Subgroups — D₅×#5140 #14478132

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#131	C₂	1	1	yes	maximal, characteristic
2	#11751241	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5140	C₂	1	1	yes	maximal, characteristic, complemented
4	#11747525	C₂	1	3	yes	maximal, complemented
5	#11747524	C₂	1	3	yes	maximal, complemented
6	D₅×#812	C₂	1	3	yes	maximal, complemented
7	C₂×D₅×C₃⋊C₁₆	C₂	1	3	yes	maximal, complemented
8	D₅×#504	—	3	1	no	maximal, Hall
9	C₃×D₅×#41	C₄	1	1	yes	characteristic
10	C₃×C₅×#131	C₂²	1	1	yes	characteristic
11	C₃×#4094	C₄	1	1	yes	characteristic
12	C₃×#4053	C₄	1	3	yes	—
13	C₃×D₅×M₁₆	C₄	1	3	yes	—
14	C₃×#4047	C₂²	1	3	yes	—
15	C₂×C₃×C₈×D₅	C₂²	1	3	yes	—
16	#91096	C₂²	1	3	yes	complemented
17	C₂×C₃⋊#672	C₂²	1	3	yes	complemented
18	C₅×#812	C₂²	1	3	yes	complemented
19	C₂×C₅×C₃⋊C₁₆	C₂²	1	3	yes	complemented
20	#90934	C₂²	1	6	yes	complemented
21	D₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
22	D₅×C₃⋊C₁₆	C₂²	1	3	yes	—
23	D₅×C₃⋊C₁₆	C₂²	1	3	yes	complemented
24	D₅×C₃⋊C₁₆	C₂²	1	3	yes	complemented
25	C₂×#5140	—	5	1	no	maximal, Hall
26	D₅×#131	D₃	1	1	yes	characteristic
27	C₅×#504	—	3	1	no	—
28	#65429	—	3	1	no	—
29	#65196	—	3	3	no	—
30	D₅×M₃₂	—	3	3	no	—
31	#65190	—	3	3	no	—
32	C₂×D₅×C₁₆	—	3	3	no	—
33	C₃×C₅×#41	C₂×C₄	1	1	yes	characteristic
34	C₃×#713	C₈	1	1	yes	characteristic
35	C₃×Q₈×D₅	C₈	1	1	yes	characteristic
36	C₃×#711	C₈	1	3	yes	—
37	C₃×D₄×D₅	C₈	1	3	yes	—
38	C₃×#709	C₂×C₄	1	3	yes	—
39	C₂×C₃×C₄×D₅	C₂×C₄	1	3	yes	—
40	C₃×C₅×M₁₆	C₂×C₄	1	3	yes	—
41	C₂×C₃×C₅×C₈	C₂³	1	3	yes	—
42	C₃×#681	C₂×C₄	1	3	yes	—
43	C₂×C₃×#168	C₂×C₄	1	3	yes	—
44	C₃×#676	C₂×C₄	1	6	yes	—
45	C₃×C₈×D₅	C₂×C₄	1	3	yes	—
46	C₃×C₈×D₅	C₂×C₄	1	3	yes	—
47	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
48	C₃×C₈×D₅	C₂³	1	3	yes	—
49	C₃⋊#672	C₂³	1	1	yes	characteristic
50	C₃⋊#672	C₂³	1	3	yes	—
51	C₅×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
52	C₅×C₃⋊C₁₆	C₂³	1	3	yes	—
53	C₂×C₃×#131	—	5	1	no	—
54	#5140	—	5	1	no	—
55	#5140	—	5	3	no	—
56	#5140	—	5	3	no	—
57	#5140	D₅	1	1	yes	characteristic, direct product factor
58	C₂×#812	—	5	3	no	—
59	C₂²×C₃⋊C₁₆	—	5	3	no	—
60	D₅×#41	Dic₃	1	1	yes	characteristic
61	C₅×#131	C₂×D₃	1	1	yes	characteristic
62	#4094	Dic₃	1	1	yes	characteristic
63	#4053	Dic₃	1	3	yes	—
64	D₅×M₁₆	Dic₃	1	3	yes	—
65	#4047	C₂×D₃	1	3	yes	—
66	C₂×C₈×D₅	C₂×D₃	1	3	yes	—
67	C₅×M₃₂	—	3	3	no	—
68	C₂×C₅×C₁₆	—	3	3	no	—
69	#3944	—	3	3	no	—
70	C₂×#672	—	3	3	no	—
71	#3930	—	3	6	no	—
72	D₅×C₁₆	—	3	1	no	—
