Subgroups — C₆₁×#62188 #29565621

Order 15616.

1756 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×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3519	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3351	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3350	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3324	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3310	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3260	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3241	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3123	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3081	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#563	—	2	2	no	—
25	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
26	C₆₁×#557	—	2	1	no	—
27	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#556	—	2	1	no	—
29	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#556	C₂²	1	2	yes	complemented
31	C₆₁×#555	C₂²	1	1	yes	characteristic
32	C₆₁×#554	C₂²	1	1	yes	characteristic
33	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
34	C₆₁×#553	—	2	1	no	—
35	C₆₁×#553	C₂²	1	2	yes	—
36	C₆₁×#552	C₂²	1	2	yes	complemented
37	C₆₁×#550	C₂²	1	1	yes	characteristic
38	C₆₁×#546	—	2	1	no	—
39	C₆₁×#546	—	2	2	no	—
40	D₄²×C₆₁	C₂²	1	1	yes	characteristic
41	D₄²×C₆₁	C₂²	1	2	yes	—
42	C₆₁×#544	C₂²	1	2	yes	complemented
43	C₆₁×#542	—	2	1	no	—
44	C₆₁×#541	—	2	2	no	—
45	C₆₁×#541	—	2	1	no	—
46	C₆₁×#541	C₂²	1	2	yes	complemented
47	C₆₁×#540	C₂²	1	2	yes	—
48	C₆₁×#538	—	2	2	no	—
49	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
51	C₆₁×#532	C₂²	1	1	yes	characteristic
52	C₆₁×#529	C₂²	1	1	yes	characteristic
53	C₆₁×#525	—	2	1	no	—
54	C₂×#121×C₆₁	—	2	1	no	—
55	C₆₁×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#501	C₂²	1	2	yes	complemented
58	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
59	C₆₁×#499	C₂²	1	2	yes	complemented
60	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#490	C₂²	1	2	yes	complemented
62	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#486	C₂²	1	2	yes	complemented
64	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
65	C₆₁×#485	C₂²	1	2	yes	complemented
66	C₆₁×#485	C₂²	1	2	yes	complemented
67	C₆₁×#483	C₂²	1	1	yes	characteristic, complemented
68	C₆₁×#483	C₂²	1	1	yes	characteristic, complemented
69	C₆₁×#482	C₂²	1	2	yes	complemented
70	C₆₁×#482	C₂²	1	2	yes	complemented
71	C₆₁×#482	C₂²	1	2	yes	complemented
72	C₆₁×#482	C₂²	1	2	yes	complemented
73	C₆₁×#481	C₂²	1	2	yes	complemented
74	C₆₁×#480	C₂²	1	2	yes	complemented
75	C₆₁×#479	C₂²	1	2	yes	complemented
76	C₆₁×#479	C₂²	1	2	yes	complemented
77	C₆₁×#478	C₂²	1	2	yes	—
78	C₆₁×#478	C₂²	1	2	yes	—
79	C₆₁×#478	C₂²	1	2	yes	complemented
80	C₆₁×#478	C₂²	1	2	yes	complemented
81	C₆₁×#478	C₂²	1	2	yes	complemented
82	C₆₁×#478	C₂²	1	2	yes	complemented
83	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
84	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
85	C₆₁×#476	C₂²	1	1	yes	characteristic
86	C₆₁×#476	C₂²	1	1	yes	characteristic
87	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
88	C₆₁×#476	C₂²	1	2	yes	complemented
89	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
90	C₆₁×#474	C₂²	1	1	yes	characteristic
91	C₆₁×#474	C₂²	1	2	yes	—
92	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
93	C₆₁×#474	C₂²	1	2	yes	complemented
94	C₆₁×#468	C₂²	1	2	yes	complemented
95	C₆₁×#468	C₂²	1	2	yes	complemented
96	C₆₁×#468	C₂²	1	2	yes	complemented
97	C₆₁×#468	C₂²	1	2	yes	complemented
98	C₆₁×#465	C₂²	1	2	yes	complemented
99	C₆₁×#465	C₂²	1	2	yes	complemented
100	C₆₁×#461	C₂²	1	1	yes	characteristic
101	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
102	C₆₁×#461	C₂²	1	2	yes	complemented
103	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
104	C₆₁×#460	C₂²	1	2	yes	complemented
105	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
106	C₆₁×#460	C₂²	1	2	yes	complemented
107	C₆₁×#450	C₂²	1	2	yes	—
108	C₆₁×#450	C₂²	1	1	yes	characteristic
