Subgroups — C₂×C₃²×D₇×C₂₉ #20300689

Order 7308.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₇×C₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₇×C₂₉	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×D₇×C₂₉	C₂×C₃	1	8	yes	direct product factor
7	C₂²×C₃²×C₂₉	—	7	1	no	maximal, Hall
8	C₂×D₇×C₂₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇×C₂₉	C₂²×C₃	1	4	yes	complemented
10	C₂×C₃²×C₂₉	—	7	2	no	—
11	C₂×C₃²×C₂₉	D₇	1	1	yes	characteristic, direct product factor
12	C₂×C₇×C₂₉	C₂×C₃²	1	1	yes	characteristic, complemented
13	D₇×C₂₉	C₂×C₃²	1	2	yes	direct product factor
14	C₂²×C₃×C₂₉	—	7	4	no	—
15	C₃²×C₂₉	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃²×D₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₇×C₂₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₂₉	—	7	8	no	—
19	C₂×C₃×C₂₉	C₃×D₇	1	4	yes	direct product factor
20	C₂×C₃²×C₇	C₂×C₂₉	1	1	yes	characteristic, complemented
21	C₃²×D₇	C₂×C₂₉	1	2	yes	direct product factor
22	C₂²×C₂₉	—	7	1	no	Hall
23	C₃×C₂₉	C₂×C₃×D₇	1	4	yes	direct product factor
24	C₂×C₃×D₇	C₃×C₂₉	1	4	yes	direct product factor
25	C₃²×C₇	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₂₉	—	7	2	no	—
27	C₂×C₂₉	C₃²×D₇	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₇	C₂×C₃×C₂₉	1	4	yes	complemented
29	C₃×D₇	C₂×C₃×C₂₉	1	8	yes	direct product factor
30	C₂²×C₃²	—	7	1	no	Hall
31	C₂₉	C₂×C₃²×D₇	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×D₇	C₃²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
33	C₃×C₇	C₂²×C₃×C₂₉	1	4	yes	complemented
34	C₂×C₃²	—	7	2	no	—
35	C₂×C₃²	D₇×C₂₉	1	1	yes	characteristic, direct product factor
36	C₂×C₇	C₂×C₃²×C₂₉	1	1	yes	characteristic, complemented
37	D₇	C₂×C₃²×C₂₉	1	2	yes	direct product factor
38	C₂²×C₃	—	7	4	no	—
39	C₃²	C₂×D₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₇	C₂²×C₃²×C₂₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	7	8	no	—
42	C₂×C₃	C₃×D₇×C₂₉	1	4	yes	direct product factor
43	C₂²	—	7	1	no	Sylow
44	C₃	C₂×C₃×D₇×C₂₉	1	4	yes	direct product factor
45	C₂	—	7	2	no	—
46	C₂	C₃²×D₇×C₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₂₉	D₇
commutator, hypocenter	C₇	C₂²×C₃²×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₂₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃²×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃²×D₇×C₂₉	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₂₉	C₂	semidirect
3. C₂×C₃×D₇×C₂₉	C₃	direct (N × H)
4. C₃²×C₇×C₂₉	C₂²	semidirect
5. C₂×C₃×C₇×C₂₉	C₂×C₃	semidirect
6. C₃×D₇×C₂₉	C₂×C₃	direct (N × H)
8. C₂×D₇×C₂₉	C₃²	direct (N × H)
9. C₃×C₇×C₂₉	C₂²×C₃	semidirect
11. C₂×C₃²×C₂₉	D₇	direct (N × H)
12. C₂×C₇×C₂₉	C₂×C₃²	semidirect
13. D₇×C₂₉	C₂×C₃²	direct (N × H)
15. C₃²×C₂₉	C₂×D₇	direct (N × H)
16. C₂×C₃²×D₇	C₂₉	direct (N × H)
17. C₇×C₂₉	C₂²×C₃²	semidirect
19. C₂×C₃×C₂₉	C₃×D₇	direct (N × H)
20. C₂×C₃²×C₇	C₂×C₂₉	semidirect
21. C₃²×D₇	C₂×C₂₉	direct (N × H)
23. C₃×C₂₉	C₂×C₃×D₇	direct (N × H)
24. C₂×C₃×D₇	C₃×C₂₉	direct (N × H)
25. C₃²×C₇	C₂²×C₂₉	semidirect
27. C₂×C₂₉	C₃²×D₇	direct (N × H)
28. C₂×C₃×C₇	C₂×C₃×C₂₉	semidirect
29. C₃×D₇	C₂×C₃×C₂₉	direct (N × H)
31. C₂₉	C₂×C₃²×D₇	direct (N × H)
32. C₂×D₇	C₃²×C₂₉	direct (N × H)
33. C₃×C₇	C₂²×C₃×C₂₉	semidirect
35. C₂×C₃²	D₇×C₂₉	direct (N × H)
36. C₂×C₇	C₂×C₃²×C₂₉	semidirect
37. D₇	C₂×C₃²×C₂₉	direct (N × H)
39. C₃²	C₂×D₇×C₂₉	direct (N × H)
40. C₇	C₂²×C₃²×C₂₉	semidirect
42. C₂×C₃	C₃×D₇×C₂₉	direct (N × H)
44. C₃	C₂×C₃×D₇×C₂₉	direct (N × H)
46. C₂	C₃²×D₇×C₂₉	direct (N × H)

Subgroups — C2×C32×D7×C29 #20300689

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×D₇×C₂₉ #20300689