Subgroups — C₅×D₃×#493 #14438763

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×D₈	C₂	1	4	yes	maximal, complemented
2	C₅×D₃×#127	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5151	C₂	1	4	yes	maximal, complemented
5	C₅×#5073	C₂	1	2	yes	maximal, complemented
6	C₅×#4695	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#493	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×D₄	—	2	4	no	—
10	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
11	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
12	C₃×C₅×#127	C₂²	1	2	yes	complemented
13	C₅×#940	—	2	4	no	—
14	C₅×#940	C₂²	1	4	yes	complemented
15	C₂×C₅×#213	C₂²	1	8	yes	complemented
16	C₅×D₃×D₈	—	2	16	no	—
17	C₂×C₅×D₂₄	C₂²	1	4	yes	complemented
18	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
19	C₅×#874	C₂²	1	2	yes	complemented
20	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
22	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
23	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	D₃×#493	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×D₈	—	3	4	no	—
26	C₂×C₅×#127	—	3	2	no	—
27	C₅×#493	—	3	1	no	—
28	C₅×#493	—	3	4	no	—
29	C₅×#493	—	3	2	no	—
30	C₅×#493	D₃	1	1	yes	characteristic, direct product factor
31	C₂×C₄×C₅×C₈	—	3	1	no	—
32	C₂³×C₅×D₃	—	2	4	no	—
33	C₂×C₃×C₅×D₄	—	2	4	no	—
34	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
35	C₂×C₅×#67	—	2	4	no	—
36	C₂×C₅×#67	—	2	8	no	—
37	C₅×D₃×D₄	—	2	16	no	—
38	C₅×D₃×D₄	—	4	16	no	—
39	C₂×C₅×D₁₂	—	2	4	no	—
40	C₂×C₅×D₁₂	C₂³	1	4	yes	—
41	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
42	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
43	C₃×C₅×D₈	—	2	8	no	—
44	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
45	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
46	C₅×#213	—	2	16	no	—
47	C₄×C₅×Dic₃	D₄	1	2	yes	—
48	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
49	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
50	C₅×D₂₄	—	2	8	no	—
51	C₅×D₃×C₈	D₄	1	8	yes	complemented
52	C₂×D₃×D₈	C₂×C₅	1	4	yes	complemented
53	D₃×#127	C₂×C₅	1	2	yes	complemented
54	C₃×#493	C₂×C₅	1	1	yes	characteristic, complemented
55	#5151	C₂×C₅	1	4	yes	complemented
56	#5073	C₂×C₅	1	2	yes	complemented
57	#4695	C₂×C₅	1	1	yes	characteristic, complemented
58	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂²×C₅×D₄	—	3	4	no	—
60	C₂²×C₅×D₄	—	6	4	no	—
61	C₂×C₅×D₈	—	3	8	no	—
62	C₂×C₅×D₈	—	3	4	no	—
63	C₂×C₅×D₈	—	6	16	no	—
64	C₂×C₅×D₈	C₂×D₃	1	4	yes	complemented
65	C₂²×C₅×C₈	—	3	2	no	—
66	C₅×#127	—	3	4	no	—
67	C₅×#127	—	3	2	no	—
68	C₅×#127	—	6	4	no	—
69	C₅×#127	C₂×D₃	1	2	yes	complemented
70	C₂×C₄²×C₅	—	3	1	no	—
71	C₄×C₅×C₈	—	3	2	no	—
72	C₄×C₅×C₈	—	3	1	no	—
73	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
74	C₂×#493	—	3	1	no	Sylow
75	C₂³×C₃×C₅	—	2	4	no	—
76	C₂²×C₅×D₃	—	2	4	no	—
77	C₂²×C₅×D₃	—	4	8	no	—
78	C₂²×C₅×D₃	—	4	16	no	—
79	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
80	C₃×C₅×D₄	—	2	8	no	—
81	C₃×C₅×D₄	—	4	8	no	—
82	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
83	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
84	C₅×#67	—	4	8	no	—
85	C₅×#67	—	4	16	no	—
86	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
88	C₅×D₁₂	—	2	8	no	—
89	C₅×D₁₂	—	4	8	no	—
