Subgroups — C₆₁×#61323 #29564756

Order 15616.

1814 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3377	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3376	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3369	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3367	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3364	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3360	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3140	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3078	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3040	C₂	1	2	yes	maximal
14	C₆₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#137×C₆₁	C₂	1	2	yes	maximal, complemented
17	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic
18	C₂×#137×C₆₁	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
20	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
21	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
22	C₆₁×#557	C₂²	1	2	yes	complemented
23	C₆₁×#556	—	2	2	no	—
24	C₆₁×#556	—	2	1	no	—
25	C₆₁×#556	—	2	1	no	—
26	C₆₁×#556	C₂²	1	2	yes	—
27	C₆₁×#556	C₂²	1	2	yes	—
28	C₆₁×#556	C₂²	1	4	yes	—
29	C₆₁×#554	—	2	1	no	—
30	C₆₁×#554	—	2	2	no	—
31	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#554	C₂²	1	2	yes	complemented
33	D₄×Q₈×C₆₁	—	2	1	no	—
34	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
35	C₆₁×#533	—	2	1	no	—
36	C₆₁×#533	—	2	2	no	—
37	C₆₁×#533	C₂²	1	1	yes	characteristic
38	C₆₁×#533	C₂²	1	2	yes	—
39	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×#126×C₆₁	—	2	2	no	—
41	C₂×#124×C₆₁	C₂²	1	2	yes	—
42	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
43	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
44	C₄×#41×C₆₁	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
46	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×#117×C₆₁	—	2	1	no	—
50	C₆₁×#491	C₂²	1	4	yes	complemented
51	C₆₁×#489	C₂²	1	4	yes	—
52	C₆₁×#489	C₂²	1	4	yes	—
53	C₆₁×#488	C₂²	1	4	yes	—
54	C₆₁×#488	C₂²	1	4	yes	—
55	C₆₁×#487	C₂²	1	2	yes	complemented
56	C₆₁×#487	C₂²	1	2	yes	complemented
57	C₆₁×#479	C₂²	1	4	yes	complemented
58	C₆₁×#479	C₂²	1	4	yes	complemented
59	C₆₁×#478	C₂²	1	4	yes	—
60	C₆₁×#477	C₂²	1	4	yes	complemented
61	C₆₁×#476	C₂²	1	2	yes	—
62	C₆₁×#475	C₂²	1	4	yes	complemented
63	C₆₁×#474	C₂²	1	2	yes	—
64	C₆₁×#464	C₂²	1	4	yes	—
65	C₆₁×#464	C₂²	1	4	yes	—
66	C₆₁×#463	C₂²	1	4	yes	—
67	C₆₁×#463	C₂²	1	4	yes	—
68	C₆₁×#462	C₂²	1	2	yes	complemented
69	C₆₁×#462	C₂²	1	2	yes	complemented
70	C₆₁×#461	C₂²	1	2	yes	complemented
71	C₆₁×#461	C₂²	1	2	yes	complemented
72	C₆₁×#446	C₂²	1	2	yes	complemented
73	C₆₁×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
75	C₆₁×#442	C₂²	1	2	yes	—
76	C₆₁×#441	C₂²	1	4	yes	complemented
77	C₆₁×#440	C₂²	1	2	yes	—
78	C₆₁×#440	C₂²	1	4	yes	complemented
79	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
82	C₄×D₈×C₆₁	C₂²	1	2	yes	—
83	C₆₁×#428	C₂²	1	2	yes	—
84	C₆₁×#428	C₂²	1	1	yes	characteristic
85	C₆₁×#423	C₂²	1	1	yes	characteristic
86	C₆₁×#423	C₂²	1	2	yes	—
87	C₆₁×#419	C₂²	1	2	yes	—
88	C₆₁×#419	C₂²	1	2	yes	—
89	C₆₁×#419	C₂²	1	2	yes	—
90	C₆₁×#418	C₂²	1	2	yes	—
