Subgroups — C₅×#8813 #11931533

Order 1280.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1844	C₂	1	6	yes	maximal
2	C₂×C₅×C₈²	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#106	—	2	12	no	—
4	C₂×C₄×C₅×C₈	C₂²	1	3	yes	—
5	C₅×#384	C₂²	1	4	yes	—
6	C₅×C₈²	C₄	1	4	yes	complemented
7	#8813	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂²×C₅×C₈	D₄	1	6	yes	—
9	C₂×C₅×C₄⋊C₄	—	2	12	no	—
10	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
11	C₅×#106	—	4	24	no	—
12	C₄×C₅×C₈	C₂×C₄	1	6	yes	—
13	C₄×C₅×C₈	Q₈	1	6	yes	—
14	#1844	C₂×C₅	1	6	yes	—
15	C₂×C₈²	C₂×C₅	1	1	yes	characteristic
16	C₂²×C₄×C₅	—	4	4	no	—
17	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
18	C₂×C₅×C₈	C₄⋊C₄	1	12	yes	—
19	C₂×C₅×C₈	SD₁₆	1	24	yes	—
20	C₅×C₄⋊C₄	—	4	24	no	—
21	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
22	C₄²×C₅	C₂×Q₈	1	3	yes	—
23	C₂×#106	—	2	12	no	—
24	C₂×C₄×C₈	C₂²×C₅	1	3	yes	—
25	#384	C₂²×C₅	1	4	yes	—
26	C₈²	C₄×C₅	1	4	yes	complemented
27	C₂³×C₅	#127	1	1	yes	characteristic
28	C₂×C₄×C₅	—	8	12	no	—
29	C₂×C₄×C₅	C₂×C₄⋊C₄	1	3	yes	—
30	C₂×C₄×C₅	C₄⋊Q₈	1	3	yes	—
31	C₂×C₄×C₅	C₂×SD₁₆	1	12	yes	—
32	C₅×C₈	#106	1	24	yes	complemented
33	C₂²×C₈	C₅×D₄	1	6	yes	—
34	C₂×C₄⋊C₄	—	2	12	no	—
35	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
36	#106	—	4	24	no	—
37	C₄×C₈	C₂×C₄×C₅	1	6	yes	—
38	C₄×C₈	C₅×Q₈	1	6	yes	—
39	C₂²×C₅	#384	1	1	yes	characteristic
40	C₂²×C₅	#492	1	6	yes	—
41	C₄×C₅	—	16	4	no	—
42	C₄×C₅	C₂×#106	1	6	yes	—
43	C₄×C₅	#498	1	6	yes	—
44	C₂²×C₄	—	4	4	no	—
45	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
46	C₂×C₈	C₅×C₄⋊C₄	1	12	yes	—
47	C₂×C₈	C₅×SD₁₆	1	24	yes	—
48	C₄⋊C₄	—	4	24	no	—
49	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
50	C₄²	C₂×C₅×Q₈	1	3	yes	—
51	C₂×C₅	#1705	1	4	yes	—
52	C₂×C₅	#1844	1	3	yes	—
53	C₂³	C₅×#127	1	1	yes	characteristic
54	C₂×C₄	—	8	12	no	—
55	C₂×C₄	C₂×C₅×C₄⋊C₄	1	3	yes	—
56	C₂×C₄	C₅×C₄⋊Q₈	1	3	yes	—
57	C₂×C₄	C₂×C₅×SD₁₆	1	12	yes	—
58	C₈	C₅×#106	1	24	yes	complemented
59	C₅	#8813	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²	C₅×#384	1	1	yes	characteristic
61	C₂²	C₅×#492	1	6	yes	—
62	C₄	—	16	4	no	—
63	C₄	C₂×C₅×#106	1	6	yes	—
64	C₄	C₅×#498	1	6	yes	—
65	C₂	C₅×#1705	1	4	yes	—
66	C₂	C₅×#1844	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	#127
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×C₈²	C₄	semidirect
7. #8813	C₅	direct (N × H)
26. C₈²	C₄×C₅	semidirect
32. C₅×C₈	#106	semidirect
58. C₈	C₅×#106	semidirect
59. C₅	#8813	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#1844	2
C₂×C₅×C₈²	2
#8813	5

Subgroups — C5×#8813 #11931533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8813 #11931533