Subgroups — #13100532

Order 1600.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#4020	C₂	1	2	yes	maximal, complemented
2	C₂×#87770	C₂	1	4	yes	maximal, complemented
3	C₄×#6029	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₂₀	—	2	4	no	—
5	C₂×C₅×D₂₀	C₂²	1	4	yes	—
6	C₄²×C₅²	C₂²	1	1	yes	characteristic
7	C₂×#6029	C₂²	1	2	yes	—
8	#87770	—	2	8	no	—
9	#65362	—	5	2	no	maximal
10	C₂²×C₅×D₅	—	2	4	no	—
11	C₂×C₄×C₅²	D₄	1	2	yes	—
12	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
13	C₅×D₂₀	—	2	8	no	—
14	C₅×D₂₀	—	4	8	no	—
15	#6029	D₄	1	4	yes	complemented
16	C₅×#127	—	5	2	no	—
17	C₂×#686	—	5	8	no	—
18	#4020	D₅	1	2	yes	complemented
19	C₄×#168	—	5	2	no	—
20	C₄×#168	—	10	2	no	—
21	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
22	C₂×C₅×D₅	—	4	4	no	—
23	C₂×C₅×D₅	—	4	8	no	—
24	C₄×C₅²	D₈	1	4	yes	complemented
25	C₄×C₅²	C₂×D₄	1	2	yes	—
26	C₂×C₅×D₄	—	5	4	no	—
27	C₂×C₅×D₄	—	10	4	no	—
28	C₂×D₂₀	—	2	4	no	—
29	C₂×D₂₀	C₂×D₅	1	4	yes	—
30	C₄²×C₅	—	2	2	no	—
31	C₄²×C₅	C₂×D₅	1	2	yes	—
32	#686	—	10	16	no	—
33	C₂×#168	—	5	4	no	—
34	C₂×#168	—	10	4	no	—
35	#493	—	25	1	no	Sylow
36	C₂×C₅²	#127	1	1	yes	characteristic
37	C₂×C₅²	C₂×D₈	1	2	yes	—
38	C₅×D₅	—	8	4	no	—
39	C₂³×C₅	—	10	4	no	—
40	C₂²×D₅	—	2	4	no	—
41	C₅×D₄	—	10	8	no	—
42	C₅×D₄	—	20	8	no	—
43	C₂×C₄×C₅	—	2	4	no	—
44	C₂×C₄×C₅	—	2	2	no	—
45	C₂×C₄×C₅	C₂²⋊D₅	1	4	yes	—
46	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
47	D₂₀	—	2	8	no	—
48	D₂₀	—	4	8	no	—
49	#168	—	5	8	no	—
50	#168	—	10	8	no	—
51	C₂×D₈	—	25	4	no	—
52	#127	—	5	2	no	—
53	C₄×C₈	—	25	1	no	—
54	C₅²	#493	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₅	—	2	2	no	—
56	C₂²×C₅	—	20	8	no	—
57	C₂²×C₅	—	20	4	no	—
58	C₂²×C₅	C₂×C₂²⋊D₅	1	2	yes	—
59	C₂×D₅	—	4	8	no	—
60	C₂×D₅	—	4	4	no	—
61	C₄×C₅	—	2	4	no	—
62	C₄×C₅	—	2	8	no	—
63	C₄×C₅	#686	1	8	yes	complemented
64	C₄×C₅	D₄×D₅	1	4	yes	—
65	C₂×D₄	—	5	4	no	—
66	C₂×D₄	—	10	4	no	—
67	D₈	—	50	8	no	—
68	C₂×C₈	—	25	2	no	—
69	C₄²	D₅²	1	1	yes	characteristic
70	C₂×C₅	—	2	4	no	—
71	C₂×C₅	—	2	2	no	—
72	C₂×C₅	—	40	4	no	—
73	C₂×C₅	C₂×#686	1	4	yes	—
74	C₂×C₅	#4086	1	2	yes	—
75	D₅	—	8	4	no	—
76	C₂³	—	10	4	no	—
77	D₄	—	10	8	no	—
78	D₄	—	20	8	no	—
79	C₂×C₄	#6037	1	2	yes	—
80	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
81	C₈	—	25	4	no	—
82	C₅	—	2	2	no	—
83	C₅	#65362	1	2	yes	complemented
84	C₂²	—	20	8	no	—
85	C₂²	—	20	4	no	—
86	C₂²	C₂×#6037	1	1	yes	characteristic
87	C₄	#87770	1	4	yes	complemented
88	C₄	#87877	1	2	yes	—
89	C₂	—	40	4	no	—
90	C₂	C₂×#87770	1	2	yes	—
91	C₂	#11717032	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#6037
commutator, cosocle	C₂×C₄×C₅²	C₂³
Frattini	C₂×C₄	C₂×D₅²
Fitting	C₄²×C₅²	C₂²
socle	C₂²×C₅²	C₂×D₄
hypercenter	C₄²	D₅²
hypocenter	C₅²	#493
LCS	G ▷ C₂×C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
1. C₅×#4020	C₂	semidirect
2. C₂×#87770	C₂	semidirect
3. C₄×#6029	C₂	semidirect
15. #6029	D₄	semidirect
18. #4020	D₅	semidirect
24. C₄×C₅²	D₈	semidirect
54. C₅²	#493	semidirect
63. C₄×C₅	#686	semidirect
83. C₅	#65362	semidirect
87. C₄	#87770	semidirect

Maximal subgroups

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

subgroup	index
C₅×#4020	2
C₂×#87770	2
C₄×#6029	2
#65362	5