Subgroups — C₆₁×#62139 #29565572

Order 15616.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3515	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3346	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3344	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3320	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3312	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3248	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3236	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3117	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₆₁×#479	C₂	1	2	yes	maximal, complemented
23	C₆₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈²×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#557	—	2	1	no	—
26	C₆₁×#557	C₂²	1	1	yes	characteristic
27	C₆₁×#557	C₂²	1	1	yes	characteristic
28	C₆₁×#554	—	2	2	no	—
29	C₆₁×#554	—	2	1	no	—
30	C₆₁×#554	C₂²	1	1	yes	characteristic
31	C₆₁×#554	C₂²	1	1	yes	characteristic
32	C₆₁×#554	C₂²	1	1	yes	characteristic
33	C₆₁×#554	C₂²	1	2	yes	—
34	C₆₁×#553	C₂²	1	2	yes	—
35	C₆₁×#552	—	2	2	no	—
36	C₆₁×#552	—	2	1	no	—
37	C₆₁×#552	C₂²	1	2	yes	—
38	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
40	C₆₁×#547	—	2	1	no	—
41	C₆₁×#547	C₂²	1	1	yes	characteristic
42	C₆₁×#541	—	2	1	no	—
43	C₆₁×#539	—	2	2	no	—
44	C₆₁×#533	—	2	2	no	—
45	C₆₁×#533	—	2	1	no	—
46	C₆₁×#533	C₂²	1	1	yes	characteristic
47	C₆₁×#533	C₂²	1	2	yes	—
48	C₆₁×#533	C₂²	1	1	yes	characteristic
49	C₆₁×#529	C₂²	1	1	yes	characteristic
50	C₆₁×#529	C₂²	1	2	yes	—
51	C₂×#125×C₆₁	C₂²	1	2	yes	—
52	C₆₁×#520	—	2	1	no	—
53	C₄×#41×C₆₁	—	2	1	no	—
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#501	C₂²	1	2	yes	—
58	C₆₁×#501	C₂²	1	2	yes	—
59	C₆₁×#500	C₂²	1	1	yes	characteristic
60	C₆₁×#498	C₂²	1	1	yes	characteristic
61	C₆₁×#491	C₂²	1	2	yes	—
62	C₆₁×#491	C₂²	1	2	yes	—
63	C₆₁×#487	C₂²	1	1	yes	characteristic
64	C₆₁×#487	C₂²	1	1	yes	characteristic
65	C₆₁×#485	C₂²	1	2	yes	—
66	C₆₁×#485	C₂²	1	2	yes	—
67	C₆₁×#484	C₂²	1	2	yes	—
68	C₆₁×#484	C₂²	1	2	yes	—
69	C₆₁×#484	C₂²	1	2	yes	—
70	C₆₁×#483	C₂²	1	2	yes	—
71	C₆₁×#483	C₂²	1	2	yes	—
72	C₆₁×#483	C₂²	1	1	yes	characteristic
73	C₆₁×#481	C₂²	1	2	yes	—
74	C₆₁×#480	C₂²	1	1	yes	characteristic
75	C₆₁×#479	C₂²	1	2	yes	—
76	C₆₁×#479	C₂²	1	2	yes	—
77	C₆₁×#479	C₂²	1	1	yes	characteristic
78	C₆₁×#479	C₂²	1	2	yes	—
79	C₆₁×#479	C₂²	1	2	yes	—
80	C₆₁×#479	C₂²	1	2	yes	—
81	C₆₁×#479	C₂²	1	2	yes	—
82	C₆₁×#479	C₂²	1	2	yes	—
83	C₆₁×#479	C₂²	1	2	yes	—
84	C₆₁×#479	C₂²	1	1	yes	characteristic
85	C₆₁×#479	C₂²	1	2	yes	—
86	C₆₁×#477	C₂²	1	1	yes	characteristic
87	C₆₁×#477	C₂²	1	1	yes	characteristic
88	C₆₁×#477	C₂²	1	1	yes	characteristic
89	C₆₁×#476	C₂²	1	1	yes	characteristic
90	C₆₁×#475	C₂²	1	1	yes	characteristic
91	C₆₁×#475	C₂²	1	1	yes	characteristic
92	C₆₁×#475	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×#467	C₂²	1	2	yes	—
97	C₆₁×#467	C₂²	1	2	yes	—
98	C₆₁×#465	C₂²	1	2	yes	—
99	C₆₁×#465	C₂²	1	2	yes	—
100	C₆₁×#464	C₂²	1	1	yes	characteristic
101	C₆₁×#464	C₂²	1	1	yes	characteristic
102	C₆₁×#464	C₂²	1	2	yes	—
103	C₆₁×#462	C₂²	1	1	yes	characteristic
104	C₆₁×#462	C₂²	1	2	yes	—
105	C₆₁×#461	C₂²	1	1	yes	characteristic
106	C₆₁×#461	C₂²	1	2	yes	—
107	C₆₁×#451	C₂²	1	2	yes	—
108	C₆₁×#451	C₂²	1	1	yes	characteristic
109	C₆₁×#448	C₂²	1	2	yes	—
110	C₆₁×#448	C₂²	1	1	yes	characteristic
111	C₆₁×#446	C₂²	1	1	yes	characteristic
112	C₆₁×#446	C₂²	1	1	yes	characteristic
113	C₆₁×#441	C₂²	1	2	yes	—
114	C₆₁×#441	C₂²	1	2	yes	—
115	C₆₁×#440	C₂²	1	2	yes	—
116	C₆₁×#440	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
