Subgroups — C₆₁×#25807 #29529240

Order 15616.

1488 conjugacy classes of subgroups.

The subgroup lattice has 912 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×#3155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#472	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#454	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#453	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3010	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3008	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2019	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×#2002	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1975	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1765	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×AGL(1,ℤ/8)×C₆₁	—	2	1	no	—
23	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
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×SD₁₆×C₆₁	—	2	1	no	—
31	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
32	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#535	C₂²	1	1	yes	characteristic
37	C₆₁×#535	C₂²	1	1	yes	characteristic, complemented
38	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#496	—	2	4	no	—
41	C₆₁×#496	—	2	1	no	—
42	C₆₁×#496	—	2	1	no	—
43	C₆₁×#495	—	2	1	no	—
44	C₆₁×#493	—	2	1	no	—
45	C₆₁×#472	—	2	4	no	—
46	C₆₁×#454	—	2	4	no	—
47	C₆₁×#453	—	2	4	no	—
48	C₆₁×#449	—	2	2	no	—
49	C₆₁×#449	—	2	2	no	—
50	C₆₁×#448	—	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×#100×C₆₁	C₂²	1	1	yes	characteristic
61	C₂×#100×C₆₁	C₂²	1	1	yes	characteristic, complemented
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×#97×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×D₄×C₆₁	—	2	1	no	—
89	C₂²×D₄×C₆₁	—	2	1	no	—
90	C₂²×D₄×C₆₁	—	4	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	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
95	#137×C₆₁	—	2	8	no	—
96	#137×C₆₁	—	2	2	no	—
97	#137×C₆₁	—	2	2	no	—
98	AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
99	AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
100	AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
101	AGL(1,ℤ/8)×C₆₁	—	2	2	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	AGL(1,ℤ/8)×C₆₁	—	4	1	no	—
109	#135×C₆₁	—	2	8	no	—
110	#135×C₆₁	—	2	2	no	—
111	#135×C₆₁	—	2	2	no	—
112	C₂×Q₁₆×C₆₁	—	2	1	no	—
113	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic, complemented
114	C₂×SD₁₆×C₆₁	—	2	8	no	—
115	C₂×SD₁₆×C₆₁	—	2	1	no	—
116	C₂×SD₁₆×C₆₁	—	2	1	no	—
117	C₂×SD₁₆×C₆₁	—	2	2	no	—
118	C₂×SD₁₆×C₆₁	—	2	1	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	2	no	—
125	C₂×SD₁₆×C₆₁	—	2	2	no	—
126	C₂×SD₁₆×C₆₁	—	4	1	no	—
127	C₂×SD₁₆×C₆₁	D₄	1	1	yes	characteristic, complemented
128	C₂×SD₁₆×C₆₁	D₄	1	4	yes	complemented
129	C₂×SD₁₆×C₆₁	D₄	1	1	yes	characteristic, complemented
130	C₂×D₈×C₆₁	—	2	1	no	—
131	C₂×D₈×C₆₁	—	2	2	no	—
132	C₂×D₈×C₆₁	—	2	1	no	—
133	C₂×D₈×C₆₁	—	2	1	no	—
134	C₂×D₈×C₆₁	—	2	1	no	—
135	C₂×D₈×C₆₁	—	2	1	no	—
136	C₂×D₈×C₆₁	—	2	2	no	—
137	C₂×D₈×C₆₁	—	2	2	no	—
138	C₂×D₈×C₆₁	—	2	1	no	—
139	C₂×D₈×C₆₁	—	2	1	no	—
140	C₂×D₈×C₆₁	—	2	2	no	—
