Subgroups — C₆₁×#34310 #29537743

Order 15616.

3764 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#518	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2366	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2363	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2361	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2358	C₂	1	4	yes	maximal, complemented
7	C₆₁×#2354	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₂²⋊C₄×C₆₁	C₂	1	2	yes	maximal, complemented
10	D₄×C₂²⋊C₄×C₆₁	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2324	C₂	1	2	yes	maximal, complemented
12	C₆₁×#2321	C₂	1	4	yes	maximal, complemented
13	C₄×#127×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#121×C₆₁	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₆₁×#390	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₆₁	C₂²	1	2	yes	—
19	C₂³×D₄×C₆₁	C₂²	1	2	yes	—
20	D₄²×C₆₁	C₄	1	16	yes	complemented
21	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#121×C₆₁	C₂²	1	2	yes	—
23	C₂×#121×C₆₁	C₂²	1	2	yes	—
24	C₂×#120×C₆₁	C₂²	1	4	yes	—
25	C₆₁×#518	—	2	16	no	—
26	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	complemented
32	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
33	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	complemented
34	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
37	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
38	C₂×#117×C₆₁	C₂²	1	2	yes	complemented
39	C₂×#117×C₆₁	C₂²	1	2	yes	complemented
40	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	complemented
42	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	complemented
43	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	complemented
44	C₂²×C₄²×C₆₁	C₂²	1	2	yes	complemented
45	C₆₁×#390	C₂²	1	1	yes	characteristic
46	C₆₁×#390	C₂²	1	2	yes	—
47	C₆₁×#390	C₂²	1	1	yes	characteristic
48	C₆₁×#390	C₂²	1	2	yes	complemented
49	C₆₁×#390	C₂²	1	4	yes	complemented
50	C₆₁×#390	C₂²	1	4	yes	complemented
51	C₆₁×#390	C₂²	1	2	yes	complemented
52	C₆₁×#390	C₂²	1	2	yes	complemented
53	C₆₁×#390	C₂²	1	2	yes	complemented
54	C₆₁×#390	C₂²	1	2	yes	complemented
55	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
56	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
57	C₆₁×#389	C₂²	1	2	yes	complemented
58	C₆₁×#388	C₂²	1	2	yes	complemented
59	C₆₁×#388	C₂²	1	2	yes	complemented
60	C₆₁×#388	C₂²	1	4	yes	complemented
61	C₆₁×#388	C₂²	1	4	yes	complemented
62	C₆₁×#388	C₂²	1	4	yes	complemented
63	C₆₁×#386	C₂²	1	4	yes	complemented
64	C₆₁×#386	C₂²	1	4	yes	complemented
65	C₆₁×#386	C₂²	1	4	yes	complemented
66	C₆₁×#386	C₂²	1	4	yes	complemented
67	C₆₁×#386	C₂²	1	4	yes	complemented
68	C₆₁×#385	C₂²	1	4	yes	complemented
69	C₆₁×#385	C₂²	1	4	yes	complemented
70	C₆₁×#384	C₂²	1	1	yes	characteristic, complemented
71	C₆₁×#380	C₂²	1	2	yes	complemented
72	C₆₁×#380	C₂²	1	2	yes	complemented
73	C₆₁×#379	C₂²	1	4	yes	complemented
74	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
79	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	complemented
84	C₄³×C₆₁	C₂²	1	1	yes	characteristic, complemented
85	C₂⁵×C₆₁	C₂³	1	4	yes	—
86	C₂²×D₄×C₆₁	—	2	8	no	—
87	C₂²×D₄×C₆₁	—	2	8	no	—
88	C₂²×D₄×C₆₁	—	4	4	no	—
89	C₂²×D₄×C₆₁	—	4	4	no	—
90	C₂²×D₄×C₆₁	C₂×C₄	1	16	yes	complemented
91	C₂²×D₄×C₆₁	C₂×C₄	1	16	yes	complemented
92	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
93	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
94	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
96	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
97	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
98	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
100	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
101	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
102	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
