Subgroups — C₆₁×#61776 #29565209

Order 15616.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3356	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3354	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3346	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3327	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3322	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3321	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3311	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3244	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3204	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3194	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3124	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3098	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#562	—	2	2	no	—
21	C₆₁×#556	—	2	1	no	—
22	C₆₁×#556	C₂²	1	2	yes	—
23	C₆₁×#555	—	2	1	no	—
24	C₆₁×#555	C₂²	1	2	yes	complemented
25	C₆₁×#554	C₂²	1	2	yes	—
26	C₆₁×#553	—	2	1	no	—
27	C₆₁×#553	C₂²	1	2	yes	—
28	C₆₁×#552	—	2	1	no	—
29	C₆₁×#552	C₂²	1	2	yes	complemented
30	C₆₁×#548	C₂²	1	2	yes	—
31	C₆₁×#547	C₂²	1	2	yes	—
32	C₆₁×#546	—	2	2	no	—
33	C₆₁×#546	C₂²	1	2	yes	—
34	C₆₁×#544	C₂²	1	1	yes	characteristic, complemented
35	C₆₁×#543	—	2	1	no	—
36	C₆₁×#542	C₂²	1	2	yes	—
37	C₆₁×#539	—	2	1	no	—
38	C₆₁×#538	—	2	1	no	—
39	C₆₁×#538	—	2	2	no	—
40	C₆₁×#537	—	2	1	no	—
41	C₆₁×#537	C₂²	1	2	yes	—
42	C₆₁×#537	C₂²	1	1	yes	characteristic, complemented
43	C₆₁×#529	—	2	2	no	—
44	C₆₁×#525	C₂²	1	1	yes	characteristic
45	C₆₁×#525	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#520	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
51	C₆₁×#501	C₂²	1	2	yes	complemented
52	C₆₁×#498	C₂²	1	2	yes	complemented
53	C₆₁×#489	C₂²	1	2	yes	complemented
54	C₆₁×#488	C₂²	1	2	yes	complemented
55	C₆₁×#485	C₂²	1	2	yes	—
56	C₆₁×#485	C₂²	1	2	yes	—
57	C₆₁×#485	C₂²	1	2	yes	complemented
58	C₆₁×#485	C₂²	1	2	yes	complemented
59	C₆₁×#484	C₂²	1	2	yes	complemented
60	C₆₁×#484	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#484	C₂²	1	2	yes	complemented
62	C₆₁×#483	C₂²	1	1	yes	characteristic
63	C₆₁×#483	C₂²	1	2	yes	complemented
64	C₆₁×#483	C₂²	1	2	yes	complemented
65	C₆₁×#482	C₂²	1	2	yes	—
66	C₆₁×#482	C₂²	1	2	yes	—
67	C₆₁×#482	C₂²	1	2	yes	—
68	C₆₁×#482	C₂²	1	2	yes	complemented
69	C₆₁×#481	C₂²	1	2	yes	—
70	C₆₁×#481	C₂²	1	2	yes	complemented
71	C₆₁×#481	C₂²	1	1	yes	characteristic, complemented
72	C₆₁×#480	C₂²	1	1	yes	characteristic
73	C₆₁×#480	C₂²	1	2	yes	—
74	C₆₁×#480	C₂²	1	2	yes	complemented
75	C₆₁×#479	C₂²	1	2	yes	complemented
76	C₆₁×#478	C₂²	1	2	yes	complemented
77	C₆₁×#477	C₂²	1	2	yes	complemented
78	C₆₁×#476	C₂²	1	2	yes	complemented
79	C₆₁×#475	C₂²	1	2	yes	complemented
80	C₆₁×#474	C₂²	1	2	yes	complemented
81	C₆₁×#470	C₂²	1	2	yes	—
82	C₆₁×#470	C₂²	1	2	yes	complemented
83	C₆₁×#469	C₂²	1	2	yes	—
84	C₆₁×#469	C₂²	1	2	yes	complemented
85	C₆₁×#468	C₂²	1	2	yes	—
86	C₆₁×#468	C₂²	1	2	yes	—
87	C₆₁×#465	C₂²	1	2	yes	complemented
88	C₆₁×#465	C₂²	1	2	yes	complemented
89	C₆₁×#464	C₂²	1	2	yes	complemented
90	C₆₁×#463	C₂²	1	2	yes	complemented
91	C₆₁×#452	C₂²	1	2	yes	complemented
92	C₆₁×#452	C₂²	1	2	yes	complemented
93	C₆₁×#451	C₂²	1	1	yes	characteristic, complemented
94	C₆₁×#450	C₂²	1	1	yes	characteristic
95	C₆₁×#449	C₂²	1	2	yes	—
96	C₆₁×#449	C₂²	1	2	yes	complemented
97	C₆₁×#448	C₂²	1	1	yes	characteristic, complemented
98	C₆₁×#447	C₂²	1	1	yes	characteristic
99	C₆₁×#440	C₂²	1	2	yes	complemented
100	C₆₁×#440	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
102	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
103	C₆₁×#436	C₂²	1	2	yes	—
104	C₆₁×#436	C₂²	1	2	yes	complemented
105	C₆₁×#435	C₂²	1	2	yes	—
106	C₆₁×#435	C₂²	1	2	yes	complemented
107	C₆₁×#433	C₂²	1	2	yes	complemented
108	C₆₁×#428	C₂²	1	2	yes	—
109	C₆₁×#428	C₂²	1	2	yes	complemented
110	C₆₁×#428	C₂²	1	2	yes	complemented
111	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
112	C₆₁×#419	C₂²	1	2	yes	complemented
113	C₆₁×#418	C₂²	1	2	yes	—
114	C₆₁×#417	C₂²	1	2	yes	complemented
115	C₆₁×#416	C₂²	1	2	yes	complemented
116	C₆₁×#408	C₂²	1	2	yes	complemented
117	C₆₁×#407	C₂²	1	1	yes	characteristic
