Subgroups — C₆₁×#36818 #29540251

Order 15616.

2056 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2850	C₂	1	2	yes	maximal, complemented
2	C₆₁×#2754	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2730	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2712	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2706	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2696	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2673	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2670	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2668	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2648	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2607	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2557	C₂	1	2	yes	maximal, complemented
13	C₆₁×#2539	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2476	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2404	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2333	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#2312	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×#124×C₆₁	C₂²	1	2	yes	—
23	C₂×#124×C₆₁	C₂²	1	2	yes	—
24	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×#123×C₆₁	C₂²	1	2	yes	—
26	C₂×#123×C₆₁	C₂²	1	2	yes	complemented
27	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
28	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#121×C₆₁	C₂²	1	2	yes	—
30	C₂×#121×C₆₁	C₂²	1	2	yes	—
31	C₂×#120×C₆₁	C₂²	1	2	yes	—
32	C₂×#120×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#120×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
37	C₆₁×#400	C₂²	1	2	yes	complemented
38	C₆₁×#399	C₂²	1	2	yes	—
39	C₆₁×#399	C₂²	1	2	yes	—
40	C₆₁×#398	C₂²	1	2	yes	complemented
41	C₆₁×#397	C₂²	1	2	yes	—
42	C₆₁×#397	C₂²	1	2	yes	—
43	C₆₁×#397	C₂²	1	2	yes	complemented
44	C₆₁×#397	C₂²	1	2	yes	complemented
45	C₆₁×#396	C₂²	1	2	yes	complemented
46	C₆₁×#394	C₂²	1	2	yes	—
47	C₆₁×#394	C₂²	1	2	yes	—
48	C₆₁×#394	C₂²	1	2	yes	—
49	C₆₁×#394	C₂²	1	2	yes	—
50	C₆₁×#394	C₂²	1	2	yes	complemented
51	C₆₁×#394	C₂²	1	2	yes	complemented
52	C₆₁×#393	C₂²	1	2	yes	—
53	C₆₁×#393	C₂²	1	2	yes	—
54	C₆₁×#393	C₂²	1	2	yes	complemented
55	C₆₁×#392	C₂²	1	2	yes	—
56	C₆₁×#392	C₂²	1	2	yes	—
57	C₆₁×#392	C₂²	1	2	yes	—
58	C₆₁×#392	C₂²	1	2	yes	—
59	C₆₁×#392	C₂²	1	2	yes	—
60	C₆₁×#392	C₂²	1	2	yes	—
61	C₆₁×#391	C₂²	1	2	yes	complemented
62	C₆₁×#391	C₂²	1	2	yes	complemented
63	C₆₁×#391	C₂²	1	2	yes	complemented
64	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
65	C₆₁×#390	C₂²	1	2	yes	—
66	C₆₁×#390	C₂²	1	2	yes	—
67	C₆₁×#390	C₂²	1	2	yes	—
68	C₆₁×#390	C₂²	1	2	yes	—
69	C₆₁×#390	C₂²	1	1	yes	characteristic, complemented
70	C₆₁×#388	C₂²	1	2	yes	—
71	C₆₁×#388	C₂²	1	2	yes	—
72	C₆₁×#388	C₂²	1	2	yes	—
73	C₆₁×#388	C₂²	1	2	yes	—
74	C₆₁×#388	C₂²	1	2	yes	—
75	C₆₁×#388	C₂²	1	2	yes	—
76	C₆₁×#388	C₂²	1	2	yes	complemented
77	C₆₁×#388	C₂²	1	2	yes	complemented
78	C₆₁×#388	C₂²	1	2	yes	complemented
79	C₆₁×#387	C₂²	1	2	yes	complemented
80	C₆₁×#387	C₂²	1	2	yes	complemented
81	C₆₁×#387	C₂²	1	2	yes	complemented
82	C₆₁×#387	C₂²	1	2	yes	complemented
83	C₆₁×#386	C₂²	1	2	yes	—
84	C₆₁×#386	C₂²	1	2	yes	—
85	C₆₁×#386	C₂²	1	2	yes	—
86	C₆₁×#386	C₂²	1	2	yes	—
