Subgroups — C₅×#7541 #11930261

Order 1280.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃₂	C₂	1	1	yes	maximal, characteristic
2	C₅×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1425	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₁₆	—	2	1	no	—
5	C₅×D₃₂	—	2	1	no	—
6	C₅×D₃₂	C₄	1	2	yes	—
7	C₂×C₅×C₃₂	C₂²	1	1	yes	characteristic
8	C₅×#368	—	2	1	no	—
9	C₅×C₆₄	—	2	1	no	—
10	#7541	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₅×D₈	—	4	1	no	—
12	C₅×D₁₆	—	2	2	no	—
13	C₅×D₁₆	—	4	1	no	—
14	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
15	C₅×#108	—	4	1	no	—
16	C₅×C₃₂	C₂×C₄	1	1	yes	characteristic
17	C₅×C₃₂	D₄	1	1	yes	characteristic
18	C₂×D₃₂	C₂×C₅	1	1	yes	characteristic
19	M₁₂₈	C₂×C₅	1	1	yes	characteristic, complemented
20	#1425	C₂×C₅	1	1	yes	characteristic, complemented
21	C₂×C₅×D₄	—	8	1	no	—
22	C₅×D₈	—	4	2	no	—
23	C₅×D₈	—	8	1	no	—
24	C₅×M₁₆	—	8	1	no	—
25	C₂×C₅×C₈	D₈	1	1	yes	characteristic
26	C₅×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
27	C₅×C₁₆	SD₁₆	1	1	yes	characteristic
28	C₂×D₁₆	—	2	1	no	—
29	D₃₂	—	2	1	no	—
30	D₃₂	C₄×C₅	1	2	yes	—
31	C₂×C₃₂	C₂²×C₅	1	1	yes	characteristic
32	#368	—	2	1	no	—
33	C₆₄	—	2	1	no	—
34	C₂³×C₅	—	16	1	no	—
35	C₅×D₄	—	8	2	no	—
36	C₅×D₄	—	16	1	no	—
37	C₂×C₄×C₅	D₁₆	1	1	yes	characteristic
38	C₅×C₈	—	16	1	no	—
39	C₅×C₈	#102	1	1	yes	characteristic
40	C₅×C₈	SD₃₂	1	1	yes	characteristic
41	C₂×D₈	—	4	1	no	—
42	D₁₆	—	2	2	no	—
43	D₁₆	—	4	1	no	—
44	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
45	#108	—	4	1	no	—
46	C₃₂	C₂×C₄×C₅	1	1	yes	characteristic
47	C₃₂	C₅×D₄	1	1	yes	characteristic
48	C₂²×C₅	—	16	2	no	—
49	C₂²×C₅	—	32	2	no	—
50	C₂²×C₅	SD₆₄	1	1	yes	characteristic
51	C₄×C₅	#357	1	1	yes	characteristic
52	C₄×C₅	D₃₂	1	1	yes	characteristic
53	C₂×D₄	—	8	1	no	—
54	D₈	—	4	2	no	—
55	D₈	—	8	1	no	—
56	M₁₆	—	8	1	no	—
57	C₂×C₈	C₅×D₈	1	1	yes	characteristic
58	C₁₆	C₅×C₂²⋊C₄	1	1	yes	characteristic
59	C₁₆	C₅×SD₁₆	1	1	yes	characteristic
60	C₂×C₅	—	2	1	no	—
61	C₂×C₅	—	32	2	no	—
62	C₂×C₅	#1415	1	1	yes	characteristic
63	C₂³	—	16	1	no	—
64	D₄	—	8	2	no	—
65	D₄	—	16	1	no	—
66	C₂×C₄	C₅×D₁₆	1	1	yes	characteristic
67	C₈	—	16	1	no	—
68	C₈	C₅×#102	1	1	yes	characteristic
69	C₈	C₅×SD₃₂	1	1	yes	characteristic
70	C₅	#7541	1	1	yes	characteristic, direct product factor, Sylow
71	C₂²	—	16	2	no	—
72	C₂²	—	32	2	no	—
73	C₂²	C₅×SD₆₄	1	1	yes	characteristic
74	C₄	C₅×#357	1	1	yes	characteristic
75	C₄	C₅×D₃₂	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	32	2	no	—
78	C₂	C₅×#1415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#1415
commutator	C₃₂	C₂×C₄×C₅
Frattini, cosocle	C₂×C₃₂	C₂²×C₅
prime radical	C₂×C₅×D₃₂	C₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₂×C₅×C₁₆ ◁ C₂×C₅×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×M₁₂₈	C₂	semidirect
3. C₅×#1425	C₂	semidirect
10. #7541	C₅	direct (N × H)
19. M₁₂₈	C₂×C₅	semidirect
20. #1425	C₂×C₅	semidirect
70. C₅	#7541	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃₂	2
C₅×M₁₂₈	2
C₅×#1425	2
#7541	5

Subgroups — C5×#7541 #11930261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7541 #11930261