91	C₆₁×#418	C₂²	1	1	yes	characteristic
92	C₆₁×#417	C₂²	1	1	yes	characteristic
93	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
95	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₁	—	2	1	no	—
97	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
98	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
99	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₆₁	—	2	1	no	—
101	#137×C₆₁	—	2	8	no	—
102	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
103	C₂×Q₁₆×C₆₁	C₂³	1	4	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	1	yes	characteristic
108	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
109	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₁	—	2	1	no	—
111	C₄⋊Q₈×C₆₁	—	2	2	no	—
112	C₄⋊Q₈×C₆₁	—	2	1	no	—
113	C₄⋊Q₈×C₆₁	—	2	2	no	—
114	C₄⋊Q₈×C₆₁	—	2	1	no	—
115	C₄⋊Q₈×C₆₁	—	2	1	no	—
116	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
122	#126×C₆₁	—	2	4	no	—
123	#126×C₆₁	—	2	4	no	—
124	#126×C₆₁	—	2	4	no	—
125	#126×C₆₁	—	2	4	no	—
126	#125×C₆₁	—	2	2	no	—
127	#125×C₆₁	—	2	2	no	—
128	#125×C₆₁	—	2	2	no	—
129	#125×C₆₁	C₂³	1	2	yes	—
130	#125×C₆₁	C₂³	1	2	yes	—
131	#125×C₆₁	C₂³	1	2	yes	—
132	#124×C₆₁	—	2	2	no	—
133	#124×C₆₁	—	2	2	no	—
134	#124×C₆₁	C₂³	1	4	yes	—
135	#124×C₆₁	C₂³	1	4	yes	—
136	C₂²⋊Q₈×C₆₁	—	2	1	no	—
137	C₂²⋊Q₈×C₆₁	—	2	2	no	—
138	C₂²⋊Q₈×C₆₁	—	2	2	no	—
139	C₂²⋊Q₈×C₆₁	—	2	2	no	—
140	C₂²⋊Q₈×C₆₁	—	2	4	no	—
141	C₂²⋊Q₈×C₆₁	—	2	1	no	—
142	C₂²⋊Q₈×C₆₁	—	2	2	no	—
143	C₂²⋊Q₈×C₆₁	—	2	2	no	—
144	C₂²⋊Q₈×C₆₁	—	2	1	no	—
145	C₂²⋊Q₈×C₆₁	—	2	1	no	—
146	C₂²⋊Q₈×C₆₁	—	2	2	no	—
147	C₂²⋊Q₈×C₆₁	—	2	2	no	—
148	C₂²⋊Q₈×C₆₁	—	2	2	no	—
149	C₂²⋊Q₈×C₆₁	—	2	2	no	—
150	C₄×Q₈×C₆₁	—	2	1	no	—
151	C₄×Q₈×C₆₁	—	2	1	no	—
152	C₄×Q₈×C₆₁	—	2	2	no	—
153	C₄×Q₈×C₆₁	—	2	1	no	—
154	C₄×Q₈×C₆₁	—	2	2	no	—
155	C₄×Q₈×C₆₁	—	2	1	no	—
156	C₄×Q₈×C₆₁	—	2	2	no	—
157	C₄×Q₈×C₆₁	—	2	2	no	—
158	C₄×Q₈×C₆₁	—	2	2	no	—
159	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
160	C₄×Q₈×C₆₁	D₄	1	2	yes	—
161	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
162	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
163	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
164	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
165	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
168	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
171	C₄×D₄×C₆₁	—	2	1	no	—
172	C₄×D₄×C₆₁	—	2	2	no	—
173	C₄×D₄×C₆₁	—	2	2	no	—
174	C₄×D₄×C₆₁	—	2	1	no	—
175	C₄×D₄×C₆₁	—	2	1	no	—
176	C₄×D₄×C₆₁	—	2	1	no	—
177	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₆₁	C₂³	1	2	yes	—
179	C₄×D₄×C₆₁	C₂³	1	2	yes	—
180	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₆₁	C₂³	1	2	yes	—
182	C₄×D₄×C₆₁	C₂³	1	2	yes	—
183	#117×C₆₁	—	2	2	no	—
184	#117×C₆₁	—	2	4	no	—
185	#117×C₆₁	—	2	2	no	—
186	#117×C₆₁	—	2	1	no	—
187	#117×C₆₁	—	2	2	no	—
188	#117×C₆₁	C₂³	1	2	yes	—
189	#117×C₆₁	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
192	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
193	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
194	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