87	C₆₁×#386	C₂²	1	2	yes	—
88	C₆₁×#386	C₂²	1	2	yes	—
89	C₆₁×#386	C₂²	1	1	yes	characteristic
90	C₆₁×#386	C₂²	1	1	yes	characteristic
91	C₆₁×#386	C₂²	1	2	yes	complemented
92	C₆₁×#386	C₂²	1	2	yes	complemented
93	C₆₁×#386	C₂²	1	2	yes	complemented
94	C₆₁×#386	C₂²	1	2	yes	complemented
95	C₆₁×#386	C₂²	1	2	yes	complemented
96	C₆₁×#385	C₂²	1	2	yes	complemented
97	C₆₁×#382	C₂²	1	2	yes	complemented
98	C₆₁×#381	C₂²	1	1	yes	characteristic
99	C₆₁×#380	C₂²	1	2	yes	—
100	C₆₁×#379	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
107	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
108	C₂×#41×C₆₁	—	2	4	no	—
109	C₂×#41×C₆₁	—	4	2	no	—
110	C₂×#41×C₆₁	—	4	2	no	—
111	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
119	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
120	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
121	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
122	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
123	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
124	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
130	#127×C₆₁	—	4	2	no	—
131	#124×C₆₁	—	4	4	no	—
132	#124×C₆₁	—	4	4	no	—
133	#124×C₆₁	—	4	2	no	—
134	#123×C₆₁	—	4	4	no	—
135	#123×C₆₁	—	4	4	no	—
136	C₂²⋊Q₈×C₆₁	—	4	4	no	—
137	#121×C₆₁	—	2	4	no	—
138	#121×C₆₁	—	4	4	no	—
139	#121×C₆₁	—	4	4	no	—
140	#120×C₆₁	—	4	4	no	—
141	#120×C₆₁	—	4	2	no	—
142	#120×C₆₁	—	4	2	no	—
143	#117×C₆₁	—	4	2	no	—
144	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
155	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
185	C₂×C₄²×C₆₁	—	4	2	no	—
186	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
187	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
194	#95×C₆₁	C₂³	1	2	yes	—
195	#95×C₆₁	C₂³	1	2	yes	—
196	#95×C₆₁	C₂³	1	2	yes	—
197	#95×C₆₁	C₂³	1	2	yes	—
198	#95×C₆₁	C₂³	1	2	yes	—
199	#95×C₆₁	C₂³	1	2	yes	—
200	#95×C₆₁	C₂³	1	2	yes	—
201	#95×C₆₁	C₂³	1	2	yes	—
202	#95×C₆₁	C₂³	1	2	yes	—
203	#95×C₆₁	C₂³	1	2	yes	—
204	#95×C₆₁	C₂³	1	2	yes	—
205	#95×C₆₁	C₂³	1	2	yes	—
206	#95×C₆₁	C₂³	1	2	yes	—
207	#95×C₆₁	C₂³	1	2	yes	—
208	#95×C₆₁	C₂³	1	2	yes	—
209	#95×C₆₁	C₂³	1	2	yes	—
210	#95×C₆₁	C₂³	1	2	yes	—
211	#95×C₆₁	C₂³	1	2	yes	—
212	#95×C₆₁	C₂³	1	2	yes	—
213	C₂⁴×C₆₁	—	2	2	no	—
214	C₂⁴×C₆₁	—	4	2	no	—
215	C₂⁴×C₆₁	—	4	2	no	—
216	C₂⁴×C₆₁	—	4	1	no	—
217	C₂⁴×C₆₁	—	4	1	no	—
218	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
219	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
220	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
223	#41×C₆₁	—	4	16	no	—
224	C₂×Q₈×C₆₁	—	2	2	no	—
225	C₂×Q₈×C₆₁	—	2	2	no	—
226	C₂×Q₈×C₆₁	—	2	4	no	—
227	C₂×Q₈×C₆₁	—	4	1	no	—
228	C₂×Q₈×C₆₁	—	4	2	no	—
229	C₂×Q₈×C₆₁	—	4	2	no	—
230	C₂×D₄×C₆₁	—	2	2	no	—
231	C₂×D₄×C₆₁	—	2	2	no	—
232	C₂×D₄×C₆₁	—	2	2	no	—
233	C₂×D₄×C₆₁	—	2	2	no	—
234	C₂×D₄×C₆₁	—	2	4	no	—
235	C₂×D₄×C₆₁	—	2	4	no	—
236	C₂×D₄×C₆₁	—	2	4	no	—
237	C₂×D₄×C₆₁	—	2	2	no	—
238	C₂×D₄×C₆₁	—	2	2	no	—
239	C₂×D₄×C₆₁	—	2	2	no	—
240	C₂×D₄×C₆₁	—	2	4	no	—
241	C₂×D₄×C₆₁	—	4	1	no	—
242	C₂×D₄×C₆₁	—	4	1	no	—
243	C₂×D₄×C₆₁	—	4	1	no	—
244	C₂×D₄×C₆₁	—	4	2	no	—
245	C₂×D₄×C₆₁	—	4	2	no	—
246	C₂×D₄×C₆₁	—	4	2	no	—
247	C₂×D₄×C₆₁	—	4	2	no	—
248	C₂×D₄×C₆₁	—	4	2	no	—
249	C₂×D₄×C₆₁	—	4	2	no	—
250	C₂×D₄×C₆₁	—	4	2	no	—
