Subgroups — C₆₁×#62056 #29565489

Order 15616.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3552	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3395	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3312	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3300	C₂	1	2	yes	maximal, complemented
11	D₄×Q₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
12	D₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3270	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3261	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3223	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3127	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3044	C₂	1	2	yes	maximal, complemented
22	C₂×C₆₁×#462	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	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
26	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#563	—	2	2	no	—
28	C₆₁×#557	—	2	1	no	—
29	C₆₁×#557	C₂²	1	1	yes	characteristic
30	C₆₁×#557	C₂²	1	1	yes	characteristic
31	C₆₁×#557	C₂²	1	1	yes	characteristic
32	C₆₁×#556	—	2	1	no	—
33	C₆₁×#556	C₂²	1	1	yes	characteristic
34	C₆₁×#556	C₂²	1	1	yes	characteristic
35	C₆₁×#554	—	2	1	no	—
36	C₆₁×#553	—	2	1	no	—
37	C₆₁×#552	—	2	2	no	—
38	C₆₁×#552	C₂²	1	2	yes	—
39	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
40	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
42	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#548	C₂²	1	2	yes	—
44	C₆₁×#547	C₂²	1	1	yes	characteristic
45	C₆₁×#544	—	2	1	no	—
46	C₆₁×#542	—	2	1	no	—
47	C₆₁×#541	—	2	2	no	—
48	C₆₁×#541	C₂²	1	2	yes	—
49	C₆₁×#541	C₂²	1	2	yes	—
50	C₆₁×#539	—	2	2	no	—
51	C₆₁×#536	C₂²	1	2	yes	—
52	C₆₁×#533	—	2	1	no	—
53	C₆₁×#533	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×#529	—	2	1	no	—
56	C₆₁×#529	C₂²	1	1	yes	characteristic
57	C₆₁×#529	C₂²	1	1	yes	characteristic
58	C₆₁×#519	C₂²	1	2	yes	—
59	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
60	C₆₁×#497	C₂²	1	2	yes	—
61	C₆₁×#494	C₂²	1	1	yes	characteristic
62	C₆₁×#494	C₂²	1	2	yes	—
63	C₆₁×#494	C₂²	1	1	yes	characteristic
64	C₆₁×#491	C₂²	1	2	yes	—
65	C₆₁×#488	C₂²	1	2	yes	—
66	C₆₁×#487	C₂²	1	1	yes	characteristic
67	C₆₁×#487	C₂²	1	1	yes	characteristic
68	C₆₁×#485	C₂²	1	2	yes	—
69	C₆₁×#485	C₂²	1	2	yes	—
70	C₆₁×#483	C₂²	1	1	yes	characteristic
71	C₆₁×#480	C₂²	1	1	yes	characteristic
72	C₆₁×#479	C₂²	1	2	yes	—
73	C₆₁×#479	C₂²	1	2	yes	—
74	C₆₁×#479	C₂²	1	1	yes	characteristic
75	C₆₁×#479	C₂²	1	1	yes	characteristic
76	C₆₁×#479	C₂²	1	2	yes	—
77	C₆₁×#475	C₂²	1	1	yes	characteristic
78	C₆₁×#474	C₂²	1	1	yes	characteristic
79	C₆₁×#470	C₂²	1	2	yes	—
80	C₆₁×#470	C₂²	1	2	yes	—
81	C₆₁×#467	C₂²	1	2	yes	—
82	C₆₁×#467	C₂²	1	2	yes	—
83	C₆₁×#467	C₂²	1	2	yes	—
84	C₆₁×#465	C₂²	1	2	yes	—
85	C₆₁×#464	C₂²	1	1	yes	characteristic
86	C₆₁×#464	C₂²	1	2	yes	—
87	C₆₁×#464	C₂²	1	2	yes	—
88	C₆₁×#464	C₂²	1	2	yes	—
89	C₆₁×#464	C₂²	1	1	yes	characteristic
90	C₆₁×#462	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	1	yes	characteristic
94	C₆₁×#462	C₂²	1	1	yes	characteristic
95	C₆₁×#462	C₂²	1	2	yes	—
96	C₆₁×#462	C₂²	1	2	yes	—
97	C₆₁×#462	C₂²	1	2	yes	—
98	C₆₁×#462	C₂²	1	2	yes	—
99	C₆₁×#462	C₂²	1	2	yes	—
100	C₆₁×#462	C₂²	1	1	yes	characteristic
101	C₆₁×#462	C₂²	1	2	yes	—
102	C₆₁×#462	C₂²	1	2	yes	—
103	C₆₁×#461	C₂²	1	1	yes	characteristic
104	C₆₁×#452	C₂²	1	2	yes	—
105	C₆₁×#452	C₂²	1	2	yes	—
106	C₆₁×#451	C₂²	1	2	yes	—
107	C₆₁×#451	C₂²	1	2	yes	—
108	C₆₁×#451	C₂²	1	2	yes	—
