Subgroups — #13102741

Order 1600.

344 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11717210	C₂	1	2	yes	maximal
2	C₅²×#107	C₂	1	1	yes	maximal, characteristic
3	#11716685	C₂	1	1	yes	maximal, characteristic
4	C₈×#1039	C₂	1	1	yes	maximal, characteristic
5	#11716675	C₂	1	2	yes	maximal
6	C₂×C₅²×C₈	C₂²	1	1	yes	characteristic
7	C₅²×C₄⋊C₄	C₂²	1	2	yes	—
8	C₄⋊#1039	—	2	2	no	—
9	C₄⋊#1039	C₂²	1	2	yes	—
10	#87806	—	2	2	no	—
11	C₄×#1039	C₂²	1	1	yes	characteristic
12	C₂×#6029	C₂²	1	1	yes	characteristic
13	#65167	—	5	6	no	maximal
14	C₂×C₄×C₅²	—	2	2	no	—
15	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
16	C₂×#1039	—	2	2	no	—
17	C₂×#1039	D₄	1	1	yes	characteristic
18	C₂×#1039	D₄	1	1	yes	characteristic
19	C₅²×C₈	Q₈	1	2	yes	—
20	#6029	Q₈	1	2	yes	—
21	#4036	—	5	12	no	—
22	C₅×#107	D₅	1	6	yes	—
23	#3950	—	5	6	no	—
24	C₈×Dic₅	—	5	6	no	—
25	#3940	—	5	12	no	—
26	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
27	C₄×C₅²	—	4	2	no	—
28	C₄×C₅²	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₅²	C₂×Q₈	1	1	yes	characteristic
30	#1039	—	2	1	no	—
31	#1039	—	2	1	no	—
32	#1039	—	4	2	no	—
33	C₂×C₅×C₈	C₂×D₅	1	6	yes	—
34	C₅×C₄⋊C₄	C₂×D₅	1	12	yes	—
35	C₄⋊Dic₅	—	5	12	no	—
36	C₄⋊Dic₅	—	10	12	no	—
37	#683	—	10	12	no	—
38	C₄×Dic₅	—	5	6	no	—
39	C₂×#168	—	5	6	no	—
40	#499	—	25	1	no	Sylow
41	C₂×C₅²	C₄⋊Q₈	1	1	yes	characteristic
42	C₂×C₅²	#135	1	1	yes	characteristic
43	C₂×C₅²	#135	1	1	yes	characteristic
44	C₂×C₄×C₅	—	2	12	no	—
45	C₂×C₄×C₅	C₂²×D₅	1	6	yes	—
46	C₂×Dic₅	—	5	6	no	—
47	C₂×Dic₅	—	5	6	no	—
48	C₂×Dic₅	—	10	12	no	—
49	C₅×C₈	Dic₁₀	1	12	yes	—
50	#168	—	5	12	no	—
51	#125	—	25	2	no	—
52	#107	—	25	1	no	—
53	#107	C₅⋊D₅	1	1	yes	characteristic
54	#106	—	25	2	no	—
55	C₄×C₈	—	25	1	no	—
56	C₅²	#499	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₅	D₄×D₅	1	6	yes	—
58	C₄×C₅	—	4	12	no	—
59	C₄×C₅	C₂×Dic₁₀	1	6	yes	—
60	C₄×C₅	Q₈×D₅	1	6	yes	—
61	Dic₅	—	10	6	no	—
62	Dic₅	—	10	6	no	—
63	Dic₅	—	20	12	no	—
64	C₂×C₈	—	25	1	no	—
65	C₂×C₈	C₂×C₅⋊D₅	1	1	yes	characteristic
66	C₄⋊C₄	—	25	2	no	—
67	C₄⋊C₄	—	50	2	no	—
68	C₄⋊C₄	—	50	2	no	—
69	C₄⋊C₄	C₂×C₅⋊D₅	1	2	yes	—
70	C₄²	—	25	1	no	—
71	C₂×C₅	#4034	1	6	yes	—
72	C₂×C₅	#4058	1	6	yes	—
73	C₂×C₅	#4065	1	6	yes	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	25	1	no	—
76	C₂×C₄	—	25	1	no	—
77	C₂×C₄	—	50	2	no	—
78	C₂×C₄	C₂²×C₅⋊D₅	1	1	yes	characteristic
79	C₈	—	25	2	no	—
80	C₈	#6045	1	2	yes	—
81	C₅	#65167	1	6	yes	complemented
82	C₂²	D₄×C₅⋊D₅	1	1	yes	characteristic
83	C₄	—	4	2	no	—
84	C₄	—	50	1	no	—
85	C₄	—	50	1	no	—
86	C₄	—	100	2	no	—
87	C₄	C₂×#6045	1	1	yes	characteristic
88	C₄	Q₈×C₅⋊D₅	1	1	yes	characteristic
89	C₂	#11717208	1	1	yes	characteristic
90	C₂	#11717232	1	1	yes	characteristic
91	C₂	#11717239	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₅⋊D₅
commutator, cosocle	C₂×C₄×C₅²	C₂³
Frattini	C₂×C₄	C₂²×C₅⋊D₅
Fitting	C₅²×#107	C₂
socle, prime radical	C₂²×C₅²	C₂×D₄
hypercenter	#107	C₅⋊D₅
hypocenter	C₅²	#499
LCS	G ▷ C₂×C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
56. C₅²	#499	semidirect
81. C₅	#65167	semidirect

Maximal subgroups

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

subgroup	index
#11717210	2
C₅²×#107	2
#11716685	2
C₈×#1039	2
#11716675	2
#65167	5