251	C₂×D₄×C₆₁	—	4	2	no	—
252	C₂×D₄×C₆₁	—	4	2	no	—
253	C₂×D₄×C₆₁	—	4	1	no	—
254	C₂×D₄×C₆₁	—	4	2	no	—
255	C₂×D₄×C₆₁	—	4	1	no	—
256	C₂×D₄×C₆₁	—	4	2	no	—
257	C₂×D₄×C₆₁	—	4	2	no	—
258	C₂×D₄×C₆₁	—	4	2	no	—
259	C₂×D₄×C₆₁	—	4	2	no	—
260	C₂×D₄×C₆₁	—	4	2	no	—
261	C₂×D₄×C₆₁	—	4	2	no	—
262	C₂×D₄×C₆₁	—	4	2	no	—
263	C₂²×C₄×C₆₁	—	2	2	no	—
264	C₂²×C₄×C₆₁	—	2	2	no	—
265	C₂²×C₄×C₆₁	—	2	2	no	—
266	C₂²×C₄×C₆₁	—	2	2	no	—
267	C₂²×C₄×C₆₁	—	2	2	no	—
268	C₂²×C₄×C₆₁	—	2	4	no	—
269	C₂²×C₄×C₆₁	—	4	2	no	—
270	C₂²×C₄×C₆₁	—	4	2	no	—
271	C₂²×C₄×C₆₁	—	4	1	no	—
272	C₂²×C₄×C₆₁	—	4	1	no	—
273	C₂²×C₄×C₆₁	—	4	1	no	—
274	C₂²×C₄×C₆₁	—	4	1	no	—
275	C₂²×C₄×C₆₁	—	4	2	no	—
276	C₂²×C₄×C₆₁	—	4	2	no	—
277	C₂²×C₄×C₆₁	—	4	2	no	—
278	C₂²×C₄×C₆₁	—	4	2	no	—
279	C₂²×C₄×C₆₁	#41	1	4	yes	—
280	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
294	C₄⋊C₄×C₆₁	—	2	2	no	—
295	C₄⋊C₄×C₆₁	—	2	4	no	—
296	C₄⋊C₄×C₆₁	—	2	4	no	—
297	C₄⋊C₄×C₆₁	—	4	2	no	—
298	C₄⋊C₄×C₆₁	—	4	2	no	—
299	C₄⋊C₄×C₆₁	—	4	2	no	—
300	C₄⋊C₄×C₆₁	—	4	2	no	—
301	C₄⋊C₄×C₆₁	—	4	2	no	—
302	C₄⋊C₄×C₆₁	—	4	2	no	—
303	C₄⋊C₄×C₆₁	—	4	2	no	—
304	C₂²⋊C₄×C₆₁	—	2	4	no	—
305	C₂²⋊C₄×C₆₁	—	2	4	no	—
306	C₂²⋊C₄×C₆₁	—	2	4	no	—
307	C₂²⋊C₄×C₆₁	—	2	4	no	—
308	C₂²⋊C₄×C₆₁	—	2	4	no	—
309	C₂²⋊C₄×C₆₁	—	2	4	no	—
310	C₂²⋊C₄×C₆₁	—	2	4	no	—
311	C₂²⋊C₄×C₆₁	—	2	4	no	—
312	C₂²⋊C₄×C₆₁	—	2	4	no	—
313	C₂²⋊C₄×C₆₁	—	2	4	no	—
314	C₂²⋊C₄×C₆₁	—	4	2	no	—
315	C₂²⋊C₄×C₆₁	—	4	2	no	—
316	C₂²⋊C₄×C₆₁	—	4	2	no	—
317	C₂²⋊C₄×C₆₁	—	4	2	no	—
318	C₂²⋊C₄×C₆₁	—	4	2	no	—
319	C₂²⋊C₄×C₆₁	—	4	1	no	—
320	C₂²⋊C₄×C₆₁	—	4	1	no	—
321	C₂²⋊C₄×C₆₁	—	4	2	no	—
322	C₂²⋊C₄×C₆₁	—	4	2	no	—
323	C₂²⋊C₄×C₆₁	—	4	2	no	—
324	C₂²⋊C₄×C₆₁	—	4	2	no	—
325	C₂²⋊C₄×C₆₁	—	4	2	no	—
326	C₂²⋊C₄×C₆₁	—	4	2	no	—
327	C₂²⋊C₄×C₆₁	—	4	2	no	—
328	C₂²⋊C₄×C₆₁	—	4	2	no	—
329	C₂²⋊C₄×C₆₁	—	4	2	no	—
330	C₂²⋊C₄×C₆₁	—	4	2	no	—
331	C₂²⋊C₄×C₆₁	—	4	2	no	—
332	C₂²⋊C₄×C₆₁	—	4	2	no	—
333	C₂²⋊C₄×C₆₁	—	4	2	no	—
334	C₄²×C₆₁	—	2	4	no	—
335	C₄²×C₆₁	—	4	1	no	—
336	C₄²×C₆₁	—	4	1	no	—
337	C₄²×C₆₁	—	4	1	no	—
338	C₄²×C₆₁	—	4	1	no	—
339	C₄²×C₆₁	—	4	1	no	—
340	C₄²×C₆₁	—	4	2	no	—
341	C₄²×C₆₁	—	4	1	no	—
342	C₂³×C₆₁	—	2	1	no	—
343	C₂³×C₆₁	—	2	2	no	—
344	C₂³×C₆₁	—	2	2	no	—
345	C₂³×C₆₁	—	2	1	no	—
346	C₂³×C₆₁	—	2	1	no	—
347	C₂³×C₆₁	—	2	1	no	—
348	C₂³×C₆₁	—	2	2	no	—
349	C₂³×C₆₁	—	2	2	no	—
350	C₂³×C₆₁	—	2	2	no	—
351	C₂³×C₆₁	—	2	2	no	—
352	C₂³×C₆₁	—	2	1	no	—
353	C₂³×C₆₁	—	2	2	no	—
354	C₂³×C₆₁	—	2	2	no	—
355	C₂³×C₆₁	—	2	2	no	—
356	C₂³×C₆₁	—	2	2	no	—
357	C₂³×C₆₁	—	2	2	no	—
358	C₂³×C₆₁	—	2	2	no	—
359	C₂³×C₆₁	—	2	2	no	—
360	C₂³×C₆₁	—	2	2	no	—
361	C₂³×C₆₁	—	2	1	no	—
362	C₂³×C₆₁	—	2	1	no	—
363	C₂³×C₆₁	—	2	2	no	—
364	C₂³×C₆₁	—	2	2	no	—
365	C₂³×C₆₁	—	2	2	no	—
366	C₂³×C₆₁	—	2	2	no	—
367	C₂³×C₆₁	—	2	2	no	—
368	C₂³×C₆₁	—	2	2	no	—
369	C₂³×C₆₁	—	4	4	no	—
370	C₂³×C₆₁	—	8	2	no	—
371	C₂³×C₆₁	—	8	2	no	—
372	C₂³×C₆₁	—	8	4	no	—
373	C₂³×C₆₁	—	8	4	no	—
374	C₂³×C₆₁	C₂×#41	1	2	yes	—
375	C₂³×C₆₁	H(5,𝔽₂)	1	2	yes	—
376	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
377	Q₈×C₆₁	—	4	4	no	—
378	Q₈×C₆₁	—	8	4	no	—
379	D₄×C₆₁	—	4	4	no	—
380	D₄×C₆₁	—	4	4	no	—
381	D₄×C₆₁	—	4	4	no	—
382	D₄×C₆₁	—	8	2	no	—
383	D₄×C₆₁	—	8	4	no	—
384	D₄×C₆₁	—	8	4	no	—
385	D₄×C₆₁	—	8	4	no	—
386	D₄×C₆₁	—	8	4	no	—
387	D₄×C₆₁	—	8	4	no	—
