Subgroups — C₆₁×#62193 #29565626

Order 15616.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3522	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3353	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3343	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3327	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3313	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3243	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3120	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3083	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#563	—	2	2	no	—
25	C₆₁×#559	—	2	1	no	—
26	C₆₁×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₆₁	C₂²	1	1	yes	characteristic
28	Q₈²×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#557	—	2	1	no	—
30	C₆₁×#557	C₂²	1	1	yes	characteristic
31	C₆₁×#556	—	2	1	no	—
32	C₆₁×#556	C₂²	1	1	yes	characteristic
33	C₆₁×#556	C₂²	1	2	yes	—
34	C₆₁×#554	—	2	1	no	—
35	C₆₁×#554	C₂²	1	1	yes	characteristic
36	C₆₁×#554	C₂²	1	1	yes	characteristic
37	C₆₁×#552	C₂²	1	2	yes	—
38	C₆₁×#550	C₂²	1	1	yes	characteristic
39	C₆₁×#548	C₂²	1	2	yes	—
40	C₆₁×#547	—	2	2	no	—
41	C₆₁×#547	C₂²	1	2	yes	—
42	C₆₁×#544	C₂²	1	2	yes	—
43	C₆₁×#542	—	2	2	no	—
44	C₆₁×#542	—	2	1	no	—
45	C₆₁×#542	C₂²	1	2	yes	—
46	C₆₁×#541	—	2	2	no	—
47	C₆₁×#541	—	2	1	no	—
48	C₆₁×#541	C₂²	1	2	yes	—
49	C₆₁×#533	C₂²	1	1	yes	characteristic
50	C₆₁×#533	C₂²	1	1	yes	characteristic
51	C₆₁×#532	—	2	1	no	—
52	C₆₁×#532	C₂²	1	1	yes	characteristic
53	C₆₁×#529	—	2	1	no	—
54	C₆₁×#529	C₂²	1	1	yes	characteristic
55	C₆₁×#520	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#501	C₂²	1	2	yes	—
58	C₆₁×#500	C₂²	1	1	yes	characteristic
59	C₆₁×#500	C₂²	1	2	yes	—
60	C₆₁×#498	C₂²	1	1	yes	characteristic
61	C₆₁×#489	C₂²	1	2	yes	—
62	C₆₁×#488	C₂²	1	2	yes	—
63	C₆₁×#486	C₂²	1	1	yes	characteristic
64	C₆₁×#486	C₂²	1	1	yes	characteristic
65	C₆₁×#485	C₂²	1	2	yes	—
66	C₆₁×#484	C₂²	1	2	yes	—
67	C₆₁×#484	C₂²	1	2	yes	—
68	C₆₁×#484	C₂²	1	1	yes	characteristic
69	C₆₁×#484	C₂²	1	1	yes	characteristic
70	C₆₁×#483	C₂²	1	2	yes	—
71	C₆₁×#482	C₂²	1	2	yes	—
72	C₆₁×#482	C₂²	1	2	yes	—
73	C₆₁×#482	C₂²	1	2	yes	—
74	C₆₁×#480	C₂²	1	2	yes	—
75	C₆₁×#479	C₂²	1	2	yes	—
76	C₆₁×#479	C₂²	1	2	yes	—
77	C₆₁×#479	C₂²	1	2	yes	—
78	C₆₁×#478	C₂²	1	2	yes	—
79	C₆₁×#478	C₂²	1	2	yes	—
80	C₆₁×#478	C₂²	1	2	yes	—
81	C₆₁×#477	C₂²	1	2	yes	—
82	C₆₁×#477	C₂²	1	1	yes	characteristic
83	C₆₁×#477	C₂²	1	1	yes	characteristic
84	C₆₁×#477	C₂²	1	1	yes	characteristic
85	C₆₁×#477	C₂²	1	1	yes	characteristic
86	C₆₁×#477	C₂²	1	2	yes	—
87	C₆₁×#477	C₂²	1	1	yes	characteristic
88	C₆₁×#477	C₂²	1	1	yes	characteristic
89	C₆₁×#475	C₂²	1	1	yes	characteristic
90	C₆₁×#475	C₂²	1	1	yes	characteristic
91	C₆₁×#475	C₂²	1	2	yes	—
92	C₆₁×#474	C₂²	1	2	yes	—
93	C₆₁×#474	C₂²	1	2	yes	—
94	C₆₁×#470	C₂²	1	2	yes	—
95	C₆₁×#468	C₂²	1	2	yes	—
96	C₆₁×#468	C₂²	1	2	yes	—
97	C₆₁×#468	C₂²	1	2	yes	—
98	C₆₁×#467	C₂²	1	2	yes	—
99	C₆₁×#465	C₂²	1	2	yes	—
100	C₆₁×#464	C₂²	1	2	yes	—
101	C₆₁×#464	C₂²	1	2	yes	—
102	C₆₁×#462	C₂²	1	1	yes	characteristic
103	C₆₁×#462	C₂²	1	1	yes	characteristic
104	C₆₁×#461	C₂²	1	2	yes	—
105	C₆₁×#460	C₂²	1	1	yes	characteristic
106	C₆₁×#460	C₂²	1	1	yes	characteristic
107	C₆₁×#452	C₂²	1	2	yes	—
108	C₆₁×#452	C₂²	1	2	yes	—
109	C₆₁×#451	C₂²	1	1	yes	characteristic
110	C₆₁×#451	C₂²	1	1	yes	characteristic
111	C₆₁×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
113	C₆₁×#441	C₂²	1	2	yes	—
