Subgroups — C₃×#10600228 #14294927

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3935	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic
4	C₃×#64744	C₂	1	4	yes	maximal
5	#10600228	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×#168	C₂²	1	2	yes	—
9	C₂²×C₃×#168	C₂²	1	2	yes	—
10	C₃×C₅×#95	C₄	1	4	yes	—
11	C₃×#3935	C₄	1	4	yes	complemented
12	C₃×C₄×#168	C₄	1	4	yes	complemented
13	C₃×#1746	—	5	1	no	maximal, Hall
14	C₅×#376	C₂×C₃	1	1	yes	characteristic
15	C₂×#3935	C₂×C₃	1	1	yes	characteristic
16	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic
17	#64744	C₂×C₃	1	4	yes	—
18	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
19	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
20	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
21	C₃×C₄²×C₅	—	2	4	no	—
22	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
23	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
24	C₂×C₃×#168	—	2	4	no	—
25	C₂×C₃×#168	—	2	4	no	—
26	C₂×C₃×#168	C₂×C₄	1	4	yes	—
27	C₂×C₃×#168	C₂×C₄	1	4	yes	—
28	C₂×C₃×#97	—	5	1	no	—
29	C₂×C₃×C₄×C₈	—	5	1	no	—
30	C₃×#376	D₅	1	1	yes	characteristic
31	C₃×#336	—	5	4	no	—
32	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
33	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
34	C₂²×#168	C₂²×C₃	1	2	yes	—
35	C₂²×#168	C₂²×C₃	1	2	yes	—
36	C₅×#95	C₃×C₄	1	4	yes	—
37	#3935	C₃×C₄	1	4	yes	complemented
38	C₄×#168	C₃×C₄	1	4	yes	complemented
39	#1746	—	5	1	no	Sylow
40	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×C₅	—	2	4	no	—
42	C₂×C₃×C₄×C₅	—	2	4	no	—
43	C₂×C₃×C₄×C₅	—	2	8	no	—
44	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
45	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	#41	1	4	yes	—
48	C₃×#168	—	2	4	no	—
49	C₃×#168	—	2	4	no	—
50	C₂²×C₃×C₈	—	5	2	no	—
51	C₂²×C₃×C₈	—	5	2	no	—
52	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
53	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
54	C₃×#97	—	5	4	no	—
55	C₃×C₄×C₈	—	5	4	no	—
56	C₃×#95	Dic₅	1	4	yes	—
57	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
58	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
59	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
60	C₄²×C₅	—	2	4	no	—
61	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
62	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
63	C₂×#168	—	2	4	no	—
64	C₂×#168	—	2	4	no	—
65	C₂×#168	C₂×C₃×C₄	1	4	yes	—
66	C₂×#168	C₂×C₃×C₄	1	4	yes	—
67	C₂×#97	—	5	1	no	—
68	C₂×C₄×C₈	—	5	1	no	—
69	#376	C₃×D₅	1	1	yes	characteristic
70	#336	—	5	4	no	—
71	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
72	C₂²×C₃×C₅	#117	1	2	yes	—
73	C₂²×C₃×C₅	#131	1	4	yes	—
74	C₃×C₄×C₅	—	2	4	no	—
75	C₃×C₄×C₅	—	4	4	no	—
76	C₃×C₄×C₅	#117	1	2	yes	—
77	C₃×C₄×C₅	#117	1	2	yes	—
78	C₂²×C₃×C₄	C₂×Dic₅	1	4	yes	—
79	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
80	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
81	C₂×C₃×C₈	—	5	4	no	—
82	C₂×C₃×C₈	—	5	4	no	—
83	C₂×C₃×C₈	—	10	4	no	—
84	C₂×C₃×C₈	—	10	4	no	—
85	C₃×C₄²	—	2	4	no	—
86	C₃×C₄²	C₄×D₅	1	2	yes	—
87	C₃×C₄²	C₄×D₅	1	2	yes	—
88	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
89	C₂×C₄×C₅	—	2	4	no	—
90	C₂×C₄×C₅	—	2	4	no	—
91	C₂×C₄×C₅	—	2	8	no	—
92	C₂×C₄×C₅	C₃×C₄²	1	4	yes	—
93	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
94	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
