Subgroups — C₂×C₅×#1380 #11935275

Order 1280.

694 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#107	C₂	1	2	yes	maximal
3	C₅×#1380	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
5	C₂²×C₅×C₄⋊C₄	—	2	2	no	—
6	C₂²×C₅×C₁₆	—	2	4	no	—
7	C₂²×C₅×C₁₆	C₄	1	4	yes	complemented
8	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
9	C₂×C₅×#107	—	2	4	no	—
10	C₂×C₅×#107	—	2	2	no	—
11	C₂×C₅×#107	C₄	1	8	yes	complemented
12	C₂×C₅×#107	C₂²	1	4	yes	—
13	C₂×#1380	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂³×C₄×C₅	—	4	2	no	—
15	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
16	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
17	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
18	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
19	C₂²×C₅×C₈	D₄	1	4	yes	—
20	C₂²×C₅×C₈	Q₈	1	2	yes	—
21	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₄	—	2	8	no	—
23	C₂×C₅×C₄⋊C₄	—	2	4	no	—
24	C₂×C₅×C₄⋊C₄	—	4	2	no	—
25	C₂×C₅×C₄⋊C₄	—	4	4	no	—
26	C₂×C₅×C₁₆	—	2	8	no	—
27	C₂×C₅×C₁₆	—	2	4	no	—
28	C₂×C₅×C₁₆	C₂×C₄	1	4	yes	complemented
29	C₅×#107	—	2	8	no	—
30	C₅×#107	—	2	4	no	—
31	C₅×#107	C₂×C₄	1	8	yes	complemented
32	C₂³×C₁₆	C₂×C₅	1	1	yes	characteristic
33	C₂²×#107	C₂×C₅	1	2	yes	—
34	#1380	C₂×C₅	1	4	yes	direct product factor
35	C₂⁴×C₅	D₈	1	1	yes	characteristic
36	C₂²×C₄×C₅	—	4	8	no	—
37	C₂²×C₄×C₅	—	4	4	no	—
38	C₂²×C₄×C₅	—	8	4	no	—
39	C₂²×C₄×C₅	—	8	4	no	—
40	C₂²×C₄×C₅	C₂²⋊C₄	1	4	yes	—
41	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
42	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
43	C₂²×C₄×C₅	SD₁₆	1	4	yes	—
44	C₂²×C₄×C₅	Q₁₆	1	2	yes	—
45	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
46	C₂×C₅×C₈	C₄²	1	4	yes	—
47	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
48	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
49	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
50	C₂×C₅×C₈	C₄⋊C₄	1	8	yes	—
51	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
53	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
54	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
55	C₅×C₄⋊C₄	—	2	8	no	—
56	C₅×C₄⋊C₄	—	4	8	no	—
57	C₅×C₄⋊C₄	—	4	4	no	—
58	C₅×C₁₆	—	2	4	no	—
59	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
60	C₂²×C₄⋊C₄	—	2	2	no	—
61	C₂²×C₁₆	—	2	4	no	—
62	C₂²×C₁₆	C₄×C₅	1	4	yes	complemented
63	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
64	C₂×#107	—	2	2	no	—
65	C₂×#107	—	2	4	no	—
66	C₂×#107	C₄×C₅	1	8	yes	complemented
67	C₂×#107	C₂²×C₅	1	4	yes	—
68	C₂³×C₅	#102	1	4	yes	—
69	C₂³×C₅	#107	1	2	yes	—
70	C₂³×C₅	D₁₆	1	2	yes	—
71	C₂³×C₅	SD₃₂	1	4	yes	—
72	C₂³×C₅	Q₃₂	1	2	yes	—
73	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
74	C₂×C₄×C₅	—	4	8	no	—
75	C₂×C₄×C₅	—	8	16	no	—
76	C₂×C₄×C₅	—	8	4	no	—
77	C₂×C₄×C₅	—	8	4	no	—
78	C₂×C₄×C₅	#95	1	4	yes	—
79	C₂×C₄×C₅	#102	1	4	yes	—
80	C₂×C₄×C₅	#103	1	8	yes	—
81	C₂×C₄×C₅	#106	1	4	yes	—
82	C₂×C₄×C₅	#107	1	2	yes	—
83	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
84	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
86	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
87	C₅×C₈	#95	1	4	yes	—
88	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
89	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
91	C₂³×C₄	—	4	2	no	—
92	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
93	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
94	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
95	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
96	C₂²×C₈	C₅×D₄	1	4	yes	—
97	C₂²×C₈	C₅×Q₈	1	2	yes	—
98	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
99	C₂×C₄⋊C₄	—	2	8	no	—
100	C₂×C₄⋊C₄	—	2	4	no	—
101	C₂×C₄⋊C₄	—	4	2	no	—
102	C₂×C₄⋊C₄	—	4	4	no	—
103	C₂×C₁₆	—	2	8	no	—
104	C₂×C₁₆	—	2	4	no	—
105	C₂×C₁₆	C₂×C₄×C₅	1	4	yes	complemented
106	#107	—	2	8	no	—
107	#107	—	2	4	no	—
108	#107	C₂×C₄×C₅	1	8	yes	complemented
109	C₂²×C₅	#340	1	4	yes	—
