Subgroups — C₆₁×#60422 #29563855

Order 15616.

2714 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#135×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3428	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3046	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3045	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3044	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3043	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3042	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3041	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3035	C₂	1	8	yes	maximal, complemented
12	C₂×C₆₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2896	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#575	—	2	8	no	—
19	C₂×#137×C₆₁	C₂²	1	2	yes	—
20	C₂×#137×C₆₁	C₂²	1	2	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
22	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	complemented
23	C₂×#135×C₆₁	—	2	8	no	—
24	C₂×#135×C₆₁	C₂²	1	4	yes	—
25	C₂×#135×C₆₁	C₂²	1	4	yes	complemented
26	C₂×#135×C₆₁	C₂²	1	4	yes	complemented
27	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
31	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
32	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#537	—	2	2	no	—
34	C₆₁×#536	C₂²	1	2	yes	—
35	C₆₁×#536	C₂²	1	2	yes	complemented
36	C₆₁×#535	C₂²	1	2	yes	—
37	C₆₁×#535	C₂²	1	2	yes	complemented
38	C₆₁×#534	—	2	2	no	—
39	C₆₁×#532	C₂²	1	4	yes	complemented
40	C₆₁×#525	—	2	2	no	—
41	C₆₁×#525	—	2	2	no	—
42	C₆₁×#520	—	2	2	no	—
43	C₆₁×#520	C₂²	1	4	yes	complemented
44	C₆₁×#519	C₂²	1	2	yes	complemented
45	C₆₁×#518	—	2	2	no	—
46	C₆₁×#518	C₂²	1	2	yes	complemented
47	C₄×#41×C₆₁	—	2	2	no	—
48	C₄×#41×C₆₁	C₂²	1	4	yes	complemented
49	C₂×#117×C₆₁	—	2	2	no	—
50	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
52	C₆₁×#464	C₂²	1	8	yes	complemented
53	C₆₁×#464	C₂²	1	8	yes	complemented
54	C₆₁×#463	C₂²	1	8	yes	complemented
55	C₆₁×#463	C₂²	1	8	yes	complemented
56	C₆₁×#462	C₂²	1	8	yes	complemented
57	C₆₁×#461	C₂²	1	8	yes	complemented
58	C₆₁×#460	C₂²	1	8	yes	complemented
59	C₆₁×#459	C₂²	1	8	yes	complemented
60	C₆₁×#424	C₂²	1	2	yes	complemented
61	C₆₁×#424	C₂²	1	2	yes	complemented
62	C₆₁×#424	C₂²	1	4	yes	complemented
63	C₂×C₄⋊C₈×C₆₁	C₂²	1	4	yes	complemented
64	C₆₁×#419	C₂²	1	2	yes	complemented
65	C₆₁×#418	C₂²	1	2	yes	complemented
66	C₆₁×#417	C₂²	1	4	yes	complemented
67	C₆₁×#416	C₂²	1	2	yes	—
68	C₆₁×#416	C₂²	1	2	yes	—
69	C₆₁×#416	C₂²	1	4	yes	complemented
70	C₆₁×#416	C₂²	1	4	yes	complemented
71	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
72	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
73	C₂×#41×C₆₁	—	2	1	no	—
74	C₂×#41×C₆₁	—	2	1	no	—
75	C₂×#41×C₆₁	—	2	1	no	—
76	C₂×#41×C₆₁	—	2	1	no	—
77	C₂×#41×C₆₁	—	2	1	no	—
78	C₂×#41×C₆₁	—	2	1	no	—
79	C₂×#41×C₆₁	—	2	4	no	—
80	C₂×#41×C₆₁	—	2	4	no	—
81	C₂×#41×C₆₁	—	2	4	no	—
82	C₂×#41×C₆₁	—	2	4	no	—
83	C₂×#41×C₆₁	—	2	4	no	—
84	C₂×#41×C₆₁	D₄	1	8	yes	complemented
85	C₂×#41×C₆₁	C₂³	1	2	yes	—
86	C₂×#41×C₆₁	C₂³	1	2	yes	—
87	C₂×#41×C₆₁	C₂³	1	2	yes	—
88	C₂×#41×C₆₁	C₂³	1	2	yes	—
89	C₂×#41×C₆₁	C₂³	1	2	yes	—
90	C₂×#41×C₆₁	C₂³	1	2	yes	—
91	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
92	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₆₁	—	2	1	no	—
95	C₂²×D₄×C₆₁	—	2	1	no	—
96	C₂²×D₄×C₆₁	—	2	1	no	—
