Subgroups — C₆₁×#34327 #29537760

Order 15616.

2584 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#548	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2372	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2368	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2364	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2353	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2337	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2332	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2325	C₂	1	2	yes	maximal, complemented
16	C₄×#124×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₂²⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#121×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₆₁×#391	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2275	C₂	1	2	yes	maximal, complemented
23	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#548	C₄	1	16	yes	complemented
27	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#124×C₆₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
31	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#121×C₆₁	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
44	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#391	C₂²	1	1	yes	characteristic
49	C₆₁×#391	C₂²	1	1	yes	characteristic
50	C₆₁×#391	C₂²	1	2	yes	—
51	C₆₁×#391	C₂²	1	1	yes	characteristic
52	C₆₁×#391	C₂²	1	1	yes	characteristic
53	C₆₁×#391	C₂²	1	2	yes	—
54	C₆₁×#391	C₂²	1	1	yes	characteristic
55	C₆₁×#391	C₂²	1	1	yes	characteristic
56	C₆₁×#391	C₂²	1	2	yes	—
57	C₆₁×#391	C₂²	1	2	yes	—
58	C₆₁×#390	C₂²	1	1	yes	characteristic
59	C₆₁×#390	C₂²	1	1	yes	characteristic
60	C₆₁×#389	C₂²	1	1	yes	characteristic
61	C₆₁×#389	C₂²	1	1	yes	characteristic
62	C₆₁×#388	C₂²	1	2	yes	—
63	C₆₁×#388	C₂²	1	2	yes	—
64	C₆₁×#388	C₂²	1	2	yes	—
65	C₆₁×#388	C₂²	1	2	yes	—
66	C₆₁×#388	C₂²	1	2	yes	—
67	C₆₁×#388	C₂²	1	2	yes	—
68	C₆₁×#388	C₂²	1	2	yes	—
69	C₆₁×#388	C₂²	1	2	yes	—
70	C₆₁×#388	C₂²	1	2	yes	—
71	C₆₁×#387	C₂²	1	2	yes	—
72	C₆₁×#387	C₂²	1	2	yes	—
73	C₆₁×#387	C₂²	1	2	yes	—
74	C₆₁×#387	C₂²	1	2	yes	—
75	C₆₁×#387	C₂²	1	2	yes	—
76	C₆₁×#387	C₂²	1	2	yes	—
77	C₆₁×#387	C₂²	1	2	yes	—
78	C₆₁×#386	C₂²	1	2	yes	—
79	C₆₁×#386	C₂²	1	2	yes	—
80	C₆₁×#386	C₂²	1	2	yes	—
81	C₆₁×#386	C₂²	1	2	yes	—
82	C₆₁×#386	C₂²	1	2	yes	—
83	C₆₁×#386	C₂²	1	2	yes	—
84	C₆₁×#386	C₂²	1	2	yes	—
85	C₆₁×#385	C₂²	1	2	yes	—
86	C₆₁×#385	C₂²	1	2	yes	—
87	C₆₁×#385	C₂²	1	2	yes	—
88	C₆₁×#383	C₂²	1	2	yes	—
89	C₆₁×#382	C₂²	1	1	yes	characteristic
90	C₆₁×#381	C₂²	1	2	yes	—
91	C₆₁×#380	C₂²	1	1	yes	characteristic
92	C₆₁×#380	C₂²	1	1	yes	characteristic
93	C₆₁×#380	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊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
105	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
107	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
108	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
109	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
118	C₆₁×#376	C₂²	1	2	yes	—
119	C₆₁×#376	C₂²	1	2	yes	—
120	C₂×#95×C₆₁	C₂²	1	2	yes	—
121	C₂×#95×C₆₁	C₂²	1	2	yes	—
122	C₂×#95×C₆₁	C₂²	1	2	yes	—
123	C₄³×C₆₁	C₂²	1	1	yes	characteristic
124	C₂×#41×C₆₁	—	4	2	no	—
125	C₂×#41×C₆₁	—	4	2	no	—
126	C₂×#41×C₆₁	C₂×C₄	1	8	yes	complemented
127	C₂²×Q₈×C₆₁	—	4	2	no	—
128	C₂²×Q₈×C₆₁	—	4	2	no	—
129	C₂²×Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
133	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
135	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
142	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
146	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
147	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
148	#124×C₆₁	C₂×C₄	1	8	yes	complemented
149	#124×C₆₁	C₂×C₄	1	16	yes	complemented
150	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
151	C₂²⋊Q₈×C₆₁	C₂×C₄	1	16	yes	complemented
152	#121×C₆₁	C₂×C₄	1	8	yes	complemented
153	#121×C₆₁	C₂×C₄	1	16	yes	complemented
