Subgroups — C₂×#4036 #65833

Order 320.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₅	C₂	1	2	yes	maximal
3	C₂×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×#683	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
6	#4036	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×C₅	C₂²	1	2	yes	—
8	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×Dic₅	C₂²	1	1	yes	characteristic
10	C₂²×Dic₅	C₂²	1	1	yes	characteristic
11	C₂²×Dic₅	C₂²	1	2	yes	—
12	C₅×C₄⋊C₄	C₂²	1	4	yes	—
13	C₄⋊Dic₅	C₂²	1	8	yes	—
14	C₄⋊Dic₅	C₂²	1	4	yes	—
15	#683	C₂²	1	8	yes	—
16	C₄×Dic₅	C₂²	1	4	yes	—
17	C₂×#125	—	5	1	no	maximal, Sylow
18	C₂³×C₅	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₅	—	2	4	no	—
20	C₂×C₄×C₅	Q₈	1	4	yes	—
21	C₂×C₄×C₅	C₂³	1	4	yes	—
22	C₂×C₄×C₅	C₂³	1	2	yes	—
23	C₂×Dic₅	—	2	2	no	—
24	C₂×Dic₅	—	2	2	no	—
25	C₂×Dic₅	—	2	4	no	—
26	C₂×Dic₅	C₂³	1	2	yes	—
27	C₂×Dic₅	C₂³	1	2	yes	—
28	C₂×Dic₅	C₂³	1	4	yes	—
29	#125	—	5	8	no	—
30	C₂×C₄⋊C₄	—	5	2	no	—
31	C₂×C₄⋊C₄	—	5	2	no	—
32	C₂×C₄⋊C₄	—	5	1	no	—
33	C₂×C₄⋊C₄	D₅	1	1	yes	characteristic
34	C₂×C₄²	—	5	1	no	—
35	C₂²×C₅	C₂×Q₈	1	2	yes	—
36	C₂²×C₅	#41	1	2	yes	—
37	C₂²×C₅	#41	1	2	yes	—
38	C₂²×C₅	C₂⁴	1	1	yes	characteristic
39	C₄×C₅	—	2	4	no	—
40	C₄×C₅	C₂×Q₈	1	4	yes	—
41	Dic₅	—	2	2	no	—
42	Dic₅	—	2	2	no	—
43	Dic₅	—	2	4	no	—
44	C₂²×C₄	—	5	1	no	—
45	C₂²×C₄	—	5	1	no	—
46	C₂²×C₄	—	5	2	no	—
47	C₂²×C₄	C₂×D₅	1	2	yes	—
48	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
49	C₄⋊C₄	—	5	8	no	—
50	C₄⋊C₄	—	5	8	no	—
51	C₄⋊C₄	—	5	4	no	—
52	C₄⋊C₄	C₂×D₅	1	4	yes	—
53	C₄²	—	5	4	no	—
54	C₂×C₅	#125	1	4	yes	complemented
55	C₂×C₅	C₂²×Q₈	1	1	yes	characteristic
56	C₂×C₅	C₂×#41	1	1	yes	characteristic
57	C₂×C₅	C₂×#41	1	1	yes	characteristic
58	C₂³	C₂²×D₅	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	—	5	2	no	—
61	C₂×C₄	—	5	2	no	—
62	C₂×C₄	—	5	4	no	—
63	C₂×C₄	—	10	2	no	—
64	C₂×C₄	—	10	2	no	—
65	C₂×C₄	—	10	4	no	—
66	C₂×C₄	Dic₁₀	1	4	yes	—
67	C₂×C₄	C₂²×D₅	1	4	yes	—
68	C₂×C₄	C₂²×D₅	1	2	yes	—
69	C₅	C₂×#125	1	1	yes	characteristic, complemented, Sylow
70	C₂²	C₂×Dic₁₀	1	2	yes	—
71	C₂²	#711	1	2	yes	—
72	C₂²	#713	1	2	yes	—
73	C₂²	C₂³×D₅	1	1	yes	characteristic
74	C₄	—	2	4	no	—
75	C₄	—	10	2	no	—
76	C₄	—	10	2	no	—
77	C₄	—	10	4	no	—
78	C₄	C₂×Dic₁₀	1	4	yes	—
79	C₂	#4036	1	4	yes	direct product factor
80	C₂	C₂²×Dic₁₀	1	1	yes	characteristic
81	C₂	C₂×#711	1	1	yes	characteristic
82	C₂	C₂×#713	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂⁴
Frattini	C₂²	C₂³×D₅
Fitting	C₂×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₅	C₂³
hypercenter	C₂×C₄⋊C₄	D₅
hypocenter	C₅	C₂×#125
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #4036	C₂	direct (N × H)
54. C₂×C₅	#125	semidirect
69. C₅	C₂×#125	semidirect
79. C₂	#4036	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×C₄⋊C₄	2
C₂×C₄⋊Dic₅	2
C₂×#683	2
C₂×C₄×Dic₅	2
#4036	2
C₂×#125	5

Subgroups — C2×#4036 #65833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4036 #65833