97	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₆₁	—	2	1	no	—
101	C₂³×C₄×C₆₁	—	2	1	no	—
102	C₂³×C₄×C₆₁	—	2	1	no	—
103	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
104	#137×C₆₁	—	2	8	no	—
105	#137×C₆₁	—	2	8	no	—
106	AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
107	AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
108	#135×C₆₁	—	2	16	no	—
109	#135×C₆₁	—	2	16	no	—
110	#135×C₆₁	—	2	16	no	—
111	C₂×Q₁₆×C₆₁	—	2	4	no	—
112	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
113	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₆₁	—	2	4	no	—
115	C₂×SD₁₆×C₆₁	—	2	4	no	—
116	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
120	C₂×D₈×C₆₁	—	2	4	no	—
121	C₂×D₈×C₆₁	C₂³	1	4	yes	—
122	C₂×D₈×C₆₁	C₂³	1	4	yes	—
123	C₂×M₁₆×C₆₁	—	2	4	no	—
124	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
125	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
126	C₂²×C₈×C₆₁	—	2	4	no	—
127	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
130	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
131	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
132	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
133	#127×C₆₁	C₂³	1	4	yes	—
134	#124×C₆₁	C₂³	1	4	yes	—
135	#124×C₆₁	C₂³	1	4	yes	—
136	#123×C₆₁	—	2	4	no	—
137	#123×C₆₁	—	2	4	no	—
138	C₂²⋊Q₈×C₆₁	—	2	4	no	—
139	C₂²⋊Q₈×C₆₁	—	2	4	no	—
140	#121×C₆₁	—	2	8	no	—
141	#121×C₆₁	—	2	4	no	—
142	#121×C₆₁	—	2	4	no	—
143	#120×C₆₁	—	2	4	no	—
144	#120×C₆₁	—	2	4	no	—
145	C₄×Q₈×C₆₁	—	2	4	no	—
146	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
147	C₄×D₄×C₆₁	—	2	8	no	—
148	C₄×D₄×C₆₁	—	2	4	no	—
149	C₄×D₄×C₆₁	—	2	8	no	—
150	C₄×D₄×C₆₁	—	2	8	no	—
151	C₄×D₄×C₆₁	C₂³	1	8	yes	—
152	#117×C₆₁	—	2	1	no	—
153	#117×C₆₁	—	2	1	no	—
154	#117×C₆₁	—	2	4	no	—
155	#117×C₆₁	—	2	4	no	—
156	#117×C₆₁	—	2	4	no	—
157	#117×C₆₁	D₄	1	2	yes	—
158	#117×C₆₁	D₄	1	2	yes	—
159	#117×C₆₁	C₂³	1	2	yes	—
160	#117×C₆₁	C₂³	1	2	yes	—
161	#117×C₆₁	C₂³	1	2	yes	—
162	#117×C₆₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
164	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
167	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
168	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
169	C₂×C₄²×C₆₁	—	2	1	no	—
170	C₂×C₄²×C₆₁	—	2	4	no	—
171	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
172	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
173	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
174	#103×C₆₁	C₂³	1	4	yes	—
175	#103×C₆₁	C₂³	1	4	yes	—
176	#103×C₆₁	C₂³	1	8	yes	—
177	#102×C₆₁	C₂³	1	4	yes	—
178	#102×C₆₁	C₂³	1	4	yes	—
179	#102×C₆₁	C₂³	1	8	yes	—
180	C₂⁴×C₆₁	—	2	1	no	—
181	C₂⁴×C₆₁	—	2	1	no	—
182	C₂⁴×C₆₁	—	2	1	no	—
183	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
184	#41×C₆₁	—	2	8	no	—
185	#41×C₆₁	—	2	8	no	—
186	#41×C₆₁	—	2	4	no	—
187	#41×C₆₁	—	2	4	no	—
188	#41×C₆₁	—	2	4	no	—
189	#41×C₆₁	—	2	4	no	—
190	#41×C₆₁	—	2	4	no	—
191	#41×C₆₁	—	2	4	no	—
192	#41×C₆₁	—	2	4	no	—
193	#41×C₆₁	—	2	4	no	—
194	#41×C₆₁	—	2	4	no	—
195	#41×C₆₁	—	2	4	no	—
196	#41×C₆₁	—	4	4	no	—
197	#41×C₆₁	—	4	4	no	—
198	#41×C₆₁	—	4	4	no	—
199	#41×C₆₁	—	4	4	no	—
200	#41×C₆₁	C₂×D₄	1	8	yes	—
201	#41×C₆₁	C₂×D₄	1	8	yes	—
202	C₂×Q₈×C₆₁	—	2	1	no	—
203	C₂×Q₈×C₆₁	—	2	1	no	—
204	C₂×Q₈×C₆₁	—	2	1	no	—
205	C₂×Q₈×C₆₁	—	2	2	no	—
206	C₂×Q₈×C₆₁	—	2	2	no	—
207	C₂×Q₈×C₆₁	—	2	2	no	—
208	C₂×Q₈×C₆₁	—	2	2	no	—
