Subgroups — C₆₁×#34743 #29538176

Order 15616.

3390 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2429	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2428	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2427	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2426	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2425	C₂	1	4	yes	maximal, complemented
10	C₆₁×#2424	C₂	1	4	yes	maximal, complemented
11	C₆₁×#2392	C₂	1	4	yes	maximal, complemented
12	C₄×#121×C₆₁	C₂	1	4	yes	maximal, complemented
13	C₆₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#532	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
21	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
24	C₆₁×#525	—	2	8	no	—
25	C₆₁×#525	—	2	8	no	—
26	C₂×#123×C₆₁	C₂²	1	2	yes	—
27	C₂×#123×C₆₁	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
30	C₂×#121×C₆₁	C₂²	1	4	yes	—
31	C₂×#121×C₆₁	C₂²	1	2	yes	—
32	C₂×#121×C₆₁	C₂²	1	2	yes	—
33	C₂×#121×C₆₁	C₂²	1	4	yes	—
34	C₂×#120×C₆₁	C₂²	1	2	yes	—
35	C₂×#120×C₆₁	C₂²	1	2	yes	—
36	C₄×#41×C₆₁	—	2	8	no	—
37	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
39	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
40	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
41	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	complemented
42	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
43	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#117×C₆₁	C₂²	1	2	yes	complemented
46	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
47	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₆₁	C₂²	1	2	yes	complemented
50	C₆₁×#398	C₂²	1	4	yes	complemented
51	C₆₁×#397	C₂²	1	4	yes	complemented
52	C₆₁×#396	C₂²	1	4	yes	—
53	C₆₁×#396	C₂²	1	4	yes	complemented
54	C₆₁×#394	C₂²	1	4	yes	—
55	C₆₁×#394	C₂²	1	4	yes	—
56	C₆₁×#394	C₂²	1	4	yes	complemented
57	C₆₁×#392	C₂²	1	4	yes	—
58	C₆₁×#391	C₂²	1	2	yes	complemented
59	C₆₁×#390	C₂²	1	4	yes	—
60	C₆₁×#390	C₂²	1	2	yes	complemented
61	C₆₁×#389	C₂²	1	2	yes	complemented
62	C₆₁×#389	C₂²	1	2	yes	complemented
63	C₆₁×#389	C₂²	1	4	yes	complemented
64	C₆₁×#388	C₂²	1	4	yes	—
65	C₆₁×#388	C₂²	1	4	yes	complemented
66	C₆₁×#386	C₂²	1	4	yes	—
67	C₆₁×#386	C₂²	1	4	yes	—
68	C₆₁×#386	C₂²	1	4	yes	complemented
69	C₆₁×#385	C₂²	1	4	yes	—
70	C₆₁×#380	C₂²	1	4	yes	complemented
71	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	complemented
72	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
73	C₄×C₂²⋊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	complemented
77	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
78	C₂×#95×C₆₁	C₂²	1	2	yes	—
79	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
80	C₂×#41×C₆₁	—	2	4	no	—
81	C₂×#41×C₆₁	—	2	4	no	—
82	C₂×#41×C₆₁	—	2	4	no	—
83	C₂×#41×C₆₁	—	2	4	no	—
84	C₂×#41×C₆₁	—	2	4	no	—
85	C₂×#41×C₆₁	D₄	1	8	yes	complemented
86	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
91	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
92	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
93	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₆₁	—	2	4	no	—
96	C₂³×C₄×C₆₁	—	2	4	no	—
