Subgroups — C₃×#10600602 #14296138

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3946	C₂	1	2	yes	maximal
3	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3935	C₂	1	1	yes	maximal, characteristic
5	C₃×#64770	C₂	1	2	yes	maximal
6	#10600602	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×C₅×#97	—	2	2	no	—
15	C₃×#3946	C₄	1	8	yes	complemented
16	C₃×#3935	—	2	2	no	—
17	C₃×#1767	—	5	1	no	maximal, Hall
18	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic
19	C₂×#3946	C₂×C₃	1	2	yes	—
20	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic
21	C₂×#3935	C₂×C₃	1	1	yes	characteristic
22	#64770	C₂×C₃	1	2	yes	—
23	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
24	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
27	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃×C₅×C₈	—	2	2	no	—
29	C₂×C₃×C₅×C₈	—	2	2	no	—
30	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
31	C₃×C₄²×C₅	D₄	1	2	yes	—
32	C₃×C₄²×C₅	Q₈	1	2	yes	—
33	C₃×C₄×Dic₅	—	2	2	no	—
34	C₃×C₄×Dic₅	—	2	4	no	—
35	C₃×C₄×Dic₅	—	2	4	no	—
36	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
37	C₂×C₃×#168	—	2	2	no	—
38	C₂×C₃×#168	—	2	2	no	—
39	C₂×C₃×#168	C₂×C₄	1	4	yes	—
40	C₂×C₃×C₄⋊C₈	—	5	2	no	—
41	C₂×C₃×#97	—	5	1	no	—
42	C₂×C₃×#97	D₅	1	1	yes	characteristic
43	C₃×C₄³	—	5	1	no	—
44	C₃×#336	—	5	2	no	—
45	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
46	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
47	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
48	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
49	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
50	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
51	C₂²×#168	C₂²×C₃	1	2	yes	—
52	C₅×#97	—	2	2	no	—
53	#3946	C₃×C₄	1	8	yes	complemented
54	#3935	—	2	2	no	—
55	#1767	—	5	1	no	Sylow
56	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×C₅	—	2	2	no	—
58	C₂×C₃×C₄×C₅	—	2	2	no	—
59	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
60	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
61	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	#41	1	2	yes	—
64	C₂×C₃×Dic₅	—	2	2	no	—
65	C₂×C₃×Dic₅	—	2	2	no	—
66	C₂×C₃×Dic₅	—	2	2	no	—
67	C₂×C₃×Dic₅	C₄²	1	2	yes	—
68	C₂×C₃×Dic₅	C₄²	1	2	yes	—
69	C₂×C₃×Dic₅	M₁₆	1	4	yes	—
70	C₂×C₃×Dic₅	M₁₆	1	4	yes	—
71	C₃×C₅×C₈	—	2	4	no	—
72	C₃×#168	—	2	4	no	—
73	C₂²×C₃×C₈	—	5	2	no	—
74	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
75	C₂×C₃×C₄²	—	5	1	no	—
76	C₂×C₃×C₄²	—	5	2	no	—
77	C₂×C₃×C₄²	—	5	2	no	—
78	C₂×C₃×C₄²	—	5	1	no	—
79	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
80	C₃×C₄⋊C₈	—	5	8	no	—
81	C₃×#97	—	2	2	no	—
82	C₃×#97	—	10	2	no	—
83	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
84	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
85	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
86	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
87	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
88	C₂×C₅×C₈	—	2	2	no	—
89	C₂×C₅×C₈	—	2	2	no	—
90	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
91	C₄²×C₅	C₃×D₄	1	2	yes	—
92	C₄²×C₅	C₃×Q₈	1	2	yes	—
93	C₄×Dic₅	—	2	2	no	—
94	C₄×Dic₅	—	2	4	no	—
95	C₄×Dic₅	—	2	4	no	—
96	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
