Subgroups — C₆₁×#25801 #29529234

Order 15616.

1444 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3154	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#471	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#454	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#455	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3008	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2020	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2004	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2003	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1974	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1764	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#577	—	2	4	no	—
19	C₆₁×#577	—	2	4	no	—
20	C₂×#137×C₆₁	—	2	1	no	—
21	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×AGL(1,ℤ/8)×C₆₁	—	2	1	no	—
25	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×#135×C₆₁	—	2	1	no	—
29	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
30	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
31	C₂²×SD₁₆×C₆₁	—	2	1	no	—
32	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
33	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
34	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#536	C₂²	1	1	yes	characteristic, complemented
37	C₆₁×#535	C₂²	1	1	yes	characteristic
38	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#497	—	2	1	no	—
41	C₆₁×#496	—	2	1	no	—
42	C₆₁×#495	—	2	1	no	—
43	C₆₁×#495	—	2	4	no	—
44	C₆₁×#492	—	2	1	no	—
45	C₆₁×#471	—	2	4	no	—
46	C₆₁×#455	—	2	4	no	—
47	C₆₁×#454	—	2	4	no	—
48	C₆₁×#452	—	2	2	no	—
49	C₆₁×#451	—	2	2	no	—
50	C₆₁×#449	—	2	2	no	—
51	C₆₁×#447	—	2	2	no	—
52	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic, complemented
53	C₂×#104×C₆₁	C₂²	1	1	yes	characteristic
54	C₂×#104×C₆₁	C₂²	1	1	yes	characteristic
55	C₂×#104×C₆₁	C₂²	1	1	yes	characteristic, complemented
56	C₆₁×#419	C₂²	1	1	yes	characteristic, complemented
57	C₆₁×#418	C₂²	1	1	yes	characteristic
58	C₆₁×#416	C₂²	1	1	yes	characteristic
59	C₂×#101×C₆₁	C₂²	1	1	yes	characteristic, complemented
60	C₂×#101×C₆₁	C₂²	1	1	yes	characteristic, complemented
61	C₂×#100×C₆₁	C₂²	1	1	yes	characteristic
62	C₂×#100×C₆₁	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#408	C₂²	1	1	yes	characteristic
64	C₆₁×#408	C₂²	1	1	yes	characteristic, complemented
65	C₆₁×#405	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#341	C₂²	1	1	yes	characteristic, complemented
68	C₆₁×#339	C₂²	1	1	yes	characteristic, complemented
69	2₋¹⁺⁴×C₆₁	—	2	2	no	—
70	2₋¹⁺⁴×C₆₁	—	2	2	no	—
71	2₋¹⁺⁴×C₆₁	—	2	2	no	—
72	2₋¹⁺⁴×C₆₁	—	4	1	no	—
73	H(5,𝔽₂)×C₆₁	—	2	2	no	—
74	H(5,𝔽₂)×C₆₁	—	2	2	no	—
75	H(5,𝔽₂)×C₆₁	—	2	2	no	—
76	H(5,𝔽₂)×C₆₁	—	4	1	no	—
77	C₂×#41×C₆₁	—	2	1	no	—
78	C₂×#41×C₆₁	—	2	1	no	—
79	C₂×#41×C₆₁	—	2	1	no	—
80	C₂×#41×C₆₁	—	2	1	no	—
81	C₂×#41×C₆₁	—	4	1	no	—
82	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
83	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₆₁	—	2	1	no	—
86	C₂²×Q₈×C₆₁	—	2	1	no	—
87	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₁	—	2	1	no	—
90	C₂²×D₄×C₆₁	—	2	1	no	—
91	C₂²×D₄×C₆₁	—	4	1	no	—
92	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
94	#137×C₆₁	—	2	8	no	—
95	#137×C₆₁	—	2	2	no	—
96	#137×C₆₁	—	2	2	no	—
97	#137×C₆₁	—	2	2	no	—
