Subgroups — C₁₃₉×#7329 #48001925

Order 35584.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₂×C₁₃₉	C₂	1	2	yes	maximal
2	C₈×C₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₁₃₉	C₄	1	4	yes	—
4	C₄×C₁₆×C₁₃₉	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
6	C₈²×C₁₃₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₃₉	C₈	1	2	yes	—
8	C₂×C₁₆×C₁₃₉	C₂×C₄	1	2	yes	—
9	C₄×C₈×C₁₃₉	C₈	1	2	yes	—
10	C₄×C₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
11	C₃₂×C₁₃₉	C₈	1	8	yes	complemented
12	C₂×C₈×C₁₃₉	C₁₆	1	4	yes	—
13	C₂×C₈×C₁₃₉	C₄²	1	1	yes	characteristic
14	C₂×C₈×C₁₃₉	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₃₉	C₂×C₈	1	1	yes	characteristic
16	C₁₆×C₁₃₉	C₁₆	1	4	yes	—
17	C₁₆×C₁₃₉	C₂×C₈	1	4	yes	—
18	C₂×C₄×C₁₃₉	C₄×C₈	1	1	yes	characteristic
19	C₂×C₄×C₁₃₉	C₂×C₁₆	1	2	yes	—
20	C₈×C₁₃₉	—	2	4	no	—
21	C₈×C₁₃₉	C₄×C₈	1	2	yes	—
22	C₈×C₁₃₉	C₂×C₁₆	1	2	yes	—
23	C₂²×C₁₃₉	C₄×C₁₆	1	1	yes	characteristic
24	C₄×C₁₃₉	C₈²	1	1	yes	characteristic
25	C₄×C₁₃₉	C₄×C₁₆	1	1	yes	characteristic
26	C₄×C₁₃₉	M₆₄	1	4	yes	—
27	C₂×C₁₃₉	C₈×C₁₆	1	1	yes	characteristic
28	C₂×C₁₃₉	#1397	1	2	yes	—
29	#7329	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₁₃₉	#7329	1	1	yes	characteristic, direct product factor, Sylow
31	C₄×C₃₂	C₂×C₁₃₉	1	2	yes	—
32	C₈×C₁₆	C₂×C₁₃₉	1	1	yes	characteristic
33	C₂×C₃₂	C₄×C₁₃₉	1	4	yes	—
34	C₄×C₁₆	C₄×C₁₃₉	1	1	yes	characteristic
35	C₄×C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
36	C₈²	C₄×C₁₃₉	1	1	yes	characteristic
37	C₂×C₁₆	C₈×C₁₃₉	1	2	yes	—
38	C₂×C₁₆	C₂×C₄×C₁₃₉	1	2	yes	—
39	C₄×C₈	C₈×C₁₃₉	1	2	yes	—
40	C₄×C₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
41	C₃₂	C₈×C₁₃₉	1	8	yes	complemented
42	C₂×C₈	C₁₆×C₁₃₉	1	4	yes	—
43	C₂×C₈	C₄²×C₁₃₉	1	1	yes	characteristic
44	C₂×C₈	C₂×C₈×C₁₃₉	1	1	yes	characteristic
45	C₄²	C₂×C₈×C₁₃₉	1	1	yes	characteristic
46	C₁₆	C₁₆×C₁₃₉	1	4	yes	—
47	C₁₆	C₂×C₈×C₁₃₉	1	4	yes	—
48	C₂×C₄	C₄×C₈×C₁₃₉	1	1	yes	characteristic
49	C₂×C₄	C₂×C₁₆×C₁₃₉	1	2	yes	—
50	C₈	—	2	4	no	—
51	C₈	C₄×C₈×C₁₃₉	1	2	yes	—
52	C₈	C₂×C₁₆×C₁₃₉	1	2	yes	—
53	C₂²	C₄×C₁₆×C₁₃₉	1	1	yes	characteristic
54	C₄	C₈²×C₁₃₉	1	1	yes	characteristic
55	C₄	C₄×C₁₆×C₁₃₉	1	1	yes	characteristic
56	C₄	M₆₄×C₁₃₉	1	4	yes	—
57	C₂	C₈×C₁₆×C₁₃₉	1	1	yes	characteristic
58	C₂	#1397×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₄×C₁₆×C₁₃₉	C₂²
commutator	C₂	C₈×C₁₆×C₁₃₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₃₉
socle, prime radical	C₂²×C₁₃₉	C₄×C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₆×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₃₂×C₁₃₉	C₈	semidirect
29. #7329	C₁₃₉	direct (N × H)
30. C₁₃₉	#7329	direct (N × H)
41. C₃₂	C₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃₂×C₁₃₉	2
C₈×C₁₆×C₁₃₉	2
#7329	139

Subgroups — C139×#7329 #48001925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#7329 #48001925