141	C₂×D₈×C₆₁	—	4	1	no	—
142	C₂×D₈×C₆₁	D₄	1	1	yes	characteristic, complemented
143	#131×C₆₁	—	2	2	no	—
144	#131×C₆₁	D₄	1	4	yes	complemented
145	C₂×M₁₆×C₆₁	—	2	1	no	—
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	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₆₁	—	2	1	no	—
151	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
153	#127×C₆₁	—	2	2	no	—
154	#127×C₆₁	—	2	1	no	—
155	#127×C₆₁	—	2	1	no	—
156	#127×C₆₁	—	2	2	no	—
157	#124×C₆₁	—	2	1	no	—
158	#124×C₆₁	—	2	1	no	—
159	#124×C₆₁	—	2	2	no	—
160	#124×C₆₁	—	2	2	no	—
161	#121×C₆₁	—	2	2	no	—
162	#121×C₆₁	—	2	2	no	—
163	#120×C₆₁	—	4	1	no	—
164	#120×C₆₁	—	4	1	no	—
165	#117×C₆₁	C₂³	1	1	yes	characteristic
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	complemented
174	#102×C₆₁	—	2	2	no	—
175	#102×C₆₁	D₄	1	2	yes	complemented
176	#101×C₆₁	—	2	2	no	—
177	#100×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	2	no	—
183	#97×C₆₁	—	2	1	no	—
184	C₄×C₈×C₆₁	—	2	1	no	—
185	C₂⁴×C₆₁	—	2	1	no	—
186	C₂⁴×C₆₁	—	2	1	no	—
187	C₂⁴×C₆₁	—	2	1	no	—
188	C₂⁴×C₆₁	—	4	1	no	—
189	#41×C₆₁	—	2	1	no	—
190	#41×C₆₁	—	2	1	no	—
191	#41×C₆₁	—	2	4	no	—
192	#41×C₆₁	—	2	4	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	—	2	1	no	—
201	#41×C₆₁	—	4	2	no	—
202	#41×C₆₁	—	4	4	no	—
203	#41×C₆₁	—	4	2	no	—
204	#41×C₆₁	—	4	2	no	—
205	#41×C₆₁	—	4	2	no	—
206	#41×C₆₁	—	4	4	no	—
207	#41×C₆₁	—	4	2	no	—
208	#41×C₆₁	—	4	2	no	—
209	#41×C₆₁	C₂×D₄	1	2	yes	—
210	#41×C₆₁	C₂×D₄	1	2	yes	—
211	C₂×Q₈×C₆₁	—	2	1	no	—
212	C₂×Q₈×C₆₁	—	2	4	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	—	4	1	no	—
218	C₂×Q₈×C₆₁	—	4	2	no	—
219	C₂×Q₈×C₆₁	—	4	2	no	—
220	C₂×Q₈×C₆₁	—	4	2	no	—
221	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
222	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
224	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
225	C₂×D₄×C₆₁	—	2	1	no	—
226	C₂×D₄×C₆₁	—	2	4	no	—
227	C₂×D₄×C₆₁	—	2	1	no	—
228	C₂×D₄×C₆₁	—	2	1	no	—
229	C₂×D₄×C₆₁	—	2	1	no	—
230	C₂×D₄×C₆₁	—	2	1	no	—
231	C₂×D₄×C₆₁	—	2	1	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	—	2	1	no	—
246	C₂×D₄×C₆₁	—	4	2	no	—
247	C₂×D₄×C₆₁	—	4	1	no	—
248	C₂×D₄×C₆₁	—	4	1	no	—
249	C₂×D₄×C₆₁	—	4	4	no	—
250	C₂×D₄×C₆₁	—	4	2	no	—
251	C₂×D₄×C₆₁	—	4	2	no	—
252	C₂×D₄×C₆₁	—	4	2	no	—
253	C₂×D₄×C₆₁	—	4	4	no	—
254	C₂×D₄×C₆₁	—	4	4	no	—
255	C₂×D₄×C₆₁	—	4	1	no	—
256	C₂×D₄×C₆₁	—	4	2	no	—
257	C₂×D₄×C₆₁	—	8	4	no	—
258	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
259	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₆₁	—	2	1	no	—
263	C₂²×C₄×C₆₁	—	2	1	no	—
264	C₂²×C₄×C₆₁	—	2	1	no	—
265	C₂²×C₄×C₆₁	—	2	1	no	—
266	C₂²×C₄×C₆₁	—	2	1	no	—
267	C₂²×C₄×C₆₁	—	4	1	no	—
268	C₂²×C₄×C₆₁	—	4	1	no	—
269	C₂²×C₄×C₆₁	—	4	1	no	—
270	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
271	Q₁₆×C₆₁	—	2	4	no	—
272	Q₁₆×C₆₁	—	2	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	4	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	D₈×C₆₁	—	2	4	no	—
285	D₈×C₆₁	—	2	2	no	—
286	D₈×C₆₁	—	4	4	no	—
287	D₈×C₆₁	—	4	2	no	—
288	D₈×C₆₁	—	4	2	no	—
289	D₈×C₆₁	—	4	2	no	—
290	D₈×C₆₁	—	4	2	no	—
291	D₈×C₆₁	—	4	2	no	—
292	D₈×C₆₁	—	4	2	no	—
