Subgroups — C₂×C₆₁×#3267 #29564458

Order 15616.

2914 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#135×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3267	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₆₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₆₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₆₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₆₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#450	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₆₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₆₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
22	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	8	yes	complemented
23	C₂×#135×C₆₁	—	2	8	no	—
24	C₂×#135×C₆₁	C₂²	1	8	yes	complemented
25	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
29	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
30	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
31	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
36	C₆₁×#547	—	2	4	no	—
37	C₆₁×#547	C₂²	1	8	yes	complemented
38	C₆₁×#546	—	2	4	no	—
39	C₆₁×#546	C₂²	1	8	yes	complemented
40	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#123×C₆₁	—	2	1	no	—
43	C₂×#123×C₆₁	—	2	1	no	—
44	C₂×#123×C₆₁	—	2	1	no	—
45	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
48	C₂×#121×C₆₁	—	2	1	no	—
49	C₂×#121×C₆₁	—	2	1	no	—
50	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×#120×C₆₁	—	2	1	no	—
52	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
56	C₂²×C₂²⋊C₄×C₆₁	—	2	1	no	—
57	C₆₁×#497	C₂²	1	8	yes	complemented
58	C₆₁×#470	C₂²	1	8	yes	complemented
59	C₆₁×#465	C₂²	1	8	yes	complemented
60	C₆₁×#463	C₂²	1	8	yes	complemented
61	C₆₁×#461	C₂²	1	8	yes	complemented
62	C₆₁×#452	C₂²	1	8	yes	complemented
63	C₆₁×#452	C₂²	1	8	yes	complemented
64	C₆₁×#450	C₂²	1	8	yes	complemented
65	C₆₁×#449	C₂²	1	8	yes	complemented
66	C₆₁×#442	C₂²	1	8	yes	complemented
67	C₆₁×#435	C₂²	1	8	yes	complemented
68	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
70	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
71	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
72	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
73	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
74	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
75	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
77	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
78	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic, complemented
79	C₂⁵×C₆₁	—	2	1	no	—
80	C₂×#41×C₆₁	—	2	2	no	—
81	C₂×#41×C₆₁	—	2	2	no	—
82	C₂×#41×C₆₁	—	2	2	no	—
83	C₂×#41×C₆₁	—	2	4	no	—
84	C₂×#41×C₆₁	—	2	4	no	—
85	C₂×#41×C₆₁	—	2	4	no	—
86	C₂×#41×C₆₁	—	4	2	no	—
87	C₂×#41×C₆₁	—	4	2	no	—
88	C₂×#41×C₆₁	—	4	2	no	—
89	C₂×#41×C₆₁	C₂³	1	4	yes	—
90	C₂×#41×C₆₁	C₂³	1	4	yes	—
91	C₂×#41×C₆₁	C₂³	1	4	yes	complemented
92	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₆₁	—	2	4	no	—
96	C₂²×D₄×C₆₁	—	2	1	no	—
97	C₂²×D₄×C₆₁	—	2	1	no	—
98	C₂²×D₄×C₆₁	—	2	1	no	—
99	C₂²×D₄×C₆₁	—	2	1	no	—
100	C₂²×D₄×C₆₁	—	2	2	no	—
101	C₂²×D₄×C₆₁	—	2	1	no	—
102	C₂²×D₄×C₆₁	—	4	2	no	—
103	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
106	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₆₁	—	2	1	no	—
109	C₂³×C₄×C₆₁	—	2	1	no	—
110	C₂³×C₄×C₆₁	—	2	1	no	—
111	C₂³×C₄×C₆₁	—	2	1	no	—
112	C₂³×C₄×C₆₁	—	2	1	no	—
113	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
115	AGL(1,ℤ/8)×C₆₁	—	2	32	no	—
116	#135×C₆₁	—	2	32	no	—
117	C₂×Q₁₆×C₆₁	—	2	4	no	—
118	C₂×Q₁₆×C₆₁	—	4	2	no	—
119	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	complemented
120	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	complemented
121	C₂×SD₁₆×C₆₁	—	2	4	no	—
122	C₂×SD₁₆×C₆₁	—	2	4	no	—
123	C₂×SD₁₆×C₆₁	—	2	4	no	—
124	C₂×SD₁₆×C₆₁	—	2	4	no	—