109	C₆₁×#450	C₂²	1	2	yes	—
110	C₆₁×#450	C₂²	1	1	yes	characteristic
111	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
113	C₆₁×#440	C₂²	1	2	yes	—
114	C₆₁×#440	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₆₁×#436	C₂²	1	2	yes	complemented
122	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
123	C₆₁×#435	C₂²	1	2	yes	complemented
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, complemented
127	C₆₁×#428	C₂²	1	2	yes	complemented
128	C₆₁×#428	C₂²	1	2	yes	complemented
129	C₆₁×#427	C₂²	1	2	yes	complemented
130	C₆₁×#424	C₂²	1	2	yes	complemented
131	C₆₁×#423	C₂²	1	1	yes	characteristic, complemented
132	C₆₁×#418	C₂²	1	2	yes	—
133	C₆₁×#418	C₂²	1	2	yes	—
134	C₂×#102×C₆₁	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂²×D₄×C₆₁	—	2	1	no	—
138	C₂²×D₄×C₆₁	—	2	2	no	—
139	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₁	—	2	1	no	—
142	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₆₁	—	2	1	no	—
152	C₄⋊Q₈×C₆₁	—	2	2	no	—
153	C₄⋊Q₈×C₆₁	—	2	1	no	—
154	C₄⋊Q₈×C₆₁	—	2	2	no	—
155	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
161	#127×C₆₁	C₂³	1	1	yes	characteristic
162	#127×C₆₁	C₂³	1	2	yes	—
163	#126×C₆₁	—	2	2	no	—
164	#126×C₆₁	—	2	2	no	—
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	2	no	—
170	#126×C₆₁	D₄	1	2	yes	—
171	#125×C₆₁	—	2	2	no	—
172	#125×C₆₁	—	2	2	no	—
173	#125×C₆₁	—	2	2	no	—
174	#125×C₆₁	—	2	1	no	—
175	#125×C₆₁	—	2	2	no	—
176	#125×C₆₁	—	2	2	no	—
177	#125×C₆₁	—	2	1	no	—
178	#125×C₆₁	D₄	1	1	yes	characteristic
179	#125×C₆₁	C₂³	1	2	yes	—
180	#125×C₆₁	C₂³	1	2	yes	—
181	#125×C₆₁	C₂³	1	2	yes	—
182	#124×C₆₁	—	2	1	no	—
183	#124×C₆₁	—	2	2	no	—
184	#124×C₆₁	—	2	2	no	—
185	#124×C₆₁	—	2	1	no	—
186	#124×C₆₁	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
201	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
202	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
203	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
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	—	2	1	no	—
211	#121×C₆₁	—	2	1	no	—
212	#121×C₆₁	—	2	2	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	#121×C₆₁	C₂³	1	2	yes	—
218	#120×C₆₁	—	2	2	no	—
219	#120×C₆₁	—	2	2	no	—
220	#120×C₆₁	—	2	2	no	—
221	C₄×Q₈×C₆₁	—	2	1	no	—
222	C₄×Q₈×C₆₁	—	2	2	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	—	2	1	no	—
228	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₆₁	—	2	1	no	—
234	C₄×D₄×C₆₁	—	2	2	no	—
235	C₄×D₄×C₆₁	—	2	2	no	—
236	C₄×D₄×C₆₁	—	2	2	no	—
237	C₄×D₄×C₆₁	—	2	1	no	—
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	—	2	1	no	—
240	C₄×D₄×C₆₁	C₂³	1	2	yes	—
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	2	yes	—
245	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₁	C₂³	1	2	yes	—
248	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
249	#117×C₆₁	—	2	1	no	—
250	#117×C₆₁	—	2	1	no	—
251	#117×C₆₁	—	2	2	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	2	yes	—
256	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
260	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
262	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
263	#107×C₆₁	C₂³	1	2	yes	—
264	#107×C₆₁	C₂³	1	2	yes	—
265	#107×C₆₁	C₂³	1	2	yes	—
266	#107×C₆₁	C₂³	1	2	yes	—
267	#107×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
272	#106×C₆₁	C₂³	1	2	yes	—
273	#106×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	2	yes	—
277	C₄⋊C₈×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	2	yes	—
282	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
289	#103×C₆₁	C₂³	1	2	yes	—
290	#102×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
295	#102×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
305	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×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	2	yes	—
312	C₂⁴×C₆₁	—	2	1	no	—
313	C₂⁴×C₆₁	—	2	2	no	—
314	#41×C₆₁	—	8	2	no	—
315	#41×C₆₁	—	8	2	no	—
316	C₂×Q₈×C₆₁	—	2	1	no	—
317	C₂×Q₈×C₆₁	—	2	1	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	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₆₁	—	2	2	no	—