293	M₁₆×C₆₁	—	2	1	no	—
294	M₁₆×C₆₁	—	2	1	no	—
295	M₁₆×C₆₁	—	2	4	no	—
296	M₁₆×C₆₁	—	2	1	no	—
297	M₁₆×C₆₁	—	2	1	no	—
298	M₁₆×C₆₁	—	2	1	no	—
299	M₁₆×C₆₁	—	2	1	no	—
300	M₁₆×C₆₁	C₂×D₄	1	2	yes	—
301	M₁₆×C₆₁	C₂×D₄	1	2	yes	—
302	C₂×C₈×C₆₁	—	2	1	no	—
303	C₂×C₈×C₆₁	—	2	1	no	—
304	C₂×C₈×C₆₁	—	2	1	no	—
305	C₂×C₈×C₆₁	—	2	1	no	—
306	C₂×C₈×C₆₁	—	2	4	no	—
307	C₂×C₈×C₆₁	—	2	1	no	—
308	C₂×C₈×C₆₁	—	2	1	no	—
309	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
310	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
311	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
312	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
313	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
315	C₂²⋊C₄×C₆₁	—	2	1	no	—
316	C₂²⋊C₄×C₆₁	—	4	4	no	—
317	C₂²⋊C₄×C₆₁	—	4	2	no	—
318	C₂²⋊C₄×C₆₁	—	4	2	no	—
319	C₄²×C₆₁	—	2	1	no	—
320	C₄²×C₆₁	—	2	1	no	—
321	C₄²×C₆₁	C₂×D₄	1	2	yes	—
322	C₂³×C₆₁	—	2	1	no	—
323	C₂³×C₆₁	—	2	1	no	—
324	C₂³×C₆₁	—	2	1	no	—
325	C₂³×C₆₁	—	2	2	no	—
326	C₂³×C₆₁	—	4	4	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	—	4	1	no	—
332	C₂³×C₆₁	—	4	1	no	—
333	C₂³×C₆₁	—	4	1	no	—
334	C₂³×C₆₁	—	4	1	no	—
335	C₂³×C₆₁	—	8	2	no	—
336	C₂³×C₆₁	—	8	2	no	—
337	C₂³×C₆₁	—	8	2	no	—
338	C₂³×C₆₁	—	16	2	no	—
339	C₂³×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
340	Q₈×C₆₁	—	2	1	no	—
341	Q₈×C₆₁	—	2	1	no	—
342	Q₈×C₆₁	—	2	2	no	—
343	Q₈×C₆₁	—	2	1	no	—
344	Q₈×C₆₁	—	2	2	no	—
345	Q₈×C₆₁	—	2	1	no	—
346	Q₈×C₆₁	—	2	1	no	—
347	Q₈×C₆₁	—	4	4	no	—
348	Q₈×C₆₁	—	4	1	no	—
349	Q₈×C₆₁	—	4	1	no	—
350	Q₈×C₆₁	#127	1	2	yes	—
351	D₄×C₆₁	—	2	2	no	—
352	D₄×C₆₁	—	2	2	no	—
353	D₄×C₆₁	—	2	1	no	—
354	D₄×C₆₁	—	2	2	no	—
355	D₄×C₆₁	—	2	1	no	—
356	D₄×C₆₁	—	2	1	no	—
357	D₄×C₆₁	—	2	2	no	—
358	D₄×C₆₁	—	2	1	no	—
359	D₄×C₆₁	—	2	1	no	—
360	D₄×C₆₁	—	4	4	no	—
361	D₄×C₆₁	—	4	4	no	—
362	D₄×C₆₁	—	4	4	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	—	4	1	no	—
373	D₄×C₆₁	—	4	1	no	—
374	D₄×C₆₁	—	4	1	no	—
375	D₄×C₆₁	—	4	1	no	—
376	D₄×C₆₁	—	4	1	no	—
377	D₄×C₆₁	—	8	8	no	—
378	D₄×C₆₁	—	16	2	no	—
379	D₄×C₆₁	—	16	2	no	—
380	D₄×C₆₁	#127	1	2	yes	—
381	C₂×C₄×C₆₁	—	2	1	no	—
382	C₂×C₄×C₆₁	—	2	2	no	—
383	C₂×C₄×C₆₁	—	2	2	no	—
384	C₂×C₄×C₆₁	—	2	2	no	—
385	C₂×C₄×C₆₁	—	2	2	no	—
386	C₂×C₄×C₆₁	—	2	2	no	—
387	C₂×C₄×C₆₁	—	2	1	no	—
388	C₂×C₄×C₆₁	—	2	1	no	—
389	C₂×C₄×C₆₁	—	4	4	no	—
390	C₂×C₄×C₆₁	—	4	4	no	—
391	C₂×C₄×C₆₁	—	4	2	no	—
392	C₂×C₄×C₆₁	—	4	4	no	—
393	C₂×C₄×C₆₁	—	4	1	no	—
394	C₂×C₄×C₆₁	—	4	1	no	—
395	C₂×C₄×C₆₁	—	4	1	no	—
396	C₂×C₄×C₆₁	—	4	1	no	—
397	C₂×C₄×C₆₁	—	4	1	no	—
398	C₂×C₄×C₆₁	—	4	1	no	—
399	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
405	C₈×C₆₁	—	2	2	no	—
406	C₈×C₆₁	—	2	2	no	—
407	C₈×C₆₁	—	2	2	no	—
408	C₈×C₆₁	—	4	1	no	—
409	C₈×C₆₁	—	4	1	no	—
410	C₈×C₆₁	#120	1	2	yes	—
411	C₈×C₆₁	#120	1	2	yes	—
412	#25807	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
413	C₂²×C₆₁	—	2	2	no	—
414	C₂²×C₆₁	—	2	2	no	—
415	C₂²×C₆₁	—	4	2	no	—
416	C₂²×C₆₁	—	4	1	no	—
417	C₂²×C₆₁	—	4	1	no	—
418	C₂²×C₆₁	—	4	2	no	—
419	C₂²×C₆₁	—	4	2	no	—
420	C₂²×C₆₁	—	4	2	no	—
421	C₂²×C₆₁	—	8	2	no	—
422	C₂²×C₆₁	—	8	2	no	—
423	C₂²×C₆₁	—	8	2	no	—
424	C₂²×C₆₁	—	8	2	no	—
425	C₂²×C₆₁	—	8	1	no	—
