Subgroups — C₅×#12879 #11935599

Order 1280.

366 conjugacy classes of subgroups.

The subgroup lattice has 170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₄⋊C₁₆	C₂	1	2	yes	maximal
2	C₄²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#1374	C₂	1	4	yes	maximal
4	C₂²×C₅×C₁₆	C₂²	1	4	yes	—
5	C₂×C₄×C₅×C₈	C₄	1	2	yes	—
6	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic
7	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₄³×C₅	C₄	1	1	yes	characteristic
10	C₅×C₄⋊C₁₆	—	2	4	no	—
11	#12879	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
14	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₅	C₈	1	2	yes	—
16	C₂×C₄²×C₅	C₈	1	1	yes	characteristic
17	C₂×C₄²×C₅	C₈	1	1	yes	characteristic
18	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
20	C₂×C₅×C₁₆	—	2	4	no	—
21	C₂×C₅×C₁₆	—	2	8	no	—
22	C₄×C₅×C₈	—	2	4	no	—
23	C₄×C₅×C₈	—	2	4	no	—
24	C₄×C₅×C₈	—	2	2	no	—
25	C₄×C₅×C₈	D₄	1	2	yes	—
26	C₄×C₅×C₈	Q₈	1	2	yes	—
27	C₂×C₄⋊C₁₆	C₂×C₅	1	2	yes	—
28	C₄²×C₈	C₂×C₅	1	1	yes	characteristic
29	#1374	C₂×C₅	1	4	yes	—
30	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
31	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
32	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
33	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
34	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₅×C₈	—	2	2	no	—
36	C₂×C₅×C₈	—	2	2	no	—
37	C₂×C₅×C₈	—	2	2	no	—
38	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
39	C₂×C₅×C₈	M₁₆	1	4	yes	—
40	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
41	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₅×C₈	#41	1	4	yes	—
43	C₄²×C₅	—	2	4	no	—
44	C₄²×C₅	—	2	2	no	—
45	C₄²×C₅	—	2	2	no	—
46	C₄²×C₅	—	2	2	no	—
47	C₄²×C₅	C₁₆	1	4	yes	complemented
48	C₄²×C₅	C₄⋊C₄	1	2	yes	—
49	C₄²×C₅	M₁₆	1	2	yes	—
50	C₅×C₁₆	—	4	4	no	—
51	C₂²×C₁₆	C₂²×C₅	1	4	yes	—
52	C₂×C₄×C₈	C₄×C₅	1	2	yes	—
53	C₂×C₄×C₈	C₄×C₅	1	1	yes	characteristic
54	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
55	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
56	C₄³	C₄×C₅	1	1	yes	characteristic
57	C₄⋊C₁₆	—	2	4	no	—
58	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
59	C₂×C₄×C₅	—	2	2	no	—
60	C₂×C₄×C₅	—	2	2	no	—
61	C₂×C₄×C₅	—	2	2	no	—
62	C₂×C₄×C₅	—	2	2	no	—
63	C₂×C₄×C₅	—	2	2	no	—
64	C₂×C₄×C₅	C₄⋊C₈	1	2	yes	—
65	C₂×C₄×C₅	C₄⋊C₈	1	2	yes	—
66	C₂×C₄×C₅	C₂×C₁₆	1	4	yes	—
67	C₂×C₄×C₅	C₂×C₁₆	1	2	yes	—
68	C₂×C₄×C₅	M₃₂	1	4	yes	—
69	C₂×C₄×C₅	M₃₂	1	2	yes	—
70	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₅	#117	1	2	yes	—
72	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
73	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
74	C₅×C₈	—	2	2	no	—
75	C₅×C₈	—	2	4	no	—
76	C₅×C₈	#124	1	2	yes	—
77	C₅×C₈	#125	1	2	yes	—
78	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
79	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
80	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
81	C₂×C₄²	C₅×C₈	1	2	yes	—
82	C₂×C₄²	C₅×C₈	1	1	yes	characteristic
83	C₂×C₄²	C₅×C₈	1	1	yes	characteristic
84	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
