Subgroups — C₆₁×#62055 #29565488

Order 15616.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3543	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3310	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3296	C₂	1	2	yes	maximal, complemented
11	D₄×SD₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
12	D₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3266	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3260	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3222	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3126	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3043	C₂	1	2	yes	maximal, complemented
22	C₂×C₆₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₁	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
27	C₆₁×#560	—	2	2	no	—
28	C₆₁×#559	C₂²	1	1	yes	characteristic
29	C₆₁×#557	—	2	1	no	—
30	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#556	—	2	1	no	—
33	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
34	C₆₁×#552	—	2	2	no	—
35	C₆₁×#552	C₂²	1	2	yes	complemented
36	C₆₁×#550	C₂²	1	1	yes	characteristic
37	C₆₁×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
39	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#546	—	2	1	no	—
41	C₆₁×#546	C₂²	1	2	yes	—
42	D₄²×C₆₁	—	2	1	no	—
43	D₄²×C₆₁	C₂²	1	2	yes	—
44	D₄²×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#541	—	2	2	no	—
46	C₆₁×#541	C₂²	1	2	yes	complemented
47	C₆₁×#540	—	2	1	no	—
48	C₆₁×#540	C₂²	1	2	yes	—
49	C₆₁×#535	—	2	1	no	—
50	C₆₁×#535	C₂²	1	2	yes	—
51	C₆₁×#534	—	2	2	no	—
52	C₆₁×#533	—	2	1	no	—
53	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
54	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×#529	—	2	1	no	—
56	C₆₁×#529	C₂²	1	1	yes	characteristic
57	C₆₁×#529	C₂²	1	1	yes	characteristic
58	C₆₁×#519	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#497	C₂²	1	2	yes	complemented
61	C₆₁×#492	C₂²	1	1	yes	characteristic
62	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#492	C₂²	1	2	yes	complemented
64	C₆₁×#490	C₂²	1	2	yes	complemented
65	C₆₁×#488	C₂²	1	2	yes	complemented
66	C₆₁×#486	C₂²	1	1	yes	characteristic
67	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
68	C₆₁×#483	C₂²	1	1	yes	characteristic, complemented
69	C₆₁×#482	C₂²	1	2	yes	complemented
70	C₆₁×#482	C₂²	1	2	yes	complemented
71	C₆₁×#480	C₂²	1	1	yes	characteristic
72	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
73	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
74	C₆₁×#479	C₂²	1	2	yes	complemented
75	C₆₁×#478	C₂²	1	2	yes	complemented
76	C₆₁×#478	C₂²	1	2	yes	complemented
77	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
79	C₆₁×#468	C₂²	1	2	yes	complemented
80	C₆₁×#468	C₂²	1	2	yes	complemented
81	C₆₁×#467	C₂²	1	2	yes	complemented
82	C₆₁×#465	C₂²	1	2	yes	—
83	C₆₁×#465	C₂²	1	2	yes	complemented
84	C₆₁×#465	C₂²	1	2	yes	complemented
85	C₆₁×#464	C₂²	1	2	yes	complemented
86	C₆₁×#464	C₂²	1	1	yes	characteristic, complemented
87	C₆₁×#464	C₂²	1	2	yes	complemented
88	C₆₁×#464	C₂²	1	2	yes	complemented
89	C₆₁×#464	C₂²	1	1	yes	characteristic, complemented
90	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#461	C₂²	1	2	yes	complemented
93	C₆₁×#461	C₂²	1	2	yes	complemented
94	C₆₁×#460	C₂²	1	1	yes	characteristic
95	C₆₁×#460	C₂²	1	1	yes	characteristic
96	C₆₁×#460	C₂²	1	2	yes	complemented
97	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
98	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
99	C₆₁×#460	C₂²	1	2	yes	complemented
100	C₆₁×#460	C₂²	1	2	yes	complemented
101	C₆₁×#460	C₂²	1	2	yes	complemented
102	C₆₁×#460	C₂²	1	2	yes	complemented
103	C₆₁×#460	C₂²	1	2	yes	complemented
104	C₆₁×#452	C₂²	1	2	yes	complemented
105	C₆₁×#452	C₂²	1	2	yes	complemented
106	C₆₁×#451	C₂²	1	1	yes	characteristic, complemented
107	C₆₁×#450	C₂²	1	2	yes	complemented
108	C₆₁×#450	C₂²	1	2	yes	complemented
109	C₆₁×#450	C₂²	1	2	yes	complemented
110	C₆₁×#450	C₂²	1	2	yes	complemented
111	C₆₁×#448	C₂²	1	1	yes	characteristic
112	C₆₁×#448	C₂²	1	2	yes	complemented
113	C₆₁×#448	C₂²	1	2	yes	complemented
114	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₆₁×#440	C₂²	1	2	yes	complemented
117	C₆₁×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
124	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
127	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
128	C₆₁×#433	C₂²	1	2	yes	complemented
129	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₆₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
132	C₆₁×#418	C₂²	1	2	yes	complemented
133	C₆₁×#416	C₂²	1	2	yes	complemented
