Subgroups — C₆₁×#61451 #29564884

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3345	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3318	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3306	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3264	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3180	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3114	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3109	C₂	1	2	yes	maximal, complemented
21	C₆₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₆₁×#442	C₂	1	2	yes	maximal, complemented
24	C₂²×#41×C₆₁	—	2	1	no	—
25	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#559	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#553	—	2	1	no	—
31	C₆₁×#553	C₂²	1	2	yes	complemented
32	C₆₁×#551	—	2	2	no	—
33	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
34	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
35	C₆₁×#548	—	2	1	no	—
36	C₆₁×#547	C₂²	1	1	yes	characteristic
37	C₆₁×#547	C₂²	1	2	yes	complemented
38	C₆₁×#546	—	2	1	no	—
39	C₆₁×#546	—	2	1	no	—
40	C₆₁×#546	—	2	2	no	—
41	C₆₁×#546	C₂²	1	2	yes	complemented
42	D₄²×C₆₁	C₂²	1	1	yes	characteristic
43	D₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
44	D₄²×C₆₁	C₂²	1	2	yes	complemented
45	C₆₁×#532	C₂²	1	2	yes	complemented
46	C₆₁×#532	C₂²	1	1	yes	characteristic, complemented
47	C₆₁×#532	C₂²	1	1	yes	characteristic, complemented
48	C₆₁×#529	—	2	1	no	—
49	C₆₁×#529	C₂²	1	2	yes	complemented
50	C₆₁×#525	—	2	2	no	—
51	C₆₁×#525	—	2	2	no	—
52	C₆₁×#525	—	2	1	no	—
53	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄×C₆₁	—	2	1	no	—
56	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
59	C₆₁×#501	C₂²	1	2	yes	complemented
60	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#496	C₂²	1	2	yes	complemented
62	C₆₁×#493	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#490	C₂²	1	2	yes	complemented
64	C₆₁×#489	C₂²	1	2	yes	complemented
65	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#483	C₂²	1	2	yes	complemented
68	C₆₁×#482	C₂²	1	2	yes	complemented
69	C₆₁×#481	C₂²	1	2	yes	complemented
70	C₆₁×#481	C₂²	1	2	yes	complemented
71	C₆₁×#481	C₂²	1	2	yes	complemented
72	C₆₁×#480	C₂²	1	2	yes	complemented
73	C₆₁×#478	C₂²	1	2	yes	complemented
74	C₆₁×#478	C₂²	1	2	yes	complemented
75	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
76	C₆₁×#476	C₂²	1	2	yes	complemented
77	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#476	C₂²	1	2	yes	complemented
79	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
80	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₆₁×#469	C₂²	1	2	yes	complemented
82	C₆₁×#469	C₂²	1	2	yes	complemented
83	C₆₁×#466	C₂²	1	2	yes	complemented
84	C₆₁×#466	C₂²	1	2	yes	complemented
85	C₆₁×#465	C₂²	1	2	yes	complemented
86	C₆₁×#465	C₂²	1	2	yes	complemented
87	C₆₁×#463	C₂²	1	2	yes	complemented
88	C₆₁×#463	C₂²	1	2	yes	complemented
89	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
90	C₆₁×#459	C₂²	1	1	yes	characteristic
91	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#459	C₂²	1	2	yes	complemented
93	C₆₁×#459	C₂²	1	2	yes	complemented
94	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
95	C₆₁×#450	C₂²	1	2	yes	complemented
96	C₆₁×#449	C₂²	1	2	yes	complemented
97	C₆₁×#447	C₂²	1	2	yes	—
98	C₆₁×#447	C₂²	1	2	yes	complemented
99	C₆₁×#447	C₂²	1	2	yes	complemented
100	C₆₁×#447	C₂²	1	2	yes	complemented
101	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
103	C₆₁×#442	C₂²	1	2	yes	—
104	C₆₁×#442	C₂²	1	1	yes	characteristic
105	C₆₁×#442	C₂²	1	2	yes	complemented
106	C₆₁×#442	C₂²	1	2	yes	complemented
107	C₆₁×#442	C₂²	1	2	yes	complemented
108	C₆₁×#442	C₂²	1	2	yes	complemented
109	C₆₁×#442	C₂²	1	1	yes	characteristic, complemented
110	C₆₁×#442	C₂²	1	2	yes	complemented
111	C₆₁×#442	C₂²	1	2	yes	complemented
112	C₆₁×#442	C₂²	1	2	yes	complemented
113	C₆₁×#442	C₂²	1	2	yes	complemented
114	C₆₁×#440	C₂²	1	1	yes	characteristic, complemented
115	C₆₁×#440	C₂²	1	2	yes	complemented
116	C₆₁×#440	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₆₁×#435	C₂²	1	2	yes	complemented
122	C₆₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#432	C₂²	1	2	yes	complemented
126	C₆₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₆₁×#428	C₂²	1	1	yes	characteristic, complemented
128	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
129	C₆₁×#418	C₂²	1	1	yes	characteristic, complemented
130	C₆₁×#417	C₂²	1	1	yes	characteristic, complemented
131	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
134	C₂×#97×C₆₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	—	2	2	no	—
138	C₂×#41×C₆₁	—	2	2	no	—
139	C₂×#41×C₆₁	—	2	1	no	—
140	C₂×#41×C₆₁	—	2	1	no	—
141	C₂×#41×C₆₁	—	4	8	no	—
142	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
143	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₆₁	—	2	1	no	—
145	C₂²×D₄×C₆₁	—	2	1	no	—
146	C₂²×D₄×C₆₁	—	2	2	no	—
147	C₂²×D₄×C₆₁	—	2	1	no	—
148	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
149	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
151	C₂³×C₄×C₆₁	—	2	2	no	—
152	C₂³×C₄×C₆₁	—	2	1	no	—
153	C₂³×C₄×C₆₁	—	2	2	no	—
154	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
155	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
158	C₂×D₈×C₆₁	—	2	8	no	—
159	C₂×D₈×C₆₁	C₂³	1	2	yes	—
160	C₂×D₈×C₆₁	C₂³	1	2	yes	—