325	C₂×D₄×C₆₁	—	2	4	no	—
326	C₂×D₄×C₆₁	—	2	2	no	—
327	C₂×D₄×C₆₁	—	2	2	no	—
328	C₂×D₄×C₆₁	—	2	2	no	—
329	C₂×D₄×C₆₁	—	2	1	no	—
330	C₂×D₄×C₆₁	—	2	2	no	—
331	C₂×D₄×C₆₁	—	2	1	no	—
332	C₂×D₄×C₆₁	—	2	2	no	—
333	C₂×D₄×C₆₁	—	2	1	no	—
334	C₂×D₄×C₆₁	—	2	2	no	—
335	C₂×D₄×C₆₁	—	4	2	no	—
336	C₂×D₄×C₆₁	—	4	1	no	—
337	C₂×D₄×C₆₁	—	8	2	no	—
338	C₂×D₄×C₆₁	—	8	4	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	2	yes	—
342	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₆₁	—	2	1	no	—
345	C₂²×C₄×C₆₁	—	2	2	no	—
346	C₂²×C₄×C₆₁	—	2	1	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	2	no	—
351	C₂²×C₄×C₆₁	—	2	2	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	SD₁₆×C₆₁	—	2	2	no	—
359	SD₁₆×C₆₁	—	2	2	no	—
360	SD₁₆×C₆₁	—	4	1	no	—
361	SD₁₆×C₆₁	—	4	2	no	—
362	SD₁₆×C₆₁	—	4	2	no	—
363	SD₁₆×C₆₁	—	4	1	no	—
364	M₁₆×C₆₁	—	4	2	no	—
365	M₁₆×C₆₁	—	4	2	no	—
366	C₂×C₈×C₆₁	—	4	2	no	—
367	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
372	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₆₁	—	2	1	no	—
374	C₄⋊C₄×C₆₁	—	2	2	no	—
375	C₄⋊C₄×C₆₁	—	2	1	no	—
376	C₄⋊C₄×C₆₁	—	2	2	no	—
377	C₄⋊C₄×C₆₁	—	2	1	no	—
378	C₄⋊C₄×C₆₁	—	2	1	no	—
379	C₄⋊C₄×C₆₁	—	2	2	no	—
380	C₄⋊C₄×C₆₁	—	2	1	no	—
381	C₄⋊C₄×C₆₁	—	2	1	no	—
382	C₄⋊C₄×C₆₁	—	2	2	no	—
383	C₄⋊C₄×C₆₁	—	2	1	no	—
384	C₄⋊C₄×C₆₁	—	2	2	no	—
385	C₄⋊C₄×C₆₁	—	2	2	no	—
386	C₄⋊C₄×C₆₁	—	2	2	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	—	2	1	no	—
389	C₄⋊C₄×C₆₁	—	2	1	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	2	no	—
396	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
409	C₂²⋊C₄×C₆₁	—	2	2	no	—
410	C₂²⋊C₄×C₆₁	—	2	1	no	—
411	C₂²⋊C₄×C₆₁	—	2	1	no	—
412	C₂²⋊C₄×C₆₁	—	2	2	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	—	2	2	no	—
416	C₂²⋊C₄×C₆₁	—	2	1	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	1	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	2	no	—
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	2	no	—
426	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
431	C₄²×C₆₁	—	2	2	no	—
432	C₄²×C₆₁	—	2	2	no	—
433	C₄²×C₆₁	—	2	1	no	—
434	C₄²×C₆₁	—	2	1	no	—
435	C₄²×C₆₁	—	2	2	no	—
436	C₄²×C₆₁	—	2	2	no	—
437	C₄²×C₆₁	—	2	2	no	—
438	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
441	C₄²×C₆₁	C₂⁴	1	2	yes	—
442	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
443	C₂³×C₆₁	—	2	1	no	—
444	C₂³×C₆₁	—	2	2	no	—
445	C₂³×C₆₁	—	2	1	no	—
446	C₂³×C₆₁	—	4	2	no	—
447	C₂³×C₆₁	—	4	4	no	—
448	C₂³×C₆₁	—	4	2	no	—
449	C₂³×C₆₁	—	8	1	no	—
450	C₂³×C₆₁	—	8	2	no	—
451	C₂³×C₆₁	—	8	2	no	—
452	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
453	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₆₁	—	2	2	no	—
455	Q₈×C₆₁	—	2	1	no	—
456	Q₈×C₆₁	—	2	1	no	—
457	Q₈×C₆₁	—	2	1	no	—
458	Q₈×C₆₁	—	2	1	no	—
459	Q₈×C₆₁	—	4	2	no	—
460	Q₈×C₆₁	—	8	1	no	—
461	Q₈×C₆₁	—	8	1	no	—
462	Q₈×C₆₁	—	8	2	no	—
463	Q₈×C₆₁	—	8	1	no	—
464	D₄×C₆₁	—	2	2	no	—
465	D₄×C₆₁	—	2	1	no	—
466	D₄×C₆₁	—	2	2	no	—
467	D₄×C₆₁	—	2	1	no	—
468	D₄×C₆₁	—	2	1	no	—
469	D₄×C₆₁	—	2	2	no	—
470	D₄×C₆₁	—	4	2	no	—
471	D₄×C₆₁	—	4	4	no	—
472	D₄×C₆₁	—	4	2	no	—
473	D₄×C₆₁	—	4	4	no	—
474	D₄×C₆₁	—	4	2	no	—
475	D₄×C₆₁	—	8	2	no	—
476	D₄×C₆₁	—	8	1	no	—
477	D₄×C₆₁	—	8	2	no	—
478	D₄×C₆₁	—	8	2	no	—
479	D₄×C₆₁	—	8	2	no	—
480	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
481	C₂×C₄×C₆₁	—	2	2	no	—
482	C₂×C₄×C₆₁	—	2	1	no	—
483	C₂×C₄×C₆₁	—	2	2	no	—
484	C₂×C₄×C₆₁	—	2	2	no	—
485	C₂×C₄×C₆₁	—	2	1	no	—
486	C₂×C₄×C₆₁	—	2	1	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	1	no	—
491	C₂×C₄×C₆₁	—	2	2	no	—
492	C₂×C₄×C₆₁	—	2	2	no	—
493	C₂×C₄×C₆₁	—	2	1	no	—
494	C₂×C₄×C₆₁	—	2	1	no	—
495	C₂×C₄×C₆₁	—	4	1	no	—
496	C₂×C₄×C₆₁	—	4	2	no	—
497	C₂×C₄×C₆₁	—	4	2	no	—
498	C₂×C₄×C₆₁	—	8	1	no	—
499	C₂×C₄×C₆₁	—	8	1	no	—
500	C₂×C₄×C₆₁	—	8	2	no	—
501	C₂×C₄×C₆₁	—	8	2	no	—
502	C₂×C₄×C₆₁	—	8	2	no	—
503	C₂×C₄×C₆₁	—	8	2	no	—
504	C₂×C₄×C₆₁	—	8	1	no	—
505	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
