482	C₂×C₄×C₆₁	—	8	1	no	—
483	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
488	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
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	#62087	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	1	no	—
502	C₂²×C₆₁	—	2	2	no	—
503	C₂²×C₆₁	—	2	2	no	—
504	C₂²×C₆₁	—	4	1	no	—
505	C₂²×C₆₁	—	4	1	no	—
506	C₂²×C₆₁	—	4	2	no	—
507	C₂²×C₆₁	—	4	2	no	—
508	C₂²×C₆₁	—	4	2	no	—
509	C₂²×C₆₁	—	4	2	no	—
510	C₂²×C₆₁	—	4	2	no	—
511	C₂²×C₆₁	—	4	2	no	—
512	C₂²×C₆₁	—	16	4	no	—
513	C₂²×C₆₁	—	16	2	no	—
514	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
515	C₄×C₆₁	—	2	1	no	—
516	C₄×C₆₁	—	2	1	no	—
517	C₄×C₆₁	—	2	2	no	—
518	C₄×C₆₁	—	2	1	no	—
519	C₄×C₆₁	—	2	1	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	1	no	—
528	C₄×C₆₁	—	4	2	no	—
529	C₄×C₆₁	—	4	2	no	—
530	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₄×C₆₁	#585	1	1	yes	characteristic
532	#3561	C₂×C₆₁	1	1	yes	characteristic, complemented
533	#3514	C₂×C₆₁	1	1	yes	characteristic, complemented
534	#3401	C₂×C₆₁	1	2	yes	complemented
535	#3367	C₂×C₆₁	1	2	yes	complemented
536	#3329	C₂×C₆₁	1	2	yes	complemented
537	#3319	C₂×C₆₁	1	2	yes	complemented
538	#3313	C₂×C₆₁	1	2	yes	complemented
539	#3273	C₂×C₆₁	1	2	yes	complemented
540	#3266	C₂×C₆₁	1	2	yes	complemented
541	#3265	C₂×C₆₁	1	2	yes	complemented
542	#3262	C₂×C₆₁	1	2	yes	complemented
543	#3254	C₂×C₆₁	1	1	yes	characteristic, complemented
544	#3225	C₂×C₆₁	1	2	yes	complemented
545	#3213	C₂×C₆₁	1	1	yes	characteristic, complemented
546	#3118	C₂×C₆₁	1	2	yes	complemented
547	#3116	C₂×C₆₁	1	1	yes	characteristic, complemented
548	#3042	C₂×C₆₁	1	2	yes	complemented
549	#3040	C₂×C₆₁	1	1	yes	characteristic, complemented
550	#2995	C₂×C₆₁	1	1	yes	characteristic, complemented
551	C₂×C₆₁	—	4	1	no	—
552	C₂×C₆₁	—	4	2	no	—
553	C₂×C₆₁	—	4	2	no	—
554	C₂×C₆₁	—	8	2	no	—
555	C₂×C₆₁	—	8	2	no	—
556	C₂×C₆₁	#3488	1	1	yes	characteristic
557	C₂×C₆₁	#3585	1	1	yes	characteristic
558	C₂×C₆₁	#3586	1	1	yes	characteristic
559	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
560	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
561	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
562	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
563	#563	—	2	1	no	—
564	#562	—	2	1	no	—
565	#559	C₂²×C₆₁	1	1	yes	characteristic, complemented
566	#556	C₂²×C₆₁	1	2	yes	complemented
567	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
568	#555	C₂²×C₆₁	1	2	yes	—
569	#551	—	2	2	no	—
570	#551	—	2	2	no	—
571	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
572	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
573	#548	—	2	1	no	—
574	#548	C₂²×C₆₁	1	2	yes	—
575	#546	—	2	1	no	—
576	#546	C₂²×C₆₁	1	2	yes	—
577	#546	C₂²×C₆₁	1	2	yes	complemented
578	D₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
579	#543	—	2	1	no	—
580	#542	—	2	2	no	—
581	#542	C₂²×C₆₁	1	2	yes	complemented
582	#542	C₂²×C₆₁	1	2	yes	complemented
583	#538	—	2	2	no	—
584	#538	—	2	1	no	—
585	#536	C₂²×C₆₁	1	2	yes	complemented
586	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
587	#532	C₂²×C₆₁	1	1	yes	characteristic
588	#529	—	2	1	no	—
589	#529	C₂²×C₆₁	1	1	yes	characteristic
590	C₂×#124	—	2	1	no	—
591	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
