Subgroups — C₆₁×#34320 #29537753

Order 15616.

2840 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#546	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2374	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2363	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2358	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2342	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2335	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2333	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2321	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×#2293	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₆₁×#390	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2273	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×D₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#546	C₄	1	16	yes	complemented
27	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#123×C₆₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₁	C₂²	1	2	yes	—
32	C₂×#120×C₆₁	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×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	1	yes	characteristic
39	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
42	C₂×#117×C₆₁	C₂²	1	2	yes	complemented
43	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
46	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
47	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
48	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
49	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
51	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
52	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
53	C₆₁×#390	C₂²	1	1	yes	characteristic
54	C₆₁×#390	C₂²	1	1	yes	characteristic
55	C₆₁×#390	C₂²	1	2	yes	—
56	C₆₁×#390	C₂²	1	1	yes	characteristic
57	C₆₁×#390	C₂²	1	1	yes	characteristic
58	C₆₁×#390	C₂²	1	2	yes	—
59	C₆₁×#390	C₂²	1	1	yes	characteristic
60	C₆₁×#390	C₂²	1	1	yes	characteristic
61	C₆₁×#390	C₂²	1	2	yes	complemented
62	C₆₁×#390	C₂²	1	2	yes	complemented
63	C₆₁×#390	C₂²	1	2	yes	complemented
64	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
65	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#389	C₂²	1	2	yes	complemented
67	C₆₁×#388	C₂²	1	2	yes	complemented
68	C₆₁×#388	C₂²	1	2	yes	complemented
69	C₆₁×#388	C₂²	1	2	yes	complemented
70	C₆₁×#388	C₂²	1	2	yes	complemented
71	C₆₁×#388	C₂²	1	2	yes	complemented
72	C₆₁×#388	C₂²	1	2	yes	complemented
73	C₆₁×#388	C₂²	1	2	yes	complemented
74	C₆₁×#388	C₂²	1	2	yes	complemented
75	C₆₁×#388	C₂²	1	2	yes	complemented
76	C₆₁×#388	C₂²	1	2	yes	complemented
77	C₆₁×#388	C₂²	1	2	yes	complemented
78	C₆₁×#387	C₂²	1	2	yes	complemented
79	C₆₁×#387	C₂²	1	2	yes	complemented
80	C₆₁×#387	C₂²	1	2	yes	complemented
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	complemented
85	C₆₁×#386	C₂²	1	2	yes	complemented
86	C₆₁×#386	C₂²	1	2	yes	complemented
87	C₆₁×#386	C₂²	1	2	yes	complemented
88	C₆₁×#385	C₂²	1	2	yes	—
89	C₆₁×#385	C₂²	1	2	yes	—
90	C₆₁×#385	C₂²	1	2	yes	complemented
91	C₆₁×#382	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#381	C₂²	1	2	yes	complemented
93	C₆₁×#380	C₂²	1	1	yes	characteristic
94	C₆₁×#380	C₂²	1	1	yes	characteristic, complemented
95	C₆₁×#380	C₂²	1	2	yes	complemented
96	C₆₁×#379	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
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	2	yes	—
108	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
114	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
115	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
116	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
117	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
118	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
119	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
123	C₄³×C₆₁	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₆₁	C₂³	1	2	yes	—
125	C₂×#41×C₆₁	—	4	2	no	—
126	C₂×#41×C₆₁	—	4	2	no	—
127	C₂×#41×C₆₁	C₂×C₄	1	8	yes	complemented
128	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₆₁	—	4	2	no	—
130	C₂²×D₄×C₆₁	—	4	2	no	—
131	C₂²×D₄×C₆₁	C₂×C₄	1	8	yes	complemented
132	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
136	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
137	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
142	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
147	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
148	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
149	#124×C₆₁	C₂×C₄	1	8	yes	complemented
150	#123×C₆₁	C₂×C₄	1	16	yes	complemented
151	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
152	#121×C₆₁	C₂×C₄	1	8	yes	complemented
153	#121×C₆₁	C₂×C₄	1	16	yes	complemented
154	#120×C₆₁	C₂×C₄	1	16	yes	complemented
155	C₄×Q₈×C₆₁	—	4	2	no	—
156	C₄×Q₈×C₆₁	—	4	2	no	—
157	C₄×D₄×C₆₁	—	2	4	no	—
158	C₄×D₄×C₆₁	—	2	4	no	—
159	C₄×D₄×C₆₁	—	4	2	no	—
160	C₄×D₄×C₆₁	—	4	2	no	—
161	C₄×D₄×C₆₁	—	4	4	no	—
