Subgroups — C₆₁×#62123 #29565556

Order 15616.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1124 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, complemented
2	C₆₁×#3483	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×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3348	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3347	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3317	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3309	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3251	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3234	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3080	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈²×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#557	C₂²	1	1	yes	characteristic
26	C₆₁×#555	—	2	1	no	—
27	C₆₁×#555	—	2	2	no	—
28	C₆₁×#555	C₂²	1	2	yes	—
29	C₆₁×#555	C₂²	1	1	yes	characteristic
30	C₆₁×#554	C₂²	1	1	yes	characteristic
31	C₆₁×#554	C₂²	1	1	yes	characteristic
32	C₆₁×#553	C₂²	1	2	yes	—
33	C₆₁×#552	—	2	2	no	—
34	C₆₁×#552	—	2	1	no	—
35	C₆₁×#552	C₂²	1	2	yes	—
36	C₆₁×#550	—	2	1	no	—
37	C₆₁×#550	C₂²	1	2	yes	—
38	C₆₁×#550	C₂²	1	1	yes	characteristic
39	C₆₁×#550	C₂²	1	1	yes	characteristic
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	C₂²	1	1	yes	characteristic
45	C₆₁×#532	—	2	2	no	—
46	C₆₁×#532	—	2	1	no	—
47	C₆₁×#532	C₂²	1	1	yes	characteristic
48	C₆₁×#532	C₂²	1	2	yes	—
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	C₄×#41×C₆₁	C₂²	1	2	yes	—
56	C₄×#41×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×#490	C₂²	1	2	yes	—
62	C₆₁×#490	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	1	yes	characteristic
66	C₆₁×#485	C₂²	1	2	yes	—
67	C₆₁×#482	C₂²	1	2	yes	—
68	C₆₁×#482	C₂²	1	2	yes	—
69	C₆₁×#482	C₂²	1	1	yes	characteristic
70	C₆₁×#482	C₂²	1	2	yes	—
71	C₆₁×#481	C₂²	1	2	yes	—
72	C₆₁×#481	C₂²	1	2	yes	—
73	C₆₁×#480	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×#479	C₂²	1	1	yes	characteristic
79	C₆₁×#478	C₂²	1	2	yes	—
80	C₆₁×#478	C₂²	1	2	yes	—
81	C₆₁×#478	C₂²	1	2	yes	—
82	C₆₁×#478	C₂²	1	2	yes	—
83	C₆₁×#478	C₂²	1	2	yes	—
84	C₆₁×#478	C₂²	1	1	yes	characteristic
85	C₆₁×#478	C₂²	1	2	yes	—
86	C₆₁×#477	C₂²	1	1	yes	characteristic
87	C₆₁×#477	C₂²	1	1	yes	characteristic
88	C₆₁×#476	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	2	yes	—
92	C₆₁×#474	C₂²	1	1	yes	characteristic
93	C₆₁×#474	C₂²	1	2	yes	—
94	C₆₁×#469	C₂²	1	2	yes	—
95	C₆₁×#469	C₂²	1	2	yes	—
96	C₆₁×#468	C₂²	1	2	yes	—
97	C₆₁×#468	C₂²	1	2	yes	—
98	C₆₁×#466	C₂²	1	2	yes	—
99	C₆₁×#465	C₂²	1	2	yes	—
100	C₆₁×#464	C₂²	1	1	yes	characteristic
101	C₆₁×#463	C₂²	1	1	yes	characteristic
102	C₆₁×#463	C₂²	1	2	yes	—
103	C₆₁×#460	C₂²	1	2	yes	—
104	C₆₁×#460	C₂²	1	1	yes	characteristic
105	C₆₁×#459	C₂²	1	2	yes	—
106	C₆₁×#459	C₂²	1	1	yes	characteristic
107	C₆₁×#452	C₂²	1	1	yes	characteristic
108	C₆₁×#452	C₂²	1	2	yes	—
109	C₆₁×#449	C₂²	1	1	yes	characteristic
110	C₆₁×#449	C₂²	1	2	yes	—
111	C₆₁×#446	C₂²	1	1	yes	characteristic
112	C₆₁×#446	C₂²	1	1	yes	characteristic
113	C₆₁×#442	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×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
121	C₆₁×#436	C₂²	1	1	yes	characteristic
122	C₆₁×#436	C₂²	1	1	yes	characteristic
123	C₆₁×#435	C₂²	1	2	yes	—
124	C₆₁×#435	C₂²	1	2	yes	—
125	C₆₁×#432	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	C₆₁×#427	C₂²	1	2	yes	—