134	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₁	—	2	2	no	—
140	C₂²×D₄×C₆₁	—	2	1	no	—
141	C₂²×D₄×C₆₁	—	2	1	no	—
142	C₂²×D₄×C₆₁	—	2	1	no	—
143	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
145	#137×C₆₁	—	4	4	no	—
146	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₆₁	—	4	4	no	—
150	C₂×SD₁₆×C₆₁	—	4	4	no	—
151	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
162	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
163	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
164	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₁	—	2	1	no	—
166	C₄⋊Q₈×C₆₁	—	2	1	no	—
167	C₄⋊Q₈×C₆₁	—	2	2	no	—
168	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
171	#127×C₆₁	—	2	1	no	—
172	#127×C₆₁	—	2	1	no	—
173	#127×C₆₁	—	2	1	no	—
174	#127×C₆₁	C₂³	1	2	yes	—
175	#127×C₆₁	C₂³	1	1	yes	characteristic
176	#127×C₆₁	C₂³	1	1	yes	characteristic
177	#127×C₆₁	C₂³	1	2	yes	—
178	#126×C₆₁	—	2	2	no	—
179	#126×C₆₁	—	2	2	no	—
180	#126×C₆₁	—	2	2	no	—
181	#126×C₆₁	—	2	2	no	—
182	#126×C₆₁	—	2	1	no	—
183	#126×C₆₁	D₄	1	2	yes	—
184	#125×C₆₁	—	2	2	no	—
185	#125×C₆₁	—	2	2	no	—
186	#125×C₆₁	—	2	2	no	—
187	#125×C₆₁	—	2	2	no	—
188	#125×C₆₁	—	2	2	no	—
189	#125×C₆₁	—	2	1	no	—
190	#125×C₆₁	—	2	1	no	—
191	#125×C₆₁	D₄	1	1	yes	characteristic
192	#125×C₆₁	C₂³	1	1	yes	characteristic
193	#125×C₆₁	C₂³	1	2	yes	—
194	#124×C₆₁	—	2	1	no	—
195	#124×C₆₁	—	2	1	no	—
196	#124×C₆₁	D₄	1	1	yes	characteristic
197	#124×C₆₁	C₂³	1	1	yes	characteristic
198	#124×C₆₁	C₂³	1	2	yes	—
199	#123×C₆₁	—	2	2	no	—
200	#123×C₆₁	—	2	1	no	—
201	#123×C₆₁	—	2	2	no	—
202	#123×C₆₁	—	2	2	no	—
203	#123×C₆₁	—	2	2	no	—
204	#123×C₆₁	—	2	2	no	—
205	#123×C₆₁	D₄	1	2	yes	—
206	C₂²⋊Q₈×C₆₁	—	2	1	no	—
207	C₂²⋊Q₈×C₆₁	—	2	2	no	—
208	C₂²⋊Q₈×C₆₁	—	2	2	no	—
209	C₂²⋊Q₈×C₆₁	—	2	2	no	—
210	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
215	#121×C₆₁	—	2	2	no	—
216	#121×C₆₁	—	2	2	no	—
217	#121×C₆₁	—	2	2	no	—
218	#121×C₆₁	—	2	1	no	—
219	#121×C₆₁	—	2	1	no	—
220	#121×C₆₁	—	2	2	no	—
221	#121×C₆₁	—	2	2	no	—
222	#121×C₆₁	—	2	2	no	—
223	#121×C₆₁	—	2	2	no	—
224	#121×C₆₁	—	2	2	no	—
225	#121×C₆₁	D₄	1	1	yes	characteristic
226	#121×C₆₁	C₂³	1	2	yes	—
227	#121×C₆₁	C₂³	1	2	yes	—
228	#121×C₆₁	C₂³	1	1	yes	characteristic
229	#120×C₆₁	—	2	2	no	—
230	#120×C₆₁	—	2	2	no	—
231	#120×C₆₁	—	2	2	no	—
232	#120×C₆₁	—	2	2	no	—
233	#120×C₆₁	—	2	2	no	—
234	#120×C₆₁	—	2	2	no	—
235	C₄×Q₈×C₆₁	—	2	1	no	—
236	C₄×Q₈×C₆₁	—	2	2	no	—
237	C₄×Q₈×C₆₁	—	2	1	no	—
238	C₄×Q₈×C₆₁	—	2	2	no	—
239	C₄×Q₈×C₆₁	—	2	1	no	—
240	C₄×Q₈×C₆₁	—	2	1	no	—
241	C₄×Q₈×C₆₁	—	2	1	no	—
242	C₄×Q₈×C₆₁	—	2	1	no	—
243	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
244	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
247	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
249	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₆₁	—	2	2	no	—
253	C₄×D₄×C₆₁	—	2	1	no	—
254	C₄×D₄×C₆₁	—	2	1	no	—
255	C₄×D₄×C₆₁	—	2	1	no	—
256	C₄×D₄×C₆₁	—	2	1	no	—
257	C₄×D₄×C₆₁	C₂³	1	2	yes	—
258	C₄×D₄×C₆₁	C₂³	1	2	yes	—
259	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₆₁	C₂³	1	2	yes	—
261	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
262	#117×C₆₁	—	2	1	no	—
263	#117×C₆₁	—	2	2	no	—
264	#117×C₆₁	—	2	2	no	—
265	#117×C₆₁	—	2	2	no	—
266	#117×C₆₁	—	2	1	no	—
267	#117×C₆₁	C₂³	1	2	yes	—
268	#117×C₆₁	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
272	C₂×C₄²×C₆₁	—	2	1	no	—
273	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
274	#107×C₆₁	C₂³	1	1	yes	characteristic
275	#107×C₆₁	C₂³	1	1	yes	characteristic
276	#107×C₆₁	C₂³	1	2	yes	—
277	#106×C₆₁	C₂³	1	1	yes	characteristic
278	#106×C₆₁	C₂³	1	2	yes	—
279	#106×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×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	1	yes	characteristic
284	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	1	yes	characteristic
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	1	yes	characteristic
290	#103×C₆₁	C₂³	1	1	yes	characteristic
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	1	yes	characteristic
293	#103×C₆₁	C₂³	1	1	yes	characteristic
294	#103×C₆₁	C₂³	1	1	yes	characteristic
295	#103×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	1	yes	characteristic
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	#102×C₆₁	C₂³	1	2	yes	—
305	#102×C₆₁	C₂³	1	1	yes	characteristic
306	#102×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
311	#97×C₆₁	C₂³	1	2	yes	—
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	C₂⁴×C₆₁	—	2	2	no	—
316	C₂⁴×C₆₁	—	2	2	no	—
317	#41×C₆₁	—	4	2	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	8	2	no	—
