Subgroups — C₂×D₅×#803 #14411209

Order 1920.

1360 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×D₅×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₂×#91087	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90952	C₂	1	2	yes	maximal, complemented
6	D₅×#803	C₂	1	8	yes	maximal, direct product factor
7	C₂×D₅×#97	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₄×D₅	C₄	1	2	yes	—
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊#168	C₂²	1	2	yes	—
12	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
13	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₃×C₄²×D₅	C₄	1	4	yes	—
16	C₃×C₄²×D₅	C₂²	1	4	yes	—
17	C₂×D₅×C₃⋊C₈	C₄	1	16	yes	complemented
18	C₂×D₅×C₃⋊C₈	C₂²	1	8	yes	—
19	#91087	C₂²	1	4	yes	complemented
20	C₅×#803	C₂²	1	4	yes	complemented
21	#90952	C₂²	1	8	yes	complemented
22	C₂²×#803	—	5	1	no	maximal, Hall
23	C₂²×C₈×D₅	—	3	2	no	—
24	C₂×C₄²×D₅	D₃	1	1	yes	characteristic
25	C₂×C₅×#97	—	3	1	no	—
26	C₂×#3947	—	3	2	no	—
27	C₂×#3935	—	3	1	no	—
28	D₅×#97	—	3	8	no	—
29	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
32	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
33	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₄×D₅	—	2	8	no	—
35	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
36	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
38	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
39	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
40	C₃×C₄²×C₅	C₂³	1	2	yes	—
41	C₂×C₃⋊#168	C₂×C₄	1	8	yes	complemented
42	C₂×C₃⋊#168	C₂³	1	4	yes	—
43	C₂×C₅×C₃⋊C₈	C₂×C₄	1	8	yes	complemented
44	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
45	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
46	C₃×C₄×Dic₅	C₂×C₄	1	8	yes	—
47	C₃×C₄×Dic₅	C₂³	1	2	yes	—
48	D₅×C₃⋊C₈	C₂×C₄	1	32	yes	complemented
49	C₂²×C₃×C₄²	—	5	1	no	—
50	C₂³×C₃⋊C₈	—	5	2	no	—
51	C₂×#803	—	5	1	no	—
52	C₂×#803	—	5	2	no	—
53	C₂×#803	—	5	8	no	—
54	C₂×#803	D₅	1	1	yes	characteristic, direct product factor
55	C₂²×C₄×D₅	Dic₃	1	2	yes	—
56	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
57	C₂²×C₅×C₈	—	3	2	no	—
58	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
59	C₂×C₄×Dic₅	Dic₃	1	2	yes	—
60	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
61	C₂²×#168	—	3	2	no	—
62	C₂×C₈×D₅	—	3	16	no	—
63	C₂×C₈×D₅	—	3	8	no	—
64	C₄²×D₅	Dic₃	1	4	yes	—
65	C₄²×D₅	C₂×D₃	1	4	yes	—
66	C₅×#97	—	3	4	no	—
67	#3947	—	3	8	no	—
68	#3935	—	3	4	no	—
69	C₂²×#97	—	15	1	no	Sylow
70	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₃×D₅	C₄²	1	4	yes	—
72	C₂²×C₃×D₅	M₁₆	1	8	yes	—
73	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
74	C₂×C₃×C₄×C₅	—	2	4	no	—
75	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
76	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