125	C₂×SD₁₆×C₆₁	—	4	2	no	—
126	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
127	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
128	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	complemented
131	C₂×D₈×C₆₁	—	2	4	no	—
132	C₂×D₈×C₆₁	D₄	1	8	yes	complemented
133	C₂×D₈×C₆₁	C₂³	1	4	yes	—
134	C₂×D₈×C₆₁	C₂³	1	4	yes	—
135	C₂×M₁₆×C₆₁	—	2	4	no	—
136	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
137	C₂²×C₈×C₆₁	—	2	4	no	—
138	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₆₁	C₂³	1	4	yes	complemented
143	C₄⋊Q₈×C₆₁	—	2	2	no	—
144	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	complemented
145	#124×C₆₁	—	2	2	no	—
146	#124×C₆₁	C₂³	1	4	yes	—
147	#123×C₆₁	—	2	8	no	—
148	#123×C₆₁	—	2	8	no	—
149	#123×C₆₁	—	2	8	no	—
150	C₂²⋊Q₈×C₆₁	—	2	2	no	—
151	C₂²⋊Q₈×C₆₁	—	2	2	no	—
152	C₂²⋊Q₈×C₆₁	—	2	2	no	—
153	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
154	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
155	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	complemented
156	#121×C₆₁	—	2	8	no	—
157	#121×C₆₁	—	2	2	no	—
158	#121×C₆₁	—	2	8	no	—
159	#121×C₆₁	C₂³	1	4	yes	—
160	#120×C₆₁	—	2	8	no	—
161	C₄×D₄×C₆₁	—	2	2	no	—
162	C₄×D₄×C₆₁	—	2	2	no	—
163	C₄×D₄×C₆₁	D₄	1	4	yes	—
164	C₄×D₄×C₆₁	C₂³	1	4	yes	—
165	C₄×D₄×C₆₁	C₂³	1	4	yes	—
166	C₄×D₄×C₆₁	C₂³	1	4	yes	complemented
167	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
168	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
169	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
170	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
171	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
172	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
173	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
179	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
185	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
188	#106×C₆₁	C₂³	1	4	yes	complemented
189	C₄⋊C₈×C₆₁	C₂³	1	4	yes	complemented
190	#103×C₆₁	C₂³	1	4	yes	complemented
191	#103×C₆₁	C₂³	1	4	yes	complemented
192	#103×C₆₁	C₂³	1	4	yes	complemented
193	#102×C₆₁	C₂³	1	4	yes	—
194	#102×C₆₁	C₂³	1	4	yes	—
195	#102×C₆₁	C₂³	1	4	yes	complemented
196	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
197	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	complemented
198	#97×C₆₁	C₂³	1	4	yes	complemented
199	C₂⁴×C₆₁	—	2	1	no	—
200	C₂⁴×C₆₁	—	2	1	no	—
201	C₂⁴×C₆₁	—	2	1	no	—
202	C₂⁴×C₆₁	—	2	4	no	—
203	C₂⁴×C₆₁	—	4	4	no	—
204	C₂⁴×C₆₁	—	4	4	no	—
205	C₂⁴×C₆₁	—	8	2	no	—
206	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
207	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
208	#41×C₆₁	—	2	8	no	—
209	#41×C₆₁	—	2	8	no	—
210	#41×C₆₁	—	2	8	no	—
211	#41×C₆₁	—	4	4	no	—
212	#41×C₆₁	—	4	4	no	—
213	#41×C₆₁	—	4	4	no	—
214	#41×C₆₁	—	4	8	no	—
215	#41×C₆₁	—	4	8	no	—
216	#41×C₆₁	—	4	8	no	—
217	C₂×Q₈×C₆₁	—	2	1	no	—
218	C₂×Q₈×C₆₁	—	2	1	no	—
219	C₂×Q₈×C₆₁	—	2	1	no	—
220	C₂×Q₈×C₆₁	—	2	2	no	—
221	C₂×Q₈×C₆₁	—	2	2	no	—
222	C₂×Q₈×C₆₁	—	2	2	no	—
223	C₂×Q₈×C₆₁	—	2	2	no	—
224	C₂×Q₈×C₆₁	—	2	2	no	—
225	C₂×Q₈×C₆₁	—	2	2	no	—
226	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
227	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
229	C₂×D₄×C₆₁	—	2	8	no	—
230	C₂×D₄×C₆₁	—	2	4	no	—
231	C₂×D₄×C₆₁	—	2	4	no	—
232	C₂×D₄×C₆₁	—	2	4	no	—
233	C₂×D₄×C₆₁	—	2	4	no	—
234	C₂×D₄×C₆₁	—	2	1	no	—
235	C₂×D₄×C₆₁	—	2	1	no	—
236	C₂×D₄×C₆₁	—	2	2	no	—
237	C₂×D₄×C₆₁	—	2	4	no	—
238	C₂×D₄×C₆₁	—	2	1	no	—
239	C₂×D₄×C₆₁	—	2	2	no	—
240	C₂×D₄×C₆₁	—	2	2	no	—
241	C₂×D₄×C₆₁	—	2	2	no	—
242	C₂×D₄×C₆₁	—	4	4	no	—
243	C₂×D₄×C₆₁	—	4	8	no	—
244	C₂×D₄×C₆₁	—	4	2	no	—
245	C₂×D₄×C₆₁	—	4	4	no	—
246	C₂×D₄×C₆₁	—	4	4	no	—
247	C₂×D₄×C₆₁	—	4	4	no	—
248	C₂×D₄×C₆₁	—	4	4	no	—
249	C₂×D₄×C₆₁	—	8	2	no	—
