Subgroups — C₆₁×#61815 #29565248

Order 15616.

1788 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3350	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3345	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3311	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3306	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3238	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3204	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3198	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3099	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3096	C₂	1	2	yes	maximal, complemented
23	C₆₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#560	—	2	2	no	—
25	C₆₁×#556	C₂²	1	1	yes	characteristic
26	C₆₁×#556	C₂²	1	2	yes	complemented
27	C₆₁×#555	C₂²	1	1	yes	characteristic
28	C₆₁×#555	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#554	C₂²	1	1	yes	characteristic
30	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#553	—	2	1	no	—
32	C₆₁×#553	—	2	1	no	—
33	C₆₁×#553	C₂²	1	2	yes	—
34	C₆₁×#550	—	2	1	no	—
35	C₆₁×#550	C₂²	1	1	yes	characteristic
36	C₆₁×#548	—	2	2	no	—
37	C₆₁×#547	C₂²	1	1	yes	characteristic
38	C₆₁×#547	C₂²	1	2	yes	complemented
39	C₆₁×#546	—	2	1	no	—
40	C₆₁×#546	C₂²	1	2	yes	—
41	D₄²×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#542	—	2	1	no	—
43	C₆₁×#542	—	2	2	no	—
44	C₆₁×#538	—	2	2	no	—
45	C₆₁×#537	C₂²	1	2	yes	—
46	C₆₁×#537	C₂²	1	2	yes	complemented
47	C₆₁×#535	—	2	1	no	—
48	C₆₁×#535	C₂²	1	2	yes	—
49	C₆₁×#533	—	2	1	no	—
50	C₆₁×#532	—	2	1	no	—
51	C₆₁×#532	C₂²	1	1	yes	characteristic
52	C₆₁×#532	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
54	C₆₁×#529	C₂²	1	1	yes	characteristic
55	C₆₁×#520	C₂²	1	2	yes	complemented
56	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
57	C₆₁×#501	C₂²	1	2	yes	complemented
58	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
59	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#489	C₂²	1	2	yes	—
61	C₆₁×#486	C₂²	1	1	yes	characteristic
62	C₆₁×#486	C₂²	1	1	yes	characteristic
63	C₆₁×#485	C₂²	1	2	yes	complemented
64	C₆₁×#485	C₂²	1	2	yes	complemented
65	C₆₁×#485	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#483	C₂²	1	2	yes	complemented
67	C₆₁×#483	C₂²	1	2	yes	complemented
68	C₆₁×#483	C₂²	1	2	yes	complemented
69	C₆₁×#482	C₂²	1	2	yes	—
70	C₆₁×#482	C₂²	1	2	yes	—
71	C₆₁×#482	C₂²	1	1	yes	characteristic
72	C₆₁×#482	C₂²	1	2	yes	complemented
73	C₆₁×#482	C₂²	1	2	yes	complemented
74	C₆₁×#482	C₂²	1	2	yes	complemented
75	C₆₁×#481	C₂²	1	2	yes	—
76	C₆₁×#481	C₂²	1	2	yes	—
77	C₆₁×#481	C₂²	1	2	yes	complemented
78	C₆₁×#481	C₂²	1	2	yes	complemented
79	C₆₁×#481	C₂²	1	2	yes	complemented
80	C₆₁×#480	C₂²	1	2	yes	—
81	C₆₁×#480	C₂²	1	2	yes	complemented
82	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
83	C₆₁×#478	C₂²	1	1	yes	characteristic, complemented
84	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
85	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
86	C₆₁×#476	C₂²	1	1	yes	characteristic
87	C₆₁×#476	C₂²	1	1	yes	characteristic
88	C₆₁×#476	C₂²	1	2	yes	complemented
89	C₆₁×#476	C₂²	1	2	yes	complemented
90	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
91	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#470	C₂²	1	2	yes	complemented
93	C₆₁×#469	C₂²	1	2	yes	—
94	C₆₁×#469	C₂²	1	2	yes	—
95	C₆₁×#468	C₂²	1	2	yes	complemented
96	C₆₁×#466	C₂²	1	2	yes	complemented
97	C₆₁×#465	C₂²	1	2	yes	—
98	C₆₁×#465	C₂²	1	2	yes	—
99	C₆₁×#465	C₂²	1	2	yes	complemented
100	C₆₁×#464	C₂²	1	1	yes	characteristic
101	C₆₁×#463	C₂²	1	1	yes	characteristic
102	C₆₁×#460	C₂²	1	1	yes	characteristic
103	C₆₁×#459	C₂²	1	1	yes	characteristic
104	C₆₁×#452	C₂²	1	2	yes	complemented
105	C₆₁×#452	C₂²	1	1	yes	characteristic, complemented
106	C₆₁×#450	C₂²	1	2	yes	—
107	C₆₁×#449	C₂²	1	1	yes	characteristic
108	C₆₁×#449	C₂²	1	2	yes	complemented
109	C₆₁×#449	C₂²	1	2	yes	complemented
110	C₆₁×#447	C₂²	1	2	yes	—
111	C₆₁×#442	C₂²	1	2	yes	complemented
112	C₆₁×#440	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
117	C₆₁×#436	C₂²	1	1	yes	characteristic
118	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
119	C₆₁×#435	C₂²	1	2	yes	complemented