78	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
79	C₂×C₃×Dic₅	—	2	4	no	—
80	C₂×C₃×Dic₅	C₄²	1	4	yes	—
81	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
82	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
83	C₃×C₄×D₅	—	2	16	no	—
84	C₃×C₄×D₅	C₄²	1	8	yes	—
85	C₃×C₄×D₅	C₂²×C₄	1	8	yes	—
86	C₃⋊#168	C₂²×C₄	1	8	yes	complemented
87	C₅×C₃⋊C₈	C₂²×C₄	1	8	yes	complemented
88	C₂³×C₃×C₄	—	5	1	no	—
89	C₂³×C₃×C₄	—	5	2	no	—
90	C₂×C₃×C₄²	—	5	2	no	—
91	C₂×C₃×C₄²	—	5	1	no	—
92	C₂×C₃×C₄²	—	5	4	no	—
93	C₂×C₃×C₄²	—	5	4	no	—
94	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
95	C₂²×C₃⋊C₈	—	5	2	no	—
96	C₂²×C₃⋊C₈	—	5	16	no	—
97	C₂²×C₃⋊C₈	—	5	8	no	—
98	C₂²×C₃⋊C₈	C₂×D₅	1	2	yes	—
99	#803	—	5	4	no	—
100	#803	—	5	8	no	—
101	#803	C₂×D₅	1	4	yes	direct product factor
102	C₂³×D₅	C₂×Dic₃	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
104	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
105	C₂²×Dic₅	C₂×Dic₃	1	2	yes	—
106	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
107	C₂×C₄×D₅	—	2	8	no	—
108	C₂×C₄×D₅	C₄×D₃	1	8	yes	—
109	C₂×C₄×D₅	C₂×Dic₃	1	8	yes	—
110	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
111	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
112	C₂×C₅×C₈	—	3	8	no	—
113	C₂×C₅×C₈	—	3	4	no	—
114	C₄²×C₅	C₂×Dic₃	1	2	yes	—
115	C₄²×C₅	C₂²×D₃	1	2	yes	—
116	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
117	C₄×Dic₅	C₂×Dic₃	1	8	yes	—
118	C₄×Dic₅	C₂²×D₃	1	2	yes	—
119	C₂×#168	—	3	8	no	—
120	C₂×#168	—	3	4	no	—
121	C₈×D₅	—	3	32	no	—
122	C₂³×C₈	—	15	2	no	—
123	C₂²×C₄²	—	5	1	no	—
124	C₂×#97	—	3	1	no	—
125	C₂×#97	—	15	8	no	—
126	C₂×#97	—	15	2	no	—
127	C₂×#97	—	15	1	no	—
128	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
129	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	—
130	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₃×D₅	#97	1	16	yes	complemented
132	C₂×C₃×D₅	C₂×C₄²	1	4	yes	—
133	C₂×C₃×D₅	C₂×M₁₆	1	8	yes	—
134	C₃×C₄×C₅	—	2	4	no	—
135	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
136	C₃×C₄×C₅	C₂³×C₄	1	2	yes	—
137	C₃×Dic₅	—	2	4	no	—
138	C₃×Dic₅	C₂×C₄²	1	4	yes	—
139	C₂⁴×C₃	—	5	1	no	—
140	C₂²×C₃×C₄	—	5	1	no	—
141	C₂²×C₃×C₄	—	5	8	no	—
142	C₂²×C₃×C₄	—	5	2	no	—
143	C₂²×C₃×C₄	—	5	2	no	—
144	C₂²×C₃×C₄	—	5	2	no	—
145	C₂²×C₃×C₄	—	5	8	no	—
146	C₂²×C₃×C₄	—	10	8	no	—
147	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
148	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
149	C₃×C₄²	—	5	8	no	—
150	C₃×C₄²	—	5	2	no	—
151	C₃×C₄²	—	5	2	no	—
152	C₃×C₄²	C₄×D₅	1	2	yes	—
153	C₃×C₄²	C₂²×D₅	1	2	yes	—
154	C₂×C₃⋊C₈	—	5	8	no	—
155	C₂×C₃⋊C₈	—	5	4	no	—
156	C₂×C₃⋊C₈	—	5	32	no	—
157	C₂×C₃⋊C₈	C₄×D₅	1	8	yes	complemented
158	C₂×C₃⋊C₈	C₂²×D₅	1	4	yes	—
159	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
160	C₂²×D₅	#208	1	8	yes	—
