Subgroups — C₃×#10599849 #14315193

Order 1920.

292 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65190	C₂	1	2	yes	maximal, complemented
2	C₃×#64989	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64728	C₂	1	2	yes	maximal, complemented
5	C₃×#64683	C₂	1	1	yes	maximal, characteristic, complemented
6	#10599849	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×#4050	C₄	1	1	yes	characteristic
8	C₃×#4047	C₂²	1	2	yes	—
9	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×#3951	C₄	1	1	yes	characteristic
13	C₃×#3944	C₂²	1	2	yes	—
14	C₃×#3937	C₄	1	2	yes	—
15	C₃×#3930	—	2	2	no	—
16	C₃×D₅×C₁₆	—	2	2	no	—
17	C₃×#2170	—	5	1	no	maximal, Hall
18	#65190	C₂×C₃	1	2	yes	complemented
19	#64989	C₂×C₃	1	1	yes	characteristic
20	C₄×C₅×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
21	#64728	C₂×C₃	1	2	yes	complemented
22	#64683	C₂×C₃	1	1	yes	characteristic, complemented
23	C₃×#709	C₂×C₄	1	2	yes	—
24	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
26	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
27	C₃×#681	C₂×C₄	1	2	yes	—
28	C₃×Dic₂₀	C₈	1	1	yes	characteristic
29	C₃×D₄₀	C₈	1	1	yes	characteristic
30	C₃×#677	C₈	1	2	yes	—
31	C₃×#676	—	2	2	no	—
32	C₃×C₈×D₅	—	2	2	no	—
33	C₃×C₅×C₁₆	—	2	1	no	—
34	C₃×C₅×C₁₆	D₄	1	1	yes	characteristic
35	C₃×C₅×C₁₆	D₄	1	1	yes	characteristic
36	C₃×#672	—	2	2	no	—
37	C₃×#504	—	5	2	no	—
38	C₃×#443	—	5	1	no	—
39	C₃×#364	—	5	1	no	—
40	C₃×#350	—	5	2	no	—
41	C₃×C₄×C₁₆	D₅	1	1	yes	characteristic, complemented
42	#4050	C₃×C₄	1	1	yes	characteristic
43	#4047	C₂²×C₃	1	2	yes	—
44	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
45	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
46	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
47	#3951	C₃×C₄	1	1	yes	characteristic
48	#3944	C₂²×C₃	1	2	yes	—
49	#3937	C₃×C₄	1	2	yes	—
50	#3930	—	2	2	no	—
51	D₅×C₁₆	—	2	2	no	—
52	#2170	—	5	1	no	Sylow
53	C₂×C₃×C₄×C₅	—	2	1	no	—
54	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
55	C₃×C₂²⋊D₅	—	2	2	no	—
56	C₃×D₂₀	C₂×C₈	1	2	yes	—
57	C₃×C₄×D₅	—	2	2	no	—
58	C₃×Dic₁₀	C₂×C₈	1	2	yes	—
59	C₃×C₅×C₈	C₂×C₈	1	1	yes	characteristic
60	C₃×C₅×C₈	C₂×C₈	1	1	yes	characteristic
61	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
62	C₃×C₅×C₈	#41	1	1	yes	characteristic
63	C₃×#168	—	2	2	no	—
64	C₃×#135	—	5	1	no	—
65	C₃×#131	—	5	2	no	—
66	C₃×M₃₂	—	5	2	no	—
67	C₃×M₃₂	—	10	2	no	—
68	C₂×C₃×C₁₆	—	10	2	no	—
69	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic
70	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic
71	C₃×#108	—	5	1	no	—
72	C₃×#104	—	5	2	no	—
73	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
74	#709	C₂×C₃×C₄	1	2	yes	—