120	C₆₁×#435	C₂²	1	2	yes	complemented
121	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₆₁×#432	C₂²	1	1	yes	characteristic, complemented
124	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#428	C₂²	1	2	yes	complemented
126	C₆₁×#428	C₂²	1	2	yes	complemented
127	C₆₁×#427	C₂²	1	2	yes	complemented
128	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
129	C₆₁×#418	C₂²	1	2	yes	—
130	C₆₁×#417	C₂²	1	2	yes	complemented
131	C₆₁×#416	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₁	C₂²	1	2	yes	—
133	C₆₁×#408	C₂²	1	2	yes	complemented
134	C₆₁×#408	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	2	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	—	2	1	no	—
138	C₂×#41×C₆₁	C₂³	1	2	yes	—
139	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
140	C₂×#41×C₆₁	C₂³	1	2	yes	—
141	C₂²×Q₈×C₆₁	—	2	1	no	—
142	C₂²×D₄×C₆₁	—	2	1	no	—
143	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₆₁	C₂³	1	2	yes	—
150	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₆₁	—	2	1	no	—
155	C₄⋊Q₈×C₆₁	—	2	1	no	—
156	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
157	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
161	#127×C₆₁	—	2	1	no	—
162	#127×C₆₁	—	2	2	no	—
163	#127×C₆₁	D₄	1	1	yes	characteristic
164	#127×C₆₁	C₂³	1	1	yes	characteristic
165	#126×C₆₁	—	2	2	no	—
166	#126×C₆₁	—	2	2	no	—
167	#126×C₆₁	—	2	2	no	—
168	#126×C₆₁	—	2	2	no	—
169	#126×C₆₁	—	2	1	no	—
170	#125×C₆₁	—	2	1	no	—
171	#125×C₆₁	—	2	1	no	—
172	#125×C₆₁	C₂³	1	1	yes	characteristic
173	#124×C₆₁	—	2	2	no	—
174	#124×C₆₁	—	2	2	no	—
175	#124×C₆₁	—	2	1	no	—
176	#124×C₆₁	—	2	2	no	—
177	#124×C₆₁	—	2	2	no	—
178	#124×C₆₁	—	2	1	no	—
179	#124×C₆₁	D₄	1	2	yes	—
180	#124×C₆₁	C₂³	1	1	yes	characteristic
181	#123×C₆₁	—	2	1	no	—
182	#123×C₆₁	—	2	2	no	—
183	#123×C₆₁	—	2	2	no	—
184	#123×C₆₁	—	2	2	no	—
185	#123×C₆₁	—	2	2	no	—
186	#123×C₆₁	—	2	2	no	—
187	C₂²⋊Q₈×C₆₁	—	2	2	no	—
188	C₂²⋊Q₈×C₆₁	—	2	2	no	—
189	C₂²⋊Q₈×C₆₁	—	2	2	no	—
190	C₂²⋊Q₈×C₆₁	—	2	1	no	—
191	C₂²⋊Q₈×C₆₁	—	2	2	no	—
192	C₂²⋊Q₈×C₆₁	—	2	2	no	—
193	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
194	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
197	#121×C₆₁	—	2	2	no	—
198	#121×C₆₁	—	2	1	no	—
199	#121×C₆₁	—	2	1	no	—
200	#121×C₆₁	—	2	2	no	—
201	#121×C₆₁	—	2	2	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	—	2	2	no	—
204	#121×C₆₁	—	2	2	no	—
205	#121×C₆₁	—	2	2	no	—
206	#121×C₆₁	—	2	1	no	—
207	#121×C₆₁	—	2	1	no	—
208	#121×C₆₁	—	2	2	no	—
209	#121×C₆₁	—	2	2	no	—
210	#121×C₆₁	D₄	1	1	yes	characteristic
211	#121×C₆₁	D₄	1	2	yes	—
212	#121×C₆₁	D₄	1	1	yes	characteristic
213	#121×C₆₁	C₂³	1	2	yes	—
214	#121×C₆₁	C₂³	1	1	yes	characteristic
215	#121×C₆₁	C₂³	1	2	yes	—
216	#121×C₆₁	C₂³	1	2	yes	—
217	#121×C₆₁	C₂³	1	2	yes	—
218	#121×C₆₁	C₂³	1	2	yes	—
219	#121×C₆₁	C₂³	1	2	yes	—
220	#120×C₆₁	—	2	2	no	—
221	#120×C₆₁	—	2	2	no	—
222	#120×C₆₁	—	2	2	no	—
223	#120×C₆₁	—	2	2	no	—
224	C₄×Q₈×C₆₁	—	2	2	no	—
225	C₄×Q₈×C₆₁	—	2	2	no	—
226	C₄×Q₈×C₆₁	—	2	1	no	—
227	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₆₁	—	2	2	no	—
231	C₄×D₄×C₆₁	—	2	1	no	—
232	C₄×D₄×C₆₁	—	2	1	no	—
233	C₄×D₄×C₆₁	—	2	2	no	—
234	C₄×D₄×C₆₁	—	2	2	no	—
235	C₄×D₄×C₆₁	—	2	1	no	—
236	C₄×D₄×C₆₁	—	2	1	no	—
237	C₄×D₄×C₆₁	—	2	1	no	—
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	—	2	2	no	—
240	C₄×D₄×C₆₁	—	2	1	no	—
241	C₄×D₄×C₆₁	C₂³	1	2	yes	—
242	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₁	C₂³	1	2	yes	—
247	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
248	#117×C₆₁	—	2	1	no	—
249	#117×C₆₁	—	2	1	no	—
250	#117×C₆₁	—	2	1	no	—
251	#117×C₆₁	—	2	1	no	—
252	#117×C₆₁	C₂³	1	2	yes	—
253	#117×C₆₁	C₂³	1	2	yes	—
254	#117×C₆₁	C₂³	1	2	yes	—
255	#117×C₆₁	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
261	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
262	C₂×C₄²×C₆₁	—	2	1	no	—
263	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
264	#107×C₆₁	C₂³	1	2	yes	—
265	#107×C₆₁	C₂³	1	2	yes	—
266	#107×C₆₁	C₂³	1	1	yes	characteristic
267	#107×C₆₁	C₂³	1	1	yes	characteristic
268	#107×C₆₁	C₂³	1	2	yes	—
269	#106×C₆₁	C₂³	1	1	yes	characteristic
270	#106×C₆₁	C₂³	1	2	yes	—
271	#106×C₆₁	C₂³	1	2	yes	—
