Subgroups — C₃×C₄×C₁₇×C₁₅₇ #44545075

Order 32028.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×C₁₅₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₇×C₁₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×C₁₅₇	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic
5	C₁₇×C₁₅₇	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₄×C₁₅₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₁₅₇	C₂×C₁₇	1	1	yes	characteristic
8	C₄×C₁₅₇	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₅₇	C₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₅₇	C₂×C₃×C₁₇	1	1	yes	characteristic
11	C₃×C₄×C₁₇	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₅₇	C₃×C₄×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃×C₁₇	C₂×C₁₅₇	1	1	yes	characteristic
14	C₄×C₁₇	C₃×C₁₅₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₇	C₄×C₁₅₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₇	C₂×C₃×C₁₅₇	1	1	yes	characteristic
17	C₁₇	C₃×C₄×C₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	C₁₇×C₁₅₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₁₇×C₁₅₇	1	1	yes	characteristic
20	C₄	C₃×C₁₇×C₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₄×C₁₇×C₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₁₇×C₁₅₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₁₇×C₁₅₇
socle, prime radical	C₂×C₃×C₁₇×C₁₅₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₇×C₁₅₇	C₃	direct (N × H)
3. C₃×C₁₇×C₁₅₇	C₄	direct (N × H)
5. C₁₇×C₁₅₇	C₃×C₄	direct (N × H)
6. C₃×C₄×C₁₅₇	C₁₇	direct (N × H)
8. C₄×C₁₅₇	C₃×C₁₇	direct (N × H)
9. C₃×C₁₅₇	C₄×C₁₇	direct (N × H)
11. C₃×C₄×C₁₇	C₁₅₇	direct (N × H)
12. C₁₅₇	C₃×C₄×C₁₇	direct (N × H)
14. C₄×C₁₇	C₃×C₁₅₇	direct (N × H)
15. C₃×C₁₇	C₄×C₁₅₇	direct (N × H)
17. C₁₇	C₃×C₄×C₁₅₇	direct (N × H)
18. C₃×C₄	C₁₇×C₁₅₇	direct (N × H)
20. C₄	C₃×C₁₇×C₁₅₇	direct (N × H)
21. C₃	C₄×C₁₇×C₁₅₇	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×C₃×C₁₇×C₁₅₇	2
C₄×C₁₇×C₁₅₇	3
C₃×C₄×C₁₅₇	17
C₃×C₄×C₁₇	157

Subgroups — C3×C4×C17×C157 #44545075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₁₇×C₁₅₇ #44545075