Subgroups — C₃×C₅×#2382 #14275416

Order 1920.

816 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×#125	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#389	C₂	1	4	yes	maximal
3	C₃×C₅×#387	C₂	1	4	yes	maximal
4	C₃×C₅×#387	C₂	1	4	yes	maximal
5	C₃×C₅×#382	C₂	1	2	yes	maximal
6	C₅×#2382	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×#125	C₄	1	8	yes	complemented
8	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×#95	C₂²	1	4	yes	—
16	C₃×C₅×#95	C₂²	1	4	yes	—
17	C₃×C₅×#95	C₂²	1	4	yes	—
18	C₃×C₅×#95	C₂²	1	4	yes	—
19	C₃×#2382	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic
21	C₅×#389	C₂×C₃	1	4	yes	—
22	C₅×#387	C₂×C₃	1	4	yes	—
23	C₅×#387	C₂×C₃	1	4	yes	—
24	C₅×#382	C₂×C₃	1	2	yes	—
25	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
26	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
27	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
28	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₃×C₅×C₄⋊C₄	—	4	4	no	—
31	C₃×C₅×C₄⋊C₄	—	4	2	no	—
32	C₃×C₅×C₄⋊C₄	—	4	2	no	—
33	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
34	C₃×C₅×C₄⋊C₄	C₂×C₄	1	16	yes	—
35	C₃×C₄²×C₅	—	4	4	no	—
36	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
37	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic
38	C₃×#389	C₂×C₅	1	4	yes	—
39	C₃×#387	C₂×C₅	1	4	yes	—
40	C₃×#387	C₂×C₅	1	4	yes	—
41	C₃×#382	C₂×C₅	1	2	yes	—
42	C₅×#125	C₃×C₄	1	8	yes	complemented
43	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
44	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
45	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
46	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
47	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
48	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
49	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
50	C₅×#95	C₂²×C₃	1	4	yes	—
51	C₅×#95	C₂²×C₃	1	4	yes	—
52	C₅×#95	C₂²×C₃	1	4	yes	—
53	C₅×#95	C₂²×C₃	1	4	yes	—
54	#2382	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
55	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
56	C₂×C₃×C₄×C₅	—	2	4	no	—
57	C₂×C₃×C₄×C₅	—	2	2	no	—
58	C₂×C₃×C₄×C₅	—	2	1	no	—
59	C₂×C₃×C₄×C₅	—	2	1	no	—
60	C₂×C₃×C₄×C₅	—	2	4	no	—
61	C₂×C₃×C₄×C₅	—	2	2	no	—
62	C₂×C₃×C₄×C₅	—	2	4	no	—
63	C₂×C₃×C₄×C₅	—	2	4	no	—
64	C₂×C₃×C₄×C₅	—	2	4	no	—
65	C₂×C₃×C₄×C₅	—	2	4	no	—
66	C₂×C₃×C₄×C₅	—	2	4	no	—
67	C₂×C₃×C₄×C₅	—	2	4	no	—
68	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
69	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
70	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
71	C₃×#125	C₄×C₅	1	8	yes	complemented
72	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
73	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
74	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
75	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
76	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
77	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
78	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
79	C₃×#95	C₂²×C₅	1	4	yes	—
80	C₃×#95	C₂²×C₅	1	4	yes	—
81	C₃×#95	C₂²×C₅	1	4	yes	—
82	C₃×#95	C₂²×C₅	1	4	yes	—
83	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
84	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
85	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
86	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
87	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
88	C₅×C₄⋊C₄	—	4	4	no	—
89	C₅×C₄⋊C₄	—	4	2	no	—
90	C₅×C₄⋊C₄	—	4	2	no	—
91	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
92	C₅×C₄⋊C₄	C₂×C₃×C₄	1	16	yes	—
93	C₄²×C₅	—	4	4	no	—
94	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
95	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic
96	#389	C₂×C₃×C₅	1	4	yes	—
97	#387	C₂×C₃×C₅	1	4	yes	—
98	#387	C₂×C₃×C₅	1	4	yes	—
99	#382	C₂×C₃×C₅	1	2	yes	—
100	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
101	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
102	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
103	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
104	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
105	C₃×C₄×C₅	—	2	2	no	—
106	C₃×C₄×C₅	—	2	8	no	—
107	C₃×C₄×C₅	—	2	4	no	—
108	C₃×C₄×C₅	—	4	4	no	—
109	C₃×C₄×C₅	—	4	4	no	—
110	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
111	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
112	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
113	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
114	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
115	C₃×C₄⋊C₄	—	4	4	no	—
116	C₃×C₄⋊C₄	—	4	2	no	—
117	C₃×C₄⋊C₄	—	4	2	no	—
118	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
119	C₃×C₄⋊C₄	C₂×C₄×C₅	1	16	yes	—
120	C₃×C₄²	—	4	4	no	—
121	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
122	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
123	C₂×C₄×C₅	—	2	4	no	—
124	C₂×C₄×C₅	—	2	2	no	—
125	C₂×C₄×C₅	—	2	1	no	—
126	C₂×C₄×C₅	—	2	1	no	—
127	C₂×C₄×C₅	—	2	4	no	—