90	C₄×C₅×D₃	D₈	1	8	yes	complemented
91	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
92	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
93	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
94	C₂×D₃×D₄	—	2	4	no	—
95	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
96	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
97	C₃×#127	C₂²×C₅	1	2	yes	complemented
98	#940	—	2	4	no	—
99	#940	C₂²×C₅	1	4	yes	complemented
100	C₂×#213	C₂²×C₅	1	8	yes	complemented
101	D₃×D₈	—	2	16	no	—
102	C₂×D₂₄	C₂²×C₅	1	4	yes	complemented
103	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
104	#874	C₂²×C₅	1	2	yes	complemented
105	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
106	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
107	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
108	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
109	C₂⁴×C₅	—	6	4	no	—
110	C₂×C₅×D₄	—	2	4	no	—
111	C₂×C₅×D₄	—	3	4	no	—
112	C₂×C₅×D₄	—	6	16	no	—
113	C₂×C₅×D₄	—	6	8	no	—
114	C₂×C₅×D₄	—	6	4	no	—
115	C₂×C₅×D₄	—	6	4	no	—
116	C₂×C₅×D₄	—	12	16	no	—
117	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
118	C₂²×C₄×C₅	—	3	2	no	—
119	C₂²×C₄×C₅	—	3	1	no	—
120	C₅×D₈	—	2	8	no	—
121	C₅×D₈	—	6	16	no	—
122	C₅×D₈	—	6	8	no	—
123	C₂×C₅×C₈	—	3	2	no	—
124	C₂×C₅×C₈	—	3	8	no	—
125	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
126	C₄²×C₅	—	3	2	no	—
127	C₄²×C₅	—	3	1	no	—
128	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
129	C₂²×D₈	—	3	4	no	—
130	C₂×#127	—	3	2	no	—
131	#493	—	3	4	no	—
132	#493	—	3	2	no	—
133	#493	—	3	1	no	—
134	#493	C₅×D₃	1	1	yes	characteristic, direct product factor
135	C₂×C₄×C₈	—	3	1	no	—
136	C₂²×C₃×C₅	—	4	4	no	—
137	C₂²×C₃×C₅	—	4	8	no	—
138	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₅×D₃	—	4	4	no	—
140	C₂×C₅×D₃	—	4	8	no	—
141	C₂×C₅×D₃	—	8	16	no	—
142	C₂×C₅×D₃	#127	1	2	yes	—
143	C₂×C₅×D₃	C₂×D₈	1	4	yes	—
144	C₃×C₄×C₅	C₂×D₈	1	4	yes	complemented
145	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
146	C₅×Dic₃	#127	1	2	yes	—
147	C₅×Dic₃	C₂×D₈	1	4	yes	complemented
148	C₂³×D₃	—	2	4	no	—
149	C₂×C₃×D₄	—	2	4	no	—
150	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
151	C₂×#67	—	2	4	no	—
152	C₂×#67	—	2	8	no	—
153	D₃×D₄	—	2	16	no	—
154	D₃×D₄	—	4	16	no	—
155	C₂×D₁₂	—	2	4	no	—
156	C₂×D₁₂	C₂³×C₅	1	4	yes	—
157	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
158	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
159	C₃×D₈	—	2	8	no	—
160	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
161	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
162	#213	—	2	16	no	—
163	C₄×Dic₃	C₅×D₄	1	2	yes	—
164	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
165	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
166	D₂₄	—	2	8	no	—
167	D₃×C₈	C₅×D₄	1	8	yes	complemented
168	C₂³×C₅	—	2	4	no	—
169	C₂³×C₅	—	3	1	no	—
170	C₂³×C₅	—	6	4	no	—
171	C₂³×C₅	—	12	8	no	—
172	C₂³×C₅	—	12	16	no	—
173	C₅×D₄	—	2	8	no	—
174	C₅×D₄	—	4	8	no	—
175	C₅×D₄	—	6	8	no	—
176	C₅×D₄	—	12	8	no	—
177	C₅×D₄	—	12	16	no	—
178	C₅×D₄	—	12	8	no	—
179	C₂×C₄×C₅	—	3	1	no	—
180	C₂×C₄×C₅	—	3	2	no	—
181	C₂×C₄×C₅	—	3	8	no	—
182	C₂×C₄×C₅	—	3	4	no	—
183	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
184	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