426	C₂²×C₆₁	—	8	1	no	—
427	C₂²×C₆₁	—	8	2	no	—
428	C₂²×C₆₁	—	8	2	no	—
429	C₂²×C₆₁	—	16	1	no	—
430	C₂²×C₆₁	—	16	1	no	—
431	C₂²×C₆₁	—	16	1	no	—
432	C₂²×C₆₁	—	16	4	no	—
433	C₂²×C₆₁	#535	1	1	yes	characteristic
434	C₂²×C₆₁	D₄²	1	1	yes	characteristic
435	C₂²×C₆₁	D₄²	1	1	yes	characteristic
436	C₄×C₆₁	—	2	2	no	—
437	C₄×C₆₁	—	4	2	no	—
438	C₄×C₆₁	—	4	1	no	—
439	C₄×C₆₁	—	4	2	no	—
440	C₄×C₆₁	—	4	1	no	—
441	C₄×C₆₁	—	4	2	no	—
442	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
443	C₄×C₆₁	C₂×#127	1	1	yes	characteristic
444	C₄×C₆₁	D₄²	1	1	yes	characteristic
445	C₄×C₆₁	D₄²	1	1	yes	characteristic
446	C₂×#577	C₂×C₆₁	1	1	yes	characteristic, complemented
447	#3155	C₂×C₆₁	1	1	yes	characteristic, complemented
448	C₂×#496	C₂×C₆₁	1	1	yes	characteristic, complemented
449	C₂×#472	C₂×C₆₁	1	1	yes	characteristic, complemented
450	C₂×#454	C₂×C₆₁	1	1	yes	characteristic, complemented
451	C₂×#453	C₂×C₆₁	1	1	yes	characteristic, complemented
452	#3010	C₂×C₆₁	1	1	yes	characteristic, complemented
453	#3008	C₂×C₆₁	1	1	yes	characteristic, complemented
454	#2019	C₂×C₆₁	1	1	yes	characteristic, complemented
455	#2018	C₂×C₆₁	1	1	yes	characteristic, complemented
456	#2004	C₂×C₆₁	1	1	yes	characteristic, complemented
457	#2002	C₂×C₆₁	1	1	yes	characteristic, complemented
458	#1977	C₂×C₆₁	1	1	yes	characteristic, complemented
459	#1975	C₂×C₆₁	1	1	yes	characteristic, complemented
460	#1765	C₂×C₆₁	1	1	yes	characteristic, complemented
461	C₂×C₆₁	—	2	1	no	—
462	C₂×C₆₁	—	2	1	no	—
463	C₂×C₆₁	—	4	2	no	—
464	C₂×C₆₁	—	8	1	no	—
465	C₂×C₆₁	—	8	1	no	—
466	C₂×C₆₁	—	8	2	no	—
467	C₂×C₆₁	—	16	1	no	—
468	C₂×C₆₁	—	16	1	no	—
469	C₂×C₆₁	#2433	1	1	yes	characteristic
470	C₂×C₆₁	#3288	1	2	yes	—
471	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
472	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	1	yes	characteristic
473	#577	—	2	4	no	—
474	#577	—	2	4	no	—
475	C₂×#137	—	2	1	no	—
476	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
477	C₂×AGL(1,ℤ/8)	—	2	1	no	—
478	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
479	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
480	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
481	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
482	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic, complemented
483	C₂×#135	—	2	1	no	—
484	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
485	C₂²×SD₁₆	—	2	1	no	—
486	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
487	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
488	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
489	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
490	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
491	#535	C₂²×C₆₁	1	1	yes	characteristic
492	#535	C₂²×C₆₁	1	1	yes	characteristic, complemented
493	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
494	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
495	#496	—	2	4	no	—
496	#496	—	2	1	no	—
497	#496	—	2	1	no	—
498	#495	—	2	1	no	—
499	#493	—	2	1	no	—
500	#472	—	2	4	no	—
501	#454	—	2	4	no	—
502	#453	—	2	4	no	—
503	#449	—	2	2	no	—
