Subgroups — C₅×#33496 #11956216

Order 1280.

526 conjugacy classes of subgroups.

The subgroup lattice has 128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×Q₈×C₁₆	C₂	1	8	yes	maximal, complemented
3	C₅×#2162	C₂	1	6	yes	maximal
4	C₂×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
5	C₅×C₈×Q₈	C₄	1	4	yes	—
6	C₅×C₈×Q₈	C₂²	1	4	yes	—
7	C₂×C₅×C₄⋊C₈	C₄	1	3	yes	—
8	C₂×C₄×C₅×C₈	C₂²	1	3	yes	—
9	C₅×C₄⋊C₁₆	C₂²	1	12	yes	—
10	C₅×C₂²⋊C₁₆	C₂²	1	4	yes	—
11	C₄×C₅×C₁₆	C₂²	1	12	yes	—
12	#33496	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₅×Q₈	C₈	1	1	yes	characteristic
14	C₂²×C₅×C₈	C₂×C₄	1	3	yes	—
15	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
16	C₄×C₅×Q₈	C₈	1	4	yes	—
17	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
18	C₂×C₅×C₄⋊C₄	C₈	1	3	yes	—
19	C₂×C₄²×C₅	C₂×C₄	1	3	yes	—
20	C₂×C₅×C₁₆	C₂³	1	8	yes	—
21	C₅×C₄⋊C₈	C₂×C₄	1	12	yes	—
22	C₄×C₅×C₈	C₂×C₄	1	6	yes	—
23	C₄×C₅×C₈	C₂³	1	6	yes	—
24	C₂×C₈×Q₈	C₂×C₅	1	1	yes	characteristic
25	Q₈×C₁₆	C₂×C₅	1	8	yes	complemented
26	#2162	C₂×C₅	1	6	yes	—
27	C₂×C₅×Q₈	C₁₆	1	8	yes	complemented
28	C₂×C₅×Q₈	C₂×C₈	1	4	yes	—
29	C₂²×C₄×C₅	C₂×C₈	1	3	yes	—
30	C₂²×C₄×C₅	C₂×C₈	1	3	yes	—
31	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₅×C₈	—	2	2	no	—
33	C₂×C₅×C₈	—	4	3	no	—
34	C₂×C₅×C₈	C₂²×C₄	1	6	yes	—
35	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
37	C₅×C₄⋊C₄	C₂×C₈	1	12	yes	—
38	C₄²×C₅	C₂×C₈	1	6	yes	—
39	C₄²×C₅	C₂²×C₄	1	6	yes	—
40	C₅×C₁₆	—	2	8	no	—
41	C₂×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
42	C₈×Q₈	C₄×C₅	1	4	yes	—
43	C₈×Q₈	C₂²×C₅	1	4	yes	—
44	C₂×C₄⋊C₈	C₄×C₅	1	3	yes	—
45	C₂×C₄×C₈	C₂²×C₅	1	3	yes	—
46	C₄⋊C₁₆	C₂²×C₅	1	12	yes	—
47	C₂²⋊C₁₆	C₂²×C₅	1	4	yes	—
48	C₄×C₁₆	C₂²×C₅	1	12	yes	—
49	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
50	C₅×Q₈	C₂×C₁₆	1	16	yes	—
51	C₂×C₄×C₅	—	2	1	no	—
52	C₂×C₄×C₅	—	2	1	no	—
53	C₂×C₄×C₅	—	4	3	no	—
54	C₂×C₄×C₅	C₂×C₁₆	1	12	yes	—
55	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
56	C₂×C₄×C₅	C₂²×C₈	1	6	yes	—
57	C₂×C₄×C₅	C₂²×C₈	1	6	yes	—
58	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
59	C₅×C₈	—	2	1	no	—
60	C₅×C₈	—	2	6	no	—
61	C₅×C₈	2₋¹⁺⁴	1	2	yes	—
62	C₂²×Q₈	C₅×C₈	1	1	yes	characteristic
63	C₂²×C₈	C₂×C₄×C₅	1	3	yes	—
64	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
65	C₄×Q₈	C₅×C₈	1	4	yes	—
66	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
67	C₂×C₄⋊C₄	C₅×C₈	1	3	yes	—
68	C₂×C₄²	C₂×C₄×C₅	1	3	yes	—
