Subgroups — C₅×PGL(2,𝔽₉) #72219564

Order 3600.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×A₆	C₂	1	1	yes	maximal, characteristic, complemented
2	PGL(2,𝔽₉)	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×AGL(1,𝔽₉)	—	10	1	no	maximal
4	A₆	C₂×C₅	1	1	yes	characteristic, complemented
5	C₅×A₅	—	12	1	no	—
6	C₅×#157	—	10	1	no	—
7	C₅×S₄	—	30	1	no	—
8	C₂×C₅×D₅	—	36	1	no	maximal
9	C₅×C₃⋊D₃	—	10	1	no	—
10	C₅×D₈	—	45	1	no	maximal
11	AGL(1,𝔽₉)	—	10	1	no	—
12	C₅×A₄	—	30	1	no	—
13	A₅	—	12	1	no	—
14	C₂×C₅²	—	36	1	no	—
15	C₅×D₅	—	36	1	no	—
16	C₅×D₅	—	36	1	no	—
17	C₃²×C₅	—	10	1	no	—
18	C₅×D₄	—	45	1	no	—
19	C₅×D₄	—	45	1	no	—
20	C₅×C₈	—	45	1	no	—
21	#157	—	10	1	no	—
22	C₅×D₃	—	120	1	no	—
23	C₅²	—	36	1	no	Sylow
24	S₄	—	30	1	no	—
25	C₂²×C₅	—	30	1	no	—
26	C₂²×C₅	—	90	1	no	—
27	C₂×D₅	—	36	1	no	—
28	C₄×C₅	—	45	1	no	—
29	C₃⋊D₃	—	10	1	no	—
30	D₈	—	45	1	no	Sylow
31	C₃×C₅	—	40	1	no	—
32	A₄	—	30	1	no	—
33	C₂×C₅	—	36	1	no	—
34	C₂×C₅	—	36	1	no	—
35	C₂×C₅	—	45	1	no	—
36	C₂×C₅	—	72	2	no	—
37	D₅	—	36	1	no	—
38	D₅	—	36	1	no	—
39	C₃²	—	10	1	no	Sylow
40	D₄	—	45	1	no	—
41	D₄	—	45	1	no	—
42	C₈	—	45	1	no	—
43	D₃	—	120	1	no	—
44	C₅	—	36	1	no	—
45	C₅	—	72	2	no	—
46	C₅	PGL(2,𝔽₉)	1	1	yes	characteristic, direct product factor
47	C₂²	—	30	1	no	—
48	C₂²	—	90	1	no	—
49	C₄	—	45	1	no	—
50	C₃	—	40	1	no	—
51	C₂	—	36	1	no	—
52	C₂	—	45	1	no	—

	subgroup	G/H
center, Fitting, hypercenter	C₅	PGL(2,𝔽₉)
commutator, cosocle, hypocenter	A₆	C₂×C₅
Frattini	C₁	G
socle	C₅×A₆	C₂
LCS	G ▷ A₆
UCS	C₁ ◁ 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.