118	C₆₁×#407	C₂²	1	1	yes	characteristic
119	C₂×#41×C₆₁	—	2	2	no	—
120	C₂×#41×C₆₁	C₂³	1	2	yes	—
121	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
122	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₆₁	—	2	1	no	—
125	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
130	C₂×D₈×C₆₁	C₂³	1	2	yes	—
131	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
132	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
133	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
134	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₆₁	—	2	1	no	—
136	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
138	#126×C₆₁	—	2	2	no	—
139	#126×C₆₁	—	2	2	no	—
140	#126×C₆₁	—	2	2	no	—
141	#126×C₆₁	—	2	2	no	—
142	#126×C₆₁	—	2	2	no	—
143	#125×C₆₁	—	2	2	no	—
144	#125×C₆₁	—	2	1	no	—
145	#125×C₆₁	—	2	2	no	—
146	#125×C₆₁	C₂³	1	2	yes	—
147	#124×C₆₁	—	2	2	no	—
148	#124×C₆₁	—	2	2	no	—
149	#124×C₆₁	—	2	2	no	—
150	#124×C₆₁	—	2	2	no	—
151	#124×C₆₁	—	2	2	no	—
152	#124×C₆₁	C₂³	1	2	yes	—
153	#123×C₆₁	—	2	2	no	—
154	#123×C₆₁	—	2	1	no	—
155	#123×C₆₁	—	2	2	no	—
156	#123×C₆₁	—	2	2	no	—
157	#123×C₆₁	—	2	2	no	—
158	#123×C₆₁	—	2	2	no	—
159	#123×C₆₁	—	2	2	no	—
160	#123×C₆₁	D₄	1	2	yes	—
161	C₂²⋊Q₈×C₆₁	—	2	2	no	—
162	C₂²⋊Q₈×C₆₁	—	2	1	no	—
163	C₂²⋊Q₈×C₆₁	—	2	1	no	—
164	C₂²⋊Q₈×C₆₁	—	2	1	no	—
165	C₂²⋊Q₈×C₆₁	—	2	2	no	—
166	C₂²⋊Q₈×C₆₁	—	2	2	no	—
167	C₂²⋊Q₈×C₆₁	—	2	2	no	—
168	C₂²⋊Q₈×C₆₁	—	2	2	no	—
169	C₂²⋊Q₈×C₆₁	—	2	2	no	—
170	C₂²⋊Q₈×C₆₁	—	2	2	no	—
171	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
172	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
173	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
174	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
175	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
176	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
177	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
179	#121×C₆₁	—	2	2	no	—
180	#121×C₆₁	—	2	2	no	—
181	#121×C₆₁	—	2	2	no	—
182	#121×C₆₁	—	2	2	no	—
183	#121×C₆₁	—	2	2	no	—
184	#121×C₆₁	—	2	1	no	—
185	#121×C₆₁	—	2	2	no	—
186	#121×C₆₁	—	2	2	no	—
187	#121×C₆₁	—	2	1	no	—
188	#121×C₆₁	—	2	1	no	—
189	#121×C₆₁	—	2	2	no	—
190	#121×C₆₁	D₄	1	1	yes	characteristic
191	#121×C₆₁	D₄	1	1	yes	characteristic
192	#121×C₆₁	C₂³	1	2	yes	—
193	#121×C₆₁	C₂³	1	2	yes	—
194	#121×C₆₁	C₂³	1	2	yes	—
195	#121×C₆₁	C₂³	1	2	yes	—
196	#121×C₆₁	C₂³	1	1	yes	characteristic
197	#121×C₆₁	C₂³	1	1	yes	characteristic
198	#120×C₆₁	—	2	1	no	—
199	#120×C₆₁	—	2	2	no	—
200	#120×C₆₁	D₄	1	2	yes	—
201	C₄×Q₈×C₆₁	—	2	1	no	—
202	C₄×Q₈×C₆₁	—	2	2	no	—
203	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
205	C₄×D₄×C₆₁	—	2	2	no	—
206	C₄×D₄×C₆₁	—	2	2	no	—
207	C₄×D₄×C₆₁	—	2	1	no	—
208	C₄×D₄×C₆₁	—	2	1	no	—
209	C₄×D₄×C₆₁	—	2	1	no	—
210	C₄×D₄×C₆₁	—	2	2	no	—
211	C₄×D₄×C₆₁	—	2	2	no	—
212	C₄×D₄×C₆₁	—	2	2	no	—
213	C₄×D₄×C₆₁	C₂³	1	2	yes	—
214	C₄×D₄×C₆₁	C₂³	1	2	yes	—
215	C₄×D₄×C₆₁	C₂³	1	2	yes	—
216	C₄×D₄×C₆₁	C₂³	1	2	yes	—
217	#117×C₆₁	—	2	1	no	—
218	#117×C₆₁	—	2	1	no	—
219	#117×C₆₁	—	2	2	no	—
220	#117×C₆₁	—	2	1	no	—
221	#117×C₆₁	—	2	2	no	—
222	#117×C₆₁	C₂³	1	1	yes	characteristic
223	#117×C₆₁	C₂³	1	2	yes	—
224	#117×C₆₁	C₂³	1	2	yes	—
225	#117×C₆₁	C₂³	1	2	yes	—
226	#117×C₆₁	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
228	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
236	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
237	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
239	C₂×C₄²×C₆₁	—	2	1	no	—
240	#107×C₆₁	C₂³	1	2	yes	—
241	#107×C₆₁	C₂³	1	2	yes	—
242	#107×C₆₁	C₂³	1	2	yes	—
243	#107×C₆₁	C₂³	1	2	yes	—
244	#107×C₆₁	C₂³	1	2	yes	—
245	#107×C₆₁	C₂³	1	2	yes	—
246	#106×C₆₁	C₂³	1	2	yes	—
247	#106×C₆₁	C₂³	1	2	yes	—
248	#106×C₆₁	C₂³	1	2	yes	—
249	#106×C₆₁	C₂³	1	2	yes	—
250	#106×C₆₁	C₂³	1	2	yes	—
251	#106×C₆₁	C₂³	1	2	yes	—
252	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
253	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
254	#103×C₆₁	C₂³	1	2	yes	—
255	#103×C₆₁	C₂³	1	2	yes	—
256	#103×C₆₁	C₂³	1	2	yes	—
257	#103×C₆₁	C₂³	1	2	yes	—
258	#103×C₆₁	C₂³	1	2	yes	—
259	#103×C₆₁	C₂³	1	2	yes	—
260	#103×C₆₁	C₂³	1	2	yes	—
261	#103×C₆₁	C₂³	1	2	yes	—
262	#102×C₆₁	C₂³	1	2	yes	—