98	#137×C₆₁	—	2	2	no	—
99	#137×C₆₁	—	2	2	no	—
100	#137×C₆₁	—	4	1	no	—
101	AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
102	AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
103	AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
104	AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
105	AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
106	AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
107	AGL(1,ℤ/8)×C₆₁	—	4	1	no	—
108	#135×C₆₁	—	2	8	no	—
109	#135×C₆₁	—	2	2	no	—
110	#135×C₆₁	—	2	2	no	—
111	C₂×Q₁₆×C₆₁	—	2	1	no	—
112	C₂×Q₁₆×C₆₁	—	2	2	no	—
113	C₂×Q₁₆×C₆₁	—	2	1	no	—
114	C₂×Q₁₆×C₆₁	—	2	1	no	—
115	C₂×Q₁₆×C₆₁	—	2	2	no	—
116	C₂×Q₁₆×C₆₁	—	4	1	no	—
117	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic
118	C₂×SD₁₆×C₆₁	—	2	8	no	—
119	C₂×SD₁₆×C₆₁	—	2	1	no	—
120	C₂×SD₁₆×C₆₁	—	2	1	no	—
121	C₂×SD₁₆×C₆₁	—	2	1	no	—
122	C₂×SD₁₆×C₆₁	—	2	1	no	—
123	C₂×SD₁₆×C₆₁	—	2	1	no	—
124	C₂×SD₁₆×C₆₁	—	2	1	no	—
125	C₂×SD₁₆×C₆₁	—	2	1	no	—
126	C₂×SD₁₆×C₆₁	—	2	1	no	—
127	C₂×SD₁₆×C₆₁	—	2	2	no	—
128	C₂×SD₁₆×C₆₁	—	2	2	no	—
129	C₂×SD₁₆×C₆₁	—	2	1	no	—
130	C₂×SD₁₆×C₆₁	—	2	2	no	—
131	C₂×SD₁₆×C₆₁	—	2	1	no	—
132	C₂×SD₁₆×C₆₁	D₄	1	1	yes	characteristic
133	C₂×SD₁₆×C₆₁	D₄	1	1	yes	characteristic
134	C₂×SD₁₆×C₆₁	D₄	1	4	yes	complemented
135	C₂×D₈×C₆₁	—	2	1	no	—
136	C₂×D₈×C₆₁	—	2	2	no	—
137	C₂×D₈×C₆₁	—	2	1	no	—
138	C₂×D₈×C₆₁	—	2	1	no	—
139	C₂×D₈×C₆₁	—	2	2	no	—
140	C₂×D₈×C₆₁	—	4	1	no	—
141	C₂×D₈×C₆₁	D₄	1	1	yes	characteristic
142	#131×C₆₁	—	2	2	no	—
143	#131×C₆₁	D₄	1	4	yes	complemented
144	C₂×M₁₆×C₆₁	—	2	1	no	—
145	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₆₁	—	2	1	no	—
150	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₆₁	—	2	1	no	—
153	#127×C₆₁	—	2	1	no	—
154	#124×C₆₁	—	2	1	no	—
155	#124×C₆₁	—	2	2	no	—
156	#124×C₆₁	—	2	1	no	—
157	#124×C₆₁	—	2	2	no	—
158	#124×C₆₁	—	2	2	no	—
159	#124×C₆₁	—	2	2	no	—
160	#123×C₆₁	—	4	1	no	—
161	C₂²⋊Q₈×C₆₁	—	2	2	no	—
162	#121×C₆₁	—	2	2	no	—
163	#120×C₆₁	—	4	1	no	—
164	#117×C₆₁	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₆₁	—	4	1	no	—
166	C₂×C₂²⋊C₄×C₆₁	—	4	1	no	—
167	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
168	#108×C₆₁	—	2	2	no	—
169	#104×C₆₁	—	2	2	no	—
170	#104×C₆₁	—	2	2	no	—
171	#104×C₆₁	D₄	1	4	yes	complemented
172	#103×C₆₁	—	2	2	no	—
173	#103×C₆₁	D₄	1	2	yes	—
174	#102×C₆₁	—	2	2	no	—
175	#102×C₆₁	D₄	1	2	yes	—
176	#101×C₆₁	—	2	2	no	—
177	#101×C₆₁	—	2	2	no	—
178	#100×C₆₁	—	2	2	no	—
179	#100×C₆₁	—	2	2	no	—
180	C₂²⋊C₈×C₆₁	—	2	2	no	—
181	C₂²⋊C₈×C₆₁	—	2	2	no	—
182	#97×C₆₁	—	2	1	no	—
183	C₄×C₈×C₆₁	—	2	2	no	—
184	C₄×C₈×C₆₁	—	2	1	no	—
185	C₂⁴×C₆₁	—	2	1	no	—
186	C₂⁴×C₆₁	—	2	1	no	—
187	C₂⁴×C₆₁	—	4	1	no	—
188	#41×C₆₁	—	2	1	no	—
189	#41×C₆₁	—	2	1	no	—
190	#41×C₆₁	—	2	4	no	—
191	#41×C₆₁	—	2	4	no	—
192	#41×C₆₁	—	2	1	no	—
193	#41×C₆₁	—	2	1	no	—
194	#41×C₆₁	—	2	1	no	—
195	#41×C₆₁	—	2	1	no	—
196	#41×C₆₁	—	2	1	no	—
197	#41×C₆₁	—	2	1	no	—
198	#41×C₆₁	—	2	1	no	—
199	#41×C₆₁	—	2	1	no	—
200	#41×C₆₁	—	4	2	no	—
201	#41×C₆₁	—	4	4	no	—
202	#41×C₆₁	—	4	2	no	—
203	#41×C₆₁	—	4	2	no	—
204	#41×C₆₁	—	4	2	no	—
205	#41×C₆₁	—	4	4	no	—
206	#41×C₆₁	—	4	2	no	—
207	#41×C₆₁	—	4	2	no	—
208	#41×C₆₁	C₂×D₄	1	2	yes	—
209	#41×C₆₁	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₆₁	—	2	1	no	—
211	C₂×Q₈×C₆₁	—	2	4	no	—