118	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
121	C₆₁×#435	C₂²	1	2	yes	—
122	C₆₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
125	C₆₁×#432	C₂²	1	2	yes	—
126	C₆₁×#431	C₂²	1	1	yes	characteristic
127	C₆₁×#428	C₂²	1	2	yes	—
128	C₂×#107×C₆₁	C₂²	1	2	yes	—
129	C₂×#106×C₆₁	C₂²	1	2	yes	—
130	C₆₁×#423	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
132	C₆₁×#419	C₂²	1	2	yes	—
133	C₂×#103×C₆₁	C₂²	1	2	yes	—
134	C₂×#103×C₆₁	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
137	C₂²×Q₈×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	2	yes	—
142	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂²×C₈×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	1	no	—
152	C₄⋊Q₈×C₆₁	—	2	2	no	—
153	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	—	2	2	no	—
161	#126×C₆₁	—	2	2	no	—
162	#126×C₆₁	—	2	1	no	—
163	#125×C₆₁	—	2	1	no	—
164	#125×C₆₁	—	2	2	no	—
165	#125×C₆₁	—	2	1	no	—
166	#125×C₆₁	—	2	2	no	—
167	#125×C₆₁	—	2	2	no	—
168	#125×C₆₁	—	2	2	no	—
169	#125×C₆₁	—	2	1	no	—
170	#125×C₆₁	—	2	1	no	—
171	#125×C₆₁	—	2	2	no	—
172	#125×C₆₁	—	2	2	no	—
173	#125×C₆₁	—	2	2	no	—
174	#125×C₆₁	C₂³	1	2	yes	—
175	#125×C₆₁	C₂³	1	2	yes	—
176	#125×C₆₁	C₂³	1	2	yes	—
177	#125×C₆₁	C₂³	1	1	yes	characteristic
178	#124×C₆₁	C₂³	1	1	yes	characteristic
179	#123×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	1	no	—
181	#123×C₆₁	—	2	2	no	—
182	#123×C₆₁	—	2	2	no	—
183	#123×C₆₁	—	2	2	no	—
184	C₂²⋊Q₈×C₆₁	—	2	1	no	—
185	C₂²⋊Q₈×C₆₁	—	2	1	no	—
186	C₂²⋊Q₈×C₆₁	—	2	1	no	—
187	C₂²⋊Q₈×C₆₁	—	2	2	no	—
188	C₂²⋊Q₈×C₆₁	—	2	1	no	—
189	C₂²⋊Q₈×C₆₁	—	2	2	no	—
190	C₂²⋊Q₈×C₆₁	—	2	1	no	—
191	C₂²⋊Q₈×C₆₁	—	2	2	no	—
192	C₂²⋊Q₈×C₆₁	—	2	2	no	—
193	C₂²⋊Q₈×C₆₁	—	2	2	no	—
194	C₂²⋊Q₈×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	—	2	2	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	2	no	—
198	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
202	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
203	#121×C₆₁	—	2	2	no	—
204	#121×C₆₁	C₂³	1	2	yes	—
205	#121×C₆₁	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₆₁	—	2	1	no	—
207	C₄×Q₈×C₆₁	—	2	1	no	—
208	C₄×Q₈×C₆₁	—	2	1	no	—
209	C₄×Q₈×C₆₁	—	2	2	no	—
210	C₄×Q₈×C₆₁	—	2	1	no	—
211	C₄×Q₈×C₆₁	—	2	2	no	—
212	C₄×Q₈×C₆₁	—	2	1	no	—
213	C₄×Q₈×C₆₁	—	2	1	no	—
214	C₄×Q₈×C₆₁	—	2	1	no	—
215	C₄×Q₈×C₆₁	—	2	1	no	—
216	C₄×Q₈×C₆₁	—	2	2	no	—
217	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
218	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₆₁	—	2	1	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	—	2	1	no	—
231	C₄×D₄×C₆₁	—	2	2	no	—
232	C₄×D₄×C₆₁	—	2	1	no	—
233	C₄×D₄×C₆₁	—	2	2	no	—
234	C₄×D₄×C₆₁	—	2	1	no	—
235	C₄×D₄×C₆₁	—	2	2	no	—
236	C₄×D₄×C₆₁	D₄	1	2	yes	—
237	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
238	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₆₁	C₂³	1	2	yes	—
240	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₁	C₂³	1	2	yes	—
242	#117×C₆₁	—	2	2	no	—
243	#117×C₆₁	—	2	1	no	—
244	#117×C₆₁	—	2	2	no	—
245	#117×C₆₁	—	2	1	no	—
246	#117×C₆₁	—	2	2	no	—
247	#117×C₆₁	D₄	1	1	yes	characteristic
248	#117×C₆₁	D₄	1	2	yes	—
249	#117×C₆₁	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
251	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
252	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₆₁	—	2	2	no	—
260	C₂×C₄²×C₆₁	—	2	1	no	—
261	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
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	2	yes	—
268	#107×C₆₁	C₂³	1	1	yes	characteristic
269	#107×C₆₁	C₂³	1	2	yes	—
