Subgroups — C₆₁×#61005 #29564438

Order 15616.

1672 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3495	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3256	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3252	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3244	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3242	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3225	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3223	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3197	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#3196	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3195	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3185	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3172	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3127	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3125	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3121	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3120	C₂	1	2	yes	maximal, complemented
19	C₆₁×#2921	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#556	—	2	2	no	—
21	C₆₁×#554	—	2	2	no	—
22	C₆₁×#552	—	2	2	no	—
23	C₆₁×#552	—	2	2	no	—
24	C₆₁×#552	—	2	2	no	—
25	C₆₁×#552	—	2	2	no	—
26	C₆₁×#551	—	2	2	no	—
27	C₆₁×#551	—	2	2	no	—
28	C₆₁×#544	C₂²	1	2	yes	—
29	C₆₁×#542	C₂²	1	2	yes	—
30	C₆₁×#542	C₂²	1	2	yes	—
31	C₆₁×#541	C₂²	1	2	yes	—
32	C₆₁×#541	C₂²	1	2	yes	—
33	C₆₁×#536	C₂²	1	2	yes	—
34	C₆₁×#533	C₂²	1	2	yes	—
35	C₆₁×#533	C₂²	1	2	yes	—
36	C₆₁×#529	C₂²	1	2	yes	—
37	C₆₁×#529	C₂²	1	2	yes	—
38	C₆₁×#525	C₂²	1	2	yes	—
39	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
40	C₆₁×#520	C₂²	1	2	yes	—
41	C₆₁×#519	C₂²	1	2	yes	—
42	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#501	C₂²	1	2	yes	complemented
44	C₆₁×#499	C₂²	1	1	yes	characteristic, complemented
45	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
46	C₆₁×#497	C₂²	1	2	yes	complemented
47	C₆₁×#495	C₂²	1	1	yes	characteristic, complemented
48	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#491	C₂²	1	2	yes	complemented
50	C₆₁×#489	C₂²	1	2	yes	complemented
51	C₆₁×#488	C₂²	1	2	yes	complemented
52	C₆₁×#487	C₂²	1	2	yes	complemented
53	C₆₁×#485	C₂²	1	2	yes	—
54	C₆₁×#485	C₂²	1	2	yes	—
55	C₆₁×#485	C₂²	1	2	yes	—
56	C₆₁×#484	C₂²	1	2	yes	—
57	C₆₁×#483	C₂²	1	2	yes	—
58	C₆₁×#483	C₂²	1	2	yes	—
59	C₆₁×#482	C₂²	1	2	yes	—
60	C₆₁×#481	C₂²	1	2	yes	—
61	C₆₁×#479	C₂²	1	2	yes	complemented
62	C₆₁×#479	C₂²	1	2	yes	complemented
63	C₆₁×#479	C₂²	1	2	yes	complemented
64	C₆₁×#478	C₂²	1	2	yes	complemented
65	C₆₁×#477	C₂²	1	2	yes	complemented
66	C₆₁×#476	C₂²	1	2	yes	complemented
67	C₆₁×#475	C₂²	1	2	yes	complemented
68	C₆₁×#475	C₂²	1	2	yes	complemented
69	C₆₁×#470	C₂²	1	2	yes	—
70	C₆₁×#470	C₂²	1	2	yes	—
71	C₆₁×#470	C₂²	1	1	yes	characteristic
72	C₆₁×#470	C₂²	1	1	yes	characteristic
73	C₆₁×#470	C₂²	1	2	yes	—
74	C₆₁×#470	C₂²	1	1	yes	characteristic
75	C₆₁×#469	C₂²	1	1	yes	characteristic
76	C₆₁×#468	C₂²	1	2	yes	—
77	C₆₁×#468	C₂²	1	2	yes	—
78	C₆₁×#468	C₂²	1	2	yes	—
79	C₆₁×#464	C₂²	1	2	yes	complemented
80	C₆₁×#464	C₂²	1	2	yes	complemented
81	C₆₁×#464	C₂²	1	2	yes	complemented
82	C₆₁×#463	C₂²	1	2	yes	complemented
83	C₆₁×#462	C₂²	1	2	yes	complemented
84	C₆₁×#462	C₂²	1	2	yes	complemented
85	C₆₁×#462	C₂²	1	2	yes	complemented
86	C₆₁×#461	C₂²	1	2	yes	complemented
87	C₆₁×#452	C₂²	1	2	yes	—
88	C₆₁×#452	C₂²	1	2	yes	—
89	C₆₁×#452	C₂²	1	2	yes	—
90	C₆₁×#451	C₂²	1	2	yes	—
91	C₆₁×#451	C₂²	1	2	yes	—
92	C₆₁×#451	C₂²	1	2	yes	—
93	C₆₁×#449	C₂²	1	2	yes	—
94	C₆₁×#448	C₂²	1	2	yes	—
95	C₆₁×#442	C₂²	1	1	yes	characteristic, complemented
96	C₆₁×#441	C₂²	1	1	yes	characteristic, complemented