97	C₂×#168	—	2	2	no	—
98	C₂×#168	—	2	2	no	—
99	C₂×#168	C₂×C₃×C₄	1	4	yes	—
100	C₂×C₄⋊C₈	—	5	2	no	—
101	C₂×#97	—	5	1	no	—
102	C₂×#97	C₃×D₅	1	1	yes	characteristic
103	C₄³	—	5	1	no	—
104	#336	—	5	2	no	—
105	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
106	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₃×C₅	#117	1	1	yes	characteristic
108	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
109	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
110	C₃×C₄×C₅	—	2	4	no	—
111	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
112	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
113	C₃×Dic₅	—	2	2	no	—
114	C₃×Dic₅	—	2	4	no	—
115	C₃×Dic₅	#97	1	4	yes	complemented
116	C₂²×C₃×C₄	—	5	1	no	—
117	C₂²×C₃×C₄	—	5	1	no	—
118	C₂²×C₃×C₄	—	5	2	no	—
119	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
120	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
121	C₂×C₃×C₈	—	2	2	no	—
122	C₂×C₃×C₈	—	2	2	no	—
123	C₂×C₃×C₈	—	5	4	no	—
124	C₂×C₃×C₈	—	10	2	no	—
125	C₂×C₃×C₈	—	10	2	no	—
126	C₂×C₃×C₈	C₄×D₅	1	4	yes	—
127	C₃×C₄²	—	5	4	no	—
128	C₃×C₄²	—	10	4	no	—
129	C₃×C₄²	—	10	4	no	—
130	C₃×C₄²	—	10	2	no	—
131	C₃×C₄²	Dic₁₀	1	2	yes	—
132	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
133	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
134	C₂×C₄×C₅	—	2	2	no	—
135	C₂×C₄×C₅	—	2	2	no	—
136	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	—
137	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
138	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
139	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
140	C₂×C₄×C₅	C₃×#41	1	2	yes	—
141	C₂×Dic₅	—	2	2	no	—
142	C₂×Dic₅	—	2	2	no	—
143	C₂×Dic₅	—	2	2	no	—
144	C₂×Dic₅	C₃×C₄²	1	2	yes	—
145	C₂×Dic₅	C₃×C₄²	1	2	yes	—
146	C₂×Dic₅	C₃×M₁₆	1	4	yes	—
147	C₂×Dic₅	C₃×M₁₆	1	4	yes	—
148	C₅×C₈	—	2	4	no	—
149	#168	—	2	4	no	—
150	C₂²×C₈	—	5	2	no	—
151	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
152	C₂×C₄²	—	5	1	no	—
153	C₂×C₄²	—	5	2	no	—
154	C₂×C₄²	—	5	2	no	—
155	C₂×C₄²	—	5	1	no	—
156	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
157	C₄⋊C₈	—	5	8	no	—
158	#97	—	2	2	no	—
159	#97	—	10	2	no	—
160	C₂×C₃×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₃×C₅	C₂×#97	1	1	yes	characteristic
162	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
163	C₂×C₃×C₅	#423	1	2	yes	—
164	C₂×C₃×C₅	#432	1	2	yes	—
165	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
166	C₂×C₃×C₄	—	2	2	no	—
167	C₂×C₃×C₄	—	2	2	no	—
168	C₂×C₃×C₄	—	5	2	no	—
169	C₂×C₃×C₄	—	5	4	no	—
170	C₂×C₃×C₄	—	5	2	no	—
171	C₂×C₃×C₄	—	5	4	no	—
172	C₂×C₃×C₄	—	10	2	no	—
173	C₂×C₃×C₄	—	10	2	no	—
174	C₂×C₃×C₄	—	10	2	no	—
175	C₂×C₃×C₄	#683	1	4	yes	—
176	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
177	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
178	C₂×C₃×C₄	#709	1	2	yes	—
179	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
180	C₃×C₈	—	2	4	no	—
181	C₃×C₈	—	10	4	no	—
182	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
183	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×C₅	C₃×#117	1	1	yes	characteristic
185	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
186	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
187	C₄×C₅	—	2	4	no	—
