Subgroups — C₂×C₆₁×#3270 #29564461

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#548	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#3270	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×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₆₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₆₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₆₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₆₁×#441	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	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#137×C₆₁	—	2	8	no	—
22	C₂×#137×C₆₁	C₂²	1	8	yes	complemented
23	C₂²×Q₁₆×C₆₁	—	2	8	no	—
24	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
29	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
30	C₂²×Q₁₆×C₆₁	C₂²	1	8	yes	complemented
31	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
32	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
33	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₆₁	—	2	4	no	—
37	D₄×Q₈×C₆₁	C₂²	1	8	yes	complemented
38	C₆₁×#548	—	2	4	no	—
39	C₆₁×#548	C₂²	1	8	yes	—
40	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
41	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#124×C₆₁	—	2	1	no	—
43	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
45	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
46	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
47	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
50	C₂×#121×C₆₁	—	2	1	no	—
51	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
53	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₆₁	—	2	1	no	—
55	C₂×C₄×D₄×C₆₁	—	2	1	no	—
56	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
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×#464	C₂²	1	8	yes	complemented
61	C₆₁×#462	C₂²	1	8	yes	complemented
62	C₆₁×#452	C₂²	1	8	yes	complemented
63	C₆₁×#451	C₂²	1	8	yes	complemented
64	C₆₁×#451	C₂²	1	8	yes	complemented
65	C₆₁×#448	C₂²	1	8	yes	complemented
66	C₆₁×#441	C₂²	1	8	yes	complemented
67	C₆₁×#435	C₂²	1	8	yes	complemented
68	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
69	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
70	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
71	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
72	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
73	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
74	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
75	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
76	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
77	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
78	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
79	C₂×#41×C₆₁	—	2	2	no	—
80	C₂×#41×C₆₁	—	2	4	no	—
81	C₂×#41×C₆₁	—	4	2	no	—
82	C₂×#41×C₆₁	C₂³	1	4	yes	—
83	C₂²×Q₈×C₆₁	—	2	1	no	—
84	C₂²×Q₈×C₆₁	—	2	1	no	—
85	C₂²×Q₈×C₆₁	—	2	2	no	—
86	C₂²×Q₈×C₆₁	—	2	2	no	—
87	C₂²×Q₈×C₆₁	—	2	2	no	—
88	C₂²×Q₈×C₆₁	—	2	1	no	—
89	C₂²×Q₈×C₆₁	—	2	4	no	—
90	C₂²×Q₈×C₆₁	—	2	4	no	—
91	C₂²×Q₈×C₆₁	—	2	4	no	—
92	C₂²×Q₈×C₆₁	—	4	2	no	—
93	C₂²×Q₈×C₆₁	—	4	2	no	—
94	C₂²×Q₈×C₆₁	—	4	2	no	—
95	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
99	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
