Subgroups — #10602148

Order 640.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#499	C₂	1	1	yes	maximal, characteristic
2	#64971	C₂	1	1	yes	maximal, characteristic
3	#64710	C₂	1	2	yes	maximal
4	#64709	C₂	1	2	yes	maximal
5	#64681	C₂	1	1	yes	maximal, characteristic
6	C₅×#125	—	2	1	no	—
7	#4015	—	2	1	no	—
8	C₅×#107	C₂²	1	1	yes	characteristic
9	C₅×#107	C₂²	1	1	yes	characteristic
10	C₅×#106	—	2	1	no	—
11	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	#3950	—	2	1	no	—
13	#3950	C₂²	1	2	yes	—
14	C₂×#672	C₂²	1	2	yes	—
15	#2255	—	5	1	no	maximal, Sylow
16	C₂×Dic₁₀	—	4	1	no	—
17	C₂×C₅×C₈	D₄	1	1	yes	characteristic
18	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
19	C₅×C₄⋊C₄	—	2	1	no	—
20	C₅×C₄⋊C₄	—	2	1	no	—
21	C₅×C₄⋊C₄	—	4	1	no	—
22	C₅×C₄⋊C₄	—	4	1	no	—
23	C₄²×C₅	D₄	1	1	yes	characteristic
24	C₄⋊Dic₅	—	2	2	no	—
25	C₄⋊Dic₅	—	4	1	no	—
26	#672	Q₈	1	4	yes	complemented
27	#500	—	5	1	no	—
28	#499	D₅	1	1	yes	characteristic
29	#367	—	5	2	no	—
30	#366	—	5	2	no	—
31	#346	—	5	1	no	—
32	C₂×C₄×C₅	—	4	1	no	—
33	C₂×C₄×C₅	—	4	1	no	—
34	C₂×C₄×C₅	D₈	1	1	yes	characteristic
35	C₂×C₄×C₅	D₈	1	1	yes	characteristic
36	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₅	—	4	2	no	—
38	Dic₁₀	—	8	2	no	—
39	C₅×C₈	Q₁₆	1	2	yes	—
40	C₅×C₈	C₂×Q₈	1	2	yes	—
41	C₄⋊Q₈	—	10	1	no	—
42	#125	—	2	1	no	—
43	C₂×C₁₆	—	5	2	no	—
44	#107	—	5	2	no	—
45	#107	—	10	1	no	—
46	#107	C₂×D₅	1	1	yes	characteristic
47	#107	C₂×D₅	1	1	yes	characteristic
48	#106	—	2	1	no	—
49	C₄×C₈	C₂×D₅	1	1	yes	characteristic
50	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
51	C₄×C₅	—	2	1	no	—
52	C₄×C₅	—	2	1	no	—
53	C₄×C₅	—	8	1	no	—
54	C₄×C₅	—	8	1	no	—
55	C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
56	C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
57	Dic₅	—	8	2	no	—
58	C₂×Q₈	—	20	1	no	—
59	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
60	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
61	C₄⋊C₄	—	2	1	no	—
62	C₄⋊C₄	—	2	1	no	—
63	C₄⋊C₄	—	4	1	no	—
64	C₄⋊C₄	—	4	1	no	—
65	C₄⋊C₄	—	10	2	no	—
66	C₄⋊C₄	—	20	1	no	—
67	C₄²	C₂²⋊D₅	1	1	yes	characteristic
68	C₁₆	—	5	4	no	—
69	C₂×C₅	#500	1	1	yes	characteristic
70	C₂×C₅	#509	1	1	yes	characteristic
71	C₂×C₅	#510	1	1	yes	characteristic
72	Q₈	—	40	2	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	20	2	no	—
76	C₂×C₄	#686	1	1	yes	characteristic
77	C₂×C₄	#686	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
79	C₈	#689	1	2	yes	—
80	C₈	Q₈×D₅	1	2	yes	—
81	C₅	#2255	1	1	yes	characteristic, complemented, Sylow
82	C₂²	C₂×#686	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	8	1	no	—
87	C₄	—	40	2	no	—
88	C₄	C₂×#689	1	1	yes	characteristic
89	C₄	#4090	1	1	yes	characteristic
90	C₂	#65367	1	1	yes	characteristic
91	C₂	#65482	1	1	yes	characteristic
92	C₂	#65484	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#686
commutator, cosocle	C₂×C₅×C₈	C₂³
Frattini	C₂×C₈	C₂²×D₅
Fitting	C₅×#499	C₂
socle, prime radical	C₂²×C₅	C₂×D₈
hypercenter	#499	D₅
hypocenter	C₅	#2255
LCS	G ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
26. #672	Q₈	semidirect
81. C₅	#2255	semidirect

Maximal subgroups

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

subgroup	index
C₅×#499	2
#64971	2
#64710	2
#64709	2
#64681	2
#2255	5