195	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
201	C₂×C₄²×C₆₁	—	2	2	no	—
202	C₂×C₄²×C₆₁	—	2	1	no	—
203	C₂×C₄²×C₆₁	—	2	2	no	—
204	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
206	#107×C₆₁	C₂³	1	2	yes	—
207	#107×C₆₁	C₂³	1	4	yes	—
208	#106×C₆₁	C₂³	1	2	yes	—
209	#106×C₆₁	C₂³	1	4	yes	—
210	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
211	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
212	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
213	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
214	#103×C₆₁	C₂³	1	2	yes	—
215	#103×C₆₁	C₂³	1	4	yes	—
216	#103×C₆₁	C₂³	1	4	yes	—
217	#103×C₆₁	C₂³	1	4	yes	—
218	#103×C₆₁	C₂³	1	4	yes	—
219	#103×C₆₁	C₂³	1	4	yes	—
220	#103×C₆₁	C₂³	1	4	yes	—
221	#102×C₆₁	C₂³	1	2	yes	—
222	#102×C₆₁	C₂³	1	2	yes	—
223	#102×C₆₁	C₂³	1	2	yes	—
224	#102×C₆₁	C₂³	1	4	yes	—
225	#102×C₆₁	C₂³	1	4	yes	—
226	#97×C₆₁	C₂³	1	2	yes	—
227	#97×C₆₁	C₂³	1	4	yes	—
228	C₄×C₈×C₆₁	C₂³	1	2	yes	—
229	C₄×C₈×C₆₁	C₂³	1	4	yes	—
230	C₂⁴×C₆₁	—	2	1	no	—
231	#41×C₆₁	—	2	2	no	—
232	#41×C₆₁	#41	1	4	yes	—
233	C₂×Q₈×C₆₁	—	2	2	no	—
234	C₂×Q₈×C₆₁	—	2	1	no	—
235	C₂×Q₈×C₆₁	—	2	2	no	—
236	C₂×Q₈×C₆₁	—	2	2	no	—
237	C₂×Q₈×C₆₁	—	2	1	no	—
238	C₂×Q₈×C₆₁	—	2	4	no	—
239	C₂×Q₈×C₆₁	—	2	4	no	—
240	C₂×Q₈×C₆₁	—	4	2	no	—
241	C₂×Q₈×C₆₁	—	4	4	no	—
242	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
246	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₆₁	—	2	1	no	—
248	C₂×D₄×C₆₁	—	2	1	no	—
249	C₂×D₄×C₆₁	—	2	2	no	—
250	C₂×D₄×C₆₁	—	2	2	no	—
251	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
252	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₁	—	2	1	no	—
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	1	no	—
258	C₂²×C₄×C₆₁	—	2	2	no	—
259	C₂²×C₄×C₆₁	—	2	2	no	—
260	C₂²×C₄×C₆₁	—	2	2	no	—
261	C₂²×C₄×C₆₁	—	2	1	no	—
262	C₂²×C₄×C₆₁	—	4	4	no	—
263	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₆₁	—	2	8	no	—
269	SD₁₆×C₆₁	—	2	4	no	—
270	SD₁₆×C₆₁	—	2	8	no	—
271	D₈×C₆₁	—	2	4	no	—
272	M₁₆×C₆₁	—	2	2	no	—
273	M₁₆×C₆₁	—	2	4	no	—
274	M₁₆×C₆₁	—	2	2	no	—
275	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
276	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
277	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₆₁	—	2	2	no	—
279	C₄⋊C₄×C₆₁	—	2	2	no	—
280	C₄⋊C₄×C₆₁	—	2	2	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	4	no	—
286	C₄⋊C₄×C₆₁	—	2	4	no	—
287	C₄⋊C₄×C₆₁	—	2	2	no	—
288	C₄⋊C₄×C₆₁	—	2	2	no	—
289	C₄⋊C₄×C₆₁	—	2	1	no	—
290	C₄⋊C₄×C₆₁	—	2	2	no	—
291	C₄⋊C₄×C₆₁	—	2	2	no	—
292	C₄⋊C₄×C₆₁	—	2	1	no	—
293	C₄⋊C₄×C₆₁	—	2	1	no	—
294	C₄⋊C₄×C₆₁	—	2	2	no	—
295	C₄⋊C₄×C₆₁	—	2	1	no	—
296	C₄⋊C₄×C₆₁	—	2	2	no	—
297	C₄⋊C₄×C₆₁	—	2	2	no	—
298	C₄⋊C₄×C₆₁	—	2	2	no	—
299	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
307	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
311	C₂²⋊C₄×C₆₁	—	2	2	no	—
312	C₂²⋊C₄×C₆₁	—	2	1	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	4	no	—
318	C₂²⋊C₄×C₆₁	—	2	4	no	—
319	C₂²⋊C₄×C₆₁	—	2	2	no	—
320	C₂²⋊C₄×C₆₁	—	2	2	no	—
321	C₂²⋊C₄×C₆₁	—	2	1	no	—
322	C₂²⋊C₄×C₆₁	—	2	1	no	—
323	C₄²×C₆₁	—	2	4	no	—
324	C₄²×C₆₁	—	2	4	no	—
325	C₄²×C₆₁	—	2	1	no	—
326	C₄²×C₆₁	—	2	2	no	—
