Subgroups — C₆₁×#61557 #29564990

Order 15616.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3356	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3316	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3311	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3275	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3173	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3125	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3121	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2947	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₁	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
26	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
27	C₆₁×#556	—	2	2	no	—
28	C₆₁×#556	—	2	1	no	—
29	C₆₁×#556	C₂²	1	1	yes	characteristic
30	C₆₁×#556	C₂²	1	2	yes	—
31	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#555	—	2	1	no	—
33	C₆₁×#555	C₂²	1	1	yes	characteristic, complemented
34	C₆₁×#554	C₂²	1	2	yes	—
35	C₆₁×#552	—	2	1	no	—
36	C₆₁×#551	—	2	2	no	—
37	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
39	C₆₁×#548	—	2	1	no	—
40	C₆₁×#548	C₂²	1	2	yes	—
41	C₆₁×#547	C₂²	1	1	yes	characteristic
42	C₆₁×#547	C₂²	1	1	yes	characteristic
43	C₆₁×#546	C₂²	1	2	yes	—
44	C₆₁×#542	—	2	2	no	—
45	C₆₁×#542	C₂²	1	2	yes	—
46	C₆₁×#542	C₂²	1	2	yes	complemented
47	C₆₁×#539	—	2	2	no	—
48	C₆₁×#533	—	2	1	no	—
49	C₆₁×#533	C₂²	1	1	yes	characteristic
50	C₆₁×#533	C₂²	1	1	yes	characteristic
51	C₆₁×#529	—	2	1	no	—
52	C₆₁×#529	C₂²	1	1	yes	characteristic
53	C₆₁×#525	—	2	1	no	—
54	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
55	C₆₁×#520	C₂²	1	2	yes	—
56	C₆₁×#519	C₂²	1	2	yes	complemented
57	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
59	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#498	C₂²	1	2	yes	complemented
61	C₆₁×#495	C₂²	1	2	yes	—
62	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#489	C₂²	1	2	yes	—
64	C₆₁×#489	C₂²	1	2	yes	complemented
65	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#485	C₂²	1	2	yes	—
68	C₆₁×#485	C₂²	1	2	yes	complemented
69	C₆₁×#483	C₂²	1	2	yes	—
70	C₆₁×#483	C₂²	1	2	yes	complemented
71	C₆₁×#482	C₂²	1	2	yes	—
72	C₆₁×#481	C₂²	1	2	yes	complemented
73	C₆₁×#477	C₂²	1	2	yes	complemented
74	C₆₁×#476	C₂²	1	1	yes	characteristic
75	C₆₁×#476	C₂²	1	2	yes	—
76	C₆₁×#476	C₂²	1	1	yes	characteristic
77	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#475	C₂²	1	2	yes	complemented
79	C₆₁×#475	C₂²	1	2	yes	complemented
80	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₆₁×#470	C₂²	1	2	yes	—
82	C₆₁×#470	C₂²	1	2	yes	—
83	C₆₁×#470	C₂²	1	2	yes	complemented
84	C₆₁×#469	C₂²	1	2	yes	—
85	C₆₁×#465	C₂²	1	2	yes	—
86	C₆₁×#465	C₂²	1	2	yes	complemented
87	C₆₁×#464	C₂²	1	2	yes	—
88	C₆₁×#464	C₂²	1	2	yes	—
89	C₆₁×#464	C₂²	1	2	yes	complemented
90	C₆₁×#463	C₂²	1	2	yes	—
91	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#461	C₂²	1	1	yes	characteristic
93	C₆₁×#461	C₂²	1	1	yes	characteristic
94	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
95	C₆₁×#452	C₂²	1	2	yes	—
96	C₆₁×#452	C₂²	1	2	yes	—
97	C₆₁×#451	C₂²	1	2	yes	complemented
98	C₆₁×#450	C₂²	1	2	yes	—
99	C₆₁×#449	C₂²	1	2	yes	—
100	C₆₁×#448	C₂²	1	2	yes	—
101	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
103	C₆₁×#442	C₂²	1	1	yes	characteristic
104	C₆₁×#442	C₂²	1	1	yes	characteristic
105	C₆₁×#441	C₂²	1	2	yes	complemented
106	C₆₁×#441	C₂²	1	2	yes	complemented
107	C₆₁×#441	C₂²	1	2	yes	complemented
108	C₆₁×#440	C₂²	1	2	yes	—
109	C₆₁×#440	C₂²	1	1	yes	characteristic
110	C₆₁×#440	C₂²	1	1	yes	characteristic
111	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
112	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
121	C₆₁×#436	C₂²	1	2	yes	—
122	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
123	C₆₁×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#433	C₂²	1	2	yes	complemented
