Subgroups — C₂×C₅×C₃₇×C₇⋊D₇ #49136457

Order 36260.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₇×C₇⋊D₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇×C₇⋊D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₇×C₃₇	—	7	8	no	maximal
6	C₃₇×C₇⋊D₇	C₂×C₅	1	2	yes	direct product factor
7	C₂×C₇²×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅×D₇×C₃₇	—	7	16	no	—
9	C₂×C₅×C₇×C₃₇	D₇	1	8	yes	complemented
10	C₇²×C₃₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₇×C₃₇	C₂×D₇	1	8	yes	complemented
12	C₂×D₇×C₃₇	—	7	8	no	—
13	C₂×C₅×C₇⋊D₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₅×C₃₇	—	49	1	no	Hall
15	C₂×C₇×C₃₇	C₅×D₇	1	8	yes	complemented
16	D₇×C₃₇	—	7	16	no	—
17	C₂×C₅×C₇²	C₂×C₃₇	1	1	yes	characteristic, complemented
18	C₅×C₇⋊D₇	C₂×C₃₇	1	2	yes	direct product factor
19	C₂×C₅×C₃₇	—	49	2	no	—
20	C₂×C₅×C₃₇	C₇⋊D₇	1	1	yes	characteristic, direct product factor
21	C₇×C₃₇	C₂×C₅×D₇	1	8	yes	complemented
22	C₅×C₇²	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇⋊D₇	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₃₇	C₂×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₃₇	—	49	1	no	Hall
26	C₂×C₅×D₇	—	7	8	no	—
27	C₂×C₇²	C₂×C₅×C₃₇	1	1	yes	characteristic, complemented
28	C₇⋊D₇	C₂×C₅×C₃₇	1	2	yes	direct product factor
29	C₂×C₃₇	—	49	2	no	—
30	C₂×C₃₇	C₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor
31	C₂×C₅×C₇	D₇×C₃₇	1	8	yes	complemented
32	C₅×D₇	—	7	16	no	—
33	C₇²	C₂²×C₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
34	C₃₇	C₂×C₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
35	C₅×C₇	C₂×D₇×C₃₇	1	8	yes	complemented
36	C₂×D₇	—	7	8	no	—
37	C₂²×C₅	—	49	1	no	Hall
38	C₂×C₇	C₅×D₇×C₃₇	1	8	yes	complemented
39	D₇	—	7	16	no	—
40	C₂×C₅	—	49	2	no	—
41	C₂×C₅	C₃₇×C₇⋊D₇	1	1	yes	characteristic, direct product factor
42	C₇	C₂×C₅×D₇×C₃₇	1	8	yes	complemented
43	C₅	C₂×C₃₇×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	—	49	1	no	Sylow
45	C₂	—	49	2	no	—
46	C₂	C₅×C₃₇×C₇⋊D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₃₇	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂²×C₅×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₃₇	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₅×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₇×C₇⋊D₇	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₃₇	C₂	semidirect
3. C₅×C₇²×C₃₇	C₂²	semidirect
4. C₂×C₃₇×C₇⋊D₇	C₅	direct (N × H)
6. C₃₇×C₇⋊D₇	C₂×C₅	direct (N × H)
7. C₂×C₇²×C₃₇	C₂×C₅	semidirect
9. C₂×C₅×C₇×C₃₇	D₇	semidirect
10. C₇²×C₃₇	C₂²×C₅	semidirect
11. C₅×C₇×C₃₇	C₂×D₇	semidirect
13. C₂×C₅×C₇⋊D₇	C₃₇	direct (N × H)
15. C₂×C₇×C₃₇	C₅×D₇	semidirect
17. C₂×C₅×C₇²	C₂×C₃₇	semidirect
18. C₅×C₇⋊D₇	C₂×C₃₇	direct (N × H)
20. C₂×C₅×C₃₇	C₇⋊D₇	direct (N × H)
21. C₇×C₃₇	C₂×C₅×D₇	semidirect
22. C₅×C₇²	C₂²×C₃₇	semidirect
23. C₂×C₇⋊D₇	C₅×C₃₇	direct (N × H)
24. C₅×C₃₇	C₂×C₇⋊D₇	direct (N × H)
27. C₂×C₇²	C₂×C₅×C₃₇	semidirect
28. C₇⋊D₇	C₂×C₅×C₃₇	direct (N × H)
30. C₂×C₃₇	C₅×C₇⋊D₇	direct (N × H)
31. C₂×C₅×C₇	D₇×C₃₇	semidirect
33. C₇²	C₂²×C₅×C₃₇	semidirect
34. C₃₇	C₂×C₅×C₇⋊D₇	direct (N × H)
35. C₅×C₇	C₂×D₇×C₃₇	semidirect
38. C₂×C₇	C₅×D₇×C₃₇	semidirect
41. C₂×C₅	C₃₇×C₇⋊D₇	direct (N × H)
42. C₇	C₂×C₅×D₇×C₃₇	semidirect
43. C₅	C₂×C₃₇×C₇⋊D₇	direct (N × H)
46. C₂	C₅×C₃₇×C₇⋊D₇	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×C₃₇×C₇⋊D₇	2
C₂×C₅×C₇²×C₃₇	2
C₂×C₃₇×C₇⋊D₇	5
C₂×C₅×D₇×C₃₇	7
C₂×C₅×C₇⋊D₇	37

Subgroups — C2×C5×C37×C7⋊D7 #49136457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₃₇×C₇⋊D₇ #49136457