Subgroups — C₂×SL(2,𝔽₉) #13088281

Order 1440.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	SL(2,𝔽₉)	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×SL(2,𝔽₅)	—	6	2	no	maximal
3	C₂×#622	—	10	1	no	maximal
4	SL(2,𝔽₅)	—	6	2	no	—
5	C₂×#226	—	15	2	no	maximal
6	C₂×C₃⋊Dic₃	—	10	1	no	—
7	#622	—	10	1	no	—
8	#622	—	10	1	no	—
9	C₂×SL(2,𝔽₃)	—	15	2	no	—
10	#226	—	15	2	no	—
11	#226	—	15	2	no	—
12	C₂×Dic₅	—	36	1	no	—
13	C₂²×C₃²	—	10	1	no	—
14	C₃⋊Dic₃	—	10	1	no	—
15	C₃⋊Dic₃	—	10	1	no	—
16	C₂×Q₁₆	—	45	1	no	Sylow
17	C₂×Dic₃	—	60	2	no	—
18	SL(2,𝔽₃)	—	15	2	no	—
19	C₂²×C₅	—	36	1	no	—
20	Dic₅	—	36	1	no	—
21	Dic₅	—	36	1	no	—
22	C₂×C₃²	—	10	1	no	—
23	C₂×C₃²	—	10	2	no	—
24	C₂×Q₈	—	15	2	no	—
25	Q₁₆	—	45	1	no	—
26	Q₁₆	—	45	2	no	—
27	Q₁₆	—	45	1	no	—
28	C₂×C₈	—	45	1	no	—
29	C₂²×C₃	—	20	2	no	—
30	Dic₃	—	60	2	no	—
31	Dic₃	—	60	2	no	—
32	C₂×C₅	—	36	1	no	—
33	C₂×C₅	—	36	2	no	—
34	C₃²	—	10	1	no	Sylow
35	Q₈	—	15	2	no	—
36	Q₈	—	45	2	no	—
37	C₂×C₄	—	45	1	no	—
38	C₈	—	45	1	no	—
39	C₈	—	45	1	no	—
40	C₂×C₃	—	20	2	no	—
41	C₂×C₃	—	20	4	no	—
42	C₅	—	36	1	no	Sylow
43	C₂²	A₆	1	1	yes	maximal normal, characteristic
44	C₄	—	45	1	no	—
45	C₄	—	45	1	no	—
46	C₃	—	20	2	no	—
47	C₂	SL(2,𝔽₉)	1	2	yes	direct product factor
48	C₂	C₂×A₆	1	1	yes	characteristic

	subgroup	G/H
center, Fitting, socle, hypercenter	C₂²	A₆
commutator, hypocenter	SL(2,𝔽₉)	C₂
Frattini, cosocle	C₂	C₂×A₆
LCS	G ▷ SL(2,𝔽₉)
UCS	C₁ ◁ C₂²

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

N	H ≅ G/N	type
1. SL(2,𝔽₉)	C₂	direct (N × H)
47. C₂	SL(2,𝔽₉)	direct (N × H)

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