Subgroups — C₆₁×#62073 #29565506

Order 15616.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3307	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3301	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3284	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3271	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3257	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3221	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3125	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3046	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₁	C₂²	1	2	yes	—
25	C₂×#135×C₆₁	C₂²	1	2	yes	—
26	C₂×#135×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#562	—	2	2	no	—
28	C₆₁×#559	—	2	1	no	—
29	C₆₁×#559	C₂²	1	1	yes	characteristic
30	C₆₁×#557	C₂²	1	1	yes	characteristic
31	C₆₁×#557	C₂²	1	1	yes	characteristic
32	C₆₁×#554	—	2	1	no	—
33	C₆₁×#553	—	2	2	no	—
34	C₆₁×#553	C₂²	1	2	yes	—
35	C₆₁×#550	—	2	1	no	—
36	C₆₁×#550	C₂²	1	1	yes	characteristic
37	C₆₁×#550	C₂²	1	1	yes	characteristic
38	C₆₁×#550	C₂²	1	2	yes	—
39	C₆₁×#550	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#548	C₂²	1	2	yes	—
42	C₆₁×#547	—	2	1	no	—
43	C₆₁×#547	C₂²	1	2	yes	—
44	C₆₁×#547	C₂²	1	1	yes	characteristic
45	C₆₁×#542	—	2	1	no	—
46	C₆₁×#542	C₂²	1	2	yes	—
47	C₆₁×#540	—	2	2	no	—
48	C₆₁×#540	—	2	1	no	—
49	C₆₁×#540	C₂²	1	2	yes	—
50	C₆₁×#539	—	2	2	no	—
51	C₆₁×#536	C₂²	1	2	yes	—
52	C₆₁×#533	C₂²	1	1	yes	characteristic
53	C₆₁×#532	—	2	1	no	—
54	C₆₁×#532	C₂²	1	1	yes	characteristic
55	C₆₁×#532	C₂²	1	1	yes	characteristic
56	C₆₁×#529	—	2	1	no	—
57	C₆₁×#529	C₂²	1	1	yes	characteristic
58	C₆₁×#520	C₂²	1	2	yes	—
59	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
60	C₆₁×#496	C₂²	1	2	yes	—
61	C₆₁×#493	C₂²	1	1	yes	characteristic
62	C₆₁×#492	C₂²	1	1	yes	characteristic
63	C₆₁×#492	C₂²	1	2	yes	—
64	C₆₁×#491	C₂²	1	2	yes	—
65	C₆₁×#488	C₂²	1	2	yes	—
66	C₆₁×#487	C₂²	1	1	yes	characteristic
67	C₆₁×#486	C₂²	1	1	yes	characteristic
68	C₆₁×#485	C₂²	1	1	yes	characteristic
69	C₆₁×#485	C₂²	1	1	yes	characteristic
70	C₆₁×#483	C₂²	1	2	yes	—
71	C₆₁×#481	C₂²	1	2	yes	—
72	C₆₁×#479	C₂²	1	2	yes	—
73	C₆₁×#478	C₂²	1	2	yes	—
74	C₆₁×#476	C₂²	1	2	yes	—
75	C₆₁×#475	C₂²	1	1	yes	characteristic
76	C₆₁×#475	C₂²	1	1	yes	characteristic
77	C₆₁×#475	C₂²	1	1	yes	characteristic
78	C₆₁×#474	C₂²	1	1	yes	characteristic
79	C₆₁×#469	C₂²	1	2	yes	—
80	C₆₁×#468	C₂²	1	2	yes	—
81	C₆₁×#466	C₂²	1	2	yes	—
82	C₆₁×#465	C₂²	1	2	yes	—
83	C₆₁×#465	C₂²	1	2	yes	—
84	C₆₁×#465	C₂²	1	2	yes	—
85	C₆₁×#464	C₂²	1	2	yes	—
86	C₆₁×#464	C₂²	1	2	yes	—
87	C₆₁×#463	C₂²	1	2	yes	—
88	C₆₁×#463	C₂²	1	2	yes	—
89	C₆₁×#463	C₂²	1	2	yes	—
90	C₆₁×#463	C₂²	1	2	yes	—
91	C₆₁×#462	C₂²	1	1	yes	characteristic
92	C₆₁×#462	C₂²	1	1	yes	characteristic
93	C₆₁×#462	C₂²	1	2	yes	—
94	C₆₁×#461	C₂²	1	1	yes	characteristic
95	C₆₁×#461	C₂²	1	2	yes	—
96	C₆₁×#461	C₂²	1	2	yes	—
97	C₆₁×#461	C₂²	1	1	yes	characteristic
98	C₆₁×#460	C₂²	1	1	yes	characteristic
99	C₆₁×#460	C₂²	1	1	yes	characteristic
100	C₆₁×#460	C₂²	1	2	yes	—
101	C₆₁×#460	C₂²	1	1	yes	characteristic
102	C₆₁×#459	C₂²	1	1	yes	characteristic
103	C₆₁×#459	C₂²	1	2	yes	—
104	C₆₁×#452	C₂²	1	1	yes	characteristic
105	C₆₁×#452	C₂²	1	1	yes	characteristic
106	C₆₁×#452	C₂²	1	2	yes	—
107	C₆₁×#449	C₂²	1	2	yes	—
108	C₆₁×#449	C₂²	1	2	yes	—
109	C₆₁×#449	C₂²	1	2	yes	—
110	C₆₁×#449	C₂²	1	2	yes	—
111	C₆₁×#449	C₂²	1	2	yes	—
112	C₆₁×#448	C₂²	1	2	yes	—
113	C₆₁×#448	C₂²	1	2	yes	—