162	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	complemented
163	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	complemented
164	#117×C₆₁	—	4	4	no	—
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	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
173	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
180	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
182	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
183	C₂×C₂²⋊C₄×C₆₁	—	4	4	no	—
184	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	16	yes	complemented
185	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
201	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₁	—	4	2	no	—
214	C₂×C₄²×C₆₁	—	4	2	no	—
215	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
223	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
225	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
226	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
227	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
229	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
230	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
231	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
234	#95×C₆₁	C₂³	1	1	yes	characteristic
235	#95×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
241	#95×C₆₁	C₂³	1	2	yes	—
242	#95×C₆₁	C₂³	1	1	yes	characteristic
243	#95×C₆₁	C₂³	1	1	yes	characteristic
244	#95×C₆₁	C₂³	1	1	yes	characteristic
245	#95×C₆₁	C₂³	1	1	yes	characteristic
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	#95×C₆₁	C₂³	1	2	yes	—
251	#95×C₆₁	C₂³	1	2	yes	—
252	#95×C₆₁	C₂³	1	2	yes	—
253	C₂⁴×C₆₁	—	2	4	no	—
254	C₂⁴×C₆₁	—	2	4	no	—
255	C₂⁴×C₆₁	—	4	2	no	—
256	C₂⁴×C₆₁	—	4	2	no	—
257	C₂⁴×C₆₁	—	4	2	no	—
258	C₂⁴×C₆₁	—	4	2	no	—
259	C₂⁴×C₆₁	C₂²×C₄	1	8	yes	—
260	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
261	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
262	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
264	#41×C₆₁	—	4	16	no	—
265	C₂×Q₈×C₆₁	—	2	2	no	—
266	C₂×Q₈×C₆₁	—	2	2	no	—
267	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
268	C₂×D₄×C₆₁	—	2	2	no	—
269	C₂×D₄×C₆₁	—	2	2	no	—
270	C₂×D₄×C₆₁	—	2	2	no	—
271	C₂×D₄×C₆₁	—	2	2	no	—
272	C₂×D₄×C₆₁	—	2	2	no	—
273	C₂×D₄×C₆₁	—	2	2	no	—
274	C₂×D₄×C₆₁	—	4	16	no	—
275	C₂×D₄×C₆₁	—	4	2	no	—
276	C₂×D₄×C₆₁	—	4	2	no	—
277	C₂×D₄×C₆₁	—	4	2	no	—
278	C₂×D₄×C₆₁	—	4	2	no	—
279	C₂×D₄×C₆₁	—	4	2	no	—
280	C₂×D₄×C₆₁	—	4	2	no	—
281	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
282	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
283	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
284	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
285	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
286	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
287	C₂²×C₄×C₆₁	—	2	2	no	—
288	C₂²×C₄×C₆₁	—	2	2	no	—
289	C₂²×C₄×C₆₁	—	2	2	no	—
290	C₂²×C₄×C₆₁	—	2	2	no	—
291	C₂²×C₄×C₆₁	—	2	2	no	—
292	C₂²×C₄×C₆₁	—	2	4	no	—
293	C₂²×C₄×C₆₁	—	2	2	no	—
294	C₂²×C₄×C₆₁	—	2	2	no	—
295	C₂²×C₄×C₆₁	—	2	2	no	—
296	C₂²×C₄×C₆₁	—	2	2	no	—
297	C₂²×C₄×C₆₁	—	2	4	no	—
298	C₂²×C₄×C₆₁	—	2	4	no	—
299	C₂²×C₄×C₆₁	—	4	1	no	—
300	C₂²×C₄×C₆₁	—	4	1	no	—
301	C₂²×C₄×C₆₁	—	4	1	no	—
302	C₂²×C₄×C₆₁	—	4	1	no	—
303	C₂²×C₄×C₆₁	—	4	2	no	—
304	C₂²×C₄×C₆₁	—	4	1	no	—
305	C₂²×C₄×C₆₁	—	4	2	no	—
306	C₂²×C₄×C₆₁	—	4	1	no	—
307	C₂²×C₄×C₆₁	—	4	2	no	—
308	C₂²×C₄×C₆₁	—	4	2	no	—
309	C₂²×C₄×C₆₁	—	4	2	no	—
310	C₂²×C₄×C₆₁	—	4	2	no	—
311	C₂²×C₄×C₆₁	—	4	2	no	—
312	C₂²×C₄×C₆₁	—	4	2	no	—
313	C₂²×C₄×C₆₁	—	4	2	no	—
314	C₂²×C₄×C₆₁	—	4	2	no	—
315	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
316	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
317	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
318	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
319	C₂²×C₄×C₆₁	#41	1	4	yes	complemented
320	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
339	C₄⋊C₄×C₆₁	—	2	2	no	—
340	C₄⋊C₄×C₆₁	—	2	2	no	—
341	C₄⋊C₄×C₆₁	—	2	2	no	—
342	C₄⋊C₄×C₆₁	—	2	2	no	—
343	C₄⋊C₄×C₆₁	—	2	4	no	—
344	C₄⋊C₄×C₆₁	—	2	2	no	—
345	C₄⋊C₄×C₆₁	—	2	2	no	—
346	C₄⋊C₄×C₆₁	—	4	2	no	—
347	C₄⋊C₄×C₆₁	—	4	2	no	—
348	C₄⋊C₄×C₆₁	—	4	2	no	—
349	C₄⋊C₄×C₆₁	—	4	2	no	—
350	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
351	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
352	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
353	C₂²⋊C₄×C₆₁	—	2	4	no	—
354	C₂²⋊C₄×C₆₁	—	2	2	no	—
355	C₂²⋊C₄×C₆₁	—	2	4	no	—
356	C₂²⋊C₄×C₆₁	—	2	4	no	—
357	C₂²⋊C₄×C₆₁	—	2	4	no	—
358	C₂²⋊C₄×C₆₁	—	2	4	no	—
359	C₂²⋊C₄×C₆₁	—	2	4	no	—
360	C₂²⋊C₄×C₆₁	—	2	4	no	—
361	C₂²⋊C₄×C₆₁	—	2	2	no	—
362	C₂²⋊C₄×C₆₁	—	2	2	no	—
363	C₂²⋊C₄×C₆₁	—	2	4	no	—
364	C₂²⋊C₄×C₆₁	—	2	4	no	—
365	C₂²⋊C₄×C₆₁	—	4	2	no	—
366	C₂²⋊C₄×C₆₁	—	4	2	no	—
367	C₂²⋊C₄×C₆₁	—	4	2	no	—
368	C₂²⋊C₄×C₆₁	—	4	2	no	—
369	C₂²⋊C₄×C₆₁	—	4	2	no	—
370	C₂²⋊C₄×C₆₁	—	4	2	no	—
371	C₂²⋊C₄×C₆₁	—	4	2	no	—
372	C₂²⋊C₄×C₆₁	—	4	2	no	—
373	C₂²⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