154	C₄×Q₈×C₆₁	—	4	2	no	—
155	C₄×Q₈×C₆₁	—	4	2	no	—
156	C₄×Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
157	C₄×D₄×C₆₁	—	2	4	no	—
158	C₄×D₄×C₆₁	—	2	8	no	—
159	C₄×D₄×C₆₁	—	2	4	no	—
160	C₄×D₄×C₆₁	—	2	8	no	—
161	C₄×D₄×C₆₁	—	4	2	no	—
162	C₄×D₄×C₆₁	—	4	2	no	—
163	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	complemented
164	C₄×D₄×C₆₁	C₂×C₄	1	16	yes	complemented
165	#117×C₆₁	—	4	2	no	—
166	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
167	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₁	—	4	2	no	—
202	C₂×C₄²×C₆₁	—	4	2	no	—
203	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
209	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
210	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
214	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
218	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
219	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
223	#95×C₆₁	C₂³	1	2	yes	—
224	#95×C₆₁	C₂³	1	1	yes	characteristic
225	#95×C₆₁	C₂³	1	2	yes	—
226	#95×C₆₁	C₂³	1	2	yes	—
227	#95×C₆₁	C₂³	1	2	yes	—
228	#95×C₆₁	C₂³	1	2	yes	—
229	#95×C₆₁	C₂³	1	2	yes	—
230	#95×C₆₁	C₂³	1	2	yes	—
231	#95×C₆₁	C₂³	1	2	yes	—
232	#95×C₆₁	C₂³	1	2	yes	—
233	#95×C₆₁	C₂³	1	2	yes	—
234	#95×C₆₁	C₂³	1	1	yes	characteristic
235	#95×C₆₁	C₂³	1	2	yes	—
236	#95×C₆₁	C₂³	1	2	yes	—
237	#95×C₆₁	C₂³	1	2	yes	—
238	#95×C₆₁	C₂³	1	2	yes	—
239	#95×C₆₁	C₂³	1	2	yes	—
240	#95×C₆₁	C₂³	1	1	yes	characteristic
241	#95×C₆₁	C₂³	1	1	yes	characteristic
242	#95×C₆₁	C₂³	1	1	yes	characteristic
243	#95×C₆₁	C₂³	1	1	yes	characteristic
244	#95×C₆₁	C₂³	1	2	yes	—
245	#95×C₆₁	C₂³	1	2	yes	—
246	#95×C₆₁	C₂³	1	2	yes	—
247	#95×C₆₁	C₂³	1	2	yes	—
248	#95×C₆₁	C₂³	1	2	yes	—
249	#95×C₆₁	C₂³	1	2	yes	—
250	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
252	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
253	#41×C₆₁	—	4	16	no	—
254	C₂×Q₈×C₆₁	—	2	2	no	—
255	C₂×Q₈×C₆₁	—	2	2	no	—
256	C₂×Q₈×C₆₁	—	2	2	no	—
257	C₂×Q₈×C₆₁	—	2	2	no	—
258	C₂×Q₈×C₆₁	—	4	2	no	—
259	C₂×Q₈×C₆₁	—	4	2	no	—
260	C₂×Q₈×C₆₁	—	4	16	no	—
261	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
262	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
263	C₂×Q₈×C₆₁	C₂²×C₄	1	8	yes	—
264	C₂×D₄×C₆₁	—	2	2	no	—
265	C₂×D₄×C₆₁	—	2	4	no	—
266	C₂×D₄×C₆₁	—	2	4	no	—
267	C₂×D₄×C₆₁	—	2	2	no	—
268	C₂×D₄×C₆₁	—	2	2	no	—
269	C₂×D₄×C₆₁	—	2	2	no	—
270	C₂×D₄×C₆₁	—	4	2	no	—
271	C₂×D₄×C₆₁	—	4	2	no	—
272	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
273	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
274	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
275	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
276	C₂²×C₄×C₆₁	—	2	2	no	—
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	4	no	—
282	C₂²×C₄×C₆₁	—	2	2	no	—
283	C₂²×C₄×C₆₁	—	2	2	no	—
284	C₂²×C₄×C₆₁	—	2	2	no	—
285	C₂²×C₄×C₆₁	—	2	2	no	—
286	C₂²×C₄×C₆₁	—	2	4	no	—
287	C₂²×C₄×C₆₁	—	2	4	no	—
288	C₂²×C₄×C₆₁	—	4	1	no	—
289	C₂²×C₄×C₆₁	—	4	1	no	—
290	C₂²×C₄×C₆₁	—	4	1	no	—
291	C₂²×C₄×C₆₁	—	4	1	no	—
292	C₂²×C₄×C₆₁	—	4	1	no	—
293	C₂²×C₄×C₆₁	—	4	1	no	—
294	C₂²×C₄×C₆₁	—	4	2	no	—
295	C₂²×C₄×C₆₁	—	4	2	no	—
296	C₂²×C₄×C₆₁	—	4	2	no	—
297	C₂²×C₄×C₆₁	—	4	2	no	—
298	C₂²×C₄×C₆₁	—	4	2	no	—
299	C₂²×C₄×C₆₁	—	4	2	no	—
300	C₂²×C₄×C₆₁	—	4	2	no	—
301	C₂²×C₄×C₆₁	—	4	2	no	—
302	C₂²×C₄×C₆₁	—	4	2	no	—
303	C₂²×C₄×C₆₁	—	4	2	no	—
304	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
305	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
306	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
307	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
308	C₂²×C₄×C₆₁	#41	1	4	yes	complemented
309	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
329	C₄⋊C₄×C₆₁	—	2	2	no	—
330	C₄⋊C₄×C₆₁	—	2	2	no	—
331	C₄⋊C₄×C₆₁	—	2	4	no	—
332	C₄⋊C₄×C₆₁	—	2	4	no	—
333	C₄⋊C₄×C₆₁	—	2	2	no	—
334	C₄⋊C₄×C₆₁	—	2	2	no	—
335	C₄⋊C₄×C₆₁	—	2	2	no	—
336	C₄⋊C₄×C₆₁	—	2	2	no	—
337	C₄⋊C₄×C₆₁	—	4	2	no	—
338	C₄⋊C₄×C₆₁	—	4	2	no	—