97	C₆₁×#441	C₂²	1	1	yes	characteristic, complemented
98	C₆₁×#441	C₂²	1	2	yes	complemented
99	C₆₁×#441	C₂²	1	1	yes	characteristic, complemented
100	C₆₁×#440	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
105	C₆₁×#433	C₂²	1	2	yes	—
106	C₆₁×#433	C₂²	1	2	yes	—
107	C₆₁×#433	C₂²	1	2	yes	—
108	C₆₁×#433	C₂²	1	2	yes	—
109	C₆₁×#423	C₂²	1	1	yes	characteristic
110	C₆₁×#423	C₂²	1	1	yes	characteristic
111	C₆₁×#407	C₂²	1	1	yes	characteristic
112	C₆₁×#407	C₂²	1	1	yes	characteristic
113	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
114	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
115	C₂×#41×C₆₁	C₂³	1	2	yes	—
116	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
117	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
118	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
119	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
122	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
124	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
127	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
128	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
132	C₄⋊Q₈×C₆₁	—	2	2	no	—
133	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
137	#126×C₆₁	—	2	2	no	—
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	#126×C₆₁	—	2	2	no	—
144	#126×C₆₁	—	2	2	no	—
145	#125×C₆₁	—	2	2	no	—
146	#125×C₆₁	—	2	2	no	—
147	#125×C₆₁	—	2	2	no	—
148	#125×C₆₁	—	2	2	no	—
149	#125×C₆₁	—	2	2	no	—
150	#125×C₆₁	—	2	2	no	—
151	#125×C₆₁	—	2	2	no	—
152	#125×C₆₁	C₂³	1	2	yes	—
153	#125×C₆₁	C₂³	1	2	yes	—
154	#124×C₆₁	—	2	2	no	—
155	#124×C₆₁	—	2	2	no	—
156	#124×C₆₁	C₂³	1	2	yes	—
157	#124×C₆₁	C₂³	1	2	yes	—
158	#123×C₆₁	—	2	2	no	—
159	#123×C₆₁	—	2	2	no	—
160	#123×C₆₁	—	2	2	no	—
161	#123×C₆₁	—	2	2	no	—
162	#123×C₆₁	—	2	2	no	—
163	#123×C₆₁	—	2	2	no	—
164	#123×C₆₁	—	2	2	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	—	2	2	no	—
172	C₂²⋊Q₈×C₆₁	—	2	2	no	—
173	C₂²⋊Q₈×C₆₁	—	2	2	no	—
174	C₂²⋊Q₈×C₆₁	—	2	2	no	—
175	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
176	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
177	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
178	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
179	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
180	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
181	#121×C₆₁	C₂³	1	2	yes	—
182	#121×C₆₁	C₂³	1	2	yes	—
183	#120×C₆₁	—	2	2	no	—
184	C₄×Q₈×C₆₁	—	2	2	no	—
185	C₄×Q₈×C₆₁	—	2	2	no	—
186	C₄×Q₈×C₆₁	—	2	2	no	—
187	C₄×Q₈×C₆₁	—	2	2	no	—
188	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
189	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
190	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
191	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
192	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
193	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
194	C₄×D₄×C₆₁	—	2	2	no	—
195	C₄×D₄×C₆₁	—	2	2	no	—
196	C₄×D₄×C₆₁	—	2	2	no	—
197	C₄×D₄×C₆₁	—	2	2	no	—
198	C₄×D₄×C₆₁	—	2	2	no	—
199	C₄×D₄×C₆₁	—	2	2	no	—
200	C₄×D₄×C₆₁	C₂³	1	2	yes	—
201	C₄×D₄×C₆₁	C₂³	1	2	yes	—
202	#117×C₆₁	—	2	2	no	—
203	#117×C₆₁	—	2	2	no	—
204	#117×C₆₁	—	2	2	no	—
205	#117×C₆₁	—	2	2	no	—
206	#117×C₆₁	—	2	2	no	—
207	#117×C₆₁	—	2	2	no	—
208	#117×C₆₁	—	2	2	no	—
209	#117×C₆₁	D₄	1	2	yes	—
210	#117×C₆₁	D₄	1	2	yes	—
211	#117×C₆₁	C₂³	1	2	yes	—
212	#117×C₆₁	C₂³	1	2	yes	—
213	#117×C₆₁	C₂³	1	2	yes	—
214	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
215	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
216	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
217	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