327	C₄²×C₆₁	—	2	2	no	—
328	C₄²×C₆₁	—	2	1	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	2	yes	—
333	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₆₁	C₂×D₄	1	2	yes	—
335	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₄²×C₆₁	C₂⁴	1	2	yes	—
337	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
338	C₄²×C₆₁	C₂⁴	1	2	yes	—
339	C₂³×C₆₁	—	2	1	no	—
340	C₂³×C₆₁	—	2	2	no	—
341	C₂³×C₆₁	—	4	2	no	—
342	C₂³×C₆₁	—	4	2	no	—
343	C₂³×C₆₁	—	4	2	no	—
344	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
345	Q₈×C₆₁	—	2	2	no	—
346	Q₈×C₆₁	—	2	2	no	—
347	Q₈×C₆₁	—	2	1	no	—
348	Q₈×C₆₁	—	2	4	no	—
349	Q₈×C₆₁	—	2	4	no	—
350	Q₈×C₆₁	—	4	2	no	—
351	Q₈×C₆₁	—	4	4	no	—
352	Q₈×C₆₁	—	4	4	no	—
353	Q₈×C₆₁	—	4	2	no	—
354	Q₈×C₆₁	—	8	2	no	—
355	Q₈×C₆₁	—	8	1	no	—
356	Q₈×C₆₁	C₂×#41	1	2	yes	—
357	D₄×C₆₁	—	2	4	no	—
358	D₄×C₆₁	—	2	2	no	—
359	D₄×C₆₁	—	2	1	no	—
360	D₄×C₆₁	—	2	2	no	—
361	D₄×C₆₁	—	4	2	no	—
362	D₄×C₆₁	C₂×#41	1	2	yes	—
363	C₂×C₄×C₆₁	—	2	1	no	—
364	C₂×C₄×C₆₁	—	2	4	no	—
365	C₂×C₄×C₆₁	—	2	2	no	—
366	C₂×C₄×C₆₁	—	2	2	no	—
367	C₂×C₄×C₆₁	—	2	4	no	—
368	C₂×C₄×C₆₁	—	2	2	no	—
369	C₂×C₄×C₆₁	—	2	1	no	—
370	C₂×C₄×C₆₁	—	2	2	no	—
371	C₂×C₄×C₆₁	—	2	1	no	—
372	C₂×C₄×C₆₁	—	4	2	no	—
373	C₂×C₄×C₆₁	—	4	1	no	—
374	C₂×C₄×C₆₁	—	4	2	no	—
375	C₂×C₄×C₆₁	—	4	4	no	—
376	C₂×C₄×C₆₁	—	4	4	no	—
377	C₂×C₄×C₆₁	—	4	2	no	—
378	C₂×C₄×C₆₁	—	4	4	no	—
379	C₂×C₄×C₆₁	—	4	4	no	—
380	C₂×C₄×C₆₁	—	4	2	no	—
381	C₂×C₄×C₆₁	—	8	2	no	—
382	C₂×C₄×C₆₁	—	8	1	no	—
383	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
390	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
393	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
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	#61323	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	—	4	1	no	—
403	C₂²×C₆₁	—	4	1	no	—
404	C₂²×C₆₁	—	4	2	no	—
405	C₂²×C₆₁	—	4	2	no	—
406	C₂²×C₆₁	—	4	2	no	—
407	C₂²×C₆₁	—	8	4	no	—
408	C₂²×C₆₁	#548	1	2	yes	—
409	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
410	C₄×C₆₁	—	2	2	no	—
411	C₄×C₆₁	—	2	1	no	—
412	C₄×C₆₁	—	2	2	no	—
413	C₄×C₆₁	—	2	1	no	—
414	C₄×C₆₁	—	2	2	no	—
415	C₄×C₆₁	—	2	1	no	—
416	C₄×C₆₁	—	2	2	no	—
417	C₄×C₆₁	—	2	2	no	—
418	C₄×C₆₁	—	4	2	no	—
419	C₄×C₆₁	—	4	1	no	—
420	C₄×C₆₁	—	4	4	no	—
421	C₄×C₆₁	—	4	2	no	—
422	C₄×C₆₁	—	4	2	no	—
423	C₄×C₆₁	—	4	1	no	—
424	C₄×C₆₁	#548	1	2	yes	—
425	C₄×C₆₁	#575	1	2	yes	—
426	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
427	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
428	Q₈×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
429	C₂×#556	C₂×C₆₁	1	1	yes	characteristic, complemented
430	#3377	C₂×C₆₁	1	4	yes	complemented
431	#3376	C₂×C₆₁	1	4	yes	complemented
432	#3369	C₂×C₆₁	1	2	yes	complemented
433	#3367	C₂×C₆₁	1	2	yes	complemented
434	#3364	C₂×C₆₁	1	2	yes	complemented
435	#3360	C₂×C₆₁	1	2	yes	complemented
436	#3140	C₂×C₆₁	1	2	yes	complemented
437	#3139	C₂×C₆₁	1	1	yes	characteristic, complemented
438	#3078	C₂×C₆₁	1	2	yes	complemented
439	#3077	C₂×C₆₁	1	1	yes	characteristic, complemented
440	#3040	C₂×C₆₁	1	2	yes	—
441	#3039	C₂×C₆₁	1	1	yes	characteristic, complemented