592	#518	C₂²×C₆₁	1	2	yes	complemented
593	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
594	#497	C₂²×C₆₁	1	2	yes	complemented
595	#496	C₂²×C₆₁	1	2	yes	—
596	#495	C₂²×C₆₁	1	2	yes	complemented
597	#489	C₂²×C₆₁	1	2	yes	complemented
598	#489	C₂²×C₆₁	1	2	yes	complemented
599	#487	C₂²×C₆₁	1	2	yes	complemented
600	#485	C₂²×C₆₁	1	2	yes	complemented
601	#485	C₂²×C₆₁	1	2	yes	complemented
602	#482	C₂²×C₆₁	1	2	yes	complemented
603	#477	C₂²×C₆₁	1	2	yes	complemented
604	#477	C₂²×C₆₁	1	2	yes	complemented
605	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
606	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
607	#474	C₂²×C₆₁	1	2	yes	complemented
608	#474	C₂²×C₆₁	1	2	yes	complemented
609	#468	C₂²×C₆₁	1	2	yes	complemented
610	#468	C₂²×C₆₁	1	2	yes	complemented
611	#468	C₂²×C₆₁	1	2	yes	complemented
612	#468	C₂²×C₆₁	1	2	yes	complemented
613	#467	C₂²×C₆₁	1	2	yes	complemented
614	#466	C₂²×C₆₁	1	2	yes	—
615	#464	C₂²×C₆₁	1	2	yes	complemented
616	#464	C₂²×C₆₁	1	2	yes	complemented
617	#464	C₂²×C₆₁	1	2	yes	complemented
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	complemented
622	#463	C₂²×C₆₁	1	2	yes	complemented
623	#463	C₂²×C₆₁	1	2	yes	complemented
624	#463	C₂²×C₆₁	1	2	yes	complemented
625	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
626	#461	C₂²×C₆₁	1	2	yes	complemented
627	#461	C₂²×C₆₁	1	2	yes	complemented
628	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
629	#461	C₂²×C₆₁	1	2	yes	complemented
630	#460	C₂²×C₆₁	1	2	yes	complemented
631	#452	C₂²×C₆₁	1	2	yes	—
632	#452	C₂²×C₆₁	1	2	yes	complemented
633	#451	C₂²×C₆₁	1	2	yes	complemented
634	#450	C₂²×C₆₁	1	2	yes	complemented
635	#449	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	#447	C₂²×C₆₁	1	2	yes	complemented
640	#446	C₂²×C₆₁	1	2	yes	complemented
641	#442	C₂²×C₆₁	1	2	yes	complemented
642	#441	C₂²×C₆₁	1	2	yes	complemented
643	#440	C₂²×C₆₁	1	2	yes	complemented
644	#440	C₂²×C₆₁	1	2	yes	complemented
645	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
646	C₄×D₈	C₂²×C₆₁	1	2	yes	—
647	#436	C₂²×C₆₁	1	2	yes	complemented
648	#435	C₂²×C₆₁	1	2	yes	complemented
649	#435	C₂²×C₆₁	1	2	yes	complemented
650	#433	C₂²×C₆₁	1	2	yes	complemented
651	#432	C₂²×C₆₁	1	1	yes	characteristic, complemented
652	#424	C₂²×C₆₁	1	2	yes	complemented
653	#423	C₂²×C₆₁	1	1	yes	characteristic, complemented
654	#419	C₂²×C₆₁	1	1	yes	characteristic, complemented
655	#419	C₂²×C₆₁	1	2	yes	complemented
656	#418	C₂²×C₆₁	1	1	yes	characteristic, complemented
657	#416	C₂²×C₆₁	1	2	yes	complemented
658	C₆₁	#62087	1	1	yes	characteristic, direct product factor, Sylow
659	C₂×#41	—	2	1	no	—
660	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
661	C₂×#41	C₂³×C₆₁	1	2	yes	—
662	C₂²×Q₈	—	2	1	no	—
663	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
664	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
665	C₂²×D₄	—	2	1	no	—
666	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
667	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
668	#137	—	4	2	no	—
669	AGL(1,ℤ/8)	—	4	2	no	—
670	AGL(1,ℤ/8)	—	4	4	no	—
671	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
672	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
673	C₂×SD₁₆	—	4	4	no	—
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×SD₁₆	C₂³×C₆₁	1	2	yes	—