212	C₂×Q₈×C₆₁	—	2	1	no	—
213	C₂×Q₈×C₆₁	—	2	1	no	—
214	C₂×Q₈×C₆₁	—	2	1	no	—
215	C₂×Q₈×C₆₁	—	2	1	no	—
216	C₂×Q₈×C₆₁	—	2	1	no	—
217	C₂×Q₈×C₆₁	—	2	1	no	—
218	C₂×Q₈×C₆₁	—	2	1	no	—
219	C₂×Q₈×C₆₁	—	2	1	no	—
220	C₂×Q₈×C₆₁	—	2	1	no	—
221	C₂×Q₈×C₆₁	—	2	1	no	—
222	C₂×Q₈×C₆₁	—	4	1	no	—
223	C₂×Q₈×C₆₁	—	4	2	no	—
224	C₂×Q₈×C₆₁	—	4	2	no	—
225	C₂×Q₈×C₆₁	—	4	2	no	—
226	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
227	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
229	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
230	C₂×D₄×C₆₁	—	2	1	no	—
231	C₂×D₄×C₆₁	—	2	4	no	—
232	C₂×D₄×C₆₁	—	2	1	no	—
233	C₂×D₄×C₆₁	—	2	1	no	—
234	C₂×D₄×C₆₁	—	2	1	no	—
235	C₂×D₄×C₆₁	—	2	1	no	—
236	C₂×D₄×C₆₁	—	2	1	no	—
237	C₂×D₄×C₆₁	—	2	1	no	—
238	C₂×D₄×C₆₁	—	2	1	no	—
239	C₂×D₄×C₆₁	—	2	1	no	—
240	C₂×D₄×C₆₁	—	2	1	no	—
241	C₂×D₄×C₆₁	—	2	1	no	—
242	C₂×D₄×C₆₁	—	2	1	no	—
243	C₂×D₄×C₆₁	—	2	1	no	—
244	C₂×D₄×C₆₁	—	2	1	no	—
245	C₂×D₄×C₆₁	—	4	2	no	—
246	C₂×D₄×C₆₁	—	4	1	no	—
247	C₂×D₄×C₆₁	—	4	1	no	—
248	C₂×D₄×C₆₁	—	4	2	no	—
249	C₂×D₄×C₆₁	—	4	2	no	—
250	C₂×D₄×C₆₁	—	4	4	no	—
251	C₂×D₄×C₆₁	—	4	4	no	—
252	C₂×D₄×C₆₁	—	4	1	no	—
253	C₂×D₄×C₆₁	—	4	2	no	—
254	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₆₁	—	2	1	no	—
259	C₂²×C₄×C₆₁	—	2	1	no	—
260	C₂²×C₄×C₆₁	—	2	1	no	—
261	C₂²×C₄×C₆₁	—	2	1	no	—
262	C₂²×C₄×C₆₁	—	2	1	no	—
263	C₂²×C₄×C₆₁	—	2	1	no	—
264	C₂²×C₄×C₆₁	—	4	1	no	—
265	C₂²×C₄×C₆₁	—	4	1	no	—
266	C₂²×C₄×C₆₁	—	4	1	no	—
267	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₆₁	—	2	4	no	—
269	Q₁₆×C₆₁	—	2	2	no	—
270	Q₁₆×C₆₁	—	4	4	no	—
271	Q₁₆×C₆₁	—	4	2	no	—
272	Q₁₆×C₆₁	—	4	2	no	—
273	SD₁₆×C₆₁	—	2	4	no	—
274	SD₁₆×C₆₁	—	2	4	no	—
275	SD₁₆×C₆₁	—	2	2	no	—
276	SD₁₆×C₆₁	—	2	4	no	—
277	SD₁₆×C₆₁	—	2	4	no	—
278	SD₁₆×C₆₁	—	2	2	no	—
279	SD₁₆×C₆₁	—	4	2	no	—
280	SD₁₆×C₆₁	—	4	2	no	—
281	SD₁₆×C₆₁	—	4	2	no	—
282	SD₁₆×C₆₁	—	4	2	no	—
283	SD₁₆×C₆₁	—	4	2	no	—
284	SD₁₆×C₆₁	—	4	2	no	—
285	D₈×C₆₁	—	2	4	no	—
286	D₈×C₆₁	—	2	2	no	—
287	D₈×C₆₁	—	4	4	no	—
288	D₈×C₆₁	—	4	2	no	—
289	D₈×C₆₁	—	4	2	no	—
290	M₁₆×C₆₁	—	2	1	no	—
291	M₁₆×C₆₁	—	2	1	no	—
292	M₁₆×C₆₁	—	2	4	no	—
293	M₁₆×C₆₁	—	2	1	no	—
294	M₁₆×C₆₁	—	2	1	no	—
295	M₁₆×C₆₁	—	2	1	no	—
296	M₁₆×C₆₁	—	2	1	no	—
297	M₁₆×C₆₁	C₂×D₄	1	2	yes	—
298	M₁₆×C₆₁	C₂×D₄	1	2	yes	—
299	C₂×C₈×C₆₁	—	2	1	no	—
300	C₂×C₈×C₆₁	—	2	1	no	—
301	C₂×C₈×C₆₁	—	2	1	no	—
302	C₂×C₈×C₆₁	—	2	1	no	—
303	C₂×C₈×C₆₁	—	2	4	no	—
304	C₂×C₈×C₆₁	—	2	1	no	—
305	C₂×C₈×C₆₁	—	2	1	no	—
306	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
307	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
308	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
309	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
310	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₆₁	—	4	2	no	—
312	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
313	C₂²⋊C₄×C₆₁	—	2	1	no	—
314	C₂²⋊C₄×C₆₁	—	4	4	no	—
315	C₂²⋊C₄×C₆₁	—	4	2	no	—
316	C₂²⋊C₄×C₆₁	—	4	4	no	—
317	C₂²⋊C₄×C₆₁	—	4	2	no	—
318	C₄²×C₆₁	—	2	1	no	—
319	C₄²×C₆₁	—	2	1	no	—
320	C₄²×C₆₁	C₂×D₄	1	2	yes	—
321	C₂³×C₆₁	—	2	1	no	—
322	C₂³×C₆₁	—	2	1	no	—
323	C₂³×C₆₁	—	2	1	no	—
324	C₂³×C₆₁	—	2	2	no	—
325	C₂³×C₆₁	—	4	4	no	—
326	C₂³×C₆₁	—	4	1	no	—
327	C₂³×C₆₁	—	4	1	no	—
328	C₂³×C₆₁	—	4	1	no	—
329	C₂³×C₆₁	—	4	1	no	—
330	C₂³×C₆₁	—	4	1	no	—
331	C₂³×C₆₁	—	8	2	no	—
332	C₂³×C₆₁	—	8	2	no	—