512	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
514	C₈×C₆₁	—	2	1	no	—
515	C₈×C₆₁	—	2	1	no	—
516	C₈×C₆₁	—	2	1	no	—
517	C₈×C₆₁	—	2	2	no	—
518	C₈×C₆₁	—	2	1	no	—
519	C₈×C₆₁	—	2	2	no	—
520	#62188	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
521	C₂²×C₆₁	—	2	1	no	—
522	C₂²×C₆₁	—	2	2	no	—
523	C₂²×C₆₁	—	2	1	no	—
524	C₂²×C₆₁	—	2	2	no	—
525	C₂²×C₆₁	—	2	2	no	—
526	C₂²×C₆₁	—	2	1	no	—
527	C₂²×C₆₁	—	2	2	no	—
528	C₂²×C₆₁	—	4	1	no	—
529	C₂²×C₆₁	—	4	1	no	—
530	C₂²×C₆₁	—	4	2	no	—
531	C₂²×C₆₁	—	4	1	no	—
532	C₂²×C₆₁	—	4	1	no	—
533	C₂²×C₆₁	—	4	2	no	—
534	C₂²×C₆₁	—	4	1	no	—
535	C₂²×C₆₁	—	4	2	no	—
536	C₂²×C₆₁	—	8	4	no	—
537	C₂²×C₆₁	—	16	4	no	—
538	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₆₁	—	2	1	no	—
540	C₄×C₆₁	—	2	1	no	—
541	C₄×C₆₁	—	2	2	no	—
542	C₄×C₆₁	—	2	2	no	—
543	C₄×C₆₁	—	2	1	no	—
544	C₄×C₆₁	—	2	1	no	—
545	C₄×C₆₁	—	2	2	no	—
546	C₄×C₆₁	—	4	2	no	—
547	C₄×C₆₁	—	4	1	no	—
548	C₄×C₆₁	—	4	2	no	—
549	C₄×C₆₁	—	4	1	no	—
550	C₄×C₆₁	—	4	1	no	—
551	C₄×C₆₁	—	4	1	no	—
552	C₄×C₆₁	—	4	1	no	—
553	C₄×C₆₁	—	4	1	no	—
554	C₄×C₆₁	—	4	2	no	—
555	C₄×C₆₁	#577	1	2	yes	—
556	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
557	C₄×C₆₁	#585	1	1	yes	characteristic
558	#3555	C₂×C₆₁	1	1	yes	characteristic, complemented
559	#3519	C₂×C₆₁	1	1	yes	characteristic
560	#3385	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#3381	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3368	C₂×C₆₁	1	1	yes	characteristic, complemented
563	#3362	C₂×C₆₁	1	1	yes	characteristic, complemented
564	#3357	C₂×C₆₁	1	1	yes	characteristic, complemented
565	#3351	C₂×C₆₁	1	2	yes	complemented
566	#3350	C₂×C₆₁	1	2	yes	complemented
567	#3340	C₂×C₆₁	1	1	yes	characteristic, complemented
568	#3324	C₂×C₆₁	1	1	yes	characteristic, complemented
569	#3324	C₂×C₆₁	1	2	yes	complemented
570	#3310	C₂×C₆₁	1	2	yes	complemented
571	#3295	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3260	C₂×C₆₁	1	2	yes	complemented
573	#3254	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3241	C₂×C₆₁	1	2	yes	complemented
575	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#3123	C₂×C₆₁	1	2	yes	complemented
577	#3101	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3081	C₂×C₆₁	1	2	yes	complemented
579	#3077	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#2993	C₂×C₆₁	1	1	yes	characteristic, complemented
581	C₂×C₆₁	—	4	1	no	—
582	C₂×C₆₁	—	4	2	no	—
583	C₂×C₆₁	—	4	2	no	—
584	C₂×C₆₁	—	8	1	no	—
585	C₂×C₆₁	—	8	2	no	—
586	C₂×C₆₁	#3489	1	1	yes	characteristic
587	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
588	C₂×C₆₁	#3585	1	1	yes	characteristic
589	#563	—	2	2	no	—
590	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
591	#557	—	2	1	no	—
592	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
593	#556	—	2	1	no	—
594	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
595	#556	C₂²×C₆₁	1	2	yes	complemented
596	#555	C₂²×C₆₁	1	1	yes	characteristic
597	#554	C₂²×C₆₁	1	1	yes	characteristic
598	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
599	#553	—	2	1	no	—
600	#553	C₂²×C₆₁	1	2	yes	—
601	#552	C₂²×C₆₁	1	2	yes	complemented
602	#550	C₂²×C₆₁	1	1	yes	characteristic
603	#546	—	2	1	no	—
604	#546	—	2	2	no	—
605	D₄²	C₂²×C₆₁	1	1	yes	characteristic
606	D₄²	C₂²×C₆₁	1	2	yes	—
607	#544	C₂²×C₆₁	1	2	yes	complemented
608	#542	—	2	1	no	—
609	#541	—	2	2	no	—
610	#541	—	2	1	no	—
611	#541	C₂²×C₆₁	1	2	yes	complemented
612	#540	C₂²×C₆₁	1	2	yes	—
613	#538	—	2	2	no	—
614	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
615	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
616	#532	C₂²×C₆₁	1	1	yes	characteristic
617	#529	C₂²×C₆₁	1	1	yes	characteristic
618	#525	—	2	1	no	—
619	C₂×#121	—	2	1	no	—
620	#518	C₂²×C₆₁	1	2	yes	—
621	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
622	#501	C₂²×C₆₁	1	2	yes	complemented
623	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
624	#499	C₂²×C₆₁	1	2	yes	complemented
625	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