681	C₂×D₈	C₂³×C₆₁	1	2	yes	—
682	C₂×D₈	C₂³×C₆₁	1	2	yes	—
683	C₂×D₈	C₂³×C₆₁	1	2	yes	—
684	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
685	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
686	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
687	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
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	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
694	#127	C₂³×C₆₁	1	1	yes	characteristic
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	D₄×C₆₁	1	2	yes	—
701	#125	—	2	1	no	—
702	#125	D₄×C₆₁	1	1	yes	characteristic
703	#124	—	2	1	no	—
704	#124	—	2	1	no	—
705	#124	—	2	2	no	—
706	#124	—	2	2	no	—
707	#124	—	2	2	no	—
708	#124	—	2	2	no	—
709	#124	—	2	2	no	—
710	#124	—	2	1	no	—
711	#124	—	2	1	no	—
712	#124	—	2	1	no	—
713	#124	D₄×C₆₁	1	1	yes	characteristic
714	#124	C₂³×C₆₁	1	2	yes	—
715	#124	C₂³×C₆₁	1	2	yes	—
716	#124	C₂³×C₆₁	1	2	yes	—
717	#124	C₂³×C₆₁	1	2	yes	—
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	—	2	2	no	—
724	#123	—	2	2	no	—
725	#123	D₄×C₆₁	1	2	yes	—
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	2	no	—
732	C₂²⋊Q₈	—	2	2	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	D₄×C₆₁	1	1	yes	characteristic
738	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
739	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
740	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
741	#121	—	2	2	no	—
742	#121	—	2	2	no	—
743	#121	—	2	1	no	—
744	#121	—	2	1	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	#120	—	2	2	no	—
752	#120	—	2	2	no	—
753	#120	—	2	2	no	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
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	2	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	1	no	—
769	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
770	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₆₁	1	2	yes	—
772	C₄×D₄	C₂³×C₆₁	1	2	yes	—
773	C₄×D₄	C₂³×C₆₁	1	2	yes	—
774	C₄×D₄	C₂³×C₆₁	1	2	yes	—
775	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
776	C₄×D₄	C₂³×C₆₁	1	2	yes	—
777	#117	—	2	1	no	—
778	#117	—	2	2	no	—
779	#117	—	2	2	no	—
780	#117	—	2	1	no	—
781	#117	C₂³×C₆₁	1	1	yes	characteristic
782	#117	C₂³×C₆₁	1	2	yes	—
783	#117	C₂³×C₆₁	1	2	yes	—
784	C₂×C₂²⋊C₄	—	2	1	no	—
785	C₂×C₂²⋊C₄	—	2	1	no	—
786	C₂×C₂²⋊C₄	—	2	2	no	—
787	C₂×C₂²⋊C₄	—	2	2	no	—
788	C₂×C₂²⋊C₄	—	2	2	no	—
789	C₂×C₂²⋊C₄	—	2	2	no	—
790	C₂×C₄²	—	2	1	no	—
791	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
792	#107	C₂³×C₆₁	1	2	yes	—
793	#107	C₂³×C₆₁	1	2	yes	—
794	#107	C₂³×C₆₁	1	2	yes	—
795	#106	C₂³×C₆₁	1	2	yes	—
796	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
797	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
798	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
799	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
800	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
801	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
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	#103	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	#102	C₂³×C₆₁	1	2	yes	—
818	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
819	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
820	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