109	C₆₁×#451	C₂²	1	2	yes	—
110	C₆₁×#451	C₂²	1	1	yes	characteristic
111	C₆₁×#451	C₂²	1	2	yes	—
112	C₆₁×#451	C₂²	1	2	yes	—
113	C₆₁×#448	C₂²	1	1	yes	characteristic
114	C₆₁×#446	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
116	C₆₁×#441	C₂²	1	2	yes	—
117	C₆₁×#441	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
119	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
121	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
122	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
124	C₆₁×#436	C₂²	1	1	yes	characteristic
125	C₆₁×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₆₁	C₂²	1	2	yes	—
127	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
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×#419	C₂²	1	2	yes	—
133	C₆₁×#416	C₂²	1	2	yes	—
134	C₂×#103×C₆₁	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	C₂³	1	2	yes	—
136	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
140	#137×C₆₁	—	4	4	no	—
141	C₂×Q₁₆×C₆₁	—	4	4	no	—
142	C₂×Q₁₆×C₆₁	—	4	4	no	—
143	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
152	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×Q₁₆×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×M₁₆×C₆₁	C₂³	1	2	yes	—
158	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₁	—	2	1	no	—
161	C₄⋊Q₈×C₆₁	—	2	1	no	—
162	C₄⋊Q₈×C₆₁	—	2	2	no	—
163	C₄⋊Q₈×C₆₁	—	2	1	no	—
164	C₄⋊Q₈×C₆₁	—	2	2	no	—
165	C₄⋊Q₈×C₆₁	—	2	1	no	—
166	C₄⋊Q₈×C₆₁	—	2	1	no	—
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	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
172	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
174	#126×C₆₁	—	2	2	no	—
175	#126×C₆₁	—	2	2	no	—
176	#126×C₆₁	—	2	2	no	—
177	#126×C₆₁	—	2	2	no	—
178	#126×C₆₁	—	2	2	no	—
179	#126×C₆₁	—	2	2	no	—
180	#126×C₆₁	—	2	2	no	—
181	#126×C₆₁	—	2	1	no	—
182	#126×C₆₁	D₄	1	2	yes	—
183	#125×C₆₁	—	2	2	no	—
184	#125×C₆₁	—	2	2	no	—
185	#125×C₆₁	—	2	2	no	—
186	#125×C₆₁	—	2	2	no	—
187	#125×C₆₁	—	2	2	no	—
188	#125×C₆₁	—	2	2	no	—
189	#125×C₆₁	—	2	2	no	—
190	#125×C₆₁	—	2	2	no	—
191	#125×C₆₁	—	2	1	no	—
192	#125×C₆₁	—	2	1	no	—
193	#125×C₆₁	—	2	1	no	—
194	#125×C₆₁	D₄	1	1	yes	characteristic
195	#125×C₆₁	C₂³	1	1	yes	characteristic
196	#125×C₆₁	C₂³	1	2	yes	—
197	#124×C₆₁	—	2	1	no	—
198	#124×C₆₁	—	2	2	no	—
199	#124×C₆₁	D₄	1	1	yes	characteristic
200	#124×C₆₁	C₂³	1	1	yes	characteristic
201	#124×C₆₁	C₂³	1	2	yes	—
202	#123×C₆₁	—	2	2	no	—
203	#123×C₆₁	—	2	1	no	—
204	#123×C₆₁	—	2	2	no	—
205	#123×C₆₁	—	2	2	no	—
206	#123×C₆₁	—	2	2	no	—
207	#123×C₆₁	D₄	1	2	yes	—
208	C₂²⋊Q₈×C₆₁	—	2	1	no	—
209	C₂²⋊Q₈×C₆₁	—	2	1	no	—
210	C₂²⋊Q₈×C₆₁	—	2	2	no	—
211	C₂²⋊Q₈×C₆₁	—	2	2	no	—
212	C₂²⋊Q₈×C₆₁	—	2	2	no	—
213	C₂²⋊Q₈×C₆₁	—	2	2	no	—
214	C₂²⋊Q₈×C₆₁	—	2	2	no	—
215	C₂²⋊Q₈×C₆₁	—	2	2	no	—
216	C₂²⋊Q₈×C₆₁	—	2	2	no	—
217	C₂²⋊Q₈×C₆₁	—	2	2	no	—
218	C₂²⋊Q₈×C₆₁	—	2	2	no	—
219	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
220	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
225	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
226	#121×C₆₁	—	2	2	no	—
227	#121×C₆₁	—	2	1	no	—
228	#121×C₆₁	D₄	1	1	yes	characteristic
229	#121×C₆₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₆₁	—	2	1	no	—
231	C₄×Q₈×C₆₁	—	2	1	no	—
232	C₄×Q₈×C₆₁	—	2	2	no	—
233	C₄×Q₈×C₆₁	—	2	1	no	—
234	C₄×Q₈×C₆₁	—	2	2	no	—
235	C₄×Q₈×C₆₁	—	2	1	no	—
236	C₄×Q₈×C₆₁	—	2	1	no	—
237	C₄×Q₈×C₆₁	—	2	1	no	—
238	C₄×Q₈×C₆₁	—	2	1	no	—
239	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
