Subgroups — C₅×#489 #65652

Order 320.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#124	C₂	1	1	yes	maximal, characteristic
3	C₅×#103	C₂	1	2	yes	maximal, complemented
4	C₅×#102	C₂	1	2	yes	maximal
5	C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×Q₈	—	2	1	no	—
7	C₂×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₂×C₅×C₈	C₂²	1	2	yes	—
10	C₅×C₄⋊C₄	—	2	1	no	—
11	C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₅×C₂²⋊C₄	—	2	1	no	—
13	C₅×C₂²⋊C₄	—	2	1	no	—
14	C₄²×C₅	C₂²	1	1	yes	characteristic
15	#489	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂³×C₅	—	2	1	no	—
17	C₅×Q₈	—	2	2	no	—
18	C₅×Q₈	—	4	2	no	—
19	C₅×D₄	—	2	2	no	—
20	C₂×C₄×C₅	—	2	1	no	—
21	C₂×C₄×C₅	—	2	2	no	—
22	C₂×C₄×C₅	D₄	1	1	yes	characteristic
23	C₂×C₄×C₅	D₄	1	1	yes	characteristic
24	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₅×C₈	—	2	2	no	—
26	C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
27	#124	C₂×C₅	1	1	yes	characteristic
28	#103	C₂×C₅	1	2	yes	complemented
29	#102	C₂×C₅	1	2	yes	—
30	#97	C₂×C₅	1	1	yes	characteristic, complemented
31	C₂²×C₅	—	4	1	no	—
32	C₂²×C₅	—	4	1	no	—
33	C₂²×C₅	—	4	1	no	—
34	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
35	C₄×C₅	—	2	1	no	—
36	C₄×C₅	—	2	1	no	—
37	C₄×C₅	—	4	1	no	—
38	C₄×C₅	—	4	2	no	—
39	C₄×C₅	#41	1	2	yes	—
40	C₂×Q₈	—	2	1	no	—
41	C₂×Q₈	C₂²×C₅	1	1	yes	characteristic
42	C₂×D₄	C₂²×C₅	1	1	yes	characteristic
43	C₂×C₈	C₂²×C₅	1	2	yes	—
44	C₄⋊C₄	—	2	1	no	—
45	C₄⋊C₄	C₂²×C₅	1	2	yes	—
46	C₂²⋊C₄	—	2	1	no	—
47	C₂²⋊C₄	—	2	1	no	—
48	C₄²	C₂²×C₅	1	1	yes	characteristic
49	C₂×C₅	—	8	1	no	—
50	C₂×C₅	#124	1	1	yes	characteristic
51	C₂×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
52	C₂×C₅	#137	1	1	yes	characteristic
53	C₂³	—	2	1	no	—
54	Q₈	—	2	2	no	—
55	Q₈	—	4	2	no	—
56	D₄	—	2	2	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	C₅×D₄	1	1	yes	characteristic
60	C₂×C₄	C₅×D₄	1	1	yes	characteristic
61	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
62	C₈	—	2	2	no	—
63	C₅	#489	1	1	yes	characteristic, direct product factor, Sylow
64	C₂²	—	4	1	no	—
65	C₂²	—	4	1	no	—
66	C₂²	—	4	1	no	—
67	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	2	1	no	—
70	C₄	—	4	1	no	—
71	C₄	—	4	2	no	—
72	C₄	C₅×#41	1	2	yes	—
73	C₂	—	8	1	no	—
74	C₂	C₅×#124	1	1	yes	characteristic
75	C₂	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
76	C₂	C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅
prime radical	C₂×C₅×D₄	C₂²
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. C₅×C₄⋊Q₈	C₂	semidirect
3. C₅×#103	C₂	semidirect
5. C₅×#97	C₂	semidirect
15. #489	C₅	direct (N × H)
26. C₄⋊Q₈	C₂×C₅	semidirect
28. #103	C₂×C₅	semidirect
30. #97	C₂×C₅	semidirect
63. C₅	#489	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×C₄⋊Q₈	2
C₅×#124	2
C₅×#103	2
C₅×#102	2
C₅×#97	2
#489	5

Subgroups — C5×#489 #65652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#489 #65652