Subgroups — #13101031

Order 1600.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11717037	C₂	1	2	yes	maximal
2	C₈×#1039	C₂	1	1	yes	maximal, characteristic
3	C₅×#3949	C₂	1	2	yes	maximal
4	#11716615	C₂	1	2	yes	maximal
5	C₂×#6039	—	2	2	no	—
6	C₂×C₅²×C₈	C₂²	1	1	yes	characteristic
7	C₄×#1039	C₂²	1	1	yes	characteristic
8	C₂×#6029	C₂²	1	1	yes	characteristic
9	C₅×C₄⋊Dic₅	C₂²	1	4	yes	—
10	#87781	—	2	2	no	—
11	#65144	—	5	2	no	maximal
12	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
13	C₂×#1039	D₄	1	2	yes	—
14	C₂×C₅×Dic₅	—	2	4	no	—
15	#6039	—	4	4	no	—
16	C₅²×C₈	Q₈	1	2	yes	complemented
17	#6029	Q₈	1	2	yes	complemented
18	#4034	—	5	4	no	—
19	C₅×#106	—	5	2	no	—
20	#3949	D₅	1	2	yes	—
21	C₈×Dic₅	—	5	2	no	—
22	C₈×Dic₅	—	10	2	no	—
23	#3940	—	5	4	no	—
24	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
25	C₄×C₅²	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₅²	C₂×Q₈	1	1	yes	characteristic
27	#1039	SD₁₆	1	4	yes	—
28	C₅×Dic₅	—	4	4	no	—
29	C₂×Dic₁₀	—	10	4	no	—
30	C₂×C₅×C₈	—	2	2	no	—
31	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
32	C₅×C₄⋊C₄	—	5	4	no	—
33	C₄⋊Dic₅	C₂×D₅	1	4	yes	—
34	#683	—	10	4	no	—
35	C₄×Dic₅	—	5	2	no	—
36	C₄×Dic₅	—	10	2	no	—
37	C₂×#168	—	5	2	no	—
38	C₂×#168	—	10	2	no	—
39	#498	—	25	1	no	Sylow
40	C₂×C₅²	C₄⋊Q₈	1	1	yes	characteristic
41	C₂×C₅²	C₂×SD₁₆	1	2	yes	—
42	C₂×C₄×C₅	—	2	2	no	—
43	C₂×C₄×C₅	—	10	4	no	—
44	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
45	C₂×Dic₅	—	2	4	no	—
46	C₂×Dic₅	—	5	4	no	—
47	C₂×Dic₅	—	10	4	no	—
48	Dic₁₀	—	20	8	no	—
49	C₅×C₈	—	2	4	no	—
50	C₅×C₈	Dic₁₀	1	4	yes	complemented
51	#168	—	5	4	no	—
52	#168	—	10	4	no	—
53	C₄⋊Q₈	—	25	2	no	—
54	#106	—	5	2	no	—
55	#106	—	25	2	no	—
56	C₄×C₈	—	25	1	no	—
57	C₅²	#498	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₅	—	2	2	no	—
59	C₂²×C₅	D₄×D₅	1	2	yes	—
60	C₄×C₅	—	2	2	no	—
61	C₄×C₅	—	2	2	no	—
62	C₄×C₅	—	20	4	no	—
63	C₄×C₅	C₂×Dic₁₀	1	2	yes	—
64	C₄×C₅	Q₈×D₅	1	2	yes	—
65	Dic₅	—	4	4	no	—
66	Dic₅	—	5	8	no	—
67	Dic₅	—	10	8	no	—
68	C₂×Q₈	—	50	2	no	—
69	C₂×C₈	—	25	1	no	—
70	C₂×C₈	D₅²	1	1	yes	characteristic
71	C₄⋊C₄	—	5	4	no	—
72	C₄⋊C₄	—	50	2	no	—
73	C₄²	—	25	1	no	—
74	C₂×C₅	—	2	4	no	—
75	C₂×C₅	—	2	2	no	—
76	C₂×C₅	#4034	1	2	yes	—
77	C₂×C₅	D₅×SD₁₆	1	4	yes	—
78	Q₈	—	100	4	no	—
79	C₂×C₄	—	10	4	no	—
80	C₂×C₄	—	25	2	no	—
81	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
82	C₈	—	25	2	no	—
83	C₈	#6039	1	2	yes	complemented
84	C₅	—	2	2	no	—
85	C₅	#65144	1	2	yes	complemented
86	C₂²	#87877	1	1	yes	characteristic
87	C₄	—	20	4	no	—
88	C₄	—	25	4	no	—
89	C₄	#87872	1	1	yes	characteristic
90	C₄	C₂×#6039	1	1	yes	characteristic
91	C₂	#11716914	1	2	yes	—
92	C₂	#11717037	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#87877
commutator, cosocle	C₂×C₄×C₅²	C₂³
Frattini	C₂×C₄	C₂×D₅²
Fitting	C₂×C₅²×C₈	C₂²
socle, prime radical	C₂²×C₅²	C₂×D₄
hypercenter	C₂×C₈	D₅²
hypocenter	C₅²	#498
LCS	G ▷ C₂×C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
16. C₅²×C₈	Q₈	semidirect
17. #6029	Q₈	semidirect
50. C₅×C₈	Dic₁₀	semidirect
57. C₅²	#498	semidirect
83. C₈	#6039	semidirect
85. C₅	#65144	semidirect

Maximal subgroups

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

subgroup	index
#11717037	2
C₈×#1039	2
C₅×#3949	2
#11716615	2
#65144	5