97	C₂³×C₄×C₆₁	—	2	4	no	—
98	C₂³×C₄×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	2	yes	—
103	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
104	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
105	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
106	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₆₁	—	2	4	no	—
108	#127×C₆₁	—	2	4	no	—
109	#124×C₆₁	—	2	4	no	—
110	#124×C₆₁	—	2	4	no	—
111	#123×C₆₁	—	2	8	no	—
112	#123×C₆₁	—	2	8	no	—
113	C₂²⋊Q₈×C₆₁	—	2	8	no	—
114	C₂²⋊Q₈×C₆₁	—	2	8	no	—
115	#121×C₆₁	—	2	16	no	—
116	#121×C₆₁	—	2	8	no	—
117	#121×C₆₁	—	2	8	no	—
118	#121×C₆₁	—	2	16	no	—
119	#120×C₆₁	—	2	8	no	—
120	#120×C₆₁	—	2	8	no	—
121	C₄×Q₈×C₆₁	—	2	8	no	—
122	C₄×D₄×C₆₁	—	2	16	no	—
123	C₄×D₄×C₆₁	—	2	16	no	—
124	C₄×D₄×C₆₁	—	2	8	no	—
125	C₄×D₄×C₆₁	—	2	16	no	—
126	C₄×D₄×C₆₁	—	2	16	no	—
127	#117×C₆₁	—	2	4	no	—
128	#117×C₆₁	—	2	8	no	—
129	#117×C₆₁	D₄	1	8	yes	complemented
130	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
139	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	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	2	yes	—
153	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
154	C₂×C₄²×C₆₁	—	2	4	no	—
155	C₂×C₄²×C₆₁	—	2	4	no	—
156	C₂×C₄²×C₆₁	—	2	8	no	—
157	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
160	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
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	2	yes	—
165	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
166	#95×C₆₁	C₂³	1	2	yes	—
167	#95×C₆₁	C₂³	1	2	yes	—
168	#95×C₆₁	C₂³	1	2	yes	—
169	#95×C₆₁	C₂³	1	2	yes	—
170	#95×C₆₁	C₂³	1	4	yes	—
171	#95×C₆₁	C₂³	1	4	yes	—
172	#95×C₆₁	C₂³	1	4	yes	—
173	#95×C₆₁	C₂³	1	4	yes	—
174	C₂⁴×C₆₁	—	2	4	no	—
175	C₂⁴×C₆₁	—	2	2	no	—
176	C₂⁴×C₆₁	—	2	2	no	—
177	C₂⁴×C₆₁	—	2	2	no	—
178	C₂⁴×C₆₁	—	4	2	no	—
179	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
180	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
181	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
182	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
183	#41×C₆₁	—	2	32	no	—
184	#41×C₆₁	—	4	16	no	—
185	C₂×Q₈×C₆₁	—	2	2	no	—
186	C₂×Q₈×C₆₁	—	2	2	no	—
187	C₂×Q₈×C₆₁	—	2	2	no	—
188	C₂×Q₈×C₆₁	—	2	2	no	—
189	C₂×Q₈×C₆₁	—	2	2	no	—
190	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
191	C₂×D₄×C₆₁	—	2	4	no	—
192	C₂×D₄×C₆₁	—	2	4	no	—
193	C₂×D₄×C₆₁	—	2	8	no	—
194	C₂×D₄×C₆₁	—	2	8	no	—
195	C₂×D₄×C₆₁	—	2	4	no	—
196	C₂×D₄×C₆₁	—	2	4	no	—
197	C₂×D₄×C₆₁	—	2	8	no	—
198	C₂×D₄×C₆₁	—	2	8	no	—
199	C₂×D₄×C₆₁	—	2	4	no	—
200	C₂×D₄×C₆₁	—	2	2	no	—
201	C₂×D₄×C₆₁	—	2	8	no	—
202	C₂×D₄×C₆₁	—	2	2	no	—
203	C₂×D₄×C₆₁	—	2	2	no	—
204	C₂×D₄×C₆₁	—	2	2	no	—
205	C₂×D₄×C₆₁	—	2	8	no	—
206	C₂×D₄×C₆₁	—	2	2	no	—
207	C₂×D₄×C₆₁	—	4	4	no	—
208	C₂×D₄×C₆₁	—	4	4	no	—
209	C₂×D₄×C₆₁	—	4	4	no	—
210	C₂×D₄×C₆₁	C₂×D₄	1	8	yes	—
211	C₂×D₄×C₆₁	C₂×D₄	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	2	no	—
217	C₂²×C₄×C₆₁	—	2	2	no	—
218	C₂²×C₄×C₆₁	—	2	2	no	—
219	C₂²×C₄×C₆₁	—	2	8	no	—
220	C₂²×C₄×C₆₁	—	2	4	no	—
221	C₂²×C₄×C₆₁	—	2	4	no	—
222	C₂²×C₄×C₆₁	—	2	4	no	—
223	C₂²×C₄×C₆₁	—	2	4	no	—
224	C₂²×C₄×C₆₁	—	2	4	no	—
