Subgroups — C₆₁×#61785 #29565218

Order 15616.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3351	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3337	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3326	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3301	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3200	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3198	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3099	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3097	C₂	1	2	yes	maximal, complemented
23	C₆₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#562	—	2	2	no	—
25	C₆₁×#559	—	2	2	no	—
26	C₆₁×#556	—	2	1	no	—
27	C₆₁×#555	—	2	1	no	—
28	C₆₁×#555	C₂²	1	1	yes	characteristic
29	C₆₁×#555	C₂²	1	1	yes	characteristic
30	C₆₁×#555	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#553	—	2	1	no	—
33	C₆₁×#553	C₂²	1	2	yes	—
34	C₆₁×#553	C₂²	1	2	yes	—
35	C₆₁×#552	C₂²	1	2	yes	complemented
36	C₆₁×#550	—	2	1	no	—
37	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
38	C₆₁×#548	C₂²	1	2	yes	complemented
39	C₆₁×#547	C₂²	1	1	yes	characteristic
40	C₆₁×#547	C₂²	1	1	yes	characteristic
41	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
42	C₆₁×#544	—	2	1	no	—
43	C₆₁×#542	—	2	2	no	—
44	C₆₁×#540	—	2	1	no	—
45	C₆₁×#538	—	2	2	no	—
46	C₆₁×#537	C₂²	1	2	yes	—
47	C₆₁×#536	C₂²	1	2	yes	—
48	C₆₁×#535	C₂²	1	2	yes	—
49	C₆₁×#533	C₂²	1	1	yes	characteristic
50	C₆₁×#533	C₂²	1	1	yes	characteristic
51	C₆₁×#532	C₂²	1	1	yes	characteristic
52	C₆₁×#529	C₂²	1	1	yes	characteristic
53	C₆₁×#525	—	2	1	no	—
54	C₆₁×#525	—	2	1	no	—
55	C₆₁×#520	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
58	C₆₁×#499	C₂²	1	2	yes	complemented
59	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#488	C₂²	1	2	yes	complemented
61	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
62	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#485	C₂²	1	2	yes	—
64	C₆₁×#485	C₂²	1	2	yes	—
65	C₆₁×#485	C₂²	1	2	yes	—
66	C₆₁×#485	C₂²	1	2	yes	complemented
67	C₆₁×#485	C₂²	1	2	yes	complemented
68	C₆₁×#485	C₂²	1	2	yes	complemented
69	C₆₁×#484	C₂²	1	1	yes	characteristic
70	C₆₁×#484	C₂²	1	2	yes	complemented
71	C₆₁×#483	C₂²	1	2	yes	—
72	C₆₁×#483	C₂²	1	2	yes	complemented
73	C₆₁×#483	C₂²	1	2	yes	complemented
74	C₆₁×#482	C₂²	1	2	yes	—
75	C₆₁×#482	C₂²	1	2	yes	—
76	C₆₁×#482	C₂²	1	2	yes	—
77	C₆₁×#482	C₂²	1	2	yes	complemented
78	C₆₁×#481	C₂²	1	2	yes	—
79	C₆₁×#481	C₂²	1	1	yes	characteristic
80	C₆₁×#481	C₂²	1	2	yes	complemented
81	C₆₁×#480	C₂²	1	2	yes	—
82	C₆₁×#479	C₂²	1	2	yes	complemented
83	C₆₁×#479	C₂²	1	2	yes	complemented
84	C₆₁×#478	C₂²	1	1	yes	characteristic
85	C₆₁×#478	C₂²	1	1	yes	characteristic
86	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
87	C₆₁×#476	C₂²	1	1	yes	characteristic
88	C₆₁×#476	C₂²	1	1	yes	characteristic
89	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
90	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
91	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#469	C₂²	1	2	yes	—
93	C₆₁×#468	C₂²	1	2	yes	—
94	C₆₁×#468	C₂²	1	2	yes	—
95	C₆₁×#468	C₂²	1	2	yes	—
96	C₆₁×#466	C₂²	1	2	yes	—
97	C₆₁×#465	C₂²	1	2	yes	—
98	C₆₁×#465	C₂²	1	2	yes	—
99	C₆₁×#465	C₂²	1	2	yes	—
100	C₆₁×#463	C₂²	1	1	yes	characteristic
101	C₆₁×#463	C₂²	1	1	yes	characteristic
102	C₆₁×#461	C₂²	1	1	yes	characteristic
103	C₆₁×#461	C₂²	1	1	yes	characteristic
104	C₆₁×#450	C₂²	1	2	yes	—
105	C₆₁×#450	C₂²	1	1	yes	characteristic
106	C₆₁×#449	C₂²	1	2	yes	—
107	C₆₁×#449	C₂²	1	2	yes	—
108	C₆₁×#448	C₂²	1	2	yes	—
109	C₆₁×#448	C₂²	1	2	yes	—
110	C₆₁×#447	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
116	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
117	C₆₁×#436	C₂²	1	2	yes	complemented
118	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
