Subgroups — C₅×#362 #64829

Order 320.

54 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
2	C₅×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₅×#108	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Q₈	—	2	1	no	—
5	C₅×Q₁₆	—	2	1	no	—
6	C₅×Q₁₆	C₄	1	2	yes	—
7	C₅×M₁₆	—	2	1	no	—
8	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₅×C₁₆	—	2	1	no	—
10	#362	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₅×Q₈	—	2	2	no	—
12	C₅×Q₈	—	4	1	no	—
13	C₂×C₄×C₅	—	4	1	no	—
14	C₂×C₄×C₅	D₄	1	1	yes	characteristic
15	C₅×C₈	—	4	1	no	—
16	C₅×C₈	C₂×C₄	1	1	yes	characteristic
17	C₅×C₈	D₄	1	1	yes	characteristic
18	C₂×Q₁₆	C₂×C₅	1	1	yes	characteristic
19	M₃₂	C₂×C₅	1	1	yes	characteristic
20	#108	C₂×C₅	1	1	yes	characteristic
21	C₂²×C₅	SD₁₆	1	1	yes	characteristic
22	C₄×C₅	—	4	2	no	—
23	C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
24	C₄×C₅	D₈	1	1	yes	characteristic
25	C₂×Q₈	—	2	1	no	—
26	Q₁₆	—	2	1	no	—
27	Q₁₆	C₄×C₅	1	2	yes	—
28	M₁₆	—	2	1	no	—
29	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
30	C₁₆	—	2	1	no	—
31	C₂×C₅	—	2	1	no	—
32	C₂×C₅	#102	1	1	yes	characteristic
33	Q₈	—	2	2	no	—
34	Q₈	—	4	1	no	—
35	C₂×C₄	—	4	1	no	—
36	C₂×C₄	C₅×D₄	1	1	yes	characteristic
37	C₈	—	4	1	no	—
38	C₈	C₂×C₄×C₅	1	1	yes	characteristic
39	C₈	C₅×D₄	1	1	yes	characteristic
40	C₅	#362	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²	C₅×SD₁₆	1	1	yes	characteristic
42	C₄	—	4	2	no	—
43	C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
44	C₄	C₅×D₈	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	C₅×#102	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#102
commutator	C₈	C₂×C₄×C₅
Frattini, cosocle	C₂×C₈	C₂²×C₅
prime radical	C₂²×C₅	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
10. #362	C₅	direct (N × H)
40. C₅	#362	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
C₅×M₃₂	2
C₅×#108	2
#362	5

Subgroups — C5×#362 #64829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#362 #64829