Subgroups — C₆₁×#61497 #29564930

Order 15616.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3520	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3344	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3299	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3296	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3266	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3178	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3121	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3120	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2947	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₁	C₂²	1	2	yes	—
25	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#557	—	2	1	no	—
27	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#556	—	2	1	no	—
30	C₆₁×#556	C₂²	1	1	yes	characteristic
31	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#554	C₂²	1	2	yes	—
33	C₆₁×#552	—	2	1	no	—
34	C₆₁×#552	—	2	2	no	—
35	C₆₁×#552	C₂²	1	2	yes	—
36	C₆₁×#551	—	2	2	no	—
37	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
38	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#548	—	2	1	no	—
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	C₂²	1	2	yes	—
45	C₆₁×#541	—	2	2	no	—
46	C₆₁×#541	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	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
59	C₆₁×#501	C₂²	1	2	yes	complemented
60	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#497	C₂²	1	2	yes	—
62	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#488	C₂²	1	2	yes	—
64	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
65	C₆₁×#487	C₂²	1	2	yes	complemented
66	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#485	C₂²	1	2	yes	complemented
68	C₆₁×#484	C₂²	1	2	yes	—
69	C₆₁×#484	C₂²	1	2	yes	complemented
70	C₆₁×#483	C₂²	1	2	yes	—
71	C₆₁×#483	C₂²	1	2	yes	complemented
72	C₆₁×#482	C₂²	1	2	yes	—
73	C₆₁×#479	C₂²	1	2	yes	complemented
74	C₆₁×#478	C₂²	1	2	yes	—
75	C₆₁×#477	C₂²	1	2	yes	complemented
76	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
77	C₆₁×#475	C₂²	1	2	yes	complemented
78	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
79	C₆₁×#474	C₂²	1	1	yes	characteristic
80	C₆₁×#474	C₂²	1	1	yes	characteristic
81	C₆₁×#470	C₂²	1	2	yes	complemented
82	C₆₁×#468	C₂²	1	2	yes	—
83	C₆₁×#467	C₂²	1	2	yes	—
84	C₆₁×#467	C₂²	1	2	yes	—
85	C₆₁×#467	C₂²	1	2	yes	complemented
86	C₆₁×#465	C₂²	1	2	yes	—
87	C₆₁×#464	C₂²	1	2	yes	—
88	C₆₁×#464	C₂²	1	2	yes	—
89	C₆₁×#462	C₂²	1	2	yes	complemented
90	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
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	2	yes	—
95	C₆₁×#452	C₂²	1	2	yes	—
96	C₆₁×#452	C₂²	1	2	yes	—
97	C₆₁×#451	C₂²	1	2	yes	—
98	C₆₁×#451	C₂²	1	2	yes	complemented
99	C₆₁×#450	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×#441	C₂²	1	2	yes	complemented
104	C₆₁×#441	C₂²	1	2	yes	complemented
105	C₆₁×#441	C₂²	1	2	yes	complemented
106	C₆₁×#440	C₂²	1	2	yes	—
107	C₆₁×#440	C₂²	1	2	yes	—
108	C₆₁×#440	C₂²	1	2	yes	—
109	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
110	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
112	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
121	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₆₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₆₁	C₂²	1	2	yes	—
124	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#433	C₂²	1	2	yes	complemented
126	C₆₁×#432	C₂²	1	1	yes	characteristic
127	C₆₁×#428	C₂²	1	2	yes	complemented
128	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
129	C₆₁×#416	C₂²	1	2	yes	—
130	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