339	C₄⋊C₄×C₆₁	—	4	2	no	—
340	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
341	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
342	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
343	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
344	C₂²⋊C₄×C₆₁	—	2	2	no	—
345	C₂²⋊C₄×C₆₁	—	2	4	no	—
346	C₂²⋊C₄×C₆₁	—	2	2	no	—
347	C₂²⋊C₄×C₆₁	—	2	4	no	—
348	C₂²⋊C₄×C₆₁	—	2	4	no	—
349	C₂²⋊C₄×C₆₁	—	2	2	no	—
350	C₂²⋊C₄×C₆₁	—	2	4	no	—
351	C₂²⋊C₄×C₆₁	—	4	2	no	—
352	C₂²⋊C₄×C₆₁	—	4	2	no	—
353	C₂²⋊C₄×C₆₁	—	4	2	no	—
354	C₂²⋊C₄×C₆₁	—	4	2	no	—
355	C₂²⋊C₄×C₆₁	—	4	2	no	—
356	C₂²⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
357	C₂²⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
358	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
359	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
360	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
361	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
362	C₂²⋊C₄×C₆₁	#41	1	4	yes	complemented
363	C₄²×C₆₁	—	2	2	no	—
364	C₄²×C₆₁	—	2	4	no	—
365	C₄²×C₆₁	—	2	2	no	—
366	C₄²×C₆₁	—	2	4	no	—
367	C₄²×C₆₁	—	2	2	no	—
368	C₄²×C₆₁	—	2	2	no	—
369	C₄²×C₆₁	—	2	2	no	—
370	C₄²×C₆₁	—	2	2	no	—
371	C₄²×C₆₁	—	2	2	no	—
372	C₄²×C₆₁	—	4	1	no	—
373	C₄²×C₆₁	—	4	1	no	—
374	C₄²×C₆₁	—	4	1	no	—
375	C₄²×C₆₁	—	4	1	no	—
376	C₄²×C₆₁	—	4	1	no	—
377	C₄²×C₆₁	—	4	2	no	—
378	C₄²×C₆₁	—	4	2	no	—
379	C₄²×C₆₁	—	4	2	no	—
380	C₄²×C₆₁	—	4	2	no	—
381	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
382	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
383	C₂³×C₆₁	—	2	1	no	—
384	C₂³×C₆₁	—	2	1	no	—
385	C₂³×C₆₁	—	2	1	no	—
386	C₂³×C₆₁	—	2	1	no	—
387	C₂³×C₆₁	—	2	1	no	—
388	C₂³×C₆₁	—	2	2	no	—
389	C₂³×C₆₁	—	2	2	no	—
390	C₂³×C₆₁	—	2	1	no	—
391	C₂³×C₆₁	—	2	1	no	—
392	C₂³×C₆₁	—	2	2	no	—
393	C₂³×C₆₁	—	2	2	no	—
394	C₂³×C₆₁	—	2	1	no	—
395	C₂³×C₆₁	—	2	2	no	—
396	C₂³×C₆₁	—	2	1	no	—
397	C₂³×C₆₁	—	2	1	no	—
398	C₂³×C₆₁	—	2	2	no	—
399	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
400	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
401	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
402	C₂³×C₆₁	C₂×#41	1	2	yes	—
403	C₂³×C₆₁	C₂×#41	1	2	yes	—
404	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
405	Q₈×C₆₁	—	2	8	no	—
406	Q₈×C₆₁	—	2	8	no	—
407	Q₈×C₆₁	—	4	8	no	—
408	D₄×C₆₁	—	2	8	no	—
409	D₄×C₆₁	—	2	16	no	—
410	D₄×C₆₁	—	2	8	no	—
411	D₄×C₆₁	—	4	8	no	—
412	C₂×C₄×C₆₁	—	2	2	no	—
413	C₂×C₄×C₆₁	—	2	1	no	—
414	C₂×C₄×C₆₁	—	2	1	no	—
415	C₂×C₄×C₆₁	—	2	2	no	—
416	C₂×C₄×C₆₁	—	2	1	no	—
417	C₂×C₄×C₆₁	—	2	1	no	—
418	C₂×C₄×C₆₁	—	2	1	no	—
419	C₂×C₄×C₆₁	—	2	1	no	—
420	C₂×C₄×C₆₁	—	2	1	no	—
421	C₂×C₄×C₆₁	—	2	1	no	—
422	C₂×C₄×C₆₁	—	2	1	no	—
423	C₂×C₄×C₆₁	—	2	1	no	—
424	C₂×C₄×C₆₁	—	2	1	no	—
425	C₂×C₄×C₆₁	—	2	2	no	—
426	C₂×C₄×C₆₁	—	2	2	no	—
427	C₂×C₄×C₆₁	—	2	1	no	—
428	C₂×C₄×C₆₁	—	2	2	no	—
429	C₂×C₄×C₆₁	—	2	2	no	—
430	C₂×C₄×C₆₁	—	2	1	no	—
431	C₂×C₄×C₆₁	—	2	1	no	—
432	C₂×C₄×C₆₁	—	2	1	no	—
433	C₂×C₄×C₆₁	—	2	1	no	—
434	C₂×C₄×C₆₁	—	2	1	no	—
435	C₂×C₄×C₆₁	—	2	1	no	—
436	C₂×C₄×C₆₁	—	2	8	no	—
437	C₂×C₄×C₆₁	—	2	8	no	—
438	C₂×C₄×C₆₁	—	2	1	no	—
439	C₂×C₄×C₆₁	—	2	2	no	—
440	C₂×C₄×C₆₁	—	2	2	no	—
441	C₂×C₄×C₆₁	—	2	1	no	—
442	C₂×C₄×C₆₁	—	2	2	no	—
443	C₂×C₄×C₆₁	—	2	2	no	—
444	C₂×C₄×C₆₁	—	2	1	no	—
445	C₂×C₄×C₆₁	—	2	1	no	—
446	C₂×C₄×C₆₁	—	2	1	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	—	2	2	no	—
451	C₂×C₄×C₆₁	—	2	2	no	—
452	C₂×C₄×C₆₁	—	2	1	no	—
453	C₂×C₄×C₆₁	—	2	2	no	—
454	C₂×C₄×C₆₁	—	2	1	no	—
455	C₂×C₄×C₆₁	—	2	2	no	—
456	C₂×C₄×C₆₁	—	2	2	no	—
457	C₂×C₄×C₆₁	—	2	1	no	—
458	C₂×C₄×C₆₁	—	2	2	no	—
459	C₂×C₄×C₆₁	—	4	8	no	—
460	C₂×C₄×C₆₁	—	4	8	no	—
461	C₂×C₄×C₆₁	—	4	4	no	—
462	C₂×C₄×C₆₁	—	4	4	no	—
463	C₂×C₄×C₆₁	—	4	4	no	—
464	C₂×C₄×C₆₁	—	4	4	no	—
465	C₂×C₄×C₆₁	—	8	4	no	—
466	C₂×C₄×C₆₁	—	8	4	no	—
467	C₂×C₄×C₆₁	—	8	4	no	—
468	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
469	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
470	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