209	C₂×Q₈×C₆₁	—	2	2	no	—
210	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
211	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
212	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
213	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
214	C₂×D₄×C₆₁	—	2	8	no	—
215	C₂×D₄×C₆₁	—	2	2	no	—
216	C₂×D₄×C₆₁	—	2	2	no	—
217	C₂×D₄×C₆₁	—	2	2	no	—
218	C₂×D₄×C₆₁	—	2	2	no	—
219	C₂×D₄×C₆₁	—	2	2	no	—
220	C₂×D₄×C₆₁	—	2	2	no	—
221	C₂×D₄×C₆₁	—	2	1	no	—
222	C₂×D₄×C₆₁	—	2	2	no	—
223	C₂×D₄×C₆₁	—	2	2	no	—
224	C₂×D₄×C₆₁	—	2	1	no	—
225	C₂×D₄×C₆₁	—	2	1	no	—
226	C₂×D₄×C₆₁	—	2	8	no	—
227	C₂×D₄×C₆₁	—	2	2	no	—
228	C₂×D₄×C₆₁	—	2	2	no	—
229	C₂×D₄×C₆₁	—	2	2	no	—
230	C₂×D₄×C₆₁	—	4	4	no	—
231	C₂×D₄×C₆₁	—	4	4	no	—
232	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
233	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
234	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
235	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₆₁	—	2	1	no	—
237	C₂²×C₄×C₆₁	—	2	8	no	—
238	C₂²×C₄×C₆₁	—	2	2	no	—
239	C₂²×C₄×C₆₁	—	2	2	no	—
240	C₂²×C₄×C₆₁	—	2	1	no	—
241	C₂²×C₄×C₆₁	—	2	1	no	—
242	C₂²×C₄×C₆₁	—	2	2	no	—
243	C₂²×C₄×C₆₁	—	2	2	no	—
244	C₂²×C₄×C₆₁	—	2	2	no	—
245	C₂²×C₄×C₆₁	—	2	2	no	—
246	C₂²×C₄×C₆₁	—	2	2	no	—
247	C₂²×C₄×C₆₁	—	2	8	no	—
248	C₂²×C₄×C₆₁	—	4	4	no	—
249	C₂²×C₄×C₆₁	—	4	4	no	—
250	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
251	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
255	C₂²×C₄×C₆₁	#41	1	4	yes	—
256	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
259	Q₁₆×C₆₁	—	2	8	no	—
260	Q₁₆×C₆₁	—	2	8	no	—
261	SD₁₆×C₆₁	—	2	8	no	—
262	SD₁₆×C₆₁	—	2	8	no	—
263	SD₁₆×C₆₁	—	2	8	no	—
264	SD₁₆×C₆₁	—	2	8	no	—
265	D₈×C₆₁	—	2	8	no	—
266	D₈×C₆₁	—	2	8	no	—
267	M₁₆×C₆₁	—	2	4	no	—
268	M₁₆×C₆₁	—	2	4	no	—
269	C₂×C₈×C₆₁	—	2	2	no	—
270	C₂×C₈×C₆₁	—	2	2	no	—
271	C₂×C₈×C₆₁	—	2	4	no	—
272	C₂×C₈×C₆₁	—	2	4	no	—
273	C₂×C₈×C₆₁	—	2	4	no	—
274	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
275	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
276	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₆₁	—	2	2	no	—
278	C₄⋊C₄×C₆₁	—	2	8	no	—
279	C₄⋊C₄×C₆₁	—	2	8	no	—
280	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
281	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
282	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
283	C₂²⋊C₄×C₆₁	—	2	2	no	—
284	C₂²⋊C₄×C₆₁	—	2	2	no	—
285	C₂²⋊C₄×C₆₁	—	2	8	no	—
286	C₂²⋊C₄×C₆₁	—	2	8	no	—
287	C₂²⋊C₄×C₆₁	—	2	8	no	—
288	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
289	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
290	C₄²×C₆₁	—	2	8	no	—
291	C₄²×C₆₁	—	2	2	no	—
292	C₄²×C₆₁	—	2	2	no	—
293	C₄²×C₆₁	C₂×D₄	1	4	yes	—
294	C₄²×C₆₁	C₂⁴	1	4	yes	—
295	C₂³×C₆₁	—	2	2	no	—
296	C₂³×C₆₁	—	2	4	no	—
297	C₂³×C₆₁	—	2	2	no	—
298	C₂³×C₆₁	—	2	2	no	—
299	C₂³×C₆₁	—	4	2	no	—
300	C₂³×C₆₁	—	4	2	no	—
301	C₂³×C₆₁	—	4	2	no	—
302	C₂³×C₆₁	—	8	2	no	—
303	C₂³×C₆₁	—	8	2	no	—
304	C₂³×C₆₁	—	8	2	no	—
305	C₂³×C₆₁	#121	1	4	yes	—
306	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
307	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
308	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₆₁	—	2	4	no	—
310	Q₈×C₆₁	—	2	2	no	—
311	Q₈×C₆₁	—	2	2	no	—
312	Q₈×C₆₁	—	2	2	no	—
313	Q₈×C₆₁	—	2	2	no	—
314	Q₈×C₆₁	—	2	2	no	—
315	Q₈×C₆₁	—	4	2	no	—
316	Q₈×C₆₁	—	4	2	no	—
317	Q₈×C₆₁	C₂²×D₄	1	4	yes	—