270	#106×C₆₁	C₂³	1	1	yes	characteristic
271	#106×C₆₁	C₂³	1	2	yes	—
272	#106×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	2	yes	—
275	#106×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	2	yes	—
277	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
279	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
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	#103×C₆₁	C₂³	1	1	yes	characteristic
285	#103×C₆₁	C₂³	1	1	yes	characteristic
286	#103×C₆₁	C₂³	1	2	yes	—
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	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	2	yes	—
293	#103×C₆₁	C₂³	1	2	yes	—
294	#103×C₆₁	C₂³	1	1	yes	characteristic
295	#103×C₆₁	C₂³	1	1	yes	characteristic
296	#103×C₆₁	C₂³	1	1	yes	characteristic
297	#103×C₆₁	C₂³	1	1	yes	characteristic
298	#103×C₆₁	C₂³	1	2	yes	—
299	#103×C₆₁	C₂³	1	2	yes	—
300	#103×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	1	yes	characteristic
302	#102×C₆₁	C₂³	1	1	yes	characteristic
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	#97×C₆₁	C₂³	1	2	yes	—
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
312	#41×C₆₁	—	2	4	no	—
313	#41×C₆₁	—	4	4	no	—
314	C₂×Q₈×C₆₁	—	2	1	no	—
315	C₂×Q₈×C₆₁	—	2	2	no	—
316	C₂×Q₈×C₆₁	—	2	1	no	—
317	C₂×Q₈×C₆₁	—	2	1	no	—
318	C₂×Q₈×C₆₁	—	2	2	no	—
319	C₂×Q₈×C₆₁	—	2	1	no	—
320	C₂×Q₈×C₆₁	—	2	4	no	—
321	C₂×Q₈×C₆₁	—	2	2	no	—
322	C₂×Q₈×C₆₁	—	4	2	no	—
323	C₂×Q₈×C₆₁	—	4	1	no	—
324	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
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×D₄×C₆₁	—	2	2	no	—
330	C₂×D₄×C₆₁	—	2	1	no	—
331	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
332	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₆₁	—	2	1	no	—
335	C₂²×C₄×C₆₁	—	2	2	no	—
336	C₂²×C₄×C₆₁	—	2	2	no	—
337	C₂²×C₄×C₆₁	—	2	1	no	—
338	C₂²×C₄×C₆₁	—	2	2	no	—
339	C₂²×C₄×C₆₁	—	2	2	no	—
340	C₂²×C₄×C₆₁	—	2	1	no	—
341	C₂²×C₄×C₆₁	—	2	2	no	—
342	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
343	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
345	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
348	Q₁₆×C₆₁	—	2	2	no	—
349	Q₁₆×C₆₁	—	4	1	no	—
350	Q₁₆×C₆₁	—	4	2	no	—
351	SD₁₆×C₆₁	—	2	2	no	—
352	SD₁₆×C₆₁	—	4	1	no	—
353	SD₁₆×C₆₁	—	4	2	no	—
354	M₁₆×C₆₁	—	4	2	no	—
355	C₂×C₈×C₆₁	—	4	2	no	—
356	C₂×C₈×C₆₁	—	4	2	no	—
357	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
362	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₆₁	—	2	1	no	—
364	C₄⋊C₄×C₆₁	—	2	2	no	—
365	C₄⋊C₄×C₆₁	—	2	1	no	—
366	C₄⋊C₄×C₆₁	—	2	1	no	—
367	C₄⋊C₄×C₆₁	—	2	2	no	—
368	C₄⋊C₄×C₆₁	—	2	1	no	—
369	C₄⋊C₄×C₆₁	—	2	2	no	—
370	C₄⋊C₄×C₆₁	—	2	2	no	—
371	C₄⋊C₄×C₆₁	—	2	2	no	—
372	C₄⋊C₄×C₆₁	—	2	1	no	—
373	C₄⋊C₄×C₆₁	—	2	2	no	—
374	C₄⋊C₄×C₆₁	—	2	1	no	—
375	C₄⋊C₄×C₆₁	—	2	2	no	—
376	C₄⋊C₄×C₆₁	—	2	1	no	—
377	C₄⋊C₄×C₆₁	—	2	2	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	1	no	—
384	C₄⋊C₄×C₆₁	—	2	2	no	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	2	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	2	no	—
389	C₄⋊C₄×C₆₁	—	2	2	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	—	2	2	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
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	1	no	—
414	C₂²⋊C₄×C₆₁	—	2	1	no	—
415	C₂²⋊C₄×C₆₁	—	2	1	no	—
416	C₂²⋊C₄×C₆₁	—	2	1	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₂²⋊C₄×C₆₁	—	2	1	no	—
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	C₄²×C₆₁	—	2	1	no	—
424	C₄²×C₆₁	—	2	2	no	—
425	C₄²×C₆₁	—	2	1	no	—
426	C₄²×C₆₁	—	2	2	no	—
427	C₄²×C₆₁	—	2	1	no	—