119	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
120	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
122	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₆₁×#431	C₂²	1	1	yes	characteristic
124	C₆₁×#431	C₂²	1	1	yes	characteristic
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×#419	C₂²	1	2	yes	complemented
130	C₆₁×#417	C₂²	1	2	yes	complemented
131	C₆₁×#416	C₂²	1	2	yes	complemented
132	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
133	C₆₁×#408	C₂²	1	2	yes	—
134	C₆₁×#408	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	C₂³	1	2	yes	—
138	C₂×#41×C₆₁	C₂³	1	2	yes	—
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	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₆₁	—	2	2	no	—
153	C₄⋊Q₈×C₆₁	—	2	1	no	—
154	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
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	#127×C₆₁	—	2	2	no	—
160	#127×C₆₁	D₄	1	1	yes	characteristic
161	#126×C₆₁	—	2	2	no	—
162	#126×C₆₁	—	2	2	no	—
163	#126×C₆₁	—	2	2	no	—
164	#126×C₆₁	—	2	1	no	—
165	#125×C₆₁	—	2	2	no	—
166	#125×C₆₁	—	2	1	no	—
167	#125×C₆₁	—	2	1	no	—
168	#125×C₆₁	C₂³	1	2	yes	—
169	#125×C₆₁	C₂³	1	1	yes	characteristic
170	#124×C₆₁	—	2	2	no	—
171	#124×C₆₁	—	2	2	no	—
172	#124×C₆₁	—	2	2	no	—
173	#124×C₆₁	—	2	2	no	—
174	#124×C₆₁	—	2	2	no	—
175	#124×C₆₁	—	2	2	no	—
176	#124×C₆₁	D₄	1	2	yes	—
177	#124×C₆₁	C₂³	1	1	yes	characteristic
178	#123×C₆₁	—	2	2	no	—
179	#123×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	2	no	—
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	1	no	—
189	C₂²⋊Q₈×C₆₁	—	2	1	no	—
190	C₂²⋊Q₈×C₆₁	—	2	1	no	—
191	C₂²⋊Q₈×C₆₁	—	2	2	no	—
192	C₂²⋊Q₈×C₆₁	—	2	1	no	—
193	C₂²⋊Q₈×C₆₁	—	2	1	no	—
194	C₂²⋊Q₈×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	—	2	2	no	—
196	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
201	#121×C₆₁	—	2	2	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	—	2	2	no	—
204	#121×C₆₁	—	2	2	no	—
205	#121×C₆₁	—	2	2	no	—
206	#121×C₆₁	—	2	1	no	—
207	#121×C₆₁	—	2	2	no	—
208	#121×C₆₁	—	2	1	no	—
209	#121×C₆₁	—	2	1	no	—
210	#121×C₆₁	—	2	1	no	—
211	#121×C₆₁	D₄	1	2	yes	—
212	#121×C₆₁	D₄	1	1	yes	characteristic
213	#121×C₆₁	D₄	1	1	yes	characteristic
214	#121×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
219	#121×C₆₁	C₂³	1	2	yes	—
220	#120×C₆₁	—	2	2	no	—
221	#120×C₆₁	—	2	2	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	C₂³	1	2	yes	—
227	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₆₁	—	2	2	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	—	2	1	no	—
231	C₄×D₄×C₆₁	—	2	1	no	—
232	C₄×D₄×C₆₁	—	2	2	no	—
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	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
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	#117×C₆₁	—	2	1	no	—
248	#117×C₆₁	—	2	1	no	—
249	#117×C₆₁	—	2	1	no	—
250	#117×C₆₁	—	2	1	no	—
251	#117×C₆₁	—	2	2	no	—
252	#117×C₆₁	—	2	1	no	—
253	#117×C₆₁	C₂³	1	2	yes	—
254	#117×C₆₁	C₂³	1	2	yes	—
255	#117×C₆₁	C₂³	1	2	yes	—
256	#117×C₆₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
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×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
263	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
264	#107×C₆₁	C₂³	1	1	yes	characteristic
265	#107×C₆₁	C₂³	1	2	yes	—
266	#107×C₆₁	C₂³	1	1	yes	characteristic
267	#107×C₆₁	C₂³	1	2	yes	—
268	#107×C₆₁	C₂³	1	2	yes	—
269	#107×C₆₁	C₂³	1	2	yes	—
270	#106×C₆₁	C₂³	1	1	yes	characteristic
271	#106×C₆₁	C₂³	1	2	yes	—
272	#106×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	2	yes	—
275	#106×C₆₁	C₂³	1	2	yes	—
276	#106×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×C₆₁	C₂³	1	2	yes	—
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	1	yes	characteristic