318	D₄×C₆₁	—	2	8	no	—
319	D₄×C₆₁	—	2	8	no	—
320	D₄×C₆₁	—	2	4	no	—
321	D₄×C₆₁	—	2	2	no	—
322	D₄×C₆₁	—	2	2	no	—
323	D₄×C₆₁	—	2	2	no	—
324	D₄×C₆₁	—	2	2	no	—
325	D₄×C₆₁	—	2	2	no	—
326	D₄×C₆₁	—	4	4	no	—
327	D₄×C₆₁	—	4	4	no	—
328	D₄×C₆₁	—	4	4	no	—
329	D₄×C₆₁	—	4	4	no	—
330	D₄×C₆₁	—	4	2	no	—
331	D₄×C₆₁	—	4	2	no	—
332	D₄×C₆₁	—	8	8	no	—
333	D₄×C₆₁	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₆₁	—	2	4	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	2	8	no	—
337	C₂×C₄×C₆₁	—	2	8	no	—
338	C₂×C₄×C₆₁	—	2	4	no	—
339	C₂×C₄×C₆₁	—	2	2	no	—
340	C₂×C₄×C₆₁	—	2	2	no	—
341	C₂×C₄×C₆₁	—	4	4	no	—
342	C₂×C₄×C₆₁	—	4	2	no	—
343	C₂×C₄×C₆₁	—	4	2	no	—
344	C₂×C₄×C₆₁	—	4	4	no	—
345	C₂×C₄×C₆₁	—	4	4	no	—
346	C₂×C₄×C₆₁	—	4	4	no	—
347	C₂×C₄×C₆₁	—	4	4	no	—
348	C₂×C₄×C₆₁	—	8	8	no	—
349	C₂×C₄×C₆₁	—	8	2	no	—
350	C₂×C₄×C₆₁	#121	1	4	yes	—
351	C₂×C₄×C₆₁	#121	1	4	yes	—
352	C₂×C₄×C₆₁	#121	1	4	yes	—
353	C₂×C₄×C₆₁	C₂²×D₄	1	8	yes	—
354	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
361	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
362	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
363	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
364	C₈×C₆₁	—	2	2	no	—
365	C₈×C₆₁	—	2	2	no	—
366	C₈×C₆₁	—	2	4	no	—
367	#60422	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂²×C₆₁	—	2	2	no	—
369	C₂²×C₆₁	—	2	2	no	—
370	C₂²×C₆₁	—	2	2	no	—
371	C₂²×C₆₁	—	2	4	no	—
372	C₂²×C₆₁	—	4	4	no	—
373	C₂²×C₆₁	—	4	4	no	—
374	C₂²×C₆₁	—	4	4	no	—
375	C₂²×C₆₁	—	4	4	no	—
376	C₂²×C₆₁	—	4	2	no	—
377	C₂²×C₆₁	—	4	2	no	—
378	C₂²×C₆₁	—	8	4	no	—
379	C₂²×C₆₁	—	8	4	no	—
380	C₂²×C₆₁	—	8	4	no	—
381	C₂²×C₆₁	C₂×#121	1	2	yes	—
382	C₂²×C₆₁	C₂×#121	1	2	yes	—
383	C₂²×C₆₁	C₂×#121	1	2	yes	—
384	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₆₁	—	2	8	no	—
386	C₄×C₆₁	—	2	4	no	—
387	C₄×C₆₁	—	4	4	no	—
388	C₄×C₆₁	—	4	2	no	—
389	C₄×C₆₁	—	4	2	no	—
390	C₄×C₆₁	C₂×#121	1	2	yes	—
391	C₄×C₆₁	C₂×#121	1	2	yes	—
392	C₄×C₆₁	C₂×#121	1	2	yes	—
393	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
394	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
395	C₂×#575	C₂×C₆₁	1	1	yes	characteristic, complemented
396	C₂²×#135	C₂×C₆₁	1	1	yes	characteristic, complemented
397	#3449	C₂×C₆₁	1	1	yes	characteristic, complemented
398	#3428	C₂×C₆₁	1	1	yes	characteristic, complemented
399	#3046	C₂×C₆₁	1	4	yes	complemented
400	#3045	C₂×C₆₁	1	4	yes	complemented
401	#3044	C₂×C₆₁	1	2	yes	complemented
402	#3043	C₂×C₆₁	1	2	yes	complemented
403	#3042	C₂×C₆₁	1	2	yes	complemented
404	#3041	C₂×C₆₁	1	2	yes	complemented
405	#3035	C₂×C₆₁	1	8	yes	complemented
406	C₂×#424	C₂×C₆₁	1	1	yes	characteristic, complemented
407	#2896	C₂×C₆₁	1	1	yes	characteristic, complemented
408	C₂×#416	C₂×C₆₁	1	1	yes	characteristic, complemented
409	C₂×C₆₁	—	2	2	no	—
410	C₂×C₆₁	—	2	2	no	—
411	C₂×C₆₁	—	2	2	no	—
412	C₂×C₆₁	—	4	4	no	—
413	C₂×C₆₁	—	8	2	no	—
414	C₂×C₆₁	—	8	2	no	—
415	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
416	C₂×C₆₁	#3584	1	2	yes	—
417	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
418	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
419	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
420	#575	—	2	8	no	—
421	C₂×#137	C₂²×C₆₁	1	2	yes	—
422	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
423	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