161	C₂²×D₅	C₄×Dic₃	1	4	yes	—
162	C₂²×D₅	C₂²×Dic₃	1	2	yes	—
163	C₂×C₄×C₅	—	2	4	no	—
164	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
165	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
166	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
168	C₂×Dic₅	—	2	4	no	—
169	C₂×Dic₅	C₄×Dic₃	1	4	yes	—
170	C₂×Dic₅	C₂²×Dic₃	1	4	yes	—
171	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
172	C₄×D₅	—	2	16	no	—
173	C₄×D₅	C₄×Dic₃	1	8	yes	—
174	C₄×D₅	C₂×C₄×D₃	1	8	yes	—
175	C₅×C₈	—	3	8	no	—
176	#168	—	3	8	no	—
177	C₂³×C₄	—	5	1	no	—
178	C₂³×C₄	—	5	2	no	—
179	C₂²×C₈	—	3	2	no	—
180	C₂²×C₈	—	15	8	no	—
181	C₂²×C₈	—	15	16	no	—
182	C₂²×C₈	—	15	2	no	—
183	C₂×C₄²	—	5	2	no	—
184	C₂×C₄²	—	5	1	no	—
185	C₂×C₄²	—	5	4	no	—
186	C₂×C₄²	—	5	4	no	—
187	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
188	#97	—	3	4	no	—
189	#97	—	15	8	no	—
190	#97	—	15	4	no	—
191	C₂×C₃×C₅	C₂×#97	1	4	yes	complemented
192	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
193	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
194	C₃×D₅	C₂×#97	1	8	yes	complemented
195	C₂³×C₃	—	5	2	no	—
196	C₂³×C₃	—	5	4	no	—
197	C₂³×C₃	—	5	8	no	—
198	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
199	C₂×C₃×C₄	—	2	4	no	—
200	C₂×C₃×C₄	—	5	2	no	—
201	C₂×C₃×C₄	—	5	4	no	—
202	C₂×C₃×C₄	—	5	8	no	—
203	C₂×C₃×C₄	—	5	8	no	—
204	C₂×C₃×C₄	—	5	4	no	—
205	C₂×C₃×C₄	—	10	16	no	—
206	C₂×C₃×C₄	—	10	4	no	—
207	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
208	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
209	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
210	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
211	C₃⋊C₈	—	5	8	no	—
212	C₃⋊C₈	C₂×C₄×D₅	1	8	yes	complemented
213	C₂²×C₅	C₂×#208	1	4	yes	—
214	C₂²×C₅	C₂×C₄×Dic₃	1	2	yes	—
215	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
216	C₂×D₅	#803	1	16	yes	direct product factor
217	C₂×D₅	C₂×#208	1	8	yes	—
218	C₂×D₅	C₂×C₄×Dic₃	1	4	yes	—
219	C₄×C₅	—	2	4	no	—
220	C₄×C₅	C₂×C₄×Dic₃	1	2	yes	—
221	C₄×C₅	C₂²×C₄×D₃	1	2	yes	—
222	Dic₅	—	2	4	no	—
223	Dic₅	C₂×C₄×Dic₃	1	4	yes	—
224	C₂⁴	—	5	1	no	—
225	C₂²×C₄	—	5	1	no	—
226	C₂²×C₄	—	5	8	no	—
227	C₂²×C₄	—	5	2	no	—
228	C₂²×C₄	—	5	2	no	—
229	C₂²×C₄	—	5	2	no	—
230	C₂²×C₄	—	5	8	no	—
231	C₂²×C₄	—	10	8	no	—
232	C₂²×C₄	D₅×Dic₃	1	2	yes	—
233	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
234	C₂×C₈	—	3	8	no	—
235	C₂×C₈	—	3	4	no	—
236	C₂×C₈	—	15	32	no	—
237	C₂×C₈	—	15	8	no	—
238	C₂×C₈	—	15	4	no	—
239	C₄²	—	5	8	no	—
240	C₄²	—	5	2	no	—
241	C₄²	—	5	2	no	—
242	C₄²	D₅×Dic₃	1	2	yes	—
243	C₄²	C₂×D₃×D₅	1	2	yes	—
244	C₃×C₅	C₂²×#97	1	1	yes	characteristic, complemented, Hall
245	C₂²×C₃	—	5	4	no	—
246	C₂²×C₃	—	5	8	no	—
247	C₂²×C₃	—	5	16	no	—
248	C₂²×C₃	C₄²×D₅	1	2	yes	—
249	C₂²×C₃	D₅×M₁₆	1	4	yes	—
