Subgroups — C₂×#64480 #10597171

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
2	#64480	C₂	1	2	yes	maximal, direct product factor
3	C₂×#1044	—	3	1	no	maximal, Hall
4	C₂×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented
5	(C₅⋊D₅)⋊C₃	C₄	1	1	yes	characteristic, complemented
6	(C₅⋊D₅)⋊C₃	C₂²	1	1	yes	characteristic
7	C₂×C₅⋊D₅	D₃	1	1	yes	characteristic
8	#1044	—	3	2	no	—
9	C₅²⋊C₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅²	Dic₃	1	1	yes	characteristic, complemented
11	C₅⋊D₅	Dic₃	1	1	yes	characteristic, complemented
12	C₅⋊D₅	C₂×D₃	1	1	yes	characteristic
13	C₂×AGL(1,𝔽₅)	—	15	2	no	—
14	C₅²	C₂×Dic₃	1	1	yes	characteristic, complemented, Sylow
15	C₂×Dic₃	—	25	1	no	maximal, Hall
16	C₂×D₅	—	15	2	no	—
17	AGL(1,𝔽₅)	—	15	4	no	—
18	C₂²×C₃	—	25	1	no	—
19	Dic₃	—	25	2	no	—
20	C₂×C₅	—	3	2	no	—
21	D₅	—	15	2	no	—
22	D₅	—	15	2	no	—
23	C₂×C₄	—	75	1	no	Sylow
24	C₂×C₃	—	25	1	no	—
25	C₂×C₃	—	25	1	no	—
26	C₂×C₃	—	25	1	no	—
27	C₅	—	3	2	no	—
28	C₂²	—	25	1	no	—
29	C₄	—	75	2	no	—
30	C₃	—	25	1	no	Sylow
31	C₂	—	25	1	no	—
32	C₂	—	25	1	no	—
33	C₂	#64480	1	1	yes	characteristic, direct product factor

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.