374	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
375	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
376	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
377	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
378	C₂²⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
379	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
380	C₂²⋊C₄×C₆₁	#41	1	4	yes	complemented
381	C₄²×C₆₁	—	2	2	no	—
382	C₄²×C₆₁	—	2	2	no	—
383	C₄²×C₆₁	—	2	2	no	—
384	C₄²×C₆₁	—	2	2	no	—
385	C₄²×C₆₁	—	2	2	no	—
386	C₄²×C₆₁	—	2	2	no	—
387	C₄²×C₆₁	—	2	2	no	—
388	C₄²×C₆₁	—	4	1	no	—
389	C₄²×C₆₁	—	4	1	no	—
390	C₄²×C₆₁	—	4	1	no	—
391	C₄²×C₆₁	—	4	1	no	—
392	C₄²×C₆₁	—	4	2	no	—
393	C₄²×C₆₁	—	4	1	no	—
394	C₄²×C₆₁	—	4	2	no	—
395	C₄²×C₆₁	—	4	2	no	—
396	C₄²×C₆₁	—	4	2	no	—
397	C₄²×C₆₁	—	4	2	no	—
398	C₄²×C₆₁	—	4	2	no	—
399	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
400	C₂³×C₆₁	—	2	1	no	—
401	C₂³×C₆₁	—	2	1	no	—
402	C₂³×C₆₁	—	2	1	no	—
403	C₂³×C₆₁	—	2	1	no	—
404	C₂³×C₆₁	—	2	2	no	—
405	C₂³×C₆₁	—	2	2	no	—
406	C₂³×C₆₁	—	2	2	no	—
407	C₂³×C₆₁	—	2	1	no	—
408	C₂³×C₆₁	—	2	1	no	—
409	C₂³×C₆₁	—	2	2	no	—
410	C₂³×C₆₁	—	2	2	no	—
411	C₂³×C₆₁	—	2	2	no	—
412	C₂³×C₆₁	—	2	1	no	—
413	C₂³×C₆₁	—	2	1	no	—
414	C₂³×C₆₁	—	2	2	no	—
415	C₂³×C₆₁	—	2	2	no	—
416	C₂³×C₆₁	—	2	1	no	—
417	C₂³×C₆₁	—	2	2	no	—
418	C₂³×C₆₁	—	2	2	no	—
419	C₂³×C₆₁	—	2	2	no	—
420	C₂³×C₆₁	—	2	1	no	—
421	C₂³×C₆₁	—	2	2	no	—
422	C₂³×C₆₁	—	2	16	no	—
423	C₂³×C₆₁	—	4	8	no	—
424	C₂³×C₆₁	—	4	8	no	—
425	C₂³×C₆₁	—	8	4	no	—
426	C₂³×C₆₁	—	8	4	no	—
427	C₂³×C₆₁	—	8	4	no	—
428	C₂³×C₆₁	—	8	4	no	—
429	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
430	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
431	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
432	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
433	C₂³×C₆₁	C₂×#41	1	2	yes	—
434	C₂³×C₆₁	C₂×#41	1	2	yes	—
435	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
436	Q₈×C₆₁	—	2	8	no	—
437	D₄×C₆₁	—	2	8	no	—
438	D₄×C₆₁	—	2	8	no	—
439	D₄×C₆₁	—	2	8	no	—
440	D₄×C₆₁	—	4	8	no	—
441	D₄×C₆₁	—	4	8	no	—
442	D₄×C₆₁	—	4	8	no	—
443	C₂×C₄×C₆₁	—	2	1	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	1	no	—
449	C₂×C₄×C₆₁	—	2	1	no	—
450	C₂×C₄×C₆₁	—	2	1	no	—
451	C₂×C₄×C₆₁	—	2	1	no	—
452	C₂×C₄×C₆₁	—	2	1	no	—
453	C₂×C₄×C₆₁	—	2	1	no	—
454	C₂×C₄×C₆₁	—	2	1	no	—
455	C₂×C₄×C₆₁	—	2	1	no	—
456	C₂×C₄×C₆₁	—	2	2	no	—
457	C₂×C₄×C₆₁	—	2	2	no	—
458	C₂×C₄×C₆₁	—	2	2	no	—
459	C₂×C₄×C₆₁	—	2	1	no	—
460	C₂×C₄×C₆₁	—	2	1	no	—
461	C₂×C₄×C₆₁	—	2	1	no	—
462	C₂×C₄×C₆₁	—	2	1	no	—
463	C₂×C₄×C₆₁	—	2	1	no	—
464	C₂×C₄×C₆₁	—	2	2	no	—
465	C₂×C₄×C₆₁	—	2	8	no	—
466	C₂×C₄×C₆₁	—	2	8	no	—
467	C₂×C₄×C₆₁	—	2	1	no	—
468	C₂×C₄×C₆₁	—	2	2	no	—
469	C₂×C₄×C₆₁	—	2	2	no	—
470	C₂×C₄×C₆₁	—	2	2	no	—
471	C₂×C₄×C₆₁	—	2	2	no	—
472	C₂×C₄×C₆₁	—	2	1	no	—
473	C₂×C₄×C₆₁	—	2	1	no	—
474	C₂×C₄×C₆₁	—	2	1	no	—
475	C₂×C₄×C₆₁	—	2	1	no	—
476	C₂×C₄×C₆₁	—	2	1	no	—
477	C₂×C₄×C₆₁	—	2	1	no	—
478	C₂×C₄×C₆₁	—	2	2	no	—
479	C₂×C₄×C₆₁	—	2	2	no	—
480	C₂×C₄×C₆₁	—	2	2	no	—
481	C₂×C₄×C₆₁	—	2	2	no	—
482	C₂×C₄×C₆₁	—	2	2	no	—
483	C₂×C₄×C₆₁	—	2	2	no	—
484	C₂×C₄×C₆₁	—	2	2	no	—
485	C₂×C₄×C₆₁	—	2	1	no	—
486	C₂×C₄×C₆₁	—	2	2	no	—
487	C₂×C₄×C₆₁	—	2	1	no	—
488	C₂×C₄×C₆₁	—	4	8	no	—
489	C₂×C₄×C₆₁	—	4	8	no	—
490	C₂×C₄×C₆₁	—	4	4	no	—
491	C₂×C₄×C₆₁	—	4	4	no	—
492	C₂×C₄×C₆₁	—	4	4	no	—
493	C₂×C₄×C₆₁	—	4	4	no	—
494	C₂×C₄×C₆₁	—	8	4	no	—
495	C₂×C₄×C₆₁	—	8	4	no	—
496	C₂×C₄×C₆₁	—	8	4	no	—
497	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
498	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
499	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
500	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
501	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
502	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
503	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
504	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
505	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
506	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
507	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
508	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
509	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
510	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
511	#34320	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
512	C₂²×C₆₁	—	2	2	no	—
513	C₂²×C₆₁	—	2	2	no	—
514	C₂²×C₆₁	—	2	2	no	—
515	C₂²×C₆₁	—	2	2	no	—
516	C₂²×C₆₁	—	2	2	no	—
517	C₂²×C₆₁	—	2	2	no	—
518	C₂²×C₆₁	—	2	2	no	—
519	C₂²×C₆₁	—	2	4	no	—
520	C₂²×C₆₁	—	2	4	no	—
521	C₂²×C₆₁	—	2	2	no	—
522	C₂²×C₆₁	—	2	4	no	—
523	C₂²×C₆₁	—	2	4	no	—
524	C₂²×C₆₁	—	2	4	no	—
525	C₂²×C₆₁	—	2	2	no	—
526	C₂²×C₆₁	—	2	4	no	—
527	C₂²×C₆₁	—	4	1	no	—
528	C₂²×C₆₁	—	4	2	no	—
529	C₂²×C₆₁	—	4	2	no	—
530	C₂²×C₆₁	—	4	1	no	—
531	C₂²×C₆₁	—	4	2	no	—
532	C₂²×C₆₁	—	4	2	no	—
533	C₂²×C₆₁	—	4	2	no	—
534	C₂²×C₆₁	—	4	1	no	—
535	C₂²×C₆₁	—	4	2	no	—
536	C₂²×C₆₁	—	4	1	no	—
537	C₂²×C₆₁	—	4	2	no	—
538	C₂²×C₆₁	—	4	2	no	—
