Subgroups — ((D₅⋊AGL(1,𝔽₅))⋊C₂)⋊C₃ #11925737

Order 1200.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6057⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	(D₅⋊AGL(1,𝔽₅))⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#1043⋊C₃	—	4	1	no	maximal
4	#6057	C₂×C₃	1	1	yes	characteristic
5	D₅²⋊C₂	—	3	1	no	—
6	D₅⋊AGL(1,𝔽₅)	—	3	1	no	—
7	(C₅⋊D₅)⋊C₃	—	4	1	no	—
8	D₅²	—	3	1	no	—
9	#1044	—	3	1	no	—
10	#1043	A₄	1	1	yes	characteristic
11	C₅²⋊C₃	—	4	1	no	Hall
12	C₅⋊D₅	C₂×A₄	1	1	yes	characteristic
13	C₅×D₅	—	6	1	no	—
14	#41⋊C₃	—	25	1	no	maximal, Hall
15	C₂×AGL(1,𝔽₅)	—	30	1	no	—
16	C₅²	#41⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	SL(2,𝔽₃)	—	25	1	no	—
18	C₂×D₅	—	30	1	no	—
19	AGL(1,𝔽₅)	—	30	1	no	—
20	AGL(1,𝔽₅)	—	30	1	no	—
21	#41	—	25	1	no	Sylow
22	C₃×C₄	—	100	1	no	—
23	C₂×C₅	—	30	1	no	—
24	D₅	—	6	1	no	—
25	D₅	—	30	1	no	—
26	Q₈	—	25	1	no	—
27	D₄	—	75	1	no	—
28	C₂×C₄	—	75	1	no	—
29	C₂×C₃	—	100	1	no	—
30	C₅	—	6	1	no	—
31	C₂²	—	75	1	no	—
32	C₄	—	25	1	no	—
33	C₄	—	75	1	no	—
34	C₃	—	100	1	no	Sylow
35	C₂	—	25	1	no	—
36	C₂	—	30	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	#6057	C₂×C₃
Fitting, socle	C₅²	#41⋊C₃
LCS	G ▷ #6057
UCS	C₁

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

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