263	#102×C₆₁	C₂³	1	2	yes	—
264	#102×C₆₁	C₂³	1	2	yes	—
265	#102×C₆₁	C₂³	1	2	yes	—
266	#102×C₆₁	C₂³	1	2	yes	—
267	#102×C₆₁	C₂³	1	2	yes	—
268	#102×C₆₁	C₂³	1	2	yes	—
269	#102×C₆₁	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
271	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
273	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
274	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
275	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
276	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
278	#97×C₆₁	C₂³	1	2	yes	—
279	C₄×C₈×C₆₁	C₂³	1	2	yes	—
280	C₂⁴×C₆₁	—	2	1	no	—
281	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
282	#41×C₆₁	—	4	2	no	—
283	#41×C₆₁	—	4	2	no	—
284	#41×C₆₁	—	4	2	no	—
285	#41×C₆₁	—	4	2	no	—
286	#41×C₆₁	—	8	4	no	—
287	C₂×Q₈×C₆₁	—	2	2	no	—
288	C₂×Q₈×C₆₁	—	2	1	no	—
289	C₂×Q₈×C₆₁	—	2	2	no	—
290	C₂×Q₈×C₆₁	—	4	2	no	—
291	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
294	C₂×D₄×C₆₁	—	2	1	no	—
295	C₂×D₄×C₆₁	—	2	2	no	—
296	C₂×D₄×C₆₁	—	2	1	no	—
297	C₂×D₄×C₆₁	—	2	1	no	—
298	C₂×D₄×C₆₁	—	2	2	no	—
299	C₂×D₄×C₆₁	—	2	2	no	—
300	C₂×D₄×C₆₁	—	2	2	no	—
301	C₂×D₄×C₆₁	—	2	2	no	—
302	C₂×D₄×C₆₁	—	2	1	no	—
303	C₂×D₄×C₆₁	—	4	2	no	—
304	C₂×D₄×C₆₁	—	8	2	no	—
305	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
306	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
307	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
308	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
309	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
310	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₁	—	2	1	no	—
312	C₂²×C₄×C₆₁	—	2	1	no	—
313	C₂²×C₄×C₆₁	—	2	1	no	—
314	C₂²×C₄×C₆₁	—	2	1	no	—
315	C₂²×C₄×C₆₁	—	2	1	no	—
316	C₂²×C₄×C₆₁	—	2	2	no	—
317	C₂²×C₄×C₆₁	—	2	2	no	—
318	C₂²×C₄×C₆₁	—	2	1	no	—
319	C₂²×C₄×C₆₁	—	2	2	no	—
320	C₂²×C₄×C₆₁	—	2	2	no	—
321	C₂²×C₄×C₆₁	—	2	2	no	—
322	C₂²×C₄×C₆₁	—	4	2	no	—
323	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
330	Q₁₆×C₆₁	—	4	2	no	—
331	SD₁₆×C₆₁	—	4	2	no	—
332	SD₁₆×C₆₁	—	4	2	no	—
333	D₈×C₆₁	—	4	2	no	—
334	M₁₆×C₆₁	—	4	2	no	—
335	M₁₆×C₆₁	—	4	2	no	—
336	M₁₆×C₆₁	—	4	2	no	—
337	C₂×C₈×C₆₁	—	4	2	no	—
338	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
339	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
340	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
341	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₆₁	—	2	1	no	—
343	C₄⋊C₄×C₆₁	—	2	2	no	—
344	C₄⋊C₄×C₆₁	—	2	2	no	—
345	C₄⋊C₄×C₆₁	—	2	2	no	—
346	C₄⋊C₄×C₆₁	—	2	1	no	—
347	C₄⋊C₄×C₆₁	—	2	2	no	—
348	C₄⋊C₄×C₆₁	—	2	1	no	—
349	C₄⋊C₄×C₆₁	—	2	2	no	—
350	C₄⋊C₄×C₆₁	—	2	1	no	—
351	C₄⋊C₄×C₆₁	—	2	1	no	—
352	C₄⋊C₄×C₆₁	—	2	2	no	—
353	C₄⋊C₄×C₆₁	—	2	2	no	—
354	C₄⋊C₄×C₆₁	—	2	1	no	—
355	C₄⋊C₄×C₆₁	—	2	2	no	—
356	C₄⋊C₄×C₆₁	—	2	2	no	—
357	C₄⋊C₄×C₆₁	—	2	2	no	—
358	C₄⋊C₄×C₆₁	—	2	2	no	—
359	C₄⋊C₄×C₆₁	—	2	2	no	—
360	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
370	C₂²⋊C₄×C₆₁	—	2	2	no	—
371	C₂²⋊C₄×C₆₁	—	2	2	no	—
372	C₂²⋊C₄×C₆₁	—	2	2	no	—
373	C₂²⋊C₄×C₆₁	—	2	2	no	—
374	C₂²⋊C₄×C₆₁	—	2	2	no	—
375	C₂²⋊C₄×C₆₁	—	2	1	no	—
376	C₂²⋊C₄×C₆₁	—	2	2	no	—
377	C₂²⋊C₄×C₆₁	—	2	1	no	—
378	C₂²⋊C₄×C₆₁	—	2	1	no	—
379	C₂²⋊C₄×C₆₁	—	2	2	no	—
380	C₂²⋊C₄×C₆₁	—	2	2	no	—
381	C₂²⋊C₄×C₆₁	—	2	2	no	—
382	C₂²⋊C₄×C₆₁	—	2	2	no	—
383	C₂²⋊C₄×C₆₁	—	2	2	no	—
384	C₂²⋊C₄×C₆₁	—	2	1	no	—
385	C₂²⋊C₄×C₆₁	—	2	2	no	—
386	C₂²⋊C₄×C₆₁	—	2	2	no	—
387	C₂²⋊C₄×C₆₁	—	2	1	no	—
388	C₂²⋊C₄×C₆₁	—	2	2	no	—
389	C₂²⋊C₄×C₆₁	—	2	2	no	—
390	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
395	C₄²×C₆₁	—	2	2	no	—
396	C₄²×C₆₁	—	2	2	no	—
397	C₄²×C₆₁	—	2	2	no	—
398	C₄²×C₆₁	—	2	2	no	—
399	C₄²×C₆₁	—	2	1	no	—
400	C₄²×C₆₁	—	2	2	no	—
401	C₄²×C₆₁	C₂⁴	1	2	yes	—
402	C₂³×C₆₁	—	2	1	no	—
403	C₂³×C₆₁	—	2	2	no	—
404	C₂³×C₆₁	—	4	1	no	—
405	C₂³×C₆₁	—	4	1	no	—
406	C₂³×C₆₁	—	4	1	no	—
407	C₂³×C₆₁	—	4	2	no	—
408	C₂³×C₆₁	—	8	1	no	—
409	C₂³×C₆₁	—	8	1	no	—
410	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
411	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
412	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
413	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
414	Q₈×C₆₁	—	2	2	no	—
415	Q₈×C₆₁	—	2	2	no	—
416	Q₈×C₆₁	—	2	2	no	—
