Subgroups — C₂×D₇₂₉ #72210204

Order 2916.

35 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₄₃	—	3	1	no	maximal
4	C₇₂₉	C₂²	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₂₄₃	D₃	1	1	yes	characteristic
6	D₂₄₃	—	3	2	no	—
7	C₂×D₈₁	—	9	1	no	—
8	C₂₄₃	C₂×D₃	1	1	yes	characteristic
9	C₂×C₈₁	D₉	1	1	yes	characteristic
10	D₈₁	—	9	2	no	—
11	C₂×D₂₇	—	27	1	no	—
12	C₈₁	C₂×D₉	1	1	yes	characteristic
13	C₂×C₂₇	D₂₇	1	1	yes	characteristic
14	D₂₇	—	27	2	no	—
15	C₂×D₉	—	81	1	no	—
16	C₂₇	C₂×D₂₇	1	1	yes	characteristic
17	C₂×C₉	D₈₁	1	1	yes	characteristic
18	D₉	—	81	2	no	—
19	C₂×D₃	—	243	1	no	—
20	C₉	C₂×D₈₁	1	1	yes	characteristic
21	C₂×C₃	D₂₄₃	1	1	yes	characteristic
22	D₃	—	243	2	no	—
23	C₂²	—	729	1	no	Sylow
24	C₃	C₂×D₂₄₃	1	1	yes	characteristic
25	C₂	—	729	2	no	—
26	C₂	D₇₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇₂₉
commutator, cosocle, hypocenter	C₇₂₉	C₂²
Frattini	C₂₄₃	C₂×D₃
Fitting	C₂×C₇₂₉	C₂
socle	C₂×C₃	D₂₄₃
LCS	G ▷ C₇₂₉
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.