Subgroups — C₇²×D₅×D₂₉ #43249355

Order 28420.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×D₂₉	—	5	1	no	maximal, Hall
6	C₇×D₅×D₂₉	C₇	1	8	yes	maximal, direct product factor
7	C₇²×D₂₉	—	5	1	no	—
8	C₇²×D₂₉	D₅	1	1	yes	characteristic, direct product factor
9	C₂×C₇²×C₂₉	—	5	1	no	—
10	C₇×D₁₄₅	C₂×C₇	1	8	yes	complemented
11	C₇×D₅×C₂₉	C₂×C₇	1	8	yes	complemented
12	C₅×C₇×D₂₉	C₂×C₇	1	8	yes	complemented
13	C₇²×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₇×C₂₉	C₂²×C₇	1	8	yes	complemented
15	C₂×C₇²×D₅	—	29	1	no	maximal, Hall
16	C₂×C₇×D₂₉	—	5	8	no	—
17	D₅×D₂₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅×C₇²	—	29	1	no	—
19	C₇²×D₅	—	29	1	no	—
20	C₇²×D₅	D₂₉	1	1	yes	characteristic, direct product factor
21	C₂×C₇×C₂₉	—	5	8	no	—
22	C₇×D₂₉	—	5	8	no	—
23	C₇×D₂₉	C₇×D₅	1	8	yes	direct product factor
24	D₁₄₅	C₂×C₇²	1	1	yes	characteristic, complemented
25	C₅×D₂₉	C₂×C₇²	1	1	yes	characteristic, complemented
26	D₅×C₂₉	C₂×C₇²	1	1	yes	characteristic, complemented
27	C₅×C₇²	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
28	C₇×C₂₉	C₂×C₇×D₅	1	8	yes	complemented
29	C₂²×C₇²	—	145	1	no	Hall
30	C₅×C₂₉	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇×D₅	—	29	8	no	—
32	C₂×D₂₉	—	5	1	no	Hall
33	C₂×C₇²	—	5	1	no	—
34	C₂×C₇²	—	29	1	no	—
35	C₂×C₇²	—	145	1	no	—
36	C₂×C₅×C₇	—	29	8	no	—
37	C₇×D₅	—	29	8	no	—
38	C₇×D₅	C₇×D₂₉	1	8	yes	direct product factor
39	C₂×C₂₉	—	5	1	no	—
40	D₂₉	—	5	1	no	—
41	D₂₉	C₇²×D₅	1	1	yes	characteristic, direct product factor
42	C₇²	D₅×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₅×C₇	C₂×C₇×D₂₉	1	8	yes	complemented
44	C₂₉	C₂×C₇²×D₅	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₇	—	145	8	no	—
46	C₂×D₅	—	29	1	no	Hall
47	C₂×C₇	—	5	8	no	—
48	C₂×C₇	—	29	8	no	—
49	C₂×C₇	—	145	8	no	—
50	C₂×C₅	—	29	1	no	—
51	D₅	—	29	1	no	—
52	D₅	C₇²×D₂₉	1	1	yes	characteristic, direct product factor
53	C₇	C₇×D₅×D₂₉	1	8	yes	direct product factor
54	C₅	C₂×C₇²×D₂₉	1	1	yes	characteristic, complemented, Sylow
55	C₂²	—	145	1	no	Sylow
56	C₂	—	5	1	no	—
57	C₂	—	29	1	no	—
58	C₂	—	145	1	no	—

	subgroup	G/H
center, hypercenter	C₇²	D₅×D₂₉
commutator, cosocle, hypocenter	C₅×C₂₉	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₂₉	C₂²
LCS	G ▷ C₅×C₂₉
UCS	C₁ ◁ C₇²

Complements

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

N	H ≅ G/N	type
1. C₅×C₇²×D₂₉	C₂	semidirect
2. C₇²×D₅×C₂₉	C₂	semidirect
3. C₇²×D₁₄₅	C₂	semidirect
4. C₅×C₇²×C₂₉	C₂²	semidirect
6. C₇×D₅×D₂₉	C₇	direct (N × H)
8. C₇²×D₂₉	D₅	direct (N × H)
10. C₇×D₁₄₅	C₂×C₇	semidirect
11. C₇×D₅×C₂₉	C₂×C₇	semidirect
12. C₅×C₇×D₂₉	C₂×C₇	semidirect
13. C₇²×C₂₉	C₂×D₅	semidirect
14. C₅×C₇×C₂₉	C₂²×C₇	semidirect
17. D₅×D₂₉	C₇²	direct (N × H)
20. C₇²×D₅	D₂₉	direct (N × H)
23. C₇×D₂₉	C₇×D₅	direct (N × H)
24. D₁₄₅	C₂×C₇²	semidirect
25. C₅×D₂₉	C₂×C₇²	semidirect
26. D₅×C₂₉	C₂×C₇²	semidirect
27. C₅×C₇²	C₂×D₂₉	semidirect
28. C₇×C₂₉	C₂×C₇×D₅	semidirect
30. C₅×C₂₉	C₂²×C₇²	semidirect
38. C₇×D₅	C₇×D₂₉	direct (N × H)
41. D₂₉	C₇²×D₅	direct (N × H)
42. C₇²	D₅×D₂₉	direct (N × H)
43. C₅×C₇	C₂×C₇×D₂₉	semidirect
44. C₂₉	C₂×C₇²×D₅	semidirect
52. D₅	C₇²×D₂₉	direct (N × H)
53. C₇	C₇×D₅×D₂₉	direct (N × H)
54. C₅	C₂×C₇²×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇²×D₂₉	2
C₇²×D₅×C₂₉	2
C₇²×D₁₄₅	2
C₂×C₇²×D₂₉	5
C₇×D₅×D₂₉	7
C₂×C₇²×D₅	29

Subgroups — C72×D5×D29 #43249355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×D₅×D₂₉ #43249355