Subgroups — D₅×#4699 #14438811

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×Dic₁₂	C₂	1	4	yes	maximal
2	D₅×#869	C₂	1	2	yes	maximal
3	#11750800	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4699	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
6	#11748018	C₂	1	4	yes	maximal, complemented
7	#11747096	C₂	1	2	yes	maximal, complemented
8	D₅×#494	—	3	1	no	maximal, Hall
9	C₂×D₅×Dic₆	C₂²	1	4	yes	—
10	C₂×Dic₆₀	C₂²	1	4	yes	—
11	#91758	C₂²	1	2	yes	—
12	C₂×C₅×Dic₁₂	C₂²	1	4	yes	—
13	C₅×#869	C₂²	1	2	yes	—
14	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
15	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
16	#91468	—	2	4	no	—
17	D₅×C₄⋊Dic₃	—	2	4	no	—
18	#91376	C₂²	1	4	yes	—
19	C₂×#6663	C₂²	1	8	yes	—
20	D₅×Dic₁₂	—	2	16	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₃×C₈×Dic₅	C₂²	1	2	yes	—
23	C₃×C₄×#168	C₂²	1	1	yes	characteristic
24	C₂×#4699	—	5	1	no	maximal, Hall
25	C₂×D₅×Q₁₆	—	3	4	no	—
26	D₅×C₄⋊Q₈	—	3	2	no	—
27	C₅×#494	—	3	1	no	—
28	#65470	—	3	4	no	—
29	#65381	—	3	2	no	—
30	#64988	—	3	1	no	—
31	C₄×C₈×D₅	D₃	1	1	yes	characteristic
32	C₂×Dic₃₀	C₂³	1	4	yes	—
33	C₂×C₅×Dic₆	C₂³	1	4	yes	—
34	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
35	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
36	C₂×#1204	—	2	4	no	—
37	C₂×D₅×Dic₃	—	2	4	no	—
38	D₅×Dic₆	—	2	16	no	—
39	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
40	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
41	C₄⋊Dic₁₅	—	2	4	no	—
42	Dic₆₀	—	2	8	no	—
43	C₅×C₄⋊Dic₃	—	2	4	no	—
44	C₅×Dic₁₂	—	2	8	no	—
45	C₃×C₄×Dic₅	D₄	1	2	yes	—
46	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×#168	C₂³	1	2	yes	—
48	C₃×C₈×D₅	D₄	1	8	yes	—
49	#6668	—	2	8	no	—
50	#6663	—	2	16	no	—
51	C₂²×Dic₁₂	—	5	4	no	—
52	C₂×#869	—	5	2	no	—
53	C₂×C₃×C₄×C₈	—	5	1	no	—
54	#4699	—	5	4	no	—
55	#4699	—	5	2	no	—
56	#4699	—	5	1	no	—
57	#4699	D₅	1	1	yes	characteristic, direct product factor
58	C₂×Q₈×D₅	—	3	4	no	—
59	C₂×C₅×Q₁₆	—	3	4	no	—
60	C₅×C₄⋊Q₈	—	3	2	no	—
61	#4090	—	3	4	no	—
62	C₂×#689	—	3	8	no	—
63	D₅×Q₁₆	—	6	16	no	—
64	C₂×Dic₂₀	—	3	4	no	—
65	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
66	D₅×C₄⋊C₄	—	6	4	no	—
67	#4034	—	6	4	no	—
68	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
69	#4015	—	3	2	no	—
70	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
71	C₈×Dic₅	C₂×D₃	1	2	yes	—
72	C₄×#168	C₂×D₃	1	1	yes	characteristic
