Subgroups — C₃²×#16812339 #44528174

Order 31140.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₅×C₁₇₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#16812339	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₁₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×Dic₁₇₃	—	5	1	no	maximal, Hall
5	C₃×D₅×C₁₇₃	C₂×C₃	1	4	yes	—
6	#16812339	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₁₇₃	—	5	1	no	—
8	C₃×C₅×C₁₇₃	C₃×C₄	1	4	yes	complemented
9	C₃×Dic₁₇₃	—	5	4	no	—
10	D₅×C₁₇₃	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₁₇₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₇₃	—	5	4	no	—
13	C₅×C₁₇₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	Dic₁₇₃	—	5	1	no	Hall
15	C₃×C₁₇₃	C₃×AGL(1,𝔽₅)	1	4	yes	complemented
16	C₂×C₁₇₃	—	5	1	no	—
17	C₃²×AGL(1,𝔽₅)	—	173	1	no	maximal, Hall
18	C₁₇₃	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
19	C₃²×D₅	D₁₇₃	1	1	yes	characteristic
20	C₃×AGL(1,𝔽₅)	—	173	4	no	—
21	C₃²×C₅	Dic₁₇₃	1	1	yes	characteristic, complemented, Hall
22	C₃²×C₄	—	865	1	no	Hall
23	C₃×D₅	C₃×D₁₇₃	1	4	yes	—
24	AGL(1,𝔽₅)	—	173	1	no	Hall
25	C₂×C₃²	—	5	1	no	—
26	C₃×C₅	C₃×Dic₁₇₃	1	4	yes	complemented
27	C₃×C₄	—	865	4	no	—
28	D₅	C₃²×D₁₇₃	1	1	yes	characteristic
29	C₃²	#16812339	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	—	5	4	no	—
31	C₅	C₃²×Dic₁₇₃	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	865	1	no	Sylow
33	C₃	C₃×#16812339	1	4	yes	direct product factor
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	#16812339
commutator, hypocenter	C₅×C₁₇₃	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₇₃	C₄
prime radical	C₃²×D₅×C₁₇₃	C₂
cosocle	D₅×C₁₇₃	C₂×C₃²
LCS	G ▷ C₅×C₁₇₃
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×#16812339	C₃	direct (N × H)
3. C₃²×C₅×C₁₇₃	C₄	semidirect
6. #16812339	C₃²	direct (N × H)
8. C₃×C₅×C₁₇₃	C₃×C₄	semidirect
11. C₃²×C₁₇₃	AGL(1,𝔽₅)	semidirect
13. C₅×C₁₇₃	C₃²×C₄	semidirect
15. C₃×C₁₇₃	C₃×AGL(1,𝔽₅)	semidirect
18. C₁₇₃	C₃²×AGL(1,𝔽₅)	semidirect
21. C₃²×C₅	Dic₁₇₃	semidirect
26. C₃×C₅	C₃×Dic₁₇₃	semidirect
29. C₃²	#16812339	direct (N × H)
31. C₅	C₃²×Dic₁₇₃	semidirect
33. C₃	C₃×#16812339	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₅×C₁₇₃	2
C₃×#16812339	3
C₃²×Dic₁₇₃	5
C₃²×AGL(1,𝔽₅)	173

Subgroups — C32×#16812339 #44528174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#16812339 #44528174