Subgroups — C₂×C₅×#100 #65574

Order 320.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×M₁₆	C₂	1	2	yes	maximal, complemented
3	C₅×#100	C₂	1	4	yes	maximal, direct product factor
4	C₂⁴×C₅	C₄	1	2	yes	—
5	C₂×C₅×D₄	—	2	2	no	—
6	C₂×C₅×D₄	—	2	2	no	—
7	C₂×C₅×D₄	C₄	1	2	yes	—
8	C₂×C₅×D₄	C₂²	1	2	yes	—
9	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₅×M₁₆	—	2	2	no	—
11	C₅×M₁₆	C₂²	1	4	yes	complemented
12	C₂×C₅×C₈	—	2	2	no	—
13	C₂×#100	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂³×C₅	—	2	2	no	—
15	C₂³×C₅	—	2	2	no	—
16	C₂³×C₅	—	4	4	no	—
17	C₂³×C₅	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₅	C₂×C₄	1	4	yes	—
19	C₅×D₄	—	2	4	no	—
20	C₅×D₄	—	2	4	no	—
21	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₅	D₄	1	2	yes	—
23	C₂×C₄×C₅	D₄	1	2	yes	—
24	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₅×C₈	—	2	4	no	—
26	C₂²×D₄	C₂×C₅	1	1	yes	characteristic
27	C₂×M₁₆	C₂×C₅	1	2	yes	complemented
28	#100	C₂×C₅	1	4	yes	direct product factor
29	C₂²×C₅	—	2	2	no	—
30	C₂²×C₅	—	2	4	no	—
31	C₂²×C₅	—	4	4	no	—
32	C₂²×C₅	—	4	4	no	—
33	C₂²×C₅	—	4	4	no	—
34	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₅	C₂²⋊C₄	1	2	yes	—
38	C₄×C₅	C₂×D₄	1	2	yes	—
39	C₂⁴	C₄×C₅	1	2	yes	—
40	C₂×D₄	—	2	2	no	—
41	C₂×D₄	—	2	2	no	—
42	C₂×D₄	C₄×C₅	1	2	yes	—
43	C₂×D₄	C₂²×C₅	1	2	yes	—
44	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
45	M₁₆	—	2	2	no	—
46	M₁₆	C₂²×C₅	1	4	yes	complemented
47	C₂×C₈	—	2	2	no	—
48	C₂×C₅	—	2	1	no	—
49	C₂×C₅	—	2	1	no	—
50	C₂×C₅	—	4	4	no	—
51	C₂×C₅	#100	1	2	yes	direct product factor
52	C₂×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂³	—	2	2	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	4	4	no	—
56	C₂³	C₂×C₄×C₅	1	1	yes	characteristic
57	C₂³	C₂×C₄×C₅	1	4	yes	—
58	D₄	—	2	4	no	—
59	D₄	—	2	4	no	—
60	C₂×C₄	C₂×C₄×C₅	1	1	yes	characteristic
61	C₂×C₄	C₅×D₄	1	2	yes	—
62	C₂×C₄	C₅×D₄	1	2	yes	—
63	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
64	C₈	—	2	4	no	—
65	C₅	C₂×#100	1	1	yes	characteristic, direct product factor, Sylow
66	C₂²	—	2	2	no	—
67	C₂²	—	2	4	no	—
68	C₂²	—	4	4	no	—
69	C₂²	—	4	4	no	—
70	C₂²	—	4	4	no	—
71	C₂²	C₅×C₂²⋊C₄	1	1	yes	characteristic
72	C₂²	C₅×C₂²⋊C₄	1	1	yes	characteristic
73	C₂²	C₂²×C₄×C₅	1	1	yes	characteristic
74	C₄	C₅×C₂²⋊C₄	1	2	yes	—
75	C₄	C₂×C₅×D₄	1	2	yes	—
76	C₂	—	2	1	no	—
77	C₂	—	2	1	no	—
78	C₂	—	4	4	no	—
79	C₂	C₅×#100	1	2	yes	direct product factor
80	C₂	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²⋊C₄
commutator	C₂²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂³×C₅
prime radical	C₂²×C₅×D₄	C₂
LCS	G ▷ C₂² ▷ 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
2. C₂×C₅×M₁₆	C₂	semidirect
3. C₅×#100	C₂	direct (N × H)
11. C₅×M₁₆	C₂²	semidirect
13. C₂×#100	C₅	direct (N × H)
27. C₂×M₁₆	C₂×C₅	semidirect
28. #100	C₂×C₅	direct (N × H)
46. M₁₆	C₂²×C₅	semidirect
51. C₂×C₅	#100	direct (N × H)
65. C₅	C₂×#100	direct (N × H)
79. C₂	C₅×#100	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₄	2
C₂×C₅×M₁₆	2
C₅×#100	2
C₂×#100	5

Subgroups — C2×C5×#100 #65574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#100 #65574