Subgroups — #18073074

Order 4864.

400 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926606	C₂	1	1	yes	maximal, characteristic
2	#14561947	C₂	1	1	yes	maximal, characteristic
3	#14561947	C₂	1	1	yes	maximal, characteristic
4	#14561928	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561919	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1281	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597318	C₂²	1	1	yes	characteristic
9	#11926606	—	2	1	no	—
10	#11926606	—	2	1	no	—
11	#11926606	—	2	1	no	—
12	#11926606	—	2	1	no	—
13	#11926597	C₂²	1	1	yes	characteristic
14	#11926597	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₉⋊C₈	C₄	1	1	yes	characteristic
16	C₂×Dic₁₉⋊C₈	C₄	1	1	yes	characteristic
17	C₂×(C₂×D₁₉)⋊C₈	C₄	1	1	yes	characteristic
18	C₂×(C₂×D₁₉)⋊C₈	C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#11926269	C₄	1	2	yes	—
21	#11926269	C₄	1	2	yes	—
22	#11926267	C₄	1	2	yes	—
23	#11926267	C₄	1	2	yes	—
24	#11926266	—	2	1	no	—
25	#11926266	—	2	1	no	—
26	#11926265	—	2	1	no	—
27	C₈×C₁₉⋊C₈	—	2	1	no	—
28	C₁₉×#431	C₂²	1	1	yes	characteristic
29	C₁₉×#431	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×(C₂×D₁₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
36	C₂×(C₂×D₁₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
37	C₂×Dic₁₉⋊C₄	C₂×C₄	1	1	yes	characteristic
38	C₂×Dic₁₉⋊C₄	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
42	#10597318	—	2	1	no	—
43	#10597318	—	2	1	no	—
44	#10597318	—	2	1	no	—
45	#10597318	—	2	1	no	—
46	C₁₉×C₄⋊C₈	—	2	1	no	—
47	C₁₉×C₄⋊C₈	—	2	1	no	—
48	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
49	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
50	C₁₉×#97	—	2	1	no	—
51	C₁₉×#97	—	2	1	no	—
52	C₄×C₈×C₁₉	—	2	1	no	—
53	C₄×C₈×C₁₉	—	2	1	no	—
54	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
55	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
56	(C₂×D₁₉)⋊C₈	—	2	1	no	—
57	(C₂×D₁₉)⋊C₈	—	2	1	no	—
58	(C₂×D₁₉)⋊C₈	—	2	1	no	—
59	(C₂×D₁₉)⋊C₈	—	2	1	no	—
60	Dic₁₉⋊C₈	—	2	1	no	—
61	Dic₁₉⋊C₈	—	2	1	no	—
62	Dic₁₉⋊C₈	—	2	1	no	—
63	Dic₁₉⋊C₈	—	2	1	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄×C₁₉⋊C₈	—	2	1	no	—
67	C₄×C₁₉⋊C₈	—	2	1	no	—
68	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
69	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
70	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
71	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
72	C₂³×D₁₉	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
77	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
78	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
