Subgroups — #18073586

Order 4864.

392 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572611	C₂	1	1	yes	maximal, characteristic
2	#14563387	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562223	C₂	1	1	yes	maximal, characteristic
4	#14561925	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561535	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561528	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1500	C₂	1	1	yes	maximal, characteristic
8	#11926675	C₄	1	1	yes	characteristic, complemented
9	Q₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic, complemented
10	#11926622	C₄	1	1	yes	characteristic, complemented
11	#11926616	—	2	1	no	—
12	D₄×C₁₉⋊C₈	—	2	1	no	—
13	D₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic, complemented
14	#11926605	—	2	1	no	—
15	#11926601	C₂²	1	1	yes	characteristic
16	#11926500	—	2	1	no	—
17	C₄×#64520	C₂²	1	1	yes	characteristic
18	C₂×#10597260	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#11926299	—	2	1	no	—
21	#11926299	—	2	1	no	—
22	#11926286	C₄	1	2	yes	complemented
23	#11926284	C₄	1	2	yes	complemented
24	#11926266	—	2	1	no	—
25	#11926265	—	2	1	no	—
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₁₉×#431	C₂²	1	1	yes	characteristic
28	C₁₉×#376	C₂²	1	1	yes	characteristic
29	C₁₉×#328	C₄	1	2	yes	—
30	C₁₉×#327	C₄	1	2	yes	—
31	C₁₉×#126	—	2	1	no	—
32	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
33	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
34	C₁₉×#123	—	2	1	no	—
35	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
36	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
37	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₄×D₄×C₁₉	—	2	1	no	—
39	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₁₉×#117	—	2	1	no	—
41	C₂×C₄²×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×#64520	—	2	1	no	—
44	C₂×#64520	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₂²×C₁₉⋊C₈	—	2	1	no	—
47	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
48	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
49	C₁₉×C₄⋊C₈	—	2	1	no	—
50	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
51	C₄×C₈×C₁₉	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	C₂×C₄	1	2	yes	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
56	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
60	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
61	#10597260	—	2	1	no	—
62	#10597260	—	2	1	no	—
63	#10597260	—	2	1	no	—
64	#10597260	C₂×C₄	1	2	yes	—
65	#10597260	C₂×C₄	1	2	yes	—
66	C₄×C₁₉⋊C₈	—	2	1	no	—
67	C₄×C₁₉⋊C₈	—	2	1	no	—
68	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
69	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
71	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
72	C₂×Q₈×C₁₉	C₄²	1	1	yes	characteristic
73	C₂×D₄×C₁₉	—	2	1	no	—
74	C₂×D₄×C₁₉	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
80	C₂×C₈×C₁₉	—	2	2	no	—
81	C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₄⋊C₄×C₁₉	C₄²	1	1	yes	characteristic
86	C₄⋊C₄×C₁₉	C₄²	1	1	yes	characteristic
87	C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₄²×C₁₉	—	2	1	no	—
93	C₄²×C₁₉	—	4	1	no	—
94	C₄²×C₁₉	—	4	1	no	—
95	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
96	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₄²×C₁₉	#41	1	1	yes	characteristic
99	#64520	—	4	2	no	—
100	#64520	—	4	2	no	—
101	C₂×C₁₉⋊C₈	—	2	1	no	—