188	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
189	C₄×C₅	C₃×C₄×Q₈	1	2	yes	—
190	Dic₅	—	2	2	no	—
191	Dic₅	—	2	4	no	—
192	Dic₅	C₃×#97	1	4	yes	complemented
193	C₂²×C₄	—	5	1	no	—
194	C₂²×C₄	—	5	1	no	—
195	C₂²×C₄	—	5	2	no	—
196	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
197	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	5	4	no	—
201	C₂×C₈	—	10	2	no	—
202	C₂×C₈	—	10	2	no	—
203	C₂×C₈	C₃×C₄×D₅	1	4	yes	—
204	C₄²	—	5	4	no	—
205	C₄²	—	10	4	no	—
206	C₄²	—	10	4	no	—
207	C₄²	—	10	2	no	—
208	C₄²	C₃×Dic₁₀	1	2	yes	—
209	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
210	C₃×C₅	#1767	1	1	yes	characteristic, complemented, Hall
211	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
212	C₂²×C₃	#4018	1	1	yes	characteristic
213	C₂²×C₃	D₅×M₁₆	1	2	yes	—
214	C₂²×C₃	D₅×M₁₆	1	2	yes	—
215	C₂²×C₃	C₂×#683	1	1	yes	characteristic
216	C₃×C₄	—	2	4	no	—
217	C₃×C₄	—	5	4	no	—
218	C₃×C₄	—	10	4	no	—
219	C₃×C₄	—	10	2	no	—
220	C₃×C₄	C₄×Dic₁₀	1	2	yes	—
221	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
222	C₂×C₅	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
223	C₂×C₅	C₂×C₃×#97	1	1	yes	characteristic
224	C₂×C₅	C₃×C₄×M₁₆	1	1	yes	characteristic
225	C₂×C₅	C₃×#423	1	2	yes	—
226	C₂×C₅	C₃×#432	1	2	yes	—
227	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	5	2	no	—
231	C₂×C₄	—	5	4	no	—
232	C₂×C₄	—	5	2	no	—
233	C₂×C₄	—	5	4	no	—
234	C₂×C₄	—	10	2	no	—
235	C₂×C₄	—	10	2	no	—
236	C₂×C₄	—	10	2	no	—
237	C₂×C₄	C₃×#683	1	4	yes	—
238	C₂×C₄	C₂×C₃×Dic₁₀	1	1	yes	characteristic
239	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
240	C₂×C₄	C₃×#709	1	2	yes	—
241	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
242	C₈	—	2	4	no	—
243	C₈	—	10	4	no	—
244	C₂×C₃	D₅×#97	1	1	yes	characteristic
245	C₂×C₃	#64994	1	2	yes	—
246	C₂×C₃	#64996	1	1	yes	characteristic
247	C₂×C₃	C₄×#683	1	1	yes	characteristic
248	C₂×C₃	#65407	1	2	yes	—
249	C₅	C₃×#1767	1	1	yes	characteristic, complemented, Sylow
250	C₂²	C₃×C₄²×D₅	1	1	yes	characteristic
251	C₂²	C₃×#4018	1	1	yes	characteristic
252	C₂²	C₃×D₅×M₁₆	1	2	yes	—
253	C₂²	C₃×D₅×M₁₆	1	2	yes	—
254	C₂²	C₂×C₃×#683	1	1	yes	characteristic
255	C₄	—	2	4	no	—
256	C₄	—	5	4	no	—
257	C₄	—	10	4	no	—
258	C₄	—	10	2	no	—
259	C₄	C₃×C₄×Dic₁₀	1	2	yes	—
260	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
261	C₃	#10600602	1	1	yes	characteristic, direct product factor, Sylow
262	C₂	C₃×D₅×#97	1	1	yes	characteristic
263	C₂	C₃×#64994	1	2	yes	—
264	C₂	C₃×#64996	1	1	yes	characteristic
265	C₂	C₃×C₄×#683	1	1	yes	characteristic
266	C₂	C₃×#65407	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	C₂×C₃×C₅×#97	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×#97	D₅
hypocenter	C₅	C₃×#1767
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
6. #10600602	C₃	direct (N × H)
15. C₃×#3946	C₄	semidirect
53. #3946	C₃×C₄	semidirect
115. C₃×Dic₅	#97	semidirect
192. Dic₅	C₃×#97	semidirect
210. C₃×C₅	#1767	semidirect
249. C₅	C₃×#1767	semidirect
261. C₃	#10600602	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×#97	2
C₂×C₃×#3946	2
C₃×C₄²×Dic₅	2
C₂×C₃×#3935	2
C₃×#64770	2
#10600602	3
C₃×#1767	5

Subgroups — C3×#10600602 #14296138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600602 #14296138