114	C₆₁×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
118	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
121	C₆₁×#436	C₂²	1	2	yes	—
122	C₆₁×#436	C₂²	1	1	yes	characteristic
123	C₆₁×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
125	C₆₁×#433	C₂²	1	2	yes	—
126	C₆₁×#431	C₂²	1	1	yes	characteristic
127	C₆₁×#428	C₂²	1	2	yes	—
128	C₆₁×#428	C₂²	1	2	yes	—
129	C₂×#107×C₆₁	C₂²	1	2	yes	—
130	C₆₁×#424	C₂²	1	2	yes	—
131	C₆₁×#423	C₂²	1	1	yes	characteristic
132	C₆₁×#419	C₂²	1	2	yes	—
133	C₆₁×#417	C₂²	1	2	yes	—
134	C₆₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	2	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
148	C₄⋊Q₈×C₆₁	—	2	1	no	—
149	C₄⋊Q₈×C₆₁	—	2	1	no	—
150	C₄⋊Q₈×C₆₁	—	2	2	no	—
151	C₄⋊Q₈×C₆₁	—	2	2	no	—
152	C₄⋊Q₈×C₆₁	—	2	1	no	—
153	C₄⋊Q₈×C₆₁	—	2	2	no	—
154	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
161	#127×C₆₁	—	2	1	no	—
162	#127×C₆₁	C₂³	1	1	yes	characteristic
163	#126×C₆₁	—	2	2	no	—
164	#126×C₆₁	—	2	2	no	—
165	#126×C₆₁	—	2	2	no	—
166	#126×C₆₁	—	2	2	no	—
167	#126×C₆₁	—	2	2	no	—
168	#126×C₆₁	—	2	2	no	—
169	#126×C₆₁	—	2	2	no	—
170	#126×C₆₁	D₄	1	2	yes	—
171	#125×C₆₁	—	2	2	no	—
172	#125×C₆₁	—	2	2	no	—
173	#125×C₆₁	—	2	2	no	—
174	#125×C₆₁	—	2	1	no	—
175	#125×C₆₁	—	2	2	no	—
176	#125×C₆₁	—	2	2	no	—
177	#125×C₆₁	—	2	1	no	—
178	#125×C₆₁	—	2	1	no	—
179	#125×C₆₁	D₄	1	1	yes	characteristic
180	#125×C₆₁	C₂³	1	2	yes	—
181	#125×C₆₁	C₂³	1	2	yes	—
182	#124×C₆₁	—	2	1	no	—
183	#124×C₆₁	—	2	1	no	—
184	#124×C₆₁	—	2	2	no	—
185	#124×C₆₁	—	2	2	no	—
186	#124×C₆₁	—	2	2	no	—
187	#124×C₆₁	—	2	1	no	—
188	#124×C₆₁	D₄	1	1	yes	characteristic
189	#124×C₆₁	C₂³	1	2	yes	—
190	#123×C₆₁	—	2	2	no	—
191	#123×C₆₁	—	2	2	no	—
192	#123×C₆₁	—	2	2	no	—
193	#123×C₆₁	—	2	2	no	—
194	#123×C₆₁	—	2	2	no	—
195	#123×C₆₁	D₄	1	2	yes	—
196	C₂²⋊Q₈×C₆₁	—	2	1	no	—
197	C₂²⋊Q₈×C₆₁	—	2	1	no	—
198	C₂²⋊Q₈×C₆₁	—	2	1	no	—
199	C₂²⋊Q₈×C₆₁	—	2	2	no	—
200	C₂²⋊Q₈×C₆₁	—	2	2	no	—
201	C₂²⋊Q₈×C₆₁	—	2	2	no	—
202	C₂²⋊Q₈×C₆₁	—	2	2	no	—
203	C₂²⋊Q₈×C₆₁	—	2	2	no	—
204	C₂²⋊Q₈×C₆₁	—	2	2	no	—
205	C₂²⋊Q₈×C₆₁	—	2	2	no	—
206	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
207	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
212	#121×C₆₁	—	2	2	no	—
213	#121×C₆₁	—	2	1	no	—
214	#121×C₆₁	—	2	2	no	—
215	#121×C₆₁	D₄	1	1	yes	characteristic
216	#121×C₆₁	C₂³	1	2	yes	—
217	#121×C₆₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₆₁	—	2	1	no	—
219	C₄×Q₈×C₆₁	—	2	1	no	—
220	C₄×Q₈×C₆₁	—	2	2	no	—
221	C₄×Q₈×C₆₁	—	2	1	no	—
222	C₄×Q₈×C₆₁	—	2	1	no	—
223	C₄×Q₈×C₆₁	—	2	1	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	1	yes	characteristic
229	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	—	2	1	no	—
240	C₄×D₄×C₆₁	—	2	1	no	—
241	C₄×D₄×C₆₁	—	2	1	no	—
242	C₄×D₄×C₆₁	—	2	2	no	—
243	C₄×D₄×C₆₁	—	2	2	no	—
244	C₄×D₄×C₆₁	—	2	2	no	—
245	C₄×D₄×C₆₁	—	2	1	no	—
246	C₄×D₄×C₆₁	C₂³	1	2	yes	—
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	#117×C₆₁	—	2	1	no	—
251	#117×C₆₁	—	2	2	no	—
252	#117×C₆₁	—	2	2	no	—
253	#117×C₆₁	C₂³	1	2	yes	—
254	#117×C₆₁	C₂³	1	2	yes	—
255	#117×C₆₁	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
261	C₂×C₄²×C₆₁	—	2	1	no	—
262	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
263	#107×C₆₁	C₂³	1	1	yes	characteristic
264	#107×C₆₁	C₂³	1	2	yes	—
265	#107×C₆₁	C₂³	1	2	yes	—
266	#107×C₆₁	C₂³	1	2	yes	—
267	#107×C₆₁	C₂³	1	1	yes	characteristic
268	#107×C₆₁	C₂³	1	2	yes	—
269	#107×C₆₁	C₂³	1	2	yes	—
270	#107×C₆₁	C₂³	1	1	yes	characteristic
271	#107×C₆₁	C₂³	1	1	yes	characteristic
