Subgroups — #13100173

Order 1600.

103 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11716841	C₂	1	2	yes	maximal
2	C₅×#3947	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅²×C₈	C₄	1	1	yes	characteristic
4	C₄×C₅×Dic₅	C₄	1	1	yes	characteristic
5	C₂×C₅×#168	C₂²	1	1	yes	characteristic
6	#87763	C₄	1	4	yes	complemented
7	#64890	—	5	1	no	maximal
8	#64686	—	5	1	no	maximal
9	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic
10	C₂×C₅×Dic₅	—	2	1	no	—
11	C₅²×C₈	—	2	1	no	—
12	C₅×#168	C₂×C₄	1	2	yes	—
13	#3998	—	5	2	no	—
14	C₅×#97	—	5	1	no	—
15	#3947	D₅	1	1	yes	characteristic
16	#3944	—	5	2	no	—
17	C₂²×C₅²	M₁₆	1	1	yes	characteristic
18	C₄×C₅²	C₄²	1	1	yes	characteristic
19	C₄×C₅²	M₁₆	1	1	yes	characteristic
20	C₅×Dic₅	—	4	1	no	—
21	C₂×C₅×C₈	—	4	1	no	—
22	C₂×C₅×C₈	—	5	1	no	—
23	C₂×C₅×C₈	Dic₅	1	1	yes	characteristic
24	C₂×C₅×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₄²×C₅	—	5	1	no	—
26	C₄×Dic₅	Dic₅	1	1	yes	characteristic
27	C₂×#168	C₂×D₅	1	1	yes	characteristic
28	#674	—	5	4	no	—
29	#672	—	5	4	no	—
30	#347	—	25	1	no	Sylow
31	C₂×C₅²	—	2	1	no	—
32	C₂×C₅²	#97	1	1	yes	characteristic
33	C₂×C₄×C₅	—	4	1	no	—
34	C₂×C₄×C₅	—	10	1	no	—
35	C₂×C₄×C₅	C₂×Dic₅	1	1	yes	characteristic
36	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
37	C₂×Dic₅	—	2	1	no	—
38	C₅×C₈	—	2	1	no	—
39	C₅×C₈	—	2	1	no	—
40	C₅×C₈	—	4	2	no	—
41	C₅×C₈	—	5	2	no	—
42	#168	C₄×D₅	1	2	yes	—
43	M₃₂	—	25	2	no	—
44	#97	—	5	1	no	—
45	C₅²	#347	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₅	—	4	1	no	—
47	C₂²×C₅	#681	1	1	yes	characteristic
48	C₂²×C₅	#700	1	1	yes	characteristic
49	C₄×C₅	—	4	1	no	—
50	C₄×C₅	—	4	1	no	—
51	C₄×C₅	—	20	1	no	—
52	C₄×C₅	#681	1	1	yes	characteristic
53	C₄×C₅	C₄×Dic₅	1	1	yes	characteristic
54	C₄×C₅	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₄×C₅	#704	1	1	yes	characteristic
56	Dic₅	—	4	1	no	—
57	C₂×C₈	—	5	1	no	—
58	C₂×C₈	#1042	1	1	yes	characteristic
59	C₄²	—	5	1	no	—
60	C₁₆	—	25	4	no	—
61	C₂×C₅	—	2	1	no	—
62	C₂×C₅	—	2	1	no	—
63	C₂×C₅	—	4	2	no	—
64	C₂×C₅	—	4	1	no	—
65	C₂×C₅	#3935	1	1	yes	characteristic
66	C₂×C₅	#4002	1	1	yes	characteristic
67	C₂×C₄	—	10	1	no	—
68	C₂×C₄	C₂×#1042	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	5	2	no	—
71	C₅	—	4	1	no	—
72	C₅	#64686	1	1	yes	characteristic, complemented
73	C₅	#64890	1	1	yes	characteristic, complemented
74	C₂²	#87849	1	1	yes	characteristic
75	C₄	—	20	1	no	—
76	C₄	C₄×#1042	1	1	yes	characteristic
77	C₄	#87853	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	#11716845	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#1042
commutator	C₄×C₅²	C₄²
Frattini	C₂×C₄	C₂×#1042
Fitting	C₂×C₅²×C₈	C₄
socle	C₂×C₅²	#97
prime radical	C₂²×C₅²	M₁₆
cosocle	C₂×C₅×#168	C₂²
hypercenter	C₂×C₈	#1042
hypocenter	C₅²	#347
LCS	G ▷ C₄×C₅² ▷ C₅²
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
6. #87763	C₄	semidirect
45. C₅²	#347	semidirect
72. C₅	#64686	semidirect
73. C₅	#64890	semidirect

Maximal subgroups

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

subgroup	index
#11716841	2
C₅×#3947	2
#64890	5
#64686	5