Finite Group Databasebeta

← C₃×C₇×C₁₃×C₉₇ #40996607

Subgroups — C₃×C₇×C₁₃×C₉₇ #40996607

Order 26481.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₁₃×C₉₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₉₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₉₇	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
5	C₇×C₉₇	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₉₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₁₃	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₉₇	C₃×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₇×C₁₃	C₃×C₉₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₃	C₇×C₉₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇	C₁₃×C₉₇	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃	C₃×C₇×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	C₃×C₁₃×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	C₇×C₁₃×C₉₇	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. C₇×C₁₃×C₉₇	C₃	direct (N × H)
2. C₃×C₁₃×C₉₇	C₇	direct (N × H)
3. C₃×C₇×C₉₇	C₁₃	direct (N × H)
4. C₁₃×C₉₇	C₃×C₇	direct (N × H)
5. C₇×C₉₇	C₃×C₁₃	direct (N × H)
6. C₃×C₉₇	C₇×C₁₃	direct (N × H)
7. C₃×C₇×C₁₃	C₉₇	direct (N × H)
8. C₉₇	C₃×C₇×C₁₃	direct (N × H)
9. C₇×C₁₃	C₃×C₉₇	direct (N × H)
10. C₃×C₁₃	C₇×C₉₇	direct (N × H)
11. C₃×C₇	C₁₃×C₉₇	direct (N × H)
12. C₁₃	C₃×C₇×C₉₇	direct (N × H)
13. C₇	C₃×C₁₃×C₉₇	direct (N × H)
14. C₃	C₇×C₁₃×C₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₃×C₉₇	3
C₃×C₁₃×C₉₇	7
C₃×C₇×C₉₇	13
C₃×C₇×C₁₃	97