Subgroups — C₆₁×#61574 #29565007

Order 15616.

2094 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3505	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3320	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3312	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3270	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3266	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3218	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3196	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3189	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3117	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3004	C₂	1	2	yes	maximal, complemented
13	C₂×C₆₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
18	C₂×#137×C₆₁	C₂²	1	4	yes	complemented
19	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
21	C₆₁×#553	—	2	2	no	—
22	C₆₁×#553	C₂²	1	2	yes	—
23	C₆₁×#552	C₂²	1	2	yes	—
24	C₆₁×#551	—	2	2	no	—
25	D₄×Q₈×C₆₁	—	2	2	no	—
26	D₄×Q₈×C₆₁	—	2	2	no	—
27	D₄×Q₈×C₆₁	C₂²	1	4	yes	—
28	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
29	C₆₁×#548	C₂²	1	2	yes	—
30	C₆₁×#546	C₂²	1	2	yes	—
31	C₆₁×#539	—	2	1	no	—
32	C₆₁×#538	—	2	1	no	—
33	C₆₁×#534	—	2	1	no	—
34	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
35	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
36	C₆₁×#529	C₂²	1	2	yes	—
37	C₆₁×#525	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
39	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
40	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#518	—	2	1	no	—
45	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₆₁	—	2	1	no	—
47	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#497	C₂²	1	4	yes	complemented
49	C₆₁×#491	C₂²	1	4	yes	complemented
50	C₆₁×#485	C₂²	1	4	yes	complemented
51	C₆₁×#484	C₂²	1	2	yes	complemented
52	C₆₁×#484	C₂²	1	2	yes	complemented
53	C₆₁×#483	C₂²	1	2	yes	complemented
54	C₆₁×#481	C₂²	1	2	yes	—
55	C₆₁×#479	C₂²	1	4	yes	complemented
56	C₆₁×#470	C₂²	1	4	yes	complemented
57	C₆₁×#468	C₂²	1	4	yes	complemented
58	C₆₁×#467	C₂²	1	4	yes	complemented
59	C₆₁×#465	C₂²	1	4	yes	complemented
60	C₆₁×#464	C₂²	1	4	yes	complemented
61	C₆₁×#462	C₂²	1	4	yes	complemented
62	C₆₁×#461	C₂²	1	4	yes	complemented
63	C₆₁×#452	C₂²	1	4	yes	complemented
64	C₆₁×#451	C₂²	1	4	yes	complemented
65	C₆₁×#451	C₂²	1	4	yes	complemented
66	C₆₁×#451	C₂²	1	2	yes	complemented
67	C₆₁×#451	C₂²	1	2	yes	complemented
68	C₆₁×#451	C₂²	1	2	yes	complemented
69	C₆₁×#451	C₂²	1	2	yes	complemented
70	C₆₁×#450	C₂²	1	2	yes	complemented
71	C₆₁×#448	C₂²	1	2	yes	—
72	C₆₁×#448	C₂²	1	2	yes	—
73	C₆₁×#448	C₂²	1	2	yes	—
74	C₆₁×#448	C₂²	1	4	yes	complemented
75	C₆₁×#448	C₂²	1	4	yes	complemented
76	C₆₁×#441	C₂²	1	4	yes	complemented
77	C₆₁×#440	C₂²	1	4	yes	complemented
78	C₆₁×#435	C₂²	1	4	yes	—
79	C₆₁×#435	C₂²	1	4	yes	complemented
80	C₆₁×#432	C₂²	1	2	yes	complemented
81	C₆₁×#419	C₂²	1	4	yes	complemented
82	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
83	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
84	C₆₁×#407	C₂²	1	2	yes	complemented
85	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
86	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
87	C₂×#41×C₆₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₆₁	—	2	1	no	—
89	C₂²×Q₈×C₆₁	—	2	1	no	—
90	C₂²×Q₈×C₆₁	—	2	1	no	—
91	C₂²×Q₈×C₆₁	—	2	1	no	—
92	C₂²×Q₈×C₆₁	—	2	2	no	—
93	C₂²×Q₈×C₆₁	—	4	4	no	—
