Subgroups — C₅²×A₄×C₁₇ #19099833

Order 5100.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅²×C₁₇	—	4	1	no	maximal, Hall
3	C₅×A₄×C₁₇	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅²×C₁₇	—	3	1	no	—
5	C₅²×C₁₇	A₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₅×C₁₇	C₃×C₅	1	6	yes	complemented
7	C₅²×A₄	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×C₁₇	—	4	6	no	—
9	A₄×C₁₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₁₇	—	3	6	no	—
11	C₂²×C₅²	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₇	C₅×A₄	1	6	yes	direct product factor
13	C₃×C₅²	—	4	1	no	Hall
14	C₂²×C₁₇	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
15	C₅×A₄	C₅×C₁₇	1	6	yes	direct product factor
16	C₃×C₁₇	—	4	1	no	Hall
17	C₂×C₅²	—	3	1	no	—
18	C₂×C₁₇	—	3	1	no	—
19	C₅²	A₄×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²×C₅	C₃×C₅×C₁₇	1	6	yes	complemented
21	C₁₇	C₅²×A₄	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×C₅	—	4	6	no	—
23	A₄	C₅²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₅	—	3	6	no	—
25	C₅	C₅×A₄×C₁₇	1	6	yes	direct product factor
26	C₂²	C₃×C₅²×C₁₇	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	4	1	no	Sylow
28	C₂	—	3	1	no	—

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