Subgroups — C₅×#7513 #11930233

Order 1280.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₅×M₁₂₈	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×C₁₆	C₄	1	1	yes	characteristic
4	C₅×M₆₄	—	2	2	no	—
5	C₂×C₅×C₃₂	C₄	1	1	yes	characteristic
6	C₂×C₅×C₃₂	C₂²	1	1	yes	characteristic
7	C₅×C₆₄	—	2	2	no	—
8	#7513	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂²×C₅×C₈	C₈	1	1	yes	characteristic
10	C₂×C₅×C₁₆	—	2	1	no	—
11	C₂×C₅×C₁₆	—	2	1	no	—
12	C₂×C₅×C₁₆	C₈	1	1	yes	characteristic
13	C₂×C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
14	C₅×C₃₂	—	2	1	no	—
15	C₅×C₃₂	D₄	1	2	yes	—
16	C₂×M₆₄	C₂×C₅	1	1	yes	characteristic
17	M₁₂₈	C₂×C₅	1	2	yes	complemented
18	C₂²×C₄×C₅	C₁₆	1	1	yes	characteristic
19	C₂×C₅×C₈	—	2	1	no	—
20	C₂×C₅×C₈	—	2	1	no	—
21	C₂×C₅×C₈	C₁₆	1	1	yes	characteristic
22	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
23	C₅×C₁₆	—	2	1	no	—
24	C₅×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
25	C₅×C₁₆	M₁₆	1	1	yes	characteristic
26	C₂²×C₁₆	C₄×C₅	1	1	yes	characteristic
27	M₆₄	—	2	2	no	—
28	C₂×C₃₂	C₄×C₅	1	1	yes	characteristic
29	C₂×C₃₂	C₂²×C₅	1	1	yes	characteristic
30	C₆₄	—	2	2	no	—
31	C₂³×C₅	C₃₂	1	1	yes	characteristic
32	C₂×C₄×C₅	—	2	1	no	—
33	C₂×C₄×C₅	—	2	1	no	—
34	C₂×C₄×C₅	C₃₂	1	1	yes	characteristic
35	C₂×C₄×C₅	C₂×C₁₆	1	1	yes	characteristic
36	C₅×C₈	—	2	1	no	—
37	C₅×C₈	C₂²⋊C₈	1	1	yes	characteristic
38	C₅×C₈	M₃₂	1	1	yes	characteristic
39	C₂²×C₈	C₅×C₈	1	1	yes	characteristic
40	C₂×C₁₆	—	2	1	no	—
41	C₂×C₁₆	—	2	1	no	—
42	C₂×C₁₆	C₅×C₈	1	1	yes	characteristic
43	C₂×C₁₆	C₂×C₄×C₅	1	1	yes	characteristic
44	C₃₂	—	2	1	no	—
45	C₃₂	C₅×D₄	1	2	yes	—
46	C₂²×C₅	—	2	1	no	—
47	C₂²×C₅	—	4	1	no	—
48	C₂²×C₅	C₂×C₃₂	1	1	yes	characteristic
49	C₄×C₅	—	2	1	no	—
50	C₄×C₅	C₂²⋊C₁₆	1	1	yes	characteristic
51	C₄×C₅	M₆₄	1	1	yes	characteristic
52	C₂²×C₄	C₅×C₁₆	1	1	yes	characteristic
53	C₂×C₈	—	2	1	no	—
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₅×C₁₆	1	1	yes	characteristic
56	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	C₅×C₂²⋊C₄	1	1	yes	characteristic
59	C₁₆	C₅×M₁₆	1	1	yes	characteristic
60	C₂×C₅	—	2	1	no	—
61	C₂×C₅	—	4	1	no	—
62	C₂×C₅	C₂²⋊C₃₂	1	1	yes	characteristic
63	C₂³	C₅×C₃₂	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₅×C₃₂	1	1	yes	characteristic
67	C₂×C₄	C₂×C₅×C₁₆	1	1	yes	characteristic
68	C₈	—	2	1	no	—
69	C₈	C₅×C₂²⋊C₈	1	1	yes	characteristic
70	C₈	C₅×M₃₂	1	1	yes	characteristic
71	C₅	#7513	1	1	yes	characteristic, direct product factor, Sylow
72	C₂²	—	2	1	no	—
73	C₂²	—	4	1	no	—
74	C₂²	C₂×C₅×C₃₂	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	C₅×C₂²⋊C₁₆	1	1	yes	characteristic
77	C₄	C₅×M₆₄	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	4	1	no	—
80	C₂	C₅×C₂²⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₅×C₁₆	C₂²⋊C₄
commutator	C₂²	C₂×C₅×C₃₂
Frattini, cosocle	C₂×C₃₂	C₂²×C₅
socle	C₂×C₅	C₂²⋊C₃₂
prime radical	C₂³×C₅	C₃₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ 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
8. #7513	C₅	direct (N × H)
17. M₁₂₈	C₂×C₅	semidirect
71. C₅	#7513	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×M₆₄	2
C₅×M₁₂₈	2
#7513	5

Subgroups — C5×#7513 #11930233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7513 #11930233