442	Q₈×M₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
443	C₄×#137	C₂×C₆₁	1	2	yes	complemented
444	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic
445	C₂×C₆₁	—	2	2	no	—
446	C₂×C₆₁	—	4	2	no	—
447	C₂×C₆₁	—	8	2	no	—
448	C₂×C₆₁	C₂×#548	1	1	yes	characteristic
449	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
450	C₂×C₆₁	#3586	1	1	yes	characteristic
451	C₂×#137	C₂²×C₆₁	1	2	yes	—
452	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
453	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
454	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
455	#557	C₂²×C₆₁	1	2	yes	complemented
456	#556	—	2	1	no	—
457	#556	—	2	2	no	—
458	#556	—	2	1	no	—
459	#556	C₂²×C₆₁	1	2	yes	—
460	#556	C₂²×C₆₁	1	2	yes	—
461	#556	C₂²×C₆₁	1	4	yes	—
462	#554	—	2	1	no	—
463	#554	—	2	2	no	—
464	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
465	#554	C₂²×C₆₁	1	2	yes	complemented
466	D₄×Q₈	—	2	1	no	—
467	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
468	#533	—	2	1	no	—
469	#533	—	2	2	no	—
470	#533	C₂²×C₆₁	1	1	yes	characteristic
471	#533	C₂²×C₆₁	1	2	yes	—
472	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
473	C₂×#126	—	2	2	no	—
474	C₂×#124	C₂²×C₆₁	1	2	yes	—
475	C₂×C₂²⋊Q₈	—	2	1	no	—
476	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
477	C₄×#41	C₂²×C₆₁	1	2	yes	—
478	C₂×C₄×Q₈	—	2	1	no	—
479	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
480	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
481	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
482	C₂×#117	—	2	1	no	—
483	#491	C₂²×C₆₁	1	4	yes	complemented
484	#489	C₂²×C₆₁	1	4	yes	—
485	#489	C₂²×C₆₁	1	4	yes	—
486	#488	C₂²×C₆₁	1	4	yes	—
487	#488	C₂²×C₆₁	1	4	yes	—
488	#487	C₂²×C₆₁	1	2	yes	complemented
489	#487	C₂²×C₆₁	1	2	yes	complemented
490	#479	C₂²×C₆₁	1	4	yes	complemented
491	#479	C₂²×C₆₁	1	4	yes	complemented
492	#478	C₂²×C₆₁	1	4	yes	—
493	#477	C₂²×C₆₁	1	4	yes	complemented
494	#476	C₂²×C₆₁	1	2	yes	—
495	#475	C₂²×C₆₁	1	4	yes	complemented
496	#474	C₂²×C₆₁	1	2	yes	—
497	#464	C₂²×C₆₁	1	4	yes	—
498	#464	C₂²×C₆₁	1	4	yes	—
499	#463	C₂²×C₆₁	1	4	yes	—
500	#463	C₂²×C₆₁	1	4	yes	—
501	#462	C₂²×C₆₁	1	2	yes	complemented
502	#462	C₂²×C₆₁	1	2	yes	complemented
503	#461	C₂²×C₆₁	1	2	yes	complemented
504	#461	C₂²×C₆₁	1	2	yes	complemented
505	#446	C₂²×C₆₁	1	2	yes	complemented
506	#446	C₂²×C₆₁	1	4	yes	complemented
507	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
508	#442	C₂²×C₆₁	1	2	yes	—
509	#441	C₂²×C₆₁	1	4	yes	complemented
510	#440	C₂²×C₆₁	1	2	yes	—
511	#440	C₂²×C₆₁	1	4	yes	complemented
512	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	complemented
513	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
514	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
515	C₄×D₈	C₂²×C₆₁	1	2	yes	—
516	#428	C₂²×C₆₁	1	2	yes	—
517	#428	C₂²×C₆₁	1	1	yes	characteristic
518	#423	C₂²×C₆₁	1	1	yes	characteristic
519	#423	C₂²×C₆₁	1	2	yes	—
520	#419	C₂²×C₆₁	1	2	yes	—
521	#419	C₂²×C₆₁	1	2	yes	—
522	#419	C₂²×C₆₁	1	2	yes	—
523	#418	C₂²×C₆₁	1	2	yes	—
524	#418	C₂²×C₆₁	1	1	yes	characteristic
525	#417	C₂²×C₆₁	1	1	yes	characteristic
