Subgroups — C₆₁×#61731 #29565164

Order 15616.

1816 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3354	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3348	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3340	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3329	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3321	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3303	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3194	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3187	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3095	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3091	C₂	1	2	yes	maximal, complemented
17	C₆₁×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
19	C₆₁×#555	—	2	2	no	—
20	C₆₁×#555	—	2	1	no	—
21	C₆₁×#555	—	2	1	no	—
22	C₆₁×#555	C₂²	1	2	yes	—
23	C₆₁×#555	C₂²	1	4	yes	—
24	C₆₁×#555	C₂²	1	2	yes	—
25	C₆₁×#554	—	2	1	no	—
26	C₆₁×#552	C₂²	1	2	yes	complemented
27	C₆₁×#551	—	2	2	no	—
28	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#548	C₂²	1	2	yes	complemented
30	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#546	—	2	1	no	—
33	C₆₁×#542	—	2	1	no	—
34	C₆₁×#539	—	2	2	no	—
35	C₆₁×#533	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#529	C₂²	1	1	yes	characteristic
38	C₂×#124×C₆₁	—	2	2	no	—
39	C₆₁×#525	C₂²	1	2	yes	—
40	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
41	C₂×#121×C₆₁	—	2	1	no	—
42	C₂×#121×C₆₁	C₂²	1	2	yes	—
43	C₆₁×#520	—	2	1	no	—
44	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×#117×C₆₁	—	2	1	no	—
47	C₂×#117×C₆₁	C₂²	1	2	yes	—
48	C₆₁×#501	C₂²	1	2	yes	complemented
49	C₆₁×#498	C₂²	1	2	yes	complemented
50	C₆₁×#489	C₂²	1	2	yes	complemented
51	C₆₁×#487	C₂²	1	2	yes	complemented
52	C₆₁×#485	C₂²	1	4	yes	complemented
53	C₆₁×#485	C₂²	1	4	yes	complemented
54	C₆₁×#485	C₂²	1	4	yes	complemented
55	C₆₁×#484	C₂²	1	2	yes	—
56	C₆₁×#484	C₂²	1	1	yes	characteristic
57	C₆₁×#483	C₂²	1	2	yes	—
58	C₆₁×#483	C₂²	1	2	yes	—
59	C₆₁×#483	C₂²	1	2	yes	—
60	C₆₁×#482	C₂²	1	4	yes	complemented
61	C₆₁×#482	C₂²	1	4	yes	complemented
62	C₆₁×#481	C₂²	1	1	yes	characteristic
63	C₆₁×#481	C₂²	1	4	yes	complemented
64	C₆₁×#480	C₂²	1	2	yes	—
65	C₆₁×#478	C₂²	1	2	yes	complemented
66	C₆₁×#477	C₂²	1	2	yes	complemented
67	C₆₁×#476	C₂²	1	2	yes	complemented
68	C₆₁×#475	C₂²	1	4	yes	complemented
69	C₆₁×#474	C₂²	1	2	yes	complemented
70	C₆₁×#469	C₂²	1	4	yes	complemented
71	C₆₁×#468	C₂²	1	4	yes	complemented
72	C₆₁×#465	C₂²	1	4	yes	complemented
73	C₆₁×#465	C₂²	1	4	yes	complemented
74	C₆₁×#463	C₂²	1	2	yes	complemented
75	C₆₁×#461	C₂²	1	2	yes	complemented
76	C₆₁×#450	C₂²	1	1	yes	characteristic
77	C₆₁×#450	C₂²	1	2	yes	—
78	C₆₁×#449	C₂²	1	4	yes	complemented
79	C₆₁×#448	C₂²	1	4	yes	complemented
80	C₆₁×#447	C₂²	1	1	yes	characteristic
81	C₆₁×#440	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
83	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
84	C₆₁×#436	C₂²	1	2	yes	complemented
85	C₆₁×#435	C₂²	1	4	yes	complemented
86	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
87	C₆₁×#432	C₂²	1	1	yes	characteristic
88	C₆₁×#431	C₂²	1	1	yes	characteristic
89	C₆₁×#428	C₂²	1	4	yes	complemented
90	C₆₁×#427	C₂²	1	4	yes	complemented
91	C₆₁×#419	C₂²	1	4	yes	complemented
92	C₆₁×#416	C₂²	1	4	yes	complemented
93	C₆₁×#407	C₂²	1	2	yes	—