73	C₂×#494	—	15	1	no	Sylow
74	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
76	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
77	C₂×Dic₁₅	—	2	4	no	—
78	Dic₃₀	—	2	8	no	—
79	C₂×C₅×Dic₃	—	2	4	no	—
80	C₅×Dic₆	—	2	8	no	—
81	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
82	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
83	C₃×C₄×D₅	Q₁₆	1	8	yes	complemented
84	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
85	#1204	—	4	8	no	—
86	D₅×Dic₃	—	4	8	no	—
87	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
88	C₃×#168	C₂×D₄	1	4	yes	—
89	C₂²×Dic₆	—	5	4	no	—
90	C₂²×C₃×C₈	—	5	2	no	—
91	C₂×C₃×C₄²	—	5	1	no	—
92	C₂×C₄⋊Dic₃	—	10	4	no	—
93	C₂×Dic₁₂	—	5	8	no	—
94	C₂×Dic₁₂	—	5	4	no	—
95	C₂×Dic₁₂	—	10	16	no	—
96	C₂×Dic₁₂	C₂×D₅	1	4	yes	—
97	#869	—	5	4	no	—
98	#869	—	5	2	no	—
99	#869	—	10	4	no	—
100	#869	C₂×D₅	1	2	yes	—
101	C₃×C₄×C₈	—	5	2	no	—
102	C₃×C₄×C₈	—	5	1	no	—
103	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
104	C₂×C₅×Q₈	—	3	4	no	—
105	Q₈×D₅	—	6	16	no	—
106	C₂×C₄×D₅	—	6	4	no	—
107	C₂×C₄×D₅	D₁₂	1	2	yes	—
108	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
109	C₂×Dic₁₀	—	3	4	no	—
110	C₂×Dic₁₀	—	6	4	no	—
111	C₅×Q₁₆	—	6	8	no	—
112	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
113	C₅×C₄⋊C₄	—	6	4	no	—
114	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
115	#689	—	6	16	no	—
116	C₄⋊Dic₅	—	6	4	no	—
117	#683	—	6	8	no	—
118	C₄×Dic₅	D₁₂	1	2	yes	—
119	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
120	C₂×#168	C₂²×D₃	1	2	yes	—
121	Dic₂₀	—	6	8	no	—
122	C₈×D₅	D₁₂	1	8	yes	—
123	C₂²×Q₁₆	—	15	4	no	—
124	C₂×C₄⋊Q₈	—	15	2	no	—
125	#494	—	3	1	no	—
126	#494	—	15	2	no	—
127	#494	—	15	4	no	—
128	#494	—	15	1	no	—
129	C₂×C₄×C₈	—	5	1	no	—
130	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₃×D₅	#127	1	2	yes	—
132	C₂×C₃×D₅	C₂×Q₁₆	1	4	yes	—
133	C₃×C₄×C₅	C₂×Q₁₆	1	4	yes	complemented
134	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
135	Dic₁₅	—	4	4	no	—
136	C₃×Dic₅	#127	1	2	yes	—
137	C₃×Dic₅	C₂×Q₁₆	1	4	yes	complemented
138	C₅×Dic₃	—	4	4	no	—
139	C₂²×C₃×C₄	—	5	2	no	—
140	C₂²×C₃×C₄	—	5	1	no	—
141	C₂²×Dic₃	—	10	4	no	—
142	C₂×Dic₆	—	5	4	no	—
143	C₂×Dic₆	—	10	16	no	—
144	C₂×Dic₆	—	10	4	no	—
145	C₂×Dic₆	C₂²×D₅	1	4	yes	—
146	C₂×C₃×C₈	—	5	2	no	—
147	C₂×C₃×C₈	—	5	8	no	—
148	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
149	C₃×C₄²	—	5	2	no	—