526	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
527	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
528	C₆₁	#61323	1	1	yes	characteristic, direct product factor, Sylow
529	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
530	C₂²×Q₈	—	2	1	no	—
531	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
533	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
534	C₂³×C₄	—	2	1	no	—
535	#137	—	2	8	no	—
536	AGL(1,ℤ/8)	—	2	4	no	—
537	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
538	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
539	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
540	C₂×D₈	C₂³×C₆₁	1	2	yes	—
541	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
542	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
543	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	—	2	2	no	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	—	2	2	no	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
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	4	no	—
557	#126	—	2	4	no	—
558	#126	—	2	4	no	—
559	#126	—	2	4	no	—
560	#125	—	2	2	no	—
561	#125	—	2	2	no	—
562	#125	—	2	2	no	—
563	#125	C₂³×C₆₁	1	2	yes	—
564	#125	C₂³×C₆₁	1	2	yes	—
565	#125	C₂³×C₆₁	1	2	yes	—
566	#124	—	2	2	no	—
567	#124	—	2	2	no	—
568	#124	C₂³×C₆₁	1	4	yes	—
569	#124	C₂³×C₆₁	1	4	yes	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	4	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	1	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
594	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
595	C₄×Q₈	D₄×C₆₁	1	2	yes	—
596	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
597	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
598	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
599	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
602	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
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	2	yes	—
615	C₄×D₄	C₂³×C₆₁	1	2	yes	—
616	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
617	#117	—	2	2	no	—
618	#117	—	2	4	no	—
619	#117	—	2	2	no	—
620	#117	—	2	1	no	—
621	#117	—	2	2	no	—
622	#117	C₂³×C₆₁	1	1	yes	characteristic
623	#117	C₂³×C₆₁	1	2	yes	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	2	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	2	no	—
629	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
630	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	—	2	2	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	2	no	—
635	C₂×C₄²	—	2	2	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
640	#107	C₂³×C₆₁	1	2	yes	—
641	#107	C₂³×C₆₁	1	4	yes	—
642	#106	C₂³×C₆₁	1	2	yes	—
643	#106	C₂³×C₆₁	1	4	yes	—
644	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
645	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
646	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
647	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
648	#103	C₂³×C₆₁	1	2	yes	—
649	#103	C₂³×C₆₁	1	4	yes	—
650	#103	C₂³×C₆₁	1	4	yes	—
651	#103	C₂³×C₆₁	1	4	yes	—
652	#103	C₂³×C₆₁	1	4	yes	—
653	#103	C₂³×C₆₁	1	4	yes	—
654	#103	C₂³×C₆₁	1	4	yes	—
