Subgroups — #65177

Order 320.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4043	C₂	1	1	yes	maximal, characteristic
2	#4038	C₂	1	1	yes	maximal, characteristic
3	C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#3952	C₂	1	1	yes	maximal, characteristic
5	#3948	C₂	1	1	yes	maximal, characteristic, complemented
6	#3942	C₂	1	1	yes	maximal, characteristic, complemented
7	#3940	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₀	C₂²	1	1	yes	characteristic
10	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	#685	—	2	1	no	—
14	#685	—	2	1	no	—
15	C₄⋊Dic₅	—	2	1	no	—
16	C₄⋊Dic₅	C₂²	1	1	yes	characteristic
17	C₄×Dic₅	—	2	1	no	—
18	C₂×#168	C₂²	1	1	yes	characteristic
19	#485	—	5	1	no	maximal, Sylow
20	C₂²×D₅	D₄	1	1	yes	characteristic
21	C₂×C₄×C₅	—	2	1	no	—
22	C₂×C₄×C₅	—	2	1	no	—
23	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₂×Dic₅	—	2	1	no	—
25	C₂×Dic₅	—	2	1	no	—
26	C₂×Dic₅	D₄	1	1	yes	characteristic
27	C₄×D₅	—	2	1	no	—
28	C₄×D₅	—	2	1	no	—
29	Dic₁₀	—	2	1	no	—
30	Dic₁₀	—	2	1	no	—
31	C₅×C₈	—	2	1	no	—
32	#168	—	2	1	no	—
33	C₂²⋊Q₈	—	5	1	no	—
34	#117	—	5	1	no	—
35	#107	D₅	1	1	yes	characteristic, complemented
36	#106	—	5	1	no	—
37	#103	—	5	1	no	—
38	#103	—	5	1	no	—
39	C₂²⋊C₈	—	5	1	no	—
40	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
41	C₂×D₅	—	2	1	no	—
42	C₂×D₅	—	2	1	no	—
43	C₂×D₅	—	2	1	no	—
44	C₄×C₅	—	4	1	no	—
45	C₄×C₅	—	4	1	no	—
46	C₄×C₅	#41	1	1	yes	characteristic
47	C₄×C₅	#41	1	1	yes	characteristic
48	Dic₅	—	2	1	no	—
49	Dic₅	—	4	1	no	—
50	Dic₅	—	4	1	no	—
51	C₂×Q₈	—	5	1	no	—
52	C₂²×C₄	—	5	1	no	—
53	C₂×C₈	—	5	1	no	—
54	C₂×C₈	C₂×D₅	1	1	yes	characteristic
55	C₄⋊C₄	—	5	1	no	—
56	C₄⋊C₄	—	10	1	no	—
57	C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
58	C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
59	C₂²⋊C₄	—	10	1	no	—
60	C₂²⋊C₄	—	10	1	no	—
61	C₄²	—	10	1	no	—
62	C₂×C₅	#123	1	1	yes	characteristic
63	C₂×C₅	#135	1	1	yes	characteristic
64	C₂×C₅	#137	1	1	yes	characteristic
65	D₅	—	4	1	no	—
66	C₂³	—	5	1	no	—
67	Q₈	—	10	1	no	—
68	Q₈	—	10	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	5	1	no	—
72	C₂×C₄	—	10	1	no	—
73	C₂×C₄	—	10	1	no	—
74	C₂×C₄	—	10	1	no	—
75	C₂×C₄	—	10	1	no	—
76	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	10	1	no	—
79	C₅	#485	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	10	1	no	—
81	C₂²	—	10	1	no	—
82	C₂²	—	10	1	no	—
83	C₂²	D₄×D₅	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	10	1	no	—
87	C₄	—	20	1	no	—
88	C₄	—	20	1	no	—
89	C₄	#709	1	1	yes	characteristic
90	C₄	#713	1	1	yes	characteristic
91	C₂	—	20	1	no	—
92	C₂	#4040	1	1	yes	characteristic
93	C₂	#4058	1	1	yes	characteristic
94	C₂	#4064	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×#107	C₂
socle	C₂²×C₅	C₂×D₄
prime radical	C₂²×D₅	D₄
hypercenter	#107	D₅
hypocenter	C₅	#485
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. C₅×#107	C₂	semidirect
5. #3948	C₂	semidirect
6. #3942	C₂	semidirect
7. #3940	C₂	semidirect
35. #107	D₅	semidirect
79. C₅	#485	semidirect

Maximal subgroups

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

subgroup	index
#4043	2
#4038	2
C₅×#107	2
#3952	2
#3948	2
#3942	2
#3940	2
#485	5