Subgroups — C₅×#13725 #11936445

Order 1280.

270 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃₂	C₂	1	4	yes	maximal, complemented
2	C₅×#2246	C₂	1	2	yes	maximal, complemented
3	C₄×C₅×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₁₆	—	2	2	no	—
5	C₂×C₅×D₁₆	C₂²	1	4	yes	—
6	C₅×#493	—	2	2	no	—
7	C₅×D₃₂	—	2	8	no	—
8	C₂×C₅×C₃₂	C₂²	1	2	yes	—
9	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
10	#13725	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₅×D₈	—	2	4	no	—
12	C₂×C₅×D₈	—	4	2	no	—
13	C₅×#127	—	4	2	no	—
14	C₅×D₁₆	—	2	8	no	—
15	C₅×D₁₆	—	4	4	no	—
16	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
17	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
18	C₄×C₅×C₈	D₄	1	1	yes	characteristic
19	C₅×C₃₂	D₄	1	4	yes	complemented
20	C₂×D₃₂	C₂×C₅	1	4	yes	complemented
21	#2246	C₂×C₅	1	2	yes	complemented
22	C₄×C₃₂	C₂×C₅	1	1	yes	characteristic, complemented
23	C₂×C₅×D₄	—	4	4	no	—
24	C₂×C₅×D₄	—	8	4	no	—
25	C₅×D₈	—	4	4	no	—
26	C₅×D₈	—	4	4	no	—
27	C₅×D₈	—	8	4	no	—
28	C₂×C₅×C₈	D₈	1	1	yes	characteristic
29	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
30	C₄²×C₅	D₈	1	1	yes	characteristic
31	C₅×C₁₆	D₈	1	2	yes	—
32	C₅×C₁₆	C₂×D₄	1	2	yes	—
33	C₂×D₁₆	—	2	2	no	—
34	C₂×D₁₆	C₂²×C₅	1	4	yes	—
35	#493	—	2	2	no	—
36	D₃₂	—	2	8	no	—
37	C₂×C₃₂	C₂²×C₅	1	2	yes	—
38	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
39	C₂³×C₅	—	8	4	no	—
40	C₅×D₄	—	8	4	no	—
41	C₅×D₄	—	8	4	no	—
42	C₅×D₄	—	16	8	no	—
43	C₂×C₄×C₅	D₁₆	1	2	yes	—
44	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
45	C₅×C₈	D₁₆	1	2	yes	—
46	C₅×C₈	#127	1	1	yes	characteristic
47	C₅×C₈	C₂×D₈	1	1	yes	characteristic
48	C₂×D₈	—	2	4	no	—
49	C₂×D₈	—	4	2	no	—
50	#127	—	4	2	no	—
51	D₁₆	—	2	8	no	—
52	D₁₆	—	4	4	no	—
53	C₂×C₁₆	C₅×D₄	1	1	yes	characteristic
54	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
55	C₄×C₈	C₅×D₄	1	1	yes	characteristic
56	C₃₂	C₅×D₄	1	4	yes	complemented
57	C₂²×C₅	—	16	4	no	—
58	C₂²×C₅	—	16	8	no	—
59	C₂²×C₅	C₂×D₁₆	1	1	yes	characteristic
60	C₄×C₅	D₃₂	1	4	yes	complemented
61	C₄×C₅	#493	1	1	yes	characteristic
62	C₄×C₅	C₂×D₁₆	1	1	yes	characteristic
63	C₂×D₄	—	4	4	no	—
64	C₂×D₄	—	8	4	no	—
65	D₈	—	4	4	no	—
66	D₈	—	4	4	no	—
67	D₈	—	8	4	no	—
68	C₂×C₈	C₅×D₈	1	1	yes	characteristic
69	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
70	C₄²	C₅×D₈	1	1	yes	characteristic
71	C₁₆	C₅×D₈	1	2	yes	—
72	C₁₆	C₂×C₅×D₄	1	2	yes	—
73	C₂×C₅	—	32	4	no	—
74	C₂×C₅	#2246	1	1	yes	characteristic
75	C₂×C₅	C₂×D₃₂	1	2	yes	—
76	C₂³	—	8	4	no	—
77	D₄	—	8	4	no	—
78	D₄	—	8	4	no	—
79	D₄	—	16	8	no	—
80	C₂×C₄	C₅×D₁₆	1	2	yes	—
81	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
82	C₈	C₅×D₁₆	1	2	yes	—
83	C₈	C₅×#127	1	1	yes	characteristic
84	C₈	C₂×C₅×D₈	1	1	yes	characteristic
85	C₅	#13725	1	1	yes	characteristic, direct product factor, Sylow
86	C₂²	—	16	4	no	—
87	C₂²	—	16	8	no	—
88	C₂²	C₂×C₅×D₁₆	1	1	yes	characteristic
89	C₄	C₅×D₃₂	1	4	yes	complemented
90	C₄	C₅×#493	1	1	yes	characteristic
91	C₄	C₂×C₅×D₁₆	1	1	yes	characteristic
92	C₂	—	32	4	no	—
93	C₂	C₅×#2246	1	1	yes	characteristic
94	C₂	C₂×C₅×D₃₂	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₅
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×C₈ ◁ C₄×C₅×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃₂	C₂	semidirect
2. C₅×#2246	C₂	semidirect
3. C₄×C₅×C₃₂	C₂	semidirect
10. #13725	C₅	direct (N × H)
19. C₅×C₃₂	D₄	semidirect
20. C₂×D₃₂	C₂×C₅	semidirect
21. #2246	C₂×C₅	semidirect
22. C₄×C₃₂	C₂×C₅	semidirect
56. C₃₂	C₅×D₄	semidirect
60. C₄×C₅	D₃₂	semidirect
85. C₅	#13725	direct (N × H)
89. C₄	C₅×D₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃₂	2
C₅×#2246	2
C₄×C₅×C₃₂	2
#13725	5

Subgroups — C5×#13725 #11936445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13725 #11936445