Subgroups — #18075404

Order 4864.

462 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14562383	C₂	1	2	yes	maximal, complemented
2	#14561949	C₂	1	2	yes	maximal
3	#14561466	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#405	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	4	yes	—
6	#11926297	—	2	2	no	—
7	#11926295	—	2	2	no	—
8	#11926270	—	2	2	no	—
9	#11926268	—	2	2	no	—
10	C₂²×M₁₆×C₁₉	C₄	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₄	1	1	yes	characteristic
12	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₁₉×#405	—	2	2	no	—
14	C₁₉×#405	—	2	2	no	—
15	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
16	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×M₁₆×C₁₉	—	2	2	no	—
21	C₂×M₁₆×C₁₉	—	2	2	no	—
22	C₂×M₁₆×C₁₉	C₈	1	4	yes	complemented
23	C₂²×C₈×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂²×C₈×C₁₉	—	2	1	no	—
26	C₂²×C₈×C₁₉	—	2	2	no	—
27	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₁₉×#117	—	2	2	no	—
32	C₁₉×#117	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₁₉×#97	—	2	2	no	—
40	C₁₉×#97	—	2	2	no	—
41	C₄×C₈×C₁₉	—	2	1	no	—
42	C₄×C₈×C₁₉	—	2	1	no	—
43	C₄×C₈×C₁₉	D₄	1	2	yes	—
44	C₄×C₈×C₁₉	D₄	1	2	yes	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
47	C₄×C₁₉⋊C₈	—	2	4	no	—
48	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	—	2	1	no	—
53	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
57	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
61	M₁₆×C₁₉	—	2	8	no	—
62	C₂×C₈×C₁₉	—	2	4	no	—
63	C₂×C₈×C₁₉	—	2	4	no	—
64	C₂×C₈×C₁₉	—	2	1	no	—
65	C₂×C₈×C₁₉	—	2	1	no	—
66	C₂×C₈×C₁₉	—	2	1	no	—
67	C₂×C₈×C₁₉	—	2	1	no	—
68	C₂×C₈×C₁₉	—	2	1	no	—
69	C₂×C₈×C₁₉	—	2	1	no	—
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
74	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
75	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
76	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
77	C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₄²×C₁₉	—	2	1	no	—
82	C₄²×C₁₉	—	2	1	no	—
83	C₄²×C₁₉	C₂×D₄	1	2	yes	—
84	C₄²×C₁₉	#41	1	2	yes	—
85	C₂×C₁₉⋊C₈	—	4	4	no	—
86	#8602	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	—	2	1	no	—
88	C₂³×C₁₉	—	2	1	no	—
89	C₂³×C₁₉	—	4	1	no	—
90	C₂³×C₁₉	—	4	1	no	—
91	C₂³×C₁₉	C₄⋊C₈	1	2	yes	—
92	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
106	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#121	1	2	yes	—
109	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
110	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
114	C₈×C₁₉	—	2	2	no	—
115	C₈×C₁₉	—	2	1	no	—
116	C₈×C₁₉	—	2	1	no	—
117	C₈×C₁₉	—	2	2	no	—
118	C₈×C₁₉	C₂²⋊C₈	1	4	yes	—
119	C₁₉⋊C₈	—	8	4	no	—
120	C₂×#405	D₁₉	1	1	yes	characteristic
121	#1564	—	19	2	no	—
122	#1458	—	19	2	no	—
123	#1275	—	19	2	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	—	2	2	no	—
127	C₂²×C₁₉	—	4	2	no	—
128	C₂²×C₁₉	—	4	2	no	—
129	C₂²×C₁₉	—	4	1	no	—
130	C₂²×C₁₉	—	4	1	no	—
131	C₂²×C₁₉	#380	1	1	yes	characteristic
132	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
133	C₂²×C₁₉	#423	1	1	yes	characteristic
134	C₄×C₁₉	—	2	2	no	—
135	C₄×C₁₉	—	2	2	no	—
136	C₄×C₁₉	—	2	2	no	—
137	C₄×C₁₉	—	4	1	no	—
138	C₄×C₁₉	—	4	1	no	—
139	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
140	C₄×C₁₉	#407	1	1	yes	characteristic
141	C₄×C₁₉	#431	1	1	yes	characteristic
142	C₄×C₁₉	#432	1	1	yes	characteristic
143	C₂²×M₁₆	Dic₁₉	1	1	yes	characteristic
144	C₂³×C₈	Dic₁₉	1	1	yes	characteristic
145	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
146	#431	—	19	4	no	—
147	#405	—	2	2	no	—
148	#405	—	2	2	no	—
149	C₂×#97	Dic₁₉	1	1	yes	characteristic
150	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
151	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
152	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
153	#335	—	38	2	no	—
154	#334	—	38	2	no	—
155	#324	—	38	2	no	—
156	#323	—	38	2	no	—
157	C₂×C₁₉	—	2	1	no	—
158	C₂×C₁₉	—	2	1	no	—
159	C₂×C₁₉	—	4	2	no	—
160	C₂×C₁₉	#1797	1	1	yes	characteristic
161	C₂×C₁₉	#1812	1	1	yes	characteristic
162	C₂×C₁₉	#1813	1	1	yes	characteristic
163	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
164	C₂×M₁₆	—	2	2	no	—
165	C₂×M₁₆	—	2	2	no	—
166	C₂×M₁₆	C₁₉⋊C₈	1	4	yes	complemented
167	C₂²×C₈	—	2	2	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	—	2	1	no	—
170	C₂²×C₈	—	2	1	no	—
171	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