471	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
472	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
473	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
474	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
475	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
476	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
477	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
478	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
479	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
480	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
481	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
482	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
483	#34327	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
484	C₂²×C₆₁	—	2	2	no	—
485	C₂²×C₆₁	—	2	2	no	—
486	C₂²×C₆₁	—	2	2	no	—
487	C₂²×C₆₁	—	2	2	no	—
488	C₂²×C₆₁	—	2	2	no	—
489	C₂²×C₆₁	—	2	2	no	—
490	C₂²×C₆₁	—	2	2	no	—
491	C₂²×C₆₁	—	2	4	no	—
492	C₂²×C₆₁	—	2	2	no	—
493	C₂²×C₆₁	—	2	4	no	—
494	C₂²×C₆₁	—	2	4	no	—
495	C₂²×C₆₁	—	2	2	no	—
496	C₂²×C₆₁	—	4	1	no	—
497	C₂²×C₆₁	—	4	2	no	—
498	C₂²×C₆₁	—	4	1	no	—
499	C₂²×C₆₁	—	4	2	no	—
500	C₂²×C₆₁	—	4	2	no	—
501	C₂²×C₆₁	—	4	1	no	—
502	C₂²×C₆₁	—	4	1	no	—
503	C₂²×C₆₁	—	4	2	no	—
504	C₂²×C₆₁	C₄×#41	1	4	yes	—
505	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
506	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
507	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
508	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
511	C₂²×C₆₁	#585	1	1	yes	characteristic
512	C₄×C₆₁	—	2	4	no	—
513	C₄×C₆₁	—	2	2	no	—
514	C₄×C₆₁	—	2	2	no	—
515	C₄×C₆₁	—	2	2	no	—
516	C₄×C₆₁	—	2	4	no	—
517	C₄×C₆₁	—	2	4	no	—
518	C₄×C₆₁	—	2	2	no	—
519	C₄×C₆₁	—	2	2	no	—
520	C₄×C₆₁	—	2	2	no	—
521	C₄×C₆₁	—	2	2	no	—
522	C₄×C₆₁	—	2	2	no	—
523	C₄×C₆₁	—	2	2	no	—
524	C₄×C₆₁	—	4	1	no	—
525	C₄×C₆₁	—	4	2	no	—
526	C₄×C₆₁	—	4	1	no	—
527	C₄×C₆₁	—	4	2	no	—
528	C₄×C₆₁	—	4	2	no	—
529	C₄×C₆₁	—	4	2	no	—
530	C₄×C₆₁	—	4	1	no	—
531	C₄×C₆₁	#518	1	4	yes	—
532	C₂×#548	C₂×C₆₁	1	1	yes	characteristic
533	#2372	C₂×C₆₁	1	2	yes	complemented
534	#2368	C₂×C₆₁	1	2	yes	complemented
535	#2367	C₂×C₆₁	1	1	yes	characteristic, complemented
536	#2364	C₂×C₆₁	1	2	yes	complemented
537	#2362	C₂×C₆₁	1	1	yes	characteristic, complemented
538	#2361	C₂×C₆₁	1	1	yes	characteristic, complemented
539	#2356	C₂×C₆₁	1	1	yes	characteristic, complemented
540	#2353	C₂×C₆₁	1	2	yes	complemented
541	#2352	C₂×C₆₁	1	1	yes	characteristic, complemented
542	Q₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#2339	C₂×C₆₁	1	1	yes	characteristic, complemented
544	#2337	C₂×C₆₁	1	2	yes	complemented
545	#2332	C₂×C₆₁	1	2	yes	complemented
546	#2325	C₂×C₆₁	1	2	yes	complemented
547	C₄×#124	C₂×C₆₁	1	1	yes	characteristic, complemented
548	C₄×C₂²⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
549	C₄×#121	C₂×C₆₁	1	1	yes	characteristic, complemented
550	#2297	C₂×C₆₁	1	1	yes	characteristic, complemented
551	#2295	C₂×C₆₁	1	1	yes	characteristic, complemented
552	C₂×#391	C₂×C₆₁	1	1	yes	characteristic, complemented
553	#2275	C₂×C₆₁	1	2	yes	complemented
554	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
555	C₂×C₆₁	—	2	4	no	—
556	C₂×C₆₁	—	4	2	no	—
557	C₂×C₆₁	—	4	4	no	—
558	C₂×C₆₁	C₂×C₄×#41	1	1	yes	characteristic
559	C₂×C₆₁	C₂×#518	1	1	yes	characteristic
560	C₂×C₆₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
561	C₂×C₆₁	#3505	1	1	yes	characteristic
562	C₂×C₆₁	#3511	1	1	yes	characteristic
563	C₂×C₆₁	#3514	1	1	yes	characteristic
564	C₂×C₆₁	#3520	1	1	yes	characteristic
565	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
566	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
567	#548	C₄×C₆₁	1	16	yes	complemented
568	C₂×#124	C₂²×C₆₁	1	2	yes	—
569	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
570	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
571	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
