Subgroups — C₂×C₇²×C₁₇×C₁₉ #44539607

Order 31654.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₇×C₁₉	C₇	1	8	yes	maximal, direct product factor
3	C₇×C₁₇×C₁₉	C₂×C₇	1	8	yes	direct product factor
4	C₂×C₇²×C₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇²×C₁₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇²×C₁₉	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
7	C₇²×C₁₇	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₁₇×C₁₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
9	C₁₇×C₁₉	C₂×C₇²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇×C₁₉	C₇×C₁₇	1	8	yes	direct product factor
11	C₂×C₇×C₁₇	C₇×C₁₉	1	8	yes	direct product factor
12	C₇×C₁₉	C₂×C₇×C₁₇	1	8	yes	direct product factor
13	C₇×C₁₇	C₂×C₇×C₁₉	1	8	yes	direct product factor
14	C₂×C₇²	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
15	C₇²	C₂×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₉	C₇²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₇	C₇²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₁₉	C₂×C₇²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₇	C₂×C₇²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₇	C₇×C₁₇×C₁₉	1	8	yes	direct product factor
21	C₇	C₂×C₇×C₁₇×C₁₉	1	8	yes	direct product factor
22	C₂	C₇²×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow

	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. C₇²×C₁₇×C₁₉	C₂	direct (N × H)
2. C₂×C₇×C₁₇×C₁₉	C₇	direct (N × H)
3. C₇×C₁₇×C₁₉	C₂×C₇	direct (N × H)
4. C₂×C₇²×C₁₉	C₁₇	direct (N × H)
5. C₂×C₇²×C₁₇	C₁₉	direct (N × H)
6. C₇²×C₁₉	C₂×C₁₇	direct (N × H)
7. C₇²×C₁₇	C₂×C₁₉	direct (N × H)
8. C₂×C₁₇×C₁₉	C₇²	direct (N × H)
9. C₁₇×C₁₉	C₂×C₇²	direct (N × H)
10. C₂×C₇×C₁₉	C₇×C₁₇	direct (N × H)
11. C₂×C₇×C₁₇	C₇×C₁₉	direct (N × H)
12. C₇×C₁₉	C₂×C₇×C₁₇	direct (N × H)
13. C₇×C₁₇	C₂×C₇×C₁₉	direct (N × H)
14. C₂×C₇²	C₁₇×C₁₉	direct (N × H)
15. C₇²	C₂×C₁₇×C₁₉	direct (N × H)
16. C₂×C₁₉	C₇²×C₁₇	direct (N × H)
17. C₂×C₁₇	C₇²×C₁₉	direct (N × H)
18. C₁₉	C₂×C₇²×C₁₇	direct (N × H)
19. C₁₇	C₂×C₇²×C₁₉	direct (N × H)
20. C₂×C₇	C₇×C₁₇×C₁₉	direct (N × H)
21. C₇	C₂×C₇×C₁₇×C₁₉	direct (N × H)
22. C₂	C₇²×C₁₇×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×C₁₇×C₁₉	2
C₂×C₇×C₁₇×C₁₉	7
C₂×C₇²×C₁₉	17
C₂×C₇²×C₁₇	19

Subgroups — C2×C72×C17×C19 #44539607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇²×C₁₇×C₁₉ #44539607