821	#97	C₂³×C₆₁	1	2	yes	—
822	#97	C₂³×C₆₁	1	2	yes	—
823	C₄×C₈	C₂³×C₆₁	1	2	yes	—
824	C₂⁴	—	2	1	no	—
825	C₂⁴	—	2	2	no	—
826	#41	—	2	2	no	—
827	#41	—	4	1	no	—
828	#41	—	4	2	no	—
829	#41	—	4	2	no	—
830	#41	—	8	2	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	1	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	2	no	—
835	C₂×Q₈	—	2	1	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×Q₈	—	4	1	no	—
838	C₂×Q₈	—	4	1	no	—
839	C₂×Q₈	—	4	2	no	—
840	C₂×Q₈	—	8	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	4	no	—
846	C₂×D₄	—	2	1	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	1	no	—
855	C₂×D₄	—	4	2	no	—
856	C₂×D₄	—	4	1	no	—
857	C₂×D₄	—	4	1	no	—
858	C₂×D₄	—	8	2	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	2	yes	—
863	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
875	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
878	Q₁₆	—	4	2	no	—
879	Q₁₆	—	4	2	no	—
880	SD₁₆	—	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	D₈	—	2	4	no	—
888	D₈	—	4	2	no	—
889	D₈	—	4	2	no	—
890	M₁₆	—	4	2	no	—
891	M₁₆	—	4	1	no	—
892	M₁₆	—	4	1	no	—
893	C₂×C₈	—	4	2	no	—
894	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
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	C₄⋊C₄	—	2	1	no	—
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	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
913	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
914	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
915	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
916	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
917	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
918	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
919	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
920	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
921	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	1	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	1	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	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
949	C₄²	—	2	1	no	—
950	C₄²	—	2	1	no	—
951	C₄²	—	2	1	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
956	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
957	C₄²	C₂⁴×C₆₁	1	2	yes	—
958	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
959	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
960	C₂³	—	2	1	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	4	4	no	—
964	C₂³	—	4	2	no	—
965	C₂³	—	8	1	no	—
966	C₂³	—	8	2	no	—
967	C₂³	—	8	1	no	—
968	C₂³	—	8	2	no	—
969	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
970	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
971	Q₈	—	2	2	no	—
972	Q₈	—	2	2	no	—
973	Q₈	—	2	1	no	—
974	Q₈	—	2	2	no	—
975	Q₈	—	2	1	no	—
976	Q₈	—	2	2	no	—
977	Q₈	—	4	1	no	—
978	Q₈	—	4	2	no	—
979	Q₈	—	8	1	no	—
980	Q₈	—	8	1	no	—
981	Q₈	—	8	2	no	—
982	Q₈	—	8	2	no	—
983	D₄	—	2	2	no	—
984	D₄	—	2	2	no	—
985	D₄	—	2	1	no	—
986	D₄	—	2	2	no	—
987	D₄	—	2	2	no	—
988	D₄	—	4	1	no	—
989	D₄	—	4	2	no	—
990	D₄	—	4	4	no	—
991	D₄	—	4	2	no	—
992	D₄	—	4	2	no	—
993	D₄	—	8	1	no	—
994	D₄	—	8	1	no	—
995	D₄	—	8	2	no	—
996	D₄	—	8	2	no	—
997	D₄	—	8	2	no	—
998	D₄	—	8	2	no	—
