Subgroups — C₆₁×#61481 #29564914

Order 15616.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3519	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3337	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3320	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3310	C₂	1	2	yes	maximal, complemented
13	D₄×SD₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3174	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3126	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3123	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2949	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#557	—	2	1	no	—
27	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#556	—	2	1	no	—
30	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#555	C₂²	1	1	yes	characteristic
32	C₆₁×#554	C₂²	1	1	yes	characteristic
33	C₆₁×#553	—	2	1	no	—
34	C₆₁×#553	C₂²	1	2	yes	—
35	C₆₁×#552	—	2	2	no	—
36	C₆₁×#552	C₂²	1	2	yes	complemented
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	—	2	2	no	—
42	D₄²×C₆₁	C₂²	1	2	yes	—
43	D₄²×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#541	—	2	2	no	—
45	C₆₁×#541	C₂²	1	2	yes	complemented
46	C₆₁×#540	C₂²	1	2	yes	—
47	C₆₁×#538	—	2	2	no	—
48	C₆₁×#533	—	2	1	no	—
49	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#532	C₂²	1	1	yes	characteristic
51	C₆₁×#529	—	2	1	no	—
52	C₆₁×#529	C₂²	1	1	yes	characteristic
53	C₆₁×#525	—	2	1	no	—
54	C₂×#121×C₆₁	—	2	1	no	—
55	C₆₁×#519	C₂²	1	2	yes	complemented
56	C₆₁×#518	C₂²	1	2	yes	—
57	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
59	C₆₁×#499	C₂²	1	2	yes	complemented
60	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
62	C₆₁×#492	C₂²	1	2	yes	complemented
63	C₆₁×#491	C₂²	1	2	yes	complemented
64	C₆₁×#490	C₂²	1	2	yes	complemented
65	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#485	C₂²	1	2	yes	complemented
68	C₆₁×#485	C₂²	1	2	yes	complemented
69	C₆₁×#484	C₂²	1	2	yes	complemented
70	C₆₁×#482	C₂²	1	2	yes	complemented
71	C₆₁×#482	C₂²	1	2	yes	complemented
72	C₆₁×#480	C₂²	1	2	yes	complemented
73	C₆₁×#479	C₂²	1	2	yes	complemented
74	C₆₁×#479	C₂²	1	2	yes	complemented
75	C₆₁×#478	C₂²	1	2	yes	—
76	C₆₁×#478	C₂²	1	2	yes	complemented
77	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
79	C₆₁×#474	C₂²	1	1	yes	characteristic
80	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₆₁×#468	C₂²	1	2	yes	complemented
82	C₆₁×#468	C₂²	1	2	yes	complemented
83	C₆₁×#465	C₂²	1	2	yes	complemented
84	C₆₁×#465	C₂²	1	2	yes	complemented
85	C₆₁×#465	C₂²	1	2	yes	complemented
86	C₆₁×#465	C₂²	1	2	yes	complemented
87	C₆₁×#461	C₂²	1	1	yes	characteristic
88	C₆₁×#461	C₂²	1	2	yes	—
89	C₆₁×#461	C₂²	1	2	yes	complemented
90	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
91	C₆₁×#460	C₂²	1	2	yes	complemented
92	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
93	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
94	C₆₁×#460	C₂²	1	2	yes	complemented
95	C₆₁×#450	C₂²	1	2	yes	—
96	C₆₁×#450	C₂²	1	2	yes	—
97	C₆₁×#450	C₂²	1	2	yes	—
98	C₆₁×#448	C₂²	1	2	yes	complemented
99	C₆₁×#448	C₂²	1	2	yes	complemented
100	C₆₁×#448	C₂²	1	2	yes	complemented
101	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
103	C₆₁×#440	C₂²	1	2	yes	—
104	C₆₁×#440	C₂²	1	2	yes	—
105	C₆₁×#440	C₂²	1	2	yes	complemented
106	C₆₁×#440	C₂²	1	2	yes	complemented
107	C₆₁×#440	C₂²	1	2	yes	complemented
108	C₆₁×#440	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₆₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#433	C₂²	1	2	yes	complemented
126	C₆₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₆₁×#427	C₂²	1	2	yes	complemented
128	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
129	C₆₁×#419	C₂²	1	2	yes	complemented
130	C₆₁×#418	C₂²	1	2	yes	—
131	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
132	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
133	C₆₁×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₁	—	2	1	no	—
140	C₂²×D₄×C₆₁	—	2	2	no	—
141	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₁	—	2	1	no	—
144	C₂×SD₁₆×C₆₁	—	2	4	no	—
145	C₂×SD₁₆×C₆₁	—	2	8	no	—
146	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