79	C₂×C₄×D₁₉	—	2	1	no	—
80	C₂×C₄×D₁₉	—	2	1	no	—
81	C₂×C₄×D₁₉	—	2	1	no	—
82	C₂×C₄×D₁₉	—	2	1	no	—
83	C₂×C₄×D₁₉	—	2	1	no	—
84	C₂×C₄×D₁₉	—	2	1	no	—
85	C₂×C₈×C₁₉	—	2	1	no	—
86	C₂×C₈×C₁₉	—	2	1	no	—
87	C₂×C₈×C₁₉	—	2	2	no	—
88	C₂×C₈×C₁₉	—	2	2	no	—
89	C₂×C₈×C₁₉	—	2	1	no	—
90	C₂×C₈×C₁₉	—	2	1	no	—
91	C₂×C₈×C₁₉	—	2	1	no	—
92	C₂×C₈×C₁₉	—	2	1	no	—
93	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₄²×C₁₉	#41	1	1	yes	characteristic
96	C₄²×C₁₉	#41	1	1	yes	characteristic
97	(C₂×D₁₉)⋊C₄	—	2	1	no	—
98	(C₂×D₁₉)⋊C₄	—	2	1	no	—
99	(C₂×D₁₉)⋊C₄	—	2	1	no	—
100	(C₂×D₁₉)⋊C₄	—	2	1	no	—
101	Dic₁₉⋊C₄	—	2	1	no	—
102	Dic₁₉⋊C₄	—	2	1	no	—
103	Dic₁₉⋊C₄	—	2	1	no	—
104	Dic₁₉⋊C₄	—	2	1	no	—
105	C₄×Dic₁₉	—	2	1	no	—
106	C₄×Dic₁₉	—	2	1	no	—
107	C₂×C₁₉⋊C₈	—	2	1	no	—
108	C₂×C₁₉⋊C₈	—	2	1	no	—
109	C₂×C₁₉⋊C₈	—	2	1	no	—
110	C₂×C₁₉⋊C₈	—	2	1	no	—
111	C₂×C₁₉⋊C₈	—	2	2	no	—
112	C₂×C₁₉⋊C₈	—	2	2	no	—
113	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
117	#8158	—	19	1	no	maximal, Sylow
118	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
119	C₂²×D₁₉	—	2	1	no	—
120	C₂²×D₁₉	—	2	1	no	—
121	C₂²×D₁₉	—	2	1	no	—
122	C₂²×D₁₉	—	4	1	no	—
123	C₂²×D₁₉	—	4	1	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	1	no	—
126	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
128	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
133	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
136	C₂×Dic₁₉	—	2	1	no	—
137	C₂×Dic₁₉	—	2	1	no	—
138	C₂×Dic₁₉	—	2	1	no	—
139	C₂×Dic₁₉	—	2	1	no	—
140	C₂×Dic₁₉	—	2	1	no	—
141	C₂×Dic₁₉	—	4	1	no	—
142	C₂×Dic₁₉	—	4	1	no	—
143	C₄×D₁₉	—	4	1	no	—
144	C₄×D₁₉	—	4	1	no	—
145	C₄×D₁₉	—	4	1	no	—
146	C₄×D₁₉	—	4	1	no	—
147	C₈×C₁₉	—	4	2	no	—
148	C₈×C₁₉	—	4	2	no	—
149	C₈×C₁₉	—	4	1	no	—
150	C₈×C₁₉	—	4	1	no	—
151	C₁₉⋊C₈	—	2	1	no	—
152	C₁₉⋊C₈	—	2	1	no	—
153	C₁₉⋊C₈	—	2	1	no	—
154	C₁₉⋊C₈	—	2	1	no	—
155	C₁₉⋊C₈	—	4	2	no	—
156	C₁₉⋊C₈	—	4	2	no	—
157	C₂×#433	—	19	1	no	—
158	#1458	—	19	1	no	—
159	#1458	—	19	1	no	—
160	#1452	—	19	1	no	—
161	#1450	—	19	1	no	—
162	#1281	—	19	1	no	—
163	#1281	D₁₉	1	1	yes	characteristic, complemented
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₁₉	#405	1	1	yes	characteristic
168	C₂²×C₁₉	#405	1	1	yes	characteristic
169	C₂×D₁₉	—	4	1	no	—
170	C₂×D₁₉	—	4	1	no	—
171	C₂×D₁₉	—	4	1	no	—
172	C₂×D₁₉	—	8	1	no	—
173	C₂×D₁₉	—	8	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	2	1	no	—
177	C₄×C₁₉	—	2	1	no	—
178	C₄×C₁₉	#408	1	1	yes	characteristic
179	C₄×C₁₉	#408	1	1	yes	characteristic
180	C₄×C₁₉	#433	1	1	yes	characteristic
181	C₄×C₁₉	#433	1	1	yes	characteristic
182	Dic₁₉	—	4	1	no	—
183	Dic₁₉	—	4	1	no	—