242	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
243	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
246	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
247	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₆₁	—	2	2	no	—
251	C₄×D₄×C₆₁	—	2	1	no	—
252	C₄×D₄×C₆₁	—	2	2	no	—
253	C₄×D₄×C₆₁	—	2	1	no	—
254	C₄×D₄×C₆₁	—	2	1	no	—
255	C₄×D₄×C₆₁	—	2	2	no	—
256	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₁	C₂³	1	2	yes	—
259	#117×C₆₁	—	2	1	no	—
260	#117×C₆₁	—	2	1	no	—
261	#117×C₆₁	—	2	2	no	—
262	#117×C₆₁	—	2	2	no	—
263	#117×C₆₁	—	2	2	no	—
264	#117×C₆₁	—	2	1	no	—
265	#117×C₆₁	C₂³	1	2	yes	—
266	#117×C₆₁	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
269	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
271	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
276	#107×C₆₁	C₂³	1	1	yes	characteristic
277	#106×C₆₁	C₂³	1	1	yes	characteristic
278	#106×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	1	yes	characteristic
299	#103×C₆₁	C₂³	1	2	yes	—
300	#103×C₆₁	C₂³	1	1	yes	characteristic
301	#103×C₆₁	C₂³	1	2	yes	—
302	#103×C₆₁	C₂³	1	2	yes	—
303	#103×C₆₁	C₂³	1	2	yes	—
304	#102×C₆₁	C₂³	1	1	yes	characteristic
305	#102×C₆₁	C₂³	1	2	yes	—
306	#102×C₆₁	C₂³	1	1	yes	characteristic
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	—	4	2	no	—
316	#41×C₆₁	—	4	2	no	—
317	C₂×Q₈×C₆₁	—	2	1	no	—
318	C₂×Q₈×C₆₁	—	2	2	no	—
319	C₂×Q₈×C₆₁	—	2	1	no	—
320	C₂×Q₈×C₆₁	—	2	2	no	—
321	C₂×Q₈×C₆₁	—	2	2	no	—
322	C₂×Q₈×C₆₁	—	2	2	no	—
323	C₂×Q₈×C₆₁	—	2	4	no	—
324	C₂×Q₈×C₆₁	—	4	1	no	—
325	C₂×Q₈×C₆₁	—	4	2	no	—
326	C₂×Q₈×C₆₁	—	4	2	no	—
327	C₂×Q₈×C₆₁	—	4	2	no	—
328	C₂×Q₈×C₆₁	—	4	2	no	—
329	C₂×Q₈×C₆₁	—	4	2	no	—
330	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₆₁	—	2	1	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₆₁	—	2	1	no	—
343	C₂²×C₄×C₆₁	—	2	1	no	—
344	C₂²×C₄×C₆₁	—	2	2	no	—
345	C₂²×C₄×C₆₁	—	2	2	no	—
346	C₂²×C₄×C₆₁	—	2	2	no	—
347	C₂²×C₄×C₆₁	—	2	1	no	—
348	C₂²×C₄×C₆₁	—	2	2	no	—
349	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
353	Q₁₆×C₆₁	—	2	2	no	—
354	Q₁₆×C₆₁	—	2	4	no	—
355	Q₁₆×C₆₁	—	2	4	no	—
356	Q₁₆×C₆₁	—	4	2	no	—
357	Q₁₆×C₆₁	—	4	2	no	—
358	Q₁₆×C₆₁	—	4	2	no	—
359	Q₁₆×C₆₁	—	4	2	no	—
360	Q₁₆×C₆₁	—	4	2	no	—
361	Q₁₆×C₆₁	—	4	1	no	—
362	Q₁₆×C₆₁	—	4	2	no	—
363	Q₁₆×C₆₁	—	4	2	no	—
364	SD₁₆×C₆₁	—	2	2	no	—
365	SD₁₆×C₆₁	—	4	1	no	—
366	SD₁₆×C₆₁	—	4	2	no	—
367	M₁₆×C₆₁	—	4	2	no	—
368	C₂×C₈×C₆₁	—	4	2	no	—
369	C₂×C₈×C₆₁	—	4	2	no	—
370	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
374	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₆₁	—	2	1	no	—
377	C₄⋊C₄×C₆₁	—	2	1	no	—
378	C₄⋊C₄×C₆₁	—	2	1	no	—
379	C₄⋊C₄×C₆₁	—	2	1	no	—
380	C₄⋊C₄×C₆₁	—	2	1	no	—
381	C₄⋊C₄×C₆₁	—	2	1	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	2	no	—
389	C₄⋊C₄×C₆₁	—	2	2	no	—
390	C₄⋊C₄×C₆₁	—	2	2	no	—
391	C₄⋊C₄×C₆₁	—	2	1	no	—
392	C₄⋊C₄×C₆₁	—	2	1	no	—
393	C₄⋊C₄×C₆₁	—	2	2	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	1	no	—
398	C₄⋊C₄×C₆₁	—	2	2	no	—
399	C₄⋊C₄×C₆₁	—	2	2	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	1	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	2	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	2	no	—
406	C₄⋊C₄×C₆₁	—	2	2	no	—
407	C₄⋊C₄×C₆₁	—	2	2	no	—
408	C₄⋊C₄×C₆₁	—	2	2	no	—
409	C₄⋊C₄×C₆₁	—	2	1	no	—
410	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	1	no	—
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	2	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	1	no	—
