Subgroups — C₃×#10600641 #14280607

Order 1920.

380 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×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#65214	C₂	1	2	yes	maximal
3	C₃×#64675	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	#10600641	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×M₁₆	C₄	1	2	yes	—
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₃×C₅×#97	C₄	1	2	yes	—
10	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₂²⋊#168	C₄	1	4	yes	—
13	C₃×C₄⋊#168	C₄	1	4	yes	—
14	C₃×C₄×#168	C₂²	1	2	yes	—
15	C₃×C₄×#168	C₂²	1	2	yes	—
16	C₃×#1453	—	5	1	no	maximal, Hall
17	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
18	#65214	C₂×C₃	1	2	yes	—
19	#64675	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	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
23	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
24	C₃×C₅×M₁₆	—	2	4	no	—
25	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
26	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
27	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
28	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
29	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
30	C₂×C₃×#168	C₂×C₄	1	4	yes	—
31	C₂×C₃×#168	C₂×C₄	1	4	yes	—
32	C₃×#431	—	5	2	no	—
33	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic
34	C₃×#322	—	5	2	no	—
35	C₃×#322	—	5	1	no	—
36	C₃×C₈²	—	5	1	no	—
37	C₂×C₅×M₁₆	C₃×C₄	1	2	yes	—
38	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
39	C₅×#97	C₃×C₄	1	2	yes	—
40	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
41	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
42	C₂²⋊#168	C₃×C₄	1	4	yes	—
43	C₄⋊#168	C₃×C₄	1	4	yes	—
44	C₄×#168	C₂²×C₃	1	2	yes	—
45	C₄×#168	C₂²×C₃	1	2	yes	—
46	#1453	—	5	1	no	Sylow
47	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
48	C₂×C₃×C₄×C₅	—	2	2	no	—
49	C₂×C₃×C₄×C₅	—	2	4	no	—
50	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
51	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
52	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
54	C₃×C₅×C₈	—	2	2	no	—
55	C₃×C₅×C₈	M₁₆	1	4	yes	—
56	C₃×#168	—	2	4	no	—
57	C₃×#168	—	2	4	no	—
58	C₂×C₃×M₁₆	Dic₅	1	2	yes	—
59	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
60	C₃×C₄⋊C₈	—	5	4	no	—
61	C₃×C₂²⋊C₈	—	5	4	no	—
62	C₃×#97	Dic₅	1	2	yes	—
63	C₃×C₄×C₈	—	5	2	no	—
64	C₃×C₄×C₈	—	5	2	no	—
65	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
66	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
67	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
68	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
69	C₅×M₁₆	—	2	4	no	—
70	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
71	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
72	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
73	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
74	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
75	C₂×#168	C₂×C₃×C₄	1	4	yes	—
76	C₂×#168	C₂×C₃×C₄	1	4	yes	—
77	#431	—	5	2	no	—
78	C₄×M₁₆	C₃×D₅	1	1	yes	characteristic
79	#322	—	5	2	no	—
80	#322	—	5	1	no	—
81	C₈²	—	5	1	no	—
82	C₂²×C₃×C₅	—	2	1	no	—
83	C₂²×C₃×C₅	—	2	2	no	—
84	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
85	C₃×C₄×C₅	—	2	1	no	—
86	C₃×C₄×C₅	—	2	2	no	—
87	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
88	C₃×C₄×C₅	#131	1	4	yes	—
89	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
90	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
91	C₃×M₁₆	—	2	4	no	—
92	C₂×C₃×C₈	—	5	4	no	—
93	C₂×C₃×C₈	—	5	4	no	—
94	C₂×C₃×C₈	C₂×Dic₅	1	2	yes	—
95	C₂×C₃×C₈	C₂×Dic₅	1	2	yes	—
96	C₃×C₄²	C₄×D₅	1	2	yes	—
97	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
98	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
99	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
100	C₂×C₄×C₅	—	2	2	no	—
101	C₂×C₄×C₅	—	2	4	no	—