161	C₂×D₈×C₆₁	C₂³	1	2	yes	—
162	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₂×D₈×C₆₁	C₂³	1	2	yes	—
164	C₂×D₈×C₆₁	C₂³	1	2	yes	—
165	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
167	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
169	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
172	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
173	#127×C₆₁	C₂³	1	1	yes	characteristic
174	#127×C₆₁	C₂³	1	2	yes	—
175	#127×C₆₁	C₂³	1	1	yes	characteristic
176	#126×C₆₁	—	2	2	no	—
177	#126×C₆₁	—	2	2	no	—
178	#125×C₆₁	—	2	1	no	—
179	#125×C₆₁	C₂³	1	2	yes	—
180	#124×C₆₁	—	2	1	no	—
181	#124×C₆₁	—	2	1	no	—
182	#124×C₆₁	—	2	2	no	—
183	#124×C₆₁	—	2	1	no	—
184	#124×C₆₁	C₂³	1	2	yes	—
185	#123×C₆₁	—	2	2	no	—
186	#123×C₆₁	—	2	2	no	—
187	#123×C₆₁	—	2	2	no	—
188	#123×C₆₁	—	2	2	no	—
189	#123×C₆₁	—	2	2	no	—
190	#123×C₆₁	—	2	2	no	—
191	#123×C₆₁	—	2	2	no	—
192	C₂²⋊Q₈×C₆₁	—	2	1	no	—
193	C₂²⋊Q₈×C₆₁	—	2	1	no	—
194	C₂²⋊Q₈×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	—	2	1	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	2	no	—
198	C₂²⋊Q₈×C₆₁	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
200	#121×C₆₁	—	2	2	no	—
201	#121×C₆₁	—	2	2	no	—
202	#121×C₆₁	—	2	1	no	—
203	#121×C₆₁	—	2	1	no	—
204	#121×C₆₁	—	2	1	no	—
205	#121×C₆₁	—	2	2	no	—
206	#121×C₆₁	—	2	1	no	—
207	#121×C₆₁	—	2	1	no	—
208	#121×C₆₁	—	2	2	no	—
209	#121×C₆₁	—	2	2	no	—
210	#121×C₆₁	C₂³	1	2	yes	—
211	#121×C₆₁	C₂³	1	2	yes	—
212	#121×C₆₁	C₂³	1	2	yes	—
213	#121×C₆₁	C₂³	1	2	yes	—
214	#121×C₆₁	C₂³	1	2	yes	—
215	#120×C₆₁	—	2	2	no	—
216	#120×C₆₁	—	2	2	no	—
217	#120×C₆₁	—	2	2	no	—
218	#120×C₆₁	—	2	2	no	—
219	#120×C₆₁	—	2	2	no	—
220	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
221	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₆₁	—	2	1	no	—
225	C₄×D₄×C₆₁	—	2	1	no	—
226	C₄×D₄×C₆₁	—	2	2	no	—
227	C₄×D₄×C₆₁	—	2	1	no	—
228	C₄×D₄×C₆₁	—	2	1	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	—	2	1	no	—
231	C₄×D₄×C₆₁	—	2	1	no	—
232	C₄×D₄×C₆₁	—	2	2	no	—
233	C₄×D₄×C₆₁	—	2	1	no	—
234	C₄×D₄×C₆₁	—	2	2	no	—
235	C₄×D₄×C₆₁	—	2	2	no	—
236	C₄×D₄×C₆₁	—	2	1	no	—
237	C₄×D₄×C₆₁	—	2	2	no	—
238	C₄×D₄×C₆₁	—	2	2	no	—
239	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
240	C₄×D₄×C₆₁	D₄	1	2	yes	—
241	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₁	C₂³	1	2	yes	—
243	C₄×D₄×C₆₁	C₂³	1	2	yes	—
244	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₁	C₂³	1	2	yes	—
246	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₁	C₂³	1	2	yes	—
248	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₁	C₂³	1	2	yes	—
250	C₄×D₄×C₆₁	C₂³	1	2	yes	—
251	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₆₁	C₂³	1	2	yes	—
255	#117×C₆₁	—	2	1	no	—
256	#117×C₆₁	—	2	2	no	—
257	#117×C₆₁	D₄	1	2	yes	—
258	#117×C₆₁	D₄	1	1	yes	characteristic
259	#117×C₆₁	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
268	C₂×C₄²×C₆₁	—	2	1	no	—
269	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
271	#107×C₆₁	C₂³	1	1	yes	characteristic
272	#107×C₆₁	C₂³	1	1	yes	characteristic
273	#107×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	1	yes	characteristic
275	#106×C₆₁	C₂³	1	2	yes	—
276	#106×C₆₁	C₂³	1	2	yes	—
277	#106×C₆₁	C₂³	1	2	yes	—
278	#106×C₆₁	C₂³	1	1	yes	characteristic
279	#106×C₆₁	C₂³	1	2	yes	—
280	#106×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
284	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
285	#103×C₆₁	C₂³	1	1	yes	characteristic
286	#103×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	2	yes	—
288	#102×C₆₁	C₂³	1	1	yes	characteristic
289	#102×C₆₁	C₂³	1	1	yes	characteristic
290	#102×C₆₁	C₂³	1	2	yes	—
291	#102×C₆₁	C₂³	1	2	yes	—
292	#102×C₆₁	C₂³	1	2	yes	—
293	#102×C₆₁	C₂³	1	2	yes	—
294	#102×C₆₁	C₂³	1	2	yes	—
295	#102×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	1	yes	characteristic
297	#102×C₆₁	C₂³	1	1	yes	characteristic
298	#102×C₆₁	C₂³	1	1	yes	characteristic
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	#102×C₆₁	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
308	#97×C₆₁	C₂³	1	1	yes	characteristic
309	#97×C₆₁	C₂³	1	2	yes	—
310	#97×C₆₁	C₂³	1	2	yes	—
311	#97×C₆₁	C₂³	1	2	yes	—
312	#97×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
315	C₂⁴×C₆₁	—	2	2	no	—
316	C₂⁴×C₆₁	—	2	1	no	—
317	C₂⁴×C₆₁	—	2	2	no	—
318	#41×C₆₁	—	2	4	no	—
319	#41×C₆₁	—	2	2	no	—
320	#41×C₆₁	—	4	1	no	—
321	#41×C₆₁	—	4	8	no	—
322	#41×C₆₁	—	4	4	no	—
323	#41×C₆₁	—	4	8	no	—
324	#41×C₆₁	—	4	4	no	—
325	#41×C₆₁	—	4	4	no	—
326	#41×C₆₁	—	8	2	no	—
327	C₂×Q₈×C₆₁	—	2	2	no	—
328	C₂×Q₈×C₆₁	—	2	1	no	—
329	C₂×Q₈×C₆₁	—	2	1	no	—
330	C₂×Q₈×C₆₁	—	4	4	no	—
331	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₆₁	—	2	4	no	—
334	C₂×D₄×C₆₁	—	2	2	no	—
335	C₂×D₄×C₆₁	—	2	4	no	—
336	C₂×D₄×C₆₁	—	2	1	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	2	no	—
340	C₂×D₄×C₆₁	—	2	2	no	—
341	C₂×D₄×C₆₁	—	2	2	no	—
342	C₂×D₄×C₆₁	—	2	1	no	—
343	C₂×D₄×C₆₁	—	2	2	no	—
344	C₂×D₄×C₆₁	—	2	2	no	—
345	C₂×D₄×C₆₁	—	2	1	no	—
346	C₂×D₄×C₆₁	—	2	2	no	—
347	C₂×D₄×C₆₁	—	2	1	no	—
348	C₂×D₄×C₆₁	—	2	2	no	—
349	C₂×D₄×C₆₁	—	2	1	no	—
350	C₂×D₄×C₆₁	—	2	1	no	—
351	C₂×D₄×C₆₁	—	4	2	no	—
352	C₂×D₄×C₆₁	—	4	2	no	—
353	C₂×D₄×C₆₁	—	4	1	no	—
354	C₂×D₄×C₆₁	—	4	8	no	—
355	C₂×D₄×C₆₁	—	4	4	no	—
356	C₂×D₄×C₆₁	—	4	4	no	—
357	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