430	C₂²⋊C₄×C₆₁	—	2	1	no	—
431	C₂²⋊C₄×C₆₁	—	2	1	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	—	2	1	no	—
434	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
439	C₄²×C₆₁	—	2	1	no	—
440	C₄²×C₆₁	—	2	1	no	—
441	C₄²×C₆₁	—	2	1	no	—
442	C₄²×C₆₁	—	2	1	no	—
443	C₄²×C₆₁	—	2	2	no	—
444	C₄²×C₆₁	—	2	2	no	—
445	C₄²×C₆₁	—	2	2	no	—
446	C₄²×C₆₁	—	2	1	no	—
447	C₄²×C₆₁	—	2	2	no	—
448	C₄²×C₆₁	—	2	2	no	—
449	C₄²×C₆₁	—	2	2	no	—
450	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₆₁	C₂⁴	1	2	yes	—
454	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
455	C₂³×C₆₁	—	2	1	no	—
456	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
457	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
458	Q₈×C₆₁	—	2	2	no	—
459	Q₈×C₆₁	—	2	1	no	—
460	Q₈×C₆₁	—	2	2	no	—
461	Q₈×C₆₁	—	2	1	no	—
462	Q₈×C₆₁	—	2	2	no	—
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	2	no	—
468	Q₈×C₆₁	—	2	1	no	—
469	Q₈×C₆₁	—	2	2	no	—
470	Q₈×C₆₁	—	4	4	no	—
471	Q₈×C₆₁	—	4	2	no	—
472	Q₈×C₆₁	—	4	2	no	—
473	Q₈×C₆₁	—	8	2	no	—
474	Q₈×C₆₁	—	8	2	no	—
475	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
476	D₄×C₆₁	—	2	4	no	—
477	D₄×C₆₁	—	2	2	no	—
478	D₄×C₆₁	—	2	1	no	—
479	D₄×C₆₁	—	2	1	no	—
480	D₄×C₆₁	—	4	2	no	—
481	D₄×C₆₁	—	8	2	no	—
482	C₂×C₄×C₆₁	—	2	2	no	—
483	C₂×C₄×C₆₁	—	2	1	no	—
484	C₂×C₄×C₆₁	—	2	2	no	—
485	C₂×C₄×C₆₁	—	2	1	no	—
486	C₂×C₄×C₆₁	—	2	2	no	—
487	C₂×C₄×C₆₁	—	2	1	no	—
488	C₂×C₄×C₆₁	—	2	2	no	—
489	C₂×C₄×C₆₁	—	2	1	no	—
490	C₂×C₄×C₆₁	—	2	1	no	—
491	C₂×C₄×C₆₁	—	2	2	no	—
492	C₂×C₄×C₆₁	—	2	1	no	—
493	C₂×C₄×C₆₁	—	2	1	no	—
494	C₂×C₄×C₆₁	—	2	1	no	—
495	C₂×C₄×C₆₁	—	2	2	no	—
496	C₂×C₄×C₆₁	—	2	1	no	—
497	C₂×C₄×C₆₁	—	2	2	no	—
498	C₂×C₄×C₆₁	—	2	2	no	—
499	C₂×C₄×C₆₁	—	4	2	no	—
500	C₂×C₄×C₆₁	—	4	4	no	—
501	C₂×C₄×C₆₁	—	4	2	no	—
502	C₂×C₄×C₆₁	—	4	2	no	—
503	C₂×C₄×C₆₁	—	8	2	no	—
504	C₂×C₄×C₆₁	—	8	2	no	—
505	C₂×C₄×C₆₁	—	8	2	no	—
506	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
515	C₈×C₆₁	—	2	1	no	—
516	C₈×C₆₁	—	2	2	no	—
517	C₈×C₆₁	—	2	2	no	—
518	C₈×C₆₁	—	2	1	no	—
519	C₈×C₆₁	—	2	1	no	—
520	C₈×C₆₁	—	2	1	no	—
521	#62056	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
522	C₂²×C₆₁	—	2	1	no	—
523	C₂²×C₆₁	—	2	1	no	—
524	C₂²×C₆₁	—	2	2	no	—
525	C₂²×C₆₁	—	2	2	no	—
526	C₂²×C₆₁	—	2	2	no	—
527	C₂²×C₆₁	—	4	1	no	—
528	C₂²×C₆₁	—	4	1	no	—
529	C₂²×C₆₁	—	4	1	no	—
530	C₂²×C₆₁	#578	1	2	yes	—
531	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
532	C₄×C₆₁	—	2	2	no	—
533	C₄×C₆₁	—	2	1	no	—
534	C₄×C₆₁	—	2	2	no	—
535	C₄×C₆₁	—	2	1	no	—
536	C₄×C₆₁	—	2	1	no	—
537	C₄×C₆₁	—	2	1	no	—
538	C₄×C₆₁	—	2	2	no	—
539	C₄×C₆₁	—	2	2	no	—
540	C₄×C₆₁	—	4	2	no	—
541	C₄×C₆₁	—	4	1	no	—
542	C₄×C₆₁	—	4	2	no	—
543	C₄×C₆₁	—	4	1	no	—
544	C₄×C₆₁	—	4	2	no	—
545	C₄×C₆₁	—	4	1	no	—
546	C₄×C₆₁	—	4	1	no	—
547	C₄×C₆₁	—	4	1	no	—
548	C₄×C₆₁	—	4	1	no	—
549	C₄×C₆₁	—	4	2	no	—
550	C₄×C₆₁	#578	1	2	yes	—
551	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
552	C₄×C₆₁	#585	1	1	yes	characteristic
553	#3552	C₂×C₆₁	1	1	yes	characteristic
554	#3523	C₂×C₆₁	1	1	yes	characteristic, complemented
555	#3398	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#3395	C₂×C₆₁	1	1	yes	characteristic, complemented
557	#3374	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#3364	C₂×C₆₁	1	1	yes	characteristic, complemented
559	#3328	C₂×C₆₁	1	1	yes	characteristic, complemented
560	#3312	C₂×C₆₁	1	2	yes	complemented
561	#3302	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3300	C₂×C₆₁	1	2	yes	complemented