219	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
220	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
222	#107×C₆₁	C₂³	1	2	yes	—
223	#107×C₆₁	C₂³	1	2	yes	—
224	#107×C₆₁	C₂³	1	2	yes	—
225	#106×C₆₁	C₂³	1	2	yes	—
226	#106×C₆₁	C₂³	1	2	yes	—
227	#106×C₆₁	C₂³	1	1	yes	characteristic
228	#106×C₆₁	C₂³	1	1	yes	characteristic
229	#106×C₆₁	C₂³	1	2	yes	—
230	#106×C₆₁	C₂³	1	1	yes	characteristic
231	#106×C₆₁	C₂³	1	1	yes	characteristic
232	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
233	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
236	#103×C₆₁	C₂³	1	2	yes	—
237	#103×C₆₁	C₂³	1	2	yes	—
238	#103×C₆₁	C₂³	1	2	yes	—
239	#103×C₆₁	C₂³	1	2	yes	—
240	#103×C₆₁	C₂³	1	2	yes	—
241	#103×C₆₁	C₂³	1	2	yes	—
242	#103×C₆₁	C₂³	1	2	yes	—
243	#103×C₆₁	C₂³	1	2	yes	—
244	#103×C₆₁	C₂³	1	2	yes	—
245	#103×C₆₁	C₂³	1	2	yes	—
246	#103×C₆₁	C₂³	1	2	yes	—
247	#103×C₆₁	C₂³	1	2	yes	—
248	#102×C₆₁	C₂³	1	2	yes	—
249	#102×C₆₁	C₂³	1	2	yes	—
250	#102×C₆₁	C₂³	1	2	yes	—
251	#102×C₆₁	C₂³	1	2	yes	—
252	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
253	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
256	#97×C₆₁	C₂³	1	1	yes	characteristic
257	#97×C₆₁	C₂³	1	1	yes	characteristic
258	#97×C₆₁	C₂³	1	2	yes	—
259	C₄×C₈×C₆₁	C₂³	1	2	yes	—
260	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
262	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
263	#41×C₆₁	—	4	2	no	—
264	#41×C₆₁	—	4	2	no	—
265	C₂×Q₈×C₆₁	—	2	2	no	—
266	C₂×Q₈×C₆₁	—	2	2	no	—
267	C₂×Q₈×C₆₁	—	2	2	no	—
268	C₂×Q₈×C₆₁	—	4	2	no	—
269	C₂×Q₈×C₆₁	—	4	2	no	—
270	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
271	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
272	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
273	C₂×D₄×C₆₁	—	2	2	no	—
274	C₂×D₄×C₆₁	—	2	2	no	—
275	C₂×D₄×C₆₁	—	2	2	no	—
276	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₆₁	—	2	2	no	—
278	C₂²×C₄×C₆₁	—	2	2	no	—
279	C₂²×C₄×C₆₁	—	2	2	no	—
280	C₂²×C₄×C₆₁	—	2	2	no	—
281	C₂²×C₄×C₆₁	—	2	2	no	—
282	C₂²×C₄×C₆₁	—	4	1	no	—
283	C₂²×C₄×C₆₁	—	4	1	no	—
284	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
290	Q₁₆×C₆₁	—	4	1	no	—
291	Q₁₆×C₆₁	—	4	2	no	—
292	Q₁₆×C₆₁	—	4	2	no	—
293	Q₁₆×C₆₁	—	4	1	no	—
294	Q₁₆×C₆₁	—	4	2	no	—
295	Q₁₆×C₆₁	—	4	1	no	—
296	SD₁₆×C₆₁	—	4	2	no	—
297	SD₁₆×C₆₁	—	4	2	no	—
298	SD₁₆×C₆₁	—	4	2	no	—
299	D₈×C₆₁	—	4	1	no	—
300	M₁₆×C₆₁	—	4	1	no	—
301	M₁₆×C₆₁	—	4	1	no	—
302	M₁₆×C₆₁	—	4	1	no	—
303	M₁₆×C₆₁	—	4	1	no	—
304	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
305	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
306	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
307	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
308	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
309	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₆₁	—	2	2	no	—
311	C₄⋊C₄×C₆₁	—	2	2	no	—
312	C₄⋊C₄×C₆₁	—	2	2	no	—
313	C₄⋊C₄×C₆₁	—	2	2	no	—
314	C₄⋊C₄×C₆₁	—	2	2	no	—
315	C₄⋊C₄×C₆₁	—	2	2	no	—
316	C₄⋊C₄×C₆₁	—	2	2	no	—
317	C₄⋊C₄×C₆₁	—	2	2	no	—
318	C₄⋊C₄×C₆₁	—	2	2	no	—
319	C₄⋊C₄×C₆₁	—	2	2	no	—
320	C₄⋊C₄×C₆₁	—	2	2	no	—
321	C₄⋊C₄×C₆₁	—	2	2	no	—
322	C₄⋊C₄×C₆₁	—	2	2	no	—
323	C₄⋊C₄×C₆₁	—	2	2	no	—
324	C₄⋊C₄×C₆₁	—	2	2	no	—
325	C₄⋊C₄×C₆₁	—	2	2	no	—
326	C₄⋊C₄×C₆₁	—	2	2	no	—
327	C₄⋊C₄×C₆₁	—	2	2	no	—
328	C₄⋊C₄×C₆₁	—	2	2	no	—
329	C₄⋊C₄×C₆₁	—	2	2	no	—
330	C₄⋊C₄×C₆₁	—	2	2	no	—
331	C₄⋊C₄×C₆₁	—	2	2	no	—
332	C₄⋊C₄×C₆₁	—	2	2	no	—
333	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
334	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
340	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
341	C₂²⋊C₄×C₆₁	—	2	2	no	—
342	C₂²⋊C₄×C₆₁	—	2	2	no	—
343	C₂²⋊C₄×C₆₁	—	2	2	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	2	no	—
