Subgroups — C₃₁⋊C₃×D₁₄₅ #41004213

Order 26970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₁₄₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₂₉×C₃₁⋊C₃	—	5	1	no	maximal, Hall
4	C₅×C₂₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂₉×C₃₁⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₂₉	—	5	1	no	Hall
7	D₅×C₃₁⋊C₃	—	29	1	no	maximal, Hall
8	C₂₉×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×D₁₄₅	—	31	1	no	maximal, Hall
10	C₅×C₃₁⋊C₃	D₂₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×C₂₉	—	31	1	no	Hall
12	D₅×C₃₁	—	29	1	no	Hall
13	D₁₄₅	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃₁⋊C₃	—	145	1	no	Hall
15	C₃×D₂₉	—	155	1	no	Hall
16	C₅×C₃₁	C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
17	C₅×C₂₉	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₃₁⋊C₃	D₁₄₅	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₂₉	—	31	1	no	Hall
20	C₂×C₃₁	—	145	1	no	Hall
21	D₂₉	—	5	1	no	Hall
22	C₃₁	C₃×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
23	C₃×D₅	—	899	1	no	Hall
24	C₂₉	D₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	—	31	1	no	Hall
26	D₅	—	29	1	no	Hall
27	C₂×C₃	—	4495	1	no	Hall
28	C₅	D₂₉×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	31	1	no	Sylow
30	C₂	—	145	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₂₉×C₃₁	C₂×C₃
LCS	G ▷ C₅×C₂₉×C₃₁
UCS	C₁

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.