Subgroups — C₃×C₅×#1813 #14274847

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#108	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#413	C₂	1	2	yes	maximal
4	C₃×C₅×#338	C₂	1	2	yes	maximal, complemented
5	C₅×#1813	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
7	C₃×C₅×#131	—	2	4	no	—
8	C₂×C₃×C₅×M₁₆	C₄	1	2	yes	—
9	C₂×C₃×C₅×M₁₆	C₂²	1	4	yes	—
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₄	1	2	yes	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×#108	—	2	4	no	—
14	C₃×C₅×#101	—	2	2	no	—
15	C₃×C₅×#100	—	2	2	no	—
16	C₃×#1813	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic
18	C₂×C₅×#108	C₂×C₃	1	2	yes	complemented
19	C₅×#413	C₂×C₃	1	2	yes	—
20	C₅×#338	C₂×C₃	1	2	yes	complemented
21	C₃×C₅×#41	—	2	2	no	—
22	C₃×C₅×#41	—	2	2	no	—
23	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
24	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
25	C₂×C₃×C₅×D₄	Q₈	1	2	yes	—
26	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
27	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
28	C₃×C₅×M₁₆	—	2	2	no	—
29	C₃×C₅×M₁₆	—	2	4	no	—
30	C₃×C₅×M₁₆	—	2	4	no	—
31	C₃×C₅×M₁₆	—	2	4	no	—
32	C₂×C₃×C₅×C₈	—	2	4	no	—
33	C₂×C₃×C₅×C₈	—	2	4	no	—
34	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
35	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
38	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic
39	C₂×C₃×#108	C₂×C₅	1	2	yes	complemented
40	C₃×#413	C₂×C₅	1	2	yes	—
41	C₃×#338	C₂×C₅	1	2	yes	complemented
42	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
43	C₅×#131	—	2	4	no	—
44	C₂×C₅×M₁₆	C₃×C₄	1	2	yes	—
45	C₂×C₅×M₁₆	C₂²×C₃	1	4	yes	—
46	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₃×C₄	1	2	yes	—
48	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
49	C₅×#108	—	2	4	no	—
50	C₅×#101	—	2	2	no	—
51	C₅×#100	—	2	2	no	—
52	#1813	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
53	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
54	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
55	C₃×C₅×Q₈	—	2	2	no	—
56	C₃×C₅×D₄	—	2	4	no	—
57	C₃×C₅×D₄	—	2	2	no	—
58	C₂×C₃×C₄×C₅	—	2	2	no	—
59	C₂×C₃×C₄×C₅	—	2	2	no	—
60	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
61	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
63	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
64	C₂×C₃×C₄×C₅	#41	1	2	yes	—
65	C₃×C₅×C₈	—	2	2	no	—
66	C₃×C₅×C₈	—	4	4	no	—
67	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
68	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
69	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
70	C₃×#131	—	2	4	no	—
71	C₂×C₃×M₁₆	C₄×C₅	1	2	yes	—
72	C₂×C₃×M₁₆	C₂²×C₅	1	4	yes	—
73	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
74	C₂²×C₃×C₈	C₄×C₅	1	2	yes	—
75	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
76	C₃×#108	—	2	4	no	—
77	C₃×#101	—	2	2	no	—
78	C₃×#100	—	2	2	no	—
79	C₅×#41	—	2	2	no	—
80	C₅×#41	—	2	2	no	—
81	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
82	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
83	C₂×C₅×D₄	C₃×Q₈	1	2	yes	—
84	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
85	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
86	C₅×M₁₆	—	2	2	no	—
87	C₅×M₁₆	—	2	4	no	—
88	C₅×M₁₆	—	2	4	no	—
89	C₅×M₁₆	—	2	4	no	—
90	C₂×C₅×C₈	—	2	4	no	—
91	C₂×C₅×C₈	—	2	4	no	—
92	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
93	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
94	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
95	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
96	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic
97	C₂×#108	C₂×C₃×C₅	1	2	yes	complemented
98	#413	C₂×C₃×C₅	1	2	yes	—
99	#338	C₂×C₃×C₅	1	2	yes	complemented
100	C₂²×C₃×C₅	—	2	2	no	—
101	C₂²×C₃×C₅	—	4	1	no	—
102	C₂²×C₃×C₅	—	4	2	no	—
103	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
105	C₃×C₄×C₅	—	2	2	no	—
106	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₃×C₄×C₅	#117	1	1	yes	characteristic
108	C₃×C₄×C₅	#121	1	2	yes	—
109	C₃×#41	—	2	2	no	—
110	C₃×#41	—	2	2	no	—
111	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
112	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
113	C₂×C₃×D₄	C₅×Q₈	1	2	yes	—
114	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
115	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
116	C₃×M₁₆	—	2	2	no	—
117	C₃×M₁₆	—	2	4	no	—
118	C₃×M₁₆	—	2	4	no	—
119	C₃×M₁₆	—	2	4	no	—
120	C₂×C₃×C₈	—	2	4	no	—
121	C₂×C₃×C₈	—	2	4	no	—
122	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
123	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
124	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
125	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
126	C₂³×C₅	C₃×C₄⋊C₄	1	2	yes	—
127	C₂³×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
128	C₅×Q₈	—	2	2	no	—
129	C₅×D₄	—	2	4	no	—
130	C₅×D₄	—	2	2	no	—
131	C₂×C₄×C₅	—	2	2	no	—
132	C₂×C₄×C₅	—	2	2	no	—
133	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
