Subgroups — C₃₁⋊C₃×C₁₀₉⋊C₃ #44477331

Order 30411.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23778336	C₃	1	1	yes	maximal, characteristic, complemented
2	#23778335	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃₁×C₁₀₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃₁⋊C₃×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃₁×C₁₀₉	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₀₉⋊C₃	—	31	1	no	maximal, Hall
7	C₃×C₁₀₉	—	31	1	no	—
8	C₁₀₉⋊C₃	—	31	1	no	—
9	C₁₀₉⋊C₃	—	31	1	no	—
10	C₁₀₉⋊C₃	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
11	C₃×C₃₁⋊C₃	—	109	1	no	maximal, Hall
12	C₁₀₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₃₁	—	109	1	no	—
14	C₃₁⋊C₃	—	109	1	no	—
15	C₃₁⋊C₃	—	109	1	no	—
16	C₃₁⋊C₃	C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor
17	C₃₁	C₃×C₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃²	—	3379	1	no	Sylow
19	C₃	—	31	1	no	—
20	C₃	—	3379	1	no	—
21	C₃	—	3379	1	no	—
22	C₃	—	109	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₁×C₁₀₉	C₃²
LCS	G ▷ C₃₁×C₁₀₉
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.