272	#107×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	2	yes	—
275	#106×C₆₁	C₂³	1	2	yes	—
276	#106×C₆₁	C₂³	1	2	yes	—
277	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
282	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	#103×C₆₁	C₂³	1	1	yes	characteristic
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	1	yes	characteristic
291	#103×C₆₁	C₂³	1	1	yes	characteristic
292	#103×C₆₁	C₂³	1	1	yes	characteristic
293	#103×C₆₁	C₂³	1	1	yes	characteristic
294	#103×C₆₁	C₂³	1	2	yes	—
295	#103×C₆₁	C₂³	1	1	yes	characteristic
296	#103×C₆₁	C₂³	1	1	yes	characteristic
297	#103×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	2	yes	—
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×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	2	yes	—
312	#41×C₆₁	—	2	4	no	—
313	#41×C₆₁	—	4	2	no	—
314	#41×C₆₁	—	8	2	no	—
315	#41×C₆₁	—	8	4	no	—
316	C₂×Q₈×C₆₁	—	2	1	no	—
317	C₂×Q₈×C₆₁	—	2	1	no	—
318	C₂×Q₈×C₆₁	—	2	1	no	—
319	C₂×Q₈×C₆₁	—	2	1	no	—
320	C₂×Q₈×C₆₁	—	2	2	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	—	4	1	no	—
325	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₆₁	—	2	2	no	—
331	C₂×D₄×C₆₁	—	2	2	no	—
332	C₂×D₄×C₆₁	—	2	2	no	—
333	C₂×D₄×C₆₁	—	2	1	no	—
334	C₂×D₄×C₆₁	—	2	1	no	—
335	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₆₁	—	2	1	no	—
339	C₂²×C₄×C₆₁	—	2	1	no	—
340	C₂²×C₄×C₆₁	—	2	2	no	—
341	C₂²×C₄×C₆₁	—	2	2	no	—
342	C₂²×C₄×C₆₁	—	2	2	no	—
343	C₂²×C₄×C₆₁	—	2	2	no	—
344	C₂²×C₄×C₆₁	—	2	2	no	—
345	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
349	Q₁₆×C₆₁	—	2	2	no	—
350	Q₁₆×C₆₁	—	2	2	no	—
351	Q₁₆×C₆₁	—	4	1	no	—
352	Q₁₆×C₆₁	—	4	1	no	—
353	SD₁₆×C₆₁	—	4	2	no	—
354	SD₁₆×C₆₁	—	4	2	no	—
355	M₁₆×C₆₁	—	4	2	no	—
356	M₁₆×C₆₁	—	4	2	no	—
357	C₂×C₈×C₆₁	—	4	2	no	—
358	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
363	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₆₁	—	2	1	no	—
365	C₄⋊C₄×C₆₁	—	2	2	no	—
366	C₄⋊C₄×C₆₁	—	2	2	no	—
367	C₄⋊C₄×C₆₁	—	2	1	no	—
368	C₄⋊C₄×C₆₁	—	2	1	no	—
369	C₄⋊C₄×C₆₁	—	2	1	no	—
370	C₄⋊C₄×C₆₁	—	2	1	no	—
371	C₄⋊C₄×C₆₁	—	2	2	no	—
372	C₄⋊C₄×C₆₁	—	2	1	no	—
373	C₄⋊C₄×C₆₁	—	2	1	no	—
374	C₄⋊C₄×C₆₁	—	2	2	no	—
375	C₄⋊C₄×C₆₁	—	2	1	no	—
376	C₄⋊C₄×C₆₁	—	2	1	no	—
377	C₄⋊C₄×C₆₁	—	2	1	no	—
378	C₄⋊C₄×C₆₁	—	2	2	no	—
379	C₄⋊C₄×C₆₁	—	2	1	no	—
380	C₄⋊C₄×C₆₁	—	2	2	no	—
381	C₄⋊C₄×C₆₁	—	2	2	no	—
382	C₄⋊C₄×C₆₁	—	2	2	no	—
383	C₄⋊C₄×C₆₁	—	2	2	no	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	2	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	—	2	2	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	2	no	—
393	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
406	C₂²⋊C₄×C₆₁	—	2	1	no	—
407	C₂²⋊C₄×C₆₁	—	2	1	no	—
408	C₂²⋊C₄×C₆₁	—	2	2	no	—
409	C₂²⋊C₄×C₆₁	—	2	2	no	—
410	C₂²⋊C₄×C₆₁	—	2	2	no	—
411	C₂²⋊C₄×C₆₁	—	2	2	no	—
412	C₂²⋊C₄×C₆₁	—	2	2	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	—	2	2	no	—
416	C₂²⋊C₄×C₆₁	—	2	2	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
420	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
424	C₄²×C₆₁	—	2	1	no	—
425	C₄²×C₆₁	—	2	1	no	—
426	C₄²×C₆₁	—	2	1	no	—
427	C₄²×C₆₁	—	2	1	no	—
428	C₄²×C₆₁	—	2	2	no	—
429	C₄²×C₆₁	—	2	2	no	—
430	C₄²×C₆₁	—	2	1	no	—
431	C₄²×C₆₁	—	2	1	no	—
432	C₄²×C₆₁	—	2	2	no	—
433	C₄²×C₆₁	—	2	2	no	—
434	C₄²×C₆₁	—	2	2	no	—
435	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
438	C₄²×C₆₁	C₂⁴	1	2	yes	—
439	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
440	C₂³×C₆₁	—	2	2	no	—
