Subgroups — C₂×C₆₁×#3343 #29564668

Order 15616.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#547	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3343	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₆₁×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×#483	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₆₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#468	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₆₁×#465	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₆₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#107×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₆₁	—	2	1	no	—
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#552	—	2	4	no	—
22	C₆₁×#552	C₂²	1	8	yes	complemented
23	C₆₁×#547	—	2	4	no	—
24	C₆₁×#547	C₂²	1	8	yes	—
25	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#126×C₆₁	—	2	1	no	—
27	C₂×#125×C₆₁	—	2	1	no	—
28	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#123×C₆₁	—	2	1	no	—
30	C₂×#123×C₆₁	—	2	1	no	—
31	C₂×#123×C₆₁	—	2	1	no	—
32	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×#117×C₆₁	—	2	1	no	—
41	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#501	C₂²	1	8	yes	complemented
46	C₆₁×#484	C₂²	1	8	yes	complemented
47	C₆₁×#483	C₂²	1	8	yes	complemented
48	C₆₁×#482	C₂²	1	8	yes	complemented
49	C₆₁×#480	C₂²	1	8	yes	complemented
50	C₆₁×#478	C₂²	1	8	yes	complemented
51	C₆₁×#477	C₂²	1	8	yes	complemented
52	C₆₁×#468	C₂²	1	8	yes	complemented
53	C₆₁×#465	C₂²	1	8	yes	complemented
54	C₆₁×#440	C₂²	1	8	yes	complemented
55	C₆₁×#435	C₂²	1	8	yes	complemented
56	C₆₁×#428	C₂²	1	8	yes	complemented
57	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
58	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
59	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
60	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
61	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
62	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
63	C₂×#107×C₆₁	C₂²	1	8	yes	complemented
64	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
65	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
66	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
67	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
68	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
69	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
70	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
71	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
72	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
73	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
76	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
77	C₂×#41×C₆₁	—	2	8	no	—
78	C₂×#41×C₆₁	—	4	8	no	—
79	C₂²×Q₈×C₆₁	—	2	1	no	—
80	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₆₁	—	2	1	no	—
82	C₂²×D₄×C₆₁	—	2	1	no	—
83	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
84	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₆₁	—	2	1	no	—
86	C₂³×C₄×C₆₁	—	2	1	no	—
87	C₂³×C₄×C₆₁	—	2	1	no	—
88	C₂³×C₄×C₆₁	—	2	1	no	—
89	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
91	C₂×SD₁₆×C₆₁	—	2	4	no	—
92	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
93	C₂×M₁₆×C₆₁	—	2	4	no	—
94	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
95	C₂²×C₈×C₆₁	—	2	4	no	—
96	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
98	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₁	—	2	2	no	—
102	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
103	#126×C₆₁	—	2	8	no	—
104	#125×C₆₁	—	2	8	no	—
105	#125×C₆₁	—	2	2	no	—
106	#125×C₆₁	C₂³	1	4	yes	—
107	#123×C₆₁	—	2	8	no	—
108	#123×C₆₁	—	2	8	no	—
109	#123×C₆₁	—	2	8	no	—
110	C₂²⋊Q₈×C₆₁	—	2	2	no	—
111	C₂²⋊Q₈×C₆₁	—	2	2	no	—
112	C₂²⋊Q₈×C₆₁	—	2	8	no	—
113	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