114	C₆₁×#446	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
116	C₆₁×#442	C₂²	1	2	yes	—
117	C₆₁×#441	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
122	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
124	C₆₁×#436	C₂²	1	1	yes	characteristic
125	C₆₁×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₆₁	C₂²	1	2	yes	—
128	C₆₁×#433	C₂²	1	2	yes	—
129	C₆₁×#431	C₂²	1	1	yes	characteristic
130	C₆₁×#424	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
132	C₆₁×#417	C₂²	1	2	yes	—
133	C₆₁×#416	C₂²	1	2	yes	—
134	C₂×#103×C₆₁	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	—	2	1	no	—
138	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
139	C₂×#41×C₆₁	C₂³	1	2	yes	—
140	C₂×#41×C₆₁	C₂³	1	2	yes	—
141	C₂×#41×C₆₁	C₂³	1	2	yes	—
142	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
143	#137×C₆₁	—	4	4	no	—
144	#135×C₆₁	—	4	4	no	—
145	#135×C₆₁	—	4	4	no	—
146	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₆₁	C₂³	1	2	yes	—
158	C₂×D₈×C₆₁	C₂³	1	2	yes	—
159	C₂×D₈×C₆₁	C₂³	1	2	yes	—
160	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₁	—	2	1	no	—
164	C₄⋊Q₈×C₆₁	—	2	1	no	—
165	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	#127×C₆₁	—	2	1	no	—
171	#127×C₆₁	—	2	2	no	—
172	#127×C₆₁	—	2	1	no	—
173	#127×C₆₁	C₂³	1	1	yes	characteristic
174	#127×C₆₁	C₂³	1	1	yes	characteristic
175	#127×C₆₁	C₂³	1	2	yes	—
176	#126×C₆₁	—	2	2	no	—
177	#126×C₆₁	—	2	2	no	—
178	#126×C₆₁	D₄	1	2	yes	—
179	#125×C₆₁	—	2	2	no	—
180	#125×C₆₁	—	2	2	no	—
181	#125×C₆₁	—	2	1	no	—
182	#125×C₆₁	—	2	1	no	—
183	#125×C₆₁	D₄	1	1	yes	characteristic
184	#125×C₆₁	C₂³	1	2	yes	—
185	#124×C₆₁	—	2	1	no	—
186	#124×C₆₁	—	2	2	no	—
187	#124×C₆₁	—	2	2	no	—
188	#124×C₆₁	—	2	1	no	—
189	#124×C₆₁	D₄	1	1	yes	characteristic
190	#124×C₆₁	C₂³	1	2	yes	—
191	#124×C₆₁	C₂³	1	2	yes	—
192	#123×C₆₁	—	2	2	no	—
193	#123×C₆₁	—	2	2	no	—
194	#123×C₆₁	—	2	2	no	—
195	#123×C₆₁	—	2	2	no	—
196	#123×C₆₁	—	2	2	no	—
197	#123×C₆₁	—	2	2	no	—
198	#123×C₆₁	—	2	2	no	—
199	#123×C₆₁	—	2	2	no	—
200	#123×C₆₁	—	2	2	no	—
201	#123×C₆₁	—	2	2	no	—
202	#123×C₆₁	D₄	1	2	yes	—
203	C₂²⋊Q₈×C₆₁	—	2	1	no	—
204	C₂²⋊Q₈×C₆₁	—	2	2	no	—
205	C₂²⋊Q₈×C₆₁	—	2	2	no	—
206	C₂²⋊Q₈×C₆₁	—	2	2	no	—
207	C₂²⋊Q₈×C₆₁	—	2	2	no	—
208	C₂²⋊Q₈×C₆₁	—	2	1	no	—
209	C₂²⋊Q₈×C₆₁	—	2	2	no	—
210	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
214	#121×C₆₁	—	2	2	no	—
215	#121×C₆₁	—	2	2	no	—
216	#121×C₆₁	—	2	2	no	—
217	#121×C₆₁	—	2	1	no	—
218	#121×C₆₁	—	2	1	no	—
219	#121×C₆₁	—	2	1	no	—
220	#121×C₆₁	—	2	2	no	—
221	#121×C₆₁	—	2	1	no	—
222	#121×C₆₁	—	2	2	no	—
223	#121×C₆₁	—	2	2	no	—
224	#121×C₆₁	—	2	2	no	—
225	#121×C₆₁	—	2	2	no	—
226	#121×C₆₁	—	2	2	no	—
227	#121×C₆₁	—	2	2	no	—
228	#121×C₆₁	D₄	1	1	yes	characteristic
229	#121×C₆₁	C₂³	1	2	yes	—
230	#121×C₆₁	C₂³	1	2	yes	—
231	#121×C₆₁	C₂³	1	2	yes	—
232	#121×C₆₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₆₁	—	2	1	no	—
234	C₄×Q₈×C₆₁	—	2	1	no	—
235	C₄×Q₈×C₆₁	—	2	1	no	—
236	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₁	—	2	1	no	—
244	C₄×D₄×C₆₁	—	2	1	no	—
245	C₄×D₄×C₆₁	—	2	1	no	—
246	C₄×D₄×C₆₁	—	2	1	no	—
247	C₄×D₄×C₆₁	—	2	1	no	—
248	C₄×D₄×C₆₁	—	2	1	no	—
249	C₄×D₄×C₆₁	—	2	2	no	—
250	C₄×D₄×C₆₁	—	2	2	no	—
251	C₄×D₄×C₆₁	—	2	2	no	—
252	C₄×D₄×C₆₁	—	2	2	no	—
253	C₄×D₄×C₆₁	—	2	2	no	—
254	C₄×D₄×C₆₁	—	2	1	no	—
255	C₄×D₄×C₆₁	—	2	1	no	—
256	C₄×D₄×C₆₁	—	2	1	no	—
257	C₄×D₄×C₆₁	C₂³	1	2	yes	—
258	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₆₁	C₂³	1	2	yes	—