156	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
157	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₁	—	2	1	no	—
161	C₄⋊Q₈×C₆₁	—	2	1	no	—
162	C₄⋊Q₈×C₆₁	—	2	2	no	—
163	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	#127×C₆₁	C₂³	1	1	yes	characteristic
168	#127×C₆₁	C₂³	1	2	yes	—
169	#126×C₆₁	—	2	2	no	—
170	#126×C₆₁	—	2	2	no	—
171	#126×C₆₁	—	2	2	no	—
172	#126×C₆₁	—	2	2	no	—
173	#126×C₆₁	—	2	2	no	—
174	#126×C₆₁	D₄	1	2	yes	—
175	#125×C₆₁	—	2	2	no	—
176	#125×C₆₁	—	2	2	no	—
177	#125×C₆₁	—	2	2	no	—
178	#125×C₆₁	—	2	2	no	—
179	#125×C₆₁	—	2	2	no	—
180	#125×C₆₁	—	2	1	no	—
181	#125×C₆₁	—	2	1	no	—
182	#125×C₆₁	D₄	1	1	yes	characteristic
183	#125×C₆₁	C₂³	1	2	yes	—
184	#125×C₆₁	C₂³	1	2	yes	—
185	#124×C₆₁	—	2	1	no	—
186	#124×C₆₁	—	2	2	no	—
187	#124×C₆₁	—	2	1	no	—
188	#124×C₆₁	D₄	1	1	yes	characteristic
189	#123×C₆₁	—	2	2	no	—
190	#123×C₆₁	—	2	2	no	—
191	#123×C₆₁	—	2	2	no	—
192	#123×C₆₁	—	2	2	no	—
193	#123×C₆₁	D₄	1	2	yes	—
194	C₂²⋊Q₈×C₆₁	—	2	1	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	—	2	2	no	—
200	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
201	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
204	#121×C₆₁	—	2	2	no	—
205	#121×C₆₁	—	2	1	no	—
206	#121×C₆₁	—	2	1	no	—
207	#121×C₆₁	—	2	2	no	—
208	#121×C₆₁	—	2	2	no	—
209	#121×C₆₁	—	2	1	no	—
210	#121×C₆₁	—	2	1	no	—
211	#121×C₆₁	—	2	2	no	—
212	#121×C₆₁	—	2	2	no	—
213	#121×C₆₁	D₄	1	1	yes	characteristic
214	#121×C₆₁	C₂³	1	2	yes	—
215	#121×C₆₁	C₂³	1	2	yes	—
216	#121×C₆₁	C₂³	1	2	yes	—
217	#120×C₆₁	—	2	2	no	—
218	#120×C₆₁	—	2	2	no	—
219	#120×C₆₁	—	2	2	no	—
220	C₄×Q₈×C₆₁	—	2	1	no	—
221	C₄×Q₈×C₆₁	—	2	2	no	—
222	C₄×Q₈×C₆₁	—	2	1	no	—
223	C₄×Q₈×C₆₁	—	2	2	no	—
224	C₄×Q₈×C₆₁	—	2	1	no	—
225	C₄×Q₈×C₆₁	—	2	1	no	—
226	C₄×Q₈×C₆₁	—	2	1	no	—
227	C₄×Q₈×C₆₁	—	2	1	no	—
228	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₆₁	—	2	2	no	—
237	C₄×D₄×C₆₁	—	2	1	no	—
238	C₄×D₄×C₆₁	—	2	2	no	—
239	C₄×D₄×C₆₁	—	2	2	no	—
240	C₄×D₄×C₆₁	—	2	2	no	—
241	C₄×D₄×C₆₁	—	2	1	no	—
242	C₄×D₄×C₆₁	—	2	1	no	—
243	C₄×D₄×C₆₁	—	2	1	no	—
244	C₄×D₄×C₆₁	C₂³	1	2	yes	—
245	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₁	C₂³	1	2	yes	—
248	C₄×D₄×C₆₁	C₂³	1	2	yes	—
249	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₆₁	C₂³	1	2	yes	—
252	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
253	#117×C₆₁	—	2	1	no	—
254	#117×C₆₁	—	2	1	no	—
255	#117×C₆₁	—	2	2	no	—
256	#117×C₆₁	—	2	2	no	—
257	#117×C₆₁	—	2	2	no	—
258	#117×C₆₁	C₂³	1	2	yes	—
259	#117×C₆₁	C₂³	1	2	yes	—
260	#117×C₆₁	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	#107×C₆₁	C₂³	1	2	yes	—
271	#107×C₆₁	C₂³	1	2	yes	—
272	#107×C₆₁	C₂³	1	2	yes	—
273	#107×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	1	yes	characteristic
275	#106×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	1	yes	characteristic
277	#106×C₆₁	C₂³	1	1	yes	characteristic
278	#106×C₆₁	C₂³	1	2	yes	—
279	#106×C₆₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
284	#103×C₆₁	C₂³	1	1	yes	characteristic
285	#103×C₆₁	C₂³	1	1	yes	characteristic
286	#103×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	2	yes	—
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	2	yes	—
293	#103×C₆₁	C₂³	1	2	yes	—
294	#102×C₆₁	C₂³	1	1	yes	characteristic
295	#102×C₆₁	C₂³	1	1	yes	characteristic
296	#102×C₆₁	C₂³	1	1	yes	characteristic
297	#102×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	#97×C₆₁	C₂³	1	2	yes	—
308	#97×C₆₁	C₂³	1	2	yes	—
309	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	2	yes	—
314	C₂⁴×C₆₁	—	2	1	no	—
315	C₂⁴×C₆₁	—	2	2	no	—
316	#41×C₆₁	—	8	2	no	—
317	#41×C₆₁	—	8	2	no	—
318	C₂×Q₈×C₆₁	—	2	1	no	—
319	C₂×Q₈×C₆₁	—	2	2	no	—
320	C₂×Q₈×C₆₁	—	2	1	no	—
321	C₂×Q₈×C₆₁	—	2	1	no	—
322	C₂×Q₈×C₆₁	—	2	2	no	—
323	C₂×Q₈×C₆₁	—	2	4	no	—
324	C₂×Q₈×C₆₁	—	4	1	no	—
325	C₂×Q₈×C₆₁	—	4	2	no	—
326	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₆₁	—	2	2	no	—
331	C₂×D₄×C₆₁	—	2	4	no	—
332	C₂×D₄×C₆₁	—	2	2	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	1	no	—
340	C₂×D₄×C₆₁	—	2	2	no	—
341	C₂×D₄×C₆₁	—	4	1	no	—
342	C₂×D₄×C₆₁	—	4	2	no	—
343	C₂×D₄×C₆₁	—	8	2	no	—
344	C₂×D₄×C₆₁	—	8	4	no	—