417	Q₈×C₆₁	—	4	1	no	—
418	Q₈×C₆₁	—	8	2	no	—
419	Q₈×C₆₁	—	8	1	no	—
420	Q₈×C₆₁	—	8	2	no	—
421	D₄×C₆₁	—	2	2	no	—
422	D₄×C₆₁	—	2	2	no	—
423	D₄×C₆₁	—	2	2	no	—
424	D₄×C₆₁	—	4	2	no	—
425	D₄×C₆₁	—	4	1	no	—
426	D₄×C₆₁	—	4	2	no	—
427	D₄×C₆₁	—	4	2	no	—
428	D₄×C₆₁	—	4	4	no	—
429	D₄×C₆₁	—	4	2	no	—
430	D₄×C₆₁	—	8	1	no	—
431	D₄×C₆₁	—	8	1	no	—
432	D₄×C₆₁	—	8	2	no	—
433	D₄×C₆₁	—	8	1	no	—
434	D₄×C₆₁	—	8	2	no	—
435	D₄×C₆₁	—	8	2	no	—
436	D₄×C₆₁	—	8	2	no	—
437	C₂×C₄×C₆₁	—	2	2	no	—
438	C₂×C₄×C₆₁	—	2	2	no	—
439	C₂×C₄×C₆₁	—	2	2	no	—
440	C₂×C₄×C₆₁	—	2	2	no	—
441	C₂×C₄×C₆₁	—	2	2	no	—
442	C₂×C₄×C₆₁	—	2	2	no	—
443	C₂×C₄×C₆₁	—	2	1	no	—
444	C₂×C₄×C₆₁	—	2	1	no	—
445	C₂×C₄×C₆₁	—	2	2	no	—
446	C₂×C₄×C₆₁	—	2	2	no	—
447	C₂×C₄×C₆₁	—	2	1	no	—
448	C₂×C₄×C₆₁	—	2	2	no	—
449	C₂×C₄×C₆₁	—	2	2	no	—
450	C₂×C₄×C₆₁	—	4	1	no	—
451	C₂×C₄×C₆₁	—	4	1	no	—
452	C₂×C₄×C₆₁	—	4	1	no	—
453	C₂×C₄×C₆₁	—	4	2	no	—
454	C₂×C₄×C₆₁	—	4	2	no	—
455	C₂×C₄×C₆₁	—	8	2	no	—
456	C₂×C₄×C₆₁	—	8	2	no	—
457	C₂×C₄×C₆₁	—	8	2	no	—
458	C₂×C₄×C₆₁	—	8	1	no	—
459	C₂×C₄×C₆₁	—	8	2	no	—
460	C₂×C₄×C₆₁	—	8	1	no	—
461	C₂×C₄×C₆₁	—	8	1	no	—
462	C₂×C₄×C₆₁	—	8	1	no	—
463	C₂×C₄×C₆₁	—	8	2	no	—
464	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
471	C₈×C₆₁	—	2	2	no	—
472	C₈×C₆₁	—	2	2	no	—
473	C₈×C₆₁	—	2	2	no	—
474	C₈×C₆₁	—	2	2	no	—
475	#61776	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
476	C₂²×C₆₁	—	2	1	no	—
477	C₂²×C₆₁	—	2	2	no	—
478	C₂²×C₆₁	—	2	1	no	—
479	C₂²×C₆₁	—	2	1	no	—
480	C₂²×C₆₁	—	2	1	no	—
481	C₂²×C₆₁	—	2	1	no	—
482	C₂²×C₆₁	—	2	2	no	—
483	C₂²×C₆₁	—	2	1	no	—
484	C₂²×C₆₁	—	2	1	no	—
485	C₂²×C₆₁	—	2	1	no	—
486	C₂²×C₆₁	—	2	1	no	—
487	C₂²×C₆₁	—	2	2	no	—
488	C₂²×C₆₁	—	4	1	no	—
489	C₂²×C₆₁	—	4	2	no	—
490	C₂²×C₆₁	—	4	1	no	—
491	C₂²×C₆₁	—	4	2	no	—
492	C₂²×C₆₁	—	4	1	no	—
493	C₂²×C₆₁	—	4	2	no	—
494	C₂²×C₆₁	—	8	2	no	—
495	C₂²×C₆₁	—	16	2	no	—
496	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
497	C₄×C₆₁	—	2	2	no	—
498	C₄×C₆₁	—	2	2	no	—
499	C₄×C₆₁	—	2	1	no	—
500	C₄×C₆₁	—	2	1	no	—
501	C₄×C₆₁	—	2	1	no	—
502	C₄×C₆₁	—	2	2	no	—
503	C₄×C₆₁	—	4	2	no	—
504	C₄×C₆₁	—	4	2	no	—
505	C₄×C₆₁	—	4	2	no	—
506	C₄×C₆₁	—	4	1	no	—
507	C₄×C₆₁	—	4	2	no	—
508	C₄×C₆₁	—	4	1	no	—
509	C₄×C₆₁	—	4	1	no	—
510	C₄×C₆₁	—	4	2	no	—
511	C₄×C₆₁	#585	1	2	yes	—
512	#3536	C₂×C₆₁	1	1	yes	characteristic, complemented
513	#3493	C₂×C₆₁	1	1	yes	characteristic, complemented
514	#3356	C₂×C₆₁	1	2	yes	complemented
515	#3354	C₂×C₆₁	1	2	yes	complemented
516	#3346	C₂×C₆₁	1	2	yes	complemented
517	#3343	C₂×C₆₁	1	2	yes	complemented
518	#3327	C₂×C₆₁	1	2	yes	complemented
519	#3322	C₂×C₆₁	1	2	yes	complemented
520	#3321	C₂×C₆₁	1	2	yes	complemented
521	#3311	C₂×C₆₁	1	2	yes	complemented
522	#3244	C₂×C₆₁	1	2	yes	complemented
523	#3204	C₂×C₆₁	1	2	yes	complemented
524	#3196	C₂×C₆₁	1	1	yes	characteristic, complemented
525	#3194	C₂×C₆₁	1	1	yes	characteristic, complemented
526	#3124	C₂×C₆₁	1	2	yes	complemented
527	#3098	C₂×C₆₁	1	2	yes	complemented
528	#3095	C₂×C₆₁	1	1	yes	characteristic, complemented
529	#3094	C₂×C₆₁	1	1	yes	characteristic, complemented
530	#2978	C₂×C₆₁	1	1	yes	characteristic, complemented
531	C₂×C₆₁	—	4	2	no	—
532	C₂×C₆₁	—	4	1	no	—
533	C₂×C₆₁	—	4	1	no	—
534	C₂×C₆₁	—	4	1	no	—
535	C₂×C₆₁	—	8	1	no	—
536	C₂×C₆₁	—	8	2	no	—
537	C₂×C₆₁	#3485	1	1	yes	characteristic
538	C₂×C₆₁	#3585	1	1	yes	characteristic
539	C₂×C₆₁	#3586	1	1	yes	characteristic
540	#562	—	2	2	no	—
541	#556	—	2	1	no	—
542	#556	C₂²×C₆₁	1	2	yes	—
543	#555	—	2	1	no	—
544	#555	C₂²×C₆₁	1	2	yes	complemented
545	#554	C₂²×C₆₁	1	2	yes	—
546	#553	—	2	1	no	—
547	#553	C₂²×C₆₁	1	2	yes	—
548	#552	—	2	1	no	—
549	#552	C₂²×C₆₁	1	2	yes	complemented
550	#548	C₂²×C₆₁	1	2	yes	—
551	#547	C₂²×C₆₁	1	2	yes	—
552	#546	—	2	2	no	—
553	#546	C₂²×C₆₁	1	2	yes	—
554	#544	C₂²×C₆₁	1	1	yes	characteristic, complemented
555	#543	—	2	1	no	—
556	#542	C₂²×C₆₁	1	2	yes	—
557	#539	—	2	1	no	—
558	#538	—	2	1	no	—
559	#538	—	2	2	no	—
560	#537	—	2	1	no	—
561	#537	C₂²×C₆₁	1	2	yes	—
562	#537	C₂²×C₆₁	1	1	yes	characteristic, complemented
563	#529	—	2	2	no	—
564	#525	C₂²×C₆₁	1	1	yes	characteristic
565	#525	C₂²×C₆₁	1	1	yes	characteristic
566	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
