Subgroups — C₅×#92150⋊C₃ #20300036

Order 7260.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×(C₁₁⋊D₁₁)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×#92150	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#92150⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
6	(C₁₁⋊D₁₁)⋊C₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#92150	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₁₁²⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	C₁₁⋊D₁₁	C₂×C₃×C₅	1	1	yes	characteristic
11	C₁₁²	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
12	C₅×D₁₁	—	66	2	no	—
13	C₃×C₄×C₅	—	121	1	no	maximal, Hall
14	C₅×C₁₁	—	6	2	no	—
15	C₂×C₃×C₅	—	121	1	no	—
16	D₁₁	—	66	2	no	—
17	C₄×C₅	—	121	1	no	Hall
18	C₃×C₅	—	121	1	no	Hall
19	C₃×C₄	—	121	1	no	Hall
20	C₁₁	—	6	2	no	—
21	C₂×C₅	—	121	1	no	—
22	C₂×C₃	—	121	1	no	—
23	C₅	#92150⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₄	—	121	1	no	Sylow
25	C₃	—	121	1	no	Sylow
26	C₂	—	121	1	no	—

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