388	D₄×C₆₁	—	8	4	no	—
389	D₄×C₆₁	—	8	4	no	—
390	C₂×C₄×C₆₁	—	2	8	no	—
391	C₂×C₄×C₆₁	—	2	1	no	—
392	C₂×C₄×C₆₁	—	2	2	no	—
393	C₂×C₄×C₆₁	—	2	1	no	—
394	C₂×C₄×C₆₁	—	2	1	no	—
395	C₂×C₄×C₆₁	—	2	1	no	—
396	C₂×C₄×C₆₁	—	2	1	no	—
397	C₂×C₄×C₆₁	—	2	1	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	1	no	—
402	C₂×C₄×C₆₁	—	2	2	no	—
403	C₂×C₄×C₆₁	—	2	2	no	—
404	C₂×C₄×C₆₁	—	2	2	no	—
405	C₂×C₄×C₆₁	—	2	2	no	—
406	C₂×C₄×C₆₁	—	2	2	no	—
407	C₂×C₄×C₆₁	—	2	2	no	—
408	C₂×C₄×C₆₁	—	2	2	no	—
409	C₂×C₄×C₆₁	—	2	2	no	—
410	C₂×C₄×C₆₁	—	2	2	no	—
411	C₂×C₄×C₆₁	—	2	2	no	—
412	C₂×C₄×C₆₁	—	2	2	no	—
413	C₂×C₄×C₆₁	—	2	2	no	—
414	C₂×C₄×C₆₁	—	2	2	no	—
415	C₂×C₄×C₆₁	—	2	2	no	—
416	C₂×C₄×C₆₁	—	2	2	no	—
417	C₂×C₄×C₆₁	—	2	2	no	—
418	C₂×C₄×C₆₁	—	2	1	no	—
419	C₂×C₄×C₆₁	—	2	1	no	—
420	C₂×C₄×C₆₁	—	2	2	no	—
421	C₂×C₄×C₆₁	—	2	2	no	—
422	C₂×C₄×C₆₁	—	2	2	no	—
423	C₂×C₄×C₆₁	—	2	2	no	—
424	C₂×C₄×C₆₁	—	2	2	no	—
425	C₂×C₄×C₆₁	—	2	2	no	—
426	C₂×C₄×C₆₁	—	2	2	no	—
427	C₂×C₄×C₆₁	—	2	2	no	—
428	C₂×C₄×C₆₁	—	2	2	no	—
429	C₂×C₄×C₆₁	—	4	4	no	—
430	C₂×C₄×C₆₁	—	4	8	no	—
431	C₂×C₄×C₆₁	—	4	4	no	—
432	C₂×C₄×C₆₁	—	8	2	no	—
433	C₂×C₄×C₆₁	—	8	4	no	—
434	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
435	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
436	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
437	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
438	#36818	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂²×C₆₁	—	2	2	no	—
440	C₂²×C₆₁	—	2	2	no	—
441	C₂²×C₆₁	—	2	2	no	—
442	C₂²×C₆₁	—	2	2	no	—
443	C₂²×C₆₁	—	2	4	no	—
444	C₂²×C₆₁	—	4	1	no	—
445	C₂²×C₆₁	—	4	1	no	—
446	C₂²×C₆₁	—	4	2	no	—
447	C₂²×C₆₁	—	4	2	no	—
448	C₂²×C₆₁	—	4	2	no	—
449	C₂²×C₆₁	—	4	2	no	—
450	C₂²×C₆₁	—	4	1	no	—
451	C₂²×C₆₁	—	4	2	no	—
452	C₂²×C₆₁	—	4	1	no	—
453	C₂²×C₆₁	—	4	2	no	—
454	C₂²×C₆₁	—	4	2	no	—
455	C₂²×C₆₁	—	4	2	no	—
456	C₂²×C₆₁	—	4	1	no	—
457	C₂²×C₆₁	—	4	2	no	—
458	C₂²×C₆₁	—	4	2	no	—
459	C₂²×C₆₁	—	4	2	no	—
460	C₂²×C₆₁	—	4	2	no	—
461	C₂²×C₆₁	—	4	2	no	—
462	C₂²×C₆₁	—	4	2	no	—
463	C₂²×C₆₁	—	4	2	no	—
464	C₂²×C₆₁	—	4	2	no	—
465	C₂²×C₆₁	—	4	2	no	—
466	C₂²×C₆₁	—	4	2	no	—
467	C₂²×C₆₁	—	4	2	no	—
468	C₂²×C₆₁	—	8	8	no	—
469	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
470	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
473	C₂²×C₆₁	#585	1	2	yes	—
474	C₄×C₆₁	—	2	2	no	—
475	C₄×C₆₁	—	2	2	no	—
476	C₄×C₆₁	—	2	2	no	—
477	C₄×C₆₁	—	2	4	no	—
478	C₄×C₆₁	—	4	1	no	—
479	C₄×C₆₁	—	4	2	no	—
480	C₄×C₆₁	—	4	2	no	—
481	C₄×C₆₁	—	4	2	no	—
482	C₄×C₆₁	—	4	2	no	—
483	C₄×C₆₁	—	4	2	no	—
484	C₄×C₆₁	—	4	2	no	—
485	C₄×C₆₁	—	4	2	no	—
486	C₄×C₆₁	—	4	2	no	—
487	C₄×C₆₁	—	4	2	no	—
488	#2850	C₂×C₆₁	1	2	yes	complemented
489	#2754	C₂×C₆₁	1	2	yes	complemented
490	#2730	C₂×C₆₁	1	2	yes	complemented
491	#2712	C₂×C₆₁	1	2	yes	complemented
492	#2706	C₂×C₆₁	1	2	yes	complemented
493	#2696	C₂×C₆₁	1	2	yes	complemented
494	#2673	C₂×C₆₁	1	2	yes	complemented
495	#2670	C₂×C₆₁	1	2	yes	complemented
496	#2668	C₂×C₆₁	1	2	yes	complemented
497	#2648	C₂×C₆₁	1	2	yes	complemented
498	#2607	C₂×C₆₁	1	1	yes	characteristic, complemented
499	#2557	C₂×C₆₁	1	2	yes	complemented
500	#2539	C₂×C₆₁	1	1	yes	characteristic, complemented
501	#2476	C₂×C₆₁	1	2	yes	complemented
502	#2431	C₂×C₆₁	1	1	yes	characteristic, complemented
