Subgroups — C₅×C₃⋊#1035 #13093751

Order 1500.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₅×#1035	—	3	1	no	maximal, Hall
3	C₃×C₅×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×ΓL(1,𝔽₁₆)	—	5	1	no	maximal
5	C₃⋊#1035	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₅×D₂₅	D₃	1	1	yes	characteristic
7	C₃×C₅×D₅	—	5	1	no	—
8	C₃×D₂₅	C₂×C₅	1	1	yes	characteristic
9	C₅×C₂₅	Dic₃	1	1	yes	characteristic, complemented, Sylow
10	C₅×AGL(1,𝔽₅)	—	15	1	no	—
11	#1035	—	3	1	no	—
12	C₃×C₅²	AGL(1,𝔽₅)	1	1	yes	characteristic
13	C₃×C₂₅	—	4	1	no	—
14	C₃×C₂₅	C₄×C₅	1	1	yes	characteristic, complemented
15	ΓL(1,𝔽₁₆)	—	5	1	no	—
16	C₅×Dic₃	—	25	1	no	—
17	C₅×D₅	—	5	1	no	—
18	D₂₅	C₅×D₃	1	1	yes	characteristic
19	C₂×C₃×C₅	—	25	1	no	—
20	C₃×D₅	—	5	1	no	—
21	C₅²	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
22	C₂₅	—	4	1	no	—
23	C₂₅	C₅×Dic₃	1	1	yes	characteristic, complemented
24	AGL(1,𝔽₅)	—	15	1	no	—
25	C₄×C₅	—	75	1	no	—
26	C₃×C₅	—	4	1	no	—
27	C₃×C₅	#1035	1	1	yes	characteristic, complemented
28	C₃×C₅	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
29	Dic₃	—	25	1	no	Hall
30	C₂×C₅	—	25	1	no	—
31	D₅	—	5	1	no	—
32	C₂×C₃	—	25	1	no	—
33	C₅	—	4	1	no	—
34	C₅	C₃⋊#1035	1	1	yes	characteristic, direct product factor
35	C₅	C₅×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
36	C₄	—	75	1	no	Sylow
37	C₃	C₅×#1035	1	1	yes	characteristic, complemented, Sylow
38	C₂	—	25	1	no	—

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.