Subgroups — C₂²×C₅×C₁₉×C₇₁ #41008686

Order 26980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₉×C₇₁	C₂	1	3	yes	maximal, direct product factor
2	C₅×C₁₉×C₇₁	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₉×C₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₉×C₇₁	C₂×C₅	1	3	yes	direct product factor
5	C₂²×C₅×C₇₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₉×C₇₁	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₇₁	C₂×C₁₉	1	3	yes	direct product factor
8	C₂²×C₅×C₁₉	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₇₁	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂²×C₇₁	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₁₉	C₂×C₇₁	1	3	yes	direct product factor
12	C₂×C₇₁	C₂×C₅×C₁₉	1	3	yes	direct product factor
13	C₅×C₁₉	C₂²×C₇₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂²×C₁₉	C₅×C₇₁	1	1	yes	characteristic, direct product factor, Hall
15	C₇₁	C₂²×C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₉	C₂×C₅×C₇₁	1	3	yes	direct product factor
17	C₂²×C₅	C₁₉×C₇₁	1	1	yes	characteristic, direct product factor, Hall
18	C₁₉	C₂²×C₅×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₂×C₁₉×C₇₁	1	3	yes	direct product factor
20	C₅	C₂²×C₁₉×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₅×C₁₉×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₁₉×C₇₁	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₁₉×C₇₁	C₂	direct (N × H)
2. C₅×C₁₉×C₇₁	C₂²	direct (N × H)
3. C₂²×C₁₉×C₇₁	C₅	direct (N × H)
4. C₂×C₁₉×C₇₁	C₂×C₅	direct (N × H)
5. C₂²×C₅×C₇₁	C₁₉	direct (N × H)
6. C₁₉×C₇₁	C₂²×C₅	direct (N × H)
7. C₂×C₅×C₇₁	C₂×C₁₉	direct (N × H)
8. C₂²×C₅×C₁₉	C₇₁	direct (N × H)
9. C₅×C₇₁	C₂²×C₁₉	direct (N × H)
10. C₂²×C₇₁	C₅×C₁₉	direct (N × H)
11. C₂×C₅×C₁₉	C₂×C₇₁	direct (N × H)
12. C₂×C₇₁	C₂×C₅×C₁₉	direct (N × H)
13. C₅×C₁₉	C₂²×C₇₁	direct (N × H)
14. C₂²×C₁₉	C₅×C₇₁	direct (N × H)
15. C₇₁	C₂²×C₅×C₁₉	direct (N × H)
16. C₂×C₁₉	C₂×C₅×C₇₁	direct (N × H)
17. C₂²×C₅	C₁₉×C₇₁	direct (N × H)
18. C₁₉	C₂²×C₅×C₇₁	direct (N × H)
19. C₂×C₅	C₂×C₁₉×C₇₁	direct (N × H)
20. C₅	C₂²×C₁₉×C₇₁	direct (N × H)
21. C₂²	C₅×C₁₉×C₇₁	direct (N × H)
22. C₂	C₂×C₅×C₁₉×C₇₁	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×C₁₉×C₇₁	2
C₂²×C₁₉×C₇₁	5
C₂²×C₅×C₇₁	19
C₂²×C₅×C₁₉	71

Subgroups — C22×C5×C19×C71 #41008686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₁₉×C₇₁ #41008686