Subgroups — C₂×C₅×D₂₁₇ #16864708

Order 4340.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₂₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₂₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₃₁	—	7	1	no	maximal, Hall
6	C₂×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
7	D₂₁₇	C₂×C₅	1	2	yes	direct product factor
8	C₂×C₅×C₃₁	D₇	1	1	yes	characteristic, complemented
9	C₅×D₃₁	—	7	2	no	—
10	C₇×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×D₇	—	31	1	no	maximal, Hall
13	C₂×D₃₁	—	7	1	no	Hall
14	C₂×C₅×C₇	D₃₁	1	1	yes	characteristic, complemented
15	C₅×D₇	—	31	2	no	—
16	C₂×C₃₁	C₅×D₇	1	1	yes	characteristic, complemented
17	D₃₁	—	7	2	no	—
18	C₅×C₇	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
19	C₃₁	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₇	—	31	1	no	Hall
21	C₂²×C₅	—	217	1	no	Hall
22	C₂×C₇	C₅×D₃₁	1	1	yes	characteristic, complemented
23	D₇	—	31	2	no	—
24	C₂×C₅	—	217	2	no	—
25	C₂×C₅	D₂₁₇	1	1	yes	characteristic, direct product factor
26	C₇	C₂×C₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
27	C₅	C₂×D₂₁₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	217	1	no	Sylow
29	C₂	—	217	2	no	—
30	C₂	C₅×D₂₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₂₁₇
commutator, cosocle, hypocenter	C₇×C₃₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₃₁	C₂
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₂×C₅

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.