260	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₆₁	C₂³	1	2	yes	—
262	C₄×D₄×C₆₁	C₂³	1	2	yes	—
263	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
264	#117×C₆₁	—	2	1	no	—
265	#117×C₆₁	—	2	2	no	—
266	#117×C₆₁	—	2	1	no	—
267	#117×C₆₁	C₂³	1	1	yes	characteristic
268	#117×C₆₁	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
270	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
271	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
272	C₂×C₄²×C₆₁	—	2	1	no	—
273	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
274	#107×C₆₁	C₂³	1	1	yes	characteristic
275	#107×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	1	yes	characteristic
277	#106×C₆₁	C₂³	1	1	yes	characteristic
278	#106×C₆₁	C₂³	1	2	yes	—
279	#106×C₆₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	1	yes	characteristic
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	1	yes	characteristic
293	#103×C₆₁	C₂³	1	2	yes	—
294	#103×C₆₁	C₂³	1	1	yes	characteristic
295	#103×C₆₁	C₂³	1	1	yes	characteristic
296	#103×C₆₁	C₂³	1	1	yes	characteristic
297	#103×C₆₁	C₂³	1	1	yes	characteristic
298	#103×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	#102×C₆₁	C₂³	1	1	yes	characteristic
305	#102×C₆₁	C₂³	1	1	yes	characteristic
306	#102×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
311	#97×C₆₁	C₂³	1	2	yes	—
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	#41×C₆₁	—	2	2	no	—
316	#41×C₆₁	—	2	4	no	—
317	#41×C₆₁	—	4	2	no	—
318	#41×C₆₁	—	4	1	no	—
319	#41×C₆₁	—	4	2	no	—
320	#41×C₆₁	—	4	2	no	—
321	#41×C₆₁	—	4	2	no	—
322	#41×C₆₁	—	4	2	no	—
323	#41×C₆₁	—	8	2	no	—
324	#41×C₆₁	—	8	2	no	—
325	#41×C₆₁	—	8	2	no	—
326	C₂×Q₈×C₆₁	—	2	1	no	—
327	C₂×Q₈×C₆₁	—	2	1	no	—
328	C₂×Q₈×C₆₁	—	2	2	no	—
329	C₂×Q₈×C₆₁	—	4	2	no	—
330	C₂×Q₈×C₆₁	—	4	2	no	—
331	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₆₁	—	2	1	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	2	no	—
340	C₂×D₄×C₆₁	—	2	2	no	—
341	C₂×D₄×C₆₁	—	2	2	no	—
342	C₂×D₄×C₆₁	—	2	2	no	—
343	C₂×D₄×C₆₁	—	2	2	no	—
344	C₂×D₄×C₆₁	—	2	1	no	—
345	C₂×D₄×C₆₁	—	2	1	no	—
346	C₂×D₄×C₆₁	—	2	1	no	—
347	C₂×D₄×C₆₁	—	2	1	no	—
348	C₂×D₄×C₆₁	—	2	2	no	—
349	C₂×D₄×C₆₁	—	2	2	no	—
350	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₆₁	—	2	2	no	—
356	C₂²×C₄×C₆₁	—	2	2	no	—
357	C₂²×C₄×C₆₁	—	2	1	no	—
358	C₂²×C₄×C₆₁	—	2	1	no	—
359	C₂²×C₄×C₆₁	—	2	2	no	—
360	C₂²×C₄×C₆₁	—	2	1	no	—
361	C₂²×C₄×C₆₁	—	2	2	no	—
362	C₂²×C₄×C₆₁	—	2	2	no	—
363	C₂²×C₄×C₆₁	—	2	2	no	—
364	C₂²×C₄×C₆₁	—	2	2	no	—
365	C₂²×C₄×C₆₁	—	2	2	no	—
366	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
370	Q₁₆×C₆₁	—	2	2	no	—
371	Q₁₆×C₆₁	—	2	4	no	—
372	Q₁₆×C₆₁	—	2	2	no	—
373	SD₁₆×C₆₁	—	2	4	no	—
374	SD₁₆×C₆₁	—	4	1	no	—
375	SD₁₆×C₆₁	—	4	2	no	—
376	SD₁₆×C₆₁	—	4	1	no	—
377	SD₁₆×C₆₁	—	4	2	no	—
378	SD₁₆×C₆₁	—	4	2	no	—
379	SD₁₆×C₆₁	—	4	2	no	—
380	SD₁₆×C₆₁	—	4	2	no	—
381	D₈×C₆₁	—	4	2	no	—
382	D₈×C₆₁	—	4	2	no	—
383	D₈×C₆₁	—	4	2	no	—
384	M₁₆×C₆₁	—	4	2	no	—
385	C₂×C₈×C₆₁	—	4	2	no	—
386	C₂×C₈×C₆₁	—	4	2	no	—
387	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
391	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	2	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	2	no	—
398	C₄⋊C₄×C₆₁	—	2	2	no	—
399	C₄⋊C₄×C₆₁	—	2	1	no	—
400	C₄⋊C₄×C₆₁	—	2	1	no	—
401	C₄⋊C₄×C₆₁	—	2	1	no	—
402	C₄⋊C₄×C₆₁	—	2	1	no	—
403	C₄⋊C₄×C₆₁	—	2	1	no	—
404	C₄⋊C₄×C₆₁	—	2	1	no	—
405	C₄⋊C₄×C₆₁	—	2	1	no	—
406	C₄⋊C₄×C₆₁	—	2	2	no	—
407	C₄⋊C₄×C₆₁	—	2	2	no	—