101	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₆₁	—	2	1	no	—
104	C₂²×D₄×C₆₁	—	2	1	no	—
105	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
106	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₁	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
113	#137×C₆₁	—	2	32	no	—
114	C₂×Q₁₆×C₆₁	—	2	4	no	—
115	C₂×Q₁₆×C₆₁	—	2	4	no	—
116	C₂×Q₁₆×C₆₁	—	2	4	no	—
117	C₂×Q₁₆×C₆₁	—	2	32	no	—
118	C₂×Q₁₆×C₆₁	—	2	4	no	—
119	C₂×Q₁₆×C₆₁	—	4	2	no	—
120	C₂×Q₁₆×C₆₁	D₄	1	8	yes	complemented
121	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
122	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
123	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
124	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
125	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
126	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
127	C₂×SD₁₆×C₆₁	—	2	4	no	—
128	C₂×SD₁₆×C₆₁	—	2	4	no	—
129	C₂×SD₁₆×C₆₁	—	4	2	no	—
130	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
131	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
132	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
133	C₂×M₁₆×C₆₁	—	2	4	no	—
134	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
135	C₂²×C₈×C₆₁	—	2	4	no	—
136	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
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	C₄⋊Q₈×C₆₁	—	2	8	no	—
142	C₄⋊Q₈×C₆₁	—	2	2	no	—
143	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
144	#124×C₆₁	—	2	8	no	—
145	#124×C₆₁	—	2	2	no	—
146	#124×C₆₁	C₂³	1	4	yes	—
147	C₂²⋊Q₈×C₆₁	—	2	2	no	—
148	C₂²⋊Q₈×C₆₁	—	2	2	no	—
149	C₂²⋊Q₈×C₆₁	—	2	2	no	—
150	C₂²⋊Q₈×C₆₁	—	2	8	no	—
151	C₂²⋊Q₈×C₆₁	—	2	8	no	—
152	C₂²⋊Q₈×C₆₁	—	2	8	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	—
156	#121×C₆₁	—	2	8	no	—
157	#121×C₆₁	—	2	2	no	—
158	#121×C₆₁	C₂³	1	4	yes	—
159	C₄×Q₈×C₆₁	—	2	2	no	—
160	C₄×Q₈×C₆₁	—	2	2	no	—
161	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
162	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
163	C₄×D₄×C₆₁	—	2	8	no	—
164	C₄×D₄×C₆₁	—	2	8	no	—
165	C₄×D₄×C₆₁	D₄	1	4	yes	—
166	C₄×D₄×C₆₁	C₂³	1	4	yes	—
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	1	no	—
173	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
174	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₆₁	—	2	1	no	—
186	C₂×C₄²×C₆₁	—	2	1	no	—
187	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
188	#106×C₆₁	C₂³	1	4	yes	—
189	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
190	#103×C₆₁	C₂³	1	4	yes	—
191	#103×C₆₁	C₂³	1	4	yes	—
192	#103×C₆₁	C₂³	1	4	yes	—
193	#103×C₆₁	C₂³	1	4	yes	—
194	#103×C₆₁	C₂³	1	4	yes	—
195	#102×C₆₁	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
197	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
198	#97×C₆₁	C₂³	1	4	yes	—
199	C₂⁴×C₆₁	—	2	1	no	—
200	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
201	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
202	#41×C₆₁	—	2	8	no	—
203	#41×C₆₁	—	4	4	no	—
204	#41×C₆₁	—	4	8	no	—
205	C₂×Q₈×C₆₁	—	2	1	no	—
206	C₂×Q₈×C₆₁	—	2	1	no	—
207	C₂×Q₈×C₆₁	—	2	4	no	—
208	C₂×Q₈×C₆₁	—	2	1	no	—
209	C₂×Q₈×C₆₁	—	2	4	no	—
210	C₂×Q₈×C₆₁	—	2	4	no	—
211	C₂×Q₈×C₆₁	—	2	1	no	—
212	C₂×Q₈×C₆₁	—	2	1	no	—
213	C₂×Q₈×C₆₁	—	2	2	no	—
214	C₂×Q₈×C₆₁	—	2	2	no	—
