Subgroups — C₃×C₅×#2073 #14275107

Order 1920.

516 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal
2	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#340	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2073	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#102	—	2	4	no	—
14	C₃×C₅×#95	—	2	2	no	—
15	C₃×#2073	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×#102	C₂×C₃	1	2	yes	—
17	C₅×#390	C₂×C₃	1	1	yes	characteristic
18	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
19	C₅×#340	C₂×C₃	1	2	yes	complemented
20	C₅×#336	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂⁴×C₃×C₅	—	2	1	no	—
22	C₂×C₃×C₅×D₄	—	2	2	no	—
23	C₂×C₃×C₅×D₄	—	2	2	no	—
24	C₂×C₃×C₅×D₄	—	2	1	no	—
25	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
26	C₂²×C₃×C₄×C₅	—	2	1	no	—
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₂×C₃×C₅×C₈	—	2	2	no	—
31	C₂×C₃×C₅×C₈	—	2	2	no	—
32	C₂×C₃×C₅×C₈	—	2	2	no	—
33	C₃×C₅×C₄⋊C₄	—	2	2	no	—
34	C₃×C₅×C₄⋊C₄	—	2	2	no	—
35	C₃×C₅×C₄⋊C₄	—	2	2	no	—
36	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
37	C₃×C₄²×C₅	—	2	2	no	—
38	C₂×C₃×#102	C₂×C₅	1	2	yes	—
39	C₃×#390	C₂×C₅	1	1	yes	characteristic
40	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
41	C₃×#340	C₂×C₅	1	2	yes	complemented
42	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
43	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
44	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
45	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
46	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
47	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
48	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
49	C₅×#102	—	2	4	no	—
50	C₅×#95	—	2	2	no	—
51	#2073	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
52	C₂³×C₃×C₅	—	2	2	no	—
53	C₂³×C₃×C₅	—	4	1	no	—
54	C₂³×C₃×C₅	—	4	1	no	—
55	C₂³×C₃×C₅	—	4	2	no	—
56	C₂³×C₃×C₅	—	4	2	no	—
57	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
58	C₃×C₅×D₄	—	2	4	no	—
59	C₃×C₅×D₄	—	4	2	no	—
60	C₂×C₃×C₄×C₅	—	2	2	no	—
61	C₂×C₃×C₄×C₅	—	2	2	no	—
62	C₂×C₃×C₄×C₅	—	2	2	no	—
63	C₂×C₃×C₄×C₅	—	4	2	no	—
64	C₂×C₃×C₄×C₅	—	4	1	no	—
65	C₂×C₃×C₄×C₅	—	4	2	no	—
66	C₂×C₃×C₄×C₅	—	4	2	no	—
67	C₂×C₃×C₄×C₅	—	4	2	no	—
68	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	#41	1	2	yes	—
70	C₂×C₃×C₄×C₅	#41	1	2	yes	—
71	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
72	C₃×C₅×C₈	—	4	2	no	—
73	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
74	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
75	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
76	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
77	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
79	C₃×#102	—	2	4	no	—
80	C₃×#95	—	2	2	no	—
81	C₂⁴×C₅	—	2	1	no	—
82	C₂×C₅×D₄	—	2	2	no	—
83	C₂×C₅×D₄	—	2	2	no	—
84	C₂×C₅×D₄	—	2	1	no	—
85	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
86	C₂²×C₄×C₅	—	2	1	no	—
87	C₂²×C₄×C₅	—	2	2	no	—
88	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
89	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
90	C₂×C₅×C₈	—	2	2	no	—
91	C₂×C₅×C₈	—	2	2	no	—
92	C₂×C₅×C₈	—	2	2	no	—
93	C₅×C₄⋊C₄	—	2	2	no	—
94	C₅×C₄⋊C₄	—	2	2	no	—
95	C₅×C₄⋊C₄	—	2	2	no	—
96	C₅×C₂²⋊C₄	—	4	4	no	—
97	C₄²×C₅	—	2	2	no	—
98	C₂×#102	C₂×C₃×C₅	1	2	yes	—
99	#390	C₂×C₃×C₅	1	1	yes	characteristic
100	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
