Subgroups — C₃×C₅×#2093 #14275127

Order 1920.

580 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#107	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal
3	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2093	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	—	2	2	no	—
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×#107	—	2	4	no	—
15	C₃×C₅×#102	—	2	4	no	—
16	C₃×#2093	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅×#107	C₂×C₃	1	2	yes	complemented
18	C₂×C₅×#102	C₂×C₃	1	2	yes	—
19	C₅×#390	C₂×C₃	1	1	yes	characteristic
20	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
21	C₅×#336	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂⁴×C₃×C₅	—	2	1	no	—
23	C₂×C₃×C₅×D₄	—	2	2	no	—
24	C₂×C₃×C₅×D₄	—	2	2	no	—
25	C₂×C₃×C₅×D₄	—	2	1	no	—
26	C₂×C₃×C₅×D₄	Q₈	1	2	yes	—
27	C₂²×C₃×C₄×C₅	—	2	1	no	—
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂×C₃×C₅×C₈	—	2	2	no	—
32	C₂×C₃×C₅×C₈	—	2	2	no	—
33	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
34	C₃×C₅×C₄⋊C₄	—	2	2	no	—
35	C₃×C₅×C₄⋊C₄	—	2	2	no	—
36	C₃×C₅×C₄⋊C₄	—	2	2	no	—
37	C₃×C₅×C₄⋊C₄	—	4	4	no	—
38	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
39	C₃×C₄²×C₅	—	2	2	no	—
40	C₂×C₃×#107	C₂×C₅	1	2	yes	complemented
41	C₂×C₃×#102	C₂×C₅	1	2	yes	—
42	C₃×#390	C₂×C₅	1	1	yes	characteristic
43	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
44	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
45	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
47	C₂×C₅×C₄⋊C₄	—	2	2	no	—
48	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
49	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
50	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
51	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
52	C₅×#107	—	2	4	no	—
53	C₅×#102	—	2	4	no	—
54	#2093	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
55	C₂³×C₃×C₅	—	2	2	no	—
56	C₂³×C₃×C₅	—	4	1	no	—
57	C₂³×C₃×C₅	—	4	1	no	—
58	C₂³×C₃×C₅	—	4	2	no	—
59	C₂³×C₃×C₅	—	4	2	no	—
60	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
61	C₃×C₅×D₄	—	2	4	no	—
62	C₃×C₅×D₄	—	4	2	no	—
63	C₂×C₃×C₄×C₅	—	2	2	no	—
64	C₂×C₃×C₄×C₅	—	2	2	no	—
65	C₂×C₃×C₄×C₅	—	4	2	no	—
66	C₂×C₃×C₄×C₅	—	4	1	no	—
67	C₂×C₃×C₄×C₅	—	4	2	no	—
68	C₂×C₃×C₄×C₅	—	4	4	no	—
69	C₂×C₃×C₄×C₅	D₈	1	4	yes	—
70	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
71	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	#41	1	2	yes	—
73	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
74	C₃×C₅×C₈	—	2	4	no	—
75	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
77	C₂×C₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
79	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
80	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
82	C₃×#107	—	2	4	no	—
83	C₃×#102	—	2	4	no	—
84	C₂⁴×C₅	—	2	1	no	—
85	C₂×C₅×D₄	—	2	2	no	—
86	C₂×C₅×D₄	—	2	2	no	—
87	C₂×C₅×D₄	—	2	1	no	—
88	C₂×C₅×D₄	C₃×Q₈	1	2	yes	—
89	C₂²×C₄×C₅	—	2	1	no	—
90	C₂²×C₄×C₅	—	2	2	no	—
91	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
92	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
93	C₂×C₅×C₈	—	2	2	no	—
94	C₂×C₅×C₈	—	2	2	no	—
95	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
96	C₅×C₄⋊C₄	—	2	2	no	—
97	C₅×C₄⋊C₄	—	2	2	no	—
98	C₅×C₄⋊C₄	—	2	2	no	—
99	C₅×C₄⋊C₄	—	4	4	no	—
100	C₅×C₂²⋊C₄	—	4	4	no	—
101	C₄²×C₅	—	2	2	no	—
102	C₂×#107	C₂×C₃×C₅	1	2	yes	complemented
103	C₂×#102	C₂×C₃×C₅	1	2	yes	—
104	#390	C₂×C₃×C₅	1	1	yes	characteristic
105	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
106	#336	C₂×C₃×C₅	1	1	yes	characteristic, complemented
