Subgroups — C₃×#10599390 #14294893

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3947	C₂	1	2	yes	maximal
2	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic
4	C₃×#64770	C₂	1	2	yes	maximal
5	C₃×#64744	C₂	1	1	yes	maximal, characteristic
6	#10599390	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
10	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
11	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃×#168	C₂²	1	2	yes	—
14	C₃×#3947	C₄	1	8	yes	complemented
15	C₃×#1745	—	5	1	no	maximal, Hall
16	C₂×#3947	C₂×C₃	1	2	yes	—
17	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic
18	C₅×#336	C₂×C₃	1	1	yes	characteristic
19	#64770	C₂×C₃	1	2	yes	—
20	#64744	C₂×C₃	1	1	yes	characteristic
21	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
22	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
26	C₂×C₃×C₅×C₈	—	2	2	no	—
27	C₂×C₃×C₅×C₈	—	2	2	no	—
28	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
29	C₃×C₄²×C₅	—	2	2	no	—
30	C₃×C₄×Dic₅	—	2	4	no	—
31	C₃×C₄×Dic₅	—	2	1	no	—
32	C₃×C₄×Dic₅	—	2	1	no	—
33	C₃×C₄×Dic₅	—	2	4	no	—
34	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
35	C₂×C₃×#168	—	2	2	no	—
36	C₂×C₃×#168	—	2	2	no	—
37	C₂×C₃×#168	C₂×C₄	1	4	yes	—
38	C₂×C₃×#97	—	5	2	no	—
39	C₃×C₄³	—	5	1	no	—
40	C₃×#336	—	5	2	no	—
41	C₃×#336	—	5	1	no	—
42	C₃×#336	D₅	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
44	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
45	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
46	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
47	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
48	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
49	C₂²×#168	C₂²×C₃	1	2	yes	—
50	#3947	C₃×C₄	1	8	yes	complemented
51	#1745	—	5	1	no	Sylow
52	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	—	2	2	no	—
54	C₂×C₃×C₄×C₅	—	2	2	no	—
55	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	—
56	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
57	C₂×C₃×C₄×C₅	#41	1	2	yes	—
58	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
60	C₂×C₃×Dic₅	—	2	2	no	—
61	C₂×C₃×Dic₅	—	2	2	no	—
62	C₂×C₃×Dic₅	—	2	2	no	—
63	C₂×C₃×Dic₅	—	2	2	no	—
64	C₂×C₃×Dic₅	C₄²	1	2	yes	—
65	C₂×C₃×Dic₅	C₄²	1	2	yes	—
66	C₂×C₃×Dic₅	M₁₆	1	4	yes	—
67	C₃×C₅×C₈	—	2	4	no	—
68	C₃×#168	—	2	4	no	—
69	C₂²×C₃×C₈	—	5	2	no	—
70	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
71	C₂×C₃×C₄²	—	5	1	no	—
72	C₂×C₃×C₄²	—	5	2	no	—
73	C₂×C₃×C₄²	—	5	2	no	—
74	C₂×C₃×C₄²	—	5	1	no	—
75	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
76	C₃×#97	—	5	8	no	—
77	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
78	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
79	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
80	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
81	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
82	C₂×C₅×C₈	—	2	2	no	—
83	C₂×C₅×C₈	—	2	2	no	—
84	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
85	C₄²×C₅	—	2	2	no	—
86	C₄×Dic₅	—	2	4	no	—
87	C₄×Dic₅	—	2	1	no	—
