Subgroups — C₃×#17987871 #28358482

Order 13950.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊D₁₅₅	C₃	1	1	yes	maximal, characteristic, complemented
3	#17987871	C₃	1	3	yes	maximal, direct product factor
4	C₃₁×C₅²⋊C₃	C₂×C₃	1	3	yes	complemented
5	C₃×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅⋊D₁₅₅	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₁₅₅	—	15	2	no	—
8	C₅²×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×D₃₁	—	25	1	no	maximal, Hall
10	C₃×C₅×C₃₁	—	3	2	no	—
11	C₃×(C₅⋊D₅)⋊C₃	—	31	1	no	maximal, Hall
12	D₁₅₅	—	15	2	no	—
13	C₃²×C₃₁	—	25	1	no	Hall
14	C₃×C₅²⋊C₃	D₃₁	1	1	yes	characteristic, complemented, Hall
15	C₃×D₃₁	—	25	3	no	—
16	C₃×D₃₁	—	25	1	no	—
17	C₅×C₃₁	—	3	2	no	—
18	C₃×C₅⋊D₅	—	31	1	no	—
19	(C₅⋊D₅)⋊C₃	—	31	3	no	—
20	C₃×C₃₁	—	25	3	no	—
21	C₃×C₃₁	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
22	C₃×C₅²	C₃×D₃₁	1	1	yes	characteristic, complemented
23	C₅²⋊C₃	C₃×D₃₁	1	3	yes	complemented
24	D₃₁	—	25	1	no	Hall
25	C₅⋊D₅	—	31	1	no	Hall
26	C₃₁	C₃×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₅	—	465	2	no	—
28	C₅²	C₃²×D₃₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃²	—	775	1	no	Hall
30	C₃×C₅	—	3	2	no	—
31	D₅	—	465	2	no	—
32	C₃²	—	25	1	no	Sylow
33	C₂×C₃	—	775	3	no	—
34	C₂×C₃	—	775	1	no	—
35	C₅	—	3	2	no	—
36	C₃	—	25	3	no	—
37	C₃	#17987871	1	1	yes	characteristic, direct product factor
38	C₂	—	775	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#17987871
commutator, cosocle, hypocenter	C₅²×C₃₁	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	C₂×C₃
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×C₅²⋊C₃	C₂	semidirect
2. C₃×C₅⋊D₁₅₅	C₃	semidirect
3. #17987871	C₃	direct (N × H)
4. C₃₁×C₅²⋊C₃	C₂×C₃	semidirect
5. C₃×C₅²×C₃₁	C₂×C₃	semidirect
6. C₅⋊D₁₅₅	C₃²	semidirect
8. C₅²×C₃₁	C₂×C₃²	semidirect
14. C₃×C₅²⋊C₃	D₃₁	semidirect
21. C₃×C₃₁	(C₅⋊D₅)⋊C₃	semidirect
22. C₃×C₅²	C₃×D₃₁	semidirect
23. C₅²⋊C₃	C₃×D₃₁	semidirect
26. C₃₁	C₃×(C₅⋊D₅)⋊C₃	semidirect
28. C₅²	C₃²×D₃₁	semidirect
37. C₃	#17987871	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃₁×C₅²⋊C₃	2
C₃×C₅⋊D₁₅₅	3
#17987871	3
C₃²×D₃₁	25
C₃×(C₅⋊D₅)⋊C₃	31

Subgroups — C3×#17987871 #28358482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987871 #28358482