348	C₂²⋊C₄×C₆₁	—	2	2	no	—
349	C₂²⋊C₄×C₆₁	—	2	2	no	—
350	C₂²⋊C₄×C₆₁	—	2	2	no	—
351	C₂²⋊C₄×C₆₁	—	2	2	no	—
352	C₂²⋊C₄×C₆₁	—	2	2	no	—
353	C₂²⋊C₄×C₆₁	—	2	2	no	—
354	C₂²⋊C₄×C₆₁	—	2	2	no	—
355	C₂²⋊C₄×C₆₁	—	2	2	no	—
356	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
357	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
358	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
359	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
360	C₄²×C₆₁	—	2	2	no	—
361	C₄²×C₆₁	—	2	2	no	—
362	C₄²×C₆₁	—	2	2	no	—
363	C₄²×C₆₁	—	2	2	no	—
364	C₄²×C₆₁	—	2	2	no	—
365	C₄²×C₆₁	—	2	2	no	—
366	C₄²×C₆₁	—	2	2	no	—
367	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₆₁	C₂×D₄	1	2	yes	—
369	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
371	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
372	C₄²×C₆₁	C₂⁴	1	2	yes	—
373	C₂³×C₆₁	—	2	2	no	—
374	C₂³×C₆₁	—	4	1	no	—
375	C₂³×C₆₁	—	4	2	no	—
376	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
377	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
378	Q₈×C₆₁	—	2	2	no	—
379	Q₈×C₆₁	—	2	2	no	—
380	Q₈×C₆₁	—	2	2	no	—
381	Q₈×C₆₁	—	2	2	no	—
382	Q₈×C₆₁	—	2	2	no	—
383	Q₈×C₆₁	—	2	2	no	—
384	Q₈×C₆₁	—	4	4	no	—
385	Q₈×C₆₁	—	8	2	no	—
386	Q₈×C₆₁	—	8	2	no	—
387	D₄×C₆₁	—	2	2	no	—
388	D₄×C₆₁	—	2	2	no	—
389	D₄×C₆₁	—	4	4	no	—
390	D₄×C₆₁	—	4	4	no	—
391	D₄×C₆₁	—	8	2	no	—
392	C₂×C₄×C₆₁	—	2	1	no	—
393	C₂×C₄×C₆₁	—	2	1	no	—
394	C₂×C₄×C₆₁	—	2	2	no	—
395	C₂×C₄×C₆₁	—	2	2	no	—
396	C₂×C₄×C₆₁	—	2	2	no	—
397	C₂×C₄×C₆₁	—	2	2	no	—
398	C₂×C₄×C₆₁	—	2	2	no	—
399	C₂×C₄×C₆₁	—	2	2	no	—
400	C₂×C₄×C₆₁	—	2	2	no	—
401	C₂×C₄×C₆₁	—	2	2	no	—
402	C₂×C₄×C₆₁	—	2	2	no	—
403	C₂×C₄×C₆₁	—	4	1	no	—
404	C₂×C₄×C₆₁	—	4	2	no	—
405	C₂×C₄×C₆₁	—	4	2	no	—
406	C₂×C₄×C₆₁	—	4	2	no	—
407	C₂×C₄×C₆₁	—	4	4	no	—
408	C₂×C₄×C₆₁	—	4	4	no	—
409	C₂×C₄×C₆₁	—	8	2	no	—
410	C₂×C₄×C₆₁	—	8	2	no	—
411	C₂×C₄×C₆₁	—	8	2	no	—
412	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
419	C₈×C₆₁	—	2	1	no	—
420	C₈×C₆₁	—	2	1	no	—
421	C₈×C₆₁	—	2	2	no	—
422	C₈×C₆₁	—	2	2	no	—
423	C₈×C₆₁	—	2	1	no	—
424	C₈×C₆₁	—	2	1	no	—
425	#61005	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
426	C₂²×C₆₁	—	2	2	no	—
427	C₂²×C₆₁	—	2	2	no	—
428	C₂²×C₆₁	—	2	2	no	—
429	C₂²×C₆₁	—	2	2	no	—
430	C₂²×C₆₁	—	2	1	no	—
431	C₂²×C₆₁	—	4	2	no	—
432	C₂²×C₆₁	—	4	2	no	—
433	C₂²×C₆₁	—	4	2	no	—
434	C₂²×C₆₁	—	8	2	no	—
435	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
436	C₄×C₆₁	—	2	2	no	—
437	C₄×C₆₁	—	2	2	no	—
438	C₄×C₆₁	—	2	2	no	—
439	C₄×C₆₁	—	2	2	no	—
440	C₄×C₆₁	—	2	2	no	—
441	C₄×C₆₁	—	2	1	no	—
442	C₄×C₆₁	—	4	2	no	—
443	C₄×C₆₁	—	4	2	no	—
444	C₄×C₆₁	—	4	2	no	—
445	C₄×C₆₁	—	4	2	no	—
446	C₄×C₆₁	—	4	2	no	—
447	C₄×C₆₁	—	4	2	no	—
448	C₄×C₆₁	—	4	2	no	—
449	C₄×C₆₁	#585	1	1	yes	characteristic
450	C₄×C₆₁	#585	1	1	yes	characteristic
451	#3495	C₂×C₆₁	1	2	yes	complemented
452	#3256	C₂×C₆₁	1	1	yes	characteristic, complemented
453	#3255	C₂×C₆₁	1	1	yes	characteristic, complemented
454	#3252	C₂×C₆₁	1	2	yes	complemented
455	#3244	C₂×C₆₁	1	2	yes	complemented
456	#3242	C₂×C₆₁	1	2	yes	complemented
457	#3225	C₂×C₆₁	1	2	yes	complemented
458	#3223	C₂×C₆₁	1	2	yes	complemented
459	#3197	C₂×C₆₁	1	1	yes	characteristic
460	#3196	C₂×C₆₁	1	2	yes	complemented
461	#3195	C₂×C₆₁	1	1	yes	characteristic, complemented
462	#3185	C₂×C₆₁	1	1	yes	characteristic, complemented
463	#3183	C₂×C₆₁	1	1	yes	characteristic, complemented
464	#3172	C₂×C₆₁	1	2	yes	complemented
465	#3127	C₂×C₆₁	1	2	yes	complemented
466	#3125	C₂×C₆₁	1	2	yes	complemented
467	#3121	C₂×C₆₁	1	2	yes	complemented
468	#3120	C₂×C₆₁	1	2	yes	complemented
469	#2921	C₂×C₆₁	1	1	yes	characteristic, complemented