88	C₄×Dic₅	—	2	1	no	—
89	C₄×Dic₅	—	2	4	no	—
90	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
91	C₂×#168	—	2	2	no	—
92	C₂×#168	—	2	2	no	—
93	C₂×#168	C₂×C₃×C₄	1	4	yes	—
94	C₂×#97	—	5	2	no	—
95	C₄³	—	5	1	no	—
96	#336	—	5	2	no	—
97	#336	—	5	1	no	—
98	#336	C₃×D₅	1	1	yes	characteristic
99	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
100	C₂²×C₃×C₅	#117	1	1	yes	characteristic
101	C₂²×C₃×C₅	#117	1	1	yes	characteristic
102	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
103	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
104	C₃×C₄×C₅	—	2	4	no	—
105	C₃×C₄×C₅	#117	1	2	yes	—
106	C₃×C₄×C₅	#117	1	2	yes	—
107	C₃×Dic₅	—	2	2	no	—
108	C₃×Dic₅	—	2	2	no	—
109	C₃×Dic₅	—	2	4	no	—
110	C₂²×C₃×C₄	—	5	1	no	—
111	C₂²×C₃×C₄	—	5	1	no	—
112	C₂²×C₃×C₄	—	5	2	no	—
113	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
114	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
115	C₂×C₃×C₈	—	2	2	no	—
116	C₂×C₃×C₈	—	2	2	no	—
117	C₂×C₃×C₈	—	5	4	no	—
118	C₂×C₃×C₈	—	10	2	no	—
119	C₂×C₃×C₈	—	10	2	no	—
120	C₂×C₃×C₈	C₄×D₅	1	4	yes	—
121	C₃×C₄²	—	2	2	no	—
122	C₃×C₄²	—	5	4	no	—
123	C₃×C₄²	—	10	4	no	—
124	C₃×C₄²	—	10	4	no	—
125	C₃×C₄²	—	10	1	no	—
126	C₃×C₄²	—	10	1	no	—
127	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
128	C₂×C₄×C₅	—	2	2	no	—
129	C₂×C₄×C₅	—	2	2	no	—
130	C₂×C₄×C₅	C₃×M₁₆	1	4	yes	—
131	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
132	C₂×C₄×C₅	C₃×#41	1	2	yes	—
133	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
134	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
135	C₂×Dic₅	—	2	2	no	—
136	C₂×Dic₅	—	2	2	no	—
137	C₂×Dic₅	—	2	2	no	—
138	C₂×Dic₅	—	2	2	no	—
139	C₂×Dic₅	C₃×C₄²	1	2	yes	—
140	C₂×Dic₅	C₃×C₄²	1	2	yes	—
141	C₂×Dic₅	C₃×M₁₆	1	4	yes	—
142	C₅×C₈	—	2	4	no	—
143	#168	—	2	4	no	—
144	C₂²×C₈	—	5	2	no	—
145	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
146	C₂×C₄²	—	5	1	no	—
147	C₂×C₄²	—	5	2	no	—
148	C₂×C₄²	—	5	2	no	—
149	C₂×C₄²	—	5	1	no	—
150	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
151	#97	—	5	8	no	—
152	C₂×C₃×C₅	#376	1	1	yes	characteristic
153	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
154	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
155	C₂×C₃×C₅	#432	1	2	yes	—
156	C₂×C₃×C₅	#432	1	2	yes	—
157	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
158	C₂×C₃×C₄	—	2	2	no	—
159	C₂×C₃×C₄	—	2	2	no	—
160	C₂×C₃×C₄	—	5	2	no	—
161	C₂×C₃×C₄	—	5	2	no	—
162	C₂×C₃×C₄	—	5	4	no	—
163	C₂×C₃×C₄	—	10	2	no	—
164	C₂×C₃×C₄	—	10	2	no	—
165	C₂×C₃×C₄	—	10	2	no	—
166	C₂×C₃×C₄	—	10	2	no	—
167	C₂×C₃×C₄	#676	1	4	yes	—
168	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
169	C₂×C₃×C₄	#711	1	1	yes	characteristic
170	C₂×C₃×C₄	#711	1	2	yes	—
171	C₂×C₃×C₄	#713	1	1	yes	characteristic
172	C₃×C₈	—	2	4	no	—
173	C₃×C₈	—	10	4	no	—
174	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
175	C₂²×C₅	C₃×#117	1	1	yes	characteristic
176	C₂²×C₅	C₃×#117	1	1	yes	characteristic
177	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
178	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
179	C₄×C₅	—	2	4	no	—