215	C₂×Q₈×C₆₁	—	2	8	no	—
216	C₂×Q₈×C₆₁	—	2	8	no	—
217	C₂×Q₈×C₆₁	—	2	8	no	—
218	C₂×Q₈×C₆₁	—	2	2	no	—
219	C₂×Q₈×C₆₁	—	2	2	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	—	4	4	no	—
225	C₂×Q₈×C₆₁	—	4	4	no	—
226	C₂×Q₈×C₆₁	—	4	4	no	—
227	C₂×Q₈×C₆₁	—	4	4	no	—
228	C₂×Q₈×C₆₁	—	4	4	no	—
229	C₂×Q₈×C₆₁	—	4	4	no	—
230	C₂×Q₈×C₆₁	—	4	8	no	—
231	C₂×Q₈×C₆₁	—	4	8	no	—
232	C₂×Q₈×C₆₁	—	4	8	no	—
233	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
234	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
235	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
240	C₂×D₄×C₆₁	—	2	4	no	—
241	C₂×D₄×C₆₁	—	2	4	no	—
242	C₂×D₄×C₆₁	—	2	4	no	—
243	C₂×D₄×C₆₁	—	2	2	no	—
244	C₂×D₄×C₆₁	—	2	1	no	—
245	C₂×D₄×C₆₁	—	2	2	no	—
246	C₂×D₄×C₆₁	—	4	4	no	—
247	C₂×D₄×C₆₁	—	4	4	no	—
248	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
249	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₁	—	2	1	no	—
251	C₂²×C₄×C₆₁	—	2	1	no	—
252	C₂²×C₄×C₆₁	—	2	2	no	—
253	C₂²×C₄×C₆₁	—	2	2	no	—
254	C₂²×C₄×C₆₁	—	2	2	no	—
255	C₂²×C₄×C₆₁	—	2	2	no	—
256	C₂²×C₄×C₆₁	—	2	4	no	—
257	C₂²×C₄×C₆₁	—	2	4	no	—
258	C₂²×C₄×C₆₁	—	2	4	no	—
259	C₂²×C₄×C₆₁	—	2	1	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	4	no	—
265	C₂²×C₄×C₆₁	—	4	4	no	—
266	C₂²×C₄×C₆₁	—	4	4	no	—
267	C₂²×C₄×C₆₁	—	4	4	no	—
268	C₂²×C₄×C₆₁	—	4	4	no	—
269	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
278	Q₁₆×C₆₁	—	2	8	no	—
279	Q₁₆×C₆₁	—	2	8	no	—
280	Q₁₆×C₆₁	—	2	8	no	—
281	Q₁₆×C₆₁	—	2	8	no	—
282	Q₁₆×C₆₁	—	4	4	no	—
283	Q₁₆×C₆₁	C₂×D₄	1	16	yes	complemented
284	SD₁₆×C₆₁	—	2	8	no	—
285	SD₁₆×C₆₁	—	2	8	no	—
286	SD₁₆×C₆₁	—	4	4	no	—
287	M₁₆×C₆₁	—	2	8	no	—
288	C₂×C₈×C₆₁	—	2	2	no	—
289	C₂×C₈×C₆₁	—	2	2	no	—
290	C₂×C₈×C₆₁	—	2	2	no	—
291	C₂×C₈×C₆₁	—	2	8	no	—
292	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
293	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
294	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
295	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
296	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₆₁	—	2	4	no	—
298	C₄⋊C₄×C₆₁	—	2	4	no	—
299	C₄⋊C₄×C₆₁	—	2	4	no	—
300	C₄⋊C₄×C₆₁	—	2	4	no	—
301	C₄⋊C₄×C₆₁	—	2	4	no	—
302	C₄⋊C₄×C₆₁	—	2	4	no	—
303	C₄⋊C₄×C₆₁	—	2	4	no	—
304	C₄⋊C₄×C₆₁	—	2	1	no	—
305	C₄⋊C₄×C₆₁	—	2	1	no	—
306	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
307	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
309	C₂²⋊C₄×C₆₁	—	2	4	no	—
310	C₂²⋊C₄×C₆₁	—	2	4	no	—
311	C₂²⋊C₄×C₆₁	—	2	4	no	—
312	C₂²⋊C₄×C₆₁	—	2	4	no	—
313	C₂²⋊C₄×C₆₁	—	2	4	no	—
314	C₂²⋊C₄×C₆₁	—	2	4	no	—
315	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
316	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
317	C₄²×C₆₁	—	2	4	no	—
318	C₄²×C₆₁	—	2	4	no	—
319	C₄²×C₆₁	C₂×D₄	1	2	yes	—
320	C₄²×C₆₁	C₂⁴	1	2	yes	—
321	C₂³×C₆₁	—	2	2	no	—
322	C₂³×C₆₁	—	2	2	no	—
323	C₂³×C₆₁	—	2	2	no	—
324	C₂³×C₆₁	—	2	2	no	—
325	C₂³×C₆₁	—	2	2	no	—
326	C₂³×C₆₁	—	2	2	no	—
327	C₂³×C₆₁	—	4	2	no	—
328	C₂³×C₆₁	—	4	2	no	—
329	C₂³×C₆₁	—	4	2	no	—
330	C₂³×C₆₁	#137	1	4	yes	complemented
331	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
332	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
333	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
334	Q₈×C₆₁	—	2	4	no	—
335	Q₈×C₆₁	—	2	4	no	—