94	C₂²×Q₈×C₆₁	—	4	4	no	—
95	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
97	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
98	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₆₁	—	2	1	no	—
103	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₆₁	—	2	1	no	—
106	C₂³×C₄×C₆₁	—	2	1	no	—
107	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
109	#137×C₆₁	—	4	8	no	—
110	C₂×Q₁₆×C₆₁	—	4	4	no	—
111	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
112	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
113	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₆₁	—	4	4	no	—
115	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
118	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
119	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
120	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₆₁	—	2	4	no	—
122	C₄⋊Q₈×C₆₁	—	2	4	no	—
123	C₄⋊Q₈×C₆₁	—	2	2	no	—
124	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
125	#126×C₆₁	—	2	2	no	—
126	#126×C₆₁	—	2	2	no	—
127	#126×C₆₁	—	2	2	no	—
128	#125×C₆₁	—	2	2	no	—
129	#125×C₆₁	C₂³	1	2	yes	—
130	#124×C₆₁	—	2	2	no	—
131	#124×C₆₁	C₂³	1	2	yes	—
132	#123×C₆₁	—	2	2	no	—
133	#123×C₆₁	—	2	2	no	—
134	#123×C₆₁	—	2	2	no	—
135	#123×C₆₁	—	2	2	no	—
136	#123×C₆₁	—	2	2	no	—
137	C₂²⋊Q₈×C₆₁	—	2	1	no	—
138	C₂²⋊Q₈×C₆₁	—	2	1	no	—
139	C₂²⋊Q₈×C₆₁	—	2	1	no	—
140	C₂²⋊Q₈×C₆₁	—	2	2	no	—
141	C₂²⋊Q₈×C₆₁	—	2	1	no	—
142	C₂²⋊Q₈×C₆₁	—	2	2	no	—
143	C₂²⋊Q₈×C₆₁	—	2	4	no	—
144	C₂²⋊Q₈×C₆₁	—	2	4	no	—
145	C₂²⋊Q₈×C₆₁	—	2	4	no	—
146	C₂²⋊Q₈×C₆₁	—	2	4	no	—
147	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
149	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
150	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
153	#121×C₆₁	—	2	2	no	—
154	#121×C₆₁	—	2	2	no	—
155	#121×C₆₁	—	2	1	no	—
156	#121×C₆₁	—	2	1	no	—
157	#121×C₆₁	—	2	2	no	—
158	#121×C₆₁	C₂³	1	2	yes	—
159	#121×C₆₁	C₂³	1	2	yes	—
160	#121×C₆₁	C₂³	1	2	yes	—
161	#120×C₆₁	—	2	2	no	—
162	#120×C₆₁	—	2	2	no	—
163	C₄×Q₈×C₆₁	—	2	2	no	—
164	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
165	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
166	C₄×D₄×C₆₁	—	2	4	no	—
167	C₄×D₄×C₆₁	—	2	4	no	—
168	C₄×D₄×C₆₁	—	2	2	no	—
169	C₄×D₄×C₆₁	—	2	2	no	—
170	C₄×D₄×C₆₁	—	2	2	no	—
171	C₄×D₄×C₆₁	—	2	2	no	—
172	C₄×D₄×C₆₁	—	2	2	no	—
173	C₄×D₄×C₆₁	D₄	1	2	yes	—
174	C₄×D₄×C₆₁	D₄	1	2	yes	—
175	C₄×D₄×C₆₁	C₂³	1	2	yes	—
176	C₄×D₄×C₆₁	C₂³	1	2	yes	—
177	C₄×D₄×C₆₁	C₂³	1	2	yes	—
178	#117×C₆₁	—	2	2	no	—
179	#117×C₆₁	—	2	2	no	—
180	#117×C₆₁	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
182	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
183	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
184	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
185	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
186	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
187	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₆₁	—	2	1	no	—
199	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
200	#107×C₆₁	C₂³	1	4	yes	—
201	#106×C₆₁	C₂³	1	4	yes	—
202	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
203	#103×C₆₁	C₂³	1	4	yes	—
204	#103×C₆₁	C₂³	1	4	yes	—
205	#103×C₆₁	C₂³	1	4	yes	—
206	#103×C₆₁	C₂³	1	4	yes	—
207	#103×C₆₁	C₂³	1	4	yes	—
208	#103×C₆₁	C₂³	1	4	yes	—
209	#103×C₆₁	C₂³	1	4	yes	—
210	#102×C₆₁	C₂³	1	4	yes	—
211	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