655	#102	C₂³×C₆₁	1	2	yes	—
656	#102	C₂³×C₆₁	1	2	yes	—
657	#102	C₂³×C₆₁	1	2	yes	—
658	#102	C₂³×C₆₁	1	4	yes	—
659	#102	C₂³×C₆₁	1	4	yes	—
660	#97	C₂³×C₆₁	1	2	yes	—
661	#97	C₂³×C₆₁	1	4	yes	—
662	C₄×C₈	C₂³×C₆₁	1	2	yes	—
663	C₄×C₈	C₂³×C₆₁	1	4	yes	—
664	C₂⁴	—	2	1	no	—
665	#41	—	2	2	no	—
666	#41	#41×C₆₁	1	4	yes	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	4	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
677	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
678	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
679	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
680	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
686	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	4	4	no	—
697	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
699	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
702	Q₁₆	—	2	8	no	—
703	SD₁₆	—	2	4	no	—
704	SD₁₆	—	2	8	no	—
705	D₈	—	2	4	no	—
706	M₁₆	—	2	2	no	—
707	M₁₆	—	2	4	no	—
708	M₁₆	—	2	2	no	—
709	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
710	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
711	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
737	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
738	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
739	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
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	2	yes	—
744	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	2	4	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	1	no	—
765	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₆₁	1	2	yes	—
767	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₆₁	1	2	yes	—
769	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
770	C₄²	C₂⁴×C₆₁	1	2	yes	—
771	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
772	C₄²	C₂⁴×C₆₁	1	2	yes	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	4	2	no	—
776	C₂³	—	4	2	no	—
777	C₂³	—	4	2	no	—
778	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
779	Q₈	—	2	2	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	4	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	4	2	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	4	no	—
787	Q₈	—	4	2	no	—
788	Q₈	—	8	2	no	—
789	Q₈	—	8	1	no	—
790	Q₈	C₂×#41×C₆₁	1	2	yes	—
791	D₄	—	2	4	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	2	no	—
795	D₄	—	4	2	no	—
796	D₄	C₂×#41×C₆₁	1	2	yes	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	8	2	no	—
816	C₂×C₄	—	8	1	no	—
817	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
826	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
827	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
828	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
829	C₈	—	2	2	no	—
830	C₈	—	2	4	no	—
831	C₈	—	2	2	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	8	4	no	—
841	C₂²	C₆₁×#548	1	2	yes	—
842	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
843	C₄	—	2	1	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	4	no	—
857	C₄	C₆₁×#548	1	2	yes	—
858	C₄	C₆₁×#575	1	2	yes	—
859	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
