Subgroups — C₆₁×#34334 #29537767

Order 15616.

2500 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2369	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2368	C₂	1	4	yes	maximal, complemented
4	C₆₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2360	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2349	C₂	1	2	yes	maximal
8	D₄×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
9	Q₈×C₂²⋊C₄×C₆₁	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2331	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2329	C₂	1	4	yes	maximal, complemented
12	C₄×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂²⋊Q₈×C₆₁	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₆₁×#391	C₂	1	2	yes	maximal, complemented
16	C₆₁×#2275	C₂	1	2	yes	maximal
17	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic
18	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
19	D₄×Q₈×C₆₁	C₄	1	16	yes	complemented
20	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
33	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
34	C₆₁×#391	C₂²	1	1	yes	characteristic
35	C₆₁×#391	C₂²	1	2	yes	—
36	C₆₁×#391	C₂²	1	4	yes	—
37	C₆₁×#391	C₂²	1	2	yes	—
38	C₆₁×#391	C₂²	1	2	yes	—
39	C₆₁×#391	C₂²	1	4	yes	—
40	C₆₁×#391	C₂²	1	1	yes	characteristic
41	C₆₁×#391	C₂²	1	4	yes	—
42	C₆₁×#391	C₂²	1	4	yes	—
43	C₆₁×#389	C₂²	1	1	yes	characteristic
44	C₆₁×#389	C₂²	1	1	yes	characteristic
45	C₆₁×#389	C₂²	1	2	yes	—
46	C₆₁×#389	C₂²	1	2	yes	—
47	C₆₁×#389	C₂²	1	4	yes	—
48	C₆₁×#389	C₂²	1	2	yes	—
49	C₆₁×#389	C₂²	1	2	yes	—
50	C₆₁×#387	C₂²	1	2	yes	—
51	C₆₁×#387	C₂²	1	2	yes	—
52	C₆₁×#387	C₂²	1	4	yes	—
53	C₆₁×#387	C₂²	1	4	yes	—
54	C₆₁×#387	C₂²	1	4	yes	—
55	C₆₁×#387	C₂²	1	4	yes	—
56	C₆₁×#385	C₂²	1	4	yes	—
57	C₆₁×#385	C₂²	1	4	yes	—
58	C₆₁×#385	C₂²	1	4	yes	—
59	C₆₁×#384	C₂²	1	1	yes	characteristic
60	C₆₁×#382	C₂²	1	2	yes	—
61	C₆₁×#380	C₂²	1	2	yes	—
62	C₆₁×#380	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
73	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
79	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
80	C₆₁×#376	C₂²	1	2	yes	—
81	C₂×#95×C₆₁	C₂²	1	4	yes	—
82	C₂×#95×C₆₁	C₂²	1	4	yes	—
83	C₄³×C₆₁	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₆₁	—	4	4	no	—
85	C₂²×Q₈×C₆₁	—	4	4	no	—
86	C₂²×Q₈×C₆₁	C₂×C₄	1	16	yes	complemented
87	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
90	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
94	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
95	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
97	C₄⋊Q₈×C₆₁	C₂×C₄	1	16	yes	complemented
98	C₂²⋊Q₈×C₆₁	C₂×C₄	1	16	yes	complemented
99	C₂²⋊Q₈×C₆₁	C₂×C₄	1	32	yes	complemented
100	C₄×Q₈×C₆₁	—	4	4	no	—
101	C₄×Q₈×C₆₁	—	4	4	no	—
102	C₄×Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
103	C₄×D₄×C₆₁	—	2	4	no	—
104	C₄×D₄×C₆₁	—	2	8	no	—
105	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	—
106	C₄×D₄×C₆₁	C₂×C₄	1	16	yes	—
107	C₄×D₄×C₆₁	Q₈	1	8	yes	complemented
108	C₂×C₄⋊C₄×C₆₁	—	4	4	no	—
109	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