213	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
214	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
215	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
216	#97×C₆₁	C₂³	1	4	yes	—
217	C₂⁴×C₆₁	—	2	1	no	—
218	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
219	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
220	#41×C₆₁	—	4	4	no	—
221	C₂×Q₈×C₆₁	—	2	4	no	—
222	C₂×Q₈×C₆₁	—	2	1	no	—
223	C₂×Q₈×C₆₁	—	2	4	no	—
224	C₂×Q₈×C₆₁	—	2	2	no	—
225	C₂×Q₈×C₆₁	—	2	2	no	—
226	C₂×Q₈×C₆₁	—	2	1	no	—
227	C₂×Q₈×C₆₁	—	2	1	no	—
228	C₂×Q₈×C₆₁	—	2	1	no	—
229	C₂×Q₈×C₆₁	—	2	4	no	—
230	C₂×Q₈×C₆₁	—	2	4	no	—
231	C₂×Q₈×C₆₁	—	2	8	no	—
232	C₂×Q₈×C₆₁	—	4	2	no	—
233	C₂×Q₈×C₆₁	—	4	2	no	—
234	C₂×Q₈×C₆₁	—	4	4	no	—
235	C₂×Q₈×C₆₁	—	4	2	no	—
236	C₂×Q₈×C₆₁	—	4	2	no	—
237	C₂×Q₈×C₆₁	—	4	4	no	—
238	C₂×Q₈×C₆₁	—	4	4	no	—
239	C₂×Q₈×C₆₁	—	4	2	no	—
240	C₂×Q₈×C₆₁	—	4	4	no	—
241	C₂×Q₈×C₆₁	—	4	4	no	—
242	C₂×Q₈×C₆₁	—	4	8	no	—
243	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
247	C₂×D₄×C₆₁	—	2	4	no	—
248	C₂×D₄×C₆₁	—	2	2	no	—
249	C₂×D₄×C₆₁	—	2	2	no	—
250	C₂×D₄×C₆₁	—	2	2	no	—
251	C₂×D₄×C₆₁	—	2	2	no	—
252	C₂×D₄×C₆₁	—	2	1	no	—
253	C₂×D₄×C₆₁	—	4	2	no	—
254	C₂×D₄×C₆₁	—	4	4	no	—
255	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₁	—	2	1	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	4	no	—
264	C₂²×C₄×C₆₁	—	2	2	no	—
265	C₂²×C₄×C₆₁	—	2	2	no	—
266	C₂²×C₄×C₆₁	—	2	1	no	—
267	C₂²×C₄×C₆₁	—	2	1	no	—
268	C₂²×C₄×C₆₁	—	2	2	no	—
269	C₂²×C₄×C₆₁	—	2	2	no	—
270	C₂²×C₄×C₆₁	—	4	2	no	—
271	C₂²×C₄×C₆₁	—	4	2	no	—
272	C₂²×C₄×C₆₁	—	4	4	no	—
273	C₂²×C₄×C₆₁	—	4	4	no	—
274	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
281	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
285	Q₁₆×C₆₁	—	2	8	no	—
286	Q₁₆×C₆₁	—	4	4	no	—
287	Q₁₆×C₆₁	—	4	4	no	—
288	SD₁₆×C₆₁	—	2	8	no	—
289	SD₁₆×C₆₁	—	4	4	no	—
290	SD₁₆×C₆₁	—	4	4	no	—
291	M₁₆×C₆₁	—	4	4	no	—
292	C₂×C₈×C₆₁	—	4	2	no	—
293	C₂×C₈×C₆₁	—	4	2	no	—
294	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
295	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
296	C₄⋊C₄×C₆₁	—	2	2	no	—
297	C₄⋊C₄×C₆₁	—	2	4	no	—
298	C₄⋊C₄×C₆₁	—	2	4	no	—
299	C₄⋊C₄×C₆₁	—	2	2	no	—
300	C₄⋊C₄×C₆₁	—	2	4	no	—
301	C₄⋊C₄×C₆₁	—	2	4	no	—
302	C₄⋊C₄×C₆₁	—	2	2	no	—
303	C₄⋊C₄×C₆₁	—	2	2	no	—
304	C₄⋊C₄×C₆₁	—	2	1	no	—
305	C₄⋊C₄×C₆₁	—	2	1	no	—
306	C₄⋊C₄×C₆₁	—	2	1	no	—
307	C₄⋊C₄×C₆₁	—	2	2	no	—
308	C₄⋊C₄×C₆₁	—	2	2	no	—
309	C₄⋊C₄×C₆₁	—	2	2	no	—
310	C₄⋊C₄×C₆₁	—	2	2	no	—
311	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
316	C₂²⋊C₄×C₆₁	—	2	2	no	—
317	C₂²⋊C₄×C₆₁	—	2	2	no	—
318	C₂²⋊C₄×C₆₁	—	2	4	no	—
319	C₂²⋊C₄×C₆₁	—	2	2	no	—
320	C₂²⋊C₄×C₆₁	—	2	2	no	—
321	C₂²⋊C₄×C₆₁	—	2	2	no	—
322	C₂²⋊C₄×C₆₁	—	2	2	no	—
323	C₂²⋊C₄×C₆₁	—	2	2	no	—
324	C₂²⋊C₄×C₆₁	—	2	2	no	—
325	C₂²⋊C₄×C₆₁	—	2	2	no	—
326	C₂²⋊C₄×C₆₁	—	2	2	no	—
327	C₂²⋊C₄×C₆₁	—	2	2	no	—
328	C₂²⋊C₄×C₆₁	—	2	2	no	—
329	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
333	C₄²×C₆₁	—	2	4	no	—
334	C₄²×C₆₁	—	2	2	no	—
335	C₄²×C₆₁	—	2	2	no	—
336	C₄²×C₆₁	C₂×D₄	1	2	yes	—
337	C₄²×C₆₁	C₂⁴	1	2	yes	—
338	C₂³×C₆₁	—	2	2	no	—
339	C₂³×C₆₁	—	2	2	no	—
340	C₂³×C₆₁	—	4	1	no	—
341	C₂³×C₆₁	—	4	1	no	—
342	C₂³×C₆₁	—	4	1	no	—
343	C₂³×C₆₁	—	4	1	no	—
344	C₂³×C₆₁	—	4	2	no	—
345	C₂³×C₆₁	—	8	1	no	—
346	C₂³×C₆₁	—	8	1	no	—
347	C₂³×C₆₁	#137	1	4	yes	complemented
348	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
