Subgroups — C₉⋊#15688384 #41001237

Order 26820.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×D₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15688384	—	3	1	no	maximal
3	C₅×C₉×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10597010	—	5	1	no	maximal, Hall
5	C₃×C₅×D₁₄₉	D₃	1	1	yes	characteristic
6	#15688384	—	9	1	no	Hall
7	C₉×D₁₄₉	D₅	1	1	yes	characteristic
8	C₃×C₅×C₁₄₉	Dic₃	1	1	yes	characteristic
9	C₃⋊#10597010	—	15	1	no	—
10	C₅×D₁₄₉	D₉	1	1	yes	characteristic
11	C₉×C₁₄₉	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₄₉	D₁₅	1	1	yes	characteristic
13	C₅×C₁₄₉	Dic₉	1	1	yes	characteristic, complemented, Hall
14	#10597010	—	45	1	no	Hall
15	C₃×C₁₄₉	Dic₁₅	1	1	yes	characteristic
16	D₁₄₉	D₄₅	1	1	yes	characteristic
17	Dic₄₅	—	149	1	no	maximal, Hall
18	C₁₄₉	Dic₄₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅×C₉	—	149	1	no	—
20	Dic₁₅	—	447	1	no	—
21	C₅×C₉	#10597010	1	1	yes	characteristic, complemented, Hall
22	Dic₉	—	745	1	no	Hall
23	C₂×C₃×C₅	—	149	1	no	—
24	Dic₅	—	1341	1	no	Hall
25	C₂×C₉	—	149	1	no	—
26	C₃×C₅	C₃⋊#10597010	1	1	yes	characteristic
27	Dic₃	—	2235	1	no	—
28	C₂×C₅	—	149	1	no	—
29	C₉	#15688384	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	149	1	no	—
31	C₅	C₉⋊#10597010	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	6705	1	no	Sylow
33	C₃	C₃⋊#15688384	1	1	yes	characteristic
34	C₂	—	149	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₉×C₁₄₉	C₄
Frattini	C₃	C₃⋊#15688384
socle	C₃×C₅×C₁₄₉	Dic₃
prime radical	C₃×C₅×D₁₄₉	D₃
cosocle	C₅×C₉×D₁₄₉	C₂
LCS	G ▷ C₅×C₉×C₁₄₉
UCS	C₁

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.