428	C₄²×C₆₁	—	2	2	no	—
429	C₄²×C₆₁	—	2	1	no	—
430	C₄²×C₆₁	—	2	2	no	—
431	C₄²×C₆₁	—	2	2	no	—
432	C₄²×C₆₁	—	2	1	no	—
433	C₄²×C₆₁	C₂×D₄	1	2	yes	—
434	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₆₁	C₂×D₄	1	2	yes	—
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	1	no	—
441	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
442	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
443	Q₈×C₆₁	—	2	2	no	—
444	Q₈×C₆₁	—	2	1	no	—
445	Q₈×C₆₁	—	2	1	no	—
446	Q₈×C₆₁	—	2	2	no	—
447	Q₈×C₆₁	—	2	1	no	—
448	Q₈×C₆₁	—	2	1	no	—
449	Q₈×C₆₁	—	2	2	no	—
450	Q₈×C₆₁	—	2	1	no	—
451	Q₈×C₆₁	—	4	4	no	—
452	Q₈×C₆₁	—	4	2	no	—
453	Q₈×C₆₁	—	4	2	no	—
454	Q₈×C₆₁	—	8	2	no	—
455	Q₈×C₆₁	—	8	1	no	—
456	Q₈×C₆₁	—	8	1	no	—
457	Q₈×C₆₁	2₋¹⁺⁴	1	2	yes	—
458	D₄×C₆₁	—	2	4	no	—
459	D₄×C₆₁	—	2	1	no	—
460	D₄×C₆₁	—	2	1	no	—
461	D₄×C₆₁	—	4	4	no	—
462	D₄×C₆₁	—	8	1	no	—
463	D₄×C₆₁	#137	1	4	yes	—
464	C₂×C₄×C₆₁	—	2	4	no	—
465	C₂×C₄×C₆₁	—	2	1	no	—
466	C₂×C₄×C₆₁	—	2	2	no	—
467	C₂×C₄×C₆₁	—	2	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	1	no	—
472	C₂×C₄×C₆₁	—	2	1	no	—
473	C₂×C₄×C₆₁	—	2	2	no	—
474	C₂×C₄×C₆₁	—	2	1	no	—
475	C₂×C₄×C₆₁	—	2	2	no	—
476	C₂×C₄×C₆₁	—	2	2	no	—
477	C₂×C₄×C₆₁	—	2	1	no	—
478	C₂×C₄×C₆₁	—	2	2	no	—
479	C₂×C₄×C₆₁	—	2	1	no	—
480	C₂×C₄×C₆₁	—	2	1	no	—
481	C₂×C₄×C₆₁	—	4	2	no	—
482	C₂×C₄×C₆₁	—	4	1	no	—
483	C₂×C₄×C₆₁	—	4	4	no	—
484	C₂×C₄×C₆₁	—	4	2	no	—
485	C₂×C₄×C₆₁	—	4	4	no	—
486	C₂×C₄×C₆₁	—	4	2	no	—
487	C₂×C₄×C₆₁	—	8	2	no	—
488	C₂×C₄×C₆₁	—	8	2	no	—
489	C₂×C₄×C₆₁	—	8	1	no	—
490	C₂×C₄×C₆₁	—	8	2	no	—
491	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
500	C₈×C₆₁	—	2	1	no	—
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	#62139	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
507	C₂²×C₆₁	—	2	2	no	—
508	C₂²×C₆₁	—	2	2	no	—
509	C₂²×C₆₁	—	2	1	no	—
510	C₂²×C₆₁	—	2	1	no	—
511	C₂²×C₆₁	—	2	1	no	—
512	C₂²×C₆₁	—	4	1	no	—
513	C₂²×C₆₁	—	4	1	no	—
514	C₂²×C₆₁	—	4	1	no	—
515	C₂²×C₆₁	C₂×#137	1	4	yes	—
516	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
517	C₄×C₆₁	—	2	1	no	—
518	C₄×C₆₁	—	2	2	no	—
519	C₄×C₆₁	—	2	1	no	—
520	C₄×C₆₁	—	2	2	no	—
521	C₄×C₆₁	—	2	1	no	—
522	C₄×C₆₁	—	2	2	no	—
523	C₄×C₆₁	—	2	1	no	—
524	C₄×C₆₁	—	2	2	no	—
525	C₄×C₆₁	—	4	1	no	—
526	C₄×C₆₁	—	4	1	no	—
527	C₄×C₆₁	—	4	2	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	2	no	—
535	C₄×C₆₁	C₂×#137	1	2	yes	—
536	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
537	C₄×C₆₁	#585	1	1	yes	characteristic
538	#3515	C₂×C₆₁	1	1	yes	characteristic
539	Q₈×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
540	#3387	C₂×C₆₁	1	1	yes	characteristic, complemented
541	#3385	C₂×C₆₁	1	1	yes	characteristic, complemented
542	#3374	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#3372	C₂×C₆₁	1	1	yes	characteristic, complemented
544	#3346	C₂×C₆₁	1	2	yes	complemented
545	#3344	C₂×C₆₁	1	2	yes	complemented
546	#3338	C₂×C₆₁	1	1	yes	characteristic, complemented
547	#3335	C₂×C₆₁	1	1	yes	characteristic, complemented
548	#3320	C₂×C₆₁	1	2	yes	complemented
549	#3312	C₂×C₆₁	1	2	yes	complemented
550	#3299	C₂×C₆₁	1	1	yes	characteristic, complemented
551	#3298	C₂×C₆₁	1	1	yes	characteristic, complemented
552	#3252	C₂×C₆₁	1	1	yes	characteristic, complemented
553	#3248	C₂×C₆₁	1	2	yes	complemented
554	#3236	C₂×C₆₁	1	2	yes	complemented
555	#3231	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#3117	C₂×C₆₁	1	2	yes	complemented
557	#3108	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#3078	C₂×C₆₁	1	1	yes	characteristic, complemented
559	C₂×#479	C₂×C₆₁	1	2	yes	complemented
