Subgroups — C₂×D₄₉₄₅ #34089922

Order 19780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₉₄₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₃×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₉₈₉	—	5	1	no	maximal, Hall
5	C₂×C₂₃×C₄₃	D₅	1	1	yes	characteristic, complemented
6	D₉₈₉	—	5	2	no	—
7	C₂₃×C₄₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
8	C₂×D₂₁₅	—	23	1	no	maximal, Hall
9	C₂×D₁₁₅	—	43	1	no	maximal, Hall
10	C₂×C₅×C₄₃	D₂₃	1	1	yes	characteristic, complemented
11	D₂₁₅	—	23	2	no	—
12	C₂×C₅×C₂₃	D₄₃	1	1	yes	characteristic, complemented
13	D₁₁₅	—	43	2	no	—
14	C₅×C₄₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₄₃	—	115	1	no	Hall
16	C₅×C₂₃	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
17	C₂×D₂₃	—	215	1	no	Hall
18	C₂×C₄₃	D₁₁₅	1	1	yes	characteristic, complemented
19	D₄₃	—	115	2	no	—
20	C₂×C₂₃	D₂₁₅	1	1	yes	characteristic, complemented
21	D₂₃	—	215	2	no	—
22	C₄₃	C₂×D₁₁₅	1	1	yes	characteristic, complemented, Sylow
23	C₂₃	C₂×D₂₁₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₅	—	989	1	no	Hall
25	C₂×C₅	D₉₈₉	1	1	yes	characteristic, complemented
26	D₅	—	989	2	no	—
27	C₅	C₂×D₉₈₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	4945	1	no	Sylow
29	C₂	—	4945	2	no	—
30	C₂	D₄₉₄₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₄₉₄₅
commutator, cosocle, hypocenter	C₅×C₂₃×C₄₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₃×C₄₃	C₂
LCS	G ▷ C₅×C₂₃×C₄₃
UCS	C₁ ◁ C₂

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.