126	C₆₁×#431	C₂²	1	1	yes	characteristic
127	C₆₁×#428	C₂²	1	1	yes	characteristic
128	C₆₁×#428	C₂²	1	2	yes	complemented
129	C₆₁×#418	C₂²	1	1	yes	characteristic
130	C₆₁×#417	C₂²	1	1	yes	characteristic
131	C₆₁×#416	C₂²	1	2	yes	—
132	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
133	C₆₁×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	C₂³	1	2	yes	—
137	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₁	—	2	1	no	—
139	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₁	—	2	1	no	—
142	#137×C₆₁	—	2	8	no	—
143	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
144	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₆₁	—	2	1	no	—
159	C₄⋊Q₈×C₆₁	—	2	1	no	—
160	C₄⋊Q₈×C₆₁	—	2	2	no	—
161	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
167	#126×C₆₁	—	2	2	no	—
168	#126×C₆₁	—	2	2	no	—
169	#126×C₆₁	—	2	2	no	—
170	#126×C₆₁	—	2	2	no	—
171	#126×C₆₁	—	2	2	no	—
172	#126×C₆₁	—	2	2	no	—
173	#126×C₆₁	D₄	1	2	yes	—
174	#125×C₆₁	—	2	2	no	—
175	#125×C₆₁	—	2	1	no	—
176	#125×C₆₁	—	2	1	no	—
177	#125×C₆₁	D₄	1	1	yes	characteristic
178	#124×C₆₁	—	2	2	no	—
179	#124×C₆₁	—	2	2	no	—
180	#124×C₆₁	—	2	2	no	—
181	#124×C₆₁	—	2	2	no	—
182	#124×C₆₁	—	2	2	no	—
183	#124×C₆₁	D₄	1	1	yes	characteristic
184	#124×C₆₁	C₂³	1	2	yes	—
185	#124×C₆₁	C₂³	1	2	yes	—
186	#123×C₆₁	—	2	2	no	—
187	#123×C₆₁	—	2	2	no	—
188	#123×C₆₁	—	2	2	no	—
189	#123×C₆₁	—	2	2	no	—
190	#123×C₆₁	—	2	2	no	—
191	#123×C₆₁	D₄	1	2	yes	—
192	C₂²⋊Q₈×C₆₁	—	2	1	no	—
193	C₂²⋊Q₈×C₆₁	—	2	1	no	—
194	C₂²⋊Q₈×C₆₁	—	2	1	no	—
195	C₂²⋊Q₈×C₆₁	—	2	1	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	2	no	—
198	C₂²⋊Q₈×C₆₁	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	—	2	2	no	—
200	C₂²⋊Q₈×C₆₁	—	2	1	no	—
201	C₂²⋊Q₈×C₆₁	—	2	1	no	—
202	C₂²⋊Q₈×C₆₁	—	2	2	no	—
203	C₂²⋊Q₈×C₆₁	—	2	2	no	—
204	C₂²⋊Q₈×C₆₁	—	2	2	no	—
205	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
206	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
210	#121×C₆₁	—	2	2	no	—
211	#121×C₆₁	—	2	1	no	—
212	#121×C₆₁	—	2	1	no	—
213	#121×C₆₁	—	2	2	no	—
214	#121×C₆₁	D₄	1	1	yes	characteristic
215	#121×C₆₁	C₂³	1	2	yes	—
216	#121×C₆₁	C₂³	1	2	yes	—
217	#120×C₆₁	—	2	2	no	—
218	C₄×Q₈×C₆₁	—	2	1	no	—
219	C₄×Q₈×C₆₁	—	2	2	no	—
220	C₄×Q₈×C₆₁	—	2	2	no	—
221	C₄×Q₈×C₆₁	—	2	2	no	—
222	C₄×Q₈×C₆₁	—	2	1	no	—
223	C₄×Q₈×C₆₁	—	2	1	no	—
224	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₆₁	—	2	1	no	—
233	C₄×D₄×C₆₁	—	2	2	no	—
234	C₄×D₄×C₆₁	—	2	1	no	—
235	C₄×D₄×C₆₁	—	2	1	no	—
236	C₄×D₄×C₆₁	—	2	2	no	—
237	C₄×D₄×C₆₁	—	2	2	no	—
238	C₄×D₄×C₆₁	—	2	2	no	—
239	C₄×D₄×C₆₁	—	2	1	no	—
240	C₄×D₄×C₆₁	—	2	1	no	—
241	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₁	C₂³	1	2	yes	—
244	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₁	C₂³	1	2	yes	—
249	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
250	#117×C₆₁	—	2	1	no	—
251	#117×C₆₁	—	2	1	no	—
252	#117×C₆₁	—	2	1	no	—
253	#117×C₆₁	—	2	1	no	—
254	#117×C₆₁	—	2	2	no	—
255	#117×C₆₁	—	2	1	no	—
256	#117×C₆₁	—	2	2	no	—
257	#117×C₆₁	—	2	2	no	—
258	#117×C₆₁	—	2	1	no	—
259	#117×C₆₁	C₂³	1	2	yes	—
260	#117×C₆₁	C₂³	1	1	yes	characteristic
261	#117×C₆₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
263	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
264	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
267	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
268	C₂×C₄²×C₆₁	—	2	1	no	—
269	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
270	#107×C₆₁	C₂³	1	1	yes	characteristic
271	#107×C₆₁	C₂³	1	1	yes	characteristic
272	#107×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	1	yes	characteristic
274	#106×C₆₁	C₂³	1	1	yes	characteristic
275	#106×C₆₁	C₂³	1	2	yes	—
276	#106×C₆₁	C₂³	1	2	yes	—
277	#106×C₆₁	C₂³	1	2	yes	—
278	#106×C₆₁	C₂³	1	2	yes	—
279	#106×C₆₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
