Subgroups — C₃×C₅×#2641 #14275675

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#394	C₂	1	8	yes	maximal, complemented
4	C₃×C₅×#390	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2641	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
8	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
9	C₃×C₅×#127	—	2	4	no	—
10	C₃×C₅×#125	—	2	4	no	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	16	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#95	C₂²	1	4	yes	—
17	C₃×#2641	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
19	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
20	C₅×#394	C₂×C₃	1	8	yes	complemented
21	C₅×#390	C₂×C₃	1	4	yes	complemented
22	C₅×#376	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
24	C₂×C₃×C₅×D₄	—	2	8	no	—
25	C₂×C₃×C₅×D₄	—	2	4	no	—
26	C₂×C₃×C₅×D₄	—	2	8	no	—
27	C₂×C₃×C₅×D₄	—	4	8	no	—
28	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
29	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
30	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
31	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₄	—	2	8	no	—
33	C₃×C₅×C₄⋊C₄	—	2	4	no	—
34	C₃×C₅×C₂²⋊C₄	—	4	16	no	—
35	C₃×C₄²×C₅	—	2	4	no	—
36	C₃×C₄²×C₅	D₄	1	4	yes	—
37	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic
38	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
39	C₃×#394	C₂×C₅	1	8	yes	complemented
40	C₃×#390	C₂×C₅	1	4	yes	complemented
41	C₃×#376	C₂×C₅	1	1	yes	characteristic, complemented
42	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
43	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
44	C₅×#127	—	2	4	no	—
45	C₅×#125	—	2	4	no	—
46	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
47	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
48	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	16	yes	—
49	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
50	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
51	C₅×#95	C₂²×C₃	1	4	yes	—
52	#2641	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
53	C₂³×C₃×C₅	—	2	4	no	—
54	C₂³×C₃×C₅	—	2	8	no	—
55	C₂³×C₃×C₅	—	2	16	no	—
56	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
57	C₃×C₅×D₄	—	4	16	no	—
58	C₃×C₅×D₄	—	4	8	no	—
59	C₂×C₃×C₄×C₅	—	2	4	no	—
60	C₂×C₃×C₄×C₅	—	2	4	no	—
61	C₂×C₃×C₄×C₅	—	2	4	no	—
62	C₂×C₃×C₄×C₅	—	2	8	no	—
63	C₂×C₃×C₄×C₅	—	2	8	no	—
64	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
65	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
66	C₂×C₃×C₄×C₅	#41	1	4	yes	—
67	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
68	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
69	C₃×#127	—	2	4	no	—
70	C₃×#125	—	2	4	no	—
71	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
72	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
73	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	16	yes	—
74	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
75	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
76	C₃×#95	C₂²×C₅	1	4	yes	—
77	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
78	C₂×C₅×D₄	—	2	8	no	—
79	C₂×C₅×D₄	—	2	4	no	—
80	C₂×C₅×D₄	—	2	8	no	—
81	C₂×C₅×D₄	—	4	8	no	—
82	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
83	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
84	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
85	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
86	C₅×C₄⋊C₄	—	2	8	no	—
87	C₅×C₄⋊C₄	—	2	4	no	—
88	C₅×C₂²⋊C₄	—	4	16	no	—
89	C₄²×C₅	—	2	4	no	—
90	C₄²×C₅	C₃×D₄	1	4	yes	—
91	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic
92	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
93	#394	C₂×C₃×C₅	1	8	yes	complemented
94	#390	C₂×C₃×C₅	1	4	yes	complemented
95	#376	C₂×C₃×C₅	1	1	yes	characteristic, complemented
96	C₂²×C₃×C₅	—	4	4	no	—
97	C₂²×C₃×C₅	—	4	8	no	—
98	C₂²×C₃×C₅	—	4	16	no	—
99	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
100	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
101	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
102	C₃×C₄×C₅	—	2	4	no	—
103	C₃×C₄×C₅	—	4	4	no	—
104	C₃×C₄×C₅	—	4	4	no	—
105	C₃×C₄×C₅	#124	1	4	yes	—
106	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
107	C₂×C₃×D₄	—	2	8	no	—
108	C₂×C₃×D₄	—	2	4	no	—
109	C₂×C₃×D₄	—	2	8	no	—
110	C₂×C₃×D₄	—	4	8	no	—
111	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
112	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
113	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
114	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
115	C₃×C₄⋊C₄	—	2	8	no	—
116	C₃×C₄⋊C₄	—	2	4	no	—
117	C₃×C₂²⋊C₄	—	4	16	no	—
118	C₃×C₄²	—	2	4	no	—
119	C₃×C₄²	C₅×D₄	1	4	yes	—
120	C₂³×C₅	—	2	4	no	—
121	C₂³×C₅	—	2	8	no	—
122	C₂³×C₅	—	2	16	no	—
123	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
124	C₅×D₄	—	4	16	no	—
125	C₅×D₄	—	4	8	no	—
126	C₂×C₄×C₅	—	2	4	no	—
127	C₂×C₄×C₅	—	2	4	no	—
