Subgroups — C₁₉×#19571 #18025530

Order 4864.

550 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3229	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2986	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1704	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1692	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1684	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1672	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1544	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#500	—	2	1	no	—
16	C₁₉×#498	C₂²	1	2	yes	—
17	C₁₉×#487	—	2	1	no	—
18	C₁₉×#487	C₂²	1	2	yes	—
19	C₁₉×#484	—	2	2	no	—
20	C₁₉×#483	—	2	2	no	—
21	C₁₉×#477	C₂²	1	2	yes	—
22	C₁₉×#477	C₂²	1	2	yes	—
23	C₁₉×#475	—	2	1	no	—
24	C₁₉×#475	—	2	1	no	—
25	C₁₉×#475	—	2	1	no	—
26	C₁₉×#475	C₂²	1	2	yes	—
27	C₁₉×#470	—	2	2	no	—
28	C₁₉×#462	—	2	1	no	—
29	C₁₉×#462	C₂²	1	2	yes	—
30	C₁₉×#446	—	2	1	no	—
31	C₁₉×#446	C₂²	1	2	yes	—
32	C₈×Q₈×C₁₉	—	2	1	no	—
33	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#433	—	2	2	no	—
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#423	C₂²	1	1	yes	characteristic
39	C₁₉×#335	C₂²	1	2	yes	—
40	C₁₉×#334	C₂²	1	2	yes	—
41	C₁₉×#333	C₂²	1	2	yes	—
42	C₁₉×#333	C₂²	1	2	yes	—
43	C₁₉×#332	C₂²	1	1	yes	characteristic
44	C₁₉×#332	C₂²	1	1	yes	characteristic
45	C₁₉×#332	C₂²	1	1	yes	characteristic
46	C₁₉×#332	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂×Q₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₁₉×C₄⋊Q₈	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₉×#125	—	2	1	no	—
59	C₁₉×#125	—	2	1	no	—
60	C₁₉×C₂²⋊Q₈	—	2	1	no	—
61	C₁₉×C₂²⋊Q₈	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
64	C₄×Q₈×C₁₉	—	2	1	no	—
65	C₄×Q₈×C₁₉	—	2	1	no	—
66	C₄×Q₈×C₁₉	—	2	1	no	—
67	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
68	C₁₉×#117	—	2	1	no	—
69	C₁₉×#117	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#107	—	2	2	no	—
74	C₁₉×#107	—	2	2	no	—
75	C₁₉×#106	—	2	2	no	—
76	C₁₉×#106	—	2	2	no	—
77	C₁₉×#106	—	2	2	no	—
78	C₁₉×C₄⋊C₈	—	2	2	no	—
79	C₁₉×C₄⋊C₈	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₉×#103	—	2	2	no	—
89	C₁₉×#103	—	2	2	no	—
90	C₁₉×#103	—	2	2	no	—
91	C₁₉×#103	—	2	2	no	—
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	1	no	—
95	C₁₉×C₂²⋊C₈	—	2	1	no	—
96	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
97	C₁₉×#97	—	2	2	no	—
98	C₄×C₈×C₁₉	—	2	2	no	—
99	C₄×C₈×C₁₉	—	2	1	no	—
100	C₄×C₈×C₁₉	—	2	1	no	—
101	C₄×C₈×C₁₉	C₂³	1	2	yes	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	4	1	no	—
107	C₂×Q₈×C₁₉	—	8	2	no	—
108	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
113	Q₁₆×C₁₉	—	8	2	no	—
114	M₁₆×C₁₉	—	8	1	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	1	no	—
117	C₂×C₈×C₁₉	—	2	1	no	—
118	C₂×C₈×C₁₉	—	2	1	no	—
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₄⋊C₄×C₁₉	—	4	1	no	—
135	C₄⋊C₄×C₁₉	—	4	1	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	4	1	no	—
140	C₄²×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₉	#41	1	1	yes	characteristic
145	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
146	#19571	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₁₉	#121	1	1	yes	characteristic
148	Q₈×C₁₉	—	2	2	no	—
149	Q₈×C₁₉	—	2	2	no	—
150	Q₈×C₁₉	—	4	2	no	—
151	Q₈×C₁₉	—	4	1	no	—
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	—	4	1	no	—
154	Q₈×C₁₉	—	4	1	no	—
155	Q₈×C₁₉	—	8	2	no	—
156	Q₈×C₁₉	—	8	2	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
174	C₈×C₁₉	—	2	2	no	—
175	C₈×C₁₉	—	2	2	no	—
176	C₈×C₁₉	—	4	1	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₈×C₁₉	—	4	1	no	—
179	C₈×C₁₉	—	4	1	no	—
180	C₈×C₁₉	—	4	1	no	—
181	#3255	C₂×C₁₉	1	1	yes	characteristic
182	#3230	C₂×C₁₉	1	1	yes	characteristic
183	#3229	C₂×C₁₉	1	1	yes	characteristic
184	#2986	C₂×C₁₉	1	1	yes	characteristic
185	#1704	C₂×C₁₉	1	2	yes	complemented
186	#1692	C₂×C₁₉	1	2	yes	complemented
187	#1684	C₂×C₁₉	1	2	yes	complemented
188	#1672	C₂×C₁₉	1	2	yes	complemented
189	#1574	C₂×C₁₉	1	1	yes	characteristic
190	#1548	C₂×C₁₉	1	1	yes	characteristic
191	#1544	C₂×C₁₉	1	1	yes	characteristic
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	4	2	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₄×C₁₉	—	8	2	no	—
204	C₄×C₁₉	#471	1	2	yes	—
205	C₄×C₁₉	#577	1	1	yes	characteristic
206	C₄×C₁₉	#578	1	1	yes	characteristic
207	C₄×C₁₉	#578	1	1	yes	characteristic
208	C₄×C₁₉	#578	1	1	yes	characteristic
209	#533	C₂²×C₁₉	1	1	yes	characteristic
210	#533	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
212	#500	—	2	1	no	—
213	#498	C₂²×C₁₉	1	2	yes	—
214	#487	—	2	1	no	—
215	#487	C₂²×C₁₉	1	2	yes	—
216	#484	—	2	2	no	—