272	#106×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	1	yes	characteristic
274	#106×C₆₁	C₂³	1	2	yes	—
275	#106×C₆₁	C₂³	1	2	yes	—
276	#106×C₆₁	C₂³	1	2	yes	—
277	#106×C₆₁	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	#103×C₆₁	C₂³	1	1	yes	characteristic
283	#103×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	1	yes	characteristic
287	#103×C₆₁	C₂³	1	1	yes	characteristic
288	#103×C₆₁	C₂³	1	2	yes	—
289	#102×C₆₁	C₂³	1	1	yes	characteristic
290	#102×C₆₁	C₂³	1	2	yes	—
291	#102×C₆₁	C₂³	1	2	yes	—
292	#102×C₆₁	C₂³	1	2	yes	—
293	#102×C₆₁	C₂³	1	2	yes	—
294	#102×C₆₁	C₂³	1	2	yes	—
295	#102×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	1	yes	characteristic
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
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	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
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	C₂⁴×C₆₁	—	2	2	no	—
313	#41×C₆₁	—	4	2	no	—
314	#41×C₆₁	—	4	2	no	—
315	#41×C₆₁	—	4	1	no	—
316	#41×C₆₁	—	4	1	no	—
317	#41×C₆₁	—	4	2	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	8	2	no	—
320	#41×C₆₁	—	8	2	no	—
321	#41×C₆₁	—	8	4	no	—
322	C₂×Q₈×C₆₁	—	2	1	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	1	no	—
325	C₂×Q₈×C₆₁	—	2	1	no	—
326	C₂×Q₈×C₆₁	—	8	2	no	—
327	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
328	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₆₁	—	2	1	no	—
331	C₂×D₄×C₆₁	—	2	1	no	—
332	C₂×D₄×C₆₁	—	2	2	no	—
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	2	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	1	no	—
340	C₂×D₄×C₆₁	—	2	1	no	—
341	C₂×D₄×C₆₁	—	2	2	no	—
342	C₂×D₄×C₆₁	—	4	2	no	—
343	C₂×D₄×C₆₁	—	4	2	no	—
344	C₂×D₄×C₆₁	—	8	2	no	—
345	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₆₁	—	2	2	no	—
355	C₂²×C₄×C₆₁	—	2	2	no	—
356	C₂²×C₄×C₆₁	—	2	2	no	—
357	C₂²×C₄×C₆₁	—	2	2	no	—
358	C₂²×C₄×C₆₁	—	2	1	no	—
359	C₂²×C₄×C₆₁	—	2	1	no	—
360	C₂²×C₄×C₆₁	—	2	1	no	—
361	C₂²×C₄×C₆₁	—	2	1	no	—
362	C₂²×C₄×C₆₁	—	2	2	no	—
363	C₂²×C₄×C₆₁	—	2	2	no	—
364	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
369	Q₁₆×C₆₁	—	4	1	no	—
370	SD₁₆×C₆₁	—	4	1	no	—
371	SD₁₆×C₆₁	—	4	1	no	—
372	SD₁₆×C₆₁	—	4	2	no	—
373	D₈×C₆₁	—	4	2	no	—
374	D₈×C₆₁	—	4	1	no	—
375	M₁₆×C₆₁	—	4	2	no	—
376	M₁₆×C₆₁	—	4	2	no	—
377	C₂×C₈×C₆₁	—	4	2	no	—
378	C₂×C₈×C₆₁	—	4	2	no	—
379	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
384	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	—	2	2	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	1	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	1	no	—
397	C₄⋊C₄×C₆₁	—	2	1	no	—
398	C₄⋊C₄×C₆₁	—	2	2	no	—
399	C₄⋊C₄×C₆₁	—	2	2	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	1	no	—
402	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₆₁	—	2	2	no	—
413	C₂²⋊C₄×C₆₁	—	2	1	no	—
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	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	1	no	—
423	C₂²⋊C₄×C₆₁	—	2	1	no	—
424	C₂²⋊C₄×C₆₁	—	2	1	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	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	1	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	C₄²×C₆₁	—	2	1	no	—
438	C₄²×C₆₁	—	2	1	no	—
439	C₄²×C₆₁	—	2	1	no	—
440	C₄²×C₆₁	—	2	2	no	—
441	C₄²×C₆₁	—	2	2	no	—
442	C₄²×C₆₁	—	2	1	no	—
443	C₄²×C₆₁	—	2	2	no	—
444	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
447	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
448	C₂³×C₆₁	—	2	1	no	—
449	C₂³×C₆₁	—	2	1	no	—
450	C₂³×C₆₁	—	2	2	no	—
451	C₂³×C₆₁	—	8	2	no	—
452	C₂³×C₆₁	—	8	2	no	—
453	C₂³×C₆₁	—	8	2	no	—
454	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
455	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
456	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
457	Q₈×C₆₁	—	2	1	no	—
458	Q₈×C₆₁	—	2	1	no	—
459	Q₈×C₆₁	—	2	1	no	—
460	Q₈×C₆₁	—	2	1	no	—
461	Q₈×C₆₁	—	4	2	no	—
462	Q₈×C₆₁	—	4	4	no	—
463	Q₈×C₆₁	—	4	2	no	—
464	Q₈×C₆₁	—	8	1	no	—
465	Q₈×C₆₁	—	8	1	no	—
466	D₄×C₆₁	—	2	2	no	—
467	D₄×C₆₁	—	2	2	no	—
468	D₄×C₆₁	—	2	1	no	—
469	D₄×C₆₁	—	2	1	no	—
470	D₄×C₆₁	—	2	1	no	—
471	D₄×C₆₁	—	2	2	no	—
472	D₄×C₆₁	—	2	1	no	—
473	D₄×C₆₁	—	2	2	no	—
