Subgroups — C₃×C₅×#2402 #14275436

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#400	C₂	1	4	yes	maximal
2	C₃×C₅×#398	C₂	1	4	yes	maximal
3	C₃×C₄×C₅×C₄⋊C₄	C₂	1	4	yes	maximal
4	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
5	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic
6	C₅×#2402	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#95	C₂²	1	4	yes	—
14	C₃×C₅×#95	C₂²	1	2	yes	—
15	C₃×C₅×#95	C₂²	1	4	yes	—
16	C₃×C₅×#95	C₂²	1	4	yes	—
17	C₃×C₅×#95	C₂²	1	2	yes	—
18	C₃×#2402	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₅×#400	C₂×C₃	1	4	yes	—
20	C₅×#398	C₂×C₃	1	4	yes	—
21	C₄×C₅×C₄⋊C₄	C₂×C₃	1	4	yes	—
22	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
23	C₅×#376	C₂×C₃	1	1	yes	characteristic
24	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
25	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
26	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
27	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
28	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₃×C₅×C₄⋊C₄	—	2	8	no	—
30	C₃×C₅×C₄⋊C₄	—	2	8	no	—
31	C₃×C₅×C₄⋊C₄	—	2	8	no	—
32	C₃×C₄²×C₅	—	2	8	no	—
33	C₃×C₄²×C₅	—	2	4	no	—
34	C₃×C₄²×C₅	Q₈	1	4	yes	—
35	C₃×#400	C₂×C₅	1	4	yes	—
36	C₃×#398	C₂×C₅	1	4	yes	—
37	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	—
38	C₃×C₄×C₄⋊C₄	C₂×C₅	1	4	yes	—
39	C₃×#376	C₂×C₅	1	1	yes	characteristic
40	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
41	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
42	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
43	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
44	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
45	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
46	C₅×#95	C₂²×C₃	1	4	yes	—
47	C₅×#95	C₂²×C₃	1	2	yes	—
48	C₅×#95	C₂²×C₃	1	4	yes	—
49	C₅×#95	C₂²×C₃	1	4	yes	—
50	C₅×#95	C₂²×C₃	1	2	yes	—
51	#2402	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
52	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	—	2	4	no	—
54	C₂×C₃×C₄×C₅	—	2	4	no	—
55	C₂×C₃×C₄×C₅	—	2	4	no	—
56	C₂×C₃×C₄×C₅	—	2	4	no	—
57	C₂×C₃×C₄×C₅	—	2	4	no	—
58	C₂×C₃×C₄×C₅	—	2	4	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	C₂×Q₈	1	4	yes	—
63	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
64	C₂×C₃×C₄×C₅	#41	1	8	yes	—
65	C₂×C₃×C₄×C₅	#41	1	4	yes	—
66	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
67	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
68	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
69	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
70	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
71	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
72	C₃×#95	C₂²×C₅	1	4	yes	—
73	C₃×#95	C₂²×C₅	1	2	yes	—
74	C₃×#95	C₂²×C₅	1	4	yes	—
75	C₃×#95	C₂²×C₅	1	4	yes	—
76	C₃×#95	C₂²×C₅	1	2	yes	—
77	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
78	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
79	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
80	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
81	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
82	C₅×C₄⋊C₄	—	2	8	no	—
83	C₅×C₄⋊C₄	—	2	8	no	—
84	C₅×C₄⋊C₄	—	2	8	no	—
85	C₄²×C₅	—	2	8	no	—
86	C₄²×C₅	—	2	4	no	—
87	C₄²×C₅	C₃×Q₈	1	4	yes	—
88	#400	C₂×C₃×C₅	1	4	yes	—
89	#398	C₂×C₃×C₅	1	4	yes	—
90	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
91	C₄×C₄⋊C₄	C₂×C₃×C₅	1	4	yes	—
92	#376	C₂×C₃×C₅	1	1	yes	characteristic
93	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
94	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
95	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
96	C₃×C₄×C₅	—	2	8	no	—
97	C₃×C₄×C₅	—	2	4	no	—
98	C₃×C₄×C₅	—	4	4	no	—
99	C₃×C₄×C₅	—	4	4	no	—
100	C₃×C₄×C₅	#125	1	4	yes	—
101	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
102	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
103	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
104	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
105	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
106	C₃×C₄⋊C₄	—	2	8	no	—
107	C₃×C₄⋊C₄	—	2	8	no	—
108	C₃×C₄⋊C₄	—	2	8	no	—
109	C₃×C₄²	—	2	8	no	—
110	C₃×C₄²	—	2	4	no	—