572	C₂×#121	C₂²×C₆₁	1	2	yes	—
573	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
574	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
575	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
576	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
577	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
578	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
579	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
580	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
581	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
582	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
583	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
584	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
585	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
586	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
587	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
588	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
589	#391	C₂²×C₆₁	1	2	yes	—
590	#391	C₂²×C₆₁	1	2	yes	—
591	#391	C₂²×C₆₁	1	2	yes	—
592	#391	C₂²×C₆₁	1	1	yes	characteristic
593	#391	C₂²×C₆₁	1	1	yes	characteristic
594	#391	C₂²×C₆₁	1	1	yes	characteristic
595	#391	C₂²×C₆₁	1	1	yes	characteristic
596	#391	C₂²×C₆₁	1	2	yes	—
597	#391	C₂²×C₆₁	1	1	yes	characteristic
598	#391	C₂²×C₆₁	1	1	yes	characteristic
599	#390	C₂²×C₆₁	1	1	yes	characteristic
600	#390	C₂²×C₆₁	1	1	yes	characteristic
601	#389	C₂²×C₆₁	1	1	yes	characteristic
602	#389	C₂²×C₆₁	1	1	yes	characteristic
603	#388	C₂²×C₆₁	1	2	yes	—
604	#388	C₂²×C₆₁	1	2	yes	—
605	#388	C₂²×C₆₁	1	2	yes	—
606	#388	C₂²×C₆₁	1	2	yes	—
607	#388	C₂²×C₆₁	1	2	yes	—
608	#388	C₂²×C₆₁	1	2	yes	—
609	#388	C₂²×C₆₁	1	2	yes	—
610	#388	C₂²×C₆₁	1	2	yes	—
611	#388	C₂²×C₆₁	1	2	yes	—
612	#387	C₂²×C₆₁	1	2	yes	—
613	#387	C₂²×C₆₁	1	2	yes	—
614	#387	C₂²×C₆₁	1	2	yes	—
615	#387	C₂²×C₆₁	1	2	yes	—
616	#387	C₂²×C₆₁	1	2	yes	—
617	#387	C₂²×C₆₁	1	2	yes	—
618	#387	C₂²×C₆₁	1	2	yes	—
619	#386	C₂²×C₆₁	1	2	yes	—
620	#386	C₂²×C₆₁	1	2	yes	—
621	#386	C₂²×C₆₁	1	2	yes	—
622	#386	C₂²×C₆₁	1	2	yes	—
623	#386	C₂²×C₆₁	1	2	yes	—
624	#386	C₂²×C₆₁	1	2	yes	—
625	#386	C₂²×C₆₁	1	2	yes	—
626	#385	C₂²×C₆₁	1	2	yes	—
627	#385	C₂²×C₆₁	1	2	yes	—
628	#385	C₂²×C₆₁	1	2	yes	—
629	#383	C₂²×C₆₁	1	2	yes	—
630	#382	C₂²×C₆₁	1	1	yes	characteristic
631	#381	C₂²×C₆₁	1	2	yes	—
632	#380	C₂²×C₆₁	1	2	yes	—
633	#380	C₂²×C₆₁	1	1	yes	characteristic
634	#380	C₂²×C₆₁	1	1	yes	characteristic
635	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
636	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
637	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
638	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
639	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
640	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
641	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
642	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
643	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
644	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
645	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
646	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
647	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
648	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
649	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
650	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
651	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
652	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
653	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
654	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
655	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
656	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
657	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
658	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
659	#376	C₂²×C₆₁	1	2	yes	—
660	#376	C₂²×C₆₁	1	2	yes	—
