Subgroups — C₁₉×#19518 #18025477

Order 4864.

580 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3231	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2981	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1699	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1691	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1683	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1673	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1552	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₁₉×#500	C₂²	1	1	yes	characteristic
16	C₁₉×#498	C₂²	1	1	yes	characteristic
17	C₁₉×#487	C₂²	1	1	yes	characteristic
18	C₁₉×#487	C₂²	1	1	yes	characteristic
19	C₁₉×#485	—	2	2	no	—
20	C₁₉×#479	—	2	2	no	—
21	C₁₉×#477	—	2	1	no	—
22	C₁₉×#476	C₂²	1	2	yes	—
23	C₁₉×#475	—	2	1	no	—
24	C₁₉×#474	C₂²	1	2	yes	—
25	C₁₉×#468	—	2	2	no	—
26	C₁₉×#465	—	2	2	no	—
27	C₁₉×#461	C₂²	1	2	yes	—
28	C₁₉×#461	C₂²	1	2	yes	—
29	C₁₉×#460	—	2	1	no	—
30	C₁₉×#460	—	2	1	no	—
31	C₁₉×#436	C₂²	1	2	yes	—
32	C₁₉×#435	—	2	2	no	—
33	C₈×D₄×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#432	C₂²	1	1	yes	characteristic
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#423	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₉×#408	—	2	2	no	—
39	C₁₉×#335	C₂²	1	2	yes	—
40	C₁₉×#335	C₂²	1	2	yes	—
41	C₁₉×#333	C₂²	1	2	yes	—
42	C₁₉×#332	C₂²	1	2	yes	—
43	C₁₉×#332	C₂²	1	2	yes	—
44	C₁₉×#332	C₂²	1	2	yes	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×SD₁₆×C₁₉	—	2	2	no	—
47	C₂×SD₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
53	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₁₉×#127	D₄	1	1	yes	characteristic
58	C₁₉×#125	—	2	1	no	—
59	C₁₉×#125	—	2	1	no	—
60	C₁₉×#124	—	2	1	no	—
61	C₁₉×C₂²⋊Q₈	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	1	no	—
65	C₁₉×#121	—	2	1	no	—
66	C₁₉×#121	D₄	1	2	yes	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	C₂³	1	2	yes	—
73	C₁₉×#117	—	2	1	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×#107	—	2	2	no	—
77	C₁₉×#107	—	2	2	no	—
78	C₁₉×#106	—	2	2	no	—
79	C₁₉×#106	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	—	2	1	no	—
82	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
83	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
85	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#103	—	2	2	no	—
88	C₁₉×#103	—	2	2	no	—
89	C₁₉×#103	—	2	2	no	—
90	C₁₉×#102	—	2	2	no	—
91	C₁₉×#102	—	2	2	no	—
92	C₁₉×C₂²⋊C₈	—	2	1	no	—
93	C₁₉×C₂²⋊C₈	—	2	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	2	no	—
95	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
96	C₁₉×#97	—	2	1	no	—
97	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	#41×C₁₉	—	8	2	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	—	2	2	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	SD₁₆×C₁₉	—	8	2	no	—
114	SD₁₆×C₁₉	—	8	2	no	—
115	M₁₆×C₁₉	—	8	2	no	—
116	M₁₆×C₁₉	—	8	1	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	8	2	no	—
121	C₂×C₈×C₁₉	—	8	1	no	—
122	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	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	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	4	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	4	1	no	—
143	C₄²×C₁₉	—	4	1	no	—
144	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₉	#41	1	1	yes	characteristic
147	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
148	#19518	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	#121	1	1	yes	characteristic
151	Q₈×C₁₉	—	4	1	no	—
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	—	4	2	no	—
154	Q₈×C₁₉	—	4	1	no	—
155	Q₈×C₁₉	—	4	1	no	—
156	Q₈×C₁₉	—	8	1	no	—
157	Q₈×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	2	2	no	—
159	D₄×C₁₉	—	2	2	no	—
160	D₄×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	8	1	no	—
162	D₄×C₁₉	—	8	2	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
180	C₈×C₁₉	—	2	2	no	—
181	C₈×C₁₉	—	2	2	no	—
182	C₈×C₁₉	—	4	2	no	—
183	C₈×C₁₉	—	4	2	no	—
184	C₈×C₁₉	—	4	2	no	—
185	#3254	C₂×C₁₉	1	1	yes	characteristic
186	#3246	C₂×C₁₉	1	1	yes	characteristic
187	#3231	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#2981	C₂×C₁₉	1	1	yes	characteristic
189	#1699	C₂×C₁₉	1	2	yes	complemented
190	#1691	C₂×C₁₉	1	2	yes	complemented
191	#1683	C₂×C₁₉	1	2	yes	complemented
192	#1673	C₂×C₁₉	1	2	yes	complemented
193	#1571	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1552	C₂×C₁₉	1	1	yes	characteristic, complemented
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	4	2	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	8	1	no	—
209	C₄×C₁₉	—	8	1	no	—
210	C₄×C₁₉	—	8	1	no	—
211	C₄×C₁₉	—	8	1	no	—
212	C₄×C₁₉	#576	1	1	yes	characteristic
213	C₄×C₁₉	#577	1	2	yes	—
214	C₄×C₁₉	#578	1	1	yes	characteristic
215	#533	C₂²×C₁₉	1	1	yes	characteristic
216	#533	C₂²×C₁₉	1	1	yes	characteristic
217	#532	C₂²×C₁₉	1	1	yes	characteristic