560	#2990	C₂×C₆₁	1	1	yes	characteristic, complemented
561	C₂×C₆₁	—	2	4	no	—
562	C₂×C₆₁	—	4	1	no	—
563	C₂×C₆₁	—	8	1	no	—
564	C₂×C₆₁	#3489	1	1	yes	characteristic
565	C₂×C₆₁	C₂²×#137	1	1	yes	characteristic
566	C₂×C₆₁	#3584	1	1	yes	characteristic
567	Q₈²	C₂²×C₆₁	1	1	yes	characteristic
568	#557	—	2	1	no	—
569	#557	C₂²×C₆₁	1	1	yes	characteristic
570	#557	C₂²×C₆₁	1	1	yes	characteristic
571	#554	—	2	1	no	—
572	#554	—	2	2	no	—
573	#554	C₂²×C₆₁	1	1	yes	characteristic
574	#554	C₂²×C₆₁	1	1	yes	characteristic
575	#554	C₂²×C₆₁	1	1	yes	characteristic
576	#554	C₂²×C₆₁	1	2	yes	—
577	#553	C₂²×C₆₁	1	2	yes	—
578	#552	—	2	2	no	—
579	#552	—	2	1	no	—
580	#552	C₂²×C₆₁	1	2	yes	—
581	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
582	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
583	#547	—	2	1	no	—
584	#547	C₂²×C₆₁	1	1	yes	characteristic
585	#541	—	2	1	no	—
586	#539	—	2	2	no	—
587	#533	—	2	2	no	—
588	#533	—	2	1	no	—
589	#533	C₂²×C₆₁	1	1	yes	characteristic
590	#533	C₂²×C₆₁	1	2	yes	—
591	#533	C₂²×C₆₁	1	1	yes	characteristic
592	#529	C₂²×C₆₁	1	1	yes	characteristic
593	#529	C₂²×C₆₁	1	2	yes	—
594	C₂×#125	C₂²×C₆₁	1	2	yes	—
595	#520	—	2	1	no	—
596	C₄×#41	—	2	1	no	—
597	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
598	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
599	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
600	#501	C₂²×C₆₁	1	2	yes	—
601	#501	C₂²×C₆₁	1	2	yes	—
602	#500	C₂²×C₆₁	1	1	yes	characteristic
603	#498	C₂²×C₆₁	1	1	yes	characteristic
604	#491	C₂²×C₆₁	1	2	yes	—
605	#491	C₂²×C₆₁	1	2	yes	—
606	#487	C₂²×C₆₁	1	1	yes	characteristic
607	#487	C₂²×C₆₁	1	1	yes	characteristic
608	#485	C₂²×C₆₁	1	2	yes	—
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	2	yes	—
613	#483	C₂²×C₆₁	1	2	yes	—
614	#483	C₂²×C₆₁	1	1	yes	characteristic
615	#483	C₂²×C₆₁	1	2	yes	—
616	#481	C₂²×C₆₁	1	2	yes	—
617	#480	C₂²×C₆₁	1	1	yes	characteristic
618	#479	C₂²×C₆₁	1	1	yes	characteristic
619	#479	C₂²×C₆₁	1	2	yes	—
620	#479	C₂²×C₆₁	1	2	yes	—
621	#479	C₂²×C₆₁	1	2	yes	—
622	#479	C₂²×C₆₁	1	2	yes	—
623	#479	C₂²×C₆₁	1	2	yes	—
624	#479	C₂²×C₆₁	1	2	yes	—
625	#479	C₂²×C₆₁	1	2	yes	—
626	#479	C₂²×C₆₁	1	2	yes	—
627	#479	C₂²×C₆₁	1	1	yes	characteristic
628	#479	C₂²×C₆₁	1	2	yes	—
629	#477	C₂²×C₆₁	1	1	yes	characteristic
630	#477	C₂²×C₆₁	1	1	yes	characteristic
631	#477	C₂²×C₆₁	1	1	yes	characteristic
632	#476	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	#470	C₂²×C₆₁	1	2	yes	—
638	#468	C₂²×C₆₁	1	2	yes	—
639	#467	C₂²×C₆₁	1	2	yes	—
640	#467	C₂²×C₆₁	1	2	yes	—
641	#465	C₂²×C₆₁	1	2	yes	—
642	#465	C₂²×C₆₁	1	2	yes	—
643	#464	C₂²×C₆₁	1	1	yes	characteristic
644	#464	C₂²×C₆₁	1	1	yes	characteristic
645	#464	C₂²×C₆₁	1	2	yes	—
646	#462	C₂²×C₆₁	1	2	yes	—
647	#462	C₂²×C₆₁	1	1	yes	characteristic
648	#461	C₂²×C₆₁	1	2	yes	—
649	#461	C₂²×C₆₁	1	1	yes	characteristic
650	#451	C₂²×C₆₁	1	1	yes	characteristic
651	#451	C₂²×C₆₁	1	2	yes	—
652	#448	C₂²×C₆₁	1	1	yes	characteristic
653	#448	C₂²×C₆₁	1	2	yes	—
654	#446	C₂²×C₆₁	1	1	yes	characteristic
655	#446	C₂²×C₆₁	1	1	yes	characteristic
656	#441	C₂²×C₆₁	1	2	yes	—
657	#441	C₂²×C₆₁	1	2	yes	—
658	#440	C₂²×C₆₁	1	2	yes	—
659	#440	C₂²×C₆₁	1	2	yes	—
660	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
661	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
662	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
663	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
664	#435	C₂²×C₆₁	1	2	yes	—
665	#435	C₂²×C₆₁	1	2	yes	—
666	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