860	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
861	C₂	—	2	2	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	2	no	—
864	C₂	C₂×C₆₁×#548	1	1	yes	characteristic
865	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
866	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×AGL(1,ℤ/8)×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×#41×C₆₁	C₂	semidirect
2. C₂×C₆₁×#556	C₂	semidirect
3. C₆₁×#3377	C₂	semidirect
4. C₆₁×#3376	C₂	semidirect
5. C₆₁×#3369	C₂	semidirect
6. C₆₁×#3367	C₂	semidirect
7. C₆₁×#3364	C₂	semidirect
8. C₆₁×#3360	C₂	semidirect
9. C₆₁×#3140	C₂	semidirect
10. C₆₁×#3139	C₂	semidirect
11. C₆₁×#3078	C₂	semidirect
12. C₆₁×#3077	C₂	semidirect
14. C₆₁×#3039	C₂	semidirect
15. Q₈×M₁₆×C₆₁	C₂	semidirect
16. C₄×#137×C₆₁	C₂	semidirect
20. Q₈²×C₆₁	C₂²	semidirect
21. C₆₁×#557	C₂²	semidirect
22. C₆₁×#557	C₂²	semidirect
31. C₆₁×#554	C₂²	semidirect
32. C₆₁×#554	C₂²	semidirect
34. D₄×Q₈×C₆₁	C₂²	semidirect
50. C₆₁×#491	C₂²	semidirect
55. C₆₁×#487	C₂²	semidirect
56. C₆₁×#487	C₂²	semidirect
57. C₆₁×#479	C₂²	semidirect
58. C₆₁×#479	C₂²	semidirect
60. C₆₁×#477	C₂²	semidirect
62. C₆₁×#475	C₂²	semidirect
68. C₆₁×#462	C₂²	semidirect
69. C₆₁×#462	C₂²	semidirect
70. C₆₁×#461	C₂²	semidirect
71. C₆₁×#461	C₂²	semidirect
72. C₆₁×#446	C₂²	semidirect
73. C₆₁×#446	C₂²	semidirect
74. C₈×Q₈×C₆₁	C₂²	semidirect
76. C₆₁×#441	C₂²	semidirect
78. C₆₁×#440	C₂²	semidirect
79. C₄×Q₁₆×C₆₁	C₂²	semidirect
81. C₄×SD₁₆×C₆₁	C₂²	semidirect
398. #61323	C₆₁	direct (N × H)
428. Q₈×#41	C₂×C₆₁	semidirect
429. C₂×#556	C₂×C₆₁	semidirect
430. #3377	C₂×C₆₁	semidirect
431. #3376	C₂×C₆₁	semidirect
432. #3369	C₂×C₆₁	semidirect
433. #3367	C₂×C₆₁	semidirect
434. #3364	C₂×C₆₁	semidirect
435. #3360	C₂×C₆₁	semidirect
436. #3140	C₂×C₆₁	semidirect
437. #3139	C₂×C₆₁	semidirect
438. #3078	C₂×C₆₁	semidirect
439. #3077	C₂×C₆₁	semidirect
441. #3039	C₂×C₆₁	semidirect
442. Q₈×M₁₆	C₂×C₆₁	semidirect
443. C₄×#137	C₂×C₆₁	semidirect
453. Q₈²	C₂²×C₆₁	semidirect
454. #557	C₂²×C₆₁	semidirect
455. #557	C₂²×C₆₁	semidirect
464. #554	C₂²×C₆₁	semidirect
465. #554	C₂²×C₆₁	semidirect
467. D₄×Q₈	C₂²×C₆₁	semidirect
483. #491	C₂²×C₆₁	semidirect
488. #487	C₂²×C₆₁	semidirect
489. #487	C₂²×C₆₁	semidirect
490. #479	C₂²×C₆₁	semidirect
491. #479	C₂²×C₆₁	semidirect
493. #477	C₂²×C₆₁	semidirect
495. #475	C₂²×C₆₁	semidirect
501. #462	C₂²×C₆₁	semidirect
502. #462	C₂²×C₆₁	semidirect
503. #461	C₂²×C₆₁	semidirect
504. #461	C₂²×C₆₁	semidirect
505. #446	C₂²×C₆₁	semidirect
506. #446	C₂²×C₆₁	semidirect
507. C₈×Q₈	C₂²×C₆₁	semidirect
509. #441	C₂²×C₆₁	semidirect
511. #440	C₂²×C₆₁	semidirect
512. C₄×Q₁₆	C₂²×C₆₁	semidirect
514. C₄×SD₁₆	C₂²×C₆₁	semidirect
528. C₆₁	#61323	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Q₈×#41×C₆₁	2
C₂×C₆₁×#556	2
C₆₁×#3377	2
C₆₁×#3376	2
C₆₁×#3369	2
C₆₁×#3367	2
C₆₁×#3364	2
C₆₁×#3360	2
C₆₁×#3140	2
C₆₁×#3139	2
C₆₁×#3078	2
C₆₁×#3077	2
C₆₁×#3040	2
C₆₁×#3039	2
Q₈×M₁₆×C₆₁	2
C₄×#137×C₆₁	2
C₄×AGL(1,ℤ/8)×C₆₁	2
#61323	61

Subgroups — C61×#61323 #29564756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61323 #29564756