345	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
349	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₆₁	—	2	1	no	—
351	C₂²×C₄×C₆₁	—	2	1	no	—
352	C₂²×C₄×C₆₁	—	2	2	no	—
353	C₂²×C₄×C₆₁	—	2	1	no	—
354	C₂²×C₄×C₆₁	—	2	1	no	—
355	C₂²×C₄×C₆₁	—	2	1	no	—
356	C₂²×C₄×C₆₁	—	2	1	no	—
357	C₂²×C₄×C₆₁	—	2	2	no	—
358	C₂²×C₄×C₆₁	—	2	2	no	—
359	C₂²×C₄×C₆₁	—	2	2	no	—
360	C₂²×C₄×C₆₁	—	2	1	no	—
361	C₂²×C₄×C₆₁	—	8	2	no	—
362	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
366	SD₁₆×C₆₁	—	2	2	no	—
367	SD₁₆×C₆₁	—	2	4	no	—
368	SD₁₆×C₆₁	—	2	2	no	—
369	SD₁₆×C₆₁	—	2	4	no	—
370	SD₁₆×C₆₁	—	2	2	no	—
371	SD₁₆×C₆₁	—	2	4	no	—
372	SD₁₆×C₆₁	—	4	2	no	—
373	SD₁₆×C₆₁	—	4	2	no	—
374	SD₁₆×C₆₁	—	4	2	no	—
375	SD₁₆×C₆₁	#41	1	4	yes	complemented
376	M₁₆×C₆₁	—	4	2	no	—
377	C₂×C₈×C₆₁	—	2	2	no	—
378	C₂×C₈×C₆₁	—	2	4	no	—
379	C₂×C₈×C₆₁	—	4	1	no	—
380	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
384	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
385	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	1	no	—
389	C₄⋊C₄×C₆₁	—	2	1	no	—
390	C₄⋊C₄×C₆₁	—	2	1	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	1	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	2	no	—
395	C₄⋊C₄×C₆₁	—	2	2	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	1	no	—
398	C₄⋊C₄×C₆₁	—	2	2	no	—
399	C₄⋊C₄×C₆₁	—	2	1	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	1	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	2	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	2	no	—
406	C₄⋊C₄×C₆₁	—	2	2	no	—
407	C₄⋊C₄×C₆₁	—	2	2	no	—
408	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
420	C₂²⋊C₄×C₆₁	—	2	2	no	—
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	2	no	—
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	1	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	1	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	1	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	—	2	2	no	—
434	C₂²⋊C₄×C₆₁	—	2	2	no	—
435	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
440	C₄²×C₆₁	—	2	1	no	—
441	C₄²×C₆₁	—	2	1	no	—
442	C₄²×C₆₁	—	2	1	no	—
443	C₄²×C₆₁	—	2	1	no	—
444	C₄²×C₆₁	—	2	2	no	—
445	C₄²×C₆₁	—	2	2	no	—
446	C₄²×C₆₁	—	2	2	no	—
447	C₄²×C₆₁	—	2	2	no	—
448	C₄²×C₆₁	—	2	2	no	—
449	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
452	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₆₁	C₂⁴	1	2	yes	—
454	C₂³×C₆₁	—	2	1	no	—
455	C₂³×C₆₁	—	2	1	no	—
456	C₂³×C₆₁	—	2	2	no	—
457	C₂³×C₆₁	—	4	2	no	—
458	C₂³×C₆₁	—	4	4	no	—
459	C₂³×C₆₁	—	4	2	no	—
460	C₂³×C₆₁	—	8	1	no	—
461	C₂³×C₆₁	—	8	2	no	—
462	C₂³×C₆₁	—	8	2	no	—
463	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
464	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
465	Q₈×C₆₁	—	2	2	no	—
466	Q₈×C₆₁	—	2	1	no	—
467	Q₈×C₆₁	—	2	1	no	—
468	Q₈×C₆₁	—	2	2	no	—
469	Q₈×C₆₁	—	2	2	no	—
470	Q₈×C₆₁	—	2	1	no	—
471	Q₈×C₆₁	—	4	2	no	—
472	Q₈×C₆₁	—	4	4	no	—
473	Q₈×C₆₁	—	4	2	no	—
474	Q₈×C₆₁	—	8	1	no	—
475	Q₈×C₆₁	C₂×#41	1	2	yes	—
476	D₄×C₆₁	—	2	4	no	—
477	D₄×C₆₁	—	2	2	no	—
478	D₄×C₆₁	—	2	1	no	—
479	D₄×C₆₁	—	2	2	no	—
480	D₄×C₆₁	—	2	1	no	—
481	D₄×C₆₁	—	2	1	no	—
482	D₄×C₆₁	—	2	2	no	—
483	D₄×C₆₁	—	4	2	no	—
484	D₄×C₆₁	—	4	4	no	—
485	D₄×C₆₁	—	4	4	no	—
486	D₄×C₆₁	—	4	2	no	—
487	D₄×C₆₁	—	8	2	no	—
488	D₄×C₆₁	—	8	1	no	—
489	D₄×C₆₁	—	8	2	no	—
490	D₄×C₆₁	—	8	2	no	—
491	D₄×C₆₁	—	8	2	no	—
492	D₄×C₆₁	C₂×#41	1	2	yes	—
493	C₂×C₄×C₆₁	—	2	2	no	—
494	C₂×C₄×C₆₁	—	2	1	no	—
495	C₂×C₄×C₆₁	—	2	2	no	—
496	C₂×C₄×C₆₁	—	2	1	no	—
497	C₂×C₄×C₆₁	—	2	2	no	—
498	C₂×C₄×C₆₁	—	2	1	no	—
499	C₂×C₄×C₆₁	—	2	2	no	—
500	C₂×C₄×C₆₁	—	2	1	no	—
501	C₂×C₄×C₆₁	—	2	2	no	—
502	C₂×C₄×C₆₁	—	2	1	no	—
503	C₂×C₄×C₆₁	—	2	1	no	—
504	C₂×C₄×C₆₁	—	2	1	no	—
505	C₂×C₄×C₆₁	—	2	2	no	—
506	C₂×C₄×C₆₁	—	2	2	no	—
507	C₂×C₄×C₆₁	—	2	1	no	—
508	C₂×C₄×C₆₁	—	4	2	no	—
509	C₂×C₄×C₆₁	—	4	4	no	—
510	C₂×C₄×C₆₁	—	4	2	no	—
511	C₂×C₄×C₆₁	—	4	2	no	—
512	C₂×C₄×C₆₁	—	4	2	no	—
513	C₂×C₄×C₆₁	—	8	1	no	—
514	C₂×C₄×C₆₁	—	8	1	no	—
515	C₂×C₄×C₆₁	—	8	2	no	—
516	C₂×C₄×C₆₁	—	8	2	no	—
517	C₂×C₄×C₆₁	—	8	2	no	—
518	C₂×C₄×C₆₁	—	8	1	no	—
519	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
528	C₈×C₆₁	—	2	1	no	—
529	C₈×C₆₁	—	2	2	no	—
530	C₈×C₆₁	—	2	1	no	—