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#102×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
297	#102×C₆₁	C₂³	1	1	yes	characteristic
298	#102×C₆₁	C₂³	1	1	yes	characteristic
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	2	yes	—
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	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	#41×C₆₁	—	4	2	no	—
314	#41×C₆₁	—	4	2	no	—
315	#41×C₆₁	—	4	2	no	—
316	#41×C₆₁	—	4	2	no	—
317	#41×C₆₁	—	8	2	no	—
318	#41×C₆₁	—	8	2	no	—
319	C₂×Q₈×C₆₁	—	2	1	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	—	4	2	no	—
324	C₂×Q₈×C₆₁	—	4	2	no	—
325	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
328	C₂×D₄×C₆₁	—	2	2	no	—
329	C₂×D₄×C₆₁	—	2	2	no	—
330	C₂×D₄×C₆₁	—	2	1	no	—
331	C₂×D₄×C₆₁	—	2	2	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	1	no	—
336	C₂×D₄×C₆₁	—	4	1	no	—
337	C₂×D₄×C₆₁	—	4	1	no	—
338	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₆₁	—	2	1	no	—
348	C₂²×C₄×C₆₁	—	2	2	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	—	2	1	no	—
354	C₂²×C₄×C₆₁	—	2	1	no	—
355	C₂²×C₄×C₆₁	—	2	2	no	—
356	C₂²×C₄×C₆₁	—	2	1	no	—
357	C₂²×C₄×C₆₁	—	2	1	no	—
358	C₂²×C₄×C₆₁	—	8	2	no	—
359	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
364	SD₁₆×C₆₁	—	4	1	no	—
365	SD₁₆×C₆₁	—	4	2	no	—
366	SD₁₆×C₆₁	—	4	1	no	—
367	SD₁₆×C₆₁	—	4	2	no	—
368	D₈×C₆₁	—	4	1	no	—
369	D₈×C₆₁	—	4	1	no	—
370	M₁₆×C₆₁	—	4	2	no	—
371	M₁₆×C₆₁	—	4	2	no	—
372	C₂×C₈×C₆₁	—	4	2	no	—
373	C₂×C₈×C₆₁	—	4	2	no	—
374	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
376	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
378	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₆₁	—	2	1	no	—
381	C₄⋊C₄×C₆₁	—	2	2	no	—
382	C₄⋊C₄×C₆₁	—	2	1	no	—
383	C₄⋊C₄×C₆₁	—	2	2	no	—
384	C₄⋊C₄×C₆₁	—	2	2	no	—
385	C₄⋊C₄×C₆₁	—	2	2	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	1	no	—
389	C₄⋊C₄×C₆₁	—	2	2	no	—
390	C₄⋊C₄×C₆₁	—	2	1	no	—
391	C₄⋊C₄×C₆₁	—	2	1	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	2	no	—
394	C₄⋊C₄×C₆₁	—	2	2	no	—
395	C₄⋊C₄×C₆₁	—	2	2	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	1	no	—
400	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
410	C₂²⋊C₄×C₆₁	—	2	2	no	—
411	C₂²⋊C₄×C₆₁	—	2	2	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	2	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	1	no	—
419	C₂²⋊C₄×C₆₁	—	2	1	no	—
420	C₂²⋊C₄×C₆₁	—	2	1	no	—
421	C₂²⋊C₄×C₆₁	—	2	1	no	—
422	C₂²⋊C₄×C₆₁	—	2	1	no	—
423	C₂²⋊C₄×C₆₁	—	2	2	no	—
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	1	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	1	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	1	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	C₄²×C₆₁	—	2	2	no	—
437	C₄²×C₆₁	—	2	2	no	—
438	C₄²×C₆₁	—	2	2	no	—
439	C₄²×C₆₁	—	2	2	no	—
440	C₄²×C₆₁	—	2	1	no	—
441	C₄²×C₆₁	—	2	2	no	—
442	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
446	C₂³×C₆₁	—	2	1	no	—
447	C₂³×C₆₁	—	2	1	no	—
448	C₂³×C₆₁	—	2	1	no	—
449	C₂³×C₆₁	—	4	2	no	—
450	C₂³×C₆₁	—	8	1	no	—
451	C₂³×C₆₁	—	8	1	no	—
452	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
453	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
454	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
455	Q₈×C₆₁	—	2	1	no	—
456	Q₈×C₆₁	—	2	1	no	—
457	Q₈×C₆₁	—	2	2	no	—
458	Q₈×C₆₁	—	2	2	no	—
459	Q₈×C₆₁	—	4	2	no	—
460	Q₈×C₆₁	—	4	2	no	—
461	Q₈×C₆₁	—	8	1	no	—
462	Q₈×C₆₁	—	8	1	no	—
463	Q₈×C₆₁	—	8	2	no	—
464	D₄×C₆₁	—	2	2	no	—
465	D₄×C₆₁	—	2	2	no	—
466	D₄×C₆₁	—	2	1	no	—
467	D₄×C₆₁	—	2	1	no	—
468	D₄×C₆₁	—	2	1	no	—
469	D₄×C₆₁	—	2	1	no	—
470	D₄×C₆₁	—	2	1	no	—
471	D₄×C₆₁	—	2	1	no	—
472	D₄×C₆₁	—	4	2	no	—
473	D₄×C₆₁	—	4	2	no	—
474	D₄×C₆₁	—	4	2	no	—
475	D₄×C₆₁	—	4	2	no	—
476	D₄×C₆₁	—	4	2	no	—
477	D₄×C₆₁	—	8	1	no	—