114	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
115	#121×C₆₁	—	2	2	no	—
116	#121×C₆₁	—	2	2	no	—
117	#121×C₆₁	C₂³	1	4	yes	—
118	#121×C₆₁	C₂³	1	4	yes	—
119	C₄×Q₈×C₆₁	—	2	2	no	—
120	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
121	C₄×D₄×C₆₁	—	2	2	no	—
122	C₄×D₄×C₆₁	D₄	1	4	yes	—
123	C₄×D₄×C₆₁	C₂³	1	4	yes	—
124	C₄×D₄×C₆₁	C₂³	1	4	yes	—
125	#117×C₆₁	—	2	2	no	—
126	#117×C₆₁	—	2	8	no	—
127	#117×C₆₁	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
129	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
131	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
132	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
133	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
134	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
135	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
136	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
137	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
138	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
139	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
140	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
145	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
158	C₂×C₄²×C₆₁	—	2	1	no	—
159	C₂×C₄²×C₆₁	—	2	1	no	—
160	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
161	#107×C₆₁	C₂³	1	4	yes	—
162	#107×C₆₁	C₂³	1	4	yes	—
163	#107×C₆₁	C₂³	1	4	yes	—
164	#107×C₆₁	C₂³	1	4	yes	—
165	#107×C₆₁	C₂³	1	4	yes	—
166	#107×C₆₁	C₂³	1	4	yes	—
167	#106×C₆₁	C₂³	1	4	yes	—
168	#106×C₆₁	C₂³	1	4	yes	—
169	#106×C₆₁	C₂³	1	4	yes	—
170	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
171	#103×C₆₁	C₂³	1	4	yes	—
172	#103×C₆₁	C₂³	1	4	yes	—
173	#103×C₆₁	C₂³	1	4	yes	—
174	#102×C₆₁	C₂³	1	4	yes	—
175	#102×C₆₁	C₂³	1	4	yes	—
176	#102×C₆₁	C₂³	1	4	yes	—
177	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
178	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
179	#97×C₆₁	C₂³	1	4	yes	—
180	C₂⁴×C₆₁	—	2	1	no	—
181	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
182	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
183	#41×C₆₁	—	4	32	no	—
184	C₂×Q₈×C₆₁	—	2	1	no	—
185	C₂×Q₈×C₆₁	—	2	4	no	—
186	C₂×Q₈×C₆₁	—	2	2	no	—
187	C₂×Q₈×C₆₁	—	2	2	no	—
188	C₂×Q₈×C₆₁	—	4	4	no	—
189	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
190	C₂×D₄×C₆₁	—	2	4	no	—
191	C₂×D₄×C₆₁	—	2	4	no	—
192	C₂×D₄×C₆₁	—	2	4	no	—
193	C₂×D₄×C₆₁	—	2	1	no	—
194	C₂×D₄×C₆₁	—	2	2	no	—
195	C₂×D₄×C₆₁	—	2	2	no	—
196	C₂×D₄×C₆₁	—	4	4	no	—
197	C₂×D₄×C₆₁	—	4	4	no	—
198	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
199	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₆₁	—	2	2	no	—
201	C₂²×C₄×C₆₁	—	2	2	no	—
202	C₂²×C₄×C₆₁	—	2	2	no	—
203	C₂²×C₄×C₆₁	—	2	2	no	—
204	C₂²×C₄×C₆₁	—	2	4	no	—
205	C₂²×C₄×C₆₁	—	2	4	no	—
206	C₂²×C₄×C₆₁	—	2	4	no	—
207	C₂²×C₄×C₆₁	—	2	1	no	—
208	C₂²×C₄×C₆₁	—	2	1	no	—
209	C₂²×C₄×C₆₁	—	2	1	no	—
210	C₂²×C₄×C₆₁	—	2	1	no	—
211	C₂²×C₄×C₆₁	—	2	1	no	—
212	C₂²×C₄×C₆₁	—	2	1	no	—
213	C₂²×C₄×C₆₁	—	2	1	no	—
214	C₂²×C₄×C₆₁	—	2	4	no	—
215	C₂²×C₄×C₆₁	—	4	4	no	—
216	C₂²×C₄×C₆₁	—	4	4	no	—
217	C₂²×C₄×C₆₁	—	4	4	no	—
218	C₂²×C₄×C₆₁	—	4	4	no	—
219	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
228	SD₁₆×C₆₁	—	2	8	no	—
229	M₁₆×C₆₁	—	2	8	no	—
230	C₂×C₈×C₆₁	—	2	2	no	—
231	C₂×C₈×C₆₁	—	2	2	no	—
232	C₂×C₈×C₆₁	—	2	2	no	—
233	C₂×C₈×C₆₁	—	2	8	no	—
234	C₂×C₈×C₆₁	#41	1	4	yes	complemented
235	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
236	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
237	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
238	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
239	C₄⋊C₄×C₆₁	—	2	1	no	—
240	C₄⋊C₄×C₆₁	—	2	1	no	—
241	C₄⋊C₄×C₆₁	—	2	1	no	—
242	C₄⋊C₄×C₆₁	—	2	1	no	—
243	C₄⋊C₄×C₆₁	—	2	4	no	—
244	C₄⋊C₄×C₆₁	—	2	4	no	—