358	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
360	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
361	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₆₁	—	2	1	no	—
365	C₂²×C₄×C₆₁	—	2	2	no	—
366	C₂²×C₄×C₆₁	—	2	2	no	—
367	C₂²×C₄×C₆₁	—	2	1	no	—
368	C₂²×C₄×C₆₁	—	2	1	no	—
369	C₂²×C₄×C₆₁	—	2	1	no	—
370	C₂²×C₄×C₆₁	—	2	2	no	—
371	C₂²×C₄×C₆₁	—	2	1	no	—
372	C₂²×C₄×C₆₁	—	2	2	no	—
373	C₂²×C₄×C₆₁	—	2	1	no	—
374	C₂²×C₄×C₆₁	—	2	2	no	—
375	C₂²×C₄×C₆₁	—	2	1	no	—
376	C₂²×C₄×C₆₁	—	2	2	no	—
377	C₂²×C₄×C₆₁	—	2	1	no	—
378	C₂²×C₄×C₆₁	—	2	2	no	—
379	C₂²×C₄×C₆₁	—	2	2	no	—
380	C₂²×C₄×C₆₁	—	4	8	no	—
381	C₂²×C₄×C₆₁	—	4	4	no	—
382	C₂²×C₄×C₆₁	—	8	4	no	—
383	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
384	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
386	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
388	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
389	SD₁₆×C₆₁	—	2	2	no	—
390	SD₁₆×C₆₁	—	2	2	no	—
391	SD₁₆×C₆₁	—	4	2	no	—
392	D₈×C₆₁	—	2	4	no	—
393	D₈×C₆₁	—	2	4	no	—
394	D₈×C₆₁	—	2	2	no	—
395	D₈×C₆₁	—	2	4	no	—
396	D₈×C₆₁	—	4	2	no	—
397	D₈×C₆₁	—	4	2	no	—
398	D₈×C₆₁	#41	1	4	yes	complemented
399	M₁₆×C₆₁	—	2	2	no	—
400	M₁₆×C₆₁	—	4	1	no	—
401	C₂×C₈×C₆₁	—	2	4	no	—
402	C₂×C₈×C₆₁	—	4	2	no	—
403	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
407	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
408	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	—	2	1	no	—
410	C₄⋊C₄×C₆₁	—	2	2	no	—
411	C₄⋊C₄×C₆₁	—	2	1	no	—
412	C₄⋊C₄×C₆₁	—	2	2	no	—
413	C₄⋊C₄×C₆₁	—	2	2	no	—
414	C₄⋊C₄×C₆₁	—	2	1	no	—
415	C₄⋊C₄×C₆₁	—	2	1	no	—
416	C₄⋊C₄×C₆₁	—	2	2	no	—
417	C₄⋊C₄×C₆₁	—	2	2	no	—
418	C₄⋊C₄×C₆₁	—	2	2	no	—
419	C₄⋊C₄×C₆₁	—	2	1	no	—
420	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
423	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
424	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	1	no	—
432	C₂²⋊C₄×C₆₁	—	2	1	no	—
433	C₂²⋊C₄×C₆₁	—	2	1	no	—
434	C₂²⋊C₄×C₆₁	—	2	2	no	—
435	C₂²⋊C₄×C₆₁	—	2	2	no	—
436	C₂²⋊C₄×C₆₁	—	2	2	no	—
437	C₂²⋊C₄×C₆₁	—	2	1	no	—
438	C₂²⋊C₄×C₆₁	—	2	2	no	—
439	C₂²⋊C₄×C₆₁	—	2	2	no	—
440	C₂²⋊C₄×C₆₁	—	2	1	no	—
441	C₂²⋊C₄×C₆₁	—	2	2	no	—
442	C₂²⋊C₄×C₆₁	—	2	1	no	—
443	C₂²⋊C₄×C₆₁	—	2	2	no	—
444	C₂²⋊C₄×C₆₁	—	2	2	no	—
445	C₂²⋊C₄×C₆₁	—	2	1	no	—
446	C₂²⋊C₄×C₆₁	—	2	2	no	—
447	C₂²⋊C₄×C₆₁	—	2	2	no	—
448	C₂²⋊C₄×C₆₁	—	2	2	no	—
449	C₂²⋊C₄×C₆₁	—	2	2	no	—
450	C₂²⋊C₄×C₆₁	—	2	2	no	—
451	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
453	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
454	C₄²×C₆₁	—	2	1	no	—
455	C₄²×C₆₁	—	2	1	no	—
456	C₄²×C₆₁	—	2	1	no	—
457	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₆₁	C₂×D₄	1	2	yes	—
460	C₄²×C₆₁	C₂×D₄	1	2	yes	—
461	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
462	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
463	C₄²×C₆₁	C₂⁴	1	2	yes	—
464	C₂³×C₆₁	—	2	1	no	—
465	C₂³×C₆₁	—	2	1	no	—
466	C₂³×C₆₁	—	2	2	no	—
467	C₂³×C₆₁	—	2	2	no	—
468	C₂³×C₆₁	—	2	1	no	—
469	C₂³×C₆₁	—	4	4	no	—
470	C₂³×C₆₁	—	4	4	no	—
471	C₂³×C₆₁	—	4	2	no	—
472	C₂³×C₆₁	—	4	2	no	—
473	C₂³×C₆₁	—	4	4	no	—
474	C₂³×C₆₁	—	4	4	no	—
475	C₂³×C₆₁	—	8	2	no	—
476	C₂³×C₆₁	—	8	2	no	—
477	C₂³×C₆₁	—	8	1	no	—
478	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
479	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
480	Q₈×C₆₁	—	2	2	no	—
481	Q₈×C₆₁	—	2	1	no	—
482	Q₈×C₆₁	—	2	1	no	—
483	Q₈×C₆₁	—	4	4	no	—
484	Q₈×C₆₁	—	4	2	no	—
485	Q₈×C₆₁	—	8	1	no	—
486	D₄×C₆₁	—	2	4	no	—
487	D₄×C₆₁	—	2	2	no	—
488	D₄×C₆₁	—	2	2	no	—
489	D₄×C₆₁	—	2	1	no	—
490	D₄×C₆₁	—	2	1	no	—
491	D₄×C₆₁	—	2	1	no	—
492	D₄×C₆₁	—	2	2	no	—
493	D₄×C₆₁	—	2	1	no	—
494	D₄×C₆₁	—	2	2	no	—
495	D₄×C₆₁	—	4	2	no	—
496	D₄×C₆₁	—	4	4	no	—
497	D₄×C₆₁	—	4	4	no	—
498	D₄×C₆₁	—	4	4	no	—
499	D₄×C₆₁	—	4	2	no	—
500	D₄×C₆₁	—	4	4	no	—
501	D₄×C₆₁	—	4	4	no	—
502	D₄×C₆₁	—	4	4	no	—
503	D₄×C₆₁	—	4	4	no	—
504	D₄×C₆₁	—	4	2	no	—
505	D₄×C₆₁	—	4	2	no	—
506	D₄×C₆₁	—	8	2	no	—
507	D₄×C₆₁	—	8	1	no	—
508	D₄×C₆₁	—	8	1	no	—
509	D₄×C₆₁	—	8	2	no	—
510	D₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	complemented
511	D₄×C₆₁	C₂×#41	1	2	yes	—
512	D₄×C₆₁	C₂×#41	1	2	yes	complemented
513	C₂×C₄×C₆₁	—	2	4	no	—
514	C₂×C₄×C₆₁	—	2	2	no	—
515	C₂×C₄×C₆₁	—	2	2	no	—
516	C₂×C₄×C₆₁	—	2	1	no	—
517	C₂×C₄×C₆₁	—	2	2	no	—
518	C₂×C₄×C₆₁	—	2	1	no	—
519	C₂×C₄×C₆₁	—	2	1	no	—
520	C₂×C₄×C₆₁	—	2	1	no	—
521	C₂×C₄×C₆₁	—	2	1	no	—
522	C₂×C₄×C₆₁	—	2	2	no	—
523	C₂×C₄×C₆₁	—	2	1	no	—
524	C₂×C₄×C₆₁	—	2	2	no	—
525	C₂×C₄×C₆₁	—	2	1	no	—
526	C₂×C₄×C₆₁	—	4	2	no	—
527	C₂×C₄×C₆₁	—	4	1	no	—
528	C₂×C₄×C₆₁	—	4	2	no	—
529	C₂×C₄×C₆₁	—	4	2	no	—
530	C₂×C₄×C₆₁	—	4	4	no	—
531	C₂×C₄×C₆₁	—	4	4	no	—
532	C₂×C₄×C₆₁	—	4	2	no	—
533	C₂×C₄×C₆₁	—	4	4	no	—
534	C₂×C₄×C₆₁	—	4	2	no	—
535	C₂×C₄×C₆₁	—	4	4	no	—
536	C₂×C₄×C₆₁	—	4	2	no	—
537	C₂×C₄×C₆₁	—	4	4	no	—
538	C₂×C₄×C₆₁	—	4	2	no	—
539	C₂×C₄×C₆₁	—	4	2	no	—
540	C₂×C₄×C₆₁	—	4	2	no	—
541	C₂×C₄×C₆₁	—	8	2	no	—
542	C₂×C₄×C₆₁	—	8	2	no	—
543	C₂×C₄×C₆₁	—	8	2	no	—
544	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
553	C₈×C₆₁	—	2	2	no	—
554	C₈×C₆₁	—	2	1	no	—
555	C₈×C₆₁	—	2	1	no	—
556	C₈×C₆₁	—	2	2	no	—
557	C₈×C₆₁	—	2	1	no	—
558	C₈×C₆₁	C₂×#41	1	2	yes	complemented
559	#61451	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
560	C₂²×C₆₁	—	2	2	no	—
561	C₂²×C₆₁	—	2	2	no	—
562	C₂²×C₆₁	—	2	1	no	—
563	C₂²×C₆₁	—	2	1	no	—
564	C₂²×C₆₁	—	2	2	no	—
565	C₂²×C₆₁	—	2	2	no	—