73	D₅×C₁₆	—	3	3	no	—
74	D₅×C₁₆	—	3	3	no	—
75	D₅×C₁₆	—	3	3	no	—
76	C₂×#504	—	15	1	no	Sylow
77	C₂²×C₃×D₅	C₂×C₈	1	3	yes	—
78	C₃×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
79	C₃×C₅×D₄	C₂×C₈	1	3	yes	—
80	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
81	C₃×C₂²⋊D₅	C₂×C₈	1	6	yes	—
82	C₂×C₃×Dic₅	C₂×C₈	1	3	yes	—
83	C₃×D₂₀	C₂×C₈	1	3	yes	—
84	C₃×C₄×D₅	C₂×C₈	1	3	yes	—
85	C₃×C₄×D₅	C₂×C₈	1	3	yes	—
86	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
87	C₃×C₄×D₅	C₂²×C₄	1	3	yes	—
88	C₃×Dic₁₀	C₂×C₈	1	3	yes	—
89	C₃×C₅×C₈	C₂²×C₄	1	3	yes	—
90	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
91	C₃×#168	C₂²×C₄	1	1	yes	characteristic
92	C₃×#168	C₂²×C₄	1	3	yes	—
93	C₂×C₃×#41	—	5	1	no	—
94	C₃×#131	—	5	1	no	—
95	C₃×#131	—	5	3	no	—
96	C₃×#131	—	5	3	no	—
97	C₃×#131	C₂×D₅	1	1	yes	characteristic
98	C₂×C₃×M₁₆	—	5	3	no	—
99	C₂²×C₃×C₈	—	5	3	no	—
100	#812	—	5	3	no	—
101	#812	—	5	6	no	—
102	#812	C₂×D₅	1	3	yes	complemented
103	C₂×C₃⋊C₁₆	—	5	3	no	—
104	C₂×C₃⋊C₁₆	—	5	3	no	—
105	C₂×C₃⋊C₁₆	—	5	3	no	—
106	C₂×C₃⋊C₁₆	—	5	1	no	—
107	C₂×C₃⋊C₁₆	—	5	3	no	—
108	C₂×C₃⋊C₁₆	C₂×D₅	1	3	yes	complemented
109	C₅×#41	C₂×Dic₃	1	1	yes	characteristic
110	#713	C₃⋊C₈	1	1	yes	characteristic
111	Q₈×D₅	C₃⋊C₈	1	1	yes	characteristic
112	#711	C₃⋊C₈	1	3	yes	—
113	D₄×D₅	C₃⋊C₈	1	3	yes	—
114	#709	C₂×Dic₃	1	3	yes	—
115	C₂×C₄×D₅	C₂×Dic₃	1	3	yes	—
116	C₅×M₁₆	C₂×Dic₃	1	3	yes	—
117	C₂×C₅×C₈	C₂²×D₃	1	3	yes	—
118	#681	C₂×Dic₃	1	3	yes	—
119	C₂×#168	C₂×Dic₃	1	3	yes	—
120	#676	C₂×Dic₃	1	6	yes	—
121	C₈×D₅	C₂×Dic₃	1	3	yes	—
122	C₈×D₅	C₂×Dic₃	1	3	yes	—
123	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
124	C₈×D₅	C₂²×D₃	1	3	yes	—
125	C₅×C₁₆	—	3	1	no	—
126	C₅×C₁₆	—	3	3	no	—
127	#672	—	3	1	no	—
128	#672	—	3	3	no	—
129	C₂×#131	—	5	1	no	—
130	#504	—	3	1	no	—
131	#504	—	15	3	no	—
132	#504	—	15	3	no	—
133	#504	—	15	1	no	—
134	C₂×M₃₂	—	15	3	no	—
135	C₂²×C₁₆	—	15	3	no	—
136	C₂²×C₃×C₅	C₂²×C₈	1	3	yes	—
137	C₂×C₃×D₅	—	2	6	no	—
138	C₂×C₃×D₅	C₂²×C₈	1	3	yes	—
139	C₂×C₃×D₅	C₂²×C₈	1	1	yes	characteristic
140	C₃×C₄×C₅	C₂²×C₈	1	3	yes	—
141	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
142	C₃×Dic₅	C₂²×C₈	1	3	yes	—
143	C₃×Dic₅	C₂²×C₈	1	1	yes	characteristic
144	C₃×#41	—	5	1	no	—
145	C₃×#41	—	5	3	no	—
146	C₃×#41	—	5	3	no	—
147	C₃×#41	C₄×D₅	1	1	yes	characteristic
148	C₂×C₃×Q₈	—	5	1	no	—
149	C₂×C₃×D₄	—	5	3	no	—
150	C₂²×C₃×C₄	—	5	3	no	—
151	C₃×M₁₆	—	5	3	no	—
152	C₃×M₁₆	—	5	6	no	—
153	C₃×M₁₆	C₄×D₅	1	3	yes	—
154	C₂×C₃×C₈	—	5	3	no	—
155	C₂×C₃×C₈	—	5	3	no	—