103	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
104	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
105	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
106	#127×C₆₁	C₂×C₄	1	8	yes	complemented
107	#121×C₆₁	C₂×C₄	1	16	yes	complemented
108	#121×C₆₁	C₂×C₄	1	16	yes	complemented
109	#120×C₆₁	C₂×C₄	1	32	yes	complemented
110	C₄×D₄×C₆₁	—	2	8	no	—
111	C₄×D₄×C₆₁	—	2	4	no	—
112	C₄×D₄×C₆₁	—	2	16	no	—
113	C₄×D₄×C₆₁	—	2	8	no	—
114	C₄×D₄×C₆₁	—	2	16	no	—
115	C₄×D₄×C₆₁	—	2	8	no	—
116	C₄×D₄×C₆₁	—	4	4	no	—
117	C₄×D₄×C₆₁	—	4	4	no	—
118	C₄×D₄×C₆₁	—	4	4	no	—
119	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	complemented
120	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	complemented
121	C₄×D₄×C₆₁	D₄	1	8	yes	complemented
122	#117×C₆₁	—	2	8	no	—
123	#117×C₆₁	—	2	8	no	—
124	C₂×C₄⋊C₄×C₆₁	—	4	4	no	—
125	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₆₁	—	2	16	no	—
138	C₂×C₂²⋊C₄×C₆₁	—	2	16	no	—
139	C₂×C₂²⋊C₄×C₆₁	—	4	8	no	—
140	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
158	C₂×C₄²×C₆₁	—	4	4	no	—
159	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
164	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
165	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
166	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
168	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
171	#95×C₆₁	C₂³	1	2	yes	—
172	#95×C₆₁	C₂³	1	2	yes	—
173	#95×C₆₁	C₂³	1	2	yes	—
174	#95×C₆₁	C₂³	1	2	yes	—
175	#95×C₆₁	C₂³	1	4	yes	—
176	#95×C₆₁	C₂³	1	2	yes	—
177	#95×C₆₁	C₂³	1	4	yes	—
178	#95×C₆₁	C₂³	1	2	yes	—
179	C₂⁴×C₆₁	—	2	8	no	—
180	C₂⁴×C₆₁	—	2	8	no	—
181	C₂⁴×C₆₁	—	4	4	no	—
182	C₂⁴×C₆₁	—	4	4	no	—
183	C₂⁴×C₆₁	—	4	4	no	—
184	C₂⁴×C₆₁	—	4	4	no	—
185	C₂⁴×C₆₁	C₂²×C₄	1	16	yes	—
186	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
187	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
188	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
189	C₂×D₄×C₆₁	—	2	8	no	—
190	C₂×D₄×C₆₁	—	2	8	no	—
191	C₂×D₄×C₆₁	—	2	64	no	—
192	C₂×D₄×C₆₁	—	2	4	no	—
193	C₂×D₄×C₆₁	—	2	4	no	—
194	C₂×D₄×C₆₁	—	2	4	no	—
195	C₂×D₄×C₆₁	—	2	4	no	—
196	C₂×D₄×C₆₁	—	2	2	no	—
197	C₂×D₄×C₆₁	—	2	2	no	—
198	C₂×D₄×C₆₁	—	4	32	no	—
199	C₂×D₄×C₆₁	—	4	2	no	—
200	C₂×D₄×C₆₁	—	4	4	no	—
201	C₂×D₄×C₆₁	—	4	4	no	—
202	C₂×D₄×C₆₁	—	4	2	no	—
203	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
204	C₂×D₄×C₆₁	C₂²×C₄	1	16	yes	—
205	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
206	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
207	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
208	C₂×D₄×C₆₁	C₂²×C₄	1	16	yes	—
209	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
210	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
211	C₂×D₄×C₆₁	#41	1	4	yes	—
212	C₂²×C₄×C₆₁	—	2	4	no	—
213	C₂²×C₄×C₆₁	—	2	4	no	—
214	C₂²×C₄×C₆₁	—	2	4	no	—
215	C₂²×C₄×C₆₁	—	2	4	no	—
216	C₂²×C₄×C₆₁	—	2	4	no	—
217	C₂²×C₄×C₆₁	—	2	8	no	—
218	C₂²×C₄×C₆₁	—	2	4	no	—
219	C₂²×C₄×C₆₁	—	2	8	no	—
220	C₂²×C₄×C₆₁	—	2	8	no	—
221	C₂²×C₄×C₆₁	—	4	2	no	—
222	C₂²×C₄×C₆₁	—	4	2	no	—
223	C₂²×C₄×C₆₁	—	4	2	no	—
224	C₂²×C₄×C₆₁	—	4	4	no	—
225	C₂²×C₄×C₆₁	—	4	4	no	—
226	C₂²×C₄×C₆₁	—	4	4	no	—
227	C₂²×C₄×C₆₁	—	4	4	no	—
228	C₂²×C₄×C₆₁	—	4	4	no	—
229	C₂²×C₄×C₆₁	—	4	4	no	—
230	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
231	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
232	C₂²×C₄×C₆₁	C₂×D₄	1	8	yes	complemented
233	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
247	C₄⋊C₄×C₆₁	—	2	4	no	—
248	C₄⋊C₄×C₆₁	—	2	4	no	—
249	C₄⋊C₄×C₆₁	—	2	4	no	—
250	C₄⋊C₄×C₆₁	—	2	2	no	—
251	C₄⋊C₄×C₆₁	—	2	2	no	—
252	C₄⋊C₄×C₆₁	—	2	4	no	—
253	C₄⋊C₄×C₆₁	—	2	2	no	—
254	C₄⋊C₄×C₆₁	—	4	4	no	—
255	C₄⋊C₄×C₆₁	—	4	2	no	—
256	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
257	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