470	C₂×C₆₁	—	4	1	no	—
471	C₂×C₆₁	—	4	2	no	—
472	C₂×C₆₁	—	8	2	no	—
473	C₂×C₆₁	#3449	1	1	yes	characteristic
474	C₂×C₆₁	#3586	1	2	yes	—
475	#556	—	2	2	no	—
476	#554	—	2	2	no	—
477	#552	—	2	2	no	—
478	#552	—	2	2	no	—
479	#552	—	2	2	no	—
480	#552	—	2	2	no	—
481	#551	—	2	2	no	—
482	#551	—	2	2	no	—
483	#544	C₂²×C₆₁	1	2	yes	—
484	#542	C₂²×C₆₁	1	2	yes	—
485	#542	C₂²×C₆₁	1	2	yes	—
486	#541	C₂²×C₆₁	1	2	yes	—
487	#541	C₂²×C₆₁	1	2	yes	—
488	#536	C₂²×C₆₁	1	2	yes	—
489	#533	C₂²×C₆₁	1	2	yes	—
490	#533	C₂²×C₆₁	1	2	yes	—
491	#529	C₂²×C₆₁	1	2	yes	—
492	#529	C₂²×C₆₁	1	2	yes	—
493	#525	C₂²×C₆₁	1	2	yes	—
494	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
495	#520	C₂²×C₆₁	1	2	yes	—
496	#519	C₂²×C₆₁	1	2	yes	—
497	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
498	#501	C₂²×C₆₁	1	2	yes	complemented
499	#499	C₂²×C₆₁	1	1	yes	characteristic, complemented
500	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
501	#497	C₂²×C₆₁	1	2	yes	complemented
502	#495	C₂²×C₆₁	1	1	yes	characteristic, complemented
503	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
504	#491	C₂²×C₆₁	1	2	yes	complemented
505	#489	C₂²×C₆₁	1	2	yes	complemented
506	#488	C₂²×C₆₁	1	2	yes	complemented
507	#487	C₂²×C₆₁	1	2	yes	complemented
508	#485	C₂²×C₆₁	1	2	yes	—
509	#485	C₂²×C₆₁	1	2	yes	—
510	#485	C₂²×C₆₁	1	2	yes	—
511	#484	C₂²×C₆₁	1	2	yes	—
512	#483	C₂²×C₆₁	1	2	yes	—
513	#483	C₂²×C₆₁	1	2	yes	—
514	#482	C₂²×C₆₁	1	2	yes	—
515	#481	C₂²×C₆₁	1	2	yes	—
516	#479	C₂²×C₆₁	1	2	yes	complemented
517	#479	C₂²×C₆₁	1	2	yes	complemented
518	#479	C₂²×C₆₁	1	2	yes	complemented
519	#478	C₂²×C₆₁	1	2	yes	complemented
520	#477	C₂²×C₆₁	1	2	yes	complemented
521	#476	C₂²×C₆₁	1	2	yes	complemented
522	#475	C₂²×C₆₁	1	2	yes	complemented
523	#475	C₂²×C₆₁	1	2	yes	complemented
524	#470	C₂²×C₆₁	1	2	yes	—
525	#470	C₂²×C₆₁	1	2	yes	—
526	#470	C₂²×C₆₁	1	1	yes	characteristic
527	#470	C₂²×C₆₁	1	1	yes	characteristic
528	#470	C₂²×C₆₁	1	2	yes	—
529	#470	C₂²×C₆₁	1	1	yes	characteristic
530	#469	C₂²×C₆₁	1	1	yes	characteristic
531	#468	C₂²×C₆₁	1	2	yes	—
532	#468	C₂²×C₆₁	1	2	yes	—
533	#468	C₂²×C₆₁	1	2	yes	—
534	#464	C₂²×C₆₁	1	2	yes	complemented
535	#464	C₂²×C₆₁	1	2	yes	complemented
536	#464	C₂²×C₆₁	1	2	yes	complemented
537	#463	C₂²×C₆₁	1	2	yes	complemented
538	#462	C₂²×C₆₁	1	2	yes	complemented
539	#462	C₂²×C₆₁	1	2	yes	complemented
540	#462	C₂²×C₆₁	1	2	yes	complemented
541	#461	C₂²×C₆₁	1	2	yes	complemented
542	#452	C₂²×C₆₁	1	2	yes	—
543	#452	C₂²×C₆₁	1	2	yes	—
544	#452	C₂²×C₆₁	1	2	yes	—
545	#451	C₂²×C₆₁	1	2	yes	—
546	#451	C₂²×C₆₁	1	2	yes	—
547	#451	C₂²×C₆₁	1	2	yes	—
548	#449	C₂²×C₆₁	1	2	yes	—
549	#448	C₂²×C₆₁	1	2	yes	—
550	#442	C₂²×C₆₁	1	1	yes	characteristic, complemented
551	#441	C₂²×C₆₁	1	1	yes	characteristic, complemented
552	#441	C₂²×C₆₁	1	1	yes	characteristic, complemented
553	#441	C₂²×C₆₁	1	2	yes	complemented
554	#441	C₂²×C₆₁	1	1	yes	characteristic, complemented
555	#440	C₂²×C₆₁	1	2	yes	complemented
556	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
557	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
558	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
559	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
560	#433	C₂²×C₆₁	1	2	yes	—
561	#433	C₂²×C₆₁	1	2	yes	—
562	#433	C₂²×C₆₁	1	2	yes	—
563	#433	C₂²×C₆₁	1	2	yes	—
564	#423	C₂²×C₆₁	1	1	yes	characteristic
565	#423	C₂²×C₆₁	1	1	yes	characteristic
566	#407	C₂²×C₆₁	1	1	yes	characteristic
567	#407	C₂²×C₆₁	1	1	yes	characteristic
568	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
569	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
570	C₆₁	#61005	1	1	yes	characteristic, direct product factor, Sylow
571	C₂×#41	C₂³×C₆₁	1	2	yes	—
