Subgroups — C₁₉×#10243 #18016202

Order 4864.

578 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3037	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#137	—	2	1	no	—
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#500	—	2	1	no	—
14	C₁₉×#486	—	2	1	no	—
15	C₁₉×#480	—	2	2	no	—
16	C₁₉×#474	—	2	2	no	—
17	C₁₉×#464	—	2	2	no	—
18	C₁₉×#462	—	2	1	no	—
19	C₁₉×#460	—	2	1	no	—
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#423	C₂²	1	1	yes	characteristic
23	C₁₉×#417	—	2	1	no	—
24	C₁₉×#398	—	2	2	no	—
25	C₁₉×#391	—	2	1	no	—
26	C₁₉×#389	—	2	2	no	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#332	—	2	2	no	—
29	C₁₉×#327	—	2	2	no	—
30	C₁₉×Q₈⋊C₈	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
34	C₁₉×#137	—	4	2	no	—
35	C₁₉×#137	—	4	2	no	—
36	C₂×Q₁₆×C₁₉	—	2	2	no	—
37	C₂×SD₁₆×C₁₉	—	2	2	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	—	4	2	no	—
44	C₁₉×C₄⋊Q₈	—	4	2	no	—
45	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
46	C₁₉×#127	D₄	1	1	yes	characteristic
47	C₁₉×#124	—	2	1	no	—
48	C₁₉×#121	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₄×Q₈×C₁₉	—	2	1	no	—
51	C₄×Q₈×C₁₉	—	2	1	no	—
52	C₄×Q₈×C₁₉	—	2	1	no	—
53	C₄×Q₈×C₁₉	—	2	1	no	—
54	C₄×D₄×C₁₉	—	2	1	no	—
55	C₄×D₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₉	—	2	1	no	—
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×#107	—	2	4	no	—
66	C₁₉×C₄⋊C₈	—	2	1	no	—
67	C₁₉×C₄⋊C₈	—	2	1	no	—
68	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
69	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
70	C₁₉×#103	—	2	2	no	—
71	C₁₉×#102	—	2	2	no	—
72	C₁₉×#102	—	2	4	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₁₉×C₂²⋊C₈	—	2	1	no	—
75	C₄×C₈×C₁₉	—	2	1	no	—
76	C₄×C₈×C₁₉	—	2	1	no	—
77	C₁₉×#95	—	2	4	no	—
78	C₁₉×#95	D₄	1	2	yes	—
79	#41×C₁₉	—	4	1	no	—
80	#41×C₁₉	—	4	1	no	—
81	#41×C₁₉	—	4	1	no	—
82	#41×C₁₉	—	4	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	—	4	1	no	—
90	C₂×Q₈×C₁₉	—	4	1	no	—
91	C₂×Q₈×C₁₉	—	4	1	no	—
92	C₂×Q₈×C₁₉	—	4	1	no	—
93	C₂×Q₈×C₁₉	—	4	1	no	—
94	C₂×Q₈×C₁₉	—	4	1	no	—
95	C₂×Q₈×C₁₉	D₈	1	2	yes	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	Q₁₆×C₁₉	—	4	4	no	—
109	SD₁₆×C₁₉	—	4	4	no	—
110	M₁₆×C₁₉	—	4	1	no	—
111	M₁₆×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₄⋊C₄×C₁₉	—	2	4	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	4	8	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	4	1	no	—
126	C₄⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₄²×C₁₉	—	4	1	no	—
130	C₄²×C₁₉	—	4	1	no	—
131	C₄²×C₁₉	—	4	1	no	—
132	C₄²×C₁₉	—	4	1	no	—
133	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₉	#41	1	1	yes	characteristic
137	#10243	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	#120	1	1	yes	characteristic
140	Q₈×C₁₉	—	2	2	no	—
141	Q₈×C₁₉	—	2	2	no	—
142	Q₈×C₁₉	—	4	1	no	—
143	Q₈×C₁₉	—	4	1	no	—
144	Q₈×C₁₉	—	4	1	no	—
145	Q₈×C₁₉	—	4	1	no	—
146	Q₈×C₁₉	—	8	1	no	—
147	Q₈×C₁₉	—	8	1	no	—
148	Q₈×C₁₉	—	8	1	no	—
149	Q₈×C₁₉	—	8	1	no	—
150	D₄×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	4	1	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	8	1	no	—
154	D₄×C₁₉	—	8	1	no	—
155	D₄×C₁₉	—	8	1	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
180	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₈×C₁₉	—	4	2	no	—
183	C₈×C₁₉	—	4	2	no	—
184	C₈×C₁₉	—	8	1	no	—
185	#3226	C₂×C₁₉	1	1	yes	characteristic
186	#3037	C₂×C₁₉	1	1	yes	characteristic
187	#2546	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1502	C₂×C₁₉	1	1	yes	characteristic
190	#1479	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1303	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	8	1	no	—
195	C₂²×C₁₉	—	8	1	no	—
196	C₂²×C₁₉	—	8	1	no	—
197	C₂²×C₁₉	#392	1	1	yes	characteristic
198	C₂²×C₁₉	#447	1	1	yes	characteristic
199	C₂²×C₁₉	#449	1	1	yes	characteristic
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	4	4	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	8	2	no	—
206	C₄×C₁₉	—	8	1	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	#447	1	1	yes	characteristic
209	C₄×C₁₉	#449	1	1	yes	characteristic
210	C₄×C₁₉	#456	1	2	yes	—
211	C₄×C₁₉	#466	1	1	yes	characteristic
212	C₄×C₁₉	#469	1	1	yes	characteristic
213	C₂×#137	—	2	1	no	—