478	D₄×C₆₁	—	8	2	no	—
479	D₄×C₆₁	—	8	2	no	—
480	D₄×C₆₁	—	8	2	no	—
481	D₄×C₆₁	—	8	2	no	—
482	D₄×C₆₁	—	8	2	no	—
483	D₄×C₆₁	—	8	2	no	—
484	C₂×C₄×C₆₁	—	2	2	no	—
485	C₂×C₄×C₆₁	—	2	2	no	—
486	C₂×C₄×C₆₁	—	2	2	no	—
487	C₂×C₄×C₆₁	—	2	2	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	1	no	—
493	C₂×C₄×C₆₁	—	2	2	no	—
494	C₂×C₄×C₆₁	—	2	1	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	2	no	—
499	C₂×C₄×C₆₁	—	2	2	no	—
500	C₂×C₄×C₆₁	—	4	1	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	2	no	—
508	C₂×C₄×C₆₁	—	8	1	no	—
509	C₂×C₄×C₆₁	—	8	2	no	—
510	C₂×C₄×C₆₁	—	8	2	no	—
511	C₂×C₄×C₆₁	—	8	2	no	—
512	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
520	C₈×C₆₁	—	2	1	no	—
521	C₈×C₆₁	—	2	2	no	—
522	C₈×C₆₁	—	2	1	no	—
523	C₈×C₆₁	—	2	1	no	—
524	C₈×C₆₁	—	2	1	no	—
525	C₈×C₆₁	—	2	2	no	—
526	#61785	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
527	C₂²×C₆₁	—	2	1	no	—
528	C₂²×C₆₁	—	2	2	no	—
529	C₂²×C₆₁	—	2	2	no	—
530	C₂²×C₆₁	—	2	2	no	—
531	C₂²×C₆₁	—	2	1	no	—
532	C₂²×C₆₁	—	2	2	no	—
533	C₂²×C₆₁	—	2	1	no	—
534	C₂²×C₆₁	—	2	2	no	—
535	C₂²×C₆₁	—	2	2	no	—
536	C₂²×C₆₁	—	4	1	no	—
537	C₂²×C₆₁	—	4	1	no	—
538	C₂²×C₆₁	—	4	1	no	—
539	C₂²×C₆₁	—	4	1	no	—
540	C₂²×C₆₁	—	4	1	no	—
541	C₂²×C₆₁	—	4	1	no	—
542	C₂²×C₆₁	—	4	1	no	—
543	C₂²×C₆₁	—	4	1	no	—
544	C₂²×C₆₁	—	4	1	no	—
545	C₂²×C₆₁	—	8	4	no	—
546	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
547	C₄×C₆₁	—	2	1	no	—
548	C₄×C₆₁	—	2	1	no	—
549	C₄×C₆₁	—	2	2	no	—
550	C₄×C₆₁	—	2	1	no	—
551	C₄×C₆₁	—	2	2	no	—
552	C₄×C₆₁	—	2	1	no	—
553	C₄×C₆₁	—	4	1	no	—
554	C₄×C₆₁	—	4	2	no	—
555	C₄×C₆₁	—	4	2	no	—
556	C₄×C₆₁	—	4	2	no	—
557	C₄×C₆₁	—	4	1	no	—
558	C₄×C₆₁	—	4	1	no	—
559	C₄×C₆₁	—	4	1	no	—
560	C₄×C₆₁	—	4	1	no	—
561	C₄×C₆₁	—	4	2	no	—
562	C₄×C₆₁	#577	1	2	yes	—
563	C₄×C₆₁	#585	1	1	yes	characteristic
564	C₄×C₆₁	#585	1	1	yes	characteristic
565	#3547	C₂×C₆₁	1	1	yes	characteristic, complemented
566	#3506	C₂×C₆₁	1	1	yes	characteristic, complemented
567	#3357	C₂×C₆₁	1	1	yes	characteristic, complemented
568	#3354	C₂×C₆₁	1	1	yes	characteristic, complemented
569	#3351	C₂×C₆₁	1	2	yes	complemented
570	#3341	C₂×C₆₁	1	1	yes	characteristic, complemented
571	#3337	C₂×C₆₁	1	2	yes	complemented
572	#3335	C₂×C₆₁	1	1	yes	characteristic, complemented
573	#3330	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3329	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3326	C₂×C₆₁	1	2	yes	complemented
576	#3303	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3301	C₂×C₆₁	1	2	yes	complemented
578	#3298	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3233	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#3231	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3200	C₂×C₆₁	1	2	yes	complemented
582	#3198	C₂×C₆₁	1	2	yes	complemented
583	#3105	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3101	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#3099	C₂×C₆₁	1	2	yes	complemented
586	#3097	C₂×C₆₁	1	2	yes	complemented
587	#2979	C₂×C₆₁	1	1	yes	characteristic, complemented
588	C₂×C₆₁	—	4	2	no	—
589	C₂×C₆₁	—	4	2	no	—
590	C₂×C₆₁	—	4	1	no	—
591	C₂×C₆₁	—	8	1	no	—
592	C₂×C₆₁	—	8	1	no	—
593	C₂×C₆₁	—	8	1	no	—
594	C₂×C₆₁	#3485	1	1	yes	characteristic
595	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
596	C₂×C₆₁	#3584	1	1	yes	characteristic
597	#562	—	2	2	no	—
598	#559	—	2	2	no	—
599	#556	—	2	1	no	—
600	#555	—	2	1	no	—
601	#555	C₂²×C₆₁	1	1	yes	characteristic
602	#555	C₂²×C₆₁	1	1	yes	characteristic
603	#555	C₂²×C₆₁	1	1	yes	characteristic, complemented
604	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
605	#553	—	2	1	no	—
606	#553	C₂²×C₆₁	1	2	yes	—
607	#553	C₂²×C₆₁	1	2	yes	—
608	#552	C₂²×C₆₁	1	2	yes	complemented
609	#550	—	2	1	no	—
610	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