441	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
442	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
443	Q₈×C₆₁	—	2	2	no	—
444	Q₈×C₆₁	—	2	1	no	—
445	Q₈×C₆₁	—	2	1	no	—
446	Q₈×C₆₁	—	2	1	no	—
447	Q₈×C₆₁	—	2	1	no	—
448	Q₈×C₆₁	—	2	1	no	—
449	Q₈×C₆₁	—	2	1	no	—
450	Q₈×C₆₁	—	2	1	no	—
451	Q₈×C₆₁	—	4	2	no	—
452	Q₈×C₆₁	—	4	2	no	—
453	Q₈×C₆₁	—	8	1	no	—
454	Q₈×C₆₁	—	8	1	no	—
455	Q₈×C₆₁	—	8	2	no	—
456	Q₈×C₆₁	—	8	1	no	—
457	Q₈×C₆₁	—	8	2	no	—
458	Q₈×C₆₁	2₋¹⁺⁴	1	2	yes	—
459	D₄×C₆₁	—	2	2	no	—
460	D₄×C₆₁	—	2	2	no	—
461	D₄×C₆₁	—	2	2	no	—
462	D₄×C₆₁	—	4	2	no	—
463	D₄×C₆₁	—	4	4	no	—
464	D₄×C₆₁	—	4	4	no	—
465	D₄×C₆₁	—	4	2	no	—
466	D₄×C₆₁	—	8	1	no	—
467	D₄×C₆₁	—	8	2	no	—
468	C₂×C₄×C₆₁	—	2	1	no	—
469	C₂×C₄×C₆₁	—	2	2	no	—
470	C₂×C₄×C₆₁	—	2	1	no	—
471	C₂×C₄×C₆₁	—	2	2	no	—
472	C₂×C₄×C₆₁	—	2	2	no	—
473	C₂×C₄×C₆₁	—	2	1	no	—
474	C₂×C₄×C₆₁	—	2	1	no	—
475	C₂×C₄×C₆₁	—	2	1	no	—
476	C₂×C₄×C₆₁	—	2	2	no	—
477	C₂×C₄×C₆₁	—	2	1	no	—
478	C₂×C₄×C₆₁	—	2	1	no	—
479	C₂×C₄×C₆₁	—	2	2	no	—
480	C₂×C₄×C₆₁	—	2	1	no	—
481	C₂×C₄×C₆₁	—	2	1	no	—
482	C₂×C₄×C₆₁	—	2	2	no	—
483	C₂×C₄×C₆₁	—	2	1	no	—
484	C₂×C₄×C₆₁	—	4	1	no	—
485	C₂×C₄×C₆₁	—	4	4	no	—
486	C₂×C₄×C₆₁	—	4	2	no	—
487	C₂×C₄×C₆₁	—	4	2	no	—
488	C₂×C₄×C₆₁	—	8	2	no	—
489	C₂×C₄×C₆₁	—	8	2	no	—
490	C₂×C₄×C₆₁	—	8	2	no	—
491	C₂×C₄×C₆₁	—	8	2	no	—
492	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
501	C₈×C₆₁	—	2	1	no	—
502	C₈×C₆₁	—	2	1	no	—
503	C₈×C₆₁	—	2	1	no	—
504	C₈×C₆₁	—	2	2	no	—
505	C₈×C₆₁	—	2	2	no	—
506	C₈×C₆₁	—	2	1	no	—
507	#62193	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
508	C₂²×C₆₁	—	2	1	no	—
509	C₂²×C₆₁	—	2	2	no	—
510	C₂²×C₆₁	—	2	1	no	—
511	C₂²×C₆₁	—	2	2	no	—
512	C₂²×C₆₁	—	2	1	no	—
513	C₂²×C₆₁	—	2	2	no	—
514	C₂²×C₆₁	—	4	2	no	—
515	C₂²×C₆₁	—	4	2	no	—
516	C₂²×C₆₁	—	4	2	no	—
517	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
518	C₄×C₆₁	—	2	1	no	—
519	C₄×C₆₁	—	2	1	no	—
520	C₄×C₆₁	—	2	2	no	—
521	C₄×C₆₁	—	2	2	no	—
522	C₄×C₆₁	—	2	1	no	—
523	C₄×C₆₁	—	2	2	no	—
524	C₄×C₆₁	—	2	1	no	—
525	C₄×C₆₁	—	2	2	no	—
526	C₄×C₆₁	—	4	1	no	—
527	C₄×C₆₁	—	4	1	no	—
528	C₄×C₆₁	—	4	2	no	—
529	C₄×C₆₁	—	4	1	no	—
530	C₄×C₆₁	—	4	2	no	—
531	C₄×C₆₁	—	4	1	no	—
532	C₄×C₆₁	—	4	1	no	—
533	C₄×C₆₁	—	4	1	no	—
534	C₄×C₆₁	—	4	1	no	—
535	C₄×C₆₁	—	4	2	no	—
536	C₄×C₆₁	#578	1	2	yes	—
537	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
538	C₄×C₆₁	#585	1	1	yes	characteristic
539	#3555	C₂×C₆₁	1	1	yes	characteristic, complemented
540	#3522	C₂×C₆₁	1	1	yes	characteristic
541	#3387	C₂×C₆₁	1	1	yes	characteristic, complemented
542	Q₈×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#3375	C₂×C₆₁	1	1	yes	characteristic, complemented
544	#3365	C₂×C₆₁	1	1	yes	characteristic, complemented
545	#3356	C₂×C₆₁	1	1	yes	characteristic, complemented
546	#3353	C₂×C₆₁	1	2	yes	complemented
547	#3343	C₂×C₆₁	1	2	yes	complemented
548	#3338	C₂×C₆₁	1	1	yes	characteristic, complemented
549	#3333	C₂×C₆₁	1	1	yes	characteristic, complemented
550	#3327	C₂×C₆₁	1	2	yes	complemented
551	#3313	C₂×C₆₁	1	2	yes	complemented
552	#3304	C₂×C₆₁	1	1	yes	characteristic, complemented
553	#3258	C₂×C₆₁	1	2	yes	complemented
554	#3254	C₂×C₆₁	1	1	yes	characteristic, complemented
555	#3243	C₂×C₆₁	1	2	yes	complemented
556	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
557	#3120	C₂×C₆₁	1	2	yes	complemented
558	#3104	C₂×C₆₁	1	1	yes	characteristic, complemented
559	#3083	C₂×C₆₁	1	2	yes	complemented