132	C₂×C₄²×C₆₁	—	4	4	no	—
133	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
141	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
143	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
144	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
145	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
147	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
148	#95×C₆₁	C₂³	1	2	yes	—
149	#95×C₆₁	C₂³	1	2	yes	—
150	#95×C₆₁	C₂³	1	4	yes	—
151	#95×C₆₁	C₂³	1	4	yes	—
152	#95×C₆₁	C₂³	1	4	yes	—
153	#95×C₆₁	C₂³	1	4	yes	—
154	#95×C₆₁	C₂³	1	4	yes	—
155	#95×C₆₁	C₂³	1	4	yes	—
156	#95×C₆₁	C₂³	1	2	yes	—
157	#95×C₆₁	C₂³	1	2	yes	—
158	#95×C₆₁	C₂³	1	2	yes	—
159	#95×C₆₁	C₂³	1	2	yes	—
160	#95×C₆₁	C₂³	1	2	yes	—
161	#95×C₆₁	C₂³	1	2	yes	—
162	#95×C₆₁	C₂³	1	2	yes	—
163	#95×C₆₁	C₂³	1	4	yes	—
164	#95×C₆₁	C₂³	1	4	yes	—
165	#95×C₆₁	C₂³	1	2	yes	—
166	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
167	C₂×Q₈×C₆₁	—	2	4	no	—
168	C₂×Q₈×C₆₁	—	2	4	no	—
169	C₂×Q₈×C₆₁	—	2	2	no	—
170	C₂×Q₈×C₆₁	—	2	2	no	—
171	C₂×Q₈×C₆₁	—	4	4	no	—
172	C₂×Q₈×C₆₁	—	4	4	no	—
173	C₂×Q₈×C₆₁	—	4	32	no	—
174	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
175	C₂×Q₈×C₆₁	C₂²×C₄	1	8	yes	—
176	C₂×Q₈×C₆₁	C₂²×C₄	1	16	yes	—
177	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
178	C₂×D₄×C₆₁	C₂×Q₈	1	4	yes	—
179	C₂×D₄×C₆₁	#41	1	4	yes	—
180	C₂²×C₄×C₆₁	—	2	4	no	—
181	C₂²×C₄×C₆₁	—	2	4	no	—
182	C₂²×C₄×C₆₁	—	2	4	no	—
183	C₂²×C₄×C₆₁	—	2	8	no	—
184	C₂²×C₄×C₆₁	—	2	4	no	—
185	C₂²×C₄×C₆₁	—	4	2	no	—
186	C₂²×C₄×C₆₁	—	4	2	no	—
187	C₂²×C₄×C₆₁	—	4	2	no	—
188	C₂²×C₄×C₆₁	—	4	4	no	—
189	C₂²×C₄×C₆₁	—	4	4	no	—
190	C₂²×C₄×C₆₁	—	4	4	no	—
191	C₂²×C₄×C₆₁	—	4	4	no	—
192	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
193	C₂²×C₄×C₆₁	C₂²×C₄	1	16	yes	—
194	C₂²×C₄×C₆₁	C₂×Q₈	1	8	yes	complemented
195	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
211	C₄⋊C₄×C₆₁	—	2	2	no	—
212	C₄⋊C₄×C₆₁	—	2	4	no	—
213	C₄⋊C₄×C₆₁	—	2	2	no	—
214	C₄⋊C₄×C₆₁	—	2	4	no	—
215	C₄⋊C₄×C₆₁	—	2	2	no	—
216	C₄⋊C₄×C₆₁	—	2	4	no	—
217	C₄⋊C₄×C₆₁	—	4	4	no	—
218	C₄⋊C₄×C₆₁	—	4	2	no	—
219	C₄⋊C₄×C₆₁	—	4	2	no	—
220	C₄⋊C₄×C₆₁	—	4	4	no	—
221	C₄⋊C₄×C₆₁	—	4	4	no	—
222	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
223	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
224	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
225	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
226	C₄⋊C₄×C₆₁	C₂²×C₄	1	16	yes	—
227	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
228	C₄⋊C₄×C₆₁	C₂×Q₈	1	4	yes	complemented
229	C₂²⋊C₄×C₆₁	—	2	4	no	—
230	C₂²⋊C₄×C₆₁	—	2	8	no	—
231	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
232	C₂²⋊C₄×C₆₁	C₂²×C₄	1	16	yes	—
233	C₂²⋊C₄×C₆₁	C₂×Q₈	1	8	yes	complemented
234	C₄²×C₆₁	—	2	2	no	—
235	C₄²×C₆₁	—	2	4	no	—
236	C₄²×C₆₁	—	2	2	no	—
237	C₄²×C₆₁	—	2	4	no	—
238	C₄²×C₆₁	—	2	2	no	—
239	C₄²×C₆₁	—	2	2	no	—
240	C₄²×C₆₁	—	4	2	no	—
241	C₄²×C₆₁	—	4	2	no	—
242	C₄²×C₆₁	—	4	4	no	—
243	C₄²×C₆₁	—	4	1	no	—
244	C₄²×C₆₁	—	4	4	no	—
245	C₄²×C₆₁	—	4	4	no	—
246	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