69	C₂×C₁₆	C₂³×C₅	1	8	yes	—
70	C₄⋊C₈	C₂×C₄×C₅	1	12	yes	—
71	C₄×C₈	C₂×C₄×C₅	1	6	yes	—
72	C₄×C₈	C₂³×C₅	1	6	yes	—
73	C₂²×C₅	—	2	1	no	—
74	C₂²×C₅	—	2	1	no	—
75	C₂²×C₅	C₂²×C₁₆	1	2	yes	—
76	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
77	C₄×C₅	—	2	6	no	—
78	C₄×C₅	—	2	1	no	—
79	C₄×C₅	C₂²×C₁₆	1	12	yes	—
80	C₄×C₅	#519	1	1	yes	characteristic
81	C₄×C₅	#568	1	1	yes	characteristic
82	C₂×Q₈	C₅×C₁₆	1	8	yes	complemented
83	C₂×Q₈	C₂×C₅×C₈	1	4	yes	—
84	C₂²×C₄	C₂×C₅×C₈	1	3	yes	—
85	C₂²×C₄	C₂×C₅×C₈	1	3	yes	—
86	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	4	3	no	—
89	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
90	C₂×C₈	C₂²×C₄×C₅	1	6	yes	—
91	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
92	C₄⋊C₄	C₂×C₅×C₈	1	12	yes	—
93	C₄²	C₂×C₅×C₈	1	6	yes	—
94	C₄²	C₂²×C₄×C₅	1	6	yes	—
95	C₁₆	—	2	8	no	—
96	C₂×C₅	—	2	2	no	—
97	C₂×C₅	#2982	1	1	yes	characteristic
98	C₂×C₅	C₂³×C₁₆	1	1	yes	characteristic
99	C₂×C₅	#3407	1	1	yes	characteristic
100	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
101	Q₈	C₂×C₅×C₁₆	1	16	yes	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	4	3	no	—
105	C₂×C₄	C₂×C₅×C₁₆	1	12	yes	—
106	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
107	C₂×C₄	C₂²×C₅×C₈	1	6	yes	—
108	C₂×C₄	C₂²×C₅×C₈	1	6	yes	—
109	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
110	C₈	—	2	1	no	—
111	C₈	—	2	6	no	—
112	C₈	C₅×2₋¹⁺⁴	1	2	yes	—
113	C₅	#33496	1	1	yes	characteristic, direct product factor, Sylow
114	C₂²	—	2	1	no	—
115	C₂²	—	2	1	no	—
116	C₂²	C₂²×C₅×C₁₆	1	2	yes	—
117	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
118	C₄	—	2	1	no	—
119	C₄	—	2	6	no	—
120	C₄	C₂²×C₅×C₁₆	1	12	yes	—
121	C₄	C₅×#519	1	1	yes	characteristic
122	C₄	C₅×#568	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	C₅×#2982	1	1	yes	characteristic
125	C₂	C₂³×C₅×C₁₆	1	1	yes	characteristic
126	C₂	C₅×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂⁴
commutator	C₂	C₂³×C₅×C₁₆
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂³×C₈
prime radical	C₂³×C₅	C₂²×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×Q₈×C₁₆	C₂	semidirect
12. #33496	C₅	direct (N × H)
25. Q₈×C₁₆	C₂×C₅	semidirect
27. C₂×C₅×Q₈	C₁₆	semidirect
82. C₂×Q₈	C₅×C₁₆	semidirect
113. C₅	#33496	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×C₈×Q₈	2
C₅×Q₈×C₁₆	2
C₅×#2162	2
#33496	5

Subgroups — C5×#33496 #11956216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33496 #11956216