504	#449	—	2	2	no	—
505	#448	—	2	2	no	—
506	#447	—	2	2	no	—
507	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic, complemented
508	C₂×#104	C₂²×C₆₁	1	1	yes	characteristic
509	C₂×#104	C₂²×C₆₁	1	1	yes	characteristic
510	C₂×#104	C₂²×C₆₁	1	1	yes	characteristic, complemented
511	#419	C₂²×C₆₁	1	1	yes	characteristic, complemented
512	#418	C₂²×C₆₁	1	1	yes	characteristic
513	#416	C₂²×C₆₁	1	1	yes	characteristic
514	C₂×#101	C₂²×C₆₁	1	1	yes	characteristic, complemented
515	C₂×#100	C₂²×C₆₁	1	1	yes	characteristic
516	C₂×#100	C₂²×C₆₁	1	1	yes	characteristic, complemented
517	C₂×#100	C₂²×C₆₁	1	1	yes	characteristic, complemented
518	#408	C₂²×C₆₁	1	1	yes	characteristic
519	#408	C₂²×C₆₁	1	1	yes	characteristic, complemented
520	#405	C₂²×C₆₁	1	1	yes	characteristic, complemented
521	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic, complemented
522	#341	C₂²×C₆₁	1	1	yes	characteristic, complemented
523	#339	C₂²×C₆₁	1	1	yes	characteristic, complemented
524	C₆₁	#25807	1	1	yes	characteristic, direct product factor, Sylow
525	2₋¹⁺⁴	—	2	2	no	—
526	2₋¹⁺⁴	—	2	2	no	—
527	2₋¹⁺⁴	—	2	2	no	—
528	2₋¹⁺⁴	—	4	1	no	—
529	H(5,𝔽₂)	—	2	2	no	—
530	H(5,𝔽₂)	—	2	2	no	—
531	H(5,𝔽₂)	—	2	2	no	—
532	H(5,𝔽₂)	—	4	1	no	—
533	C₂×#41	—	2	1	no	—
534	C₂×#41	—	2	1	no	—
535	C₂×#41	—	2	1	no	—
536	C₂×#41	—	2	1	no	—
537	C₂×#41	—	4	1	no	—
538	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
539	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
540	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
541	C₂²×Q₈	—	2	1	no	—
542	C₂²×Q₈	—	2	1	no	—
543	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
544	C₂²×D₄	—	2	1	no	—
545	C₂²×D₄	—	2	1	no	—
546	C₂²×D₄	—	4	1	no	—
547	C₂²×D₄	—	4	1	no	—
548	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
550	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
551	#137	—	2	8	no	—
552	#137	—	2	2	no	—
553	#137	—	2	2	no	—
554	AGL(1,ℤ/8)	—	2	8	no	—
555	AGL(1,ℤ/8)	—	2	2	no	—
556	AGL(1,ℤ/8)	—	2	2	no	—
557	AGL(1,ℤ/8)	—	2	2	no	—
558	AGL(1,ℤ/8)	—	2	2	no	—
559	AGL(1,ℤ/8)	—	2	2	no	—
560	AGL(1,ℤ/8)	—	2	2	no	—
561	AGL(1,ℤ/8)	—	2	2	no	—
562	AGL(1,ℤ/8)	—	2	2	no	—
563	AGL(1,ℤ/8)	—	4	1	no	—
564	AGL(1,ℤ/8)	—	4	1	no	—
565	#135	—	2	8	no	—
566	#135	—	2	2	no	—
567	#135	—	2	2	no	—
568	C₂×Q₁₆	—	2	1	no	—
569	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic, complemented
570	C₂×SD₁₆	—	2	8	no	—
571	C₂×SD₁₆	—	2	1	no	—
572	C₂×SD₁₆	—	2	1	no	—
573	C₂×SD₁₆	—	2	2	no	—
574	C₂×SD₁₆	—	2	1	no	—
575	C₂×SD₁₆	—	2	1	no	—
576	C₂×SD₁₆	—	2	1	no	—
577	C₂×SD₁₆	—	2	1	no	—
578	C₂×SD₁₆	—	2	1	no	—
579	C₂×SD₁₆	—	2	1	no	—
580	C₂×SD₁₆	—	2	2	no	—
581	C₂×SD₁₆	—	2	2	no	—
582	C₂×SD₁₆	—	4	1	no	—
583	C₂×SD₁₆	D₄×C₆₁	1	1	yes	characteristic, complemented
584	C₂×SD₁₆	D₄×C₆₁	1	4	yes	complemented
585	C₂×SD₁₆	D₄×C₆₁	1	1	yes	characteristic, complemented
586	C₂×D₈	—	2	1	no	—
587	C₂×D₈	—	2	2	no	—
588	C₂×D₈	—	2	1	no	—
589	C₂×D₈	—	2	1	no	—
590	C₂×D₈	—	2	1	no	—
591	C₂×D₈	—	2	1	no	—
592	C₂×D₈	—	2	2	no	—
593	C₂×D₈	—	2	2	no	—
594	C₂×D₈	—	2	1	no	—
595	C₂×D₈	—	2	1	no	—
596	C₂×D₈	—	2	2	no	—
597	C₂×D₈	—	4	1	no	—
598	C₂×D₈	D₄×C₆₁	1	1	yes	characteristic, complemented