566	C₂²×C₆₁	—	2	1	no	—
567	C₂²×C₆₁	—	4	1	no	—
568	C₂²×C₆₁	—	4	1	no	—
569	C₂²×C₆₁	—	4	1	no	—
570	C₂²×C₆₁	—	4	1	no	—
571	C₂²×C₆₁	—	4	2	no	—
572	C₂²×C₆₁	—	4	2	no	—
573	C₂²×C₆₁	—	4	1	no	—
574	C₂²×C₆₁	—	4	2	no	—
575	C₂²×C₆₁	—	4	2	no	—
576	C₂²×C₆₁	—	4	1	no	—
577	C₂²×C₆₁	—	4	2	no	—
578	C₂²×C₆₁	—	4	1	no	—
579	C₂²×C₆₁	—	4	2	no	—
580	C₂²×C₆₁	—	8	8	no	—
581	C₂²×C₆₁	—	8	8	no	—
582	C₂²×C₆₁	—	8	4	no	—
583	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
584	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
585	C₄×C₆₁	—	2	1	no	—
586	C₄×C₆₁	—	2	2	no	—
587	C₄×C₆₁	—	2	1	no	—
588	C₄×C₆₁	—	2	1	no	—
589	C₄×C₆₁	—	2	2	no	—
590	C₄×C₆₁	—	2	1	no	—
591	C₄×C₆₁	—	2	2	no	—
592	C₄×C₆₁	—	4	1	no	—
593	C₄×C₆₁	—	4	2	no	—
594	C₄×C₆₁	—	4	1	no	—
595	C₄×C₆₁	—	4	1	no	—
596	C₄×C₆₁	—	4	2	no	—
597	C₄×C₆₁	—	4	1	no	—
598	C₄×C₆₁	—	4	1	no	—
599	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
600	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
601	C₄×C₆₁	#585	1	1	yes	characteristic
602	#3481	C₂×C₆₁	1	1	yes	characteristic, complemented
603	D₄×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
604	#3399	C₂×C₆₁	1	1	yes	characteristic, complemented
605	#3384	C₂×C₆₁	1	1	yes	characteristic, complemented
606	#3373	C₂×C₆₁	1	1	yes	characteristic, complemented
607	#3366	C₂×C₆₁	1	1	yes	characteristic, complemented
608	#3345	C₂×C₆₁	1	2	yes	complemented
609	#3335	C₂×C₆₁	1	1	yes	characteristic, complemented
610	#3318	C₂×C₆₁	1	2	yes	complemented
611	#3306	C₂×C₆₁	1	2	yes	complemented
612	#3295	C₂×C₆₁	1	1	yes	characteristic, complemented
613	#3294	C₂×C₆₁	1	1	yes	characteristic, complemented
614	D₄×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
615	#3264	C₂×C₆₁	1	2	yes	complemented
616	#3184	C₂×C₆₁	1	1	yes	characteristic, complemented
617	#3180	C₂×C₆₁	1	2	yes	complemented
618	#3115	C₂×C₆₁	1	1	yes	characteristic, complemented
619	#3114	C₂×C₆₁	1	2	yes	complemented
620	#3109	C₂×C₆₁	1	1	yes	characteristic, complemented
621	#3109	C₂×C₆₁	1	2	yes	complemented
622	#2970	C₂×C₆₁	1	1	yes	characteristic, complemented
623	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic, complemented
624	C₂×#442	C₂×C₆₁	1	2	yes	complemented
625	C₂×C₆₁	—	2	4	no	—
626	C₂×C₆₁	—	4	1	no	—
627	C₂×C₆₁	—	4	2	no	—
628	C₂×C₆₁	—	4	2	no	—
629	C₂×C₆₁	—	8	2	no	—
630	C₂×C₆₁	—	8	2	no	—
631	C₂×C₆₁	—	8	1	no	—
632	C₂×C₆₁	D₄×#41	1	1	yes	characteristic
633	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
634	C₂×C₆₁	#3585	1	1	yes	characteristic
635	C₂²×#41	—	2	1	no	—
636	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
637	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
638	#559	C₂²×C₆₁	1	1	yes	characteristic, complemented
639	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
640	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
641	#553	—	2	1	no	—
642	#553	C₂²×C₆₁	1	2	yes	complemented
643	#551	—	2	2	no	—
644	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
645	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
646	#548	—	2	1	no	—
647	#547	C₂²×C₆₁	1	1	yes	characteristic
648	#547	C₂²×C₆₁	1	2	yes	complemented
649	#546	—	2	1	no	—
650	#546	—	2	1	no	—
651	#546	—	2	2	no	—
652	#546	C₂²×C₆₁	1	2	yes	complemented
653	D₄²	C₂²×C₆₁	1	1	yes	characteristic
654	D₄²	C₂²×C₆₁	1	2	yes	complemented
655	D₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
656	#532	C₂²×C₆₁	1	2	yes	complemented
657	#532	C₂²×C₆₁	1	1	yes	characteristic, complemented
658	#532	C₂²×C₆₁	1	1	yes	characteristic, complemented
659	#529	—	2	1	no	—
660	#529	C₂²×C₆₁	1	2	yes	complemented
661	#525	—	2	2	no	—
662	#525	—	2	2	no	—
663	#525	—	2	1	no	—
664	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
665	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
666	C₂×C₄×D₄	—	2	1	no	—
667	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
668	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
669	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
670	#501	C₂²×C₆₁	1	2	yes	complemented
671	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
672	#496	C₂²×C₆₁	1	2	yes	complemented
673	#493	C₂²×C₆₁	1	1	yes	characteristic, complemented
674	#490	C₂²×C₆₁	1	2	yes	complemented
675	#489	C₂²×C₆₁	1	2	yes	complemented
676	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
677	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
678	#483	C₂²×C₆₁	1	2	yes	complemented
679	#482	C₂²×C₆₁	1	2	yes	complemented
680	#481	C₂²×C₆₁	1	2	yes	complemented
681	#481	C₂²×C₆₁	1	2	yes	complemented
682	#481	C₂²×C₆₁	1	2	yes	complemented
683	#480	C₂²×C₆₁	1	2	yes	complemented
684	#478	C₂²×C₆₁	1	2	yes	complemented
685	#478	C₂²×C₆₁	1	2	yes	complemented
686	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
687	#476	C₂²×C₆₁	1	2	yes	complemented
688	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
689	#476	C₂²×C₆₁	1	2	yes	complemented
690	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
691	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
692	#469	C₂²×C₆₁	1	2	yes	complemented
693	#469	C₂²×C₆₁	1	2	yes	complemented
694	#466	C₂²×C₆₁	1	2	yes	complemented
695	#466	C₂²×C₆₁	1	2	yes	complemented
696	#465	C₂²×C₆₁	1	2	yes	complemented
697	#465	C₂²×C₆₁	1	2	yes	complemented
698	#463	C₂²×C₆₁	1	2	yes	complemented
699	#463	C₂²×C₆₁	1	2	yes	complemented
700	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
