Subgroups — C₃×#10601646 #14291773

Order 1920.

320 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#65297	C₂	1	2	yes	maximal
3	C₃×#64971	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64701	C₂	1	2	yes	maximal, complemented
5	C₃×#64678	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601646	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×C₈	—	2	1	no	—
8	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₃×#4015	C₂²	1	2	yes	—
10	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
12	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×#3964	—	2	2	no	—
14	C₃×#3950	—	2	1	no	—
15	C₃×#3950	—	2	1	no	—
16	C₃×#3940	—	2	2	no	—
17	C₃×C₄⋊#168	C₂²	1	2	yes	—
18	C₃×#1675	—	5	1	no	maximal, Hall
19	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic
20	#65297	C₂×C₃	1	2	yes	—
21	#64971	C₂×C₃	1	1	yes	characteristic, complemented
22	#64701	C₂×C₃	1	2	yes	complemented
23	#64678	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
25	C₂²×C₃×C₄×C₅	—	2	1	no	—
26	C₂×C₃×Dic₁₀	—	2	2	no	—
27	C₂×C₃×C₅×C₈	—	2	1	no	—
28	C₂×C₃×C₅×C₈	—	4	2	no	—
29	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
30	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
31	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
32	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
33	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
34	C₃×C₄⋊Dic₅	—	2	2	no	—
35	C₃×C₄⋊Dic₅	—	2	2	no	—
36	C₂×C₃×#168	—	2	2	no	—
37	C₃×#500	—	5	1	no	—
38	C₃×#476	—	5	2	no	—
39	C₃×C₈×D₄	D₅	1	1	yes	characteristic
40	C₃×#335	—	5	1	no	—
41	C₃×#333	—	5	2	no	—
42	C₂²×C₅×C₈	—	2	1	no	—
43	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
44	#4015	C₂²×C₃	1	2	yes	—
45	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
46	C₅×C₂²⋊C₈	—	2	1	no	—
47	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
48	#3964	—	2	2	no	—
49	#3950	—	2	1	no	—
50	#3950	—	2	1	no	—
51	#3940	—	2	2	no	—
52	C₄⋊#168	C₂²×C₃	1	2	yes	—
53	#1675	—	5	1	no	Sylow
54	C₂³×C₃×C₅	—	2	1	no	—
55	C₃×C₅×D₄	—	2	1	no	—
56	C₃×C₅×D₄	Q₁₆	1	2	yes	—
57	C₂×C₃×C₄×C₅	—	2	1	no	—
58	C₂×C₃×C₄×C₅	—	4	1	no	—
59	C₂×C₃×C₄×C₅	—	4	1	no	—
60	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
61	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
63	C₂×C₃×Dic₅	—	4	2	no	—
64	C₃×Dic₁₀	—	8	2	no	—
65	C₃×C₅×C₈	—	2	1	no	—
66	C₃×C₅×C₈	—	4	1	no	—
67	C₃×C₅×C₈	SD₁₆	1	2	yes	—
68	C₃×#168	—	4	2	no	—
69	C₂²×C₃×C₈	—	2	1	no	—
70	C₃×C₄⋊Q₈	—	5	2	no	—
71	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
72	C₃×#107	—	10	1	no	—
73	C₃×#107	—	10	1	no	—
74	C₃×#106	—	10	2	no	—
75	C₃×C₄⋊C₈	—	5	2	no	—
76	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
77	C₃×#102	—	10	2	no	—
78	C₃×C₂²⋊C₈	—	2	1	no	—
79	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
80	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	—	2	1	no	—
82	C₂×Dic₁₀	—	2	2	no	—
83	C₂×C₅×C₈	—	2	1	no	—
84	C₂×C₅×C₈	—	4	2	no	—
85	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
86	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