349	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
350	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
351	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
352	Q₈×C₆₁	—	2	4	no	—
353	Q₈×C₆₁	—	2	2	no	—
354	Q₈×C₆₁	—	2	2	no	—
355	Q₈×C₆₁	—	2	4	no	—
356	Q₈×C₆₁	—	2	4	no	—
357	Q₈×C₆₁	—	2	2	no	—
358	Q₈×C₆₁	—	4	8	no	—
359	Q₈×C₆₁	—	4	4	no	—
360	Q₈×C₆₁	—	4	4	no	—
361	Q₈×C₆₁	—	4	2	no	—
362	Q₈×C₆₁	—	4	2	no	—
363	Q₈×C₆₁	—	8	1	no	—
364	Q₈×C₆₁	H(5,𝔽₂)	1	4	yes	—
365	D₄×C₆₁	—	2	4	no	—
366	D₄×C₆₁	—	2	4	no	—
367	D₄×C₆₁	—	2	4	no	—
368	D₄×C₆₁	—	4	4	no	—
369	D₄×C₆₁	—	4	4	no	—
370	D₄×C₆₁	—	8	1	no	—
371	D₄×C₆₁	—	8	2	no	—
372	D₄×C₆₁	—	8	2	no	—
373	C₂×C₄×C₆₁	—	2	4	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	—	2	2	no	—
378	C₂×C₄×C₆₁	—	2	4	no	—
379	C₂×C₄×C₆₁	—	2	2	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	—	4	2	no	—
387	C₂×C₄×C₆₁	—	4	1	no	—
388	C₂×C₄×C₆₁	—	4	1	no	—
389	C₂×C₄×C₆₁	—	4	1	no	—
390	C₂×C₄×C₆₁	—	4	1	no	—
391	C₂×C₄×C₆₁	—	4	1	no	—
392	C₂×C₄×C₆₁	—	4	4	no	—
393	C₂×C₄×C₆₁	—	4	4	no	—
394	C₂×C₄×C₆₁	—	4	8	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	—	4	2	no	—
399	C₂×C₄×C₆₁	—	8	2	no	—
400	C₂×C₄×C₆₁	—	8	2	no	—
401	C₂×C₄×C₆₁	—	8	1	no	—
402	C₂×C₄×C₆₁	—	8	1	no	—
403	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
410	C₈×C₆₁	—	2	4	no	—
411	C₈×C₆₁	—	2	4	no	—
412	#61574	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
413	C₂²×C₆₁	—	2	1	no	—
414	C₂²×C₆₁	—	2	1	no	—
415	C₂²×C₆₁	—	2	1	no	—
416	C₂²×C₆₁	—	2	1	no	—
417	C₂²×C₆₁	—	2	1	no	—
418	C₂²×C₆₁	—	2	1	no	—
419	C₂²×C₆₁	—	2	2	no	—
420	C₂²×C₆₁	—	2	2	no	—
421	C₂²×C₆₁	—	2	2	no	—
422	C₂²×C₆₁	—	4	4	no	—
423	C₂²×C₆₁	—	4	4	no	—
424	C₂²×C₆₁	—	4	2	no	—
425	C₂²×C₆₁	—	4	2	no	—
426	C₂²×C₆₁	—	4	2	no	—
427	C₂²×C₆₁	—	16	2	no	—
428	C₂²×C₆₁	C₂×#137	1	2	yes	—
429	C₂²×C₆₁	C₂×#137	1	2	yes	—
430	C₂²×C₆₁	C₂×#137	1	2	yes	—
431	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
432	C₄×C₆₁	—	2	2	no	—
433	C₄×C₆₁	—	2	4	no	—
434	C₄×C₆₁	—	2	1	no	—
435	C₄×C₆₁	—	2	2	no	—
436	C₄×C₆₁	—	2	1	no	—
437	C₄×C₆₁	—	2	1	no	—
438	C₄×C₆₁	—	2	2	no	—
439	C₄×C₆₁	—	4	2	no	—
440	C₄×C₆₁	—	4	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	C₂×H(5,𝔽₂)	1	2	yes	—
446	#3505	C₂×C₆₁	1	1	yes	characteristic
447	C₂×D₄×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
448	#3320	C₂×C₆₁	1	4	yes	complemented
449	#3312	C₂×C₆₁	1	4	yes	complemented
450	#3270	C₂×C₆₁	1	4	yes	complemented
451	#3266	C₂×C₆₁	1	4	yes	complemented
452	#3218	C₂×C₆₁	1	2	yes	complemented
453	#3196	C₂×C₆₁	1	2	yes	complemented
454	#3189	C₂×C₆₁	1	1	yes	characteristic, complemented
455	#3187	C₂×C₆₁	1	1	yes	characteristic, complemented
456	#3117	C₂×C₆₁	1	2	yes	complemented
457	#3004	C₂×C₆₁	1	2	yes	complemented
458	C₂×#451	C₂×C₆₁	1	1	yes	characteristic, complemented
459	C₂×#448	C₂×C₆₁	1	1	yes	characteristic, complemented
460	#2973	C₂×C₆₁	1	1	yes	characteristic, complemented
461	C₂×C₆₁	—	2	2	no	—
462	C₂×C₆₁	—	2	2	no	—
463	C₂×C₆₁	—	2	2	no	—
464	C₂×C₆₁	—	4	2	no	—
465	C₂×C₆₁	—	8	2	no	—
466	C₂×C₆₁	#3484	1	1	yes	characteristic
467	C₂×C₆₁	C₂²×#137	1	1	yes	characteristic
468	C₂×C₆₁	#3586	1	1	yes	characteristic
469	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
470	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
471	C₂×#137	C₂²×C₆₁	1	4	yes	complemented
472	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
473	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