567	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
568	#520	C₂²×C₆₁	1	1	yes	characteristic, complemented
569	#520	C₂²×C₆₁	1	1	yes	characteristic, complemented
570	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
571	#501	C₂²×C₆₁	1	2	yes	complemented
572	#498	C₂²×C₆₁	1	2	yes	complemented
573	#489	C₂²×C₆₁	1	2	yes	complemented
574	#488	C₂²×C₆₁	1	2	yes	complemented
575	#485	C₂²×C₆₁	1	2	yes	—
576	#485	C₂²×C₆₁	1	2	yes	—
577	#485	C₂²×C₆₁	1	2	yes	complemented
578	#485	C₂²×C₆₁	1	2	yes	complemented
579	#484	C₂²×C₆₁	1	1	yes	characteristic, complemented
580	#484	C₂²×C₆₁	1	2	yes	complemented
581	#484	C₂²×C₆₁	1	2	yes	complemented
582	#483	C₂²×C₆₁	1	1	yes	characteristic
583	#483	C₂²×C₆₁	1	2	yes	complemented
584	#483	C₂²×C₆₁	1	2	yes	complemented
585	#482	C₂²×C₆₁	1	2	yes	—
586	#482	C₂²×C₆₁	1	2	yes	—
587	#482	C₂²×C₆₁	1	2	yes	—
588	#482	C₂²×C₆₁	1	2	yes	complemented
589	#481	C₂²×C₆₁	1	2	yes	—
590	#481	C₂²×C₆₁	1	2	yes	complemented
591	#481	C₂²×C₆₁	1	1	yes	characteristic, complemented
592	#480	C₂²×C₆₁	1	1	yes	characteristic
593	#480	C₂²×C₆₁	1	2	yes	—
594	#480	C₂²×C₆₁	1	2	yes	complemented
595	#479	C₂²×C₆₁	1	2	yes	complemented
596	#478	C₂²×C₆₁	1	2	yes	complemented
597	#477	C₂²×C₆₁	1	2	yes	complemented
598	#476	C₂²×C₆₁	1	2	yes	complemented
599	#475	C₂²×C₆₁	1	2	yes	complemented
600	#474	C₂²×C₆₁	1	2	yes	complemented
601	#470	C₂²×C₆₁	1	2	yes	—
602	#470	C₂²×C₆₁	1	2	yes	complemented
603	#469	C₂²×C₆₁	1	2	yes	—
604	#469	C₂²×C₆₁	1	2	yes	complemented
605	#468	C₂²×C₆₁	1	2	yes	—
606	#468	C₂²×C₆₁	1	2	yes	—
607	#465	C₂²×C₆₁	1	2	yes	complemented
608	#465	C₂²×C₆₁	1	2	yes	complemented
609	#464	C₂²×C₆₁	1	2	yes	complemented
610	#463	C₂²×C₆₁	1	2	yes	complemented
611	#452	C₂²×C₆₁	1	2	yes	complemented
612	#452	C₂²×C₆₁	1	2	yes	complemented
613	#451	C₂²×C₆₁	1	1	yes	characteristic, complemented
614	#450	C₂²×C₆₁	1	1	yes	characteristic
615	#449	C₂²×C₆₁	1	2	yes	—
616	#449	C₂²×C₆₁	1	2	yes	complemented
617	#448	C₂²×C₆₁	1	1	yes	characteristic, complemented
618	#447	C₂²×C₆₁	1	1	yes	characteristic
619	#440	C₂²×C₆₁	1	2	yes	complemented
620	#440	C₂²×C₆₁	1	2	yes	complemented
621	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
622	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
623	#436	C₂²×C₆₁	1	2	yes	—
624	#436	C₂²×C₆₁	1	2	yes	complemented
625	#435	C₂²×C₆₁	1	2	yes	—
626	#435	C₂²×C₆₁	1	2	yes	complemented
627	#433	C₂²×C₆₁	1	2	yes	complemented
628	#428	C₂²×C₆₁	1	2	yes	—
629	#428	C₂²×C₆₁	1	2	yes	complemented
630	#428	C₂²×C₆₁	1	2	yes	complemented
631	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
632	#419	C₂²×C₆₁	1	2	yes	complemented
633	#418	C₂²×C₆₁	1	2	yes	—
634	#417	C₂²×C₆₁	1	2	yes	complemented
635	#416	C₂²×C₆₁	1	2	yes	complemented
636	#408	C₂²×C₆₁	1	2	yes	complemented
637	#407	C₂²×C₆₁	1	1	yes	characteristic
638	#407	C₂²×C₆₁	1	1	yes	characteristic
639	C₆₁	#61776	1	1	yes	characteristic, direct product factor, Sylow
640	C₂×#41	—	2	2	no	—
641	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
642	C₂×#41	C₂³×C₆₁	1	2	yes	—
643	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
644	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
645	C₂²×D₄	—	2	1	no	—
646	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
647	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
648	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
649	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
650	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
651	C₂×D₈	C₂³×C₆₁	1	2	yes	—
652	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
653	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
654	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
655	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
656	C₄⋊Q₈	—	2	1	no	—
657	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
658	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	—	2	2	no	—
663	#126	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	1	no	—
667	#125	C₂³×C₆₁	1	2	yes	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	2	no	—
672	#124	—	2	2	no	—
673	#124	C₂³×C₆₁	1	2	yes	—
674	#123	—	2	2	no	—