245	C₄⋊C₄×C₆₁	—	2	1	no	—
246	C₄⋊C₄×C₆₁	—	2	4	no	—
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	4	no	—
251	C₄⋊C₄×C₆₁	—	2	4	no	—
252	C₄⋊C₄×C₆₁	—	2	4	no	—
253	C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
255	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
261	C₂²⋊C₄×C₆₁	—	2	4	no	—
262	C₂²⋊C₄×C₆₁	—	2	4	no	—
263	C₂²⋊C₄×C₆₁	—	2	4	no	—
264	C₂²⋊C₄×C₆₁	—	2	4	no	—
265	C₂²⋊C₄×C₆₁	—	2	4	no	—
266	C₂²⋊C₄×C₆₁	—	2	4	no	—
267	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
268	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
269	C₄²×C₆₁	—	2	4	no	—
270	C₄²×C₆₁	—	2	4	no	—
271	C₄²×C₆₁	C₂×D₄	1	2	yes	—
272	C₄²×C₆₁	C₂⁴	1	2	yes	—
273	C₂³×C₆₁	—	2	2	no	—
274	C₂³×C₆₁	—	2	2	no	—
275	C₂³×C₆₁	—	2	2	no	—
276	C₂³×C₆₁	—	2	2	no	—
277	C₂³×C₆₁	—	2	2	no	—
278	C₂³×C₆₁	—	2	2	no	—
279	C₂³×C₆₁	—	4	2	no	—
280	C₂³×C₆₁	—	4	2	no	—
281	C₂³×C₆₁	—	4	2	no	—
282	C₂³×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
283	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
284	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
285	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
286	Q₈×C₆₁	—	2	2	no	—
287	Q₈×C₆₁	—	2	2	no	—
288	Q₈×C₆₁	—	4	8	no	—
289	Q₈×C₆₁	—	4	2	no	—
290	D₄×C₆₁	—	2	8	no	—
291	D₄×C₆₁	—	2	2	no	—
292	D₄×C₆₁	—	2	2	no	—
293	D₄×C₆₁	—	4	8	no	—
294	D₄×C₆₁	—	4	8	no	—
295	D₄×C₆₁	—	4	2	no	—
296	C₂×C₄×C₆₁	—	2	2	no	—
297	C₂×C₄×C₆₁	—	2	2	no	—
298	C₂×C₄×C₆₁	—	2	2	no	—
299	C₂×C₄×C₆₁	—	2	2	no	—
300	C₂×C₄×C₆₁	—	2	4	no	—
301	C₂×C₄×C₆₁	—	2	4	no	—
302	C₂×C₄×C₆₁	—	2	2	no	—
303	C₂×C₄×C₆₁	—	2	2	no	—
304	C₂×C₄×C₆₁	—	2	2	no	—
305	C₂×C₄×C₆₁	—	2	2	no	—
306	C₂×C₄×C₆₁	—	2	2	no	—
307	C₂×C₄×C₆₁	—	2	2	no	—
308	C₂×C₄×C₆₁	—	2	2	no	—
309	C₂×C₄×C₆₁	—	2	2	no	—
310	C₂×C₄×C₆₁	—	2	2	no	—
311	C₂×C₄×C₆₁	—	2	2	no	—
312	C₂×C₄×C₆₁	—	2	2	no	—
313	C₂×C₄×C₆₁	—	4	8	no	—
314	C₂×C₄×C₆₁	—	4	8	no	—
315	C₂×C₄×C₆₁	—	4	2	no	—
316	C₂×C₄×C₆₁	—	4	8	no	—
317	C₂×C₄×C₆₁	—	4	2	no	—
318	C₂×C₄×C₆₁	—	4	2	no	—
319	C₂×C₄×C₆₁	—	4	2	no	—
320	C₂×C₄×C₆₁	—	4	2	no	—
321	C₂×C₄×C₆₁	—	4	2	no	—
322	C₂×C₄×C₆₁	—	4	8	no	—
323	C₂×C₄×C₆₁	—	4	2	no	—
324	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
330	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
331	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
332	C₈×C₆₁	—	2	2	no	—
333	C₈×C₆₁	—	2	2	no	—
334	C₈×C₆₁	—	2	2	no	—
335	C₈×C₆₁	C₂×#41	1	4	yes	complemented
336	C₂×#3343	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
337	C₂²×C₆₁	—	2	8	no	—
338	C₂²×C₆₁	—	2	2	no	—
339	C₂²×C₆₁	—	2	2	no	—
340	C₂²×C₆₁	—	2	2	no	—
341	C₂²×C₆₁	—	2	2	no	—
342	C₂²×C₆₁	—	2	2	no	—
343	C₂²×C₆₁	—	4	4	no	—
344	C₂²×C₆₁	—	4	2	no	—
345	C₂²×C₆₁	—	4	2	no	—
346	C₂²×C₆₁	—	4	2	no	—
347	C₂²×C₆₁	—	8	4	no	—
348	C₂²×C₆₁	#547	1	2	yes	—
349	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
350	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
351	C₂²×C₆₁	#578	1	2	yes	—
352	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
353	C₄×C₆₁	—	2	2	no	—
354	C₄×C₆₁	—	2	2	no	—
355	C₄×C₆₁	—	2	2	no	—
356	C₄×C₆₁	—	2	2	no	—
357	C₄×C₆₁	—	4	2	no	—
358	C₄×C₆₁	—	4	2	no	—
359	C₄×C₆₁	—	4	2	no	—
360	C₄×C₆₁	—	4	2	no	—
361	C₄×C₆₁	—	4	2	no	—
362	C₄×C₆₁	—	4	2	no	—
363	C₄×C₆₁	—	4	2	no	—
364	C₄×C₆₁	#547	1	2	yes	—
365	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
366	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
367	C₂×#552	C₂×C₆₁	1	1	yes	characteristic, complemented
368	C₂×#547	C₂×C₆₁	1	1	yes	characteristic
369	#3343	C₂×C₆₁	1	16	yes	direct product factor
370	C₂×#501	C₂×C₆₁	1	1	yes	characteristic, complemented
371	C₂×#484	C₂×C₆₁	1	1	yes	characteristic, complemented
372	C₂×#482	C₂×C₆₁	1	1	yes	characteristic, complemented
373	C₂×#483	C₂×C₆₁	1	1	yes	characteristic, complemented
374	C₂×#480	C₂×C₆₁	1	1	yes	characteristic, complemented
375	C₂×#477	C₂×C₆₁	1	1	yes	characteristic, complemented