572	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
573	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
574	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
575	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
576	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
577	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
578	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
579	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
580	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
583	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
584	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
585	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
586	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
587	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
588	C₄⋊Q₈	—	2	2	no	—
589	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
591	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
592	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
593	#126	—	2	2	no	—
594	#126	—	2	2	no	—
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#126	—	2	2	no	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#125	—	2	2	no	—
602	#125	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	—	2	2	no	—
605	#125	—	2	2	no	—
606	#125	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	C₂³×C₆₁	1	2	yes	—
609	#125	C₂³×C₆₁	1	2	yes	—
610	#124	—	2	2	no	—
611	#124	—	2	2	no	—
612	#124	C₂³×C₆₁	1	2	yes	—
613	#124	C₂³×C₆₁	1	2	yes	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	#123	—	2	2	no	—
618	#123	—	2	2	no	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
632	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
633	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
634	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
635	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
636	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
637	#121	C₂³×C₆₁	1	2	yes	—
638	#121	C₂³×C₆₁	1	2	yes	—
639	#120	—	2	2	no	—
640	C₄×Q₈	—	2	2	no	—
641	C₄×Q₈	—	2	2	no	—
642	C₄×Q₈	—	2	2	no	—
643	C₄×Q₈	—	2	2	no	—
644	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
645	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
646	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
647	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
648	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
649	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	C₂³×C₆₁	1	2	yes	—
657	C₄×D₄	C₂³×C₆₁	1	2	yes	—
658	#117	—	2	2	no	—
659	#117	—	2	2	no	—
660	#117	—	2	2	no	—
661	#117	—	2	2	no	—
662	#117	—	2	2	no	—
663	#117	—	2	2	no	—
664	#117	—	2	2	no	—
665	#117	D₄×C₆₁	1	2	yes	—
666	#117	D₄×C₆₁	1	2	yes	—
667	#117	C₂³×C₆₁	1	2	yes	—
668	#117	C₂³×C₆₁	1	2	yes	—
669	#117	C₂³×C₆₁	1	2	yes	—
670	C₂×C₄⋊C₄	—	2	2	no	—
671	C₂×C₄⋊C₄	—	2	2	no	—
672	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
674	C₂×C₂²⋊C₄	—	2	2	no	—
675	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
676	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
678	#107	C₂³×C₆₁	1	2	yes	—
679	#107	C₂³×C₆₁	1	2	yes	—
680	#107	C₂³×C₆₁	1	2	yes	—
681	#106	C₂³×C₆₁	1	2	yes	—
682	#106	C₂³×C₆₁	1	2	yes	—
683	#106	C₂³×C₆₁	1	1	yes	characteristic
684	#106	C₂³×C₆₁	1	1	yes	characteristic
685	#106	C₂³×C₆₁	1	2	yes	—
686	#106	C₂³×C₆₁	1	1	yes	characteristic
687	#106	C₂³×C₆₁	1	1	yes	characteristic
688	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
689	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
690	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
691	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