661	C₂×#95	C₂²×C₆₁	1	2	yes	—
662	C₂×#95	C₂²×C₆₁	1	2	yes	—
663	C₂×#95	C₂²×C₆₁	1	2	yes	—
664	C₄³	C₂²×C₆₁	1	1	yes	characteristic
665	C₆₁	#34327	1	1	yes	characteristic, direct product factor, Sylow
666	C₂×#41	—	4	2	no	—
667	C₂×#41	—	4	2	no	—
668	C₂×#41	C₂×C₄×C₆₁	1	8	yes	complemented
669	C₂²×Q₈	—	4	2	no	—
670	C₂²×Q₈	—	4	2	no	—
671	C₂²×Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
672	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
673	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
674	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
675	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
676	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
677	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
678	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
679	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
684	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
685	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
686	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
688	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
689	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
690	#124	C₂×C₄×C₆₁	1	8	yes	complemented
691	#124	C₂×C₄×C₆₁	1	16	yes	complemented
692	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
693	C₂²⋊Q₈	C₂×C₄×C₆₁	1	16	yes	complemented
694	#121	C₂×C₄×C₆₁	1	8	yes	complemented
695	#121	C₂×C₄×C₆₁	1	16	yes	complemented
696	C₄×Q₈	—	4	2	no	—
697	C₄×Q₈	—	4	2	no	—
698	C₄×Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
699	C₄×D₄	—	2	4	no	—
700	C₄×D₄	—	2	8	no	—
701	C₄×D₄	—	2	4	no	—
702	C₄×D₄	—	2	8	no	—
703	C₄×D₄	—	4	2	no	—
704	C₄×D₄	—	4	2	no	—
705	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	complemented
706	C₄×D₄	C₂×C₄×C₆₁	1	16	yes	complemented
707	#117	—	4	2	no	—
708	C₂×C₄⋊C₄	—	4	2	no	—
709	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
743	C₂×C₄²	—	4	2	no	—
744	C₂×C₄²	—	4	2	no	—
745	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
748	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
749	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
750	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
755	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
756	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
757	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
758	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
759	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
760	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
765	#95	C₂³×C₆₁	1	2	yes	—
766	#95	C₂³×C₆₁	1	1	yes	characteristic
767	#95	C₂³×C₆₁	1	2	yes	—
768	#95	C₂³×C₆₁	1	2	yes	—
769	#95	C₂³×C₆₁	1	2	yes	—
770	#95	C₂³×C₆₁	1	2	yes	—
771	#95	C₂³×C₆₁	1	2	yes	—
772	#95	C₂³×C₆₁	1	2	yes	—
773	#95	C₂³×C₆₁	1	2	yes	—
774	#95	C₂³×C₆₁	1	2	yes	—
775	#95	C₂³×C₆₁	1	2	yes	—
776	#95	C₂³×C₆₁	1	1	yes	characteristic
777	#95	C₂³×C₆₁	1	2	yes	—
778	#95	C₂³×C₆₁	1	2	yes	—
779	#95	C₂³×C₆₁	1	2	yes	—
780	#95	C₂³×C₆₁	1	2	yes	—
781	#95	C₂³×C₆₁	1	2	yes	—
782	#95	C₂³×C₆₁	1	1	yes	characteristic
783	#95	C₂³×C₆₁	1	1	yes	characteristic
784	#95	C₂³×C₆₁	1	1	yes	characteristic
785	#95	C₂³×C₆₁	1	1	yes	characteristic
786	#95	C₂³×C₆₁	1	2	yes	—
787	#95	C₂³×C₆₁	1	2	yes	—
788	#95	C₂³×C₆₁	1	2	yes	—
789	#95	C₂³×C₆₁	1	2	yes	—
790	#95	C₂³×C₆₁	1	2	yes	—
791	#95	C₂³×C₆₁	1	2	yes	—
792	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
793	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
794	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
795	#41	—	4	16	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	2	no	—
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	4	2	no	—
801	C₂×Q₈	—	4	2	no	—
802	C₂×Q₈	—	4	16	no	—
803	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
804	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
805	C₂×Q₈	C₂²×C₄×C₆₁	1	8	yes	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	4	2	no	—
813	C₂×D₄	—	4	2	no	—