111	C₃×C₄²	C₅×Q₈	1	4	yes	—
112	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
113	C₂×C₄×C₅	—	2	4	no	—
114	C₂×C₄×C₅	—	2	4	no	—
115	C₂×C₄×C₅	—	2	4	no	—
116	C₂×C₄×C₅	—	2	4	no	—
117	C₂×C₄×C₅	—	2	4	no	—
118	C₂×C₄×C₅	—	2	4	no	—
119	C₂×C₄×C₅	—	2	4	no	—
120	C₂×C₄×C₅	—	2	4	no	—
121	C₂×C₄×C₅	—	2	4	no	—
122	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
123	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
124	C₂×C₄×C₅	C₃×#41	1	8	yes	—
125	C₂×C₄×C₅	C₃×#41	1	4	yes	—
126	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
127	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
128	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
129	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
130	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
131	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
132	#95	C₂²×C₃×C₅	1	4	yes	—
133	#95	C₂²×C₃×C₅	1	2	yes	—
134	#95	C₂²×C₃×C₅	1	4	yes	—
135	#95	C₂²×C₃×C₅	1	4	yes	—
136	#95	C₂²×C₃×C₅	1	2	yes	—
137	C₂×C₃×C₅	C₂×#125	1	1	yes	characteristic
138	C₂×C₃×C₅	#529	1	4	yes	—
139	C₂×C₃×C₅	#533	1	2	yes	—
140	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
141	C₂×C₃×C₄	—	2	4	no	—
142	C₂×C₃×C₄	—	2	4	no	—
143	C₂×C₃×C₄	—	2	4	no	—
144	C₂×C₃×C₄	—	2	4	no	—
145	C₂×C₃×C₄	—	2	4	no	—
146	C₂×C₃×C₄	—	2	4	no	—
147	C₂×C₃×C₄	—	2	4	no	—
148	C₂×C₃×C₄	—	2	4	no	—
149	C₂×C₃×C₄	—	2	4	no	—
150	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
151	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
152	C₂×C₃×C₄	C₅×#41	1	8	yes	—
153	C₂×C₃×C₄	C₅×#41	1	4	yes	—
154	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
155	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
156	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
157	C₄×C₅	—	2	8	no	—
158	C₄×C₅	—	2	4	no	—
159	C₄×C₅	—	4	4	no	—
160	C₄×C₅	—	4	4	no	—
161	C₄×C₅	C₃×#125	1	4	yes	—
162	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
163	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
164	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
165	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
166	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
167	C₄⋊C₄	—	2	8	no	—
168	C₄⋊C₄	—	2	8	no	—
169	C₄⋊C₄	—	2	8	no	—
170	C₄²	—	2	8	no	—
171	C₄²	—	2	4	no	—
172	C₄²	C₃×C₅×Q₈	1	4	yes	—
173	C₃×C₅	#2402	1	1	yes	characteristic, direct product factor, Hall
174	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
175	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
176	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
177	C₃×C₄	—	2	8	no	—
178	C₃×C₄	—	2	4	no	—
179	C₃×C₄	—	4	4	no	—
180	C₃×C₄	—	4	4	no	—
181	C₃×C₄	C₅×#125	1	4	yes	—
182	C₂×C₅	C₂×C₃×#125	1	1	yes	characteristic
183	C₂×C₅	C₃×#529	1	4	yes	—
184	C₂×C₅	C₃×#533	1	2	yes	—
185	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
186	C₂×C₄	—	2	4	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	4	no	—
195	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
196	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
197	C₂×C₄	C₃×C₅×#41	1	8	yes	—
198	C₂×C₄	C₃×C₅×#41	1	4	yes	—
199	C₂×C₃	C₂×C₅×#125	1	1	yes	characteristic
200	C₂×C₃	C₅×#529	1	4	yes	—
201	C₂×C₃	C₅×#533	1	2	yes	—
202	C₅	C₃×#2402	1	1	yes	characteristic, direct product factor, Sylow
203	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
204	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
205	C₂²	C₂×C₃×C₅×#41	1	4	yes	—
206	C₄	—	2	8	no	—
207	C₄	—	2	4	no	—
208	C₄	—	4	4	no	—
209	C₄	—	4	4	no	—
210	C₄	C₃×C₅×#125	1	4	yes	—
211	C₃	C₅×#2402	1	1	yes	characteristic, direct product factor, Sylow
212	C₂	C₂×C₃×C₅×#125	1	1	yes	characteristic
213	C₂	C₃×C₅×#529	1	4	yes	—
214	C₂	C₃×C₅×#533	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
6. C₅×#2402	C₃	direct (N × H)
18. C₃×#2402	C₅	direct (N × H)
51. #2402	C₃×C₅	direct (N × H)
173. C₃×C₅	#2402	direct (N × H)
202. C₅	C₃×#2402	direct (N × H)
211. C₃	C₅×#2402	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#400	2
C₃×C₅×#398	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₅×#376	2
C₅×#2402	3
C₃×#2402	5

Subgroups — C3×C5×#2402 #14275436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2402 #14275436