Subgroups — C₂×D₂₆₇₉ #24924285

Order 10716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₆₇₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈₉₃	—	3	1	no	maximal, Hall
4	C₃×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₄₇	D₃	1	1	yes	characteristic, complemented
6	D₈₉₃	—	3	2	no	—
7	C₁₉×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₄₁	—	19	1	no	maximal, Hall
9	C₂×C₃×C₄₇	D₁₉	1	1	yes	characteristic, complemented
10	D₁₄₁	—	19	2	no	—
11	C₂×D₅₇	—	47	1	no	maximal, Hall
12	C₂×D₄₇	—	57	1	no	Hall
13	C₃×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₁₉	D₄₇	1	1	yes	characteristic, complemented
15	D₅₇	—	47	2	no	—
16	C₂×C₄₇	D₅₇	1	1	yes	characteristic, complemented
17	D₄₇	—	57	2	no	—
18	C₂×D₁₉	—	141	1	no	Hall
19	C₃×C₁₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
20	C₄₇	C₂×D₅₇	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₉	D₁₄₁	1	1	yes	characteristic, complemented
22	D₁₉	—	141	2	no	—
23	C₁₉	C₂×D₁₄₁	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	893	1	no	Hall
25	C₂×C₃	D₈₉₃	1	1	yes	characteristic, complemented
26	D₃	—	893	2	no	—
27	C₂²	—	2679	1	no	Sylow
28	C₃	C₂×D₈₉₃	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	2679	2	no	—
30	C₂	D₂₆₇₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₂₆₇₉
commutator, cosocle, hypocenter	C₃×C₁₉×C₄₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₄₇	C₂
LCS	G ▷ C₃×C₁₉×C₄₇
UCS	C₁ ◁ C₂

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