626	#490	C₂²×C₆₁	1	2	yes	complemented
627	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
628	#486	C₂²×C₆₁	1	2	yes	complemented
629	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
630	#485	C₂²×C₆₁	1	2	yes	complemented
631	#485	C₂²×C₆₁	1	2	yes	complemented
632	#483	C₂²×C₆₁	1	1	yes	characteristic, complemented
633	#483	C₂²×C₆₁	1	1	yes	characteristic, complemented
634	#482	C₂²×C₆₁	1	2	yes	complemented
635	#482	C₂²×C₆₁	1	2	yes	complemented
636	#482	C₂²×C₆₁	1	2	yes	complemented
637	#482	C₂²×C₆₁	1	2	yes	complemented
638	#481	C₂²×C₆₁	1	2	yes	complemented
639	#480	C₂²×C₆₁	1	2	yes	complemented
640	#479	C₂²×C₆₁	1	2	yes	complemented
641	#479	C₂²×C₆₁	1	2	yes	complemented
642	#478	C₂²×C₆₁	1	2	yes	—
643	#478	C₂²×C₆₁	1	2	yes	—
644	#478	C₂²×C₆₁	1	2	yes	complemented
645	#478	C₂²×C₆₁	1	2	yes	complemented
646	#478	C₂²×C₆₁	1	2	yes	complemented
647	#478	C₂²×C₆₁	1	2	yes	complemented
648	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
649	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
650	#476	C₂²×C₆₁	1	1	yes	characteristic
651	#476	C₂²×C₆₁	1	1	yes	characteristic
652	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
653	#476	C₂²×C₆₁	1	2	yes	complemented
654	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
655	#474	C₂²×C₆₁	1	1	yes	characteristic
656	#474	C₂²×C₆₁	1	2	yes	—
657	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
658	#474	C₂²×C₆₁	1	2	yes	complemented
659	#468	C₂²×C₆₁	1	2	yes	complemented
660	#468	C₂²×C₆₁	1	2	yes	complemented
661	#468	C₂²×C₆₁	1	2	yes	complemented
662	#468	C₂²×C₆₁	1	2	yes	complemented
663	#465	C₂²×C₆₁	1	2	yes	complemented
664	#465	C₂²×C₆₁	1	2	yes	complemented
665	#461	C₂²×C₆₁	1	1	yes	characteristic
666	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
667	#461	C₂²×C₆₁	1	2	yes	complemented
668	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
669	#460	C₂²×C₆₁	1	2	yes	complemented
670	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
671	#460	C₂²×C₆₁	1	2	yes	complemented
672	#450	C₂²×C₆₁	1	1	yes	characteristic
673	#450	C₂²×C₆₁	1	1	yes	characteristic
674	#450	C₂²×C₆₁	1	2	yes	—
675	#450	C₂²×C₆₁	1	2	yes	—
676	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
677	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
678	#440	C₂²×C₆₁	1	2	yes	—
679	#440	C₂²×C₆₁	1	2	yes	complemented
680	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
682	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
683	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
684	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
685	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
686	#436	C₂²×C₆₁	1	2	yes	complemented
687	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
688	#435	C₂²×C₆₁	1	2	yes	complemented
689	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
690	#433	C₂²×C₆₁	1	2	yes	complemented
691	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
692	#428	C₂²×C₆₁	1	2	yes	complemented
693	#428	C₂²×C₆₁	1	2	yes	complemented
694	#427	C₂²×C₆₁	1	2	yes	complemented
695	#424	C₂²×C₆₁	1	2	yes	complemented
696	#423	C₂²×C₆₁	1	1	yes	characteristic, complemented
697	#418	C₂²×C₆₁	1	2	yes	—
698	#418	C₂²×C₆₁	1	2	yes	—
699	C₂×#102	C₂²×C₆₁	1	2	yes	—
700	C₆₁	#62188	1	1	yes	characteristic, direct product factor, Sylow
701	C₂×#41	—	2	1	no	—
702	C₂×#41	—	2	1	no	—
703	C₂²×D₄	—	2	1	no	—
704	C₂²×D₄	—	2	2	no	—
705	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
706	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
707	C₂³×C₄	—	2	1	no	—
708	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
710	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
714	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
715	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
716	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	—	2	2	no	—
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	—	2	2	no	—
721	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
727	#127	C₂³×C₆₁	1	1	yes	characteristic
