Subgroups — C₅×#408 #65571

Order 320.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₂²⋊C₈	C₂	1	4	yes	maximal, complemented
5	C₅×#41	—	2	2	no	—
6	C₅×#41	—	2	2	no	—
7	C₂×C₅×Q₈	C₄	1	1	yes	characteristic
8	C₂×C₅×D₄	C₄	1	2	yes	—
9	C₂×C₅×D₄	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₅	C₂²	1	2	yes	—
11	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₅×M₁₆	—	2	2	no	—
13	C₂×C₅×C₈	—	2	2	no	—
14	C₂×C₅×C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₈	C₂²	1	2	yes	—
16	#408	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₅	C₂×C₄	1	2	yes	—
18	C₂³×C₅	C₂×C₄	1	1	yes	characteristic
19	C₅×Q₈	—	2	2	no	—
20	C₅×D₄	—	2	4	no	—
21	C₅×D₄	—	2	2	no	—
22	C₂×C₄×C₅	—	2	2	no	—
23	C₂×C₄×C₅	—	2	2	no	—
24	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×C₅	D₄	1	2	yes	—
27	C₂×C₄×C₅	D₄	1	2	yes	—
28	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₅×C₈	—	2	2	no	—
30	C₅×C₈	—	2	2	no	—
31	C₂×#41	C₂×C₅	1	1	yes	characteristic
32	C₂×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
33	C₂²×C₈	C₂×C₅	1	1	yes	characteristic, complemented
34	C₂²⋊C₈	C₂×C₅	1	4	yes	complemented
35	C₂²×C₅	—	2	2	no	—
36	C₂²×C₅	—	2	2	no	—
37	C₂²×C₅	—	2	4	no	—
38	C₂²×C₅	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
40	C₄×C₅	—	2	2	no	—
41	C₄×C₅	C₂²⋊C₄	1	2	yes	—
42	C₄×C₅	C₂×D₄	1	1	yes	characteristic
43	C₄×C₅	C₂×D₄	1	1	yes	characteristic
44	#41	—	2	2	no	—
45	#41	—	2	2	no	—
46	C₂×Q₈	C₄×C₅	1	1	yes	characteristic
47	C₂×D₄	C₄×C₅	1	2	yes	—
48	C₂×D₄	C₄×C₅	1	1	yes	characteristic
49	C₂²×C₄	C₂²×C₅	1	2	yes	—
50	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
51	M₁₆	—	2	2	no	—
52	C₂×C₈	—	2	2	no	—
53	C₂×C₈	C₂²×C₅	1	2	yes	—
54	C₂×C₈	C₂²×C₅	1	2	yes	—
55	C₂×C₅	—	2	2	no	—
56	C₂×C₅	—	4	2	no	—
57	C₂×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₅	#131	1	2	yes	—
59	C₂³	C₂×C₄×C₅	1	2	yes	—
60	C₂³	C₂×C₄×C₅	1	1	yes	characteristic
61	Q₈	—	2	2	no	—
62	D₄	—	2	4	no	—
63	D₄	—	2	2	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	C₂×C₄×C₅	1	2	yes	—
67	C₂×C₄	C₂×C₄×C₅	1	1	yes	characteristic
68	C₂×C₄	C₅×D₄	1	2	yes	—
69	C₂×C₄	C₅×D₄	1	2	yes	—
70	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₈	—	2	2	no	—
73	C₅	#408	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	2	2	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	2	4	no	—
77	C₂²	C₅×C₂²⋊C₄	1	2	yes	—
78	C₂²	C₂²×C₄×C₅	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	C₅×C₂²⋊C₄	1	2	yes	—
81	C₄	C₂×C₅×D₄	1	1	yes	characteristic
82	C₄	C₂×C₅×D₄	1	1	yes	characteristic
83	C₂	—	2	2	no	—
84	C₂	—	4	2	no	—
85	C₂	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
86	C₂	C₅×#131	1	2	yes	—

	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×#41	C₂
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
2. C₂×C₅×M₁₆	C₂	semidirect
3. C₂²×C₅×C₈	C₂	semidirect
4. C₅×C₂²⋊C₈	C₂	semidirect
16. #408	C₅	direct (N × H)
32. C₂×M₁₆	C₂×C₅	semidirect
33. C₂²×C₈	C₂×C₅	semidirect
34. C₂²⋊C₈	C₂×C₅	semidirect
73. C₅	#408	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×#41	2
C₂×C₅×M₁₆	2
C₂²×C₅×C₈	2
C₅×C₂²⋊C₈	2
#408	5

Subgroups — C5×#408 #65571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#408 #65571