Subgroups — C₂×Q₈⋊(C₅²⋊C₃) #11925673

Order 1200.

74 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, direct product factor
2	C₂×C₅²×Q₈	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂²×C₅²⋊C₃	—	4	1	no	maximal
4	C₅²×Q₈	—	3	1	no	—
5	C₅²×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×C₄×C₅²	—	3	1	no	—
7	C₂×C₅²⋊C₃	—	4	2	no	—
8	C₂×C₅²⋊C₃	—	4	1	no	—
9	C₂²×C₅²	A₄	1	1	yes	characteristic
10	C₄×C₅²	—	3	1	no	—
11	C₄×C₅²	—	3	1	no	—
12	C₂×C₅×Q₈	—	3	2	no	—
13	C₅²⋊C₃	—	4	1	no	Hall
14	C₂×C₅²	SL(2,𝔽₃)	1	2	yes	complemented
15	C₂×C₅²	C₂×A₄	1	1	yes	characteristic
16	C₂×SL(2,𝔽₃)	—	25	1	no	maximal, Hall
17	C₅×Q₈	—	3	6	no	—
18	C₅×Q₈	—	3	2	no	—
19	C₂×C₄×C₅	—	3	6	no	—
20	C₅²	C₂×SL(2,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
21	SL(2,𝔽₃)	—	25	1	no	—
22	C₂²×C₅	—	3	2	no	—
23	C₄×C₅	—	3	6	no	—
24	C₄×C₅	—	3	6	no	—
25	C₂×Q₈	C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂²×C₃	—	100	1	no	—
27	C₂×C₅	—	3	4	no	—
28	C₂×C₅	—	3	2	no	—
29	Q₈	—	3	1	no	—
30	Q₈	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
31	C₂×C₄	—	3	1	no	—
32	C₂×C₃	—	100	2	no	—
33	C₂×C₃	—	100	1	no	—
34	C₅	—	3	2	no	—
35	C₂²	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic
36	C₄	—	3	1	no	—
37	C₄	—	3	1	no	—
38	C₃	—	100	1	no	Sylow
39	C₂	Q₈⋊(C₅²⋊C₃)	1	2	yes	direct product factor
40	C₂	C₂×C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic

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

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.