Subgroups — #18072021

Order 4864.

630 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926600	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926595	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
4	#14561470	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₁₉	—	2	1	no	—
9	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
10	#11926600	—	2	2	no	—
11	#11926600	C₄	1	4	yes	—
12	#11926595	—	2	2	no	—
13	#11926595	—	2	2	no	—
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₉⋊C₈	—	2	1	no	—
17	C₂×Dic₁₉⋊C₈	C₄	1	2	yes	—
18	C₄⋊C₈×D₁₉	—	2	2	no	—
19	C₄⋊C₈×D₁₉	C₄	1	4	yes	—
20	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
21	C₂×(C₂×D₁₉)⋊C₈	C₄	1	2	yes	—
22	C₂×#10597272	—	2	1	no	—
23	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
36	C₂×C₄×Dic₁₉	Q₈	1	1	yes	characteristic
37	C₂²×C₁₉⋊C₈	—	2	1	no	—
38	C₂²×C₁₉⋊C₈	—	2	1	no	—
39	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₁₉	—	2	4	no	—
41	C₂×C₈×D₁₉	—	4	2	no	—
42	C₂×C₈×D₁₉	—	4	2	no	—
43	C₄²×D₁₉	C₂×C₄	1	2	yes	—
44	C₄²×D₁₉	C₂×C₄	1	2	yes	—
45	C₄²×D₁₉	D₄	1	2	yes	—
46	C₄²×D₁₉	D₄	1	2	yes	—
47	C₁₉×C₄⋊C₈	—	2	1	no	—
48	C₁₉×C₄⋊C₈	—	2	1	no	—
49	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
50	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
51	C₄×C₈×C₁₉	—	2	1	no	—
52	C₄×C₈×C₁₉	—	2	1	no	—
53	(C₂×D₁₉)⋊C₈	—	2	4	no	—
54	(C₂×D₁₉)⋊C₈	—	2	4	no	—
55	#10597272	—	2	4	no	—
56	Dic₁₉⋊C₈	—	2	4	no	—
57	Dic₁₉⋊C₈	—	2	4	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
61	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
62	C₄×C₁₉⋊C₈	—	2	1	no	—
63	C₄×C₁₉⋊C₈	—	2	1	no	—
64	C₂³×D₁₉	C₄⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
68	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×D₁₉	—	2	4	no	—
72	C₂×C₄×D₁₉	—	2	2	no	—
73	C₂×C₄×D₁₉	—	2	2	no	—
74	C₂×C₄×D₁₉	—	2	1	no	—
75	C₂×C₄×D₁₉	—	2	1	no	—
76	C₂×C₄×D₁₉	—	2	1	no	—
77	C₂×C₄×D₁₉	—	2	1	no	—
78	C₂×C₄×D₁₉	C₄²	1	2	yes	—
79	C₂×C₄×D₁₉	C₂²⋊C₄	1	2	yes	—
80	C₂×C₄×D₁₉	C₂²⋊C₄	1	2	yes	—
81	C₂×C₄×D₁₉	C₂²⋊C₄	1	2	yes	—
82	C₂×C₄×D₁₉	C₄⋊C₄	1	2	yes	—
83	C₂×C₄×D₁₉	C₄⋊C₄	1	2	yes	—
84	C₂×C₈×C₁₉	—	2	2	no	—
85	C₂×C₈×C₁₉	—	2	2	no	—
86	C₂×C₈×C₁₉	—	2	2	no	—
87	C₂×C₈×C₁₉	—	2	2	no	—
88	C₂×C₈×C₁₉	—	2	2	no	—
89	C₂×C₈×C₁₉	—	4	1	no	—
90	C₂×C₈×C₁₉	—	4	1	no	—
91	C₂×C₈×C₁₉	—	4	1	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₄×Dic₁₉	C₄²	1	2	yes	—
98	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
99	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
100	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
101	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