87	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
88	C₅×C₂²⋊C₄	—	2	1	no	—
89	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
90	C₄⋊Dic₅	—	2	2	no	—
91	C₄⋊Dic₅	—	2	2	no	—
92	C₂×#168	—	2	2	no	—
93	#500	—	5	1	no	—
94	#476	—	5	2	no	—
95	C₈×D₄	C₃×D₅	1	1	yes	characteristic
96	#335	—	5	1	no	—
97	#333	—	5	2	no	—
98	C₂²×C₃×C₅	—	2	2	no	—
99	C₂²×C₃×C₅	—	4	1	no	—
100	C₂²×C₃×C₅	—	4	1	no	—
101	C₂²×C₃×C₅	#121	1	1	yes	characteristic
102	C₃×C₄×C₅	—	2	1	no	—
103	C₃×C₄×C₅	—	4	1	no	—
104	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
105	C₃×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
106	C₃×C₄×C₅	#135	1	1	yes	characteristic
107	C₃×C₄×C₅	#137	1	1	yes	characteristic
108	C₃×Dic₅	—	8	2	no	—
109	C₂×C₃×Q₈	—	10	2	no	—
110	C₂×C₃×D₄	D₂₀	1	1	yes	characteristic
111	C₂²×C₃×C₄	—	2	1	no	—
112	C₂×C₃×C₈	—	2	1	no	—
113	C₂×C₃×C₈	—	4	2	no	—
114	C₂×C₃×C₈	—	10	2	no	—
115	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
116	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
117	C₃×C₄⋊C₄	—	10	2	no	—
118	C₃×C₄⋊C₄	—	10	2	no	—
119	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
120	C₃×C₂²⋊C₄	—	2	1	no	—
121	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
122	C₂³×C₅	—	2	1	no	—
123	C₅×D₄	—	2	1	no	—
124	C₅×D₄	C₃×Q₁₆	1	2	yes	—
125	C₂×C₄×C₅	—	2	1	no	—
126	C₂×C₄×C₅	—	4	1	no	—
127	C₂×C₄×C₅	—	4	1	no	—
128	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
129	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
130	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
131	C₂×Dic₅	—	4	2	no	—
132	Dic₁₀	—	8	2	no	—
133	C₅×C₈	—	2	1	no	—
134	C₅×C₈	—	4	1	no	—
135	C₅×C₈	C₃×SD₁₆	1	2	yes	—
136	#168	—	4	2	no	—
137	C₂²×C₈	—	2	1	no	—
138	C₄⋊Q₈	—	5	2	no	—
139	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
140	#107	—	10	1	no	—
141	#107	—	10	1	no	—
142	#106	—	10	2	no	—
143	C₄⋊C₈	—	5	2	no	—
144	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
145	#102	—	10	2	no	—
146	C₂²⋊C₈	—	2	1	no	—
147	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
148	C₂×C₃×C₅	—	4	2	no	—
149	C₂×C₃×C₅	#461	1	1	yes	characteristic
150	C₂×C₃×C₅	#467	1	1	yes	characteristic
151	C₂×C₃×C₅	#472	1	1	yes	characteristic
152	C₂³×C₃	—	2	1	no	—
153	C₃×Q₈	—	40	2	no	—
154	C₃×D₄	—	2	1	no	—
155	C₃×D₄	Dic₂₀	1	2	yes	—
156	C₂×C₃×C₄	—	2	1	no	—
157	C₂×C₃×C₄	—	4	1	no	—
158	C₂×C₃×C₄	—	4	1	no	—
159	C₂×C₃×C₄	—	20	2	no	—
160	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
161	C₂×C₃×C₄	#709	1	1	yes	characteristic
162	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
163	C₃×C₈	—	2	1	no	—
164	C₃×C₈	—	4	1	no	—
165	C₃×C₈	—	20	2	no	—
166	C₃×C₈	#687	1	2	yes	—
167	C₂²×C₅	—	2	2	no	—
168	C₂²×C₅	—	4	1	no	—
169	C₂²×C₅	—	4	1	no	—
170	C₂²×C₅	C₃×#121	1	1	yes	characteristic
171	C₄×C₅	—	2	1	no	—
172	C₄×C₅	—	4	1	no	—
173	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
174	C₄×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
175	C₄×C₅	C₃×#135	1	1	yes	characteristic
176	C₄×C₅	C₃×#137	1	1	yes	characteristic
177	Dic₅	—	8	2	no	—