320	C₂×Q₈×C₆₁	—	2	1	no	—
321	C₂×Q₈×C₆₁	—	2	2	no	—
322	C₂×Q₈×C₆₁	—	2	1	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	4	no	—
325	C₂×Q₈×C₆₁	—	4	1	no	—
326	C₂×Q₈×C₆₁	—	4	2	no	—
327	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₆₁	—	2	1	no	—
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	2	2	no	—
335	C₂×D₄×C₆₁	—	2	2	no	—
336	C₂×D₄×C₆₁	—	2	1	no	—
337	C₂×D₄×C₆₁	—	2	1	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	2	no	—
340	C₂×D₄×C₆₁	—	2	1	no	—
341	C₂×D₄×C₆₁	—	2	2	no	—
342	C₂×D₄×C₆₁	—	2	2	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	—	4	2	no	—
347	C₂×D₄×C₆₁	—	4	2	no	—
348	C₂×D₄×C₆₁	—	4	2	no	—
349	C₂×D₄×C₆₁	—	4	2	no	—
350	C₂×D₄×C₆₁	—	8	2	no	—
351	C₂×D₄×C₆₁	—	8	2	no	—
352	C₂×D₄×C₆₁	—	8	2	no	—
353	C₂×D₄×C₆₁	—	8	4	no	—
354	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
355	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
357	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₆₁	—	2	1	no	—
360	C₂²×C₄×C₆₁	—	2	1	no	—
361	C₂²×C₄×C₆₁	—	2	2	no	—
362	C₂²×C₄×C₆₁	—	2	1	no	—
363	C₂²×C₄×C₆₁	—	2	2	no	—
364	C₂²×C₄×C₆₁	—	2	2	no	—
365	C₂²×C₄×C₆₁	—	2	2	no	—
366	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
370	Q₁₆×C₆₁	—	2	2	no	—
371	Q₁₆×C₆₁	—	4	1	no	—
372	Q₁₆×C₆₁	—	4	2	no	—
373	SD₁₆×C₆₁	—	2	2	no	—
374	SD₁₆×C₆₁	—	2	4	no	—
375	SD₁₆×C₆₁	—	2	4	no	—
376	SD₁₆×C₆₁	—	4	2	no	—
377	SD₁₆×C₆₁	—	4	2	no	—
378	SD₁₆×C₆₁	—	4	2	no	—
379	SD₁₆×C₆₁	—	4	2	no	—
380	SD₁₆×C₆₁	—	4	1	no	—
381	SD₁₆×C₆₁	—	4	2	no	—
382	SD₁₆×C₆₁	—	4	2	no	—
383	SD₁₆×C₆₁	—	4	2	no	—
384	M₁₆×C₆₁	—	4	2	no	—
385	C₂×C₈×C₆₁	—	4	2	no	—
386	C₂×C₈×C₆₁	—	4	2	no	—
387	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
392	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	1	no	—
397	C₄⋊C₄×C₆₁	—	2	1	no	—
398	C₄⋊C₄×C₆₁	—	2	2	no	—
399	C₄⋊C₄×C₆₁	—	2	2	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	1	no	—
402	C₄⋊C₄×C₆₁	—	2	1	no	—
403	C₄⋊C₄×C₆₁	—	2	1	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	1	no	—
406	C₄⋊C₄×C₆₁	—	2	2	no	—
407	C₄⋊C₄×C₆₁	—	2	1	no	—
408	C₄⋊C₄×C₆₁	—	2	1	no	—
409	C₄⋊C₄×C₆₁	—	2	2	no	—
410	C₄⋊C₄×C₆₁	—	2	2	no	—
411	C₄⋊C₄×C₆₁	—	2	2	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	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
426	C₂²⋊C₄×C₆₁	—	2	1	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	—	2	1	no	—
434	C₂²⋊C₄×C₆₁	—	2	1	no	—
435	C₂²⋊C₄×C₆₁	—	2	1	no	—
436	C₂²⋊C₄×C₆₁	—	2	2	no	—
437	C₂²⋊C₄×C₆₁	—	2	2	no	—
438	C₂²⋊C₄×C₆₁	—	2	1	no	—
439	C₂²⋊C₄×C₆₁	—	2	2	no	—
440	C₂²⋊C₄×C₆₁	—	2	2	no	—
441	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
446	C₄²×C₆₁	—	2	1	no	—
447	C₄²×C₆₁	—	2	1	no	—
448	C₄²×C₆₁	—	2	1	no	—
449	C₄²×C₆₁	—	2	1	no	—
450	C₄²×C₆₁	—	2	2	no	—
451	C₄²×C₆₁	—	2	2	no	—
452	C₄²×C₆₁	—	2	2	no	—
453	C₄²×C₆₁	—	2	1	no	—
454	C₄²×C₆₁	—	2	2	no	—
455	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
458	C₄²×C₆₁	C₂⁴	1	2	yes	—
459	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
460	C₂³×C₆₁	—	2	1	no	—
461	C₂³×C₆₁	—	2	2	no	—
462	C₂³×C₆₁	—	2	2	no	—
463	C₂³×C₆₁	—	4	4	no	—
464	C₂³×C₆₁	—	8	2	no	—
465	C₂³×C₆₁	—	8	2	no	—
466	C₂³×C₆₁	—	8	2	no	—
467	C₂³×C₆₁	—	8	2	no	—
468	C₂³×C₆₁	—	8	2	no	—
469	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
470	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
471	Q₈×C₆₁	—	2	2	no	—
472	Q₈×C₆₁	—	2	1	no	—
473	Q₈×C₆₁	—	2	1	no	—
474	Q₈×C₆₁	—	2	2	no	—
475	Q₈×C₆₁	—	2	1	no	—
476	Q₈×C₆₁	—	2	2	no	—
477	Q₈×C₆₁	—	2	1	no	—
478	Q₈×C₆₁	—	2	1	no	—
479	Q₈×C₆₁	—	4	4	no	—
480	Q₈×C₆₁	—	4	2	no	—
481	Q₈×C₆₁	—	4	2	no	—
482	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
483	D₄×C₆₁	—	2	4	no	—
484	D₄×C₆₁	—	2	2	no	—
485	D₄×C₆₁	—	2	1	no	—
486	D₄×C₆₁	—	2	2	no	—
487	D₄×C₆₁	—	2	2	no	—
488	D₄×C₆₁	—	2	1	no	—
489	D₄×C₆₁	—	2	2	no	—
490	D₄×C₆₁	—	2	2	no	—
491	D₄×C₆₁	—	4	2	no	—
492	D₄×C₆₁	—	4	2	no	—
493	D₄×C₆₁	—	4	2	no	—
494	D₄×C₆₁	—	8	2	no	—
495	D₄×C₆₁	—	8	2	no	—
496	D₄×C₆₁	—	8	2	no	—
497	D₄×C₆₁	—	8	1	no	—
498	D₄×C₆₁	—	8	2	no	—
499	D₄×C₆₁	—	8	1	no	—
500	D₄×C₆₁	—	8	2	no	—
501	D₄×C₆₁	—	8	2	no	—
502	D₄×C₆₁	—	8	2	no	—
503	D₄×C₆₁	—	8	2	no	—
504	D₄×C₆₁	—	8	2	no	—
505	C₂×C₄×C₆₁	—	2	2	no	—
506	C₂×C₄×C₆₁	—	2	1	no	—
507	C₂×C₄×C₆₁	—	2	2	no	—
508	C₂×C₄×C₆₁	—	2	1	no	—
509	C₂×C₄×C₆₁	—	2	2	no	—
510	C₂×C₄×C₆₁	—	2	1	no	—
511	C₂×C₄×C₆₁	—	2	2	no	—
512	C₂×C₄×C₆₁	—	2	1	no	—
513	C₂×C₄×C₆₁	—	2	2	no	—
514	C₂×C₄×C₆₁	—	2	1	no	—
515	C₂×C₄×C₆₁	—	2	1	no	—
516	C₂×C₄×C₆₁	—	2	2	no	—
517	C₂×C₄×C₆₁	—	2	1	no	—
518	C₂×C₄×C₆₁	—	2	1	no	—
519	C₂×C₄×C₆₁	—	2	1	no	—
520	C₂×C₄×C₆₁	—	4	2	no	—
521	C₂×C₄×C₆₁	—	4	4	no	—
522	C₂×C₄×C₆₁	—	4	2	no	—
523	C₂×C₄×C₆₁	—	4	2	no	—
524	C₂×C₄×C₆₁	—	8	2	no	—