728	#127	C₂³×C₆₁	1	2	yes	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	D₄×C₆₁	1	2	yes	—
737	#125	—	2	2	no	—
738	#125	—	2	2	no	—
739	#125	—	2	2	no	—
740	#125	—	2	1	no	—
741	#125	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	—	2	1	no	—
744	#125	D₄×C₆₁	1	1	yes	characteristic
745	#125	C₂³×C₆₁	1	2	yes	—
746	#125	C₂³×C₆₁	1	2	yes	—
747	#125	C₂³×C₆₁	1	2	yes	—
748	#124	—	2	1	no	—
749	#124	—	2	2	no	—
750	#124	—	2	2	no	—
751	#124	—	2	1	no	—
752	#124	D₄×C₆₁	1	1	yes	characteristic
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	D₄×C₆₁	1	2	yes	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
768	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
769	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
771	#121	—	2	2	no	—
772	#121	—	2	1	no	—
773	#121	—	2	1	no	—
774	#121	—	2	1	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	D₄×C₆₁	1	1	yes	characteristic
781	#121	C₂³×C₆₁	1	2	yes	—
782	#121	C₂³×C₆₁	1	2	yes	—
783	#121	C₂³×C₆₁	1	2	yes	—
784	#120	—	2	2	no	—
785	#120	—	2	2	no	—
786	#120	—	2	2	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	2	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	—	2	1	no	—
794	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
797	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
798	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₆₁	1	2	yes	—
811	C₄×D₄	C₂³×C₆₁	1	2	yes	—
812	C₄×D₄	C₂³×C₆₁	1	2	yes	—
813	C₄×D₄	C₂³×C₆₁	1	2	yes	—
814	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
815	#117	—	2	1	no	—
816	#117	—	2	1	no	—
817	#117	—	2	2	no	—
818	#117	C₂³×C₆₁	1	2	yes	—
819	#117	C₂³×C₆₁	1	2	yes	—
820	#117	C₂³×C₆₁	1	2	yes	—
821	#117	C₂³×C₆₁	1	2	yes	—
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
824	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
825	C₂×C₂²⋊C₄	—	2	1	no	—
826	C₂×C₂²⋊C₄	—	2	2	no	—
827	C₂×C₂²⋊C₄	—	2	2	no	—
828	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
829	#107	C₂³×C₆₁	1	2	yes	—
830	#107	C₂³×C₆₁	1	2	yes	—
831	#107	C₂³×C₆₁	1	2	yes	—
832	#107	C₂³×C₆₁	1	2	yes	—
833	#107	C₂³×C₆₁	1	2	yes	—
834	#107	C₂³×C₆₁	1	2	yes	—
835	#106	C₂³×C₆₁	1	1	yes	characteristic
836	#106	C₂³×C₆₁	1	2	yes	—
837	#106	C₂³×C₆₁	1	1	yes	characteristic
838	#106	C₂³×C₆₁	1	2	yes	—
839	#106	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	2	yes	—
843	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
848	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
849	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
850	#103	C₂³×C₆₁	1	1	yes	characteristic
851	#103	C₂³×C₆₁	1	2	yes	—
852	#103	C₂³×C₆₁	1	1	yes	characteristic
853	#103	C₂³×C₆₁	1	1	yes	characteristic
854	#103	C₂³×C₆₁	1	1	yes	characteristic
855	#103	C₂³×C₆₁	1	2	yes	—
856	#102	C₂³×C₆₁	1	1	yes	characteristic
857	#102	C₂³×C₆₁	1	2	yes	—
858	#102	C₂³×C₆₁	1	2	yes	—
859	#102	C₂³×C₆₁	1	2	yes	—
860	#102	C₂³×C₆₁	1	1	yes	characteristic
861	#102	C₂³×C₆₁	1	2	yes	—
862	#102	C₂³×C₆₁	1	2	yes	—
863	#102	C₂³×C₆₁	1	2	yes	—
864	#102	C₂³×C₆₁	1	2	yes	—
865	#102	C₂³×C₆₁	1	2	yes	—
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	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
873	C₂²⋊C₈	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	2	yes	—
878	C₂⁴	—	2	1	no	—
879	C₂⁴	—	2	2	no	—
880	#41	—	8	2	no	—
881	#41	—	8	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	1	no	—
903	C₂×D₄	—	8	2	no	—
904	C₂×D₄	—	8	4	no	—
905	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
906	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
907	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
908	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
909	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	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	SD₁₆	—	2	2	no	—
925	SD₁₆	—	2	2	no	—
926	SD₁₆	—	4	1	no	—
927	SD₁₆	—	4	2	no	—
928	SD₁₆	—	4	2	no	—
929	SD₁₆	—	4	1	no	—
930	M₁₆	—	4	2	no	—
931	M₁₆	—	4	2	no	—
932	C₂×C₈	—	4	2	no	—
933	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