408	C₄⋊C₄×C₆₁	—	2	1	no	—
409	C₄⋊C₄×C₆₁	—	2	2	no	—
410	C₄⋊C₄×C₆₁	—	2	1	no	—
411	C₄⋊C₄×C₆₁	—	2	2	no	—
412	C₄⋊C₄×C₆₁	—	2	1	no	—
413	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₆₁	—	2	1	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	1	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	1	no	—
430	C₂²⋊C₄×C₆₁	—	2	1	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	—	2	2	no	—
434	C₂²⋊C₄×C₆₁	—	2	2	no	—
435	C₂²⋊C₄×C₆₁	—	2	2	no	—
436	C₂²⋊C₄×C₆₁	—	2	2	no	—
437	C₂²⋊C₄×C₆₁	—	2	2	no	—
438	C₂²⋊C₄×C₆₁	—	2	2	no	—
439	C₂²⋊C₄×C₆₁	—	2	2	no	—
440	C₂²⋊C₄×C₆₁	—	2	2	no	—
441	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
446	C₄²×C₆₁	—	2	1	no	—
447	C₄²×C₆₁	—	2	1	no	—
448	C₄²×C₆₁	—	2	1	no	—
449	C₄²×C₆₁	—	2	1	no	—
450	C₄²×C₆₁	—	2	2	no	—
451	C₄²×C₆₁	—	2	1	no	—
452	C₄²×C₆₁	—	2	2	no	—
453	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₆₁	C₂⁴	1	2	yes	—
457	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₆₁	—	2	2	no	—
459	C₂³×C₆₁	—	2	1	no	—
460	C₂³×C₆₁	—	2	2	no	—
461	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
462	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
463	Q₈×C₆₁	—	2	2	no	—
464	Q₈×C₆₁	—	2	1	no	—
465	Q₈×C₆₁	—	2	1	no	—
466	Q₈×C₆₁	—	2	2	no	—
467	Q₈×C₆₁	—	2	1	no	—
468	Q₈×C₆₁	—	2	1	no	—
469	Q₈×C₆₁	—	2	2	no	—
470	Q₈×C₆₁	—	2	1	no	—
471	Q₈×C₆₁	—	4	2	no	—
472	Q₈×C₆₁	—	8	1	no	—
473	Q₈×C₆₁	—	8	2	no	—
474	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
475	D₄×C₆₁	—	2	2	no	—
476	D₄×C₆₁	—	2	2	no	—
477	D₄×C₆₁	—	2	1	no	—
478	D₄×C₆₁	—	2	2	no	—
479	D₄×C₆₁	—	2	2	no	—
480	D₄×C₆₁	—	2	2	no	—
481	D₄×C₆₁	—	2	1	no	—
482	D₄×C₆₁	—	4	2	no	—
483	D₄×C₆₁	—	4	4	no	—
484	D₄×C₆₁	—	4	2	no	—
485	D₄×C₆₁	—	4	2	no	—
486	D₄×C₆₁	—	4	2	no	—
487	D₄×C₆₁	—	8	1	no	—
488	D₄×C₆₁	—	8	1	no	—
489	D₄×C₆₁	—	8	2	no	—
490	D₄×C₆₁	—	8	2	no	—
491	D₄×C₆₁	—	8	2	no	—
492	D₄×C₆₁	—	8	2	no	—
493	D₄×C₆₁	—	8	2	no	—
494	D₄×C₆₁	—	8	2	no	—
495	D₄×C₆₁	—	8	2	no	—
496	D₄×C₆₁	—	8	2	no	—
497	C₂×C₄×C₆₁	—	2	1	no	—
498	C₂×C₄×C₆₁	—	2	2	no	—
499	C₂×C₄×C₆₁	—	2	1	no	—
500	C₂×C₄×C₆₁	—	2	2	no	—
501	C₂×C₄×C₆₁	—	2	2	no	—
502	C₂×C₄×C₆₁	—	2	1	no	—
503	C₂×C₄×C₆₁	—	2	1	no	—
504	C₂×C₄×C₆₁	—	2	1	no	—
505	C₂×C₄×C₆₁	—	2	1	no	—
506	C₂×C₄×C₆₁	—	2	1	no	—
507	C₂×C₄×C₆₁	—	2	1	no	—
508	C₂×C₄×C₆₁	—	2	2	no	—
509	C₂×C₄×C₆₁	—	2	2	no	—
510	C₂×C₄×C₆₁	—	2	1	no	—
511	C₂×C₄×C₆₁	—	4	1	no	—
512	C₂×C₄×C₆₁	—	4	2	no	—
513	C₂×C₄×C₆₁	—	4	4	no	—
514	C₂×C₄×C₆₁	—	4	2	no	—
515	C₂×C₄×C₆₁	—	8	1	no	—
516	C₂×C₄×C₆₁	—	8	2	no	—
517	C₂×C₄×C₆₁	—	8	2	no	—
518	C₂×C₄×C₆₁	—	8	2	no	—
519	C₂×C₄×C₆₁	—	8	2	no	—
520	C₂×C₄×C₆₁	—	8	2	no	—
521	C₂×C₄×C₆₁	—	8	2	no	—
522	C₂×C₄×C₆₁	—	8	2	no	—
523	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
532	C₈×C₆₁	—	2	1	no	—
533	C₈×C₆₁	—	2	2	no	—
534	C₈×C₆₁	—	2	2	no	—
535	C₈×C₆₁	—	2	1	no	—
536	C₈×C₆₁	—	2	1	no	—
537	C₈×C₆₁	—	2	1	no	—
538	#62073	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
539	C₂²×C₆₁	—	2	1	no	—
540	C₂²×C₆₁	—	2	2	no	—
541	C₂²×C₆₁	—	2	2	no	—
542	C₂²×C₆₁	—	2	1	no	—
543	C₂²×C₆₁	—	2	1	no	—
544	C₂²×C₆₁	—	2	2	no	—
545	C₂²×C₆₁	—	4	1	no	—
546	C₂²×C₆₁	—	4	2	no	—
547	C₂²×C₆₁	—	4	2	no	—
548	C₂²×C₆₁	—	4	1	no	—
549	C₂²×C₆₁	—	4	2	no	—
550	C₂²×C₆₁	—	4	2	no	—
551	C₂²×C₆₁	—	4	1	no	—
552	C₂²×C₆₁	—	4	2	no	—
553	C₂²×C₆₁	—	4	2	no	—
554	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₆₁	—	2	1	no	—
556	C₄×C₆₁	—	2	1	no	—
557	C₄×C₆₁	—	2	2	no	—
558	C₄×C₆₁	—	2	1	no	—
559	C₄×C₆₁	—	2	2	no	—
560	C₄×C₆₁	—	2	2	no	—
561	C₄×C₆₁	—	2	1	no	—