131	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
133	C₆₁×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₆₁	—	2	1	no	—
138	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
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	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
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	—	2	4	no	—
148	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
156	C₂²×C₈×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	2	yes	—
164	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
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	2	no	—
176	#125×C₆₁	—	2	2	no	—
177	#125×C₆₁	—	2	2	no	—
178	#125×C₆₁	—	2	2	no	—
179	#125×C₆₁	—	2	2	no	—
180	#125×C₆₁	—	2	1	no	—
181	#125×C₆₁	—	2	1	no	—
182	#125×C₆₁	—	2	1	no	—
183	#125×C₆₁	D₄	1	1	yes	characteristic
184	#125×C₆₁	C₂³	1	2	yes	—
185	#124×C₆₁	—	2	1	no	—
186	#124×C₆₁	—	2	2	no	—
187	#124×C₆₁	D₄	1	1	yes	characteristic
188	#124×C₆₁	C₂³	1	2	yes	—
189	#123×C₆₁	—	2	2	no	—
190	#123×C₆₁	—	2	2	no	—
191	#123×C₆₁	—	2	2	no	—
192	#123×C₆₁	—	2	2	no	—
193	#123×C₆₁	—	2	2	no	—
194	#123×C₆₁	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₆₁	—	2	1	no	—
196	C₂²⋊Q₈×C₆₁	—	2	1	no	—
197	C₂²⋊Q₈×C₆₁	—	2	1	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	—	2	2	no	—
206	C₂²⋊Q₈×C₆₁	—	2	2	no	—
207	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
213	#121×C₆₁	—	2	1	no	—
214	#121×C₆₁	—	2	2	no	—
215	#121×C₆₁	D₄	1	1	yes	characteristic
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	1	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	—	2	1	no	—
225	C₄×Q₈×C₆₁	—	2	1	no	—
226	C₄×Q₈×C₆₁	—	2	1	no	—
227	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₆₁	—	2	2	no	—
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	—	2	2	no	—
240	C₄×D₄×C₆₁	—	2	2	no	—
241	C₄×D₄×C₆₁	—	2	2	no	—
242	C₄×D₄×C₆₁	—	2	1	no	—
243	C₄×D₄×C₆₁	—	2	1	no	—
244	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₁	C₂³	1	2	yes	—
246	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₁	C₂³	1	2	yes	—
250	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
251	#117×C₆₁	—	2	1	no	—
252	#117×C₆₁	—	2	1	no	—
253	#117×C₆₁	—	2	2	no	—
254	#117×C₆₁	—	2	1	no	—
255	#117×C₆₁	—	2	2	no	—
256	#117×C₆₁	—	2	2	no	—
257	#117×C₆₁	—	2	2	no	—
258	#117×C₆₁	C₂³	1	2	yes	—
259	#117×C₆₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
262	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
271	#107×C₆₁	C₂³	1	2	yes	—
272	#107×C₆₁	C₂³	1	2	yes	—
273	#107×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	1	yes	characteristic
275	#106×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	1	yes	characteristic
277	#106×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
286	#103×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	1	yes	characteristic
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	2	yes	—
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	#103×C₆₁	C₂³	1	2	yes	—
296	#103×C₆₁	C₂³	1	2	yes	—
297	#103×C₆₁	C₂³	1	2	yes	—
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	2	yes	—
308	#97×C₆₁	C₂³	1	2	yes	—
309	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	2	yes	—
314	C₂⁴×C₆₁	—	2	1	no	—
315	#41×C₆₁	—	2	4	no	—
316	#41×C₆₁	—	4	2	no	—
317	#41×C₆₁	—	8	2	no	—
318	C₂×Q₈×C₆₁	—	2	1	no	—
319	C₂×Q₈×C₆₁	—	2	2	no	—
320	C₂×Q₈×C₆₁	—	2	1	no	—
321	C₂×Q₈×C₆₁	—	2	1	no	—
322	C₂×Q₈×C₆₁	—	2	2	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	4	no	—
325	C₂×Q₈×C₆₁	—	4	1	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	1	yes	characteristic
331	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	2	2	no	—
335	C₂×D₄×C₆₁	—	2	2	no	—
336	C₂×D₄×C₆₁	—	2	1	no	—