247	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
248	C₄²×C₆₁	C₂×Q₈	1	4	yes	complemented
249	C₂³×C₆₁	—	2	2	no	—
250	C₂³×C₆₁	—	2	2	no	—
251	C₂³×C₆₁	—	2	2	no	—
252	C₂³×C₆₁	—	2	2	no	—
253	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
254	C₂³×C₆₁	C₂²×Q₈	1	4	yes	—
255	C₂³×C₆₁	C₂×#41	1	4	yes	—
256	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
257	Q₈×C₆₁	—	2	8	no	—
258	Q₈×C₆₁	—	2	16	no	—
259	Q₈×C₆₁	—	4	16	no	—
260	D₄×C₆₁	C₄×Q₈	1	16	yes	complemented
261	C₂×C₄×C₆₁	—	2	1	no	—
262	C₂×C₄×C₆₁	—	2	1	no	—
263	C₂×C₄×C₆₁	—	2	2	no	—
264	C₂×C₄×C₆₁	—	2	1	no	—
265	C₂×C₄×C₆₁	—	2	1	no	—
266	C₂×C₄×C₆₁	—	2	2	no	—
267	C₂×C₄×C₆₁	—	2	4	no	—
268	C₂×C₄×C₆₁	—	2	4	no	—
269	C₂×C₄×C₆₁	—	2	2	no	—
270	C₂×C₄×C₆₁	—	2	2	no	—
271	C₂×C₄×C₆₁	—	2	2	no	—
272	C₂×C₄×C₆₁	—	2	1	no	—
273	C₂×C₄×C₆₁	—	2	1	no	—
274	C₂×C₄×C₆₁	—	2	2	no	—
275	C₂×C₄×C₆₁	—	2	2	no	—
276	C₂×C₄×C₆₁	—	2	2	no	—
277	C₂×C₄×C₆₁	—	2	1	no	—
278	C₂×C₄×C₆₁	—	2	1	no	—
279	C₂×C₄×C₆₁	—	2	16	no	—
280	C₂×C₄×C₆₁	—	2	1	no	—
281	C₂×C₄×C₆₁	—	2	2	no	—
282	C₂×C₄×C₆₁	—	2	2	no	—
283	C₂×C₄×C₆₁	—	2	4	no	—
284	C₂×C₄×C₆₁	—	2	2	no	—
285	C₂×C₄×C₆₁	—	2	2	no	—
286	C₂×C₄×C₆₁	—	2	1	no	—
287	C₂×C₄×C₆₁	—	2	2	no	—
288	C₂×C₄×C₆₁	—	2	4	no	—
289	C₂×C₄×C₆₁	—	2	2	no	—
290	C₂×C₄×C₆₁	—	2	2	no	—
291	C₂×C₄×C₆₁	—	2	2	no	—
292	C₂×C₄×C₆₁	—	2	1	no	—
293	C₂×C₄×C₆₁	—	2	4	no	—
294	C₂×C₄×C₆₁	—	2	2	no	—
295	C₂×C₄×C₆₁	—	4	16	no	—
296	C₂×C₄×C₆₁	—	4	8	no	—
297	C₂×C₄×C₆₁	—	4	8	no	—
298	C₂×C₄×C₆₁	—	8	8	no	—
299	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
300	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
301	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
302	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
303	C₂×C₄×C₆₁	C₂³×C₄	1	8	yes	—
304	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
305	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
306	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
307	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
308	C₂×C₄×C₆₁	C₂²×Q₈	1	4	yes	—
309	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
310	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
311	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
312	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
313	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
314	#34334	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂²×C₆₁	—	2	4	no	—
316	C₂²×C₆₁	—	2	4	no	—
317	C₂²×C₆₁	—	2	4	no	—
318	C₂²×C₆₁	—	2	4	no	—
319	C₂²×C₆₁	—	2	4	no	—
320	C₂²×C₆₁	—	2	4	no	—
321	C₂²×C₆₁	C₂×C₄×Q₈	1	8	yes	—
322	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
323	C₂²×C₆₁	C₂³×Q₈	1	1	yes	characteristic
324	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
325	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
327	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
328	C₂²×C₆₁	#585	1	1	yes	characteristic
329	C₄×C₆₁	—	2	4	no	—
330	C₄×C₆₁	—	2	4	no	—
331	C₄×C₆₁	—	2	8	no	—
332	C₄×C₆₁	—	2	2	no	—
333	C₄×C₆₁	—	2	4	no	—
334	C₄×C₆₁	—	2	2	no	—
335	C₄×C₆₁	—	2	4	no	—