474	#553	—	2	2	no	—
475	#553	C₂²×C₆₁	1	2	yes	—
476	#552	C₂²×C₆₁	1	2	yes	—
477	#551	—	2	2	no	—
478	D₄×Q₈	—	2	2	no	—
479	D₄×Q₈	—	2	2	no	—
480	D₄×Q₈	C₂²×C₆₁	1	4	yes	—
481	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
482	#548	C₂²×C₆₁	1	2	yes	—
483	#546	C₂²×C₆₁	1	2	yes	—
484	#539	—	2	1	no	—
485	#538	—	2	1	no	—
486	#534	—	2	1	no	—
487	C₂×C₄⋊Q₈	—	2	1	no	—
488	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
489	#529	C₂²×C₆₁	1	2	yes	—
490	#525	C₂²×C₆₁	1	2	yes	—
491	C₂×C₂²⋊Q₈	—	2	1	no	—
492	C₂×C₂²⋊Q₈	—	2	1	no	—
493	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
494	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
495	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
496	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
497	#518	—	2	1	no	—
498	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
499	C₂×C₄×D₄	—	2	1	no	—
500	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
501	#497	C₂²×C₆₁	1	4	yes	complemented
502	#491	C₂²×C₆₁	1	4	yes	complemented
503	#485	C₂²×C₆₁	1	4	yes	complemented
504	#484	C₂²×C₆₁	1	2	yes	complemented
505	#484	C₂²×C₆₁	1	2	yes	complemented
506	#483	C₂²×C₆₁	1	2	yes	complemented
507	#481	C₂²×C₆₁	1	2	yes	—
508	#479	C₂²×C₆₁	1	4	yes	complemented
509	#470	C₂²×C₆₁	1	4	yes	complemented
510	#468	C₂²×C₆₁	1	4	yes	complemented
511	#467	C₂²×C₆₁	1	4	yes	complemented
512	#465	C₂²×C₆₁	1	4	yes	complemented
513	#464	C₂²×C₆₁	1	4	yes	complemented
514	#462	C₂²×C₆₁	1	4	yes	complemented
515	#461	C₂²×C₆₁	1	4	yes	complemented
516	#452	C₂²×C₆₁	1	4	yes	complemented
517	#451	C₂²×C₆₁	1	2	yes	complemented
518	#451	C₂²×C₆₁	1	2	yes	complemented
519	#451	C₂²×C₆₁	1	2	yes	complemented
520	#451	C₂²×C₆₁	1	2	yes	complemented
521	#451	C₂²×C₆₁	1	4	yes	complemented
522	#451	C₂²×C₆₁	1	4	yes	complemented
523	#450	C₂²×C₆₁	1	2	yes	complemented
524	#448	C₂²×C₆₁	1	2	yes	—
525	#448	C₂²×C₆₁	1	2	yes	—
526	#448	C₂²×C₆₁	1	2	yes	—
527	#448	C₂²×C₆₁	1	4	yes	complemented
528	#448	C₂²×C₆₁	1	4	yes	complemented
529	#441	C₂²×C₆₁	1	4	yes	complemented
530	#440	C₂²×C₆₁	1	4	yes	complemented
531	#435	C₂²×C₆₁	1	4	yes	—
532	#435	C₂²×C₆₁	1	4	yes	complemented
533	#432	C₂²×C₆₁	1	2	yes	complemented
534	#419	C₂²×C₆₁	1	4	yes	complemented
535	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
536	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
537	#407	C₂²×C₆₁	1	2	yes	complemented
538	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
539	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
540	C₆₁	#61574	1	1	yes	characteristic, direct product factor, Sylow
541	C₂×#41	C₂³×C₆₁	1	2	yes	—
542	C₂²×Q₈	—	2	1	no	—
543	C₂²×Q₈	—	2	1	no	—
544	C₂²×Q₈	—	2	1	no	—
545	C₂²×Q₈	—	2	1	no	—
546	C₂²×Q₈	—	2	2	no	—
547	C₂²×Q₈	—	4	4	no	—
548	C₂²×Q₈	—	4	4	no	—
549	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
550	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
551	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
552	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
553	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
554	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
555	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
558	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
559	C₂³×C₄	—	2	1	no	—
560	C₂³×C₄	—	2	1	no	—
561	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
563	#137	—	4	8	no	—
564	C₂×Q₁₆	—	4	4	no	—