156	C₂×C₃×C₈	—	5	3	no	—
157	C₂×C₃×C₈	—	5	1	no	—
158	C₂×C₃×C₈	—	5	3	no	—
159	C₂×C₃×C₈	C₂²×D₅	1	3	yes	—
160	C₃⋊C₁₆	—	5	1	no	—
161	C₃⋊C₁₆	—	5	3	no	—
162	C₃⋊C₁₆	C₂²×D₅	1	1	yes	characteristic
163	C₃⋊C₁₆	C₂²×D₅	1	3	yes	—
164	C₂²×D₅	C₂×C₃⋊C₈	1	3	yes	—
165	C₅×Q₈	C₂×C₃⋊C₈	1	1	yes	characteristic
166	C₅×D₄	C₂×C₃⋊C₈	1	3	yes	—
167	C₂×C₄×C₅	C₂²×Dic₃	1	3	yes	—
168	C₂²⋊D₅	C₂×C₃⋊C₈	1	6	yes	—
169	C₂×Dic₅	C₂×C₃⋊C₈	1	3	yes	—
170	D₂₀	C₂×C₃⋊C₈	1	3	yes	—
171	C₄×D₅	C₂×C₃⋊C₈	1	3	yes	—
172	C₄×D₅	C₂×C₃⋊C₈	1	3	yes	—
173	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
174	C₄×D₅	C₂²×Dic₃	1	3	yes	—
175	Dic₁₀	C₂×C₃⋊C₈	1	3	yes	—
176	C₅×C₈	C₂²×Dic₃	1	3	yes	—
177	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
178	#168	C₂²×Dic₃	1	1	yes	characteristic
179	#168	C₂²×Dic₃	1	3	yes	—
180	C₂×#41	—	5	1	no	—
181	#131	—	5	1	no	—
182	#131	—	5	3	no	—
183	#131	—	5	3	no	—
184	#131	D₃×D₅	1	1	yes	characteristic
185	C₂×M₁₆	—	5	3	no	—
186	C₂²×C₈	—	5	3	no	—
187	M₃₂	—	3	3	no	—
188	M₃₂	—	15	6	no	—
189	M₃₂	—	15	3	no	—
190	C₂×C₁₆	—	3	3	no	—
191	C₂×C₁₆	—	15	1	no	—
192	C₂×C₁₆	—	15	3	no	—
193	C₂×C₁₆	—	15	3	no	—
194	C₂×C₁₆	—	15	3	no	—
195	C₂×C₁₆	—	15	3	no	—
196	C₂×C₃×C₅	—	2	3	no	—
197	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
198	C₃×D₅	—	2	3	no	—
199	C₃×D₅	#504	1	2	yes	complemented
200	C₂³×C₃	—	5	3	no	—
201	C₃×Q₈	—	5	3	no	—
202	C₃×Q₈	C₈×D₅	1	1	yes	characteristic
203	C₃×D₄	—	5	6	no	—
204	C₃×D₄	—	5	3	no	—
205	C₃×D₄	C₈×D₅	1	3	yes	—
206	C₂×C₃×C₄	—	5	3	no	—
207	C₂×C₃×C₄	—	5	1	no	—
208	C₂×C₃×C₄	—	5	3	no	—
209	C₂×C₃×C₄	—	5	3	no	—
210	C₂×C₃×C₄	—	5	3	no	—
211	C₂×C₃×C₄	C₂×C₄×D₅	1	3	yes	—
212	C₃×C₈	—	5	1	no	—
213	C₃×C₈	—	5	3	no	—
214	C₃×C₈	C₂×C₄×D₅	1	3	yes	—
215	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
216	C₂²×C₅	C₂²×C₃⋊C₈	1	3	yes	—
217	C₂×D₅	—	2	6	no	—
218	C₂×D₅	C₂²×C₃⋊C₈	1	3	yes	—
219	C₂×D₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
220	C₄×C₅	C₂²×C₃⋊C₈	1	3	yes	—
221	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
222	Dic₅	C₂²×C₃⋊C₈	1	3	yes	—
223	Dic₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
224	#41	—	5	1	no	—
225	#41	—	5	3	no	—
226	#41	—	5	3	no	—
227	#41	D₅×Dic₃	1	1	yes	characteristic
228	C₂×Q₈	—	5	1	no	—
229	C₂×D₄	—	5	3	no	—
230	C₂²×C₄	—	5	3	no	—
231	M₁₆	—	5	3	no	—
232	M₁₆	—	5	6	no	—
233	M₁₆	D₅×Dic₃	1	3	yes	—
234	C₂×C₈	—	5	3	no	—
235	C₂×C₈	—	5	3	no	—
236	C₂×C₈	—	5	3	no	—
237	C₂×C₈	—	5	1	no	—
238	C₂×C₈	—	5	3	no	—
239	C₂×C₈	C₂×D₃×D₅	1	3	yes	—
240	C₁₆	—	3	1	no	—
241	C₁₆	—	3	3	no	—
242	C₁₆	—	15	1	no	—