284	#103×C₆₁	C₂³	1	1	yes	characteristic
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×C₆₁	C₂³	1	2	yes	—
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	1	yes	characteristic
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	2	yes	—
293	#103×C₆₁	C₂³	1	2	yes	—
294	#103×C₆₁	C₂³	1	2	yes	—
295	#102×C₆₁	C₂³	1	1	yes	characteristic
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	1	yes	characteristic
298	#102×C₆₁	C₂³	1	1	yes	characteristic
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	1	yes	characteristic
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	#97×C₆₁	C₂³	1	1	yes	characteristic
308	#97×C₆₁	C₂³	1	1	yes	characteristic
309	#97×C₆₁	C₂³	1	2	yes	—
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₁	C₂³	1	2	yes	—
313	C₄×C₈×C₆₁	C₂³	1	2	yes	—
314	C₂⁴×C₆₁	—	2	1	no	—
315	#41×C₆₁	—	2	2	no	—
316	#41×C₆₁	—	2	4	no	—
317	#41×C₆₁	—	4	2	no	—
318	#41×C₆₁	—	4	1	no	—
319	#41×C₆₁	—	8	2	no	—
320	C₂×Q₈×C₆₁	—	2	2	no	—
321	C₂×Q₈×C₆₁	—	2	1	no	—
322	C₂×Q₈×C₆₁	—	2	1	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	2	no	—
325	C₂×Q₈×C₆₁	—	2	4	no	—
326	C₂×Q₈×C₆₁	—	4	2	no	—
327	C₂×Q₈×C₆₁	—	8	2	no	—
328	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₆₁	—	2	2	no	—
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	2	1	no	—
335	C₂×D₄×C₆₁	—	2	2	no	—
336	C₂×D₄×C₆₁	—	2	2	no	—
337	C₂×D₄×C₆₁	—	2	1	no	—
338	C₂×D₄×C₆₁	—	4	1	no	—
339	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₆₁	—	2	2	no	—
345	C₂²×C₄×C₆₁	—	2	1	no	—
346	C₂²×C₄×C₆₁	—	2	2	no	—
347	C₂²×C₄×C₆₁	—	2	1	no	—
348	C₂²×C₄×C₆₁	—	2	1	no	—
349	C₂²×C₄×C₆₁	—	2	2	no	—
350	C₂²×C₄×C₆₁	—	2	1	no	—
351	C₂²×C₄×C₆₁	—	2	1	no	—
352	C₂²×C₄×C₆₁	—	2	1	no	—
353	C₂²×C₄×C₆₁	—	2	2	no	—
354	C₂²×C₄×C₆₁	—	2	1	no	—
355	C₂²×C₄×C₆₁	—	2	1	no	—
356	C₂²×C₄×C₆₁	—	8	2	no	—
357	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
361	Q₁₆×C₆₁	—	2	4	no	—
362	Q₁₆×C₆₁	—	2	4	no	—
363	Q₁₆×C₆₁	—	4	2	no	—
364	SD₁₆×C₆₁	—	2	2	no	—
365	SD₁₆×C₆₁	—	2	4	no	—
366	SD₁₆×C₆₁	—	4	2	no	—
367	SD₁₆×C₆₁	—	4	2	no	—
368	SD₁₆×C₆₁	#41	1	4	yes	complemented
369	D₈×C₆₁	—	2	2	no	—
370	D₈×C₆₁	—	2	2	no	—
371	M₁₆×C₆₁	—	2	2	no	—
372	M₁₆×C₆₁	—	2	4	no	—
373	M₁₆×C₆₁	—	4	1	no	—
374	C₂×C₈×C₆₁	—	4	2	no	—
375	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
376	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
379	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₆₁	—	2	2	no	—
382	C₄⋊C₄×C₆₁	—	2	1	no	—
383	C₄⋊C₄×C₆₁	—	2	2	no	—
384	C₄⋊C₄×C₆₁	—	2	2	no	—
385	C₄⋊C₄×C₆₁	—	2	2	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	1	no	—
389	C₄⋊C₄×C₆₁	—	2	1	no	—
390	C₄⋊C₄×C₆₁	—	2	1	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	2	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	2	no	—
398	C₄⋊C₄×C₆₁	—	2	2	no	—
399	C₄⋊C₄×C₆₁	—	2	1	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	2	no	—
402	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	—	2	2	no	—
416	C₂²⋊C₄×C₆₁	—	2	2	no	—
417	C₂²⋊C₄×C₆₁	—	2	1	no	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₂²⋊C₄×C₆₁	—	2	2	no	—
420	C₂²⋊C₄×C₆₁	—	2	1	no	—
421	C₂²⋊C₄×C₆₁	—	2	1	no	—
422	C₂²⋊C₄×C₆₁	—	2	1	no	—
423	C₂²⋊C₄×C₆₁	—	2	1	no	—
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	2	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	1	no	—
428	C₂²⋊C₄×C₆₁	—	2	1	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
438	C₄²×C₆₁	—	2	1	no	—
439	C₄²×C₆₁	—	2	1	no	—
440	C₄²×C₆₁	—	2	1	no	—
441	C₄²×C₆₁	—	2	2	no	—
442	C₄²×C₆₁	—	2	2	no	—
443	C₄²×C₆₁	—	2	2	no	—
444	C₄²×C₆₁	—	2	2	no	—
445	C₄²×C₆₁	—	2	2	no	—
446	C₄²×C₆₁	—	2	2	no	—
447	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
450	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
451	C₄²×C₆₁	C₂⁴	1	2	yes	—
452	C₂³×C₆₁	—	2	1	no	—
453	C₂³×C₆₁	—	2	1	no	—
454	C₂³×C₆₁	—	2	1	no	—
455	C₂³×C₆₁	—	4	2	no	—
456	C₂³×C₆₁	—	4	2	no	—
457	C₂³×C₆₁	—	8	1	no	—