250	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
251	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
252	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
253	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
254	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
255	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₁	—	2	2	no	—
257	C₂²×C₄×C₆₁	—	2	2	no	—
258	C₂²×C₄×C₆₁	—	2	2	no	—
259	C₂²×C₄×C₆₁	—	2	2	no	—
260	C₂²×C₄×C₆₁	—	2	1	no	—
261	C₂²×C₄×C₆₁	—	2	1	no	—
262	C₂²×C₄×C₆₁	—	2	1	no	—
263	C₂²×C₄×C₆₁	—	2	1	no	—
264	C₂²×C₄×C₆₁	—	2	1	no	—
265	C₂²×C₄×C₆₁	—	2	4	no	—
266	C₂²×C₄×C₆₁	—	2	4	no	—
267	C₂²×C₄×C₆₁	—	2	4	no	—
268	C₂²×C₄×C₆₁	—	2	4	no	—
269	C₂²×C₄×C₆₁	—	2	4	no	—
270	C₂²×C₄×C₆₁	—	4	4	no	—
271	C₂²×C₄×C₆₁	—	4	4	no	—
272	C₂²×C₄×C₆₁	—	4	4	no	—
273	C₂²×C₄×C₆₁	—	4	4	no	—
274	C₂²×C₄×C₆₁	—	8	2	no	—
275	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
284	Q₁₆×C₆₁	—	2	8	no	—
285	Q₁₆×C₆₁	—	4	4	no	—
286	SD₁₆×C₆₁	—	2	8	no	—
287	SD₁₆×C₆₁	—	2	8	no	—
288	SD₁₆×C₆₁	—	2	8	no	—
289	SD₁₆×C₆₁	—	2	8	no	—
290	SD₁₆×C₆₁	—	4	4	no	—
291	D₈×C₆₁	—	2	8	no	—
292	D₈×C₆₁	C₂×D₄	1	16	yes	complemented
293	M₁₆×C₆₁	—	2	8	no	—
294	C₂×C₈×C₆₁	—	2	2	no	—
295	C₂×C₈×C₆₁	—	2	2	no	—
296	C₂×C₈×C₆₁	—	2	2	no	—
297	C₂×C₈×C₆₁	—	2	8	no	—
298	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
299	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
300	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
301	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
302	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₆₁	—	2	4	no	—
304	C₄⋊C₄×C₆₁	—	2	4	no	—
305	C₄⋊C₄×C₆₁	—	2	4	no	—
306	C₄⋊C₄×C₆₁	—	2	4	no	—
307	C₄⋊C₄×C₆₁	—	2	4	no	—
308	C₄⋊C₄×C₆₁	—	2	1	no	—
309	C₄⋊C₄×C₆₁	—	2	1	no	—
310	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
311	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
313	C₂²⋊C₄×C₆₁	—	2	4	no	—
314	C₂²⋊C₄×C₆₁	—	2	4	no	—
315	C₂²⋊C₄×C₆₁	—	2	4	no	—
316	C₂²⋊C₄×C₆₁	—	2	4	no	—
317	C₂²⋊C₄×C₆₁	—	2	4	no	—
318	C₂²⋊C₄×C₆₁	—	2	4	no	—
319	C₂²⋊C₄×C₆₁	—	2	4	no	—
320	C₂²⋊C₄×C₆₁	—	2	4	no	—
321	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
322	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
323	C₄²×C₆₁	C₂×D₄	1	2	yes	—
324	C₄²×C₆₁	C₂⁴	1	2	yes	—
325	C₂³×C₆₁	—	2	2	no	—
326	C₂³×C₆₁	—	2	2	no	—
327	C₂³×C₆₁	—	2	4	no	—
328	C₂³×C₆₁	—	2	4	no	—
329	C₂³×C₆₁	—	2	2	no	—
330	C₂³×C₆₁	—	2	2	no	—
331	C₂³×C₆₁	—	2	2	no	—
332	C₂³×C₆₁	—	2	2	no	—
333	C₂³×C₆₁	—	2	2	no	—
334	C₂³×C₆₁	—	2	2	no	—
335	C₂³×C₆₁	—	2	2	no	—
336	C₂³×C₆₁	—	4	8	no	—
337	C₂³×C₆₁	—	4	8	no	—
338	C₂³×C₆₁	—	4	2	no	—
339	C₂³×C₆₁	—	4	2	no	—
340	C₂³×C₆₁	—	4	2	no	—
341	C₂³×C₆₁	—	4	2	no	—
342	C₂³×C₆₁	—	4	2	no	—
343	C₂³×C₆₁	—	4	2	no	—
344	C₂³×C₆₁	—	4	2	no	—
345	C₂³×C₆₁	—	8	4	no	—
346	C₂³×C₆₁	—	8	16	no	—
347	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
348	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
349	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
350	Q₈×C₆₁	—	2	2	no	—
351	Q₈×C₆₁	—	2	2	no	—
352	Q₈×C₆₁	—	2	2	no	—
353	Q₈×C₆₁	—	2	2	no	—
354	Q₈×C₆₁	—	2	2	no	—
355	Q₈×C₆₁	—	2	2	no	—
356	Q₈×C₆₁	—	4	2	no	—
357	Q₈×C₆₁	—	4	2	no	—
358	Q₈×C₆₁	—	4	2	no	—
359	D₄×C₆₁	—	2	4	no	—
360	D₄×C₆₁	—	2	4	no	—
361	D₄×C₆₁	—	2	2	no	—
362	D₄×C₆₁	—	2	2	no	—
363	D₄×C₆₁	—	2	2	no	—
364	D₄×C₆₁	—	2	2	no	—
365	D₄×C₆₁	—	4	4	no	—
366	D₄×C₆₁	—	4	8	no	—
367	D₄×C₆₁	—	4	8	no	—
368	D₄×C₆₁	—	4	8	no	—
369	D₄×C₆₁	—	4	8	no	—
370	D₄×C₆₁	—	4	2	no	—
371	D₄×C₆₁	—	8	4	no	—
372	D₄×C₆₁	C₂²×D₄	1	4	yes	—
373	D₄×C₆₁	C₂²×D₄	1	4	yes	—
374	C₂×C₄×C₆₁	—	2	2	no	—
375	C₂×C₄×C₆₁	—	2	2	no	—
376	C₂×C₄×C₆₁	—	2	2	no	—
377	C₂×C₄×C₆₁	—	2	2	no	—
378	C₂×C₄×C₆₁	—	2	4	no	—
379	C₂×C₄×C₆₁	—	2	4	no	—
380	C₂×C₄×C₆₁	—	2	2	no	—
381	C₂×C₄×C₆₁	—	2	2	no	—
382	C₂×C₄×C₆₁	—	2	2	no	—
383	C₂×C₄×C₆₁	—	2	2	no	—
384	C₂×C₄×C₆₁	—	2	2	no	—
385	C₂×C₄×C₆₁	—	2	2	no	—