180	C₄×C₅	C₃×#117	1	2	yes	—
181	C₄×C₅	C₃×#117	1	2	yes	—
182	Dic₅	—	2	2	no	—
183	Dic₅	—	2	2	no	—
184	Dic₅	—	2	4	no	—
185	C₂²×C₄	—	5	1	no	—
186	C₂²×C₄	—	5	1	no	—
187	C₂²×C₄	—	5	2	no	—
188	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
189	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	5	4	no	—
193	C₂×C₈	—	10	2	no	—
194	C₂×C₈	—	10	2	no	—
195	C₂×C₈	C₃×C₄×D₅	1	4	yes	—
196	C₄²	—	2	2	no	—
197	C₄²	—	5	4	no	—
198	C₄²	—	10	4	no	—
199	C₄²	—	10	4	no	—
200	C₄²	—	10	1	no	—
201	C₄²	—	10	1	no	—
202	C₃×C₅	#1745	1	1	yes	characteristic, complemented, Hall
203	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
204	C₂²×C₃	#4023	1	1	yes	characteristic
205	C₂²×C₃	#4038	1	1	yes	characteristic
206	C₂²×C₃	C₂×#676	1	2	yes	—
207	C₂²×C₃	D₅×M₁₆	1	2	yes	—
208	C₃×C₄	—	2	4	no	—
209	C₃×C₄	—	10	4	no	—
210	C₃×C₄	—	10	2	no	—
211	C₃×C₄	—	10	2	no	—
212	C₃×C₄	#4023	1	2	yes	—
213	C₃×C₄	#4038	1	2	yes	—
214	C₂×C₅	C₃×#376	1	1	yes	characteristic
215	C₂×C₅	C₃×C₄×M₁₆	1	1	yes	characteristic
216	C₂×C₅	C₃×C₄×M₁₆	1	1	yes	characteristic
217	C₂×C₅	C₃×#432	1	2	yes	—
218	C₂×C₅	C₃×#432	1	2	yes	—
219	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	5	2	no	—
223	C₂×C₄	—	5	2	no	—
224	C₂×C₄	—	5	4	no	—
225	C₂×C₄	—	10	2	no	—
226	C₂×C₄	—	10	2	no	—
227	C₂×C₄	—	10	2	no	—
228	C₂×C₄	—	10	2	no	—
229	C₂×C₄	C₃×#676	1	4	yes	—
230	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
231	C₂×C₄	C₃×#711	1	1	yes	characteristic
232	C₂×C₄	C₃×#711	1	2	yes	—
233	C₂×C₄	C₃×#713	1	1	yes	characteristic
234	C₈	—	2	4	no	—
235	C₈	—	10	4	no	—
236	C₂×C₃	#64937	1	1	yes	characteristic
237	C₂×C₃	C₄×#676	1	1	yes	characteristic
238	C₂×C₃	#64996	1	1	yes	characteristic
239	C₂×C₃	#65008	1	2	yes	—
240	C₂×C₃	#65124	1	2	yes	—
241	C₅	C₃×#1745	1	1	yes	characteristic, complemented, Sylow
242	C₂²	C₃×C₄²×D₅	1	1	yes	characteristic
243	C₂²	C₃×#4023	1	1	yes	characteristic
244	C₂²	C₃×#4038	1	1	yes	characteristic
245	C₂²	C₂×C₃×#676	1	2	yes	—
246	C₂²	C₃×D₅×M₁₆	1	2	yes	—
247	C₄	—	2	4	no	—
248	C₄	—	10	4	no	—
249	C₄	—	10	2	no	—
250	C₄	—	10	2	no	—
251	C₄	C₃×#4023	1	2	yes	—
252	C₄	C₃×#4038	1	2	yes	—
253	C₃	#10599390	1	1	yes	characteristic, direct product factor, Sylow
254	C₂	C₃×#64937	1	1	yes	characteristic
255	C₂	C₃×C₄×#676	1	1	yes	characteristic
256	C₂	C₃×#64996	1	1	yes	characteristic
257	C₂	C₃×#65008	1	2	yes	—
258	C₂	C₃×#65124	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#336	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#336	D₅
hypocenter	C₅	C₃×#1745
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×#336

Complements

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

N	H ≅ G/N	type
6. #10599390	C₃	direct (N × H)
14. C₃×#3947	C₄	semidirect
50. #3947	C₃×C₄	semidirect
202. C₃×C₅	#1745	semidirect
241. C₅	C₃×#1745	semidirect
253. C₃	#10599390	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×#3947	2
C₃×C₄²×Dic₅	2
C₃×C₅×#336	2
C₃×#64770	2
C₃×#64744	2
#10599390	3
C₃×#1745	5

Subgroups — C3×#10599390 #14294893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599390 #14294893