Subgroups — C₅×#448 #65611

Order 320.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₅×#121	C₂	1	1	yes	maximal, characteristic
4	C₅×#103	C₂	1	2	yes	maximal, complemented
5	C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×Q₈	—	2	4	no	—
7	C₂×C₅×Q₈	—	2	1	no	—
8	C₂×C₅×Q₈	C₂²	1	2	yes	—
9	C₂×C₅×D₄	—	2	1	no	—
10	C₂×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅	—	2	1	no	—
12	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₅×SD₁₆	—	2	4	no	—
14	C₂×C₅×C₈	C₂²	1	2	yes	—
15	C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₅×C₂²⋊C₄	—	2	1	no	—
17	#448	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂³×C₅	—	2	1	no	—
19	C₂³×C₅	D₄	1	1	yes	characteristic
20	C₅×Q₈	—	2	4	no	—
21	C₅×Q₈	—	2	2	no	—
22	C₅×Q₈	D₄	1	4	yes	complemented
23	C₅×D₄	—	2	2	no	—
24	C₅×D₄	—	4	2	no	—
25	C₂×C₄×C₅	—	2	4	no	—
26	C₂×C₄×C₅	—	2	2	no	—
27	C₂×C₄×C₅	—	2	2	no	—
28	C₂×C₄×C₅	—	2	1	no	—
29	C₂×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₅×C₈	—	2	2	no	—
32	C₂²×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
33	C₂×SD₁₆	C₂×C₅	1	2	yes	complemented
34	#121	C₂×C₅	1	1	yes	characteristic
35	#103	C₂×C₅	1	2	yes	complemented
36	C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
37	C₂²×C₅	—	2	1	no	—
38	C₂²×C₅	—	2	1	no	—
39	C₂²×C₅	—	4	1	no	—
40	C₂²×C₅	—	4	1	no	—
41	C₂²×C₅	—	4	1	no	—
42	C₂²×C₅	SD₁₆	1	2	yes	complemented
43	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
44	C₄×C₅	—	2	4	no	—
45	C₄×C₅	—	2	1	no	—
46	C₄×C₅	—	4	1	no	—
47	C₄×C₅	C₂×D₄	1	2	yes	—
48	C₂×Q₈	—	2	4	no	—
49	C₂×Q₈	—	2	1	no	—
50	C₂×Q₈	C₂²×C₅	1	2	yes	—
51	C₂×D₄	—	2	1	no	—
52	C₂×D₄	C₂²×C₅	1	1	yes	characteristic
53	C₂²×C₄	—	2	1	no	—
54	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
55	SD₁₆	—	2	4	no	—
56	C₂×C₈	C₂²×C₅	1	2	yes	—
57	C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
58	C₂²⋊C₄	—	2	1	no	—
59	C₂×C₅	—	2	2	no	—
60	C₂×C₅	—	8	1	no	—
61	C₂×C₅	#120	1	1	yes	characteristic
62	C₂×C₅	C₂×SD₁₆	1	1	yes	characteristic
63	C₂×C₅	#137	1	1	yes	characteristic
64	C₂³	—	2	1	no	—
65	C₂³	C₅×D₄	1	1	yes	characteristic
66	Q₈	—	2	4	no	—
67	Q₈	—	2	2	no	—
68	Q₈	C₅×D₄	1	4	yes	complemented
69	D₄	—	2	2	no	—
70	D₄	—	4	2	no	—
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	C₅×D₄	1	1	yes	characteristic
76	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
77	C₈	—	2	2	no	—
78	C₅	#448	1	1	yes	characteristic, direct product factor, Sylow
79	C₂²	—	2	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	4	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	C₅×SD₁₆	1	2	yes	complemented
85	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	C₂×C₅×D₄	1	2	yes	—
90	C₂	—	2	2	no	—
91	C₂	—	8	1	no	—
92	C₂	C₅×#120	1	1	yes	characteristic
93	C₂	C₂×C₅×SD₁₆	1	1	yes	characteristic
94	C₂	C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅
prime radical	C₅×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×Q₈	C₂	semidirect
2. C₂×C₅×SD₁₆	C₂	semidirect
4. C₅×#103	C₂	semidirect
5. C₅×C₂²⋊C₈	C₂	semidirect
17. #448	C₅	direct (N × H)
22. C₅×Q₈	D₄	semidirect
32. C₂²×Q₈	C₂×C₅	semidirect
33. C₂×SD₁₆	C₂×C₅	semidirect
35. #103	C₂×C₅	semidirect
36. C₂²⋊C₈	C₂×C₅	semidirect
42. C₂²×C₅	SD₁₆	semidirect
68. Q₈	C₅×D₄	semidirect
78. C₅	#448	direct (N × H)
84. C₂²	C₅×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×Q₈	2
C₂×C₅×SD₁₆	2
C₅×#121	2
C₅×#103	2
C₅×C₂²⋊C₈	2
#448	5

Subgroups — C5×#448 #65611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#448 #65611