102	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
103	C₂×C₁₉⋊C₈	—	2	2	no	—
104	C₂×C₁₉⋊C₈	—	2	2	no	—
105	C₂×C₁₉⋊C₈	—	2	2	no	—
106	C₂×C₁₉⋊C₈	—	2	2	no	—
107	C₂×C₁₉⋊C₈	—	2	2	no	—
108	C₂×C₁₉⋊C₈	—	4	1	no	—
109	C₂×C₁₉⋊C₈	—	4	1	no	—
110	C₂×C₁₉⋊C₈	—	4	1	no	—
111	C₂×C₁₉⋊C₈	—	4	1	no	—
112	C₈×D₁₉	—	4	8	no	—
113	#7879	—	19	1	no	maximal, Sylow
114	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂²×D₁₉	—	2	2	no	—
116	C₂²×D₁₉	—	2	1	no	—
117	C₂²×D₁₉	—	2	1	no	—
118	C₂²×D₁₉	#95	1	2	yes	—
119	C₂²×D₁₉	#108	1	4	yes	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
122	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₉	#131	1	2	yes	—
128	C₂×C₄×C₁₉	#131	1	2	yes	—
129	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
130	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
133	C₂×Dic₁₉	—	2	2	no	—
134	C₂×Dic₁₉	—	2	1	no	—
135	C₂×Dic₁₉	—	2	1	no	—
136	C₂×Dic₁₉	—	2	2	no	—
137	C₂×Dic₁₉	#95	1	2	yes	—
138	C₂×Dic₁₉	#95	1	2	yes	—
139	C₂×Dic₁₉	#95	1	2	yes	—
140	C₄×D₁₉	—	2	4	no	—
141	C₄×D₁₉	—	2	4	no	—
142	C₄×D₁₉	—	2	2	no	—
143	C₄×D₁₉	—	2	2	no	—
144	C₄×D₁₉	—	2	4	no	—
145	C₄×D₁₉	—	2	2	no	—
146	C₄×D₁₉	—	2	2	no	—
147	C₄×D₁₉	—	2	2	no	—
148	C₄×D₁₉	—	2	2	no	—
149	C₈×C₁₉	—	4	2	no	—
150	C₈×C₁₉	—	4	2	no	—
151	C₈×C₁₉	—	4	2	no	—
152	C₁₉⋊C₈	—	4	2	no	—
153	C₁₉⋊C₈	—	4	2	no	—
154	C₁₉⋊C₈	—	4	2	no	—
155	C₂×#432	—	19	1	no	—
156	C₂×#431	—	19	1	no	—
157	C₂²×C₄⋊C₈	—	19	1	no	—
158	#1277	—	19	1	no	—
159	#1277	—	19	1	no	—
160	#1277	—	19	1	no	—
161	#1277	D₁₉	1	1	yes	characteristic, complemented
162	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
163	C₂²×C₁₉	#424	1	2	yes	—
164	C₂²×C₁₉	#428	1	1	yes	characteristic
165	C₂²×C₁₉	#428	1	1	yes	characteristic
166	C₂²×C₁₉	C₂×#108	1	2	yes	—
167	C₂×D₁₉	—	2	4	no	—
168	C₂×D₁₉	—	2	4	no	—
169	C₂×D₁₉	—	2	2	no	—
170	C₂×D₁₉	—	2	2	no	—
171	C₂×D₁₉	#341	1	4	yes	—
172	C₄×C₁₉	—	2	1	no	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	#405	1	1	yes	characteristic
175	C₄×C₁₉	#405	1	1	yes	characteristic
176	C₄×C₁₉	#408	1	2	yes	—
177	C₄×C₁₉	#417	1	1	yes	characteristic
178	C₄×C₁₉	#417	1	1	yes	characteristic
179	C₄×C₁₉	#418	1	1	yes	characteristic
180	C₄×C₁₉	#419	1	1	yes	characteristic
181	Dic₁₉	—	2	2	no	—
182	Dic₁₉	—	2	2	no	—
183	Dic₁₉	—	2	2	no	—
184	C₂³×C₈	—	38	1	no	—
185	C₂²×C₄²	—	19	1	no	—
186	#432	—	19	4	no	—
187	#432	—	38	2	no	—
188	#431	—	38	2	no	—
189	#431	—	38	2	no	—
190	C₂×C₄⋊C₈	—	19	1	no	—
191	C₂×C₄⋊C₈	—	19	1	no	—
192	C₂×C₄⋊C₈	—	19	4	no	—
193	C₂×C₄⋊C₈	—	19	2	no	—
194	C₂×C₄⋊C₈	—	38	2	no	—
195	C₂×C₄⋊C₈	—	38	1	no	—
196	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