458	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
460	Q₈×C₆₁	—	2	2	no	—
461	Q₈×C₆₁	—	2	1	no	—
462	Q₈×C₆₁	—	2	2	no	—
463	Q₈×C₆₁	—	2	2	no	—
464	Q₈×C₆₁	—	2	2	no	—
465	Q₈×C₆₁	—	2	2	no	—
466	Q₈×C₆₁	—	4	4	no	—
467	Q₈×C₆₁	—	4	2	no	—
468	Q₈×C₆₁	—	8	1	no	—
469	Q₈×C₆₁	—	8	2	no	—
470	Q₈×C₆₁	—	8	2	no	—
471	Q₈×C₆₁	C₂×#41	1	2	yes	—
472	D₄×C₆₁	—	2	2	no	—
473	D₄×C₆₁	—	2	1	no	—
474	D₄×C₆₁	—	2	1	no	—
475	D₄×C₆₁	—	2	1	no	—
476	D₄×C₆₁	—	2	1	no	—
477	D₄×C₆₁	—	2	1	no	—
478	D₄×C₆₁	—	4	2	no	—
479	D₄×C₆₁	—	4	2	no	—
480	D₄×C₆₁	—	4	2	no	—
481	D₄×C₆₁	—	4	4	no	—
482	D₄×C₆₁	—	8	2	no	—
483	D₄×C₆₁	—	8	2	no	—
484	D₄×C₆₁	C₂×#41	1	2	yes	—
485	C₂×C₄×C₆₁	—	2	1	no	—
486	C₂×C₄×C₆₁	—	2	2	no	—
487	C₂×C₄×C₆₁	—	2	1	no	—
488	C₂×C₄×C₆₁	—	2	2	no	—
489	C₂×C₄×C₆₁	—	2	2	no	—
490	C₂×C₄×C₆₁	—	2	1	no	—
491	C₂×C₄×C₆₁	—	2	1	no	—
492	C₂×C₄×C₆₁	—	2	2	no	—
493	C₂×C₄×C₆₁	—	2	2	no	—
494	C₂×C₄×C₆₁	—	2	2	no	—
495	C₂×C₄×C₆₁	—	2	1	no	—
496	C₂×C₄×C₆₁	—	2	1	no	—
497	C₂×C₄×C₆₁	—	2	2	no	—
498	C₂×C₄×C₆₁	—	2	1	no	—
499	C₂×C₄×C₆₁	—	4	1	no	—
500	C₂×C₄×C₆₁	—	4	2	no	—
501	C₂×C₄×C₆₁	—	4	4	no	—
502	C₂×C₄×C₆₁	—	4	4	no	—
503	C₂×C₄×C₆₁	—	4	2	no	—
504	C₂×C₄×C₆₁	—	4	2	no	—
505	C₂×C₄×C₆₁	—	4	2	no	—
506	C₂×C₄×C₆₁	—	8	1	no	—
507	C₂×C₄×C₆₁	—	8	1	no	—
508	C₂×C₄×C₆₁	—	8	1	no	—
509	C₂×C₄×C₆₁	—	8	2	no	—
510	C₂×C₄×C₆₁	—	8	1	no	—
511	C₂×C₄×C₆₁	—	8	2	no	—
512	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
521	C₈×C₆₁	—	2	1	no	—
522	C₈×C₆₁	—	2	2	no	—
523	C₈×C₆₁	—	2	1	no	—
524	C₈×C₆₁	—	2	2	no	—
525	C₈×C₆₁	—	2	1	no	—
526	C₈×C₆₁	C₂×#41	1	2	yes	—
527	#61557	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
528	C₂²×C₆₁	—	2	1	no	—
529	C₂²×C₆₁	—	2	2	no	—
530	C₂²×C₆₁	—	2	2	no	—
531	C₂²×C₆₁	—	2	1	no	—
532	C₂²×C₆₁	—	2	2	no	—
533	C₂²×C₆₁	—	2	1	no	—
534	C₂²×C₆₁	—	2	2	no	—
535	C₂²×C₆₁	—	4	1	no	—
536	C₂²×C₆₁	—	4	1	no	—
537	C₂²×C₆₁	—	4	1	no	—
538	C₂²×C₆₁	—	4	1	no	—
539	C₂²×C₆₁	—	4	1	no	—
540	C₂²×C₆₁	—	4	1	no	—
541	C₂²×C₆₁	—	4	1	no	—
542	C₂²×C₆₁	—	4	1	no	—
543	C₂²×C₆₁	—	8	4	no	—
544	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
545	C₄×C₆₁	—	2	1	no	—
546	C₄×C₆₁	—	2	1	no	—
547	C₄×C₆₁	—	2	2	no	—
548	C₄×C₆₁	—	2	1	no	—
549	C₄×C₆₁	—	2	2	no	—
550	C₄×C₆₁	—	2	2	no	—
551	C₄×C₆₁	—	2	1	no	—
552	C₄×C₆₁	—	2	2	no	—
553	C₄×C₆₁	—	4	1	no	—
554	C₄×C₆₁	—	4	2	no	—
555	C₄×C₆₁	—	4	2	no	—
556	C₄×C₆₁	—	4	2	no	—
557	C₄×C₆₁	—	4	1	no	—
558	C₄×C₆₁	—	4	1	no	—
559	C₄×C₆₁	—	4	1	no	—
560	C₄×C₆₁	—	4	2	no	—
561	C₄×C₆₁	#577	1	2	yes	—
562	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
563	C₄×C₆₁	#585	1	1	yes	characteristic
564	#3520	C₂×C₆₁	1	1	yes	characteristic, complemented
565	#3518	C₂×C₆₁	1	1	yes	characteristic, complemented
566	#3393	C₂×C₆₁	1	1	yes	characteristic, complemented
567	Q₈×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
568	#3369	C₂×C₆₁	1	1	yes	characteristic, complemented
569	#3367	C₂×C₆₁	1	1	yes	characteristic, complemented
570	#3356	C₂×C₆₁	1	2	yes	complemented
571	#3354	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3316	C₂×C₆₁	1	2	yes	complemented
573	#3311	C₂×C₆₁	1	2	yes	complemented
574	#3303	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3298	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#3276	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3275	C₂×C₆₁	1	2	yes	complemented
578	#3185	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3173	C₂×C₆₁	1	2	yes	complemented
580	#3125	C₂×C₆₁	1	2	yes	complemented
581	#3121	C₂×C₆₁	1	2	yes	complemented
582	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
583	#3101	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#2969	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#2947	C₂×C₆₁	1	2	yes	complemented
586	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic, complemented
587	C₂×C₆₁	—	4	2	no	—
588	C₂×C₆₁	—	4	1	no	—
589	C₂×C₆₁	—	4	2	no	—
590	C₂×C₆₁	—	8	1	no	—
591	C₂×C₆₁	—	8	1	no	—