503	#2404	C₂×C₆₁	1	1	yes	characteristic, complemented
504	#2333	C₂×C₆₁	1	1	yes	characteristic, complemented
505	#2312	C₂×C₆₁	1	1	yes	characteristic, complemented
506	#2297	C₂×C₆₁	1	1	yes	characteristic, complemented
507	C₂×C₆₁	—	4	2	no	—
508	C₂×C₆₁	—	4	2	no	—
509	C₂×C₆₁	—	8	1	no	—
510	C₂×C₆₁	—	8	2	no	—
511	C₂×C₆₁	—	8	2	no	—
512	C₂×C₆₁	#3455	1	1	yes	characteristic
513	C₂×C₆₁	#3490	1	1	yes	characteristic
514	C₂×C₆₁	#3508	1	1	yes	characteristic
515	C₂×C₆₁	#3542	1	2	yes	—
516	C₂×C₆₁	#3558	1	2	yes	—
517	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
518	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic, complemented
519	C₂×#124	C₂²×C₆₁	1	2	yes	—
520	C₂×#124	C₂²×C₆₁	1	2	yes	—
521	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
522	C₂×#123	C₂²×C₆₁	1	2	yes	—
523	C₂×#123	C₂²×C₆₁	1	2	yes	complemented
524	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
525	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
526	C₂×#121	C₂²×C₆₁	1	2	yes	—
527	C₂×#121	C₂²×C₆₁	1	2	yes	—
528	C₂×#120	C₂²×C₆₁	1	1	yes	characteristic
529	C₂×#120	C₂²×C₆₁	1	1	yes	characteristic
530	C₂×#120	C₂²×C₆₁	1	2	yes	—
531	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic, complemented
532	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
533	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
534	#400	C₂²×C₆₁	1	2	yes	complemented
535	#399	C₂²×C₆₁	1	2	yes	—
536	#399	C₂²×C₆₁	1	2	yes	—
537	#398	C₂²×C₆₁	1	2	yes	complemented
538	#397	C₂²×C₆₁	1	2	yes	—
539	#397	C₂²×C₆₁	1	2	yes	—
540	#397	C₂²×C₆₁	1	2	yes	complemented
541	#397	C₂²×C₆₁	1	2	yes	complemented
542	#396	C₂²×C₆₁	1	2	yes	complemented
543	#394	C₂²×C₆₁	1	2	yes	—
544	#394	C₂²×C₆₁	1	2	yes	—
545	#394	C₂²×C₆₁	1	2	yes	—
546	#394	C₂²×C₆₁	1	2	yes	—
547	#394	C₂²×C₆₁	1	2	yes	complemented
548	#394	C₂²×C₆₁	1	2	yes	complemented
549	#393	C₂²×C₆₁	1	2	yes	—
550	#393	C₂²×C₆₁	1	2	yes	—
551	#393	C₂²×C₆₁	1	2	yes	complemented
552	#392	C₂²×C₆₁	1	2	yes	—
553	#392	C₂²×C₆₁	1	2	yes	—
554	#392	C₂²×C₆₁	1	2	yes	—
555	#392	C₂²×C₆₁	1	2	yes	—
556	#392	C₂²×C₆₁	1	2	yes	—
557	#392	C₂²×C₆₁	1	2	yes	—
558	#391	C₂²×C₆₁	1	2	yes	complemented
559	#391	C₂²×C₆₁	1	2	yes	complemented
560	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
561	#391	C₂²×C₆₁	1	2	yes	complemented
562	#390	C₂²×C₆₁	1	2	yes	—
563	#390	C₂²×C₆₁	1	2	yes	—
564	#390	C₂²×C₆₁	1	2	yes	—
565	#390	C₂²×C₆₁	1	2	yes	—
566	#390	C₂²×C₆₁	1	1	yes	characteristic, complemented
567	#388	C₂²×C₆₁	1	2	yes	—
568	#388	C₂²×C₆₁	1	2	yes	—
569	#388	C₂²×C₆₁	1	2	yes	—
570	#388	C₂²×C₆₁	1	2	yes	—
571	#388	C₂²×C₆₁	1	2	yes	—
572	#388	C₂²×C₆₁	1	2	yes	—
573	#388	C₂²×C₆₁	1	2	yes	complemented
574	#388	C₂²×C₆₁	1	2	yes	complemented
575	#388	C₂²×C₆₁	1	2	yes	complemented
576	#387	C₂²×C₆₁	1	2	yes	complemented
577	#387	C₂²×C₆₁	1	2	yes	complemented
578	#387	C₂²×C₆₁	1	2	yes	complemented
579	#387	C₂²×C₆₁	1	2	yes	complemented
580	#386	C₂²×C₆₁	1	2	yes	—
581	#386	C₂²×C₆₁	1	2	yes	—
582	#386	C₂²×C₆₁	1	2	yes	—
583	#386	C₂²×C₆₁	1	2	yes	—
584	#386	C₂²×C₆₁	1	1	yes	characteristic
585	#386	C₂²×C₆₁	1	1	yes	characteristic
586	#386	C₂²×C₆₁	1	2	yes	—
587	#386	C₂²×C₆₁	1	2	yes	—
588	#386	C₂²×C₆₁	1	2	yes	complemented
589	#386	C₂²×C₆₁	1	2	yes	complemented