701	#459	C₂²×C₆₁	1	1	yes	characteristic
702	#459	C₂²×C₆₁	1	2	yes	complemented
703	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
704	#459	C₂²×C₆₁	1	2	yes	complemented
705	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
706	#450	C₂²×C₆₁	1	2	yes	complemented
707	#449	C₂²×C₆₁	1	2	yes	complemented
708	#447	C₂²×C₆₁	1	2	yes	—
709	#447	C₂²×C₆₁	1	2	yes	complemented
710	#447	C₂²×C₆₁	1	2	yes	complemented
711	#447	C₂²×C₆₁	1	2	yes	complemented
712	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
713	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
714	#442	C₂²×C₆₁	1	2	yes	—
715	#442	C₂²×C₆₁	1	1	yes	characteristic
716	#442	C₂²×C₆₁	1	2	yes	complemented
717	#442	C₂²×C₆₁	1	2	yes	complemented
718	#442	C₂²×C₆₁	1	1	yes	characteristic, complemented
719	#442	C₂²×C₆₁	1	2	yes	complemented
720	#442	C₂²×C₆₁	1	2	yes	complemented
721	#442	C₂²×C₆₁	1	2	yes	complemented
722	#442	C₂²×C₆₁	1	2	yes	complemented
723	#442	C₂²×C₆₁	1	2	yes	complemented
724	#442	C₂²×C₆₁	1	2	yes	complemented
725	#440	C₂²×C₆₁	1	1	yes	characteristic, complemented
726	#440	C₂²×C₆₁	1	2	yes	complemented
727	#440	C₂²×C₆₁	1	1	yes	characteristic, complemented
728	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
729	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
730	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
731	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
732	#435	C₂²×C₆₁	1	2	yes	complemented
733	#435	C₂²×C₆₁	1	2	yes	complemented
734	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
735	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
736	#432	C₂²×C₆₁	1	2	yes	complemented
737	#432	C₂²×C₆₁	1	1	yes	characteristic, complemented
738	#428	C₂²×C₆₁	1	1	yes	characteristic, complemented
739	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
740	#418	C₂²×C₆₁	1	1	yes	characteristic, complemented
741	#417	C₂²×C₆₁	1	1	yes	characteristic, complemented
742	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
743	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
744	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
745	C₂×#97	C₂²×C₆₁	1	2	yes	complemented
746	C₆₁	#61451	1	1	yes	characteristic, direct product factor, Sylow
747	C₂×#41	—	2	1	no	—
748	C₂×#41	—	2	1	no	—
749	C₂×#41	—	2	2	no	—
750	C₂×#41	—	2	2	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	2	1	no	—
753	C₂×#41	—	4	8	no	—
754	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
755	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
756	C₂²×Q₈	—	2	1	no	—
757	C₂²×D₄	—	2	1	no	—
758	C₂²×D₄	—	2	1	no	—
759	C₂²×D₄	—	2	2	no	—
760	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
761	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
762	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
763	C₂³×C₄	—	2	2	no	—
764	C₂³×C₄	—	2	1	no	—
765	C₂³×C₄	—	2	2	no	—
766	AGL(1,ℤ/8)	—	2	4	no	—
767	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
768	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
769	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
770	C₂×D₈	—	2	8	no	—
771	C₂×D₈	C₂³×C₆₁	1	2	yes	—
772	C₂×D₈	C₂³×C₆₁	1	2	yes	—
773	C₂×D₈	C₂³×C₆₁	1	2	yes	—
774	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
775	C₂×D₈	C₂³×C₆₁	1	2	yes	—
776	C₂×D₈	C₂³×C₆₁	1	2	yes	—
777	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
778	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
779	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
780	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
781	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
782	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
783	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
784	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
785	#127	C₂³×C₆₁	1	1	yes	characteristic
786	#127	C₂³×C₆₁	1	2	yes	—
787	#127	C₂³×C₆₁	1	1	yes	characteristic
788	#126	—	2	2	no	—
789	#126	—	2	2	no	—
790	#125	—	2	1	no	—
791	#125	C₂³×C₆₁	1	2	yes	—
792	#124	—	2	1	no	—
793	#124	—	2	1	no	—
794	#124	—	2	2	no	—
795	#124	—	2	1	no	—
796	#124	C₂³×C₆₁	1	2	yes	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	—	2	1	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	1	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	—	2	2	no	—
811	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	2	no	—
818	#121	—	2	1	no	—
819	#121	—	2	2	no	—
820	#121	—	2	1	no	—
821	#121	—	2	2	no	—
822	#121	C₂³×C₆₁	1	2	yes	—
823	#121	C₂³×C₆₁	1	2	yes	—
824	#121	C₂³×C₆₁	1	2	yes	—
825	#121	C₂³×C₆₁	1	2	yes	—
826	#121	C₂³×C₆₁	1	2	yes	—
827	#120	—	2	2	no	—
828	#120	—	2	2	no	—
829	#120	—	2	2	no	—
830	#120	—	2	2	no	—
831	#120	—	2	2	no	—
832	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
833	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
834	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
835	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
852	C₄×D₄	D₄×C₆₁	1	2	yes	—
853	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₆₁	1	2	yes	—
856	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
857	C₄×D₄	C₂³×C₆₁	1	2	yes	—
858	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₆₁	1	2	yes	—
860	C₄×D₄	C₂³×C₆₁	1	2	yes	—
861	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
862	C₄×D₄	C₂³×C₆₁	1	2	yes	—
863	C₄×D₄	C₂³×C₆₁	1	2	yes	—
864	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
