Subgroups — C₃×#10598840 #14280433

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#64974	C₂	1	2	yes	maximal
2	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64674	C₂	1	2	yes	maximal, complemented
5	C₃×C₈×#168	C₂	1	1	yes	maximal, characteristic, complemented
6	#10598840	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₈×D₅	C₄	1	2	yes	—
8	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
10	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₃×#3952	C₄	1	4	yes	—
12	C₃×#3946	C₄	1	4	yes	—
13	C₃×C₈×Dic₅	C₄	1	2	yes	—
14	C₃×C₄×#168	C₂²	1	1	yes	characteristic
15	C₃×C₄×#168	C₂²	1	2	yes	—
16	C₃×#1450	—	5	1	no	maximal, Hall
17	#64974	C₂×C₃	1	2	yes	—
18	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic
19	C₅×C₈²	C₂×C₃	1	1	yes	characteristic, complemented
20	#64674	C₂×C₃	1	2	yes	complemented
21	C₈×#168	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
25	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
26	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
27	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
28	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
29	C₂×C₃×#168	C₂×C₄	1	4	yes	—
30	C₂×C₃×#168	C₂×C₄	1	2	yes	—
31	C₃×C₈×D₅	C₈	1	8	yes	complemented
32	C₃×#431	—	5	2	no	—
33	C₂×C₃×C₄×C₈	—	5	1	no	—
34	C₃×#322	—	5	2	no	—
35	C₃×C₈²	—	5	1	no	—
36	C₃×C₈²	D₅	1	1	yes	characteristic, complemented
37	C₂×C₈×D₅	C₃×C₄	1	2	yes	—
38	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
39	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
40	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
41	#3952	C₃×C₄	1	4	yes	—
42	#3946	C₃×C₄	1	4	yes	—
43	C₈×Dic₅	C₃×C₄	1	2	yes	—
44	C₄×#168	C₂²×C₃	1	2	yes	—
45	C₄×#168	C₂²×C₃	1	1	yes	characteristic
46	#1450	—	5	1	no	Sylow
47	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
48	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
50	C₂×C₃×Dic₅	C₄²	1	2	yes	—
51	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
52	C₃×C₄×D₅	—	2	4	no	—
53	C₃×C₄×D₅	C₂×C₈	1	4	yes	—
54	C₃×C₅×C₈	—	2	4	no	—
55	C₃×C₅×C₈	C₂×C₈	1	4	yes	—
56	C₃×#168	—	2	4	no	—
57	C₃×#168	C₂×C₈	1	4	yes	—
58	C₂²×C₃×C₈	—	5	2	no	—
59	C₂×C₃×C₄²	—	5	1	no	—
60	C₃×C₄⋊C₈	—	5	4	no	—
61	C₃×C₂²⋊C₈	—	5	4	no	—
62	C₃×C₄×C₈	—	5	2	no	—
63	C₃×C₄×C₈	—	5	1	no	—
64	C₃×C₄×C₈	—	5	2	no	—
65	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
66	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
67	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
68	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
69	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
70	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
71	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
72	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
73	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
74	C₂×#168	C₂×C₃×C₄	1	4	yes	—
75	C₂×#168	C₂×C₃×C₄	1	2	yes	—
76	C₈×D₅	C₃×C₈	1	8	yes	complemented
77	#431	—	5	2	no	—
78	C₂×C₄×C₈	—	5	1	no	—
79	#322	—	5	2	no	—
80	C₈²	—	5	1	no	—
81	C₈²	C₃×D₅	1	1	yes	characteristic, complemented
82	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
83	C₂×C₃×D₅	—	2	2	no	—
84	C₂×C₃×D₅	C₄×C₈	1	2	yes	—
85	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
86	C₃×C₄×C₅	#131	1	4	yes	—
87	C₃×Dic₅	—	2	2	no	—
88	C₃×Dic₅	C₄×C₈	1	2	yes	—
89	C₂²×C₃×C₄	—	5	1	no	—
90	C₂²×C₃×C₄	—	5	2	no	—
91	C₂×C₃×C₈	—	5	2	no	—
92	C₂×C₃×C₈	—	5	8	no	—
93	C₂×C₃×C₈	—	5	4	no	—
94	C₂×C₃×C₈	C₄×D₅	1	4	yes	—
95	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
96	C₃×C₄²	—	5	1	no	—
97	C₃×C₄²	—	5	2	no	—
98	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
99	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
100	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
101	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
102	C₂×Dic₅	C₃×C₄²	1	2	yes	—
103	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
104	C₄×D₅	—	2	4	no	—
105	C₄×D₅	C₂×C₃×C₈	1	4	yes	—
106	C₅×C₈	—	2	4	no	—
107	C₅×C₈	C₂×C₃×C₈	1	4	yes	—
108	#168	—	2	4	no	—
109	#168	C₂×C₃×C₈	1	4	yes	—
110	C₂²×C₈	—	5	2	no	—
111	C₂×C₄²	—	5	1	no	—
112	C₄⋊C₈	—	5	4	no	—
113	C₂²⋊C₈	—	5	4	no	—
114	C₄×C₈	—	5	2	no	—
115	C₄×C₈	—	5	2	no	—
116	C₄×C₈	—	5	1	no	—
117	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
118	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
119	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
120	C₂×C₃×C₅	#405	1	2	yes	—
121	C₃×D₅	—	2	2	no	—
122	C₂³×C₃	—	5	1	no	—
123	C₂×C₃×C₄	—	5	1	no	—
124	C₂×C₃×C₄	—	5	4	no	—
125	C₂×C₃×C₄	—	5	2	no	—
126	C₂×C₃×C₄	—	10	4	no	—
127	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
128	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
129	C₃×C₈	—	2	4	no	—
130	C₃×C₈	—	5	4	no	—
131	C₃×C₈	—	10	4	no	—
132	C₃×C₈	C₈×D₅	1	4	yes	—
133	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
134	C₂×D₅	—	2	2	no	—
135	C₂×D₅	C₃×C₄×C₈	1	2	yes	—
136	C₄×C₅	C₂²×C₃×C₈	1	2	yes	—
137	C₄×C₅	C₃×#131	1	4	yes	—
138	Dic₅	—	2	2	no	—
139	Dic₅	C₃×C₄×C₈	1	2	yes	—
140	C₂²×C₄	—	5	1	no	—
141	C₂²×C₄	—	5	2	no	—
142	C₂×C₈	—	5	2	no	—
143	C₂×C₈	—	5	8	no	—
144	C₂×C₈	—	5	4	no	—
145	C₂×C₈	C₃×C₄×D₅	1	4	yes	—
146	C₂×C₈	C₃×C₄×D₅	1	2	yes	—
147	C₄²	—	5	1	no	—
148	C₄²	—	5	2	no	—
149	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
150	C₃×C₅	#1450	1	1	yes	characteristic, complemented, Hall
151	C₂²×C₃	—	5	2	no	—
152	C₂²×C₃	—	10	2	no	—
153	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
154	C₃×C₄	—	5	2	no	—
155	C₃×C₄	—	10	2	no	—
156	C₃×C₄	C₂×C₈×D₅	1	2	yes	—
157	C₃×C₄	#4047	1	4	yes	—
158	C₂×C₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
159	C₂×C₅	C₃×#405	1	2	yes	—
160	D₅	—	2	2	no	—
161	C₂³	—	5	1	no	—
162	C₂×C₄	—	5	1	no	—
163	C₂×C₄	—	5	4	no	—
164	C₂×C₄	—	5	2	no	—
165	C₂×C₄	—	10	4	no	—
166	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
167	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
168	C₈	—	2	4	no	—
169	C₈	—	5	4	no	—
170	C₈	—	10	4	no	—
171	C₈	C₃×C₈×D₅	1	4	yes	—
172	C₂×C₃	—	10	2	no	—
173	C₂×C₃	C₄×C₈×D₅	1	1	yes	characteristic
174	C₂×C₃	#64978	1	2	yes	—
175	C₅	C₃×#1450	1	1	yes	characteristic, complemented, Sylow
176	C₂²	—	5	2	no	—
177	C₂²	—	10	2	no	—
178	C₂²	C₃×C₄²×D₅	1	1	yes	characteristic
179	C₄	—	5	2	no	—
180	C₄	—	10	2	no	—
181	C₄	C₂×C₃×C₈×D₅	1	2	yes	—
182	C₄	C₃×#4047	1	4	yes	—
183	C₃	#10598840	1	1	yes	characteristic, direct product factor, Sylow
184	C₂	—	10	2	no	—
185	C₂	C₃×C₄×C₈×D₅	1	1	yes	characteristic
186	C₂	C₃×#64978	1	2	yes	—