590	#386	C₂²×C₆₁	1	2	yes	complemented
591	#386	C₂²×C₆₁	1	2	yes	complemented
592	#386	C₂²×C₆₁	1	2	yes	complemented
593	#385	C₂²×C₆₁	1	2	yes	complemented
594	#382	C₂²×C₆₁	1	2	yes	complemented
595	#381	C₂²×C₆₁	1	1	yes	characteristic
596	#380	C₂²×C₆₁	1	2	yes	—
597	#379	C₂²×C₆₁	1	2	yes	—
598	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
599	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
600	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
601	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
602	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
603	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
604	C₆₁	#36818	1	1	yes	characteristic, direct product factor, Sylow
605	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
606	C₂×#41	—	2	4	no	—
607	C₂×#41	—	4	2	no	—
608	C₂×#41	—	4	2	no	—
609	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
610	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
611	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
612	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
613	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
614	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
615	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
616	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
617	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
618	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
619	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
620	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
621	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
622	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
625	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
627	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
628	#127	—	4	2	no	—
629	#124	—	4	4	no	—
630	#124	—	4	4	no	—
631	#124	—	4	2	no	—
632	#123	—	4	4	no	—
633	#123	—	4	4	no	—
634	C₂²⋊Q₈	—	4	4	no	—
635	#121	—	2	4	no	—
636	#121	—	4	4	no	—
637	#121	—	4	4	no	—
638	#120	—	4	4	no	—
639	#120	—	4	2	no	—
640	#120	—	4	2	no	—
641	#117	—	4	2	no	—
642	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
652	C₂×C₂²⋊C₄	—	2	4	no	—
653	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
683	C₂×C₄²	—	4	2	no	—
684	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
685	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
688	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
692	#95	C₂³×C₆₁	1	2	yes	—
693	#95	C₂³×C₆₁	1	2	yes	—
694	#95	C₂³×C₆₁	1	2	yes	—
695	#95	C₂³×C₆₁	1	2	yes	—
696	#95	C₂³×C₆₁	1	2	yes	—
697	#95	C₂³×C₆₁	1	2	yes	—
698	#95	C₂³×C₆₁	1	2	yes	—
699	#95	C₂³×C₆₁	1	2	yes	—
700	#95	C₂³×C₆₁	1	2	yes	—
701	#95	C₂³×C₆₁	1	2	yes	—
702	#95	C₂³×C₆₁	1	2	yes	—
703	#95	C₂³×C₆₁	1	2	yes	—
704	#95	C₂³×C₆₁	1	2	yes	—
705	#95	C₂³×C₆₁	1	2	yes	—
706	#95	C₂³×C₆₁	1	2	yes	—
707	#95	C₂³×C₆₁	1	2	yes	—
708	#95	C₂³×C₆₁	1	2	yes	—
709	#95	C₂³×C₆₁	1	2	yes	—
710	#95	C₂³×C₆₁	1	2	yes	—
711	C₂⁴	—	2	2	no	—
712	C₂⁴	—	4	2	no	—
713	C₂⁴	—	4	2	no	—
714	C₂⁴	—	4	1	no	—
715	C₂⁴	—	4	1	no	—
716	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
717	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
718	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
