Subgroups — #10597080

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#3874	C₂	1	1	yes	maximal, characteristic, complemented
3	#64470	C₂	1	1	yes	maximal, characteristic, complemented
4	#6038	—	3	1	no	maximal, Hall
5	C₂×C₅²⋊C₃	C₂²	1	1	yes	characteristic
6	(C₅⋊D₅)⋊C₃	—	2	1	no	—
7	#3874	—	2	1	no	—
8	C₂×C₅⋊D₅	D₃	1	1	yes	characteristic, complemented
9	C₂×C₅×D₅	—	3	1	no	—
10	C₅×Dic₅	—	3	1	no	—
11	C₅²⋊C₃	D₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅²	C₂×D₃	1	1	yes	characteristic
13	C₅⋊D₅	—	2	1	no	—
14	C₅×D₅	—	6	1	no	—
15	C₂²⋊D₅	—	15	1	no	—
16	D₂₀	—	15	1	no	—
17	C₅²	#67	1	1	yes	characteristic, complemented, Sylow
18	#67	—	25	1	no	maximal, Hall
19	C₂²×C₅	—	15	1	no	—
20	C₂×D₅	—	3	1	no	—
21	C₂×D₅	—	15	1	no	—
22	C₂×D₅	—	30	1	no	—
23	C₄×C₅	—	15	1	no	—
24	Dic₅	—	3	1	no	—
25	C₂²×C₃	—	25	1	no	—
26	C₂×D₃	—	50	1	no	—
27	Dic₃	—	50	1	no	—
28	C₂×C₅	—	3	1	no	—
29	C₂×C₅	—	6	1	no	—
30	C₂×C₅	—	30	1	no	—
31	D₅	—	6	1	no	—
32	D₅	—	30	1	no	—
33	D₅	—	30	1	no	—
34	D₄	—	75	1	no	Sylow
35	C₂×C₃	—	50	1	no	—
36	C₂×C₃	—	50	1	no	—
37	D₃	—	50	1	no	—
38	C₅	—	3	1	no	—
39	C₅	—	6	1	no	—
40	C₂²	—	15	1	no	—
41	C₂²	—	25	1	no	—
42	C₄	—	15	1	no	—
43	C₃	—	50	1	no	Sylow
44	C₂	—	30	1	no	—
45	C₂	—	50	1	no	—
46	C₂	#3874⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#3874⋊C₂
commutator, cosocle	C₂×C₅²⋊C₃	C₂²
Fitting, socle	C₂×C₅²	C₂×D₃
hypocenter	C₅²⋊C₃	D₄
LCS	G ▷ C₂×C₅²⋊C₃ ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂

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.