560	#3078	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#2993	C₂×C₆₁	1	1	yes	characteristic, complemented
562	C₂×C₆₁	—	4	1	no	—
563	C₂×C₆₁	—	4	2	no	—
564	C₂×C₆₁	—	8	2	no	—
565	C₂×C₆₁	#3489	1	1	yes	characteristic
566	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
567	C₂×C₆₁	#3585	1	1	yes	characteristic
568	#563	—	2	2	no	—
569	#559	—	2	1	no	—
570	#559	C₂²×C₆₁	1	1	yes	characteristic
571	Q₈²	C₂²×C₆₁	1	1	yes	characteristic
572	Q₈²	C₂²×C₆₁	1	1	yes	characteristic
573	#557	—	2	1	no	—
574	#557	C₂²×C₆₁	1	1	yes	characteristic
575	#556	—	2	1	no	—
576	#556	C₂²×C₆₁	1	2	yes	—
577	#556	C₂²×C₆₁	1	1	yes	characteristic
578	#554	—	2	1	no	—
579	#554	C₂²×C₆₁	1	1	yes	characteristic
580	#554	C₂²×C₆₁	1	1	yes	characteristic
581	#552	C₂²×C₆₁	1	2	yes	—
582	#550	C₂²×C₆₁	1	1	yes	characteristic
583	#548	C₂²×C₆₁	1	2	yes	—
584	#547	—	2	2	no	—
585	#547	C₂²×C₆₁	1	2	yes	—
586	#544	C₂²×C₆₁	1	2	yes	—
587	#542	—	2	2	no	—
588	#542	—	2	1	no	—
589	#542	C₂²×C₆₁	1	2	yes	—
590	#541	—	2	2	no	—
591	#541	—	2	1	no	—
592	#541	C₂²×C₆₁	1	2	yes	—
593	#533	C₂²×C₆₁	1	1	yes	characteristic
594	#533	C₂²×C₆₁	1	1	yes	characteristic
595	#532	—	2	1	no	—
596	#532	C₂²×C₆₁	1	1	yes	characteristic
597	#529	—	2	1	no	—
598	#529	C₂²×C₆₁	1	1	yes	characteristic
599	#520	C₂²×C₆₁	1	2	yes	—
600	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
601	#501	C₂²×C₆₁	1	2	yes	—
602	#500	C₂²×C₆₁	1	1	yes	characteristic
603	#500	C₂²×C₆₁	1	2	yes	—
604	#498	C₂²×C₆₁	1	1	yes	characteristic
605	#489	C₂²×C₆₁	1	2	yes	—
606	#488	C₂²×C₆₁	1	2	yes	—
607	#486	C₂²×C₆₁	1	1	yes	characteristic
608	#486	C₂²×C₆₁	1	1	yes	characteristic
609	#485	C₂²×C₆₁	1	2	yes	—
610	#484	C₂²×C₆₁	1	2	yes	—
611	#484	C₂²×C₆₁	1	2	yes	—
612	#484	C₂²×C₆₁	1	1	yes	characteristic
613	#484	C₂²×C₆₁	1	1	yes	characteristic
614	#483	C₂²×C₆₁	1	2	yes	—
615	#482	C₂²×C₆₁	1	2	yes	—
616	#482	C₂²×C₆₁	1	2	yes	—
617	#482	C₂²×C₆₁	1	2	yes	—
618	#480	C₂²×C₆₁	1	2	yes	—
619	#479	C₂²×C₆₁	1	2	yes	—
620	#479	C₂²×C₆₁	1	2	yes	—
621	#479	C₂²×C₆₁	1	2	yes	—
622	#478	C₂²×C₆₁	1	2	yes	—
623	#478	C₂²×C₆₁	1	2	yes	—
624	#478	C₂²×C₆₁	1	2	yes	—
625	#477	C₂²×C₆₁	1	1	yes	characteristic
626	#477	C₂²×C₆₁	1	1	yes	characteristic
627	#477	C₂²×C₆₁	1	1	yes	characteristic
628	#477	C₂²×C₆₁	1	1	yes	characteristic
629	#477	C₂²×C₆₁	1	2	yes	—
630	#477	C₂²×C₆₁	1	2	yes	—
631	#477	C₂²×C₆₁	1	1	yes	characteristic
632	#477	C₂²×C₆₁	1	1	yes	characteristic
633	#475	C₂²×C₆₁	1	1	yes	characteristic
634	#475	C₂²×C₆₁	1	1	yes	characteristic
635	#475	C₂²×C₆₁	1	2	yes	—
636	#474	C₂²×C₆₁	1	2	yes	—
637	#474	C₂²×C₆₁	1	2	yes	—
638	#470	C₂²×C₆₁	1	2	yes	—
639	#468	C₂²×C₆₁	1	2	yes	—
640	#468	C₂²×C₆₁	1	2	yes	—
641	#468	C₂²×C₆₁	1	2	yes	—
642	#467	C₂²×C₆₁	1	2	yes	—
643	#465	C₂²×C₆₁	1	2	yes	—
644	#464	C₂²×C₆₁	1	2	yes	—
645	#464	C₂²×C₆₁	1	2	yes	—
646	#462	C₂²×C₆₁	1	1	yes	characteristic
647	#462	C₂²×C₆₁	1	1	yes	characteristic
648	#461	C₂²×C₆₁	1	2	yes	—
649	#460	C₂²×C₆₁	1	1	yes	characteristic
650	#460	C₂²×C₆₁	1	1	yes	characteristic
651	#452	C₂²×C₆₁	1	2	yes	—
652	#452	C₂²×C₆₁	1	2	yes	—
653	#451	C₂²×C₆₁	1	1	yes	characteristic
654	#451	C₂²×C₆₁	1	1	yes	characteristic
655	#446	C₂²×C₆₁	1	1	yes	characteristic
656	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
657	#441	C₂²×C₆₁	1	2	yes	—
658	#440	C₂²×C₆₁	1	2	yes	—
659	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
660	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
661	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
662	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