565	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
566	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
567	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
568	C₂×SD₁₆	—	4	4	no	—
569	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
570	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
571	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
572	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
573	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
574	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
575	C₄⋊Q₈	—	2	4	no	—
576	C₄⋊Q₈	—	2	4	no	—
577	C₄⋊Q₈	—	2	2	no	—
578	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
579	#126	—	2	2	no	—
580	#126	—	2	2	no	—
581	#126	—	2	2	no	—
582	#125	—	2	2	no	—
583	#125	C₂³×C₆₁	1	2	yes	—
584	#124	—	2	2	no	—
585	#124	C₂³×C₆₁	1	2	yes	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	4	no	—
598	C₂²⋊Q₈	—	2	4	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₂²⋊Q₈	—	2	4	no	—
601	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
602	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
603	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
605	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
606	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	1	no	—
611	#121	—	2	2	no	—
612	#121	C₂³×C₆₁	1	2	yes	—
613	#121	C₂³×C₆₁	1	2	yes	—
614	#121	C₂³×C₆₁	1	2	yes	—
615	#120	—	2	2	no	—
616	#120	—	2	2	no	—
617	C₄×Q₈	—	2	2	no	—
618	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
619	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	D₄×C₆₁	1	2	yes	—
628	C₄×D₄	D₄×C₆₁	1	2	yes	—
629	C₄×D₄	C₂³×C₆₁	1	2	yes	—
630	C₄×D₄	C₂³×C₆₁	1	2	yes	—
631	C₄×D₄	C₂³×C₆₁	1	2	yes	—
632	#117	—	2	2	no	—
633	#117	—	2	2	no	—
634	#117	C₂³×C₆₁	1	2	yes	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	2	no	—
650	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
652	C₂×C₄²	—	2	1	no	—
653	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
654	#107	C₂³×C₆₁	1	4	yes	—
655	#106	C₂³×C₆₁	1	4	yes	—
656	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
657	#103	C₂³×C₆₁	1	4	yes	—
658	#103	C₂³×C₆₁	1	4	yes	—
659	#103	C₂³×C₆₁	1	4	yes	—
660	#103	C₂³×C₆₁	1	4	yes	—
661	#103	C₂³×C₆₁	1	4	yes	—
662	#103	C₂³×C₆₁	1	4	yes	—
663	#103	C₂³×C₆₁	1	4	yes	—
664	#102	C₂³×C₆₁	1	4	yes	—
665	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
666	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
668	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
669	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
670	#97	C₂³×C₆₁	1	4	yes	—
671	C₂⁴	—	2	1	no	—
672	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
673	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
674	#41	—	4	4	no	—
675	C₂×Q₈	—	2	4	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	4	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	1	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	4	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	2	8	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	—	4	2	no	—
688	C₂×Q₈	—	4	4	no	—
689	C₂×Q₈	—	4	2	no	—
690	C₂×Q₈	—	4	2	no	—
691	C₂×Q₈	—	4	4	no	—
692	C₂×Q₈	—	4	4	no	—
693	C₂×Q₈	—	4	2	no	—
694	C₂×Q₈	—	4	4	no	—
695	C₂×Q₈	—	4	4	no	—
696	C₂×Q₈	—	4	8	no	—
697	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
698	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