611	#548	C₂²×C₆₁	1	2	yes	complemented
612	#547	C₂²×C₆₁	1	1	yes	characteristic
613	#547	C₂²×C₆₁	1	1	yes	characteristic
614	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
615	#544	—	2	1	no	—
616	#542	—	2	2	no	—
617	#540	—	2	1	no	—
618	#538	—	2	2	no	—
619	#537	C₂²×C₆₁	1	2	yes	—
620	#536	C₂²×C₆₁	1	2	yes	—
621	#535	C₂²×C₆₁	1	2	yes	—
622	#533	C₂²×C₆₁	1	1	yes	characteristic
623	#533	C₂²×C₆₁	1	1	yes	characteristic
624	#532	C₂²×C₆₁	1	1	yes	characteristic
625	#529	C₂²×C₆₁	1	1	yes	characteristic
626	#525	—	2	1	no	—
627	#525	—	2	1	no	—
628	#520	C₂²×C₆₁	1	2	yes	—
629	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
630	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
631	#499	C₂²×C₆₁	1	2	yes	complemented
632	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
633	#488	C₂²×C₆₁	1	2	yes	complemented
634	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
635	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
636	#485	C₂²×C₆₁	1	2	yes	—
637	#485	C₂²×C₆₁	1	2	yes	—
638	#485	C₂²×C₆₁	1	2	yes	—
639	#485	C₂²×C₆₁	1	2	yes	complemented
640	#485	C₂²×C₆₁	1	2	yes	complemented
641	#485	C₂²×C₆₁	1	2	yes	complemented
642	#484	C₂²×C₆₁	1	1	yes	characteristic
643	#484	C₂²×C₆₁	1	2	yes	complemented
644	#483	C₂²×C₆₁	1	2	yes	—
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	2	yes	—
649	#482	C₂²×C₆₁	1	2	yes	—
650	#482	C₂²×C₆₁	1	2	yes	complemented
651	#481	C₂²×C₆₁	1	2	yes	—
652	#481	C₂²×C₆₁	1	1	yes	characteristic
653	#481	C₂²×C₆₁	1	2	yes	complemented
654	#480	C₂²×C₆₁	1	2	yes	—
655	#479	C₂²×C₆₁	1	2	yes	complemented
656	#479	C₂²×C₆₁	1	2	yes	complemented
657	#478	C₂²×C₆₁	1	1	yes	characteristic
658	#478	C₂²×C₆₁	1	1	yes	characteristic
659	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	#476	C₂²×C₆₁	1	1	yes	characteristic
661	#476	C₂²×C₆₁	1	1	yes	characteristic
662	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
663	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
664	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
665	#469	C₂²×C₆₁	1	2	yes	—
666	#468	C₂²×C₆₁	1	2	yes	—
667	#468	C₂²×C₆₁	1	2	yes	—
668	#468	C₂²×C₆₁	1	2	yes	—
669	#466	C₂²×C₆₁	1	2	yes	—
670	#465	C₂²×C₆₁	1	2	yes	—
671	#465	C₂²×C₆₁	1	2	yes	—
672	#465	C₂²×C₆₁	1	2	yes	—
673	#463	C₂²×C₆₁	1	1	yes	characteristic
674	#463	C₂²×C₆₁	1	1	yes	characteristic
675	#461	C₂²×C₆₁	1	1	yes	characteristic
676	#461	C₂²×C₆₁	1	1	yes	characteristic
677	#450	C₂²×C₆₁	1	2	yes	—
678	#450	C₂²×C₆₁	1	1	yes	characteristic
679	#449	C₂²×C₆₁	1	2	yes	—
680	#449	C₂²×C₆₁	1	2	yes	—
681	#448	C₂²×C₆₁	1	2	yes	—
682	#448	C₂²×C₆₁	1	2	yes	—
683	#447	C₂²×C₆₁	1	1	yes	characteristic
684	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
686	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
687	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
688	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
689	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
690	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
691	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
692	#436	C₂²×C₆₁	1	2	yes	complemented
693	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
694	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
695	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
696	#431	C₂²×C₆₁	1	1	yes	characteristic
697	#431	C₂²×C₆₁	1	1	yes	characteristic
698	#428	C₂²×C₆₁	1	2	yes	complemented
699	#428	C₂²×C₆₁	1	2	yes	complemented
700	#427	C₂²×C₆₁	1	2	yes	complemented
701	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
702	#419	C₂²×C₆₁	1	2	yes	complemented
703	#417	C₂²×C₆₁	1	2	yes	complemented
704	#416	C₂²×C₆₁	1	2	yes	complemented
705	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
706	#408	C₂²×C₆₁	1	2	yes	—
707	#408	C₂²×C₆₁	1	2	yes	—