95	C₂×C₄×C₅	C₃×#41	1	4	yes	—
96	#168	—	2	4	no	—
97	#168	—	2	4	no	—
98	C₂²×C₈	—	5	2	no	—
99	C₂²×C₈	—	5	2	no	—
100	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
101	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
102	#97	—	5	4	no	—
103	C₄×C₈	—	5	4	no	—
104	#95	C₃×Dic₅	1	4	yes	—
105	C₂×C₃×C₅	#376	1	1	yes	characteristic
106	C₂×C₃×C₅	#405	1	2	yes	—
107	C₂×C₃×C₅	#433	1	4	yes	—
108	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
109	C₂×C₃×C₄	—	2	4	no	—
110	C₂×C₃×C₄	—	2	4	no	—
111	C₂×C₃×C₄	—	2	8	no	—
112	C₂×C₃×C₄	C₄×Dic₅	1	4	yes	—
113	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
114	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
115	C₂×C₃×C₄	#709	1	4	yes	—
116	C₃×C₈	—	10	4	no	—
117	C₃×C₈	—	10	4	no	—
118	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
119	C₂²×C₅	C₃×#117	1	2	yes	—
120	C₂²×C₅	C₃×#131	1	4	yes	—
121	C₄×C₅	—	2	4	no	—
122	C₄×C₅	—	4	4	no	—
123	C₄×C₅	C₃×#117	1	2	yes	—
124	C₄×C₅	C₃×#117	1	2	yes	—
125	C₂²×C₄	C₂×C₃×Dic₅	1	4	yes	—
126	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
127	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
128	C₂×C₈	—	5	4	no	—
129	C₂×C₈	—	5	4	no	—
130	C₂×C₈	—	10	4	no	—
131	C₂×C₈	—	10	4	no	—
132	C₄²	—	2	4	no	—
133	C₄²	C₃×C₄×D₅	1	2	yes	—
134	C₄²	C₃×C₄×D₅	1	2	yes	—
135	C₃×C₅	#1746	1	1	yes	characteristic, complemented, Hall
136	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
137	C₂²×C₃	#4072	1	2	yes	—
138	C₂²×C₃	#4094	1	4	yes	—
139	C₃×C₄	—	2	4	no	—
140	C₃×C₄	—	4	4	no	—
141	C₃×C₄	#4018	1	2	yes	—
142	C₃×C₄	#4018	1	2	yes	—
143	C₂×C₅	C₃×#376	1	1	yes	characteristic
144	C₂×C₅	C₃×#405	1	2	yes	—
145	C₂×C₅	C₃×#433	1	4	yes	—
146	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
147	C₂×C₄	—	2	4	no	—
148	C₂×C₄	—	2	8	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	C₃×C₄×Dic₅	1	4	yes	—
151	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
152	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
153	C₂×C₄	C₃×#709	1	4	yes	—
154	C₈	—	10	4	no	—
155	C₈	—	10	4	no	—
156	C₂×C₃	#65221	1	1	yes	characteristic
157	C₂×C₃	#65286	1	2	yes	—
158	C₂×C₃	#65289	1	4	yes	—
159	C₅	C₃×#1746	1	1	yes	characteristic, complemented, Sylow
160	C₂²	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
161	C₂²	C₃×#4072	1	2	yes	—
162	C₂²	C₃×#4094	1	4	yes	—
163	C₄	—	2	4	no	—
164	C₄	—	4	4	no	—
165	C₄	C₃×#4018	1	2	yes	—
166	C₄	C₃×#4018	1	2	yes	—
167	C₃	#10600228	1	1	yes	characteristic, direct product factor, Sylow
168	C₂	C₃×#65221	1	1	yes	characteristic
169	C₂	C₃×#65286	1	2	yes	—
170	C₂	C₃×#65289	1	4	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#376	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#376	D₅
hypocenter	C₅	C₃×#1746
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×#376

Complements

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

N	H ≅ G/N	type
5. #10600228	C₃	direct (N × H)
11. C₃×#3935	C₄	semidirect
12. C₃×C₄×#168	C₄	semidirect
37. #3935	C₃×C₄	semidirect
38. C₄×#168	C₃×C₄	semidirect
135. C₃×C₅	#1746	semidirect
159. C₅	C₃×#1746	semidirect
167. C₃	#10600228	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×#376	2
C₂×C₃×#3935	2
C₂×C₃×C₄×#168	2
C₃×#64744	2
#10600228	3
C₃×#1746	5

Subgroups — C3×#10600228 #14294927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600228 #14294927