474	D₄×C₆₁	—	4	2	no	—
475	D₄×C₆₁	—	4	2	no	—
476	D₄×C₆₁	—	4	2	no	—
477	D₄×C₆₁	—	4	2	no	—
478	D₄×C₆₁	—	4	2	no	—
479	D₄×C₆₁	—	4	2	no	—
480	D₄×C₆₁	—	8	1	no	—
481	D₄×C₆₁	—	8	2	no	—
482	D₄×C₆₁	—	8	1	no	—
483	D₄×C₆₁	—	8	2	no	—
484	D₄×C₆₁	—	8	2	no	—
485	D₄×C₆₁	—	8	2	no	—
486	D₄×C₆₁	—	8	2	no	—
487	D₄×C₆₁	—	8	2	no	—
488	D₄×C₆₁	—	8	2	no	—
489	D₄×C₆₁	—	8	2	no	—
490	C₂×C₄×C₆₁	—	2	2	no	—
491	C₂×C₄×C₆₁	—	2	2	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	1	no	—
498	C₂×C₄×C₆₁	—	2	1	no	—
499	C₂×C₄×C₆₁	—	2	1	no	—
500	C₂×C₄×C₆₁	—	2	1	no	—
501	C₂×C₄×C₆₁	—	2	1	no	—
502	C₂×C₄×C₆₁	—	2	2	no	—
503	C₂×C₄×C₆₁	—	2	2	no	—
504	C₂×C₄×C₆₁	—	2	2	no	—
505	C₂×C₄×C₆₁	—	2	1	no	—
506	C₂×C₄×C₆₁	—	4	1	no	—
507	C₂×C₄×C₆₁	—	4	2	no	—
508	C₂×C₄×C₆₁	—	4	2	no	—
509	C₂×C₄×C₆₁	—	4	2	no	—
510	C₂×C₄×C₆₁	—	4	2	no	—
511	C₂×C₄×C₆₁	—	8	2	no	—
512	C₂×C₄×C₆₁	—	8	2	no	—
513	C₂×C₄×C₆₁	—	8	2	no	—
514	C₂×C₄×C₆₁	—	8	2	no	—
515	C₂×C₄×C₆₁	—	8	2	no	—
516	C₂×C₄×C₆₁	—	8	2	no	—
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	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
525	C₈×C₆₁	—	2	1	no	—
526	C₈×C₆₁	—	2	1	no	—
527	C₈×C₆₁	—	2	2	no	—
528	C₈×C₆₁	—	2	2	no	—
529	C₈×C₆₁	—	2	1	no	—
530	C₈×C₆₁	—	2	1	no	—
531	#61815	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
532	C₂²×C₆₁	—	2	1	no	—
533	C₂²×C₆₁	—	2	2	no	—
534	C₂²×C₆₁	—	2	2	no	—
535	C₂²×C₆₁	—	2	1	no	—
536	C₂²×C₆₁	—	2	2	no	—
537	C₂²×C₆₁	—	2	2	no	—
538	C₂²×C₆₁	—	2	1	no	—
539	C₂²×C₆₁	—	2	2	no	—
540	C₂²×C₆₁	—	2	2	no	—
541	C₂²×C₆₁	—	4	1	no	—
542	C₂²×C₆₁	—	4	2	no	—
543	C₂²×C₆₁	—	4	1	no	—
544	C₂²×C₆₁	—	4	1	no	—
545	C₂²×C₆₁	—	4	2	no	—
546	C₂²×C₆₁	—	4	1	no	—
547	C₂²×C₆₁	—	4	1	no	—
548	C₂²×C₆₁	—	4	1	no	—
549	C₂²×C₆₁	—	4	2	no	—
550	C₂²×C₆₁	—	16	4	no	—
551	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₆₁	—	2	1	no	—
553	C₄×C₆₁	—	2	1	no	—
554	C₄×C₆₁	—	2	1	no	—
555	C₄×C₆₁	—	2	2	no	—
556	C₄×C₆₁	—	2	2	no	—
557	C₄×C₆₁	—	2	1	no	—
558	C₄×C₆₁	—	4	1	no	—
559	C₄×C₆₁	—	4	2	no	—
560	C₄×C₆₁	—	4	2	no	—
561	C₄×C₆₁	—	4	1	no	—
562	C₄×C₆₁	—	4	1	no	—
563	C₄×C₆₁	—	4	1	no	—
564	C₄×C₆₁	—	4	1	no	—
565	C₄×C₆₁	—	4	1	no	—
566	C₄×C₆₁	—	4	2	no	—
567	C₄×C₆₁	#577	1	2	yes	—
568	C₄×C₆₁	#585	1	1	yes	characteristic
569	C₄×C₆₁	#585	1	1	yes	characteristic
570	#3546	C₂×C₆₁	1	1	yes	characteristic, complemented
571	#3511	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3356	C₂×C₆₁	1	1	yes	characteristic, complemented
573	#3354	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3350	C₂×C₆₁	1	2	yes	complemented
575	#3345	C₂×C₆₁	1	2	yes	complemented
576	#3340	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3335	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3333	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3325	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#3311	C₂×C₆₁	1	2	yes	complemented
581	#3306	C₂×C₆₁	1	2	yes	complemented
582	#3305	C₂×C₆₁	1	1	yes	characteristic, complemented
583	#3295	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3238	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#3227	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#3204	C₂×C₆₁	1	2	yes	complemented
587	#3198	C₂×C₆₁	1	2	yes	complemented
588	#3115	C₂×C₆₁	1	1	yes	characteristic, complemented
589	#3102	C₂×C₆₁	1	1	yes	characteristic, complemented
590	#3099	C₂×C₆₁	1	2	yes	complemented
591	#3096	C₂×C₆₁	1	2	yes	complemented
592	#2981	C₂×C₆₁	1	1	yes	characteristic, complemented
593	C₂×C₆₁	—	4	1	no	—
594	C₂×C₆₁	—	4	2	no	—
595	C₂×C₆₁	—	4	2	no	—
596	C₂×C₆₁	—	8	1	no	—
597	C₂×C₆₁	—	8	2	no	—
598	C₂×C₆₁	—	8	1	no	—
599	C₂×C₆₁	#3485	1	1	yes	characteristic
600	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
601	C₂×C₆₁	#3585	1	1	yes	characteristic
602	#560	—	2	2	no	—
603	#556	C₂²×C₆₁	1	1	yes	characteristic
604	#556	C₂²×C₆₁	1	2	yes	complemented
605	#555	C₂²×C₆₁	1	1	yes	characteristic
606	#555	C₂²×C₆₁	1	1	yes	characteristic, complemented
607	#554	C₂²×C₆₁	1	1	yes	characteristic
608	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
609	#553	—	2	1	no	—
610	#553	—	2	1	no	—
611	#553	C₂²×C₆₁	1	2	yes	—
612	#550	—	2	1	no	—
613	#550	C₂²×C₆₁	1	1	yes	characteristic
614	#548	—	2	2	no	—
615	#547	C₂²×C₆₁	1	1	yes	characteristic