675	#123	—	2	1	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	D₄×C₆₁	1	2	yes	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	1	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
693	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
694	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
696	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
698	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
699	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	—	2	1	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	1	no	—
709	#121	—	2	1	no	—
710	#121	—	2	2	no	—
711	#121	D₄×C₆₁	1	1	yes	characteristic
712	#121	D₄×C₆₁	1	1	yes	characteristic
713	#121	C₂³×C₆₁	1	2	yes	—
714	#121	C₂³×C₆₁	1	2	yes	—
715	#121	C₂³×C₆₁	1	1	yes	characteristic
716	#121	C₂³×C₆₁	1	1	yes	characteristic
717	#121	C₂³×C₆₁	1	2	yes	—
718	#121	C₂³×C₆₁	1	2	yes	—
719	#120	—	2	1	no	—
720	#120	—	2	2	no	—
721	#120	D₄×C₆₁	1	2	yes	—
722	C₄×Q₈	—	2	1	no	—
723	C₄×Q₈	—	2	2	no	—
724	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
725	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	—	2	1	no	—
731	C₄×D₄	—	2	2	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	C₂³×C₆₁	1	2	yes	—
735	C₄×D₄	C₂³×C₆₁	1	2	yes	—
736	C₄×D₄	C₂³×C₆₁	1	2	yes	—
737	C₄×D₄	C₂³×C₆₁	1	2	yes	—
738	#117	—	2	1	no	—
739	#117	—	2	1	no	—
740	#117	—	2	1	no	—
741	#117	—	2	2	no	—
742	#117	—	2	2	no	—
743	#117	C₂³×C₆₁	1	2	yes	—
744	#117	C₂³×C₆₁	1	2	yes	—
745	#117	C₂³×C₆₁	1	1	yes	characteristic
746	#117	C₂³×C₆₁	1	2	yes	—
747	#117	C₂³×C₆₁	1	1	yes	characteristic
748	C₂×C₄⋊C₄	—	2	1	no	—
749	C₂×C₄⋊C₄	—	2	1	no	—
750	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
756	C₂×C₂²⋊C₄	—	2	1	no	—
757	C₂×C₂²⋊C₄	—	2	1	no	—
758	C₂×C₂²⋊C₄	—	2	1	no	—
759	C₂×C₂²⋊C₄	—	2	2	no	—
760	C₂×C₄²	—	2	1	no	—
761	#107	C₂³×C₆₁	1	2	yes	—
762	#107	C₂³×C₆₁	1	2	yes	—
763	#107	C₂³×C₆₁	1	2	yes	—
764	#107	C₂³×C₆₁	1	2	yes	—
765	#107	C₂³×C₆₁	1	2	yes	—
766	#107	C₂³×C₆₁	1	2	yes	—
767	#106	C₂³×C₆₁	1	2	yes	—
768	#106	C₂³×C₆₁	1	2	yes	—
769	#106	C₂³×C₆₁	1	2	yes	—
770	#106	C₂³×C₆₁	1	2	yes	—
771	#106	C₂³×C₆₁	1	2	yes	—
772	#106	C₂³×C₆₁	1	2	yes	—
773	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
774	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
775	#103	C₂³×C₆₁	1	2	yes	—
776	#103	C₂³×C₆₁	1	2	yes	—
777	#103	C₂³×C₆₁	1	2	yes	—
778	#103	C₂³×C₆₁	1	2	yes	—
779	#103	C₂³×C₆₁	1	2	yes	—
780	#103	C₂³×C₆₁	1	2	yes	—
781	#103	C₂³×C₆₁	1	2	yes	—
782	#103	C₂³×C₆₁	1	2	yes	—
783	#102	C₂³×C₆₁	1	2	yes	—
784	#102	C₂³×C₆₁	1	2	yes	—
785	#102	C₂³×C₆₁	1	2	yes	—
786	#102	C₂³×C₆₁	1	2	yes	—
787	#102	C₂³×C₆₁	1	2	yes	—
788	#102	C₂³×C₆₁	1	2	yes	—
789	#102	C₂³×C₆₁	1	2	yes	—
790	#102	C₂³×C₆₁	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
793	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
794	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
795	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
796	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
797	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
798	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
799	#97	C₂³×C₆₁	1	2	yes	—
800	C₄×C₈	C₂³×C₆₁	1	2	yes	—
801	C₂⁴	—	2	1	no	—
802	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
803	#41	—	4	2	no	—
804	#41	—	4	2	no	—
805	#41	—	4	2	no	—
806	#41	—	4	2	no	—
807	#41	—	8	4	no	—
808	C₂×Q₈	—	2	2	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	2	no	—
811	C₂×Q₈	—	4	2	no	—
812	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
813	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
814	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	1	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	—	8	2	no	—
826	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
827	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
828	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
829	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
830	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
831	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
845	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
846	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
851	Q₁₆	—	4	2	no	—
852	SD₁₆	—	4	2	no	—