94	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
95	C₂×#41×C₆₁	—	2	1	no	—
96	C₂×#41×C₆₁	C₂³	1	2	yes	—
97	C₂²×Q₈×C₆₁	—	2	1	no	—
98	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
99	C₂²×D₄×C₆₁	—	2	2	no	—
100	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
101	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₆₁	—	2	1	no	—
103	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
106	C₂×D₈×C₆₁	C₂³	1	2	yes	—
107	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
108	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₆₁	—	2	1	no	—
110	C₄⋊Q₈×C₆₁	—	2	1	no	—
111	C₄⋊Q₈×C₆₁	—	2	1	no	—
112	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
116	#126×C₆₁	—	2	2	no	—
117	#126×C₆₁	—	2	2	no	—
118	#126×C₆₁	—	2	1	no	—
119	#125×C₆₁	—	2	2	no	—
120	#125×C₆₁	—	2	1	no	—
121	#125×C₆₁	C₂³	1	1	yes	characteristic
122	#124×C₆₁	—	2	1	no	—
123	#124×C₆₁	—	2	2	no	—
124	#124×C₆₁	—	2	4	no	—
125	#124×C₆₁	—	2	4	no	—
126	#124×C₆₁	—	2	4	no	—
127	#124×C₆₁	—	2	4	no	—
128	#124×C₆₁	C₂³	1	1	yes	characteristic
129	#123×C₆₁	—	2	2	no	—
130	#123×C₆₁	—	2	2	no	—
131	#123×C₆₁	—	2	1	no	—
132	#123×C₆₁	—	2	2	no	—
133	#123×C₆₁	—	2	2	no	—
134	C₂²⋊Q₈×C₆₁	—	2	1	no	—
135	C₂²⋊Q₈×C₆₁	—	2	2	no	—
136	C₂²⋊Q₈×C₆₁	—	2	2	no	—
137	C₂²⋊Q₈×C₆₁	—	2	2	no	—
138	C₂²⋊Q₈×C₆₁	—	2	1	no	—
139	C₂²⋊Q₈×C₆₁	—	2	2	no	—
140	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
141	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
142	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
143	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
144	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
145	#121×C₆₁	—	2	2	no	—
146	#121×C₆₁	—	2	1	no	—
147	#121×C₆₁	—	2	2	no	—
148	#121×C₆₁	—	2	2	no	—
149	#121×C₆₁	—	2	4	no	—
150	#121×C₆₁	—	2	2	no	—
151	#121×C₆₁	—	2	2	no	—
152	#121×C₆₁	C₂³	1	2	yes	—
153	#121×C₆₁	C₂³	1	4	yes	—
154	#121×C₆₁	C₂³	1	4	yes	—
155	#121×C₆₁	C₂³	1	1	yes	characteristic
156	#120×C₆₁	—	2	2	no	—
157	C₄×Q₈×C₆₁	—	2	1	no	—
158	C₄×Q₈×C₆₁	—	2	1	no	—
159	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
160	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
161	C₄×D₄×C₆₁	—	2	1	no	—
162	C₄×D₄×C₆₁	—	2	2	no	—
163	C₄×D₄×C₆₁	—	2	1	no	—
164	C₄×D₄×C₆₁	—	2	2	no	—
165	C₄×D₄×C₆₁	—	2	2	no	—
166	C₄×D₄×C₆₁	—	2	1	no	—
167	C₄×D₄×C₆₁	—	2	1	no	—
168	C₄×D₄×C₆₁	D₄	1	2	yes	—
169	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
170	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
171	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₆₁	C₂³	1	2	yes	—
173	C₄×D₄×C₆₁	C₂³	1	2	yes	—
174	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₆₁	C₂³	1	2	yes	—
177	#117×C₆₁	—	2	1	no	—
178	#117×C₆₁	—	2	2	no	—
179	#117×C₆₁	—	2	2	no	—
180	#117×C₆₁	—	2	2	no	—
181	#117×C₆₁	—	2	4	no	—
182	#117×C₆₁	—	2	2	no	—
183	#117×C₆₁	—	2	2	no	—
184	#117×C₆₁	—	2	1	no	—
185	#117×C₆₁	C₂³	1	2	yes	—
186	#117×C₆₁	C₂³	1	4	yes	—
187	#117×C₆₁	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
189	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
190	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
199	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
200	C₂×C₄²×C₆₁	—	2	2	no	—
201	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
202	#107×C₆₁	C₂³	1	4	yes	—
203	#107×C₆₁	C₂³	1	4	yes	—
204	#107×C₆₁	C₂³	1	2	yes	—
