Subgroups — C₃×PSL(2,𝔽₂₉) #49141699

Order 36540.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	PSL(2,𝔽₂₉)	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×D₂₉⋊C₇	—	30	1	no	maximal
3	C₃×C₂₉⋊C₇	—	30	1	no	—
4	D₂₉⋊C₇	—	30	1	no	—
5	C₂₉⋊C₇	—	30	1	no	Hall
6	C₃×A₅	—	203	2	no	maximal, Hall
7	C₃×D₂₉	—	30	1	no	—
8	C₃×D₁₅	—	406	1	no	maximal
9	C₃×C₂₉	—	30	1	no	—
10	C₂×C₃×D₇	—	435	1	no	maximal
11	A₅	—	203	2	no	—
12	D₂₉	—	30	1	no	—
13	C₃²×C₅	—	406	1	no	Hall
14	C₂×C₃×C₇	—	435	1	no	—
15	C₃×D₇	—	435	2	no	—
16	C₃×A₄	—	1015	1	no	Hall
17	D₁₅	—	406	1	no	—
18	C₃×D₅	—	1218	1	no	—
19	C₂₉	—	30	1	no	Sylow
20	C₂×D₇	—	435	1	no	Hall
21	C₃×C₇	—	435	1	no	—
22	C₃×D₃	—	2030	1	no	—
23	C₃×C₅	—	812	1	no	—
24	C₃×C₅	—	406	1	no	—
25	C₃×C₅	—	406	1	no	—
26	C₂×C₇	—	435	1	no	—
27	D₇	—	435	2	no	—
28	C₂²×C₃	—	1015	1	no	—
29	A₄	—	1015	2	no	—
30	A₄	—	1015	1	no	—
31	D₅	—	1218	1	no	—
32	C₃²	—	406	1	no	Sylow
33	C₇	—	435	1	no	Sylow
34	C₂×C₃	—	435	1	no	—
35	D₃	—	2030	1	no	—
36	C₅	—	406	1	no	Sylow
37	C₂²	—	1015	1	no	Sylow
38	C₃	—	812	1	no	—
39	C₃	—	406	1	no	—
40	C₃	PSL(2,𝔽₂₉)	1	1	yes	maximal normal, characteristic, direct product factor
41	C₂	—	435	1	no	—

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

N	H ≅ G/N	type
1. PSL(2,𝔽₂₉)	C₃	direct (N × H)
40. C₃	PSL(2,𝔽₂₉)	direct (N × H)

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