130	C₆₁×#423	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
132	C₆₁×#417	C₂²	1	2	yes	—
133	C₆₁×#417	C₂²	1	2	yes	—
134	C₆₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	—	2	2	no	—
138	C₂×#41×C₆₁	—	2	1	no	—
139	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
140	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₆₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₆₁	—	2	1	no	—
152	C₄⋊Q₈×C₆₁	—	2	1	no	—
153	C₄⋊Q₈×C₆₁	—	2	2	no	—
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	1	yes	characteristic
158	#127×C₆₁	—	2	1	no	—
159	#127×C₆₁	—	2	2	no	—
160	#127×C₆₁	C₂³	1	1	yes	characteristic
161	#127×C₆₁	C₂³	1	2	yes	—
162	#126×C₆₁	—	2	2	no	—
163	#126×C₆₁	—	2	2	no	—
164	#126×C₆₁	—	2	2	no	—
165	#126×C₆₁	—	2	1	no	—
166	#125×C₆₁	—	2	2	no	—
167	#125×C₆₁	—	2	2	no	—
168	#125×C₆₁	—	2	1	no	—
169	#125×C₆₁	—	2	2	no	—
170	#125×C₆₁	—	2	2	no	—
171	#125×C₆₁	C₂³	1	2	yes	—
172	#125×C₆₁	C₂³	1	2	yes	—
173	#125×C₆₁	C₂³	1	2	yes	—
174	#125×C₆₁	C₂³	1	1	yes	characteristic
175	#124×C₆₁	—	2	2	no	—
176	#124×C₆₁	—	2	2	no	—
177	#124×C₆₁	—	2	2	no	—
178	#124×C₆₁	—	2	2	no	—
179	#124×C₆₁	—	2	1	no	—
180	#124×C₆₁	C₂³	1	1	yes	characteristic
181	#123×C₆₁	—	2	2	no	—
182	#123×C₆₁	—	2	1	no	—
183	#123×C₆₁	—	2	2	no	—
184	#123×C₆₁	—	2	2	no	—
185	#123×C₆₁	—	2	2	no	—
186	C₂²⋊Q₈×C₆₁	—	2	1	no	—
187	C₂²⋊Q₈×C₆₁	—	2	1	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	C₂³	1	1	yes	characteristic
193	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
194	#121×C₆₁	—	2	1	no	—
195	#121×C₆₁	—	2	2	no	—
196	#121×C₆₁	—	2	2	no	—
197	#121×C₆₁	—	2	1	no	—
198	#121×C₆₁	—	2	2	no	—
199	#121×C₆₁	—	2	1	no	—
200	#121×C₆₁	—	2	2	no	—
201	#121×C₆₁	—	2	2	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	—	2	2	no	—
204	#121×C₆₁	C₂³	1	2	yes	—
205	#121×C₆₁	C₂³	1	2	yes	—
206	#121×C₆₁	C₂³	1	2	yes	—
207	#121×C₆₁	C₂³	1	2	yes	—
208	#121×C₆₁	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₆₁	—	2	1	no	—
210	C₄×Q₈×C₆₁	—	2	1	no	—
211	C₄×Q₈×C₆₁	—	2	1	no	—
212	C₄×Q₈×C₆₁	—	2	1	no	—
213	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₆₁	—	2	1	no	—
221	C₄×D₄×C₆₁	—	2	2	no	—
222	C₄×D₄×C₆₁	—	2	1	no	—
223	C₄×D₄×C₆₁	—	2	2	no	—
224	C₄×D₄×C₆₁	—	2	1	no	—
225	C₄×D₄×C₆₁	—	2	1	no	—
226	C₄×D₄×C₆₁	—	2	2	no	—
227	C₄×D₄×C₆₁	—	2	1	no	—
228	C₄×D₄×C₆₁	—	2	2	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	D₄	1	2	yes	—
233	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
234	C₄×D₄×C₆₁	C₂³	1	2	yes	—
235	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₆₁	C₂³	1	2	yes	—
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	1	no	—
243	#117×C₆₁	—	2	2	no	—
244	#117×C₆₁	—	2	2	no	—
245	#117×C₆₁	—	2	1	no	—
246	#117×C₆₁	—	2	2	no	—
247	#117×C₆₁	—	2	2	no	—
248	#117×C₆₁	—	2	1	no	—
249	#117×C₆₁	D₄	1	1	yes	characteristic
250	#117×C₆₁	D₄	1	2	yes	—
251	#117×C₆₁	C₂³	1	2	yes	—
252	#117×C₆₁	C₂³	1	1	yes	characteristic
253	#117×C₆₁	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
256	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
259	C₂×C₄²×C₆₁	—	2	1	no	—
260	C₂×C₄²×C₆₁	—	2	2	no	—
261	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
263	#107×C₆₁	C₂³	1	2	yes	—
264	#107×C₆₁	C₂³	1	2	yes	—
265	#107×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
271	#106×C₆₁	C₂³	1	2	yes	—
272	#106×C₆₁	C₂³	1	1	yes	characteristic
