Subgroups — C₅×D₃×#494 #14438793

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×Q₁₆	C₂	1	4	yes	maximal
2	C₅×D₃×C₄⋊Q₈	C₂	1	2	yes	maximal
3	C₃×C₅×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5183	C₂	1	4	yes	maximal, complemented
5	C₅×#5092	C₂	1	2	yes	maximal, complemented
6	C₅×#4699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅×#494	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×Q₈	C₂²	1	4	yes	—
10	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	—
11	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₅×#944	C₂²	1	4	yes	—
13	C₂×C₅×#216	C₂²	1	8	yes	—
14	C₅×D₃×Q₁₆	—	2	16	no	—
15	C₂×C₅×Dic₁₂	C₂²	1	4	yes	—
16	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
17	C₅×D₃×C₄⋊C₄	—	2	4	no	—
18	C₅×#888	—	2	4	no	—
19	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₅×#869	C₂²	1	2	yes	—
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₅×C₈×Dic₃	C₂²	1	2	yes	—
23	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	D₃×#494	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×Q₁₆	—	3	4	no	—
26	C₂×C₅×C₄⋊Q₈	—	3	2	no	—
27	C₅×#494	—	3	1	no	—
28	C₅×#494	—	3	4	no	—
29	C₅×#494	—	3	2	no	—
30	C₅×#494	D₃	1	1	yes	characteristic, direct product factor
31	C₂×C₄×C₅×C₈	—	3	1	no	—
32	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
33	C₅×D₃×Q₈	—	2	16	no	—
34	C₂×C₄×C₅×D₃	—	2	4	no	—
35	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
36	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
37	C₂×C₅×Dic₆	—	2	4	no	—
38	C₂×C₅×Dic₆	C₂³	1	4	yes	—
39	C₃×C₅×Q₁₆	—	2	8	no	—
40	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
41	C₃×C₅×C₄⋊C₄	—	2	4	no	—
42	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
43	C₅×#216	—	2	16	no	—
44	C₅×C₄⋊Dic₃	—	2	4	no	—
45	C₅×Dic₃⋊C₄	—	2	8	no	—
46	C₄×C₅×Dic₃	D₄	1	2	yes	—
47	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
48	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
49	C₅×Dic₁₂	—	2	8	no	—
50	C₅×D₃×C₈	D₄	1	8	yes	—
51	C₂×D₃×Q₁₆	C₂×C₅	1	4	yes	—
52	D₃×C₄⋊Q₈	C₂×C₅	1	2	yes	—
53	C₃×#494	C₂×C₅	1	1	yes	characteristic, complemented
54	#5183	C₂×C₅	1	4	yes	complemented
55	#5092	C₂×C₅	1	2	yes	complemented
56	#4699	C₂×C₅	1	1	yes	characteristic, complemented
57	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic
58	C₂²×C₅×Q₈	—	3	4	no	—
59	C₂×C₅×Q₁₆	—	3	8	no	—
60	C₂×C₅×Q₁₆	—	3	4	no	—
61	C₂×C₅×Q₁₆	—	6	16	no	—
62	C₂×C₅×Q₁₆	C₂×D₃	1	4	yes	—
63	C₂²×C₅×C₈	—	3	2	no	—
64	C₅×C₄⋊Q₈	—	3	4	no	—
65	C₅×C₄⋊Q₈	—	3	2	no	—
66	C₅×C₄⋊Q₈	—	6	4	no	—
67	C₅×C₄⋊Q₈	C₂×D₃	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	—	6	4	no	—
69	C₂×C₄²×C₅	—	3	1	no	—
70	C₄×C₅×C₈	—	3	2	no	—
71	C₄×C₅×C₈	—	3	1	no	—
72	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
73	C₂×#494	—	3	1	no	Sylow
74	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
75	C₃×C₅×Q₈	—	2	8	no	—
76	C₂×C₃×C₄×C₅	—	2	4	no	—
77	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
78	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
79	C₂×C₅×Dic₃	—	2	4	no	—
80	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
81	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
82	C₄×C₅×D₃	—	4	8	no	—
83	C₄×C₅×D₃	Q₁₆	1	8	yes	complemented
84	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
85	C₅×Dic₆	—	2	8	no	—
86	C₅×Dic₆	—	4	8	no	—
87	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
88	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
89	C₂×D₃×Q₈	C₂²×C₅	1	4	yes	—
90	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
91	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
92	#944	C₂²×C₅	1	4	yes	—
93	C₂×#216	C₂²×C₅	1	8	yes	—
94	D₃×Q₁₆	—	2	16	no	—
95	C₂×Dic₁₂	C₂²×C₅	1	4	yes	—