386	C₂×C₄×C₆₁	—	2	2	no	—
387	C₂×C₄×C₆₁	—	2	2	no	—
388	C₂×C₄×C₆₁	—	2	2	no	—
389	C₂×C₄×C₆₁	—	4	8	no	—
390	C₂×C₄×C₆₁	—	4	8	no	—
391	C₂×C₄×C₆₁	—	4	8	no	—
392	C₂×C₄×C₆₁	—	4	8	no	—
393	C₂×C₄×C₆₁	—	4	2	no	—
394	C₂×C₄×C₆₁	—	4	2	no	—
395	C₂×C₄×C₆₁	—	4	2	no	—
396	C₂×C₄×C₆₁	—	4	2	no	—
397	C₂×C₄×C₆₁	—	4	2	no	—
398	C₂×C₄×C₆₁	—	8	4	no	—
399	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
407	C₈×C₆₁	—	2	2	no	—
408	C₈×C₆₁	—	2	2	no	—
409	C₈×C₆₁	—	2	2	no	—
410	C₈×C₆₁	C₂²×D₄	1	4	yes	—
411	C₂×#3267	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂²×C₆₁	—	2	2	no	—
413	C₂²×C₆₁	—	2	2	no	—
414	C₂²×C₆₁	—	2	4	no	—
415	C₂²×C₆₁	—	2	4	no	—
416	C₂²×C₆₁	—	2	2	no	—
417	C₂²×C₆₁	—	2	2	no	—
418	C₂²×C₆₁	—	2	2	no	—
419	C₂²×C₆₁	—	2	2	no	—
420	C₂²×C₆₁	—	4	4	no	—
421	C₂²×C₆₁	—	4	4	no	—
422	C₂²×C₆₁	—	4	8	no	—
423	C₂²×C₆₁	—	4	8	no	—
424	C₂²×C₆₁	—	4	2	no	—
425	C₂²×C₆₁	—	4	2	no	—
426	C₂²×C₆₁	—	4	2	no	—
427	C₂²×C₆₁	—	4	2	no	—
428	C₂²×C₆₁	—	4	2	no	—
429	C₂²×C₆₁	—	4	2	no	—
430	C₂²×C₆₁	—	4	2	no	—
431	C₂²×C₆₁	—	8	16	no	—
432	C₂²×C₆₁	—	8	4	no	—
433	C₂²×C₆₁	D₄²	1	2	yes	—
434	C₂²×C₆₁	#575	1	2	yes	—
435	C₂²×C₆₁	#577	1	2	yes	—
436	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
437	C₄×C₆₁	—	2	2	no	—
438	C₄×C₆₁	—	2	2	no	—
439	C₄×C₆₁	—	2	2	no	—
440	C₄×C₆₁	—	2	2	no	—
441	C₄×C₆₁	—	4	2	no	—
442	C₄×C₆₁	—	4	2	no	—
443	C₄×C₆₁	—	4	2	no	—
444	C₄×C₆₁	—	4	2	no	—
445	C₄×C₆₁	—	4	2	no	—
446	C₄×C₆₁	D₄²	1	2	yes	—
447	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
448	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂²×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic, complemented
450	C₂²×#135	C₂×C₆₁	1	1	yes	characteristic, complemented
451	C₂×#547	C₂×C₆₁	1	1	yes	characteristic, complemented
452	C₂×#546	C₂×C₆₁	1	1	yes	characteristic, complemented
453	#3267	C₂×C₆₁	1	16	yes	direct product factor
454	C₂×#497	C₂×C₆₁	1	1	yes	characteristic, complemented
455	C₂×#470	C₂×C₆₁	1	1	yes	characteristic, complemented
456	C₂×#465	C₂×C₆₁	1	1	yes	characteristic, complemented
457	C₂×#463	C₂×C₆₁	1	1	yes	characteristic, complemented
458	C₂×#461	C₂×C₆₁	1	1	yes	characteristic, complemented
459	C₂×#452	C₂×C₆₁	1	1	yes	characteristic, complemented
460	C₂×#452	C₂×C₆₁	1	1	yes	characteristic, complemented
461	C₂×#449	C₂×C₆₁	1	1	yes	characteristic, complemented
462	C₂×#450	C₂×C₆₁	1	1	yes	characteristic, complemented
463	C₂×#442	C₂×C₆₁	1	1	yes	characteristic, complemented
464	C₂×#435	C₂×C₆₁	1	1	yes	characteristic, complemented
465	C₂×C₆₁	—	4	2	no	—
466	C₂×C₆₁	—	4	2	no	—
467	C₂×C₆₁	—	4	4	no	—
468	C₂×C₆₁	—	4	4	no	—
469	C₂×C₆₁	—	8	2	no	—
470	C₂×C₆₁	#3267	1	4	yes	direct product factor
471	C₂×C₆₁	C₂×D₄²	1	1	yes	characteristic
472	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
473	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
474	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
475	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
476	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
477	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
478	C₂×AGL(1,ℤ/8)	—	2	8	no	—
479	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	8	yes	complemented
480	C₂×#135	—	2	8	no	—
481	C₂×#135	C₂²×C₆₁	1	8	yes	complemented
482	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
483	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
484	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
485	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
486	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
487	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
488	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
489	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
490	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
