Subgroups — C₅×#436 #65599

Order 320.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×M₁₆	C₂	1	2	yes	maximal, complemented
2	C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
3	C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×D₄	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₅	C₂²	1	2	yes	—
8	C₅×M₁₆	—	2	4	no	—
9	C₂×C₅×C₈	C₂²	1	2	yes	—
10	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₅×C₂²⋊C₄	C₄	1	2	yes	—
14	C₄²×C₅	C₂²	1	1	yes	characteristic
15	#436	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂³×C₅	C₂×C₄	1	2	yes	—
17	C₅×D₄	—	2	2	no	—
18	C₂×C₄×C₅	—	2	2	no	—
19	C₂×C₄×C₅	—	2	2	no	—
20	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₅×C₈	—	2	2	no	—
25	C₅×C₈	—	2	1	no	—
26	C₅×C₈	D₄	1	2	yes	complemented
27	C₂×M₁₆	C₂×C₅	1	2	yes	complemented
28	C₄×D₄	C₂×C₅	1	1	yes	characteristic
29	C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
30	C₂²⋊C₈	C₂×C₅	1	2	yes	complemented
31	C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
32	C₂²×C₅	—	2	2	no	—
33	C₂²×C₅	—	2	2	no	—
34	C₂²×C₅	—	2	2	no	—
35	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₅	—	2	2	no	—
37	C₄×C₅	—	2	1	no	—
38	C₄×C₅	M₁₆	1	2	yes	complemented
39	C₄×C₅	C₂×D₄	1	1	yes	characteristic
40	C₄×C₅	#41	1	1	yes	characteristic
41	C₂×D₄	C₄×C₅	1	1	yes	characteristic
42	C₂²×C₄	C₂²×C₅	1	2	yes	—
43	M₁₆	—	2	4	no	—
44	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
45	C₂×C₈	C₂²×C₅	1	2	yes	—
46	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
47	C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
48	C₂²⋊C₄	C₄×C₅	1	2	yes	—
49	C₄²	C₂²×C₅	1	1	yes	characteristic
50	C₂×C₅	—	4	2	no	—
51	C₂×C₅	C₄×D₄	1	1	yes	characteristic
52	C₂×C₅	C₂×M₁₆	1	1	yes	characteristic
53	C₂×C₅	#131	1	1	yes	characteristic
54	C₂³	C₂×C₄×C₅	1	2	yes	—
55	D₄	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	C₂×C₄×C₅	1	1	yes	characteristic
59	C₂×C₄	C₂×C₄×C₅	1	2	yes	—
60	C₂×C₄	C₂×C₄×C₅	1	1	yes	characteristic
61	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
62	C₈	—	2	2	no	—
63	C₈	—	2	1	no	—
64	C₈	C₅×D₄	1	2	yes	complemented
65	C₅	#436	1	1	yes	characteristic, direct product factor, Sylow
66	C₂²	—	2	2	no	—
67	C₂²	—	2	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	C₂²×C₄×C₅	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	2	1	no	—
72	C₄	C₅×M₁₆	1	2	yes	complemented
73	C₄	C₂×C₅×D₄	1	1	yes	characteristic
74	C₄	C₅×#41	1	1	yes	characteristic
75	C₂	—	4	2	no	—
76	C₂	C₄×C₅×D₄	1	1	yes	characteristic
77	C₂	C₂×C₅×M₁₆	1	1	yes	characteristic
78	C₂	C₅×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³
commutator	C₂²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂³×C₅
socle	C₂²×C₅	C₂²×C₄
prime radical	C₂×C₅×D₄	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×M₁₆	C₂	semidirect
3. C₅×C₄⋊C₈	C₂	semidirect
4. C₅×C₂²⋊C₈	C₂	semidirect
5. C₄×C₅×C₈	C₂	semidirect
15. #436	C₅	direct (N × H)
26. C₅×C₈	D₄	semidirect
27. C₂×M₁₆	C₂×C₅	semidirect
29. C₄⋊C₈	C₂×C₅	semidirect
30. C₂²⋊C₈	C₂×C₅	semidirect
31. C₄×C₈	C₂×C₅	semidirect
38. C₄×C₅	M₁₆	semidirect
64. C₈	C₅×D₄	semidirect
65. C₅	#436	direct (N × H)
72. C₄	C₅×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×M₁₆	2
C₄×C₅×D₄	2
C₅×C₄⋊C₈	2
C₅×C₂²⋊C₈	2
C₄×C₅×C₈	2
#436	5

Subgroups — C5×#436 #65599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#436 #65599