Subgroups — D₅×C₁₉×D₇₁ #41008697

Order 26980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₃₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₉×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₉×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×D₇₁	—	5	1	no	maximal, Hall
6	C₂×C₁₉×C₇₁	—	5	1	no	—
7	C₁₉×D₇₁	—	5	1	no	—
8	C₁₉×D₇₁	D₅	1	1	yes	characteristic, direct product factor
9	D₅×D₇₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₉×C₇₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	D₃₅₅	C₂×C₁₉	1	1	yes	characteristic, complemented
12	C₅×D₇₁	C₂×C₁₉	1	1	yes	characteristic, complemented
13	D₅×C₇₁	C₂×C₁₉	1	1	yes	characteristic, complemented
14	C₂×D₅×C₁₉	—	71	1	no	maximal, Hall
15	C₅×C₇₁	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×D₇₁	—	5	1	no	Hall
17	C₂×C₅×C₁₉	—	71	1	no	—
18	D₅×C₁₉	—	71	1	no	—
19	D₅×C₁₉	D₇₁	1	1	yes	characteristic, direct product factor
20	C₂×C₇₁	—	5	1	no	—
21	D₇₁	—	5	1	no	—
22	D₇₁	D₅×C₁₉	1	1	yes	characteristic, direct product factor
23	C₅×C₁₉	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₁₉	—	355	1	no	Hall
25	C₇₁	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₉	—	5	1	no	—
27	C₂×C₁₉	—	71	1	no	—
28	C₂×C₁₉	—	355	1	no	—
29	C₂×D₅	—	71	1	no	Hall
30	C₁₉	D₅×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₅	—	71	1	no	—
32	D₅	—	71	1	no	—
33	D₅	C₁₉×D₇₁	1	1	yes	characteristic, direct product factor
34	C₅	C₂×C₁₉×D₇₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	355	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	71	1	no	—
38	C₂	—	355	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₅×D₇₁
commutator, cosocle, hypocenter	C₅×C₇₁	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₇₁	C₂²
LCS	G ▷ C₅×C₇₁
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₃₅₅	C₂	semidirect
2. D₅×C₁₉×C₇₁	C₂	semidirect
3. C₅×C₁₉×D₇₁	C₂	semidirect
4. C₅×C₁₉×C₇₁	C₂²	semidirect
8. C₁₉×D₇₁	D₅	direct (N × H)
9. D₅×D₇₁	C₁₉	direct (N × H)
10. C₁₉×C₇₁	C₂×D₅	semidirect
11. D₃₅₅	C₂×C₁₉	semidirect
12. C₅×D₇₁	C₂×C₁₉	semidirect
13. D₅×C₇₁	C₂×C₁₉	semidirect
15. C₅×C₇₁	C₂²×C₁₉	semidirect
19. D₅×C₁₉	D₇₁	direct (N × H)
22. D₇₁	D₅×C₁₉	direct (N × H)
23. C₅×C₁₉	C₂×D₇₁	semidirect
25. C₇₁	C₂×D₅×C₁₉	semidirect
30. C₁₉	D₅×D₇₁	direct (N × H)
33. D₅	C₁₉×D₇₁	direct (N × H)
34. C₅	C₂×C₁₉×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×D₃₅₅	2
D₅×C₁₉×C₇₁	2
C₅×C₁₉×D₇₁	2
C₂×C₁₉×D₇₁	5
D₅×D₇₁	19
C₂×D₅×C₁₉	71

Subgroups — D5×C19×D71 #41008697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₉×D₇₁ #41008697