243	C₁₆	—	15	3	no	—
244	C₃×C₅	C₂×#504	1	1	yes	characteristic, complemented, Hall
245	C₂²×C₃	—	5	1	no	—
246	C₂²×C₃	—	5	3	no	—
247	C₂²×C₃	—	10	6	no	—
248	C₂²×C₃	C₂×C₈×D₅	1	3	yes	—
249	C₃×C₄	—	5	1	no	—
250	C₃×C₄	—	5	3	no	—
251	C₃×C₄	C₂×C₈×D₅	1	3	yes	—
252	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
253	C₂×C₅	—	2	3	no	—
254	C₂×C₅	C₂³×C₃⋊C₈	1	1	yes	characteristic
255	D₅	—	2	3	no	—
256	D₅	#5140	1	2	yes	direct product factor
257	C₂³	—	5	3	no	—
258	Q₈	—	5	3	no	—
259	Q₈	D₅×C₃⋊C₈	1	1	yes	characteristic
260	D₄	—	5	6	no	—
261	D₄	—	5	3	no	—
262	D₄	D₅×C₃⋊C₈	1	3	yes	—
263	C₂×C₄	—	5	3	no	—
264	C₂×C₄	—	5	1	no	—
265	C₂×C₄	—	5	3	no	—
266	C₂×C₄	—	5	3	no	—
267	C₂×C₄	—	5	3	no	—
268	C₂×C₄	C₂×D₅×Dic₃	1	3	yes	—
269	C₈	—	5	1	no	—
270	C₈	—	5	3	no	—
271	C₈	C₂×D₅×Dic₃	1	3	yes	—
272	C₈	C₂²×D₃×D₅	1	1	yes	characteristic
273	C₂×C₃	—	2	3	no	—
274	C₂×C₃	—	5	2	no	—
275	C₂×C₃	—	10	3	no	—
276	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
277	C₅	C₂×#5140	1	1	yes	characteristic, complemented, Sylow
278	C₂²	—	5	1	no	—
279	C₂²	—	5	3	no	—
280	C₂²	—	10	6	no	—
281	C₂²	C₂×D₅×C₃⋊C₈	1	3	yes	—
282	C₄	—	5	1	no	—
283	C₄	—	5	3	no	—
284	C₄	C₂×D₅×C₃⋊C₈	1	3	yes	—
285	C₄	C₂²×D₅×Dic₃	1	1	yes	characteristic
286	C₃	D₅×#504	1	1	yes	characteristic, complemented, Sylow
287	C₂	—	2	3	no	—
288	C₂	—	5	2	no	—
289	C₂	—	10	3	no	—
290	C₂	C₂²×D₅×C₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×D₃×D₅
commutator, socle	C₂×C₃×C₅	C₂³×C₈
Fitting	C₃×C₅×#131	C₂²
prime radical	C₃×D₅×#41	C₄
cosocle	C₃×C₅×C₈	C₂⁴
hypercenter	#131	D₃×D₅
hypocenter	C₃×C₅	C₂×#504
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
2. #11751241	C₂	semidirect
3. C₅×#5140	C₂	semidirect
4. #11747525	C₂	semidirect
5. #11747524	C₂	semidirect
6. D₅×#812	C₂	semidirect
7. C₂×D₅×C₃⋊C₁₆	C₂	semidirect
16. #91096	C₂²	semidirect
17. C₂×C₃⋊#672	C₂²	semidirect
18. C₅×#812	C₂²	semidirect
19. C₂×C₅×C₃⋊C₁₆	C₂²	semidirect
20. #90934	C₂²	semidirect
23. D₅×C₃⋊C₁₆	C₂²	semidirect
24. D₅×C₃⋊C₁₆	C₂²	semidirect
57. #5140	D₅	direct (N × H)
102. #812	C₂×D₅	semidirect
108. C₂×C₃⋊C₁₆	C₂×D₅	semidirect
199. C₃×D₅	#504	semidirect
244. C₃×C₅	C₂×#504	semidirect
256. D₅	#5140	direct (N × H)
277. C₅	C₂×#5140	semidirect
286. C₃	D₅×#504	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₅×#131	2
#11751241	2
C₅×#5140	2
#11747525	2
#11747524	2
D₅×#812	2
C₂×D₅×C₃⋊C₁₆	2
D₅×#504	3
C₂×#5140	5

Subgroups — D5×#5140 #14478132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#5140 #14478132