Finite Group Databasebeta

← C₃×C₁₇²×C₃₁ #41001850

Subgroups — C₃×C₁₇²×C₃₁ #41001850

Order 26877.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₁₇×C₃₁	C₁₇	1	18	yes	maximal, direct product factor
3	C₃×C₁₇²	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇×C₃₁	C₃×C₁₇	1	18	yes	direct product factor
5	C₁₇²	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₃×C₃₁	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₁₇	C₁₇×C₃₁	1	18	yes	direct product factor
8	C₃₁	C₃×C₁₇²	1	1	yes	characteristic, direct product factor, Sylow
9	C₁₇	C₃×C₁₇×C₃₁	1	18	yes	direct product factor
10	C₃	C₁₇²×C₃₁	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. C₁₇²×C₃₁	C₃	direct (N × H)
2. C₃×C₁₇×C₃₁	C₁₇	direct (N × H)
3. C₃×C₁₇²	C₃₁	direct (N × H)
4. C₁₇×C₃₁	C₃×C₁₇	direct (N × H)
5. C₁₇²	C₃×C₃₁	direct (N × H)
6. C₃×C₃₁	C₁₇²	direct (N × H)
7. C₃×C₁₇	C₁₇×C₃₁	direct (N × H)
8. C₃₁	C₃×C₁₇²	direct (N × H)
9. C₁₇	C₃×C₁₇×C₃₁	direct (N × H)
10. C₃	C₁₇²×C₃₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₇²×C₃₁	3
C₃×C₁₇×C₃₁	17
C₃×C₁₇²	31