719	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
720	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
721	#41	—	4	16	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	4	no	—
725	C₂×Q₈	—	4	1	no	—
726	C₂×Q₈	—	4	2	no	—
727	C₂×Q₈	—	4	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	4	1	no	—
740	C₂×D₄	—	4	1	no	—
741	C₂×D₄	—	4	1	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	2	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	2	no	—
751	C₂×D₄	—	4	1	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	1	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	—	4	1	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	#41×C₆₁	1	4	yes	—
778	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	1	no	—
814	C₂²⋊C₄	—	4	1	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₄²	—	2	4	no	—
833	C₄²	—	4	1	no	—
834	C₄²	—	4	1	no	—
835	C₄²	—	4	1	no	—
836	C₄²	—	4	1	no	—
837	C₄²	—	4	1	no	—
838	C₄²	—	4	2	no	—
839	C₄²	—	4	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	4	4	no	—
868	C₂³	—	8	2	no	—
869	C₂³	—	8	2	no	—
870	C₂³	—	8	4	no	—
871	C₂³	—	8	4	no	—
872	C₂³	C₂×#41×C₆₁	1	2	yes	—
873	C₂³	H(5,𝔽₂)×C₆₁	1	2	yes	—
874	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
875	Q₈	—	4	4	no	—
876	Q₈	—	8	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	4	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	4	no	—
882	D₄	—	8	4	no	—
883	D₄	—	8	4	no	—
884	D₄	—	8	4	no	—
885	D₄	—	8	4	no	—
886	D₄	—	8	4	no	—
887	D₄	—	8	4	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	8	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	8	2	no	—
931	C₂×C₄	—	8	4	no	—
932	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
933	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
934	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
935	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	1	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	8	8	no	—
966	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
967	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
968	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
969	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
970	C₂²	C₆₁×#585	1	2	yes	—
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	4	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₂	—	4	2	no	—
986	C₂	—	4	2	no	—
987	C₂	—	8	2	no	—
988	C₂	—	8	2	no	—
989	C₂	—	8	1	no	—
990	C₂	C₆₁×#3455	1	1	yes	characteristic
991	C₂	C₆₁×#3490	1	1	yes	characteristic
992	C₂	C₆₁×#3508	1	1	yes	characteristic
993	C₂	C₆₁×#3542	1	2	yes	—
994	C₂	C₆₁×#3558	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2850	C₂	semidirect
2. C₆₁×#2754	C₂	semidirect
3. C₆₁×#2730	C₂	semidirect
4. C₆₁×#2712	C₂	semidirect
5. C₆₁×#2706	C₂	semidirect
6. C₆₁×#2696	C₂	semidirect
7. C₆₁×#2673	C₂	semidirect
8. C₆₁×#2670	C₂	semidirect
9. C₆₁×#2668	C₂	semidirect
10. C₆₁×#2648	C₂	semidirect
11. C₆₁×#2607	C₂	semidirect
12. C₆₁×#2557	C₂	semidirect
13. C₆₁×#2539	C₂	semidirect
14. C₆₁×#2476	C₂	semidirect
15. C₆₁×#2431	C₂	semidirect
16. C₆₁×#2404	C₂	semidirect
17. C₆₁×#2333	C₂	semidirect
18. C₆₁×#2312	C₂	semidirect
19. C₆₁×#2297	C₂	semidirect
21. C₂×#127×C₆₁	C₂²	semidirect