102	C₂×C₁₉⋊C₈	—	2	1	no	—
103	C₂×C₁₉⋊C₈	—	2	2	no	—
104	C₂×C₁₉⋊C₈	—	2	2	no	—
105	C₂×C₁₉⋊C₈	—	4	1	no	—
106	C₂×C₁₉⋊C₈	—	4	1	no	—
107	C₂×C₁₉⋊C₈	—	4	2	no	—
108	C₂×C₁₉⋊C₈	—	4	1	no	—
109	C₂×C₁₉⋊C₈	—	4	1	no	—
110	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
114	#8248	—	19	1	no	maximal, Sylow
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
117	Q₈×C₁₉	—	4	1	no	—
118	D₄×C₁₉	—	4	1	no	—
119	D₄×C₁₉	—	4	2	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	4	1	no	—
127	C₂×C₄×C₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	4	1	no	—
129	C₂×C₄×C₁₉	—	4	2	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
133	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
138	C₈×C₁₉	—	4	2	no	—
139	C₁₉⋊C₈	—	2	1	no	—
140	C₁₉⋊C₈	—	2	1	no	—
141	C₁₉⋊C₈	—	2	1	no	—
142	C₁₉⋊C₈	—	2	1	no	—
143	C₁₉⋊C₈	—	4	2	no	—
144	C₁₉⋊C₈	—	4	2	no	—
145	C₁₉⋊C₈	—	4	1	no	—
146	C₁₉⋊C₈	—	4	1	no	—
147	#2966	—	19	1	no	—
148	#1746	—	19	1	no	—
149	#1524	—	19	1	no	—
150	#1500	D₁₉	1	1	yes	characteristic
151	#1451	—	19	1	no	—
152	#1302	—	19	1	no	—
153	#1300	—	19	1	no	—
154	C₂²×C₁₉	—	2	1	no	—
155	C₂²×C₁₉	—	2	1	no	—
156	C₂²×C₁₉	—	4	1	no	—
157	C₂²×C₁₉	—	4	1	no	—
158	C₂²×C₁₉	—	4	1	no	—
159	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₁₉	#444	1	2	yes	—
161	C₄×C₁₉	—	2	1	no	—
162	C₄×C₁₉	—	2	1	no	—
163	C₄×C₁₉	—	2	1	no	—
164	C₄×C₁₉	—	2	1	no	—
165	C₄×C₁₉	—	2	1	no	—
166	C₄×C₁₉	—	4	1	no	—
167	C₄×C₁₉	—	4	1	no	—
168	C₄×C₁₉	—	4	1	no	—
169	C₄×C₁₉	—	8	2	no	—
170	C₄×C₁₉	#421	1	1	yes	characteristic
171	C₄×C₁₉	#421	1	1	yes	characteristic
172	#529	C₂×D₁₉	1	1	yes	characteristic
173	#446	—	19	1	no	—
174	C₈×Q₈	—	19	1	no	—
175	#436	—	19	1	no	—
176	#435	—	38	1	no	—
177	C₈×D₄	—	19	1	no	—
178	C₈×D₄	—	38	1	no	—
179	#433	—	38	1	no	—
180	#432	—	19	1	no	—
181	#431	C₂×D₁₉	1	1	yes	characteristic
182	#405	—	38	1	no	—
183	C₄×M₁₆	—	19	1	no	—
184	C₂×#97	—	19	1	no	—
185	C₂×C₄×C₈	—	19	1	no	—
186	#376	C₂×D₁₉	1	1	yes	characteristic
187	#336	—	38	1	no	—
188	#336	—	38	1	no	—
189	#330	—	19	2	no	—
190	#329	—	19	2	no	—
191	#328	Dic₁₉	1	2	yes	—
192	#327	Dic₁₉	1	2	yes	—
193	#322	—	38	1	no	—
194	#322	—	38	1	no	—
195	C₂×C₁₉	—	2	2	no	—
196	C₂×C₁₉	—	8	1	no	—
197	C₂×C₁₉	#1757	1	1	yes	characteristic
198	C₂×C₁₉	#1759	1	1	yes	characteristic
199	C₂×C₁₉	#1765	1	1	yes	characteristic
200	C₂×M₁₆	—	38	1	no	—
201	C₂×M₁₆	—	38	1	no	—
202	C₂²×C₈	—	19	1	no	—
203	C₂²×C₈	—	19	1	no	—
204	C₂²×C₈	—	38	1	no	—
205	C₂²×C₈	—	38	1	no	—
206	#126	—	2	1	no	—
207	#125	C₄×D₁₉	1	1	yes	characteristic
208	#124	C₄×D₁₉	1	1	yes	characteristic
209	#123	—	2	1	no	—
210	C₂²⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
211	#121	C₂×Dic₁₉	1	1	yes	characteristic
212	C₄×Q₈	C₄×D₁₉	1	1	yes	characteristic
213	C₄×D₄	—	2	1	no	—
214	C₄×D₄	C₄×D₁₉	1	1	yes	characteristic
215	#117	—	2	1	no	—
216	C₂×C₄²	—	2	1	no	—
217	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
218	C₄⋊C₈	—	2	1	no	—
219	C₄⋊C₈	—	19	1	no	—
220	C₄⋊C₈	—	19	1	no	—
221	C₄⋊C₈	—	38	1	no	—
222	C₄⋊C₈	—	38	1	no	—
223	C₂²⋊C₈	—	38	1	no	—
224	C₂²⋊C₈	—	38	1	no	—
225	C₂²⋊C₈	—	38	1	no	—
226	C₂²⋊C₈	C₂×Dic₁₉	1	2	yes	—
227	#97	—	19	2	no	—
228	#97	—	19	2	no	—
229	#97	—	38	1	no	—
230	#97	—	38	1	no	—
231	#97	—	38	1	no	—
232	C₄×C₈	—	2	1	no	—
233	C₄×C₈	—	19	1	no	—
234	C₄×C₈	—	19	1	no	—
235	C₄×C₈	—	19	1	no	—
236	C₄×C₈	—	19	1	no	—
237	C₄×C₈	—	38	1	no	—
238	C₄×C₈	—	38	1	no	—
239	#95	—	2	1	no	—
240	#95	C₂×Dic₁₉	1	2	yes	—
