Subgroups — C₅²×C₂²⋊(C₃₁⋊C₃) #22604930

Order 9300.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×C₃₁⋊C₃	—	4	1	no	maximal, Hall
3	C₅×C₂²⋊(C₃₁⋊C₃)	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅²×C₃₁	—	3	1	no	—
5	C₅²×C₃₁	A₄	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₅×C₃₁	C₃×C₅	1	6	yes	complemented
7	C₅×C₃₁⋊C₃	—	4	6	no	—
8	C₂²⋊(C₃₁⋊C₃)	C₅²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₃₁	—	3	6	no	—
10	C₅²×A₄	—	31	1	no	maximal, Hall
11	C₅×C₃₁	C₅×A₄	1	6	yes	complemented
12	C₂²×C₃₁	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
13	C₂²×C₅²	C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₃₁⋊C₃	—	4	1	no	Hall
15	C₃×C₅²	—	124	1	no	Hall
16	C₂×C₃₁	—	3	1	no	—
17	C₅×A₄	—	31	6	no	—
18	C₂×C₅²	—	3	1	no	—
19	C₃₁	C₅²×A₄	1	1	yes	characteristic, complemented, Sylow
20	C₅²	C₂²⋊(C₃₁⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₅	C₅×C₃₁⋊C₃	1	6	yes	complemented
22	C₃×C₅	—	124	6	no	—
23	A₄	—	31	1	no	Hall
24	C₂×C₅	—	3	6	no	—
25	C₅	C₅×C₂²⋊(C₃₁⋊C₃)	1	6	yes	direct product factor
26	C₂²	C₅²×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	124	1	no	Sylow
28	C₂	—	3	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.