Subgroups — C₄×C₅×C₃₇×C₄₉ #49136355

Order 36260.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₇×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₇×C₄₉	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₃₇×C₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₅×C₇×C₃₇	C₇	1	1	yes	maximal, characteristic
5	C₂×C₃₇×C₄₉	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₇×C₃₇	C₂×C₇	1	1	yes	characteristic
7	C₃₇×C₄₉	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₇×C₃₇	C₄×C₇	1	1	yes	characteristic
9	C₄×C₇×C₃₇	C₅×C₇	1	1	yes	characteristic
10	C₄×C₅×C₄₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₄×C₅×C₃₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₇×C₃₇	C₂×C₅×C₇	1	1	yes	characteristic
13	C₂×C₅×C₄₉	C₂×C₃₇	1	1	yes	characteristic
14	C₂×C₅×C₃₇	C₂×C₄₉	1	1	yes	characteristic
15	C₇×C₃₇	C₄×C₅×C₇	1	1	yes	characteristic
16	C₅×C₄₉	C₄×C₃₇	1	1	yes	characteristic, direct product factor, Hall
17	C₄×C₄₉	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₃₇	C₄×C₄₉	1	1	yes	characteristic, direct product factor, Hall
19	C₄×C₃₇	C₅×C₄₉	1	1	yes	characteristic, direct product factor, Hall
20	C₄×C₅×C₇	C₇×C₃₇	1	1	yes	characteristic
21	C₂×C₄₉	C₂×C₅×C₃₇	1	1	yes	characteristic
22	C₂×C₃₇	C₂×C₅×C₄₉	1	1	yes	characteristic
23	C₂×C₅×C₇	C₂×C₇×C₃₇	1	1	yes	characteristic
24	C₄₉	C₄×C₅×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₃₇	C₄×C₅×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₅×C₇	C₄×C₇×C₃₇	1	1	yes	characteristic
27	C₄×C₇	C₅×C₇×C₃₇	1	1	yes	characteristic
28	C₄×C₅	C₃₇×C₄₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇	C₂×C₅×C₇×C₃₇	1	1	yes	characteristic
30	C₂×C₅	C₂×C₃₇×C₄₉	1	1	yes	characteristic
31	C₇	C₄×C₅×C₇×C₃₇	1	1	yes	characteristic
32	C₅	C₄×C₃₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₄	C₅×C₃₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅×C₃₇×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₇	C₂×C₅×C₇×C₃₇
socle, prime radical	C₂×C₅×C₇×C₃₇	C₂×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×C₃₇×C₄₉	C₄	direct (N × H)
3. C₄×C₃₇×C₄₉	C₅	direct (N × H)
7. C₃₇×C₄₉	C₄×C₅	direct (N × H)
10. C₄×C₅×C₄₉	C₃₇	direct (N × H)
11. C₄×C₅×C₃₇	C₄₉	direct (N × H)
16. C₅×C₄₉	C₄×C₃₇	direct (N × H)
17. C₄×C₄₉	C₅×C₃₇	direct (N × H)
18. C₅×C₃₇	C₄×C₄₉	direct (N × H)
19. C₄×C₃₇	C₅×C₄₉	direct (N × H)
24. C₄₉	C₄×C₅×C₃₇	direct (N × H)
25. C₃₇	C₄×C₅×C₄₉	direct (N × H)
28. C₄×C₅	C₃₇×C₄₉	direct (N × H)
32. C₅	C₄×C₃₇×C₄₉	direct (N × H)
33. C₄	C₅×C₃₇×C₄₉	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×C₅×C₃₇×C₄₉	2
C₄×C₃₇×C₄₉	5
C₄×C₅×C₇×C₃₇	7
C₄×C₅×C₄₉	37

Subgroups — C4×C5×C37×C49 #49136355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₃₇×C₄₉ #49136355