999	D₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	8	1	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	—	8	2	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	—	8	1	no	—
1023	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
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	2	yes	—
1028	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1029	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1030	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1031	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₈	—	2	2	no	—
1035	C₈	—	2	2	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	16	4	no	—
1052	C₂²	—	16	2	no	—
1053	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	2	no	—
1069	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1070	C₄	C₆₁×#585	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	4	2	no	—
1073	C₂	—	4	2	no	—
1074	C₂	—	8	2	no	—
1075	C₂	—	8	2	no	—
1076	C₂	C₆₁×#3488	1	1	yes	characteristic
1077	C₂	C₆₁×#3585	1	1	yes	characteristic
1078	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×#3514	C₂	semidirect
3. C₆₁×#3401	C₂	semidirect
4. C₆₁×#3367	C₂	semidirect
5. C₆₁×#3329	C₂	semidirect
6. C₆₁×#3319	C₂	semidirect
7. C₆₁×#3313	C₂	semidirect
8. C₆₁×#3273	C₂	semidirect
9. C₆₁×#3266	C₂	semidirect
10. C₆₁×#3265	C₂	semidirect
11. C₆₁×#3262	C₂	semidirect
12. C₆₁×#3254	C₂	semidirect
13. C₆₁×#3225	C₂	semidirect
14. C₆₁×#3213	C₂	semidirect
15. C₆₁×#3118	C₂	semidirect
16. C₆₁×#3116	C₂	semidirect
17. C₆₁×#3042	C₂	semidirect
18. C₆₁×#3040	C₂	semidirect
19. C₆₁×#2995	C₂	semidirect
23. C₂²×SD₁₆×C₆₁	C₂²	semidirect
26. C₆₁×#559	C₂²	semidirect
27. C₆₁×#556	C₂²	semidirect
28. C₆₁×#556	C₂²	semidirect
32. D₄×Q₈×C₆₁	C₂²	semidirect
33. D₄×Q₈×C₆₁	C₂²	semidirect
38. C₆₁×#546	C₂²	semidirect
39. D₄²×C₆₁	C₂²	semidirect
42. C₆₁×#542	C₂²	semidirect
43. C₆₁×#542	C₂²	semidirect
46. C₆₁×#536	C₂²	semidirect
47. C₆₁×#533	C₂²	semidirect
52. C₂×#124×C₆₁	C₂²	semidirect
53. C₆₁×#518	C₂²	semidirect
55. C₆₁×#497	C₂²	semidirect
57. C₆₁×#495	C₂²	semidirect
58. C₆₁×#489	C₂²	semidirect
59. C₆₁×#489	C₂²	semidirect
60. C₆₁×#487	C₂²	semidirect
61. C₆₁×#485	C₂²	semidirect
62. C₆₁×#485	C₂²	semidirect
63. C₆₁×#482	C₂²	semidirect
64. C₆₁×#477	C₂²	semidirect
65. C₆₁×#477	C₂²	semidirect
66. C₆₁×#477	C₂²	semidirect
67. C₆₁×#476	C₂²	semidirect
68. C₆₁×#474	C₂²	semidirect
69. C₆₁×#474	C₂²	semidirect
70. C₆₁×#468	C₂²	semidirect
71. C₆₁×#468	C₂²	semidirect
72. C₆₁×#468	C₂²	semidirect
73. C₆₁×#468	C₂²	semidirect
74. C₆₁×#467	C₂²	semidirect
76. C₆₁×#464	C₂²	semidirect
77. C₆₁×#464	C₂²	semidirect
78. C₆₁×#464	C₂²	semidirect
82. C₆₁×#463	C₂²	semidirect
83. C₆₁×#463	C₂²	semidirect
84. C₆₁×#463	C₂²	semidirect
85. C₆₁×#463	C₂²	semidirect
86. C₆₁×#462	C₂²	semidirect
87. C₆₁×#461	C₂²	semidirect
88. C₆₁×#461	C₂²	semidirect
89. C₆₁×#461	C₂²	semidirect
90. C₆₁×#461	C₂²	semidirect
91. C₆₁×#460	C₂²	semidirect
93. C₆₁×#452	C₂²	semidirect
94. C₆₁×#451	C₂²	semidirect
95. C₆₁×#450	C₂²	semidirect
97. C₆₁×#448	C₂²	semidirect
98. C₆₁×#448	C₂²	semidirect
100. C₆₁×#447	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₆₁×#442	C₂²	semidirect
103. C₆₁×#441	C₂²	semidirect
104. C₆₁×#440	C₂²	semidirect
105. C₆₁×#440	C₂²	semidirect
106. C₄×SD₁₆×C₆₁	C₂²	semidirect
108. C₆₁×#436	C₂²	semidirect
109. C₆₁×#435	C₂²	semidirect
110. C₆₁×#435	C₂²	semidirect
111. C₆₁×#433	C₂²	semidirect
