Subgroups — C₃²×#16809857 #44475652

Order 30276.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₉⋊D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃×#16809857	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₂₉²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₉⋊D₂₉	C₂×C₃	1	4	yes	—
5	#16809857	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₂₉²	C₃×C₄	1	4	yes	complemented
7	C₂₉⋊D₂₉	C₂×C₃²	1	1	yes	characteristic
8	C₃²×#1181	—	29	30	no	maximal
9	C₂₉²	C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
10	C₃²×D₂₉	—	29	30	no	—
11	C₃×#1181	—	29	120	no	—
12	C₃²×C₂₉	#1181	1	30	yes	complemented
13	C₃×D₂₉	—	29	120	no	—
14	#1181	—	29	30	no	—
15	C₃×C₂₉	C₃×#1181	1	120	yes	complemented
16	D₂₉	—	29	30	no	—
17	C₃²×C₄	—	841	1	no	Hall
18	C₂₉	C₃²×#1181	1	30	yes	complemented
19	C₂×C₃²	—	841	1	no	—
20	C₃×C₄	—	841	4	no	—
21	C₃²	#16809857	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₃	—	841	4	no	—
23	C₄	—	841	1	no	Sylow
24	C₃	C₃×#16809857	1	4	yes	direct product factor
25	C₂	—	841	1	no	—

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.