491	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
492	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
493	#547	—	2	4	no	—
494	#547	C₂²×C₆₁	1	8	yes	complemented
495	#546	—	2	4	no	—
496	#546	C₂²×C₆₁	1	8	yes	complemented
497	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
498	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
499	C₂×#123	—	2	1	no	—
500	C₂×#123	—	2	1	no	—
501	C₂×#123	—	2	1	no	—
502	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
503	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
504	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
505	C₂×#121	—	2	1	no	—
506	C₂×#121	—	2	1	no	—
507	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
508	C₂×#120	—	2	1	no	—
509	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
510	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
511	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
512	C₂²×C₄⋊C₄	—	2	1	no	—
513	C₂²×C₂²⋊C₄	—	2	1	no	—
514	#497	C₂²×C₆₁	1	8	yes	complemented
515	#470	C₂²×C₆₁	1	8	yes	complemented
516	#465	C₂²×C₆₁	1	8	yes	complemented
517	#463	C₂²×C₆₁	1	8	yes	complemented
518	#461	C₂²×C₆₁	1	8	yes	complemented
519	#452	C₂²×C₆₁	1	8	yes	complemented
520	#452	C₂²×C₆₁	1	8	yes	complemented
521	#450	C₂²×C₆₁	1	8	yes	complemented
522	#449	C₂²×C₆₁	1	8	yes	complemented
523	#442	C₂²×C₆₁	1	8	yes	complemented
524	#435	C₂²×C₆₁	1	8	yes	complemented
525	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
526	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
527	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
528	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
529	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
530	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
531	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
532	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
533	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
534	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
535	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic, complemented
536	C₆₁	C₂×#3267	1	1	yes	characteristic, direct product factor, Sylow
537	C₂⁵	—	2	1	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	—	2	2	no	—
540	C₂×#41	—	2	2	no	—
541	C₂×#41	—	2	4	no	—
542	C₂×#41	—	2	4	no	—
543	C₂×#41	—	2	4	no	—
544	C₂×#41	—	4	2	no	—
545	C₂×#41	—	4	2	no	—
546	C₂×#41	—	4	2	no	—
547	C₂×#41	C₂³×C₆₁	1	4	yes	—
548	C₂×#41	C₂³×C₆₁	1	4	yes	—
549	C₂×#41	C₂³×C₆₁	1	4	yes	complemented
550	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
551	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
552	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
553	C₂²×D₄	—	2	4	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	1	no	—
559	C₂²×D₄	—	2	2	no	—
560	C₂²×D₄	—	4	2	no	—
561	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
562	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
564	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
565	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
566	C₂³×C₄	—	2	1	no	—
567	C₂³×C₄	—	2	1	no	—
568	C₂³×C₄	—	2	1	no	—
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	—	2	1	no	—
571	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
573	AGL(1,ℤ/8)	—	2	32	no	—
574	#135	—	2	32	no	—
575	C₂×Q₁₆	—	2	4	no	—
576	C₂×Q₁₆	—	4	2	no	—
577	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	complemented
578	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	complemented
579	C₂×SD₁₆	—	2	4	no	—
580	C₂×SD₁₆	—	2	4	no	—
581	C₂×SD₁₆	—	2	4	no	—
582	C₂×SD₁₆	—	2	4	no	—
583	C₂×SD₁₆	—	4	2	no	—
584	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
585	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
586	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