376	C₂×#478	C₂×C₆₁	1	1	yes	characteristic, complemented
377	C₂×#468	C₂×C₆₁	1	1	yes	characteristic, complemented
378	C₂×#465	C₂×C₆₁	1	1	yes	characteristic, complemented
379	C₂×#440	C₂×C₆₁	1	1	yes	characteristic, complemented
380	C₂×#435	C₂×C₆₁	1	1	yes	characteristic, complemented
381	C₂×#428	C₂×C₆₁	1	1	yes	characteristic, complemented
382	C₂²×#107	C₂×C₆₁	1	1	yes	characteristic, complemented
383	C₂×C₆₁	—	2	4	no	—
384	C₂×C₆₁	—	4	2	no	—
385	C₂×C₆₁	—	8	2	no	—
386	C₂×C₆₁	#3343	1	4	yes	direct product factor
387	C₂×C₆₁	C₂×#547	1	1	yes	characteristic
388	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
390	C₂²×#41	—	2	1	no	—
391	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
392	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
393	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
394	#552	—	2	4	no	—
395	#552	C₂²×C₆₁	1	8	yes	complemented
396	#547	—	2	4	no	—
397	#547	C₂²×C₆₁	1	8	yes	—
398	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
399	C₂×#126	—	2	1	no	—
400	C₂×#125	—	2	1	no	—
401	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
402	C₂×#123	—	2	1	no	—
403	C₂×#123	—	2	1	no	—
404	C₂×#123	—	2	1	no	—
405	C₂×C₂²⋊Q₈	—	2	1	no	—
406	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
407	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
408	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
409	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
410	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
411	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
413	C₂×#117	—	2	1	no	—
414	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
416	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
417	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
418	#501	C₂²×C₆₁	1	8	yes	complemented
419	#484	C₂²×C₆₁	1	8	yes	complemented
420	#483	C₂²×C₆₁	1	8	yes	complemented
421	#482	C₂²×C₆₁	1	8	yes	complemented
422	#480	C₂²×C₆₁	1	8	yes	complemented
423	#478	C₂²×C₆₁	1	8	yes	complemented
424	#477	C₂²×C₆₁	1	8	yes	complemented
425	#468	C₂²×C₆₁	1	8	yes	complemented
426	#465	C₂²×C₆₁	1	8	yes	complemented
427	#440	C₂²×C₆₁	1	8	yes	complemented
428	#435	C₂²×C₆₁	1	8	yes	complemented
429	#428	C₂²×C₆₁	1	8	yes	complemented
430	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
431	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
432	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
433	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
434	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
435	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
436	C₂×#107	C₂²×C₆₁	1	8	yes	complemented
437	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
438	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
439	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
440	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
441	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
442	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
443	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
444	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
445	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
446	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
447	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
448	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
449	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
450	C₆₁	C₂×#3343	1	1	yes	characteristic, direct product factor, Sylow
451	C₂×#41	—	2	8	no	—
452	C₂×#41	—	4	8	no	—
453	C₂²×Q₈	—	2	1	no	—
454	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	—	2	1	no	—
457	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	—	2	1	no	—
463	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
465	C₂×SD₁₆	—	2	4	no	—