424	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	complemented
425	C₂×#135	—	2	8	no	—
426	C₂×#135	C₂²×C₆₁	1	4	yes	—
427	C₂×#135	C₂²×C₆₁	1	4	yes	complemented
428	C₂×#135	C₂²×C₆₁	1	4	yes	complemented
429	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
430	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
431	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
432	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
433	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
434	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
435	#537	—	2	2	no	—
436	#536	C₂²×C₆₁	1	2	yes	—
437	#536	C₂²×C₆₁	1	2	yes	complemented
438	#535	C₂²×C₆₁	1	2	yes	—
439	#535	C₂²×C₆₁	1	2	yes	complemented
440	#534	—	2	2	no	—
441	#532	C₂²×C₆₁	1	4	yes	complemented
442	#525	—	2	2	no	—
443	#525	—	2	2	no	—
444	#520	—	2	2	no	—
445	#520	C₂²×C₆₁	1	4	yes	complemented
446	#519	C₂²×C₆₁	1	2	yes	complemented
447	#518	—	2	2	no	—
448	#518	C₂²×C₆₁	1	2	yes	complemented
449	C₄×#41	—	2	2	no	—
450	C₄×#41	C₂²×C₆₁	1	4	yes	complemented
451	C₂×#117	—	2	2	no	—
452	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
453	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
454	#464	C₂²×C₆₁	1	8	yes	complemented
455	#464	C₂²×C₆₁	1	8	yes	complemented
456	#463	C₂²×C₆₁	1	8	yes	complemented
457	#463	C₂²×C₆₁	1	8	yes	complemented
458	#462	C₂²×C₆₁	1	8	yes	complemented
459	#461	C₂²×C₆₁	1	8	yes	complemented
460	#460	C₂²×C₆₁	1	8	yes	complemented
461	#459	C₂²×C₆₁	1	8	yes	complemented
462	#424	C₂²×C₆₁	1	2	yes	complemented
463	#424	C₂²×C₆₁	1	2	yes	complemented
464	#424	C₂²×C₆₁	1	4	yes	complemented
465	C₂×C₄⋊C₈	C₂²×C₆₁	1	4	yes	complemented
466	#419	C₂²×C₆₁	1	2	yes	complemented
467	#418	C₂²×C₆₁	1	2	yes	complemented
468	#417	C₂²×C₆₁	1	4	yes	complemented
469	#416	C₂²×C₆₁	1	2	yes	—
470	#416	C₂²×C₆₁	1	2	yes	—
471	#416	C₂²×C₆₁	1	4	yes	complemented
472	#416	C₂²×C₆₁	1	4	yes	complemented
473	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
474	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
475	C₆₁	#60422	1	1	yes	characteristic, direct product factor, Sylow
476	C₂×#41	—	2	1	no	—
477	C₂×#41	—	2	1	no	—
478	C₂×#41	—	2	1	no	—
479	C₂×#41	—	2	1	no	—
480	C₂×#41	—	2	1	no	—
481	C₂×#41	—	2	1	no	—
482	C₂×#41	—	2	4	no	—
483	C₂×#41	—	2	4	no	—
484	C₂×#41	—	2	4	no	—
485	C₂×#41	—	2	4	no	—
486	C₂×#41	—	2	4	no	—
487	C₂×#41	D₄×C₆₁	1	8	yes	complemented
488	C₂×#41	C₂³×C₆₁	1	2	yes	—
489	C₂×#41	C₂³×C₆₁	1	2	yes	—
490	C₂×#41	C₂³×C₆₁	1	2	yes	—
491	C₂×#41	C₂³×C₆₁	1	2	yes	—
492	C₂×#41	C₂³×C₆₁	1	2	yes	—
493	C₂×#41	C₂³×C₆₁	1	2	yes	—
494	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
495	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
496	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
507	#137	—	2	8	no	—
508	#137	—	2	8	no	—
509	AGL(1,ℤ/8)	—	2	8	no	—
510	AGL(1,ℤ/8)	—	2	8	no	—
511	#135	—	2	16	no	—
512	#135	—	2	16	no	—
513	#135	—	2	16	no	—
514	C₂×Q₁₆	—	2	4	no	—
515	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
516	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
517	C₂×SD₁₆	—	2	4	no	—
518	C₂×SD₁₆	—	2	4	no	—
519	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
520	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
521	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
522	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
523	C₂×D₈	—	2	4	no	—
524	C₂×D₈	C₂³×C₆₁	1	4	yes	—