75	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
76	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
77	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
78	#681	C₂×C₃×C₄	1	2	yes	—
79	Dic₂₀	C₃×C₈	1	1	yes	characteristic
80	D₄₀	C₃×C₈	1	1	yes	characteristic
81	#677	C₃×C₈	1	2	yes	—
82	#676	—	2	2	no	—
83	C₈×D₅	—	2	2	no	—
84	C₅×C₁₆	—	2	1	no	—
85	C₅×C₁₆	C₃×D₄	1	1	yes	characteristic
86	C₅×C₁₆	C₃×D₄	1	1	yes	characteristic
87	#672	—	2	2	no	—
88	#504	—	5	2	no	—
89	#443	—	5	1	no	—
90	#364	—	5	1	no	—
91	#350	—	5	2	no	—
92	C₄×C₁₆	C₃×D₅	1	1	yes	characteristic, complemented
93	C₂²×C₃×C₅	#131	1	1	yes	characteristic
94	C₂×C₃×D₅	—	2	2	no	—
95	C₃×C₄×C₅	—	2	2	no	—
96	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
97	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
98	C₃×Dic₅	—	2	2	no	—
99	C₃×#41	—	5	2	no	—
100	C₃×Q₁₆	—	5	1	no	—
101	C₃×SD₁₆	—	5	2	no	—
102	C₃×D₈	—	5	1	no	—
103	C₃×M₁₆	—	5	2	no	—
104	C₃×M₁₆	—	10	2	no	—
105	C₂×C₃×C₈	—	10	2	no	—
106	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
107	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
108	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
109	C₃×C₁₆	—	2	1	no	—
110	C₃×C₁₆	—	10	2	no	—
111	C₃×C₁₆	D₂₀	1	1	yes	characteristic
112	C₃×C₁₆	D₂₀	1	1	yes	characteristic
113	C₂×C₄×C₅	—	2	1	no	—
114	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
115	C₂²⋊D₅	—	2	2	no	—
116	D₂₀	C₂×C₃×C₈	1	2	yes	—
117	C₄×D₅	—	2	2	no	—
118	Dic₁₀	C₂×C₃×C₈	1	2	yes	—
119	C₅×C₈	C₂×C₃×C₈	1	1	yes	characteristic
120	C₅×C₈	C₂×C₃×C₈	1	1	yes	characteristic
121	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
122	C₅×C₈	C₃×#41	1	1	yes	characteristic
123	#168	—	2	2	no	—
124	#135	—	5	1	no	—
125	#131	—	5	2	no	—
126	M₃₂	—	5	2	no	—
127	M₃₂	—	10	2	no	—
128	C₂×C₁₆	—	10	2	no	—
129	C₂×C₁₆	C₂×C₃×D₅	1	1	yes	characteristic
130	C₂×C₁₆	C₂×C₃×D₅	1	1	yes	characteristic
131	#108	—	5	1	no	—
132	#104	—	5	2	no	—
133	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
134	C₂×C₃×C₅	—	2	1	no	—
135	C₂×C₃×C₅	C₈×D₄	1	1	yes	characteristic
136	C₃×D₅	—	4	2	no	—
137	C₃×Q₈	—	5	2	no	—
138	C₃×D₄	—	5	2	no	—
139	C₃×D₄	—	10	2	no	—
140	C₂×C₃×C₄	—	2	1	no	—
141	C₂×C₃×C₄	—	10	2	no	—
142	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
143	C₃×C₈	—	10	2	no	—
144	C₃×C₈	C₈×D₅	1	1	yes	characteristic
145	C₃×C₈	C₈×D₅	1	1	yes	characteristic
146	C₃×C₈	C₂×D₂₀	1	1	yes	characteristic
147	C₃×C₈	#709	1	1	yes	characteristic
148	C₂²×C₅	C₃×#131	1	1	yes	characteristic
149	C₂×D₅	—	2	2	no	—
150	C₄×C₅	—	2	2	no	—
151	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
152	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
153	Dic₅	—	2	2	no	—