101	#340	C₂×C₃×C₅	1	2	yes	complemented
102	#336	C₂×C₃×C₅	1	1	yes	characteristic, complemented
103	C₂²×C₃×C₅	—	4	2	no	—
104	C₂²×C₃×C₅	—	4	4	no	—
105	C₂²×C₃×C₅	—	8	2	no	—
106	C₂²×C₃×C₅	—	8	1	no	—
107	C₂²×C₃×C₅	—	8	1	no	—
108	C₂²×C₃×C₅	#121	1	1	yes	characteristic
109	C₂²×C₃×C₅	#123	1	1	yes	characteristic
110	C₂²×C₃×C₅	#124	1	1	yes	characteristic
111	C₂²×C₃×C₅	#135	1	2	yes	—
112	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
113	C₃×C₄×C₅	—	4	2	no	—
114	C₃×C₄×C₅	—	8	2	no	—
115	C₃×C₄×C₅	—	8	1	no	—
116	C₃×C₄×C₅	#123	1	2	yes	—
117	C₃×C₄×C₅	#126	1	2	yes	—
118	C₂⁴×C₃	—	2	1	no	—
119	C₂×C₃×D₄	—	2	2	no	—
120	C₂×C₃×D₄	—	2	2	no	—
121	C₂×C₃×D₄	—	2	1	no	—
122	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
123	C₂²×C₃×C₄	—	2	2	no	—
124	C₂²×C₃×C₄	—	2	1	no	—
125	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
126	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
127	C₂×C₃×C₈	—	2	2	no	—
128	C₂×C₃×C₈	—	2	2	no	—
129	C₂×C₃×C₈	—	2	2	no	—
130	C₃×C₄⋊C₄	—	2	2	no	—
131	C₃×C₄⋊C₄	—	2	2	no	—
132	C₃×C₄⋊C₄	—	2	2	no	—
133	C₃×C₂²⋊C₄	—	4	4	no	—
134	C₃×C₄²	—	2	2	no	—
135	C₂³×C₅	—	2	2	no	—
136	C₂³×C₅	—	4	1	no	—
137	C₂³×C₅	—	4	1	no	—
138	C₂³×C₅	—	4	2	no	—
139	C₂³×C₅	—	4	2	no	—
140	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
141	C₅×D₄	—	2	4	no	—
142	C₅×D₄	—	4	2	no	—
143	C₂×C₄×C₅	—	2	2	no	—
144	C₂×C₄×C₅	—	2	2	no	—
145	C₂×C₄×C₅	—	2	2	no	—
146	C₂×C₄×C₅	—	4	2	no	—
147	C₂×C₄×C₅	—	4	1	no	—
148	C₂×C₄×C₅	—	4	2	no	—
149	C₂×C₄×C₅	—	4	2	no	—
150	C₂×C₄×C₅	—	4	2	no	—
151	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
152	C₂×C₄×C₅	C₃×#41	1	2	yes	—
153	C₂×C₄×C₅	C₃×#41	1	2	yes	—
154	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
155	C₅×C₈	—	4	2	no	—
156	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
157	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
158	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
159	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
160	C₂×C₂²⋊C₄	—	2	2	no	—
161	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
162	#102	—	2	4	no	—
163	#95	—	2	2	no	—
164	C₂×C₃×C₅	—	8	2	no	—
165	C₂×C₃×C₅	#397	1	1	yes	characteristic
166	C₂×C₃×C₅	#463	1	2	yes	—
167	C₂×C₃×C₅	#482	1	2	yes	—
168	C₂×C₃×C₅	#488	1	1	yes	characteristic
169	C₂×C₃×C₅	#490	1	1	yes	characteristic
170	C₂³×C₃	—	2	2	no	—
171	C₂³×C₃	—	4	1	no	—
172	C₂³×C₃	—	4	1	no	—
173	C₂³×C₃	—	4	2	no	—
174	C₂³×C₃	—	4	2	no	—
175	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
176	C₃×D₄	—	2	4	no	—
177	C₃×D₄	—	4	2	no	—
178	C₂×C₃×C₄	—	2	2	no	—
179	C₂×C₃×C₄	—	2	2	no	—
180	C₂×C₃×C₄	—	2	2	no	—
181	C₂×C₃×C₄	—	4	2	no	—
182	C₂×C₃×C₄	—	4	1	no	—
183	C₂×C₃×C₄	—	4	2	no	—
184	C₂×C₃×C₄	—	4	2	no	—
185	C₂×C₃×C₄	—	4	2	no	—
186	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
187	C₂×C₃×C₄	C₅×#41	1	2	yes	—
188	C₂×C₃×C₄	C₅×#41	1	2	yes	—
189	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
190	C₃×C₈	—	4	2	no	—
191	C₂²×C₅	—	4	2	no	—
192	C₂²×C₅	—	4	4	no	—
193	C₂²×C₅	—	8	2	no	—
194	C₂²×C₅	—	8	1	no	—
195	C₂²×C₅	—	8	1	no	—
196	C₂²×C₅	C₃×#121	1	1	yes	characteristic
197	C₂²×C₅	C₃×#123	1	1	yes	characteristic
198	C₂²×C₅	C₃×#124	1	1	yes	characteristic
199	C₂²×C₅	C₃×#135	1	2	yes	—
200	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
201	C₄×C₅	—	4	2	no	—
202	C₄×C₅	—	8	2	no	—
203	C₄×C₅	—	8	1	no	—
204	C₄×C₅	C₃×#123	1	2	yes	—
205	C₄×C₅	C₃×#126	1	2	yes	—
206	C₂⁴	—	2	1	no	—
207	C₂×D₄	—	2	2	no	—