128	C₂×C₄×C₅	—	2	2	no	—
129	C₂×C₄×C₅	—	2	4	no	—
130	C₂×C₄×C₅	—	2	4	no	—
131	C₂×C₄×C₅	—	2	4	no	—
132	C₂×C₄×C₅	—	2	4	no	—
133	C₂×C₄×C₅	—	2	4	no	—
134	C₂×C₄×C₅	—	2	4	no	—
135	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
136	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
137	C₂×C₄×C₅	C₂²×C₃×C₄	1	8	yes	—
138	#125	C₃×C₄×C₅	1	8	yes	complemented
139	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
140	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
141	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
142	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
143	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
144	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
145	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
146	#95	C₂²×C₃×C₅	1	4	yes	—
147	#95	C₂²×C₃×C₅	1	4	yes	—
148	#95	C₂²×C₃×C₅	1	4	yes	—
149	#95	C₂²×C₃×C₅	1	4	yes	—
150	C₂×C₃×C₅	#519	1	1	yes	characteristic
151	C₂×C₃×C₅	#520	1	2	yes	—
152	C₂×C₃×C₅	#562	1	1	yes	characteristic
153	C₂×C₃×C₅	#563	1	2	yes	—
154	C₂×C₃×C₅	#564	1	1	yes	characteristic
155	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
156	C₂×C₃×C₄	—	2	4	no	—
157	C₂×C₃×C₄	—	2	2	no	—
158	C₂×C₃×C₄	—	2	1	no	—
159	C₂×C₃×C₄	—	2	1	no	—
160	C₂×C₃×C₄	—	2	4	no	—
161	C₂×C₃×C₄	—	2	2	no	—
162	C₂×C₃×C₄	—	2	4	no	—
163	C₂×C₃×C₄	—	2	4	no	—
164	C₂×C₃×C₄	—	2	4	no	—
165	C₂×C₃×C₄	—	2	4	no	—
166	C₂×C₃×C₄	—	2	4	no	—
167	C₂×C₃×C₄	—	2	4	no	—
168	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
169	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
170	C₂×C₃×C₄	C₂²×C₄×C₅	1	8	yes	—
171	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
172	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
173	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
174	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
175	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
176	C₄×C₅	—	2	2	no	—
177	C₄×C₅	—	2	8	no	—
178	C₄×C₅	—	2	4	no	—
179	C₄×C₅	—	4	4	no	—
180	C₄×C₅	—	4	4	no	—
181	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
182	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
183	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
184	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
185	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
186	C₄⋊C₄	—	4	4	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
190	C₄⋊C₄	C₂×C₃×C₄×C₅	1	16	yes	—
191	C₄²	—	4	4	no	—
192	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
193	C₃×C₅	#2382	1	1	yes	characteristic, direct product factor, Hall
194	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
195	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
196	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
197	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
198	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
199	C₃×C₄	—	2	2	no	—
200	C₃×C₄	—	2	8	no	—
201	C₃×C₄	—	2	4	no	—
202	C₃×C₄	—	4	4	no	—
203	C₃×C₄	—	4	4	no	—
204	C₂×C₅	C₃×#519	1	1	yes	characteristic
205	C₂×C₅	C₃×#520	1	2	yes	—
206	C₂×C₅	C₃×#562	1	1	yes	characteristic
207	C₂×C₅	C₃×#563	1	2	yes	—
208	C₂×C₅	C₃×#564	1	1	yes	characteristic
209	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
210	C₂×C₄	—	2	4	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	2	4	no	—
218	C₂×C₄	—	2	4	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	4	no	—
221	C₂×C₄	—	2	4	no	—
222	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
223	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
224	C₂×C₄	C₂²×C₃×C₄×C₅	1	8	yes	—
225	C₂×C₃	C₅×#519	1	1	yes	characteristic
226	C₂×C₃	C₅×#520	1	2	yes	—
227	C₂×C₃	C₅×#562	1	1	yes	characteristic
228	C₂×C₃	C₅×#563	1	2	yes	—
229	C₂×C₃	C₅×#564	1	1	yes	characteristic
230	C₅	C₃×#2382	1	1	yes	characteristic, direct product factor, Sylow
231	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
232	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
233	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
234	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
235	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
236	C₄	—	2	2	no	—
237	C₄	—	2	8	no	—
238	C₄	—	2	4	no	—
239	C₄	—	4	4	no	—
240	C₄	—	4	4	no	—
241	C₃	C₅×#2382	1	1	yes	characteristic, direct product factor, Sylow
242	C₂	C₃×C₅×#519	1	1	yes	characteristic
243	C₂	C₃×C₅×#520	1	2	yes	—
244	C₂	C₃×C₅×#562	1	1	yes	characteristic
245	C₂	C₃×C₅×#563	1	2	yes	—
246	C₂	C₃×C₅×#564	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#2382	C₃	direct (N × H)
7. C₃×C₅×#125	C₄	semidirect
19. C₃×#2382	C₅	direct (N × H)
42. C₅×#125	C₃×C₄	semidirect
54. #2382	C₃×C₅	direct (N × H)
71. C₃×#125	C₄×C₅	semidirect
138. #125	C₃×C₄×C₅	semidirect
193. C₃×C₅	#2382	direct (N × H)
230. C₅	C₃×#2382	direct (N × H)
241. C₃	C₅×#2382	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×#125	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#382	2
C₅×#2382	3
C₃×#2382	5

Subgroups — C3×C5×#2382 #14275416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2382 #14275416