562	C₄×C₆₁	—	2	2	no	—
563	C₄×C₆₁	—	4	1	no	—
564	C₄×C₆₁	—	4	1	no	—
565	C₄×C₆₁	—	4	1	no	—
566	C₄×C₆₁	—	4	1	no	—
567	C₄×C₆₁	—	4	2	no	—
568	C₄×C₆₁	—	4	1	no	—
569	C₄×C₆₁	—	4	1	no	—
570	C₄×C₆₁	—	4	2	no	—
571	C₄×C₆₁	#577	1	2	yes	—
572	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
573	C₄×C₆₁	#585	1	1	yes	characteristic
574	#3554	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3517	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#3399	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3392	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3374	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3365	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#3332	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3307	C₂×C₆₁	1	2	yes	complemented
582	#3301	C₂×C₆₁	1	2	yes	complemented
583	#3298	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3287	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#3284	C₂×C₆₁	1	2	yes	complemented
586	#3278	C₂×C₆₁	1	1	yes	characteristic, complemented
587	#3271	C₂×C₆₁	1	2	yes	complemented
588	#3257	C₂×C₆₁	1	2	yes	complemented
589	#3246	C₂×C₆₁	1	1	yes	characteristic, complemented
590	#3221	C₂×C₆₁	1	2	yes	complemented
591	#3207	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#3125	C₂×C₆₁	1	2	yes	complemented
593	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
594	#3046	C₂×C₆₁	1	2	yes	complemented
595	#3035	C₂×C₆₁	1	1	yes	characteristic, complemented
596	#2994	C₂×C₆₁	1	1	yes	characteristic, complemented
597	C₂×C₆₁	—	4	1	no	—
598	C₂×C₆₁	—	4	2	no	—
599	C₂×C₆₁	—	8	1	no	—
600	C₂×C₆₁	—	8	2	no	—
601	C₂×C₆₁	—	8	2	no	—
602	C₂×C₆₁	#3488	1	1	yes	characteristic
603	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
604	C₂×C₆₁	#3584	1	1	yes	characteristic
605	C₂×#137	C₂²×C₆₁	1	2	yes	—
606	C₂×#135	C₂²×C₆₁	1	2	yes	—
607	C₂×#135	C₂²×C₆₁	1	2	yes	—
608	#562	—	2	2	no	—
609	#559	—	2	1	no	—
610	#559	C₂²×C₆₁	1	1	yes	characteristic
611	#557	C₂²×C₆₁	1	1	yes	characteristic
612	#557	C₂²×C₆₁	1	1	yes	characteristic
613	#554	—	2	1	no	—
614	#553	—	2	2	no	—
615	#553	C₂²×C₆₁	1	2	yes	—
616	#550	—	2	1	no	—
617	#550	C₂²×C₆₁	1	1	yes	characteristic
618	#550	C₂²×C₆₁	1	2	yes	—
619	#550	C₂²×C₆₁	1	1	yes	characteristic
620	#550	C₂²×C₆₁	1	1	yes	characteristic
621	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
622	#548	C₂²×C₆₁	1	2	yes	—
623	#547	—	2	1	no	—
624	#547	C₂²×C₆₁	1	2	yes	—
625	#547	C₂²×C₆₁	1	1	yes	characteristic
626	#542	—	2	1	no	—
627	#542	C₂²×C₆₁	1	2	yes	—
628	#540	—	2	2	no	—
629	#540	—	2	1	no	—
630	#540	C₂²×C₆₁	1	2	yes	—
631	#539	—	2	2	no	—
632	#536	C₂²×C₆₁	1	2	yes	—
633	#533	C₂²×C₆₁	1	1	yes	characteristic
634	#532	—	2	1	no	—
635	#532	C₂²×C₆₁	1	1	yes	characteristic
636	#532	C₂²×C₆₁	1	1	yes	characteristic
637	#529	—	2	1	no	—
638	#529	C₂²×C₆₁	1	1	yes	characteristic
639	#520	C₂²×C₆₁	1	2	yes	—
640	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
641	#496	C₂²×C₆₁	1	2	yes	—
642	#493	C₂²×C₆₁	1	1	yes	characteristic
643	#492	C₂²×C₆₁	1	1	yes	characteristic
644	#492	C₂²×C₆₁	1	2	yes	—
645	#491	C₂²×C₆₁	1	2	yes	—
646	#488	C₂²×C₆₁	1	2	yes	—
647	#487	C₂²×C₆₁	1	1	yes	characteristic
648	#486	C₂²×C₆₁	1	1	yes	characteristic
649	#485	C₂²×C₆₁	1	1	yes	characteristic
650	#485	C₂²×C₆₁	1	1	yes	characteristic
651	#483	C₂²×C₆₁	1	2	yes	—
652	#481	C₂²×C₆₁	1	2	yes	—
653	#479	C₂²×C₆₁	1	2	yes	—
654	#478	C₂²×C₆₁	1	2	yes	—
655	#476	C₂²×C₆₁	1	2	yes	—