599	#131	—	2	2	no	—
600	#131	D₄×C₆₁	1	4	yes	complemented
601	C₂×M₁₆	—	2	1	no	—
602	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
603	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
604	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
605	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
606	C₂²×C₈	—	2	1	no	—
607	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
608	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
609	#127	—	2	2	no	—
610	#127	—	2	1	no	—
611	#127	—	2	1	no	—
612	#127	—	2	2	no	—
613	#124	—	2	2	no	—
614	#124	—	2	1	no	—
615	#124	—	2	1	no	—
616	#124	—	2	2	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#120	—	4	1	no	—
620	#120	—	4	1	no	—
621	#117	C₂³×C₆₁	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	—	4	1	no	—
623	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
624	#108	—	2	2	no	—
625	#104	—	2	2	no	—
626	#104	—	2	2	no	—
627	#104	D₄×C₆₁	1	4	yes	complemented
628	#103	—	2	2	no	—
629	#103	D₄×C₆₁	1	2	yes	complemented
630	#102	—	2	2	no	—
631	#102	D₄×C₆₁	1	2	yes	complemented
632	#101	—	2	2	no	—
633	#100	—	2	2	no	—
634	#100	—	2	2	no	—
635	#100	—	2	2	no	—
636	C₂²⋊C₈	—	2	2	no	—
637	C₂²⋊C₈	—	2	2	no	—
638	#97	—	2	2	no	—
639	#97	—	2	1	no	—
640	C₄×C₈	—	2	1	no	—
641	C₂⁴	—	2	1	no	—
642	C₂⁴	—	2	1	no	—
643	C₂⁴	—	2	1	no	—
644	C₂⁴	—	4	1	no	—
645	#41	—	2	1	no	—
646	#41	—	2	1	no	—
647	#41	—	2	4	no	—
648	#41	—	2	4	no	—
649	#41	—	2	1	no	—
650	#41	—	2	1	no	—
651	#41	—	2	1	no	—
652	#41	—	2	1	no	—
653	#41	—	2	1	no	—
654	#41	—	2	1	no	—
655	#41	—	2	1	no	—
656	#41	—	2	1	no	—
657	#41	—	4	2	no	—
658	#41	—	4	4	no	—
659	#41	—	4	2	no	—
660	#41	—	4	2	no	—
661	#41	—	4	2	no	—
662	#41	—	4	4	no	—
663	#41	—	4	2	no	—
664	#41	—	4	2	no	—
665	#41	C₂×D₄×C₆₁	1	2	yes	—
666	#41	C₂×D₄×C₆₁	1	2	yes	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	4	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	4	1	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×Q₈	—	4	2	no	—
677	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
678	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
679	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
680	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	4	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	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	1	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	4	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	1	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	8	4	no	—
714	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
715	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
716	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
717	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	4	1	no	—
724	C₂²×C₄	—	4	1	no	—
725	C₂²×C₄	—	4	1	no	—
726	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
727	Q₁₆	—	2	4	no	—
728	Q₁₆	—	2	2	no	—
729	SD₁₆	—	2	4	no	—
730	SD₁₆	—	2	4	no	—
731	SD₁₆	—	2	2	no	—
732	SD₁₆	—	2	4	no	—
733	SD₁₆	—	2	4	no	—
734	SD₁₆	—	2	2	no	—
735	SD₁₆	—	4	4	no	—
736	SD₁₆	—	4	2	no	—
737	SD₁₆	—	4	2	no	—
738	SD₁₆	—	4	2	no	—