865	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
866	C₄×D₄	C₂³×C₆₁	1	2	yes	—
867	#117	—	2	1	no	—
868	#117	—	2	2	no	—
869	#117	D₄×C₆₁	1	2	yes	—
870	#117	D₄×C₆₁	1	1	yes	characteristic
871	#117	C₂³×C₆₁	1	1	yes	characteristic
872	C₂×C₄⋊C₄	—	2	1	no	—
873	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
874	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
875	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
876	C₂×C₂²⋊C₄	—	2	2	no	—
877	C₂×C₂²⋊C₄	—	2	1	no	—
878	C₂×C₂²⋊C₄	—	2	2	no	—
879	C₂×C₂²⋊C₄	—	2	2	no	—
880	C₂×C₄²	—	2	1	no	—
881	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
882	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
883	#107	C₂³×C₆₁	1	1	yes	characteristic
884	#107	C₂³×C₆₁	1	1	yes	characteristic
885	#107	C₂³×C₆₁	1	2	yes	—
886	#106	C₂³×C₆₁	1	1	yes	characteristic
887	#106	C₂³×C₆₁	1	2	yes	—
888	#106	C₂³×C₆₁	1	2	yes	—
889	#106	C₂³×C₆₁	1	2	yes	—
890	#106	C₂³×C₆₁	1	1	yes	characteristic
891	#106	C₂³×C₆₁	1	2	yes	—
892	#106	C₂³×C₆₁	1	2	yes	—
893	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
894	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
895	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
896	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
897	#103	C₂³×C₆₁	1	1	yes	characteristic
898	#103	C₂³×C₆₁	1	1	yes	characteristic
899	#103	C₂³×C₆₁	1	2	yes	—
900	#102	C₂³×C₆₁	1	1	yes	characteristic
901	#102	C₂³×C₆₁	1	1	yes	characteristic
902	#102	C₂³×C₆₁	1	2	yes	—
903	#102	C₂³×C₆₁	1	2	yes	—
904	#102	C₂³×C₆₁	1	2	yes	—
905	#102	C₂³×C₆₁	1	2	yes	—
906	#102	C₂³×C₆₁	1	2	yes	—
907	#102	C₂³×C₆₁	1	2	yes	—
908	#102	C₂³×C₆₁	1	1	yes	characteristic
909	#102	C₂³×C₆₁	1	1	yes	characteristic
910	#102	C₂³×C₆₁	1	1	yes	characteristic
911	#102	C₂³×C₆₁	1	1	yes	characteristic
912	#102	C₂³×C₆₁	1	2	yes	—
913	#102	C₂³×C₆₁	1	2	yes	—
914	#102	C₂³×C₆₁	1	2	yes	—
915	#102	C₂³×C₆₁	1	2	yes	—
916	#102	C₂³×C₆₁	1	2	yes	—
917	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
919	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
920	#97	C₂³×C₆₁	1	1	yes	characteristic
921	#97	C₂³×C₆₁	1	2	yes	—
922	#97	C₂³×C₆₁	1	2	yes	—
923	#97	C₂³×C₆₁	1	2	yes	—
924	#97	C₂³×C₆₁	1	1	yes	characteristic
925	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
926	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
927	C₂⁴	—	2	2	no	—
928	C₂⁴	—	2	1	no	—
929	C₂⁴	—	2	2	no	—
930	#41	—	2	4	no	—
931	#41	—	2	2	no	—
932	#41	—	4	1	no	—
933	#41	—	4	8	no	—
934	#41	—	4	4	no	—
935	#41	—	4	8	no	—
936	#41	—	4	4	no	—
937	#41	—	4	4	no	—
938	#41	—	8	2	no	—
939	C₂×Q₈	—	2	2	no	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	4	4	no	—
943	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
944	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
945	C₂×D₄	—	2	4	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	4	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	1	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	—	4	2	no	—
965	C₂×D₄	—	4	1	no	—
966	C₂×D₄	—	4	8	no	—
967	C₂×D₄	—	4	4	no	—
968	C₂×D₄	—	4	4	no	—
969	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
970	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
971	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
972	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
973	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
974	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
975	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	4	8	no	—
993	C₂²×C₄	—	4	4	no	—
994	C₂²×C₄	—	8	4	no	—
995	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
996	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
997	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
998	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
1000	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1001	SD₁₆	—	2	2	no	—
1002	SD₁₆	—	2	2	no	—
1003	SD₁₆	—	4	2	no	—
1004	D₈	—	2	4	no	—
1005	D₈	—	2	4	no	—
1006	D₈	—	2	2	no	—
1007	D₈	—	2	4	no	—
1008	D₈	—	4	2	no	—
1009	D₈	—	4	2	no	—
1010	D₈	#41×C₆₁	1	4	yes	complemented
1011	M₁₆	—	2	2	no	—
1012	M₁₆	—	4	1	no	—
1013	C₂×C₈	—	2	4	no	—
1014	C₂×C₈	—	4	2	no	—
1015	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1016	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1017	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1018	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1019	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1020	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1033	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1034	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1035	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1036	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1037	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1038	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1039	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1040	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1041	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1064	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1065	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1070	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1071	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1072	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1073	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1074	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1075	C₄²	C₂⁴×C₆₁	1	2	yes	—