205	#106×C₆₁	C₂³	1	2	yes	—
206	#106×C₆₁	C₂³	1	4	yes	—
207	#106×C₆₁	C₂³	1	4	yes	—
208	#106×C₆₁	C₂³	1	4	yes	—
209	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
210	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
211	#103×C₆₁	C₂³	1	4	yes	—
212	#103×C₆₁	C₂³	1	4	yes	—
213	#103×C₆₁	C₂³	1	2	yes	—
214	#103×C₆₁	C₂³	1	4	yes	—
215	#103×C₆₁	C₂³	1	4	yes	—
216	#102×C₆₁	C₂³	1	2	yes	—
217	#102×C₆₁	C₂³	1	4	yes	—
218	#102×C₆₁	C₂³	1	2	yes	—
219	#102×C₆₁	C₂³	1	2	yes	—
220	#102×C₆₁	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
223	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
225	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
226	#97×C₆₁	C₂³	1	2	yes	—
227	C₄×C₈×C₆₁	C₂³	1	2	yes	—
228	C₂⁴×C₆₁	—	2	1	no	—
229	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
230	#41×C₆₁	—	4	4	no	—
231	#41×C₆₁	—	4	4	no	—
232	C₂×Q₈×C₆₁	—	2	1	no	—
233	C₂×Q₈×C₆₁	—	2	2	no	—
234	C₂×Q₈×C₆₁	—	2	2	no	—
235	C₂×Q₈×C₆₁	—	2	2	no	—
236	C₂×Q₈×C₆₁	—	4	4	no	—
237	C₂×Q₈×C₆₁	—	8	2	no	—
238	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
239	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
240	C₂×D₄×C₆₁	—	2	1	no	—
241	C₂×D₄×C₆₁	—	2	2	no	—
242	C₂×D₄×C₆₁	—	2	2	no	—
243	C₂×D₄×C₆₁	—	2	4	no	—
244	C₂×D₄×C₆₁	—	2	4	no	—
245	C₂×D₄×C₆₁	—	2	1	no	—
246	C₂×D₄×C₆₁	—	4	2	no	—
247	C₂×D₄×C₆₁	—	4	2	no	—
248	C₂×D₄×C₆₁	—	8	4	no	—
249	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
253	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₆₁	—	2	1	no	—
255	C₂²×C₄×C₆₁	—	2	2	no	—
256	C₂²×C₄×C₆₁	—	2	2	no	—
257	C₂²×C₄×C₆₁	—	2	2	no	—
258	C₂²×C₄×C₆₁	—	2	1	no	—
259	C₂²×C₄×C₆₁	—	2	2	no	—
260	C₂²×C₄×C₆₁	—	2	2	no	—
261	C₂²×C₄×C₆₁	—	2	2	no	—
262	C₂²×C₄×C₆₁	—	4	4	no	—
263	C₂²×C₄×C₆₁	—	4	4	no	—
264	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
272	SD₁₆×C₆₁	—	4	2	no	—
273	SD₁₆×C₆₁	—	4	4	no	—
274	D₈×C₆₁	—	4	2	no	—
275	M₁₆×C₆₁	—	4	4	no	—
276	C₂×C₈×C₆₁	—	4	4	no	—
277	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
278	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
279	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
280	C₄⋊C₄×C₆₁	—	2	1	no	—
281	C₄⋊C₄×C₆₁	—	2	2	no	—
282	C₄⋊C₄×C₆₁	—	2	2	no	—
283	C₄⋊C₄×C₆₁	—	2	2	no	—
284	C₄⋊C₄×C₆₁	—	2	1	no	—
285	C₄⋊C₄×C₆₁	—	2	2	no	—
286	C₄⋊C₄×C₆₁	—	2	2	no	—
287	C₄⋊C₄×C₆₁	—	2	1	no	—
288	C₄⋊C₄×C₆₁	—	2	2	no	—
289	C₄⋊C₄×C₆₁	—	2	2	no	—
290	C₄⋊C₄×C₆₁	—	2	1	no	—
291	C₄⋊C₄×C₆₁	—	2	1	no	—
292	C₄⋊C₄×C₆₁	—	2	1	no	—
293	C₄⋊C₄×C₆₁	—	2	2	no	—
294	C₄⋊C₄×C₆₁	—	2	1	no	—
295	C₄⋊C₄×C₆₁	—	2	2	no	—
296	C₄⋊C₄×C₆₁	—	2	1	no	—
297	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
305	C₂²⋊C₄×C₆₁	—	2	1	no	—
306	C₂²⋊C₄×C₆₁	—	2	4	no	—
307	C₂²⋊C₄×C₆₁	—	2	4	no	—
308	C₂²⋊C₄×C₆₁	—	2	2	no	—
309	C₂²⋊C₄×C₆₁	—	2	2	no	—
310	C₂²⋊C₄×C₆₁	—	2	2	no	—
311	C₂²⋊C₄×C₆₁	—	2	2	no	—
312	C₂²⋊C₄×C₆₁	—	2	2	no	—
313	C₂²⋊C₄×C₆₁	—	2	4	no	—
314	C₂²⋊C₄×C₆₁	—	2	4	no	—
315	C₂²⋊C₄×C₆₁	—	2	2	no	—
316	C₂²⋊C₄×C₆₁	—	2	2	no	—
317	C₂²⋊C₄×C₆₁	—	2	1	no	—
318	C₂²⋊C₄×C₆₁	—	2	1	no	—
319	C₂²⋊C₄×C₆₁	—	2	1	no	—
320	C₂²⋊C₄×C₆₁	—	2	2	no	—
321	C₂²⋊C₄×C₆₁	—	2	1	no	—
322	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
326	C₄²×C₆₁	—	2	4	no	—
327	C₄²×C₆₁	—	2	4	no	—
328	C₄²×C₆₁	—	2	2	no	—
329	C₄²×C₆₁	—	2	2	no	—
330	C₄²×C₆₁	—	2	1	no	—
331	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂³×C₆₁	—	2	4	no	—
336	C₂³×C₆₁	—	2	1	no	—
