Subgroups — C₂²×C₅²⋊(C₃₁⋊C₃) #22604932

Order 9300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²⋊(C₃₁⋊C₃)	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²⋊(C₃₁⋊C₃)	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅²×C₃₁	C₂×C₃	1	3	yes	complemented
5	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₅×C₃₁	—	3	2	no	—
7	C₂²×C₃₁⋊C₃	—	25	1	no	maximal, Hall
8	C₂×C₅×C₃₁	—	3	6	no	—
9	C₂²×C₅²⋊C₃	—	31	1	no	maximal, Hall
10	C₂×C₃₁⋊C₃	—	25	3	no	—
11	C₅×C₃₁	—	3	2	no	—
12	C₂×C₅²⋊C₃	—	31	3	no	—
13	C₂²×C₃₁	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₅²	C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₃₁⋊C₃	—	25	1	no	Hall
16	C₅²⋊C₃	—	31	1	no	Hall
17	C₂×C₃₁	C₂×C₅²⋊C₃	1	3	yes	complemented
18	C₂×C₅²	C₂×C₃₁⋊C₃	1	3	yes	complemented
19	C₃₁	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₅²	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₅	—	3	2	no	—
22	C₂²×C₃	—	775	1	no	Hall
23	C₂×C₅	—	3	6	no	—
24	C₂×C₃	—	775	3	no	—
25	C₅	—	3	2	no	—
26	C₂²	C₅²⋊(C₃₁⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
27	C₃	—	775	1	no	Sylow
28	C₂	C₂×C₅²⋊(C₃₁⋊C₃)	1	3	yes	direct product factor

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