667	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
668	#432	C₂²×C₆₁	1	2	yes	—
669	#431	C₂²×C₆₁	1	1	yes	characteristic
670	#428	C₂²×C₆₁	1	2	yes	—
671	C₂×#107	C₂²×C₆₁	1	2	yes	—
672	C₂×#106	C₂²×C₆₁	1	2	yes	—
673	#423	C₂²×C₆₁	1	1	yes	characteristic
674	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
675	#419	C₂²×C₆₁	1	2	yes	—
676	C₂×#103	C₂²×C₆₁	1	2	yes	—
677	C₂×#103	C₂²×C₆₁	1	2	yes	—
678	C₆₁	#62139	1	1	yes	characteristic, direct product factor, Sylow
679	C₂×#41	—	2	1	no	—
680	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
681	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
682	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
683	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
684	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
685	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
687	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
688	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
689	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
690	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
691	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	2	no	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	2	no	—
697	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
699	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	1	no	—
707	#125	—	2	1	no	—
708	#125	—	2	2	no	—
709	#125	—	2	1	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	1	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	1	no	—
717	#125	—	2	2	no	—
718	#125	C₂³×C₆₁	1	1	yes	characteristic
719	#125	C₂³×C₆₁	1	2	yes	—
720	#125	C₂³×C₆₁	1	2	yes	—
721	#125	C₂³×C₆₁	1	2	yes	—
722	#124	C₂³×C₆₁	1	1	yes	characteristic
723	#123	—	2	2	no	—
724	#123	—	2	1	no	—
725	#123	—	2	2	no	—
726	#123	—	2	2	no	—
727	#123	—	2	2	no	—
728	C₂²⋊Q₈	—	2	1	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
743	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
744	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
745	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
746	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
747	#121	—	2	2	no	—
748	#121	C₂³×C₆₁	1	2	yes	—
749	#121	C₂³×C₆₁	1	1	yes	characteristic
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	2	no	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	2	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	2	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
763	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
764	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
767	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
769	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
770	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
781	C₄×D₄	D₄×C₆₁	1	2	yes	—
782	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
783	C₄×D₄	C₂³×C₆₁	1	2	yes	—
784	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
785	C₄×D₄	C₂³×C₆₁	1	2	yes	—
786	#117	—	2	2	no	—
787	#117	—	2	1	no	—
788	#117	—	2	2	no	—
789	#117	—	2	1	no	—
790	#117	—	2	2	no	—
791	#117	D₄×C₆₁	1	1	yes	characteristic
792	#117	D₄×C₆₁	1	2	yes	—
793	#117	C₂³×C₆₁	1	2	yes	—
794	C₂×C₄⋊C₄	—	2	2	no	—
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄⋊C₄	—	2	2	no	—
797	C₂×C₄⋊C₄	—	2	2	no	—
798	C₂×C₄⋊C₄	—	2	1	no	—
799	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
800	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
802	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
803	C₂×C₄²	—	2	2	no	—
804	C₂×C₄²	—	2	1	no	—
