Subgroups — #1044×C₃₁₇ #44540186

Order 31700.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₃₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₃₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	AGL(1,𝔽₅)×C₃₁₇	—	5	2	no	maximal
4	D₅×C₃₁₇	—	5	2	no	—
5	D₅×C₃₁₇	—	10	2	no	—
6	C₅×C₃₁₇	—	2	2	no	—
7	C₅×C₃₁₇	AGL(1,𝔽₅)	1	2	yes	complemented
8	C₄×C₃₁₇	—	25	1	no	Hall
9	C₂×C₃₁₇	—	25	1	no	—
10	C₃₁₇	#1044	1	1	yes	characteristic, direct product factor, Sylow
11	#1044	C₃₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅⋊D₅	C₂×C₃₁₇	1	1	yes	characteristic
13	C₅²	C₄×C₃₁₇	1	1	yes	characteristic, complemented, Sylow
14	AGL(1,𝔽₅)	—	5	2	no	—
15	D₅	—	5	2	no	—
16	D₅	—	10	2	no	—
17	C₅	—	2	2	no	—
18	C₅	AGL(1,𝔽₅)×C₃₁₇	1	2	yes	complemented
19	C₄	—	25	1	no	Sylow
20	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.