525	C₂×D₈	C₂³×C₆₁	1	4	yes	—
526	C₂×M₁₆	—	2	4	no	—
527	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
528	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
529	C₂²×C₈	—	2	4	no	—
530	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
533	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
534	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
536	#127	C₂³×C₆₁	1	4	yes	—
537	#124	C₂³×C₆₁	1	4	yes	—
538	#124	C₂³×C₆₁	1	4	yes	—
539	#123	—	2	4	no	—
540	#123	—	2	4	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	#121	—	2	8	no	—
544	#121	—	2	4	no	—
545	#121	—	2	4	no	—
546	#120	—	2	4	no	—
547	#120	—	2	4	no	—
548	C₄×Q₈	—	2	4	no	—
549	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
550	C₄×D₄	—	2	8	no	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	8	no	—
553	C₄×D₄	—	2	8	no	—
554	C₄×D₄	C₂³×C₆₁	1	8	yes	—
555	#117	—	2	1	no	—
556	#117	—	2	1	no	—
557	#117	—	2	4	no	—
558	#117	—	2	4	no	—
559	#117	—	2	4	no	—
560	#117	D₄×C₆₁	1	2	yes	—
561	#117	D₄×C₆₁	1	2	yes	—
562	#117	C₂³×C₆₁	1	2	yes	—
563	#117	C₂³×C₆₁	1	2	yes	—
564	#117	C₂³×C₆₁	1	2	yes	—
565	#117	C₂³×C₆₁	1	2	yes	—
566	C₂×C₄⋊C₄	—	2	4	no	—
567	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	4	no	—
571	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
572	C₂×C₄²	—	2	1	no	—
573	C₂×C₄²	—	2	4	no	—
574	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
575	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
576	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
577	#103	C₂³×C₆₁	1	4	yes	—
578	#103	C₂³×C₆₁	1	4	yes	—
579	#103	C₂³×C₆₁	1	8	yes	—
580	#102	C₂³×C₆₁	1	4	yes	—
581	#102	C₂³×C₆₁	1	4	yes	—
582	#102	C₂³×C₆₁	1	8	yes	—
583	C₂⁴	—	2	1	no	—
584	C₂⁴	—	2	1	no	—
585	C₂⁴	—	2	1	no	—
586	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
587	#41	—	2	8	no	—
588	#41	—	2	8	no	—
589	#41	—	2	4	no	—
590	#41	—	2	4	no	—
591	#41	—	2	4	no	—
592	#41	—	2	4	no	—
593	#41	—	2	4	no	—
594	#41	—	2	4	no	—
595	#41	—	2	4	no	—
596	#41	—	2	4	no	—
597	#41	—	2	4	no	—
598	#41	—	2	4	no	—
599	#41	—	4	4	no	—
600	#41	—	4	4	no	—
601	#41	—	4	4	no	—
602	#41	—	4	4	no	—
603	#41	C₂×D₄×C₆₁	1	8	yes	—
604	#41	C₂×D₄×C₆₁	1	8	yes	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
614	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
615	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
616	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
617	C₂×D₄	—	2	8	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	8	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
636	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
637	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
638	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	8	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	8	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
654	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
658	C₂²×C₄	#41×C₆₁	1	4	yes	—
659	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
662	Q₁₆	—	2	8	no	—
663	Q₁₆	—	2	8	no	—
664	SD₁₆	—	2	8	no	—
665	SD₁₆	—	2	8	no	—
666	SD₁₆	—	2	8	no	—
667	SD₁₆	—	2	8	no	—
668	D₈	—	2	8	no	—
669	D₈	—	2	8	no	—
670	M₁₆	—	2	4	no	—
671	M₁₆	—	2	4	no	—
672	C₂×C₈	—	2	2	no	—
673	C₂×C₈	—	2	2	no	—
674	C₂×C₈	—	2	4	no	—
675	C₂×C₈	—	2	4	no	—
676	C₂×C₈	—	2	4	no	—
677	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