337	C₂×D₄×C₆₁	—	4	1	no	—
338	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₆₁	—	2	1	no	—
343	C₂²×C₄×C₆₁	—	2	1	no	—
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	2	no	—
348	C₂²×C₄×C₆₁	—	2	1	no	—
349	C₂²×C₄×C₆₁	—	2	1	no	—
350	C₂²×C₄×C₆₁	—	2	2	no	—
351	C₂²×C₄×C₆₁	—	2	1	no	—
352	C₂²×C₄×C₆₁	—	2	1	no	—
353	C₂²×C₄×C₆₁	—	8	2	no	—
354	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
358	Q₁₆×C₆₁	—	2	4	no	—
359	Q₁₆×C₆₁	—	2	4	no	—
360	Q₁₆×C₆₁	—	4	2	no	—
361	Q₁₆×C₆₁	—	4	2	no	—
362	SD₁₆×C₆₁	—	2	2	no	—
363	SD₁₆×C₆₁	—	2	2	no	—
364	SD₁₆×C₆₁	—	2	4	no	—
365	SD₁₆×C₆₁	—	2	2	no	—
366	SD₁₆×C₆₁	—	4	2	no	—
367	SD₁₆×C₆₁	#41	1	4	yes	complemented
368	M₁₆×C₆₁	—	2	4	no	—
369	C₂×C₈×C₆₁	—	2	2	no	—
370	C₂×C₈×C₆₁	—	4	2	no	—
371	C₂×C₈×C₆₁	—	4	1	no	—
372	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
376	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
377	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₆₁	—	2	2	no	—
379	C₄⋊C₄×C₆₁	—	2	1	no	—
380	C₄⋊C₄×C₆₁	—	2	1	no	—
381	C₄⋊C₄×C₆₁	—	2	2	no	—
382	C₄⋊C₄×C₆₁	—	2	2	no	—
383	C₄⋊C₄×C₆₁	—	2	1	no	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	2	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	1	no	—
389	C₄⋊C₄×C₆₁	—	2	2	no	—
390	C₄⋊C₄×C₆₁	—	2	2	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	1	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	2	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	1	no	—
397	C₄⋊C₄×C₆₁	—	2	2	no	—
398	C₄⋊C₄×C₆₁	—	2	1	no	—
399	C₄⋊C₄×C₆₁	—	2	2	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	2	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	2	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	2	no	—
406	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₂²⋊C₄×C₆₁	—	2	2	no	—
420	C₂²⋊C₄×C₆₁	—	2	2	no	—
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	2	no	—
424	C₂²⋊C₄×C₆₁	—	2	1	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	1	no	—
427	C₂²⋊C₄×C₆₁	—	2	1	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	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	C₂×D₄	1	2	yes	—
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	C₄²×C₆₁	—	2	1	no	—
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	—	4	2	no	—
455	C₂³×C₆₁	—	4	2	no	—
456	C₂³×C₆₁	—	8	1	no	—
457	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
458	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₆₁	—	2	2	no	—
460	Q₈×C₆₁	—	2	1	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	1	no	—
466	Q₈×C₆₁	—	2	2	no	—
467	Q₈×C₆₁	—	4	4	no	—
468	Q₈×C₆₁	—	4	2	no	—
469	Q₈×C₆₁	—	4	2	no	—
470	Q₈×C₆₁	—	4	2	no	—
471	Q₈×C₆₁	—	8	2	no	—
472	Q₈×C₆₁	C₂×#41	1	2	yes	—
473	D₄×C₆₁	—	2	4	no	—
474	D₄×C₆₁	—	2	2	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	4	no	—
480	D₄×C₆₁	—	8	2	no	—
481	D₄×C₆₁	C₂×#41	1	2	yes	—
482	C₂×C₄×C₆₁	—	2	2	no	—
483	C₂×C₄×C₆₁	—	2	1	no	—
484	C₂×C₄×C₆₁	—	2	2	no	—
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	1	no	—
490	C₂×C₄×C₆₁	—	2	2	no	—
491	C₂×C₄×C₆₁	—	2	2	no	—
492	C₂×C₄×C₆₁	—	2	1	no	—
493	C₂×C₄×C₆₁	—	2	1	no	—
494	C₂×C₄×C₆₁	—	2	2	no	—
495	C₂×C₄×C₆₁	—	2	1	no	—
496	C₂×C₄×C₆₁	—	2	2	no	—
497	C₂×C₄×C₆₁	—	2	1	no	—
498	C₂×C₄×C₆₁	—	4	2	no	—
499	C₂×C₄×C₆₁	—	4	4	no	—
500	C₂×C₄×C₆₁	—	4	4	no	—
501	C₂×C₄×C₆₁	—	4	2	no	—
502	C₂×C₄×C₆₁	—	4	2	no	—
503	C₂×C₄×C₆₁	—	4	2	no	—
504	C₂×C₄×C₆₁	—	8	1	no	—
505	C₂×C₄×C₆₁	—	8	1	no	—
506	C₂×C₄×C₆₁	—	8	2	no	—
507	C₂×C₄×C₆₁	—	8	1	no	—
508	C₂×C₄×C₆₁	—	8	2	no	—
509	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
518	C₈×C₆₁	—	2	1	no	—
519	C₈×C₆₁	—	2	2	no	—
520	C₈×C₆₁	—	2	1	no	—
521	C₈×C₆₁	—	2	2	no	—
522	C₈×C₆₁	—	2	1	no	—
523	C₈×C₆₁	C₂×#41	1	2	yes	—