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	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	2	yes	—
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	1	yes	characteristic
288	#103×C₆₁	C₂³	1	1	yes	characteristic
289	#103×C₆₁	C₂³	1	1	yes	characteristic
290	#103×C₆₁	C₂³	1	2	yes	—
291	#102×C₆₁	C₂³	1	2	yes	—
292	#102×C₆₁	C₂³	1	2	yes	—
293	#102×C₆₁	C₂³	1	2	yes	—
294	#102×C₆₁	C₂³	1	2	yes	—
295	#102×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	1	yes	characteristic
298	#102×C₆₁	C₂³	1	1	yes	characteristic
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	1	yes	characteristic
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	#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	2	no	—
313	#41×C₆₁	—	2	4	no	—
314	#41×C₆₁	—	4	2	no	—
315	#41×C₆₁	—	4	1	no	—
316	#41×C₆₁	—	4	2	no	—
317	#41×C₆₁	—	4	4	no	—
318	#41×C₆₁	—	4	4	no	—
319	#41×C₆₁	—	8	4	no	—
320	#41×C₆₁	—	8	2	no	—
321	C₂×Q₈×C₆₁	—	2	1	no	—
322	C₂×Q₈×C₆₁	—	2	1	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	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×D₄×C₆₁	—	2	1	no	—
329	C₂×D₄×C₆₁	—	2	2	no	—
330	C₂×D₄×C₆₁	—	2	2	no	—
331	C₂×D₄×C₆₁	—	2	1	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	2	no	—
338	C₂×D₄×C₆₁	—	2	1	no	—
339	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
343	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₆₁	—	2	2	no	—
345	C₂²×C₄×C₆₁	—	2	2	no	—
346	C₂²×C₄×C₆₁	—	2	1	no	—
347	C₂²×C₄×C₆₁	—	2	2	no	—
348	C₂²×C₄×C₆₁	—	2	2	no	—
349	C₂²×C₄×C₆₁	—	2	1	no	—
350	C₂²×C₄×C₆₁	—	2	1	no	—
351	C₂²×C₄×C₆₁	—	2	2	no	—
352	C₂²×C₄×C₆₁	—	2	1	no	—
353	C₂²×C₄×C₆₁	—	2	2	no	—
354	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
357	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
360	Q₁₆×C₆₁	—	2	2	no	—
361	SD₁₆×C₆₁	—	2	2	no	—
362	SD₁₆×C₆₁	—	4	2	no	—
363	SD₁₆×C₆₁	—	4	1	no	—
364	D₈×C₆₁	—	4	2	no	—
365	D₈×C₆₁	—	4	1	no	—
366	M₁₆×C₆₁	—	4	2	no	—
367	M₁₆×C₆₁	—	4	2	no	—
368	C₂×C₈×C₆₁	—	4	2	no	—
369	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
374	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₆₁	—	2	2	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	2	no	—
385	C₄⋊C₄×C₆₁	—	2	2	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	2	no	—
389	C₄⋊C₄×C₆₁	—	2	1	no	—
390	C₄⋊C₄×C₆₁	—	2	2	no	—
391	C₄⋊C₄×C₆₁	—	2	1	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	2	no	—
396	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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	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	2	yes	—
404	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
407	C₂²⋊C₄×C₆₁	—	2	2	no	—
408	C₂²⋊C₄×C₆₁	—	2	1	no	—
409	C₂²⋊C₄×C₆₁	—	2	2	no	—
410	C₂²⋊C₄×C₆₁	—	2	2	no	—
411	C₂²⋊C₄×C₆₁	—	2	1	no	—
412	C₂²⋊C₄×C₆₁	—	2	1	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	1	no	—
417	C₂²⋊C₄×C₆₁	—	2	1	no	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₂²⋊C₄×C₆₁	—	2	1	no	—
420	C₂²⋊C₄×C₆₁	—	2	2	no	—
421	C₂²⋊C₄×C₆₁	—	2	1	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	2	no	—
424	C₂²⋊C₄×C₆₁	—	2	1	no	—
425	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
428	C₄²×C₆₁	—	2	1	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	—	2	2	no	—
434	C₄²×C₆₁	—	2	2	no	—
435	C₄²×C₆₁	—	2	1	no	—
436	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₆₁	C₂×D₄	1	2	yes	—
438	C₄²×C₆₁	C₂×D₄	1	2	yes	—
