Subgroups — C₅×#15690394 #29506052

Order 15300.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#15690394	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×#10597479	—	5	1	no	maximal
5	C₅²×D₅₁	—	6	2	no	—
6	C₅×#66772	—	9	1	no	maximal, Hall
7	C₅×C₃⋊D₅₁	—	2	2	no	—
8	C₅×C₃⋊D₅₁	D₅	1	1	yes	characteristic
9	C₅×C₃⋊D₅₁	C₂×C₅	1	1	yes	characteristic
10	C₃×C₅²×C₁₇	—	2	2	no	—
11	C₅×#4379	—	17	1	no	maximal, Hall
12	C₅²×D₁₇	—	9	1	no	—
13	C₃²×C₅×C₁₇	—	2	2	no	—
14	C₃²×C₅×C₁₇	Dic₅	1	1	yes	characteristic, complemented
15	C₃²×C₅×C₁₇	C₄×C₅	1	1	yes	characteristic, complemented
16	#10597479	—	5	1	no	Hall
17	C₅×D₅₁	—	6	2	no	—
18	C₅×D₅₁	—	6	2	no	—
19	C₅×D₅₁	—	6	8	no	—
20	C₅²×C₃⋊D₃	—	17	1	no	—
21	C₅²×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
22	#66772	—	9	1	no	—
23	C₅×#595	—	45	1	no	—
24	C₃⋊D₅₁	C₅×D₅	1	1	yes	characteristic
25	C₃×C₅×C₁₇	—	2	8	no	—
26	C₃×C₅×C₁₇	—	2	2	no	—
27	C₃×C₅×C₁₇	—	2	2	no	—
28	C₃²×C₅²	#595	1	1	yes	characteristic, complemented, Hall
29	#4379	—	17	1	no	—
30	C₅×#157	—	85	1	no	—
31	C₅×D₁₇	—	9	1	no	—
32	C₅×D₁₇	—	9	1	no	—
33	C₅×D₁₇	—	18	2	no	—
34	C₃²×C₁₇	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
35	C₅²×D₃	—	102	2	no	—
36	D₅₁	—	6	2	no	—
37	C₅×Dic₅	—	153	1	no	Hall
38	C₅×C₃⋊D₃	—	17	1	no	—
39	C₅×C₃⋊D₃	—	17	1	no	—
40	C₅×C₃⋊D₃	—	34	2	no	—
41	C₅×C₁₇	—	2	2	no	—
42	C₅×C₁₇	C₅×#157	1	1	yes	characteristic, complemented
43	C₅×C₁₇	#4379	1	1	yes	characteristic, complemented
44	C₃×C₅²	—	2	2	no	—
45	#595	—	45	1	no	Hall
46	C₃×C₁₇	—	2	2	no	—
47	C₂×C₅²	—	153	1	no	—
48	C₃²×C₅	—	2	2	no	—
49	C₃²×C₅	C₅×#595	1	1	yes	characteristic, complemented
50	C₃²×C₅	#66772	1	1	yes	characteristic, complemented
51	#157	—	85	1	no	Hall
52	D₁₇	—	9	1	no	—
53	C₅×D₃	—	102	8	no	—
54	C₅×D₃	—	102	2	no	—
55	C₅×D₃	—	102	2	no	—
56	C₅²	#10597479	1	1	yes	characteristic, complemented, Sylow
57	C₄×C₅	—	765	1	no	—
58	Dic₅	—	153	1	no	—
59	C₃⋊D₃	—	17	1	no	—
60	C₁₇	C₅×#4379	1	1	yes	characteristic, complemented, Sylow
61	C₃×C₅	—	2	8	no	—
62	C₃×C₅	—	2	2	no	—
63	C₃×C₅	—	2	2	no	—
64	C₂×C₅	—	306	2	no	—
65	C₂×C₅	—	153	1	no	—
66	C₂×C₅	—	153	1	no	—
67	C₃²	C₅×#66772	1	1	yes	characteristic, complemented, Sylow
68	D₃	—	102	2	no	—
69	C₅	—	2	2	no	—
70	C₅	C₅×#10597479	1	1	yes	characteristic, complemented
71	C₅	#15690394	1	1	yes	characteristic, direct product factor
72	C₄	—	765	1	no	Sylow
73	C₃	—	2	2	no	—
74	C₂	—	153	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#15690394
commutator, hypocenter	C₃²×C₅×C₁₇	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₇	C₄
prime radical	C₅²×C₃⋊D₅₁	C₂
cosocle	C₅×C₃⋊D₅₁	C₂×C₅
LCS	G ▷ C₃²×C₅×C₁₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₁₇	C₄	semidirect
3. #15690394	C₅	direct (N × H)
14. C₃²×C₅×C₁₇	Dic₅	semidirect
15. C₃²×C₅×C₁₇	C₄×C₅	semidirect
21. C₅²×C₁₇	#157	semidirect
28. C₃²×C₅²	#595	semidirect
34. C₃²×C₁₇	C₅×Dic₅	semidirect
42. C₅×C₁₇	C₅×#157	semidirect
43. C₅×C₁₇	#4379	semidirect
49. C₃²×C₅	C₅×#595	semidirect
50. C₃²×C₅	#66772	semidirect
56. C₅²	#10597479	semidirect
60. C₁₇	C₅×#4379	semidirect
67. C₃²	C₅×#66772	semidirect
70. C₅	C₅×#10597479	semidirect
71. C₅	#15690394	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×C₃⋊D₅₁	2
#15690394	5
C₅×#10597479	5
C₅×#66772	9
C₅×#4379	17

Subgroups — C5×#15690394 #29506052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#15690394 #29506052