96	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
97	D₃×C₄⋊C₄	—	2	4	no	—
98	#888	—	2	4	no	—
99	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
100	#869	C₂²×C₅	1	2	yes	—
101	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
102	C₈×Dic₃	C₂²×C₅	1	2	yes	—
103	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
104	C₂×C₅×Q₈	—	3	4	no	—
105	C₂×C₅×Q₈	—	6	4	no	—
106	C₂×C₅×Q₈	—	6	16	no	—
107	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
108	C₂²×C₄×C₅	—	3	2	no	—
109	C₂²×C₄×C₅	—	3	1	no	—
110	C₂²×C₄×C₅	—	6	4	no	—
111	C₅×Q₁₆	—	2	8	no	—
112	C₅×Q₁₆	—	6	16	no	—
113	C₅×Q₁₆	—	6	8	no	—
114	C₂×C₅×C₈	—	3	2	no	—
115	C₂×C₅×C₈	—	3	8	no	—
116	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
117	C₅×C₄⋊C₄	—	2	4	no	—
118	C₅×C₄⋊C₄	—	6	8	no	—
119	C₅×C₄⋊C₄	—	6	4	no	—
120	C₄²×C₅	—	3	2	no	—
121	C₄²×C₅	—	3	1	no	—
122	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
123	C₂²×Q₁₆	—	3	4	no	—
124	C₂×C₄⋊Q₈	—	3	2	no	—
125	#494	—	3	4	no	—
126	#494	—	3	2	no	—
127	#494	—	3	1	no	—
128	#494	C₅×D₃	1	1	yes	characteristic, direct product factor
129	C₂×C₄×C₈	—	3	1	no	—
130	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₅×D₃	#127	1	2	yes	—
132	C₂×C₅×D₃	C₂×Q₁₆	1	4	yes	—
133	C₃×C₄×C₅	—	4	4	no	—
134	C₃×C₄×C₅	C₂×Q₁₆	1	4	yes	complemented
135	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
136	C₅×Dic₃	—	4	4	no	—
137	C₅×Dic₃	#127	1	2	yes	—
138	C₅×Dic₃	C₂×Q₁₆	1	4	yes	complemented
139	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
140	D₃×Q₈	—	2	16	no	—
141	C₂×C₄×D₃	—	2	4	no	—
142	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
143	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
144	C₂×Dic₆	—	2	4	no	—
145	C₂×Dic₆	C₂³×C₅	1	4	yes	—
146	C₃×Q₁₆	—	2	8	no	—
147	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
148	C₃×C₄⋊C₄	—	2	4	no	—
149	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
150	#216	—	2	16	no	—
151	C₄⋊Dic₃	—	2	4	no	—
152	Dic₃⋊C₄	—	2	8	no	—
153	C₄×Dic₃	C₅×D₄	1	2	yes	—
154	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
155	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
156	Dic₁₂	—	2	8	no	—
157	D₃×C₈	C₅×D₄	1	8	yes	—
158	C₂³×C₅	—	3	1	no	—
159	C₅×Q₈	—	2	8	no	—
160	C₅×Q₈	—	6	8	no	—
161	C₅×Q₈	—	12	8	no	—
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	3	2	no	—
164	C₂×C₄×C₅	—	3	1	no	—
165	C₂×C₄×C₅	—	3	8	no	—
166	C₂×C₄×C₅	—	3	4	no	—
167	C₂×C₄×C₅	—	6	4	no	—
168	C₂×C₄×C₅	—	12	8	no	—
169	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
170	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
171	C₅×C₈	—	3	4	no	—
172	C₅×C₈	D₃×D₄	1	4	yes	—
173	C₂²×Q₈	—	3	4	no	—
174	C₂×Q₁₆	—	3	8	no	—
175	C₂×Q₁₆	—	3	4	no	—
176	C₂×Q₁₆	—	6	16	no	—
177	C₂×Q₁₆	C₂×C₅×D₃	1	4	yes	—
178	C₂²×C₈	—	3	2	no	—
179	C₄⋊Q₈	—	3	4	no	—
180	C₄⋊Q₈	—	3	2	no	—
181	C₄⋊Q₈	—	6	4	no	—
182	C₄⋊Q₈	C₂×C₅×D₃	1	2	yes	—
183	C₂×C₄⋊C₄	—	6	4	no	—
184	C₂×C₄²	—	3	1	no	—
185	C₄×C₈	—	3	2	no	—
186	C₄×C₈	—	3	1	no	—
187	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
188	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
189	C₂×C₃×C₅	C₂²×Q₁₆	1	2	yes	—
190	C₅×D₃	#494	1	4	yes	direct product factor
191	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
192	C₃×Q₈	—	2	8	no	—
193	C₂×C₃×C₄	—	2	4	no	—
194	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
195	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
196	C₂×Dic₃	—	2	4	no	—
197	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
198	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
199	C₄×D₃	—	4	8	no	—
200	C₄×D₃	C₅×Q₁₆	1	8	yes	complemented
201	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
202	Dic₆	—	2	8	no	—
203	Dic₆	—	4	8	no	—
204	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