197	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
198	C₂×C₂²⋊C₈	—	19	2	no	—
199	C₂×C₂²⋊C₈	—	38	1	no	—
200	C₂×#97	—	38	1	no	—
201	C₂×C₄×C₈	—	19	1	no	—
202	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
203	C₂×C₁₉	#1573	1	2	yes	—
204	C₂×C₁₉	#1573	1	2	yes	—
205	C₂×C₁₉	#1729	1	1	yes	characteristic
206	C₂×C₁₉	#1736	1	1	yes	characteristic
207	C₂×C₁₉	C₂×#341	1	1	yes	characteristic
208	D₁₉	—	2	4	no	—
209	C₂³×C₄	—	19	1	no	—
210	C₂³×C₄	—	19	1	no	—
211	C₂³×C₄	—	19	1	no	—
212	C₂²×C₈	—	2	1	no	—
213	C₂²×C₈	—	2	1	no	—
214	C₂²×C₈	—	19	2	no	—
215	C₂²×C₈	—	38	4	no	—
216	C₂²×C₈	—	38	1	no	—
217	C₂²×C₈	—	38	1	no	—
218	C₂²×C₈	—	76	2	no	—
219	C₂²×C₈	—	76	2	no	—
220	C₂²×C₈	C₄×D₁₉	1	2	yes	—
221	C₂×C₄²	—	19	1	no	—
222	C₂×C₄²	—	19	1	no	—
223	C₂×C₄²	—	19	1	no	—
224	C₂×C₄²	—	19	2	no	—
225	C₂×C₄²	—	19	2	no	—
226	C₂×C₄²	—	19	2	no	—
227	C₂×C₄²	—	19	2	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	—	19	2	no	—
232	C₄⋊C₈	—	19	2	no	—
233	C₄⋊C₈	—	38	4	no	—
234	C₄⋊C₈	—	38	4	no	—
235	C₄⋊C₈	—	38	1	no	—
236	C₄⋊C₈	—	38	1	no	—
237	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
238	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
239	C₂²⋊C₈	—	38	4	no	—
240	C₂²⋊C₈	—	38	4	no	—
241	#97	—	38	4	no	—
242	C₄×C₈	—	2	1	no	—
243	C₄×C₈	—	2	1	no	—
244	C₄×C₈	—	38	1	no	—
245	C₄×C₈	—	38	1	no	—
246	C₁₉	#7879	1	1	yes	characteristic, complemented, Sylow
247	C₂⁴	—	19	1	no	—
248	C₂²×C₄	—	19	1	no	—
249	C₂²×C₄	—	19	1	no	—
250	C₂²×C₄	—	19	1	no	—
251	C₂²×C₄	—	19	2	no	—
252	C₂²×C₄	—	19	2	no	—
253	C₂²×C₄	—	19	2	no	—
254	C₂²×C₄	—	19	2	no	—
255	C₂²×C₄	—	19	2	no	—
256	C₂²×C₄	—	19	2	no	—
257	C₂²×C₄	—	38	4	no	—
258	C₂²×C₄	—	38	2	no	—
259	C₂²×C₄	—	38	2	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	C₂×C₄×D₁₉	1	1	yes	characteristic
265	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
266	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	4	1	no	—
273	C₂×C₈	—	4	1	no	—
274	C₂×C₈	—	4	1	no	—
275	C₂×C₈	—	4	1	no	—
276	C₂×C₈	—	38	2	no	—
277	C₂×C₈	—	38	2	no	—
278	C₂×C₈	—	38	2	no	—
279	C₂×C₈	—	38	2	no	—
280	C₂×C₈	—	38	2	no	—
281	C₂×C₈	—	76	8	no	—
282	C₂×C₈	—	76	1	no	—
283	C₂×C₈	—	76	1	no	—
284	C₂×C₈	—	76	1	no	—
285	C₂×C₈	—	76	1	no	—
286	C₄²	—	19	2	no	—
287	C₄²	—	19	2	no	—
288	C₄²	—	19	2	no	—
289	C₄²	—	19	2	no	—
290	C₄²	—	19	2	no	—
291	C₄²	—	19	2	no	—
292	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
293	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
294	C₄²	D₄×D₁₉	1	1	yes	characteristic
295	C₄²	D₄×D₁₉	1	1	yes	characteristic
296	C₂³	—	19	4	no	—
297	C₂³	—	19	2	no	—
