Finite Group Databasebeta

← C₁₃×C₁₆×C₁₄₉ #72207756

Subgroups — C₁₃×C₁₆×C₁₄₉ #72207756

Order 30992.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₃×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₁₄₉	C₄	1	1	yes	characteristic
3	C₂×C₁₃×C₁₄₉	C₈	1	1	yes	characteristic
4	C₁₆×C₁₄₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₃×C₁₄₉	C₁₆	1	1	yes	characteristic, direct product factor, Hall
6	C₈×C₁₄₉	C₂×C₁₃	1	1	yes	characteristic
7	C₄×C₁₄₉	C₄×C₁₃	1	1	yes	characteristic
8	C₂×C₁₄₉	C₈×C₁₃	1	1	yes	characteristic
9	C₁₃×C₁₆	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₄₉	C₁₃×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
11	C₈×C₁₃	C₂×C₁₄₉	1	1	yes	characteristic
12	C₄×C₁₃	C₄×C₁₄₉	1	1	yes	characteristic
13	C₂×C₁₃	C₈×C₁₄₉	1	1	yes	characteristic
14	C₁₆	C₁₃×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₁₃	C₁₆×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₈	C₂×C₁₃×C₁₄₉	1	1	yes	characteristic
17	C₄	C₄×C₁₃×C₁₄₉	1	1	yes	characteristic
18	C₂	C₈×C₁₃×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₁₃×C₁₄₉
socle, prime radical	C₂×C₁₃×C₁₄₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₆×C₁₄₉	C₁₃	direct (N × H)
5. C₁₃×C₁₄₉	C₁₆	direct (N × H)
9. C₁₃×C₁₆	C₁₄₉	direct (N × H)
10. C₁₄₉	C₁₃×C₁₆	direct (N × H)
14. C₁₆	C₁₃×C₁₄₉	direct (N × H)
15. C₁₃	C₁₆×C₁₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×C₁₃×C₁₄₉	2
C₁₆×C₁₄₉	13
C₁₃×C₁₆	149