739	SD₁₆	—	4	2	no	—
740	D₈	—	2	4	no	—
741	D₈	—	2	2	no	—
742	D₈	—	4	4	no	—
743	D₈	—	4	2	no	—
744	D₈	—	4	2	no	—
745	D₈	—	4	2	no	—
746	D₈	—	4	2	no	—
747	D₈	—	4	2	no	—
748	D₈	—	4	2	no	—
749	M₁₆	—	2	1	no	—
750	M₁₆	—	2	1	no	—
751	M₁₆	—	2	4	no	—
752	M₁₆	—	2	1	no	—
753	M₁₆	—	2	1	no	—
754	M₁₆	—	2	1	no	—
755	M₁₆	—	2	1	no	—
756	M₁₆	C₂×D₄×C₆₁	1	2	yes	—
757	M₁₆	C₂×D₄×C₆₁	1	2	yes	—
758	C₂×C₈	—	2	1	no	—
759	C₂×C₈	—	2	1	no	—
760	C₂×C₈	—	2	1	no	—
761	C₂×C₈	—	2	1	no	—
762	C₂×C₈	—	2	4	no	—
763	C₂×C₈	—	2	1	no	—
764	C₂×C₈	—	2	1	no	—
765	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
766	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
767	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
768	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
769	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
770	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	4	4	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	C₂×D₄×C₆₁	1	2	yes	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	4	4	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	1	no	—
785	C₂³	—	4	1	no	—
786	C₂³	—	4	1	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	1	no	—
790	C₂³	—	4	1	no	—
791	C₂³	—	8	2	no	—
792	C₂³	—	8	2	no	—
793	C₂³	—	8	2	no	—
794	C₂³	—	16	2	no	—
795	C₂³	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
796	Q₈	—	2	1	no	—
797	Q₈	—	2	2	no	—
798	Q₈	—	2	1	no	—
799	Q₈	—	2	1	no	—
800	Q₈	—	2	1	no	—
801	Q₈	—	2	2	no	—
802	Q₈	—	2	1	no	—
803	Q₈	—	4	4	no	—
804	Q₈	—	4	1	no	—
805	Q₈	—	4	1	no	—
806	Q₈	#127×C₆₁	1	2	yes	—
807	D₄	—	2	2	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	1	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	1	no	—
812	D₄	—	2	1	no	—
813	D₄	—	2	1	no	—
814	D₄	—	2	2	no	—
815	D₄	—	2	1	no	—
816	D₄	—	4	4	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	4	no	—
819	D₄	—	4	1	no	—
820	D₄	—	4	1	no	—
821	D₄	—	4	1	no	—
822	D₄	—	4	1	no	—
823	D₄	—	4	1	no	—
824	D₄	—	4	1	no	—
825	D₄	—	4	1	no	—
826	D₄	—	4	1	no	—
827	D₄	—	4	1	no	—
828	D₄	—	4	1	no	—
829	D₄	—	4	1	no	—
830	D₄	—	4	1	no	—
831	D₄	—	4	1	no	—
832	D₄	—	4	1	no	—
833	D₄	—	8	8	no	—
834	D₄	—	16	2	no	—
835	D₄	—	16	2	no	—
836	D₄	#127×C₆₁	1	2	yes	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	2	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	4	1	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
856	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
859	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
860	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
861	C₈	—	2	2	no	—
862	C₈	—	2	2	no	—
863	C₈	—	2	2	no	—
864	C₈	—	4	1	no	—
865	C₈	—	4	1	no	—
866	C₈	#120×C₆₁	1	2	yes	—
867	C₈	#120×C₆₁	1	2	yes	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	8	2	no	—
877	C₂²	—	8	2	no	—
878	C₂²	—	8	2	no	—
879	C₂²	—	8	2	no	—
880	C₂²	—	8	2	no	—
881	C₂²	—	8	2	no	—
882	C₂²	—	8	1	no	—
883	C₂²	—	8	1	no	—
884	C₂²	—	16	1	no	—
885	C₂²	—	16	1	no	—
886	C₂²	—	16	1	no	—
887	C₂²	—	16	4	no	—
888	C₂²	C₆₁×#535	1	1	yes	characteristic
889	C₂²	D₄²×C₆₁	1	1	yes	characteristic
890	C₂²	D₄²×C₆₁	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