663	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
664	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
665	#436	C₂²×C₆₁	1	1	yes	characteristic
666	#436	C₂²×C₆₁	1	2	yes	—
667	#435	C₂²×C₆₁	1	2	yes	—
668	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
669	#433	C₂²×C₆₁	1	2	yes	—
670	#431	C₂²×C₆₁	1	1	yes	characteristic
671	#428	C₂²×C₆₁	1	2	yes	—
672	#428	C₂²×C₆₁	1	2	yes	—
673	C₂×#107	C₂²×C₆₁	1	2	yes	—
674	#424	C₂²×C₆₁	1	2	yes	—
675	#423	C₂²×C₆₁	1	1	yes	characteristic
676	#419	C₂²×C₆₁	1	2	yes	—
677	#417	C₂²×C₆₁	1	2	yes	—
678	#416	C₂²×C₆₁	1	2	yes	—
679	C₆₁	#62193	1	1	yes	characteristic, direct product factor, Sylow
680	C₂×#41	—	2	2	no	—
681	C₂×#41	—	2	1	no	—
682	C₂×#41	C₂³×C₆₁	1	2	yes	—
683	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
684	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
685	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
686	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
687	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
688	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
690	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
691	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
692	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	2	no	—
696	C₄⋊Q₈	—	2	2	no	—
697	C₄⋊Q₈	—	2	1	no	—
698	C₄⋊Q₈	—	2	2	no	—
699	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
705	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
706	#127	—	2	1	no	—
707	#127	C₂³×C₆₁	1	1	yes	characteristic
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	D₄×C₆₁	1	2	yes	—
716	#125	—	2	1	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	1	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	1	no	—
724	#125	D₄×C₆₁	1	1	yes	characteristic
725	#125	C₂³×C₆₁	1	2	yes	—
726	#125	C₂³×C₆₁	1	2	yes	—
727	#124	—	2	1	no	—
728	#124	—	2	1	no	—
729	#124	—	2	2	no	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	—	2	1	no	—
733	#124	D₄×C₆₁	1	1	yes	characteristic
734	#124	C₂³×C₆₁	1	2	yes	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	D₄×C₆₁	1	2	yes	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
752	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
753	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
754	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
757	#121	—	2	2	no	—
758	#121	—	2	1	no	—
759	#121	—	2	2	no	—
760	#121	D₄×C₆₁	1	1	yes	characteristic
761	#121	C₂³×C₆₁	1	2	yes	—
762	#121	C₂³×C₆₁	1	2	yes	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	2	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
775	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
778	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
781	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
782	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	C₂³×C₆₁	1	2	yes	—
792	C₄×D₄	C₂³×C₆₁	1	2	yes	—
793	C₄×D₄	C₂³×C₆₁	1	2	yes	—
794	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
795	#117	—	2	1	no	—
796	#117	—	2	2	no	—
797	#117	—	2	2	no	—
798	#117	C₂³×C₆₁	1	2	yes	—
799	#117	C₂³×C₆₁	1	2	yes	—
800	#117	C₂³×C₆₁	1	2	yes	—
801	C₂×C₄⋊C₄	—	2	1	no	—
802	C₂×C₄⋊C₄	—	2	2	no	—
803	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
804	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
805	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
806	C₂×C₄²	—	2	1	no	—
807	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
808	#107	C₂³×C₆₁	1	1	yes	characteristic
