Subgroups — C₂×D₅₉₄₅ #37558113

Order 23780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₉₄₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₉×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₉×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁₈₉	—	5	1	no	maximal, Hall
5	C₂×C₂₉×C₄₁	D₅	1	1	yes	characteristic, complemented
6	D₁₁₈₉	—	5	2	no	—
7	C₂₉×C₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
8	C₂×D₂₀₅	—	29	1	no	maximal, Hall
9	C₂×D₁₄₅	—	41	1	no	maximal, Hall
10	C₂×C₅×C₄₁	D₂₉	1	1	yes	characteristic, complemented
11	D₂₀₅	—	29	2	no	—
12	C₂×C₅×C₂₉	D₄₁	1	1	yes	characteristic, complemented
13	D₁₄₅	—	41	2	no	—
14	C₅×C₄₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
15	C₂×D₄₁	—	145	1	no	Hall
16	C₅×C₂₉	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
17	C₂×D₂₉	—	205	1	no	Hall
18	C₂×C₄₁	D₁₄₅	1	1	yes	characteristic, complemented
19	D₄₁	—	145	2	no	—
20	C₂×C₂₉	D₂₀₅	1	1	yes	characteristic, complemented
21	D₂₉	—	205	2	no	—
22	C₄₁	C₂×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
23	C₂₉	C₂×D₂₀₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₅	—	1189	1	no	Hall
25	C₂×C₅	D₁₁₈₉	1	1	yes	characteristic, complemented
26	D₅	—	1189	2	no	—
27	C₅	C₂×D₁₁₈₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	5945	1	no	Sylow
29	C₂	—	5945	2	no	—
30	C₂	D₅₉₄₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅₉₄₅
commutator, cosocle, hypocenter	C₅×C₂₉×C₄₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₉×C₄₁	C₂
LCS	G ▷ C₅×C₂₉×C₄₁
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.