692	#103	C₂³×C₆₁	1	2	yes	—
693	#103	C₂³×C₆₁	1	2	yes	—
694	#103	C₂³×C₆₁	1	2	yes	—
695	#103	C₂³×C₆₁	1	2	yes	—
696	#103	C₂³×C₆₁	1	2	yes	—
697	#103	C₂³×C₆₁	1	2	yes	—
698	#103	C₂³×C₆₁	1	2	yes	—
699	#103	C₂³×C₆₁	1	2	yes	—
700	#103	C₂³×C₆₁	1	2	yes	—
701	#103	C₂³×C₆₁	1	2	yes	—
702	#103	C₂³×C₆₁	1	2	yes	—
703	#103	C₂³×C₆₁	1	2	yes	—
704	#102	C₂³×C₆₁	1	2	yes	—
705	#102	C₂³×C₆₁	1	2	yes	—
706	#102	C₂³×C₆₁	1	2	yes	—
707	#102	C₂³×C₆₁	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
709	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
710	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
711	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
712	#97	C₂³×C₆₁	1	1	yes	characteristic
713	#97	C₂³×C₆₁	1	1	yes	characteristic
714	#97	C₂³×C₆₁	1	2	yes	—
715	C₄×C₈	C₂³×C₆₁	1	2	yes	—
716	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
717	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
718	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
719	#41	—	4	2	no	—
720	#41	—	4	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	4	2	no	—
725	C₂×Q₈	—	4	2	no	—
726	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
727	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
728	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
741	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
742	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
743	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
746	Q₁₆	—	4	1	no	—
747	Q₁₆	—	4	2	no	—
748	Q₁₆	—	4	2	no	—
749	Q₁₆	—	4	1	no	—
750	Q₁₆	—	4	2	no	—
751	Q₁₆	—	4	1	no	—
752	SD₁₆	—	4	2	no	—
753	SD₁₆	—	4	2	no	—
754	SD₁₆	—	4	2	no	—
755	D₈	—	4	1	no	—
756	M₁₆	—	4	1	no	—
757	M₁₆	—	4	1	no	—
758	M₁₆	—	4	1	no	—
759	M₁₆	—	4	1	no	—
760	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
761	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
762	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
763	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
764	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
765	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
792	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
796	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
813	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
824	C₄²	C₂×D₄×C₆₁	1	2	yes	—
825	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
826	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
827	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
828	C₄²	C₂⁴×C₆₁	1	2	yes	—
829	C₂³	—	2	2	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	2	no	—
832	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
833	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	2	2	no	—
837	Q₈	—	2	2	no	—
838	Q₈	—	2	2	no	—
839	Q₈	—	2	2	no	—
840	Q₈	—	4	4	no	—
841	Q₈	—	8	2	no	—
842	Q₈	—	8	2	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	2	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	D₄	—	8	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
869	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
874	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
875	C₈	—	2	1	no	—
876	C₈	—	2	1	no	—
877	C₈	—	2	2	no	—
878	C₈	—	2	2	no	—
879	C₈	—	2	1	no	—
880	C₈	—	2	1	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	8	2	no	—
890	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	1	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	C₆₁×#585	1	1	yes	characteristic
905	C₄	C₆₁×#585	1	1	yes	characteristic
906	C₂	—	4	1	no	—
907	C₂	—	4	2	no	—
908	C₂	—	8	2	no	—
909	C₂	C₆₁×#3449	1	1	yes	characteristic
910	C₂	C₆₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3197	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3495	C₂	semidirect