805	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
806	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
807	#107	C₂³×C₆₁	1	1	yes	characteristic
808	#107	C₂³×C₆₁	1	2	yes	—
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	#106	C₂³×C₆₁	1	1	yes	characteristic
815	#106	C₂³×C₆₁	1	2	yes	—
816	#106	C₂³×C₆₁	1	2	yes	—
817	#106	C₂³×C₆₁	1	2	yes	—
818	#106	C₂³×C₆₁	1	2	yes	—
819	#106	C₂³×C₆₁	1	1	yes	characteristic
820	#106	C₂³×C₆₁	1	2	yes	—
821	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
823	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
824	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
825	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
828	#103	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	2	yes	—
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	2	yes	—
836	#103	C₂³×C₆₁	1	2	yes	—
837	#103	C₂³×C₆₁	1	2	yes	—
838	#103	C₂³×C₆₁	1	1	yes	characteristic
839	#103	C₂³×C₆₁	1	1	yes	characteristic
840	#103	C₂³×C₆₁	1	1	yes	characteristic
841	#103	C₂³×C₆₁	1	1	yes	characteristic
842	#103	C₂³×C₆₁	1	2	yes	—
843	#103	C₂³×C₆₁	1	2	yes	—
844	#103	C₂³×C₆₁	1	2	yes	—
845	#102	C₂³×C₆₁	1	1	yes	characteristic
846	#102	C₂³×C₆₁	1	1	yes	characteristic
847	#102	C₂³×C₆₁	1	2	yes	—
848	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
849	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
850	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
851	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
852	#97	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	#41	—	2	4	no	—
857	#41	—	4	4	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	1	no	—
864	C₂×Q₈	—	2	4	no	—
865	C₂×Q₈	—	2	2	no	—
866	C₂×Q₈	—	4	2	no	—
867	C₂×Q₈	—	4	1	no	—
868	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
869	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
870	C₂×Q₈	C₂⁴×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×D₄	—	2	2	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
876	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
877	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
887	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
888	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
889	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
891	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
892	Q₁₆	—	2	2	no	—
893	Q₁₆	—	4	1	no	—
894	Q₁₆	—	4	2	no	—
895	SD₁₆	—	2	2	no	—
896	SD₁₆	—	4	1	no	—
897	SD₁₆	—	4	2	no	—
898	M₁₆	—	4	2	no	—
899	C₂×C₈	—	4	2	no	—
900	C₂×C₈	—	4	2	no	—
901	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
906	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
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	1	yes	characteristic
944	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
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	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
952	C₂²⋊C₄	—	2	2	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	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	1	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	C₄²	—	2	1	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	1	no	—
977	C₄²	C₂×D₄×C₆₁	1	2	yes	—
978	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
979	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
980	C₄²	C₂×D₄×C₆₁	1	2	yes	—
981	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
982	C₄²	C₂⁴×C₆₁	1	2	yes	—
983	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
984	C₂³	—	2	1	no	—
985	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