241	C₁₉	#8248	1	1	yes	characteristic, complemented, Sylow
242	C₂×Q₈	C₄×Dic₁₉	1	1	yes	characteristic
243	C₂×D₄	—	2	1	no	—
244	C₂×D₄	C₄×Dic₁₉	1	1	yes	characteristic
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
248	C₂²×C₄	#64543	1	1	yes	characteristic
249	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
250	M₁₆	—	76	2	no	—
251	M₁₆	—	76	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	19	1	no	—
254	C₂×C₈	—	19	1	no	—
255	C₂×C₈	—	19	1	no	—
256	C₂×C₈	—	19	1	no	—
257	C₂×C₈	—	38	1	no	—
258	C₂×C₈	—	38	1	no	—
259	C₂×C₈	—	38	2	no	—
260	C₂×C₈	—	38	2	no	—
261	C₂×C₈	—	76	1	no	—
262	C₂×C₈	—	76	1	no	—
263	C₂×C₈	—	76	2	no	—
264	C₂×C₈	—	76	1	no	—
265	C₂×C₈	—	76	1	no	—
266	C₄⋊C₄	—	2	1	no	—
267	C₄⋊C₄	—	2	1	no	—
268	C₄⋊C₄	—	2	1	no	—
269	C₄⋊C₄	—	2	1	no	—
270	C₄⋊C₄	C₄×Dic₁₉	1	1	yes	characteristic
271	C₄⋊C₄	C₄×Dic₁₉	1	1	yes	characteristic
272	C₂²⋊C₄	—	2	1	no	—
273	C₂²⋊C₄	—	2	1	no	—
274	C₂²⋊C₄	—	2	1	no	—
275	C₂²⋊C₄	—	2	1	no	—
276	C₂²⋊C₄	—	2	1	no	—
277	C₄²	—	2	1	no	—
278	C₄²	—	4	1	no	—
279	C₄²	—	4	1	no	—
280	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
281	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
282	C₄²	D₄×D₁₉	1	1	yes	characteristic
283	C₄²	#64543	1	1	yes	characteristic
284	C₂³	—	2	1	no	—
285	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
286	Q₈	—	4	1	no	—
287	D₄	—	4	1	no	—
288	D₄	—	4	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	1	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	#10597323	1	1	yes	characteristic
302	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
303	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
304	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
305	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
306	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
307	C₈	—	4	2	no	—
308	C₈	—	38	1	no	—
309	C₈	—	38	1	no	—
310	C₈	—	38	1	no	—
311	C₈	—	38	1	no	—
312	C₈	—	76	2	no	—
313	C₈	—	76	2	no	—
314	C₈	—	76	1	no	—
315	C₈	—	76	1	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	4	1	no	—
319	C₂²	—	4	1	no	—
320	C₂²	—	4	1	no	—
321	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
322	C₂²	#11926666	1	2	yes	—
323	C₄	—	2	1	no	—
324	C₄	—	2	1	no	—
325	C₄	—	2	1	no	—
326	C₄	—	2	1	no	—
327	C₄	—	2	1	no	—
328	C₄	—	4	1	no	—
329	C₄	—	4	1	no	—
330	C₄	—	4	1	no	—
331	C₄	—	8	2	no	—
332	C₄	#11926559	1	1	yes	characteristic
333	C₄	#11926559	1	1	yes	characteristic
334	C₂	—	2	2	no	—
335	C₂	—	8	1	no	—
336	C₂	#14563437	1	1	yes	characteristic
337	C₂	#14563447	1	1	yes	characteristic
338	C₂	#14563482	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1500	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₁₉×#121	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1500	D₁₉
hypocenter	C₁₉	#8248
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1500

Complements

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

N	H ≅ G/N	type
2. #14563387	C₂	semidirect
4. #14561925	C₂	semidirect
5. #14561535	C₂	semidirect
6. #14561528	C₂	semidirect
8. #11926675	C₄	semidirect
9. Q₈×C₁₉⋊C₈	C₄	semidirect
10. #11926622	C₄	semidirect
13. D₄×C₁₉⋊C₈	C₄	semidirect
22. #11926286	C₄	semidirect
23. #11926284	C₄	semidirect
241. C₁₉	#8248	semidirect

Maximal subgroups

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

subgroup	index
#14572611	2
#14563387	2
#14562223	2
#14561925	2
#14561535	2
#14561528	2
C₁₉×#1500	2
#8248	19