616	#547	C₂²×C₆₁	1	2	yes	complemented
617	#546	—	2	1	no	—
618	#546	C₂²×C₆₁	1	2	yes	—
619	D₄²	C₂²×C₆₁	1	1	yes	characteristic
620	#542	—	2	1	no	—
621	#542	—	2	2	no	—
622	#538	—	2	2	no	—
623	#537	C₂²×C₆₁	1	2	yes	—
624	#537	C₂²×C₆₁	1	2	yes	complemented
625	#535	—	2	1	no	—
626	#535	C₂²×C₆₁	1	2	yes	—
627	#533	—	2	1	no	—
628	#532	—	2	1	no	—
629	#532	C₂²×C₆₁	1	1	yes	characteristic
630	#532	C₂²×C₆₁	1	1	yes	characteristic
631	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
632	#529	C₂²×C₆₁	1	1	yes	characteristic
633	#520	C₂²×C₆₁	1	2	yes	complemented
634	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
635	#501	C₂²×C₆₁	1	2	yes	complemented
636	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
637	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
638	#489	C₂²×C₆₁	1	2	yes	—
639	#486	C₂²×C₆₁	1	1	yes	characteristic
640	#486	C₂²×C₆₁	1	1	yes	characteristic
641	#485	C₂²×C₆₁	1	2	yes	complemented
642	#485	C₂²×C₆₁	1	2	yes	complemented
643	#485	C₂²×C₆₁	1	1	yes	characteristic, complemented
644	#483	C₂²×C₆₁	1	2	yes	complemented
645	#483	C₂²×C₆₁	1	2	yes	complemented
646	#483	C₂²×C₆₁	1	2	yes	complemented
647	#482	C₂²×C₆₁	1	2	yes	—
648	#482	C₂²×C₆₁	1	1	yes	characteristic
649	#482	C₂²×C₆₁	1	2	yes	—
650	#482	C₂²×C₆₁	1	2	yes	complemented
651	#482	C₂²×C₆₁	1	2	yes	complemented
652	#482	C₂²×C₆₁	1	2	yes	complemented
653	#481	C₂²×C₆₁	1	2	yes	—
654	#481	C₂²×C₆₁	1	2	yes	—
655	#481	C₂²×C₆₁	1	2	yes	complemented
656	#481	C₂²×C₆₁	1	2	yes	complemented
657	#481	C₂²×C₆₁	1	2	yes	complemented
658	#480	C₂²×C₆₁	1	2	yes	—
659	#480	C₂²×C₆₁	1	2	yes	complemented
660	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
661	#478	C₂²×C₆₁	1	1	yes	characteristic, complemented
662	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
663	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
664	#476	C₂²×C₆₁	1	1	yes	characteristic
665	#476	C₂²×C₆₁	1	1	yes	characteristic
666	#476	C₂²×C₆₁	1	2	yes	complemented
667	#476	C₂²×C₆₁	1	2	yes	complemented
668	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
669	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
670	#470	C₂²×C₆₁	1	2	yes	complemented
671	#469	C₂²×C₆₁	1	2	yes	—
672	#469	C₂²×C₆₁	1	2	yes	—
673	#468	C₂²×C₆₁	1	2	yes	complemented
674	#466	C₂²×C₆₁	1	2	yes	complemented
675	#465	C₂²×C₆₁	1	2	yes	—
676	#465	C₂²×C₆₁	1	2	yes	—
677	#465	C₂²×C₆₁	1	2	yes	complemented
678	#464	C₂²×C₆₁	1	1	yes	characteristic
679	#463	C₂²×C₆₁	1	1	yes	characteristic
680	#460	C₂²×C₆₁	1	1	yes	characteristic
681	#459	C₂²×C₆₁	1	1	yes	characteristic
682	#452	C₂²×C₆₁	1	2	yes	complemented
683	#452	C₂²×C₆₁	1	1	yes	characteristic, complemented
684	#450	C₂²×C₆₁	1	2	yes	—
685	#449	C₂²×C₆₁	1	1	yes	characteristic
686	#449	C₂²×C₆₁	1	2	yes	complemented
687	#449	C₂²×C₆₁	1	2	yes	complemented
688	#447	C₂²×C₆₁	1	2	yes	—
689	#442	C₂²×C₆₁	1	2	yes	complemented
690	#440	C₂²×C₆₁	1	2	yes	complemented
691	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
692	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
693	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
694	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
695	#436	C₂²×C₆₁	1	1	yes	characteristic
696	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
697	#435	C₂²×C₆₁	1	2	yes	complemented
698	#435	C₂²×C₆₁	1	2	yes	complemented
699	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
700	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
701	#432	C₂²×C₆₁	1	1	yes	characteristic, complemented
702	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
703	#428	C₂²×C₆₁	1	2	yes	complemented
704	#428	C₂²×C₆₁	1	2	yes	complemented
705	#427	C₂²×C₆₁	1	2	yes	complemented
706	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
707	#418	C₂²×C₆₁	1	2	yes	—
708	#417	C₂²×C₆₁	1	2	yes	complemented
709	#416	C₂²×C₆₁	1	2	yes	complemented
710	C₂×#102	C₂²×C₆₁	1	2	yes	—
711	#408	C₂²×C₆₁	1	2	yes	complemented
712	#408	C₂²×C₆₁	1	2	yes	complemented
713	C₆₁	#61815	1	1	yes	characteristic, direct product factor, Sylow
714	C₂×#41	—	2	2	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	1	no	—
717	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