525	C₂×C₄×C₆₁	—	8	2	no	—
526	C₂×C₄×C₆₁	—	8	2	no	—
527	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
536	C₈×C₆₁	—	2	1	no	—
537	C₈×C₆₁	—	2	2	no	—
538	C₈×C₆₁	—	2	2	no	—
539	C₈×C₆₁	—	2	1	no	—
540	C₈×C₆₁	—	2	1	no	—
541	C₈×C₆₁	—	2	1	no	—
542	#62055	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
543	C₂²×C₆₁	—	2	1	no	—
544	C₂²×C₆₁	—	2	1	no	—
545	C₂²×C₆₁	—	2	2	no	—
546	C₂²×C₆₁	—	2	2	no	—
547	C₂²×C₆₁	—	2	2	no	—
548	C₂²×C₆₁	—	4	2	no	—
549	C₂²×C₆₁	—	4	1	no	—
550	C₂²×C₆₁	—	4	2	no	—
551	C₂²×C₆₁	—	4	1	no	—
552	C₂²×C₆₁	—	4	2	no	—
553	C₂²×C₆₁	—	4	2	no	—
554	C₂²×C₆₁	—	4	1	no	—
555	C₂²×C₆₁	—	4	2	no	—
556	C₂²×C₆₁	—	4	2	no	—
557	C₂²×C₆₁	—	16	4	no	—
558	C₂²×C₆₁	—	16	4	no	—
559	C₂²×C₆₁	#577	1	2	yes	—
560	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₆₁	—	2	2	no	—
562	C₄×C₆₁	—	2	1	no	—
563	C₄×C₆₁	—	2	2	no	—
564	C₄×C₆₁	—	2	1	no	—
565	C₄×C₆₁	—	2	1	no	—
566	C₄×C₆₁	—	2	1	no	—
567	C₄×C₆₁	—	2	2	no	—
568	C₄×C₆₁	—	2	2	no	—
569	C₄×C₆₁	—	4	1	no	—
570	C₄×C₆₁	—	4	2	no	—
571	C₄×C₆₁	—	4	1	no	—
572	C₄×C₆₁	—	4	1	no	—
573	C₄×C₆₁	—	4	1	no	—
574	C₄×C₆₁	—	4	1	no	—
575	C₄×C₆₁	—	4	1	no	—
576	C₄×C₆₁	—	4	2	no	—
577	C₄×C₆₁	#577	1	2	yes	—
578	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₄×C₆₁	#585	1	1	yes	characteristic
580	#3543	C₂×C₆₁	1	1	yes	characteristic
581	#3523	C₂×C₆₁	1	1	yes	characteristic, complemented
582	#3400	C₂×C₆₁	1	1	yes	characteristic, complemented
583	#3392	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3368	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#3365	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#3324	C₂×C₆₁	1	1	yes	characteristic, complemented
587	#3310	C₂×C₆₁	1	2	yes	complemented
588	#3304	C₂×C₆₁	1	1	yes	characteristic, complemented
589	#3296	C₂×C₆₁	1	2	yes	complemented
590	D₄×SD₁₆	C₂×C₆₁	1	2	yes	complemented
591	D₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#3278	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#3266	C₂×C₆₁	1	2	yes	complemented
594	#3260	C₂×C₆₁	1	2	yes	complemented
595	#3248	C₂×C₆₁	1	1	yes	characteristic, complemented
596	#3222	C₂×C₆₁	1	2	yes	complemented
597	#3208	C₂×C₆₁	1	1	yes	characteristic, complemented
598	#3126	C₂×C₆₁	1	2	yes	complemented
599	#3108	C₂×C₆₁	1	1	yes	characteristic, complemented
600	#3043	C₂×C₆₁	1	2	yes	complemented
601	C₂×#460	C₂×C₆₁	1	1	yes	characteristic, complemented
602	#2994	C₂×C₆₁	1	1	yes	characteristic, complemented
603	C₂×C₆₁	—	2	2	no	—
604	C₂×C₆₁	—	4	2	no	—
605	C₂×C₆₁	—	8	2	no	—
606	C₂×C₆₁	—	8	1	no	—
607	C₂×C₆₁	—	8	2	no	—
608	C₂×C₆₁	#3488	1	1	yes	characteristic
609	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
610	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
611	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
612	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
613	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
614	#560	—	2	2	no	—
615	#559	C₂²×C₆₁	1	1	yes	characteristic
616	#557	—	2	1	no	—
617	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
618	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
619	#556	—	2	1	no	—
620	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
621	#552	—	2	2	no	—
622	#552	C₂²×C₆₁	1	2	yes	complemented
623	#550	C₂²×C₆₁	1	1	yes	characteristic
624	#550	C₂²×C₆₁	1	1	yes	characteristic
625	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
626	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
627	#546	—	2	1	no	—
628	#546	C₂²×C₆₁	1	2	yes	—
629	D₄²	—	2	1	no	—
630	D₄²	C₂²×C₆₁	1	2	yes	—
631	D₄²	C₂²×C₆₁	1	1	yes	characteristic
632	#541	—	2	2	no	—
633	#541	C₂²×C₆₁	1	2	yes	complemented
634	#540	—	2	1	no	—
635	#540	C₂²×C₆₁	1	2	yes	—
636	#535	—	2	1	no	—
637	#535	C₂²×C₆₁	1	2	yes	—
638	#534	—	2	2	no	—
639	#533	—	2	1	no	—
640	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
641	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
642	#529	—	2	1	no	—
643	#529	C₂²×C₆₁	1	1	yes	characteristic
644	#529	C₂²×C₆₁	1	1	yes	characteristic
645	#519	C₂²×C₆₁	1	2	yes	complemented
646	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
647	#497	C₂²×C₆₁	1	2	yes	complemented
648	#492	C₂²×C₆₁	1	1	yes	characteristic
649	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
650	#492	C₂²×C₆₁	1	2	yes	complemented
651	#490	C₂²×C₆₁	1	2	yes	complemented
652	#488	C₂²×C₆₁	1	2	yes	complemented
653	#486	C₂²×C₆₁	1	1	yes	characteristic
654	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
655	#483	C₂²×C₆₁	1	1	yes	characteristic, complemented
656	#482	C₂²×C₆₁	1	2	yes	complemented
657	#482	C₂²×C₆₁	1	2	yes	complemented
658	#480	C₂²×C₆₁	1	1	yes	characteristic