178	C₂×Q₈	—	10	2	no	—
179	C₂×D₄	C₃×D₂₀	1	1	yes	characteristic
180	C₂²×C₄	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	10	2	no	—
184	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
185	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
186	C₄⋊C₄	—	10	2	no	—
187	C₄⋊C₄	—	10	2	no	—
188	C₄⋊C₄	C₃×D₂₀	1	1	yes	characteristic
189	C₂²⋊C₄	—	2	1	no	—
190	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
191	C₃×C₅	#1675	1	1	yes	characteristic, complemented, Hall
192	C₂²×C₃	—	2	2	no	—
193	C₂²×C₃	—	4	1	no	—
194	C₂²×C₃	—	4	1	no	—
195	C₂²×C₃	#4076	1	1	yes	characteristic
196	C₃×C₄	—	2	1	no	—
197	C₃×C₄	—	4	1	no	—
198	C₃×C₄	—	40	2	no	—
199	C₃×C₄	#4050	1	1	yes	characteristic
200	C₃×C₄	C₂×Dic₂₀	1	1	yes	characteristic
201	C₃×C₄	C₂×#687	1	1	yes	characteristic
202	C₃×C₄	#4097	1	1	yes	characteristic
203	C₂×C₅	—	4	2	no	—
204	C₂×C₅	C₃×#461	1	1	yes	characteristic
205	C₂×C₅	C₃×#467	1	1	yes	characteristic
206	C₂×C₅	C₃×#472	1	1	yes	characteristic
207	C₂³	—	2	1	no	—
208	Q₈	—	40	2	no	—
209	D₄	—	2	1	no	—
210	D₄	C₃×Dic₂₀	1	2	yes	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	20	2	no	—
215	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
216	C₂×C₄	C₃×#709	1	1	yes	characteristic
217	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
218	C₈	—	2	1	no	—
219	C₈	—	4	1	no	—
220	C₈	—	20	2	no	—
221	C₈	C₃×#687	1	2	yes	—
222	C₂×C₃	—	4	2	no	—
223	C₂×C₃	#65308	1	1	yes	characteristic
224	C₂×C₃	#65405	1	1	yes	characteristic
225	C₂×C₃	#65431	1	1	yes	characteristic
226	C₅	C₃×#1675	1	1	yes	characteristic, complemented, Sylow
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	1	no	—
230	C₂²	C₃×#4076	1	1	yes	characteristic
231	C₄	—	2	1	no	—
232	C₄	—	4	1	no	—
233	C₄	—	40	2	no	—
234	C₄	C₃×#4050	1	1	yes	characteristic
235	C₄	C₂×C₃×Dic₂₀	1	1	yes	characteristic
236	C₄	C₂×C₃×#687	1	1	yes	characteristic
237	C₄	C₃×#4097	1	1	yes	characteristic
238	C₃	#10601646	1	1	yes	characteristic, direct product factor, Sylow
239	C₂	—	4	2	no	—
240	C₂	C₃×#65308	1	1	yes	characteristic
241	C₂	C₃×#65405	1	1	yes	characteristic
242	C₂	C₃×#65431	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#4076
commutator, cosocle	C₄²×C₅	C₂³×C₃
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×C₈×D₄	C₂
socle	C₂²×C₃×C₅	#121
prime radical	C₂×C₃×C₅×D₄	D₄
hypercenter	C₃×C₈×D₄	D₅
hypocenter	C₅	C₃×#1675
LCS	G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₈×D₄

Complements

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

N	H ≅ G/N	type
3. C₃×#64971	C₂	semidirect
4. C₃×#64701	C₂	semidirect
5. C₃×#64678	C₂	semidirect
6. #10601646	C₃	direct (N × H)
21. #64971	C₂×C₃	semidirect
22. #64701	C₂×C₃	semidirect
23. #64678	C₂×C₃	semidirect
191. C₃×C₅	#1675	semidirect
226. C₅	C₃×#1675	semidirect
238. C₃	#10601646	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×C₈×D₄	2
C₃×#65297	2
C₃×#64971	2
C₃×#64701	2
C₃×#64678	2
#10601646	3
C₃×#1675	5

Subgroups — C3×#10601646 #14291773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601646 #14291773