258	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	complemented
259	C₂²⋊C₄×C₆₁	—	2	8	no	—
260	C₂²⋊C₄×C₆₁	—	2	4	no	—
261	C₂²⋊C₄×C₆₁	—	2	8	no	—
262	C₂²⋊C₄×C₆₁	—	2	4	no	—
263	C₂²⋊C₄×C₆₁	—	2	4	no	—
264	C₂²⋊C₄×C₆₁	—	2	8	no	—
265	C₂²⋊C₄×C₆₁	—	2	8	no	—
266	C₂²⋊C₄×C₆₁	—	2	4	no	—
267	C₂²⋊C₄×C₆₁	—	2	8	no	—
268	C₂²⋊C₄×C₆₁	—	4	4	no	—
269	C₂²⋊C₄×C₆₁	—	4	4	no	—
270	C₂²⋊C₄×C₆₁	—	4	2	no	—
271	C₂²⋊C₄×C₆₁	—	4	4	no	—
272	C₂²⋊C₄×C₆₁	—	4	4	no	—
273	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
274	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
275	C₂²⋊C₄×C₆₁	C₂²×C₄	1	16	yes	—
276	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	complemented
277	C₄²×C₆₁	—	2	8	no	—
278	C₄²×C₆₁	—	2	4	no	—
279	C₄²×C₆₁	—	2	2	no	—
280	C₄²×C₆₁	—	2	2	no	—
281	C₄²×C₆₁	—	2	4	no	—
282	C₄²×C₆₁	—	2	2	no	—
283	C₄²×C₆₁	—	2	2	no	—
284	C₄²×C₆₁	—	4	2	no	—
285	C₄²×C₆₁	—	4	2	no	—
286	C₄²×C₆₁	—	4	1	no	—
287	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
288	C₄²×C₆₁	C₂×D₄	1	4	yes	complemented
289	C₂³×C₆₁	—	2	2	no	—
290	C₂³×C₆₁	—	2	2	no	—
291	C₂³×C₆₁	—	2	2	no	—
292	C₂³×C₆₁	—	2	2	no	—
293	C₂³×C₆₁	—	2	2	no	—
294	C₂³×C₆₁	—	2	4	no	—
295	C₂³×C₆₁	—	2	2	no	—
296	C₂³×C₆₁	—	2	4	no	—
297	C₂³×C₆₁	—	2	2	no	—
298	C₂³×C₆₁	—	2	4	no	—
299	C₂³×C₆₁	—	2	4	no	—
300	C₂³×C₆₁	—	2	4	no	—
301	C₂³×C₆₁	—	2	2	no	—
302	C₂³×C₆₁	—	2	2	no	—
303	C₂³×C₆₁	—	2	2	no	—
304	C₂³×C₆₁	—	2	4	no	—
305	C₂³×C₆₁	—	2	32	no	—
306	C₂³×C₆₁	—	4	16	no	—
307	C₂³×C₆₁	—	4	16	no	—
308	C₂³×C₆₁	—	8	8	no	—
309	C₂³×C₆₁	—	8	8	no	—
310	C₂³×C₆₁	—	8	8	no	—
311	C₂³×C₆₁	—	8	8	no	—
312	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
313	C₂³×C₆₁	C₂³×C₄	1	8	yes	—
314	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
315	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
316	C₂³×C₆₁	C₂×#41	1	4	yes	—
317	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
318	D₄×C₆₁	—	2	32	no	—
319	D₄×C₆₁	—	2	16	no	—
320	D₄×C₆₁	—	2	8	no	—
321	D₄×C₆₁	—	2	16	no	—
322	D₄×C₆₁	—	4	16	no	—
323	D₄×C₆₁	—	4	8	no	—
324	D₄×C₆₁	C₄×D₄	1	16	yes	complemented
325	C₂×C₄×C₆₁	—	2	2	no	—
326	C₂×C₄×C₆₁	—	2	1	no	—
327	C₂×C₄×C₆₁	—	2	2	no	—
328	C₂×C₄×C₆₁	—	2	1	no	—
329	C₂×C₄×C₆₁	—	2	1	no	—
330	C₂×C₄×C₆₁	—	2	2	no	—
331	C₂×C₄×C₆₁	—	2	1	no	—
332	C₂×C₄×C₆₁	—	2	1	no	—
333	C₂×C₄×C₆₁	—	2	1	no	—
334	C₂×C₄×C₆₁	—	2	2	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	2	1	no	—
337	C₂×C₄×C₆₁	—	2	1	no	—
338	C₂×C₄×C₆₁	—	2	2	no	—
339	C₂×C₄×C₆₁	—	2	16	no	—
340	C₂×C₄×C₆₁	—	2	16	no	—
341	C₂×C₄×C₆₁	—	2	2	no	—
342	C₂×C₄×C₆₁	—	2	4	no	—
343	C₂×C₄×C₆₁	—	2	2	no	—
344	C₂×C₄×C₆₁	—	2	1	no	—
345	C₂×C₄×C₆₁	—	2	2	no	—
346	C₂×C₄×C₆₁	—	2	2	no	—
347	C₂×C₄×C₆₁	—	2	1	no	—
348	C₂×C₄×C₆₁	—	2	2	no	—
349	C₂×C₄×C₆₁	—	2	4	no	—
350	C₂×C₄×C₆₁	—	2	2	no	—
351	C₂×C₄×C₆₁	—	2	2	no	—
352	C₂×C₄×C₆₁	—	2	4	no	—
353	C₂×C₄×C₆₁	—	2	2	no	—
354	C₂×C₄×C₆₁	—	2	1	no	—
355	C₂×C₄×C₆₁	—	2	2	no	—
356	C₂×C₄×C₆₁	—	4	8	no	—
357	C₂×C₄×C₆₁	—	4	8	no	—
358	C₂×C₄×C₆₁	—	8	8	no	—
359	C₂×C₄×C₆₁	—	8	8	no	—
360	C₂×C₄×C₆₁	—	8	8	no	—
361	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
362	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
363	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
364	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
365	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
366	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
367	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
371	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
372	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
373	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
374	#34310	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂²×C₆₁	—	2	4	no	—
376	C₂²×C₆₁	—	2	4	no	—
377	C₂²×C₆₁	—	2	4	no	—
378	C₂²×C₆₁	—	2	4	no	—
379	C₂²×C₆₁	—	2	4	no	—
380	C₂²×C₆₁	—	2	4	no	—
381	C₂²×C₆₁	—	2	4	no	—
382	C₂²×C₆₁	—	2	8	no	—
383	C₂²×C₆₁	—	2	4	no	—
384	C₂²×C₆₁	—	2	8	no	—