110	C₂²×C₅	#357	1	8	yes	—
111	C₂²×C₅	#358	1	8	yes	—
112	C₂²×C₅	#366	1	4	yes	—
113	C₂²×C₅	#367	1	4	yes	—
114	C₂²×C₅	C₂×#102	1	2	yes	—
115	C₂²×C₅	C₂×#107	1	1	yes	characteristic
116	C₂²×C₅	C₂×D₁₆	1	1	yes	characteristic
117	C₂²×C₅	C₂×SD₃₂	1	2	yes	—
118	C₂²×C₅	C₂×Q₃₂	1	1	yes	characteristic
119	C₄×C₅	—	8	8	no	—
120	C₄×C₅	#340	1	4	yes	—
121	C₄×C₅	C₂×#95	1	1	yes	characteristic
122	C₄×C₅	C₂×#103	1	2	yes	—
123	C₄×C₅	C₂×#106	1	1	yes	characteristic
124	C₂⁴	C₅×D₈	1	1	yes	characteristic
125	C₂²×C₄	—	4	4	no	—
126	C₂²×C₄	—	4	8	no	—
127	C₂²×C₄	—	8	4	no	—
128	C₂²×C₄	—	8	4	no	—
129	C₂²×C₄	C₅×C₂²⋊C₄	1	4	yes	—
130	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
131	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
132	C₂²×C₄	C₅×SD₁₆	1	4	yes	—
133	C₂²×C₄	C₅×Q₁₆	1	2	yes	—
134	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
135	C₂×C₈	C₄²×C₅	1	4	yes	—
136	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
137	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
138	C₂×C₈	C₅×C₄⋊C₄	1	8	yes	—
139	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
140	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
141	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
142	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
143	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
144	C₄⋊C₄	—	2	8	no	—
145	C₄⋊C₄	—	4	4	no	—
146	C₄⋊C₄	—	4	8	no	—
147	C₁₆	—	2	4	no	—
148	C₂×C₅	#1380	1	8	yes	direct product factor
149	C₂×C₅	C₂×#340	1	1	yes	characteristic
150	C₂×C₅	C₂×#357	1	2	yes	—
151	C₂×C₅	C₂×#358	1	2	yes	—
152	C₂×C₅	C₂×#366	1	1	yes	characteristic
153	C₂×C₅	C₂×#367	1	1	yes	characteristic
154	C₂³	C₅×#102	1	4	yes	—
155	C₂³	C₅×#107	1	2	yes	—
156	C₂³	C₅×D₁₆	1	2	yes	—
157	C₂³	C₅×SD₃₂	1	4	yes	—
158	C₂³	C₅×Q₃₂	1	2	yes	—
159	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
160	C₂×C₄	—	4	8	no	—
161	C₂×C₄	—	8	16	no	—
162	C₂×C₄	—	8	4	no	—
163	C₂×C₄	—	8	4	no	—
164	C₂×C₄	C₅×#95	1	4	yes	—
165	C₂×C₄	C₅×#102	1	4	yes	—
166	C₂×C₄	C₅×#103	1	8	yes	—
167	C₂×C₄	C₅×#106	1	4	yes	—
168	C₂×C₄	C₅×#107	1	2	yes	—
169	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
172	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
173	C₈	C₅×#95	1	4	yes	—
174	C₈	C₂×C₄²×C₅	1	1	yes	characteristic
175	C₈	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
176	C₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
177	C₅	C₂×#1380	1	1	yes	characteristic, direct product factor, Sylow
178	C₂²	C₅×#340	1	4	yes	—
179	C₂²	C₅×#357	1	8	yes	—
180	C₂²	C₅×#358	1	8	yes	—
181	C₂²	C₅×#366	1	4	yes	—
182	C₂²	C₅×#367	1	4	yes	—
183	C₂²	C₂×C₅×#102	1	2	yes	—
184	C₂²	C₂×C₅×#107	1	1	yes	characteristic
185	C₂²	C₂×C₅×D₁₆	1	1	yes	characteristic
186	C₂²	C₂×C₅×SD₃₂	1	2	yes	—
187	C₂²	C₂×C₅×Q₃₂	1	1	yes	characteristic
188	C₄	—	8	8	no	—
189	C₄	C₅×#340	1	4	yes	—
190	C₄	C₂×C₅×#95	1	1	yes	characteristic
191	C₄	C₂×C₅×#103	1	2	yes	—
192	C₄	C₂×C₅×#106	1	1	yes	characteristic
193	C₂	C₅×#1380	1	8	yes	direct product factor
194	C₂	C₂×C₅×#340	1	1	yes	characteristic
195	C₂	C₂×C₅×#357	1	2	yes	—
196	C₂	C₂×C₅×#358	1	2	yes	—
197	C₂	C₂×C₅×#366	1	1	yes	characteristic
198	C₂	C₂×C₅×#367	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₅	D₈
commutator	C₈	C₂×C₄²×C₅
Frattini, cosocle	C₂²×C₈	C₂³×C₅
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1380	C₂	direct (N × H)
7. C₂²×C₅×C₁₆	C₄	semidirect
11. C₂×C₅×#107	C₄	semidirect
13. C₂×#1380	C₅	direct (N × H)
28. C₂×C₅×C₁₆	C₂×C₄	semidirect
31. C₅×#107	C₂×C₄	semidirect
34. #1380	C₂×C₅	direct (N × H)
62. C₂²×C₁₆	C₄×C₅	semidirect
66. C₂×#107	C₄×C₅	semidirect
105. C₂×C₁₆	C₂×C₄×C₅	semidirect
108. #107	C₂×C₄×C₅	semidirect
148. C₂×C₅	#1380	direct (N × H)
177. C₅	C₂×#1380	direct (N × H)
193. C₂	C₅×#1380	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×C₁₆	2
C₂²×C₅×#107	2
C₅×#1380	2
C₂×#1380	5

Subgroups — C2×C5×#1380 #11935275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1380 #11935275