172	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
173	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
174	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
175	#117	—	2	2	no	—
176	#117	—	2	2	no	—
177	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
178	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
179	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
180	C₂×C₂²⋊C₄	D₇₆	1	1	yes	characteristic
181	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
182	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
183	C₄⋊C₈	—	38	4	no	—
184	C₂²⋊C₈	—	38	4	no	—
185	#97	—	2	2	no	—
186	#97	—	2	2	no	—
187	C₄×C₈	—	2	1	no	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	—	38	4	no	—
190	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
191	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
192	C₁₉	#8602	1	1	yes	characteristic, complemented, Sylow
193	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
194	C₂²×C₄	—	2	1	no	—
195	C₂²×C₄	—	2	1	no	—
196	C₂²×C₄	—	2	1	no	—
197	C₂²×C₄	—	2	1	no	—
198	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
199	C₂²×C₄	#64520	1	2	yes	—
200	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
201	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
202	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
203	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
204	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
205	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
206	M₁₆	—	2	8	no	—
207	C₂×C₈	—	2	4	no	—
208	C₂×C₈	—	2	4	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	—	2	1	no	—
212	C₂×C₈	—	2	1	no	—
213	C₂×C₈	—	2	1	no	—
214	C₂×C₈	—	2	1	no	—
215	C₂×C₈	—	76	4	no	—
216	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
217	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
218	C₂×C₈	#64520	1	2	yes	—
219	C₂×C₈	#64520	1	2	yes	—
220	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
221	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
222	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
223	C₄⋊C₄	—	2	2	no	—
224	C₄⋊C₄	—	2	2	no	—
225	C₂²⋊C₄	—	2	2	no	—
226	C₂²⋊C₄	—	2	2	no	—
227	C₄²	—	2	1	no	—
228	C₄²	—	2	1	no	—
229	C₄²	#64541	1	2	yes	—
230	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
231	C₂³	—	2	1	no	—
232	C₂³	—	2	1	no	—
233	C₂³	—	4	1	no	—
234	C₂³	—	4	1	no	—
235	C₂³	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
236	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	4	1	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
250	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
251	C₂×C₄	C₂×#64520	1	1	yes	characteristic
252	C₂×C₄	C₂×#64520	1	1	yes	characteristic
253	C₂×C₄	C₂×#64520	1	1	yes	characteristic
254	C₂×C₄	#10597370	1	2	yes	—
255	C₂×C₄	#10597372	1	1	yes	characteristic
256	C₂×C₄	#10597376	1	2	yes	—
257	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
258	C₈	—	2	2	no	—
259	C₈	—	2	2	no	—
260	C₈	—	2	1	no	—
261	C₈	—	2	1	no	—
262	C₈	—	152	4	no	—
263	C₈	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
264	C₂²	—	2	1	no	—
265	C₂²	—	2	1	no	—
266	C₂²	—	2	2	no	—
267	C₂²	—	4	2	no	—
268	C₂²	—	4	2	no	—
269	C₂²	—	4	1	no	—
270	C₂²	—	4	1	no	—
271	C₂²	#11926404	1	1	yes	characteristic
272	C₂²	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
273	C₂²	#11926568	1	1	yes	characteristic
274	C₄	—	2	2	no	—
275	C₄	—	2	2	no	—
276	C₄	—	2	2	no	—
277	C₄	—	4	1	no	—
278	C₄	—	4	1	no	—
279	C₄	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
280	C₄	#11926508	1	1	yes	characteristic
281	C₄	#11926597	1	1	yes	characteristic
282	C₄	#11926601	1	1	yes	characteristic
283	C₂	—	2	1	no	—
284	C₂	—	2	1	no	—
285	C₂	—	4	2	no	—
286	C₂	#14563615	1	1	yes	characteristic
287	C₂	#14563681	1	1	yes	characteristic
288	C₂	#14563685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597372
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#405	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#405	D₁₉
hypocenter	C₁₉	#8602
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
1. #14562383	C₂	semidirect
3. #14561466	C₂	semidirect
22. C₂×M₁₆×C₁₉	C₈	semidirect
166. C₂×M₁₆	C₁₉⋊C₈	semidirect
192. C₁₉	#8602	semidirect

Maximal subgroups

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

subgroup	index
#14562383	2
#14561949	2
#14561466	2
C₂×C₁₉×#405	2
#8602	19