385	C₂²×C₆₁	—	2	8	no	—
386	C₂²×C₆₁	—	2	4	no	—
387	C₂²×C₆₁	—	4	4	no	—
388	C₂²×C₆₁	—	4	2	no	—
389	C₂²×C₆₁	—	4	4	no	—
390	C₂²×C₆₁	—	4	2	no	—
391	C₂²×C₆₁	—	4	4	no	—
392	C₂²×C₆₁	—	4	2	no	—
393	C₂²×C₆₁	—	4	4	no	—
394	C₂²×C₆₁	—	4	2	no	—
395	C₂²×C₆₁	—	8	32	no	—
396	C₂²×C₆₁	C₂×C₄×D₄	1	8	yes	—
397	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
398	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
399	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
400	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂²×C₆₁	#585	1	1	yes	characteristic
404	C₄×C₆₁	—	2	4	no	—
405	C₄×C₆₁	—	2	4	no	—
406	C₄×C₆₁	—	2	2	no	—
407	C₄×C₆₁	—	2	2	no	—
408	C₄×C₆₁	—	2	4	no	—
409	C₄×C₆₁	—	2	2	no	—
410	C₄×C₆₁	—	2	2	no	—
411	C₄×C₆₁	—	4	2	no	—
412	C₄×C₆₁	—	4	2	no	—
413	C₄×C₆₁	—	4	4	no	—
414	C₄×C₆₁	—	4	1	no	—
415	C₄×C₆₁	—	4	2	no	—
416	C₄×C₆₁	C₂×C₄×D₄	1	4	yes	—
417	C₄×C₆₁	#518	1	4	yes	complemented
418	C₂×D₄²	C₂×C₆₁	1	1	yes	characteristic
419	C₂×#518	C₂×C₆₁	1	2	yes	complemented
420	#2366	C₂×C₆₁	1	1	yes	characteristic, complemented
421	#2363	C₂×C₆₁	1	2	yes	complemented
422	#2361	C₂×C₆₁	1	2	yes	complemented
423	#2358	C₂×C₆₁	1	4	yes	complemented
424	#2354	C₂×C₆₁	1	1	yes	characteristic, complemented
425	D₄×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
426	D₄×C₂²⋊C₄	C₂×C₆₁	1	2	yes	complemented
427	D₄×C₂²⋊C₄	C₂×C₆₁	1	2	yes	complemented
428	#2324	C₂×C₆₁	1	2	yes	complemented
429	#2321	C₂×C₆₁	1	4	yes	complemented
430	C₄×#127	C₂×C₆₁	1	1	yes	characteristic, complemented
431	C₄×#121	C₂×C₆₁	1	2	yes	complemented
432	#2293	C₂×C₆₁	1	1	yes	characteristic, complemented
433	C₂×#390	C₂×C₆₁	1	2	yes	complemented
434	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
435	C₂×C₆₁	—	2	8	no	—
436	C₂×C₆₁	—	4	8	no	—
437	C₂×C₆₁	—	4	4	no	—
438	C₂×C₆₁	C₂²×C₄×D₄	1	1	yes	characteristic
439	C₂×C₆₁	C₂×#518	1	1	yes	characteristic
440	C₂×C₆₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂×C₆₁	#3496	1	1	yes	characteristic
442	C₂×C₆₁	#3498	1	1	yes	characteristic
443	C₂×C₆₁	#3514	1	1	yes	characteristic
444	C₂×C₆₁	#3519	1	1	yes	characteristic
445	C₂³×D₄	C₂²×C₆₁	1	2	yes	—
446	C₂³×D₄	C₂²×C₆₁	1	2	yes	—
447	D₄²	C₄×C₆₁	1	16	yes	complemented
448	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
449	C₂×#121	C₂²×C₆₁	1	2	yes	—
450	C₂×#121	C₂²×C₆₁	1	2	yes	—
451	C₂×#120	C₂²×C₆₁	1	4	yes	—
452	#518	—	2	16	no	—
453	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
455	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
456	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
459	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	complemented
460	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	complemented
461	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
462	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
463	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
464	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
465	C₂×#117	C₂²×C₆₁	1	2	yes	complemented
466	C₂×#117	C₂²×C₆₁	1	2	yes	complemented
467	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
468	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	complemented
469	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	complemented
470	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	complemented
471	C₂²×C₄²	C₂²×C₆₁	1	2	yes	complemented
472	#390	C₂²×C₆₁	1	1	yes	characteristic
473	#390	C₂²×C₆₁	1	2	yes	—
474	#390	C₂²×C₆₁	1	1	yes	characteristic
475	#390	C₂²×C₆₁	1	2	yes	complemented
476	#390	C₂²×C₆₁	1	2	yes	complemented
477	#390	C₂²×C₆₁	1	2	yes	complemented
478	#390	C₂²×C₆₁	1	4	yes	complemented
479	#390	C₂²×C₆₁	1	2	yes	complemented
480	#390	C₂²×C₆₁	1	4	yes	complemented
481	#390	C₂²×C₆₁	1	2	yes	complemented
482	#389	C₂²×C₆₁	1	2	yes	complemented
483	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