208	C₂×D₄	—	2	2	no	—
209	C₂×D₄	—	2	1	no	—
210	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
211	C₂²×C₄	—	2	2	no	—
212	C₂²×C₄	—	2	1	no	—
213	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
214	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
215	C₂×C₈	—	2	2	no	—
216	C₂×C₈	—	2	2	no	—
217	C₂×C₈	—	2	2	no	—
218	C₄⋊C₄	—	2	2	no	—
219	C₄⋊C₄	—	2	2	no	—
220	C₄⋊C₄	—	2	2	no	—
221	C₂²⋊C₄	—	4	4	no	—
222	C₄²	—	2	2	no	—
223	C₃×C₅	#2073	1	1	yes	characteristic, direct product factor, Hall
224	C₂²×C₃	—	4	2	no	—
225	C₂²×C₃	—	4	4	no	—
226	C₂²×C₃	—	8	2	no	—
227	C₂²×C₃	—	8	1	no	—
228	C₂²×C₃	—	8	1	no	—
229	C₂²×C₃	C₅×#121	1	1	yes	characteristic
230	C₂²×C₃	C₅×#123	1	1	yes	characteristic
231	C₂²×C₃	C₅×#124	1	1	yes	characteristic
232	C₂²×C₃	C₅×#135	1	2	yes	—
233	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
234	C₃×C₄	—	4	2	no	—
235	C₃×C₄	—	8	2	no	—
236	C₃×C₄	—	8	1	no	—
237	C₃×C₄	C₅×#123	1	2	yes	—
238	C₃×C₄	C₅×#126	1	2	yes	—
239	C₂×C₅	—	8	2	no	—
240	C₂×C₅	C₃×#397	1	1	yes	characteristic
241	C₂×C₅	C₃×#463	1	2	yes	—
242	C₂×C₅	C₃×#482	1	2	yes	—
243	C₂×C₅	C₃×#488	1	1	yes	characteristic
244	C₂×C₅	C₃×#490	1	1	yes	characteristic
245	C₂³	—	2	2	no	—
246	C₂³	—	4	1	no	—
247	C₂³	—	4	1	no	—
248	C₂³	—	4	2	no	—
249	C₂³	—	4	2	no	—
250	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
251	D₄	—	2	4	no	—
252	D₄	—	4	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	4	1	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
262	C₂×C₄	C₃×C₅×#41	1	2	yes	—
263	C₂×C₄	C₃×C₅×#41	1	2	yes	—
264	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
265	C₈	—	4	2	no	—
266	C₂×C₃	—	8	2	no	—
267	C₂×C₃	C₅×#397	1	1	yes	characteristic
268	C₂×C₃	C₅×#463	1	2	yes	—
269	C₂×C₃	C₅×#482	1	2	yes	—
270	C₂×C₃	C₅×#488	1	1	yes	characteristic
271	C₂×C₃	C₅×#490	1	1	yes	characteristic
272	C₅	C₃×#2073	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²	—	4	4	no	—
274	C₂²	—	4	2	no	—
275	C₂²	—	8	2	no	—
276	C₂²	—	8	1	no	—
277	C₂²	—	8	1	no	—
278	C₂²	C₃×C₅×#121	1	1	yes	characteristic
279	C₂²	C₃×C₅×#123	1	1	yes	characteristic
280	C₂²	C₃×C₅×#124	1	1	yes	characteristic
281	C₂²	C₃×C₅×#135	1	2	yes	—
282	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
283	C₄	—	4	2	no	—
284	C₄	—	8	2	no	—
285	C₄	—	8	1	no	—
286	C₄	C₃×C₅×#123	1	2	yes	—
287	C₄	C₃×C₅×#126	1	2	yes	—
288	C₃	C₅×#2073	1	1	yes	characteristic, direct product factor, Sylow
289	C₂	—	8	2	no	—
290	C₂	C₃×C₅×#397	1	1	yes	characteristic
291	C₂	C₃×C₅×#463	1	2	yes	—
292	C₂	C₃×C₅×#482	1	2	yes	—
293	C₂	C₃×C₅×#488	1	1	yes	characteristic
294	C₂	C₃×C₅×#490	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#382	C₂	semidirect
4. C₃×C₅×#340	C₂	semidirect
5. C₃×C₅×#336	C₂	semidirect
6. C₅×#2073	C₃	direct (N × H)
15. C₃×#2073	C₅	direct (N × H)
18. C₅×#382	C₂×C₃	semidirect
19. C₅×#340	C₂×C₃	semidirect
20. C₅×#336	C₂×C₃	semidirect
40. C₃×#382	C₂×C₅	semidirect
41. C₃×#340	C₂×C₅	semidirect
42. C₃×#336	C₂×C₅	semidirect
51. #2073	C₃×C₅	direct (N × H)
100. #382	C₂×C₃×C₅	semidirect
101. #340	C₂×C₃×C₅	semidirect
102. #336	C₂×C₃×C₅	semidirect
223. C₃×C₅	#2073	direct (N × H)
272. C₅	C₃×#2073	direct (N × H)
288. C₃	C₅×#2073	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×C₃×C₅×#102	2
C₃×C₅×#390	2
C₃×C₅×#382	2
C₃×C₅×#340	2
C₃×C₅×#336	2
C₅×#2073	3
C₃×#2073	5

Subgroups — C3×C5×#2073 #14275107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2073 #14275107