539	C₂²×C₆₁	—	8	16	no	—
540	C₂²×C₆₁	C₄×#41	1	4	yes	—
541	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
542	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
543	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
544	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
545	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂²×C₆₁	#585	1	1	yes	characteristic
548	C₄×C₆₁	—	2	2	no	—
549	C₄×C₆₁	—	2	2	no	—
550	C₄×C₆₁	—	2	2	no	—
551	C₄×C₆₁	—	2	4	no	—
552	C₄×C₆₁	—	2	2	no	—
553	C₄×C₆₁	—	2	4	no	—
554	C₄×C₆₁	—	2	2	no	—
555	C₄×C₆₁	—	2	2	no	—
556	C₄×C₆₁	—	2	2	no	—
557	C₄×C₆₁	—	2	2	no	—
558	C₄×C₆₁	—	2	2	no	—
559	C₄×C₆₁	—	4	1	no	—
560	C₄×C₆₁	—	4	1	no	—
561	C₄×C₆₁	—	4	2	no	—
562	C₄×C₆₁	—	4	2	no	—
563	C₄×C₆₁	—	4	2	no	—
564	C₄×C₆₁	—	4	1	no	—
565	C₄×C₆₁	—	4	2	no	—
566	C₄×C₆₁	#518	1	4	yes	—
567	C₂×#546	C₂×C₆₁	1	1	yes	characteristic
568	#2374	C₂×C₆₁	1	2	yes	complemented
569	#2367	C₂×C₆₁	1	1	yes	characteristic, complemented
570	#2363	C₂×C₆₁	1	1	yes	characteristic, complemented
571	#2363	C₂×C₆₁	1	2	yes	complemented
572	#2360	C₂×C₆₁	1	1	yes	characteristic, complemented
573	#2358	C₂×C₆₁	1	2	yes	complemented
574	#2357	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#2352	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#2342	C₂×C₆₁	1	2	yes	complemented
577	#2341	C₂×C₆₁	1	1	yes	characteristic, complemented
578	D₄×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#2335	C₂×C₆₁	1	2	yes	complemented
580	#2333	C₂×C₆₁	1	2	yes	complemented
581	#2321	C₂×C₆₁	1	2	yes	complemented
582	C₄×#124	C₂×C₆₁	1	1	yes	characteristic, complemented
583	C₄×C₂²⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
584	C₄×#121	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#2297	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#2293	C₂×C₆₁	1	1	yes	characteristic, complemented
587	C₂×#390	C₂×C₆₁	1	1	yes	characteristic, complemented
588	#2273	C₂×C₆₁	1	2	yes	complemented
589	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
590	C₂×C₆₁	—	2	4	no	—
591	C₂×C₆₁	—	4	2	no	—
592	C₂×C₆₁	—	4	4	no	—
593	C₂×C₆₁	—	4	4	no	—
594	C₂×C₆₁	C₂×C₄×#41	1	1	yes	characteristic
595	C₂×C₆₁	C₂×#518	1	1	yes	characteristic
596	C₂×C₆₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂×C₆₁	#3505	1	1	yes	characteristic
598	C₂×C₆₁	#3508	1	1	yes	characteristic
599	C₂×C₆₁	#3514	1	1	yes	characteristic
600	C₂×C₆₁	#3519	1	1	yes	characteristic
601	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
602	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
603	#546	C₄×C₆₁	1	16	yes	complemented
604	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
605	C₂×#123	C₂²×C₆₁	1	2	yes	—
606	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
607	C₂×#121	C₂²×C₆₁	1	2	yes	—
608	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
609	C₂×#120	C₂²×C₆₁	1	2	yes	—
610	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
611	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
612	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
614	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
615	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
617	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
618	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
619	C₂×#117	C₂²×C₆₁	1	2	yes	complemented
620	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic, complemented
621	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
622	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
623	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
624	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
625	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
626	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
627	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
628	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
629	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
630	#390	C₂²×C₆₁	1	2	yes	—
631	#390	C₂²×C₆₁	1	1	yes	characteristic
632	#390	C₂²×C₆₁	1	1	yes	characteristic
633	#390	C₂²×C₆₁	1	1	yes	characteristic
634	#390	C₂²×C₆₁	1	1	yes	characteristic
635	#390	C₂²×C₆₁	1	2	yes	—
636	#390	C₂²×C₆₁	1	1	yes	characteristic
637	#390	C₂²×C₆₁	1	1	yes	characteristic
638	#390	C₂²×C₆₁	1	2	yes	complemented
639	#390	C₂²×C₆₁	1	2	yes	complemented
640	#390	C₂²×C₆₁	1	2	yes	complemented
641	#389	C₂²×C₆₁	1	2	yes	complemented
642	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
643	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
644	#388	C₂²×C₆₁	1	2	yes	complemented
645	#388	C₂²×C₆₁	1	2	yes	complemented
646	#388	C₂²×C₆₁	1	2	yes	complemented
647	#388	C₂²×C₆₁	1	2	yes	complemented
648	#388	C₂²×C₆₁	1	2	yes	complemented
649	#388	C₂²×C₆₁	1	2	yes	complemented
650	#388	C₂²×C₆₁	1	2	yes	complemented
651	#388	C₂²×C₆₁	1	2	yes	complemented
652	#388	C₂²×C₆₁	1	2	yes	complemented
653	#388	C₂²×C₆₁	1	2	yes	complemented
654	#388	C₂²×C₆₁	1	2	yes	complemented
655	#387	C₂²×C₆₁	1	2	yes	complemented