128	C₂×C₄×C₅	—	2	4	no	—
129	C₂×C₄×C₅	—	2	8	no	—
130	C₂×C₄×C₅	—	2	8	no	—
131	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
132	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
133	C₂×C₄×C₅	C₃×#41	1	4	yes	—
134	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
135	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
136	#127	—	2	4	no	—
137	#125	—	2	4	no	—
138	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
139	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
140	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	16	yes	—
141	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
142	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
143	#95	C₂²×C₃×C₅	1	4	yes	—
144	C₂×C₃×C₅	—	8	4	no	—
145	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
146	C₂×C₃×C₅	#535	1	2	yes	—
147	C₂×C₃×C₅	#540	1	4	yes	—
148	C₂³×C₃	—	2	4	no	—
149	C₂³×C₃	—	2	8	no	—
150	C₂³×C₃	—	2	16	no	—
151	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
152	C₃×D₄	—	4	16	no	—
153	C₃×D₄	—	4	8	no	—
154	C₂×C₃×C₄	—	2	4	no	—
155	C₂×C₃×C₄	—	2	4	no	—
156	C₂×C₃×C₄	—	2	4	no	—
157	C₂×C₃×C₄	—	2	8	no	—
158	C₂×C₃×C₄	—	2	8	no	—
159	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
160	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
161	C₂×C₃×C₄	C₅×#41	1	4	yes	—
162	C₂²×C₅	—	4	4	no	—
163	C₂²×C₅	—	4	8	no	—
164	C₂²×C₅	—	4	16	no	—
165	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
166	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
167	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
168	C₄×C₅	—	2	4	no	—
169	C₄×C₅	—	4	4	no	—
170	C₄×C₅	—	4	4	no	—
171	C₄×C₅	C₃×#124	1	4	yes	—
172	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
173	C₂×D₄	—	2	8	no	—
174	C₂×D₄	—	2	4	no	—
175	C₂×D₄	—	2	8	no	—
176	C₂×D₄	—	4	8	no	—
177	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
178	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
179	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
180	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
181	C₄⋊C₄	—	2	8	no	—
182	C₄⋊C₄	—	2	4	no	—
183	C₂²⋊C₄	—	4	16	no	—
184	C₄²	—	2	4	no	—
185	C₄²	C₃×C₅×D₄	1	4	yes	—
186	C₃×C₅	#2641	1	1	yes	characteristic, direct product factor, Hall
187	C₂²×C₃	—	4	4	no	—
188	C₂²×C₃	—	4	8	no	—
189	C₂²×C₃	—	4	16	no	—
190	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
191	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
192	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
193	C₃×C₄	—	2	4	no	—
194	C₃×C₄	—	4	4	no	—
195	C₃×C₄	—	4	4	no	—
196	C₃×C₄	C₅×#124	1	4	yes	—
197	C₂×C₅	—	8	4	no	—
198	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
199	C₂×C₅	C₃×#535	1	2	yes	—
200	C₂×C₅	C₃×#540	1	4	yes	—
201	C₂³	—	2	4	no	—
202	C₂³	—	2	8	no	—
203	C₂³	—	2	16	no	—
204	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
205	D₄	—	4	16	no	—
206	D₄	—	4	8	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	2	4	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	8	no	—
211	C₂×C₄	—	2	8	no	—
212	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
213	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
214	C₂×C₄	C₃×C₅×#41	1	4	yes	—
215	C₂×C₃	—	8	4	no	—
216	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
217	C₂×C₃	C₅×#535	1	2	yes	—
218	C₂×C₃	C₅×#540	1	4	yes	—
219	C₅	C₃×#2641	1	1	yes	characteristic, direct product factor, Sylow
220	C₂²	—	4	4	no	—
221	C₂²	—	4	8	no	—
222	C₂²	—	4	16	no	—
223	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
224	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
225	C₂²	C₃×C₅×H(5,𝔽₂)	1	4	yes	—
226	C₄	—	2	4	no	—
227	C₄	—	4	4	no	—
228	C₄	—	4	4	no	—
229	C₄	C₃×C₅×#124	1	4	yes	—
230	C₃	C₅×#2641	1	1	yes	characteristic, direct product factor, Sylow
231	C₂	—	8	4	no	—
232	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
233	C₂	C₃×C₅×#535	1	2	yes	—
234	C₂	C₃×C₅×#540	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#127	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#125	C₂	semidirect
3. C₃×C₅×#394	C₂	semidirect
4. C₃×C₅×#390	C₂	semidirect
5. C₃×C₅×#376	C₂	semidirect
6. C₅×#2641	C₃	direct (N × H)
17. C₃×#2641	C₅	direct (N × H)
19. C₂×C₅×#125	C₂×C₃	semidirect
20. C₅×#394	C₂×C₃	semidirect
21. C₅×#390	C₂×C₃	semidirect
22. C₅×#376	C₂×C₃	semidirect
38. C₂×C₃×#125	C₂×C₅	semidirect
39. C₃×#394	C₂×C₅	semidirect
40. C₃×#390	C₂×C₅	semidirect
41. C₃×#376	C₂×C₅	semidirect
52. #2641	C₃×C₅	direct (N × H)
92. C₂×#125	C₂×C₃×C₅	semidirect
93. #394	C₂×C₃×C₅	semidirect
94. #390	C₂×C₃×C₅	semidirect
95. #376	C₂×C₃×C₅	semidirect
186. C₃×C₅	#2641	direct (N × H)
219. C₅	C₃×#2641	direct (N × H)
230. C₃	C₅×#2641	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×#127	2
C₂×C₃×C₅×#125	2
C₃×C₅×#394	2
C₃×C₅×#390	2
C₃×C₅×#376	2
C₅×#2641	3
C₃×#2641	5

Subgroups — C3×C5×#2641 #14275675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2641 #14275675