225	C₂²×C₄×C₆₁	—	2	4	no	—
226	C₂²×C₄×C₆₁	—	2	4	no	—
227	C₂²×C₄×C₆₁	—	2	4	no	—
228	C₂²×C₄×C₆₁	—	2	8	no	—
229	C₂²×C₄×C₆₁	—	2	4	no	—
230	C₂²×C₄×C₆₁	—	2	4	no	—
231	C₂²×C₄×C₆₁	—	2	4	no	—
232	C₂²×C₄×C₆₁	—	4	4	no	—
233	C₂²×C₄×C₆₁	—	4	2	no	—
234	C₂²×C₄×C₆₁	—	4	2	no	—
235	C₂²×C₄×C₆₁	—	4	16	no	—
236	C₂²×C₄×C₆₁	C₂×D₄	1	8	yes	—
237	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
238	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₆₁	#41	1	4	yes	—
240	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
251	C₄⋊C₄×C₆₁	—	2	8	no	—
252	C₄⋊C₄×C₆₁	—	2	4	no	—
253	C₄⋊C₄×C₆₁	—	2	8	no	—
254	C₄⋊C₄×C₆₁	—	2	8	no	—
255	C₄⋊C₄×C₆₁	—	2	8	no	—
256	C₄⋊C₄×C₆₁	—	2	8	no	—
257	C₄⋊C₄×C₆₁	—	4	4	no	—
258	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
259	C₂²⋊C₄×C₆₁	—	2	4	no	—
260	C₂²⋊C₄×C₆₁	—	2	8	no	—
261	C₂²⋊C₄×C₆₁	—	2	8	no	—
262	C₂²⋊C₄×C₆₁	—	2	4	no	—
263	C₂²⋊C₄×C₆₁	—	2	8	no	—
264	C₂²⋊C₄×C₆₁	—	2	8	no	—
265	C₂²⋊C₄×C₆₁	—	2	8	no	—
266	C₂²⋊C₄×C₆₁	—	2	8	no	—
267	C₂²⋊C₄×C₆₁	—	2	8	no	—
268	C₂²⋊C₄×C₆₁	—	2	4	no	—
269	C₂²⋊C₄×C₆₁	—	2	4	no	—
270	C₂²⋊C₄×C₆₁	—	2	8	no	—
271	C₂²⋊C₄×C₆₁	—	4	4	no	—
272	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
273	C₂²⋊C₄×C₆₁	#41	1	8	yes	complemented
274	C₄²×C₆₁	—	2	2	no	—
275	C₄²×C₆₁	—	2	2	no	—
276	C₄²×C₆₁	—	2	4	no	—
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	C₂×D₄	1	8	yes	—
283	C₂³×C₆₁	—	2	2	no	—
284	C₂³×C₆₁	—	2	2	no	—
285	C₂³×C₆₁	—	2	8	no	—
286	C₂³×C₆₁	—	2	2	no	—
287	C₂³×C₆₁	—	2	2	no	—
288	C₂³×C₆₁	—	2	2	no	—
289	C₂³×C₆₁	—	2	2	no	—
290	C₂³×C₆₁	—	2	2	no	—
291	C₂³×C₆₁	—	2	2	no	—
292	C₂³×C₆₁	—	2	4	no	—
293	C₂³×C₆₁	—	2	4	no	—
294	C₂³×C₆₁	—	2	2	no	—
295	C₂³×C₆₁	—	2	2	no	—
296	C₂³×C₆₁	—	2	2	no	—
297	C₂³×C₆₁	—	2	2	no	—
298	C₂³×C₆₁	—	2	4	no	—
299	C₂³×C₆₁	—	2	2	no	—
300	C₂³×C₆₁	—	2	4	no	—
301	C₂³×C₆₁	—	4	8	no	—
302	C₂³×C₆₁	—	4	8	no	—
303	C₂³×C₆₁	—	4	4	no	—
304	C₂³×C₆₁	—	4	4	no	—
305	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
306	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
307	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
308	C₂³×C₆₁	C₂×#41	1	4	yes	—
309	C₂³×C₆₁	C₂×#41	1	2	yes	—
310	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
311	Q₈×C₆₁	—	2	8	no	—
312	Q₈×C₆₁	—	4	4	no	—
313	D₄×C₆₁	—	2	16	no	—
314	D₄×C₆₁	—	2	8	no	—
315	D₄×C₆₁	—	4	16	no	—
316	D₄×C₆₁	—	4	16	no	—
317	D₄×C₆₁	—	4	16	no	—
318	D₄×C₆₁	—	4	8	no	—
319	D₄×C₆₁	—	4	4	no	—
320	C₂×C₄×C₆₁	—	2	2	no	—
321	C₂×C₄×C₆₁	—	2	2	no	—
322	C₂×C₄×C₆₁	—	2	2	no	—
323	C₂×C₄×C₆₁	—	2	4	no	—
324	C₂×C₄×C₆₁	—	2	2	no	—
325	C₂×C₄×C₆₁	—	2	4	no	—
326	C₂×C₄×C₆₁	—	2	2	no	—
327	C₂×C₄×C₆₁	—	2	2	no	—
328	C₂×C₄×C₆₁	—	2	16	no	—
329	C₂×C₄×C₆₁	—	2	2	no	—
330	C₂×C₄×C₆₁	—	2	2	no	—
331	C₂×C₄×C₆₁	—	2	4	no	—
332	C₂×C₄×C₆₁	—	2	2	no	—
333	C₂×C₄×C₆₁	—	2	2	no	—
334	C₂×C₄×C₆₁	—	2	2	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	2	2	no	—
337	C₂×C₄×C₆₁	—	2	2	no	—
338	C₂×C₄×C₆₁	—	2	4	no	—
339	C₂×C₄×C₆₁	—	2	2	no	—
340	C₂×C₄×C₆₁	—	2	2	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	—	4	16	no	—
345	C₂×C₄×C₆₁	—	4	8	no	—
346	C₂×C₄×C₆₁	—	4	8	no	—
347	C₂×C₄×C₆₁	—	4	4	no	—
348	C₂×C₄×C₆₁	—	4	8	no	—
