Finite Group Databasebeta

← C₃²×C₁₃×C₇₁ #22552182

Subgroups — C₃²×C₁₃×C₇₁ #22552182

Order 8307.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₇₁	C₃	1	4	yes	maximal, direct product factor
2	C₁₃×C₇₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
3	C₃²×C₇₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇₁	C₃×C₁₃	1	4	yes	direct product factor
5	C₃²×C₁₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇₁	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
7	C₃×C₁₃	C₃×C₇₁	1	4	yes	direct product factor
8	C₁₃	C₃²×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
9	C₃²	C₁₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₁₃×C₇₁	1	4	yes	direct product factor

	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. C₃×C₁₃×C₇₁	C₃	direct (N × H)
2. C₁₃×C₇₁	C₃²	direct (N × H)
3. C₃²×C₇₁	C₁₃	direct (N × H)
4. C₃×C₇₁	C₃×C₁₃	direct (N × H)
5. C₃²×C₁₃	C₇₁	direct (N × H)
6. C₇₁	C₃²×C₁₃	direct (N × H)
7. C₃×C₁₃	C₃×C₇₁	direct (N × H)
8. C₁₃	C₃²×C₇₁	direct (N × H)
9. C₃²	C₁₃×C₇₁	direct (N × H)
10. C₃	C₃×C₁₃×C₇₁	direct (N × H)