205	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
206	C₂²×C₅	—	3	2	no	—
207	C₂²×C₅	—	3	4	no	—
208	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
209	C₄×C₅	—	3	2	no	—
210	C₄×C₅	—	3	4	no	—
211	C₄×C₅	—	4	4	no	—
212	C₄×C₅	—	12	4	no	—
213	C₄×C₅	D₃×Q₁₆	1	4	yes	complemented
214	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
215	C₂×Q₈	—	3	4	no	—
216	C₂×Q₈	—	6	4	no	—
217	C₂×Q₈	—	6	16	no	—
218	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
219	C₂²×C₄	—	3	2	no	—
220	C₂²×C₄	—	3	1	no	—
221	C₂²×C₄	—	6	4	no	—
222	Q₁₆	—	2	8	no	—
223	Q₁₆	—	6	16	no	—
224	Q₁₆	—	6	8	no	—
225	C₂×C₈	—	3	2	no	—
226	C₂×C₈	—	3	8	no	—
227	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
228	C₄⋊C₄	—	2	4	no	—
229	C₄⋊C₄	—	6	8	no	—
230	C₄⋊C₄	—	6	4	no	—
231	C₄²	—	3	2	no	—
232	C₄²	—	3	1	no	—
233	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
234	C₃×C₅	C₂×#494	1	1	yes	characteristic, complemented, Hall
235	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
236	C₂×D₃	C₅×#127	1	2	yes	—
237	C₂×D₃	C₂×C₅×Q₁₆	1	4	yes	—
238	C₃×C₄	—	4	4	no	—
239	C₃×C₄	C₂×C₅×Q₁₆	1	4	yes	complemented
240	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
241	Dic₃	—	4	4	no	—
242	Dic₃	C₅×#127	1	2	yes	—
243	Dic₃	C₂×C₅×Q₁₆	1	4	yes	complemented
244	C₂×C₅	—	3	4	no	—
245	C₂×C₅	D₃×#127	1	1	yes	characteristic
246	C₂×C₅	C₂×D₃×Q₁₆	1	2	yes	—
247	C₂³	—	3	1	no	—
248	Q₈	—	2	8	no	—
249	Q₈	—	6	8	no	—
250	Q₈	—	12	8	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	3	2	no	—
253	C₂×C₄	—	3	1	no	—
254	C₂×C₄	—	3	8	no	—
255	C₂×C₄	—	3	4	no	—
256	C₂×C₄	—	6	4	no	—
257	C₂×C₄	—	12	8	no	—
258	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
259	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
260	C₈	—	3	4	no	—
261	C₈	C₅×D₃×D₄	1	4	yes	—
262	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
263	C₂×C₃	C₂²×C₅×Q₁₆	1	2	yes	—
264	D₃	C₅×#494	1	4	yes	direct product factor
265	C₅	D₃×#494	1	1	yes	characteristic, direct product factor, Sylow
266	C₂²	—	3	2	no	—
267	C₂²	—	3	4	no	—
268	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
269	C₄	—	3	2	no	—
270	C₄	—	3	4	no	—
271	C₄	—	4	4	no	—
272	C₄	—	12	4	no	—
273	C₄	C₅×D₃×Q₁₆	1	4	yes	complemented
274	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
275	C₃	C₂×C₅×#494	1	1	yes	characteristic, complemented, Sylow
276	C₂	—	3	4	no	—
277	C₂	C₅×D₃×#127	1	1	yes	characteristic
278	C₂	C₂×C₅×D₃×Q₁₆	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#494	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
hypercenter	C₅×#494	D₃
hypocenter	C₃	C₂×C₅×#494
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#494

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#494	C₂	semidirect
4. C₅×#5183	C₂	semidirect
5. C₅×#5092	C₂	semidirect
6. C₅×#4699	C₂	semidirect
24. D₃×#494	C₅	direct (N × H)
30. C₅×#494	D₃	direct (N × H)
53. C₃×#494	C₂×C₅	semidirect
54. #5183	C₂×C₅	semidirect
55. #5092	C₂×C₅	semidirect
56. #4699	C₂×C₅	semidirect
83. C₄×C₅×D₃	Q₁₆	semidirect
128. #494	C₅×D₃	direct (N × H)
134. C₃×C₄×C₅	C₂×Q₁₆	semidirect
138. C₅×Dic₃	C₂×Q₁₆	semidirect
190. C₅×D₃	#494	direct (N × H)
200. C₄×D₃	C₅×Q₁₆	semidirect
213. C₄×C₅	D₃×Q₁₆	semidirect
234. C₃×C₅	C₂×#494	semidirect
239. C₃×C₄	C₂×C₅×Q₁₆	semidirect
243. Dic₃	C₂×C₅×Q₁₆	semidirect
264. D₃	C₅×#494	direct (N × H)
265. C₅	D₃×#494	direct (N × H)
273. C₄	C₅×D₃×Q₁₆	semidirect
275. C₃	C₂×C₅×#494	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×Q₁₆	2
C₅×D₃×C₄⋊Q₈	2
C₃×C₅×#494	2
C₅×#5183	2
C₅×#5092	2
C₅×#4699	2
C₄×C₅×D₃×C₈	2
C₂×C₅×#494	3
D₃×#494	5

Subgroups — C5×D3×#494 #14438793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#494 #14438793