218	#500	C₂²×C₁₉	1	1	yes	characteristic
219	#498	C₂²×C₁₉	1	1	yes	characteristic
220	#487	C₂²×C₁₉	1	1	yes	characteristic
221	#487	C₂²×C₁₉	1	1	yes	characteristic
222	#485	—	2	2	no	—
223	#479	—	2	2	no	—
224	#477	—	2	1	no	—
225	#476	C₂²×C₁₉	1	2	yes	—
226	#475	—	2	1	no	—
227	#474	C₂²×C₁₉	1	2	yes	—
228	#468	—	2	2	no	—
229	#465	—	2	2	no	—
230	#461	C₂²×C₁₉	1	2	yes	—
231	#461	C₂²×C₁₉	1	2	yes	—
232	#460	—	2	1	no	—
233	#460	—	2	1	no	—
234	#436	C₂²×C₁₉	1	2	yes	—
235	#435	—	2	2	no	—
236	C₈×D₄	C₂²×C₁₉	1	2	yes	—
237	#432	C₂²×C₁₉	1	1	yes	characteristic
238	#431	C₂²×C₁₉	1	1	yes	characteristic
239	#423	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
241	#408	—	2	2	no	—
242	#335	C₂²×C₁₉	1	2	yes	—
243	#335	C₂²×C₁₉	1	2	yes	—
244	#333	C₂²×C₁₉	1	2	yes	—
245	#332	C₂²×C₁₉	1	2	yes	—
246	#332	C₂²×C₁₉	1	2	yes	—
247	#332	C₂²×C₁₉	1	2	yes	—
248	C₂×C₁₉	—	4	1	no	—
249	C₂×C₁₉	—	8	2	no	—
250	C₂×C₁₉	#3042	1	1	yes	characteristic
251	C₂×C₁₉	#3061	1	1	yes	characteristic
252	C₂×C₁₉	#3069	1	1	yes	characteristic
253	C₂×#41	—	2	1	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	2	2	no	—
260	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
261	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
262	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
263	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
264	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
265	#127	D₄×C₁₉	1	1	yes	characteristic
266	#125	—	2	1	no	—
267	#125	—	2	1	no	—
268	#124	—	2	1	no	—
269	C₂²⋊Q₈	—	2	1	no	—
270	C₂²⋊Q₈	—	2	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	—	2	1	no	—
273	#121	—	2	1	no	—
274	#121	D₄×C₁₉	1	2	yes	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	—	2	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	C₂³×C₁₉	1	2	yes	—
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
284	#107	—	2	2	no	—
285	#107	—	2	2	no	—
286	#106	—	2	2	no	—
287	#106	—	2	2	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
291	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
292	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
293	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
294	#103	—	2	2	no	—
295	#103	—	2	2	no	—
296	#103	—	2	2	no	—
297	#103	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	C₂²⋊C₈	—	2	1	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	—	2	2	no	—
303	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
304	#97	—	2	1	no	—
305	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
306	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
307	C₁₉	#19518	1	1	yes	characteristic, direct product factor, Sylow
308	#41	—	8	2	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
322	SD₁₆	—	8	2	no	—
323	SD₁₆	—	8	2	no	—
324	M₁₆	—	8	2	no	—
325	M₁₆	—	8	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	8	2	no	—
330	C₂×C₈	—	8	1	no	—
331	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
332	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₄²	—	4	1	no	—
352	C₄²	—	4	1	no	—
353	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₄²	#41×C₁₉	1	1	yes	characteristic
356	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	C₁₉×#121	1	1	yes	characteristic
359	Q₈	—	4	1	no	—
360	Q₈	—	4	1	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	8	1	no	—
365	Q₈	—	8	1	no	—
366	D₄	—	2	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	8	1	no	—
369	D₄	—	8	1	no	—
370	D₄	—	8	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
383	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
384	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₈	—	4	2	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	1	no	—
406	C₄	—	8	1	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	1	no	—
409	C₄	C₁₉×#576	1	1	yes	characteristic
410	C₄	C₁₉×#577	1	2	yes	—
411	C₄	C₁₉×#578	1	1	yes	characteristic
412	C₂	—	4	1	no	—
413	C₂	—	8	2	no	—
414	C₂	C₁₉×#3042	1	1	yes	characteristic
415	C₂	C₁₉×#3061	1	1	yes	characteristic
416	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
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
3. C₁₉×#3231	C₂	semidirect
5. C₁₉×#1699	C₂	semidirect
6. C₁₉×#1691	C₂	semidirect
7. C₁₉×#1683	C₂	semidirect
8. C₁₉×#1673	C₂	semidirect
9. C₁₉×#1571	C₂	semidirect
10. C₁₉×#1559	C₂	semidirect
11. C₁₉×#1552	C₂	semidirect
148. #19518	C₁₉	direct (N × H)
187. #3231	C₂×C₁₉	semidirect
189. #1699	C₂×C₁₉	semidirect
190. #1691	C₂×C₁₉	semidirect
191. #1683	C₂×C₁₉	semidirect
192. #1673	C₂×C₁₉	semidirect
193. #1571	C₂×C₁₉	semidirect
194. #1559	C₂×C₁₉	semidirect
195. #1552	C₂×C₁₉	semidirect
307. C₁₉	#19518	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×#3254	2
C₁₉×#3246	2
C₁₉×#3231	2
C₁₉×#2981	2
C₁₉×#1699	2
C₁₉×#1691	2
C₁₉×#1683	2
C₁₉×#1673	2
C₁₉×#1571	2
C₁₉×#1559	2
C₁₉×#1552	2
#19518	19

Subgroups — C19×#19518 #18025477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19518 #18025477