814	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
815	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
816	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
817	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	4	no	—
829	C₂²×C₄	—	2	4	no	—
830	C₂²×C₄	—	4	1	no	—
831	C₂²×C₄	—	4	1	no	—
832	C₂²×C₄	—	4	1	no	—
833	C₂²×C₄	—	4	1	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	1	no	—
839	C₂²×C₄	—	4	1	no	—
840	C₂²×C₄	—	4	2	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
847	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
848	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
849	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
850	C₂²×C₄	#41×C₆₁	1	4	yes	complemented
851	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	4	no	—
874	C₄⋊C₄	—	2	4	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	4	2	no	—
880	C₄⋊C₄	—	4	2	no	—
881	C₄⋊C₄	—	4	2	no	—
882	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
883	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
884	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
885	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	4	2	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	—	4	2	no	—
896	C₂²⋊C₄	—	4	2	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
900	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
902	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
903	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
904	C₂²⋊C₄	#41×C₆₁	1	4	yes	complemented
905	C₄²	—	2	2	no	—
906	C₄²	—	2	4	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	4	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	4	1	no	—
915	C₄²	—	4	1	no	—
916	C₄²	—	4	1	no	—
917	C₄²	—	4	1	no	—
918	C₄²	—	4	2	no	—
919	C₄²	—	4	2	no	—
920	C₄²	—	4	2	no	—
921	C₄²	—	4	1	no	—
922	C₄²	—	4	2	no	—
923	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
924	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
925	C₂³	—	2	1	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	2	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	2	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	2	no	—
941	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
942	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
943	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
944	C₂³	C₂×#41×C₆₁	1	2	yes	—
945	C₂³	C₂×#41×C₆₁	1	2	yes	—
946	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
947	Q₈	—	2	8	no	—
948	Q₈	—	2	8	no	—
949	Q₈	—	4	8	no	—
950	D₄	—	2	8	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	8	no	—
953	D₄	—	4	8	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	8	no	—
979	C₂×C₄	—	2	8	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	4	8	no	—
1002	C₂×C₄	—	4	8	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	4	no	—
1005	C₂×C₄	—	4	4	no	—
1006	C₂×C₄	—	4	4	no	—
1007	C₂×C₄	—	8	4	no	—
1008	C₂×C₄	—	8	4	no	—
1009	C₂×C₄	—	8	4	no	—
1010	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1011	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
1012	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1013	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
1014	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1015	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
1016	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1017	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1018	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1019	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1020	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1021	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1022	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1023	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1024	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	4	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	4	no	—
