Subgroups — C₄×C₇×C₁₃×C₈₉ #44569293

Order 32396.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₃×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₃×C₈₉	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₃×C₈₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₇×C₈₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₃×C₈₉	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₈₉	C₂×C₁₃	1	1	yes	characteristic
7	C₁₃×C₈₉	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₈₉	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
9	C₄×C₇×C₁₃	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₈₉	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₇×C₁₃	C₂×C₈₉	1	1	yes	characteristic
12	C₂×C₈₉	C₂×C₇×C₁₃	1	1	yes	characteristic
13	C₇×C₁₃	C₄×C₈₉	1	1	yes	characteristic, direct product factor, Hall
14	C₈₉	C₄×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₄×C₁₃	C₇×C₈₉	1	1	yes	characteristic, direct product factor, Hall
16	C₄×C₇	C₁₃×C₈₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₃	C₂×C₇×C₈₉	1	1	yes	characteristic
18	C₂×C₇	C₂×C₁₃×C₈₉	1	1	yes	characteristic
19	C₁₃	C₄×C₇×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₄×C₁₃×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₇×C₁₃×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₇×C₁₃×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₇×C₁₃×C₈₉
socle, prime radical	C₂×C₇×C₁₃×C₈₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₃×C₈₉	C₄	direct (N × H)
3. C₄×C₁₃×C₈₉	C₇	direct (N × H)
4. C₄×C₇×C₈₉	C₁₃	direct (N × H)
7. C₁₃×C₈₉	C₄×C₇	direct (N × H)
8. C₇×C₈₉	C₄×C₁₃	direct (N × H)
9. C₄×C₇×C₁₃	C₈₉	direct (N × H)
10. C₄×C₈₉	C₇×C₁₃	direct (N × H)
13. C₇×C₁₃	C₄×C₈₉	direct (N × H)
14. C₈₉	C₄×C₇×C₁₃	direct (N × H)
15. C₄×C₁₃	C₇×C₈₉	direct (N × H)
16. C₄×C₇	C₁₃×C₈₉	direct (N × H)
19. C₁₃	C₄×C₇×C₈₉	direct (N × H)
20. C₇	C₄×C₁₃×C₈₉	direct (N × H)
21. C₄	C₇×C₁₃×C₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×C₁₃×C₈₉	2
C₄×C₁₃×C₈₉	7
C₄×C₇×C₈₉	13
C₄×C₇×C₁₃	89

Subgroups — C4×C7×C13×C89 #44569293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₁₃×C₈₉ #44569293