708	C₆₁	#61785	1	1	yes	characteristic, direct product factor, Sylow
709	C₂×#41	—	2	1	no	—
710	C₂×#41	—	2	1	no	—
711	C₂×#41	C₂³×C₆₁	1	2	yes	—
712	C₂×#41	C₂³×C₆₁	1	2	yes	—
713	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
714	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
715	C₂³×C₄	—	2	1	no	—
716	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
717	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
718	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
720	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
721	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
722	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
723	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
724	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
725	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
726	C₄⋊Q₈	—	2	2	no	—
727	C₄⋊Q₈	—	2	1	no	—
728	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
731	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
732	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
733	#127	—	2	2	no	—
734	#127	D₄×C₆₁	1	1	yes	characteristic
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	1	no	—
739	#125	—	2	2	no	—
740	#125	—	2	1	no	—
741	#125	—	2	1	no	—
742	#125	C₂³×C₆₁	1	1	yes	characteristic
743	#125	C₂³×C₆₁	1	2	yes	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	2	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#124	D₄×C₆₁	1	2	yes	—
751	#124	C₂³×C₆₁	1	1	yes	characteristic
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	1	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	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	C₂³×C₆₁	1	1	yes	characteristic
771	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
775	#121	—	2	1	no	—
776	#121	—	2	1	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	1	no	—
783	#121	—	2	2	no	—
784	#121	—	2	1	no	—
785	#121	D₄×C₆₁	1	1	yes	characteristic
786	#121	D₄×C₆₁	1	1	yes	characteristic
787	#121	D₄×C₆₁	1	2	yes	—
788	#121	C₂³×C₆₁	1	1	yes	characteristic
789	#121	C₂³×C₆₁	1	2	yes	—
790	#121	C₂³×C₆₁	1	2	yes	—
791	#121	C₂³×C₆₁	1	2	yes	—
792	#121	C₂³×C₆₁	1	2	yes	—
793	#121	C₂³×C₆₁	1	2	yes	—
794	#120	—	2	2	no	—
795	#120	—	2	2	no	—
796	C₄×Q₈	—	2	2	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₆₁	1	2	yes	—
821	#117	—	2	1	no	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	1	no	—
825	#117	—	2	2	no	—
826	#117	—	2	1	no	—
827	#117	C₂³×C₆₁	1	2	yes	—
828	#117	C₂³×C₆₁	1	2	yes	—
829	#117	C₂³×C₆₁	1	2	yes	—
830	#117	C₂³×C₆₁	1	2	yes	—
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
834	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
835	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
836	C₂×C₂²⋊C₄	—	2	1	no	—
837	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
838	#107	C₂³×C₆₁	1	1	yes	characteristic
839	#107	C₂³×C₆₁	1	2	yes	—
840	#107	C₂³×C₆₁	1	1	yes	characteristic
841	#107	C₂³×C₆₁	1	2	yes	—
842	#107	C₂³×C₆₁	1	2	yes	—
843	#107	C₂³×C₆₁	1	2	yes	—
844	#106	C₂³×C₆₁	1	1	yes	characteristic
845	#106	C₂³×C₆₁	1	2	yes	—
846	#106	C₂³×C₆₁	1	2	yes	—
847	#106	C₂³×C₆₁	1	2	yes	—
848	#106	C₂³×C₆₁	1	2	yes	—
849	#106	C₂³×C₆₁	1	2	yes	—
850	#106	C₂³×C₆₁	1	1	yes	characteristic
851	#106	C₂³×C₆₁	1	2	yes	—
852	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
856	#103	C₂³×C₆₁	1	1	yes	characteristic
857	#103	C₂³×C₆₁	1	2	yes	—
858	#103	C₂³×C₆₁	1	2	yes	—
859	#103	C₂³×C₆₁	1	2	yes	—
860	#103	C₂³×C₆₁	1	2	yes	—
861	#103	C₂³×C₆₁	1	2	yes	—
862	#103	C₂³×C₆₁	1	2	yes	—
863	#103	C₂³×C₆₁	1	1	yes	characteristic
864	#103	C₂³×C₆₁	1	2	yes	—
865	#103	C₂³×C₆₁	1	2	yes	—
866	#102	C₂³×C₆₁	1	1	yes	characteristic
867	#102	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	1	yes	characteristic
871	#102	C₂³×C₆₁	1	1	yes	characteristic