524	#61497	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
525	C₂²×C₆₁	—	2	1	no	—
526	C₂²×C₆₁	—	2	1	no	—
527	C₂²×C₆₁	—	2	2	no	—
528	C₂²×C₆₁	—	2	2	no	—
529	C₂²×C₆₁	—	2	2	no	—
530	C₂²×C₆₁	—	2	2	no	—
531	C₂²×C₆₁	—	4	1	no	—
532	C₂²×C₆₁	—	4	1	no	—
533	C₂²×C₆₁	—	4	1	no	—
534	C₂²×C₆₁	—	4	1	no	—
535	C₂²×C₆₁	—	4	1	no	—
536	C₂²×C₆₁	—	8	4	no	—
537	C₂²×C₆₁	#578	1	2	yes	—
538	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₆₁	—	2	2	no	—
540	C₄×C₆₁	—	2	1	no	—
541	C₄×C₆₁	—	2	2	no	—
542	C₄×C₆₁	—	2	1	no	—
543	C₄×C₆₁	—	2	2	no	—
544	C₄×C₆₁	—	2	1	no	—
545	C₄×C₆₁	—	2	1	no	—
546	C₄×C₆₁	—	2	2	no	—
547	C₄×C₆₁	—	4	2	no	—
548	C₄×C₆₁	—	4	1	no	—
549	C₄×C₆₁	—	4	2	no	—
550	C₄×C₆₁	—	4	1	no	—
551	C₄×C₆₁	—	4	1	no	—
552	C₄×C₆₁	—	4	2	no	—
553	C₄×C₆₁	—	4	2	no	—
554	C₄×C₆₁	—	4	1	no	—
555	C₄×C₆₁	—	4	1	no	—
556	C₄×C₆₁	#577	1	2	yes	—
557	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
558	C₄×C₆₁	#585	1	1	yes	characteristic
559	#3523	C₂×C₆₁	1	1	yes	characteristic, complemented
560	#3520	C₂×C₆₁	1	1	yes	characteristic
561	#3398	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3386	C₂×C₆₁	1	1	yes	characteristic, complemented
563	#3364	C₂×C₆₁	1	1	yes	characteristic, complemented
564	#3359	C₂×C₆₁	1	1	yes	characteristic, complemented
565	#3353	C₂×C₆₁	1	1	yes	characteristic, complemented
566	#3344	C₂×C₆₁	1	2	yes	complemented
567	#3302	C₂×C₆₁	1	1	yes	characteristic, complemented
568	#3299	C₂×C₆₁	1	2	yes	complemented
569	#3298	C₂×C₆₁	1	1	yes	characteristic, complemented
570	#3296	C₂×C₆₁	1	2	yes	complemented
571	#3276	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3266	C₂×C₆₁	1	2	yes	complemented
573	#3178	C₂×C₆₁	1	2	yes	complemented
574	#3170	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3121	C₂×C₆₁	1	2	yes	complemented
576	#3120	C₂×C₆₁	1	2	yes	complemented
577	#3113	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3110	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#2966	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#2947	C₂×C₆₁	1	2	yes	complemented
581	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
582	C₂×C₆₁	—	2	2	no	—
583	C₂×C₆₁	—	4	2	no	—
584	C₂×C₆₁	—	4	2	no	—
585	C₂×C₆₁	—	8	1	no	—
586	C₂×C₆₁	D₄×#41	1	1	yes	characteristic
587	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
588	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
589	C₂×#137	C₂²×C₆₁	1	2	yes	—
590	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
591	#557	—	2	1	no	—
592	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
593	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
594	#556	—	2	1	no	—
595	#556	C₂²×C₆₁	1	1	yes	characteristic
596	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
597	#554	C₂²×C₆₁	1	2	yes	—
598	#552	—	2	1	no	—
599	#552	—	2	2	no	—
600	#552	C₂²×C₆₁	1	2	yes	—
601	#551	—	2	2	no	—
602	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
603	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
604	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
605	#548	—	2	1	no	—
606	#547	C₂²×C₆₁	1	1	yes	characteristic
607	#547	C₂²×C₆₁	1	1	yes	characteristic
608	#546	C₂²×C₆₁	1	2	yes	—
609	#542	C₂²×C₆₁	1	2	yes	—
610	#541	—	2	2	no	—
611	#541	C₂²×C₆₁	1	2	yes	complemented
612	#539	—	2	2	no	—
613	#533	—	2	1	no	—
614	#533	C₂²×C₆₁	1	1	yes	characteristic
615	#533	C₂²×C₆₁	1	1	yes	characteristic
616	#529	—	2	1	no	—
617	#529	C₂²×C₆₁	1	1	yes	characteristic
618	#525	—	2	1	no	—
619	C₂×C₂²⋊Q₈	—	2	1	no	—
620	#520	C₂²×C₆₁	1	2	yes	—
621	#519	C₂²×C₆₁	1	2	yes	complemented
622	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
623	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
624	#501	C₂²×C₆₁	1	2	yes	complemented