656	#387	C₂²×C₆₁	1	2	yes	complemented
657	#387	C₂²×C₆₁	1	2	yes	complemented
658	#386	C₂²×C₆₁	1	2	yes	—
659	#386	C₂²×C₆₁	1	2	yes	—
660	#386	C₂²×C₆₁	1	2	yes	—
661	#386	C₂²×C₆₁	1	2	yes	complemented
662	#386	C₂²×C₆₁	1	2	yes	complemented
663	#386	C₂²×C₆₁	1	2	yes	complemented
664	#386	C₂²×C₆₁	1	2	yes	complemented
665	#385	C₂²×C₆₁	1	2	yes	—
666	#385	C₂²×C₆₁	1	2	yes	—
667	#385	C₂²×C₆₁	1	2	yes	complemented
668	#382	C₂²×C₆₁	1	1	yes	characteristic, complemented
669	#381	C₂²×C₆₁	1	2	yes	complemented
670	#380	C₂²×C₆₁	1	1	yes	characteristic
671	#380	C₂²×C₆₁	1	2	yes	complemented
672	#380	C₂²×C₆₁	1	1	yes	characteristic, complemented
673	#379	C₂²×C₆₁	1	2	yes	—
674	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
675	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
676	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
677	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
678	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
679	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
680	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
681	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
682	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
683	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
684	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
685	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
686	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
687	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
688	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
689	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
690	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
691	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
692	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
693	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
694	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
695	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
696	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
697	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
698	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
699	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
700	C₄³	C₂²×C₆₁	1	1	yes	characteristic, complemented
701	C₆₁	#34320	1	1	yes	characteristic, direct product factor, Sylow
702	C₂⁵	C₂³×C₆₁	1	2	yes	—
703	C₂×#41	—	4	2	no	—
704	C₂×#41	—	4	2	no	—
705	C₂×#41	C₂×C₄×C₆₁	1	8	yes	complemented
706	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
707	C₂²×D₄	—	4	2	no	—
708	C₂²×D₄	—	4	2	no	—
709	C₂²×D₄	C₂×C₄×C₆₁	1	8	yes	complemented
710	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
711	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
712	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
713	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
714	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
715	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
716	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
717	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
718	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
719	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
720	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
721	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
722	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
723	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
724	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
725	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
726	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
727	#124	C₂×C₄×C₆₁	1	8	yes	complemented
728	#123	C₂×C₄×C₆₁	1	16	yes	complemented
729	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
730	#121	C₂×C₄×C₆₁	1	8	yes	complemented
731	#121	C₂×C₄×C₆₁	1	16	yes	complemented
732	#120	C₂×C₄×C₆₁	1	16	yes	complemented
733	C₄×Q₈	—	4	2	no	—
734	C₄×Q₈	—	4	2	no	—
735	C₄×D₄	—	2	4	no	—
736	C₄×D₄	—	2	4	no	—
737	C₄×D₄	—	4	2	no	—
738	C₄×D₄	—	4	2	no	—
739	C₄×D₄	—	4	4	no	—
740	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	complemented
741	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	complemented
742	#117	—	4	4	no	—
743	#117	—	4	2	no	—
744	C₂×C₄⋊C₄	—	4	2	no	—
745	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
756	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
759	C₂×C₂²⋊C₄	—	2	8	no	—
760	C₂×C₂²⋊C₄	—	2	8	no	—
761	C₂×C₂²⋊C₄	—	4	4	no	—
762	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	16	yes	complemented
763	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
773	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
775	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
789	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
791	C₂×C₄²	—	4	2	no	—
792	C₂×C₄²	—	4	2	no	—
793	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
795	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
