Subgroups — C₂×C₅×#95 #65538

Order 320.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅	C₂	1	3	yes	maximal
2	C₅×#95	C₂	1	4	yes	maximal, direct product factor
3	C₂⁴×C₅	C₂²	1	1	yes	characteristic
4	C₂²×C₄×C₅	—	2	12	no	—
5	C₂²×C₄×C₅	C₄	1	12	yes	complemented
6	C₂²×C₄×C₅	C₂²	1	6	yes	—
7	C₂×#95	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂³×C₅	C₂×C₄	1	6	yes	—
9	C₂³×C₅	D₄	1	6	yes	—
10	C₂³×C₅	Q₈	1	2	yes	—
11	C₂³×C₅	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₅	—	2	24	no	—
13	C₂×C₄×C₅	—	2	12	no	—
14	C₂×C₄×C₅	C₂×C₄	1	12	yes	complemented
15	C₂³×C₄	C₂×C₅	1	3	yes	—
16	#95	C₂×C₅	1	4	yes	direct product factor
17	C₂²×C₅	C₄²	1	4	yes	—
18	C₂²×C₅	C₂²⋊C₄	1	12	yes	—
19	C₂²×C₅	C₄⋊C₄	1	12	yes	—
20	C₂²×C₅	C₂²×C₄	1	3	yes	—
21	C₂²×C₅	C₂×D₄	1	3	yes	—
22	C₂²×C₅	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₅	—	2	12	no	—
24	C₂⁴	C₂²×C₅	1	1	yes	characteristic
25	C₂²×C₄	—	2	12	no	—
26	C₂²×C₄	C₄×C₅	1	12	yes	complemented
27	C₂²×C₄	C₂²×C₅	1	6	yes	—
28	C₂×C₅	#95	1	8	yes	direct product factor
29	C₂×C₅	C₂×C₄²	1	1	yes	characteristic
30	C₂×C₅	C₂×C₂²⋊C₄	1	3	yes	—
31	C₂×C₅	C₂×C₄⋊C₄	1	3	yes	—
32	C₂³	C₂×C₄×C₅	1	6	yes	—
33	C₂³	C₅×D₄	1	6	yes	—
34	C₂³	C₅×Q₈	1	2	yes	—
35	C₂³	C₂³×C₅	1	1	yes	characteristic
36	C₂×C₄	—	2	24	no	—
37	C₂×C₄	—	2	12	no	—
38	C₂×C₄	C₂×C₄×C₅	1	12	yes	complemented
39	C₅	C₂×#95	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²	C₄²×C₅	1	4	yes	—
41	C₂²	C₅×C₂²⋊C₄	1	12	yes	—
42	C₂²	C₅×C₄⋊C₄	1	12	yes	—
43	C₂²	C₂²×C₄×C₅	1	3	yes	—
44	C₂²	C₂×C₅×D₄	1	3	yes	—
45	C₂²	C₂×C₅×Q₈	1	1	yes	characteristic
46	C₄	—	2	12	no	—
47	C₂	C₅×#95	1	8	yes	direct product factor
48	C₂	C₂×C₄²×C₅	1	1	yes	characteristic
49	C₂	C₂×C₅×C₂²⋊C₄	1	3	yes	—
50	C₂	C₂×C₅×C₄⋊C₄	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₅	C₂²
commutator	C₂	C₂×C₄²×C₅
Frattini, cosocle	C₂³	C₂³×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#95	C₂	direct (N × H)
5. C₂²×C₄×C₅	C₄	semidirect
7. C₂×#95	C₅	direct (N × H)
14. C₂×C₄×C₅	C₂×C₄	semidirect
16. #95	C₂×C₅	direct (N × H)
26. C₂²×C₄	C₄×C₅	semidirect
28. C₂×C₅	#95	direct (N × H)
38. C₂×C₄	C₂×C₄×C₅	semidirect
39. C₅	C₂×#95	direct (N × H)
47. C₂	C₅×#95	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₄×C₅	2
C₅×#95	2
C₂×#95	5

Subgroups — C2×C5×#95 #65538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#95 #65538