656	#475	C₂²×C₆₁	1	1	yes	characteristic
657	#475	C₂²×C₆₁	1	1	yes	characteristic
658	#475	C₂²×C₆₁	1	1	yes	characteristic
659	#474	C₂²×C₆₁	1	1	yes	characteristic
660	#469	C₂²×C₆₁	1	2	yes	—
661	#468	C₂²×C₆₁	1	2	yes	—
662	#466	C₂²×C₆₁	1	2	yes	—
663	#465	C₂²×C₆₁	1	2	yes	—
664	#465	C₂²×C₆₁	1	2	yes	—
665	#465	C₂²×C₆₁	1	2	yes	—
666	#464	C₂²×C₆₁	1	2	yes	—
667	#464	C₂²×C₆₁	1	2	yes	—
668	#463	C₂²×C₆₁	1	2	yes	—
669	#463	C₂²×C₆₁	1	2	yes	—
670	#463	C₂²×C₆₁	1	2	yes	—
671	#463	C₂²×C₆₁	1	2	yes	—
672	#462	C₂²×C₆₁	1	1	yes	characteristic
673	#462	C₂²×C₆₁	1	1	yes	characteristic
674	#462	C₂²×C₆₁	1	2	yes	—
675	#461	C₂²×C₆₁	1	1	yes	characteristic
676	#461	C₂²×C₆₁	1	1	yes	characteristic
677	#461	C₂²×C₆₁	1	2	yes	—
678	#461	C₂²×C₆₁	1	2	yes	—
679	#460	C₂²×C₆₁	1	1	yes	characteristic
680	#460	C₂²×C₆₁	1	1	yes	characteristic
681	#460	C₂²×C₆₁	1	2	yes	—
682	#460	C₂²×C₆₁	1	1	yes	characteristic
683	#459	C₂²×C₆₁	1	1	yes	characteristic
684	#459	C₂²×C₆₁	1	2	yes	—
685	#452	C₂²×C₆₁	1	1	yes	characteristic
686	#452	C₂²×C₆₁	1	1	yes	characteristic
687	#452	C₂²×C₆₁	1	2	yes	—
688	#449	C₂²×C₆₁	1	2	yes	—
689	#449	C₂²×C₆₁	1	2	yes	—
690	#449	C₂²×C₆₁	1	2	yes	—
691	#449	C₂²×C₆₁	1	2	yes	—
692	#449	C₂²×C₆₁	1	2	yes	—
693	#448	C₂²×C₆₁	1	2	yes	—
694	#448	C₂²×C₆₁	1	2	yes	—
695	#446	C₂²×C₆₁	1	1	yes	characteristic
696	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
697	#442	C₂²×C₆₁	1	2	yes	—
698	#441	C₂²×C₆₁	1	2	yes	—
699	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
700	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
701	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
702	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
703	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
704	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
705	#436	C₂²×C₆₁	1	1	yes	characteristic
706	#435	C₂²×C₆₁	1	2	yes	—
707	C₈×D₄	C₂²×C₆₁	1	2	yes	—
708	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
709	#433	C₂²×C₆₁	1	2	yes	—
710	#431	C₂²×C₆₁	1	1	yes	characteristic
711	#424	C₂²×C₆₁	1	2	yes	—
712	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
713	#417	C₂²×C₆₁	1	2	yes	—
714	#416	C₂²×C₆₁	1	2	yes	—
715	C₂×#103	C₂²×C₆₁	1	2	yes	—
716	C₆₁	#62073	1	1	yes	characteristic, direct product factor, Sylow
717	C₂×#41	—	2	1	no	—
718	C₂×#41	—	2	1	no	—
719	C₂×#41	—	2	1	no	—
720	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
721	C₂×#41	C₂³×C₆₁	1	2	yes	—
722	C₂×#41	C₂³×C₆₁	1	2	yes	—
723	C₂×#41	C₂³×C₆₁	1	2	yes	—
724	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
725	#137	—	4	4	no	—
726	#135	—	4	4	no	—
727	#135	—	4	4	no	—
728	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
729	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
737	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₆₁	1	2	yes	—
740	C₂×D₈	C₂³×C₆₁	1	2	yes	—
741	C₂×D₈	C₂³×C₆₁	1	2	yes	—
742	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
743	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
744	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
752	#127	—	2	1	no	—
753	#127	—	2	2	no	—
754	#127	—	2	1	no	—
755	#127	C₂³×C₆₁	1	1	yes	characteristic
756	#127	C₂³×C₆₁	1	1	yes	characteristic
757	#127	C₂³×C₆₁	1	2	yes	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	D₄×C₆₁	1	2	yes	—
761	#125	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	—	2	1	no	—
764	#125	—	2	1	no	—
765	#125	D₄×C₆₁	1	1	yes	characteristic
766	#125	C₂³×C₆₁	1	2	yes	—
