Subgroups — C₂×C₄×C₈×C₁₃₉ #22580487

Order 8896.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₁₃₉	C₂	1	2	yes	maximal
2	C₂×C₄²×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₁₃₉	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₁₃₉	C₄	1	2	yes	—
5	C₂²×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₃₉	C₄	1	8	yes	direct product factor
7	C₂×C₈×C₁₃₉	C₂²	1	4	yes	—
8	C₄²×C₁₃₉	C₄	1	2	yes	—
9	C₄²×C₁₃₉	C₂²	1	2	yes	—
10	C₂³×C₁₃₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₃₉	C₈	1	8	yes	direct product factor
12	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
16	C₈×C₁₃₉	C₂×C₄	1	8	yes	direct product factor
17	C₂²×C₁₃₉	C₄²	1	2	yes	—
18	C₂²×C₁₃₉	C₂×C₈	1	4	yes	—
19	C₂²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
20	C₄×C₁₃₉	C₄²	1	2	yes	—
21	C₄×C₁₃₉	C₂×C₈	1	8	yes	direct product factor
22	C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
23	C₂×C₁₃₉	C₄×C₈	1	4	yes	direct product factor
24	C₂×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
25	C₂×C₁₃₉	C₂²×C₈	1	2	yes	—
26	C₁₃₉	C₂×C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₄×C₈	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₈	C₂×C₁₃₉	1	2	yes	—
29	C₂×C₄²	C₂×C₁₃₉	1	1	yes	characteristic
30	C₄×C₈	C₂×C₁₃₉	1	4	yes	direct product factor
31	C₂²×C₄	C₄×C₁₃₉	1	2	yes	—
32	C₂²×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
33	C₂×C₈	C₄×C₁₃₉	1	8	yes	direct product factor
34	C₂×C₈	C₂²×C₁₃₉	1	4	yes	—
35	C₄²	C₄×C₁₃₉	1	2	yes	—
36	C₄²	C₂²×C₁₃₉	1	2	yes	—
37	C₂³	C₂×C₄×C₁₃₉	1	1	yes	characteristic
38	C₂×C₄	C₈×C₁₃₉	1	8	yes	direct product factor
39	C₂×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
40	C₂×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
41	C₂×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
42	C₂×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
43	C₈	C₂×C₄×C₁₃₉	1	8	yes	direct product factor
44	C₂²	C₄²×C₁₃₉	1	2	yes	—
45	C₂²	C₂×C₈×C₁₃₉	1	4	yes	—
46	C₂²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
47	C₄	C₄²×C₁₃₉	1	2	yes	—
48	C₄	C₂×C₈×C₁₃₉	1	8	yes	direct product factor
49	C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
50	C₂	C₄×C₈×C₁₃₉	1	4	yes	direct product factor
51	C₂	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
52	C₂	C₂²×C₈×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₄	C₂³×C₁₃₉
socle	C₂³×C₁₃₉	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₈×C₁₃₉	C₂	direct (N × H)
6. C₂×C₈×C₁₃₉	C₄	direct (N × H)
11. C₂×C₄×C₁₃₉	C₈	direct (N × H)
16. C₈×C₁₃₉	C₂×C₄	direct (N × H)
21. C₄×C₁₃₉	C₂×C₈	direct (N × H)
23. C₂×C₁₃₉	C₄×C₈	direct (N × H)
26. C₁₃₉	C₂×C₄×C₈	direct (N × H)
27. C₂×C₄×C₈	C₁₃₉	direct (N × H)
30. C₄×C₈	C₂×C₁₃₉	direct (N × H)
33. C₂×C₈	C₄×C₁₃₉	direct (N × H)
38. C₂×C₄	C₈×C₁₃₉	direct (N × H)
43. C₈	C₂×C₄×C₁₃₉	direct (N × H)
48. C₄	C₂×C₈×C₁₃₉	direct (N × H)
50. C₂	C₄×C₈×C₁₃₉	direct (N × H)

Subgroups — C2×C4×C8×C139 #22580487

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄×C₈×C₁₃₉ #22580487