Finite Group Databasebeta

← C₂×C₃₁×C₁₇₃ #24924340

Subgroups — C₂×C₃₁×C₁₇₃ #24924340

Order 10726.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₁₇₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₇₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇₃	C₂×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
4	C₂×C₃₁	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃₁	C₂×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	C₃₁×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×C₁₇₃	C₂	direct (N × H)
2. C₂×C₁₇₃	C₃₁	direct (N × H)
3. C₁₇₃	C₂×C₃₁	direct (N × H)
4. C₂×C₃₁	C₁₇₃	direct (N × H)
5. C₃₁	C₂×C₁₇₃	direct (N × H)
6. C₂	C₃₁×C₁₇₃	direct (N × H)