625	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
626	#497	C₂²×C₆₁	1	2	yes	—
627	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
628	#488	C₂²×C₆₁	1	2	yes	—
629	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
630	#487	C₂²×C₆₁	1	2	yes	complemented
631	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
632	#485	C₂²×C₆₁	1	2	yes	complemented
633	#484	C₂²×C₆₁	1	2	yes	—
634	#484	C₂²×C₆₁	1	2	yes	complemented
635	#483	C₂²×C₆₁	1	2	yes	—
636	#483	C₂²×C₆₁	1	2	yes	complemented
637	#482	C₂²×C₆₁	1	2	yes	—
638	#479	C₂²×C₆₁	1	2	yes	complemented
639	#478	C₂²×C₆₁	1	2	yes	—
640	#477	C₂²×C₆₁	1	2	yes	complemented
641	#475	C₂²×C₆₁	1	2	yes	complemented
642	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
643	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
644	#474	C₂²×C₆₁	1	1	yes	characteristic
645	#474	C₂²×C₆₁	1	1	yes	characteristic
646	#470	C₂²×C₆₁	1	2	yes	complemented
647	#468	C₂²×C₆₁	1	2	yes	—
648	#467	C₂²×C₆₁	1	2	yes	—
649	#467	C₂²×C₆₁	1	2	yes	—
650	#467	C₂²×C₆₁	1	2	yes	complemented
651	#465	C₂²×C₆₁	1	2	yes	—
652	#464	C₂²×C₆₁	1	2	yes	—
653	#464	C₂²×C₆₁	1	2	yes	—
654	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
655	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
656	#462	C₂²×C₆₁	1	2	yes	complemented
657	#461	C₂²×C₆₁	1	1	yes	characteristic
658	#461	C₂²×C₆₁	1	2	yes	—
659	#461	C₂²×C₆₁	1	1	yes	characteristic
660	#452	C₂²×C₆₁	1	2	yes	—
661	#452	C₂²×C₆₁	1	2	yes	—
662	#451	C₂²×C₆₁	1	2	yes	—
663	#451	C₂²×C₆₁	1	2	yes	complemented
664	#450	C₂²×C₆₁	1	2	yes	—
665	#448	C₂²×C₆₁	1	2	yes	—
666	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
667	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
668	#441	C₂²×C₆₁	1	2	yes	complemented
669	#441	C₂²×C₆₁	1	2	yes	complemented
670	#441	C₂²×C₆₁	1	2	yes	complemented
671	#440	C₂²×C₆₁	1	2	yes	—
672	#440	C₂²×C₆₁	1	2	yes	—
673	#440	C₂²×C₆₁	1	2	yes	—
674	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
675	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
676	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
677	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
678	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
679	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
680	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
682	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
683	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
684	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
686	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
687	#435	C₂²×C₆₁	1	2	yes	—
688	C₈×D₄	C₂²×C₆₁	1	2	yes	—
689	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
690	#433	C₂²×C₆₁	1	2	yes	complemented
691	#432	C₂²×C₆₁	1	1	yes	characteristic
692	#428	C₂²×C₆₁	1	2	yes	complemented
693	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
694	#416	C₂²×C₆₁	1	2	yes	—
695	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
696	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
697	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
698	#405	C₂²×C₆₁	1	2	yes	complemented
699	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
700	C₆₁	#61497	1	1	yes	characteristic, direct product factor, Sylow
701	C₂×#41	—	2	1	no	—
702	C₂×#41	C₂³×C₆₁	1	2	yes	—
703	C₂²×Q₈	—	2	1	no	—
704	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
705	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
706	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
707	C₂³×C₄	—	2	1	no	—
708	#137	—	2	8	no	—
709	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
712	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