250	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
251	C₃×C₄	—	2	4	no	—
252	C₃×C₄	—	5	4	no	—
253	C₃×C₄	—	10	4	no	—
254	C₃×C₄	C₄²×D₅	1	2	yes	—
255	C₃×C₄	C₂²×C₄×D₅	1	2	yes	—
256	C₂×C₅	C₂×#803	1	4	yes	complemented
257	C₂×C₅	C₂²×#208	1	2	yes	—
258	C₂×C₅	C₂²×C₄×Dic₃	1	1	yes	characteristic
259	D₅	C₂×#803	1	8	yes	direct product factor
260	C₂³	—	5	2	no	—
261	C₂³	—	5	8	no	—
262	C₂³	—	5	4	no	—
263	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
264	C₂×C₄	—	2	4	no	—
265	C₂×C₄	—	5	2	no	—
266	C₂×C₄	—	5	4	no	—
267	C₂×C₄	—	5	8	no	—
268	C₂×C₄	—	5	8	no	—
269	C₂×C₄	—	5	4	no	—
270	C₂×C₄	—	10	16	no	—
271	C₂×C₄	—	10	4	no	—
272	C₂×C₄	C₄×D₃×D₅	1	4	yes	—
273	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
274	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
275	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
276	C₈	—	3	8	no	—
277	C₈	—	15	8	no	—
278	C₂×C₃	—	5	8	no	—
279	C₂×C₃	D₅×#97	1	4	yes	complemented
280	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
281	C₂×C₃	C₂×D₅×M₁₆	1	2	yes	—
282	C₅	C₂²×#803	1	1	yes	characteristic, complemented, Sylow
283	C₂²	—	5	4	no	—
284	C₂²	—	5	8	no	—
285	C₂²	—	5	16	no	—
286	C₂²	D₅×#208	1	4	yes	—
287	C₂²	C₄×D₅×Dic₃	1	2	yes	—
288	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
289	C₄	—	2	4	no	—
290	C₄	—	5	4	no	—
291	C₄	—	10	4	no	—
292	C₄	C₄×D₅×Dic₃	1	2	yes	—
293	C₄	C₂×C₄×D₃×D₅	1	2	yes	—
294	C₃	C₂×D₅×#97	1	1	yes	characteristic, complemented, Sylow
295	C₂	—	5	8	no	—
296	C₂	D₅×#803	1	4	yes	direct product factor
297	C₂	C₂×D₅×#208	1	2	yes	—
298	C₂	C₂×C₄×D₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₂²×#97
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. C₂×#91087	C₂	semidirect
4. C₂×C₅×#803	C₂	semidirect
5. C₂×#90952	C₂	semidirect
6. D₅×#803	C₂	direct (N × H)
17. C₂×D₅×C₃⋊C₈	C₄	semidirect
19. #91087	C₂²	semidirect
20. C₅×#803	C₂²	semidirect
21. #90952	C₂²	semidirect
41. C₂×C₃⋊#168	C₂×C₄	semidirect
43. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
48. D₅×C₃⋊C₈	C₂×C₄	semidirect
54. C₂×#803	D₅	direct (N × H)
86. C₃⋊#168	C₂²×C₄	semidirect
87. C₅×C₃⋊C₈	C₂²×C₄	semidirect
101. #803	C₂×D₅	direct (N × H)
131. C₂×C₃×D₅	#97	semidirect
157. C₂×C₃⋊C₈	C₄×D₅	semidirect
191. C₂×C₃×C₅	C₂×#97	semidirect
194. C₃×D₅	C₂×#97	semidirect
212. C₃⋊C₈	C₂×C₄×D₅	semidirect
216. C₂×D₅	#803	direct (N × H)
244. C₃×C₅	C₂²×#97	semidirect
256. C₂×C₅	C₂×#803	semidirect
259. D₅	C₂×#803	direct (N × H)
279. C₂×C₃	D₅×#97	semidirect
282. C₅	C₂²×#803	semidirect
294. C₃	C₂×D₅×#97	semidirect
296. C₂	D₅×#803	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×C₄²×D₅	2
C₂²×D₅×C₃⋊C₈	2
C₂×#91087	2
C₂×C₅×#803	2
C₂×#90952	2
D₅×#803	2
C₂×D₅×#97	3
C₂²×#803	5

Subgroups — C2×D5×#803 #14411209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×#803 #14411209