217	#483	—	2	2	no	—
218	#477	C₂²×C₁₉	1	2	yes	—
219	#477	C₂²×C₁₉	1	2	yes	—
220	#475	—	2	1	no	—
221	#475	—	2	1	no	—
222	#475	—	2	1	no	—
223	#475	C₂²×C₁₉	1	2	yes	—
224	#470	—	2	2	no	—
225	#462	—	2	1	no	—
226	#462	C₂²×C₁₉	1	2	yes	—
227	#446	—	2	1	no	—
228	#446	C₂²×C₁₉	1	2	yes	—
229	C₈×Q₈	—	2	1	no	—
230	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
231	#433	—	2	2	no	—
232	#431	C₂²×C₁₉	1	1	yes	characteristic
233	#431	C₂²×C₁₉	1	1	yes	characteristic
234	#431	C₂²×C₁₉	1	1	yes	characteristic
235	#423	C₂²×C₁₉	1	1	yes	characteristic
236	#335	C₂²×C₁₉	1	2	yes	—
237	#334	C₂²×C₁₉	1	2	yes	—
238	#333	C₂²×C₁₉	1	2	yes	—
239	#333	C₂²×C₁₉	1	2	yes	—
240	#332	C₂²×C₁₉	1	1	yes	characteristic
241	#332	C₂²×C₁₉	1	1	yes	characteristic
242	#332	C₂²×C₁₉	1	1	yes	characteristic
243	#332	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×C₁₉	—	4	1	no	—
245	C₂×C₁₉	#3044	1	1	yes	characteristic
246	C₂×C₁₉	#3063	1	1	yes	characteristic
247	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
248	C₂²×Q₈	—	2	1	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
255	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
256	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
257	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
258	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
259	#125	—	2	1	no	—
260	#125	—	2	1	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	—	2	1	no	—
264	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
269	#117	—	2	1	no	—
270	#117	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
274	#107	—	2	2	no	—
275	#107	—	2	2	no	—
276	#106	—	2	2	no	—
277	#106	—	2	2	no	—
278	#106	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
283	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
284	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
285	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
286	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
287	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
289	#103	—	2	2	no	—
290	#103	—	2	2	no	—
291	#103	—	2	2	no	—
292	#103	—	2	2	no	—
293	#103	—	2	2	no	—
294	#103	—	2	2	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	—	2	1	no	—
297	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
298	#97	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	C₂³×C₁₉	1	2	yes	—
303	C₁₉	#19571	1	1	yes	characteristic, direct product factor, Sylow
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×Q₈	—	8	2	no	—
310	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
315	Q₁₆	—	8	2	no	—
316	M₁₆	—	8	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
323	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	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	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	1	no	—
344	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₄²	#41×C₁₉	1	1	yes	characteristic
347	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
348	C₂³	C₁₉×#121	1	1	yes	characteristic
349	Q₈	—	2	2	no	—
350	Q₈	—	2	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	1	no	—
353	Q₈	—	4	1	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	8	2	no	—
357	Q₈	—	8	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
370	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
371	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	2	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	1	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	1	no	—
381	C₈	—	4	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	8	1	no	—
392	C₄	—	8	1	no	—
393	C₄	—	8	2	no	—
394	C₄	C₁₉×#471	1	2	yes	—
395	C₄	C₁₉×#577	1	1	yes	characteristic
396	C₄	C₁₉×#578	1	1	yes	characteristic
397	C₄	C₁₉×#578	1	1	yes	characteristic
398	C₄	C₁₉×#578	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	C₁₉×#3044	1	1	yes	characteristic
401	C₂	C₁₉×#3063	1	1	yes	characteristic
402	C₂	C₂×C₁₉×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#121
LCS	G ▷ 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
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1692	C₂	semidirect
7. C₁₉×#1684	C₂	semidirect
8. C₁₉×#1672	C₂	semidirect
146. #19571	C₁₉	direct (N × H)
185. #1704	C₂×C₁₉	semidirect
186. #1692	C₂×C₁₉	semidirect
187. #1684	C₂×C₁₉	semidirect
188. #1672	C₂×C₁₉	semidirect
303. C₁₉	#19571	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×#3255	2
C₁₉×#3230	2
C₁₉×#3229	2
C₁₉×#2986	2
C₁₉×#1704	2
C₁₉×#1692	2
C₁₉×#1684	2
C₁₉×#1672	2
C₁₉×#1574	2
C₁₉×#1548	2
C₁₉×#1544	2
#19571	19

Subgroups — C19×#19571 #18025530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19571 #18025530