713	C₂×SD₁₆	—	2	4	no	—
714	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
717	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
720	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
721	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
722	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
723	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	—	2	2	no	—
727	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
730	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
731	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
732	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	D₄×C₆₁	1	2	yes	—
740	#125	—	2	1	no	—
741	#125	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	2	no	—
747	#125	—	2	1	no	—
748	#125	—	2	1	no	—
749	#125	D₄×C₆₁	1	1	yes	characteristic
750	#125	C₂³×C₆₁	1	2	yes	—
751	#124	—	2	1	no	—
752	#124	—	2	2	no	—
753	#124	D₄×C₆₁	1	1	yes	characteristic
754	#124	C₂³×C₆₁	1	2	yes	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	D₄×C₆₁	1	2	yes	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	D₄×C₆₁	1	1	yes	characteristic
782	#121	C₂³×C₆₁	1	2	yes	—
783	#120	—	2	2	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	2	no	—
786	C₄×Q₈	—	2	2	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
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	1	yes	characteristic
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₆₁	1	2	yes	—
815	C₄×D₄	C₂³×C₆₁	1	2	yes	—
816	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
817	#117	—	2	1	no	—
818	#117	—	2	1	no	—
819	#117	—	2	2	no	—
820	#117	—	2	1	no	—
821	#117	—	2	2	no	—
822	#117	—	2	2	no	—
823	#117	—	2	2	no	—
824	#117	C₂³×C₆₁	1	2	yes	—
825	#117	C₂³×C₆₁	1	2	yes	—
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	—	2	2	no	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
830	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
831	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
832	C₂×C₂²⋊C₄	—	2	1	no	—
833	C₂×C₂²⋊C₄	—	2	2	no	—
834	C₂×C₄²	—	2	1	no	—
835	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
836	#107	C₂³×C₆₁	1	2	yes	—
837	#107	C₂³×C₆₁	1	2	yes	—
838	#107	C₂³×C₆₁	1	2	yes	—
839	#107	C₂³×C₆₁	1	2	yes	—
840	#106	C₂³×C₆₁	1	1	yes	characteristic
841	#106	C₂³×C₆₁	1	1	yes	characteristic
842	#106	C₂³×C₆₁	1	1	yes	characteristic
843	#106	C₂³×C₆₁	1	1	yes	characteristic
844	#106	C₂³×C₆₁	1	2	yes	—
845	#106	C₂³×C₆₁	1	2	yes	—
846	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
849	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
850	#103	C₂³×C₆₁	1	1	yes	characteristic
851	#103	C₂³×C₆₁	1	1	yes	characteristic
852	#103	C₂³×C₆₁	1	1	yes	characteristic
853	#103	C₂³×C₆₁	1	1	yes	characteristic
854	#103	C₂³×C₆₁	1	2	yes	—
855	#103	C₂³×C₆₁	1	2	yes	—
856	#103	C₂³×C₆₁	1	2	yes	—
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	2	yes	—
863	#103	C₂³×C₆₁	1	2	yes	—
864	#102	C₂³×C₆₁	1	1	yes	characteristic
865	#102	C₂³×C₆₁	1	1	yes	characteristic
866	#102	C₂³×C₆₁	1	1	yes	characteristic
867	#102	C₂³×C₆₁	1	1	yes	characteristic
868	#102	C₂³×C₆₁	1	2	yes	—
869	#102	C₂³×C₆₁	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
873	#97	C₂³×C₆₁	1	2	yes	—
874	#97	C₂³×C₆₁	1	2	yes	—
875	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₆₁	1	2	yes	—
880	C₂⁴	—	2	1	no	—
881	#41	—	2	4	no	—
882	#41	—	4	2	no	—
883	#41	—	8	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	4	no	—
891	C₂×Q₈	—	4	1	no	—
892	C₂×Q₈	—	4	2	no	—
893	C₂×Q₈	—	8	2	no	—
894	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
896	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
898	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	4	1	no	—