336	Q₈×C₆₁	—	2	2	no	—
337	Q₈×C₆₁	—	2	2	no	—
338	Q₈×C₆₁	—	2	2	no	—
339	Q₈×C₆₁	—	2	2	no	—
340	Q₈×C₆₁	—	2	2	no	—
341	Q₈×C₆₁	—	2	2	no	—
342	Q₈×C₆₁	—	2	2	no	—
343	Q₈×C₆₁	—	2	2	no	—
344	Q₈×C₆₁	—	4	8	no	—
345	Q₈×C₆₁	—	4	8	no	—
346	Q₈×C₆₁	—	4	8	no	—
347	Q₈×C₆₁	—	4	2	no	—
348	Q₈×C₆₁	—	4	2	no	—
349	Q₈×C₆₁	—	4	2	no	—
350	Q₈×C₆₁	C₂²×D₄	1	4	yes	—
351	Q₈×C₆₁	C₂²×D₄	1	4	yes	—
352	D₄×C₆₁	—	2	8	no	—
353	D₄×C₆₁	—	2	2	no	—
354	D₄×C₆₁	—	2	2	no	—
355	D₄×C₆₁	—	4	8	no	—
356	D₄×C₆₁	—	4	8	no	—
357	D₄×C₆₁	—	4	2	no	—
358	C₂×C₄×C₆₁	—	2	2	no	—
359	C₂×C₄×C₆₁	—	2	2	no	—
360	C₂×C₄×C₆₁	—	2	4	no	—
361	C₂×C₄×C₆₁	—	2	4	no	—
362	C₂×C₄×C₆₁	—	2	2	no	—
363	C₂×C₄×C₆₁	—	2	2	no	—
364	C₂×C₄×C₆₁	—	2	2	no	—
365	C₂×C₄×C₆₁	—	2	2	no	—
366	C₂×C₄×C₆₁	—	2	4	no	—
367	C₂×C₄×C₆₁	—	2	4	no	—
368	C₂×C₄×C₆₁	—	2	2	no	—
369	C₂×C₄×C₆₁	—	2	2	no	—
370	C₂×C₄×C₆₁	—	2	2	no	—
371	C₂×C₄×C₆₁	—	2	2	no	—
372	C₂×C₄×C₆₁	—	2	2	no	—
373	C₂×C₄×C₆₁	—	2	2	no	—
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	—	4	8	no	—
378	C₂×C₄×C₆₁	—	4	8	no	—
379	C₂×C₄×C₆₁	—	4	8	no	—
380	C₂×C₄×C₆₁	—	4	8	no	—
381	C₂×C₄×C₆₁	—	4	2	no	—
382	C₂×C₄×C₆₁	—	4	2	no	—
383	C₂×C₄×C₆₁	—	4	2	no	—
384	C₂×C₄×C₆₁	—	4	2	no	—
385	C₂×C₄×C₆₁	—	4	2	no	—
386	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
393	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
394	C₈×C₆₁	—	2	2	no	—
395	C₈×C₆₁	—	2	2	no	—
396	C₈×C₆₁	—	2	2	no	—
397	C₈×C₆₁	C₂²×D₄	1	4	yes	—
398	C₂×#3270	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂²×C₆₁	—	2	2	no	—
400	C₂²×C₆₁	—	2	8	no	—
401	C₂²×C₆₁	—	2	2	no	—
402	C₂²×C₆₁	—	2	2	no	—
403	C₂²×C₆₁	—	2	2	no	—
404	C₂²×C₆₁	—	2	2	no	—
405	C₂²×C₆₁	—	4	4	no	—
406	C₂²×C₆₁	—	4	2	no	—
407	C₂²×C₆₁	—	4	2	no	—
408	C₂²×C₆₁	—	4	2	no	—
409	C₂²×C₆₁	—	8	4	no	—
410	C₂²×C₆₁	D₄²	1	2	yes	—
411	C₂²×C₆₁	C₂×#137	1	2	yes	—
412	C₂²×C₆₁	C₂×#137	1	4	yes	complemented
413	C₂²×C₆₁	#578	1	2	yes	—
414	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₆₁	—	2	2	no	—
416	C₄×C₆₁	—	2	2	no	—
417	C₄×C₆₁	—	2	4	no	—
418	C₄×C₆₁	—	2	4	no	—
419	C₄×C₆₁	—	2	2	no	—
420	C₄×C₆₁	—	2	2	no	—
421	C₄×C₆₁	—	4	2	no	—
422	C₄×C₆₁	—	4	2	no	—
423	C₄×C₆₁	—	4	2	no	—
424	C₄×C₆₁	—	4	2	no	—
425	C₄×C₆₁	—	4	2	no	—
426	C₄×C₆₁	D₄²	1	2	yes	—
427	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
428	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂²×#137	C₂×C₆₁	1	1	yes	characteristic, complemented
430	C₂³×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
431	C₂×D₄×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
432	C₂×#548	C₂×C₆₁	1	1	yes	characteristic
433	#3270	C₂×C₆₁	1	16	yes	direct product factor
434	C₂×#497	C₂×C₆₁	1	1	yes	characteristic, complemented
435	C₂×#470	C₂×C₆₁	1	1	yes	characteristic, complemented
436	C₂×#465	C₂×C₆₁	1	1	yes	characteristic, complemented
437	C₂×#464	C₂×C₆₁	1	1	yes	characteristic, complemented
438	C₂×#462	C₂×C₆₁	1	1	yes	characteristic, complemented
439	C₂×#452	C₂×C₆₁	1	1	yes	characteristic, complemented
440	C₂×#451	C₂×C₆₁	1	1	yes	characteristic, complemented
441	C₂×#451	C₂×C₆₁	1	1	yes	characteristic, complemented
442	C₂×#448	C₂×C₆₁	1	1	yes	characteristic, complemented
443	C₂×#441	C₂×C₆₁	1	1	yes	characteristic, complemented
444	C₂×#435	C₂×C₆₁	1	1	yes	characteristic, complemented
445	C₂×C₆₁	—	2	4	no	—
