Subgroups — C₂×D₇₂₃₉ #44394205

Order 28956.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₂₃₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₉×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₄₁₃	—	3	1	no	maximal, Hall
4	C₃×C₁₉×C₁₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₁₂₇	D₃	1	1	yes	characteristic, complemented
6	D₂₄₁₃	—	3	2	no	—
7	C₁₉×C₁₂₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃₈₁	—	19	1	no	maximal, Hall
9	C₂×C₃×C₁₂₇	D₁₉	1	1	yes	characteristic, complemented
10	D₃₈₁	—	19	2	no	—
11	C₂×D₁₂₇	—	57	1	no	Hall
12	C₃×C₁₂₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₂₇	D₅₇	1	1	yes	characteristic, complemented
14	D₁₂₇	—	57	2	no	—
15	C₂×D₅₇	—	127	1	no	maximal, Hall
16	C₁₂₇	C₂×D₅₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₁₉	D₁₂₇	1	1	yes	characteristic, complemented
18	D₅₇	—	127	2	no	—
19	C₂×D₁₉	—	381	1	no	Hall
20	C₃×C₁₉	C₂×D₁₂₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₉	D₃₈₁	1	1	yes	characteristic, complemented
22	D₁₉	—	381	2	no	—
23	C₁₉	C₂×D₃₈₁	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	2413	1	no	Hall
25	C₂×C₃	D₂₄₁₃	1	1	yes	characteristic, complemented
26	D₃	—	2413	2	no	—
27	C₂²	—	7239	1	no	Sylow
28	C₃	C₂×D₂₄₁₃	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	7239	2	no	—
30	C₂	D₇₂₃₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇₂₃₉
commutator, cosocle, hypocenter	C₃×C₁₉×C₁₂₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₁₂₇	C₂
LCS	G ▷ C₃×C₁₉×C₁₂₇
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.