718	C₂×#41	C₂³×C₆₁	1	2	yes	—
719	C₂×#41	C₂³×C₆₁	1	2	yes	—
720	C₂²×Q₈	—	2	1	no	—
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
723	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
725	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
726	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
727	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
728	C₂×D₈	C₂³×C₆₁	1	2	yes	—
729	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
730	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
731	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
732	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
733	C₄⋊Q₈	—	2	1	no	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
737	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
740	#127	—	2	1	no	—
741	#127	—	2	2	no	—
742	#127	D₄×C₆₁	1	1	yes	characteristic
743	#127	C₂³×C₆₁	1	1	yes	characteristic
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	1	no	—
749	#125	—	2	1	no	—
750	#125	—	2	1	no	—
751	#125	C₂³×C₆₁	1	1	yes	characteristic
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	—	2	1	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	1	no	—
758	#124	D₄×C₆₁	1	2	yes	—
759	#124	C₂³×C₆₁	1	1	yes	characteristic
760	#123	—	2	1	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
773	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
776	#121	—	2	2	no	—
777	#121	—	2	1	no	—
778	#121	—	2	1	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	D₄×C₆₁	1	1	yes	characteristic
790	#121	D₄×C₆₁	1	2	yes	—
791	#121	D₄×C₆₁	1	1	yes	characteristic
792	#121	C₂³×C₆₁	1	1	yes	characteristic
793	#121	C₂³×C₆₁	1	2	yes	—
794	#121	C₂³×C₆₁	1	2	yes	—
795	#121	C₂³×C₆₁	1	2	yes	—
796	#121	C₂³×C₆₁	1	2	yes	—
797	#121	C₂³×C₆₁	1	2	yes	—
798	#121	C₂³×C₆₁	1	2	yes	—
799	#120	—	2	2	no	—
800	#120	—	2	2	no	—
801	#120	—	2	2	no	—
802	#120	—	2	2	no	—
803	C₄×Q₈	—	2	2	no	—
804	C₄×Q₈	—	2	2	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₆₁	1	2	yes	—
824	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₆₁	1	2	yes	—
826	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
827	#117	—	2	1	no	—
828	#117	—	2	1	no	—
829	#117	—	2	1	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	#117	C₂³×C₆₁	1	2	yes	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
837	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
838	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
839	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
843	#107	C₂³×C₆₁	1	2	yes	—
844	#107	C₂³×C₆₁	1	2	yes	—
845	#107	C₂³×C₆₁	1	1	yes	characteristic
846	#107	C₂³×C₆₁	1	1	yes	characteristic
847	#107	C₂³×C₆₁	1	2	yes	—
848	#106	C₂³×C₆₁	1	1	yes	characteristic
849	#106	C₂³×C₆₁	1	2	yes	—
850	#106	C₂³×C₆₁	1	2	yes	—
851	#106	C₂³×C₆₁	1	2	yes	—
852	#106	C₂³×C₆₁	1	1	yes	characteristic
853	#106	C₂³×C₆₁	1	2	yes	—
854	#106	C₂³×C₆₁	1	2	yes	—
855	#106	C₂³×C₆₁	1	2	yes	—
856	#106	C₂³×C₆₁	1	2	yes	—
857	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
861	#103	C₂³×C₆₁	1	1	yes	characteristic
862	#103	C₂³×C₆₁	1	2	yes	—
863	#103	C₂³×C₆₁	1	1	yes	characteristic
864	#103	C₂³×C₆₁	1	2	yes	—
865	#103	C₂³×C₆₁	1	1	yes	characteristic
866	#103	C₂³×C₆₁	1	1	yes	characteristic
867	#103	C₂³×C₆₁	1	2	yes	—
868	#102	C₂³×C₆₁	1	1	yes	characteristic
869	#102	C₂³×C₆₁	1	2	yes	—
870	#102	C₂³×C₆₁	1	2	yes	—
871	#102	C₂³×C₆₁	1	2	yes	—
872	#102	C₂³×C₆₁	1	2	yes	—
873	#102	C₂³×C₆₁	1	2	yes	—
874	#102	C₂³×C₆₁	1	2	yes	—
875	#102	C₂³×C₆₁	1	1	yes	characteristic
876	#102	C₂³×C₆₁	1	2	yes	—
877	#102	C₂³×C₆₁	1	2	yes	—
878	#102	C₂³×C₆₁	1	1	yes	characteristic
879	#102	C₂³×C₆₁	1	1	yes	characteristic
880	#102	C₂³×C₆₁	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
882	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
883	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
888	#97	C₂³×C₆₁	1	2	yes	—
889	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
891	C₂⁴	—	2	2	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	4	1	no	—
895	#41	—	4	1	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	8	2	no	—
899	#41	—	8	2	no	—
900	#41	—	8	4	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	8	2	no	—
