Subgroups — C₅×#7476 #11930196

Order 1280.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#368	C₂	1	2	yes	maximal
3	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
4	C₂×C₅×#108	—	2	2	no	—
5	C₅×M₆₄	—	2	2	no	—
6	C₂×C₅×C₃₂	C₄	1	2	yes	—
7	C₅×#368	—	2	2	no	—
8	C₅×#368	C₄	1	4	yes	—
9	#7476	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₅×M₁₆	—	4	2	no	—
11	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
12	C₂×C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
14	C₂×C₅×C₁₆	D₄	1	2	yes	—
15	C₂×C₅×C₁₆	Q₈	1	1	yes	characteristic
16	C₅×#108	—	2	4	no	—
17	C₅×#108	—	4	2	no	—
18	C₅×C₃₂	—	2	2	no	—
19	C₂×M₆₄	C₂×C₅	1	1	yes	characteristic
20	C₂×#368	C₂×C₅	1	2	yes	—
21	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
22	C₅×M₁₆	—	4	4	no	—
23	C₅×M₁₆	—	8	2	no	—
24	C₂×C₅×C₈	—	8	2	no	—
25	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
26	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₅×C₈	SD₁₆	1	2	yes	—
28	C₂×C₅×C₈	Q₁₆	1	1	yes	characteristic
29	C₅×C₁₆	C₄²	1	1	yes	characteristic
30	C₅×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
31	C₅×C₁₆	C₄⋊C₄	1	2	yes	—
32	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
33	C₂×#108	—	2	2	no	—
34	M₆₄	—	2	2	no	—
35	C₂×C₃₂	C₄×C₅	1	2	yes	—
36	#368	—	2	2	no	—
37	#368	C₄×C₅	1	4	yes	—
38	C₂³×C₅	Q₃₂	1	1	yes	characteristic
39	C₂×C₄×C₅	#102	1	2	yes	—
40	C₂×C₄×C₅	#107	1	1	yes	characteristic
41	C₂×C₄×C₅	D₁₆	1	1	yes	characteristic
42	C₂×C₄×C₅	SD₃₂	1	2	yes	—
43	C₅×C₈	—	8	4	no	—
44	C₅×C₈	#95	1	1	yes	characteristic
45	C₅×C₈	#103	1	2	yes	—
46	C₅×C₈	#106	1	1	yes	characteristic
47	C₂×M₁₆	—	4	2	no	—
48	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
49	C₂×C₁₆	C₂×C₄×C₅	1	1	yes	characteristic
50	C₂×C₁₆	C₂×C₄×C₅	1	2	yes	—
51	C₂×C₁₆	C₅×D₄	1	2	yes	—
52	C₂×C₁₆	C₅×Q₈	1	1	yes	characteristic
53	#108	—	2	4	no	—
54	#108	—	4	2	no	—
55	C₃₂	—	2	2	no	—
56	C₂²×C₅	—	4	1	no	—
57	C₂²×C₅	#358	1	2	yes	—
58	C₂²×C₅	#366	1	1	yes	characteristic
59	C₄×C₅	#340	1	1	yes	characteristic
60	C₄×C₅	#357	1	2	yes	—
61	C₄×C₅	#367	1	1	yes	characteristic
62	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
63	M₁₆	—	4	4	no	—
64	M₁₆	—	8	2	no	—
65	C₂×C₈	—	8	2	no	—
66	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
67	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₈	C₅×SD₁₆	1	2	yes	—
69	C₂×C₈	C₅×Q₁₆	1	1	yes	characteristic
70	C₁₆	C₄²×C₅	1	1	yes	characteristic
71	C₁₆	C₅×C₂²⋊C₄	1	1	yes	characteristic
72	C₁₆	C₅×C₄⋊C₄	1	2	yes	—
73	C₂×C₅	—	2	2	no	—
74	C₂×C₅	—	2	1	no	—
75	C₂×C₅	#1380	1	1	yes	characteristic
76	C₂³	C₅×Q₃₂	1	1	yes	characteristic
77	C₂×C₄	C₅×#102	1	2	yes	—
78	C₂×C₄	C₅×#107	1	1	yes	characteristic
79	C₂×C₄	C₅×D₁₆	1	1	yes	characteristic
80	C₂×C₄	C₅×SD₃₂	1	2	yes	—
81	C₈	—	8	4	no	—
82	C₈	C₅×#95	1	1	yes	characteristic
83	C₈	C₅×#103	1	2	yes	—
84	C₈	C₅×#106	1	1	yes	characteristic
85	C₅	#7476	1	1	yes	characteristic, direct product factor, Sylow
86	C₂²	—	4	1	no	—
87	C₂²	C₅×#358	1	2	yes	—
88	C₂²	C₅×#366	1	1	yes	characteristic
89	C₄	C₅×#340	1	1	yes	characteristic
90	C₄	C₅×#357	1	2	yes	—
91	C₄	C₅×#367	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	—	2	1	no	—
94	C₂	C₅×#1380	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#367
commutator	C₁₆	C₄²×C₅
Frattini, cosocle	C₂²×C₁₆	C₂²×C₅
socle	C₂×C₅	#1380
prime radical	C₂³×C₅	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂²×C₅×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
9. #7476	C₅	direct (N × H)
85. C₅	#7476	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×M₆₄	2
C₂×C₅×#368	2
#7476	5

Subgroups — C5×#7476 #11930196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7476 #11930196