466	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
467	C₂×M₁₆	—	2	4	no	—
468	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
469	C₂²×C₈	—	2	4	no	—
470	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
472	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
477	#126	—	2	8	no	—
478	#125	—	2	8	no	—
479	#125	—	2	2	no	—
480	#125	C₂³×C₆₁	1	4	yes	—
481	#123	—	2	8	no	—
482	#123	—	2	8	no	—
483	#123	—	2	8	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	8	no	—
487	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
488	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	C₂³×C₆₁	1	4	yes	—
492	#121	C₂³×C₆₁	1	4	yes	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	D₄×C₆₁	1	4	yes	—
497	C₄×D₄	C₂³×C₆₁	1	4	yes	—
498	C₄×D₄	C₂³×C₆₁	1	4	yes	—
499	#117	—	2	2	no	—
500	#117	—	2	8	no	—
501	#117	C₂³×C₆₁	1	4	yes	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	2	no	—
506	C₂×C₄⋊C₄	—	2	2	no	—
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
521	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
522	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
523	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
532	C₂×C₄²	—	2	1	no	—
533	C₂×C₄²	—	2	1	no	—
534	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
535	#107	C₂³×C₆₁	1	4	yes	—
536	#107	C₂³×C₆₁	1	4	yes	—
537	#107	C₂³×C₆₁	1	4	yes	—
538	#107	C₂³×C₆₁	1	4	yes	—
539	#107	C₂³×C₆₁	1	4	yes	—
540	#107	C₂³×C₆₁	1	4	yes	—
541	#106	C₂³×C₆₁	1	4	yes	—
542	#106	C₂³×C₆₁	1	4	yes	—
543	#106	C₂³×C₆₁	1	4	yes	—
544	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
545	#103	C₂³×C₆₁	1	4	yes	—
546	#103	C₂³×C₆₁	1	4	yes	—
547	#103	C₂³×C₆₁	1	4	yes	—
548	#102	C₂³×C₆₁	1	4	yes	—
549	#102	C₂³×C₆₁	1	4	yes	—
550	#102	C₂³×C₆₁	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
552	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
553	#97	C₂³×C₆₁	1	4	yes	—
554	C₂⁴	—	2	1	no	—
555	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
556	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
557	#41	—	4	32	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	4	no	—
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	4	4	no	—
563	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
573	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	—	4	4	no	—
593	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
598	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
602	SD₁₆	—	2	8	no	—
603	M₁₆	—	2	8	no	—
604	C₂×C₈	—	2	2	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	8	no	—
608	C₂×C₈	#41×C₆₁	1	4	yes	complemented
609	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
610	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
611	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
612	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
629	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
630	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
631	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
633	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
634	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
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	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
642	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	C₂×D₄×C₆₁	1	2	yes	—
646	C₄²	C₂⁴×C₆₁	1	2	yes	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
657	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
658	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
659	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	4	8	no	—
663	Q₈	—	4	2	no	—
664	D₄	—	2	8	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	2	no	—
667	D₄	—	4	8	no	—
668	D₄	—	4	8	no	—