333	C₂³×C₆₁	—	16	2	no	—
334	C₂³×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
335	Q₈×C₆₁	—	2	1	no	—
336	Q₈×C₆₁	—	2	1	no	—
337	Q₈×C₆₁	—	2	2	no	—
338	Q₈×C₆₁	—	2	1	no	—
339	Q₈×C₆₁	—	2	1	no	—
340	Q₈×C₆₁	—	2	2	no	—
341	Q₈×C₆₁	—	2	1	no	—
342	Q₈×C₆₁	—	4	4	no	—
343	Q₈×C₆₁	—	4	1	no	—
344	Q₈×C₆₁	—	4	1	no	—
345	Q₈×C₆₁	—	4	1	no	—
346	Q₈×C₆₁	—	4	1	no	—
347	Q₈×C₆₁	—	4	1	no	—
348	Q₈×C₆₁	—	4	1	no	—
349	Q₈×C₆₁	#127	1	2	yes	—
350	D₄×C₆₁	—	2	2	no	—
351	D₄×C₆₁	—	2	2	no	—
352	D₄×C₆₁	—	2	1	no	—
353	D₄×C₆₁	—	2	2	no	—
354	D₄×C₆₁	—	2	1	no	—
355	D₄×C₆₁	—	2	1	no	—
356	D₄×C₆₁	—	2	2	no	—
357	D₄×C₆₁	—	2	1	no	—
358	D₄×C₆₁	—	2	1	no	—
359	D₄×C₆₁	—	4	4	no	—
360	D₄×C₆₁	—	4	4	no	—
361	D₄×C₆₁	—	4	4	no	—
362	D₄×C₆₁	—	4	1	no	—
363	D₄×C₆₁	—	4	1	no	—
364	D₄×C₆₁	—	4	1	no	—
365	D₄×C₆₁	—	4	1	no	—
366	D₄×C₆₁	—	4	1	no	—
367	D₄×C₆₁	—	4	1	no	—
368	D₄×C₆₁	—	4	1	no	—
369	D₄×C₆₁	—	4	1	no	—
370	D₄×C₆₁	—	4	1	no	—
371	D₄×C₆₁	—	4	1	no	—
372	D₄×C₆₁	—	16	2	no	—
373	D₄×C₆₁	#127	1	2	yes	—
374	C₂×C₄×C₆₁	—	2	1	no	—
375	C₂×C₄×C₆₁	—	2	2	no	—
376	C₂×C₄×C₆₁	—	2	2	no	—
377	C₂×C₄×C₆₁	—	2	2	no	—
378	C₂×C₄×C₆₁	—	2	2	no	—
379	C₂×C₄×C₆₁	—	2	2	no	—
380	C₂×C₄×C₆₁	—	2	1	no	—
381	C₂×C₄×C₆₁	—	2	1	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	—	4	4	no	—
386	C₂×C₄×C₆₁	—	4	1	no	—
387	C₂×C₄×C₆₁	—	4	1	no	—
388	C₂×C₄×C₆₁	—	4	1	no	—
389	C₂×C₄×C₆₁	—	4	1	no	—
390	C₂×C₄×C₆₁	—	4	1	no	—
391	C₂×C₄×C₆₁	—	4	1	no	—
392	C₂×C₄×C₆₁	—	4	1	no	—
393	C₂×C₄×C₆₁	—	4	1	no	—
394	C₂×C₄×C₆₁	—	4	1	no	—
395	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
401	C₈×C₆₁	—	2	2	no	—
402	C₈×C₆₁	—	2	2	no	—
403	C₈×C₆₁	—	2	2	no	—
404	C₈×C₆₁	—	4	1	no	—
405	C₈×C₆₁	—	4	1	no	—
406	C₈×C₆₁	#120	1	2	yes	—
407	C₈×C₆₁	#120	1	2	yes	—
408	#25801	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
409	C₂²×C₆₁	—	2	2	no	—
410	C₂²×C₆₁	—	2	2	no	—
411	C₂²×C₆₁	—	4	2	no	—
412	C₂²×C₆₁	—	4	1	no	—
413	C₂²×C₆₁	—	4	1	no	—
414	C₂²×C₆₁	—	4	2	no	—
415	C₂²×C₆₁	—	4	2	no	—
416	C₂²×C₆₁	—	4	2	no	—
417	C₂²×C₆₁	—	8	2	no	—
418	C₂²×C₆₁	—	8	2	no	—
419	C₂²×C₆₁	—	8	2	no	—
420	C₂²×C₆₁	—	8	1	no	—
421	C₂²×C₆₁	—	8	2	no	—
422	C₂²×C₆₁	—	16	1	no	—
423	C₂²×C₆₁	—	16	1	no	—
424	C₂²×C₆₁	—	16	4	no	—
425	C₂²×C₆₁	#535	1	1	yes	characteristic
426	C₂²×C₆₁	D₄²	1	1	yes	characteristic
427	C₂²×C₆₁	D₄²	1	1	yes	characteristic
428	C₄×C₆₁	—	2	2	no	—
429	C₄×C₆₁	—	4	2	no	—
430	C₄×C₆₁	—	4	1	no	—
431	C₄×C₆₁	—	4	2	no	—
432	C₄×C₆₁	—	4	1	no	—
433	C₄×C₆₁	—	4	2	no	—
434	C₄×C₆₁	—	8	1	no	—
435	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
436	C₄×C₆₁	C₂×#127	1	1	yes	characteristic
437	C₄×C₆₁	D₄²	1	1	yes	characteristic
438	C₄×C₆₁	D₄²	1	1	yes	characteristic
439	C₂×#577	C₂×C₆₁	1	1	yes	characteristic, complemented
440	#3154	C₂×C₆₁	1	1	yes	characteristic, complemented
441	C₂×#495	C₂×C₆₁	1	1	yes	characteristic, complemented
442	C₂×#471	C₂×C₆₁	1	1	yes	characteristic, complemented
443	C₂×#454	C₂×C₆₁	1	1	yes	characteristic, complemented
444	C₂×#455	C₂×C₆₁	1	1	yes	characteristic, complemented
445	#3011	C₂×C₆₁	1	1	yes	characteristic, complemented
446	#3008	C₂×C₆₁	1	1	yes	characteristic, complemented
447	#2020	C₂×C₆₁	1	1	yes	characteristic, complemented
448	#2018	C₂×C₆₁	1	1	yes	characteristic, complemented
449	#2004	C₂×C₆₁	1	1	yes	characteristic, complemented
450	#2003	C₂×C₆₁	1	1	yes	characteristic, complemented
