Subgroups — C₅×#13190 #11935910

Order 1280.

522 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₂²⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂×C₅×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₅×C₈	C₂²	1	2	yes	—
6	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
7	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
8	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
9	C₅×C₈×D₄	—	2	2	no	—
10	C₅×C₈×D₄	—	2	2	no	—
11	C₂×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₅×C₄⋊C₁₆	—	2	2	no	—
15	C₅×C₂²⋊C₁₆	—	2	8	no	—
16	C₅×#346	—	2	2	no	—
17	#13190	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₅×D₄	C₈	1	1	yes	characteristic
19	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
20	C₂²×C₅×C₈	—	2	4	no	—
21	C₂²×C₅×C₈	—	2	2	no	—
22	C₂²×C₅×C₈	—	2	2	no	—
23	C₂²×C₅×C₈	—	2	4	no	—
24	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
25	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
27	C₄×C₅×D₄	—	2	2	no	—
28	C₄×C₅×D₄	—	2	2	no	—
29	C₂×C₅×C₄⋊C₄	C₈	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₄	C₈	1	2	yes	—
31	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂×C₅×C₁₆	—	2	2	no	—
33	C₂×C₅×C₁₆	—	2	2	no	—
34	C₂×C₅×C₁₆	—	2	4	no	—
35	C₂×C₅×C₁₆	—	2	2	no	—
36	C₂×C₅×C₁₆	D₄	1	4	yes	complemented
37	C₅×C₄⋊C₈	—	2	2	no	—
38	C₅×C₂²⋊C₈	—	2	4	no	—
39	C₄×C₅×C₈	D₄	1	2	yes	—
40	C₄×C₅×C₈	D₄	1	2	yes	—
41	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic
42	C₂×C₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
43	C₂×C₂²⋊C₁₆	C₂×C₅	1	4	yes	complemented
44	C₂×#346	C₂×C₅	1	1	yes	characteristic, complemented
45	C₂⁴×C₅	C₂×C₈	1	2	yes	—
46	C₂×C₅×D₄	—	2	4	no	—
47	C₂×C₅×D₄	—	2	2	no	—
48	C₂²×C₄×C₅	—	2	2	no	—
49	C₂²×C₄×C₅	—	2	4	no	—
50	C₂²×C₄×C₅	—	2	2	no	—
51	C₂²×C₄×C₅	—	2	4	no	—
52	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
53	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
54	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₅×C₈	—	2	2	no	—
57	C₂×C₅×C₈	—	2	2	no	—
58	C₂×C₅×C₈	—	2	4	no	—
59	C₂×C₅×C₈	—	4	4	no	—
60	C₂×C₅×C₈	—	4	2	no	—
61	C₂×C₅×C₈	—	4	2	no	—
62	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
63	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
64	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
65	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
66	C₂×C₅×C₈	#41	1	2	yes	—
67	C₅×C₄⋊C₄	—	2	2	no	—
68	C₅×C₂²⋊C₄	—	2	4	no	—
69	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
70	C₄²×C₅	M₁₆	1	2	yes	—
71	C₅×C₁₆	—	2	4	no	—
72	C₅×C₁₆	—	4	2	no	—
73	C₂³×C₈	C₂²×C₅	1	2	yes	—
74	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
75	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
76	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
77	C₈×D₄	—	2	2	no	—
78	C₈×D₄	—	2	2	no	—
79	C₂×C₄⋊C₈	C₄×C₅	1	1	yes	characteristic
80	C₂×C₂²⋊C₈	C₄×C₅	1	2	yes	—
81	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
82	C₄⋊C₁₆	—	2	2	no	—
83	C₂²⋊C₁₆	—	2	8	no	—
84	#346	—	2	2	no	—
85	C₂³×C₅	—	2	2	no	—
86	C₂³×C₅	—	2	4	no	—
87	C₂³×C₅	—	2	2	no	—
88	C₂³×C₅	—	2	4	no	—
89	C₂³×C₅	M₃₂	1	4	yes	—
90	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
91	C₅×D₄	—	2	8	no	—
92	C₂×C₄×C₅	—	2	2	no	—
93	C₂×C₄×C₅	—	2	2	no	—
94	C₂×C₄×C₅	—	2	2	no	—
95	C₂×C₄×C₅	—	2	4	no	—
96	C₂×C₄×C₅	—	4	2	no	—
97	C₂×C₄×C₅	—	4	2	no	—
98	C₂×C₄×C₅	—	4	4	no	—
99	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
100	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
101	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
103	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
104	C₂×C₄×C₅	#131	1	2	yes	—
105	C₅×C₈	—	2	2	no	—
106	C₅×C₈	—	4	2	no	—
107	C₅×C₈	#121	1	2	yes	—
108	C₅×C₈	#124	1	1	yes	characteristic
109	C₅×C₈	#127	1	1	yes	characteristic
110	C₂²×D₄	C₅×C₈	1	1	yes	characteristic
111	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
112	C₂²×C₈	—	2	4	no	—
113	C₂²×C₈	—	2	2	no	—
114	C₂²×C₈	—	2	2	no	—
115	C₂²×C₈	—	2	4	no	—
116	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