439	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
441	C₄²×C₆₁	C₂⁴	1	2	yes	—
442	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
443	C₂³×C₆₁	—	2	1	no	—
444	C₂³×C₆₁	—	2	2	no	—
445	C₂³×C₆₁	—	2	1	no	—
446	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
447	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
448	Q₈×C₆₁	—	2	2	no	—
449	Q₈×C₆₁	—	2	1	no	—
450	Q₈×C₆₁	—	2	1	no	—
451	Q₈×C₆₁	—	2	1	no	—
452	Q₈×C₆₁	—	4	2	no	—
453	Q₈×C₆₁	—	8	1	no	—
454	Q₈×C₆₁	—	8	2	no	—
455	Q₈×C₆₁	—	8	1	no	—
456	Q₈×C₆₁	2₋¹⁺⁴	1	2	yes	—
457	D₄×C₆₁	—	2	2	no	—
458	D₄×C₆₁	—	2	1	no	—
459	D₄×C₆₁	—	2	1	no	—
460	D₄×C₆₁	—	2	2	no	—
461	D₄×C₆₁	—	2	1	no	—
462	D₄×C₆₁	—	2	2	no	—
463	D₄×C₆₁	—	2	1	no	—
464	D₄×C₆₁	—	4	2	no	—
465	D₄×C₆₁	—	4	2	no	—
466	D₄×C₆₁	—	4	4	no	—
467	D₄×C₆₁	—	4	4	no	—
468	D₄×C₆₁	—	4	4	no	—
469	D₄×C₆₁	—	4	2	no	—
470	D₄×C₆₁	—	8	2	no	—
471	D₄×C₆₁	—	8	1	no	—
472	D₄×C₆₁	—	8	1	no	—
473	D₄×C₆₁	—	8	2	no	—
474	D₄×C₆₁	—	8	2	no	—
475	D₄×C₆₁	—	8	2	no	—
476	C₂×C₄×C₆₁	—	2	1	no	—
477	C₂×C₄×C₆₁	—	2	2	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	—	2	2	no	—
482	C₂×C₄×C₆₁	—	2	1	no	—
483	C₂×C₄×C₆₁	—	2	1	no	—
484	C₂×C₄×C₆₁	—	2	1	no	—
485	C₂×C₄×C₆₁	—	2	2	no	—
486	C₂×C₄×C₆₁	—	2	2	no	—
487	C₂×C₄×C₆₁	—	2	2	no	—
488	C₂×C₄×C₆₁	—	2	1	no	—
489	C₂×C₄×C₆₁	—	2	1	no	—
490	C₂×C₄×C₆₁	—	4	2	no	—
491	C₂×C₄×C₆₁	—	4	2	no	—
492	C₂×C₄×C₆₁	—	4	1	no	—
493	C₂×C₄×C₆₁	—	4	2	no	—
494	C₂×C₄×C₆₁	—	4	4	no	—
495	C₂×C₄×C₆₁	—	4	4	no	—
496	C₂×C₄×C₆₁	—	4	2	no	—
497	C₂×C₄×C₆₁	—	4	4	no	—
498	C₂×C₄×C₆₁	—	4	4	no	—
499	C₂×C₄×C₆₁	—	4	2	no	—
500	C₂×C₄×C₆₁	—	4	2	no	—
501	C₂×C₄×C₆₁	—	8	2	no	—
502	C₂×C₄×C₆₁	—	8	2	no	—
503	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
512	C₈×C₆₁	—	2	1	no	—
513	C₈×C₆₁	—	2	1	no	—
514	C₈×C₆₁	—	2	2	no	—
515	C₈×C₆₁	—	2	2	no	—
516	C₈×C₆₁	—	2	1	no	—
517	C₈×C₆₁	—	2	1	no	—
518	#62123	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
519	C₂²×C₆₁	—	2	2	no	—
520	C₂²×C₆₁	—	2	1	no	—
521	C₂²×C₆₁	—	2	1	no	—
522	C₂²×C₆₁	—	2	2	no	—
523	C₂²×C₆₁	—	2	1	no	—
524	C₂²×C₆₁	—	2	2	no	—
525	C₂²×C₆₁	—	4	1	no	—
526	C₂²×C₆₁	—	4	2	no	—
527	C₂²×C₆₁	—	4	1	no	—
528	C₂²×C₆₁	—	4	2	no	—
529	C₂²×C₆₁	—	4	1	no	—
530	C₂²×C₆₁	—	4	1	no	—
531	C₂²×C₆₁	—	4	2	no	—
532	C₂²×C₆₁	—	4	1	no	—
533	C₂²×C₆₁	—	4	1	no	—
534	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₆₁	—	2	1	no	—
536	C₄×C₆₁	—	2	2	no	—
537	C₄×C₆₁	—	2	1	no	—
538	C₄×C₆₁	—	2	1	no	—
539	C₄×C₆₁	—	2	2	no	—
540	C₄×C₆₁	—	2	2	no	—
541	C₄×C₆₁	—	2	1	no	—
542	C₄×C₆₁	—	2	2	no	—
543	C₄×C₆₁	—	4	1	no	—
544	C₄×C₆₁	—	4	2	no	—
545	C₄×C₆₁	—	4	1	no	—
546	C₄×C₆₁	—	4	2	no	—
547	C₄×C₆₁	—	4	1	no	—
548	C₄×C₆₁	—	4	1	no	—
549	C₄×C₆₁	—	4	1	no	—
550	C₄×C₆₁	—	4	2	no	—
551	C₄×C₆₁	#575	1	2	yes	—
552	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₄×C₆₁	#585	1	1	yes	characteristic
554	#3515	C₂×C₆₁	1	1	yes	characteristic, complemented
555	#3483	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#3387	C₂×C₆₁	1	1	yes	characteristic, complemented
557	#3385	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#3368	C₂×C₆₁	1	1	yes	characteristic, complemented
559	#3366	C₂×C₆₁	1	1	yes	characteristic, complemented
560	#3357	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#3354	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3348	C₂×C₆₁	1	2	yes	complemented
563	#3347	C₂×C₆₁	1	2	yes	complemented
564	#3333	C₂×C₆₁	1	1	yes	characteristic, complemented