531	C₈×C₆₁	—	2	1	no	—
532	C₈×C₆₁	—	2	2	no	—
533	C₈×C₆₁	C₂×#41	1	2	yes	—
534	#61481	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
535	C₂²×C₆₁	—	2	1	no	—
536	C₂²×C₆₁	—	2	1	no	—
537	C₂²×C₆₁	—	2	2	no	—
538	C₂²×C₆₁	—	2	2	no	—
539	C₂²×C₆₁	—	2	2	no	—
540	C₂²×C₆₁	—	2	2	no	—
541	C₂²×C₆₁	—	4	1	no	—
542	C₂²×C₆₁	—	4	1	no	—
543	C₂²×C₆₁	—	4	1	no	—
544	C₂²×C₆₁	—	4	2	no	—
545	C₂²×C₆₁	—	4	1	no	—
546	C₂²×C₆₁	—	4	2	no	—
547	C₂²×C₆₁	—	4	2	no	—
548	C₂²×C₆₁	—	4	1	no	—
549	C₂²×C₆₁	—	8	4	no	—
550	C₂²×C₆₁	—	16	4	no	—
551	C₂²×C₆₁	#577	1	2	yes	—
552	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
553	C₄×C₆₁	—	2	1	no	—
554	C₄×C₆₁	—	2	2	no	—
555	C₄×C₆₁	—	2	2	no	—
556	C₄×C₆₁	—	2	1	no	—
557	C₄×C₆₁	—	2	1	no	—
558	C₄×C₆₁	—	2	1	no	—
559	C₄×C₆₁	—	2	2	no	—
560	C₄×C₆₁	—	2	2	no	—
561	C₄×C₆₁	—	4	1	no	—
562	C₄×C₆₁	—	4	2	no	—
563	C₄×C₆₁	—	4	1	no	—
564	C₄×C₆₁	—	4	1	no	—
565	C₄×C₆₁	—	4	1	no	—
566	C₄×C₆₁	—	4	1	no	—
567	C₄×C₆₁	—	4	2	no	—
568	C₄×C₆₁	—	4	2	no	—
569	C₄×C₆₁	#577	1	2	yes	—
570	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
571	C₄×C₆₁	#585	1	1	yes	characteristic
572	#3523	C₂×C₆₁	1	1	yes	characteristic, complemented
573	#3519	C₂×C₆₁	1	1	yes	characteristic
574	#3392	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3381	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#3372	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3368	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3340	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3337	C₂×C₆₁	1	2	yes	complemented
580	#3329	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3324	C₂×C₆₁	1	1	yes	characteristic, complemented
582	#3320	C₂×C₆₁	1	2	yes	complemented
583	#3310	C₂×C₆₁	1	2	yes	complemented
584	D₄×SD₁₆	C₂×C₆₁	1	2	yes	complemented
585	D₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#3174	C₂×C₆₁	1	2	yes	complemented
587	#3167	C₂×C₆₁	1	1	yes	characteristic, complemented
588	#3126	C₂×C₆₁	1	2	yes	complemented
589	#3123	C₂×C₆₁	1	2	yes	complemented
590	#3112	C₂×C₆₁	1	1	yes	characteristic, complemented
591	#3110	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#2966	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#2949	C₂×C₆₁	1	2	yes	complemented
594	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
595	C₂×C₆₁	—	2	2	no	—
596	C₂×C₆₁	—	4	2	no	—
597	C₂×C₆₁	—	4	2	no	—
598	C₂×C₆₁	—	8	1	no	—
599	C₂×C₆₁	—	8	2	no	—
600	C₂×C₆₁	D₄×#41	1	1	yes	characteristic
601	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
602	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
603	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
604	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
605	#557	—	2	1	no	—
606	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
607	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
608	#556	—	2	1	no	—
609	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
610	#555	C₂²×C₆₁	1	1	yes	characteristic
611	#554	C₂²×C₆₁	1	1	yes	characteristic
612	#553	—	2	1	no	—
613	#553	C₂²×C₆₁	1	2	yes	—
614	#552	—	2	2	no	—
615	#552	C₂²×C₆₁	1	2	yes	complemented
616	#550	C₂²×C₆₁	1	1	yes	characteristic
617	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
618	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
619	#546	—	2	1	no	—
620	#546	—	2	2	no	—
621	D₄²	C₂²×C₆₁	1	2	yes	—
622	D₄²	C₂²×C₆₁	1	1	yes	characteristic
623	#541	—	2	2	no	—
624	#541	C₂²×C₆₁	1	2	yes	complemented
625	#540	C₂²×C₆₁	1	2	yes	—
626	#538	—	2	2	no	—
627	#533	—	2	1	no	—
628	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
629	#532	C₂²×C₆₁	1	1	yes	characteristic
630	#529	—	2	1	no	—
631	#529	C₂²×C₆₁	1	1	yes	characteristic
632	#525	—	2	1	no	—
633	C₂×#121	—	2	1	no	—
634	#519	C₂²×C₆₁	1	2	yes	complemented
635	#518	C₂²×C₆₁	1	2	yes	—
636	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
637	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
638	#499	C₂²×C₆₁	1	2	yes	complemented
639	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
640	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
641	#492	C₂²×C₆₁	1	2	yes	complemented
642	#491	C₂²×C₆₁	1	2	yes	complemented
643	#490	C₂²×C₆₁	1	2	yes	complemented
