Subgroups — #41⋊(C₅²⋊C₃) #11925674

Order 1200.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×#41	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄×C₅²⋊C₃	—	4	1	no	maximal
4	C₅²×Q₈	C₂×C₃	1	1	yes	characteristic
5	C₅²×D₄	—	3	1	no	—
6	C₂×C₄×C₅²	—	3	1	no	—
7	C₂×C₅²⋊C₃	—	4	1	no	—
8	C₂²×C₅²	—	3	1	no	—
9	C₄×C₅²	—	3	1	no	—
10	C₄×C₅²	A₄	1	1	yes	characteristic
11	C₅×#41	—	3	2	no	—
12	C₅²⋊C₃	—	4	1	no	Hall
13	C₂×C₅²	—	6	1	no	—
14	C₂×C₅²	C₂×A₄	1	1	yes	characteristic
15	#41⋊C₃	—	25	1	no	maximal, Hall
16	C₅×Q₈	—	3	2	no	—
17	C₅×D₄	—	3	6	no	—
18	C₂×C₄×C₅	—	3	6	no	—
19	C₅²	#41⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	SL(2,𝔽₃)	—	25	1	no	—
21	C₂²×C₅	—	3	6	no	—
22	C₄×C₅	—	3	6	no	—
23	C₄×C₅	—	3	2	no	—
24	#41	C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₄	—	100	1	no	—
26	C₂×C₅	—	3	2	no	—
27	C₂×C₅	—	6	6	no	—
28	Q₈	C₂×C₅²⋊C₃	1	1	yes	characteristic
29	D₄	—	3	1	no	—
30	C₂×C₄	—	3	1	no	—
31	C₂×C₃	—	100	1	no	—
32	C₅	—	3	2	no	—
33	C₂²	—	3	1	no	—
34	C₄	—	3	1	no	—
35	C₄	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic
36	C₃	—	100	1	no	Sylow
37	C₂	—	6	1	no	—
38	C₂	C₂×C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	C₂²⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₅²×Q₈	C₂×C₃
Frattini	C₂	C₂×C₂²⋊(C₅²⋊C₃)
Fitting	C₅²×#41	C₃
socle	C₂×C₅²	C₂×A₄
LCS	G ▷ C₅²×Q₈
UCS	C₁ ◁ C₄

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.