451	#1977	C₂×C₆₁	1	1	yes	characteristic, complemented
452	#1974	C₂×C₆₁	1	1	yes	characteristic, complemented
453	#1764	C₂×C₆₁	1	1	yes	characteristic, complemented
454	C₂×C₆₁	—	2	1	no	—
455	C₂×C₆₁	—	2	1	no	—
456	C₂×C₆₁	—	4	2	no	—
457	C₂×C₆₁	—	8	1	no	—
458	C₂×C₆₁	—	8	1	no	—
459	C₂×C₆₁	—	8	2	no	—
460	C₂×C₆₁	—	16	1	no	—
461	C₂×C₆₁	#2433	1	1	yes	characteristic
462	C₂×C₆₁	#3290	1	2	yes	—
463	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
464	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	1	yes	characteristic
465	#577	—	2	4	no	—
466	#577	—	2	4	no	—
467	C₂×#137	—	2	1	no	—
468	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
469	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
470	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
471	C₂×AGL(1,ℤ/8)	—	2	1	no	—
472	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
473	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
474	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic, complemented
475	C₂×#135	—	2	1	no	—
476	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
477	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
478	C₂²×SD₁₆	—	2	1	no	—
479	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
480	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
481	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
482	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
483	#536	C₂²×C₆₁	1	1	yes	characteristic, complemented
484	#535	C₂²×C₆₁	1	1	yes	characteristic
485	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
486	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
487	#497	—	2	1	no	—
488	#496	—	2	1	no	—
489	#495	—	2	1	no	—
490	#495	—	2	4	no	—
491	#492	—	2	1	no	—
492	#471	—	2	4	no	—
493	#455	—	2	4	no	—
494	#454	—	2	4	no	—
495	#452	—	2	2	no	—
496	#451	—	2	2	no	—
497	#449	—	2	2	no	—
498	#447	—	2	2	no	—
499	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic, complemented
500	C₂×#104	C₂²×C₆₁	1	1	yes	characteristic
501	C₂×#104	C₂²×C₆₁	1	1	yes	characteristic
502	C₂×#104	C₂²×C₆₁	1	1	yes	characteristic, complemented
503	#419	C₂²×C₆₁	1	1	yes	characteristic, complemented
504	#418	C₂²×C₆₁	1	1	yes	characteristic
505	#416	C₂²×C₆₁	1	1	yes	characteristic
506	C₂×#101	C₂²×C₆₁	1	1	yes	characteristic, complemented
507	C₂×#101	C₂²×C₆₁	1	1	yes	characteristic, complemented
508	C₂×#100	C₂²×C₆₁	1	1	yes	characteristic
509	C₂×#100	C₂²×C₆₁	1	1	yes	characteristic, complemented
510	#408	C₂²×C₆₁	1	1	yes	characteristic
511	#408	C₂²×C₆₁	1	1	yes	characteristic, complemented
512	#405	C₂²×C₆₁	1	1	yes	characteristic, complemented
513	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
514	#341	C₂²×C₆₁	1	1	yes	characteristic, complemented
515	#339	C₂²×C₆₁	1	1	yes	characteristic, complemented
516	C₆₁	#25801	1	1	yes	characteristic, direct product factor, Sylow
517	2₋¹⁺⁴	—	2	2	no	—
518	2₋¹⁺⁴	—	2	2	no	—
519	2₋¹⁺⁴	—	2	2	no	—
520	2₋¹⁺⁴	—	4	1	no	—
521	H(5,𝔽₂)	—	2	2	no	—
522	H(5,𝔽₂)	—	2	2	no	—
523	H(5,𝔽₂)	—	2	2	no	—
524	H(5,𝔽₂)	—	4	1	no	—
525	C₂×#41	—	2	1	no	—
526	C₂×#41	—	2	1	no	—
527	C₂×#41	—	2	1	no	—
528	C₂×#41	—	2	1	no	—
529	C₂×#41	—	4	1	no	—
530	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
531	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
