Subgroups — C₅×#7454 #11930174

Order 1280.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2253	C₂	1	1	yes	maximal, characteristic
2	C₅×#1422	C₂	1	1	yes	maximal, characteristic
3	C₅×#1373	C₂	1	1	yes	maximal, characteristic
4	C₅×#499	—	2	1	no	—
5	C₅×M₆₄	—	2	1	no	—
6	C₅×#367	C₄	1	2	yes	—
7	C₅×#366	—	2	1	no	—
8	C₅×#364	—	2	1	no	—
9	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
10	#7454	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₅×#125	—	4	1	no	—
12	C₅×M₃₂	—	4	1	no	—
13	C₂×C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
14	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
15	C₅×#107	—	2	2	no	—
16	C₅×#106	—	4	1	no	—
17	C₄×C₅×C₈	D₄	1	1	yes	characteristic
18	C₅×C₃₂	—	4	1	no	—
19	#2253	C₂×C₅	1	1	yes	characteristic
20	#1422	C₂×C₅	1	1	yes	characteristic
21	#1373	C₂×C₅	1	1	yes	characteristic
22	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₅×C₈	D₈	1	1	yes	characteristic
24	C₅×C₄⋊C₄	—	4	2	no	—
25	C₅×C₄⋊C₄	—	8	2	no	—
26	C₄²×C₅	SD₁₆	1	1	yes	characteristic
27	C₅×C₁₆	—	2	1	no	—
28	C₅×C₁₆	—	8	1	no	—
29	C₅×C₁₆	SD₁₆	1	1	yes	characteristic
30	C₅×C₁₆	Q₁₆	1	1	yes	characteristic
31	#499	—	2	1	no	—
32	M₆₄	—	2	1	no	—
33	#367	C₄×C₅	1	2	yes	—
34	#366	—	2	1	no	—
35	#364	—	2	1	no	—
36	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
37	C₂×C₄×C₅	—	2	1	no	—
38	C₂×C₄×C₅	—	8	2	no	—
39	C₂×C₄×C₅	#102	1	1	yes	characteristic
40	C₅×C₈	#101	1	1	yes	characteristic
41	C₅×C₈	#103	1	1	yes	characteristic
42	C₅×C₈	SD₃₂	1	1	yes	characteristic
43	C₅×C₈	Q₃₂	1	1	yes	characteristic
44	#125	—	4	1	no	—
45	M₃₂	—	4	1	no	—
46	C₂×C₁₆	C₂×C₄×C₅	1	1	yes	characteristic
47	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
48	#107	—	2	2	no	—
49	#106	—	4	1	no	—
50	C₄×C₈	C₅×D₄	1	1	yes	characteristic
51	C₃₂	—	4	1	no	—
52	C₂²×C₅	#361	1	1	yes	characteristic
53	C₄×C₅	—	4	1	no	—
54	C₄×C₅	—	16	2	no	—
55	C₄×C₅	#332	1	1	yes	characteristic
56	C₄×C₅	#358	1	1	yes	characteristic
57	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₈	C₅×D₈	1	1	yes	characteristic
59	C₄⋊C₄	—	4	2	no	—
60	C₄⋊C₄	—	8	2	no	—
61	C₄²	C₅×SD₁₆	1	1	yes	characteristic
62	C₁₆	—	2	1	no	—
63	C₁₆	—	8	1	no	—
64	C₁₆	C₅×SD₁₆	1	1	yes	characteristic
65	C₁₆	C₅×Q₁₆	1	1	yes	characteristic
66	C₂×C₅	—	2	1	no	—
67	C₂×C₅	#1365	1	1	yes	characteristic
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	8	2	no	—
70	C₂×C₄	C₅×#102	1	1	yes	characteristic
71	C₈	C₅×#101	1	1	yes	characteristic
72	C₈	C₅×#103	1	1	yes	characteristic
73	C₈	C₅×SD₃₂	1	1	yes	characteristic
74	C₈	C₅×Q₃₂	1	1	yes	characteristic
75	C₅	#7454	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²	C₅×#361	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	16	2	no	—
79	C₄	C₅×#332	1	1	yes	characteristic
80	C₄	C₅×#358	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	C₅×#1365	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#1365
commutator	C₂×C₁₆	C₂×C₄×C₅
Frattini, cosocle	C₄×C₁₆	C₂²×C₅
prime radical	C₂²×C₅	#361
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×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. #7454	C₅	direct (N × H)
75. C₅	#7454	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×#2253	2
C₅×#1422	2
C₅×#1373	2
#7454	5

Subgroups — C5×#7454 #11930174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7454 #11930174