Subgroups — C₅×#676 #87783

Order 400.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×D₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅	C₄	1	1	yes	characteristic
5	C₄×C₅²	C₂²	1	1	yes	characteristic
6	C₅×Dic₅	C₄	1	1	yes	characteristic
7	C₅×M₁₆	—	5	1	no	maximal
8	#676	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
10	C₅×D₅	—	2	1	no	—
11	C₂×C₄×C₅	—	5	1	no	—
12	C₄×D₅	C₂×C₅	1	1	yes	characteristic
13	C₅×C₈	—	2	2	no	—
14	C₅×C₈	—	5	1	no	—
15	C₅×C₈	D₅	1	1	yes	characteristic, complemented
16	C₅×C₈	C₂×C₅	1	1	yes	characteristic, complemented
17	#168	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅²	M₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅	—	5	1	no	—
20	C₂×D₅	C₄×C₅	1	1	yes	characteristic
21	C₄×C₅	—	2	2	no	—
22	C₄×C₅	—	5	1	no	—
23	C₄×C₅	C₂×D₅	1	1	yes	characteristic
24	C₄×C₅	C₂²×C₅	1	1	yes	characteristic
25	Dic₅	C₄×C₅	1	1	yes	characteristic
26	M₁₆	—	5	1	no	Sylow
27	C₂×C₅	—	2	2	no	—
28	C₂×C₅	—	10	1	no	—
29	C₂×C₅	C₄×D₅	1	1	yes	characteristic
30	C₂×C₅	C₂×C₄×C₅	1	1	yes	characteristic
31	D₅	—	2	1	no	—
32	C₂×C₄	—	5	1	no	—
33	C₈	—	5	1	no	—
34	C₈	C₅×D₅	1	1	yes	characteristic, complemented
35	C₅	—	2	2	no	—
36	C₅	#676	1	1	yes	characteristic, direct product factor
37	C₅	C₅×M₁₆	1	1	yes	characteristic, complemented
38	C₂²	—	5	1	no	—
39	C₄	—	5	1	no	—
40	C₄	C₂×C₅×D₅	1	1	yes	characteristic
41	C₂	—	10	1	no	—
42	C₂	C₄×C₅×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×D₅
commutator	C₂×C₅	C₂×C₄×C₅
Frattini	C₄	C₂×C₅×D₅
Fitting	C₅²×C₈	C₂
socle	C₂×C₅²	C₂×C₄
prime radical	C₂×C₅×D₅	C₄
cosocle	C₄×C₅	C₂²×C₅
hypercenter	C₅×C₈	D₅
hypocenter	C₅	C₅×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₅ ◁ C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₅²×C₈	C₂	semidirect
3. C₅×#168	C₂	semidirect
8. #676	C₅	direct (N × H)
15. C₅×C₈	D₅	semidirect
16. C₅×C₈	C₂×C₅	semidirect
17. #168	C₂×C₅	semidirect
18. C₅²	M₁₆	semidirect
34. C₈	C₅×D₅	semidirect
36. C₅	#676	direct (N × H)
37. C₅	C₅×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×D₅	2
C₅²×C₈	2
C₅×#168	2
C₅×M₁₆	5
#676	5

Subgroups — C5×#676 #87783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#676 #87783