532	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
533	C₂²×Q₈	—	2	1	no	—
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
536	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	—	4	1	no	—
540	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
542	#137	—	2	8	no	—
543	#137	—	2	2	no	—
544	#137	—	2	2	no	—
545	#137	—	2	2	no	—
546	#137	—	2	2	no	—
547	#137	—	2	2	no	—
548	#137	—	4	1	no	—
549	AGL(1,ℤ/8)	—	2	8	no	—
550	AGL(1,ℤ/8)	—	2	2	no	—
551	AGL(1,ℤ/8)	—	2	2	no	—
552	AGL(1,ℤ/8)	—	2	2	no	—
553	AGL(1,ℤ/8)	—	2	2	no	—
554	AGL(1,ℤ/8)	—	2	2	no	—
555	AGL(1,ℤ/8)	—	4	1	no	—
556	#135	—	2	8	no	—
557	#135	—	2	2	no	—
558	#135	—	2	2	no	—
559	C₂×Q₁₆	—	2	1	no	—
560	C₂×Q₁₆	—	2	2	no	—
561	C₂×Q₁₆	—	2	1	no	—
562	C₂×Q₁₆	—	2	1	no	—
563	C₂×Q₁₆	—	2	2	no	—
564	C₂×Q₁₆	—	4	1	no	—
565	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic
566	C₂×SD₁₆	—	2	8	no	—
567	C₂×SD₁₆	—	2	1	no	—
568	C₂×SD₁₆	—	2	1	no	—
569	C₂×SD₁₆	—	2	1	no	—
570	C₂×SD₁₆	—	2	1	no	—
571	C₂×SD₁₆	—	2	1	no	—
572	C₂×SD₁₆	—	2	1	no	—
573	C₂×SD₁₆	—	2	1	no	—
574	C₂×SD₁₆	—	2	1	no	—
575	C₂×SD₁₆	—	2	2	no	—
576	C₂×SD₁₆	—	2	2	no	—
577	C₂×SD₁₆	—	2	1	no	—
578	C₂×SD₁₆	—	2	2	no	—
579	C₂×SD₁₆	—	2	1	no	—
580	C₂×SD₁₆	D₄×C₆₁	1	1	yes	characteristic
581	C₂×SD₁₆	D₄×C₆₁	1	1	yes	characteristic
582	C₂×SD₁₆	D₄×C₆₁	1	4	yes	complemented
583	C₂×D₈	—	2	1	no	—
584	C₂×D₈	—	2	2	no	—
585	C₂×D₈	—	2	1	no	—
586	C₂×D₈	—	2	1	no	—
587	C₂×D₈	—	2	2	no	—
588	C₂×D₈	—	4	1	no	—
589	C₂×D₈	D₄×C₆₁	1	1	yes	characteristic
590	#131	—	2	2	no	—
591	#131	D₄×C₆₁	1	4	yes	complemented
592	C₂×M₁₆	—	2	1	no	—
593	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
594	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
595	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
596	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
597	C₂²×C₈	—	2	1	no	—
598	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
599	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
600	C₄⋊Q₈	—	2	1	no	—
601	#127	—	2	1	no	—
602	#124	—	2	2	no	—
603	#124	—	2	1	no	—
604	#124	—	2	2	no	—
605	#124	—	2	1	no	—
606	#124	—	2	2	no	—
607	#124	—	2	2	no	—
608	#123	—	4	1	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	#121	—	2	2	no	—
611	#120	—	4	1	no	—
612	#117	C₂³×C₆₁	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	—	4	1	no	—
614	C₂×C₂²⋊C₄	—	4	1	no	—
615	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
616	#108	—	2	2	no	—
617	#104	—	2	2	no	—
618	#104	—	2	2	no	—
619	#104	D₄×C₆₁	1	4	yes	complemented
620	#103	—	2	2	no	—
621	#103	D₄×C₆₁	1	2	yes	—
622	#102	—	2	2	no	—
623	#102	D₄×C₆₁	1	2	yes	—
624	#101	—	2	2	no	—
625	#101	—	2	2	no	—
626	#100	—	2	2	no	—
627	#100	—	2	2	no	—
628	C₂²⋊C₈	—	2	2	no	—
629	C₂²⋊C₈	—	2	2	no	—
630	#97	—	2	1	no	—
631	C₄×C₈	—	2	2	no	—
632	C₄×C₈	—	2	1	no	—
633	C₂⁴	—	2	1	no	—
634	C₂⁴	—	2	1	no	—
635	C₂⁴	—	4	1	no	—
636	#41	—	2	1	no	—
637	#41	—	2	1	no	—
638	#41	—	2	4	no	—
639	#41	—	2	4	no	—
640	#41	—	2	1	no	—
641	#41	—	2	1	no	—
642	#41	—	2	1	no	—
643	#41	—	2	1	no	—
644	#41	—	2	1	no	—
645	#41	—	2	1	no	—
646	#41	—	2	1	no	—
647	#41	—	2	1	no	—
648	#41	—	4	2	no	—
649	#41	—	4	4	no	—
650	#41	—	4	2	no	—
651	#41	—	4	2	no	—
652	#41	—	4	2	no	—
653	#41	—	4	4	no	—
654	#41	—	4	2	no	—
655	#41	—	4	2	no	—
656	#41	C₂×D₄×C₆₁	1	2	yes	—