484	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
485	#388	C₂²×C₆₁	1	2	yes	complemented
486	#388	C₂²×C₆₁	1	4	yes	complemented
487	#388	C₂²×C₆₁	1	4	yes	complemented
488	#388	C₂²×C₆₁	1	4	yes	complemented
489	#388	C₂²×C₆₁	1	2	yes	complemented
490	#386	C₂²×C₆₁	1	4	yes	complemented
491	#386	C₂²×C₆₁	1	4	yes	complemented
492	#386	C₂²×C₆₁	1	4	yes	complemented
493	#386	C₂²×C₆₁	1	4	yes	complemented
494	#386	C₂²×C₆₁	1	4	yes	complemented
495	#385	C₂²×C₆₁	1	4	yes	complemented
496	#385	C₂²×C₆₁	1	4	yes	complemented
497	#384	C₂²×C₆₁	1	1	yes	characteristic, complemented
498	#380	C₂²×C₆₁	1	2	yes	complemented
499	#380	C₂²×C₆₁	1	2	yes	complemented
500	#379	C₂²×C₆₁	1	4	yes	complemented
501	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
502	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
503	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
504	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
505	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
506	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
507	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
508	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
509	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
510	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	complemented
511	C₄³	C₂²×C₆₁	1	1	yes	characteristic, complemented
512	C₆₁	#34310	1	1	yes	characteristic, direct product factor, Sylow
513	C₂⁵	C₂³×C₆₁	1	4	yes	—
514	C₂²×D₄	—	2	8	no	—
515	C₂²×D₄	—	2	8	no	—
516	C₂²×D₄	—	4	4	no	—
517	C₂²×D₄	—	4	4	no	—
518	C₂²×D₄	C₂×C₄×C₆₁	1	16	yes	complemented
519	C₂²×D₄	C₂×C₄×C₆₁	1	16	yes	complemented
520	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
521	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
522	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
523	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
524	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
525	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
526	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
528	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
529	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
530	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
531	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
532	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
533	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
534	#127	C₂×C₄×C₆₁	1	8	yes	complemented
535	#121	C₂×C₄×C₆₁	1	16	yes	complemented
536	#121	C₂×C₄×C₆₁	1	16	yes	complemented
537	#120	C₂×C₄×C₆₁	1	32	yes	complemented
538	C₄×D₄	—	2	8	no	—
539	C₄×D₄	—	2	4	no	—
540	C₄×D₄	—	2	16	no	—
541	C₄×D₄	—	2	8	no	—
542	C₄×D₄	—	2	16	no	—
543	C₄×D₄	—	2	8	no	—
544	C₄×D₄	—	4	4	no	—
545	C₄×D₄	—	4	4	no	—
546	C₄×D₄	—	4	4	no	—
547	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	complemented
548	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	complemented
549	C₄×D₄	D₄×C₆₁	1	8	yes	complemented
550	#117	—	2	8	no	—
551	#117	—	2	8	no	—
552	C₂×C₄⋊C₄	—	4	4	no	—
553	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
561	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
565	C₂×C₂²⋊C₄	—	2	16	no	—
566	C₂×C₂²⋊C₄	—	2	16	no	—
567	C₂×C₂²⋊C₄	—	4	8	no	—
568	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
586	C₂×C₄²	—	4	4	no	—
587	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
588	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
589	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
593	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
596	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
597	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
599	#95	C₂³×C₆₁	1	2	yes	—
600	#95	C₂³×C₆₁	1	2	yes	—
601	#95	C₂³×C₆₁	1	2	yes	—
602	#95	C₂³×C₆₁	1	2	yes	—
603	#95	C₂³×C₆₁	1	4	yes	—
604	#95	C₂³×C₆₁	1	2	yes	—
605	#95	C₂³×C₆₁	1	4	yes	—