592	C₂×C₆₁	D₄×#41	1	1	yes	characteristic
593	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
594	C₂×C₆₁	#3586	1	1	yes	characteristic
595	C₂×#137	C₂²×C₆₁	1	2	yes	—
596	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
597	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
598	#556	—	2	2	no	—
599	#556	—	2	1	no	—
600	#556	C₂²×C₆₁	1	1	yes	characteristic
601	#556	C₂²×C₆₁	1	2	yes	—
602	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
603	#555	—	2	1	no	—
604	#555	C₂²×C₆₁	1	1	yes	characteristic, complemented
605	#554	C₂²×C₆₁	1	2	yes	—
606	#552	—	2	1	no	—
607	#551	—	2	2	no	—
608	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
609	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
610	#548	—	2	1	no	—
611	#548	C₂²×C₆₁	1	2	yes	—
612	#547	C₂²×C₆₁	1	1	yes	characteristic
613	#547	C₂²×C₆₁	1	1	yes	characteristic
614	#546	C₂²×C₆₁	1	2	yes	—
615	#542	—	2	2	no	—
616	#542	C₂²×C₆₁	1	2	yes	—
617	#542	C₂²×C₆₁	1	2	yes	complemented
618	#539	—	2	2	no	—
619	#533	—	2	1	no	—
620	#533	C₂²×C₆₁	1	1	yes	characteristic
621	#533	C₂²×C₆₁	1	1	yes	characteristic
622	#529	—	2	1	no	—
623	#529	C₂²×C₆₁	1	1	yes	characteristic
624	#525	—	2	1	no	—
625	C₂×C₂²⋊Q₈	—	2	1	no	—
626	#520	C₂²×C₆₁	1	2	yes	—
627	#519	C₂²×C₆₁	1	2	yes	complemented
628	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
629	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
630	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
631	#498	C₂²×C₆₁	1	2	yes	complemented
632	#495	C₂²×C₆₁	1	2	yes	—
633	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
634	#489	C₂²×C₆₁	1	2	yes	—
635	#489	C₂²×C₆₁	1	2	yes	complemented
636	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
637	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
638	#485	C₂²×C₆₁	1	2	yes	—
639	#485	C₂²×C₆₁	1	2	yes	complemented
640	#483	C₂²×C₆₁	1	2	yes	—
641	#483	C₂²×C₆₁	1	2	yes	complemented
642	#482	C₂²×C₆₁	1	2	yes	—
643	#481	C₂²×C₆₁	1	2	yes	complemented
644	#477	C₂²×C₆₁	1	2	yes	complemented
645	#476	C₂²×C₆₁	1	1	yes	characteristic
646	#476	C₂²×C₆₁	1	1	yes	characteristic
647	#476	C₂²×C₆₁	1	2	yes	—
648	#475	C₂²×C₆₁	1	2	yes	complemented
649	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
650	#475	C₂²×C₆₁	1	2	yes	complemented
651	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
652	#470	C₂²×C₆₁	1	2	yes	—
653	#470	C₂²×C₆₁	1	2	yes	—
654	#470	C₂²×C₆₁	1	2	yes	complemented
655	#469	C₂²×C₆₁	1	2	yes	—
656	#465	C₂²×C₆₁	1	2	yes	—
657	#465	C₂²×C₆₁	1	2	yes	complemented
658	#464	C₂²×C₆₁	1	2	yes	—
659	#464	C₂²×C₆₁	1	2	yes	—
660	#464	C₂²×C₆₁	1	2	yes	complemented
661	#463	C₂²×C₆₁	1	2	yes	—
662	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
663	#461	C₂²×C₆₁	1	1	yes	characteristic
664	#461	C₂²×C₆₁	1	1	yes	characteristic
665	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
666	#452	C₂²×C₆₁	1	2	yes	—
667	#452	C₂²×C₆₁	1	2	yes	—
668	#451	C₂²×C₆₁	1	2	yes	complemented
669	#450	C₂²×C₆₁	1	2	yes	—
670	#449	C₂²×C₆₁	1	2	yes	—
671	#448	C₂²×C₆₁	1	2	yes	—
672	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
673	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
674	#442	C₂²×C₆₁	1	1	yes	characteristic
675	#442	C₂²×C₆₁	1	1	yes	characteristic
676	#441	C₂²×C₆₁	1	2	yes	complemented
677	#441	C₂²×C₆₁	1	2	yes	complemented
678	#441	C₂²×C₆₁	1	2	yes	complemented
679	#440	C₂²×C₆₁	1	2	yes	—
680	#440	C₂²×C₆₁	1	1	yes	characteristic
681	#440	C₂²×C₆₁	1	1	yes	characteristic
682	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
683	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
684	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
685	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
686	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
687	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
688	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
