Subgroups — C₂²×C₅×C₇²×C₂₉ #43249296

Order 28420.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇²×C₂₉	C₂	1	3	yes	maximal, direct product factor
2	C₅×C₇²×C₂₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₇²×C₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₅×C₇×C₂₉	C₇	1	8	yes	maximal, direct product factor
5	C₂×C₇²×C₂₉	C₂×C₅	1	3	yes	direct product factor
6	C₂×C₅×C₇×C₂₉	C₂×C₇	1	24	yes	direct product factor
7	C₇²×C₂₉	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₇×C₂₉	C₂²×C₇	1	8	yes	direct product factor
9	C₂²×C₅×C₇²	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₇×C₂₉	C₅×C₇	1	8	yes	direct product factor
11	C₂²×C₅×C₂₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₇²	C₂×C₂₉	1	3	yes	direct product factor
13	C₂×C₇×C₂₉	C₂×C₅×C₇	1	24	yes	direct product factor
14	C₂×C₅×C₂₉	C₂×C₇²	1	3	yes	direct product factor
15	C₅×C₇²	C₂²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₂₉	C₂²×C₅×C₇	1	8	yes	direct product factor
17	C₂²×C₇²	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₂₉	C₂²×C₇²	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₅×C₇	C₇×C₂₉	1	8	yes	direct product factor
20	C₂²×C₂₉	C₅×C₇²	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇²	C₂×C₅×C₂₉	1	3	yes	direct product factor
22	C₂×C₅×C₇	C₂×C₇×C₂₉	1	24	yes	direct product factor
23	C₂×C₂₉	C₂×C₅×C₇²	1	3	yes	direct product factor
24	C₇²	C₂²×C₅×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₅×C₇	C₂²×C₇×C₂₉	1	8	yes	direct product factor
26	C₂₉	C₂²×C₅×C₇²	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²×C₇	C₅×C₇×C₂₉	1	8	yes	direct product factor
28	C₂²×C₅	C₇²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇	C₂×C₅×C₇×C₂₉	1	24	yes	direct product factor
30	C₂×C₅	C₂×C₇²×C₂₉	1	3	yes	direct product factor
31	C₇	C₂²×C₅×C₇×C₂₉	1	8	yes	direct product factor
32	C₅	C₂²×C₇²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²	C₅×C₇²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅×C₇²×C₂₉	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×C₇²×C₂₉	C₂	direct (N × H)
2. C₅×C₇²×C₂₉	C₂²	direct (N × H)
3. C₂²×C₇²×C₂₉	C₅	direct (N × H)
4. C₂²×C₅×C₇×C₂₉	C₇	direct (N × H)
5. C₂×C₇²×C₂₉	C₂×C₅	direct (N × H)
6. C₂×C₅×C₇×C₂₉	C₂×C₇	direct (N × H)
7. C₇²×C₂₉	C₂²×C₅	direct (N × H)
8. C₅×C₇×C₂₉	C₂²×C₇	direct (N × H)
9. C₂²×C₅×C₇²	C₂₉	direct (N × H)
10. C₂²×C₇×C₂₉	C₅×C₇	direct (N × H)
11. C₂²×C₅×C₂₉	C₇²	direct (N × H)
12. C₂×C₅×C₇²	C₂×C₂₉	direct (N × H)
13. C₂×C₇×C₂₉	C₂×C₅×C₇	direct (N × H)
14. C₂×C₅×C₂₉	C₂×C₇²	direct (N × H)
15. C₅×C₇²	C₂²×C₂₉	direct (N × H)
16. C₇×C₂₉	C₂²×C₅×C₇	direct (N × H)
17. C₂²×C₇²	C₅×C₂₉	direct (N × H)
18. C₅×C₂₉	C₂²×C₇²	direct (N × H)
19. C₂²×C₅×C₇	C₇×C₂₉	direct (N × H)
20. C₂²×C₂₉	C₅×C₇²	direct (N × H)
21. C₂×C₇²	C₂×C₅×C₂₉	direct (N × H)
22. C₂×C₅×C₇	C₂×C₇×C₂₉	direct (N × H)
23. C₂×C₂₉	C₂×C₅×C₇²	direct (N × H)
24. C₇²	C₂²×C₅×C₂₉	direct (N × H)
25. C₅×C₇	C₂²×C₇×C₂₉	direct (N × H)
26. C₂₉	C₂²×C₅×C₇²	direct (N × H)
27. C₂²×C₇	C₅×C₇×C₂₉	direct (N × H)
28. C₂²×C₅	C₇²×C₂₉	direct (N × H)
29. C₂×C₇	C₂×C₅×C₇×C₂₉	direct (N × H)
30. C₂×C₅	C₂×C₇²×C₂₉	direct (N × H)
31. C₇	C₂²×C₅×C₇×C₂₉	direct (N × H)
32. C₅	C₂²×C₇²×C₂₉	direct (N × H)
33. C₂²	C₅×C₇²×C₂₉	direct (N × H)
34. C₂	C₂×C₅×C₇²×C₂₉	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×C₇²×C₂₉	2
C₂²×C₇²×C₂₉	5
C₂²×C₅×C₇×C₂₉	7
C₂²×C₅×C₇²	29

Subgroups — C22×C5×C72×C29 #43249296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₇²×C₂₉ #43249296