606	#95	C₂³×C₆₁	1	2	yes	—
607	C₂⁴	—	2	8	no	—
608	C₂⁴	—	2	8	no	—
609	C₂⁴	—	4	4	no	—
610	C₂⁴	—	4	4	no	—
611	C₂⁴	—	4	4	no	—
612	C₂⁴	—	4	4	no	—
613	C₂⁴	C₂²×C₄×C₆₁	1	16	yes	—
614	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
615	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
616	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
617	C₂×D₄	—	2	8	no	—
618	C₂×D₄	—	2	8	no	—
619	C₂×D₄	—	2	64	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	4	32	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	2	no	—
631	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
632	C₂×D₄	C₂²×C₄×C₆₁	1	16	yes	—
633	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
634	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
635	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
636	C₂×D₄	C₂²×C₄×C₆₁	1	16	yes	—
637	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
638	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
639	C₂×D₄	#41×C₆₁	1	4	yes	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	8	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	8	no	—
648	C₂²×C₄	—	2	8	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	—	4	4	no	—
654	C₂²×C₄	—	4	4	no	—
655	C₂²×C₄	—	4	4	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
659	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
660	C₂²×C₄	C₂×D₄×C₆₁	1	8	yes	complemented
661	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
666	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	4	4	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
685	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
686	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	complemented
687	C₂²⋊C₄	—	2	8	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	8	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	8	no	—
693	C₂²⋊C₄	—	2	8	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	8	no	—
696	C₂²⋊C₄	—	4	4	no	—
697	C₂²⋊C₄	—	4	4	no	—
698	C₂²⋊C₄	—	4	4	no	—
699	C₂²⋊C₄	—	4	4	no	—
700	C₂²⋊C₄	—	4	2	no	—
701	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
702	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
703	C₂²⋊C₄	C₂²×C₄×C₆₁	1	16	yes	—
704	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	complemented
705	C₄²	—	2	8	no	—
706	C₄²	—	2	4	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	2	no	—
709	C₄²	—	2	4	no	—
710	C₄²	—	2	2	no	—
711	C₄²	—	2	2	no	—
712	C₄²	—	4	2	no	—
713	C₄²	—	4	2	no	—
714	C₄²	—	4	1	no	—
715	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
716	C₄²	C₂×D₄×C₆₁	1	4	yes	complemented
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	4	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	32	no	—
734	C₂³	—	4	16	no	—
735	C₂³	—	4	16	no	—
736	C₂³	—	8	8	no	—
737	C₂³	—	8	8	no	—
738	C₂³	—	8	8	no	—
739	C₂³	—	8	8	no	—
740	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
741	C₂³	C₂³×C₄×C₆₁	1	8	yes	—
742	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
743	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
744	C₂³	C₂×#41×C₆₁	1	4	yes	—
745	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
746	D₄	—	2	32	no	—
747	D₄	—	2	16	no	—
748	D₄	—	2	8	no	—
749	D₄	—	2	16	no	—
750	D₄	—	4	16	no	—
751	D₄	—	4	8	no	—
752	D₄	C₄×D₄×C₆₁	1	16	yes	complemented
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	16	no	—
768	C₂×C₄	—	2	16	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	8	no	—
786	C₂×C₄	—	8	8	no	—
787	C₂×C₄	—	8	8	no	—
788	C₂×C₄	—	8	8	no	—
789	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
790	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
791	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
792	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
793	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
795	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
