Subgroups — C₂×D₂₆₈₅ #24924410

Order 10740.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₆₈₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈₉₅	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₅₃₇	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₇₉	D₃	1	1	yes	characteristic, complemented
7	D₈₉₅	—	3	2	no	—
8	C₂×C₃×C₁₇₉	D₅	1	1	yes	characteristic, complemented
9	D₅₃₇	—	5	2	no	—
10	C₅×C₁₇₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₁₇₉	—	15	1	no	Hall
12	C₃×C₁₇₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₇₉	D₁₅	1	1	yes	characteristic, complemented
14	D₁₇₉	—	15	2	no	—
15	C₁₇₉	C₂×D₁₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₁₅	—	179	1	no	maximal, Hall
17	C₂×C₃×C₅	D₁₇₉	1	1	yes	characteristic, complemented
18	D₁₅	—	179	2	no	—
19	C₂×D₅	—	537	1	no	Hall
20	C₃×C₅	C₂×D₁₇₉	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃	—	895	1	no	Hall
22	C₂×C₅	D₅₃₇	1	1	yes	characteristic, complemented
23	D₅	—	537	2	no	—
24	C₂×C₃	D₈₉₅	1	1	yes	characteristic, complemented
25	D₃	—	895	2	no	—
26	C₅	C₂×D₅₃₇	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	2685	1	no	Sylow
28	C₃	C₂×D₈₉₅	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	2685	2	no	—
30	C₂	D₂₆₈₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₂₆₈₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₇₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₇₉	C₂
LCS	G ▷ C₃×C₅×C₁₇₉
UCS	C₁ ◁ C₂

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