797	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
798	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
800	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
801	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
802	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
803	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
804	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
805	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
806	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
807	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
808	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
809	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
810	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
811	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
812	#95	C₂³×C₆₁	1	1	yes	characteristic
813	#95	C₂³×C₆₁	1	1	yes	characteristic
814	#95	C₂³×C₆₁	1	2	yes	—
815	#95	C₂³×C₆₁	1	2	yes	—
816	#95	C₂³×C₆₁	1	2	yes	—
817	#95	C₂³×C₆₁	1	2	yes	—
818	#95	C₂³×C₆₁	1	2	yes	—
819	#95	C₂³×C₆₁	1	2	yes	—
820	#95	C₂³×C₆₁	1	1	yes	characteristic
821	#95	C₂³×C₆₁	1	1	yes	characteristic
822	#95	C₂³×C₆₁	1	1	yes	characteristic
823	#95	C₂³×C₆₁	1	1	yes	characteristic
824	#95	C₂³×C₆₁	1	2	yes	—
825	#95	C₂³×C₆₁	1	2	yes	—
826	#95	C₂³×C₆₁	1	2	yes	—
827	#95	C₂³×C₆₁	1	2	yes	—
828	#95	C₂³×C₆₁	1	2	yes	—
829	#95	C₂³×C₆₁	1	2	yes	—
830	#95	C₂³×C₆₁	1	2	yes	—
831	C₂⁴	—	2	4	no	—
832	C₂⁴	—	2	4	no	—
833	C₂⁴	—	4	2	no	—
834	C₂⁴	—	4	2	no	—
835	C₂⁴	—	4	2	no	—
836	C₂⁴	—	4	2	no	—
837	C₂⁴	C₂²×C₄×C₆₁	1	8	yes	—
838	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
839	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
840	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
841	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
842	#41	—	4	16	no	—
843	C₂×Q₈	—	2	2	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	4	16	no	—
853	C₂×D₄	—	4	2	no	—
854	C₂×D₄	—	4	2	no	—
855	C₂×D₄	—	4	2	no	—
856	C₂×D₄	—	4	2	no	—
857	C₂×D₄	—	4	2	no	—
858	C₂×D₄	—	4	2	no	—
859	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
860	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
861	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
862	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
863	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
864	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	4	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	—	2	4	no	—
876	C₂²×C₄	—	2	4	no	—
877	C₂²×C₄	—	4	1	no	—
878	C₂²×C₄	—	4	1	no	—
879	C₂²×C₄	—	4	1	no	—
880	C₂²×C₄	—	4	1	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	1	no	—
885	C₂²×C₄	—	4	2	no	—
886	C₂²×C₄	—	4	1	no	—
887	C₂²×C₄	—	4	2	no	—
888	C₂²×C₄	—	4	2	no	—
889	C₂²×C₄	—	4	2	no	—
890	C₂²×C₄	—	4	2	no	—
891	C₂²×C₄	—	4	2	no	—
892	C₂²×C₄	—	4	2	no	—
893	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
894	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
895	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
896	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
897	C₂²×C₄	#41×C₆₁	1	4	yes	complemented
898	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
901	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
907	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	4	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	4	2	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	—	4	2	no	—
928	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
929	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
930	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
931	C₂²⋊C₄	—	2	4	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	4	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	2	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
952	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
953	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
954	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
955	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
956	C₂²⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
957	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
958	C₂²⋊C₄	#41×C₆₁	1	4	yes	complemented
959	C₄²	—	2	2	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	4	1	no	—
967	C₄²	—	4	1	no	—
968	C₄²	—	4	1	no	—
969	C₄²	—	4	1	no	—
970	C₄²	—	4	2	no	—
971	C₄²	—	4	2	no	—
972	C₄²	—	4	2	no	—
973	C₄²	—	4	2	no	—
974	C₄²	—	4	2	no	—
975	C₄²	—	4	2	no	—
976	C₄²	—	4	1	no	—
977	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	1	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	16	no	—
1001	C₂³	—	4	8	no	—
1002	C₂³	—	4	8	no	—
1003	C₂³	—	8	4	no	—
1004	C₂³	—	8	4	no	—
1005	C₂³	—	8	4	no	—
1006	C₂³	—	8	4	no	—
1007	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
1008	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
1009	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
1010	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
1011	C₂³	C₂×#41×C₆₁	1	2	yes	—