150	C₃×C₄²	—	5	1	no	—
151	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
152	C₄⋊Dic₃	—	2	4	no	—
153	C₄⋊Dic₃	—	10	8	no	—
154	C₄⋊Dic₃	—	10	4	no	—
155	Dic₁₂	—	2	8	no	—
156	Dic₁₂	—	10	16	no	—
157	Dic₁₂	—	10	8	no	—
158	C₂²×D₅	C₂×D₁₂	1	1	yes	characteristic
159	C₅×Q₈	—	6	8	no	—
160	C₂×C₄×C₅	—	6	4	no	—
161	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
162	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
163	C₂×Dic₅	—	6	4	no	—
164	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
165	C₂×Dic₅	C₂×D₁₂	1	2	yes	—
166	C₄×D₅	—	12	8	no	—
167	C₄×D₅	Dic₁₂	1	8	yes	complemented
168	C₄×D₅	C₂×D₁₂	1	4	yes	—
169	Dic₁₀	—	6	8	no	—
170	Dic₁₀	—	12	8	no	—
171	C₅×C₈	C₂×D₁₂	1	4	yes	—
172	#168	C₂×D₁₂	1	4	yes	—
173	C₂²×Q₈	—	15	4	no	—
174	C₂×Q₁₆	—	3	4	no	—
175	C₂×Q₁₆	—	15	8	no	—
176	C₂×Q₁₆	—	15	4	no	—
177	C₂×Q₁₆	—	30	16	no	—
178	C₂²×C₈	—	5	2	no	—
179	C₄⋊Q₈	—	3	2	no	—
180	C₄⋊Q₈	—	15	4	no	—
181	C₄⋊Q₈	—	15	2	no	—
182	C₄⋊Q₈	—	30	4	no	—
183	C₂×C₄⋊C₄	—	30	4	no	—
184	C₂×C₄²	—	5	1	no	—
185	C₄×C₈	—	5	2	no	—
186	C₄×C₈	—	5	1	no	—
187	C₄×C₈	D₃×D₅	1	1	yes	characteristic
188	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
189	C₂×C₃×C₅	C₂²×Q₁₆	1	2	yes	—
190	C₃×D₅	#494	1	4	yes	complemented
191	C₂³×C₃	—	5	1	no	—
192	C₂×C₃×C₄	—	5	2	no	—
193	C₂×C₃×C₄	—	5	1	no	—
194	C₂×C₃×C₄	—	5	4	no	—
195	C₂×C₃×C₄	—	5	8	no	—
196	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
197	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
198	C₂×Dic₃	—	2	4	no	—
199	C₂×Dic₃	—	10	4	no	—
200	C₂×Dic₃	—	20	8	no	—
201	Dic₆	—	2	8	no	—
202	Dic₆	—	10	8	no	—
203	Dic₆	—	20	8	no	—
204	C₃×C₈	—	5	4	no	—
205	C₃×C₈	D₄×D₅	1	4	yes	—
206	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
207	C₂×D₅	#874	1	2	yes	—
208	C₂×D₅	C₂×Dic₁₂	1	4	yes	—
209	C₄×C₅	—	12	4	no	—
210	C₄×C₅	C₂×Dic₁₂	1	4	yes	complemented
211	C₄×C₅	C₂²×D₁₂	1	2	yes	—
212	Dic₅	—	12	4	no	—
213	Dic₅	#874	1	2	yes	—
214	Dic₅	C₂×Dic₁₂	1	4	yes	complemented
215	C₂×Q₈	—	3	4	no	—
216	C₂×Q₈	—	15	4	no	—
217	C₂×Q₈	—	30	4	no	—
218	C₂×Q₈	—	30	16	no	—
219	C₂²×C₄	—	5	2	no	—
220	C₂²×C₄	—	5	1	no	—
221	C₂²×C₄	—	30	4	no	—
222	Q₁₆	—	6	8	no	—
223	Q₁₆	—	30	16	no	—
224	Q₁₆	—	30	8	no	—
225	C₂×C₈	—	5	2	no	—
226	C₂×C₈	—	5	8	no	—
227	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
228	C₄⋊C₄	—	6	4	no	—
229	C₄⋊C₄	—	30	8	no	—
230	C₄⋊C₄	—	30	4	no	—
231	C₄²	—	5	2	no	—
232	C₄²	—	5	1	no	—