102	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
103	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
104	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
105	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
106	C₅×C₈	—	2	2	no	—
107	C₅×C₈	C₃×M₁₆	1	4	yes	—
108	#168	—	2	4	no	—
109	#168	—	2	4	no	—
110	C₂×M₁₆	C₃×Dic₅	1	2	yes	—
111	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
112	C₄⋊C₈	—	5	4	no	—
113	C₂²⋊C₈	—	5	4	no	—
114	#97	C₃×Dic₅	1	2	yes	—
115	C₄×C₈	—	5	2	no	—
116	C₄×C₈	—	5	2	no	—
117	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
118	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
119	C₂×C₃×C₅	—	4	1	no	—
120	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
121	C₂×C₃×C₅	#405	1	2	yes	—
122	C₂³×C₃	C₄×Dic₅	1	1	yes	characteristic
123	C₂×C₃×C₄	—	2	4	no	—
124	C₂×C₃×C₄	—	2	2	no	—
125	C₂×C₃×C₄	C₄×Dic₅	1	1	yes	characteristic
126	C₂×C₃×C₄	C₄×Dic₅	1	2	yes	—
127	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
128	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
129	C₃×C₈	—	2	2	no	—
130	C₃×C₈	—	10	4	no	—
131	C₃×C₈	—	10	4	no	—
132	C₃×C₈	#681	1	4	yes	—
133	C₂²×C₅	—	2	1	no	—
134	C₂²×C₅	—	2	2	no	—
135	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
136	C₄×C₅	—	2	1	no	—
137	C₄×C₅	—	2	2	no	—
138	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
139	C₄×C₅	C₃×#131	1	4	yes	—
140	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
141	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
142	M₁₆	—	2	4	no	—
143	C₂×C₈	—	5	4	no	—
144	C₂×C₈	—	5	4	no	—
145	C₂×C₈	C₂×C₃×Dic₅	1	2	yes	—
146	C₂×C₈	C₂×C₃×Dic₅	1	2	yes	—
147	C₄²	C₃×C₄×D₅	1	2	yes	—
148	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
149	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
150	C₃×C₅	#1453	1	1	yes	characteristic, complemented, Hall
151	C₂²×C₃	—	2	2	no	—
152	C₂²×C₃	—	2	1	no	—
153	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
154	C₃×C₄	—	2	2	no	—
155	C₃×C₄	—	2	1	no	—
156	C₃×C₄	#4053	1	4	yes	—
157	C₃×C₄	C₂×#681	1	2	yes	—
158	C₂×C₅	—	4	1	no	—
159	C₂×C₅	C₃×C₄×M₁₆	1	1	yes	characteristic
160	C₂×C₅	C₃×#405	1	2	yes	—
161	C₂³	C₃×C₄×Dic₅	1	1	yes	characteristic
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	C₃×C₄×Dic₅	1	1	yes	characteristic
165	C₂×C₄	C₃×C₄×Dic₅	1	2	yes	—
166	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
167	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
168	C₈	—	2	2	no	—
169	C₈	—	10	4	no	—
170	C₈	—	10	4	no	—
171	C₈	C₃×#681	1	4	yes	—
172	C₂×C₃	—	4	1	no	—
173	C₂×C₃	C₄×#681	1	1	yes	characteristic
174	C₂×C₃	#65411	1	2	yes	—
175	C₅	C₃×#1453	1	1	yes	characteristic, complemented, Sylow
176	C₂²	—	2	2	no	—
177	C₂²	—	2	1	no	—
178	C₂²	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
179	C₄	—	2	2	no	—
180	C₄	—	2	1	no	—
181	C₄	C₃×#4053	1	4	yes	—
182	C₄	C₂×C₃×#681	1	2	yes	—
183	C₃	#10600641	1	1	yes	characteristic, direct product factor, Sylow
184	C₂	—	4	1	no	—
185	C₂	C₃×C₄×#681	1	1	yes	characteristic
186	C₂	C₃×#65411	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂²×D₅
commutator	C₂²×C₅	C₂×C₃×C₄²
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂³×C₃×C₅	C₄²
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₃×C₄×M₁₆	D₅
hypocenter	C₅	C₃×#1453
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₃×#64675	C₂	semidirect
4. C₃×#64674	C₂	semidirect
5. C₃×C₈×#168	C₂	semidirect
6. #10600641	C₃	direct (N × H)
19. #64675	C₂×C₃	semidirect
20. #64674	C₂×C₃	semidirect
21. C₈×#168	C₂×C₃	semidirect
150. C₃×C₅	#1453	semidirect
175. C₅	C₃×#1453	semidirect
183. C₃	#10600641	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×C₄×C₅×M₁₆	2
C₃×#65214	2
C₃×#64675	2
C₃×#64674	2
C₃×C₈×#168	2
#10600641	3
C₃×#1453	5

Subgroups — C3×#10600641 #14280607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600641 #14280607