938	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	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	2	no	—
962	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
966	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
995	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1005	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₆₁	1	2	yes	—
1008	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	4	4	no	—
1014	C₂³	—	4	2	no	—
1015	C₂³	—	8	1	no	—
1016	C₂³	—	8	2	no	—
1017	C₂³	—	8	2	no	—
1018	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1019	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	4	2	no	—
1026	Q₈	—	8	1	no	—
1027	Q₈	—	8	1	no	—
1028	Q₈	—	8	2	no	—
1029	Q₈	—	8	1	no	—
1030	D₄	—	2	2	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	2	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	4	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	8	1	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	4	1	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	8	1	no	—
1065	C₂×C₄	—	8	1	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	2	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
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	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1079	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1080	C₈	—	2	1	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	2	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	8	4	no	—
1102	C₂²	—	16	4	no	—
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	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	C₆₁×#577	1	2	yes	—
1121	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1122	C₄	C₆₁×#585	1	1	yes	characteristic
1123	C₂	—	4	1	no	—
1124	C₂	—	4	2	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	8	1	no	—
1127	C₂	—	8	2	no	—
1128	C₂	C₆₁×#3489	1	1	yes	characteristic
1129	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1130	C₂	C₆₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3519	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×#3555	C₂	semidirect
3. C₆₁×#3385	C₂	semidirect
4. C₆₁×#3381	C₂	semidirect
5. C₆₁×#3368	C₂	semidirect
6. C₆₁×#3362	C₂	semidirect
7. C₆₁×#3357	C₂	semidirect
8. C₆₁×#3351	C₂	semidirect
9. C₆₁×#3350	C₂	semidirect
10. C₆₁×#3340	C₂	semidirect
11. C₆₁×#3324	C₂	semidirect
12. C₆₁×#3324	C₂	semidirect
13. C₆₁×#3310	C₂	semidirect
14. C₆₁×#3295	C₂	semidirect
15. C₆₁×#3260	C₂	semidirect
16. C₆₁×#3254	C₂	semidirect
17. C₆₁×#3241	C₂	semidirect
18. C₆₁×#3228	C₂	semidirect
19. C₆₁×#3123	C₂	semidirect
20. C₆₁×#3101	C₂	semidirect
21. C₆₁×#3081	C₂	semidirect
22. C₆₁×#3077	C₂	semidirect
23. C₆₁×#2993	C₂	semidirect
25. Q₈²×C₆₁	C₂²	semidirect
27. C₆₁×#557	C₂²	semidirect
29. C₆₁×#556	C₂²	semidirect
30. C₆₁×#556	C₂²	semidirect
33. C₆₁×#554	C₂²	semidirect
36. C₆₁×#552	C₂²	semidirect
42. C₆₁×#544	C₂²	semidirect
46. C₆₁×#541	C₂²	semidirect
49. C₆₁×#533	C₂²	semidirect
50. C₆₁×#533	C₂²	semidirect
57. C₆₁×#501	C₂²	semidirect
58. C₆₁×#500	C₂²	semidirect
59. C₆₁×#499	C₂²	semidirect
60. C₆₁×#498	C₂²	semidirect
61. C₆₁×#490	C₂²	semidirect
62. C₆₁×#486	C₂²	semidirect
63. C₆₁×#486	C₂²	semidirect
64. C₆₁×#486	C₂²	semidirect
65. C₆₁×#485	C₂²	semidirect
66. C₆₁×#485	C₂²	semidirect
67. C₆₁×#483	C₂²	semidirect
68. C₆₁×#483	C₂²	semidirect
69. C₆₁×#482	C₂²	semidirect
70. C₆₁×#482	C₂²	semidirect
71. C₆₁×#482	C₂²	semidirect
72. C₆₁×#482	C₂²	semidirect
73. C₆₁×#481	C₂²	semidirect
74. C₆₁×#480	C₂²	semidirect
75. C₆₁×#479	C₂²	semidirect
76. C₆₁×#479	C₂²	semidirect
79. C₆₁×#478	C₂²	semidirect
80. C₆₁×#478	C₂²	semidirect
81. C₆₁×#478	C₂²	semidirect
82. C₆₁×#478	C₂²	semidirect
83. C₆₁×#477	C₂²	semidirect
84. C₆₁×#477	C₂²	semidirect
87. C₆₁×#476	C₂²	semidirect
88. C₆₁×#476	C₂²	semidirect
89. C₆₁×#476	C₂²	semidirect
92. C₆₁×#474	C₂²	semidirect
93. C₆₁×#474	C₂²	semidirect
94. C₆₁×#468	C₂²	semidirect
95. C₆₁×#468	C₂²	semidirect
96. C₆₁×#468	C₂²	semidirect
97. C₆₁×#468	C₂²	semidirect
98. C₆₁×#465	C₂²	semidirect