563	D₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
564	D₄×Q₁₆	C₂×C₆₁	1	2	yes	complemented
565	#3276	C₂×C₆₁	1	1	yes	characteristic, complemented
566	#3270	C₂×C₆₁	1	2	yes	complemented
567	#3261	C₂×C₆₁	1	2	yes	complemented
568	#3248	C₂×C₆₁	1	1	yes	characteristic, complemented
569	#3223	C₂×C₆₁	1	2	yes	complemented
570	#3209	C₂×C₆₁	1	1	yes	characteristic, complemented
571	#3127	C₂×C₆₁	1	2	yes	complemented
572	#3108	C₂×C₆₁	1	1	yes	characteristic, complemented
573	#3044	C₂×C₆₁	1	2	yes	complemented
574	C₂×#462	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#2994	C₂×C₆₁	1	1	yes	characteristic, complemented
576	C₂×C₆₁	—	2	2	no	—
577	C₂×C₆₁	—	4	2	no	—
578	C₂×C₆₁	—	8	1	no	—
579	C₂×C₆₁	#3488	1	1	yes	characteristic
580	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
581	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
582	C₂×#137	C₂²×C₆₁	1	2	yes	—
583	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
584	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
585	#563	—	2	2	no	—
586	#557	—	2	1	no	—
587	#557	C₂²×C₆₁	1	1	yes	characteristic
588	#557	C₂²×C₆₁	1	1	yes	characteristic
589	#557	C₂²×C₆₁	1	1	yes	characteristic
590	#556	—	2	1	no	—
591	#556	C₂²×C₆₁	1	1	yes	characteristic
592	#556	C₂²×C₆₁	1	1	yes	characteristic
593	#554	—	2	1	no	—
594	#553	—	2	1	no	—
595	#552	—	2	2	no	—
596	#552	C₂²×C₆₁	1	2	yes	—
597	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
598	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
599	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
600	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
601	#548	C₂²×C₆₁	1	2	yes	—
602	#547	C₂²×C₆₁	1	1	yes	characteristic
603	#544	—	2	1	no	—
604	#542	—	2	1	no	—
605	#541	—	2	2	no	—
606	#541	C₂²×C₆₁	1	2	yes	—
607	#541	C₂²×C₆₁	1	2	yes	—
608	#539	—	2	2	no	—
609	#536	C₂²×C₆₁	1	2	yes	—
610	#533	—	2	1	no	—
611	#533	C₂²×C₆₁	1	1	yes	characteristic
612	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
613	#529	—	2	1	no	—
614	#529	C₂²×C₆₁	1	1	yes	characteristic
615	#529	C₂²×C₆₁	1	1	yes	characteristic
616	#519	C₂²×C₆₁	1	2	yes	—
617	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
618	#497	C₂²×C₆₁	1	2	yes	—
619	#494	C₂²×C₆₁	1	1	yes	characteristic
620	#494	C₂²×C₆₁	1	2	yes	—
621	#494	C₂²×C₆₁	1	1	yes	characteristic
622	#491	C₂²×C₆₁	1	2	yes	—
623	#488	C₂²×C₆₁	1	2	yes	—
624	#487	C₂²×C₆₁	1	1	yes	characteristic
625	#487	C₂²×C₆₁	1	1	yes	characteristic
626	#485	C₂²×C₆₁	1	2	yes	—
627	#485	C₂²×C₆₁	1	2	yes	—
628	#483	C₂²×C₆₁	1	1	yes	characteristic
629	#480	C₂²×C₆₁	1	1	yes	characteristic
630	#479	C₂²×C₆₁	1	1	yes	characteristic
631	#479	C₂²×C₆₁	1	1	yes	characteristic
632	#479	C₂²×C₆₁	1	2	yes	—
633	#479	C₂²×C₆₁	1	2	yes	—
634	#479	C₂²×C₆₁	1	2	yes	—
635	#475	C₂²×C₆₁	1	1	yes	characteristic
636	#474	C₂²×C₆₁	1	1	yes	characteristic
637	#470	C₂²×C₆₁	1	2	yes	—
638	#470	C₂²×C₆₁	1	2	yes	—
639	#467	C₂²×C₆₁	1	2	yes	—
640	#467	C₂²×C₆₁	1	2	yes	—
641	#467	C₂²×C₆₁	1	2	yes	—
642	#465	C₂²×C₆₁	1	2	yes	—
643	#464	C₂²×C₆₁	1	1	yes	characteristic
644	#464	C₂²×C₆₁	1	1	yes	characteristic
645	#464	C₂²×C₆₁	1	2	yes	—
646	#464	C₂²×C₆₁	1	2	yes	—
647	#464	C₂²×C₆₁	1	2	yes	—
648	#462	C₂²×C₆₁	1	1	yes	characteristic
649	#462	C₂²×C₆₁	1	1	yes	characteristic
650	#462	C₂²×C₆₁	1	1	yes	characteristic
651	#462	C₂²×C₆₁	1	2	yes	—
652	#462	C₂²×C₆₁	1	2	yes	—
653	#462	C₂²×C₆₁	1	2	yes	—
654	#462	C₂²×C₆₁	1	1	yes	characteristic
655	#462	C₂²×C₆₁	1	2	yes	—