337	C₂³×C₆₁	—	2	2	no	—
338	C₂³×C₆₁	—	4	2	no	—
339	C₂³×C₆₁	—	4	2	no	—
340	C₂³×C₆₁	—	4	2	no	—
341	C₂³×C₆₁	—	4	2	no	—
342	C₂³×C₆₁	—	4	2	no	—
343	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
344	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
345	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₆₁	—	2	2	no	—
347	Q₈×C₆₁	—	2	4	no	—
348	Q₈×C₆₁	—	4	2	no	—
349	Q₈×C₆₁	—	8	2	no	—
350	Q₈×C₆₁	—	8	2	no	—
351	Q₈×C₆₁	—	8	2	no	—
352	D₄×C₆₁	—	2	2	no	—
353	D₄×C₆₁	—	2	2	no	—
354	D₄×C₆₁	—	2	2	no	—
355	D₄×C₆₁	—	2	2	no	—
356	D₄×C₆₁	—	2	2	no	—
357	D₄×C₆₁	—	4	2	no	—
358	D₄×C₆₁	—	4	2	no	—
359	D₄×C₆₁	—	4	4	no	—
360	D₄×C₆₁	—	4	2	no	—
361	D₄×C₆₁	—	8	4	no	—
362	D₄×C₆₁	—	8	4	no	—
363	D₄×C₆₁	—	8	2	no	—
364	C₂×C₄×C₆₁	—	2	2	no	—
365	C₂×C₄×C₆₁	—	2	2	no	—
366	C₂×C₄×C₆₁	—	2	4	no	—
367	C₂×C₄×C₆₁	—	2	4	no	—
368	C₂×C₄×C₆₁	—	2	2	no	—
369	C₂×C₄×C₆₁	—	2	2	no	—
370	C₂×C₄×C₆₁	—	2	1	no	—
371	C₂×C₄×C₆₁	—	2	2	no	—
372	C₂×C₄×C₆₁	—	2	4	no	—
373	C₂×C₄×C₆₁	—	2	1	no	—
374	C₂×C₄×C₆₁	—	2	2	no	—
375	C₂×C₄×C₆₁	—	2	1	no	—
376	C₂×C₄×C₆₁	—	4	2	no	—
377	C₂×C₄×C₆₁	—	4	2	no	—
378	C₂×C₄×C₆₁	—	4	2	no	—
379	C₂×C₄×C₆₁	—	4	4	no	—
380	C₂×C₄×C₆₁	—	4	2	no	—
381	C₂×C₄×C₆₁	—	4	4	no	—
382	C₂×C₄×C₆₁	—	4	4	no	—
383	C₂×C₄×C₆₁	—	4	4	no	—
384	C₂×C₄×C₆₁	—	4	2	no	—
385	C₂×C₄×C₆₁	—	8	2	no	—
386	C₂×C₄×C₆₁	—	8	2	no	—
387	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
395	C₈×C₆₁	—	2	2	no	—
396	C₈×C₆₁	—	2	4	no	—
397	C₈×C₆₁	—	2	2	no	—
398	#61731	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂²×C₆₁	—	2	1	no	—
400	C₂²×C₆₁	—	2	1	no	—
401	C₂²×C₆₁	—	2	2	no	—
402	C₂²×C₆₁	—	2	2	no	—
403	C₂²×C₆₁	—	2	2	no	—
404	C₂²×C₆₁	—	2	2	no	—
405	C₂²×C₆₁	—	2	2	no	—
406	C₂²×C₆₁	—	2	2	no	—
407	C₂²×C₆₁	—	4	1	no	—
408	C₂²×C₆₁	—	4	2	no	—
409	C₂²×C₆₁	—	4	2	no	—
410	C₂²×C₆₁	—	4	1	no	—
411	C₂²×C₆₁	—	4	1	no	—
412	C₂²×C₆₁	—	4	2	no	—
413	C₂²×C₆₁	—	8	4	no	—
414	C₂²×C₆₁	—	8	4	no	—
415	C₂²×C₆₁	#577	1	2	yes	—
416	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
417	C₄×C₆₁	—	2	1	no	—
418	C₄×C₆₁	—	2	2	no	—
419	C₄×C₆₁	—	2	2	no	—
420	C₄×C₆₁	—	2	1	no	—
421	C₄×C₆₁	—	2	1	no	—
422	C₄×C₆₁	—	2	1	no	—
423	C₄×C₆₁	—	4	2	no	—
424	C₄×C₆₁	—	4	1	no	—
425	C₄×C₆₁	—	4	2	no	—
426	C₄×C₆₁	—	4	1	no	—
427	C₄×C₆₁	—	4	2	no	—
428	C₄×C₆₁	—	4	4	no	—
429	C₄×C₆₁	—	4	1	no	—
430	C₄×C₆₁	#575	1	2	yes	—
431	C₄×C₆₁	#585	1	2	yes	—
432	#3520	C₂×C₆₁	1	1	yes	characteristic, complemented
433	C₂×#555	C₂×C₆₁	1	1	yes	characteristic, complemented
434	#3354	C₂×C₆₁	1	2	yes	complemented
435	#3348	C₂×C₆₁	1	4	yes	complemented
436	#3340	C₂×C₆₁	1	2	yes	complemented
437	#3329	C₂×C₆₁	1	2	yes	complemented
438	#3321	C₂×C₆₁	1	4	yes	complemented
439	#3303	C₂×C₆₁	1	2	yes	complemented
440	#3238	C₂×C₆₁	1	1	yes	characteristic, complemented
441	#3229	C₂×C₆₁	1	1	yes	characteristic, complemented
442	#3194	C₂×C₆₁	1	2	yes	complemented
443	#3187	C₂×C₆₁	1	2	yes	complemented
444	#3110	C₂×C₆₁	1	1	yes	characteristic, complemented
445	#3105	C₂×C₆₁	1	1	yes	characteristic, complemented
446	#3095	C₂×C₆₁	1	2	yes	complemented
447	#3091	C₂×C₆₁	1	2	yes	complemented
448	#2974	C₂×C₆₁	1	1	yes	characteristic, complemented
449	C₂×C₆₁	—	2	2	no	—
450	C₂×C₆₁	—	4	2	no	—
451	C₂×C₆₁	—	4	2	no	—
452	C₂×C₆₁	—	8	1	no	—
453	C₂×C₆₁	—	8	2	no	—
454	C₂×C₆₁	#3485	1	1	yes	characteristic
455	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
