Subgroups — D₅×D₄₁₃ #22551900

Order 8260.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₀₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₅×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₄₁₃	—	5	1	no	maximal, Hall
6	D₅×D₅₉	—	7	1	no	maximal, Hall
7	C₂×C₇×C₅₉	—	5	1	no	—
8	D₄₁₃	—	5	1	no	—
9	D₄₁₃	D₅	1	1	yes	characteristic, direct product factor
10	D₂₉₅	—	7	1	no	—
11	C₅×D₅₉	—	7	1	no	—
12	D₅×C₅₉	D₇	1	1	yes	characteristic, complemented
13	C₇×C₅₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₅₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
15	C₂×D₅₉	—	35	1	no	Hall
16	D₅×D₇	—	59	1	no	maximal, Hall
17	C₂×C₅₉	—	5	1	no	—
18	D₅₉	—	7	1	no	—
19	D₅₉	—	35	1	no	—
20	D₃₅	—	59	1	no	—
21	C₅×D₇	—	59	1	no	—
22	C₇×D₅	D₅₉	1	1	yes	characteristic, complemented
23	C₅₉	D₅×D₇	1	1	yes	characteristic, complemented, Sylow
24	C₅×C₇	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
25	C₂×D₇	—	295	1	no	Hall
26	C₂×D₅	—	413	1	no	Hall
27	C₂×C₇	—	5	1	no	—
28	D₇	—	295	1	no	—
29	D₇	—	59	1	no	—
30	C₂×C₅	—	413	1	no	—
31	D₅	—	413	1	no	—
32	D₅	D₄₁₃	1	1	yes	characteristic, direct product factor
33	C₇	D₅×D₅₉	1	1	yes	characteristic, complemented, Sylow
34	C₅	C₂×D₄₁₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	2065	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	2065	1	no	—
38	C₂	—	413	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇×C₅₉	C₂²
LCS	G ▷ C₅×C₇×C₅₉
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.