565	#3332	C₂×C₆₁	1	1	yes	characteristic, complemented
566	#3317	C₂×C₆₁	1	2	yes	complemented
567	#3309	C₂×C₆₁	1	2	yes	complemented
568	#3251	C₂×C₆₁	1	2	yes	complemented
569	#3247	C₂×C₆₁	1	1	yes	characteristic, complemented
570	#3234	C₂×C₆₁	1	2	yes	complemented
571	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3111	C₂×C₆₁	1	2	yes	complemented
573	#3102	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3080	C₂×C₆₁	1	2	yes	complemented
575	#3076	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#2989	C₂×C₆₁	1	1	yes	characteristic, complemented
577	C₂×C₆₁	—	4	2	no	—
578	C₂×C₆₁	—	4	1	no	—
579	C₂×C₆₁	—	8	2	no	—
580	C₂×C₆₁	—	8	1	no	—
581	C₂×C₆₁	—	8	1	no	—
582	C₂×C₆₁	#3489	1	1	yes	characteristic
583	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
584	C₂×C₆₁	#3585	1	1	yes	characteristic
585	Q₈²	C₂²×C₆₁	1	1	yes	characteristic
586	#557	C₂²×C₆₁	1	1	yes	characteristic
587	#555	—	2	1	no	—
588	#555	—	2	2	no	—
589	#555	C₂²×C₆₁	1	2	yes	—
590	#555	C₂²×C₆₁	1	1	yes	characteristic
591	#554	C₂²×C₆₁	1	1	yes	characteristic
592	#554	C₂²×C₆₁	1	1	yes	characteristic
593	#553	C₂²×C₆₁	1	2	yes	—
594	#552	—	2	2	no	—
595	#552	—	2	1	no	—
596	#552	C₂²×C₆₁	1	2	yes	—
597	#550	—	2	1	no	—
598	#550	C₂²×C₆₁	1	1	yes	characteristic
599	#550	C₂²×C₆₁	1	2	yes	—
600	#550	C₂²×C₆₁	1	1	yes	characteristic
601	#547	—	2	1	no	—
602	#547	C₂²×C₆₁	1	1	yes	characteristic
603	#541	—	2	1	no	—
604	#539	—	2	2	no	—
605	#533	C₂²×C₆₁	1	1	yes	characteristic
606	#532	—	2	1	no	—
607	#532	—	2	2	no	—
608	#532	C₂²×C₆₁	1	1	yes	characteristic
609	#532	C₂²×C₆₁	1	2	yes	—
610	#529	C₂²×C₆₁	1	1	yes	characteristic
611	#529	C₂²×C₆₁	1	2	yes	—
612	C₂×#125	C₂²×C₆₁	1	2	yes	—
613	#520	—	2	1	no	—
614	C₄×#41	—	2	1	no	—
615	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
616	C₄×#41	C₂²×C₆₁	1	2	yes	—
617	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
618	#501	C₂²×C₆₁	1	2	yes	—
619	#501	C₂²×C₆₁	1	2	yes	—
620	#500	C₂²×C₆₁	1	1	yes	characteristic
621	#498	C₂²×C₆₁	1	1	yes	characteristic
622	#490	C₂²×C₆₁	1	2	yes	—
623	#490	C₂²×C₆₁	1	2	yes	—
624	#486	C₂²×C₆₁	1	1	yes	characteristic
625	#486	C₂²×C₆₁	1	1	yes	characteristic
626	#485	C₂²×C₆₁	1	1	yes	characteristic
627	#485	C₂²×C₆₁	1	2	yes	—
628	#482	C₂²×C₆₁	1	1	yes	characteristic
629	#482	C₂²×C₆₁	1	2	yes	—
630	#482	C₂²×C₆₁	1	2	yes	—
631	#482	C₂²×C₆₁	1	2	yes	—
632	#481	C₂²×C₆₁	1	2	yes	—
633	#481	C₂²×C₆₁	1	2	yes	—
634	#480	C₂²×C₆₁	1	2	yes	—
635	#480	C₂²×C₆₁	1	2	yes	—
636	#479	C₂²×C₆₁	1	2	yes	—
637	#479	C₂²×C₆₁	1	1	yes	characteristic
638	#479	C₂²×C₆₁	1	2	yes	—
639	#479	C₂²×C₆₁	1	2	yes	—
640	#478	C₂²×C₆₁	1	2	yes	—
641	#478	C₂²×C₆₁	1	2	yes	—
642	#478	C₂²×C₆₁	1	2	yes	—
643	#478	C₂²×C₆₁	1	2	yes	—
644	#478	C₂²×C₆₁	1	2	yes	—
645	#478	C₂²×C₆₁	1	1	yes	characteristic
646	#478	C₂²×C₆₁	1	2	yes	—
647	#477	C₂²×C₆₁	1	1	yes	characteristic
648	#477	C₂²×C₆₁	1	1	yes	characteristic
649	#476	C₂²×C₆₁	1	1	yes	characteristic
650	#476	C₂²×C₆₁	1	1	yes	characteristic
651	#475	C₂²×C₆₁	1	1	yes	characteristic
652	#475	C₂²×C₆₁	1	2	yes	—
653	#474	C₂²×C₆₁	1	1	yes	characteristic
654	#474	C₂²×C₆₁	1	2	yes	—
655	#469	C₂²×C₆₁	1	2	yes	—
656	#469	C₂²×C₆₁	1	2	yes	—
657	#468	C₂²×C₆₁	1	2	yes	—
658	#468	C₂²×C₆₁	1	2	yes	—
659	#466	C₂²×C₆₁	1	2	yes	—
660	#465	C₂²×C₆₁	1	2	yes	—
661	#464	C₂²×C₆₁	1	1	yes	characteristic
662	#463	C₂²×C₆₁	1	1	yes	characteristic
663	#463	C₂²×C₆₁	1	2	yes	—