107	C₂²×C₃×C₅	—	4	2	no	—
108	C₂²×C₃×C₅	—	4	4	no	—
109	C₂²×C₃×C₅	—	8	2	no	—
110	C₂²×C₃×C₅	—	8	1	no	—
111	C₂²×C₃×C₅	—	8	1	no	—
112	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
113	C₂²×C₃×C₅	#123	1	1	yes	characteristic
114	C₂²×C₃×C₅	#127	1	1	yes	characteristic
115	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
116	C₂²×C₃×C₅	#137	1	2	yes	—
117	C₃×C₄×C₅	—	2	4	no	—
118	C₃×C₄×C₅	—	8	1	no	—
119	C₃×C₄×C₅	—	8	2	no	—
120	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
121	C₃×C₄×C₅	#123	1	2	yes	—
122	C₂⁴×C₃	—	2	1	no	—
123	C₂×C₃×D₄	—	2	2	no	—
124	C₂×C₃×D₄	—	2	2	no	—
125	C₂×C₃×D₄	—	2	1	no	—
126	C₂×C₃×D₄	C₅×Q₈	1	2	yes	—
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	2	2	no	—
129	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
130	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
131	C₂×C₃×C₈	—	2	2	no	—
132	C₂×C₃×C₈	—	2	2	no	—
133	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
134	C₃×C₄⋊C₄	—	2	2	no	—
135	C₃×C₄⋊C₄	—	2	2	no	—
136	C₃×C₄⋊C₄	—	2	2	no	—
137	C₃×C₄⋊C₄	—	4	4	no	—
138	C₃×C₂²⋊C₄	—	4	4	no	—
139	C₃×C₄²	—	2	2	no	—
140	C₂³×C₅	—	2	2	no	—
141	C₂³×C₅	—	4	1	no	—
142	C₂³×C₅	—	4	1	no	—
143	C₂³×C₅	—	4	2	no	—
144	C₂³×C₅	—	4	2	no	—
145	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
146	C₅×D₄	—	2	4	no	—
147	C₅×D₄	—	4	2	no	—
148	C₂×C₄×C₅	—	2	2	no	—
149	C₂×C₄×C₅	—	2	2	no	—
150	C₂×C₄×C₅	—	4	2	no	—
151	C₂×C₄×C₅	—	4	1	no	—
152	C₂×C₄×C₅	—	4	2	no	—
153	C₂×C₄×C₅	—	4	4	no	—
154	C₂×C₄×C₅	C₃×D₈	1	4	yes	—
155	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
156	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₅	C₃×#41	1	2	yes	—
158	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
159	C₅×C₈	—	2	4	no	—
160	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
161	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
162	C₂×C₄⋊C₄	—	2	2	no	—
163	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
164	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
165	C₂×C₂²⋊C₄	—	2	2	no	—
166	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
167	#107	—	2	4	no	—
168	#102	—	2	4	no	—
169	C₂×C₃×C₅	—	8	2	no	—
170	C₂×C₃×C₅	#399	1	1	yes	characteristic
171	C₂×C₃×C₅	#474	1	2	yes	—
172	C₂×C₃×C₅	#480	1	2	yes	—
173	C₂×C₃×C₅	#493	1	1	yes	characteristic
174	C₂×C₃×C₅	#497	1	1	yes	characteristic
175	C₂³×C₃	—	2	2	no	—
176	C₂³×C₃	—	4	1	no	—
177	C₂³×C₃	—	4	1	no	—
178	C₂³×C₃	—	4	2	no	—
179	C₂³×C₃	—	4	2	no	—
180	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
181	C₃×D₄	—	2	4	no	—
182	C₃×D₄	—	4	2	no	—
183	C₂×C₃×C₄	—	2	2	no	—
184	C₂×C₃×C₄	—	2	2	no	—
185	C₂×C₃×C₄	—	4	2	no	—
186	C₂×C₃×C₄	—	4	1	no	—
187	C₂×C₃×C₄	—	4	2	no	—
188	C₂×C₃×C₄	—	4	4	no	—
189	C₂×C₃×C₄	C₅×D₈	1	4	yes	—
190	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
191	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
192	C₂×C₃×C₄	C₅×#41	1	2	yes	—
193	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
194	C₃×C₈	—	2	4	no	—
195	C₂²×C₅	—	4	2	no	—
196	C₂²×C₅	—	4	4	no	—
197	C₂²×C₅	—	8	2	no	—
198	C₂²×C₅	—	8	1	no	—
199	C₂²×C₅	—	8	1	no	—
200	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
201	C₂²×C₅	C₃×#123	1	1	yes	characteristic
202	C₂²×C₅	C₃×#127	1	1	yes	characteristic
203	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
204	C₂²×C₅	C₃×#137	1	2	yes	—
205	C₄×C₅	—	2	4	no	—
206	C₄×C₅	—	8	1	no	—
207	C₄×C₅	—	8	2	no	—
208	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
209	C₄×C₅	C₃×#123	1	2	yes	—
210	C₂⁴	—	2	1	no	—
211	C₂×D₄	—	2	2	no	—
212	C₂×D₄	—	2	2	no	—
213	C₂×D₄	—	2	1	no	—
214	C₂×D₄	C₃×C₅×Q₈	1	2	yes	—
215	C₂²×C₄	—	2	1	no	—
