Subgroups — C₂×C₉×C₁₃×C₁₃₇ #44545379

Order 32058.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃×C₁₃₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₃×C₁₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₁₃₇	C₂×C₃	1	1	yes	characteristic
4	C₂×C₁₃×C₁₃₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₉×C₁₃₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₁₃₇	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×C₁₃₇	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₁₃₇	C₃×C₁₃	1	1	yes	characteristic
9	C₃×C₁₃₇	C₂×C₃×C₁₃	1	1	yes	characteristic
10	C₂×C₁₃₇	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₉×C₁₃	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₃₇	C₂×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₉×C₁₃	C₂×C₁₃₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₁₃	C₃×C₁₃₇	1	1	yes	characteristic
15	C₃×C₁₃	C₂×C₃×C₁₃₇	1	1	yes	characteristic
16	C₂×C₁₃	C₉×C₁₃₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₉	C₁₃×C₁₃₇	1	1	yes	characteristic, direct product factor, Hall
18	C₁₃	C₂×C₉×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₉	C₂×C₁₃×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₁₃×C₁₃₇	1	1	yes	characteristic
21	C₃	C₂×C₃×C₁₃×C₁₃₇	1	1	yes	characteristic
22	C₂	C₉×C₁₃×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₁₃×C₁₃₇
socle, prime radical	C₂×C₃×C₁₃×C₁₃₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₃×C₁₃₇	C₂	direct (N × H)
4. C₂×C₁₃×C₁₃₇	C₉	direct (N × H)
5. C₂×C₉×C₁₃₇	C₁₃	direct (N × H)
6. C₁₃×C₁₃₇	C₂×C₉	direct (N × H)
7. C₉×C₁₃₇	C₂×C₁₃	direct (N × H)
10. C₂×C₁₃₇	C₉×C₁₃	direct (N × H)
11. C₂×C₉×C₁₃	C₁₃₇	direct (N × H)
12. C₁₃₇	C₂×C₉×C₁₃	direct (N × H)
13. C₉×C₁₃	C₂×C₁₃₇	direct (N × H)
16. C₂×C₁₃	C₉×C₁₃₇	direct (N × H)
17. C₂×C₉	C₁₃×C₁₃₇	direct (N × H)
18. C₁₃	C₂×C₉×C₁₃₇	direct (N × H)
19. C₉	C₂×C₁₃×C₁₃₇	direct (N × H)
22. C₂	C₉×C₁₃×C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₁₃×C₁₃₇	2
C₂×C₃×C₁₃×C₁₃₇	3
C₂×C₉×C₁₃₇	13
C₂×C₉×C₁₃	137

Subgroups — C2×C9×C13×C137 #44545379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₃×C₁₃₇ #44545379