853	SD₁₆	—	4	2	no	—
854	D₈	—	4	2	no	—
855	M₁₆	—	4	2	no	—
856	M₁₆	—	4	2	no	—
857	M₁₆	—	4	2	no	—
858	C₂×C₈	—	4	2	no	—
859	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
860	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
861	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
862	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
882	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
883	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
884	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
885	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
886	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
887	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
888	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
889	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
890	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	1	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	1	no	—
899	C₂²⋊C₄	—	2	1	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	1	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	1	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
912	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
913	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
914	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
915	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	2	no	—
918	C₄²	—	2	2	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	1	no	—
921	C₄²	—	2	2	no	—
922	C₄²	C₂⁴×C₆₁	1	2	yes	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	4	1	no	—
926	C₂³	—	4	1	no	—
927	C₂³	—	4	1	no	—
928	C₂³	—	4	2	no	—
929	C₂³	—	8	1	no	—
930	C₂³	—	8	1	no	—
931	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
932	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
933	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
934	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
935	Q₈	—	2	2	no	—
936	Q₈	—	2	2	no	—
937	Q₈	—	2	2	no	—
938	Q₈	—	4	1	no	—
939	Q₈	—	8	2	no	—
940	Q₈	—	8	1	no	—
941	Q₈	—	8	2	no	—
942	D₄	—	2	2	no	—
943	D₄	—	2	2	no	—
944	D₄	—	2	2	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	1	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	4	no	—
950	D₄	—	4	2	no	—
951	D₄	—	8	1	no	—
952	D₄	—	8	1	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	1	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	D₄	—	8	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	1	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	—	8	2	no	—
977	C₂×C₄	—	8	2	no	—
978	C₂×C₄	—	8	2	no	—
979	C₂×C₄	—	8	1	no	—
980	C₂×C₄	—	8	2	no	—
981	C₂×C₄	—	8	1	no	—
982	C₂×C₄	—	8	1	no	—
983	C₂×C₄	—	8	1	no	—
984	C₂×C₄	—	8	2	no	—
985	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
986	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
988	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
989	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
991	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
992	C₈	—	2	2	no	—
993	C₈	—	2	2	no	—
994	C₈	—	2	2	no	—
995	C₈	—	2	2	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	1	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	8	2	no	—
1015	C₂²	—	16	2	no	—
1016	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	1	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	2	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	2	no	—
1031	C₄	C₆₁×#585	1	2	yes	—
1032	C₂	—	4	1	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	1	no	—
1035	C₂	—	4	2	no	—
1036	C₂	—	8	2	no	—
1037	C₂	—	8	1	no	—
1038	C₂	C₆₁×#3485	1	1	yes	characteristic
1039	C₂	C₆₁×#3585	1	1	yes	characteristic
1040	C₂	C₆₁×#3586	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3536	C₂	semidirect
2. C₆₁×#3493	C₂	semidirect
3. C₆₁×#3356	C₂	semidirect
4. C₆₁×#3354	C₂	semidirect
5. C₆₁×#3346	C₂	semidirect
6. C₆₁×#3343	C₂	semidirect
7. C₆₁×#3327	C₂	semidirect
8. C₆₁×#3322	C₂	semidirect
9. C₆₁×#3321	C₂	semidirect
10. C₆₁×#3311	C₂	semidirect
11. C₆₁×#3244	C₂	semidirect
12. C₆₁×#3204	C₂	semidirect
13. C₆₁×#3196	C₂	semidirect
14. C₆₁×#3194	C₂	semidirect
15. C₆₁×#3124	C₂	semidirect
16. C₆₁×#3098	C₂	semidirect
17. C₆₁×#3095	C₂	semidirect