456	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
457	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
458	#555	—	2	1	no	—
459	#555	—	2	2	no	—
460	#555	—	2	1	no	—
461	#555	C₂²×C₆₁	1	2	yes	—
462	#555	C₂²×C₆₁	1	2	yes	—
463	#555	C₂²×C₆₁	1	4	yes	—
464	#554	—	2	1	no	—
465	#552	C₂²×C₆₁	1	2	yes	complemented
466	#551	—	2	2	no	—
467	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
468	#548	C₂²×C₆₁	1	2	yes	complemented
469	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
470	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
471	#546	—	2	1	no	—
472	#542	—	2	1	no	—
473	#539	—	2	2	no	—
474	#533	C₂²×C₆₁	1	1	yes	characteristic
475	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
476	#529	C₂²×C₆₁	1	1	yes	characteristic
477	C₂×#124	—	2	2	no	—
478	#525	C₂²×C₆₁	1	2	yes	—
479	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
480	C₂×#121	—	2	1	no	—
481	C₂×#121	C₂²×C₆₁	1	2	yes	—
482	#520	—	2	1	no	—
483	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
484	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
485	C₂×#117	—	2	1	no	—
486	C₂×#117	C₂²×C₆₁	1	2	yes	—
487	#501	C₂²×C₆₁	1	2	yes	complemented
488	#498	C₂²×C₆₁	1	2	yes	complemented
489	#489	C₂²×C₆₁	1	2	yes	complemented
490	#487	C₂²×C₆₁	1	2	yes	complemented
491	#485	C₂²×C₆₁	1	4	yes	complemented
492	#485	C₂²×C₆₁	1	4	yes	complemented
493	#485	C₂²×C₆₁	1	4	yes	complemented
494	#484	C₂²×C₆₁	1	2	yes	—
495	#484	C₂²×C₆₁	1	1	yes	characteristic
496	#483	C₂²×C₆₁	1	2	yes	—
497	#483	C₂²×C₆₁	1	2	yes	—
498	#483	C₂²×C₆₁	1	2	yes	—
499	#482	C₂²×C₆₁	1	4	yes	complemented
500	#482	C₂²×C₆₁	1	4	yes	complemented
501	#481	C₂²×C₆₁	1	1	yes	characteristic
502	#481	C₂²×C₆₁	1	4	yes	complemented
503	#480	C₂²×C₆₁	1	2	yes	—
504	#478	C₂²×C₆₁	1	2	yes	complemented
505	#477	C₂²×C₆₁	1	2	yes	complemented
506	#476	C₂²×C₆₁	1	2	yes	complemented
507	#475	C₂²×C₆₁	1	4	yes	complemented
508	#474	C₂²×C₆₁	1	2	yes	complemented
509	#469	C₂²×C₆₁	1	4	yes	complemented
510	#468	C₂²×C₆₁	1	4	yes	complemented
511	#465	C₂²×C₆₁	1	4	yes	complemented
512	#465	C₂²×C₆₁	1	4	yes	complemented
513	#463	C₂²×C₆₁	1	2	yes	complemented
514	#461	C₂²×C₆₁	1	2	yes	complemented
515	#450	C₂²×C₆₁	1	1	yes	characteristic
516	#450	C₂²×C₆₁	1	2	yes	—
517	#449	C₂²×C₆₁	1	4	yes	complemented
518	#448	C₂²×C₆₁	1	4	yes	complemented
519	#447	C₂²×C₆₁	1	1	yes	characteristic
520	#440	C₂²×C₆₁	1	4	yes	complemented
521	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
522	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
523	#436	C₂²×C₆₁	1	2	yes	complemented
524	#435	C₂²×C₆₁	1	4	yes	complemented
525	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
526	#432	C₂²×C₆₁	1	1	yes	characteristic
527	#431	C₂²×C₆₁	1	1	yes	characteristic
528	#428	C₂²×C₆₁	1	4	yes	complemented
529	#427	C₂²×C₆₁	1	4	yes	complemented
530	#419	C₂²×C₆₁	1	4	yes	complemented
531	#416	C₂²×C₆₁	1	4	yes	complemented
532	#407	C₂²×C₆₁	1	2	yes	—
533	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
534	C₆₁	#61731	1	1	yes	characteristic, direct product factor, Sylow
535	C₂×#41	—	2	1	no	—
536	C₂×#41	C₂³×C₆₁	1	2	yes	—
537	C₂²×Q₈	—	2	1	no	—
538	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
539	C₂²×D₄	—	2	2	no	—
540	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
542	C₂³×C₄	—	2	1	no	—