349	C₂×C₄×C₆₁	—	4	8	no	—
350	C₂×C₄×C₆₁	—	4	8	no	—
351	C₂×C₄×C₆₁	#121	1	16	yes	complemented
352	C₂×C₄×C₆₁	C₂²×D₄	1	8	yes	—
353	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
354	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
359	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
360	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
361	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
362	#34743	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
363	C₂²×C₆₁	—	2	2	no	—
364	C₂²×C₆₁	—	2	2	no	—
365	C₂²×C₆₁	—	2	4	no	—
366	C₂²×C₆₁	—	2	4	no	—
367	C₂²×C₆₁	—	2	4	no	—
368	C₂²×C₆₁	—	2	4	no	—
369	C₂²×C₆₁	—	2	4	no	—
370	C₂²×C₆₁	—	2	4	no	—
371	C₂²×C₆₁	—	2	8	no	—
372	C₂²×C₆₁	—	4	16	no	—
373	C₂²×C₆₁	—	4	2	no	—
374	C₂²×C₆₁	—	4	2	no	—
375	C₂²×C₆₁	—	4	2	no	—
376	C₂²×C₆₁	—	4	2	no	—
377	C₂²×C₆₁	—	4	4	no	—
378	C₂²×C₆₁	—	4	2	no	—
379	C₂²×C₆₁	—	4	2	no	—
380	C₂²×C₆₁	—	4	2	no	—
381	C₂²×C₆₁	—	4	2	no	—
382	C₂²×C₆₁	—	4	2	no	—
383	C₂²×C₆₁	—	4	4	no	—
384	C₂²×C₆₁	—	4	4	no	—
385	C₂²×C₆₁	C₂×#121	1	4	yes	—
386	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
387	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
388	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
389	C₂²×C₆₁	C₂²×#41	1	2	yes	—
390	C₂²×C₆₁	#585	1	2	yes	—
391	C₄×C₆₁	—	2	4	no	—
392	C₄×C₆₁	—	2	4	no	—
393	C₄×C₆₁	—	2	8	no	—
394	C₄×C₆₁	—	2	4	no	—
395	C₄×C₆₁	—	4	2	no	—
396	C₄×C₆₁	—	4	2	no	—
397	C₄×C₆₁	—	4	2	no	—
398	C₄×C₆₁	—	4	2	no	—
399	C₄×C₆₁	—	4	4	no	—
400	C₄×C₆₁	C₂×#121	1	4	yes	—
401	C₄×C₆₁	C₂×#121	1	4	yes	—
402	C₂×#532	C₂×C₆₁	1	1	yes	characteristic, complemented
403	C₂×#525	C₂×C₆₁	1	1	yes	characteristic, complemented
404	C₂×#525	C₂×C₆₁	1	1	yes	characteristic, complemented
405	C₂×C₄×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
406	#2429	C₂×C₆₁	1	2	yes	complemented
407	#2428	C₂×C₆₁	1	2	yes	complemented
408	#2427	C₂×C₆₁	1	2	yes	complemented
409	#2426	C₂×C₆₁	1	2	yes	complemented
410	#2425	C₂×C₆₁	1	4	yes	complemented
411	#2424	C₂×C₆₁	1	4	yes	complemented
412	#2392	C₂×C₆₁	1	4	yes	complemented
413	C₄×#121	C₂×C₆₁	1	4	yes	complemented
414	#2297	C₂×C₆₁	1	1	yes	characteristic, complemented
415	#2296	C₂×C₆₁	1	1	yes	characteristic, complemented
416	C₂×C₄×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
417	C₂×C₆₁	—	2	4	no	—
418	C₂×C₆₁	—	4	4	no	—
419	C₂×C₆₁	—	4	4	no	—
420	C₂×C₆₁	—	8	2	no	—
421	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
422	C₂×C₆₁	#3444	1	1	yes	characteristic
423	C₂×C₆₁	#3455	1	1	yes	characteristic
424	C₂×C₆₁	D₄×#41	1	2	yes	—
425	C₂×C₆₁	D₄×#41	1	2	yes	—
426	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
427	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
428	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
429	#532	—	2	8	no	—
430	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
431	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic, complemented
432	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
433	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
434	#525	—	2	8	no	—
435	#525	—	2	8	no	—
436	C₂×#123	C₂²×C₆₁	1	2	yes	—