1035	C₂²	—	2	4	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	C₄×#41×C₆₁	1	4	yes	—
1046	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
1047	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1048	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1049	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1050	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1051	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1052	C₂²	C₆₁×#585	1	1	yes	characteristic
1053	C₄	—	2	4	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	4	no	—
1058	C₄	—	2	4	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	C₆₁×#518	1	4	yes	—
1073	C₂	—	2	4	no	—
1074	C₂	—	4	2	no	—
1075	C₂	—	4	4	no	—
1076	C₂	C₂×C₄×#41×C₆₁	1	1	yes	characteristic
1077	C₂	C₂×C₆₁×#518	1	1	yes	characteristic
1078	C₂	C₄×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1079	C₂	C₆₁×#3505	1	1	yes	characteristic
1080	C₂	C₆₁×#3511	1	1	yes	characteristic
1081	C₂	C₆₁×#3514	1	1	yes	characteristic
1082	C₂	C₆₁×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#548	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2372	C₂	semidirect
3. C₆₁×#2368	C₂	semidirect
4. C₆₁×#2367	C₂	semidirect
5. C₆₁×#2364	C₂	semidirect
6. C₆₁×#2362	C₂	semidirect
7. C₆₁×#2361	C₂	semidirect
8. C₆₁×#2356	C₂	semidirect
9. C₆₁×#2353	C₂	semidirect
10. C₆₁×#2352	C₂	semidirect
11. Q₈×C₂²⋊C₄×C₆₁	C₂	semidirect
12. C₆₁×#2339	C₂	semidirect
13. C₆₁×#2337	C₂	semidirect
14. C₆₁×#2332	C₂	semidirect
15. C₆₁×#2325	C₂	semidirect
16. C₄×#124×C₆₁	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₆₁	C₂	semidirect
18. C₄×#121×C₆₁	C₂	semidirect
19. C₆₁×#2297	C₂	semidirect
20. C₆₁×#2295	C₂	semidirect
21. C₂×C₆₁×#391	C₂	semidirect
22. C₆₁×#2275	C₂	semidirect
23. C₄²×D₄×C₆₁	C₂	semidirect
26. C₆₁×#548	C₄	semidirect
126. C₂×#41×C₆₁	C₂×C₄	semidirect
129. C₂²×Q₈×C₆₁	C₂×C₄	semidirect
148. #124×C₆₁	C₂×C₄	semidirect
149. #124×C₆₁	C₂×C₄	semidirect
150. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
151. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
152. #121×C₆₁	C₂×C₄	semidirect
153. #121×C₆₁	C₂×C₄	semidirect
156. C₄×Q₈×C₆₁	C₂×C₄	semidirect
163. C₄×D₄×C₆₁	C₂×C₄	semidirect
164. C₄×D₄×C₆₁	C₂×C₄	semidirect
308. C₂²×C₄×C₆₁	#41	semidirect
362. C₂²⋊C₄×C₆₁	#41	semidirect
483. #34327	C₆₁	direct (N × H)
533. #2372	C₂×C₆₁	semidirect
534. #2368	C₂×C₆₁	semidirect
535. #2367	C₂×C₆₁	semidirect
536. #2364	C₂×C₆₁	semidirect
537. #2362	C₂×C₆₁	semidirect
538. #2361	C₂×C₆₁	semidirect
539. #2356	C₂×C₆₁	semidirect
540. #2353	C₂×C₆₁	semidirect
541. #2352	C₂×C₆₁	semidirect
542. Q₈×C₂²⋊C₄	C₂×C₆₁	semidirect
543. #2339	C₂×C₆₁	semidirect
544. #2337	C₂×C₆₁	semidirect
545. #2332	C₂×C₆₁	semidirect
546. #2325	C₂×C₆₁	semidirect
547. C₄×#124	C₂×C₆₁	semidirect
548. C₄×C₂²⋊Q₈	C₂×C₆₁	semidirect
549. C₄×#121	C₂×C₆₁	semidirect
550. #2297	C₂×C₆₁	semidirect
551. #2295	C₂×C₆₁	semidirect
552. C₂×#391	C₂×C₆₁	semidirect
553. #2275	C₂×C₆₁	semidirect
554. C₄²×D₄	C₂×C₆₁	semidirect
567. #548	C₄×C₆₁	semidirect
665. C₆₁	#34327	direct (N × H)
668. C₂×#41	C₂×C₄×C₆₁	semidirect
671. C₂²×Q₈	C₂×C₄×C₆₁	semidirect
690. #124	C₂×C₄×C₆₁	semidirect
691. #124	C₂×C₄×C₆₁	semidirect
692. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
693. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
694. #121	C₂×C₄×C₆₁	semidirect
695. #121	C₂×C₄×C₆₁	semidirect
698. C₄×Q₈	C₂×C₄×C₆₁	semidirect
705. C₄×D₄	C₂×C₄×C₆₁	semidirect
706. C₄×D₄	C₂×C₄×C₆₁	semidirect
850. C₂²×C₄	#41×C₆₁	semidirect
904. C₂²⋊C₄	#41×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₆₁×#548	2
C₆₁×#2372	2
C₆₁×#2368	2
C₆₁×#2367	2
C₆₁×#2364	2
C₆₁×#2362	2
C₆₁×#2361	2
C₆₁×#2356	2
C₆₁×#2353	2
C₆₁×#2352	2
Q₈×C₂²⋊C₄×C₆₁	2
C₆₁×#2339	2
C₆₁×#2337	2
C₆₁×#2332	2
C₆₁×#2325	2
C₄×#124×C₆₁	2
C₄×C₂²⋊Q₈×C₆₁	2
C₄×#121×C₆₁	2
C₆₁×#2297	2
C₆₁×#2295	2
C₂×C₆₁×#391	2
C₆₁×#2275	2
C₄²×D₄×C₆₁	2
#34327	61

Subgroups — C61×#34327 #29537760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34327 #29537760