543	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
545	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
546	C₂×D₈	C₂³×C₆₁	1	2	yes	—
547	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
548	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
553	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
556	#126	—	2	2	no	—
557	#126	—	2	2	no	—
558	#126	—	2	1	no	—
559	#125	—	2	2	no	—
560	#125	—	2	1	no	—
561	#125	C₂³×C₆₁	1	1	yes	characteristic
562	#124	—	2	1	no	—
563	#124	—	2	4	no	—
564	#124	—	2	4	no	—
565	#124	—	2	4	no	—
566	#124	—	2	4	no	—
567	#124	—	2	2	no	—
568	#124	C₂³×C₆₁	1	1	yes	characteristic
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	1	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
581	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
582	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
583	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
584	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	4	no	—
588	#121	—	2	2	no	—
589	#121	—	2	1	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	C₂³×C₆₁	1	4	yes	—
593	#121	C₂³×C₆₁	1	4	yes	—
594	#121	C₂³×C₆₁	1	1	yes	characteristic
595	#121	C₂³×C₆₁	1	2	yes	—
596	#120	—	2	2	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
609	C₄×D₄	D₄×C₆₁	1	2	yes	—
610	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
611	C₄×D₄	C₂³×C₆₁	1	2	yes	—
612	C₄×D₄	C₂³×C₆₁	1	2	yes	—
613	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₆₁	1	2	yes	—
617	#117	—	2	2	no	—
618	#117	—	2	2	no	—
619	#117	—	2	1	no	—
620	#117	—	2	2	no	—
621	#117	—	2	4	no	—
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	—	2	1	no	—
625	#117	C₂³×C₆₁	1	4	yes	—
626	#117	C₂³×C₆₁	1	4	yes	—
627	#117	C₂³×C₆₁	1	2	yes	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
640	C₂×C₄²	—	2	2	no	—
641	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
642	#107	C₂³×C₆₁	1	4	yes	—
643	#107	C₂³×C₆₁	1	4	yes	—
644	#107	C₂³×C₆₁	1	2	yes	—
645	#106	C₂³×C₆₁	1	2	yes	—
646	#106	C₂³×C₆₁	1	4	yes	—
647	#106	C₂³×C₆₁	1	4	yes	—
648	#106	C₂³×C₆₁	1	4	yes	—
649	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
650	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
651	#103	C₂³×C₆₁	1	4	yes	—
652	#103	C₂³×C₆₁	1	4	yes	—
653	#103	C₂³×C₆₁	1	2	yes	—
654	#103	C₂³×C₆₁	1	4	yes	—
655	#103	C₂³×C₆₁	1	4	yes	—
656	#102	C₂³×C₆₁	1	2	yes	—
657	#102	C₂³×C₆₁	1	4	yes	—
658	#102	C₂³×C₆₁	1	2	yes	—
659	#102	C₂³×C₆₁	1	2	yes	—
660	#102	C₂³×C₆₁	1	4	yes	—
661	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
662	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
663	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
664	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
665	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
666	#97	C₂³×C₆₁	1	2	yes	—
667	C₄×C₈	C₂³×C₆₁	1	2	yes	—
668	C₂⁴	—	2	1	no	—
669	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
670	#41	—	4	4	no	—
671	#41	—	4	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	—	8	2	no	—
678	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
679	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂×D₄	—	8	4	no	—
689	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
690	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
691	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