437	C₂×#123	C₂²×C₆₁	1	2	yes	—
438	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
439	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
440	C₂×#121	C₂²×C₆₁	1	2	yes	—
441	C₂×#121	C₂²×C₆₁	1	2	yes	—
442	C₂×#121	C₂²×C₆₁	1	4	yes	—
443	C₂×#121	C₂²×C₆₁	1	4	yes	—
444	C₂×#120	C₂²×C₆₁	1	2	yes	—
445	C₂×#120	C₂²×C₆₁	1	2	yes	—
446	C₄×#41	—	2	8	no	—
447	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
448	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
449	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
450	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
451	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	complemented
452	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
453	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
454	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
455	C₂×#117	C₂²×C₆₁	1	2	yes	complemented
456	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
457	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
458	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
459	C₂²×C₄²	C₂²×C₆₁	1	2	yes	complemented
460	#398	C₂²×C₆₁	1	4	yes	complemented
461	#397	C₂²×C₆₁	1	4	yes	complemented
462	#396	C₂²×C₆₁	1	4	yes	—
463	#396	C₂²×C₆₁	1	4	yes	complemented
464	#394	C₂²×C₆₁	1	4	yes	—
465	#394	C₂²×C₆₁	1	4	yes	—
466	#394	C₂²×C₆₁	1	4	yes	complemented
467	#392	C₂²×C₆₁	1	4	yes	—
468	#391	C₂²×C₆₁	1	2	yes	complemented
469	#390	C₂²×C₆₁	1	4	yes	—
470	#390	C₂²×C₆₁	1	2	yes	complemented
471	#389	C₂²×C₆₁	1	4	yes	complemented
472	#389	C₂²×C₆₁	1	2	yes	complemented
473	#389	C₂²×C₆₁	1	2	yes	complemented
474	#388	C₂²×C₆₁	1	4	yes	—
475	#388	C₂²×C₆₁	1	4	yes	complemented
476	#386	C₂²×C₆₁	1	4	yes	—
477	#386	C₂²×C₆₁	1	4	yes	—
478	#386	C₂²×C₆₁	1	4	yes	complemented
479	#385	C₂²×C₆₁	1	4	yes	—
480	#380	C₂²×C₆₁	1	4	yes	complemented
481	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	complemented
482	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
487	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
488	C₂×#95	C₂²×C₆₁	1	2	yes	—
489	C₆₁	#34743	1	1	yes	characteristic, direct product factor, Sylow
490	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
491	C₂×#41	—	2	4	no	—
492	C₂×#41	—	2	4	no	—
493	C₂×#41	—	2	4	no	—
494	C₂×#41	—	2	4	no	—
495	C₂×#41	—	2	4	no	—
496	C₂×#41	D₄×C₆₁	1	8	yes	complemented
497	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
498	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
499	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
500	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
502	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
503	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
504	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
505	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
506	C₂³×C₄	—	2	4	no	—
507	C₂³×C₄	—	2	4	no	—
508	C₂³×C₄	—	2	4	no	—
509	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
510	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
511	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
512	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