657	#41	C₂×D₄×C₆₁	1	2	yes	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	4	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	4	1	no	—
671	C₂×Q₈	—	4	2	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
675	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
676	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
677	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	1	no	—
695	C₂×D₄	—	4	1	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	4	no	—
700	C₂×D₄	—	4	1	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
703	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
704	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
705	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	1	no	—
714	C₂²×C₄	—	4	1	no	—
715	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
716	Q₁₆	—	2	4	no	—
717	Q₁₆	—	2	2	no	—
718	Q₁₆	—	4	4	no	—
719	Q₁₆	—	4	2	no	—
720	Q₁₆	—	4	2	no	—
721	SD₁₆	—	2	4	no	—
722	SD₁₆	—	2	4	no	—
723	SD₁₆	—	2	2	no	—
724	SD₁₆	—	2	4	no	—
725	SD₁₆	—	2	4	no	—
726	SD₁₆	—	2	2	no	—
727	SD₁₆	—	4	2	no	—
728	SD₁₆	—	4	2	no	—
729	SD₁₆	—	4	2	no	—
730	SD₁₆	—	4	2	no	—
731	SD₁₆	—	4	2	no	—
732	SD₁₆	—	4	2	no	—
733	D₈	—	2	4	no	—
734	D₈	—	2	2	no	—
735	D₈	—	4	4	no	—
736	D₈	—	4	2	no	—
737	D₈	—	4	2	no	—
738	M₁₆	—	2	1	no	—
739	M₁₆	—	2	1	no	—
740	M₁₆	—	2	4	no	—
741	M₁₆	—	2	1	no	—
742	M₁₆	—	2	1	no	—
743	M₁₆	—	2	1	no	—
744	M₁₆	—	2	1	no	—
745	M₁₆	C₂×D₄×C₆₁	1	2	yes	—
746	M₁₆	C₂×D₄×C₆₁	1	2	yes	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	2	1	no	—
749	C₂×C₈	—	2	1	no	—
750	C₂×C₈	—	2	1	no	—
751	C₂×C₈	—	2	4	no	—
752	C₂×C₈	—	2	1	no	—
753	C₂×C₈	—	2	1	no	—
754	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
755	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
756	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
757	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
758	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	4	4	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	4	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	C₂×D₄×C₆₁	1	2	yes	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	1	no	—
775	C₂³	—	4	1	no	—
776	C₂³	—	4	1	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	8	2	no	—
780	C₂³	—	8	2	no	—
781	C₂³	—	16	2	no	—
782	C₂³	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
783	Q₈	—	2	1	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	4	4	no	—
791	Q₈	—	4	1	no	—
792	Q₈	—	4	1	no	—
793	Q₈	—	4	1	no	—
794	Q₈	—	4	1	no	—
795	Q₈	—	4	1	no	—
796	Q₈	—	4	1	no	—
797	Q₈	#127×C₆₁	1	2	yes	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	1	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	1	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	1	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	1	no	—
811	D₄	—	4	1	no	—
812	D₄	—	4	1	no	—
813	D₄	—	4	1	no	—
814	D₄	—	4	1	no	—
815	D₄	—	4	1	no	—
816	D₄	—	4	1	no	—
817	D₄	—	4	1	no	—
818	D₄	—	4	1	no	—
819	D₄	—	4	1	no	—
820	D₄	—	16	2	no	—
821	D₄	#127×C₆₁	1	2	yes	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
848	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
849	C₈	—	2	2	no	—
850	C₈	—	2	2	no	—
851	C₈	—	2	2	no	—
852	C₈	—	4	1	no	—
853	C₈	—	4	1	no	—
854	C₈	#120×C₆₁	1	2	yes	—
855	C₈	#120×C₆₁	1	2	yes	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	8	2	no	—