1076	C₂³	—	2	1	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	2	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	4	4	no	—
1082	C₂³	—	4	4	no	—
1083	C₂³	—	4	2	no	—
1084	C₂³	—	4	2	no	—
1085	C₂³	—	4	4	no	—
1086	C₂³	—	4	4	no	—
1087	C₂³	—	8	2	no	—
1088	C₂³	—	8	2	no	—
1089	C₂³	—	8	1	no	—
1090	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1091	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	1	no	—
1094	Q₈	—	2	1	no	—
1095	Q₈	—	4	4	no	—
1096	Q₈	—	4	2	no	—
1097	Q₈	—	8	1	no	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	2	no	—
1101	D₄	—	2	1	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	2	no	—
1105	D₄	—	2	1	no	—
1106	D₄	—	2	2	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	4	no	—
1109	D₄	—	4	4	no	—
1110	D₄	—	4	4	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	4	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	8	2	no	—
1119	D₄	—	8	1	no	—
1120	D₄	—	8	1	no	—
1121	D₄	—	8	2	no	—
1122	D₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	complemented
1123	D₄	C₂×#41×C₆₁	1	2	yes	—
1124	D₄	C₂×#41×C₆₁	1	2	yes	complemented
1125	C₂×C₄	—	2	4	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	4	no	—
1143	C₂×C₄	—	4	4	no	—
1144	C₂×C₄	—	4	2	no	—
1145	C₂×C₄	—	4	4	no	—
1146	C₂×C₄	—	4	2	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	8	2	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	2	no	—
1156	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1157	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1158	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1159	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1160	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1161	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1164	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1165	C₈	—	2	2	no	—
1166	C₈	—	2	1	no	—
1167	C₈	—	2	1	no	—
1168	C₈	—	2	2	no	—
1169	C₈	—	2	1	no	—
1170	C₈	C₂×#41×C₆₁	1	2	yes	complemented
1171	C₂²	—	2	2	no	—
1172	C₂²	—	2	2	no	—
1173	C₂²	—	2	1	no	—
1174	C₂²	—	2	1	no	—
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	1	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	1	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	2	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	8	8	no	—
1192	C₂²	—	8	8	no	—
1193	C₂²	—	8	4	no	—
1194	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	4	yes	—
1195	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1196	C₄	—	2	1	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	2	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	1	no	—
1210	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
1211	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1212	C₄	C₆₁×#585	1	1	yes	characteristic
1213	C₂	—	2	4	no	—
1214	C₂	—	4	1	no	—
1215	C₂	—	4	2	no	—
1216	C₂	—	4	2	no	—
1217	C₂	—	8	2	no	—
1218	C₂	—	8	1	no	—
1219	C₂	—	8	2	no	—
1220	C₂	D₄×#41×C₆₁	1	1	yes	characteristic
1221	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
1222	C₂	C₆₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3481	C₂	semidirect
2. D₄×#41×C₆₁	C₂	semidirect
3. C₆₁×#3399	C₂	semidirect
4. C₆₁×#3384	C₂	semidirect
5. C₆₁×#3373	C₂	semidirect
6. C₆₁×#3366	C₂	semidirect
7. C₆₁×#3345	C₂	semidirect
8. C₆₁×#3335	C₂	semidirect
9. C₆₁×#3318	C₂	semidirect
10. C₆₁×#3306	C₂	semidirect
11. C₆₁×#3295	C₂	semidirect
12. C₆₁×#3294	C₂	semidirect
13. D₄×D₈×C₆₁	C₂	semidirect
14. C₆₁×#3264	C₂	semidirect
15. C₆₁×#3184	C₂	semidirect
16. C₆₁×#3180	C₂	semidirect
17. C₆₁×#3115	C₂	semidirect
18. C₆₁×#3114	C₂	semidirect
19. C₆₁×#3109	C₂	semidirect
20. C₆₁×#3109	C₂	semidirect
21. C₆₁×#2970	C₂	semidirect
22. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
23. C₂×C₆₁×#442	C₂	semidirect
27. C₆₁×#559	C₂²	semidirect
28. C₆₁×#554	C₂²	semidirect
29. C₆₁×#554	C₂²	semidirect
31. C₆₁×#553	C₂²	semidirect
33. C₆₁×#550	C₂²	semidirect
34. D₄×Q₈×C₆₁	C₂²	semidirect
37. C₆₁×#547	C₂²	semidirect
41. C₆₁×#546	C₂²	semidirect
43. D₄²×C₆₁	C₂²	semidirect
44. D₄²×C₆₁	C₂²	semidirect
45. C₆₁×#532	C₂²	semidirect
46. C₆₁×#532	C₂²	semidirect
47. C₆₁×#532	C₂²	semidirect
49. C₆₁×#529	C₂²	semidirect
54. C₄×#41×C₆₁	C₂²	semidirect
56. C₂×C₄×D₄×C₆₁	C₂²	semidirect
57. C₂×C₄×D₄×C₆₁	C₂²	semidirect
58. C₂×C₄×D₄×C₆₁	C₂²	semidirect
59. C₆₁×#501	C₂²	semidirect
60. C₆₁×#498	C₂²	semidirect
61. C₆₁×#496	C₂²	semidirect
62. C₆₁×#493	C₂²	semidirect
63. C₆₁×#490	C₂²	semidirect
64. C₆₁×#489	C₂²	semidirect
65. C₆₁×#486	C₂²	semidirect
66. C₆₁×#486	C₂²	semidirect
67. C₆₁×#483	C₂²	semidirect
68. C₆₁×#482	C₂²	semidirect
69. C₆₁×#481	C₂²	semidirect
70. C₆₁×#481	C₂²	semidirect
71. C₆₁×#481	C₂²	semidirect
72. C₆₁×#480	C₂²	semidirect
73. C₆₁×#478	C₂²	semidirect
74. C₆₁×#478	C₂²	semidirect
75. C₆₁×#476	C₂²	semidirect
76. C₆₁×#476	C₂²	semidirect
77. C₆₁×#476	C₂²	semidirect
78. C₆₁×#476	C₂²	semidirect
79. C₆₁×#475	C₂²	semidirect
80. C₆₁×#474	C₂²	semidirect
81. C₆₁×#469	C₂²	semidirect
82. C₆₁×#469	C₂²	semidirect
83. C₆₁×#466	C₂²	semidirect
84. C₆₁×#466	C₂²	semidirect
85. C₆₁×#465	C₂²	semidirect
86. C₆₁×#465	C₂²	semidirect
87. C₆₁×#463	C₂²	semidirect
88. C₆₁×#463	C₂²	semidirect
89. C₆₁×#460	C₂²	semidirect
91. C₆₁×#459	C₂²	semidirect
92. C₆₁×#459	C₂²	semidirect
