Subgroups — #41001270

Order 26820.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₅×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#19128973	—	5	1	no	maximal, Hall
4	D₁₅×C₁₄₉	—	6	2	no	—
5	#15688383	—	9	1	no	maximal, Hall
6	C₃⋊D₃×C₁₄₉	—	5	1	no	—
7	C₃×C₅×C₁₄₉	—	2	2	no	—
8	D₅×C₁₄₉	—	9	1	no	—
9	C₃²×C₁₄₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₄₉	—	30	2	no	—
11	C₅×C₁₄₉	#157	1	1	yes	characteristic, complemented, Hall
12	Dic₁₄₉	—	45	1	no	Hall
13	C₃×C₁₄₉	—	2	2	no	—
14	C₂×C₁₄₉	—	45	1	no	—
15	#4380	—	149	1	no	maximal, Hall
16	C₁₄₉	#4380	1	1	yes	characteristic, complemented, Sylow
17	C₃⋊D₁₅	D₁₄₉	1	1	yes	characteristic
18	C₃²×C₅	Dic₁₄₉	1	1	yes	characteristic, complemented, Hall
19	#157	—	745	1	no	Hall
20	D₁₅	—	6	2	no	—
21	AGL(1,𝔽₅)	—	1341	1	no	Hall
22	C₃⋊D₃	—	5	1	no	—
23	C₃×C₅	—	2	2	no	—
24	D₅	—	9	1	no	—
25	C₃²	#15688383	1	1	yes	characteristic, complemented, Sylow
26	D₃	—	30	2	no	—
27	C₅	#19128973	1	1	yes	characteristic, complemented, Sylow
28	C₄	—	6705	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	45	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₁₄₉	C₄
prime radical, cosocle	C₃⋊D₁₅×C₁₄₉	C₂
LCS	G ▷ C₃²×C₅×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.