678	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
679	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	8	no	—
682	C₄⋊C₄	—	2	8	no	—
683	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
684	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
685	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	8	no	—
689	C₂²⋊C₄	—	2	8	no	—
690	C₂²⋊C₄	—	2	8	no	—
691	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
692	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	8	no	—
695	C₄²	—	2	2	no	—
696	C₄²	C₂×D₄×C₆₁	1	4	yes	—
697	C₄²	C₂⁴×C₆₁	1	4	yes	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	4	2	no	—
703	C₂³	—	4	2	no	—
704	C₂³	—	4	2	no	—
705	C₂³	—	8	2	no	—
706	C₂³	—	8	2	no	—
707	C₂³	—	8	2	no	—
708	C₂³	#121×C₆₁	1	4	yes	—
709	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
710	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
711	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
712	Q₈	—	2	2	no	—
713	Q₈	—	2	4	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	4	2	no	—
720	Q₈	C₂²×D₄×C₆₁	1	4	yes	—
721	D₄	—	2	8	no	—
722	D₄	—	2	8	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	4	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	4	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	4	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	2	no	—
735	D₄	—	8	8	no	—
736	D₄	C₂²×D₄×C₆₁	1	4	yes	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	8	no	—
740	C₂×C₄	—	2	8	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	4	no	—
749	C₂×C₄	—	4	4	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	8	8	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	#121×C₆₁	1	4	yes	—
754	C₂×C₄	#121×C₆₁	1	4	yes	—
755	C₂×C₄	#121×C₆₁	1	4	yes	—
756	C₂×C₄	C₂²×D₄×C₆₁	1	8	yes	—
757	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
758	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
759	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
760	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
763	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
764	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
765	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
766	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
767	C₈	—	2	2	no	—
768	C₈	—	2	2	no	—
769	C₈	—	2	4	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	4	4	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	4	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	8	4	no	—
781	C₂²	—	8	4	no	—
782	C₂²	—	8	4	no	—
783	C₂²	C₂×#121×C₆₁	1	2	yes	—
784	C₂²	C₂×#121×C₆₁	1	2	yes	—
785	C₂²	C₂×#121×C₆₁	1	2	yes	—
786	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
787	C₄	—	2	8	no	—
788	C₄	—	2	4	no	—
789	C₄	—	4	4	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	C₂×#121×C₆₁	1	2	yes	—
793	C₄	C₂×#121×C₆₁	1	2	yes	—
794	C₄	C₂×#121×C₆₁	1	2	yes	—
795	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
796	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
797	C₂	—	2	2	no	—
798	C₂	—	2	2	no	—
799	C₂	—	2	2	no	—
800	C₂	—	4	4	no	—
801	C₂	—	8	2	no	—
802	C₂	—	8	2	no	—
803	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
804	C₂	C₆₁×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂²×C₆₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#575	C₂	semidirect
2. C₂²×#135×C₆₁	C₂	semidirect
3. C₆₁×#3449	C₂	semidirect