699	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
700	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	4	no	—
709	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
710	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
711	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	4	no	—
727	C₂²×C₄	—	4	4	no	—
728	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
729	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
739	Q₁₆	—	2	8	no	—
740	Q₁₆	—	4	4	no	—
741	Q₁₆	—	4	4	no	—
742	SD₁₆	—	2	8	no	—
743	SD₁₆	—	4	4	no	—
744	SD₁₆	—	4	4	no	—
745	M₁₆	—	4	4	no	—
746	C₂×C₈	—	4	2	no	—
747	C₂×C₈	—	4	2	no	—
748	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
749	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
766	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
768	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
784	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
785	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
786	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
787	C₄²	—	2	4	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	C₂×D₄×C₆₁	1	2	yes	—
791	C₄²	C₂⁴×C₆₁	1	2	yes	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	4	1	no	—
795	C₂³	—	4	1	no	—
796	C₂³	—	4	1	no	—
797	C₂³	—	4	1	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	8	1	no	—
800	C₂³	—	8	1	no	—
801	C₂³	#137×C₆₁	1	4	yes	complemented
802	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
803	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
804	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
805	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
806	Q₈	—	2	4	no	—
807	Q₈	—	2	2	no	—
808	Q₈	—	2	2	no	—
809	Q₈	—	2	4	no	—
810	Q₈	—	2	4	no	—
811	Q₈	—	2	2	no	—
812	Q₈	—	4	8	no	—
813	Q₈	—	4	4	no	—
814	Q₈	—	4	4	no	—
815	Q₈	—	4	2	no	—
816	Q₈	—	4	2	no	—
817	Q₈	—	8	1	no	—
818	Q₈	H(5,𝔽₂)×C₆₁	1	4	yes	—
819	D₄	—	2	4	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	8	1	no	—
825	D₄	—	8	2	no	—
826	D₄	—	8	2	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	8	2	no	—
854	C₂×C₄	—	8	2	no	—
855	C₂×C₄	—	8	1	no	—
856	C₂×C₄	—	8	1	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	1	yes	characteristic
861	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
863	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
864	C₈	—	2	4	no	—
865	C₈	—	2	4	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	4	4	no	—
876	C₂²	—	4	4	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	16	2	no	—
881	C₂²	C₂×#137×C₆₁	1	2	yes	—
882	C₂²	C₂×#137×C₆₁	1	2	yes	—
883	C₂²	C₂×#137×C₆₁	1	2	yes	—
884	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
899	C₂	—	2	2	no	—
900	C₂	—	2	2	no	—
901	C₂	—	2	2	no	—
902	C₂	—	4	2	no	—
903	C₂	—	8	2	no	—
904	C₂	C₆₁×#3484	1	1	yes	characteristic
905	C₂	C₂²×#137×C₆₁	1	1	yes	characteristic
906	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3505	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×D₄×Q₈×C₆₁	C₂	semidirect
3. C₆₁×#3320	C₂	semidirect
4. C₆₁×#3312	C₂	semidirect
5. C₆₁×#3270	C₂	semidirect
6. C₆₁×#3266	C₂	semidirect
7. C₆₁×#3218	C₂	semidirect
8. C₆₁×#3196	C₂	semidirect
9. C₆₁×#3189	C₂	semidirect
10. C₆₁×#3187	C₂	semidirect
11. C₆₁×#3117	C₂	semidirect
12. C₆₁×#3004	C₂	semidirect
13. C₂×C₆₁×#451	C₂	semidirect
14. C₂×C₆₁×#448	C₂	semidirect
15. C₆₁×#2973	C₂	semidirect
17. C₂³×Q₈×C₆₁	C₂²	semidirect
18. C₂×#137×C₆₁	C₂²	semidirect