24. C₂×#124×C₆₁	C₂²	semidirect
26. C₂×#123×C₆₁	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
34. C₂×#117×C₆₁	C₂²	semidirect
36. C₂²×C₄²×C₆₁	C₂²	semidirect
37. C₆₁×#400	C₂²	semidirect
40. C₆₁×#398	C₂²	semidirect
43. C₆₁×#397	C₂²	semidirect
44. C₆₁×#397	C₂²	semidirect
45. C₆₁×#396	C₂²	semidirect
50. C₆₁×#394	C₂²	semidirect
51. C₆₁×#394	C₂²	semidirect
54. C₆₁×#393	C₂²	semidirect
61. C₆₁×#391	C₂²	semidirect
62. C₆₁×#391	C₂²	semidirect
63. C₆₁×#391	C₂²	semidirect
64. C₆₁×#391	C₂²	semidirect
69. C₆₁×#390	C₂²	semidirect
76. C₆₁×#388	C₂²	semidirect
77. C₆₁×#388	C₂²	semidirect
78. C₆₁×#388	C₂²	semidirect
79. C₆₁×#387	C₂²	semidirect
80. C₆₁×#387	C₂²	semidirect
81. C₆₁×#387	C₂²	semidirect
82. C₆₁×#387	C₂²	semidirect
91. C₆₁×#386	C₂²	semidirect
92. C₆₁×#386	C₂²	semidirect
93. C₆₁×#386	C₂²	semidirect
94. C₆₁×#386	C₂²	semidirect
95. C₆₁×#386	C₂²	semidirect
96. C₆₁×#385	C₂²	semidirect
97. C₆₁×#382	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
438. #36818	C₆₁	direct (N × H)
488. #2850	C₂×C₆₁	semidirect
489. #2754	C₂×C₆₁	semidirect
490. #2730	C₂×C₆₁	semidirect
491. #2712	C₂×C₆₁	semidirect
492. #2706	C₂×C₆₁	semidirect
493. #2696	C₂×C₆₁	semidirect
494. #2673	C₂×C₆₁	semidirect
495. #2670	C₂×C₆₁	semidirect
496. #2668	C₂×C₆₁	semidirect
497. #2648	C₂×C₆₁	semidirect
498. #2607	C₂×C₆₁	semidirect
499. #2557	C₂×C₆₁	semidirect
500. #2539	C₂×C₆₁	semidirect
501. #2476	C₂×C₆₁	semidirect
502. #2431	C₂×C₆₁	semidirect
503. #2404	C₂×C₆₁	semidirect
504. #2333	C₂×C₆₁	semidirect
505. #2312	C₂×C₆₁	semidirect
506. #2297	C₂×C₆₁	semidirect
518. C₂×#127	C₂²×C₆₁	semidirect
521. C₂×#124	C₂²×C₆₁	semidirect
523. C₂×#123	C₂²×C₆₁	semidirect
524. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
531. C₂×#117	C₂²×C₆₁	semidirect
533. C₂²×C₄²	C₂²×C₆₁	semidirect
534. #400	C₂²×C₆₁	semidirect
537. #398	C₂²×C₆₁	semidirect
540. #397	C₂²×C₆₁	semidirect
541. #397	C₂²×C₆₁	semidirect
542. #396	C₂²×C₆₁	semidirect
547. #394	C₂²×C₆₁	semidirect
548. #394	C₂²×C₆₁	semidirect
551. #393	C₂²×C₆₁	semidirect
558. #391	C₂²×C₆₁	semidirect
559. #391	C₂²×C₆₁	semidirect
560. #391	C₂²×C₆₁	semidirect
561. #391	C₂²×C₆₁	semidirect
566. #390	C₂²×C₆₁	semidirect
573. #388	C₂²×C₆₁	semidirect
574. #388	C₂²×C₆₁	semidirect
575. #388	C₂²×C₆₁	semidirect
576. #387	C₂²×C₆₁	semidirect
577. #387	C₂²×C₆₁	semidirect
578. #387	C₂²×C₆₁	semidirect
579. #387	C₂²×C₆₁	semidirect
588. #386	C₂²×C₆₁	semidirect
589. #386	C₂²×C₆₁	semidirect
590. #386	C₂²×C₆₁	semidirect
591. #386	C₂²×C₆₁	semidirect
592. #386	C₂²×C₆₁	semidirect
593. #385	C₂²×C₆₁	semidirect
594. #382	C₂²×C₆₁	semidirect
601. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
602. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
603. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
604. C₆₁	#36818	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×#2850	2
C₆₁×#2754	2
C₆₁×#2730	2
C₆₁×#2712	2
C₆₁×#2706	2
C₆₁×#2696	2
C₆₁×#2673	2
C₆₁×#2670	2
C₆₁×#2668	2
C₆₁×#2648	2
C₆₁×#2607	2
C₆₁×#2557	2
C₆₁×#2539	2
C₆₁×#2476	2
C₆₁×#2431	2
C₆₁×#2404	2
C₆₁×#2333	2
C₆₁×#2312	2
C₆₁×#2297	2
#36818	61

Subgroups — C61×#36818 #29540251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36818 #29540251