154	#41	—	5	2	no	—
155	Q₁₆	—	5	1	no	—
156	SD₁₆	—	5	2	no	—
157	D₈	—	5	1	no	—
158	M₁₆	—	5	2	no	—
159	M₁₆	—	10	2	no	—
160	C₂×C₈	—	10	2	no	—
161	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
162	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
163	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
164	C₁₆	—	2	1	no	—
165	C₁₆	—	10	2	no	—
166	C₁₆	C₃×D₂₀	1	1	yes	characteristic
167	C₁₆	C₃×D₂₀	1	1	yes	characteristic
168	C₃×C₅	#2170	1	1	yes	characteristic, complemented, Hall
169	C₂²×C₃	—	10	2	no	—
170	C₂²×C₃	#4047	1	1	yes	characteristic
171	C₃×C₄	—	2	2	no	—
172	C₃×C₄	—	10	2	no	—
173	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
174	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
175	C₂×C₅	—	2	1	no	—
176	C₂×C₅	C₃×C₈×D₄	1	1	yes	characteristic
177	D₅	—	4	2	no	—
178	Q₈	—	5	2	no	—
179	D₄	—	5	2	no	—
180	D₄	—	10	2	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	10	2	no	—
183	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
184	C₈	—	10	2	no	—
185	C₈	C₃×C₈×D₅	1	1	yes	characteristic
186	C₈	C₃×C₈×D₅	1	1	yes	characteristic
187	C₈	C₂×C₃×D₂₀	1	1	yes	characteristic
188	C₈	C₃×#709	1	1	yes	characteristic
189	C₂×C₃	—	2	1	no	—
190	C₂×C₃	—	20	2	no	—
191	C₂×C₃	C₈×D₂₀	1	1	yes	characteristic
192	C₅	C₃×#2170	1	1	yes	characteristic, complemented, Sylow
193	C₂²	—	10	2	no	—
194	C₂²	C₃×#4047	1	1	yes	characteristic
195	C₄	—	2	2	no	—
196	C₄	—	10	2	no	—
197	C₄	C₃×C₄×D₂₀	1	1	yes	characteristic
198	C₄	C₂×C₃×C₈×D₅	1	1	yes	characteristic
199	C₃	#10599849	1	1	yes	characteristic, direct product factor, Sylow
200	C₂	—	2	1	no	—
201	C₂	—	20	2	no	—
202	C₂	C₃×C₈×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₁₆	D₂₀
commutator	C₄×C₅	C₂²×C₃×C₈
Frattini	C₂×C₈	C₂²×C₃×D₅
Fitting	C₃×C₄×C₅×C₁₆	C₂
socle	C₂×C₃×C₅	C₈×D₄
prime radical	C₃×#4050	C₄
cosocle	C₂×C₅×C₈	C₂³×C₃
hypercenter	C₃×C₄×C₁₆	D₅
hypocenter	C₅	C₃×#2170
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₁₆ ◁ C₂×C₃×C₁₆ ◁ C₃×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×#65190	C₂	semidirect
3. C₃×C₄×C₅×C₁₆	C₂	semidirect
4. C₃×#64728	C₂	semidirect
5. C₃×#64683	C₂	semidirect
6. #10599849	C₃	direct (N × H)
18. #65190	C₂×C₃	semidirect
20. C₄×C₅×C₁₆	C₂×C₃	semidirect
21. #64728	C₂×C₃	semidirect
22. #64683	C₂×C₃	semidirect
41. C₃×C₄×C₁₆	D₅	semidirect
92. C₄×C₁₆	C₃×D₅	semidirect
168. C₃×C₅	#2170	semidirect
192. C₅	C₃×#2170	semidirect
199. C₃	#10599849	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×#65190	2
C₃×#64989	2
C₃×C₄×C₅×C₁₆	2
C₃×#64728	2
C₃×#64683	2
#10599849	3
C₃×#2170	5

Subgroups — C3×#10599849 #14315193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599849 #14315193