Subgroups — C₂×C₅×#101 #65575

Order 320.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×M₁₆	C₂	1	2	yes	maximal
3	C₅×#101	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×Q₈	—	2	2	no	—
5	C₂×C₅×Q₈	—	2	2	no	—
6	C₂×C₅×Q₈	C₄	1	2	yes	—
7	C₂×C₅×Q₈	C₂²	1	2	yes	—
8	C₂²×C₄×C₅	C₄	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	—
12	C₂×C₅×C₈	—	2	2	no	—
13	C₂×#101	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂³×C₅	C₂×C₄	1	1	yes	characteristic
15	C₅×Q₈	—	2	4	no	—
16	C₅×Q₈	—	2	4	no	—
17	C₂×C₄×C₅	—	2	2	no	—
18	C₂×C₄×C₅	—	2	2	no	—
19	C₂×C₄×C₅	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₅	D₄	1	2	yes	—
22	C₂×C₄×C₅	D₄	1	2	yes	—
23	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₅×C₈	—	2	4	no	—
25	C₂²×Q₈	C₂×C₅	1	1	yes	characteristic
26	C₂×M₁₆	C₂×C₅	1	2	yes	—
27	#101	C₂×C₅	1	4	yes	direct product factor
28	C₂²×C₅	—	2	2	no	—
29	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₅	—	2	4	no	—
33	C₄×C₅	C₂²⋊C₄	1	2	yes	—
34	C₄×C₅	C₂×D₄	1	2	yes	—
35	C₂×Q₈	—	2	2	no	—
36	C₂×Q₈	—	2	2	no	—
37	C₂×Q₈	C₄×C₅	1	2	yes	—
38	C₂×Q₈	C₂²×C₅	1	2	yes	—
39	C₂²×C₄	C₄×C₅	1	2	yes	—
40	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
41	M₁₆	—	2	2	no	—
42	M₁₆	C₂²×C₅	1	4	yes	—
43	C₂×C₈	—	2	2	no	—
44	C₂×C₅	—	2	1	no	—
45	C₂×C₅	—	2	1	no	—
46	C₂×C₅	#101	1	2	yes	direct product factor
47	C₂×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₂³	C₂×C₄×C₅	1	1	yes	characteristic
49	Q₈	—	2	4	no	—
50	Q₈	—	2	4	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	C₂×C₄×C₅	1	4	yes	—
54	C₂×C₄	C₂×C₄×C₅	1	1	yes	characteristic
55	C₂×C₄	C₅×D₄	1	2	yes	—
56	C₂×C₄	C₅×D₄	1	2	yes	—
57	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
58	C₈	—	2	4	no	—
59	C₅	C₂×#101	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²	—	2	2	no	—
61	C₂²	C₅×C₂²⋊C₄	1	1	yes	characteristic
62	C₂²	C₅×C₂²⋊C₄	1	1	yes	characteristic
63	C₂²	C₂²×C₄×C₅	1	1	yes	characteristic
64	C₄	—	2	4	no	—
65	C₄	C₅×C₂²⋊C₄	1	2	yes	—
66	C₄	C₂×C₅×D₄	1	2	yes	—
67	C₂	—	2	1	no	—
68	C₂	—	2	1	no	—
69	C₂	C₅×#101	1	2	yes	direct product factor
70	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	C₂³×C₅	C₂×C₄
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
3. C₅×#101	C₂	direct (N × H)
13. C₂×#101	C₅	direct (N × H)
27. #101	C₂×C₅	direct (N × H)
46. C₂×C₅	#101	direct (N × H)
59. C₅	C₂×#101	direct (N × H)
69. C₂	C₅×#101	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×Q₈	2
C₂×C₅×M₁₆	2
C₅×#101	2
C₂×#101	5

Subgroups — C2×C5×#101 #65575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#101 #65575