587	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
588	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	complemented
589	C₂×D₈	—	2	4	no	—
590	C₂×D₈	D₄×C₆₁	1	8	yes	complemented
591	C₂×D₈	C₂³×C₆₁	1	4	yes	—
592	C₂×D₈	C₂³×C₆₁	1	4	yes	—
593	C₂×M₁₆	—	2	4	no	—
594	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
595	C₂²×C₈	—	2	4	no	—
596	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
597	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
598	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
599	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
600	C₂²×C₈	C₂³×C₆₁	1	4	yes	complemented
601	C₄⋊Q₈	—	2	2	no	—
602	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	complemented
603	#124	—	2	2	no	—
604	#124	C₂³×C₆₁	1	4	yes	—
605	#123	—	2	8	no	—
606	#123	—	2	8	no	—
607	#123	—	2	8	no	—
608	C₂²⋊Q₈	—	2	2	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
612	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
613	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	complemented
614	#121	—	2	8	no	—
615	#121	—	2	2	no	—
616	#121	—	2	8	no	—
617	#121	C₂³×C₆₁	1	4	yes	—
618	#120	—	2	8	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	D₄×C₆₁	1	4	yes	—
622	C₄×D₄	C₂³×C₆₁	1	4	yes	—
623	C₄×D₄	C₂³×C₆₁	1	4	yes	—
624	C₄×D₄	C₂³×C₆₁	1	4	yes	complemented
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	8	no	—
631	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	8	no	—
643	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
646	#106	C₂³×C₆₁	1	4	yes	complemented
647	C₄⋊C₈	C₂³×C₆₁	1	4	yes	complemented
648	#103	C₂³×C₆₁	1	4	yes	complemented
649	#103	C₂³×C₆₁	1	4	yes	complemented
650	#103	C₂³×C₆₁	1	4	yes	complemented
651	#102	C₂³×C₆₁	1	4	yes	—
652	#102	C₂³×C₆₁	1	4	yes	—
653	#102	C₂³×C₆₁	1	4	yes	complemented
654	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
655	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	complemented
656	#97	C₂³×C₆₁	1	4	yes	complemented
657	C₂⁴	—	2	1	no	—
658	C₂⁴	—	2	1	no	—
659	C₂⁴	—	2	1	no	—
660	C₂⁴	—	2	4	no	—
661	C₂⁴	—	4	4	no	—
662	C₂⁴	—	4	4	no	—
663	C₂⁴	—	8	2	no	—
664	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
665	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
666	#41	—	2	8	no	—
667	#41	—	2	8	no	—
668	#41	—	2	8	no	—
669	#41	—	4	4	no	—
670	#41	—	4	4	no	—
671	#41	—	4	4	no	—
672	#41	—	4	8	no	—
673	#41	—	4	8	no	—
674	#41	—	4	8	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
685	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
686	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
687	C₂×D₄	—	2	8	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	4	4	no	—
701	C₂×D₄	—	4	8	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	4	4	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	8	2	no	—
708	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
709	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
710	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
711	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
712	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
713	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	4	4	no	—
729	C₂²×C₄	—	4	4	no	—
730	C₂²×C₄	—	4	4	no	—
731	C₂²×C₄	—	4	4	no	—
732	C₂²×C₄	—	8	2	no	—
733	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
737	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
738	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
742	Q₁₆	—	2	8	no	—
743	Q₁₆	—	4	4	no	—
744	SD₁₆	—	2	8	no	—
745	SD₁₆	—	2	8	no	—
746	SD₁₆	—	2	8	no	—
747	SD₁₆	—	2	8	no	—
748	SD₁₆	—	4	4	no	—
749	D₈	—	2	8	no	—
750	D₈	C₂×D₄×C₆₁	1	16	yes	complemented
751	M₁₆	—	2	8	no	—
752	C₂×C₈	—	2	2	no	—
753	C₂×C₈	—	2	2	no	—
754	C₂×C₈	—	2	2	no	—
755	C₂×C₈	—	2	8	no	—
756	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
