Subgroups — C₅×#7475 #11930195

Order 1280.

170 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	C₅×#2158	C₂	1	2	yes	maximal
3	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
4	C₅×#427	—	2	2	no	—
5	C₅×M₆₄	—	2	2	no	—
6	C₂×C₅×C₃₂	C₄	1	2	yes	complemented
7	C₅×#367	C₄	1	4	yes	complemented
8	C₅×#366	—	2	2	no	—
9	#7475	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
11	C₅×#117	—	4	2	no	—
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×#107	—	2	4	no	—
17	C₅×#106	—	4	2	no	—
18	C₅×C₃₂	—	2	2	no	—
19	C₂×M₆₄	C₂×C₅	1	1	yes	characteristic
20	#2158	C₂×C₅	1	2	yes	—
21	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
22	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
23	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₅×C₈	SD₁₆	1	2	yes	—
25	C₂×C₅×C₈	Q₁₆	1	1	yes	characteristic
26	C₅×C₄⋊C₄	—	4	4	no	—
27	C₅×C₂²⋊C₄	—	8	2	no	—
28	C₄²×C₅	—	8	2	no	—
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	#427	—	2	2	no	—
34	M₆₄	—	2	2	no	—
35	C₂×C₃₂	C₄×C₅	1	2	yes	complemented
36	#367	C₄×C₅	1	4	yes	complemented
37	#366	—	2	2	no	—
38	C₂³×C₅	D₁₆	1	1	yes	characteristic
39	C₂×C₄×C₅	—	8	4	no	—
40	C₂×C₄×C₅	#102	1	2	yes	—
41	C₂×C₄×C₅	#107	1	1	yes	characteristic
42	C₂×C₄×C₅	SD₃₂	1	2	yes	—
43	C₂×C₄×C₅	Q₃₂	1	1	yes	characteristic
44	C₅×C₈	#95	1	1	yes	characteristic
45	C₅×C₈	#103	1	2	yes	—
46	C₅×C₈	#106	1	1	yes	characteristic
47	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
48	#117	—	4	2	no	—
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	#107	—	2	4	no	—
54	#106	—	4	2	no	—
55	C₃₂	—	2	2	no	—
56	C₂²×C₅	—	4	1	no	—
57	C₂²×C₅	#357	1	2	yes	—
58	C₂²×C₅	#366	1	1	yes	characteristic
59	C₄×C₅	—	16	4	no	—
60	C₄×C₅	#340	1	1	yes	characteristic
61	C₄×C₅	#358	1	2	yes	—
62	C₄×C₅	#367	1	1	yes	characteristic
63	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
64	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
65	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₈	C₅×SD₁₆	1	2	yes	—
67	C₂×C₈	C₅×Q₁₆	1	1	yes	characteristic
68	C₄⋊C₄	—	4	4	no	—
69	C₂²⋊C₄	—	8	2	no	—
70	C₄²	—	8	2	no	—
71	C₁₆	C₄²×C₅	1	1	yes	characteristic
72	C₁₆	C₅×C₂²⋊C₄	1	1	yes	characteristic
73	C₁₆	C₅×C₄⋊C₄	1	2	yes	—
74	C₂×C₅	—	2	2	no	—
75	C₂×C₅	—	2	1	no	—
76	C₂×C₅	#1380	1	1	yes	characteristic
77	C₂³	C₅×D₁₆	1	1	yes	characteristic
78	C₂×C₄	—	8	4	no	—
79	C₂×C₄	C₅×#102	1	2	yes	—
80	C₂×C₄	C₅×#107	1	1	yes	characteristic
81	C₂×C₄	C₅×SD₃₂	1	2	yes	—
82	C₂×C₄	C₅×Q₃₂	1	1	yes	characteristic
83	C₈	C₅×#95	1	1	yes	characteristic
84	C₈	C₅×#103	1	2	yes	—
85	C₈	C₅×#106	1	1	yes	characteristic
86	C₅	#7475	1	1	yes	characteristic, direct product factor, Sylow
87	C₂²	—	4	1	no	—
88	C₂²	C₅×#357	1	2	yes	—
89	C₂²	C₅×#366	1	1	yes	characteristic
90	C₄	—	16	4	no	—
91	C₄	C₅×#340	1	1	yes	characteristic
92	C₄	C₅×#358	1	2	yes	—
93	C₄	C₅×#367	1	1	yes	characteristic
94	C₂	—	2	2	no	—
95	C₂	—	2	1	no	—
96	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	D₁₆
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
6. C₂×C₅×C₃₂	C₄	semidirect
7. C₅×#367	C₄	semidirect
9. #7475	C₅	direct (N × H)
35. C₂×C₃₂	C₄×C₅	semidirect
36. #367	C₄×C₅	semidirect
86. C₅	#7475	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
C₅×#2158	2
#7475	5

Subgroups — C5×#7475 #11930195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7475 #11930195