184	Dic₁₉	—	4	1	no	—
185	C₂×#117	—	19	1	no	—
186	#433	—	38	1	no	—
187	#433	—	38	1	no	—
188	#433	—	38	1	no	—
189	#433	—	38	1	no	—
190	#431	—	19	1	no	—
191	#431	—	19	1	no	—
192	#431	C₂×D₁₉	1	1	yes	characteristic
193	#431	C₂×D₁₉	1	1	yes	characteristic
194	C₂×C₄⋊C₈	—	19	1	no	—
195	C₂×C₄⋊C₈	—	19	1	no	—
196	C₂×C₂²⋊C₈	—	19	1	no	—
197	C₂×C₂²⋊C₈	—	19	1	no	—
198	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
199	C₂×C₄×C₈	—	19	1	no	—
200	#324	—	19	2	no	—
201	#324	—	19	2	no	—
202	#323	—	19	2	no	—
203	#323	—	19	2	no	—
204	#322	—	38	1	no	—
205	#322	—	38	1	no	—
206	#322	—	38	1	no	—
207	C₈²	—	38	1	no	—
208	C₂×C₁₉	—	2	1	no	—
209	C₂×C₁₉	—	2	1	no	—
210	C₂×C₁₉	#1750	1	1	yes	characteristic
211	C₂×C₁₉	#1757	1	1	yes	characteristic
212	C₂×C₁₉	#1757	1	1	yes	characteristic
213	D₁₉	—	8	1	no	—
214	C₂³×C₄	—	19	1	no	—
215	C₂²×C₈	—	19	1	no	—
216	C₂²×C₈	—	19	1	no	—
217	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
218	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
219	#117	—	38	1	no	—
220	#117	—	38	1	no	—
221	#117	—	38	1	no	—
222	#117	—	38	1	no	—
223	C₂×C₄⋊C₄	—	19	1	no	—
224	C₂×C₄⋊C₄	—	19	1	no	—
225	C₂×C₂²⋊C₄	—	19	1	no	—
226	C₂×C₂²⋊C₄	—	19	1	no	—
227	C₂×C₄²	—	19	1	no	—
228	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
229	C₄⋊C₈	—	2	1	no	—
230	C₄⋊C₈	—	2	1	no	—
231	C₄⋊C₈	—	38	1	no	—
232	C₄⋊C₈	—	38	1	no	—
233	C₄⋊C₈	—	38	1	no	—
234	C₄⋊C₈	—	38	1	no	—
235	C₄⋊C₈	—	38	1	no	—
236	C₄⋊C₈	—	38	1	no	—
237	C₂²⋊C₈	—	19	2	no	—
238	C₂²⋊C₈	—	19	2	no	—
239	C₂²⋊C₈	—	38	1	no	—
240	C₂²⋊C₈	—	38	1	no	—
241	C₂²⋊C₈	—	38	1	no	—
242	C₂²⋊C₈	—	38	1	no	—
243	C₂²⋊C₈	C₄×D₁₉	1	2	yes	—
244	C₂²⋊C₈	C₄×D₁₉	1	2	yes	—
245	#97	—	2	1	no	—
246	#97	—	2	1	no	—
247	C₄×C₈	—	2	1	no	—
248	C₄×C₈	—	2	1	no	—
249	C₄×C₈	—	19	1	no	—
250	C₄×C₈	—	19	1	no	—
251	C₄×C₈	—	19	1	no	—
252	C₄×C₈	—	19	1	no	—
253	C₄×C₈	—	38	1	no	—
254	C₄×C₈	—	38	1	no	—
255	C₁₉	#8158	1	1	yes	characteristic, complemented, Sylow
256	C₂⁴	—	19	1	no	—
257	C₂²×C₄	—	19	1	no	—
258	C₂²×C₄	—	19	1	no	—
259	C₂²×C₄	—	19	1	no	—
260	C₂²×C₄	—	38	1	no	—
261	C₂²×C₄	—	38	1	no	—
262	C₂²×C₄	—	38	1	no	—
263	C₂²×C₄	—	38	1	no	—
264	C₂²×C₄	—	38	1	no	—
265	C₂²×C₄	—	38	1	no	—
266	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	19	1	no	—
278	C₂×C₈	—	19	1	no	—
279	C₂×C₈	—	19	1	no	—
280	C₂×C₈	—	19	1	no	—
281	C₂×C₈	—	38	1	no	—
282	C₂×C₈	—	38	1	no	—
283	C₂×C₈	—	38	1	no	—
284	C₂×C₈	—	38	1	no	—
285	C₂×C₈	—	38	2	no	—
286	C₂×C₈	—	38	2	no	—
287	C₄⋊C₄	—	38	1	no	—
288	C₄⋊C₄	—	38	1	no	—
289	C₄⋊C₄	—	38	1	no	—
290	C₄⋊C₄	—	38	1	no	—
291	C₂²⋊C₄	—	38	1	no	—
292	C₂²⋊C₄	—	38	1	no	—
293	C₂²⋊C₄	—	38	1	no	—