906	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
907	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
908	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	8	2	no	—
924	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
925	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
926	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
927	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
928	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
929	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
930	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
931	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
932	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
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	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
944	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
948	Q₁₆	—	4	1	no	—
949	SD₁₆	—	4	1	no	—
950	SD₁₆	—	4	1	no	—
951	SD₁₆	—	4	2	no	—
952	D₈	—	4	2	no	—
953	D₈	—	4	1	no	—
954	M₁₆	—	4	2	no	—
955	M₁₆	—	4	2	no	—
956	C₂×C₈	—	4	2	no	—
957	C₂×C₈	—	4	2	no	—
958	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
963	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	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	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
984	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1024	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1025	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1026	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	8	2	no	—
1031	C₂³	—	8	2	no	—
1032	C₂³	—	8	2	no	—
1033	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1034	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1035	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	4	2	no	—
1041	Q₈	—	4	4	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	8	1	no	—
1044	Q₈	—	8	1	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	2	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	8	1	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	1	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	2	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	4	1	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1103	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1104	C₈	—	2	1	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	2	2	no	—
1107	C₈	—	2	2	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	16	4	no	—
1129	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1130	C₄	—	2	1	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	C₆₁×#577	1	2	yes	—
1146	C₄	C₆₁×#585	1	1	yes	characteristic
1147	C₄	C₆₁×#585	1	1	yes	characteristic
1148	C₂	—	4	2	no	—
1149	C₂	—	4	1	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	8	1	no	—
1152	C₂	—	8	2	no	—
1153	C₂	—	8	1	no	—
1154	C₂	C₆₁×#3485	1	1	yes	characteristic
1155	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1156	C₂	C₆₁×#3585	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3546	C₂	semidirect
2. C₆₁×#3511	C₂	semidirect
3. C₆₁×#3356	C₂	semidirect
4. C₆₁×#3354	C₂	semidirect
5. C₆₁×#3350	C₂	semidirect
6. C₆₁×#3345	C₂	semidirect
7. C₆₁×#3340	C₂	semidirect
8. C₆₁×#3335	C₂	semidirect
9. C₆₁×#3333	C₂	semidirect
10. C₆₁×#3325	C₂	semidirect
11. C₆₁×#3311	C₂	semidirect
12. C₆₁×#3306	C₂	semidirect
13. C₆₁×#3305	C₂	semidirect
14. C₆₁×#3295	C₂	semidirect
15. C₆₁×#3238	C₂	semidirect
16. C₆₁×#3227	C₂	semidirect
17. C₆₁×#3204	C₂	semidirect
18. C₆₁×#3198	C₂	semidirect
19. C₆₁×#3115	C₂	semidirect
20. C₆₁×#3102	C₂	semidirect
21. C₆₁×#3099	C₂	semidirect
22. C₆₁×#3096	C₂	semidirect
23. C₆₁×#2981	C₂	semidirect
26. C₆₁×#556	C₂²	semidirect
28. C₆₁×#555	C₂²	semidirect
30. C₆₁×#554	C₂²	semidirect
38. C₆₁×#547	C₂²	semidirect
46. C₆₁×#537	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
55. C₆₁×#520	C₂²	semidirect
56. C₄×#41×C₆₁	C₂²	semidirect
57. C₆₁×#501	C₂²	semidirect
58. C₆₁×#498	C₂²	semidirect
59. C₆₁×#498	C₂²	semidirect
63. C₆₁×#485	C₂²	semidirect
64. C₆₁×#485	C₂²	semidirect
65. C₆₁×#485	C₂²	semidirect
66. C₆₁×#483	C₂²	semidirect
67. C₆₁×#483	C₂²	semidirect
68. C₆₁×#483	C₂²	semidirect