233	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
234	C₃×C₅	C₂×#494	1	1	yes	characteristic, complemented, Hall
235	C₂²×C₃	—	5	2	no	—
236	C₂²×C₃	—	5	4	no	—
237	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
238	C₃×C₄	—	5	2	no	—
239	C₃×C₄	—	5	4	no	—
240	C₃×C₄	D₅×Q₁₆	1	4	yes	complemented
241	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
242	Dic₃	—	4	4	no	—
243	Dic₃	—	20	4	no	—
244	C₂×C₅	C₂×#874	1	1	yes	characteristic
245	C₂×C₅	C₂²×Dic₁₂	1	2	yes	—
246	D₅	#4699	1	4	yes	direct product factor
247	C₂³	—	5	1	no	—
248	Q₈	—	6	8	no	—
249	Q₈	—	30	8	no	—
250	Q₈	—	60	8	no	—
251	C₂×C₄	—	5	2	no	—
252	C₂×C₄	—	5	1	no	—
253	C₂×C₄	—	5	4	no	—
254	C₂×C₄	—	5	8	no	—
255	C₂×C₄	—	6	4	no	—
256	C₂×C₄	—	30	4	no	—
257	C₂×C₄	—	60	8	no	—
258	C₂×C₄	D₅×D₁₂	1	2	yes	—
259	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
260	C₈	—	5	4	no	—
261	C₈	D₅×D₁₂	1	4	yes	—
262	C₂×C₃	—	5	4	no	—
263	C₂×C₃	D₅×#127	1	1	yes	characteristic
264	C₂×C₃	C₂×D₅×Q₁₆	1	2	yes	—
265	C₅	C₂×#4699	1	1	yes	characteristic, complemented, Sylow
266	C₂²	—	5	4	no	—
267	C₂²	—	5	2	no	—
268	C₂²	C₂×D₅×D₁₂	1	1	yes	characteristic
269	C₄	—	5	4	no	—
270	C₄	—	5	2	no	—
271	C₄	—	12	4	no	—
272	C₄	—	60	4	no	—
273	C₄	D₅×Dic₁₂	1	4	yes	complemented
274	C₄	C₂×D₅×D₁₂	1	2	yes	—
275	C₃	D₅×#494	1	1	yes	characteristic, complemented, Sylow
276	C₂	—	5	4	no	—
277	C₂	D₅×#874	1	1	yes	characteristic
278	C₂	C₂×D₅×Dic₁₂	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₅×D₁₂
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×D₅	C₂×D₄
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#494
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #11750800	C₂	semidirect
4. C₅×#4699	C₂	semidirect
6. #11748018	C₂	semidirect
7. #11747096	C₂	semidirect
57. #4699	D₅	direct (N × H)
83. C₃×C₄×D₅	Q₁₆	semidirect
133. C₃×C₄×C₅	C₂×Q₁₆	semidirect
137. C₃×Dic₅	C₂×Q₁₆	semidirect
167. C₄×D₅	Dic₁₂	semidirect
190. C₃×D₅	#494	semidirect
210. C₄×C₅	C₂×Dic₁₂	semidirect
214. Dic₅	C₂×Dic₁₂	semidirect
234. C₃×C₅	C₂×#494	semidirect
240. C₃×C₄	D₅×Q₁₆	semidirect
246. D₅	#4699	direct (N × H)
265. C₅	C₂×#4699	semidirect
273. C₄	D₅×Dic₁₂	semidirect
275. C₃	D₅×#494	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×Dic₁₂	2
D₅×#869	2
#11750800	2
C₅×#4699	2
C₃×C₄×C₈×D₅	2
#11748018	2
#11747096	2
D₅×#494	3
C₂×#4699	5

Subgroups — D5×#4699 #14438811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#4699 #14438811