656	#462	C₂²×C₆₁	1	1	yes	characteristic
657	#462	C₂²×C₆₁	1	2	yes	—
658	#462	C₂²×C₆₁	1	2	yes	—
659	#462	C₂²×C₆₁	1	2	yes	—
660	#462	C₂²×C₆₁	1	2	yes	—
661	#461	C₂²×C₆₁	1	1	yes	characteristic
662	#452	C₂²×C₆₁	1	2	yes	—
663	#452	C₂²×C₆₁	1	2	yes	—
664	#451	C₂²×C₆₁	1	2	yes	—
665	#451	C₂²×C₆₁	1	1	yes	characteristic
666	#451	C₂²×C₆₁	1	2	yes	—
667	#451	C₂²×C₆₁	1	2	yes	—
668	#451	C₂²×C₆₁	1	2	yes	—
669	#451	C₂²×C₆₁	1	2	yes	—
670	#451	C₂²×C₆₁	1	2	yes	—
671	#448	C₂²×C₆₁	1	1	yes	characteristic
672	#446	C₂²×C₆₁	1	1	yes	characteristic
673	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
674	#441	C₂²×C₆₁	1	2	yes	—
675	#441	C₂²×C₆₁	1	2	yes	—
676	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
677	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
678	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
679	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
680	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
682	#436	C₂²×C₆₁	1	1	yes	characteristic
683	#435	C₂²×C₆₁	1	2	yes	—
684	C₈×D₄	C₂²×C₆₁	1	2	yes	—
685	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
686	#433	C₂²×C₆₁	1	2	yes	—
687	#431	C₂²×C₆₁	1	1	yes	characteristic
688	#424	C₂²×C₆₁	1	2	yes	—
689	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
690	#419	C₂²×C₆₁	1	2	yes	—
691	#416	C₂²×C₆₁	1	2	yes	—
692	C₂×#103	C₂²×C₆₁	1	2	yes	—
693	C₆₁	#62056	1	1	yes	characteristic, direct product factor, Sylow
694	C₂×#41	C₂³×C₆₁	1	2	yes	—
695	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
696	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
697	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
698	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
699	#137	—	4	4	no	—
700	C₂×Q₁₆	—	4	4	no	—
701	C₂×Q₁₆	—	4	4	no	—
702	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
703	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
704	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
705	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
706	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
707	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
708	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
709	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
711	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
712	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
716	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
717	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
718	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	—	2	1	no	—
721	C₄⋊Q₈	—	2	2	no	—
722	C₄⋊Q₈	—	2	1	no	—
723	C₄⋊Q₈	—	2	2	no	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
727	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
731	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
732	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	1	no	—
741	#126	D₄×C₆₁	1	2	yes	—
742	#125	—	2	1	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	2	no	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	1	no	—
752	#125	—	2	1	no	—
753	#125	D₄×C₆₁	1	1	yes	characteristic
754	#125	C₂³×C₆₁	1	1	yes	characteristic
755	#125	C₂³×C₆₁	1	2	yes	—
756	#124	—	2	1	no	—
757	#124	—	2	2	no	—
758	#124	D₄×C₆₁	1	1	yes	characteristic
759	#124	C₂³×C₆₁	1	1	yes	characteristic
760	#124	C₂³×C₆₁	1	2	yes	—
761	#123	—	2	2	no	—
762	#123	—	2	1	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	D₄×C₆₁	1	2	yes	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
