Subgroups — #564×D₁₃₉ #31820546

Order 17792.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃₉⋊#564	C₂	1	15	yes	maximal, complemented
2	#125×D₁₃₉	C₂	1	15	yes	maximal
3	#564×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#17984834	C₂²	1	15	yes	—
5	#17984833	C₂²	1	30	yes	—
6	#17984832	C₂²	1	60	yes	—
7	C₄⋊C₄×D₁₃₉	C₂²	1	30	yes	—
8	C₄²×D₁₃₉	C₂²	1	5	yes	—
9	#125×C₁₃₉	C₂²	1	15	yes	—
10	C₂×C₄×D₁₃₉	C₂³	1	15	yes	—
11	C₄⋊Dic₁₃₉	C₂³	1	30	yes	—
12	Dic₁₃₉⋊C₄	C₂³	1	60	yes	—
13	C₄×Dic₁₃₉	C₂³	1	15	yes	—
14	C₄⋊C₄×C₁₃₉	C₂³	1	30	yes	—
15	C₄²×C₁₃₉	C₂³	1	5	yes	—
16	C₂²×D₁₃₉	C₂⁴	1	1	yes	characteristic
17	C₂×Dic₁₃₉	C₂⁴	1	15	yes	—
18	C₄×D₁₃₉	—	2	30	no	—
19	C₂×C₄×C₁₃₉	C₂⁴	1	15	yes	—
20	C₂²×C₁₃₉	C₂⁵	1	1	yes	characteristic
21	C₂×D₁₃₉	2₋¹⁺⁴	1	6	yes	—
22	C₄×C₁₃₉	—	2	15	no	—
23	Dic₁₃₉	—	2	15	no	—
24	C₂×C₁₃₉	C₂×2₋¹⁺⁴	1	3	yes	—
25	D₁₃₉	#564	1	4	yes	direct product factor
26	C₁₃₉	C₂×#564	1	1	yes	characteristic, complemented, Sylow
27	C₂×#564	—	139	1	no	maximal, Sylow
28	#564	—	139	15	no	—
29	#564	D₁₃₉	1	1	yes	characteristic, direct product factor
30	C₂×#125	—	139	15	no	—
31	#125	—	139	60	no	—
32	#125	—	139	30	no	—
33	#125	—	139	15	no	—
34	#125	C₂×D₁₃₉	1	15	yes	—
35	C₂×C₄⋊C₄	—	139	30	no	—
36	C₂×C₄²	—	139	5	no	—
37	C₂²×C₄	—	139	15	no	—
38	C₄⋊C₄	—	139	60	no	—
39	C₄⋊C₄	—	139	30	no	—
40	C₄⋊C₄	C₂²×D₁₃₉	1	30	yes	—
41	C₄²	—	139	15	no	—
42	C₄²	C₂²×D₁₃₉	1	5	yes	—
43	C₂³	—	139	1	no	—
44	C₂×C₄	—	278	30	no	—
45	C₂×C₄	—	139	15	no	—
46	C₂×C₄	C₂³×D₁₃₉	1	15	yes	—
47	C₂²	—	139	6	no	—
48	C₂²	C₂⁴×D₁₃₉	1	1	yes	characteristic
49	C₄	—	2	15	no	—
50	C₄	—	278	15	no	—
51	C₂	—	139	4	no	—
52	C₂	2₋¹⁺⁴×D₁₃₉	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₉
commutator, socle, cosocle	C₂²×C₁₃₉	C₂⁵
Fitting	#564×C₁₃₉	C₂
prime radical	C₂²×D₁₃₉	C₂⁴
hypercenter	#564	D₁₃₉
hypocenter	C₁₃₉	C₂×#564
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ #564

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃₉⋊#564	C₂	semidirect
3. #564×C₁₃₉	C₂	semidirect
25. D₁₃₉	#564	direct (N × H)
26. C₁₃₉	C₂×#564	semidirect
29. #564	D₁₃₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃₉⋊#564	2
#125×D₁₃₉	2
#564×C₁₃₉	2
C₂×#564	139

Subgroups — #564×D139 #31820546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #564×D₁₃₉ #31820546