117	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
118	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
119	C₄×D₄	—	2	2	no	—
120	C₄×D₄	—	2	2	no	—
121	C₂×C₄⋊C₄	C₅×C₈	1	1	yes	characteristic
122	C₂×C₂²⋊C₄	C₅×C₈	1	2	yes	—
123	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
124	C₂×C₁₆	—	2	2	no	—
125	C₂×C₁₆	—	2	2	no	—
126	C₂×C₁₆	—	2	4	no	—
127	C₂×C₁₆	—	2	2	no	—
128	C₂×C₁₆	C₅×D₄	1	4	yes	complemented
129	C₄⋊C₈	—	2	2	no	—
130	C₂²⋊C₈	—	2	4	no	—
131	C₄×C₈	C₅×D₄	1	2	yes	—
132	C₄×C₈	C₅×D₄	1	2	yes	—
133	C₂²×C₅	—	2	4	no	—
134	C₂²×C₅	—	2	8	no	—
135	C₂²×C₅	—	4	2	no	—
136	C₂²×C₅	—	4	4	no	—
137	C₂²×C₅	—	4	2	no	—
138	C₂²×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
139	C₂²×C₅	C₈×D₄	1	2	yes	—
140	C₂²×C₅	C₂×M₃₂	1	2	yes	—
141	C₂²×C₅	#504	1	2	yes	—
142	C₄×C₅	—	2	2	no	—
143	C₄×C₅	—	2	2	no	—
144	C₄×C₅	—	4	2	no	—
145	C₄×C₅	#390	1	1	yes	characteristic
146	C₄×C₅	#408	1	1	yes	characteristic
147	C₄×C₅	#436	1	2	yes	—
148	C₂⁴	C₂×C₅×C₈	1	2	yes	—
149	C₂×D₄	—	2	4	no	—
150	C₂×D₄	—	2	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	2	4	no	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	2	4	no	—
155	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
156	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
158	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	—	2	4	no	—
162	C₂×C₈	—	4	4	no	—
163	C₂×C₈	—	4	2	no	—
164	C₂×C₈	—	4	2	no	—
165	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
166	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
167	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
168	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
169	C₂×C₈	C₅×#41	1	2	yes	—
170	C₄⋊C₄	—	2	2	no	—
171	C₂²⋊C₄	—	2	4	no	—
172	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
173	C₄²	C₅×M₁₆	1	2	yes	—
174	C₁₆	—	2	4	no	—
175	C₁₆	—	4	2	no	—
176	C₂×C₅	—	4	4	no	—
177	C₂×C₅	#1954	1	1	yes	characteristic
178	C₂×C₅	#2112	1	1	yes	characteristic
179	C₂×C₅	#2113	1	1	yes	characteristic
180	C₂×C₅	#2168	1	4	yes	—
181	C₂³	—	2	2	no	—
182	C₂³	—	2	4	no	—
183	C₂³	—	2	2	no	—
184	C₂³	—	2	4	no	—
185	C₂³	C₅×M₃₂	1	4	yes	—
186	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
187	D₄	—	2	8	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	4	no	—
195	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
196	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
197	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
199	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
200	C₂×C₄	C₅×#131	1	2	yes	—
201	C₈	—	2	2	no	—
202	C₈	—	4	2	no	—
203	C₈	C₅×#121	1	2	yes	—
204	C₈	C₅×#124	1	1	yes	characteristic
205	C₈	C₅×#127	1	1	yes	characteristic
206	C₅	#13190	1	1	yes	characteristic, direct product factor, Sylow
207	C₂²	—	2	4	no	—
208	C₂²	—	2	8	no	—
209	C₂²	—	4	2	no	—
210	C₂²	—	4	4	no	—
211	C₂²	—	4	2	no	—
212	C₂²	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
213	C₂²	C₅×C₈×D₄	1	2	yes	—
214	C₂²	C₂×C₅×M₃₂	1	2	yes	—
215	C₂²	C₅×#504	1	2	yes	—
216	C₄	—	2	2	no	—
217	C₄	—	2	2	no	—
218	C₄	—	4	2	no	—
219	C₄	C₅×#390	1	1	yes	characteristic
220	C₄	C₅×#408	1	1	yes	characteristic
221	C₄	C₅×#436	1	2	yes	—
222	C₂	—	4	4	no	—
223	C₂	C₅×#1954	1	1	yes	characteristic
224	C₂	C₅×#2112	1	1	yes	characteristic
225	C₂	C₅×#2113	1	1	yes	characteristic
226	C₂	C₅×#2168	1	4	yes	—

	subgroup	G/H
center	C₂²×C₅×C₈	C₂³
commutator	C₂³	C₂²×C₅×C₈
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂³×C₅	C₂²×C₈
prime radical	C₂²×C₅×D₄	C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×C₄⋊C₁₆	C₂	semidirect
3. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
4. C₂×C₅×#346	C₂	semidirect
17. #13190	C₅	direct (N × H)
36. C₂×C₅×C₁₆	D₄	semidirect
42. C₂×C₄⋊C₁₆	C₂×C₅	semidirect
43. C₂×C₂²⋊C₁₆	C₂×C₅	semidirect
44. C₂×#346	C₂×C₅	semidirect
128. C₂×C₁₆	C₅×D₄	semidirect
206. C₅	#13190	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×D₄	2
C₂×C₅×C₄⋊C₁₆	2
C₂×C₅×C₂²⋊C₁₆	2
C₂×C₅×#346	2
#13190	5

Subgroups — C5×#13190 #11935910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13190 #11935910