644	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
645	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
646	#485	C₂²×C₆₁	1	2	yes	complemented
647	#485	C₂²×C₆₁	1	2	yes	complemented
648	#484	C₂²×C₆₁	1	2	yes	complemented
649	#482	C₂²×C₆₁	1	2	yes	complemented
650	#482	C₂²×C₆₁	1	2	yes	complemented
651	#480	C₂²×C₆₁	1	2	yes	complemented
652	#479	C₂²×C₆₁	1	2	yes	complemented
653	#479	C₂²×C₆₁	1	2	yes	complemented
654	#478	C₂²×C₆₁	1	2	yes	—
655	#478	C₂²×C₆₁	1	2	yes	complemented
656	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
657	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
658	#474	C₂²×C₆₁	1	1	yes	characteristic
659	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	#468	C₂²×C₆₁	1	2	yes	complemented
661	#468	C₂²×C₆₁	1	2	yes	complemented
662	#465	C₂²×C₆₁	1	2	yes	complemented
663	#465	C₂²×C₆₁	1	2	yes	complemented
664	#465	C₂²×C₆₁	1	2	yes	complemented
665	#465	C₂²×C₆₁	1	2	yes	complemented
666	#461	C₂²×C₆₁	1	1	yes	characteristic
667	#461	C₂²×C₆₁	1	2	yes	—
668	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
669	#461	C₂²×C₆₁	1	2	yes	complemented
670	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
671	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
672	#460	C₂²×C₆₁	1	2	yes	complemented
673	#460	C₂²×C₆₁	1	2	yes	complemented
674	#450	C₂²×C₆₁	1	2	yes	—
675	#450	C₂²×C₆₁	1	2	yes	—
676	#450	C₂²×C₆₁	1	2	yes	—
677	#448	C₂²×C₆₁	1	2	yes	complemented
678	#448	C₂²×C₆₁	1	2	yes	complemented
679	#448	C₂²×C₆₁	1	2	yes	complemented
680	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
681	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
682	#440	C₂²×C₆₁	1	2	yes	—
683	#440	C₂²×C₆₁	1	2	yes	—
684	#440	C₂²×C₆₁	1	2	yes	complemented
685	#440	C₂²×C₆₁	1	2	yes	complemented
686	#440	C₂²×C₆₁	1	2	yes	complemented
687	#440	C₂²×C₆₁	1	2	yes	complemented
688	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
689	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
691	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
692	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
693	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
694	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
695	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
696	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
697	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
698	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
699	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
700	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
701	#435	C₂²×C₆₁	1	2	yes	complemented
702	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
703	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
704	#433	C₂²×C₆₁	1	2	yes	complemented
705	#432	C₂²×C₆₁	1	1	yes	characteristic, complemented
706	#427	C₂²×C₆₁	1	2	yes	complemented
707	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
708	#419	C₂²×C₆₁	1	2	yes	complemented
709	#418	C₂²×C₆₁	1	2	yes	—
710	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
711	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
712	#405	C₂²×C₆₁	1	2	yes	complemented
713	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
714	C₆₁	#61481	1	1	yes	characteristic, direct product factor, Sylow
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	1	no	—
717	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
718	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
719	C₂²×D₄	—	2	1	no	—
720	C₂²×D₄	—	2	2	no	—
721	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
722	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
723	C₂³×C₄	—	2	1	no	—
724	C₂×SD₁₆	—	2	4	no	—
725	C₂×SD₁₆	—	2	8	no	—
726	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
736	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
737	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
738	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
739	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
740	C₄⋊Q₈	—	2	1	no	—
741	C₄⋊Q₈	—	2	1	no	—
742	C₄⋊Q₈	—	2	2	no	—
743	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