185	C₅×C₈	—	3	4	no	—
186	C₅×C₈	D₃×D₄	1	4	yes	complemented
187	C₂²×D₄	—	3	4	no	—
188	C₂²×D₄	—	6	4	no	—
189	C₂×D₈	—	3	8	no	—
190	C₂×D₈	—	3	4	no	—
191	C₂×D₈	—	6	16	no	—
192	C₂×D₈	C₂×C₅×D₃	1	4	yes	complemented
193	C₂²×C₈	—	3	2	no	—
194	#127	—	3	4	no	—
195	#127	—	3	2	no	—
196	#127	—	6	4	no	—
197	#127	C₂×C₅×D₃	1	2	yes	complemented
198	C₂×C₄²	—	3	1	no	—
199	C₄×C₈	—	3	2	no	—
200	C₄×C₈	—	3	1	no	—
201	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
202	C₂×C₃×C₅	—	8	4	no	—
203	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
204	C₂×C₃×C₅	C₂²×D₈	1	2	yes	—
205	C₅×D₃	—	8	4	no	—
206	C₅×D₃	#493	1	4	yes	direct product factor
207	C₂³×C₃	—	2	4	no	—
208	C₂²×D₃	—	2	4	no	—
209	C₂²×D₃	—	4	8	no	—
210	C₂²×D₃	—	4	16	no	—
211	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
212	C₃×D₄	—	2	8	no	—
213	C₃×D₄	—	4	8	no	—
214	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
215	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
216	#67	—	4	8	no	—
217	#67	—	4	16	no	—
218	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
219	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
220	D₁₂	—	2	8	no	—
221	D₁₂	—	4	8	no	—
222	C₄×D₃	C₅×D₈	1	8	yes	complemented
223	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
224	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
225	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
226	C₂²×C₅	—	3	2	no	—
227	C₂²×C₅	—	3	4	no	—
228	C₂²×C₅	—	4	4	no	—
229	C₂²×C₅	—	4	8	no	—
230	C₂²×C₅	—	12	4	no	—
231	C₂²×C₅	—	12	8	no	—
232	C₂²×C₅	—	24	16	no	—
233	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
234	C₄×C₅	—	3	2	no	—
235	C₄×C₅	—	3	4	no	—
236	C₄×C₅	D₃×D₈	1	4	yes	complemented
237	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
238	C₂⁴	—	6	4	no	—
239	C₂×D₄	—	2	4	no	—
240	C₂×D₄	—	3	4	no	—
241	C₂×D₄	—	6	16	no	—
242	C₂×D₄	—	6	8	no	—
243	C₂×D₄	—	6	4	no	—
244	C₂×D₄	—	6	4	no	—
245	C₂×D₄	—	12	16	no	—
246	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
247	C₂²×C₄	—	3	2	no	—
248	C₂²×C₄	—	3	1	no	—
249	D₈	—	2	8	no	—
250	D₈	—	6	16	no	—
251	D₈	—	6	8	no	—
252	C₂×C₈	—	3	2	no	—
253	C₂×C₈	—	3	8	no	—
254	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
255	C₄²	—	3	2	no	—
256	C₄²	—	3	1	no	—
257	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
258	C₃×C₅	C₂×#493	1	1	yes	characteristic, complemented, Hall
259	C₂²×C₃	—	4	4	no	—
260	C₂²×C₃	—	4	8	no	—
261	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
262	C₂×D₃	—	4	4	no	—
263	C₂×D₃	—	4	8	no	—
264	C₂×D₃	—	8	16	no	—
265	C₂×D₃	C₅×#127	1	2	yes	—
266	C₂×D₃	C₂×C₅×D₈	1	4	yes	—
267	C₃×C₄	C₂×C₅×D₈	1	4	yes	complemented
268	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
269	Dic₃	C₅×#127	1	2	yes	—
270	Dic₃	C₂×C₅×D₈	1	4	yes	complemented
271	C₂×C₅	—	3	4	no	—
272	C₂×C₅	—	8	4	no	—
273	C₂×C₅	—	24	4	no	—
274	C₂×C₅	D₃×#127	1	1	yes	characteristic
275	C₂×C₅	C₂×D₃×D₈	1	2	yes	—
276	C₂³	—	2	4	no	—
277	C₂³	—	3	1	no	—
278	C₂³	—	6	4	no	—
279	C₂³	—	12	8	no	—
280	C₂³	—	12	16	no	—
281	D₄	—	2	8	no	—
282	D₄	—	4	8	no	—
283	D₄	—	6	8	no	—
284	D₄	—	12	8	no	—
285	D₄	—	12	16	no	—
286	D₄	—	12	8	no	—
287	C₂×C₄	—	3	1	no	—
288	C₂×C₄	—	3	2	no	—
289	C₂×C₄	—	3	8	no	—
290	C₂×C₄	—	3	4	no	—
291	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
