Subgroups — C₅×#13726 #11936446

Order 1280.

230 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₆₄	C₂	1	4	yes	maximal
2	C₅×#2247	C₂	1	2	yes	maximal
3	C₄×C₅×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Q₃₂	—	2	2	no	—
5	C₂×C₅×Q₃₂	C₂²	1	4	yes	—
6	C₅×#494	—	2	2	no	—
7	C₅×Q₆₄	—	2	8	no	—
8	C₂×C₅×C₃₂	C₂²	1	2	yes	—
9	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
10	#13726	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₅×Q₁₆	—	2	4	no	—
12	C₂×C₅×Q₁₆	—	4	2	no	—
13	C₅×C₄⋊Q₈	—	4	2	no	—
14	C₅×Q₃₂	—	2	8	no	—
15	C₅×Q₃₂	—	4	4	no	—
16	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
17	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
18	C₄×C₅×C₈	D₄	1	1	yes	characteristic
19	C₅×C₃₂	D₄	1	4	yes	—
20	C₂×Q₆₄	C₂×C₅	1	4	yes	—
21	#2247	C₂×C₅	1	2	yes	—
22	C₄×C₃₂	C₂×C₅	1	1	yes	characteristic
23	C₂×C₅×Q₈	—	4	4	no	—
24	C₅×Q₁₆	—	4	4	no	—
25	C₅×Q₁₆	—	4	4	no	—
26	C₅×Q₁₆	—	8	4	no	—
27	C₂×C₅×C₈	D₈	1	1	yes	characteristic
28	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
29	C₅×C₄⋊C₄	—	8	4	no	—
30	C₄²×C₅	D₈	1	1	yes	characteristic
31	C₅×C₁₆	D₈	1	2	yes	—
32	C₅×C₁₆	C₂×D₄	1	2	yes	—
33	C₂×Q₃₂	—	2	2	no	—
34	C₂×Q₃₂	C₂²×C₅	1	4	yes	—
35	#494	—	2	2	no	—
36	Q₆₄	—	2	8	no	—
37	C₂×C₃₂	C₂²×C₅	1	2	yes	—
38	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
39	C₅×Q₈	—	8	4	no	—
40	C₅×Q₈	—	8	4	no	—
41	C₂×C₄×C₅	—	8	4	no	—
42	C₂×C₄×C₅	D₁₆	1	2	yes	—
43	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
44	C₅×C₈	D₁₆	1	2	yes	—
45	C₅×C₈	#127	1	1	yes	characteristic
46	C₅×C₈	C₂×D₈	1	1	yes	characteristic
47	C₂×Q₁₆	—	2	4	no	—
48	C₂×Q₁₆	—	4	2	no	—
49	C₄⋊Q₈	—	4	2	no	—
50	Q₃₂	—	2	8	no	—
51	Q₃₂	—	4	4	no	—
52	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
53	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
54	C₄×C₈	C₅×D₄	1	1	yes	characteristic
55	C₃₂	C₅×D₄	1	4	yes	—
56	C₂²×C₅	C₂×D₁₆	1	1	yes	characteristic
57	C₄×C₅	—	16	4	no	—
58	C₄×C₅	Q₆₄	1	4	yes	complemented
59	C₄×C₅	#493	1	1	yes	characteristic
60	C₄×C₅	C₂×D₁₆	1	1	yes	characteristic
61	C₂×Q₈	—	4	4	no	—
62	Q₁₆	—	4	4	no	—
63	Q₁₆	—	4	4	no	—
64	Q₁₆	—	8	4	no	—
65	C₂×C₈	C₅×D₈	1	1	yes	characteristic
66	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
67	C₄⋊C₄	—	8	4	no	—
68	C₄²	C₅×D₈	1	1	yes	characteristic
69	C₁₆	C₅×D₈	1	2	yes	—
70	C₁₆	C₂×C₅×D₄	1	2	yes	—
71	C₂×C₅	#2246	1	1	yes	characteristic
72	C₂×C₅	C₂×Q₆₄	1	2	yes	—
73	Q₈	—	8	4	no	—
74	Q₈	—	8	4	no	—
75	C₂×C₄	—	8	4	no	—
76	C₂×C₄	C₅×D₁₆	1	2	yes	—
77	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
78	C₈	C₅×D₁₆	1	2	yes	—
79	C₈	C₅×#127	1	1	yes	characteristic
80	C₈	C₂×C₅×D₈	1	1	yes	characteristic
81	C₅	#13726	1	1	yes	characteristic, direct product factor, Sylow
82	C₂²	C₂×C₅×D₁₆	1	1	yes	characteristic
83	C₄	—	16	4	no	—
84	C₄	C₅×Q₆₄	1	4	yes	complemented
85	C₄	C₅×#493	1	1	yes	characteristic
86	C₄	C₂×C₅×D₁₆	1	1	yes	characteristic
87	C₂	C₅×#2246	1	1	yes	characteristic
88	C₂	C₂×C₅×Q₆₄	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₅	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₅
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×C₈ ◁ C₄×C₅×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
10. #13726	C₅	direct (N × H)
58. C₄×C₅	Q₆₄	semidirect
81. C₅	#13726	direct (N × H)
84. C₄	C₅×Q₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Q₆₄	2
C₅×#2247	2
C₄×C₅×C₃₂	2
#13726	5

Subgroups — C5×#13726 #11936446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13726 #11936446