745	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
747	#127	C₂³×C₆₁	1	1	yes	characteristic
748	#127	C₂³×C₆₁	1	2	yes	—
749	#126	—	2	2	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	D₄×C₆₁	1	2	yes	—
755	#125	—	2	1	no	—
756	#125	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	—	2	2	no	—
759	#125	—	2	2	no	—
760	#125	—	2	2	no	—
761	#125	—	2	1	no	—
762	#125	D₄×C₆₁	1	1	yes	characteristic
763	#125	C₂³×C₆₁	1	2	yes	—
764	#125	C₂³×C₆₁	1	2	yes	—
765	#124	—	2	1	no	—
766	#124	—	2	2	no	—
767	#124	—	2	1	no	—
768	#124	D₄×C₆₁	1	1	yes	characteristic
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	D₄×C₆₁	1	2	yes	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
781	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
782	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
783	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
784	#121	—	2	2	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	D₄×C₆₁	1	1	yes	characteristic
794	#121	C₂³×C₆₁	1	2	yes	—
795	#121	C₂³×C₆₁	1	2	yes	—
796	#121	C₂³×C₆₁	1	2	yes	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	2	no	—
802	C₄×Q₈	—	2	2	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
813	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
814	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
815	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₆₁	1	2	yes	—
829	C₄×D₄	C₂³×C₆₁	1	2	yes	—
830	C₄×D₄	C₂³×C₆₁	1	2	yes	—
831	C₄×D₄	C₂³×C₆₁	1	2	yes	—
832	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
833	#117	—	2	1	no	—
834	#117	—	2	1	no	—
835	#117	—	2	2	no	—
836	#117	—	2	2	no	—
837	#117	—	2	2	no	—
838	#117	C₂³×C₆₁	1	2	yes	—
839	#117	C₂³×C₆₁	1	2	yes	—
840	#117	C₂³×C₆₁	1	2	yes	—
841	C₂×C₄⋊C₄	—	2	1	no	—
842	C₂×C₄⋊C₄	—	2	1	no	—
843	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
845	C₂×C₂²⋊C₄	—	2	1	no	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	C₂×C₄²	—	2	1	no	—
849	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
850	#107	C₂³×C₆₁	1	2	yes	—
851	#107	C₂³×C₆₁	1	2	yes	—
852	#107	C₂³×C₆₁	1	2	yes	—
853	#107	C₂³×C₆₁	1	2	yes	—
854	#106	C₂³×C₆₁	1	1	yes	characteristic
855	#106	C₂³×C₆₁	1	1	yes	characteristic
856	#106	C₂³×C₆₁	1	1	yes	characteristic
857	#106	C₂³×C₆₁	1	1	yes	characteristic
858	#106	C₂³×C₆₁	1	2	yes	—
859	#106	C₂³×C₆₁	1	2	yes	—
860	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
864	#103	C₂³×C₆₁	1	1	yes	characteristic
865	#103	C₂³×C₆₁	1	1	yes	characteristic
866	#103	C₂³×C₆₁	1	1	yes	characteristic
867	#103	C₂³×C₆₁	1	1	yes	characteristic
868	#103	C₂³×C₆₁	1	2	yes	—
869	#103	C₂³×C₆₁	1	2	yes	—
870	#103	C₂³×C₆₁	1	2	yes	—
871	#103	C₂³×C₆₁	1	2	yes	—
872	#103	C₂³×C₆₁	1	2	yes	—
873	#103	C₂³×C₆₁	1	2	yes	—
874	#102	C₂³×C₆₁	1	1	yes	characteristic
875	#102	C₂³×C₆₁	1	1	yes	characteristic
876	#102	C₂³×C₆₁	1	1	yes	characteristic
877	#102	C₂³×C₆₁	1	1	yes	characteristic
878	#102	C₂³×C₆₁	1	2	yes	—
879	#102	C₂³×C₆₁	1	2	yes	—
880	#102	C₂³×C₆₁	1	2	yes	—
881	#102	C₂³×C₆₁	1	2	yes	—
882	#102	C₂³×C₆₁	1	2	yes	—
883	#102	C₂³×C₆₁	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
887	#97	C₂³×C₆₁	1	2	yes	—
888	#97	C₂³×C₆₁	1	2	yes	—
889	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₆₁	1	2	yes	—
894	C₂⁴	—	2	1	no	—
895	C₂⁴	—	2	2	no	—
896	#41	—	8	2	no	—
897	#41	—	8	2	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	4	no	—
904	C₂×Q₈	—	4	1	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
907	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
908	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
909	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	4	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	4	1	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	8	2	no	—
924	C₂×D₄	—	8	4	no	—
925	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
926	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
927	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
929	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	8	2	no	—
942	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
943	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	2	2	no	—
949	SD₁₆	—	2	4	no	—
950	SD₁₆	—	2	2	no	—