446	C₂×C₆₁	—	4	2	no	—
447	C₂×C₆₁	—	8	2	no	—
448	C₂×C₆₁	#3270	1	4	yes	direct product factor
449	C₂×C₆₁	C₂×D₄²	1	1	yes	characteristic
450	C₂×C₆₁	C₂²×#137	1	1	yes	characteristic
451	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
452	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
453	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
454	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
455	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
456	C₂×#137	—	2	8	no	—
457	C₂×#137	C₂²×C₆₁	1	8	yes	complemented
458	C₂²×Q₁₆	—	2	8	no	—
459	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
460	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
461	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
462	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
463	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
464	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
465	C₂²×Q₁₆	C₂²×C₆₁	1	8	yes	complemented
466	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
467	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
468	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
469	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
470	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
471	D₄×Q₈	—	2	4	no	—
472	D₄×Q₈	C₂²×C₆₁	1	8	yes	complemented
473	#548	—	2	4	no	—
474	#548	C₂²×C₆₁	1	8	yes	—
475	C₂×C₄⋊Q₈	—	2	1	no	—
476	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
477	C₂×#124	—	2	1	no	—
478	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
479	C₂×C₂²⋊Q₈	—	2	1	no	—
480	C₂×C₂²⋊Q₈	—	2	1	no	—
481	C₂×C₂²⋊Q₈	—	2	1	no	—
482	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
483	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
484	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
485	C₂×#121	—	2	1	no	—
486	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
487	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
488	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
489	C₂×C₄×D₄	—	2	1	no	—
490	C₂×C₄×D₄	—	2	1	no	—
491	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
492	#497	C₂²×C₆₁	1	8	yes	complemented
493	#470	C₂²×C₆₁	1	8	yes	complemented
494	#465	C₂²×C₆₁	1	8	yes	complemented
495	#464	C₂²×C₆₁	1	8	yes	complemented
496	#462	C₂²×C₆₁	1	8	yes	complemented
497	#452	C₂²×C₆₁	1	8	yes	complemented
498	#451	C₂²×C₆₁	1	8	yes	complemented
499	#451	C₂²×C₆₁	1	8	yes	complemented
500	#448	C₂²×C₆₁	1	8	yes	complemented
501	#441	C₂²×C₆₁	1	8	yes	complemented
502	#435	C₂²×C₆₁	1	8	yes	complemented
503	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
504	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
505	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
506	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
507	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
508	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
509	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
510	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
511	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
512	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
513	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
514	C₆₁	C₂×#3270	1	1	yes	characteristic, direct product factor, Sylow