779	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
780	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
781	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
782	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
783	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
784	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
785	#121	—	2	2	no	—
786	#121	—	2	1	no	—
787	#121	D₄×C₆₁	1	1	yes	characteristic
788	#121	C₂³×C₆₁	1	1	yes	characteristic
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
803	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
804	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
805	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
807	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₆₁	1	2	yes	—
818	#117	—	2	1	no	—
819	#117	—	2	1	no	—
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	—	2	2	no	—
823	#117	—	2	1	no	—
824	#117	C₂³×C₆₁	1	2	yes	—
825	#117	C₂³×C₆₁	1	2	yes	—
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	—	2	1	no	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
833	#107	C₂³×C₆₁	1	1	yes	characteristic
834	#107	C₂³×C₆₁	1	2	yes	—
835	#107	C₂³×C₆₁	1	1	yes	characteristic
836	#106	C₂³×C₆₁	1	1	yes	characteristic
837	#106	C₂³×C₆₁	1	1	yes	characteristic
838	#106	C₂³×C₆₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
840	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
845	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
846	#103	C₂³×C₆₁	1	2	yes	—
847	#103	C₂³×C₆₁	1	2	yes	—
848	#103	C₂³×C₆₁	1	2	yes	—
849	#103	C₂³×C₆₁	1	2	yes	—
850	#103	C₂³×C₆₁	1	2	yes	—
851	#103	C₂³×C₆₁	1	1	yes	characteristic
852	#103	C₂³×C₆₁	1	2	yes	—
853	#103	C₂³×C₆₁	1	2	yes	—
854	#103	C₂³×C₆₁	1	1	yes	characteristic
855	#103	C₂³×C₆₁	1	1	yes	characteristic
856	#103	C₂³×C₆₁	1	1	yes	characteristic
857	#103	C₂³×C₆₁	1	1	yes	characteristic
858	#103	C₂³×C₆₁	1	2	yes	—
859	#103	C₂³×C₆₁	1	1	yes	characteristic
860	#103	C₂³×C₆₁	1	2	yes	—
861	#103	C₂³×C₆₁	1	2	yes	—
862	#103	C₂³×C₆₁	1	2	yes	—
863	#102	C₂³×C₆₁	1	1	yes	characteristic
864	#102	C₂³×C₆₁	1	2	yes	—
865	#102	C₂³×C₆₁	1	1	yes	characteristic
866	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
870	#97	C₂³×C₆₁	1	2	yes	—
871	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₆₁	1	2	yes	—
874	#41	—	4	2	no	—
875	#41	—	4	2	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	4	no	—
883	C₂×Q₈	—	4	1	no	—
884	C₂×Q₈	—	4	2	no	—
885	C₂×Q₈	—	4	2	no	—
886	C₂×Q₈	—	4	2	no	—
887	C₂×Q₈	—	4	2	no	—
888	C₂×Q₈	—	4	2	no	—
889	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
891	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
894	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
899	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
909	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
912	Q₁₆	—	2	2	no	—
913	Q₁₆	—	2	4	no	—
914	Q₁₆	—	2	4	no	—
915	Q₁₆	—	4	2	no	—
916	Q₁₆	—	4	2	no	—
917	Q₁₆	—	4	2	no	—
918	Q₁₆	—	4	2	no	—
919	Q₁₆	—	4	2	no	—
920	Q₁₆	—	4	1	no	—
921	Q₁₆	—	4	2	no	—
922	Q₁₆	—	4	2	no	—
923	SD₁₆	—	2	2	no	—
924	SD₁₆	—	4	1	no	—
925	SD₁₆	—	4	2	no	—
926	M₁₆	—	4	2	no	—
927	C₂×C₈	—	4	2	no	—
928	C₂×C₈	—	4	2	no	—
929	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
933	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	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	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
971	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