951	SD₁₆	—	2	4	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	#41×C₆₁	1	4	yes	complemented
956	M₁₆	—	4	2	no	—
957	C₂×C₈	—	2	2	no	—
958	C₂×C₈	—	2	4	no	—
959	C₂×C₈	—	4	1	no	—
960	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
964	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
965	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
994	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
997	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1019	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1030	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₆₁	1	2	yes	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	4	2	no	—
1038	C₂³	—	4	4	no	—
1039	C₂³	—	4	2	no	—
1040	C₂³	—	8	1	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1044	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	4	4	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	8	1	no	—
1055	Q₈	C₂×#41×C₆₁	1	2	yes	—
1056	D₄	—	2	4	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	C₂×#41×C₆₁	1	2	yes	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	4	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	8	1	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	1	no	—
1099	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1107	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1108	C₈	—	2	1	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	2	no	—
1113	C₈	C₂×#41×C₆₁	1	2	yes	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	8	4	no	—
1129	C₂²	—	16	4	no	—
1130	C₂²	C₆₁×#577	1	2	yes	—
1131	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	C₆₁×#577	1	2	yes	—
1149	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1150	C₄	C₆₁×#585	1	1	yes	characteristic
1151	C₂	—	2	2	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	1	no	—
1155	C₂	—	8	2	no	—
1156	C₂	D₄×#41×C₆₁	1	1	yes	characteristic
1157	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1158	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×#3519	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
1. C₆₁×#3523	C₂	semidirect
3. C₆₁×#3392	C₂	semidirect
4. C₆₁×#3381	C₂	semidirect
5. C₆₁×#3372	C₂	semidirect
6. C₆₁×#3368	C₂	semidirect
7. C₆₁×#3340	C₂	semidirect
8. C₆₁×#3337	C₂	semidirect
9. C₆₁×#3329	C₂	semidirect
10. C₆₁×#3324	C₂	semidirect
11. C₆₁×#3320	C₂	semidirect
12. C₆₁×#3310	C₂	semidirect
13. D₄×SD₁₆×C₆₁	C₂	semidirect
14. D₄×SD₁₆×C₆₁	C₂	semidirect
15. C₆₁×#3174	C₂	semidirect
16. C₆₁×#3167	C₂	semidirect
17. C₆₁×#3126	C₂	semidirect
18. C₆₁×#3123	C₂	semidirect
19. C₆₁×#3112	C₂	semidirect
20. C₆₁×#3110	C₂	semidirect
21. C₆₁×#2966	C₂	semidirect
22. C₆₁×#2949	C₂	semidirect
23. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
27. C₆₁×#557	C₂²	semidirect
28. C₆₁×#557	C₂²	semidirect
30. C₆₁×#556	C₂²	semidirect
36. C₆₁×#552	C₂²	semidirect
38. D₄×Q₈×C₆₁	C₂²	semidirect
39. D₄×Q₈×C₆₁	C₂²	semidirect
45. C₆₁×#541	C₂²	semidirect
49. C₆₁×#533	C₂²	semidirect
55. C₆₁×#519	C₂²	semidirect
57. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
59. C₆₁×#499	C₂²	semidirect
60. C₆₁×#498	C₂²	semidirect
61. C₆₁×#492	C₂²	semidirect
62. C₆₁×#492	C₂²	semidirect
63. C₆₁×#491	C₂²	semidirect
64. C₆₁×#490	C₂²	semidirect
65. C₆₁×#487	C₂²	semidirect
66. C₆₁×#486	C₂²	semidirect
67. C₆₁×#485	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
69. C₆₁×#484	C₂²	semidirect
70. C₆₁×#482	C₂²	semidirect
71. C₆₁×#482	C₂²	semidirect
72. C₆₁×#480	C₂²	semidirect
73. C₆₁×#479	C₂²	semidirect
74. C₆₁×#479	C₂²	semidirect
76. C₆₁×#478	C₂²	semidirect
77. C₆₁×#477	C₂²	semidirect
78. C₆₁×#477	C₂²	semidirect
80. C₆₁×#474	C₂²	semidirect
81. C₆₁×#468	C₂²	semidirect
82. C₆₁×#468	C₂²	semidirect
83. C₆₁×#465	C₂²	semidirect
84. C₆₁×#465	C₂²	semidirect
85. C₆₁×#465	C₂²	semidirect
86. C₆₁×#465	C₂²	semidirect
89. C₆₁×#461	C₂²	semidirect
90. C₆₁×#461	C₂²	semidirect
91. C₆₁×#460	C₂²	semidirect
92. C₆₁×#460	C₂²	semidirect
93. C₆₁×#460	C₂²	semidirect
94. C₆₁×#460	C₂²	semidirect
98. C₆₁×#448	C₂²	semidirect
99. C₆₁×#448	C₂²	semidirect
100. C₆₁×#448	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₈×Q₈×C₆₁	C₂²	semidirect
