Subgroups — C₅²×#10597480 #29506046

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×#10597480	C₅	1	6	yes	maximal, direct product factor
4	C₅²×D₃×C₁₇	—	6	2	no	—
5	C₅²×Dic₁₇	—	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	—	17	1	no	maximal, Hall
9	C₂×C₅²×C₁₇	—	9	1	no	—
10	C₃²×C₅×C₁₇	C₄×C₅	1	6	yes	complemented
11	#10597480	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₅×D₃×C₁₇	—	6	12	no	—
13	C₅²×C₃⋊D₃	D₁₇	1	1	yes	characteristic
14	C₅²×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
15	C₅×Dic₁₇	—	9	6	no	—
16	C₁₇×C₃⋊D₃	C₂×C₅²	1	1	yes	characteristic
17	C₃×C₅×C₁₇	—	2	12	no	—
18	C₃²×C₅²	Dic₁₇	1	1	yes	characteristic, complemented, Hall
19	C₅×#157	—	17	6	no	—
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	—	153	1	no	Hall
25	C₅×C₃⋊D₃	C₅×D₁₇	1	6	yes	—
26	C₅×C₁₇	C₅×#157	1	6	yes	complemented
27	C₃×C₅²	—	2	2	no	—
28	Dic₁₇	—	9	1	no	Hall
29	C₃×C₁₇	—	2	2	no	—
30	C₂×C₅²	—	9	1	no	—
31	C₃²×C₅	C₅×Dic₁₇	1	6	yes	complemented
32	#157	—	17	1	no	Hall
33	C₂×C₁₇	—	9	1	no	—
34	C₅×D₃	—	6	12	no	—
35	C₅²	#10597480	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×C₅	—	153	6	no	—
37	C₃⋊D₃	C₅²×D₁₇	1	1	yes	characteristic
38	C₁₇	C₅²×#157	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	2	12	no	—
40	C₂×C₅	—	9	6	no	—
41	C₃²	C₅²×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	6	2	no	—
43	C₅	C₅×#10597480	1	6	yes	direct product factor
44	C₄	—	153	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	#10597480
commutator, hypocenter	C₃²×C₁₇	C₄×C₅²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₇	C₄
prime radical	C₅²×C₁₇×C₃⋊D₃	C₂
cosocle	C₁₇×C₃⋊D₃	C₂×C₅²
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₁₇	C₄	semidirect
3. C₅×#10597480	C₅	direct (N × H)
10. C₃²×C₅×C₁₇	C₄×C₅	semidirect
11. #10597480	C₅²	direct (N × H)
14. C₅²×C₁₇	#157	semidirect
18. C₃²×C₅²	Dic₁₇	semidirect
21. C₃²×C₁₇	C₄×C₅²	semidirect
26. C₅×C₁₇	C₅×#157	semidirect
31. C₃²×C₅	C₅×Dic₁₇	semidirect
35. C₅²	#10597480	direct (N × H)
38. C₁₇	C₅²×#157	semidirect
41. C₃²	C₅²×Dic₁₇	semidirect
43. C₅	C₅×#10597480	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×#10597480	5
C₅²×Dic₁₇	9
C₅²×#157	17

Subgroups — C52×#10597480 #29506046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×#10597480 #29506046