872	#102	C₂³×C₆₁	1	1	yes	characteristic
873	#102	C₂³×C₆₁	1	1	yes	characteristic
874	#102	C₂³×C₆₁	1	2	yes	—
875	#102	C₂³×C₆₁	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
878	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
883	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₆₁	1	2	yes	—
886	C₂⁴	—	2	1	no	—
887	#41	—	4	2	no	—
888	#41	—	4	2	no	—
889	#41	—	4	2	no	—
890	#41	—	4	2	no	—
891	#41	—	8	2	no	—
892	#41	—	8	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	4	2	no	—
898	C₂×Q₈	—	4	2	no	—
899	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
900	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	4	1	no	—
911	C₂×D₄	—	4	1	no	—
912	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
913	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
914	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
916	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
917	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
918	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	8	2	no	—
933	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
934	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
938	SD₁₆	—	4	1	no	—
939	SD₁₆	—	4	2	no	—
940	SD₁₆	—	4	1	no	—
941	SD₁₆	—	4	2	no	—
942	D₈	—	4	1	no	—
943	D₈	—	4	1	no	—
944	M₁₆	—	4	2	no	—
945	M₁₆	—	4	2	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	—	4	2	no	—
948	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
950	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
952	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	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	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
979	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
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	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1017	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1018	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1019	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	4	2	no	—
1024	C₂³	—	8	1	no	—
1025	C₂³	—	8	1	no	—
1026	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1027	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1028	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	4	2	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	1	no	—
1036	Q₈	—	8	1	no	—
1037	Q₈	—	8	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	4	1	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	8	1	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1093	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1094	C₈	—	2	1	no	—
1095	C₈	—	2	2	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	1	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	8	4	no	—
1119	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1120	C₄	—	2	1	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	C₆₁×#577	1	2	yes	—
1136	C₄	C₆₁×#585	1	1	yes	characteristic
1137	C₄	C₆₁×#585	1	1	yes	characteristic
1138	C₂	—	4	1	no	—
1139	C₂	—	4	2	no	—
1140	C₂	—	4	2	no	—
1141	C₂	—	8	1	no	—
1142	C₂	—	8	1	no	—
1143	C₂	—	8	1	no	—
1144	C₂	C₆₁×#3485	1	1	yes	characteristic
1145	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1146	C₂	C₆₁×#3584	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×#3547	C₂	semidirect
2. C₆₁×#3506	C₂	semidirect
3. C₆₁×#3357	C₂	semidirect
4. C₆₁×#3354	C₂	semidirect
5. C₆₁×#3351	C₂	semidirect
6. C₆₁×#3341	C₂	semidirect
7. C₆₁×#3337	C₂	semidirect
8. C₆₁×#3335	C₂	semidirect
9. C₆₁×#3330	C₂	semidirect
10. C₆₁×#3329	C₂	semidirect
11. C₆₁×#3326	C₂	semidirect
12. C₆₁×#3303	C₂	semidirect
13. C₆₁×#3301	C₂	semidirect
14. C₆₁×#3298	C₂	semidirect
15. C₆₁×#3233	C₂	semidirect
16. C₆₁×#3231	C₂	semidirect
17. C₆₁×#3200	C₂	semidirect