18. C₆₁×#3094	C₂	semidirect
19. C₆₁×#2978	C₂	semidirect
24. C₆₁×#555	C₂²	semidirect
29. C₆₁×#552	C₂²	semidirect
34. C₆₁×#544	C₂²	semidirect
42. C₆₁×#537	C₂²	semidirect
48. C₆₁×#520	C₂²	semidirect
49. C₆₁×#520	C₂²	semidirect
51. C₆₁×#501	C₂²	semidirect
52. C₆₁×#498	C₂²	semidirect
53. C₆₁×#489	C₂²	semidirect
54. C₆₁×#488	C₂²	semidirect
57. C₆₁×#485	C₂²	semidirect
58. C₆₁×#485	C₂²	semidirect
59. C₆₁×#484	C₂²	semidirect
60. C₆₁×#484	C₂²	semidirect
61. C₆₁×#484	C₂²	semidirect
63. C₆₁×#483	C₂²	semidirect
64. C₆₁×#483	C₂²	semidirect
68. C₆₁×#482	C₂²	semidirect
70. C₆₁×#481	C₂²	semidirect
71. C₆₁×#481	C₂²	semidirect
74. C₆₁×#480	C₂²	semidirect
75. C₆₁×#479	C₂²	semidirect
76. C₆₁×#478	C₂²	semidirect
77. C₆₁×#477	C₂²	semidirect
78. C₆₁×#476	C₂²	semidirect
79. C₆₁×#475	C₂²	semidirect
80. C₆₁×#474	C₂²	semidirect
82. C₆₁×#470	C₂²	semidirect
84. C₆₁×#469	C₂²	semidirect
87. C₆₁×#465	C₂²	semidirect
88. C₆₁×#465	C₂²	semidirect
89. C₆₁×#464	C₂²	semidirect
90. C₆₁×#463	C₂²	semidirect
91. C₆₁×#452	C₂²	semidirect
92. C₆₁×#452	C₂²	semidirect
93. C₆₁×#451	C₂²	semidirect
96. C₆₁×#449	C₂²	semidirect
97. C₆₁×#448	C₂²	semidirect
99. C₆₁×#440	C₂²	semidirect
100. C₆₁×#440	C₂²	semidirect
101. C₄×Q₁₆×C₆₁	C₂²	semidirect
102. C₄×D₈×C₆₁	C₂²	semidirect
104. C₆₁×#436	C₂²	semidirect
106. C₆₁×#435	C₂²	semidirect
107. C₆₁×#433	C₂²	semidirect
109. C₆₁×#428	C₂²	semidirect
110. C₆₁×#428	C₂²	semidirect
111. C₂×#107×C₆₁	C₂²	semidirect
112. C₆₁×#419	C₂²	semidirect
114. C₆₁×#417	C₂²	semidirect
115. C₆₁×#416	C₂²	semidirect
116. C₆₁×#408	C₂²	semidirect
475. #61776	C₆₁	direct (N × H)
512. #3536	C₂×C₆₁	semidirect
513. #3493	C₂×C₆₁	semidirect
514. #3356	C₂×C₆₁	semidirect
515. #3354	C₂×C₆₁	semidirect
516. #3346	C₂×C₆₁	semidirect
517. #3343	C₂×C₆₁	semidirect
518. #3327	C₂×C₆₁	semidirect
519. #3322	C₂×C₆₁	semidirect
520. #3321	C₂×C₆₁	semidirect
521. #3311	C₂×C₆₁	semidirect
522. #3244	C₂×C₆₁	semidirect
523. #3204	C₂×C₆₁	semidirect
524. #3196	C₂×C₆₁	semidirect
525. #3194	C₂×C₆₁	semidirect
526. #3124	C₂×C₆₁	semidirect
527. #3098	C₂×C₆₁	semidirect
528. #3095	C₂×C₆₁	semidirect
529. #3094	C₂×C₆₁	semidirect
530. #2978	C₂×C₆₁	semidirect
544. #555	C₂²×C₆₁	semidirect
549. #552	C₂²×C₆₁	semidirect
554. #544	C₂²×C₆₁	semidirect
562. #537	C₂²×C₆₁	semidirect
568. #520	C₂²×C₆₁	semidirect
569. #520	C₂²×C₆₁	semidirect
571. #501	C₂²×C₆₁	semidirect
572. #498	C₂²×C₆₁	semidirect
573. #489	C₂²×C₆₁	semidirect
574. #488	C₂²×C₆₁	semidirect
577. #485	C₂²×C₆₁	semidirect
578. #485	C₂²×C₆₁	semidirect
579. #484	C₂²×C₆₁	semidirect
580. #484	C₂²×C₆₁	semidirect
581. #484	C₂²×C₆₁	semidirect
583. #483	C₂²×C₆₁	semidirect
584. #483	C₂²×C₆₁	semidirect
588. #482	C₂²×C₆₁	semidirect
590. #481	C₂²×C₆₁	semidirect
591. #481	C₂²×C₆₁	semidirect
594. #480	C₂²×C₆₁	semidirect
595. #479	C₂²×C₆₁	semidirect
596. #478	C₂²×C₆₁	semidirect
597. #477	C₂²×C₆₁	semidirect
598. #476	C₂²×C₆₁	semidirect
599. #475	C₂²×C₆₁	semidirect
600. #474	C₂²×C₆₁	semidirect
602. #470	C₂²×C₆₁	semidirect
604. #469	C₂²×C₆₁	semidirect
607. #465	C₂²×C₆₁	semidirect
608. #465	C₂²×C₆₁	semidirect
609. #464	C₂²×C₆₁	semidirect
610. #463	C₂²×C₆₁	semidirect
611. #452	C₂²×C₆₁	semidirect
612. #452	C₂²×C₆₁	semidirect
613. #451	C₂²×C₆₁	semidirect
616. #449	C₂²×C₆₁	semidirect
617. #448	C₂²×C₆₁	semidirect
619. #440	C₂²×C₆₁	semidirect
620. #440	C₂²×C₆₁	semidirect
621. C₄×Q₁₆	C₂²×C₆₁	semidirect
622. C₄×D₈	C₂²×C₆₁	semidirect
624. #436	C₂²×C₆₁	semidirect
626. #435	C₂²×C₆₁	semidirect
627. #433	C₂²×C₆₁	semidirect
629. #428	C₂²×C₆₁	semidirect
630. #428	C₂²×C₆₁	semidirect
631. C₂×#107	C₂²×C₆₁	semidirect
632. #419	C₂²×C₆₁	semidirect
634. #417	C₂²×C₆₁	semidirect
635. #416	C₂²×C₆₁	semidirect
636. #408	C₂²×C₆₁	semidirect
639. C₆₁	#61776	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×#3536	2
C₆₁×#3493	2
C₆₁×#3356	2
C₆₁×#3354	2
C₆₁×#3346	2
C₆₁×#3343	2
C₆₁×#3327	2
C₆₁×#3322	2
C₆₁×#3321	2
C₆₁×#3311	2
C₆₁×#3244	2
C₆₁×#3204	2
C₆₁×#3196	2
C₆₁×#3194	2
C₆₁×#3124	2
C₆₁×#3098	2
C₆₁×#3095	2
C₆₁×#3094	2
C₆₁×#2978	2
#61776	61

Subgroups — C61×#61776 #29565209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61776 #29565209