Subgroups — C₂×C₃²×C₇×D₂₉ #20300690

Order 7308.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×D₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₇×D₂₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₂₉	C₂×C₃	1	4	yes	complemented
6	C₃×C₇×D₂₉	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃²×D₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×D₂₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇×C₂₉	C₂²×C₃	1	4	yes	complemented
10	C₂×C₃²×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
11	C₃²×D₂₉	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₇×C₂₉	C₂×C₃²	1	1	yes	characteristic, complemented
13	C₇×D₂₉	C₂×C₃²	1	2	yes	direct product factor
14	C₂×C₃×D₂₉	C₃×C₇	1	4	yes	direct product factor
15	C₃²×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃²×C₇	—	29	1	no	maximal, Hall
17	C₇×C₂₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₂₉	C₂×C₃×C₇	1	4	yes	complemented
19	C₃×D₂₉	C₂×C₃×C₇	1	8	yes	direct product factor
20	C₂×C₃²×C₇	—	29	2	no	—
21	C₂×C₃²×C₇	D₂₉	1	1	yes	characteristic, direct product factor
22	C₂×D₂₉	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₂₉	C₂²×C₃×C₇	1	4	yes	complemented
24	C₂²×C₃×C₇	—	29	4	no	—
25	C₃²×C₇	C₂×D₂₉	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₂₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
27	D₂₉	C₂×C₃²×C₇	1	2	yes	direct product factor
28	C₂×C₃×C₇	—	29	8	no	—
29	C₂×C₃×C₇	C₃×D₂₉	1	4	yes	direct product factor
30	C₂²×C₃²	—	29	1	no	Hall
31	C₂₉	C₂²×C₃²×C₇	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₇	—	29	1	no	Hall
33	C₃×C₇	C₂×C₃×D₂₉	1	4	yes	direct product factor
34	C₂×C₃²	—	29	2	no	—
35	C₂×C₃²	C₇×D₂₉	1	1	yes	characteristic, direct product factor
36	C₂×C₇	—	29	2	no	—
37	C₂×C₇	C₃²×D₂₉	1	1	yes	characteristic, direct product factor
38	C₂²×C₃	—	29	4	no	—
39	C₃²	C₂×C₇×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₇	C₂×C₃²×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	29	8	no	—
42	C₂×C₃	C₃×C₇×D₂₉	1	4	yes	direct product factor
43	C₂²	—	29	1	no	Sylow
44	C₃	C₂×C₃×C₇×D₂₉	1	4	yes	direct product factor
45	C₂	—	29	2	no	—
46	C₂	C₃²×C₇×D₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₇	D₂₉
commutator, hypocenter	C₂₉	C₂²×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₂₉	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₃²×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×D₂₉	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₂₉	C₂	semidirect
3. C₂×C₃×C₇×D₂₉	C₃	direct (N × H)
4. C₃²×C₇×C₂₉	C₂²	semidirect
5. C₂×C₃×C₇×C₂₉	C₂×C₃	semidirect
6. C₃×C₇×D₂₉	C₂×C₃	direct (N × H)
7. C₂×C₃²×D₂₉	C₇	direct (N × H)
8. C₂×C₇×D₂₉	C₃²	direct (N × H)
9. C₃×C₇×C₂₉	C₂²×C₃	semidirect
10. C₂×C₃²×C₂₉	C₂×C₇	semidirect
11. C₃²×D₂₉	C₂×C₇	direct (N × H)
12. C₂×C₇×C₂₉	C₂×C₃²	semidirect
13. C₇×D₂₉	C₂×C₃²	direct (N × H)
14. C₂×C₃×D₂₉	C₃×C₇	direct (N × H)
15. C₃²×C₂₉	C₂²×C₇	semidirect
17. C₇×C₂₉	C₂²×C₃²	semidirect
18. C₂×C₃×C₂₉	C₂×C₃×C₇	semidirect
19. C₃×D₂₉	C₂×C₃×C₇	direct (N × H)
21. C₂×C₃²×C₇	D₂₉	direct (N × H)
22. C₂×D₂₉	C₃²×C₇	direct (N × H)
23. C₃×C₂₉	C₂²×C₃×C₇	semidirect
25. C₃²×C₇	C₂×D₂₉	direct (N × H)
26. C₂×C₂₉	C₂×C₃²×C₇	semidirect
27. D₂₉	C₂×C₃²×C₇	direct (N × H)
29. C₂×C₃×C₇	C₃×D₂₉	direct (N × H)
31. C₂₉	C₂²×C₃²×C₇	semidirect
33. C₃×C₇	C₂×C₃×D₂₉	direct (N × H)
35. C₂×C₃²	C₇×D₂₉	direct (N × H)
37. C₂×C₇	C₃²×D₂₉	direct (N × H)
39. C₃²	C₂×C₇×D₂₉	direct (N × H)
40. C₇	C₂×C₃²×D₂₉	direct (N × H)
42. C₂×C₃	C₃×C₇×D₂₉	direct (N × H)
44. C₃	C₂×C₃×C₇×D₂₉	direct (N × H)
46. C₂	C₃²×C₇×D₂₉	direct (N × H)

Subgroups — C2×C32×C7×D29 #20300690

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×C₇×D₂₉ #20300690