664	#460	C₂²×C₆₁	1	1	yes	characteristic
665	#460	C₂²×C₆₁	1	2	yes	—
666	#459	C₂²×C₆₁	1	1	yes	characteristic
667	#459	C₂²×C₆₁	1	2	yes	—
668	#452	C₂²×C₆₁	1	2	yes	—
669	#452	C₂²×C₆₁	1	1	yes	characteristic
670	#449	C₂²×C₆₁	1	2	yes	—
671	#449	C₂²×C₆₁	1	1	yes	characteristic
672	#446	C₂²×C₆₁	1	1	yes	characteristic
673	#446	C₂²×C₆₁	1	1	yes	characteristic
674	#442	C₂²×C₆₁	1	2	yes	—
675	#441	C₂²×C₆₁	1	2	yes	—
676	#440	C₂²×C₆₁	1	2	yes	—
677	#440	C₂²×C₆₁	1	2	yes	—
678	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
679	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
681	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
682	#436	C₂²×C₆₁	1	1	yes	characteristic
683	#436	C₂²×C₆₁	1	1	yes	characteristic
684	#435	C₂²×C₆₁	1	2	yes	—
685	#435	C₂²×C₆₁	1	2	yes	—
686	#432	C₂²×C₆₁	1	2	yes	—
687	#431	C₂²×C₆₁	1	1	yes	characteristic
688	#428	C₂²×C₆₁	1	2	yes	—
689	#428	C₂²×C₆₁	1	2	yes	—
690	#427	C₂²×C₆₁	1	2	yes	—
691	#423	C₂²×C₆₁	1	2	yes	—
692	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
693	#417	C₂²×C₆₁	1	2	yes	—
694	#417	C₂²×C₆₁	1	2	yes	—
695	#416	C₂²×C₆₁	1	2	yes	—
696	C₆₁	#62123	1	1	yes	characteristic, direct product factor, Sylow
697	C₂×#41	—	2	1	no	—
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	2	2	no	—
700	C₂×#41	—	2	1	no	—
701	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
702	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
703	C₂×#41	C₂³×C₆₁	1	2	yes	—
704	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
705	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
708	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
709	C₂×D₈	C₂³×C₆₁	1	2	yes	—
710	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
711	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
712	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
713	C₄⋊Q₈	—	2	1	no	—
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	—	2	2	no	—
716	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
717	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
720	#127	—	2	1	no	—
721	#127	—	2	2	no	—
722	#127	C₂³×C₆₁	1	1	yes	characteristic
723	#127	C₂³×C₆₁	1	2	yes	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	1	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	1	no	—
731	#125	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	C₂³×C₆₁	1	1	yes	characteristic
734	#125	C₂³×C₆₁	1	2	yes	—
735	#125	C₂³×C₆₁	1	2	yes	—
736	#125	C₂³×C₆₁	1	2	yes	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	—	2	2	no	—
740	#124	—	2	2	no	—
741	#124	—	2	1	no	—
742	#124	C₂³×C₆₁	1	1	yes	characteristic
743	#123	—	2	2	no	—
744	#123	—	2	1	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
755	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
756	#121	—	2	1	no	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	—	2	1	no	—
760	#121	—	2	2	no	—
761	#121	—	2	1	no	—
762	#121	—	2	2	no	—
763	#121	—	2	2	no	—
764	#121	—	2	2	no	—
765	#121	—	2	2	no	—
766	#121	C₂³×C₆₁	1	2	yes	—
767	#121	C₂³×C₆₁	1	1	yes	characteristic
768	#121	C₂³×C₆₁	1	2	yes	—
769	#121	C₂³×C₆₁	1	2	yes	—
770	#121	C₂³×C₆₁	1	2	yes	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
779	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
780	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
795	C₄×D₄	D₄×C₆₁	1	2	yes	—
796	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₆₁	1	2	yes	—
