Finite Group Databasebeta

← C₁₃×C₁₉×D₇₁ #47975109

Subgroups — C₁₃×C₁₉×D₇₁ #47975109

Order 35074.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₇₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×D₇₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₉×C₇₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₇₁	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃×C₁₉	—	71	1	no	maximal, Hall
7	C₁₃×C₁₉	D₇₁	1	1	yes	characteristic, direct product factor, Hall
8	D₇₁	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
9	C₇₁	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₉	—	71	1	no	Hall
11	C₂×C₁₃	—	71	1	no	Hall
12	C₁₉	C₁₃×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₃	C₁₉×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	71	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	D₇₁
commutator, cosocle, hypocenter	C₇₁	C₂×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₉×C₇₁	C₂
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×C₇₁	C₂	semidirect
2. C₁₉×D₇₁	C₁₃	direct (N × H)
3. C₁₃×D₇₁	C₁₉	direct (N × H)
4. C₁₉×C₇₁	C₂×C₁₃	semidirect
5. C₁₃×C₇₁	C₂×C₁₉	semidirect
7. C₁₃×C₁₉	D₇₁	direct (N × H)
8. D₇₁	C₁₃×C₁₉	direct (N × H)
9. C₇₁	C₂×C₁₃×C₁₉	semidirect
12. C₁₉	C₁₃×D₇₁	direct (N × H)
13. C₁₃	C₁₉×D₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₁₉×C₇₁	2
C₁₉×D₇₁	13
C₁₃×D₇₁	19
C₂×C₁₃×C₁₉	71