798	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
799	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
800	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
801	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	8	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	8	no	—
812	C₂²	—	2	8	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	4	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	32	no	—
823	C₂²	C₂×C₄×D₄×C₆₁	1	8	yes	—
824	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
825	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
826	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
827	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
828	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
829	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
830	C₂²	C₆₁×#585	1	1	yes	characteristic
831	C₄	—	2	4	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	4	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	4	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	C₂×C₄×D₄×C₆₁	1	4	yes	—
844	C₄	C₆₁×#518	1	4	yes	complemented
845	C₂	—	2	8	no	—
846	C₂	—	4	4	no	—
847	C₂	—	4	8	no	—
848	C₂	C₂²×C₄×D₄×C₆₁	1	1	yes	characteristic
849	C₂	C₂×C₆₁×#518	1	1	yes	characteristic
850	C₂	C₄×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
851	C₂	C₆₁×#3496	1	1	yes	characteristic
852	C₂	C₆₁×#3498	1	1	yes	characteristic
853	C₂	C₆₁×#3514	1	1	yes	characteristic
854	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×D₄²×C₆₁	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. C₂×C₆₁×#518	C₂	semidirect
3. C₆₁×#2366	C₂	semidirect
4. C₆₁×#2363	C₂	semidirect
5. C₆₁×#2361	C₂	semidirect
6. C₆₁×#2358	C₂	semidirect
7. C₆₁×#2354	C₂	semidirect
8. D₄×C₄⋊C₄×C₆₁	C₂	semidirect
9. D₄×C₂²⋊C₄×C₆₁	C₂	semidirect
10. D₄×C₂²⋊C₄×C₆₁	C₂	semidirect
11. C₆₁×#2324	C₂	semidirect
12. C₆₁×#2321	C₂	semidirect
13. C₄×#127×C₆₁	C₂	semidirect
14. C₄×#121×C₆₁	C₂	semidirect
15. C₆₁×#2293	C₂	semidirect
16. C₂×C₆₁×#390	C₂	semidirect
17. C₄²×D₄×C₆₁	C₂	semidirect
20. D₄²×C₆₁	C₄	semidirect
31. C₂×C₄×D₄×C₆₁	C₂²	semidirect
32. C₂×C₄×D₄×C₆₁	C₂²	semidirect
33. C₂×C₄×D₄×C₆₁	C₂²	semidirect
34. C₂×C₄×D₄×C₆₁	C₂²	semidirect
35. C₂×C₄×D₄×C₆₁	C₂²	semidirect
36. C₂×C₄×D₄×C₆₁	C₂²	semidirect
37. C₂×C₄×D₄×C₆₁	C₂²	semidirect
38. C₂×#117×C₆₁	C₂²	semidirect
39. C₂×#117×C₆₁	C₂²	semidirect
40. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
41. C₂²×C₂²⋊C₄×C₆₁	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₆₁	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₆₁	C₂²	semidirect
44. C₂²×C₄²×C₆₁	C₂²	semidirect
48. C₆₁×#390	C₂²	semidirect
49. C₆₁×#390	C₂²	semidirect
50. C₆₁×#390	C₂²	semidirect
51. C₆₁×#390	C₂²	semidirect
52. C₆₁×#390	C₂²	semidirect
53. C₆₁×#390	C₂²	semidirect
54. C₆₁×#390	C₂²	semidirect
55. C₆₁×#389	C₂²	semidirect
56. C₆₁×#389	C₂²	semidirect
57. C₆₁×#389	C₂²	semidirect
58. C₆₁×#388	C₂²	semidirect
59. C₆₁×#388	C₂²	semidirect
60. C₆₁×#388	C₂²	semidirect
61. C₆₁×#388	C₂²	semidirect
62. C₆₁×#388	C₂²	semidirect
63. C₆₁×#386	C₂²	semidirect
64. C₆₁×#386	C₂²	semidirect
65. C₆₁×#386	C₂²	semidirect
66. C₆₁×#386	C₂²	semidirect
67. C₆₁×#386	C₂²	semidirect
68. C₆₁×#385	C₂²	semidirect
69. C₆₁×#385	C₂²	semidirect
70. C₆₁×#384	C₂²	semidirect
71. C₆₁×#380	C₂²	semidirect
72. C₆₁×#380	C₂²	semidirect
73. C₆₁×#379	C₂²	semidirect
74. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
75. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
76. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
77. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
78. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
79. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
80. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
81. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
