Subgroups — C₃×C₄×C₃₇×C₇₁ #44538599

Order 31524.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₇×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₃₇×C₇₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₃₇×C₇₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃₇×C₇₁	C₂×C₃	1	1	yes	characteristic
5	C₃₇×C₇₁	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₄×C₇₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₄×C₃₇	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₇₁	C₂×C₃₇	1	1	yes	characteristic
9	C₄×C₇₁	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₃₇	C₂×C₇₁	1	1	yes	characteristic
11	C₃×C₇₁	C₄×C₃₇	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₃₇	C₃×C₇₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₇₁	C₂×C₃×C₃₇	1	1	yes	characteristic
14	C₃×C₃₇	C₄×C₇₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃₇	C₂×C₃×C₇₁	1	1	yes	characteristic
16	C₇₁	C₃×C₄×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₇	C₃×C₄×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	C₃₇×C₇₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₃₇×C₇₁	1	1	yes	characteristic
20	C₄	C₃×C₃₇×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₄×C₃₇×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₃₇×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₃₇×C₇₁
socle, prime radical	C₂×C₃×C₃₇×C₇₁	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×C₃₇×C₇₁	C₃	direct (N × H)
3. C₃×C₃₇×C₇₁	C₄	direct (N × H)
5. C₃₇×C₇₁	C₃×C₄	direct (N × H)
6. C₃×C₄×C₇₁	C₃₇	direct (N × H)
7. C₃×C₄×C₃₇	C₇₁	direct (N × H)
9. C₄×C₇₁	C₃×C₃₇	direct (N × H)
11. C₃×C₇₁	C₄×C₃₇	direct (N × H)
12. C₄×C₃₇	C₃×C₇₁	direct (N × H)
14. C₃×C₃₇	C₄×C₇₁	direct (N × H)
16. C₇₁	C₃×C₄×C₃₇	direct (N × H)
17. C₃₇	C₃×C₄×C₇₁	direct (N × H)
18. C₃×C₄	C₃₇×C₇₁	direct (N × H)
20. C₄	C₃×C₃₇×C₇₁	direct (N × H)
21. C₃	C₄×C₃₇×C₇₁	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×C₃₇×C₇₁	2
C₄×C₃₇×C₇₁	3
C₃×C₄×C₇₁	37
C₃×C₄×C₃₇	71

Subgroups — C3×C4×C37×C71 #44538599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₃₇×C₇₁ #44538599