Subgroups — C₃²×C₅²×Dic₂₉ #39908020

Order 26100.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅²×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅²×Dic₂₉	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×C₅×Dic₂₉	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₃×C₅²×C₂₉	C₂×C₃	1	4	yes	—
6	C₅²×Dic₂₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₅×C₂₉	C₂×C₅	1	6	yes	—
8	C₃×C₅²×C₂₉	C₃×C₄	1	4	yes	complemented
9	C₃×C₅×Dic₂₉	C₃×C₅	1	24	yes	direct product factor
10	C₂×C₅²×C₂₉	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₅×C₂₉	C₄×C₅	1	6	yes	complemented
12	C₃²×Dic₂₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₃²×C₄×C₅²	—	29	1	no	maximal, Hall
14	C₂×C₃×C₅×C₂₉	C₂×C₃×C₅	1	24	yes	—
15	C₅²×C₂₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
16	C₅×Dic₂₉	C₃²×C₅	1	6	yes	direct product factor
17	C₂×C₃²×C₂₉	C₂×C₅²	1	1	yes	characteristic
18	C₂×C₃²×C₅²	D₂₉	1	1	yes	characteristic
19	C₃×C₅×C₂₉	C₃×C₄×C₅	1	24	yes	complemented
20	C₃×Dic₂₉	C₃×C₅²	1	4	yes	direct product factor
21	C₃×C₄×C₅²	—	29	4	no	—
22	C₂×C₅×C₂₉	C₂×C₃²×C₅	1	6	yes	—
23	C₃²×C₂₉	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
24	C₃²×C₅²	Dic₂₉	1	1	yes	characteristic, direct product factor, Hall
25	C₃²×C₄×C₅	—	29	6	no	—
26	C₂×C₃×C₂₉	C₂×C₃×C₅²	1	4	yes	—
27	C₂×C₃×C₅²	C₃×D₂₉	1	4	yes	—
28	C₅×C₂₉	C₃²×C₄×C₅	1	6	yes	complemented
29	Dic₂₉	C₃²×C₅²	1	1	yes	characteristic, direct product factor, Hall
30	C₄×C₅²	—	29	1	no	Hall
31	C₂×C₃²×C₅	C₅×D₂₉	1	6	yes	—
32	C₃×C₂₉	C₃×C₄×C₅²	1	4	yes	complemented
33	C₃×C₅²	C₃×Dic₂₉	1	4	yes	direct product factor
34	C₃×C₄×C₅	—	29	24	no	—
35	C₂×C₂₉	C₂×C₃²×C₅²	1	1	yes	characteristic
36	C₂×C₅²	C₃²×D₂₉	1	1	yes	characteristic
37	C₃²×C₅	C₅×Dic₂₉	1	6	yes	direct product factor
38	C₃²×C₄	—	29	1	no	Hall
39	C₂×C₃×C₅	C₃×C₅×D₂₉	1	24	yes	—
40	C₂₉	C₃²×C₄×C₅²	1	1	yes	characteristic, complemented, Sylow
41	C₅²	C₃²×Dic₂₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₄×C₅	—	29	6	no	—
43	C₂×C₃²	C₅²×D₂₉	1	1	yes	characteristic
44	C₃×C₅	C₃×C₅×Dic₂₉	1	24	yes	direct product factor
45	C₃×C₄	—	29	4	no	—
46	C₂×C₅	C₃²×C₅×D₂₉	1	6	yes	—
47	C₃²	C₅²×Dic₂₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₃	C₃×C₅²×D₂₉	1	4	yes	—
49	C₅	C₃²×C₅×Dic₂₉	1	6	yes	direct product factor
50	C₄	—	29	1	no	Sylow
51	C₃	C₃×C₅²×Dic₂₉	1	4	yes	direct product factor
52	C₂	C₃²×C₅²×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅²	D₂₉
commutator, hypocenter	C₂₉	C₃²×C₄×C₅²
Frattini	C₂	C₃²×C₅²×D₂₉
Fitting, socle, prime radical	C₂×C₃²×C₅²×C₂₉	C₂
cosocle	C₂×C₂₉	C₂×C₃²×C₅²
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₃²×C₅²

Complements

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

N	H ≅ G/N	type
2. C₃×C₅²×Dic₂₉	C₃	direct (N × H)
3. C₃²×C₅²×C₂₉	C₄	semidirect
4. C₃²×C₅×Dic₂₉	C₅	direct (N × H)
6. C₅²×Dic₂₉	C₃²	direct (N × H)
8. C₃×C₅²×C₂₉	C₃×C₄	semidirect
9. C₃×C₅×Dic₂₉	C₃×C₅	direct (N × H)
11. C₃²×C₅×C₂₉	C₄×C₅	semidirect
12. C₃²×Dic₂₉	C₅²	direct (N × H)
15. C₅²×C₂₉	C₃²×C₄	semidirect
16. C₅×Dic₂₉	C₃²×C₅	direct (N × H)
19. C₃×C₅×C₂₉	C₃×C₄×C₅	semidirect
20. C₃×Dic₂₉	C₃×C₅²	direct (N × H)
23. C₃²×C₂₉	C₄×C₅²	semidirect
24. C₃²×C₅²	Dic₂₉	direct (N × H)
28. C₅×C₂₉	C₃²×C₄×C₅	semidirect
29. Dic₂₉	C₃²×C₅²	direct (N × H)
32. C₃×C₂₉	C₃×C₄×C₅²	semidirect
33. C₃×C₅²	C₃×Dic₂₉	direct (N × H)
37. C₃²×C₅	C₅×Dic₂₉	direct (N × H)
40. C₂₉	C₃²×C₄×C₅²	semidirect
41. C₅²	C₃²×Dic₂₉	direct (N × H)
44. C₃×C₅	C₃×C₅×Dic₂₉	direct (N × H)
47. C₃²	C₅²×Dic₂₉	direct (N × H)
49. C₅	C₃²×C₅×Dic₂₉	direct (N × H)
51. C₃	C₃×C₅²×Dic₂₉	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×C₃²×C₅²×C₂₉	2
C₃×C₅²×Dic₂₉	3
C₃²×C₅×Dic₂₉	5
C₃²×C₄×C₅²	29

Subgroups — C32×C52×Dic29 #39908020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅²×Dic₂₉ #39908020