4. C₆₁×#3428	C₂	semidirect
5. C₆₁×#3046	C₂	semidirect
6. C₆₁×#3045	C₂	semidirect
7. C₆₁×#3044	C₂	semidirect
8. C₆₁×#3043	C₂	semidirect
9. C₆₁×#3042	C₂	semidirect
10. C₆₁×#3041	C₂	semidirect
11. C₆₁×#3035	C₂	semidirect
12. C₂×C₆₁×#424	C₂	semidirect
13. C₆₁×#2896	C₂	semidirect
14. C₂×C₆₁×#416	C₂	semidirect
20. C₂×#137×C₆₁	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
25. C₂×#135×C₆₁	C₂²	semidirect
26. C₂×#135×C₆₁	C₂²	semidirect
27. C₂²×Q₁₆×C₆₁	C₂²	semidirect
28. C₂²×SD₁₆×C₆₁	C₂²	semidirect
29. C₂²×SD₁₆×C₆₁	C₂²	semidirect
30. C₂²×D₈×C₆₁	C₂²	semidirect
35. C₆₁×#536	C₂²	semidirect
37. C₆₁×#535	C₂²	semidirect
39. C₆₁×#532	C₂²	semidirect
43. C₆₁×#520	C₂²	semidirect
44. C₆₁×#519	C₂²	semidirect
46. C₆₁×#518	C₂²	semidirect
48. C₄×#41×C₆₁	C₂²	semidirect
52. C₆₁×#464	C₂²	semidirect
53. C₆₁×#464	C₂²	semidirect
54. C₆₁×#463	C₂²	semidirect
55. C₆₁×#463	C₂²	semidirect
56. C₆₁×#462	C₂²	semidirect
57. C₆₁×#461	C₂²	semidirect
58. C₆₁×#460	C₂²	semidirect
59. C₆₁×#459	C₂²	semidirect
60. C₆₁×#424	C₂²	semidirect
61. C₆₁×#424	C₂²	semidirect
62. C₆₁×#424	C₂²	semidirect
63. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
64. C₆₁×#419	C₂²	semidirect
65. C₆₁×#418	C₂²	semidirect
66. C₆₁×#417	C₂²	semidirect
69. C₆₁×#416	C₂²	semidirect
70. C₆₁×#416	C₂²	semidirect
71. C₂×#103×C₆₁	C₂²	semidirect
72. C₂×#102×C₆₁	C₂²	semidirect
84. C₂×#41×C₆₁	D₄	semidirect
367. #60422	C₆₁	direct (N × H)
395. C₂×#575	C₂×C₆₁	semidirect
396. C₂²×#135	C₂×C₆₁	semidirect
397. #3449	C₂×C₆₁	semidirect
398. #3428	C₂×C₆₁	semidirect
399. #3046	C₂×C₆₁	semidirect
400. #3045	C₂×C₆₁	semidirect
401. #3044	C₂×C₆₁	semidirect
402. #3043	C₂×C₆₁	semidirect
403. #3042	C₂×C₆₁	semidirect
404. #3041	C₂×C₆₁	semidirect
405. #3035	C₂×C₆₁	semidirect
406. C₂×#424	C₂×C₆₁	semidirect
407. #2896	C₂×C₆₁	semidirect
408. C₂×#416	C₂×C₆₁	semidirect
422. C₂×#137	C₂²×C₆₁	semidirect
424. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
427. C₂×#135	C₂²×C₆₁	semidirect
428. C₂×#135	C₂²×C₆₁	semidirect
429. C₂²×Q₁₆	C₂²×C₆₁	semidirect
430. C₂²×SD₁₆	C₂²×C₆₁	semidirect
431. C₂²×SD₁₆	C₂²×C₆₁	semidirect
432. C₂²×D₈	C₂²×C₆₁	semidirect
437. #536	C₂²×C₆₁	semidirect
439. #535	C₂²×C₆₁	semidirect
441. #532	C₂²×C₆₁	semidirect
445. #520	C₂²×C₆₁	semidirect
446. #519	C₂²×C₆₁	semidirect
448. #518	C₂²×C₆₁	semidirect
450. C₄×#41	C₂²×C₆₁	semidirect
454. #464	C₂²×C₆₁	semidirect
455. #464	C₂²×C₆₁	semidirect
456. #463	C₂²×C₆₁	semidirect
457. #463	C₂²×C₆₁	semidirect
458. #462	C₂²×C₆₁	semidirect
459. #461	C₂²×C₆₁	semidirect
460. #460	C₂²×C₆₁	semidirect
461. #459	C₂²×C₆₁	semidirect
462. #424	C₂²×C₆₁	semidirect
463. #424	C₂²×C₆₁	semidirect
464. #424	C₂²×C₆₁	semidirect
465. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
466. #419	C₂²×C₆₁	semidirect
467. #418	C₂²×C₆₁	semidirect
468. #417	C₂²×C₆₁	semidirect
471. #416	C₂²×C₆₁	semidirect
472. #416	C₂²×C₆₁	semidirect
473. C₂×#103	C₂²×C₆₁	semidirect
474. C₂×#102	C₂²×C₆₁	semidirect
475. C₆₁	#60422	direct (N × H)
487. C₂×#41	D₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#575	2
C₂²×#135×C₆₁	2
C₆₁×#3449	2
C₆₁×#3428	2
C₆₁×#3046	2
C₆₁×#3045	2
C₆₁×#3044	2
C₆₁×#3043	2
C₆₁×#3042	2
C₆₁×#3041	2
C₆₁×#3035	2
C₂×C₆₁×#424	2
C₆₁×#2896	2
C₂×C₆₁×#416	2
#60422	61

Subgroups — C61×#60422 #29563855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60422 #29563855