Subgroups — C₁₉×#8398 #18014357

Order 4864.

782 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#554	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1549	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1486	C₂	1	2	yes	maximal
5	C₁₉×#1461	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#554	—	2	4	no	—
7	C₁₉×#554	—	2	4	no	—
8	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#125	C₄	1	2	yes	—
10	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
11	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
12	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
16	C₁₉×#431	C₂²	1	2	yes	—
17	C₁₉×#423	C₂²	1	2	yes	—
18	C₂×C₁₉×#101	—	2	1	no	—
19	C₁₉×#343	—	2	1	no	—
20	C₁₉×#332	—	2	4	no	—
21	C₁₉×D₄⋊C₈	—	2	4	no	—
22	C₁₉×#324	—	2	2	no	—
23	C₂²×Q₈×C₁₉	—	2	1	no	—
24	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	—	2	2	no	—
28	C₂×M₁₆×C₁₉	—	2	2	no	—
29	C₁₉×C₄⋊Q₈	—	2	2	no	—
30	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
31	C₁₉×#125	—	2	4	no	—
32	C₁₉×#125	—	2	4	no	—
33	C₁₉×C₂²⋊Q₈	—	2	8	no	—
34	C₁₉×C₂²⋊Q₈	—	2	16	no	—
35	C₄×Q₈×C₁₉	—	2	2	no	—
36	C₄×Q₈×C₁₉	—	2	2	no	—
37	C₄×D₄×C₁₉	—	2	4	no	—
38	C₄×D₄×C₁₉	—	2	4	no	—
39	C₄×D₄×C₁₉	—	2	2	no	—
40	C₄×D₄×C₁₉	D₄	1	4	yes	—
41	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×C₄⋊C₈	—	2	2	no	—
54	C₁₉×C₄⋊C₈	—	2	2	no	—
55	C₁₉×C₄⋊C₈	—	2	2	no	—
56	C₁₉×#101	—	4	2	no	—
57	C₁₉×C₂²⋊C₈	—	2	2	no	—
58	C₄×C₈×C₁₉	—	2	2	no	—
59	C₂⁴×C₁₉	—	2	1	no	—
60	C₂×Q₈×C₁₉	—	2	2	no	—
61	C₂×Q₈×C₁₉	—	2	4	no	—
62	C₂×Q₈×C₁₉	—	2	2	no	—
63	C₂×Q₈×C₁₉	—	2	1	no	—
64	C₂×Q₈×C₁₉	—	2	1	no	—
65	C₂×Q₈×C₁₉	—	8	2	no	—
66	C₂×D₄×C₁₉	—	2	4	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	8	no	—
72	C₂²×C₄×C₁₉	—	2	4	no	—
73	C₂²×C₄×C₁₉	—	4	2	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	8	4	no	—
77	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	M₁₆×C₁₉	—	4	2	no	—
83	M₁₆×C₁₉	—	4	2	no	—
84	C₂×C₈×C₁₉	—	4	2	no	—
85	C₂×C₈×C₁₉	—	4	2	no	—
86	C₄⋊C₄×C₁₉	—	2	8	no	—
87	C₄⋊C₄×C₁₉	—	2	8	no	—
88	C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₄⋊C₄×C₁₉	—	2	2	no	—
90	C₄⋊C₄×C₁₉	—	2	2	no	—
91	C₄⋊C₄×C₁₉	—	2	4	no	—
92	C₄⋊C₄×C₁₉	—	2	4	no	—
93	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
94	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
95	C₂²⋊C₄×C₁₉	—	2	8	no	—
96	C₂²⋊C₄×C₁₉	—	2	4	no	—
97	C₄²×C₁₉	—	2	2	no	—
98	C₄²×C₁₉	—	2	2	no	—
99	C₄²×C₁₉	C₂×D₄	1	2	yes	—
100	C₄²×C₁₉	C₂×D₄	1	2	yes	—
101	#8398	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂³×C₁₉	—	2	4	no	—
103	C₂³×C₁₉	—	2	2	no	—
104	C₂³×C₁₉	—	4	2	no	—
105	C₂³×C₁₉	—	4	1	no	—
106	C₂³×C₁₉	—	4	1	no	—
107	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	Q₈×C₁₉	—	4	2	no	—
109	Q₈×C₁₉	—	4	2	no	—
110	Q₈×C₁₉	—	8	4	no	—
111	D₄×C₁₉	—	2	4	no	—
112	D₄×C₁₉	—	2	2	no	—
113	D₄×C₁₉	#101	1	4	yes	complemented
114	C₂×C₄×C₁₉	—	2	2	no	—
115	C₂×C₄×C₁₉	—	2	2	no	—
116	C₂×C₄×C₁₉	—	2	2	no	—
117	C₂×C₄×C₁₉	—	2	2	no	—
118	C₂×C₄×C₁₉	—	2	4	no	—
119	C₂×C₄×C₁₉	—	2	2	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	4	1	no	—
122	C₂×C₄×C₁₉	—	4	4	no	—
123	C₂×C₄×C₁₉	—	4	1	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	4	no	—