865	C₂²	—	8	2	no	—
866	C₂²	—	8	2	no	—
867	C₂²	—	8	2	no	—
868	C₂²	—	8	1	no	—
869	C₂²	—	16	1	no	—
870	C₂²	—	16	1	no	—
871	C₂²	—	16	4	no	—
872	C₂²	C₆₁×#535	1	1	yes	characteristic
873	C₂²	D₄²×C₆₁	1	1	yes	characteristic
874	C₂²	D₄²×C₆₁	1	1	yes	characteristic
875	C₄	—	2	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	8	1	no	—
882	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
883	C₄	C₂×#127×C₆₁	1	1	yes	characteristic
884	C₄	D₄²×C₆₁	1	1	yes	characteristic
885	C₄	D₄²×C₆₁	1	1	yes	characteristic
886	C₂	—	2	1	no	—
887	C₂	—	2	1	no	—
888	C₂	—	4	2	no	—
889	C₂	—	8	1	no	—
890	C₂	—	8	1	no	—
891	C₂	—	8	2	no	—
892	C₂	—	16	1	no	—
893	C₂	C₆₁×#2433	1	1	yes	characteristic
894	C₂	C₆₁×#3290	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#577	C₂	semidirect
2. C₆₁×#3154	C₂	semidirect
3. C₂×C₆₁×#495	C₂	semidirect
4. C₂×C₆₁×#471	C₂	semidirect
5. C₂×C₆₁×#454	C₂	semidirect
6. C₂×C₆₁×#455	C₂	semidirect
7. C₆₁×#3011	C₂	semidirect
8. C₆₁×#3008	C₂	semidirect
9. C₆₁×#2020	C₂	semidirect
10. C₆₁×#2018	C₂	semidirect
11. C₆₁×#2004	C₂	semidirect
12. C₆₁×#2003	C₂	semidirect
13. C₆₁×#1977	C₂	semidirect
14. C₆₁×#1974	C₂	semidirect
15. C₆₁×#1764	C₂	semidirect
27. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
30. C₂²×Q₁₆×C₆₁	C₂²	semidirect
33. C₂²×SD₁₆×C₆₁	C₂²	semidirect
36. C₆₁×#536	C₂²	semidirect
39. C₂×#124×C₆₁	C₂²	semidirect
52. C₂×#108×C₆₁	C₂²	semidirect
55. C₂×#104×C₆₁	C₂²	semidirect
56. C₆₁×#419	C₂²	semidirect
59. C₂×#101×C₆₁	C₂²	semidirect
60. C₂×#101×C₆₁	C₂²	semidirect
62. C₂×#100×C₆₁	C₂²	semidirect
64. C₆₁×#408	C₂²	semidirect
65. C₆₁×#405	C₂²	semidirect
66. C₂×C₄×C₈×C₆₁	C₂²	semidirect
67. C₆₁×#341	C₂²	semidirect
68. C₆₁×#339	C₂²	semidirect
134. C₂×SD₁₆×C₆₁	D₄	semidirect
143. #131×C₆₁	D₄	semidirect
171. #104×C₆₁	D₄	semidirect
408. #25801	C₆₁	direct (N × H)
439. C₂×#577	C₂×C₆₁	semidirect
440. #3154	C₂×C₆₁	semidirect
441. C₂×#495	C₂×C₆₁	semidirect
442. C₂×#471	C₂×C₆₁	semidirect
443. C₂×#454	C₂×C₆₁	semidirect
444. C₂×#455	C₂×C₆₁	semidirect
445. #3011	C₂×C₆₁	semidirect
446. #3008	C₂×C₆₁	semidirect
447. #2020	C₂×C₆₁	semidirect
448. #2018	C₂×C₆₁	semidirect
449. #2004	C₂×C₆₁	semidirect
450. #2003	C₂×C₆₁	semidirect
451. #1977	C₂×C₆₁	semidirect
452. #1974	C₂×C₆₁	semidirect
453. #1764	C₂×C₆₁	semidirect
474. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
477. C₂²×Q₁₆	C₂²×C₆₁	semidirect
480. C₂²×SD₁₆	C₂²×C₆₁	semidirect
483. #536	C₂²×C₆₁	semidirect
486. C₂×#124	C₂²×C₆₁	semidirect
499. C₂×#108	C₂²×C₆₁	semidirect
502. C₂×#104	C₂²×C₆₁	semidirect
503. #419	C₂²×C₆₁	semidirect
506. C₂×#101	C₂²×C₆₁	semidirect
507. C₂×#101	C₂²×C₆₁	semidirect
509. C₂×#100	C₂²×C₆₁	semidirect
511. #408	C₂²×C₆₁	semidirect
512. #405	C₂²×C₆₁	semidirect
513. C₂×C₄×C₈	C₂²×C₆₁	semidirect
514. #341	C₂²×C₆₁	semidirect
515. #339	C₂²×C₆₁	semidirect
516. C₆₁	#25801	direct (N × H)
582. C₂×SD₁₆	D₄×C₆₁	semidirect
591. #131	D₄×C₆₁	semidirect
619. #104	D₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#577	2
C₆₁×#3154	2
C₂×C₆₁×#495	2
C₂×C₆₁×#471	2
C₂×C₆₁×#454	2
C₂×C₆₁×#455	2
C₆₁×#3011	2
C₆₁×#3008	2
C₆₁×#2020	2
C₆₁×#2018	2
C₆₁×#2004	2
C₆₁×#2003	2
C₆₁×#1977	2
C₆₁×#1974	2
C₆₁×#1764	2
#25801	61

Subgroups — C61×#25801 #29529234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25801 #29529234