986	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
987	Q₈	—	2	2	no	—
988	Q₈	—	2	1	no	—
989	Q₈	—	2	1	no	—
990	Q₈	—	2	2	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	1	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	4	4	no	—
996	Q₈	—	4	2	no	—
997	Q₈	—	4	2	no	—
998	Q₈	—	8	2	no	—
999	Q₈	—	8	1	no	—
1000	Q₈	—	8	1	no	—
1001	Q₈	2₋¹⁺⁴×C₆₁	1	2	yes	—
1002	D₄	—	2	4	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	2	1	no	—
1005	D₄	—	4	4	no	—
1006	D₄	—	8	1	no	—
1007	D₄	#137×C₆₁	1	4	yes	—
1008	C₂×C₄	—	2	4	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	4	1	no	—
1027	C₂×C₄	—	4	4	no	—
1028	C₂×C₄	—	4	2	no	—
1029	C₂×C₄	—	4	4	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	1	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1037	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1040	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1041	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1042	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1043	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	2	no	—
1049	C₈	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	C₂×#137×C₆₁	1	4	yes	—
1059	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1060	C₄	—	2	1	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	2	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	C₂×#137×C₆₁	1	2	yes	—
1079	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1080	C₄	C₆₁×#585	1	1	yes	characteristic
1081	C₂	—	2	4	no	—
1082	C₂	—	4	1	no	—
1083	C₂	—	8	1	no	—
1084	C₂	C₆₁×#3489	1	1	yes	characteristic
1085	C₂	C₂²×#137×C₆₁	1	1	yes	characteristic
1086	C₂	C₆₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3515	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×#41×C₆₁	C₂	semidirect
3. C₆₁×#3387	C₂	semidirect
4. C₆₁×#3385	C₂	semidirect
5. C₆₁×#3374	C₂	semidirect
6. C₆₁×#3372	C₂	semidirect
7. C₆₁×#3346	C₂	semidirect
8. C₆₁×#3344	C₂	semidirect
9. C₆₁×#3338	C₂	semidirect
10. C₆₁×#3335	C₂	semidirect
11. C₆₁×#3320	C₂	semidirect
12. C₆₁×#3312	C₂	semidirect
13. C₆₁×#3299	C₂	semidirect
14. C₆₁×#3298	C₂	semidirect
15. C₆₁×#3252	C₂	semidirect
16. C₆₁×#3248	C₂	semidirect
17. C₆₁×#3236	C₂	semidirect
18. C₆₁×#3231	C₂	semidirect
19. C₆₁×#3117	C₂	semidirect
20. C₆₁×#3108	C₂	semidirect
21. C₆₁×#3078	C₂	semidirect
22. C₂×C₆₁×#479	C₂	semidirect
23. C₆₁×#2990	C₂	semidirect
506. #62139	C₆₁	direct (N × H)
539. Q₈×#41	C₂×C₆₁	semidirect
540. #3387	C₂×C₆₁	semidirect
541. #3385	C₂×C₆₁	semidirect
542. #3374	C₂×C₆₁	semidirect
543. #3372	C₂×C₆₁	semidirect
544. #3346	C₂×C₆₁	semidirect
545. #3344	C₂×C₆₁	semidirect
546. #3338	C₂×C₆₁	semidirect
547. #3335	C₂×C₆₁	semidirect
548. #3320	C₂×C₆₁	semidirect
549. #3312	C₂×C₆₁	semidirect
550. #3299	C₂×C₆₁	semidirect
551. #3298	C₂×C₆₁	semidirect
552. #3252	C₂×C₆₁	semidirect
553. #3248	C₂×C₆₁	semidirect
554. #3236	C₂×C₆₁	semidirect
555. #3231	C₂×C₆₁	semidirect
556. #3117	C₂×C₆₁	semidirect
557. #3108	C₂×C₆₁	semidirect
558. #3078	C₂×C₆₁	semidirect
559. C₂×#479	C₂×C₆₁	semidirect
560. #2990	C₂×C₆₁	semidirect
678. C₆₁	#62139	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×#3515	2
Q₈×#41×C₆₁	2
C₆₁×#3387	2
C₆₁×#3385	2
C₆₁×#3374	2
C₆₁×#3372	2
C₆₁×#3346	2
C₆₁×#3344	2
C₆₁×#3338	2
C₆₁×#3335	2
C₆₁×#3320	2
C₆₁×#3312	2
C₆₁×#3299	2
C₆₁×#3298	2
C₆₁×#3252	2
C₆₁×#3248	2
C₆₁×#3236	2
C₆₁×#3231	2
C₆₁×#3117	2
C₆₁×#3108	2
C₆₁×#3078	2
C₂×C₆₁×#479	2
C₆₁×#2990	2
#62139	61

Subgroups — C61×#62139 #29565572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62139 #29565572