514	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
515	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
516	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
517	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
518	C₄⋊Q₈	—	2	4	no	—
519	#127	—	2	4	no	—
520	#124	—	2	4	no	—
521	#124	—	2	4	no	—
522	#123	—	2	8	no	—
523	#123	—	2	8	no	—
524	C₂²⋊Q₈	—	2	8	no	—
525	C₂²⋊Q₈	—	2	8	no	—
526	#121	—	2	8	no	—
527	#121	—	2	16	no	—
528	#121	—	2	8	no	—
529	#121	—	2	16	no	—
530	#120	—	2	8	no	—
531	#120	—	2	8	no	—
532	C₄×Q₈	—	2	8	no	—
533	C₄×D₄	—	2	16	no	—
534	C₄×D₄	—	2	16	no	—
535	C₄×D₄	—	2	8	no	—
536	C₄×D₄	—	2	16	no	—
537	C₄×D₄	—	2	16	no	—
538	#117	—	2	4	no	—
539	#117	—	2	8	no	—
540	#117	D₄×C₆₁	1	8	yes	complemented
541	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
543	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
547	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
548	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
549	C₂×C₂²⋊C₄	—	2	8	no	—
550	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
565	C₂×C₄²	—	2	4	no	—
566	C₂×C₄²	—	2	4	no	—
567	C₂×C₄²	—	2	8	no	—
568	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
569	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
571	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
572	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
573	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
577	#95	C₂³×C₆₁	1	2	yes	—
578	#95	C₂³×C₆₁	1	2	yes	—
579	#95	C₂³×C₆₁	1	2	yes	—
580	#95	C₂³×C₆₁	1	2	yes	—
581	#95	C₂³×C₆₁	1	4	yes	—
582	#95	C₂³×C₆₁	1	4	yes	—
583	#95	C₂³×C₆₁	1	4	yes	—
584	#95	C₂³×C₆₁	1	4	yes	—
585	C₂⁴	—	2	4	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	4	2	no	—
590	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
591	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
592	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
593	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
594	#41	—	2	32	no	—
595	#41	—	4	16	no	—
596	C₂×Q₈	—	2	2	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	2	2	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	8	no	—
605	C₂×D₄	—	2	8	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	8	no	—
609	C₂×D₄	—	2	8	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	C₂×D₄×C₆₁	1	8	yes	—
622	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	8	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	8	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	4	4	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	16	no	—
647	C₂²×C₄	C₂×D₄×C₆₁	1	8	yes	—
648	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
649	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
650	C₂²×C₄	#41×C₆₁	1	4	yes	—
651	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
657	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
662	C₄⋊C₄	—	2	8	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	2	8	no	—
666	C₄⋊C₄	—	2	8	no	—
667	C₄⋊C₄	—	2	8	no	—
668	C₄⋊C₄	—	4	4	no	—
669	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	8	no	—