515	C₂×#41	—	2	2	no	—
516	C₂×#41	—	2	4	no	—
517	C₂×#41	—	4	2	no	—
518	C₂×#41	C₂³×C₆₁	1	4	yes	—
519	C₂²×Q₈	—	2	1	no	—
520	C₂²×Q₈	—	2	1	no	—
521	C₂²×Q₈	—	2	1	no	—
522	C₂²×Q₈	—	2	2	no	—
523	C₂²×Q₈	—	2	2	no	—
524	C₂²×Q₈	—	2	2	no	—
525	C₂²×Q₈	—	2	4	no	—
526	C₂²×Q₈	—	2	4	no	—
527	C₂²×Q₈	—	2	4	no	—
528	C₂²×Q₈	—	4	2	no	—
529	C₂²×Q₈	—	4	2	no	—
530	C₂²×Q₈	—	4	2	no	—
531	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
534	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
535	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
536	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
537	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
542	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
543	C₂³×C₄	—	2	1	no	—
544	C₂³×C₄	—	2	1	no	—
545	C₂³×C₄	—	2	1	no	—
546	C₂³×C₄	—	2	1	no	—
547	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
549	#137	—	2	32	no	—
550	C₂×Q₁₆	—	2	4	no	—
551	C₂×Q₁₆	—	2	4	no	—
552	C₂×Q₁₆	—	2	4	no	—
553	C₂×Q₁₆	—	2	32	no	—
554	C₂×Q₁₆	—	2	4	no	—
555	C₂×Q₁₆	—	4	2	no	—
556	C₂×Q₁₆	D₄×C₆₁	1	8	yes	complemented
557	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
558	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
559	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
560	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
561	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
562	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
563	C₂×SD₁₆	—	2	4	no	—
564	C₂×SD₁₆	—	2	4	no	—
565	C₂×SD₁₆	—	4	2	no	—
566	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
567	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
568	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
569	C₂×M₁₆	—	2	4	no	—
570	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
571	C₂²×C₈	—	2	4	no	—
572	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
573	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
574	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
575	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
576	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
577	C₄⋊Q₈	—	2	8	no	—
578	C₄⋊Q₈	—	2	2	no	—
579	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
580	#124	—	2	8	no	—
581	#124	—	2	2	no	—
582	#124	C₂³×C₆₁	1	4	yes	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	8	no	—
587	C₂²⋊Q₈	—	2	8	no	—
588	C₂²⋊Q₈	—	2	8	no	—
589	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
590	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
591	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
592	#121	—	2	8	no	—
593	#121	—	2	2	no	—
594	#121	C₂³×C₆₁	1	4	yes	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
598	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
599	C₄×D₄	—	2	8	no	—
600	C₄×D₄	—	2	8	no	—
601	C₄×D₄	D₄×C₆₁	1	4	yes	—
602	C₄×D₄	C₂³×C₆₁	1	4	yes	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
621	C₂×C₄²	—	2	1	no	—
622	C₂×C₄²	—	2	1	no	—
623	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
624	#106	C₂³×C₆₁	1	4	yes	—
625	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
626	#103	C₂³×C₆₁	1	4	yes	—
627	#103	C₂³×C₆₁	1	4	yes	—
628	#103	C₂³×C₆₁	1	4	yes	—
629	#103	C₂³×C₆₁	1	4	yes	—
630	#103	C₂³×C₆₁	1	4	yes	—
