Subgroups — #13099862

Order 1600.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11716915	C₂	1	1	yes	maximal, characteristic
2	#11716883	C₂	1	1	yes	maximal, characteristic, complemented
3	#11716863	C₂	1	1	yes	maximal, characteristic, complemented
4	#87877	—	2	1	no	—
5	#87856	—	2	1	no	—
6	C₈×C₅⋊D₅	C₂²	1	1	yes	characteristic
7	C₅×D₄₀	C₄	1	2	yes	—
8	#87770	—	2	1	no	—
9	#87765	—	2	1	no	—
10	#64906	—	5	2	no	maximal
11	C₂×D₅²	—	4	1	no	—
12	C₄×C₅⋊D₅	D₄	1	1	yes	characteristic
13	C₅×D₂₀	—	2	2	no	—
14	#6037	—	4	1	no	—
15	#6033	—	4	1	no	—
16	C₅²×C₈	C₂×C₄	1	1	yes	characteristic
17	#6029	D₄	1	1	yes	characteristic
18	D₅×D₈	—	5	2	no	—
19	#3995	—	5	2	no	—
20	#3995	—	10	2	no	—
21	#3990	—	5	2	no	—
22	C₂×C₅⋊D₅	SD₁₆	1	1	yes	characteristic
23	C₂×C₅×D₅	—	4	2	no	—
24	D₅²	—	8	2	no	—
25	C₄×C₅²	C₂²⋊C₄	1	1	yes	characteristic
26	#1039	D₈	1	1	yes	characteristic
27	D₄×D₅	—	10	2	no	—
28	#700	—	10	2	no	—
29	#700	—	10	4	no	—
30	C₅×D₈	—	5	2	no	—
31	#686	—	10	2	no	—
32	D₄₀	AGL(1,𝔽₅)	1	2	yes	—
33	C₈×D₅	—	5	2	no	—
34	C₈×D₅	—	10	2	no	—
35	#674	—	10	2	no	—
36	#361	—	25	1	no	Sylow
37	C₂×C₅²	#102	1	1	yes	characteristic
38	C₅⋊D₅	—	2	1	no	—
39	C₅×D₅	—	8	2	no	—
40	C₂²×D₅	—	20	2	no	—
41	C₅×D₄	—	10	2	no	—
42	C₂²⋊D₅	—	20	2	no	—
43	D₂₀	—	2	2	no	—
44	C₄×D₅	—	5	2	no	—
45	C₄×D₅	—	10	2	no	—
46	#170	—	20	2	no	—
47	#170	—	20	4	no	—
48	C₅×C₈	—	2	2	no	—
49	C₅×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
50	#168	—	5	2	no	—
51	#168	—	10	2	no	—
52	C₂×D₈	—	25	1	no	—
53	M₃₂	—	25	1	no	—
54	#108	—	25	1	no	—
55	C₅²	#361	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₅	—	20	2	no	—
57	C₂×D₅	—	4	2	no	—
58	C₂×D₅	—	5	2	no	—
59	C₂×D₅	—	10	2	no	—
60	C₂×D₅	—	40	4	no	—
61	C₄×C₅	—	2	2	no	—
62	C₄×C₅	C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
63	Dic₅	—	5	2	no	—
64	Dic₅	—	10	2	no	—
65	C₂×D₄	—	50	1	no	—
66	D₈	—	5	2	no	—
67	D₈	—	50	1	no	—
68	M₁₆	—	50	1	no	—
69	C₂×C₈	—	25	1	no	—
70	C₁₆	—	50	1	no	—
71	C₂×C₅	—	2	2	no	—
72	C₂×C₅	—	40	2	no	—
73	C₂×C₅	#4007	1	2	yes	—
74	D₅	—	8	2	no	—
75	D₅	—	10	2	no	—
76	D₅	—	20	2	no	—
77	C₂³	—	100	1	no	—
78	D₄	—	10	2	no	—
79	D₄	—	100	1	no	—
80	C₂×C₄	—	25	1	no	—
81	C₈	—	25	1	no	—
82	C₈	—	100	1	no	—
83	C₈	D₅⋊AGL(1,𝔽₅)	1	1	yes	characteristic
84	C₅	—	2	2	no	—
85	C₅	#64906	1	2	yes	complemented
86	C₂²	—	20	2	no	—
87	C₂²	—	25	1	no	—
88	C₂²	—	200	2	no	—
89	C₄	—	25	1	no	—
90	C₄	#87831	1	1	yes	characteristic
91	C₂	—	40	2	no	—
92	C₂	—	50	1	no	—
93	C₂	#11716765	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11716765
commutator, Fitting	C₅²×C₈	C₂×C₄
Frattini, hypercenter	C₈	D₅⋊AGL(1,𝔽₅)
socle	C₂×C₅²	#102
prime radical	#11716915	C₂
cosocle	C₈×C₅⋊D₅	C₂²
hypocenter	C₅²	#361
LCS	G ▷ C₅²×C₈ ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. #11716883	C₂	semidirect
3. #11716863	C₂	semidirect
55. C₅²	#361	semidirect
85. C₅	#64906	semidirect

Maximal subgroups

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

subgroup	index
#11716915	2
#11716883	2
#11716863	2
#64906	5