298	C₂³	—	38	2	no	—
299	C₂³	—	38	1	no	—
300	C₂³	—	38	1	no	—
301	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	19	2	no	—
304	C₂×C₄	—	19	2	no	—
305	C₂×C₄	—	19	2	no	—
306	C₂×C₄	—	38	4	no	—
307	C₂×C₄	—	38	4	no	—
308	C₂×C₄	—	38	2	no	—
309	C₂×C₄	—	38	1	no	—
310	C₂×C₄	—	38	1	no	—
311	C₂×C₄	—	38	2	no	—
312	C₂×C₄	—	38	2	no	—
313	C₂×C₄	—	38	2	no	—
314	C₂×C₄	—	38	2	no	—
315	C₂×C₄	—	38	2	no	—
316	C₂×C₄	—	38	2	no	—
317	C₂×C₄	—	38	2	no	—
318	C₂×C₄	—	38	4	no	—
319	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
320	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
321	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
322	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
323	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
324	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
325	C₂×C₄	#10597347	1	2	yes	—
326	C₂×C₄	#10597353	1	2	yes	—
327	C₂×C₄	#10597357	1	1	yes	characteristic
328	C₂×C₄	#10597360	1	1	yes	characteristic
329	C₂×C₄	#10597361	1	1	yes	characteristic
330	C₂×C₄	#10597364	1	1	yes	characteristic
331	C₈	—	4	2	no	—
332	C₈	—	4	2	no	—
333	C₈	—	4	2	no	—
334	C₈	—	76	2	no	—
335	C₈	—	76	2	no	—
336	C₈	—	76	2	no	—
337	C₂²	—	19	4	no	—
338	C₂²	—	38	2	no	—
339	C₂²	—	38	2	no	—
340	C₂²	—	38	4	no	—
341	C₂²	—	38	4	no	—
342	C₂²	#95×D₁₉	1	1	yes	characteristic
343	C₂²	#11926569	1	2	yes	—
344	C₂²	#11926583	1	1	yes	characteristic
345	C₂²	#11926585	1	1	yes	characteristic
346	C₂²	#108×D₁₉	1	2	yes	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	38	2	no	—
350	C₄	—	38	2	no	—
351	C₄	—	38	2	no	—
352	C₄	#11926498	1	1	yes	characteristic
353	C₄	#11926501	1	1	yes	characteristic
354	C₄	#11926509	1	2	yes	—
355	C₄	#11926542	1	1	yes	characteristic
356	C₄	#11926544	1	1	yes	characteristic
357	C₄	#11926547	1	1	yes	characteristic
358	C₄	#11926551	1	1	yes	characteristic
359	C₂	—	38	4	no	—
360	C₂	#14562417	1	2	yes	—
361	C₂	#14562419	1	2	yes	—
362	C₂	#14563330	1	1	yes	characteristic
363	C₂	#14563353	1	1	yes	characteristic
364	C₂	D₁₉×#341	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1277	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×D₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1277	D₁₉
hypocenter	C₁₉	#7879
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
4. #14561470	C₂	semidirect
5. #14561469	C₂	semidirect
6. #14561469	C₂	semidirect
7. C₁₉×#1277	C₂	semidirect
161. #1277	D₁₉	semidirect
246. C₁₉	#7879	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926600	2
C₂×#11926595	2
C₂×C₄⋊C₈×D₁₉	2
#14561470	2
#14561469	2
C₁₉×#1277	2
#7879	19