689	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
690	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
691	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
692	#436	C₂²×C₆₁	1	2	yes	—
693	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
694	#435	C₂²×C₆₁	1	2	yes	—
695	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
696	#433	C₂²×C₆₁	1	2	yes	complemented
697	#431	C₂²×C₆₁	1	1	yes	characteristic
698	#428	C₂²×C₆₁	1	1	yes	characteristic
699	#428	C₂²×C₆₁	1	2	yes	complemented
700	#418	C₂²×C₆₁	1	1	yes	characteristic
701	#417	C₂²×C₆₁	1	1	yes	characteristic
702	#416	C₂²×C₆₁	1	2	yes	—
703	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
704	#405	C₂²×C₆₁	1	2	yes	complemented
705	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
706	C₆₁	#61557	1	1	yes	characteristic, direct product factor, Sylow
707	C₂×#41	—	2	1	no	—
708	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
709	C₂×#41	C₂³×C₆₁	1	2	yes	—
710	C₂²×Q₈	—	2	1	no	—
711	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
712	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
713	C₂³×C₄	—	2	1	no	—
714	#137	—	2	8	no	—
715	AGL(1,ℤ/8)	—	2	4	no	—
716	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
718	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
727	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
728	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	—	2	2	no	—
733	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
738	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	D₄×C₆₁	1	2	yes	—
746	#125	—	2	2	no	—
747	#125	—	2	1	no	—
748	#125	—	2	1	no	—
749	#125	D₄×C₆₁	1	1	yes	characteristic
750	#124	—	2	2	no	—
751	#124	—	2	2	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	D₄×C₆₁	1	1	yes	characteristic
756	#124	C₂³×C₆₁	1	2	yes	—
757	#124	C₂³×C₆₁	1	2	yes	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	D₄×C₆₁	1	2	yes	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
778	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
780	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
781	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	D₄×C₆₁	1	1	yes	characteristic
787	#121	C₂³×C₆₁	1	2	yes	—
788	#121	C₂³×C₆₁	1	2	yes	—
789	#120	—	2	2	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	2	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
799	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
800	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
801	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
802	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
803	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₆₁	1	2	yes	—
820	C₄×D₄	C₂³×C₆₁	1	2	yes	—
821	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	2	1	no	—
828	#117	—	2	2	no	—
829	#117	—	2	2	no	—
830	#117	—	2	1	no	—
831	#117	C₂³×C₆₁	1	1	yes	characteristic
832	#117	C₂³×C₆₁	1	2	yes	—
833	#117	C₂³×C₆₁	1	2	yes	—
834	C₂×C₄⋊C₄	—	2	2	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
837	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
838	C₂×C₂²⋊C₄	—	2	1	no	—
839	C₂×C₂²⋊C₄	—	2	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
842	#107	C₂³×C₆₁	1	1	yes	characteristic
843	#107	C₂³×C₆₁	1	1	yes	characteristic
844	#107	C₂³×C₆₁	1	2	yes	—
845	#106	C₂³×C₆₁	1	1	yes	characteristic
846	#106	C₂³×C₆₁	1	1	yes	characteristic
847	#106	C₂³×C₆₁	1	2	yes	—
848	#106	C₂³×C₆₁	1	2	yes	—
849	#106	C₂³×C₆₁	1	2	yes	—
850	#106	C₂³×C₆₁	1	2	yes	—
851	#106	C₂³×C₆₁	1	2	yes	—
852	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
855	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
856	#103	C₂³×C₆₁	1	1	yes	characteristic
857	#103	C₂³×C₆₁	1	2	yes	—
858	#103	C₂³×C₆₁	1	2	yes	—
859	#103	C₂³×C₆₁	1	2	yes	—
860	#103	C₂³×C₆₁	1	2	yes	—
861	#103	C₂³×C₆₁	1	2	yes	—
862	#103	C₂³×C₆₁	1	1	yes	characteristic