214	#532	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	—	2	1	no	—
216	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
218	#500	—	2	1	no	—
219	#486	—	2	1	no	—
220	#480	—	2	2	no	—
221	#474	—	2	2	no	—
222	#464	—	2	2	no	—
223	#462	—	2	1	no	—
224	#460	—	2	1	no	—
225	#431	C₂²×C₁₉	1	1	yes	characteristic
226	#431	C₂²×C₁₉	1	1	yes	characteristic
227	#423	C₂²×C₁₉	1	1	yes	characteristic
228	#417	—	2	1	no	—
229	#398	—	2	2	no	—
230	#391	—	2	1	no	—
231	#389	—	2	2	no	—
232	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
233	#332	—	2	2	no	—
234	#327	—	2	2	no	—
235	Q₈⋊C₈	—	2	2	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	16	1	no	—
239	C₂×C₁₉	#1999	1	1	yes	characteristic
240	C₂×C₁₉	#2005	1	1	yes	characteristic
241	C₂×C₁₉	#2009	1	1	yes	characteristic
242	C₂×#41	—	2	1	no	—
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
245	#137	—	4	2	no	—
246	#137	—	4	2	no	—
247	C₂×Q₁₆	—	2	2	no	—
248	C₂×SD₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	4	2	no	—
255	C₄⋊Q₈	—	4	2	no	—
256	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
257	#127	D₄×C₁₉	1	1	yes	characteristic
258	#124	—	2	1	no	—
259	#121	—	2	1	no	—
260	#121	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
276	#107	—	2	4	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
280	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
281	#103	—	2	2	no	—
282	#102	—	2	2	no	—
283	#102	—	2	4	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	—	2	1	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	—	2	1	no	—
288	#95	—	2	4	no	—
289	#95	D₄×C₁₉	1	2	yes	—
290	C₁₉	#10243	1	1	yes	characteristic, direct product factor, Sylow
291	#41	—	4	1	no	—
292	#41	—	4	1	no	—
293	#41	—	4	1	no	—
294	#41	—	4	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×Q₈	—	4	1	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	D₈×C₁₉	1	2	yes	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	Q₁₆	—	4	4	no	—
321	SD₁₆	—	4	4	no	—
322	M₁₆	—	4	1	no	—
323	M₁₆	—	4	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	4	1	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	4	8	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₄²	#41×C₁₉	1	1	yes	characteristic
349	C₂³	—	4	1	no	—
350	C₂³	C₁₉×#120	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	Q₈	—	2	2	no	—
353	Q₈	—	4	1	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	8	1	no	—
358	Q₈	—	8	1	no	—
359	Q₈	—	8	1	no	—
360	Q₈	—	8	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	1	no	—
366	D₄	—	8	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
384	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
385	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
386	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
387	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
388	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
389	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
391	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
392	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₈	—	8	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₁₉×#392	1	1	yes	characteristic
402	C₂²	C₁₉×#447	1	1	yes	characteristic
403	C₂²	C₁₉×#449	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	1	no	—
412	C₄	C₁₉×#447	1	1	yes	characteristic
413	C₄	C₁₉×#449	1	1	yes	characteristic
414	C₄	C₁₉×#456	1	2	yes	—
415	C₄	C₁₉×#466	1	1	yes	characteristic
416	C₄	C₁₉×#469	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	16	1	no	—
420	C₂	C₁₉×#1999	1	1	yes	characteristic
421	C₂	C₁₉×#2005	1	1	yes	characteristic
422	C₂	C₁₉×#2009	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ 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
3. C₁₉×#2546	C₂	semidirect
4. C₁₉×#1546	C₂	semidirect
6. C₁₉×#1479	C₂	semidirect
7. C₁₉×#1303	C₂	semidirect
137. #10243	C₁₉	direct (N × H)
187. #2546	C₂×C₁₉	semidirect
188. #1546	C₂×C₁₉	semidirect
190. #1479	C₂×C₁₉	semidirect
191. #1303	C₂×C₁₉	semidirect
290. C₁₉	#10243	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3226	2
C₁₉×#3037	2
C₁₉×#2546	2
C₁₉×#1546	2
C₁₉×#1502	2
C₁₉×#1479	2
C₁₉×#1303	2
#10243	19

Subgroups — C19×#10243 #18016202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10243 #18016202