1012	C₂³	C₂×#41×C₆₁	1	2	yes	—
1013	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
1014	Q₈	—	2	8	no	—
1015	D₄	—	2	8	no	—
1016	D₄	—	2	8	no	—
1017	D₄	—	2	8	no	—
1018	D₄	—	4	8	no	—
1019	D₄	—	4	8	no	—
1020	D₄	—	4	8	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	8	no	—
1044	C₂×C₄	—	2	8	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	4	8	no	—
1067	C₂×C₄	—	4	8	no	—
1068	C₂×C₄	—	4	4	no	—
1069	C₂×C₄	—	4	4	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	8	4	no	—
1073	C₂×C₄	—	8	4	no	—
1074	C₂×C₄	—	8	4	no	—
1075	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1076	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1077	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
1078	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1079	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
1080	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1081	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
1082	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1083	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1084	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1085	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1086	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1087	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1088	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	4	no	—
1097	C₂²	—	2	4	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	4	no	—
1100	C₂²	—	2	4	no	—
1101	C₂²	—	2	4	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	4	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	8	16	no	—
1117	C₂²	C₄×#41×C₆₁	1	4	yes	—
1118	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
1119	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1120	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1121	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1122	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1123	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1124	C₂²	C₆₁×#585	1	1	yes	characteristic
1125	C₄	—	2	2	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	4	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	4	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	C₆₁×#518	1	4	yes	—
1144	C₂	—	2	4	no	—
1145	C₂	—	4	4	no	—
1146	C₂	—	4	4	no	—
1147	C₂	—	4	2	no	—
1148	C₂	C₂×C₄×#41×C₆₁	1	1	yes	characteristic
1149	C₂	C₂×C₆₁×#518	1	1	yes	characteristic
1150	C₂	C₄×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1151	C₂	C₆₁×#3505	1	1	yes	characteristic
1152	C₂	C₆₁×#3508	1	1	yes	characteristic
1153	C₂	C₆₁×#3514	1	1	yes	characteristic
1154	C₂	C₆₁×#3519	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×#546	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×#2374	C₂	semidirect
3. C₆₁×#2367	C₂	semidirect
4. C₆₁×#2363	C₂	semidirect
5. C₆₁×#2363	C₂	semidirect
6. C₆₁×#2360	C₂	semidirect
7. C₆₁×#2358	C₂	semidirect
8. C₆₁×#2357	C₂	semidirect
9. C₆₁×#2352	C₂	semidirect
10. C₆₁×#2342	C₂	semidirect
11. C₆₁×#2341	C₂	semidirect
12. D₄×C₂²⋊C₄×C₆₁	C₂	semidirect
13. C₆₁×#2335	C₂	semidirect
14. C₆₁×#2333	C₂	semidirect
15. C₆₁×#2321	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×#2293	C₂	semidirect
21. C₂×C₆₁×#390	C₂	semidirect
22. C₆₁×#2273	C₂	semidirect
23. C₄²×D₄×C₆₁	C₂	semidirect
26. C₆₁×#546	C₄	semidirect
33. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
34. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
41. C₂×C₄×D₄×C₆₁	C₂²	semidirect
42. C₂×#117×C₆₁	C₂²	semidirect
43. C₂×#117×C₆₁	C₂²	semidirect
50. C₂²×C₄²×C₆₁	C₂²	semidirect
51. C₆₁×#391	C₂²	semidirect
52. C₆₁×#391	C₂²	semidirect
61. C₆₁×#390	C₂²	semidirect
62. C₆₁×#390	C₂²	semidirect
63. C₆₁×#390	C₂²	semidirect
64. C₆₁×#389	C₂²	semidirect
65. C₆₁×#389	C₂²	semidirect
66. C₆₁×#389	C₂²	semidirect
67. C₆₁×#388	C₂²	semidirect
68. C₆₁×#388	C₂²	semidirect
69. C₆₁×#388	C₂²	semidirect
70. C₆₁×#388	C₂²	semidirect
71. C₆₁×#388	C₂²	semidirect
72. C₆₁×#388	C₂²	semidirect
73. C₆₁×#388	C₂²	semidirect
74. C₆₁×#388	C₂²	semidirect
75. C₆₁×#388	C₂²	semidirect
76. C₆₁×#388	C₂²	semidirect
77. C₆₁×#388	C₂²	semidirect
78. C₆₁×#387	C₂²	semidirect
79. C₆₁×#387	C₂²	semidirect
80. C₆₁×#387	C₂²	semidirect
84. C₆₁×#386	C₂²	semidirect
85. C₆₁×#386	C₂²	semidirect
86. C₆₁×#386	C₂²	semidirect
87. C₆₁×#386	C₂²	semidirect
90. C₆₁×#385	C₂²	semidirect
91. C₆₁×#382	C₂²	semidirect
92. C₆₁×#381	C₂²	semidirect
94. C₆₁×#380	C₂²	semidirect
95. C₆₁×#380	C₂²	semidirect
97. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
98. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
99. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
100. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
101. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
102. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
103. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
110. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
111. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
112. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
113. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
114. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
115. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
116. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
117. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
123. C₄³×C₆₁	C₂²	semidirect
127. C₂×#41×C₆₁	C₂×C₄	semidirect
131. C₂²×D₄×C₆₁	C₂×C₄	semidirect
149. #124×C₆₁	C₂×C₄	semidirect
150. #123×C₆₁	C₂×C₄	semidirect
151. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
152. #121×C₆₁	C₂×C₄	semidirect
153. #121×C₆₁	C₂×C₄	semidirect
154. #120×C₆₁	C₂×C₄	semidirect
162. C₄×D₄×C₆₁	C₂×C₄	semidirect
163. C₄×D₄×C₆₁	C₂×C₄	semidirect
184. C₂×C₂²⋊C₄×C₆₁	C₂×C₄	semidirect
319. C₂²×C₄×C₆₁	#41	semidirect
380. C₂²⋊C₄×C₆₁	#41	semidirect
511. #34320	C₆₁	direct (N × H)
568. #2374	C₂×C₆₁	semidirect
569. #2367	C₂×C₆₁	semidirect
570. #2363	C₂×C₆₁	semidirect
571. #2363	C₂×C₆₁	semidirect
572. #2360	C₂×C₆₁	semidirect
573. #2358	C₂×C₆₁	semidirect
574. #2357	C₂×C₆₁	semidirect
575. #2352	C₂×C₆₁	semidirect
576. #2342	C₂×C₆₁	semidirect
577. #2341	C₂×C₆₁	semidirect
578. D₄×C₂²⋊C₄	C₂×C₆₁	semidirect
579. #2335	C₂×C₆₁	semidirect
580. #2333	C₂×C₆₁	semidirect
581. #2321	C₂×C₆₁	semidirect
582. C₄×#124	C₂×C₆₁	semidirect
583. C₄×C₂²⋊Q₈	C₂×C₆₁	semidirect
584. C₄×#121	C₂×C₆₁	semidirect
585. #2297	C₂×C₆₁	semidirect
586. #2293	C₂×C₆₁	semidirect
587. C₂×#390	C₂×C₆₁	semidirect
588. #2273	C₂×C₆₁	semidirect
589. C₄²×D₄	C₂×C₆₁	semidirect
603. #546	C₄×C₆₁	semidirect
610. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
611. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
618. C₂×C₄×D₄	C₂²×C₆₁	semidirect
619. C₂×#117	C₂²×C₆₁	semidirect
620. C₂×#117	C₂²×C₆₁	semidirect
627. C₂²×C₄²	C₂²×C₆₁	semidirect
628. #391	C₂²×C₆₁	semidirect
629. #391	C₂²×C₆₁	semidirect
638. #390	C₂²×C₆₁	semidirect
639. #390	C₂²×C₆₁	semidirect
640. #390	C₂²×C₆₁	semidirect
641. #389	C₂²×C₆₁	semidirect
642. #389	C₂²×C₆₁	semidirect
643. #389	C₂²×C₆₁	semidirect
644. #388	C₂²×C₆₁	semidirect
645. #388	C₂²×C₆₁	semidirect
646. #388	C₂²×C₆₁	semidirect
647. #388	C₂²×C₆₁	semidirect
648. #388	C₂²×C₆₁	semidirect
649. #388	C₂²×C₆₁	semidirect
650. #388	C₂²×C₆₁	semidirect
651. #388	C₂²×C₆₁	semidirect
652. #388	C₂²×C₆₁	semidirect
653. #388	C₂²×C₆₁	semidirect
654. #388	C₂²×C₆₁	semidirect
655. #387	C₂²×C₆₁	semidirect
656. #387	C₂²×C₆₁	semidirect
657. #387	C₂²×C₆₁	semidirect
661. #386	C₂²×C₆₁	semidirect
662. #386	C₂²×C₆₁	semidirect
663. #386	C₂²×C₆₁	semidirect
664. #386	C₂²×C₆₁	semidirect
667. #385	C₂²×C₆₁	semidirect
668. #382	C₂²×C₆₁	semidirect
669. #381	C₂²×C₆₁	semidirect
671. #380	C₂²×C₆₁	semidirect
672. #380	C₂²×C₆₁	semidirect
674. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
675. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
676. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
677. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
678. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
679. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
680. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
687. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
688. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
689. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
690. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
691. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
692. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
693. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
694. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
695. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
696. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
697. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
698. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
699. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
700. C₄³	C₂²×C₆₁	semidirect
701. C₆₁	#34320	direct (N × H)
705. C₂×#41	C₂×C₄×C₆₁	semidirect
709. C₂²×D₄	C₂×C₄×C₆₁	semidirect
727. #124	C₂×C₄×C₆₁	semidirect
728. #123	C₂×C₄×C₆₁	semidirect
729. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
730. #121	C₂×C₄×C₆₁	semidirect
731. #121	C₂×C₄×C₆₁	semidirect
732. #120	C₂×C₄×C₆₁	semidirect
740. C₄×D₄	C₂×C₄×C₆₁	semidirect
741. C₄×D₄	C₂×C₄×C₆₁	semidirect
762. C₂×C₂²⋊C₄	C₂×C₄×C₆₁	semidirect
897. C₂²×C₄	#41×C₆₁	semidirect
958. 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×#546	2
C₆₁×#2374	2
C₆₁×#2367	2
C₆₁×#2363	2
C₆₁×#2360	2
C₆₁×#2358	2
C₆₁×#2357	2
C₆₁×#2352	2
C₆₁×#2342	2
C₆₁×#2341	2
D₄×C₂²⋊C₄×C₆₁	2
C₆₁×#2335	2
C₆₁×#2333	2
C₆₁×#2321	2
C₄×#124×C₆₁	2
C₄×C₂²⋊Q₈×C₆₁	2
C₄×#121×C₆₁	2
C₆₁×#2297	2
C₆₁×#2293	2
C₂×C₆₁×#390	2
C₆₁×#2273	2
C₄²×D₄×C₆₁	2
#34320	61

Subgroups — C61×#34320 #29537753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34320 #29537753