Subgroups — #12014014

Order 1280.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1713	C₂	1	1	yes	maximal, characteristic
2	#10602105	C₂	1	4	yes	maximal
3	#10598858	C₂	1	1	yes	maximal, characteristic
4	C₈×#672	C₂	1	1	yes	maximal, characteristic
5	C₅×#500	—	2	2	no	—
6	C₅×#494	C₂²	1	2	yes	—
7	C₂×#3961	—	2	8	no	—
8	#64988	C₂²	1	2	yes	—
9	#64971	—	2	2	no	—
10	C₅×C₈²	C₂²	1	1	yes	characteristic
11	C₄×#672	C₂²	1	2	yes	—
12	#12516	—	5	1	no	maximal, Sylow
13	C₂×C₅×Q₁₆	—	2	4	no	—
14	C₅×C₄⋊Q₈	—	2	2	no	—
15	C₂×Dic₂₀	—	2	4	no	—
16	#4015	—	2	2	no	—
17	C₅×#107	—	4	4	no	—
18	C₄×C₅×C₈	D₄	1	2	yes	—
19	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
20	#3961	—	4	16	no	—
21	#3950	—	4	4	no	—
22	C₂×#672	D₄	1	4	yes	—
23	#2247	—	5	4	no	—
24	#1713	—	5	1	no	—
25	#1713	D₅	1	1	yes	characteristic
26	C₈×C₁₆	—	5	1	no	—
27	C₂×C₅×Q₈	—	4	2	no	—
28	C₂×Dic₁₀	—	4	2	no	—
29	C₅×Q₁₆	—	4	8	no	—
30	C₂×C₅×C₈	D₈	1	4	yes	—
31	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
32	C₅×C₄⋊C₄	—	4	4	no	—
33	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
34	C₄⋊Dic₅	—	4	4	no	—
35	Dic₂₀	—	4	8	no	—
36	#672	D₈	1	8	yes	—
37	C₂×Q₃₂	—	10	8	no	—
38	#500	—	2	2	no	—
39	#500	—	10	2	no	—
40	#494	—	5	2	no	—
41	#494	C₂×D₅	1	2	yes	—
42	C₄×C₁₆	—	5	2	no	—
43	C₈²	C₂×D₅	1	1	yes	characteristic
44	C₅×Q₈	—	8	4	no	—
45	C₂×C₄×C₅	—	8	2	no	—
46	C₂×C₄×C₅	#127	1	1	yes	characteristic
47	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
48	C₂×Dic₅	—	8	2	no	—
49	Dic₁₀	—	8	4	no	—
50	C₅×C₈	Q₃₂	1	8	yes	complemented
51	C₅×C₈	C₂×D₈	1	4	yes	—
52	C₂×Q₁₆	—	2	4	no	—
53	C₂×Q₁₆	—	10	4	no	—
54	C₄⋊Q₈	—	2	2	no	—
55	C₄⋊Q₈	—	10	2	no	—
56	Q₃₂	—	20	16	no	—
57	C₂×C₁₆	—	5	4	no	—
58	#107	—	4	4	no	—
59	#107	—	20	4	no	—
60	C₄×C₈	C₂²⋊D₅	1	2	yes	—
61	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
62	C₂²×C₅	#493	1	1	yes	characteristic
63	C₄×C₅	—	16	2	no	—
64	C₄×C₅	#493	1	2	yes	—
65	C₄×C₅	C₂×Q₃₂	1	4	yes	—
66	Dic₅	—	16	2	no	—
67	C₂×Q₈	—	4	2	no	—
68	C₂×Q₈	—	20	2	no	—
69	Q₁₆	—	4	8	no	—
70	Q₁₆	—	20	8	no	—
71	C₂×C₈	#686	1	4	yes	—
72	C₂×C₈	D₄×D₅	1	2	yes	—
73	C₄⋊C₄	—	4	4	no	—
74	C₄⋊C₄	—	20	4	no	—
75	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
76	C₁₆	—	5	8	no	—
77	C₂×C₅	#1712	1	1	yes	characteristic
78	C₂×C₅	#2247	1	2	yes	—
79	Q₈	—	8	4	no	—
80	Q₈	—	40	4	no	—
81	C₂×C₄	—	8	2	no	—
82	C₂×C₄	—	40	2	no	—
83	C₂×C₄	C₂×#686	1	2	yes	—
84	C₂×C₄	#4086	1	1	yes	characteristic
85	C₈	#3961	1	8	yes	complemented
86	C₈	D₅×D₈	1	4	yes	—
87	C₅	#12516	1	1	yes	characteristic, complemented, Sylow
88	C₂²	#65362	1	1	yes	characteristic
89	C₄	—	16	2	no	—
90	C₄	—	80	2	no	—
91	C₄	#65440	1	2	yes	—
92	C₄	C₂×#3961	1	4	yes	—
93	C₂	#10602069	1	1	yes	characteristic
94	C₂	#10602105	1	2	yes	—

	subgroup	G/H
center	C₂²	#65362
commutator, cosocle	C₄×C₅×C₈	C₂³
Frattini	C₄×C₈	C₂²×D₅
Fitting	C₅×#1713	C₂
socle, prime radical	C₂²×C₅	#493
hypercenter	#1713	D₅
hypocenter	C₅	#12516
LCS	G ▷ C₄×C₅×C₈ ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

Complements

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

N	H ≅ G/N	type
50. C₅×C₈	Q₃₂	semidirect
85. C₈	#3961	semidirect
87. C₅	#12516	semidirect

Maximal subgroups

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

subgroup	index
C₅×#1713	2
#10602105	2
#10598858	2
C₈×#672	2
#12516	5