Subgroups — C₅×#495 #65658

Order 320.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#124	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×Q₈	C₂²	1	2	yes	—
7	C₂×C₅×D₄	C₂²	1	2	yes	—
8	C₅×Q₁₆	—	2	2	no	—
9	C₅×SD₁₆	—	2	4	no	—
10	C₅×D₈	—	2	2	no	—
11	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×C₂²⋊C₄	—	2	4	no	—
14	C₄²×C₅	C₂²	1	1	yes	characteristic
15	#495	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂³×C₅	—	2	2	no	—
17	C₅×Q₈	—	2	2	no	—
18	C₅×Q₈	—	2	2	no	—
19	C₅×D₄	—	2	2	no	—
20	C₅×D₄	—	2	2	no	—
21	C₂×C₄×C₅	—	2	2	no	—
22	C₂×C₄×C₅	D₄	1	2	yes	—
23	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₅×C₈	D₄	1	2	yes	—
25	C₅×C₈	D₄	1	2	yes	—
26	C₂×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
27	C₂×SD₁₆	C₂×C₅	1	2	yes	complemented
28	C₂×D₈	C₂×C₅	1	1	yes	characteristic
29	#124	C₂×C₅	1	2	yes	complemented
30	C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
31	C₂²×C₅	—	4	2	no	—
32	C₂²×C₅	—	4	4	no	—
33	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
34	C₄×C₅	—	2	2	no	—
35	C₄×C₅	—	4	2	no	—
36	C₄×C₅	C₂×D₄	1	1	yes	characteristic
37	C₄×C₅	C₂×D₄	1	1	yes	characteristic
38	C₂×Q₈	C₂²×C₅	1	2	yes	—
39	C₂×D₄	C₂²×C₅	1	2	yes	—
40	Q₁₆	—	2	2	no	—
41	SD₁₆	—	2	4	no	—
42	D₈	—	2	2	no	—
43	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
44	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
45	C₂²⋊C₄	—	2	4	no	—
46	C₄²	C₂²×C₅	1	1	yes	characteristic
47	C₂×C₅	—	8	2	no	—
48	C₂×C₅	#127	1	1	yes	characteristic
49	C₂×C₅	#135	1	2	yes	—
50	C₂³	—	2	2	no	—
51	Q₈	—	2	2	no	—
52	Q₈	—	2	2	no	—
53	D₄	—	2	2	no	—
54	D₄	—	2	2	no	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	C₅×D₄	1	2	yes	—
57	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
58	C₈	C₅×D₄	1	2	yes	—
59	C₈	C₅×D₄	1	2	yes	—
60	C₅	#495	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²	—	4	2	no	—
62	C₂²	—	4	4	no	—
63	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	4	2	no	—
66	C₄	C₂×C₅×D₄	1	1	yes	characteristic
67	C₄	C₂×C₅×D₄	1	1	yes	characteristic
68	C₂	—	8	2	no	—
69	C₂	C₅×#127	1	1	yes	characteristic
70	C₂	C₅×#135	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅
prime radical	C₂×C₅×D₈	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₁₆	C₂	semidirect
2. C₂×C₅×SD₁₆	C₂	semidirect
4. C₅×#124	C₂	semidirect
5. C₄×C₅×C₈	C₂	semidirect
15. #495	C₅	direct (N × H)
26. C₂×Q₁₆	C₂×C₅	semidirect
27. C₂×SD₁₆	C₂×C₅	semidirect
29. #124	C₂×C₅	semidirect
30. C₄×C₈	C₂×C₅	semidirect
60. C₅	#495	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×Q₁₆	2
C₂×C₅×SD₁₆	2
C₂×C₅×D₈	2
C₅×#124	2
C₄×C₅×C₈	2
#495	5

Subgroups — C5×#495 #65658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#495 #65658