85	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
86	C₂×C₁₆	—	2	4	no	—
87	C₂×C₁₆	—	2	8	no	—
88	C₄×C₈	—	2	4	no	—
89	C₄×C₈	—	2	4	no	—
90	C₄×C₈	—	2	2	no	—
91	C₄×C₈	C₅×D₄	1	2	yes	—
92	C₄×C₈	C₅×Q₈	1	2	yes	—
93	C₂²×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
94	C₂²×C₅	#431	1	2	yes	—
95	C₂²×C₅	C₂²×C₁₆	1	1	yes	characteristic
96	C₂²×C₅	C₂×M₃₂	1	1	yes	characteristic
97	C₂²×C₅	C₂×M₃₂	1	2	yes	—
98	C₄×C₅	—	2	2	no	—
99	C₄×C₅	—	2	4	no	—
100	C₄×C₅	—	2	4	no	—
101	C₄×C₅	C₄⋊C₁₆	1	4	yes	—
102	C₄×C₅	#382	1	1	yes	characteristic
103	C₄×C₅	#423	1	1	yes	characteristic
104	C₄×C₅	#432	1	2	yes	—
105	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
106	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
107	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
108	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
109	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
110	C₂×C₈	—	2	2	no	—
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	—	2	2	no	—
113	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
114	C₂×C₈	C₅×M₁₆	1	4	yes	—
115	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
116	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
117	C₂×C₈	C₅×#41	1	4	yes	—
118	C₄²	—	2	2	no	—
119	C₄²	—	2	2	no	—
120	C₄²	—	2	4	no	—
121	C₄²	—	2	2	no	—
122	C₄²	C₅×C₁₆	1	4	yes	complemented
123	C₄²	C₅×C₄⋊C₄	1	2	yes	—
124	C₄²	C₅×M₁₆	1	2	yes	—
125	C₁₆	—	4	4	no	—
126	C₂×C₅	#1831	1	1	yes	characteristic
127	C₂×C₅	C₂×C₄⋊C₁₆	1	1	yes	characteristic
128	C₂×C₅	#2150	1	1	yes	characteristic
129	C₂×C₅	#2162	1	2	yes	—
130	C₂×C₅	#2163	1	2	yes	—
131	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	C₅×C₄⋊C₈	1	2	yes	—
138	C₂×C₄	C₅×C₄⋊C₈	1	2	yes	—
139	C₂×C₄	C₂×C₅×C₁₆	1	4	yes	—
140	C₂×C₄	C₂×C₅×C₁₆	1	2	yes	—
141	C₂×C₄	C₅×M₃₂	1	4	yes	—
142	C₂×C₄	C₅×M₃₂	1	2	yes	—
143	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄	C₅×#117	1	2	yes	—
145	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
146	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
147	C₈	—	2	2	no	—
148	C₈	—	2	4	no	—
149	C₈	C₅×#124	1	2	yes	—
150	C₈	C₅×#125	1	2	yes	—
151	C₅	#12879	1	1	yes	characteristic, direct product factor, Sylow
152	C₂²	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
153	C₂²	C₅×#431	1	2	yes	—
154	C₂²	C₂²×C₅×C₁₆	1	1	yes	characteristic
155	C₂²	C₂×C₅×M₃₂	1	1	yes	characteristic
156	C₂²	C₂×C₅×M₃₂	1	2	yes	—
157	C₄	—	2	2	no	—
158	C₄	—	2	4	no	—
159	C₄	—	2	4	no	—
160	C₄	C₅×C₄⋊C₁₆	1	4	yes	—
161	C₄	C₅×#382	1	1	yes	characteristic
162	C₄	C₅×#423	1	1	yes	characteristic
163	C₄	C₅×#432	1	2	yes	—
164	C₂	C₅×#1831	1	1	yes	characteristic
165	C₂	C₂×C₅×C₄⋊C₁₆	1	1	yes	characteristic
166	C₂	C₅×#2150	1	1	yes	characteristic
167	C₂	C₅×#2162	1	2	yes	—
168	C₂	C₅×#2163	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
11. #12879	C₅	direct (N × H)
47. C₄²×C₅	C₁₆	semidirect
122. C₄²	C₅×C₁₆	semidirect
151. C₅	#12879	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×C₄⋊C₁₆	2
C₄²×C₅×C₈	2
C₅×#1374	2
#12879	5

Subgroups — C5×#12879 #11935599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12879 #11935599