336	C₄×C₆₁	—	2	2	no	—
337	C₄×C₆₁	—	2	2	no	—
338	C₄×C₆₁	—	4	1	no	—
339	C₄×C₆₁	—	4	4	no	—
340	C₄×C₆₁	—	4	2	no	—
341	C₄×C₆₁	—	4	2	no	—
342	C₄×C₆₁	—	4	2	no	—
343	C₄×C₆₁	C₂×C₄×Q₈	1	4	yes	—
344	C₄×C₆₁	#518	1	4	yes	—
345	C₂×D₄×Q₈	C₂×C₆₁	1	1	yes	characteristic
346	#2369	C₂×C₆₁	1	2	yes	complemented
347	#2368	C₂×C₆₁	1	4	yes	complemented
348	#2365	C₂×C₆₁	1	1	yes	characteristic, complemented
349	#2360	C₂×C₆₁	1	2	yes	complemented
350	#2355	C₂×C₆₁	1	1	yes	characteristic, complemented
351	#2349	C₂×C₆₁	1	2	yes	—
352	D₄×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic
353	Q₈×C₂²⋊C₄	C₂×C₆₁	1	2	yes	complemented
354	#2331	C₂×C₆₁	1	2	yes	complemented
355	#2329	C₂×C₆₁	1	4	yes	complemented
356	C₄×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
357	C₄×C₂²⋊Q₈	C₂×C₆₁	1	2	yes	complemented
358	#2295	C₂×C₆₁	1	1	yes	characteristic, complemented
359	C₂×#391	C₂×C₆₁	1	2	yes	complemented
360	#2275	C₂×C₆₁	1	2	yes	—
361	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic
362	C₂×C₆₁	—	2	8	no	—
363	C₂×C₆₁	C₂²×C₄×Q₈	1	1	yes	characteristic
364	C₂×C₆₁	C₂×#518	1	1	yes	characteristic
365	C₂×C₆₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
366	C₂×C₆₁	#3501	1	1	yes	characteristic
367	C₂×C₆₁	#3503	1	1	yes	characteristic
368	C₂×C₆₁	#3514	1	1	yes	characteristic
369	C₂×C₆₁	#3520	1	1	yes	characteristic
370	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
371	D₄×Q₈	C₄×C₆₁	1	16	yes	complemented
372	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
373	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
374	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	—
375	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
376	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
377	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
378	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
379	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
380	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
384	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
385	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
386	#391	C₂²×C₆₁	1	2	yes	—
387	#391	C₂²×C₆₁	1	4	yes	—
388	#391	C₂²×C₆₁	1	4	yes	—
389	#391	C₂²×C₆₁	1	4	yes	—
390	#391	C₂²×C₆₁	1	1	yes	characteristic
391	#391	C₂²×C₆₁	1	2	yes	—
392	#391	C₂²×C₆₁	1	2	yes	—
393	#391	C₂²×C₆₁	1	4	yes	—
394	#391	C₂²×C₆₁	1	1	yes	characteristic
395	#389	C₂²×C₆₁	1	2	yes	—
396	#389	C₂²×C₆₁	1	2	yes	—
397	#389	C₂²×C₆₁	1	4	yes	—
398	#389	C₂²×C₆₁	1	2	yes	—
399	#389	C₂²×C₆₁	1	2	yes	—
400	#389	C₂²×C₆₁	1	1	yes	characteristic
401	#389	C₂²×C₆₁	1	1	yes	characteristic
402	#387	C₂²×C₆₁	1	2	yes	—
403	#387	C₂²×C₆₁	1	4	yes	—
404	#387	C₂²×C₆₁	1	4	yes	—
405	#387	C₂²×C₆₁	1	4	yes	—
406	#387	C₂²×C₆₁	1	4	yes	—
407	#387	C₂²×C₆₁	1	2	yes	—
408	#385	C₂²×C₆₁	1	4	yes	—
409	#385	C₂²×C₆₁	1	4	yes	—
410	#385	C₂²×C₆₁	1	4	yes	—
411	#384	C₂²×C₆₁	1	1	yes	characteristic
412	#382	C₂²×C₆₁	1	2	yes	—
413	#380	C₂²×C₆₁	1	4	yes	—
414	#380	C₂²×C₆₁	1	2	yes	—
415	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