659	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
661	#479	C₂²×C₆₁	1	2	yes	complemented
662	#478	C₂²×C₆₁	1	2	yes	complemented
663	#478	C₂²×C₆₁	1	2	yes	complemented
664	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
665	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
666	#468	C₂²×C₆₁	1	2	yes	complemented
667	#468	C₂²×C₆₁	1	2	yes	complemented
668	#467	C₂²×C₆₁	1	2	yes	complemented
669	#465	C₂²×C₆₁	1	2	yes	—
670	#465	C₂²×C₆₁	1	2	yes	complemented
671	#465	C₂²×C₆₁	1	2	yes	complemented
672	#464	C₂²×C₆₁	1	1	yes	characteristic, complemented
673	#464	C₂²×C₆₁	1	1	yes	characteristic, complemented
674	#464	C₂²×C₆₁	1	2	yes	complemented
675	#464	C₂²×C₆₁	1	2	yes	complemented
676	#464	C₂²×C₆₁	1	2	yes	complemented
677	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
678	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
679	#461	C₂²×C₆₁	1	2	yes	complemented
680	#461	C₂²×C₆₁	1	2	yes	complemented
681	#460	C₂²×C₆₁	1	1	yes	characteristic
682	#460	C₂²×C₆₁	1	1	yes	characteristic
683	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
684	#460	C₂²×C₆₁	1	2	yes	complemented
685	#460	C₂²×C₆₁	1	2	yes	complemented
686	#460	C₂²×C₆₁	1	2	yes	complemented
687	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
688	#460	C₂²×C₆₁	1	2	yes	complemented
689	#460	C₂²×C₆₁	1	2	yes	complemented
690	#460	C₂²×C₆₁	1	2	yes	complemented
691	#452	C₂²×C₆₁	1	2	yes	complemented
692	#452	C₂²×C₆₁	1	2	yes	complemented
693	#451	C₂²×C₆₁	1	1	yes	characteristic, complemented
694	#450	C₂²×C₆₁	1	2	yes	complemented
695	#450	C₂²×C₆₁	1	2	yes	complemented
696	#450	C₂²×C₆₁	1	2	yes	complemented
697	#450	C₂²×C₆₁	1	2	yes	complemented
698	#448	C₂²×C₆₁	1	1	yes	characteristic
699	#448	C₂²×C₆₁	1	2	yes	complemented
700	#448	C₂²×C₆₁	1	2	yes	complemented
701	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
702	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
703	#440	C₂²×C₆₁	1	2	yes	complemented
704	#440	C₂²×C₆₁	1	2	yes	complemented
705	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
706	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
707	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
708	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
709	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
710	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
711	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
712	#435	C₂²×C₆₁	1	2	yes	complemented
713	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
714	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
715	#433	C₂²×C₆₁	1	2	yes	complemented
716	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
717	#424	C₂²×C₆₁	1	2	yes	complemented
718	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
719	#418	C₂²×C₆₁	1	2	yes	complemented
720	#416	C₂²×C₆₁	1	2	yes	complemented
721	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
722	C₆₁	#62055	1	1	yes	characteristic, direct product factor, Sylow
723	C₂×#41	—	2	1	no	—
724	C₂×#41	C₂³×C₆₁	1	2	yes	—
725	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
726	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
727	C₂²×D₄	—	2	2	no	—
728	C₂²×D₄	—	2	1	no	—
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	—	2	1	no	—
731	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
732	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
733	#137	—	4	4	no	—
734	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
735	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
736	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
737	C₂×SD₁₆	—	4	4	no	—
738	C₂×SD₁₆	—	4	4	no	—
739	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
740	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
748	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
750	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
751	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
752	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
753	C₄⋊Q₈	—	2	1	no	—
754	C₄⋊Q₈	—	2	1	no	—
755	C₄⋊Q₈	—	2	2	no	—
756	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
757	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
758	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
759	#127	—	2	1	no	—
760	#127	—	2	1	no	—
761	#127	—	2	1	no	—
762	#127	C₂³×C₆₁	1	2	yes	—
763	#127	C₂³×C₆₁	1	1	yes	characteristic
764	#127	C₂³×C₆₁	1	1	yes	characteristic
765	#127	C₂³×C₆₁	1	2	yes	—
766	#126	—	2	2	no	—
767	#126	—	2	2	no	—
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#126	—	2	1	no	—
771	#126	D₄×C₆₁	1	2	yes	—
772	#125	—	2	1	no	—
773	#125	—	2	2	no	—