2. C₆₁×#3256	C₂	semidirect
3. C₆₁×#3255	C₂	semidirect
4. C₆₁×#3252	C₂	semidirect
5. C₆₁×#3244	C₂	semidirect
6. C₆₁×#3242	C₂	semidirect
7. C₆₁×#3225	C₂	semidirect
8. C₆₁×#3223	C₂	semidirect
10. C₆₁×#3196	C₂	semidirect
11. C₆₁×#3195	C₂	semidirect
12. C₆₁×#3185	C₂	semidirect
13. C₆₁×#3183	C₂	semidirect
14. C₆₁×#3172	C₂	semidirect
15. C₆₁×#3127	C₂	semidirect
16. C₆₁×#3125	C₂	semidirect
17. C₆₁×#3121	C₂	semidirect
18. C₆₁×#3120	C₂	semidirect
19. C₆₁×#2921	C₂	semidirect
43. C₆₁×#501	C₂²	semidirect
44. C₆₁×#499	C₂²	semidirect
45. C₆₁×#498	C₂²	semidirect
46. C₆₁×#497	C₂²	semidirect
47. C₆₁×#495	C₂²	semidirect
48. C₆₁×#494	C₂²	semidirect
49. C₆₁×#491	C₂²	semidirect
50. C₆₁×#489	C₂²	semidirect
51. C₆₁×#488	C₂²	semidirect
52. C₆₁×#487	C₂²	semidirect
61. C₆₁×#479	C₂²	semidirect
62. C₆₁×#479	C₂²	semidirect
63. C₆₁×#479	C₂²	semidirect
64. C₆₁×#478	C₂²	semidirect
65. C₆₁×#477	C₂²	semidirect
66. C₆₁×#476	C₂²	semidirect
67. C₆₁×#475	C₂²	semidirect
68. C₆₁×#475	C₂²	semidirect
79. C₆₁×#464	C₂²	semidirect
80. C₆₁×#464	C₂²	semidirect
81. C₆₁×#464	C₂²	semidirect
82. C₆₁×#463	C₂²	semidirect
83. C₆₁×#462	C₂²	semidirect
84. C₆₁×#462	C₂²	semidirect
85. C₆₁×#462	C₂²	semidirect
86. C₆₁×#461	C₂²	semidirect
95. C₆₁×#442	C₂²	semidirect
96. C₆₁×#441	C₂²	semidirect
97. C₆₁×#441	C₂²	semidirect
98. C₆₁×#441	C₂²	semidirect
99. C₆₁×#441	C₂²	semidirect
100. C₆₁×#440	C₂²	semidirect
101. C₄×Q₁₆×C₆₁	C₂²	semidirect
102. C₄×Q₁₆×C₆₁	C₂²	semidirect
103. C₄×SD₁₆×C₆₁	C₂²	semidirect
104. C₄×SD₁₆×C₆₁	C₂²	semidirect
425. #61005	C₆₁	direct (N × H)
451. #3495	C₂×C₆₁	semidirect
452. #3256	C₂×C₆₁	semidirect
453. #3255	C₂×C₆₁	semidirect
454. #3252	C₂×C₆₁	semidirect
455. #3244	C₂×C₆₁	semidirect
456. #3242	C₂×C₆₁	semidirect
457. #3225	C₂×C₆₁	semidirect
458. #3223	C₂×C₆₁	semidirect
460. #3196	C₂×C₆₁	semidirect
461. #3195	C₂×C₆₁	semidirect
462. #3185	C₂×C₆₁	semidirect
463. #3183	C₂×C₆₁	semidirect
464. #3172	C₂×C₆₁	semidirect
465. #3127	C₂×C₆₁	semidirect
466. #3125	C₂×C₆₁	semidirect
467. #3121	C₂×C₆₁	semidirect
468. #3120	C₂×C₆₁	semidirect
469. #2921	C₂×C₆₁	semidirect
498. #501	C₂²×C₆₁	semidirect
499. #499	C₂²×C₆₁	semidirect
500. #498	C₂²×C₆₁	semidirect
501. #497	C₂²×C₆₁	semidirect
502. #495	C₂²×C₆₁	semidirect
503. #494	C₂²×C₆₁	semidirect
504. #491	C₂²×C₆₁	semidirect
505. #489	C₂²×C₆₁	semidirect
506. #488	C₂²×C₆₁	semidirect
507. #487	C₂²×C₆₁	semidirect
516. #479	C₂²×C₆₁	semidirect
517. #479	C₂²×C₆₁	semidirect
518. #479	C₂²×C₆₁	semidirect
519. #478	C₂²×C₆₁	semidirect
520. #477	C₂²×C₆₁	semidirect
521. #476	C₂²×C₆₁	semidirect
522. #475	C₂²×C₆₁	semidirect
523. #475	C₂²×C₆₁	semidirect
534. #464	C₂²×C₆₁	semidirect
535. #464	C₂²×C₆₁	semidirect
536. #464	C₂²×C₆₁	semidirect
537. #463	C₂²×C₆₁	semidirect
538. #462	C₂²×C₆₁	semidirect
539. #462	C₂²×C₆₁	semidirect
540. #462	C₂²×C₆₁	semidirect
541. #461	C₂²×C₆₁	semidirect
550. #442	C₂²×C₆₁	semidirect
551. #441	C₂²×C₆₁	semidirect
552. #441	C₂²×C₆₁	semidirect
553. #441	C₂²×C₆₁	semidirect
554. #441	C₂²×C₆₁	semidirect
555. #440	C₂²×C₆₁	semidirect
556. C₄×Q₁₆	C₂²×C₆₁	semidirect
557. C₄×Q₁₆	C₂²×C₆₁	semidirect
558. C₄×SD₁₆	C₂²×C₆₁	semidirect
559. C₄×SD₁₆	C₂²×C₆₁	semidirect
570. C₆₁	#61005	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×#3495	2
C₆₁×#3256	2
C₆₁×#3255	2
C₆₁×#3252	2
C₆₁×#3244	2
C₆₁×#3242	2
C₆₁×#3225	2
C₆₁×#3223	2
C₆₁×#3197	2
C₆₁×#3196	2
C₆₁×#3195	2
C₆₁×#3185	2
C₆₁×#3183	2
C₆₁×#3172	2
C₆₁×#3127	2
C₆₁×#3125	2
C₆₁×#3121	2
C₆₁×#3120	2
C₆₁×#2921	2
#61005	61

Subgroups — C61×#61005 #29564438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61005 #29564438