Subgroups — #10597077

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3874	C₂	1	1	yes	maximal, characteristic
2	#1039⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#64470	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×Dic₅	—	3	1	no	maximal, Hall
5	C₂×C₅²⋊C₃	C₂²	1	1	yes	characteristic
6	#3874	C₄	1	2	yes	complemented
7	C₂×C₅×D₅	—	3	1	no	—
8	#1039	D₃	1	1	yes	characteristic, complemented
9	C₅×Dic₅	—	3	1	no	—
10	C₅²⋊C₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅²	C₂×D₃	1	1	yes	characteristic
12	C₅×D₅	—	3	2	no	—
13	C₂×Dic₅	—	15	1	no	—
14	C₄×D₅	—	15	1	no	—
15	C₅²	C₄×D₃	1	1	yes	characteristic, complemented, Sylow
16	C₄×D₃	—	25	1	no	maximal, Hall
17	C₂²×C₅	—	15	1	no	—
18	C₂×D₅	—	3	1	no	—
19	C₄×C₅	—	15	1	no	—
20	Dic₅	—	3	1	no	—
21	Dic₅	—	15	1	no	—
22	Dic₅	—	30	1	no	—
23	C₂×D₃	—	50	1	no	—
24	C₃×C₄	—	25	1	no	—
25	Dic₃	—	50	1	no	—
26	C₂×C₅	—	3	1	no	—
27	C₂×C₅	—	6	1	no	—
28	C₂×C₅	—	15	2	no	—
29	D₅	—	3	2	no	—
30	C₂×C₄	—	75	1	no	Sylow
31	C₂×C₃	—	100	1	no	—
32	D₃	—	50	2	no	—
33	C₅	—	3	1	no	—
34	C₅	—	6	1	no	—
35	C₂²	—	15	1	no	—
36	C₄	—	15	1	no	—
37	C₄	—	25	1	no	—
38	C₃	—	100	1	no	Sylow
39	C₂	—	15	2	no	—
40	C₂	#3874⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#3874⋊C₂
commutator, hypocenter	C₅²⋊C₃	C₂×C₄
Fitting, socle	C₂×C₅²	C₂×D₃
prime radical	C₂×#3874	C₂
cosocle	C₂×C₅²⋊C₃	C₂²
LCS	G ▷ 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.