292	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
293	C₈	—	3	4	no	—
294	C₈	C₅×D₃×D₄	1	4	yes	complemented
295	C₂×C₃	—	8	4	no	—
296	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
297	C₂×C₃	C₂²×C₅×D₈	1	2	yes	—
298	D₃	—	8	4	no	—
299	D₃	C₅×#493	1	4	yes	direct product factor
300	C₅	D₃×#493	1	1	yes	characteristic, direct product factor, Sylow
301	C₂²	—	3	2	no	—
302	C₂²	—	3	4	no	—
303	C₂²	—	4	4	no	—
304	C₂²	—	4	8	no	—
305	C₂²	—	12	4	no	—
306	C₂²	—	12	8	no	—
307	C₂²	—	24	16	no	—
308	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
309	C₄	—	3	2	no	—
310	C₄	—	3	4	no	—
311	C₄	C₅×D₃×D₈	1	4	yes	complemented
312	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
313	C₃	C₂×C₅×#493	1	1	yes	characteristic, complemented, Sylow
314	C₂	—	3	4	no	—
315	C₂	—	8	4	no	—
316	C₂	—	24	4	no	—
317	C₂	C₅×D₃×#127	1	1	yes	characteristic
318	C₂	C₂×C₅×D₃×D₈	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#493	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#493	D₃
hypocenter	C₃	C₂×C₅×#493
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#493

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×D₈	C₂	semidirect
2. C₅×D₃×#127	C₂	semidirect
3. C₃×C₅×#493	C₂	semidirect
4. C₅×#5151	C₂	semidirect
5. C₅×#5073	C₂	semidirect
6. C₅×#4695	C₂	semidirect
7. C₄×C₅×D₃×C₈	C₂	semidirect
11. C₂×C₃×C₅×D₈	C₂²	semidirect
12. C₃×C₅×#127	C₂²	semidirect
14. C₅×#940	C₂²	semidirect
15. C₂×C₅×#213	C₂²	semidirect
17. C₂×C₅×D₂₄	C₂²	semidirect
19. C₅×#874	C₂²	semidirect
21. C₃×C₄×C₅×C₈	C₂²	semidirect
22. C₅×C₈×Dic₃	C₂²	semidirect
23. C₄×C₅×C₃⋊C₈	C₂²	semidirect
24. D₃×#493	C₅	direct (N × H)
30. C₅×#493	D₃	direct (N × H)
51. C₅×D₃×C₈	D₄	semidirect
52. C₂×D₃×D₈	C₂×C₅	semidirect
53. D₃×#127	C₂×C₅	semidirect
54. C₃×#493	C₂×C₅	semidirect
55. #5151	C₂×C₅	semidirect
56. #5073	C₂×C₅	semidirect
57. #4695	C₂×C₅	semidirect
58. C₄×D₃×C₈	C₂×C₅	semidirect
64. C₂×C₅×D₈	C₂×D₃	semidirect
69. C₅×#127	C₂×D₃	semidirect
73. C₄×C₅×C₈	C₂×D₃	semidirect
90. C₄×C₅×D₃	D₈	semidirect
92. C₃×C₅×C₈	C₂×D₄	semidirect
93. C₅×C₃⋊C₈	C₂×D₄	semidirect
96. C₂×C₃×D₈	C₂²×C₅	semidirect
97. C₃×#127	C₂²×C₅	semidirect
99. #940	C₂²×C₅	semidirect
100. C₂×#213	C₂²×C₅	semidirect
102. C₂×D₂₄	C₂²×C₅	semidirect
104. #874	C₂²×C₅	semidirect
106. C₃×C₄×C₈	C₂²×C₅	semidirect
107. C₈×Dic₃	C₂²×C₅	semidirect
108. C₄×C₃⋊C₈	C₂²×C₅	semidirect
134. #493	C₅×D₃	direct (N × H)
144. C₃×C₄×C₅	C₂×D₈	semidirect
147. C₅×Dic₃	C₂×D₈	semidirect
167. D₃×C₈	C₅×D₄	semidirect
186. C₅×C₈	D₃×D₄	semidirect
192. C₂×D₈	C₂×C₅×D₃	semidirect
197. #127	C₂×C₅×D₃	semidirect
201. C₄×C₈	C₂×C₅×D₃	semidirect
206. C₅×D₃	#493	direct (N × H)
222. C₄×D₃	C₅×D₈	semidirect
224. C₃×C₈	C₂×C₅×D₄	semidirect
225. C₃⋊C₈	C₂×C₅×D₄	semidirect
236. C₄×C₅	D₃×D₈	semidirect
258. C₃×C₅	C₂×#493	semidirect
267. C₃×C₄	C₂×C₅×D₈	semidirect
270. Dic₃	C₂×C₅×D₈	semidirect
294. C₈	C₅×D₃×D₄	semidirect
299. D₃	C₅×#493	direct (N × H)
300. C₅	D₃×#493	direct (N × H)
311. C₄	C₅×D₃×D₈	semidirect
313. C₃	C₂×C₅×#493	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×D₈	2
C₅×D₃×#127	2
C₃×C₅×#493	2
C₅×#5151	2
C₅×#5073	2
C₅×#4695	2
C₄×C₅×D₃×C₈	2
C₂×C₅×#493	3
D₃×#493	5

Subgroups — C5×D3×#493 #14438763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#493 #14438763