669	D₄	—	4	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	8	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	8	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	4	8	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
703	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
704	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
705	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
706	C₈	—	2	2	no	—
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₈	C₂×#41×C₆₁	1	4	yes	complemented
710	C₂²	—	2	2	no	—
711	C₂²	—	2	8	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	4	4	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	8	4	no	—
721	C₂²	C₆₁×#547	1	2	yes	—
722	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	4	yes	—
723	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
724	C₂²	C₆₁×#578	1	2	yes	—
725	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
726	C₄	—	2	2	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	C₆₁×#547	1	2	yes	—
738	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
739	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
740	C₂	—	2	4	no	—
741	C₂	—	4	2	no	—
742	C₂	—	8	2	no	—
743	C₂	C₆₁×#3343	1	4	yes	direct product factor
744	C₂	C₂×C₆₁×#547	1	1	yes	characteristic
745	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
746	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#547	C₂
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. C₂×C₆₁×#552	C₂	semidirect
3. C₆₁×#3343	C₂	direct (N × H)
4. C₂×C₆₁×#501	C₂	semidirect
5. C₂×C₆₁×#484	C₂	semidirect
6. C₂×C₆₁×#482	C₂	semidirect
7. C₂×C₆₁×#483	C₂	semidirect
8. C₂×C₆₁×#480	C₂	semidirect
9. C₂×C₆₁×#477	C₂	semidirect
10. C₂×C₆₁×#478	C₂	semidirect
11. C₂×C₆₁×#468	C₂	semidirect
12. C₂×C₆₁×#465	C₂	semidirect
13. C₂×C₆₁×#440	C₂	semidirect
14. C₂×C₆₁×#435	C₂	semidirect
15. C₂×C₆₁×#428	C₂	semidirect
16. C₂²×#107×C₆₁	C₂	semidirect
22. C₆₁×#552	C₂²	semidirect
45. C₆₁×#501	C₂²	semidirect
46. C₆₁×#484	C₂²	semidirect
47. C₆₁×#483	C₂²	semidirect
48. C₆₁×#482	C₂²	semidirect
49. C₆₁×#480	C₂²	semidirect
50. C₆₁×#478	C₂²	semidirect
51. C₆₁×#477	C₂²	semidirect
52. C₆₁×#468	C₂²	semidirect
53. C₆₁×#465	C₂²	semidirect
54. C₆₁×#440	C₂²	semidirect
55. C₆₁×#435	C₂²	semidirect
56. C₆₁×#428	C₂²	semidirect
63. C₂×#107×C₆₁	C₂²	semidirect
234. C₂×C₈×C₆₁	#41	semidirect
335. C₈×C₆₁	C₂×#41	semidirect
336. C₂×#3343	C₆₁	direct (N × H)
367. C₂×#552	C₂×C₆₁	semidirect
369. #3343	C₂×C₆₁	direct (N × H)
370. C₂×#501	C₂×C₆₁	semidirect
371. C₂×#484	C₂×C₆₁	semidirect
372. C₂×#482	C₂×C₆₁	semidirect
373. C₂×#483	C₂×C₆₁	semidirect
374. C₂×#480	C₂×C₆₁	semidirect
375. C₂×#477	C₂×C₆₁	semidirect
376. C₂×#478	C₂×C₆₁	semidirect
377. C₂×#468	C₂×C₆₁	semidirect
378. C₂×#465	C₂×C₆₁	semidirect
379. C₂×#440	C₂×C₆₁	semidirect
380. C₂×#435	C₂×C₆₁	semidirect
381. C₂×#428	C₂×C₆₁	semidirect
382. C₂²×#107	C₂×C₆₁	semidirect
386. C₂×C₆₁	#3343	direct (N × H)
395. #552	C₂²×C₆₁	semidirect
418. #501	C₂²×C₆₁	semidirect
419. #484	C₂²×C₆₁	semidirect
420. #483	C₂²×C₆₁	semidirect
421. #482	C₂²×C₆₁	semidirect
422. #480	C₂²×C₆₁	semidirect
423. #478	C₂²×C₆₁	semidirect
424. #477	C₂²×C₆₁	semidirect
425. #468	C₂²×C₆₁	semidirect
426. #465	C₂²×C₆₁	semidirect
427. #440	C₂²×C₆₁	semidirect
428. #435	C₂²×C₆₁	semidirect
429. #428	C₂²×C₆₁	semidirect
436. C₂×#107	C₂²×C₆₁	semidirect
450. C₆₁	C₂×#3343	direct (N × H)
608. C₂×C₈	#41×C₆₁	semidirect
709. C₈	C₂×#41×C₆₁	semidirect
743. C₂	C₆₁×#3343	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#552	2
C₂×C₆₁×#547	2
C₆₁×#3343	2
C₂×C₆₁×#501	2
C₂×C₆₁×#484	2
C₂×C₆₁×#482	2
C₂×C₆₁×#483	2
C₂×C₆₁×#480	2
C₂×C₆₁×#477	2
C₂×C₆₁×#478	2
C₂×C₆₁×#468	2
C₂×C₆₁×#465	2
C₂×C₆₁×#440	2
C₂×C₆₁×#435	2
C₂×C₆₁×#428	2
C₂²×#107×C₆₁	2
C₂×#3343	61

Subgroups — C2×C61×#3343 #29564668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3343 #29564668