Subgroups — D₅×D₈₇ #13181971

Order 1740.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₂₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₈₇	—	5	1	no	maximal, Hall
7	D₁₄₅	—	3	1	no	—
8	C₅×D₂₉	—	3	1	no	—
9	D₅×C₂₉	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₂₉	—	5	1	no	—
11	D₈₇	—	5	1	no	—
12	D₈₇	D₅	1	1	yes	characteristic, direct product factor
13	C₅×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₂₉	—	15	1	no	Hall
15	C₃×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	D₃×D₅	—	29	1	no	maximal, Hall
17	C₂×C₂₉	—	5	1	no	—
18	D₂₉	—	3	1	no	—
19	D₂₉	—	15	1	no	—
20	D₁₅	—	29	1	no	—
21	C₃×D₅	D₂₉	1	1	yes	characteristic, complemented
22	C₅×D₃	—	29	1	no	—
23	C₂₉	D₃×D₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₅	—	87	1	no	Hall
25	C₃×C₅	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃	—	145	1	no	Hall
27	C₂×C₅	—	87	1	no	—
28	D₅	—	87	1	no	—
29	D₅	D₈₇	1	1	yes	characteristic, direct product factor
30	C₂×C₃	—	5	1	no	—
31	D₃	—	29	1	no	—
32	D₃	—	145	1	no	—
33	C₅	C₂×D₈₇	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	435	1	no	Sylow
35	C₃	D₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	5	1	no	—
37	C₂	—	87	1	no	—
38	C₂	—	435	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₂₉	C₂²
LCS	G ▷ C₃×C₅×C₂₉
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.