Subgroups — C₅×#328 #64795

Order 320.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#95	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
5	C₂²×C₄×C₅	—	2	1	no	—
6	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₅×C₈	—	2	1	no	—
8	C₅×C₄⋊C₄	—	2	1	no	—
9	C₅×C₄⋊C₄	C₄	1	1	yes	characteristic, complemented
10	C₅×C₂²⋊C₄	—	2	1	no	—
11	#328	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂³×C₅	D₄	1	1	yes	characteristic
13	C₅×Q₈	—	4	1	no	—
14	C₂×C₄×C₅	—	2	2	no	—
15	C₂×C₄×C₅	—	2	1	no	—
16	C₂×C₄×C₅	—	2	1	no	—
17	C₂×C₄×C₅	—	4	1	no	—
18	C₂×C₄×C₅	—	4	1	no	—
19	C₂×C₄×C₅	—	4	1	no	—
20	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₅	D₄	1	1	yes	characteristic
22	C₅×C₈	—	4	1	no	—
23	C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
24	C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
25	#95	C₂×C₅	1	1	yes	characteristic
26	C₂²×C₅	—	2	1	no	—
27	C₂²×C₅	—	2	1	no	—
28	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₅	SD₁₆	1	1	yes	characteristic
30	C₂²×C₅	Q₁₆	1	1	yes	characteristic
31	C₄×C₅	—	2	1	no	—
32	C₄×C₅	—	2	1	no	—
33	C₄×C₅	—	4	2	no	—
34	C₄×C₅	—	4	1	no	—
35	C₄×C₅	—	4	1	no	—
36	C₂×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
37	C₂²×C₄	—	2	1	no	—
38	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
39	C₂×C₈	—	2	1	no	—
40	C₄⋊C₄	—	2	1	no	—
41	C₄⋊C₄	C₄×C₅	1	1	yes	characteristic, complemented
42	C₂²⋊C₄	—	2	1	no	—
43	C₂×C₅	—	2	1	no	—
44	C₂×C₅	—	2	1	no	—
45	C₂×C₅	#99	1	1	yes	characteristic
46	C₂×C₅	#103	1	1	yes	characteristic
47	C₂×C₅	#104	1	1	yes	characteristic
48	C₂³	C₅×D₄	1	1	yes	characteristic
49	Q₈	—	4	1	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	4	1	no	—
55	C₂×C₄	—	4	1	no	—
56	C₂×C₄	C₂×C₄×C₅	1	1	yes	characteristic
57	C₂×C₄	C₅×D₄	1	1	yes	characteristic
58	C₈	—	4	1	no	—
59	C₅	#328	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²	—	2	1	no	—
61	C₂²	—	2	1	no	—
62	C₂²	C₅×C₂²⋊C₄	1	1	yes	characteristic
63	C₂²	C₅×SD₁₆	1	1	yes	characteristic
64	C₂²	C₅×Q₁₆	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	—	2	1	no	—
67	C₄	—	4	2	no	—
68	C₄	—	4	1	no	—
69	C₄	—	4	1	no	—
70	C₂	—	2	1	no	—
71	C₂	—	2	1	no	—
72	C₂	C₅×#99	1	1	yes	characteristic
73	C₂	C₅×#103	1	1	yes	characteristic
74	C₂	C₅×#104	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×Q₈	C₄	semidirect
9. C₅×C₄⋊C₄	C₄	semidirect
11. #328	C₅	direct (N × H)
36. C₂×Q₈	C₄×C₅	semidirect
41. C₄⋊C₄	C₄×C₅	semidirect
59. C₅	#328	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×C₂²⋊Q₈	2
C₅×C₂²⋊C₈	2
C₅×#95	2
#328	5

Subgroups — C5×#328 #64795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#328 #64795