Subgroups — C₃×#10601239 #14299039

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3946	C₂	1	4	yes	maximal
3	C₃×#65221	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic
5	#10601239	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
9	C₂²×C₃×#168	C₂²	1	2	yes	—
10	C₃×C₅×C₄⋊C₈	—	2	2	no	—
11	C₃×#3963	C₄	1	2	yes	—
12	C₃×#3963	C₄	1	2	yes	—
13	C₃×#3946	—	2	8	no	—
14	C₃×C₄⋊#168	—	2	2	no	—
15	C₃×#1843	—	5	1	no	maximal, Hall
16	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
17	C₂×#3946	C₂×C₃	1	4	yes	—
18	#65221	C₂×C₃	1	1	yes	characteristic
19	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
24	C₂×C₃×C₅×C₈	—	2	4	no	—
25	C₂×C₃×C₅×C₈	—	2	2	no	—
26	C₃×C₄²×C₅	D₄	1	2	yes	—
27	C₃×C₄²×C₅	Q₈	1	2	yes	—
28	C₃×C₄×Dic₅	D₄	1	4	yes	—
29	C₃×C₄×Dic₅	Q₈	1	4	yes	—
30	C₂×C₃×#168	—	2	2	no	—
31	C₂×C₃×#168	—	2	4	no	—
32	C₂×C₃×C₄⋊C₈	—	5	4	no	—
33	C₂×C₃×C₄⋊C₈	—	5	1	no	—
34	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic
35	C₃×#376	—	5	1	no	—
36	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
37	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
38	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
39	C₂²×#168	C₂²×C₃	1	2	yes	—
40	C₅×C₄⋊C₈	—	2	2	no	—
41	#3963	C₃×C₄	1	2	yes	—
42	#3963	C₃×C₄	1	2	yes	—
43	#3946	—	2	8	no	—
44	C₄⋊#168	—	2	2	no	—
45	#1843	—	5	1	no	Sylow
46	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	—	2	2	no	—
48	C₂×C₃×C₄×C₅	—	2	2	no	—
49	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
50	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
51	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
52	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
55	C₂×C₃×Dic₅	—	2	4	no	—
56	C₂×C₃×Dic₅	—	2	4	no	—
57	C₂×C₃×Dic₅	C₄⋊C₄	1	8	yes	—
58	C₃×C₅×C₈	—	4	2	no	—
59	C₃×#168	—	4	2	no	—
60	C₂²×C₃×C₈	—	5	2	no	—
61	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
62	C₂×C₃×C₄²	—	5	2	no	—
63	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
64	C₃×C₄⋊C₈	—	2	2	no	—
65	C₃×C₄⋊C₈	—	10	8	no	—
66	C₃×C₄⋊C₈	—	10	2	no	—
67	C₃×#95	—	5	2	no	—
68	C₃×#95	—	5	2	no	—
69	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
72	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
73	C₂×C₅×C₈	—	2	4	no	—
74	C₂×C₅×C₈	—	2	2	no	—
75	C₄²×C₅	C₃×D₄	1	2	yes	—
76	C₄²×C₅	C₃×Q₈	1	2	yes	—
77	C₄×Dic₅	C₃×D₄	1	4	yes	—
78	C₄×Dic₅	C₃×Q₈	1	4	yes	—
79	C₂×#168	—	2	2	no	—
80	C₂×#168	—	2	4	no	—
81	C₂×C₄⋊C₈	—	5	4	no	—
82	C₂×C₄⋊C₈	—	5	1	no	—
83	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic
84	#376	—	5	1	no	—
85	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
86	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₃×C₅	#131	1	2	yes	—
88	C₂²×C₃×C₅	#131	1	2	yes	—
89	C₃×C₄×C₅	—	2	2	no	—
90	C₃×C₄×C₅	—	2	2	no	—
91	C₃×C₄×C₅	#127	1	1	yes	characteristic
92	C₃×C₄×C₅	C₄⋊Q₈	1	2	yes	—
93	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
94	C₃×Dic₅	—	2	8	no	—
95	C₂²×C₃×C₄	—	5	4	no	—
96	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
97	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
98	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
99	C₂×C₃×C₈	—	2	4	no	—
100	C₂×C₃×C₈	—	2	2	no	—
101	C₂×C₃×C₈	—	10	4	no	—
102	C₂×C₃×C₈	—	10	2	no	—
103	C₃×C₄²	—	5	4	no	—
104	C₃×C₄²	—	5	4	no	—
105	C₃×C₄²	Dic₁₀	1	2	yes	—
106	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
107	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
108	C₂×C₄×C₅	—	2	2	no	—
109	C₂×C₄×C₅	—	2	2	no	—
110	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
111	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
112	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
113	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
114	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
115	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
116	C₂×Dic₅	—	2	4	no	—
117	C₂×Dic₅	—	2	4	no	—
118	C₂×Dic₅	C₃×C₄⋊C₄	1	8	yes	—
119	C₅×C₈	—	4	2	no	—
120	#168	—	4	2	no	—
121	C₂²×C₈	—	5	2	no	—