973	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
974	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
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	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1010	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1011	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1012	C₄²	C₂⁴×C₆₁	1	2	yes	—
1013	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1014	C₂³	—	2	1	no	—
1015	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1016	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	2	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	4	4	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	4	2	no	—
1032	Q₈	—	8	2	no	—
1033	Q₈	—	8	2	no	—
1034	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
1035	D₄	—	2	4	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	8	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	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	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1066	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1073	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	2	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	C₆₁×#578	1	2	yes	—
1089	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	C₆₁×#578	1	2	yes	—
1109	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1110	C₄	C₆₁×#585	1	1	yes	characteristic
1111	C₂	—	2	2	no	—
1112	C₂	—	4	2	no	—
1113	C₂	—	8	1	no	—
1114	C₂	C₆₁×#3488	1	1	yes	characteristic
1115	C₂	C₂×C₆₁×#578	1	1	yes	characteristic
1116	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3552	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
2. C₆₁×#3523	C₂	semidirect
3. C₆₁×#3398	C₂	semidirect
4. C₆₁×#3395	C₂	semidirect
5. C₆₁×#3374	C₂	semidirect
6. C₆₁×#3364	C₂	semidirect
7. C₆₁×#3328	C₂	semidirect
8. C₆₁×#3312	C₂	semidirect
9. C₆₁×#3302	C₂	semidirect
10. C₆₁×#3300	C₂	semidirect
11. D₄×Q₁₆×C₆₁	C₂	semidirect
12. D₄×Q₁₆×C₆₁	C₂	semidirect
13. C₆₁×#3276	C₂	semidirect
14. C₆₁×#3270	C₂	semidirect
15. C₆₁×#3261	C₂	semidirect
16. C₆₁×#3248	C₂	semidirect
17. C₆₁×#3223	C₂	semidirect
18. C₆₁×#3209	C₂	semidirect
19. C₆₁×#3127	C₂	semidirect
20. C₆₁×#3108	C₂	semidirect
21. C₆₁×#3044	C₂	semidirect
22. C₂×C₆₁×#462	C₂	semidirect
23. C₆₁×#2994	C₂	semidirect
521. #62056	C₆₁	direct (N × H)
554. #3523	C₂×C₆₁	semidirect
555. #3398	C₂×C₆₁	semidirect
556. #3395	C₂×C₆₁	semidirect
557. #3374	C₂×C₆₁	semidirect
558. #3364	C₂×C₆₁	semidirect
559. #3328	C₂×C₆₁	semidirect
560. #3312	C₂×C₆₁	semidirect
561. #3302	C₂×C₆₁	semidirect
562. #3300	C₂×C₆₁	semidirect
563. D₄×Q₁₆	C₂×C₆₁	semidirect
564. D₄×Q₁₆	C₂×C₆₁	semidirect
565. #3276	C₂×C₆₁	semidirect
566. #3270	C₂×C₆₁	semidirect
567. #3261	C₂×C₆₁	semidirect
568. #3248	C₂×C₆₁	semidirect
569. #3223	C₂×C₆₁	semidirect
570. #3209	C₂×C₆₁	semidirect
571. #3127	C₂×C₆₁	semidirect
572. #3108	C₂×C₆₁	semidirect
573. #3044	C₂×C₆₁	semidirect
574. C₂×#462	C₂×C₆₁	semidirect
575. #2994	C₂×C₆₁	semidirect
693. C₆₁	#62056	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×#3552	2
C₆₁×#3523	2
C₆₁×#3398	2
C₆₁×#3395	2
C₆₁×#3374	2
C₆₁×#3364	2
C₆₁×#3328	2
C₆₁×#3312	2
C₆₁×#3302	2
C₆₁×#3300	2
D₄×Q₁₆×C₆₁	2
C₆₁×#3276	2
C₆₁×#3270	2
C₆₁×#3261	2
C₆₁×#3248	2
C₆₁×#3223	2
C₆₁×#3209	2
C₆₁×#3127	2
C₆₁×#3108	2
C₆₁×#3044	2
C₂×C₆₁×#462	2
C₆₁×#2994	2
#62056	61

Subgroups — C61×#62056 #29565489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62056 #29565489