	subgroup	G/H
center	C₃×C₄×C₈	C₂×D₅
commutator	C₂×C₅	C₂×C₃×C₄×C₈
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×C₈²	C₂
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂²×C₃×D₅	C₄²
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₃×C₈²	D₅
hypocenter	C₅	C₃×#1450
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄×C₈ ◁ C₃×C₈²

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₈²	C₂	semidirect
4. C₃×#64674	C₂	semidirect
5. C₃×C₈×#168	C₂	semidirect
6. #10598840	C₃	direct (N × H)
19. C₅×C₈²	C₂×C₃	semidirect
20. #64674	C₂×C₃	semidirect
21. C₈×#168	C₂×C₃	semidirect
31. C₃×C₈×D₅	C₈	semidirect
36. C₃×C₈²	D₅	semidirect
76. C₈×D₅	C₃×C₈	semidirect
81. C₈²	C₃×D₅	semidirect
150. C₃×C₅	#1450	semidirect
175. C₅	C₃×#1450	semidirect
183. C₃	#10598840	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×#64974	2
C₃×C₄×C₈×D₅	2
C₃×C₅×C₈²	2
C₃×#64674	2
C₃×C₈×#168	2
#10598840	3
C₃×#1450	5

Subgroups — C3×#10598840 #14280433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10598840 #14280433