Subgroups — #22581143

Order 8896.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984823	C₂	1	3	yes	maximal, complemented
2	#17984757	C₂	1	3	yes	maximal, complemented
3	H(5,𝔽₂)×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₃₉	C₂²	1	1	yes	characteristic, complemented
5	Dic₁₃₉⋊C₄	—	2	3	no	—
6	C₂²⋊Dic₁₃₉	—	2	3	no	—
7	C₂²⋊Dic₁₃₉	C₂²	1	3	yes	complemented
8	#41×C₁₃₉	—	2	3	no	—
9	C₂×D₄×C₁₃₉	—	2	3	no	—
10	C₂×D₄×C₁₃₉	C₂²	1	3	yes	—
11	C₂×Dic₁₃₉	—	2	3	no	—
12	C₂×Dic₁₃₉	—	2	3	no	—
13	C₂³×C₁₃₉	—	2	1	no	—
14	C₂³×C₁₃₉	D₄	1	3	yes	—
15	C₂³×C₁₃₉	C₂³	1	1	yes	characteristic
16	Q₈×C₁₃₉	—	2	1	no	—
17	D₄×C₁₃₉	—	2	3	no	—
18	D₄×C₁₃₉	—	2	6	no	—
19	C₂×C₄×C₁₃₉	—	2	3	no	—
20	C₂×C₄×C₁₃₉	D₄	1	3	yes	—
21	C₂²×C₁₃₉	—	2	3	no	—
22	C₂²×C₁₃₉	—	4	1	no	—
23	C₂²×C₁₃₉	—	4	3	no	—
24	C₂²×C₁₃₉	—	8	1	no	—
25	C₂²×C₁₃₉	C₂×D₄	1	3	yes	—
26	C₄×C₁₃₉	—	2	3	no	—
27	Dic₁₃₉	—	4	3	no	—
28	Dic₁₃₉	—	4	1	no	—
29	C₂×C₁₃₉	—	2	3	no	—
30	C₂×C₁₃₉	—	4	3	no	—
31	C₂×C₁₃₉	#120	1	1	yes	characteristic
32	C₁₃₉	#458	1	1	yes	characteristic, complemented, Sylow
33	#458	—	139	1	no	maximal, Sylow
34	H(5,𝔽₂)	D₁₃₉	1	1	yes	characteristic
35	#123	—	139	3	no	—
36	#99	—	139	3	no	—
37	#41	—	2	3	no	—
38	C₂×D₄	—	2	3	no	—
39	C₂×D₄	C₂×D₁₃₉	1	3	yes	—
40	C₂²×C₄	—	139	1	no	—
41	C₄⋊C₄	—	278	3	no	—
42	C₂²⋊C₄	—	278	3	no	—
43	C₂²⋊C₄	—	139	3	no	—
44	C₂³	—	2	1	no	—
45	C₂³	C₂²⋊D₁₃₉	1	3	yes	—
46	C₂³	C₂²×D₁₃₉	1	1	yes	characteristic
47	Q₈	—	2	1	no	—
48	D₄	—	2	3	no	—
49	D₄	—	2	6	no	—
50	C₂×C₄	—	2	3	no	—
51	C₂×C₄	—	278	3	no	—
52	C₂×C₄	—	278	3	no	—
53	C₂×C₄	C₂²⋊D₁₃₉	1	3	yes	—
54	C₂²	—	2	3	no	—
55	C₂²	—	4	1	no	—
56	C₂²	—	4	3	no	—
57	C₂²	—	8	1	no	—
58	C₂²	C₂×C₂²⋊D₁₃₉	1	3	yes	—
59	C₄	—	2	3	no	—
60	C₄	—	556	3	no	—
61	C₄	—	556	1	no	—
62	C₂	—	2	3	no	—
63	C₂	—	4	3	no	—
64	C₂	#17984811	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17984811
commutator	C₂³×C₁₃₉	C₂³
Frattini	C₂³	C₂²×D₁₃₉
Fitting	H(5,𝔽₂)×C₁₃₉	C₂
socle	C₂×C₁₃₉	#120
hypercenter	H(5,𝔽₂)	D₁₃₉
hypocenter	C₁₃₉	#458
LCS	G ▷ C₂³×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. #17984823	C₂	semidirect
2. #17984757	C₂	semidirect
4. C₂²×Dic₁₃₉	C₂²	semidirect
7. C₂²⋊Dic₁₃₉	C₂²	semidirect
32. C₁₃₉	#458	semidirect