672	C₂²⋊C₄	—	2	8	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	8	no	—
675	C₂²⋊C₄	—	2	8	no	—
676	C₂²⋊C₄	—	2	8	no	—
677	C₂²⋊C₄	—	2	8	no	—
678	C₂²⋊C₄	—	2	8	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	4	4	no	—
683	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
684	C₂²⋊C₄	#41×C₆₁	1	8	yes	complemented
685	C₄²	—	2	2	no	—
686	C₄²	—	2	2	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	8	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	4	no	—
693	C₄²	C₂×D₄×C₆₁	1	8	yes	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	8	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	4	8	no	—
713	C₂³	—	4	8	no	—
714	C₂³	—	4	4	no	—
715	C₂³	—	4	4	no	—
716	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
717	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
718	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
719	C₂³	C₂×#41×C₆₁	1	4	yes	—
720	C₂³	C₂×#41×C₆₁	1	2	yes	—
721	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
722	Q₈	—	2	8	no	—
723	Q₈	—	4	4	no	—
724	D₄	—	2	16	no	—
725	D₄	—	2	8	no	—
726	D₄	—	4	16	no	—
727	D₄	—	4	16	no	—
728	D₄	—	4	16	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	4	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	16	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	4	16	no	—
756	C₂×C₄	—	4	8	no	—
757	C₂×C₄	—	4	8	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	—	4	8	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	#121×C₆₁	1	16	yes	complemented
763	C₂×C₄	C₂²×D₄×C₆₁	1	8	yes	—
764	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
765	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
766	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
767	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
768	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
769	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
770	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
771	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
772	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	2	8	no	—
782	C₂²	—	4	16	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	4	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	4	no	—
795	C₂²	C₂×#121×C₆₁	1	4	yes	—
796	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
797	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
798	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
799	C₂²	C₂²×#41×C₆₁	1	2	yes	—
800	C₂²	C₆₁×#585	1	2	yes	—
801	C₄	—	2	4	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	8	no	—
804	C₄	—	2	4	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	4	no	—
810	C₄	C₂×#121×C₆₁	1	4	yes	—
811	C₄	C₂×#121×C₆₁	1	4	yes	—
812	C₂	—	2	4	no	—
813	C₂	—	4	4	no	—
814	C₂	—	4	4	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
817	C₂	C₆₁×#3444	1	1	yes	characteristic
818	C₂	C₆₁×#3455	1	1	yes	characteristic
819	C₂	D₄×#41×C₆₁	1	2	yes	—
820	C₂	D₄×#41×C₆₁	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#532	C₂	semidirect
2. C₂×C₆₁×#525	C₂	semidirect
3. C₂×C₆₁×#525	C₂	semidirect
4. C₂×C₄×#41×C₆₁	C₂	semidirect
5. C₆₁×#2429	C₂	semidirect
6. C₆₁×#2428	C₂	semidirect