93. C₆₁×#459	C₂²	semidirect
94. C₆₁×#459	C₂²	semidirect
95. C₆₁×#450	C₂²	semidirect
96. C₆₁×#449	C₂²	semidirect
98. C₆₁×#447	C₂²	semidirect
99. C₆₁×#447	C₂²	semidirect
100. C₆₁×#447	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₆₁×#446	C₂²	semidirect
105. C₆₁×#442	C₂²	semidirect
106. C₆₁×#442	C₂²	semidirect
107. C₆₁×#442	C₂²	semidirect
108. C₆₁×#442	C₂²	semidirect
109. C₆₁×#442	C₂²	semidirect
110. C₆₁×#442	C₂²	semidirect
111. C₆₁×#442	C₂²	semidirect
112. C₆₁×#442	C₂²	semidirect
113. C₆₁×#442	C₂²	semidirect
114. C₆₁×#440	C₂²	semidirect
115. C₆₁×#440	C₂²	semidirect
116. C₆₁×#440	C₂²	semidirect
117. C₄×SD₁₆×C₆₁	C₂²	semidirect
118. C₄×SD₁₆×C₆₁	C₂²	semidirect
120. C₄×D₈×C₆₁	C₂²	semidirect
121. C₆₁×#435	C₂²	semidirect
122. C₆₁×#435	C₂²	semidirect
123. C₈×D₄×C₆₁	C₂²	semidirect
124. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#432	C₂²	semidirect
126. C₆₁×#432	C₂²	semidirect
127. C₆₁×#428	C₂²	semidirect
128. C₂×#106×C₆₁	C₂²	semidirect
129. C₆₁×#418	C₂²	semidirect
130. C₆₁×#417	C₂²	semidirect
131. C₂×#102×C₆₁	C₂²	semidirect
132. C₂×#102×C₆₁	C₂²	semidirect
133. C₄×M₁₆×C₆₁	C₂²	semidirect
134. C₂×#97×C₆₁	C₂²	semidirect
398. D₈×C₆₁	#41	semidirect
510. D₄×C₆₁	AGL(1,ℤ/8)	semidirect
512. D₄×C₆₁	C₂×#41	semidirect
558. C₈×C₆₁	C₂×#41	semidirect
559. #61451	C₆₁	direct (N × H)
602. #3481	C₂×C₆₁	semidirect
603. D₄×#41	C₂×C₆₁	semidirect
604. #3399	C₂×C₆₁	semidirect
605. #3384	C₂×C₆₁	semidirect
606. #3373	C₂×C₆₁	semidirect
607. #3366	C₂×C₆₁	semidirect
608. #3345	C₂×C₆₁	semidirect
609. #3335	C₂×C₆₁	semidirect
610. #3318	C₂×C₆₁	semidirect
611. #3306	C₂×C₆₁	semidirect
612. #3295	C₂×C₆₁	semidirect
613. #3294	C₂×C₆₁	semidirect
614. D₄×D₈	C₂×C₆₁	semidirect
615. #3264	C₂×C₆₁	semidirect
616. #3184	C₂×C₆₁	semidirect
617. #3180	C₂×C₆₁	semidirect
618. #3115	C₂×C₆₁	semidirect
619. #3114	C₂×C₆₁	semidirect
620. #3109	C₂×C₆₁	semidirect
621. #3109	C₂×C₆₁	semidirect
622. #2970	C₂×C₆₁	semidirect
623. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
624. C₂×#442	C₂×C₆₁	semidirect
638. #559	C₂²×C₆₁	semidirect
639. #554	C₂²×C₆₁	semidirect
640. #554	C₂²×C₆₁	semidirect
642. #553	C₂²×C₆₁	semidirect
644. #550	C₂²×C₆₁	semidirect
645. D₄×Q₈	C₂²×C₆₁	semidirect
648. #547	C₂²×C₆₁	semidirect
652. #546	C₂²×C₆₁	semidirect
654. D₄²	C₂²×C₆₁	semidirect
655. D₄²	C₂²×C₆₁	semidirect
656. #532	C₂²×C₆₁	semidirect
657. #532	C₂²×C₆₁	semidirect
658. #532	C₂²×C₆₁	semidirect
660. #529	C₂²×C₆₁	semidirect
665. C₄×#41	C₂²×C₆₁	semidirect
667. C₂×C₄×D₄	C₂²×C₆₁	semidirect
668. C₂×C₄×D₄	C₂²×C₆₁	semidirect
669. C₂×C₄×D₄	C₂²×C₆₁	semidirect
670. #501	C₂²×C₆₁	semidirect
671. #498	C₂²×C₆₁	semidirect
672. #496	C₂²×C₆₁	semidirect
673. #493	C₂²×C₆₁	semidirect
674. #490	C₂²×C₆₁	semidirect
675. #489	C₂²×C₆₁	semidirect
676. #486	C₂²×C₆₁	semidirect
677. #486	C₂²×C₆₁	semidirect
678. #483	C₂²×C₆₁	semidirect
679. #482	C₂²×C₆₁	semidirect
680. #481	C₂²×C₆₁	semidirect
681. #481	C₂²×C₆₁	semidirect
682. #481	C₂²×C₆₁	semidirect
683. #480	C₂²×C₆₁	semidirect
684. #478	C₂²×C₆₁	semidirect
685. #478	C₂²×C₆₁	semidirect
686. #476	C₂²×C₆₁	semidirect
687. #476	C₂²×C₆₁	semidirect
688. #476	C₂²×C₆₁	semidirect
689. #476	C₂²×C₆₁	semidirect
690. #475	C₂²×C₆₁	semidirect
691. #474	C₂²×C₆₁	semidirect
692. #469	C₂²×C₆₁	semidirect
693. #469	C₂²×C₆₁	semidirect
694. #466	C₂²×C₆₁	semidirect
695. #466	C₂²×C₆₁	semidirect
696. #465	C₂²×C₆₁	semidirect
697. #465	C₂²×C₆₁	semidirect
698. #463	C₂²×C₆₁	semidirect
699. #463	C₂²×C₆₁	semidirect
700. #460	C₂²×C₆₁	semidirect
702. #459	C₂²×C₆₁	semidirect
703. #459	C₂²×C₆₁	semidirect
704. #459	C₂²×C₆₁	semidirect
705. #459	C₂²×C₆₁	semidirect
706. #450	C₂²×C₆₁	semidirect
707. #449	C₂²×C₆₁	semidirect
709. #447	C₂²×C₆₁	semidirect
710. #447	C₂²×C₆₁	semidirect
711. #447	C₂²×C₆₁	semidirect
712. #446	C₂²×C₆₁	semidirect
713. #446	C₂²×C₆₁	semidirect
716. #442	C₂²×C₆₁	semidirect
717. #442	C₂²×C₆₁	semidirect
718. #442	C₂²×C₆₁	semidirect
719. #442	C₂²×C₆₁	semidirect
720. #442	C₂²×C₆₁	semidirect
721. #442	C₂²×C₆₁	semidirect
722. #442	C₂²×C₆₁	semidirect
723. #442	C₂²×C₆₁	semidirect
724. #442	C₂²×C₆₁	semidirect
725. #440	C₂²×C₆₁	semidirect
726. #440	C₂²×C₆₁	semidirect
727. #440	C₂²×C₆₁	semidirect
728. C₄×SD₁₆	C₂²×C₆₁	semidirect
729. C₄×SD₁₆	C₂²×C₆₁	semidirect
731. C₄×D₈	C₂²×C₆₁	semidirect
732. #435	C₂²×C₆₁	semidirect
733. #435	C₂²×C₆₁	semidirect
734. C₈×D₄	C₂²×C₆₁	semidirect
735. C₈×D₄	C₂²×C₆₁	semidirect
736. #432	C₂²×C₆₁	semidirect
737. #432	C₂²×C₆₁	semidirect
738. #428	C₂²×C₆₁	semidirect
739. C₂×#106	C₂²×C₆₁	semidirect
740. #418	C₂²×C₆₁	semidirect
741. #417	C₂²×C₆₁	semidirect
742. C₂×#102	C₂²×C₆₁	semidirect
743. C₂×#102	C₂²×C₆₁	semidirect
744. C₄×M₁₆	C₂²×C₆₁	semidirect
745. C₂×#97	C₂²×C₆₁	semidirect
746. C₆₁	#61451	direct (N × H)
1010. D₈	#41×C₆₁	semidirect
1122. D₄	AGL(1,ℤ/8)×C₆₁	semidirect
1124. D₄	C₂×#41×C₆₁	semidirect
1170. C₈	C₂×#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3481	2
D₄×#41×C₆₁	2
C₆₁×#3399	2
C₆₁×#3384	2
C₆₁×#3373	2
C₆₁×#3366	2
C₆₁×#3345	2
C₆₁×#3335	2
C₆₁×#3318	2
C₆₁×#3306	2
C₆₁×#3295	2
C₆₁×#3294	2
D₄×D₈×C₆₁	2
C₆₁×#3264	2
C₆₁×#3184	2
C₆₁×#3180	2
C₆₁×#3115	2
C₆₁×#3114	2
C₆₁×#3109	2
C₆₁×#2970	2
C₄×AGL(1,ℤ/8)×C₆₁	2
C₂×C₆₁×#442	2
#61451	61

Subgroups — C61×#61451 #29564884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61451 #29564884