631	#102	C₂³×C₆₁	1	4	yes	—
632	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
633	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
634	#97	C₂³×C₆₁	1	4	yes	—
635	C₂⁴	—	2	1	no	—
636	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
637	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
638	#41	—	2	8	no	—
639	#41	—	4	4	no	—
640	#41	—	4	8	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	2	4	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	8	no	—
652	C₂×Q₈	—	2	8	no	—
653	C₂×Q₈	—	2	8	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	4	4	no	—
661	C₂×Q₈	—	4	4	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	—	4	4	no	—
664	C₂×Q₈	—	4	4	no	—
665	C₂×Q₈	—	4	4	no	—
666	C₂×Q₈	—	4	8	no	—
667	C₂×Q₈	—	4	8	no	—
668	C₂×Q₈	—	4	8	no	—
669	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
670	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
671	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
672	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
674	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	4	4	no	—
683	C₂×D₄	—	4	4	no	—
684	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
685	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	4	4	no	—
702	C₂²×C₄	—	4	4	no	—
703	C₂²×C₄	—	4	4	no	—
704	C₂²×C₄	—	4	4	no	—
705	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
714	Q₁₆	—	2	8	no	—
715	Q₁₆	—	2	8	no	—
716	Q₁₆	—	2	8	no	—
717	Q₁₆	—	2	8	no	—
718	Q₁₆	—	4	4	no	—
719	Q₁₆	C₂×D₄×C₆₁	1	16	yes	complemented
720	SD₁₆	—	2	8	no	—
721	SD₁₆	—	2	8	no	—
722	SD₁₆	—	4	4	no	—
723	M₁₆	—	2	8	no	—
724	C₂×C₈	—	2	2	no	—
725	C₂×C₈	—	2	2	no	—
726	C₂×C₈	—	2	2	no	—
727	C₂×C₈	—	2	8	no	—
728	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
729	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
730	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
731	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
732	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
743	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
752	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
753	C₄²	—	2	4	no	—
754	C₄²	—	2	4	no	—
755	C₄²	C₂×D₄×C₆₁	1	2	yes	—
756	C₄²	C₂⁴×C₆₁	1	2	yes	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	—	4	2	no	—
766	C₂³	#137×C₆₁	1	4	yes	complemented
767	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
768	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
769	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
770	Q₈	—	2	4	no	—
771	Q₈	—	2	4	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	2	2	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	4	8	no	—
781	Q₈	—	4	8	no	—
782	Q₈	—	4	8	no	—
783	Q₈	—	4	2	no	—
784	Q₈	—	4	2	no	—
785	Q₈	—	4	2	no	—
786	Q₈	C₂²×D₄×C₆₁	1	4	yes	—
787	Q₈	C₂²×D₄×C₆₁	1	4	yes	—
788	D₄	—	2	8	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	2	no	—
791	D₄	—	4	8	no	—
792	D₄	—	4	8	no	—
793	D₄	—	4	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	8	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
828	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
829	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
830	C₈	—	2	2	no	—