757	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
758	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
759	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
760	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
769	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
770	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
780	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
781	C₄²	C₂×D₄×C₆₁	1	2	yes	—
782	C₄²	C₂⁴×C₆₁	1	2	yes	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	4	no	—
786	C₂³	—	2	4	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	4	8	no	—
795	C₂³	—	4	8	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	2	no	—
800	C₂³	—	4	2	no	—
801	C₂³	—	4	2	no	—
802	C₂³	—	4	2	no	—
803	C₂³	—	8	4	no	—
804	C₂³	—	8	16	no	—
805	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
806	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
807	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
808	Q₈	—	2	2	no	—
809	Q₈	—	2	2	no	—
810	Q₈	—	2	2	no	—
811	Q₈	—	2	2	no	—
812	Q₈	—	2	2	no	—
813	Q₈	—	2	2	no	—
814	Q₈	—	4	2	no	—
815	Q₈	—	4	2	no	—
816	Q₈	—	4	2	no	—
817	D₄	—	2	4	no	—
818	D₄	—	2	4	no	—
819	D₄	—	2	2	no	—
820	D₄	—	2	2	no	—
821	D₄	—	2	2	no	—
822	D₄	—	2	2	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	8	no	—
825	D₄	—	4	8	no	—
826	D₄	—	4	8	no	—
827	D₄	—	4	8	no	—
828	D₄	—	4	2	no	—
829	D₄	—	8	4	no	—
830	D₄	C₂²×D₄×C₆₁	1	4	yes	—
831	D₄	C₂²×D₄×C₆₁	1	4	yes	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	4	8	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	8	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	8	4	no	—
857	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
858	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
860	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
863	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
864	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
865	C₈	—	2	2	no	—
866	C₈	—	2	2	no	—
867	C₈	—	2	2	no	—
868	C₈	C₂²×D₄×C₆₁	1	4	yes	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	4	no	—
882	C₂²	—	4	4	no	—
883	C₂²	—	4	8	no	—
884	C₂²	—	4	8	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	8	16	no	—
889	C₂²	—	8	4	no	—
890	C₂²	D₄²×C₆₁	1	2	yes	—
891	C₂²	C₆₁×#575	1	2	yes	—
892	C₂²	C₆₁×#577	1	2	yes	—
893	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	D₄²×C₆₁	1	2	yes	—
904	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
905	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
906	C₂	—	4	2	no	—
907	C₂	—	4	2	no	—
908	C₂	—	4	4	no	—
909	C₂	—	4	4	no	—
910	C₂	—	8	2	no	—
911	C₂	C₆₁×#3267	1	4	yes	direct product factor
912	C₂	C₂×D₄²×C₆₁	1	1	yes	characteristic
913	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
914	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
2. C₂²×#135×C₆₁	C₂	semidirect
3. C₂×C₆₁×#547	C₂	semidirect
4. C₂×C₆₁×#546	C₂	semidirect
5. C₆₁×#3267	C₂	direct (N × H)
6. C₂×C₆₁×#497	C₂	semidirect
7. C₂×C₆₁×#470	C₂	semidirect
8. C₂×C₆₁×#465	C₂	semidirect
9. C₂×C₆₁×#463	C₂	semidirect
10. C₂×C₆₁×#461	C₂	semidirect
11. C₂×C₆₁×#452	C₂	semidirect
12. C₂×C₆₁×#452	C₂	semidirect
13. C₂×C₆₁×#449	C₂	semidirect
14. C₂×C₆₁×#450	C₂	semidirect
15. C₂×C₆₁×#442	C₂	semidirect
16. C₂×C₆₁×#435	C₂	semidirect
19. C₂²×#41×C₆₁	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
24. C₂×#135×C₆₁	C₂²	semidirect
25. C₂²×Q₁₆×C₆₁	C₂²	semidirect
26. C₂²×Q₁₆×C₆₁	C₂²	semidirect
31. C₂²×SD₁₆×C₆₁	C₂²	semidirect
35. C₂³×C₈×C₆₁	C₂²	semidirect
37. C₆₁×#547	C₂²	semidirect
39. C₆₁×#546	C₂²	semidirect
40. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
47. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
54. C₂×C₄×D₄×C₆₁	C₂²	semidirect
57. C₆₁×#497	C₂²	semidirect
58. C₆₁×#470	C₂²	semidirect