863	#103	C₂³×C₆₁	1	2	yes	—
864	#103	C₂³×C₆₁	1	2	yes	—
865	#103	C₂³×C₆₁	1	2	yes	—
866	#103	C₂³×C₆₁	1	2	yes	—
867	#102	C₂³×C₆₁	1	1	yes	characteristic
868	#102	C₂³×C₆₁	1	2	yes	—
869	#102	C₂³×C₆₁	1	1	yes	characteristic
870	#102	C₂³×C₆₁	1	1	yes	characteristic
871	#102	C₂³×C₆₁	1	1	yes	characteristic
872	#102	C₂³×C₆₁	1	1	yes	characteristic
873	#102	C₂³×C₆₁	1	1	yes	characteristic
874	#102	C₂³×C₆₁	1	2	yes	—
875	#102	C₂³×C₆₁	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
879	#97	C₂³×C₆₁	1	1	yes	characteristic
880	#97	C₂³×C₆₁	1	1	yes	characteristic
881	#97	C₂³×C₆₁	1	2	yes	—
882	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₆₁	1	2	yes	—
885	C₄×C₈	C₂³×C₆₁	1	2	yes	—
886	C₂⁴	—	2	1	no	—
887	#41	—	2	2	no	—
888	#41	—	2	4	no	—
889	#41	—	4	2	no	—
890	#41	—	4	1	no	—
891	#41	—	8	2	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	4	no	—
898	C₂×Q₈	—	4	2	no	—
899	C₂×Q₈	—	8	2	no	—
900	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
902	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
903	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	4	1	no	—
911	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
912	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
913	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
914	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	8	2	no	—
929	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
933	Q₁₆	—	2	4	no	—
934	Q₁₆	—	2	4	no	—
935	Q₁₆	—	4	2	no	—
936	SD₁₆	—	2	2	no	—
937	SD₁₆	—	2	4	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	2	no	—
940	SD₁₆	#41×C₆₁	1	4	yes	complemented
941	D₈	—	2	2	no	—
942	D₈	—	2	2	no	—
943	M₁₆	—	2	2	no	—
944	M₁₆	—	2	4	no	—
945	M₁₆	—	4	1	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
948	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
950	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
951	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
978	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1020	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₆₁	1	2	yes	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	4	2	no	—
1029	C₂³	—	8	1	no	—
1030	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1031	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	4	4	no	—
1039	Q₈	—	4	2	no	—
1040	Q₈	—	8	1	no	—
1041	Q₈	—	8	2	no	—
1042	Q₈	—	8	2	no	—
1043	Q₈	C₂×#41×C₆₁	1	2	yes	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	4	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	C₂×#41×C₆₁	1	2	yes	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	4	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	8	1	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1092	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1093	C₈	—	2	1	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	C₂×#41×C₆₁	1	2	yes	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	8	4	no	—
1115	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	2	no	—
1132	C₄	C₆₁×#577	1	2	yes	—
1133	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1134	C₄	C₆₁×#585	1	1	yes	characteristic
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	1	no	—
1140	C₂	D₄×#41×C₆₁	1	1	yes	characteristic
1141	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1142	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×#3520	C₂	semidirect
2. C₆₁×#3518	C₂	semidirect
3. C₆₁×#3393	C₂	semidirect
4. Q₈×SD₁₆×C₆₁	C₂	semidirect
5. C₆₁×#3369	C₂	semidirect
6. C₆₁×#3367	C₂	semidirect
7. C₆₁×#3356	C₂	semidirect
8. C₆₁×#3354	C₂	semidirect
9. C₆₁×#3316	C₂	semidirect
10. C₆₁×#3311	C₂	semidirect
11. C₆₁×#3303	C₂	semidirect
12. C₆₁×#3298	C₂	semidirect
13. C₆₁×#3276	C₂	semidirect
14. C₆₁×#3275	C₂	semidirect
15. C₆₁×#3185	C₂	semidirect
16. C₆₁×#3173	C₂	semidirect
17. C₆₁×#3125	C₂	semidirect
18. C₆₁×#3121	C₂	semidirect
19. C₆₁×#3107	C₂	semidirect