417	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
418	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
420	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
421	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
422	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
423	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
425	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
426	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
427	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
428	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
429	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
430	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
431	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
432	#376	C₂²×C₆₁	1	2	yes	—
433	C₂×#95	C₂²×C₆₁	1	4	yes	—
434	C₂×#95	C₂²×C₆₁	1	4	yes	—
435	C₄³	C₂²×C₆₁	1	1	yes	characteristic
436	C₆₁	#34334	1	1	yes	characteristic, direct product factor, Sylow
437	C₂²×Q₈	—	4	4	no	—
438	C₂²×Q₈	—	4	4	no	—
439	C₂²×Q₈	C₂×C₄×C₆₁	1	16	yes	complemented
440	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
441	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
443	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
445	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
446	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
447	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
448	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
449	C₄⋊Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
450	C₄⋊Q₈	C₂×C₄×C₆₁	1	16	yes	complemented
451	C₂²⋊Q₈	C₂×C₄×C₆₁	1	16	yes	complemented
452	C₂²⋊Q₈	C₂×C₄×C₆₁	1	32	yes	complemented
453	C₄×Q₈	—	4	4	no	—
454	C₄×Q₈	—	4	4	no	—
455	C₄×Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
456	C₄×D₄	—	2	4	no	—
457	C₄×D₄	—	2	8	no	—
458	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	—
459	C₄×D₄	C₂×C₄×C₆₁	1	16	yes	—
460	C₄×D₄	Q₈×C₆₁	1	8	yes	complemented
461	C₂×C₄⋊C₄	—	4	4	no	—
462	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
485	C₂×C₄²	—	4	4	no	—
486	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
488	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
490	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
493	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
494	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
496	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
497	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
498	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
500	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
501	#95	C₂³×C₆₁	1	2	yes	—
502	#95	C₂³×C₆₁	1	2	yes	—
503	#95	C₂³×C₆₁	1	4	yes	—
504	#95	C₂³×C₆₁	1	4	yes	—
505	#95	C₂³×C₆₁	1	4	yes	—
506	#95	C₂³×C₆₁	1	4	yes	—
507	#95	C₂³×C₆₁	1	4	yes	—
508	#95	C₂³×C₆₁	1	4	yes	—
509	#95	C₂³×C₆₁	1	2	yes	—
510	#95	C₂³×C₆₁	1	2	yes	—
511	#95	C₂³×C₆₁	1	2	yes	—
512	#95	C₂³×C₆₁	1	2	yes	—
513	#95	C₂³×C₆₁	1	2	yes	—
514	#95	C₂³×C₆₁	1	2	yes	—
515	#95	C₂³×C₆₁	1	2	yes	—
516	#95	C₂³×C₆₁	1	4	yes	—
517	#95	C₂³×C₆₁	1	4	yes	—