59. C₆₁×#465	C₂²	semidirect
60. C₆₁×#463	C₂²	semidirect
61. C₆₁×#461	C₂²	semidirect
62. C₆₁×#452	C₂²	semidirect
63. C₆₁×#452	C₂²	semidirect
64. C₆₁×#450	C₂²	semidirect
65. C₆₁×#449	C₂²	semidirect
66. C₆₁×#442	C₂²	semidirect
67. C₆₁×#435	C₂²	semidirect
68. C₂×#106×C₆₁	C₂²	semidirect
69. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
70. C₂×#103×C₆₁	C₂²	semidirect
71. C₂×#103×C₆₁	C₂²	semidirect
72. C₂×#103×C₆₁	C₂²	semidirect
75. C₂×#102×C₆₁	C₂²	semidirect
77. C₂×C₂²⋊C₈×C₆₁	C₂²	semidirect
78. C₂×#97×C₆₁	C₂²	semidirect
91. C₂×#41×C₆₁	C₂³	semidirect
119. C₂×Q₁₆×C₆₁	C₂³	semidirect
120. C₂×Q₁₆×C₆₁	C₂³	semidirect
130. C₂×SD₁₆×C₆₁	C₂³	semidirect
132. C₂×D₈×C₆₁	D₄	semidirect
142. C₂²×C₈×C₆₁	C₂³	semidirect
144. C₄⋊Q₈×C₆₁	C₂³	semidirect
155. C₂²⋊Q₈×C₆₁	C₂³	semidirect
166. C₄×D₄×C₆₁	C₂³	semidirect
188. #106×C₆₁	C₂³	semidirect
189. C₄⋊C₈×C₆₁	C₂³	semidirect
190. #103×C₆₁	C₂³	semidirect
191. #103×C₆₁	C₂³	semidirect
192. #103×C₆₁	C₂³	semidirect
195. #102×C₆₁	C₂³	semidirect
197. C₂²⋊C₈×C₆₁	C₂³	semidirect
198. #97×C₆₁	C₂³	semidirect
292. D₈×C₆₁	C₂×D₄	semidirect
411. C₂×#3267	C₆₁	direct (N × H)
449. C₂²×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
450. C₂²×#135	C₂×C₆₁	semidirect
451. C₂×#547	C₂×C₆₁	semidirect
452. C₂×#546	C₂×C₆₁	semidirect
453. #3267	C₂×C₆₁	direct (N × H)
454. C₂×#497	C₂×C₆₁	semidirect
455. C₂×#470	C₂×C₆₁	semidirect
456. C₂×#465	C₂×C₆₁	semidirect
457. C₂×#463	C₂×C₆₁	semidirect
458. C₂×#461	C₂×C₆₁	semidirect
459. C₂×#452	C₂×C₆₁	semidirect
460. C₂×#452	C₂×C₆₁	semidirect
461. C₂×#449	C₂×C₆₁	semidirect
462. C₂×#450	C₂×C₆₁	semidirect
463. C₂×#442	C₂×C₆₁	semidirect
464. C₂×#435	C₂×C₆₁	semidirect
470. C₂×C₆₁	#3267	direct (N × H)
476. C₂²×#41	C₂²×C₆₁	semidirect
479. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
481. C₂×#135	C₂²×C₆₁	semidirect
482. C₂²×Q₁₆	C₂²×C₆₁	semidirect
483. C₂²×Q₁₆	C₂²×C₆₁	semidirect
488. C₂²×SD₁₆	C₂²×C₆₁	semidirect
492. C₂³×C₈	C₂²×C₆₁	semidirect
494. #547	C₂²×C₆₁	semidirect
496. #546	C₂²×C₆₁	semidirect
497. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
504. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
511. C₂×C₄×D₄	C₂²×C₆₁	semidirect
514. #497	C₂²×C₆₁	semidirect
515. #470	C₂²×C₆₁	semidirect
516. #465	C₂²×C₆₁	semidirect
517. #463	C₂²×C₆₁	semidirect
518. #461	C₂²×C₆₁	semidirect
519. #452	C₂²×C₆₁	semidirect
520. #452	C₂²×C₆₁	semidirect
521. #450	C₂²×C₆₁	semidirect
522. #449	C₂²×C₆₁	semidirect
523. #442	C₂²×C₆₁	semidirect
524. #435	C₂²×C₆₁	semidirect
525. C₂×#106	C₂²×C₆₁	semidirect
526. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
527. C₂×#103	C₂²×C₆₁	semidirect
528. C₂×#103	C₂²×C₆₁	semidirect
529. C₂×#103	C₂²×C₆₁	semidirect
532. C₂×#102	C₂²×C₆₁	semidirect
534. C₂×C₂²⋊C₈	C₂²×C₆₁	semidirect
535. C₂×#97	C₂²×C₆₁	semidirect
536. C₆₁	C₂×#3267	direct (N × H)
549. C₂×#41	C₂³×C₆₁	semidirect
577. C₂×Q₁₆	C₂³×C₆₁	semidirect
578. C₂×Q₁₆	C₂³×C₆₁	semidirect
588. C₂×SD₁₆	C₂³×C₆₁	semidirect
590. C₂×D₈	D₄×C₆₁	semidirect
600. C₂²×C₈	C₂³×C₆₁	semidirect
602. C₄⋊Q₈	C₂³×C₆₁	semidirect
613. C₂²⋊Q₈	C₂³×C₆₁	semidirect
624. C₄×D₄	C₂³×C₆₁	semidirect
646. #106	C₂³×C₆₁	semidirect
647. C₄⋊C₈	C₂³×C₆₁	semidirect
648. #103	C₂³×C₆₁	semidirect
649. #103	C₂³×C₆₁	semidirect
650. #103	C₂³×C₆₁	semidirect
653. #102	C₂³×C₆₁	semidirect
655. C₂²⋊C₈	C₂³×C₆₁	semidirect
656. #97	C₂³×C₆₁	semidirect
750. D₈	C₂×D₄×C₆₁	semidirect
911. C₂	C₆₁×#3267	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₆₁	2
C₂²×#135×C₆₁	2
C₂×C₆₁×#547	2
C₂×C₆₁×#546	2
C₆₁×#3267	2
C₂×C₆₁×#497	2
C₂×C₆₁×#470	2
C₂×C₆₁×#465	2
C₂×C₆₁×#463	2
C₂×C₆₁×#461	2
C₂×C₆₁×#452	2
C₂×C₆₁×#449	2
C₂×C₆₁×#450	2
C₂×C₆₁×#442	2
C₂×C₆₁×#435	2
C₂×#3267	61

Subgroups — C2×C61×#3267 #29564458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3267 #29564458