126	C₂×C₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	8	8	no	—
129	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#120	1	2	yes	—
132	C₂×C₄×C₁₉	#120	1	2	yes	—
133	C₂×C₄×C₁₉	#135	1	2	yes	—
134	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
136	C₈×C₁₉	—	8	2	no	—
137	C₈×C₁₉	—	8	2	no	—
138	C₂×#554	C₂×C₁₉	1	1	yes	characteristic
139	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
140	#1549	C₂×C₁₉	1	2	yes	complemented
141	#1486	C₂×C₁₉	1	2	yes	—
142	#1461	C₂×C₁₉	1	1	yes	characteristic, complemented
143	C₂²×C₁₉	—	2	1	no	—
144	C₂²×C₁₉	—	2	1	no	—
145	C₂²×C₁₉	—	2	4	no	—
146	C₂²×C₁₉	—	4	4	no	—
147	C₂²×C₁₉	—	4	4	no	—
148	C₂²×C₁₉	—	4	2	no	—
149	C₂²×C₁₉	—	4	2	no	—
150	C₂²×C₁₉	#379	1	1	yes	characteristic
151	C₂²×C₁₉	#416	1	1	yes	characteristic
152	C₂²×C₁₉	#417	1	1	yes	characteristic
153	C₄×C₁₉	—	2	2	no	—
154	C₄×C₁₉	—	2	1	no	—
155	C₄×C₁₉	—	4	4	no	—
156	C₄×C₁₉	—	4	2	no	—
157	C₄×C₁₉	—	4	2	no	—
158	C₄×C₁₉	—	4	2	no	—
159	C₄×C₁₉	C₂×#101	1	2	yes	—
160	C₄×C₁₉	#449	1	2	yes	—
161	C₄×C₁₉	#452	1	2	yes	—
162	#554	—	2	4	no	—
163	#554	—	2	4	no	—
164	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
165	C₂×#125	C₄×C₁₉	1	2	yes	—
166	C₂×C₂²⋊Q₈	—	2	1	no	—
167	C₂×C₂²⋊Q₈	—	2	2	no	—
168	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
169	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
170	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
171	C₂²×C₄⋊C₄	—	2	1	no	—
172	#431	C₂²×C₁₉	1	2	yes	—
173	#423	C₂²×C₁₉	1	2	yes	—
174	C₂×#101	—	2	1	no	—
175	#343	—	2	1	no	—
176	#332	—	2	4	no	—
177	D₄⋊C₈	—	2	4	no	—
178	#324	—	2	2	no	—
179	C₂×C₁₉	—	2	1	no	—
180	C₂×C₁₉	—	2	1	no	—
181	C₂×C₁₉	—	4	4	no	—
182	C₂×C₁₉	#1784	1	1	yes	characteristic
183	C₂×C₁₉	#1788	1	1	yes	characteristic
184	C₂×C₁₉	#1795	1	1	yes	characteristic
185	C₂²×Q₈	—	2	1	no	—
186	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
187	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
188	C₂³×C₄	—	2	1	no	—
189	C₂³×C₄	—	2	2	no	—
190	C₂×M₁₆	—	2	2	no	—
191	C₄⋊Q₈	—	2	2	no	—
192	C₄⋊Q₈	D₄×C₁₉	1	4	yes	—
193	#125	—	2	4	no	—
194	#125	—	2	4	no	—
195	C₂²⋊Q₈	—	2	8	no	—
196	C₂²⋊Q₈	—	2	16	no	—
197	C₄×Q₈	—	2	2	no	—
198	C₄×Q₈	—	2	2	no	—
199	C₄×D₄	—	2	4	no	—
200	C₄×D₄	—	2	4	no	—
201	C₄×D₄	—	2	2	no	—
202	C₄×D₄	D₄×C₁₉	1	4	yes	—
203	C₂×C₄⋊C₄	—	2	8	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	—	2	1	no	—
207	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
208	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
209	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
210	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
211	C₂×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₂²⋊C₄	—	2	1	no	—
213	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
214	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
215	C₄⋊C₈	—	2	2	no	—
216	C₄⋊C₈	—	2	2	no	—
217	C₄⋊C₈	—	2	2	no	—
218	#101	—	4	2	no	—
219	C₂²⋊C₈	—	2	2	no	—
220	C₄×C₈	—	2	2	no	—
221	C₁₉	#8398	1	1	yes	characteristic, direct product factor, Sylow
222	C₂⁴	—	2	1	no	—
223	C₂×Q₈	—	2	2	no	—
224	C₂×Q₈	—	2	4	no	—