904	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
905	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
906	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
907	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	8	2	no	—
920	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
921	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
924	Q₁₆	—	2	4	no	—
925	Q₁₆	—	2	4	no	—
926	Q₁₆	—	4	2	no	—
927	Q₁₆	—	4	2	no	—
928	SD₁₆	—	2	2	no	—
929	SD₁₆	—	2	2	no	—
930	SD₁₆	—	2	4	no	—
931	SD₁₆	—	2	2	no	—
932	SD₁₆	—	4	2	no	—
933	SD₁₆	#41×C₆₁	1	4	yes	complemented
934	M₁₆	—	2	4	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	4	2	no	—
937	C₂×C₈	—	4	1	no	—
938	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
942	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
943	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	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	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
973	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
974	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
977	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1014	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1016	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1017	C₄²	C₂⁴×C₆₁	1	2	yes	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	4	2	no	—
1021	C₂³	—	4	2	no	—
1022	C₂³	—	8	1	no	—
1023	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1024	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	2	no	—
1031	Q₈	—	2	1	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	4	4	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	4	2	no	—
1036	Q₈	—	4	2	no	—
1037	Q₈	—	8	2	no	—
1038	Q₈	C₂×#41×C₆₁	1	2	yes	—
1039	D₄	—	2	4	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	8	2	no	—
1047	D₄	C₂×#41×C₆₁	1	2	yes	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	4	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	—	8	1	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1078	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1080	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1083	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1084	C₈	—	2	1	no	—
1085	C₈	—	2	2	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	2	no	—
1088	C₈	—	2	1	no	—
1089	C₈	C₂×#41×C₆₁	1	2	yes	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	8	4	no	—
1102	C₂²	C₆₁×#578	1	2	yes	—
1103	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1104	C₄	—	2	1	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	C₆₁×#577	1	2	yes	—
1122	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1123	C₄	C₆₁×#585	1	1	yes	characteristic
1124	C₂	—	2	2	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	4	2	no	—
1127	C₂	—	8	1	no	—
1128	C₂	D₄×#41×C₆₁	1	1	yes	characteristic
1129	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1130	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3520	C₂
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×#3523	C₂	semidirect
3. C₆₁×#3398	C₂	semidirect
4. C₆₁×#3386	C₂	semidirect
5. C₆₁×#3364	C₂	semidirect
6. C₆₁×#3359	C₂	semidirect
7. C₆₁×#3353	C₂	semidirect
8. C₆₁×#3344	C₂	semidirect
9. C₆₁×#3302	C₂	semidirect
10. C₆₁×#3299	C₂	semidirect
11. C₆₁×#3298	C₂	semidirect
12. C₆₁×#3296	C₂	semidirect
13. C₆₁×#3276	C₂	semidirect
14. C₆₁×#3266	C₂	semidirect
15. C₆₁×#3178	C₂	semidirect
16. C₆₁×#3170	C₂	semidirect
17. C₆₁×#3121	C₂	semidirect
18. C₆₁×#3120	C₂	semidirect
19. C₆₁×#3113	C₂	semidirect
20. C₆₁×#3110	C₂	semidirect
21. C₆₁×#2966	C₂	semidirect
22. C₆₁×#2947	C₂	semidirect
23. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