774	#125	—	2	2	no	—
775	#125	—	2	2	no	—
776	#125	—	2	2	no	—
777	#125	—	2	2	no	—
778	#125	—	2	1	no	—
779	#125	D₄×C₆₁	1	1	yes	characteristic
780	#125	C₂³×C₆₁	1	1	yes	characteristic
781	#125	C₂³×C₆₁	1	2	yes	—
782	#124	—	2	1	no	—
783	#124	—	2	1	no	—
784	#124	D₄×C₆₁	1	1	yes	characteristic
785	#124	C₂³×C₆₁	1	1	yes	characteristic
786	#124	C₂³×C₆₁	1	2	yes	—
787	#123	—	2	2	no	—
788	#123	—	2	1	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	D₄×C₆₁	1	2	yes	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
800	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	D₄×C₆₁	1	1	yes	characteristic
814	#121	C₂³×C₆₁	1	1	yes	characteristic
815	#121	C₂³×C₆₁	1	2	yes	—
816	#121	C₂³×C₆₁	1	2	yes	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	C₄×Q₈	—	2	1	no	—
824	C₄×Q₈	—	2	2	no	—
825	C₄×Q₈	—	2	2	no	—
826	C₄×Q₈	—	2	1	no	—
827	C₄×Q₈	—	2	1	no	—
828	C₄×Q₈	—	2	1	no	—
829	C₄×Q₈	—	2	1	no	—
830	C₄×Q₈	—	2	1	no	—
831	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
832	C₄×Q₈	C₂³×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	2	yes	—
836	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
837	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
838	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
839	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₆₁	1	2	yes	—
847	C₄×D₄	C₂³×C₆₁	1	2	yes	—
848	C₄×D₄	C₂³×C₆₁	1	2	yes	—
849	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
850	#117	—	2	1	no	—
851	#117	—	2	2	no	—
852	#117	—	2	2	no	—
853	#117	—	2	2	no	—
854	#117	—	2	1	no	—
855	#117	C₂³×C₆₁	1	2	yes	—
856	#117	C₂³×C₆₁	1	2	yes	—
857	C₂×C₄⋊C₄	—	2	1	no	—
858	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
862	#107	C₂³×C₆₁	1	1	yes	characteristic
863	#107	C₂³×C₆₁	1	1	yes	characteristic
864	#107	C₂³×C₆₁	1	2	yes	—
865	#106	C₂³×C₆₁	1	1	yes	characteristic
866	#106	C₂³×C₆₁	1	2	yes	—
867	#106	C₂³×C₆₁	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
869	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
870	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
871	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
873	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
874	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
875	#103	C₂³×C₆₁	1	1	yes	characteristic
876	#103	C₂³×C₆₁	1	2	yes	—
877	#103	C₂³×C₆₁	1	1	yes	characteristic
878	#103	C₂³×C₆₁	1	1	yes	characteristic
879	#103	C₂³×C₆₁	1	2	yes	—
880	#103	C₂³×C₆₁	1	1	yes	characteristic
881	#103	C₂³×C₆₁	1	1	yes	characteristic
882	#103	C₂³×C₆₁	1	1	yes	characteristic
883	#103	C₂³×C₆₁	1	2	yes	—
884	#102	C₂³×C₆₁	1	2	yes	—
885	#102	C₂³×C₆₁	1	2	yes	—
886	#102	C₂³×C₆₁	1	2	yes	—
887	#102	C₂³×C₆₁	1	2	yes	—
888	#102	C₂³×C₆₁	1	2	yes	—
889	#102	C₂³×C₆₁	1	1	yes	characteristic
890	#102	C₂³×C₆₁	1	2	yes	—
891	#102	C₂³×C₆₁	1	2	yes	—
892	#102	C₂³×C₆₁	1	2	yes	—
893	#102	C₂³×C₆₁	1	1	yes	characteristic
894	#102	C₂³×C₆₁	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
897	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
898	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
899	#97	C₂³×C₆₁	1	2	yes	—
900	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
902	C₄×C₈	C₂³×C₆₁	1	2	yes	—
903	C₂⁴	—	2	2	no	—
904	C₂⁴	—	2	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	8	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	2	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	4	no	—
913	C₂×Q₈	—	4	1	no	—
914	C₂×Q₈	—	4	2	no	—
915	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
918	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
919	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	4	2	no	—
935	C₂×D₄	—	4	2	no	—
936	C₂×D₄	—	4	2	no	—
937	C₂×D₄	—	4	2	no	—
938	C₂×D₄	—	8	2	no	—
939	C₂×D₄	—	8	2	no	—
940	C₂×D₄	—	8	2	no	—
941	C₂×D₄	—	8	4	no	—
942	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
943	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
945	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
955	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
958	Q₁₆	—	2	2	no	—
959	Q₁₆	—	4	1	no	—
960	Q₁₆	—	4	2	no	—
961	SD₁₆	—	2	2	no	—
962	SD₁₆	—	2	4	no	—
963	SD₁₆	—	2	4	no	—
964	SD₁₆	—	4	2	no	—
965	SD₁₆	—	4	2	no	—
966	SD₁₆	—	4	2	no	—
967	SD₁₆	—	4	2	no	—
968	SD₁₆	—	4	1	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	—	4	2	no	—
971	SD₁₆	—	4	2	no	—
972	M₁₆	—	4	2	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	—	4	2	no	—
975	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
