Subgroups — C₅×#485 #65648

Order 320.

96 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×#117	C₂	1	1	yes	maximal, characteristic
3	C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₅×C₄⋊C₄	—	2	1	no	—
13	C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₅×C₂²⋊C₄	—	2	1	no	—
17	C₅×C₂²⋊C₄	—	2	1	no	—
18	C₄²×C₅	—	2	1	no	—
19	#485	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂³×C₅	D₄	1	1	yes	characteristic
21	C₅×Q₈	—	2	1	no	—
22	C₅×Q₈	—	2	1	no	—
23	C₂×C₄×C₅	—	2	1	no	—
24	C₂×C₄×C₅	—	2	1	no	—
25	C₂×C₄×C₅	—	2	1	no	—
26	C₂×C₄×C₅	—	2	1	no	—
27	C₂×C₄×C₅	—	2	1	no	—
28	C₂×C₄×C₅	—	2	1	no	—
29	C₂×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₅×C₈	—	2	1	no	—
32	C₅×C₈	—	2	1	no	—
33	C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
34	#117	C₂×C₅	1	1	yes	characteristic
35	#107	C₂×C₅	1	1	yes	characteristic, complemented
36	#106	C₂×C₅	1	1	yes	characteristic, complemented
37	#103	C₂×C₅	1	1	yes	characteristic, complemented
38	#103	C₂×C₅	1	1	yes	characteristic, complemented
39	C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
40	C₂²×C₅	—	2	1	no	—
41	C₂²×C₅	—	2	1	no	—
42	C₂²×C₅	—	2	1	no	—
43	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
44	C₄×C₅	—	2	1	no	—
45	C₄×C₅	—	4	1	no	—
46	C₄×C₅	—	4	1	no	—
47	C₄×C₅	—	4	1	no	—
48	C₄×C₅	—	4	1	no	—
49	C₄×C₅	#41	1	1	yes	characteristic
50	C₄×C₅	#41	1	1	yes	characteristic
51	C₂×Q₈	C₂²×C₅	1	1	yes	characteristic
52	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
53	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
54	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
57	C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
58	C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
59	C₂²⋊C₄	—	2	1	no	—
60	C₂²⋊C₄	—	2	1	no	—
61	C₄²	—	2	1	no	—
62	C₂×C₅	—	4	1	no	—
63	C₂×C₅	#123	1	1	yes	characteristic
64	C₂×C₅	#135	1	1	yes	characteristic
65	C₂×C₅	#137	1	1	yes	characteristic
66	C₂³	C₅×D₄	1	1	yes	characteristic
67	Q₈	—	2	1	no	—
68	Q₈	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	C₅×D₄	1	1	yes	characteristic
76	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₅	#485	1	1	yes	characteristic, direct product factor, Sylow
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	4	1	no	—
89	C₄	C₅×#41	1	1	yes	characteristic
90	C₄	C₅×#41	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	C₅×#123	1	1	yes	characteristic
93	C₂	C₅×#135	1	1	yes	characteristic
94	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	C₂³×C₅	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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
3. C₅×#107	C₂	semidirect
4. C₅×#106	C₂	semidirect
5. C₅×#103	C₂	semidirect
6. C₅×#103	C₂	semidirect
19. #485	C₅	direct (N × H)
35. #107	C₂×C₅	semidirect
36. #106	C₂×C₅	semidirect
37. #103	C₂×C₅	semidirect
38. #103	C₂×C₅	semidirect
79. C₅	#485	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×#117	2
C₅×#107	2
C₅×#106	2
C₅×#103	2
C₅×C₂²⋊C₈	2
#485	5

Subgroups — C5×#485 #65648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#485 #65648