27. C₆₁×#557	C₂²	semidirect
28. C₆₁×#557	C₂²	semidirect
31. C₆₁×#556	C₂²	semidirect
39. D₄×Q₈×C₆₁	C₂²	semidirect
46. C₆₁×#541	C₂²	semidirect
56. C₆₁×#519	C₂²	semidirect
59. C₆₁×#501	C₂²	semidirect
60. C₆₁×#500	C₂²	semidirect
62. C₆₁×#494	C₂²	semidirect
64. C₆₁×#487	C₂²	semidirect
65. C₆₁×#487	C₂²	semidirect
66. C₆₁×#487	C₂²	semidirect
67. C₆₁×#485	C₂²	semidirect
69. C₆₁×#484	C₂²	semidirect
71. C₆₁×#483	C₂²	semidirect
73. C₆₁×#479	C₂²	semidirect
75. C₆₁×#477	C₂²	semidirect
76. C₆₁×#475	C₂²	semidirect
77. C₆₁×#475	C₂²	semidirect
78. C₆₁×#475	C₂²	semidirect
81. C₆₁×#470	C₂²	semidirect
85. C₆₁×#467	C₂²	semidirect
89. C₆₁×#462	C₂²	semidirect
90. C₆₁×#462	C₂²	semidirect
91. C₆₁×#462	C₂²	semidirect
98. C₆₁×#451	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₈×Q₈×C₆₁	C₂²	semidirect
103. C₆₁×#441	C₂²	semidirect
104. C₆₁×#441	C₂²	semidirect
105. C₆₁×#441	C₂²	semidirect
109. C₄×Q₁₆×C₆₁	C₂²	semidirect
110. C₄×Q₁₆×C₆₁	C₂²	semidirect
111. C₄×Q₁₆×C₆₁	C₂²	semidirect
121. C₆₁×#436	C₂²	semidirect
124. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#433	C₂²	semidirect
127. C₆₁×#428	C₂²	semidirect
131. C₂×#103×C₆₁	C₂²	semidirect
133. C₆₁×#405	C₂²	semidirect
367. SD₁₆×C₆₁	#41	semidirect
524. #61497	C₆₁	direct (N × H)
559. #3523	C₂×C₆₁	semidirect
561. #3398	C₂×C₆₁	semidirect
562. #3386	C₂×C₆₁	semidirect
563. #3364	C₂×C₆₁	semidirect
564. #3359	C₂×C₆₁	semidirect
565. #3353	C₂×C₆₁	semidirect
566. #3344	C₂×C₆₁	semidirect
567. #3302	C₂×C₆₁	semidirect
568. #3299	C₂×C₆₁	semidirect
569. #3298	C₂×C₆₁	semidirect
570. #3296	C₂×C₆₁	semidirect
571. #3276	C₂×C₆₁	semidirect
572. #3266	C₂×C₆₁	semidirect
573. #3178	C₂×C₆₁	semidirect
574. #3170	C₂×C₆₁	semidirect
575. #3121	C₂×C₆₁	semidirect
576. #3120	C₂×C₆₁	semidirect
577. #3113	C₂×C₆₁	semidirect
578. #3110	C₂×C₆₁	semidirect
579. #2966	C₂×C₆₁	semidirect
580. #2947	C₂×C₆₁	semidirect
581. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
592. #557	C₂²×C₆₁	semidirect
593. #557	C₂²×C₆₁	semidirect
596. #556	C₂²×C₆₁	semidirect
604. D₄×Q₈	C₂²×C₆₁	semidirect
611. #541	C₂²×C₆₁	semidirect
621. #519	C₂²×C₆₁	semidirect
624. #501	C₂²×C₆₁	semidirect
625. #500	C₂²×C₆₁	semidirect
627. #494	C₂²×C₆₁	semidirect
629. #487	C₂²×C₆₁	semidirect
630. #487	C₂²×C₆₁	semidirect
631. #487	C₂²×C₆₁	semidirect
632. #485	C₂²×C₆₁	semidirect
634. #484	C₂²×C₆₁	semidirect
636. #483	C₂²×C₆₁	semidirect
638. #479	C₂²×C₆₁	semidirect
640. #477	C₂²×C₆₁	semidirect
641. #475	C₂²×C₆₁	semidirect
642. #475	C₂²×C₆₁	semidirect
643. #475	C₂²×C₆₁	semidirect
646. #470	C₂²×C₆₁	semidirect
650. #467	C₂²×C₆₁	semidirect
654. #462	C₂²×C₆₁	semidirect
655. #462	C₂²×C₆₁	semidirect
656. #462	C₂²×C₆₁	semidirect
663. #451	C₂²×C₆₁	semidirect
666. #446	C₂²×C₆₁	semidirect
667. C₈×Q₈	C₂²×C₆₁	semidirect
668. #441	C₂²×C₆₁	semidirect
669. #441	C₂²×C₆₁	semidirect
670. #441	C₂²×C₆₁	semidirect
674. C₄×Q₁₆	C₂²×C₆₁	semidirect
675. C₄×Q₁₆	C₂²×C₆₁	semidirect
676. C₄×Q₁₆	C₂²×C₆₁	semidirect
686. #436	C₂²×C₆₁	semidirect
689. C₈×D₄	C₂²×C₆₁	semidirect
690. #433	C₂²×C₆₁	semidirect
692. #428	C₂²×C₆₁	semidirect
696. C₂×#103	C₂²×C₆₁	semidirect
698. #405	C₂²×C₆₁	semidirect
700. C₆₁	#61497	direct (N × H)
933. 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×#3523	2
C₆₁×#3520	2
C₆₁×#3398	2
C₆₁×#3386	2
C₆₁×#3364	2
C₆₁×#3359	2
C₆₁×#3353	2
C₆₁×#3344	2
C₆₁×#3302	2
C₆₁×#3299	2
C₆₁×#3298	2
C₆₁×#3296	2
C₆₁×#3276	2
C₆₁×#3266	2
C₆₁×#3178	2
C₆₁×#3170	2
C₆₁×#3121	2
C₆₁×#3120	2
C₆₁×#3113	2
C₆₁×#3110	2
C₆₁×#2966	2
C₆₁×#2947	2
C₂×C₄×SD₁₆×C₆₁	2
#61497	61

Subgroups — C61×#61497 #29564930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61497 #29564930