898	C₄	C₂×#127×C₆₁	1	1	yes	characteristic
899	C₄	D₄²×C₆₁	1	1	yes	characteristic
900	C₄	D₄²×C₆₁	1	1	yes	characteristic
901	C₂	—	2	1	no	—
902	C₂	—	2	1	no	—
903	C₂	—	4	2	no	—
904	C₂	—	8	1	no	—
905	C₂	—	8	1	no	—
906	C₂	—	8	2	no	—
907	C₂	—	16	1	no	—
908	C₂	—	16	1	no	—
909	C₂	C₆₁×#2433	1	1	yes	characteristic
910	C₂	C₆₁×#3288	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×#3155	C₂	semidirect
3. C₂×C₆₁×#496	C₂	semidirect
4. C₂×C₆₁×#472	C₂	semidirect
5. C₂×C₆₁×#454	C₂	semidirect
6. C₂×C₆₁×#453	C₂	semidirect
7. C₆₁×#3010	C₂	semidirect
8. C₆₁×#3008	C₂	semidirect
9. C₆₁×#2019	C₂	semidirect
10. C₆₁×#2018	C₂	semidirect
11. C₆₁×#2004	C₂	semidirect
12. C₆₁×#2002	C₂	semidirect
13. C₆₁×#1977	C₂	semidirect
14. C₆₁×#1975	C₂	semidirect
15. C₆₁×#1765	C₂	semidirect
27. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
32. C₂²×SD₁₆×C₆₁	C₂²	semidirect
34. C₂²×D₈×C₆₁	C₂²	semidirect
37. C₆₁×#535	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
61. C₂×#100×C₆₁	C₂²	semidirect
62. C₂×#100×C₆₁	C₂²	semidirect
64. C₆₁×#408	C₂²	semidirect
65. C₆₁×#405	C₂²	semidirect
66. C₂×#97×C₆₁	C₂²	semidirect
67. C₆₁×#341	C₂²	semidirect
68. C₆₁×#339	C₂²	semidirect
113. C₂×Q₁₆×C₆₁	D₄	semidirect
127. C₂×SD₁₆×C₆₁	D₄	semidirect
128. C₂×SD₁₆×C₆₁	D₄	semidirect
129. C₂×SD₁₆×C₆₁	D₄	semidirect
142. C₂×D₈×C₆₁	D₄	semidirect
144. #131×C₆₁	D₄	semidirect
171. #104×C₆₁	D₄	semidirect
173. #103×C₆₁	D₄	semidirect
175. #102×C₆₁	D₄	semidirect
412. #25807	C₆₁	direct (N × H)
446. C₂×#577	C₂×C₆₁	semidirect
447. #3155	C₂×C₆₁	semidirect
448. C₂×#496	C₂×C₆₁	semidirect
449. C₂×#472	C₂×C₆₁	semidirect
450. C₂×#454	C₂×C₆₁	semidirect
451. C₂×#453	C₂×C₆₁	semidirect
452. #3010	C₂×C₆₁	semidirect
453. #3008	C₂×C₆₁	semidirect
454. #2019	C₂×C₆₁	semidirect
455. #2018	C₂×C₆₁	semidirect
456. #2004	C₂×C₆₁	semidirect
457. #2002	C₂×C₆₁	semidirect
458. #1977	C₂×C₆₁	semidirect
459. #1975	C₂×C₆₁	semidirect
460. #1765	C₂×C₆₁	semidirect
482. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
487. C₂²×SD₁₆	C₂²×C₆₁	semidirect
489. C₂²×D₈	C₂²×C₆₁	semidirect
492. #535	C₂²×C₆₁	semidirect
494. C₂×#124	C₂²×C₆₁	semidirect
507. C₂×#108	C₂²×C₆₁	semidirect
510. C₂×#104	C₂²×C₆₁	semidirect
511. #419	C₂²×C₆₁	semidirect
514. C₂×#101	C₂²×C₆₁	semidirect
516. C₂×#100	C₂²×C₆₁	semidirect
517. C₂×#100	C₂²×C₆₁	semidirect
519. #408	C₂²×C₆₁	semidirect
520. #405	C₂²×C₆₁	semidirect
521. C₂×#97	C₂²×C₆₁	semidirect
522. #341	C₂²×C₆₁	semidirect
523. #339	C₂²×C₆₁	semidirect
524. C₆₁	#25807	direct (N × H)
569. C₂×Q₁₆	D₄×C₆₁	semidirect
583. C₂×SD₁₆	D₄×C₆₁	semidirect
584. C₂×SD₁₆	D₄×C₆₁	semidirect
585. C₂×SD₁₆	D₄×C₆₁	semidirect
598. C₂×D₈	D₄×C₆₁	semidirect
600. #131	D₄×C₆₁	semidirect
627. #104	D₄×C₆₁	semidirect
629. #103	D₄×C₆₁	semidirect
631. #102	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×#3155	2
C₂×C₆₁×#496	2
C₂×C₆₁×#472	2
C₂×C₆₁×#454	2
C₂×C₆₁×#453	2
C₆₁×#3010	2
C₆₁×#3008	2
C₆₁×#2019	2
C₆₁×#2018	2
C₆₁×#2004	2
C₆₁×#2002	2
C₆₁×#1977	2
C₆₁×#1975	2
C₆₁×#1765	2
#25807	61

Subgroups — C61×#25807 #29529240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25807 #29529240