Subgroups — C₅²×C₁₇×#157 #29506044

Order 15300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×C₁₇×#157	C₅	1	6	yes	maximal, direct product factor
4	C₅²×D₃×C₁₇	—	6	2	no	—
5	C₄×C₅²×C₁₇	—	9	1	no	maximal, Hall
6	C₅×C₁₇×C₃⋊D₃	C₂×C₅	1	6	yes	—
7	C₃×C₅²×C₁₇	—	2	2	no	—
8	C₅²×#157	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅²×C₁₇	—	9	1	no	—
10	C₃²×C₅×C₁₇	C₄×C₅	1	6	yes	complemented
11	C₁₇×#157	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₅×D₃×C₁₇	—	6	12	no	—
13	C₅²×C₃⋊D₃	C₂×C₁₇	1	1	yes	characteristic
14	C₅²×C₁₇	#157	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₅×C₁₇	—	9	6	no	—
16	C₁₇×C₃⋊D₃	C₂×C₅²	1	1	yes	characteristic
17	C₃×C₅×C₁₇	—	2	12	no	—
18	C₃²×C₅²	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
19	C₅×#157	C₅×C₁₇	1	6	yes	direct product factor
20	C₂×C₅×C₁₇	—	9	6	no	—
21	C₃²×C₁₇	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
22	C₅²×D₃	—	6	2	no	—
23	D₃×C₁₇	—	6	2	no	—
24	C₄×C₅²	—	9	1	no	Hall
25	C₅×C₃⋊D₃	C₂×C₅×C₁₇	1	6	yes	—
26	C₅×C₁₇	C₅×#157	1	6	yes	direct product factor
27	C₃×C₅²	—	2	2	no	—
28	C₄×C₁₇	—	9	1	no	Hall
29	C₃×C₁₇	—	2	2	no	—
30	C₂×C₅²	—	9	1	no	—
31	C₃²×C₅	C₄×C₅×C₁₇	1	6	yes	complemented
32	#157	C₅²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₁₇	—	9	1	no	—
34	C₅×D₃	—	6	12	no	—
35	C₅²	C₁₇×#157	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×C₅	—	9	6	no	—
37	C₃⋊D₃	C₂×C₅²×C₁₇	1	1	yes	characteristic
38	C₁₇	C₅²×#157	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₅	—	2	12	no	—
40	C₂×C₅	—	9	6	no	—
41	C₃²	C₄×C₅²×C₁₇	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	6	2	no	—
43	C₅	C₅×C₁₇×#157	1	6	yes	direct product factor
44	C₄	—	9	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅²×C₁₇	#157
commutator, hypocenter	C₃²	C₄×C₅²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₇	C₄
prime radical	C₅²×C₁₇×C₃⋊D₃	C₂
cosocle	C₃⋊D₃	C₂×C₅²×C₁₇
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅²×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₁₇	C₄	semidirect
3. C₅×C₁₇×#157	C₅	direct (N × H)
8. C₅²×#157	C₁₇	direct (N × H)
10. C₃²×C₅×C₁₇	C₄×C₅	semidirect
11. C₁₇×#157	C₅²	direct (N × H)
14. C₅²×C₁₇	#157	direct (N × H)
18. C₃²×C₅²	C₄×C₁₇	semidirect
19. C₅×#157	C₅×C₁₇	direct (N × H)
21. C₃²×C₁₇	C₄×C₅²	semidirect
26. C₅×C₁₇	C₅×#157	direct (N × H)
31. C₃²×C₅	C₄×C₅×C₁₇	semidirect
32. #157	C₅²×C₁₇	direct (N × H)
35. C₅²	C₁₇×#157	direct (N × H)
38. C₁₇	C₅²×#157	direct (N × H)
41. C₃²	C₄×C₅²×C₁₇	semidirect
43. C₅	C₅×C₁₇×#157	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₁₇×C₃⋊D₃	2
C₅×C₁₇×#157	5
C₄×C₅²×C₁₇	9
C₅²×#157	17

Subgroups — C52×C17×#157 #29506044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₁₇×#157 #29506044