225	C₂×Q₈	—	2	2	no	—
226	C₂×Q₈	—	2	1	no	—
227	C₂×Q₈	—	2	1	no	—
228	C₂×Q₈	—	8	2	no	—
229	C₂×D₄	—	2	4	no	—
230	C₂×D₄	—	2	1	no	—
231	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
232	C₂²×C₄	—	2	1	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	8	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	4	2	no	—
237	C₂²×C₄	—	4	1	no	—
238	C₂²×C₄	—	4	1	no	—
239	C₂²×C₄	—	8	4	no	—
240	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
241	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
243	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
244	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
245	M₁₆	—	4	2	no	—
246	M₁₆	—	4	2	no	—
247	C₂×C₈	—	4	2	no	—
248	C₂×C₈	—	4	2	no	—
249	C₄⋊C₄	—	2	8	no	—
250	C₄⋊C₄	—	2	8	no	—
251	C₄⋊C₄	—	2	1	no	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	2	4	no	—
255	C₄⋊C₄	—	2	4	no	—
256	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
257	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
258	C₂²⋊C₄	—	2	8	no	—
259	C₂²⋊C₄	—	2	4	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	C₂×D₄×C₁₉	1	2	yes	—
263	C₄²	C₂×D₄×C₁₉	1	2	yes	—
264	C₂³	—	2	4	no	—
265	C₂³	—	2	2	no	—
266	C₂³	—	4	2	no	—
267	C₂³	—	4	1	no	—
268	C₂³	—	4	1	no	—
269	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
270	Q₈	—	4	2	no	—
271	Q₈	—	4	2	no	—
272	Q₈	—	8	4	no	—
273	D₄	—	2	4	no	—
274	D₄	—	2	2	no	—
275	D₄	C₁₉×#101	1	4	yes	complemented
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	4	1	no	—
284	C₂×C₄	—	4	4	no	—
285	C₂×C₄	—	4	1	no	—
286	C₂×C₄	—	4	1	no	—
287	C₂×C₄	—	4	4	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	8	8	no	—
291	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
292	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
293	C₂×C₄	C₁₉×#120	1	2	yes	—
294	C₂×C₄	C₁₉×#120	1	2	yes	—
295	C₂×C₄	C₁₉×#135	1	2	yes	—
296	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
298	C₈	—	8	2	no	—
299	C₈	—	8	2	no	—
300	C₂²	—	2	1	no	—
301	C₂²	—	2	1	no	—
302	C₂²	—	2	4	no	—
303	C₂²	—	4	4	no	—
304	C₂²	—	4	4	no	—
305	C₂²	—	4	2	no	—
306	C₂²	—	4	2	no	—
307	C₂²	C₁₉×#379	1	1	yes	characteristic
308	C₂²	C₁₉×#416	1	1	yes	characteristic
309	C₂²	C₁₉×#417	1	1	yes	characteristic
310	C₄	—	2	1	no	—
311	C₄	—	2	2	no	—
312	C₄	—	4	2	no	—
313	C₄	—	4	2	no	—
314	C₄	—	4	4	no	—
315	C₄	—	4	2	no	—
316	C₄	C₂×C₁₉×#101	1	2	yes	—
317	C₄	C₁₉×#449	1	2	yes	—
318	C₄	C₁₉×#452	1	2	yes	—
319	C₂	—	2	1	no	—
320	C₂	—	2	1	no	—
321	C₂	—	4	4	no	—
322	C₂	C₁₉×#1784	1	1	yes	characteristic
323	C₂	C₁₉×#1788	1	1	yes	characteristic
324	C₂	C₁₉×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1801	C₂	semidirect
3. C₁₉×#1549	C₂	semidirect
5. C₁₉×#1461	C₂	semidirect
101. #8398	C₁₉	direct (N × H)
113. D₄×C₁₉	#101	semidirect
139. #1801	C₂×C₁₉	semidirect
140. #1549	C₂×C₁₉	semidirect
142. #1461	C₂×C₁₉	semidirect
221. C₁₉	#8398	direct (N × H)
275. D₄	C₁₉×#101	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#554	2
C₁₉×#1801	2
C₁₉×#1549	2
C₁₉×#1486	2
C₁₉×#1461	2
#8398	19

Subgroups — C19×#8398 #18014357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8398 #18014357