767	#124	—	2	1	no	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	—	2	1	no	—
771	#124	D₄×C₆₁	1	1	yes	characteristic
772	#124	C₂³×C₆₁	1	2	yes	—
773	#124	C₂³×C₆₁	1	2	yes	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	D₄×C₆₁	1	2	yes	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
793	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
794	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
795	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	1	no	—
802	#121	—	2	1	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	D₄×C₆₁	1	1	yes	characteristic
811	#121	C₂³×C₆₁	1	2	yes	—
812	#121	C₂³×C₆₁	1	2	yes	—
813	#121	C₂³×C₆₁	1	2	yes	—
814	#121	C₂³×C₆₁	1	2	yes	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	—	2	1	no	—
818	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
821	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
822	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
823	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
824	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₆₁	1	2	yes	—
842	C₄×D₄	C₂³×C₆₁	1	2	yes	—
843	C₄×D₄	C₂³×C₆₁	1	2	yes	—
844	C₄×D₄	C₂³×C₆₁	1	2	yes	—
845	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
846	#117	—	2	1	no	—
847	#117	—	2	2	no	—
848	#117	—	2	1	no	—
849	#117	C₂³×C₆₁	1	1	yes	characteristic
850	#117	C₂³×C₆₁	1	2	yes	—
851	C₂×C₄⋊C₄	—	2	2	no	—
852	C₂×C₄⋊C₄	—	2	2	no	—
853	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
854	C₂×C₄²	—	2	1	no	—
855	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
856	#107	C₂³×C₆₁	1	1	yes	characteristic
857	#107	C₂³×C₆₁	1	1	yes	characteristic
858	#106	C₂³×C₆₁	1	1	yes	characteristic
859	#106	C₂³×C₆₁	1	1	yes	characteristic
860	#106	C₂³×C₆₁	1	2	yes	—
861	#106	C₂³×C₆₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
867	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
869	#103	C₂³×C₆₁	1	1	yes	characteristic
870	#103	C₂³×C₆₁	1	2	yes	—
871	#103	C₂³×C₆₁	1	2	yes	—
872	#103	C₂³×C₆₁	1	2	yes	—
873	#103	C₂³×C₆₁	1	2	yes	—
874	#103	C₂³×C₆₁	1	1	yes	characteristic
875	#103	C₂³×C₆₁	1	2	yes	—
876	#103	C₂³×C₆₁	1	1	yes	characteristic
877	#103	C₂³×C₆₁	1	1	yes	characteristic
878	#103	C₂³×C₆₁	1	1	yes	characteristic
879	#103	C₂³×C₆₁	1	1	yes	characteristic
880	#103	C₂³×C₆₁	1	2	yes	—
881	#102	C₂³×C₆₁	1	2	yes	—
882	#102	C₂³×C₆₁	1	2	yes	—
883	#102	C₂³×C₆₁	1	2	yes	—
884	#102	C₂³×C₆₁	1	2	yes	—
885	#102	C₂³×C₆₁	1	2	yes	—
886	#102	C₂³×C₆₁	1	1	yes	characteristic
887	#102	C₂³×C₆₁	1	1	yes	characteristic
888	#102	C₂³×C₆₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
893	#97	C₂³×C₆₁	1	2	yes	—
894	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₆₁	1	2	yes	—
897	#41	—	2	2	no	—
898	#41	—	2	4	no	—
899	#41	—	4	2	no	—
900	#41	—	4	1	no	—
901	#41	—	4	2	no	—
902	#41	—	4	2	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	8	2	no	—
906	#41	—	8	2	no	—
907	#41	—	8	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	2	no	—
911	C₂×Q₈	—	4	2	no	—
912	C₂×Q₈	—	4	2	no	—
913	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
915	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
916	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
933	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
934	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
936	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
949	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
952	Q₁₆	—	2	2	no	—
953	Q₁₆	—	2	4	no	—