20. C₆₁×#3101	C₂	semidirect
21. C₆₁×#2969	C₂	semidirect
22. C₆₁×#2947	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
26. Q₈²×C₆₁	C₂²	semidirect
31. C₆₁×#556	C₂²	semidirect
33. C₆₁×#555	C₂²	semidirect
38. D₄×Q₈×C₆₁	C₂²	semidirect
46. C₆₁×#542	C₂²	semidirect
56. C₆₁×#519	C₂²	semidirect
59. C₆₁×#498	C₂²	semidirect
60. C₆₁×#498	C₂²	semidirect
62. C₆₁×#494	C₂²	semidirect
64. C₆₁×#489	C₂²	semidirect
65. C₆₁×#487	C₂²	semidirect
66. C₆₁×#487	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
70. C₆₁×#483	C₂²	semidirect
72. C₆₁×#481	C₂²	semidirect
73. C₆₁×#477	C₂²	semidirect
77. C₆₁×#475	C₂²	semidirect
78. C₆₁×#475	C₂²	semidirect
79. C₆₁×#475	C₂²	semidirect
80. C₆₁×#474	C₂²	semidirect
83. C₆₁×#470	C₂²	semidirect
86. C₆₁×#465	C₂²	semidirect
89. C₆₁×#464	C₂²	semidirect
91. C₆₁×#462	C₂²	semidirect
94. C₆₁×#461	C₂²	semidirect
97. C₆₁×#451	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₈×Q₈×C₆₁	C₂²	semidirect
105. C₆₁×#441	C₂²	semidirect
106. C₆₁×#441	C₂²	semidirect
107. C₆₁×#441	C₂²	semidirect
111. C₄×Q₁₆×C₆₁	C₂²	semidirect
112. C₄×Q₁₆×C₆₁	C₂²	semidirect
118. C₄×SD₁₆×C₆₁	C₂²	semidirect
122. C₆₁×#436	C₂²	semidirect
124. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#433	C₂²	semidirect
128. C₆₁×#428	C₂²	semidirect
132. C₂×#103×C₆₁	C₂²	semidirect
133. C₆₁×#405	C₂²	semidirect
368. SD₁₆×C₆₁	#41	semidirect
527. #61557	C₆₁	direct (N × H)
564. #3520	C₂×C₆₁	semidirect
565. #3518	C₂×C₆₁	semidirect
566. #3393	C₂×C₆₁	semidirect
567. Q₈×SD₁₆	C₂×C₆₁	semidirect
568. #3369	C₂×C₆₁	semidirect
569. #3367	C₂×C₆₁	semidirect
570. #3356	C₂×C₆₁	semidirect
571. #3354	C₂×C₆₁	semidirect
572. #3316	C₂×C₆₁	semidirect
573. #3311	C₂×C₆₁	semidirect
574. #3303	C₂×C₆₁	semidirect
575. #3298	C₂×C₆₁	semidirect
576. #3276	C₂×C₆₁	semidirect
577. #3275	C₂×C₆₁	semidirect
578. #3185	C₂×C₆₁	semidirect
579. #3173	C₂×C₆₁	semidirect
580. #3125	C₂×C₆₁	semidirect
581. #3121	C₂×C₆₁	semidirect
582. #3107	C₂×C₆₁	semidirect
583. #3101	C₂×C₆₁	semidirect
584. #2969	C₂×C₆₁	semidirect
585. #2947	C₂×C₆₁	semidirect
586. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
597. Q₈²	C₂²×C₆₁	semidirect
602. #556	C₂²×C₆₁	semidirect
604. #555	C₂²×C₆₁	semidirect
609. D₄×Q₈	C₂²×C₆₁	semidirect
617. #542	C₂²×C₆₁	semidirect
627. #519	C₂²×C₆₁	semidirect
630. #498	C₂²×C₆₁	semidirect
631. #498	C₂²×C₆₁	semidirect
633. #494	C₂²×C₆₁	semidirect
635. #489	C₂²×C₆₁	semidirect
636. #487	C₂²×C₆₁	semidirect
637. #487	C₂²×C₆₁	semidirect
639. #485	C₂²×C₆₁	semidirect
641. #483	C₂²×C₆₁	semidirect
643. #481	C₂²×C₆₁	semidirect
644. #477	C₂²×C₆₁	semidirect
648. #475	C₂²×C₆₁	semidirect
649. #475	C₂²×C₆₁	semidirect
650. #475	C₂²×C₆₁	semidirect
651. #474	C₂²×C₆₁	semidirect
654. #470	C₂²×C₆₁	semidirect
657. #465	C₂²×C₆₁	semidirect
660. #464	C₂²×C₆₁	semidirect
662. #462	C₂²×C₆₁	semidirect
665. #461	C₂²×C₆₁	semidirect
668. #451	C₂²×C₆₁	semidirect
672. #446	C₂²×C₆₁	semidirect
673. C₈×Q₈	C₂²×C₆₁	semidirect
676. #441	C₂²×C₆₁	semidirect
677. #441	C₂²×C₆₁	semidirect
678. #441	C₂²×C₆₁	semidirect
682. C₄×Q₁₆	C₂²×C₆₁	semidirect
683. C₄×Q₁₆	C₂²×C₆₁	semidirect
689. C₄×SD₁₆	C₂²×C₆₁	semidirect
693. #436	C₂²×C₆₁	semidirect
695. C₈×D₄	C₂²×C₆₁	semidirect
696. #433	C₂²×C₆₁	semidirect
699. #428	C₂²×C₆₁	semidirect
703. C₂×#103	C₂²×C₆₁	semidirect
704. #405	C₂²×C₆₁	semidirect
706. C₆₁	#61557	direct (N × H)
940. SD₁₆	#41×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#3520	2
C₆₁×#3518	2
C₆₁×#3393	2
Q₈×SD₁₆×C₆₁	2
C₆₁×#3369	2
C₆₁×#3367	2
C₆₁×#3356	2
C₆₁×#3354	2
C₆₁×#3316	2
C₆₁×#3311	2
C₆₁×#3303	2
C₆₁×#3298	2
C₆₁×#3276	2
C₆₁×#3275	2
C₆₁×#3185	2
C₆₁×#3173	2
C₆₁×#3125	2
C₆₁×#3121	2
C₆₁×#3107	2
C₆₁×#3101	2
C₆₁×#2969	2
C₆₁×#2947	2
C₄×AGL(1,ℤ/8)×C₆₁	2
#61557	61

Subgroups — C61×#61557 #29564990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61557 #29564990