112. C₆₁×#432	C₂²	semidirect
113. C₆₁×#424	C₂²	semidirect
114. C₆₁×#423	C₂²	semidirect
115. C₆₁×#419	C₂²	semidirect
116. C₆₁×#419	C₂²	semidirect
117. C₆₁×#418	C₂²	semidirect
118. C₆₁×#416	C₂²	semidirect
496. #62087	C₆₁	direct (N × H)
532. #3561	C₂×C₆₁	semidirect
533. #3514	C₂×C₆₁	semidirect
534. #3401	C₂×C₆₁	semidirect
535. #3367	C₂×C₆₁	semidirect
536. #3329	C₂×C₆₁	semidirect
537. #3319	C₂×C₆₁	semidirect
538. #3313	C₂×C₆₁	semidirect
539. #3273	C₂×C₆₁	semidirect
540. #3266	C₂×C₆₁	semidirect
541. #3265	C₂×C₆₁	semidirect
542. #3262	C₂×C₆₁	semidirect
543. #3254	C₂×C₆₁	semidirect
544. #3225	C₂×C₆₁	semidirect
545. #3213	C₂×C₆₁	semidirect
546. #3118	C₂×C₆₁	semidirect
547. #3116	C₂×C₆₁	semidirect
548. #3042	C₂×C₆₁	semidirect
549. #3040	C₂×C₆₁	semidirect
550. #2995	C₂×C₆₁	semidirect
562. C₂²×SD₁₆	C₂²×C₆₁	semidirect
565. #559	C₂²×C₆₁	semidirect
566. #556	C₂²×C₆₁	semidirect
567. #556	C₂²×C₆₁	semidirect
571. D₄×Q₈	C₂²×C₆₁	semidirect
572. D₄×Q₈	C₂²×C₆₁	semidirect
577. #546	C₂²×C₆₁	semidirect
578. D₄²	C₂²×C₆₁	semidirect
581. #542	C₂²×C₆₁	semidirect
582. #542	C₂²×C₆₁	semidirect
585. #536	C₂²×C₆₁	semidirect
586. #533	C₂²×C₆₁	semidirect
591. C₂×#124	C₂²×C₆₁	semidirect
592. #518	C₂²×C₆₁	semidirect
594. #497	C₂²×C₆₁	semidirect
596. #495	C₂²×C₆₁	semidirect
597. #489	C₂²×C₆₁	semidirect
598. #489	C₂²×C₆₁	semidirect
599. #487	C₂²×C₆₁	semidirect
600. #485	C₂²×C₆₁	semidirect
601. #485	C₂²×C₆₁	semidirect
602. #482	C₂²×C₆₁	semidirect
603. #477	C₂²×C₆₁	semidirect
604. #477	C₂²×C₆₁	semidirect
605. #477	C₂²×C₆₁	semidirect
606. #476	C₂²×C₆₁	semidirect
607. #474	C₂²×C₆₁	semidirect
608. #474	C₂²×C₆₁	semidirect
609. #468	C₂²×C₆₁	semidirect
610. #468	C₂²×C₆₁	semidirect
611. #468	C₂²×C₆₁	semidirect
612. #468	C₂²×C₆₁	semidirect
613. #467	C₂²×C₆₁	semidirect
615. #464	C₂²×C₆₁	semidirect
616. #464	C₂²×C₆₁	semidirect
617. #464	C₂²×C₆₁	semidirect
621. #463	C₂²×C₆₁	semidirect
622. #463	C₂²×C₆₁	semidirect
623. #463	C₂²×C₆₁	semidirect
624. #463	C₂²×C₆₁	semidirect
625. #462	C₂²×C₆₁	semidirect
626. #461	C₂²×C₆₁	semidirect
627. #461	C₂²×C₆₁	semidirect
628. #461	C₂²×C₆₁	semidirect
629. #461	C₂²×C₆₁	semidirect
630. #460	C₂²×C₆₁	semidirect
632. #452	C₂²×C₆₁	semidirect
633. #451	C₂²×C₆₁	semidirect
634. #450	C₂²×C₆₁	semidirect
636. #448	C₂²×C₆₁	semidirect
637. #448	C₂²×C₆₁	semidirect
639. #447	C₂²×C₆₁	semidirect
640. #446	C₂²×C₆₁	semidirect
641. #442	C₂²×C₆₁	semidirect
642. #441	C₂²×C₆₁	semidirect
643. #440	C₂²×C₆₁	semidirect
644. #440	C₂²×C₆₁	semidirect
645. C₄×SD₁₆	C₂²×C₆₁	semidirect
647. #436	C₂²×C₆₁	semidirect
648. #435	C₂²×C₆₁	semidirect
649. #435	C₂²×C₆₁	semidirect
650. #433	C₂²×C₆₁	semidirect
651. #432	C₂²×C₆₁	semidirect
652. #424	C₂²×C₆₁	semidirect
653. #423	C₂²×C₆₁	semidirect
654. #419	C₂²×C₆₁	semidirect
655. #419	C₂²×C₆₁	semidirect
656. #418	C₂²×C₆₁	semidirect
657. #416	C₂²×C₆₁	semidirect
658. C₆₁	#62087	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×#3514	2
C₆₁×#3401	2
C₆₁×#3367	2
C₆₁×#3329	2
C₆₁×#3319	2
C₆₁×#3313	2
C₆₁×#3273	2
C₆₁×#3266	2
C₆₁×#3265	2
C₆₁×#3262	2
C₆₁×#3254	2
C₆₁×#3225	2
C₆₁×#3213	2
C₆₁×#3118	2
C₆₁×#3116	2
C₆₁×#3042	2
C₆₁×#3040	2
C₆₁×#2995	2
#62087	61

Subgroups — C61×#62087 #29565520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62087 #29565520