809	#107	C₂³×C₆₁	1	2	yes	—
810	#107	C₂³×C₆₁	1	2	yes	—
811	#107	C₂³×C₆₁	1	2	yes	—
812	#107	C₂³×C₆₁	1	1	yes	characteristic
813	#107	C₂³×C₆₁	1	2	yes	—
814	#107	C₂³×C₆₁	1	2	yes	—
815	#107	C₂³×C₆₁	1	1	yes	characteristic
816	#107	C₂³×C₆₁	1	1	yes	characteristic
817	#107	C₂³×C₆₁	1	2	yes	—
818	#106	C₂³×C₆₁	1	2	yes	—
819	#106	C₂³×C₆₁	1	2	yes	—
820	#106	C₂³×C₆₁	1	2	yes	—
821	#106	C₂³×C₆₁	1	2	yes	—
822	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
823	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
827	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
828	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
829	#103	C₂³×C₆₁	1	1	yes	characteristic
830	#103	C₂³×C₆₁	1	2	yes	—
831	#103	C₂³×C₆₁	1	1	yes	characteristic
832	#103	C₂³×C₆₁	1	2	yes	—
833	#103	C₂³×C₆₁	1	2	yes	—
834	#103	C₂³×C₆₁	1	2	yes	—
835	#103	C₂³×C₆₁	1	1	yes	characteristic
836	#103	C₂³×C₆₁	1	1	yes	characteristic
837	#103	C₂³×C₆₁	1	1	yes	characteristic
838	#103	C₂³×C₆₁	1	1	yes	characteristic
839	#103	C₂³×C₆₁	1	2	yes	—
840	#103	C₂³×C₆₁	1	1	yes	characteristic
841	#103	C₂³×C₆₁	1	1	yes	characteristic
842	#103	C₂³×C₆₁	1	2	yes	—
843	#102	C₂³×C₆₁	1	2	yes	—
844	#102	C₂³×C₆₁	1	2	yes	—
845	#102	C₂³×C₆₁	1	2	yes	—
846	#102	C₂³×C₆₁	1	2	yes	—
847	#102	C₂³×C₆₁	1	2	yes	—
848	#102	C₂³×C₆₁	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
850	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
851	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
852	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
853	#97	C₂³×C₆₁	1	2	yes	—
854	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
855	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
856	C₄×C₈	C₂³×C₆₁	1	2	yes	—
857	#41	—	2	4	no	—
858	#41	—	4	2	no	—
859	#41	—	8	2	no	—
860	#41	—	8	4	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	1	no	—
864	C₂×Q₈	—	2	1	no	—
865	C₂×Q₈	—	2	2	no	—
866	C₂×Q₈	—	2	2	no	—
867	C₂×Q₈	—	2	1	no	—
868	C₂×Q₈	—	2	2	no	—
869	C₂×Q₈	—	4	1	no	—
870	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
871	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
872	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
873	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
874	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	1	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
881	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
882	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
891	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
894	Q₁₆	—	2	2	no	—
895	Q₁₆	—	2	2	no	—
896	Q₁₆	—	4	1	no	—
897	Q₁₆	—	4	1	no	—
898	SD₁₆	—	4	2	no	—
899	SD₁₆	—	4	2	no	—
900	M₁₆	—	4	2	no	—
901	M₁₆	—	4	2	no	—
902	C₂×C₈	—	4	2	no	—
903	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
907	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
908	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
940	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
941	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
949	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
965	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
966	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
967	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
968	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
981	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
982	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
983	C₄²	C₂⁴×C₆₁	1	2	yes	—