798	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₆₁	1	2	yes	—
800	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₆₁	1	2	yes	—
802	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₆₁	1	2	yes	—
804	#117	—	2	1	no	—
805	#117	—	2	2	no	—
806	#117	—	2	2	no	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	—	2	1	no	—
810	#117	—	2	2	no	—
811	#117	D₄×C₆₁	1	1	yes	characteristic
812	#117	D₄×C₆₁	1	2	yes	—
813	#117	C₂³×C₆₁	1	1	yes	characteristic
814	#117	C₂³×C₆₁	1	2	yes	—
815	#117	C₂³×C₆₁	1	2	yes	—
816	C₂×C₄⋊C₄	—	2	2	no	—
817	C₂×C₄⋊C₄	—	2	2	no	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
820	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
821	C₂×C₄²	—	2	1	no	—
822	C₂×C₄²	—	2	2	no	—
823	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
824	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
825	#107	C₂³×C₆₁	1	2	yes	—
826	#107	C₂³×C₆₁	1	2	yes	—
827	#107	C₂³×C₆₁	1	1	yes	characteristic
828	#107	C₂³×C₆₁	1	2	yes	—
829	#107	C₂³×C₆₁	1	2	yes	—
830	#107	C₂³×C₆₁	1	1	yes	characteristic
831	#107	C₂³×C₆₁	1	2	yes	—
832	#106	C₂³×C₆₁	1	2	yes	—
833	#106	C₂³×C₆₁	1	2	yes	—
834	#106	C₂³×C₆₁	1	1	yes	characteristic
835	#106	C₂³×C₆₁	1	2	yes	—
836	#106	C₂³×C₆₁	1	2	yes	—
837	#106	C₂³×C₆₁	1	1	yes	characteristic
838	#106	C₂³×C₆₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
840	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
845	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
846	#103	C₂³×C₆₁	1	2	yes	—
847	#103	C₂³×C₆₁	1	2	yes	—
848	#103	C₂³×C₆₁	1	1	yes	characteristic
849	#103	C₂³×C₆₁	1	1	yes	characteristic
850	#103	C₂³×C₆₁	1	1	yes	characteristic
851	#103	C₂³×C₆₁	1	1	yes	characteristic
852	#103	C₂³×C₆₁	1	2	yes	—
853	#102	C₂³×C₆₁	1	2	yes	—
854	#102	C₂³×C₆₁	1	2	yes	—
855	#102	C₂³×C₆₁	1	2	yes	—
856	#102	C₂³×C₆₁	1	2	yes	—
857	#102	C₂³×C₆₁	1	2	yes	—
858	#102	C₂³×C₆₁	1	2	yes	—
859	#102	C₂³×C₆₁	1	1	yes	characteristic
860	#102	C₂³×C₆₁	1	1	yes	characteristic
861	#102	C₂³×C₆₁	1	1	yes	characteristic
862	#102	C₂³×C₆₁	1	1	yes	characteristic
863	#102	C₂³×C₆₁	1	2	yes	—
864	#102	C₂³×C₆₁	1	2	yes	—
865	#102	C₂³×C₆₁	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
870	#97	C₂³×C₆₁	1	2	yes	—
871	#97	C₂³×C₆₁	1	2	yes	—
872	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
874	#41	—	2	2	no	—
875	#41	—	2	4	no	—
876	#41	—	4	2	no	—
877	#41	—	4	1	no	—
878	#41	—	4	2	no	—
879	#41	—	4	4	no	—
880	#41	—	4	4	no	—
881	#41	—	8	4	no	—
882	#41	—	8	2	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
902	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
903	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
904	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
905	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
918	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
919	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
922	Q₁₆	—	2	2	no	—
923	SD₁₆	—	2	2	no	—
924	SD₁₆	—	4	2	no	—
925	SD₁₆	—	4	1	no	—
926	D₈	—	4	2	no	—
927	D₈	—	4	1	no	—
928	M₁₆	—	4	2	no	—
929	M₁₆	—	4	2	no	—
930	C₂×C₈	—	4	2	no	—
931	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
936	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
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	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
962	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
