Subgroups — C₂×C₅×D₅×C₃₀₇ #44502003

Order 30700.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₃₀₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₃₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₃₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅×C₃₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₅×C₃₀₇	—	5	1	no	maximal
6	C₂×C₅×C₃₀₇	—	2	2	no	—
7	C₂×C₅×C₃₀₇	—	5	2	no	—
8	C₂×C₅×C₃₀₇	D₅	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₃₀₇	C₂×C₅	1	1	yes	characteristic, complemented
10	D₅×C₃₀₇	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₃₀₇	—	2	2	no	—
12	C₅×C₃₀₇	C₂×D₅	1	1	yes	characteristic, direct product factor
13	C₅×C₃₀₇	C₂²×C₅	1	1	yes	characteristic, complemented
14	C₂²×C₃₀₇	—	5	1	no	Hall
15	C₂×C₃₀₇	—	5	2	no	—
16	C₂×C₃₀₇	C₅×D₅	1	1	yes	characteristic, direct product factor
17	C₃₀₇	C₂×C₅×D₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₅×D₅	C₃₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅²	C₂×C₃₀₇	1	1	yes	characteristic, complemented
20	C₅×D₅	C₂×C₃₀₇	1	2	yes	direct product factor
21	C₅²	C₂²×C₃₀₇	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₅	—	5	1	no	—
23	C₂×D₅	C₅×C₃₀₇	1	1	yes	characteristic, direct product factor
24	C₂×C₅	—	2	2	no	—
25	C₂×C₅	—	5	2	no	—
26	C₂×C₅	D₅×C₃₀₇	1	1	yes	characteristic, direct product factor
27	C₂×C₅	C₂×C₅×C₃₀₇	1	1	yes	characteristic, complemented
28	D₅	C₂×C₅×C₃₀₇	1	2	yes	direct product factor
29	C₅	—	2	2	no	—
30	C₅	C₂²×C₅×C₃₀₇	1	1	yes	characteristic, complemented
31	C₅	C₂×D₅×C₃₀₇	1	1	yes	characteristic, direct product factor
32	C₂²	—	5	1	no	Sylow
33	C₂	—	5	2	no	—
34	C₂	C₅×D₅×C₃₀₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₃₀₇	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₅×C₃₀₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₃₀₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₅×C₃₀₇

Complements

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

N	H ≅ G/N	type
1. C₅×D₅×C₃₀₇	C₂	direct (N × H)
2. C₂×C₅²×C₃₀₇	C₂	semidirect
3. C₅²×C₃₀₇	C₂²	semidirect
4. C₂×D₅×C₃₀₇	C₅	direct (N × H)
8. C₂×C₅×C₃₀₇	D₅	direct (N × H)
9. C₂×C₅×C₃₀₇	C₂×C₅	semidirect
10. D₅×C₃₀₇	C₂×C₅	direct (N × H)
12. C₅×C₃₀₇	C₂×D₅	direct (N × H)
13. C₅×C₃₀₇	C₂²×C₅	semidirect
16. C₂×C₃₀₇	C₅×D₅	direct (N × H)
17. C₃₀₇	C₂×C₅×D₅	direct (N × H)
18. C₂×C₅×D₅	C₃₀₇	direct (N × H)
19. C₂×C₅²	C₂×C₃₀₇	semidirect
20. C₅×D₅	C₂×C₃₀₇	direct (N × H)
21. C₅²	C₂²×C₃₀₇	semidirect
23. C₂×D₅	C₅×C₃₀₇	direct (N × H)
26. C₂×C₅	D₅×C₃₀₇	direct (N × H)
27. C₂×C₅	C₂×C₅×C₃₀₇	semidirect
28. D₅	C₂×C₅×C₃₀₇	direct (N × H)
30. C₅	C₂²×C₅×C₃₀₇	semidirect
31. C₅	C₂×D₅×C₃₀₇	direct (N × H)
34. C₂	C₅×D₅×C₃₀₇	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×D₅×C₃₀₇	2
C₂×C₅²×C₃₀₇	2
C₂×D₅×C₃₀₇	5
C₂²×C₅×C₃₀₇	5
C₂×C₅×D₅	307

Subgroups — C2×C5×D5×C307 #44502003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₅×C₃₀₇ #44502003