980	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1004	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1005	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1008	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1009	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1010	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1011	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1030	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1031	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1033	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	2	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1044	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1045	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1046	C₄²	C₂⁴×C₆₁	1	2	yes	—
1047	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	4	4	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	—	8	2	no	—
1054	C₂³	—	8	2	no	—
1055	C₂³	—	8	2	no	—
1056	C₂³	—	8	2	no	—
1057	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1058	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	1	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	2	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	4	4	no	—
1068	Q₈	—	4	2	no	—
1069	Q₈	—	4	2	no	—
1070	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
1071	D₄	—	2	4	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	4	2	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	1	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	4	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1119	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1120	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1123	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1124	C₈	—	2	1	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	2	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	1	no	—
1129	C₈	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	16	4	no	—
1145	C₂²	—	16	4	no	—
1146	C₂²	C₆₁×#577	1	2	yes	—
1147	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	1	no	—
1164	C₄	C₆₁×#577	1	2	yes	—
1165	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1166	C₄	C₆₁×#585	1	1	yes	characteristic
1167	C₂	—	2	2	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	8	1	no	—
1170	C₂	—	8	2	no	—
1171	C₂	—	8	2	no	—
1172	C₂	C₆₁×#3488	1	1	yes	characteristic
1173	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1174	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3543	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3523	C₂	semidirect
3. C₆₁×#3400	C₂	semidirect
4. C₆₁×#3392	C₂	semidirect
5. C₆₁×#3368	C₂	semidirect
6. C₆₁×#3365	C₂	semidirect
7. C₆₁×#3324	C₂	semidirect
8. C₆₁×#3310	C₂	semidirect
9. C₆₁×#3304	C₂	semidirect
10. C₆₁×#3296	C₂	semidirect
11. D₄×SD₁₆×C₆₁	C₂	semidirect
12. D₄×SD₁₆×C₆₁	C₂	semidirect
13. C₆₁×#3278	C₂	semidirect
14. C₆₁×#3266	C₂	semidirect
15. C₆₁×#3260	C₂	semidirect
16. C₆₁×#3248	C₂	semidirect
17. C₆₁×#3222	C₂	semidirect
18. C₆₁×#3208	C₂	semidirect
19. C₆₁×#3126	C₂	semidirect
20. C₆₁×#3108	C₂	semidirect
21. C₆₁×#3043	C₂	semidirect
22. C₂×C₆₁×#460	C₂	semidirect
23. C₆₁×#2994	C₂	semidirect
24. C₂×#137×C₆₁	C₂²	semidirect
25. C₂²×SD₁₆×C₆₁	C₂²	semidirect
26. C₂²×SD₁₆×C₆₁	C₂²	semidirect
30. C₆₁×#557	C₂²	semidirect
31. C₆₁×#557	C₂²	semidirect
33. C₆₁×#556	C₂²	semidirect
35. C₆₁×#552	C₂²	semidirect
38. D₄×Q₈×C₆₁	C₂²	semidirect
39. D₄×Q₈×C₆₁	C₂²	semidirect
46. C₆₁×#541	C₂²	semidirect
53. C₆₁×#533	C₂²	semidirect
58. C₆₁×#519	C₂²	semidirect
59. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
60. C₆₁×#497	C₂²	semidirect
62. C₆₁×#492	C₂²	semidirect
63. C₆₁×#492	C₂²	semidirect
64. C₆₁×#490	C₂²	semidirect
65. C₆₁×#488	C₂²	semidirect
67. C₆₁×#486	C₂²	semidirect
68. C₆₁×#483	C₂²	semidirect
69. C₆₁×#482	C₂²	semidirect
70. C₆₁×#482	C₂²	semidirect
72. C₆₁×#479	C₂²	semidirect
73. C₆₁×#479	C₂²	semidirect
74. C₆₁×#479	C₂²	semidirect
75. C₆₁×#478	C₂²	semidirect
76. C₆₁×#478	C₂²	semidirect
77. C₆₁×#475	C₂²	semidirect
78. C₆₁×#474	C₂²	semidirect
79. C₆₁×#468	C₂²	semidirect
80. C₆₁×#468	C₂²	semidirect
81. C₆₁×#467	C₂²	semidirect
83. C₆₁×#465	C₂²	semidirect
84. C₆₁×#465	C₂²	semidirect
85. C₆₁×#464	C₂²	semidirect
86. C₆₁×#464	C₂²	semidirect
87. C₆₁×#464	C₂²	semidirect
88. C₆₁×#464	C₂²	semidirect
89. C₆₁×#464	C₂²	semidirect
90. C₆₁×#462	C₂²	semidirect
91. C₆₁×#461	C₂²	semidirect
92. C₆₁×#461	C₂²	semidirect
93. C₆₁×#461	C₂²	semidirect
96. C₆₁×#460	C₂²	semidirect
97. C₆₁×#460	C₂²	semidirect
98. C₆₁×#460	C₂²	semidirect
99. C₆₁×#460	C₂²	semidirect
100. C₆₁×#460	C₂²	semidirect
101. C₆₁×#460	C₂²	semidirect
102. C₆₁×#460	C₂²	semidirect
103. C₆₁×#460	C₂²	semidirect
104. C₆₁×#452	C₂²	semidirect