72. C₆₁×#482	C₂²	semidirect
73. C₆₁×#482	C₂²	semidirect
74. C₆₁×#482	C₂²	semidirect
77. C₆₁×#481	C₂²	semidirect
78. C₆₁×#481	C₂²	semidirect
79. C₆₁×#481	C₂²	semidirect
81. C₆₁×#480	C₂²	semidirect
82. C₆₁×#479	C₂²	semidirect
83. C₆₁×#478	C₂²	semidirect
84. C₆₁×#477	C₂²	semidirect
85. C₆₁×#477	C₂²	semidirect
88. C₆₁×#476	C₂²	semidirect
89. C₆₁×#476	C₂²	semidirect
90. C₆₁×#475	C₂²	semidirect
91. C₆₁×#474	C₂²	semidirect
92. C₆₁×#470	C₂²	semidirect
95. C₆₁×#468	C₂²	semidirect
96. C₆₁×#466	C₂²	semidirect
99. C₆₁×#465	C₂²	semidirect
104. C₆₁×#452	C₂²	semidirect
105. C₆₁×#452	C₂²	semidirect
108. C₆₁×#449	C₂²	semidirect
109. C₆₁×#449	C₂²	semidirect
111. C₆₁×#442	C₂²	semidirect
112. C₆₁×#440	C₂²	semidirect
113. C₄×Q₁₆×C₆₁	C₂²	semidirect
115. C₄×SD₁₆×C₆₁	C₂²	semidirect
118. C₆₁×#436	C₂²	semidirect
119. C₆₁×#435	C₂²	semidirect
120. C₆₁×#435	C₂²	semidirect
122. C₈×D₄×C₆₁	C₂²	semidirect
123. C₆₁×#432	C₂²	semidirect
124. C₆₁×#431	C₂²	semidirect
125. C₆₁×#428	C₂²	semidirect
126. C₆₁×#428	C₂²	semidirect
127. C₆₁×#427	C₂²	semidirect
128. C₂×#106×C₆₁	C₂²	semidirect
130. C₆₁×#417	C₂²	semidirect
131. C₆₁×#416	C₂²	semidirect
133. C₆₁×#408	C₂²	semidirect
134. C₆₁×#408	C₂²	semidirect
531. #61815	C₆₁	direct (N × H)
570. #3546	C₂×C₆₁	semidirect
571. #3511	C₂×C₆₁	semidirect
572. #3356	C₂×C₆₁	semidirect
573. #3354	C₂×C₆₁	semidirect
574. #3350	C₂×C₆₁	semidirect
575. #3345	C₂×C₆₁	semidirect
576. #3340	C₂×C₆₁	semidirect
577. #3335	C₂×C₆₁	semidirect
578. #3333	C₂×C₆₁	semidirect
579. #3325	C₂×C₆₁	semidirect
580. #3311	C₂×C₆₁	semidirect
581. #3306	C₂×C₆₁	semidirect
582. #3305	C₂×C₆₁	semidirect
583. #3295	C₂×C₆₁	semidirect
584. #3238	C₂×C₆₁	semidirect
585. #3227	C₂×C₆₁	semidirect
586. #3204	C₂×C₆₁	semidirect
587. #3198	C₂×C₆₁	semidirect
588. #3115	C₂×C₆₁	semidirect
589. #3102	C₂×C₆₁	semidirect
590. #3099	C₂×C₆₁	semidirect
591. #3096	C₂×C₆₁	semidirect
592. #2981	C₂×C₆₁	semidirect
604. #556	C₂²×C₆₁	semidirect
606. #555	C₂²×C₆₁	semidirect
608. #554	C₂²×C₆₁	semidirect
616. #547	C₂²×C₆₁	semidirect
624. #537	C₂²×C₆₁	semidirect
631. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
633. #520	C₂²×C₆₁	semidirect
634. C₄×#41	C₂²×C₆₁	semidirect
635. #501	C₂²×C₆₁	semidirect
636. #498	C₂²×C₆₁	semidirect
637. #498	C₂²×C₆₁	semidirect
641. #485	C₂²×C₆₁	semidirect
642. #485	C₂²×C₆₁	semidirect
643. #485	C₂²×C₆₁	semidirect
644. #483	C₂²×C₆₁	semidirect
645. #483	C₂²×C₆₁	semidirect
646. #483	C₂²×C₆₁	semidirect
650. #482	C₂²×C₆₁	semidirect
651. #482	C₂²×C₆₁	semidirect
652. #482	C₂²×C₆₁	semidirect
655. #481	C₂²×C₆₁	semidirect
656. #481	C₂²×C₆₁	semidirect
657. #481	C₂²×C₆₁	semidirect
659. #480	C₂²×C₆₁	semidirect
660. #479	C₂²×C₆₁	semidirect
661. #478	C₂²×C₆₁	semidirect
662. #477	C₂²×C₆₁	semidirect
663. #477	C₂²×C₆₁	semidirect
666. #476	C₂²×C₆₁	semidirect
667. #476	C₂²×C₆₁	semidirect
668. #475	C₂²×C₆₁	semidirect
669. #474	C₂²×C₆₁	semidirect
670. #470	C₂²×C₆₁	semidirect
673. #468	C₂²×C₆₁	semidirect
674. #466	C₂²×C₆₁	semidirect
677. #465	C₂²×C₆₁	semidirect
682. #452	C₂²×C₆₁	semidirect
683. #452	C₂²×C₆₁	semidirect
686. #449	C₂²×C₆₁	semidirect
687. #449	C₂²×C₆₁	semidirect
689. #442	C₂²×C₆₁	semidirect
690. #440	C₂²×C₆₁	semidirect
691. C₄×Q₁₆	C₂²×C₆₁	semidirect
693. C₄×SD₁₆	C₂²×C₆₁	semidirect
696. #436	C₂²×C₆₁	semidirect
697. #435	C₂²×C₆₁	semidirect
698. #435	C₂²×C₆₁	semidirect
700. C₈×D₄	C₂²×C₆₁	semidirect
701. #432	C₂²×C₆₁	semidirect
702. #431	C₂²×C₆₁	semidirect
703. #428	C₂²×C₆₁	semidirect
704. #428	C₂²×C₆₁	semidirect
705. #427	C₂²×C₆₁	semidirect
706. C₂×#106	C₂²×C₆₁	semidirect
708. #417	C₂²×C₆₁	semidirect
709. #416	C₂²×C₆₁	semidirect
711. #408	C₂²×C₆₁	semidirect
712. #408	C₂²×C₆₁	semidirect
713. C₆₁	#61815	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×#3546	2
C₆₁×#3511	2
C₆₁×#3356	2
C₆₁×#3354	2
C₆₁×#3350	2
C₆₁×#3345	2
C₆₁×#3340	2
C₆₁×#3335	2
C₆₁×#3333	2
C₆₁×#3325	2
C₆₁×#3311	2
C₆₁×#3306	2
C₆₁×#3305	2
C₆₁×#3295	2
C₆₁×#3238	2
C₆₁×#3227	2
C₆₁×#3204	2
C₆₁×#3198	2
C₆₁×#3115	2
C₆₁×#3102	2
C₆₁×#3099	2
C₆₁×#3096	2
C₆₁×#2981	2
#61815	61

Subgroups — C61×#61815 #29565248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61815 #29565248