134	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
135	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
136	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
137	C₂×C₄×C₅	C₃×#41	1	2	yes	—
138	C₅×C₈	—	2	2	no	—
139	C₅×C₈	—	4	4	no	—
140	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	—
141	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	—
142	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
143	#131	—	2	4	no	—
144	C₂×M₁₆	C₃×C₄×C₅	1	2	yes	—
145	C₂×M₁₆	C₂²×C₃×C₅	1	4	yes	—
146	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
147	C₂²×C₈	C₃×C₄×C₅	1	2	yes	—
148	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
149	#108	—	2	4	no	—
150	#101	—	2	2	no	—
151	#100	—	2	2	no	—
152	C₂×C₃×C₅	—	2	1	no	—
153	C₂×C₃×C₅	—	2	2	no	—
154	C₂×C₃×C₅	—	4	2	no	—
155	C₂×C₃×C₅	#380	1	1	yes	characteristic
156	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
157	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
158	C₃×Q₈	—	2	2	no	—
159	C₃×D₄	—	2	4	no	—
160	C₃×D₄	—	2	2	no	—
161	C₂×C₃×C₄	—	2	2	no	—
162	C₂×C₃×C₄	—	2	2	no	—
163	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
164	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
165	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
166	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
167	C₂×C₃×C₄	C₅×#41	1	2	yes	—
168	C₃×C₈	—	2	2	no	—
169	C₃×C₈	—	4	4	no	—
170	C₃×C₈	C₅×C₂²⋊C₄	1	2	yes	—
171	C₃×C₈	C₅×C₂²⋊C₄	1	2	yes	—
172	C₂²×C₅	—	2	2	no	—
173	C₂²×C₅	—	4	1	no	—
174	C₂²×C₅	—	4	2	no	—
175	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
177	C₄×C₅	—	2	2	no	—
178	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
179	C₄×C₅	C₃×#117	1	1	yes	characteristic
180	C₄×C₅	C₃×#121	1	2	yes	—
181	#41	—	2	2	no	—
182	#41	—	2	2	no	—
183	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
184	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
185	C₂×D₄	C₃×C₅×Q₈	1	2	yes	—
186	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
187	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
188	M₁₆	—	2	2	no	—
189	M₁₆	—	2	4	no	—
190	M₁₆	—	2	4	no	—
191	M₁₆	—	2	4	no	—
192	C₂×C₈	—	2	4	no	—
193	C₂×C₈	—	2	4	no	—
194	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
195	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
196	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
197	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
198	C₃×C₅	#1813	1	1	yes	characteristic, direct product factor, Hall
199	C₂²×C₃	—	2	2	no	—
200	C₂²×C₃	—	4	1	no	—
201	C₂²×C₃	—	4	2	no	—
202	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
203	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
204	C₃×C₄	—	2	2	no	—
205	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
206	C₃×C₄	C₅×#117	1	1	yes	characteristic
207	C₃×C₄	C₅×#121	1	2	yes	—
208	C₂×C₅	—	2	1	no	—
209	C₂×C₅	—	2	2	no	—
210	C₂×C₅	—	4	2	no	—
211	C₂×C₅	C₃×#380	1	1	yes	characteristic
212	C₂³	C₃×C₅×C₄⋊C₄	1	2	yes	—
213	C₂³	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
214	Q₈	—	2	2	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
220	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
221	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
222	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
223	C₂×C₄	C₃×C₅×#41	1	2	yes	—
224	C₈	—	2	2	no	—
225	C₈	—	4	4	no	—
226	C₈	C₃×C₅×C₂²⋊C₄	1	2	yes	—
227	C₈	C₃×C₅×C₂²⋊C₄	1	2	yes	—
228	C₂×C₃	—	2	1	no	—
229	C₂×C₃	—	2	2	no	—
230	C₂×C₃	—	4	2	no	—
231	C₂×C₃	C₅×#380	1	1	yes	characteristic
232	C₅	C₃×#1813	1	1	yes	characteristic, direct product factor, Sylow
233	C₂²	—	2	2	no	—
234	C₂²	—	4	1	no	—
235	C₂²	—	4	2	no	—
236	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
237	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
238	C₄	—	2	2	no	—
239	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
240	C₄	C₃×C₅×#117	1	1	yes	characteristic
241	C₄	C₃×C₅×#121	1	2	yes	—
242	C₃	C₅×#1813	1	1	yes	characteristic, direct product factor, Sylow
243	C₂	—	2	1	no	—
244	C₂	—	2	2	no	—
245	C₂	—	4	2	no	—
246	C₂	C₃×C₅×#380	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₅	#117
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂×C₃×C₅	#380
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₅ ◁ C₂×C₃×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#108	C₂	semidirect
4. C₃×C₅×#338	C₂	semidirect
5. C₅×#1813	C₃	direct (N × H)
16. C₃×#1813	C₅	direct (N × H)
18. C₂×C₅×#108	C₂×C₃	semidirect
20. C₅×#338	C₂×C₃	semidirect
39. C₂×C₃×#108	C₂×C₅	semidirect
41. C₃×#338	C₂×C₅	semidirect
52. #1813	C₃×C₅	direct (N × H)
97. C₂×#108	C₂×C₃×C₅	semidirect
99. #338	C₂×C₃×C₅	semidirect
198. C₃×C₅	#1813	direct (N × H)
232. C₅	C₃×#1813	direct (N × H)
242. C₃	C₅×#1813	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×#131	2
C₂×C₃×C₅×#108	2
C₃×C₅×#413	2
C₃×C₅×#338	2
C₅×#1813	3
C₃×#1813	5

Subgroups — C3×C5×#1813 #14274847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1813 #14274847