692	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
693	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	4	4	no	—
703	C₂²×C₄	—	4	4	no	—
704	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
707	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
708	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
712	SD₁₆	—	4	2	no	—
713	SD₁₆	—	4	4	no	—
714	D₈	—	4	2	no	—
715	M₁₆	—	4	4	no	—
716	C₂×C₈	—	4	4	no	—
717	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
718	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
719	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
738	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
739	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
741	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
743	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
744	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
763	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
764	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
765	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
766	C₄²	—	2	4	no	—
767	C₄²	—	2	4	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	1	no	—
771	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
773	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
774	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
775	C₂³	—	2	4	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	4	2	no	—
779	C₂³	—	4	2	no	—
780	C₂³	—	4	2	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	2	no	—
783	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
784	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
785	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
786	Q₈	—	2	2	no	—
787	Q₈	—	2	4	no	—
788	Q₈	—	4	2	no	—
789	Q₈	—	8	2	no	—
790	Q₈	—	8	2	no	—
791	Q₈	—	8	2	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	2	no	—
796	D₄	—	2	2	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	2	no	—
801	D₄	—	8	4	no	—
802	D₄	—	8	4	no	—
803	D₄	—	8	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	8	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
830	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
834	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
835	C₈	—	2	2	no	—
836	C₈	—	2	4	no	—
837	C₈	—	2	2	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	8	4	no	—
853	C₂²	—	8	4	no	—
854	C₂²	C₆₁×#577	1	2	yes	—
855	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	4	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	1	no	—
869	C₄	C₆₁×#575	1	2	yes	—
870	C₄	C₆₁×#585	1	2	yes	—
871	C₂	—	2	2	no	—
872	C₂	—	4	2	no	—
873	C₂	—	4	2	no	—
874	C₂	—	8	2	no	—
875	C₂	—	8	1	no	—
876	C₂	C₆₁×#3485	1	1	yes	characteristic
877	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
878	C₂	C₂×C₆₁×#577	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 ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3520	C₂	semidirect
2. C₂×C₆₁×#555	C₂	semidirect
3. C₆₁×#3354	C₂	semidirect
4. C₆₁×#3348	C₂	semidirect
5. C₆₁×#3340	C₂	semidirect
6. C₆₁×#3329	C₂	semidirect
7. C₆₁×#3321	C₂	semidirect
8. C₆₁×#3303	C₂	semidirect
9. C₆₁×#3238	C₂	semidirect
10. C₆₁×#3229	C₂	semidirect
11. C₆₁×#3194	C₂	semidirect
12. C₆₁×#3187	C₂	semidirect
13. C₆₁×#3110	C₂	semidirect
14. C₆₁×#3105	C₂	semidirect