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	C₂²×D₄×C₆₁	1	4	yes	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	8	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	8	4	no	—
845	C₂²	D₄²×C₆₁	1	2	yes	—
846	C₂²	C₂×#137×C₆₁	1	2	yes	—
847	C₂²	C₂×#137×C₆₁	1	4	yes	complemented
848	C₂²	C₆₁×#578	1	2	yes	—
849	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	D₄²×C₆₁	1	2	yes	—
862	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
863	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
864	C₂	—	2	4	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	C₆₁×#3270	1	4	yes	direct product factor
868	C₂	C₂×D₄²×C₆₁	1	1	yes	characteristic
869	C₂	C₂²×#137×C₆₁	1	1	yes	characteristic
870	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×#548	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. C₂²×#137×C₆₁	C₂	semidirect
2. C₂³×Q₁₆×C₆₁	C₂	semidirect
3. C₂×D₄×Q₈×C₆₁	C₂	semidirect
5. C₆₁×#3270	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×#464	C₂	semidirect
10. C₂×C₆₁×#462	C₂	semidirect
11. C₂×C₆₁×#452	C₂	semidirect
12. C₂×C₆₁×#451	C₂	semidirect
13. C₂×C₆₁×#451	C₂	semidirect
14. C₂×C₆₁×#448	C₂	semidirect
15. C₂×C₆₁×#441	C₂	semidirect
16. C₂×C₆₁×#435	C₂	semidirect
22. C₂×#137×C₆₁	C₂²	semidirect
30. C₂²×Q₁₆×C₆₁	C₂²	semidirect
37. D₄×Q₈×C₆₁	C₂²	semidirect
57. C₆₁×#497	C₂²	semidirect
58. C₆₁×#470	C₂²	semidirect
59. C₆₁×#465	C₂²	semidirect
60. C₆₁×#464	C₂²	semidirect
61. C₆₁×#462	C₂²	semidirect
62. C₆₁×#452	C₂²	semidirect
63. C₆₁×#451	C₂²	semidirect
64. C₆₁×#451	C₂²	semidirect
65. C₆₁×#448	C₂²	semidirect
66. C₆₁×#441	C₂²	semidirect
67. C₆₁×#435	C₂²	semidirect
120. C₂×Q₁₆×C₆₁	D₄	semidirect
283. Q₁₆×C₆₁	C₂×D₄	semidirect
330. C₂³×C₆₁	#137	semidirect
398. C₂×#3270	C₆₁	direct (N × H)
412. C₂²×C₆₁	C₂×#137	semidirect
429. C₂²×#137	C₂×C₆₁	semidirect
430. C₂³×Q₁₆	C₂×C₆₁	semidirect
431. C₂×D₄×Q₈	C₂×C₆₁	semidirect
433. #3270	C₂×C₆₁	direct (N × H)
434. C₂×#497	C₂×C₆₁	semidirect
435. C₂×#470	C₂×C₆₁	semidirect
436. C₂×#465	C₂×C₆₁	semidirect
437. C₂×#464	C₂×C₆₁	semidirect
438. C₂×#462	C₂×C₆₁	semidirect
439. C₂×#452	C₂×C₆₁	semidirect
440. C₂×#451	C₂×C₆₁	semidirect
441. C₂×#451	C₂×C₆₁	semidirect
442. C₂×#448	C₂×C₆₁	semidirect
443. C₂×#441	C₂×C₆₁	semidirect
444. C₂×#435	C₂×C₆₁	semidirect
448. C₂×C₆₁	#3270	direct (N × H)
457. C₂×#137	C₂²×C₆₁	semidirect
465. C₂²×Q₁₆	C₂²×C₆₁	semidirect
472. D₄×Q₈	C₂²×C₆₁	semidirect
492. #497	C₂²×C₆₁	semidirect
493. #470	C₂²×C₆₁	semidirect
494. #465	C₂²×C₆₁	semidirect
495. #464	C₂²×C₆₁	semidirect
496. #462	C₂²×C₆₁	semidirect
497. #452	C₂²×C₆₁	semidirect
498. #451	C₂²×C₆₁	semidirect
499. #451	C₂²×C₆₁	semidirect
500. #448	C₂²×C₆₁	semidirect
501. #441	C₂²×C₆₁	semidirect
502. #435	C₂²×C₆₁	semidirect
514. C₆₁	C₂×#3270	direct (N × H)
556. C₂×Q₁₆	D₄×C₆₁	semidirect
719. Q₁₆	C₂×D₄×C₆₁	semidirect
766. C₂³	#137×C₆₁	semidirect
847. C₂²	C₂×#137×C₆₁	semidirect
867. C₂	C₆₁×#3270	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×#137×C₆₁	2
C₂³×Q₁₆×C₆₁	2
C₂×D₄×Q₈×C₆₁	2
C₂×C₆₁×#548	2
C₆₁×#3270	2
C₂×C₆₁×#497	2
C₂×C₆₁×#470	2
C₂×C₆₁×#465	2
C₂×C₆₁×#464	2
C₂×C₆₁×#462	2
C₂×C₆₁×#452	2
C₂×C₆₁×#451	2
C₂×C₆₁×#448	2
C₂×C₆₁×#441	2
C₂×C₆₁×#435	2
C₂×#3270	61

Subgroups — C2×C61×#3270 #29564461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3270 #29564461