Subgroups — C₅×D₃₇×D₄₉ #49136366

Order 36260.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₈₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃₇×D₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₄₉×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₃₇×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₇×D₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₇×D₃₇	—	7	1	no	maximal
7	D₁₈₁₃	C₂×C₅	1	1	yes	characteristic, complemented
8	C₄₉×D₃₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃₇×D₄₉	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×D₂₅₉	—	7	1	no	—
11	C₅×D₇×C₃₇	—	7	1	no	—
12	C₅×C₇×D₃₇	D₇	1	1	yes	characteristic
13	C₃₇×C₄₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₇×C₃₇	C₂×D₇	1	1	yes	characteristic
15	D₇×D₃₇	—	7	1	no	—
16	C₂×C₅×D₄₉	—	37	1	no	maximal, Hall
17	C₂×C₅×D₃₇	—	49	1	no	Hall
18	D₂₅₉	—	7	1	no	—
19	C₇×D₃₇	C₅×D₇	1	1	yes	characteristic
20	D₇×C₃₇	—	7	1	no	—
21	C₂×C₅×C₄₉	—	37	1	no	—
22	C₅×D₄₉	—	37	1	no	—
23	C₅×D₄₉	D₃₇	1	1	yes	characteristic, direct product factor
24	C₂×C₅×C₃₇	—	49	1	no	—
25	C₅×D₃₇	—	49	1	no	—
26	C₅×D₃₇	D₄₉	1	1	yes	characteristic, direct product factor
27	C₇×C₃₇	C₂×C₅×D₇	1	1	yes	characteristic
28	C₅×C₄₉	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
29	C₂×D₄₉	—	37	1	no	Hall
30	C₅×C₃₇	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
31	C₂×D₃₇	—	49	1	no	Hall
32	C₂×C₅×D₇	—	259	1	no	—
33	C₂×C₄₉	—	37	1	no	—
34	D₄₉	—	37	1	no	—
35	D₄₉	C₅×D₃₇	1	1	yes	characteristic, direct product factor
36	C₂×C₃₇	—	49	1	no	—
37	D₃₇	—	49	1	no	—
38	D₃₇	C₅×D₄₉	1	1	yes	characteristic, direct product factor
39	C₂×C₅×C₇	—	37	1	no	—
40	C₅×D₇	—	259	1	no	—
41	C₅×D₇	—	7	1	no	—
42	C₄₉	C₂×C₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
43	C₃₇	C₂×C₅×D₄₉	1	1	yes	characteristic, complemented, Sylow
44	C₅×C₇	D₇×D₃₇	1	1	yes	characteristic
45	C₂×D₇	—	259	1	no	—
46	C₂²×C₅	—	1813	1	no	Hall
47	C₂×C₇	—	37	1	no	—
48	D₇	—	259	1	no	—
49	D₇	—	7	1	no	—
50	C₂×C₅	—	1813	1	no	—
51	C₂×C₅	—	37	1	no	—
52	C₂×C₅	—	49	1	no	—
53	C₇	C₅×D₇×D₃₇	1	1	yes	characteristic
54	C₅	D₃₇×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²	—	1813	1	no	Sylow
56	C₂	—	1813	1	no	—
57	C₂	—	37	1	no	—
58	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃₇×D₄₉
commutator, cosocle, hypocenter	C₃₇×C₄₉	C₂²×C₅
Frattini	C₇	C₅×D₇×D₃₇
Fitting	C₅×C₃₇×C₄₉	C₂²
socle	C₅×C₇×C₃₇	C₂×D₇
LCS	G ▷ C₃₇×C₄₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₈₁₃	C₂	semidirect
2. C₅×C₃₇×D₄₉	C₂	semidirect
3. C₅×C₄₉×D₃₇	C₂	semidirect
4. C₅×C₃₇×C₄₉	C₂²	semidirect
5. D₃₇×D₄₉	C₅	direct (N × H)
7. D₁₈₁₃	C₂×C₅	semidirect
8. C₄₉×D₃₇	C₂×C₅	semidirect
9. C₃₇×D₄₉	C₂×C₅	semidirect
13. C₃₇×C₄₉	C₂²×C₅	semidirect
23. C₅×D₄₉	D₃₇	direct (N × H)
26. C₅×D₃₇	D₄₉	direct (N × H)
28. C₅×C₄₉	C₂×D₃₇	semidirect
30. C₅×C₃₇	C₂×D₄₉	semidirect
35. D₄₉	C₅×D₃₇	direct (N × H)
38. D₃₇	C₅×D₄₉	direct (N × H)
42. C₄₉	C₂×C₅×D₃₇	semidirect
43. C₃₇	C₂×C₅×D₄₉	semidirect
54. C₅	D₃₇×D₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₁₈₁₃	2
C₅×C₃₇×D₄₉	2
C₅×C₄₉×D₃₇	2
D₃₇×D₄₉	5
C₅×D₇×D₃₇	7
C₂×C₅×D₄₉	37

Subgroups — C5×D37×D49 #49136366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₇×D₄₉ #49136366