105. C₆₁×#440	C₂²	semidirect
106. C₆₁×#440	C₂²	semidirect
107. C₆₁×#440	C₂²	semidirect
108. C₆₁×#440	C₂²	semidirect
114. C₄×SD₁₆×C₆₁	C₂²	semidirect
115. C₄×SD₁₆×C₆₁	C₂²	semidirect
116. C₄×SD₁₆×C₆₁	C₂²	semidirect
117. C₄×SD₁₆×C₆₁	C₂²	semidirect
118. C₄×SD₁₆×C₆₁	C₂²	semidirect
119. C₄×SD₁₆×C₆₁	C₂²	semidirect
120. C₄×SD₁₆×C₆₁	C₂²	semidirect
121. C₆₁×#436	C₂²	semidirect
122. C₆₁×#435	C₂²	semidirect
123. C₈×D₄×C₆₁	C₂²	semidirect
124. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#433	C₂²	semidirect
126. C₆₁×#432	C₂²	semidirect
127. C₆₁×#427	C₂²	semidirect
128. C₂×#106×C₆₁	C₂²	semidirect
129. C₆₁×#419	C₂²	semidirect
131. C₂×#103×C₆₁	C₂²	semidirect
133. C₆₁×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₆₁	C₂²	semidirect
375. SD₁₆×C₆₁	#41	semidirect
534. #61481	C₆₁	direct (N × H)
572. #3523	C₂×C₆₁	semidirect
574. #3392	C₂×C₆₁	semidirect
575. #3381	C₂×C₆₁	semidirect
576. #3372	C₂×C₆₁	semidirect
577. #3368	C₂×C₆₁	semidirect
578. #3340	C₂×C₆₁	semidirect
579. #3337	C₂×C₆₁	semidirect
580. #3329	C₂×C₆₁	semidirect
581. #3324	C₂×C₆₁	semidirect
582. #3320	C₂×C₆₁	semidirect
583. #3310	C₂×C₆₁	semidirect
584. D₄×SD₁₆	C₂×C₆₁	semidirect
585. D₄×SD₁₆	C₂×C₆₁	semidirect
586. #3174	C₂×C₆₁	semidirect
587. #3167	C₂×C₆₁	semidirect
588. #3126	C₂×C₆₁	semidirect
589. #3123	C₂×C₆₁	semidirect
590. #3112	C₂×C₆₁	semidirect
591. #3110	C₂×C₆₁	semidirect
592. #2966	C₂×C₆₁	semidirect
593. #2949	C₂×C₆₁	semidirect
594. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
606. #557	C₂²×C₆₁	semidirect
607. #557	C₂²×C₆₁	semidirect
609. #556	C₂²×C₆₁	semidirect
615. #552	C₂²×C₆₁	semidirect
617. D₄×Q₈	C₂²×C₆₁	semidirect
618. D₄×Q₈	C₂²×C₆₁	semidirect
624. #541	C₂²×C₆₁	semidirect
628. #533	C₂²×C₆₁	semidirect
634. #519	C₂²×C₆₁	semidirect
636. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
638. #499	C₂²×C₆₁	semidirect
639. #498	C₂²×C₆₁	semidirect
640. #492	C₂²×C₆₁	semidirect
641. #492	C₂²×C₆₁	semidirect
642. #491	C₂²×C₆₁	semidirect
643. #490	C₂²×C₆₁	semidirect
644. #487	C₂²×C₆₁	semidirect
645. #486	C₂²×C₆₁	semidirect
646. #485	C₂²×C₆₁	semidirect
647. #485	C₂²×C₆₁	semidirect
648. #484	C₂²×C₆₁	semidirect
649. #482	C₂²×C₆₁	semidirect
650. #482	C₂²×C₆₁	semidirect
651. #480	C₂²×C₆₁	semidirect
652. #479	C₂²×C₆₁	semidirect
653. #479	C₂²×C₆₁	semidirect
655. #478	C₂²×C₆₁	semidirect
656. #477	C₂²×C₆₁	semidirect
657. #477	C₂²×C₆₁	semidirect
659. #474	C₂²×C₆₁	semidirect
660. #468	C₂²×C₆₁	semidirect
661. #468	C₂²×C₆₁	semidirect
662. #465	C₂²×C₆₁	semidirect
663. #465	C₂²×C₆₁	semidirect
664. #465	C₂²×C₆₁	semidirect
665. #465	C₂²×C₆₁	semidirect
668. #461	C₂²×C₆₁	semidirect
669. #461	C₂²×C₆₁	semidirect
670. #460	C₂²×C₆₁	semidirect
671. #460	C₂²×C₆₁	semidirect
672. #460	C₂²×C₆₁	semidirect
673. #460	C₂²×C₆₁	semidirect
677. #448	C₂²×C₆₁	semidirect
678. #448	C₂²×C₆₁	semidirect
679. #448	C₂²×C₆₁	semidirect
680. #446	C₂²×C₆₁	semidirect
681. C₈×Q₈	C₂²×C₆₁	semidirect
684. #440	C₂²×C₆₁	semidirect
685. #440	C₂²×C₆₁	semidirect
686. #440	C₂²×C₆₁	semidirect
687. #440	C₂²×C₆₁	semidirect
693. C₄×SD₁₆	C₂²×C₆₁	semidirect
694. C₄×SD₁₆	C₂²×C₆₁	semidirect
695. C₄×SD₁₆	C₂²×C₆₁	semidirect
696. C₄×SD₁₆	C₂²×C₆₁	semidirect
697. C₄×SD₁₆	C₂²×C₆₁	semidirect
698. C₄×SD₁₆	C₂²×C₆₁	semidirect
699. C₄×SD₁₆	C₂²×C₆₁	semidirect
700. #436	C₂²×C₆₁	semidirect
701. #435	C₂²×C₆₁	semidirect
702. C₈×D₄	C₂²×C₆₁	semidirect
703. C₈×D₄	C₂²×C₆₁	semidirect
704. #433	C₂²×C₆₁	semidirect
705. #432	C₂²×C₆₁	semidirect
706. #427	C₂²×C₆₁	semidirect
707. C₂×#106	C₂²×C₆₁	semidirect
708. #419	C₂²×C₆₁	semidirect
710. C₂×#103	C₂²×C₆₁	semidirect
712. #405	C₂²×C₆₁	semidirect
713. C₂×C₄×C₈	C₂²×C₆₁	semidirect
714. C₆₁	#61481	direct (N × H)
955. SD₁₆	#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×#3523	2
C₆₁×#3519	2
C₆₁×#3392	2
C₆₁×#3381	2
C₆₁×#3372	2
C₆₁×#3368	2
C₆₁×#3340	2
C₆₁×#3337	2
C₆₁×#3329	2
C₆₁×#3324	2
C₆₁×#3320	2
C₆₁×#3310	2
D₄×SD₁₆×C₆₁	2
C₆₁×#3174	2
C₆₁×#3167	2
C₆₁×#3126	2
C₆₁×#3123	2
C₆₁×#3112	2
C₆₁×#3110	2
C₆₁×#2966	2
C₆₁×#2949	2
C₂×C₄×SD₁₆×C₆₁	2
#61481	61

Subgroups — C61×#61481 #29564914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61481 #29564914