105. C₆₁×#452	C₂²	semidirect
106. C₆₁×#451	C₂²	semidirect
107. C₆₁×#450	C₂²	semidirect
108. C₆₁×#450	C₂²	semidirect
109. C₆₁×#450	C₂²	semidirect
110. C₆₁×#450	C₂²	semidirect
112. C₆₁×#448	C₂²	semidirect
113. C₆₁×#448	C₂²	semidirect
114. C₆₁×#446	C₂²	semidirect
115. C₈×Q₈×C₆₁	C₂²	semidirect
116. C₆₁×#440	C₂²	semidirect
117. C₆₁×#440	C₂²	semidirect
118. C₄×Q₁₆×C₆₁	C₂²	semidirect
119. C₄×Q₁₆×C₆₁	C₂²	semidirect
120. C₄×SD₁₆×C₆₁	C₂²	semidirect
121. C₄×SD₁₆×C₆₁	C₂²	semidirect
122. C₄×SD₁₆×C₆₁	C₂²	semidirect
123. C₄×SD₁₆×C₆₁	C₂²	semidirect
124. C₆₁×#436	C₂²	semidirect
125. C₆₁×#435	C₂²	semidirect
126. C₈×D₄×C₆₁	C₂²	semidirect
127. C₈×D₄×C₆₁	C₂²	semidirect
128. C₆₁×#433	C₂²	semidirect
129. C₆₁×#431	C₂²	semidirect
130. C₆₁×#424	C₂²	semidirect
131. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
132. C₆₁×#418	C₂²	semidirect
133. C₆₁×#416	C₂²	semidirect
134. C₂×#102×C₆₁	C₂²	semidirect
542. #62055	C₆₁	direct (N × H)
581. #3523	C₂×C₆₁	semidirect
582. #3400	C₂×C₆₁	semidirect
583. #3392	C₂×C₆₁	semidirect
584. #3368	C₂×C₆₁	semidirect
585. #3365	C₂×C₆₁	semidirect
586. #3324	C₂×C₆₁	semidirect
587. #3310	C₂×C₆₁	semidirect
588. #3304	C₂×C₆₁	semidirect
589. #3296	C₂×C₆₁	semidirect
590. D₄×SD₁₆	C₂×C₆₁	semidirect
591. D₄×SD₁₆	C₂×C₆₁	semidirect
592. #3278	C₂×C₆₁	semidirect
593. #3266	C₂×C₆₁	semidirect
594. #3260	C₂×C₆₁	semidirect
595. #3248	C₂×C₆₁	semidirect
596. #3222	C₂×C₆₁	semidirect
597. #3208	C₂×C₆₁	semidirect
598. #3126	C₂×C₆₁	semidirect
599. #3108	C₂×C₆₁	semidirect
600. #3043	C₂×C₆₁	semidirect
601. C₂×#460	C₂×C₆₁	semidirect
602. #2994	C₂×C₆₁	semidirect
611. C₂×#137	C₂²×C₆₁	semidirect
612. C₂²×SD₁₆	C₂²×C₆₁	semidirect
613. C₂²×SD₁₆	C₂²×C₆₁	semidirect
617. #557	C₂²×C₆₁	semidirect
618. #557	C₂²×C₆₁	semidirect
620. #556	C₂²×C₆₁	semidirect
622. #552	C₂²×C₆₁	semidirect
625. D₄×Q₈	C₂²×C₆₁	semidirect
626. D₄×Q₈	C₂²×C₆₁	semidirect
633. #541	C₂²×C₆₁	semidirect
640. #533	C₂²×C₆₁	semidirect
645. #519	C₂²×C₆₁	semidirect
646. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
647. #497	C₂²×C₆₁	semidirect
649. #492	C₂²×C₆₁	semidirect
650. #492	C₂²×C₆₁	semidirect
651. #490	C₂²×C₆₁	semidirect
652. #488	C₂²×C₆₁	semidirect
654. #486	C₂²×C₆₁	semidirect
655. #483	C₂²×C₆₁	semidirect
656. #482	C₂²×C₆₁	semidirect
657. #482	C₂²×C₆₁	semidirect
659. #479	C₂²×C₆₁	semidirect
660. #479	C₂²×C₆₁	semidirect
661. #479	C₂²×C₆₁	semidirect
662. #478	C₂²×C₆₁	semidirect
663. #478	C₂²×C₆₁	semidirect
664. #475	C₂²×C₆₁	semidirect
665. #474	C₂²×C₆₁	semidirect
666. #468	C₂²×C₆₁	semidirect
667. #468	C₂²×C₆₁	semidirect
668. #467	C₂²×C₆₁	semidirect
670. #465	C₂²×C₆₁	semidirect
671. #465	C₂²×C₆₁	semidirect
672. #464	C₂²×C₆₁	semidirect
673. #464	C₂²×C₆₁	semidirect
674. #464	C₂²×C₆₁	semidirect
675. #464	C₂²×C₆₁	semidirect
676. #464	C₂²×C₆₁	semidirect
677. #462	C₂²×C₆₁	semidirect
678. #461	C₂²×C₆₁	semidirect
679. #461	C₂²×C₆₁	semidirect
680. #461	C₂²×C₆₁	semidirect
683. #460	C₂²×C₆₁	semidirect
684. #460	C₂²×C₆₁	semidirect
685. #460	C₂²×C₆₁	semidirect
686. #460	C₂²×C₆₁	semidirect
687. #460	C₂²×C₆₁	semidirect
688. #460	C₂²×C₆₁	semidirect
689. #460	C₂²×C₆₁	semidirect
690. #460	C₂²×C₆₁	semidirect
691. #452	C₂²×C₆₁	semidirect
692. #452	C₂²×C₆₁	semidirect
693. #451	C₂²×C₆₁	semidirect
694. #450	C₂²×C₆₁	semidirect
695. #450	C₂²×C₆₁	semidirect
696. #450	C₂²×C₆₁	semidirect
697. #450	C₂²×C₆₁	semidirect
699. #448	C₂²×C₆₁	semidirect
700. #448	C₂²×C₆₁	semidirect
701. #446	C₂²×C₆₁	semidirect
702. C₈×Q₈	C₂²×C₆₁	semidirect
703. #440	C₂²×C₆₁	semidirect
704. #440	C₂²×C₆₁	semidirect
705. C₄×Q₁₆	C₂²×C₆₁	semidirect
706. C₄×Q₁₆	C₂²×C₆₁	semidirect
707. C₄×SD₁₆	C₂²×C₆₁	semidirect
708. C₄×SD₁₆	C₂²×C₆₁	semidirect
709. C₄×SD₁₆	C₂²×C₆₁	semidirect
710. C₄×SD₁₆	C₂²×C₆₁	semidirect
711. #436	C₂²×C₆₁	semidirect
712. #435	C₂²×C₆₁	semidirect
713. C₈×D₄	C₂²×C₆₁	semidirect
714. C₈×D₄	C₂²×C₆₁	semidirect
715. #433	C₂²×C₆₁	semidirect
716. #431	C₂²×C₆₁	semidirect
717. #424	C₂²×C₆₁	semidirect
718. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
719. #418	C₂²×C₆₁	semidirect
720. #416	C₂²×C₆₁	semidirect
721. C₂×#102	C₂²×C₆₁	semidirect
722. C₆₁	#62055	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3543	2
C₆₁×#3523	2
C₆₁×#3400	2
C₆₁×#3392	2
C₆₁×#3368	2
C₆₁×#3365	2
C₆₁×#3324	2
C₆₁×#3310	2
C₆₁×#3304	2
C₆₁×#3296	2
D₄×SD₁₆×C₆₁	2
C₆₁×#3278	2
C₆₁×#3266	2
C₆₁×#3260	2
C₆₁×#3248	2
C₆₁×#3222	2
C₆₁×#3208	2
C₆₁×#3126	2
C₆₁×#3108	2
C₆₁×#3043	2
C₂×C₆₁×#460	2
C₆₁×#2994	2
#62055	61

Subgroups — C61×#62055 #29565488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62055 #29565488