294	C₂²⋊C₄	—	38	1	no	—
295	C₄²	—	38	1	no	—
296	C₄²	—	38	1	no	—
297	C₄²	D₄×D₁₉	1	1	yes	characteristic
298	C₄²	D₄×D₁₉	1	1	yes	characteristic
299	C₄²	#64543	1	1	yes	characteristic
300	C₄²	#64545	1	1	yes	characteristic
301	C₂³	—	38	1	no	—
302	C₂³	—	38	1	no	—
303	C₂³	—	38	1	no	—
304	C₂³	—	76	1	no	—
305	C₂³	—	76	1	no	—
306	C₂³	C₄²×D₁₉	1	1	yes	characteristic
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	38	1	no	—
310	C₂×C₄	—	38	1	no	—
311	C₂×C₄	—	38	1	no	—
312	C₂×C₄	—	38	1	no	—
313	C₂×C₄	—	38	1	no	—
314	C₂×C₄	—	76	1	no	—
315	C₂×C₄	—	76	1	no	—
316	C₂×C₄	—	76	1	no	—
317	C₂×C₄	—	76	1	no	—
318	C₂×C₄	—	76	1	no	—
319	C₂×C₄	—	76	1	no	—
320	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
321	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
322	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
323	C₂×C₄	#10597338	1	1	yes	characteristic
324	C₂×C₄	#10597339	1	1	yes	characteristic
325	C₂×C₄	#10597339	1	1	yes	characteristic
326	C₂×C₄	#10597347	1	1	yes	characteristic
327	C₂×C₄	#10597347	1	1	yes	characteristic
328	C₂×C₄	#10597353	1	1	yes	characteristic
329	C₂×C₄	#10597353	1	1	yes	characteristic
330	C₈	—	4	2	no	—
331	C₈	—	4	2	no	—
332	C₈	—	4	1	no	—
333	C₈	—	4	1	no	—
334	C₈	—	38	1	no	—
335	C₈	—	38	1	no	—
336	C₈	—	38	1	no	—
337	C₈	—	38	1	no	—
338	C₈	—	76	2	no	—
339	C₈	—	76	2	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	76	1	no	—
343	C₂²	—	76	1	no	—
344	C₂²	—	76	1	no	—
345	C₂²	—	152	1	no	—
346	C₂²	—	152	1	no	—
347	C₂²	#11926391	1	1	yes	characteristic
348	C₂²	#11926498	1	1	yes	characteristic
349	C₂²	#11926501	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	76	1	no	—
355	C₄	—	76	1	no	—
356	C₄	—	76	1	no	—
357	C₄	#11926509	1	1	yes	characteristic
358	C₄	#11926509	1	1	yes	characteristic
359	C₄	#11926604	1	1	yes	characteristic
360	C₄	#11926604	1	1	yes	characteristic
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	—	152	1	no	—
364	C₂	#14563400	1	1	yes	characteristic
365	C₂	#14563434	1	1	yes	characteristic
366	C₂	#14563434	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1281	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1281	D₁₉
hypocenter	C₁₉	#8158
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

Complements

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

N	H ≅ G/N	type
4. #14561928	C₂	semidirect
5. #14561919	C₂	semidirect
6. #14561480	C₂	semidirect
7. C₁₉×#1281	C₂	semidirect
163. #1281	D₁₉	semidirect
255. C₁₉	#8158	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926606	2
#14561947	2
#14561928	2
#14561919	2
#14561480	2
C₁₉×#1281	2
#8158	19