18. C₆₁×#3198	C₂	semidirect
19. C₆₁×#3105	C₂	semidirect
20. C₆₁×#3101	C₂	semidirect
21. C₆₁×#3099	C₂	semidirect
22. C₆₁×#3097	C₂	semidirect
23. C₆₁×#2979	C₂	semidirect
30. C₆₁×#555	C₂²	semidirect
31. C₆₁×#554	C₂²	semidirect
35. C₆₁×#552	C₂²	semidirect
37. D₄×Q₈×C₆₁	C₂²	semidirect
38. C₆₁×#548	C₂²	semidirect
41. C₆₁×#547	C₂²	semidirect
57. C₆₁×#500	C₂²	semidirect
58. C₆₁×#499	C₂²	semidirect
59. C₆₁×#498	C₂²	semidirect
60. C₆₁×#488	C₂²	semidirect
61. C₆₁×#487	C₂²	semidirect
62. C₆₁×#487	C₂²	semidirect
66. C₆₁×#485	C₂²	semidirect
67. C₆₁×#485	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
70. C₆₁×#484	C₂²	semidirect
72. C₆₁×#483	C₂²	semidirect
73. C₆₁×#483	C₂²	semidirect
77. C₆₁×#482	C₂²	semidirect
80. C₆₁×#481	C₂²	semidirect
82. C₆₁×#479	C₂²	semidirect
83. C₆₁×#479	C₂²	semidirect
86. C₆₁×#477	C₂²	semidirect
89. C₆₁×#476	C₂²	semidirect
90. C₆₁×#475	C₂²	semidirect
91. C₆₁×#474	C₂²	semidirect
117. C₆₁×#436	C₂²	semidirect
118. C₆₁×#436	C₂²	semidirect
119. C₆₁×#436	C₂²	semidirect
120. C₈×D₄×C₆₁	C₂²	semidirect
121. C₈×D₄×C₆₁	C₂²	semidirect
122. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#428	C₂²	semidirect
126. C₆₁×#428	C₂²	semidirect
127. C₆₁×#427	C₂²	semidirect
128. C₂×#106×C₆₁	C₂²	semidirect
129. C₆₁×#419	C₂²	semidirect
130. C₆₁×#417	C₂²	semidirect
131. C₆₁×#416	C₂²	semidirect
132. C₂×#103×C₆₁	C₂²	semidirect
526. #61785	C₆₁	direct (N × H)
565. #3547	C₂×C₆₁	semidirect
566. #3506	C₂×C₆₁	semidirect
567. #3357	C₂×C₆₁	semidirect
568. #3354	C₂×C₆₁	semidirect
569. #3351	C₂×C₆₁	semidirect
570. #3341	C₂×C₆₁	semidirect
571. #3337	C₂×C₆₁	semidirect
572. #3335	C₂×C₆₁	semidirect
573. #3330	C₂×C₆₁	semidirect
574. #3329	C₂×C₆₁	semidirect
575. #3326	C₂×C₆₁	semidirect
576. #3303	C₂×C₆₁	semidirect
577. #3301	C₂×C₆₁	semidirect
578. #3298	C₂×C₆₁	semidirect
579. #3233	C₂×C₆₁	semidirect
580. #3231	C₂×C₆₁	semidirect
581. #3200	C₂×C₆₁	semidirect
582. #3198	C₂×C₆₁	semidirect
583. #3105	C₂×C₆₁	semidirect
584. #3101	C₂×C₆₁	semidirect
585. #3099	C₂×C₆₁	semidirect
586. #3097	C₂×C₆₁	semidirect
587. #2979	C₂×C₆₁	semidirect
603. #555	C₂²×C₆₁	semidirect
604. #554	C₂²×C₆₁	semidirect
608. #552	C₂²×C₆₁	semidirect
610. D₄×Q₈	C₂²×C₆₁	semidirect
611. #548	C₂²×C₆₁	semidirect
614. #547	C₂²×C₆₁	semidirect
630. #500	C₂²×C₆₁	semidirect
631. #499	C₂²×C₆₁	semidirect
632. #498	C₂²×C₆₁	semidirect
633. #488	C₂²×C₆₁	semidirect
634. #487	C₂²×C₆₁	semidirect
635. #487	C₂²×C₆₁	semidirect
639. #485	C₂²×C₆₁	semidirect
640. #485	C₂²×C₆₁	semidirect
641. #485	C₂²×C₆₁	semidirect
643. #484	C₂²×C₆₁	semidirect
645. #483	C₂²×C₆₁	semidirect
646. #483	C₂²×C₆₁	semidirect
650. #482	C₂²×C₆₁	semidirect
653. #481	C₂²×C₆₁	semidirect
655. #479	C₂²×C₆₁	semidirect
656. #479	C₂²×C₆₁	semidirect
659. #477	C₂²×C₆₁	semidirect
662. #476	C₂²×C₆₁	semidirect
663. #475	C₂²×C₆₁	semidirect
664. #474	C₂²×C₆₁	semidirect
690. #436	C₂²×C₆₁	semidirect
691. #436	C₂²×C₆₁	semidirect
692. #436	C₂²×C₆₁	semidirect
693. C₈×D₄	C₂²×C₆₁	semidirect
694. C₈×D₄	C₂²×C₆₁	semidirect
695. C₈×D₄	C₂²×C₆₁	semidirect
698. #428	C₂²×C₆₁	semidirect
699. #428	C₂²×C₆₁	semidirect
700. #427	C₂²×C₆₁	semidirect
701. C₂×#106	C₂²×C₆₁	semidirect
702. #419	C₂²×C₆₁	semidirect
703. #417	C₂²×C₆₁	semidirect
704. #416	C₂²×C₆₁	semidirect
705. C₂×#103	C₂²×C₆₁	semidirect
708. C₆₁	#61785	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×#3547	2
C₆₁×#3506	2
C₆₁×#3357	2
C₆₁×#3354	2
C₆₁×#3351	2
C₆₁×#3341	2
C₆₁×#3337	2
C₆₁×#3335	2
C₆₁×#3330	2
C₆₁×#3329	2
C₆₁×#3326	2
C₆₁×#3303	2
C₆₁×#3301	2
C₆₁×#3298	2
C₆₁×#3233	2
C₆₁×#3231	2
C₆₁×#3200	2
C₆₁×#3198	2
C₆₁×#3105	2
C₆₁×#3101	2
C₆₁×#3099	2
C₆₁×#3097	2
C₆₁×#2979	2
#61785	61

Subgroups — C61×#61785 #29565218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61785 #29565218