988	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	1	no	—
998	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
999	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1000	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1001	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1002	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₆₁	1	2	yes	—
1004	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1009	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1010	Q₈	—	2	2	no	—
1011	Q₈	—	2	1	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	4	2	no	—
1015	Q₈	—	8	1	no	—
1016	Q₈	—	8	2	no	—
1017	Q₈	—	8	1	no	—
1018	Q₈	2₋¹⁺⁴×C₆₁	1	2	yes	—
1019	D₄	—	2	2	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	4	2	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	4	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	8	2	no	—
1033	D₄	—	8	1	no	—
1034	D₄	—	8	1	no	—
1035	D₄	—	8	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	4	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1066	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1073	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	C₆₁×#575	1	2	yes	—
1113	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1114	C₄	C₆₁×#585	1	1	yes	characteristic
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	8	2	no	—
1118	C₂	—	8	1	no	—
1119	C₂	—	8	1	no	—
1120	C₂	C₆₁×#3489	1	1	yes	characteristic
1121	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
1122	C₂	C₆₁×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3515	C₂	semidirect
2. C₆₁×#3483	C₂	semidirect
3. C₆₁×#3387	C₂	semidirect
4. C₆₁×#3385	C₂	semidirect
5. C₆₁×#3368	C₂	semidirect
6. C₆₁×#3366	C₂	semidirect
7. C₆₁×#3357	C₂	semidirect
8. C₆₁×#3354	C₂	semidirect
9. C₆₁×#3348	C₂	semidirect
10. C₆₁×#3347	C₂	semidirect
11. C₆₁×#3333	C₂	semidirect
12. C₆₁×#3332	C₂	semidirect
13. C₆₁×#3317	C₂	semidirect
14. C₆₁×#3309	C₂	semidirect
15. C₆₁×#3251	C₂	semidirect
16. C₆₁×#3247	C₂	semidirect
17. C₆₁×#3234	C₂	semidirect
18. C₆₁×#3228	C₂	semidirect
19. C₆₁×#3111	C₂	semidirect
20. C₆₁×#3102	C₂	semidirect
21. C₆₁×#3080	C₂	semidirect
22. C₆₁×#3076	C₂	semidirect
23. C₆₁×#2989	C₂	semidirect
518. #62123	C₆₁	direct (N × H)
554. #3515	C₂×C₆₁	semidirect
555. #3483	C₂×C₆₁	semidirect
556. #3387	C₂×C₆₁	semidirect
557. #3385	C₂×C₆₁	semidirect
558. #3368	C₂×C₆₁	semidirect
559. #3366	C₂×C₆₁	semidirect
560. #3357	C₂×C₆₁	semidirect
561. #3354	C₂×C₆₁	semidirect
562. #3348	C₂×C₆₁	semidirect
563. #3347	C₂×C₆₁	semidirect
564. #3333	C₂×C₆₁	semidirect
565. #3332	C₂×C₆₁	semidirect
566. #3317	C₂×C₆₁	semidirect
567. #3309	C₂×C₆₁	semidirect
568. #3251	C₂×C₆₁	semidirect
569. #3247	C₂×C₆₁	semidirect
570. #3234	C₂×C₆₁	semidirect
571. #3228	C₂×C₆₁	semidirect
572. #3111	C₂×C₆₁	semidirect
573. #3102	C₂×C₆₁	semidirect
574. #3080	C₂×C₆₁	semidirect
575. #3076	C₂×C₆₁	semidirect
576. #2989	C₂×C₆₁	semidirect
696. C₆₁	#62123	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
C₆₁×#3483	2
C₆₁×#3387	2
C₆₁×#3385	2
C₆₁×#3368	2
C₆₁×#3366	2
C₆₁×#3357	2
C₆₁×#3354	2
C₆₁×#3348	2
C₆₁×#3347	2
C₆₁×#3333	2
C₆₁×#3332	2
C₆₁×#3317	2
C₆₁×#3309	2
C₆₁×#3251	2
C₆₁×#3247	2
C₆₁×#3234	2
C₆₁×#3228	2
C₆₁×#3111	2
C₆₁×#3102	2
C₆₁×#3080	2
C₆₁×#3076	2
C₆₁×#2989	2
#62123	61

Subgroups — C61×#62123 #29565556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62123 #29565556