984	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
985	C₂³	—	2	2	no	—
986	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
987	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
988	Q₈	—	2	2	no	—
989	Q₈	—	2	1	no	—
990	Q₈	—	2	1	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	1	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	4	2	no	—
997	Q₈	—	4	2	no	—
998	Q₈	—	8	1	no	—
999	Q₈	—	8	1	no	—
1000	Q₈	—	8	2	no	—
1001	Q₈	—	8	1	no	—
1002	Q₈	—	8	2	no	—
1003	Q₈	2₋¹⁺⁴×C₆₁	1	2	yes	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	2	no	—
1007	D₄	—	4	2	no	—
1008	D₄	—	4	4	no	—
1009	D₄	—	4	4	no	—
1010	D₄	—	4	2	no	—
1011	D₄	—	8	1	no	—
1012	D₄	—	8	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	4	1	no	—
1030	C₂×C₄	—	4	4	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	8	2	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1038	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1039	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1041	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1042	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1045	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₈	—	2	2	no	—
1051	C₈	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	1	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	C₆₁×#578	1	2	yes	—
1081	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1082	C₄	C₆₁×#585	1	1	yes	characteristic
1083	C₂	—	4	1	no	—
1084	C₂	—	4	2	no	—
1085	C₂	—	8	2	no	—
1086	C₂	C₆₁×#3489	1	1	yes	characteristic
1087	C₂	C₂×C₆₁×#578	1	1	yes	characteristic
1088	C₂	C₆₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3522	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×#3555	C₂	semidirect
3. C₆₁×#3387	C₂	semidirect
4. Q₈×Q₁₆×C₆₁	C₂	semidirect
5. C₆₁×#3375	C₂	semidirect
6. C₆₁×#3365	C₂	semidirect
7. C₆₁×#3356	C₂	semidirect
8. C₆₁×#3353	C₂	semidirect
9. C₆₁×#3343	C₂	semidirect
10. C₆₁×#3338	C₂	semidirect
11. C₆₁×#3333	C₂	semidirect
12. C₆₁×#3327	C₂	semidirect
13. C₆₁×#3313	C₂	semidirect
14. C₆₁×#3304	C₂	semidirect
15. C₆₁×#3258	C₂	semidirect
16. C₆₁×#3254	C₂	semidirect
17. C₆₁×#3243	C₂	semidirect
18. C₆₁×#3228	C₂	semidirect
19. C₆₁×#3120	C₂	semidirect
20. C₆₁×#3104	C₂	semidirect
21. C₆₁×#3083	C₂	semidirect
22. C₆₁×#3078	C₂	semidirect
23. C₆₁×#2993	C₂	semidirect
507. #62193	C₆₁	direct (N × H)
539. #3555	C₂×C₆₁	semidirect
541. #3387	C₂×C₆₁	semidirect
542. Q₈×Q₁₆	C₂×C₆₁	semidirect
543. #3375	C₂×C₆₁	semidirect
544. #3365	C₂×C₆₁	semidirect
545. #3356	C₂×C₆₁	semidirect
546. #3353	C₂×C₆₁	semidirect
547. #3343	C₂×C₆₁	semidirect
548. #3338	C₂×C₆₁	semidirect
549. #3333	C₂×C₆₁	semidirect
550. #3327	C₂×C₆₁	semidirect
551. #3313	C₂×C₆₁	semidirect
552. #3304	C₂×C₆₁	semidirect
553. #3258	C₂×C₆₁	semidirect
554. #3254	C₂×C₆₁	semidirect
555. #3243	C₂×C₆₁	semidirect
556. #3228	C₂×C₆₁	semidirect
557. #3120	C₂×C₆₁	semidirect
558. #3104	C₂×C₆₁	semidirect
559. #3083	C₂×C₆₁	semidirect
560. #3078	C₂×C₆₁	semidirect
561. #2993	C₂×C₆₁	semidirect
679. C₆₁	#62193	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×#3555	2
C₆₁×#3522	2
C₆₁×#3387	2
Q₈×Q₁₆×C₆₁	2
C₆₁×#3375	2
C₆₁×#3365	2
C₆₁×#3356	2
C₆₁×#3353	2
C₆₁×#3343	2
C₆₁×#3338	2
C₆₁×#3333	2
C₆₁×#3327	2
C₆₁×#3313	2
C₆₁×#3304	2
C₆₁×#3258	2
C₆₁×#3254	2
C₆₁×#3243	2
C₆₁×#3228	2
C₆₁×#3120	2
C₆₁×#3104	2
C₆₁×#3083	2
C₆₁×#3078	2
C₆₁×#2993	2
#62193	61

Subgroups — C61×#62193 #29565626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62193 #29565626