7. C₆₁×#2427	C₂	semidirect
8. C₆₁×#2426	C₂	semidirect
9. C₆₁×#2425	C₂	semidirect
10. C₆₁×#2424	C₂	semidirect
11. C₆₁×#2392	C₂	semidirect
12. C₄×#121×C₆₁	C₂	semidirect
13. C₆₁×#2297	C₂	semidirect
14. C₆₁×#2296	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₆₁	C₂	semidirect
20. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
21. C₂×#127×C₆₁	C₂²	semidirect
22. C₂×#124×C₆₁	C₂²	semidirect
23. C₂×#124×C₆₁	C₂²	semidirect
37. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
41. C₂×C₄×D₄×C₆₁	C₂²	semidirect
42. C₂×C₄×D₄×C₆₁	C₂²	semidirect
45. C₂×#117×C₆₁	C₂²	semidirect
49. C₂²×C₄²×C₆₁	C₂²	semidirect
50. C₆₁×#398	C₂²	semidirect
51. C₆₁×#397	C₂²	semidirect
53. C₆₁×#396	C₂²	semidirect
56. C₆₁×#394	C₂²	semidirect
58. C₆₁×#391	C₂²	semidirect
60. C₆₁×#390	C₂²	semidirect
61. C₆₁×#389	C₂²	semidirect
62. C₆₁×#389	C₂²	semidirect
63. C₆₁×#389	C₂²	semidirect
65. C₆₁×#388	C₂²	semidirect
68. C₆₁×#386	C₂²	semidirect
70. C₆₁×#380	C₂²	semidirect
71. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
77. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
85. C₂×#41×C₆₁	D₄	semidirect
129. #117×C₆₁	D₄	semidirect
273. C₂²⋊C₄×C₆₁	#41	semidirect
351. C₂×C₄×C₆₁	#121	semidirect
362. #34743	C₆₁	direct (N × H)
402. C₂×#532	C₂×C₆₁	semidirect
403. C₂×#525	C₂×C₆₁	semidirect
404. C₂×#525	C₂×C₆₁	semidirect
405. C₂×C₄×#41	C₂×C₆₁	semidirect
406. #2429	C₂×C₆₁	semidirect
407. #2428	C₂×C₆₁	semidirect
408. #2427	C₂×C₆₁	semidirect
409. #2426	C₂×C₆₁	semidirect
410. #2425	C₂×C₆₁	semidirect
411. #2424	C₂×C₆₁	semidirect
412. #2392	C₂×C₆₁	semidirect
413. C₄×#121	C₂×C₆₁	semidirect
414. #2297	C₂×C₆₁	semidirect
415. #2296	C₂×C₆₁	semidirect
416. C₂×C₄×C₂²⋊C₄	C₂×C₆₁	semidirect
430. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
431. C₂×#127	C₂²×C₆₁	semidirect
432. C₂×#124	C₂²×C₆₁	semidirect
433. C₂×#124	C₂²×C₆₁	semidirect
447. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
451. C₂×C₄×D₄	C₂²×C₆₁	semidirect
452. C₂×C₄×D₄	C₂²×C₆₁	semidirect
455. C₂×#117	C₂²×C₆₁	semidirect
459. C₂²×C₄²	C₂²×C₆₁	semidirect
460. #398	C₂²×C₆₁	semidirect
461. #397	C₂²×C₆₁	semidirect
463. #396	C₂²×C₆₁	semidirect
466. #394	C₂²×C₆₁	semidirect
468. #391	C₂²×C₆₁	semidirect
470. #390	C₂²×C₆₁	semidirect
471. #389	C₂²×C₆₁	semidirect
472. #389	C₂²×C₆₁	semidirect
473. #389	C₂²×C₆₁	semidirect
475. #388	C₂²×C₆₁	semidirect
478. #386	C₂²×C₆₁	semidirect
480. #380	C₂²×C₆₁	semidirect
481. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
486. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
487. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
489. C₆₁	#34743	direct (N × H)
496. C₂×#41	D₄×C₆₁	semidirect
540. #117	D₄×C₆₁	semidirect
684. C₂²⋊C₄	#41×C₆₁	semidirect
762. C₂×C₄	#121×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×#532	2
C₂×C₆₁×#525	2
C₂×C₄×#41×C₆₁	2
C₆₁×#2429	2
C₆₁×#2428	2
C₆₁×#2427	2
C₆₁×#2426	2
C₆₁×#2425	2
C₆₁×#2424	2
C₆₁×#2392	2
C₄×#121×C₆₁	2
C₆₁×#2297	2
C₆₁×#2296	2
C₂×C₄×C₂²⋊C₄×C₆₁	2
#34743	61

Subgroups — C61×#34743 #29538176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34743 #29538176