Subgroups — C₂×C₅×#168 #87787

Order 400.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₅×#168	C₂	direct (N × H)
7. C₂×#168	C₅	direct (N × H)
8. C₂×C₅²	C₈	semidirect
14. #168	C₂×C₅	direct (N × H)
15. C₅²	C₂×C₈	semidirect
28. C₂×C₅	#168	direct (N × H)
29. C₂×C₅	C₅×C₈	semidirect
35. C₅	C₂×#168	direct (N × H)
36. C₅	C₂×C₅×C₈	semidirect
40. C₂	C₅×#168	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅²	2
C₅×#168	2
C₂×C₅×C₈	5
C₂×#168	5

Subgroups — C2×C5×#168 #87787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#168 #87787