15. C₆₁×#3095	C₂	semidirect
16. C₆₁×#3091	C₂	semidirect
17. C₆₁×#2974	C₂	semidirect
18. C₆₁×#556	C₂²	semidirect
26. C₆₁×#552	C₂²	semidirect
28. D₄×Q₈×C₆₁	C₂²	semidirect
29. C₆₁×#548	C₂²	semidirect
30. C₆₁×#547	C₂²	semidirect
31. C₆₁×#547	C₂²	semidirect
48. C₆₁×#501	C₂²	semidirect
49. C₆₁×#498	C₂²	semidirect
50. C₆₁×#489	C₂²	semidirect
51. C₆₁×#487	C₂²	semidirect
52. C₆₁×#485	C₂²	semidirect
53. C₆₁×#485	C₂²	semidirect
54. C₆₁×#485	C₂²	semidirect
60. C₆₁×#482	C₂²	semidirect
61. C₆₁×#482	C₂²	semidirect
63. C₆₁×#481	C₂²	semidirect
65. C₆₁×#478	C₂²	semidirect
66. C₆₁×#477	C₂²	semidirect
67. C₆₁×#476	C₂²	semidirect
68. C₆₁×#475	C₂²	semidirect
69. C₆₁×#474	C₂²	semidirect
70. C₆₁×#469	C₂²	semidirect
71. C₆₁×#468	C₂²	semidirect
72. C₆₁×#465	C₂²	semidirect
73. C₆₁×#465	C₂²	semidirect
74. C₆₁×#463	C₂²	semidirect
75. C₆₁×#461	C₂²	semidirect
78. C₆₁×#449	C₂²	semidirect
79. C₆₁×#448	C₂²	semidirect
81. C₆₁×#440	C₂²	semidirect
82. C₄×SD₁₆×C₆₁	C₂²	semidirect
83. C₄×D₈×C₆₁	C₂²	semidirect
84. C₆₁×#436	C₂²	semidirect
85. C₆₁×#435	C₂²	semidirect
86. C₈×D₄×C₆₁	C₂²	semidirect
89. C₆₁×#428	C₂²	semidirect
90. C₆₁×#427	C₂²	semidirect
91. C₆₁×#419	C₂²	semidirect
92. C₆₁×#416	C₂²	semidirect
398. #61731	C₆₁	direct (N × H)
432. #3520	C₂×C₆₁	semidirect
433. C₂×#555	C₂×C₆₁	semidirect
434. #3354	C₂×C₆₁	semidirect
435. #3348	C₂×C₆₁	semidirect
436. #3340	C₂×C₆₁	semidirect
437. #3329	C₂×C₆₁	semidirect
438. #3321	C₂×C₆₁	semidirect
439. #3303	C₂×C₆₁	semidirect
440. #3238	C₂×C₆₁	semidirect
441. #3229	C₂×C₆₁	semidirect
442. #3194	C₂×C₆₁	semidirect
443. #3187	C₂×C₆₁	semidirect
444. #3110	C₂×C₆₁	semidirect
445. #3105	C₂×C₆₁	semidirect
446. #3095	C₂×C₆₁	semidirect
447. #3091	C₂×C₆₁	semidirect
448. #2974	C₂×C₆₁	semidirect
457. #556	C₂²×C₆₁	semidirect
465. #552	C₂²×C₆₁	semidirect
467. D₄×Q₈	C₂²×C₆₁	semidirect
468. #548	C₂²×C₆₁	semidirect
469. #547	C₂²×C₆₁	semidirect
470. #547	C₂²×C₆₁	semidirect
487. #501	C₂²×C₆₁	semidirect
488. #498	C₂²×C₆₁	semidirect
489. #489	C₂²×C₆₁	semidirect
490. #487	C₂²×C₆₁	semidirect
491. #485	C₂²×C₆₁	semidirect
492. #485	C₂²×C₆₁	semidirect
493. #485	C₂²×C₆₁	semidirect
499. #482	C₂²×C₆₁	semidirect
500. #482	C₂²×C₆₁	semidirect
502. #481	C₂²×C₆₁	semidirect
504. #478	C₂²×C₆₁	semidirect
505. #477	C₂²×C₆₁	semidirect
506. #476	C₂²×C₆₁	semidirect
507. #475	C₂²×C₆₁	semidirect
508. #474	C₂²×C₆₁	semidirect
509. #469	C₂²×C₆₁	semidirect
510. #468	C₂²×C₆₁	semidirect
511. #465	C₂²×C₆₁	semidirect
512. #465	C₂²×C₆₁	semidirect
513. #463	C₂²×C₆₁	semidirect
514. #461	C₂²×C₆₁	semidirect
517. #449	C₂²×C₆₁	semidirect
518. #448	C₂²×C₆₁	semidirect
520. #440	C₂²×C₆₁	semidirect
521. C₄×SD₁₆	C₂²×C₆₁	semidirect
522. C₄×D₈	C₂²×C₆₁	semidirect
523. #436	C₂²×C₆₁	semidirect
524. #435	C₂²×C₆₁	semidirect
525. C₈×D₄	C₂²×C₆₁	semidirect
528. #428	C₂²×C₆₁	semidirect
529. #427	C₂²×C₆₁	semidirect
530. #419	C₂²×C₆₁	semidirect
531. #416	C₂²×C₆₁	semidirect
534. C₆₁	#61731	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×#3520	2
C₂×C₆₁×#555	2
C₆₁×#3354	2
C₆₁×#3348	2
C₆₁×#3340	2
C₆₁×#3329	2
C₆₁×#3321	2
C₆₁×#3303	2
C₆₁×#3238	2
C₆₁×#3229	2
C₆₁×#3194	2
C₆₁×#3187	2
C₆₁×#3110	2
C₆₁×#3105	2
C₆₁×#3095	2
C₆₁×#3091	2
C₆₁×#2974	2
#61731	61

Subgroups — C61×#61731 #29565164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61731 #29565164