Subgroups — C₂²×C₇₁×C₅²⋊C₃ #36319149

Order 21300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₁×C₅²⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅²×C₇₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇₁×C₅²⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅²×C₇₁	C₂×C₃	1	3	yes	complemented
5	C₅²×C₇₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₅×C₇₁	—	3	2	no	—
7	C₂²×C₃×C₇₁	—	25	1	no	maximal, Hall
8	C₂×C₅×C₇₁	—	3	6	no	—
9	C₂×C₃×C₇₁	—	25	3	no	—
10	C₅×C₇₁	—	3	2	no	—
11	C₂²×C₅²⋊C₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₇₁	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₇₁	—	25	1	no	Hall
14	C₂×C₅²⋊C₃	C₂×C₇₁	1	3	yes	direct product factor
15	C₂×C₇₁	C₂×C₅²⋊C₃	1	3	yes	direct product factor
16	C₂²×C₅²	C₃×C₇₁	1	1	yes	characteristic, complemented, Hall
17	C₅²⋊C₃	C₂²×C₇₁	1	1	yes	characteristic, direct product factor, Hall
18	C₇₁	C₂²×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅²	C₂×C₃×C₇₁	1	3	yes	complemented
20	C₅²	C₂²×C₃×C₇₁	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₅	—	3	2	no	—
22	C₂²×C₃	—	25	1	no	Hall
23	C₂×C₅	—	3	6	no	—
24	C₂×C₃	—	25	3	no	—
25	C₅	—	3	2	no	—
26	C₂²	C₇₁×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₃	—	25	1	no	Sylow
28	C₂	C₂×C₇₁×C₅²⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₇₁	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂²×C₃×C₇₁
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₇₁	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²×C₇₁

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.