Subgroups — C₂×D₁₆₃₇₇ #72304514

Order 65508.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆₃₇₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅₃×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅₄₅₉	—	3	1	no	maximal, Hall
4	C₃×C₅₃×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅₃×C₁₀₃	D₃	1	1	yes	characteristic, complemented
6	D₅₄₅₉	—	3	2	no	—
7	C₅₃×C₁₀₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃₀₉	—	53	1	no	maximal, Hall
9	C₂×D₁₅₉	—	103	1	no	maximal, Hall
10	C₂×C₃×C₁₀₃	D₅₃	1	1	yes	characteristic, complemented
11	D₃₀₉	—	53	2	no	—
12	C₂×D₁₀₃	—	159	1	no	Hall
13	C₂×C₃×C₅₃	D₁₀₃	1	1	yes	characteristic, complemented
14	D₁₅₉	—	103	2	no	—
15	C₃×C₁₀₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
16	C₂×D₅₃	—	309	1	no	Hall
17	C₂×C₁₀₃	D₁₅₉	1	1	yes	characteristic, complemented
18	D₁₀₃	—	159	2	no	—
19	C₃×C₅₃	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅₃	D₃₀₉	1	1	yes	characteristic, complemented
21	D₅₃	—	309	2	no	—
22	C₁₀₃	C₂×D₁₅₉	1	1	yes	characteristic, complemented, Sylow
23	C₅₃	C₂×D₃₀₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	5459	1	no	Hall
25	C₂×C₃	D₅₄₅₉	1	1	yes	characteristic, complemented
26	D₃	—	5459	2	no	—
27	C₂²	—	16377	1	no	Sylow
28	C₃	C₂×D₅₄₅₉	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	16377	2	no	—
30	C₂	D₁₆₃₇₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₆₃₇₇
commutator, cosocle, hypocenter	C₃×C₅₃×C₁₀₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅₃×C₁₀₃	C₂
LCS	G ▷ C₃×C₅₃×C₁₀₃
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.