Subgroups — #44475672

Order 30276.

288 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, complemented
2	C₂₉×C₃⋊D₈₇	C₂	1	2	yes	maximal, complemented
3	D₈₇⋊D₂₉	—	3	4	no	maximal
4	C₃²×C₂₉²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂₉×D₈₇	—	3	8	no	—
6	C₃×C₂₉⋊D₂₉	D₃	1	4	yes	complemented
7	D₂₉²	—	9	1	no	Hall
8	C₃×C₂₉²	C₂×D₃	1	4	yes	complemented
9	C₂₉⋊D₂₉	C₃⋊D₃	1	1	yes	characteristic, complemented
10	C₂₉×D₂₉	—	9	2	no	—
11	C₃⋊D₃×D₂₉	—	29	2	no	maximal
12	C₂₉²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
13	C₃⋊D₈₇	D₂₉	1	2	yes	complemented
14	C₃⋊D₃×C₂₉	—	29	2	no	—
15	C₃²×D₂₉	—	29	2	no	—
16	C₃²×D₂₉	—	58	14	no	—
17	D₃×D₂₉	—	87	8	no	—
18	C₃²×C₂₉	—	2	14	no	—
19	C₃²×C₂₉	C₂×D₂₉	1	2	yes	complemented
20	D₈₇	—	3	8	no	—
21	C₃×D₂₉	—	29	8	no	—
22	C₃×D₂₉	—	58	56	no	—
23	D₃×C₂₉	—	87	8	no	—
24	C₂×D₂₉	—	261	2	no	—
25	C₃×C₂₉	—	2	56	no	—
26	C₃×C₂₉	D₃×D₂₉	1	8	yes	complemented
27	C₂×C₂₉	—	261	2	no	—
28	D₂₉	—	9	2	no	—
29	D₂₉	—	29	2	no	—
30	D₂₉	—	58	14	no	—
31	C₂×C₃⋊D₃	—	841	1	no	Hall
32	C₂₉	—	2	14	no	—
33	C₂₉	C₃⋊D₃×D₂₉	1	2	yes	complemented
34	C₂×C₃²	—	841	1	no	—
35	C₃⋊D₃	—	29	2	no	—
36	C₂×D₃	—	2523	4	no	—
37	C₃²	D₂₉²	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃	—	841	4	no	—
39	D₃	—	87	8	no	—
40	C₂²	—	7569	1	no	Sylow
41	C₃	D₈₇⋊D₂₉	1	4	yes	complemented
42	C₂	—	261	2	no	—
43	C₂	—	841	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₂₉²	C₂²
LCS	G ▷ C₃²×C₂₉²
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.