Subgroups — C₅×#4178 #11717618

Order 810.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#732	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×#272	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×C₉	—	3	1	no	maximal
4	#4178	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×H(3,𝔽₃)	—	2	1	no	—
6	C₅×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
7	C₃×C₅×C₉	D₃	1	1	yes	characteristic, complemented
8	C₃×C₅×D₃	—	3	1	no	—
9	C₃×C₅×D₃	—	9	1	no	—
10	C₂×C₅×C₉	—	9	1	no	—
11	#732	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
12	#272	C₃×C₅	1	1	yes	characteristic, complemented
13	D₃×C₉	—	3	1	no	—
14	C₃²×C₅	—	3	1	no	—
15	C₃²×C₅	—	6	1	no	—
16	C₃²×C₅	C₃×D₃	1	1	yes	characteristic
17	C₅×C₉	—	3	1	no	—
18	C₂×C₃×C₅	—	9	1	no	—
19	C₅×D₃	—	3	1	no	—
20	C₅×D₃	—	9	1	no	—
21	H(3,𝔽₃)	—	2	1	no	—
22	H(3,𝔽₃)	C₂×C₃×C₅	1	1	yes	characteristic
23	C₃×C₉	C₅×D₃	1	1	yes	characteristic, complemented
24	C₃×D₃	—	3	1	no	—
25	C₃×D₃	—	9	1	no	—
26	C₂×C₉	—	9	1	no	—
27	C₃×C₅	—	3	1	no	—
28	C₃×C₅	—	9	1	no	—
29	C₃×C₅	—	18	1	no	—
30	C₃×C₅	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
31	C₂×C₅	—	9	1	no	Hall
32	C₃²	—	3	1	no	—
33	C₃²	—	6	1	no	—
34	C₃²	C₃×C₅×D₃	1	1	yes	characteristic
35	C₉	—	3	1	no	—
36	C₂×C₃	—	9	1	no	—
37	D₃	—	3	1	no	—
38	D₃	—	9	1	no	—
39	C₅	#4178	1	1	yes	characteristic, direct product factor, Sylow
40	C₃	—	3	1	no	—
41	C₃	—	9	1	no	—
42	C₃	—	18	1	no	—
43	C₃	C₅×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
44	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, socle, hypercenter	C₃×C₅	(C₃⋊D₃)⋊C₃
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂×C₃×C₅
Frattini	C₃²	C₃×C₅×D₃
Fitting	C₅×#732	C₂
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃×C₅

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

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