216	C₂²×C₄	—	2	2	no	—
217	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
218	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
219	C₂×C₈	—	2	2	no	—
220	C₂×C₈	—	2	2	no	—
221	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
222	C₄⋊C₄	—	2	2	no	—
223	C₄⋊C₄	—	2	2	no	—
224	C₄⋊C₄	—	2	2	no	—
225	C₄⋊C₄	—	4	4	no	—
226	C₂²⋊C₄	—	4	4	no	—
227	C₄²	—	2	2	no	—
228	C₃×C₅	#2093	1	1	yes	characteristic, direct product factor, Hall
229	C₂²×C₃	—	4	2	no	—
230	C₂²×C₃	—	4	4	no	—
231	C₂²×C₃	—	8	2	no	—
232	C₂²×C₃	—	8	1	no	—
233	C₂²×C₃	—	8	1	no	—
234	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
235	C₂²×C₃	C₅×#123	1	1	yes	characteristic
236	C₂²×C₃	C₅×#127	1	1	yes	characteristic
237	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
238	C₂²×C₃	C₅×#137	1	2	yes	—
239	C₃×C₄	—	2	4	no	—
240	C₃×C₄	—	8	1	no	—
241	C₃×C₄	—	8	2	no	—
242	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
243	C₃×C₄	C₅×#123	1	2	yes	—
244	C₂×C₅	—	8	2	no	—
245	C₂×C₅	C₃×#399	1	1	yes	characteristic
246	C₂×C₅	C₃×#474	1	2	yes	—
247	C₂×C₅	C₃×#480	1	2	yes	—
248	C₂×C₅	C₃×#493	1	1	yes	characteristic
249	C₂×C₅	C₃×#497	1	1	yes	characteristic
250	C₂³	—	2	2	no	—
251	C₂³	—	4	1	no	—
252	C₂³	—	4	1	no	—
253	C₂³	—	4	2	no	—
254	C₂³	—	4	2	no	—
255	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
256	D₄	—	2	4	no	—
257	D₄	—	4	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	4	1	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	4	4	no	—
264	C₂×C₄	C₃×C₅×D₈	1	4	yes	—
265	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
266	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
267	C₂×C₄	C₃×C₅×#41	1	2	yes	—
268	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
269	C₈	—	2	4	no	—
270	C₂×C₃	—	8	2	no	—
271	C₂×C₃	C₅×#399	1	1	yes	characteristic
272	C₂×C₃	C₅×#474	1	2	yes	—
273	C₂×C₃	C₅×#480	1	2	yes	—
274	C₂×C₃	C₅×#493	1	1	yes	characteristic
275	C₂×C₃	C₅×#497	1	1	yes	characteristic
276	C₅	C₃×#2093	1	1	yes	characteristic, direct product factor, Sylow
277	C₂²	—	4	4	no	—
278	C₂²	—	4	2	no	—
279	C₂²	—	8	2	no	—
280	C₂²	—	8	1	no	—
281	C₂²	—	8	1	no	—
282	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
283	C₂²	C₃×C₅×#123	1	1	yes	characteristic
284	C₂²	C₃×C₅×#127	1	1	yes	characteristic
285	C₂²	C₂×C₃×C₅×D₈	1	2	yes	—
286	C₂²	C₃×C₅×#137	1	2	yes	—
287	C₄	—	2	4	no	—
288	C₄	—	8	1	no	—
289	C₄	—	8	2	no	—
290	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
291	C₄	C₃×C₅×#123	1	2	yes	—
292	C₃	C₅×#2093	1	1	yes	characteristic, direct product factor, Sylow
293	C₂	—	8	2	no	—
294	C₂	C₃×C₅×#399	1	1	yes	characteristic
295	C₂	C₃×C₅×#474	1	2	yes	—
296	C₂	C₃×C₅×#480	1	2	yes	—
297	C₂	C₃×C₅×#493	1	1	yes	characteristic
298	C₂	C₃×C₅×#497	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
1. C₂×C₃×C₅×#107	C₂	semidirect
4. C₃×C₅×#384	C₂	semidirect
5. C₃×C₅×#336	C₂	semidirect
6. C₅×#2093	C₃	direct (N × H)
16. C₃×#2093	C₅	direct (N × H)
17. C₂×C₅×#107	C₂×C₃	semidirect
20. C₅×#384	C₂×C₃	semidirect
21. C₅×#336	C₂×C₃	semidirect
40. C₂×C₃×#107	C₂×C₅	semidirect
43. C₃×#384	C₂×C₅	semidirect
44. C₃×#336	C₂×C₅	semidirect
54. #2093	C₃×C₅	direct (N × H)
102. C₂×#107	C₂×C₃×C₅	semidirect
105. #384	C₂×C₃×C₅	semidirect
106. #336	C₂×C₃×C₅	semidirect
228. C₃×C₅	#2093	direct (N × H)
276. C₅	C₃×#2093	direct (N × H)
292. C₃	C₅×#2093	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×#107	2
C₂×C₃×C₅×#102	2
C₃×C₅×#390	2
C₃×C₅×#384	2
C₃×C₅×#336	2
C₅×#2093	3
C₃×#2093	5

Subgroups — C3×C5×#2093 #14275127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2093 #14275127