84. C₄³×C₆₁	C₂²	semidirect
90. C₂²×D₄×C₆₁	C₂×C₄	semidirect
91. C₂²×D₄×C₆₁	C₂×C₄	semidirect
106. #127×C₆₁	C₂×C₄	semidirect
107. #121×C₆₁	C₂×C₄	semidirect
108. #121×C₆₁	C₂×C₄	semidirect
109. #120×C₆₁	C₂×C₄	semidirect
119. C₄×D₄×C₆₁	C₂×C₄	semidirect
120. C₄×D₄×C₆₁	C₂×C₄	semidirect
121. C₄×D₄×C₆₁	D₄	semidirect
232. C₂²×C₄×C₆₁	C₂×D₄	semidirect
258. C₄⋊C₄×C₆₁	C₂×D₄	semidirect
276. C₂²⋊C₄×C₆₁	C₂×D₄	semidirect
288. C₄²×C₆₁	C₂×D₄	semidirect
324. D₄×C₆₁	C₄×D₄	semidirect
374. #34310	C₆₁	direct (N × H)
417. C₄×C₆₁	#518	semidirect
419. C₂×#518	C₂×C₆₁	semidirect
420. #2366	C₂×C₆₁	semidirect
421. #2363	C₂×C₆₁	semidirect
422. #2361	C₂×C₆₁	semidirect
423. #2358	C₂×C₆₁	semidirect
424. #2354	C₂×C₆₁	semidirect
425. D₄×C₄⋊C₄	C₂×C₆₁	semidirect
426. D₄×C₂²⋊C₄	C₂×C₆₁	semidirect
427. D₄×C₂²⋊C₄	C₂×C₆₁	semidirect
428. #2324	C₂×C₆₁	semidirect
429. #2321	C₂×C₆₁	semidirect
430. C₄×#127	C₂×C₆₁	semidirect
431. C₄×#121	C₂×C₆₁	semidirect
432. #2293	C₂×C₆₁	semidirect
433. C₂×#390	C₂×C₆₁	semidirect
434. C₄²×D₄	C₂×C₆₁	semidirect
447. D₄²	C₄×C₆₁	semidirect
458. C₂×C₄×D₄	C₂²×C₆₁	semidirect
459. C₂×C₄×D₄	C₂²×C₆₁	semidirect
460. C₂×C₄×D₄	C₂²×C₆₁	semidirect
461. C₂×C₄×D₄	C₂²×C₆₁	semidirect
462. C₂×C₄×D₄	C₂²×C₆₁	semidirect
463. C₂×C₄×D₄	C₂²×C₆₁	semidirect
464. C₂×C₄×D₄	C₂²×C₆₁	semidirect
465. C₂×#117	C₂²×C₆₁	semidirect
466. C₂×#117	C₂²×C₆₁	semidirect
467. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
468. C₂²×C₂²⋊C₄	C₂²×C₆₁	semidirect
469. C₂²×C₂²⋊C₄	C₂²×C₆₁	semidirect
470. C₂²×C₂²⋊C₄	C₂²×C₆₁	semidirect
471. C₂²×C₄²	C₂²×C₆₁	semidirect
475. #390	C₂²×C₆₁	semidirect
476. #390	C₂²×C₆₁	semidirect
477. #390	C₂²×C₆₁	semidirect
478. #390	C₂²×C₆₁	semidirect
479. #390	C₂²×C₆₁	semidirect
480. #390	C₂²×C₆₁	semidirect
481. #390	C₂²×C₆₁	semidirect
482. #389	C₂²×C₆₁	semidirect
483. #389	C₂²×C₆₁	semidirect
484. #389	C₂²×C₆₁	semidirect
485. #388	C₂²×C₆₁	semidirect
486. #388	C₂²×C₆₁	semidirect
487. #388	C₂²×C₆₁	semidirect
488. #388	C₂²×C₆₁	semidirect
489. #388	C₂²×C₆₁	semidirect
490. #386	C₂²×C₆₁	semidirect
491. #386	C₂²×C₆₁	semidirect
492. #386	C₂²×C₆₁	semidirect
493. #386	C₂²×C₆₁	semidirect
494. #386	C₂²×C₆₁	semidirect
495. #385	C₂²×C₆₁	semidirect
496. #385	C₂²×C₆₁	semidirect
497. #384	C₂²×C₆₁	semidirect
498. #380	C₂²×C₆₁	semidirect
499. #380	C₂²×C₆₁	semidirect
500. #379	C₂²×C₆₁	semidirect
501. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
502. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
503. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
504. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
505. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
506. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
507. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
508. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
509. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
510. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
511. C₄³	C₂²×C₆₁	semidirect
512. C₆₁	#34310	direct (N × H)
518. C₂²×D₄	C₂×C₄×C₆₁	semidirect
519. C₂²×D₄	C₂×C₄×C₆₁	semidirect
534. #127	C₂×C₄×C₆₁	semidirect
535. #121	C₂×C₄×C₆₁	semidirect
536. #121	C₂×C₄×C₆₁	semidirect
537. #120	C₂×C₄×C₆₁	semidirect
547. C₄×D₄	C₂×C₄×C₆₁	semidirect
548. C₄×D₄	C₂×C₄×C₆₁	semidirect
549. C₄×D₄	D₄×C₆₁	semidirect
660. C₂²×C₄	C₂×D₄×C₆₁	semidirect
686. C₄⋊C₄	C₂×D₄×C₆₁	semidirect
704. C₂²⋊C₄	C₂×D₄×C₆₁	semidirect
716. C₄²	C₂×D₄×C₆₁	semidirect
752. D₄	C₄×D₄×C₆₁	semidirect
844. C₄	C₆₁×#518	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₆₁	2
C₂×C₆₁×#518	2
C₆₁×#2366	2
C₆₁×#2363	2
C₆₁×#2361	2
C₆₁×#2358	2
C₆₁×#2354	2
D₄×C₄⋊C₄×C₆₁	2
D₄×C₂²⋊C₄×C₆₁	2
C₆₁×#2324	2
C₆₁×#2321	2
C₄×#127×C₆₁	2
C₄×#121×C₆₁	2
C₆₁×#2293	2
C₂×C₆₁×#390	2
C₄²×D₄×C₆₁	2
#34310	61

Subgroups — C61×#34310 #29537743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34310 #29537743