518	#95	C₂³×C₆₁	1	2	yes	—
519	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	2	no	—
524	C₂×Q₈	—	4	4	no	—
525	C₂×Q₈	—	4	4	no	—
526	C₂×Q₈	—	4	32	no	—
527	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
528	C₂×Q₈	C₂²×C₄×C₆₁	1	8	yes	—
529	C₂×Q₈	C₂²×C₄×C₆₁	1	16	yes	—
530	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
531	C₂×D₄	C₂×Q₈×C₆₁	1	4	yes	—
532	C₂×D₄	#41×C₆₁	1	4	yes	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	8	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	4	4	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
546	C₂²×C₄	C₂²×C₄×C₆₁	1	16	yes	—
547	C₂²×C₄	C₂×Q₈×C₆₁	1	8	yes	complemented
548	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
558	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	4	4	no	—
571	C₄⋊C₄	—	4	4	no	—
572	C₄⋊C₄	—	4	4	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
576	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
577	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
578	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
579	C₄⋊C₄	C₂²×C₄×C₆₁	1	16	yes	—
580	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
581	C₄⋊C₄	C₂×Q₈×C₆₁	1	4	yes	complemented
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	8	no	—
584	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
585	C₂²⋊C₄	C₂²×C₄×C₆₁	1	16	yes	—
586	C₂²⋊C₄	C₂×Q₈×C₆₁	1	8	yes	complemented
587	C₄²	—	2	2	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	4	2	no	—
594	C₄²	—	4	2	no	—
595	C₄²	—	4	4	no	—
596	C₄²	—	4	4	no	—
597	C₄²	—	4	4	no	—
598	C₄²	—	4	1	no	—
599	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
600	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
601	C₄²	C₂×Q₈×C₆₁	1	4	yes	complemented
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
607	C₂³	C₂²×Q₈×C₆₁	1	4	yes	—
608	C₂³	C₂×#41×C₆₁	1	4	yes	—
609	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
610	Q₈	—	2	8	no	—
611	Q₈	—	2	16	no	—
612	Q₈	—	4	16	no	—
613	D₄	C₄×Q₈×C₆₁	1	16	yes	complemented
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	16	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	4	16	no	—
649	C₂×C₄	—	4	8	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	8	8	no	—
652	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
653	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
656	C₂×C₄	C₂³×C₄×C₆₁	1	8	yes	—
657	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
658	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
659	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
660	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
661	C₂×C₄	C₂²×Q₈×C₆₁	1	4	yes	—
662	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
663	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
664	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
665	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
666	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	4	no	—
673	C₂²	C₂×C₄×Q₈×C₆₁	1	8	yes	—
674	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
675	C₂²	C₂³×Q₈×C₆₁	1	1	yes	characteristic