99. C₆₁×#465	C₂²	semidirect
101. C₆₁×#461	C₂²	semidirect
102. C₆₁×#461	C₂²	semidirect
103. C₆₁×#460	C₂²	semidirect
104. C₆₁×#460	C₂²	semidirect
105. C₆₁×#460	C₂²	semidirect
106. C₆₁×#460	C₂²	semidirect
111. C₆₁×#446	C₂²	semidirect
112. C₈×Q₈×C₆₁	C₂²	semidirect
114. C₆₁×#440	C₂²	semidirect
118. C₄×SD₁₆×C₆₁	C₂²	semidirect
119. C₄×SD₁₆×C₆₁	C₂²	semidirect
120. C₄×SD₁₆×C₆₁	C₂²	semidirect
121. C₆₁×#436	C₂²	semidirect
122. C₆₁×#436	C₂²	semidirect
123. C₆₁×#435	C₂²	semidirect
124. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#433	C₂²	semidirect
126. C₆₁×#431	C₂²	semidirect
127. C₆₁×#428	C₂²	semidirect
128. C₆₁×#428	C₂²	semidirect
129. C₆₁×#427	C₂²	semidirect
130. C₆₁×#424	C₂²	semidirect
131. C₆₁×#423	C₂²	semidirect
520. #62188	C₆₁	direct (N × H)
558. #3555	C₂×C₆₁	semidirect
560. #3385	C₂×C₆₁	semidirect
561. #3381	C₂×C₆₁	semidirect
562. #3368	C₂×C₆₁	semidirect
563. #3362	C₂×C₆₁	semidirect
564. #3357	C₂×C₆₁	semidirect
565. #3351	C₂×C₆₁	semidirect
566. #3350	C₂×C₆₁	semidirect
567. #3340	C₂×C₆₁	semidirect
568. #3324	C₂×C₆₁	semidirect
569. #3324	C₂×C₆₁	semidirect
570. #3310	C₂×C₆₁	semidirect
571. #3295	C₂×C₆₁	semidirect
572. #3260	C₂×C₆₁	semidirect
573. #3254	C₂×C₆₁	semidirect
574. #3241	C₂×C₆₁	semidirect
575. #3228	C₂×C₆₁	semidirect
576. #3123	C₂×C₆₁	semidirect
577. #3101	C₂×C₆₁	semidirect
578. #3081	C₂×C₆₁	semidirect
579. #3077	C₂×C₆₁	semidirect
580. #2993	C₂×C₆₁	semidirect
590. Q₈²	C₂²×C₆₁	semidirect
592. #557	C₂²×C₆₁	semidirect
594. #556	C₂²×C₆₁	semidirect
595. #556	C₂²×C₆₁	semidirect
598. #554	C₂²×C₆₁	semidirect
601. #552	C₂²×C₆₁	semidirect
607. #544	C₂²×C₆₁	semidirect
611. #541	C₂²×C₆₁	semidirect
614. #533	C₂²×C₆₁	semidirect
615. #533	C₂²×C₆₁	semidirect
622. #501	C₂²×C₆₁	semidirect
623. #500	C₂²×C₆₁	semidirect
624. #499	C₂²×C₆₁	semidirect
625. #498	C₂²×C₆₁	semidirect
626. #490	C₂²×C₆₁	semidirect
627. #486	C₂²×C₆₁	semidirect
628. #486	C₂²×C₆₁	semidirect
629. #486	C₂²×C₆₁	semidirect
630. #485	C₂²×C₆₁	semidirect
631. #485	C₂²×C₆₁	semidirect
632. #483	C₂²×C₆₁	semidirect
633. #483	C₂²×C₆₁	semidirect
634. #482	C₂²×C₆₁	semidirect
635. #482	C₂²×C₆₁	semidirect
636. #482	C₂²×C₆₁	semidirect
637. #482	C₂²×C₆₁	semidirect
638. #481	C₂²×C₆₁	semidirect
639. #480	C₂²×C₆₁	semidirect
640. #479	C₂²×C₆₁	semidirect
641. #479	C₂²×C₆₁	semidirect
644. #478	C₂²×C₆₁	semidirect
645. #478	C₂²×C₆₁	semidirect
646. #478	C₂²×C₆₁	semidirect
647. #478	C₂²×C₆₁	semidirect
648. #477	C₂²×C₆₁	semidirect
649. #477	C₂²×C₆₁	semidirect
652. #476	C₂²×C₆₁	semidirect
653. #476	C₂²×C₆₁	semidirect
654. #476	C₂²×C₆₁	semidirect
657. #474	C₂²×C₆₁	semidirect
658. #474	C₂²×C₆₁	semidirect
659. #468	C₂²×C₆₁	semidirect
660. #468	C₂²×C₆₁	semidirect
661. #468	C₂²×C₆₁	semidirect
662. #468	C₂²×C₆₁	semidirect
663. #465	C₂²×C₆₁	semidirect
664. #465	C₂²×C₆₁	semidirect
666. #461	C₂²×C₆₁	semidirect
667. #461	C₂²×C₆₁	semidirect
668. #460	C₂²×C₆₁	semidirect
669. #460	C₂²×C₆₁	semidirect
670. #460	C₂²×C₆₁	semidirect
671. #460	C₂²×C₆₁	semidirect
676. #446	C₂²×C₆₁	semidirect
677. C₈×Q₈	C₂²×C₆₁	semidirect
679. #440	C₂²×C₆₁	semidirect
683. C₄×SD₁₆	C₂²×C₆₁	semidirect
684. C₄×SD₁₆	C₂²×C₆₁	semidirect
685. C₄×SD₁₆	C₂²×C₆₁	semidirect
686. #436	C₂²×C₆₁	semidirect
687. #436	C₂²×C₆₁	semidirect
688. #435	C₂²×C₆₁	semidirect
689. C₈×D₄	C₂²×C₆₁	semidirect
690. #433	C₂²×C₆₁	semidirect
691. #431	C₂²×C₆₁	semidirect
692. #428	C₂²×C₆₁	semidirect
693. #428	C₂²×C₆₁	semidirect
694. #427	C₂²×C₆₁	semidirect
695. #424	C₂²×C₆₁	semidirect
696. #423	C₂²×C₆₁	semidirect
700. C₆₁	#62188	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×#3555	2
C₆₁×#3519	2
C₆₁×#3385	2
C₆₁×#3381	2
C₆₁×#3368	2
C₆₁×#3362	2
C₆₁×#3357	2
C₆₁×#3351	2
C₆₁×#3350	2
C₆₁×#3340	2
C₆₁×#3324	2
C₆₁×#3310	2
C₆₁×#3295	2
C₆₁×#3260	2
C₆₁×#3254	2
C₆₁×#3241	2
C₆₁×#3228	2
C₆₁×#3123	2
C₆₁×#3101	2
C₆₁×#3081	2
C₆₁×#3077	2
C₆₁×#2993	2
#62188	61

Subgroups — C61×#62188 #29565621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62188 #29565621