122	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
123	C₂×C₄²	—	5	2	no	—
124	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
125	C₄⋊C₈	—	2	2	no	—
126	C₄⋊C₈	—	10	8	no	—
127	C₄⋊C₈	—	10	2	no	—
128	#95	—	5	2	no	—
129	#95	—	5	2	no	—
130	C₂×C₃×C₅	#384	1	1	yes	characteristic
131	C₂×C₃×C₅	#424	1	4	yes	—
132	C₂×C₃×C₅	#424	1	1	yes	characteristic
133	C₂×C₃×C₅	#424	1	1	yes	characteristic
134	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
135	C₂×C₃×C₄	—	2	2	no	—
136	C₂×C₃×C₄	—	2	2	no	—
137	C₂×C₃×C₄	—	5	8	no	—
138	C₂×C₃×C₄	—	10	4	no	—
139	C₂×C₃×C₄	—	10	4	no	—
140	C₂×C₃×C₄	#683	1	2	yes	—
141	C₂×C₃×C₄	#683	1	2	yes	—
142	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
143	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
144	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
145	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
146	C₃×C₈	—	4	2	no	—
147	C₃×C₈	—	20	2	no	—
148	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
149	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×C₅	C₃×#131	1	2	yes	—
151	C₂²×C₅	C₃×#131	1	2	yes	—
152	C₄×C₅	—	2	2	no	—
153	C₄×C₅	—	2	2	no	—
154	C₄×C₅	C₃×#127	1	1	yes	characteristic
155	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
156	C₄×C₅	C₃×C₄⋊Q₈	1	2	yes	—
157	Dic₅	—	2	8	no	—
158	C₂²×C₄	—	5	4	no	—
159	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
160	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
161	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
162	C₂×C₈	—	2	4	no	—
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	10	4	no	—
165	C₂×C₈	—	10	2	no	—
166	C₄²	—	5	4	no	—
167	C₄²	—	5	4	no	—
168	C₄²	C₃×Dic₁₀	1	2	yes	—
169	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
170	C₃×C₅	#1843	1	1	yes	characteristic, complemented, Hall
171	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
172	C₂²×C₃	#4047	1	2	yes	—
173	C₂²×C₃	#4053	1	2	yes	—
174	C₂²×C₃	C₂×#683	1	1	yes	characteristic
175	C₃×C₄	—	2	2	no	—
176	C₃×C₄	—	2	2	no	—
177	C₃×C₄	—	10	8	no	—
178	C₃×C₄	#4034	1	2	yes	—
179	C₃×C₄	#4086	1	1	yes	characteristic
180	C₃×C₄	#4090	1	1	yes	characteristic
181	C₂×C₅	C₃×#384	1	1	yes	characteristic
182	C₂×C₅	C₃×#424	1	4	yes	—
183	C₂×C₅	C₃×#424	1	1	yes	characteristic
184	C₂×C₅	C₃×#424	1	1	yes	characteristic
185	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	5	8	no	—
189	C₂×C₄	—	10	4	no	—
190	C₂×C₄	—	10	4	no	—
191	C₂×C₄	C₃×#683	1	2	yes	—
192	C₂×C₄	C₃×#683	1	2	yes	—
193	C₂×C₄	C₂×C₃×Dic₁₀	1	1	yes	characteristic
194	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
195	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
196	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
197	C₈	—	4	2	no	—
198	C₈	—	20	2	no	—
199	C₂×C₃	#65128	1	4	yes	—
200	C₂×C₃	#65265	1	1	yes	characteristic
201	C₂×C₃	#65391	1	1	yes	characteristic
202	C₂×C₃	#65408	1	1	yes	characteristic
203	C₅	C₃×#1843	1	1	yes	characteristic, complemented, Sylow
204	C₂²	C₃×D₅×C₄⋊C₄	1	2	yes	—
205	C₂²	C₃×#4047	1	2	yes	—
206	C₂²	C₃×#4053	1	2	yes	—
207	C₂²	C₂×C₃×#683	1	1	yes	characteristic
208	C₄	—	2	2	no	—
209	C₄	—	2	2	no	—
210	C₄	—	10	8	no	—
211	C₄	C₃×#4034	1	2	yes	—
212	C₄	C₃×#4086	1	1	yes	characteristic
213	C₄	C₃×#4090	1	1	yes	characteristic
214	C₃	#10601239	1	1	yes	characteristic, direct product factor, Sylow
215	C₂	C₃×#65128	1	4	yes	—
216	C₂	C₃×#65265	1	1	yes	characteristic
217	C₂	C₃×#65391	1	1	yes	characteristic
218	C₂	C₃×#65408	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂³×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₃×#1843
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
5. #10601239	C₃	direct (N × H)
170. C₃×C₅	#1843	semidirect
203. C₅	C₃×#1843	semidirect
214. C₃	#10601239	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×#3946	2
C₃×#65221	2
C₂×C₃×C₄⋊#168	2
#10601239	3
C₃×#1843	5

Subgroups — C3×#10601239 #14299039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601239 #14299039