954	Q₁₆	—	2	2	no	—
955	SD₁₆	—	2	4	no	—
956	SD₁₆	—	4	1	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	1	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	SD₁₆	—	4	2	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	D₈	—	4	2	no	—
966	M₁₆	—	4	2	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	—	4	2	no	—
969	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
973	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
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	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
996	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
998	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₆₁	1	2	yes	—
1039	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1044	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	8	1	no	—
1055	Q₈	—	8	2	no	—
1056	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	4	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	8	1	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1113	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1114	C₈	—	2	1	no	—
1115	C₈	—	2	2	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	1	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	C₆₁×#577	1	2	yes	—
1153	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1154	C₄	C₆₁×#585	1	1	yes	characteristic
1155	C₂	—	4	1	no	—
1156	C₂	—	4	2	no	—
1157	C₂	—	8	1	no	—
1158	C₂	—	8	2	no	—
1159	C₂	—	8	2	no	—
1160	C₂	C₆₁×#3488	1	1	yes	characteristic
1161	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1162	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3554	C₂	semidirect
2. C₆₁×#3517	C₂	semidirect
3. C₆₁×#3399	C₂	semidirect
4. C₆₁×#3392	C₂	semidirect
5. C₆₁×#3374	C₂	semidirect
6. C₆₁×#3365	C₂	semidirect
7. C₆₁×#3332	C₂	semidirect
8. C₆₁×#3307	C₂	semidirect
9. C₆₁×#3301	C₂	semidirect
10. C₆₁×#3298	C₂	semidirect
11. C₆₁×#3287	C₂	semidirect
12. C₆₁×#3284	C₂	semidirect
13. C₆₁×#3278	C₂	semidirect
14. C₆₁×#3271	C₂	semidirect
15. C₆₁×#3257	C₂	semidirect
16. C₆₁×#3246	C₂	semidirect
17. C₆₁×#3221	C₂	semidirect
18. C₆₁×#3207	C₂	semidirect
19. C₆₁×#3125	C₂	semidirect
20. C₆₁×#3107	C₂	semidirect
21. C₆₁×#3046	C₂	semidirect
22. C₆₁×#3035	C₂	semidirect
23. C₆₁×#2994	C₂	semidirect
538. #62073	C₆₁	direct (N × H)
574. #3554	C₂×C₆₁	semidirect
575. #3517	C₂×C₆₁	semidirect
576. #3399	C₂×C₆₁	semidirect
577. #3392	C₂×C₆₁	semidirect
578. #3374	C₂×C₆₁	semidirect
579. #3365	C₂×C₆₁	semidirect
580. #3332	C₂×C₆₁	semidirect
581. #3307	C₂×C₆₁	semidirect
582. #3301	C₂×C₆₁	semidirect
583. #3298	C₂×C₆₁	semidirect
584. #3287	C₂×C₆₁	semidirect
585. #3284	C₂×C₆₁	semidirect
586. #3278	C₂×C₆₁	semidirect
587. #3271	C₂×C₆₁	semidirect
588. #3257	C₂×C₆₁	semidirect
589. #3246	C₂×C₆₁	semidirect
590. #3221	C₂×C₆₁	semidirect
591. #3207	C₂×C₆₁	semidirect
592. #3125	C₂×C₆₁	semidirect
593. #3107	C₂×C₆₁	semidirect
594. #3046	C₂×C₆₁	semidirect
595. #3035	C₂×C₆₁	semidirect
596. #2994	C₂×C₆₁	semidirect
716. C₆₁	#62073	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×#3554	2
C₆₁×#3517	2
C₆₁×#3399	2
C₆₁×#3392	2
C₆₁×#3374	2
C₆₁×#3365	2
C₆₁×#3332	2
C₆₁×#3307	2
C₆₁×#3301	2
C₆₁×#3298	2
C₆₁×#3287	2
C₆₁×#3284	2
C₆₁×#3278	2
C₆₁×#3271	2
C₆₁×#3257	2
C₆₁×#3246	2
C₆₁×#3221	2
C₆₁×#3207	2
C₆₁×#3125	2
C₆₁×#3107	2
C₆₁×#3046	2
C₆₁×#3035	2
C₆₁×#2994	2
#62073	61

Subgroups — C61×#62073 #29565506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62073 #29565506