19. C₂²×Q₁₆×C₆₁	C₂²	semidirect
20. C₂²×SD₁₆×C₆₁	C₂²	semidirect
28. D₄×Q₈×C₆₁	C₂²	semidirect
35. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
42. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
45. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
48. C₆₁×#497	C₂²	semidirect
49. C₆₁×#491	C₂²	semidirect
50. C₆₁×#485	C₂²	semidirect
51. C₆₁×#484	C₂²	semidirect
52. C₆₁×#484	C₂²	semidirect
53. C₆₁×#483	C₂²	semidirect
55. C₆₁×#479	C₂²	semidirect
56. C₆₁×#470	C₂²	semidirect
57. C₆₁×#468	C₂²	semidirect
58. C₆₁×#467	C₂²	semidirect
59. C₆₁×#465	C₂²	semidirect
60. C₆₁×#464	C₂²	semidirect
61. C₆₁×#462	C₂²	semidirect
62. C₆₁×#461	C₂²	semidirect
63. C₆₁×#452	C₂²	semidirect
64. C₆₁×#451	C₂²	semidirect
65. C₆₁×#451	C₂²	semidirect
66. C₆₁×#451	C₂²	semidirect
67. C₆₁×#451	C₂²	semidirect
68. C₆₁×#451	C₂²	semidirect
69. C₆₁×#451	C₂²	semidirect
70. C₆₁×#450	C₂²	semidirect
74. C₆₁×#448	C₂²	semidirect
75. C₆₁×#448	C₂²	semidirect
76. C₆₁×#441	C₂²	semidirect
77. C₆₁×#440	C₂²	semidirect
79. C₆₁×#435	C₂²	semidirect
80. C₆₁×#432	C₂²	semidirect
81. C₆₁×#419	C₂²	semidirect
82. C₂×#103×C₆₁	C₂²	semidirect
83. C₂×#103×C₆₁	C₂²	semidirect
84. C₆₁×#407	C₂²	semidirect
347. C₂³×C₆₁	#137	semidirect
412. #61574	C₆₁	direct (N × H)
447. C₂×D₄×Q₈	C₂×C₆₁	semidirect
448. #3320	C₂×C₆₁	semidirect
449. #3312	C₂×C₆₁	semidirect
450. #3270	C₂×C₆₁	semidirect
451. #3266	C₂×C₆₁	semidirect
452. #3218	C₂×C₆₁	semidirect
453. #3196	C₂×C₆₁	semidirect
454. #3189	C₂×C₆₁	semidirect
455. #3187	C₂×C₆₁	semidirect
456. #3117	C₂×C₆₁	semidirect
457. #3004	C₂×C₆₁	semidirect
458. C₂×#451	C₂×C₆₁	semidirect
459. C₂×#448	C₂×C₆₁	semidirect
460. #2973	C₂×C₆₁	semidirect
470. C₂³×Q₈	C₂²×C₆₁	semidirect
471. C₂×#137	C₂²×C₆₁	semidirect
472. C₂²×Q₁₆	C₂²×C₆₁	semidirect
473. C₂²×SD₁₆	C₂²×C₆₁	semidirect
481. D₄×Q₈	C₂²×C₆₁	semidirect
488. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
495. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
498. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
501. #497	C₂²×C₆₁	semidirect
502. #491	C₂²×C₆₁	semidirect
503. #485	C₂²×C₆₁	semidirect
504. #484	C₂²×C₆₁	semidirect
505. #484	C₂²×C₆₁	semidirect
506. #483	C₂²×C₆₁	semidirect
508. #479	C₂²×C₆₁	semidirect
509. #470	C₂²×C₆₁	semidirect
510. #468	C₂²×C₆₁	semidirect
511. #467	C₂²×C₆₁	semidirect
512. #465	C₂²×C₆₁	semidirect
513. #464	C₂²×C₆₁	semidirect
514. #462	C₂²×C₆₁	semidirect
515. #461	C₂²×C₆₁	semidirect
516. #452	C₂²×C₆₁	semidirect
517. #451	C₂²×C₆₁	semidirect
518. #451	C₂²×C₆₁	semidirect
519. #451	C₂²×C₆₁	semidirect
520. #451	C₂²×C₆₁	semidirect
521. #451	C₂²×C₆₁	semidirect
522. #451	C₂²×C₆₁	semidirect
523. #450	C₂²×C₆₁	semidirect
527. #448	C₂²×C₆₁	semidirect
528. #448	C₂²×C₆₁	semidirect
529. #441	C₂²×C₆₁	semidirect
530. #440	C₂²×C₆₁	semidirect
532. #435	C₂²×C₆₁	semidirect
533. #432	C₂²×C₆₁	semidirect
534. #419	C₂²×C₆₁	semidirect
535. C₂×#103	C₂²×C₆₁	semidirect
536. C₂×#103	C₂²×C₆₁	semidirect
537. #407	C₂²×C₆₁	semidirect
540. C₆₁	#61574	direct (N × H)
801. C₂³	#137×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3505	2
C₂×D₄×Q₈×C₆₁	2
C₆₁×#3320	2
C₆₁×#3312	2
C₆₁×#3270	2
C₆₁×#3266	2
C₆₁×#3218	2
C₆₁×#3196	2
C₆₁×#3189	2
C₆₁×#3187	2
C₆₁×#3117	2
C₆₁×#3004	2
C₂×C₆₁×#451	2
C₂×C₆₁×#448	2
C₆₁×#2973	2
#61574	61

Subgroups — C61×#61574 #29565007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61574 #29565007