676	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
677	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
678	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
679	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
680	C₂²	C₆₁×#585	1	1	yes	characteristic
681	C₄	—	2	4	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	8	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	4	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	C₂×C₄×Q₈×C₆₁	1	4	yes	—
696	C₄	C₆₁×#518	1	4	yes	—
697	C₂	—	2	8	no	—
698	C₂	C₂²×C₄×Q₈×C₆₁	1	1	yes	characteristic
699	C₂	C₂×C₆₁×#518	1	1	yes	characteristic
700	C₂	C₄×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
701	C₂	C₆₁×#3501	1	1	yes	characteristic
702	C₂	C₆₁×#3503	1	1	yes	characteristic
703	C₂	C₆₁×#3514	1	1	yes	characteristic
704	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	C₂²×D₄×C₆₁	C₂³
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×#2369	C₂	semidirect
3. C₆₁×#2368	C₂	semidirect
4. C₆₁×#2365	C₂	semidirect
5. C₆₁×#2360	C₂	semidirect
6. C₆₁×#2355	C₂	semidirect
9. Q₈×C₂²⋊C₄×C₆₁	C₂	semidirect
10. C₆₁×#2331	C₂	semidirect
11. C₆₁×#2329	C₂	semidirect
12. C₄×C₄⋊Q₈×C₆₁	C₂	semidirect
13. C₄×C₂²⋊Q₈×C₆₁	C₂	semidirect
14. C₆₁×#2295	C₂	semidirect
15. C₂×C₆₁×#391	C₂	semidirect
19. D₄×Q₈×C₆₁	C₄	semidirect
86. C₂²×Q₈×C₆₁	C₂×C₄	semidirect
96. C₄⋊Q₈×C₆₁	C₂×C₄	semidirect
97. C₄⋊Q₈×C₆₁	C₂×C₄	semidirect
98. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
99. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
102. C₄×Q₈×C₆₁	C₂×C₄	semidirect
107. C₄×D₄×C₆₁	Q₈	semidirect
194. C₂²×C₄×C₆₁	C₂×Q₈	semidirect
228. C₄⋊C₄×C₆₁	C₂×Q₈	semidirect
233. C₂²⋊C₄×C₆₁	C₂×Q₈	semidirect
248. C₄²×C₆₁	C₂×Q₈	semidirect
260. D₄×C₆₁	C₄×Q₈	semidirect
314. #34334	C₆₁	direct (N × H)
346. #2369	C₂×C₆₁	semidirect
347. #2368	C₂×C₆₁	semidirect
348. #2365	C₂×C₆₁	semidirect
349. #2360	C₂×C₆₁	semidirect
350. #2355	C₂×C₆₁	semidirect
353. Q₈×C₂²⋊C₄	C₂×C₆₁	semidirect
354. #2331	C₂×C₆₁	semidirect
355. #2329	C₂×C₆₁	semidirect
356. C₄×C₄⋊Q₈	C₂×C₆₁	semidirect
357. C₄×C₂²⋊Q₈	C₂×C₆₁	semidirect
358. #2295	C₂×C₆₁	semidirect
359. C₂×#391	C₂×C₆₁	semidirect
371. D₄×Q₈	C₄×C₆₁	semidirect
436. C₆₁	#34334	direct (N × H)
439. C₂²×Q₈	C₂×C₄×C₆₁	semidirect
449. C₄⋊Q₈	C₂×C₄×C₆₁	semidirect
450. C₄⋊Q₈	C₂×C₄×C₆₁	semidirect
451. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
452. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
455. C₄×Q₈	C₂×C₄×C₆₁	semidirect
460. C₄×D₄	Q₈×C₆₁	semidirect
547. C₂²×C₄	C₂×Q₈×C₆₁	semidirect
581. C₄⋊C₄	C₂×Q₈×C₆₁	semidirect
586. C₂²⋊C₄	C₂×Q₈×C₆₁	semidirect
601. C₄²	C₂×Q₈×C₆₁	semidirect
613. D₄	C₄×Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₆₁	2
C₆₁×#2369	2
C₆₁×#2368	2
C₆₁×#2365	2
C₆₁×#2360	2
C₆₁×#2355	2
C₆₁×#2349	2
D₄×C₄⋊C₄×C₆₁	2
Q₈×C₂²⋊C₄×C₆₁	2
C₆₁×#2331	2
C₆₁×#2329	2
C₄×C₄⋊Q₈×C₆₁	2
C₄×C₂²⋊Q₈×C₆₁	2
C₆₁×#2295	2
C₂×C₆₁×#391	2
C₆₁×#2275	2
C₄²×D₄×C₆₁	2
#34334	61

Subgroups — C61×#34334 #29537767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34334 #29537767