Subgroups — C₁₉×#19507 #18025466

Order 4864.

588 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3235	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2981	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1703	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1689	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1683	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1669	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1554	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#501	—	2	1	no	—
16	C₁₉×#500	—	2	1	no	—
17	C₁₉×#494	C₂²	1	1	yes	characteristic
18	C₁₉×#494	C₂²	1	1	yes	characteristic
19	C₁₉×#490	—	2	1	no	—
20	C₁₉×#487	C₂²	1	1	yes	characteristic
21	C₁₉×#487	C₂²	1	1	yes	characteristic
22	C₁₉×#486	—	2	1	no	—
23	C₁₉×#482	—	2	2	no	—
24	C₁₉×#480	—	2	2	no	—
25	C₁₉×#476	C₂²	1	2	yes	—
26	C₁₉×#474	C₂²	1	2	yes	—
27	C₁₉×#474	C₂²	1	2	yes	—
28	C₁₉×#474	C₂²	1	2	yes	—
29	C₁₉×#462	—	2	2	no	—
30	C₁₉×#451	—	2	2	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×#432	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#408	—	2	2	no	—
39	C₁₉×#335	C₂²	1	2	yes	—
40	C₁₉×#334	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	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂×Q₁₆×C₁₉	—	2	2	no	—
48	C₂×Q₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
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	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₉×#127	D₄	1	1	yes	characteristic
60	C₁₉×#125	—	2	1	no	—
61	C₁₉×#124	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×#121	—	2	1	no	—
65	C₁₉×#121	D₄	1	2	yes	—
66	C₄×Q₈×C₁₉	—	2	1	no	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₄×D₄×C₁₉	C₂³	1	2	yes	—
70	C₁₉×#117	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#107	—	2	2	no	—
75	C₁₉×#107	—	2	2	no	—
76	C₁₉×#107	—	2	2	no	—
77	C₁₉×#106	—	2	2	no	—
78	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
79	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
81	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
82	C₁₉×#103	—	2	2	no	—
83	C₁₉×#103	—	2	2	no	—
84	C₁₉×#102	—	2	2	no	—
85	C₁₉×#102	—	2	2	no	—
86	C₁₉×#102	—	2	2	no	—
87	C₁₉×#102	—	2	2	no	—
88	C₁₉×C₂²⋊C₈	—	2	1	no	—
89	C₁₉×C₂²⋊C₈	—	2	1	no	—
90	C₁₉×C₂²⋊C₈	—	2	1	no	—
91	C₁₉×C₂²⋊C₈	—	2	2	no	—
92	C₁₉×C₂²⋊C₈	—	2	2	no	—
93	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
94	C₁₉×#97	—	2	1	no	—
95	C₁₉×#97	—	2	1	no	—
96	C₄×C₈×C₁₉	—	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×Q₈×C₁₉	—	4	1	no	—
106	C₂×Q₈×C₁₉	—	8	2	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
116	Q₁₆×C₁₉	—	8	2	no	—
117	Q₁₆×C₁₉	—	8	2	no	—
118	M₁₆×C₁₉	—	8	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	8	2	no	—
123	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
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	—	2	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	—	4	1	no	—
138	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	4	1	no	—
143	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₉	#41	1	1	yes	characteristic
146	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
147	#19507	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	#121	1	1	yes	characteristic
150	Q₈×C₁₉	—	4	2	no	—
151	Q₈×C₁₉	—	4	2	no	—
152	Q₈×C₁₉	—	4	2	no	—
153	Q₈×C₁₉	—	8	1	no	—
154	Q₈×C₁₉	—	8	1	no	—
155	Q₈×C₁₉	—	8	2	no	—
156	D₄×C₁₉	—	2	4	no	—
157	D₄×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	8	1	no	—
159	D₄×C₁₉	—	8	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	8	2	no	—
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
177	C₈×C₁₉	—	2	2	no	—
178	C₈×C₁₉	—	2	2	no	—
179	C₈×C₁₉	—	4	2	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₈×C₁₉	—	4	2	no	—
182	#3235	C₂×C₁₉	1	1	yes	characteristic
183	#3226	C₂×C₁₉	1	1	yes	characteristic
184	#3209	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#2981	C₂×C₁₉	1	1	yes	characteristic
186	#1703	C₂×C₁₉	1	2	yes	complemented
187	#1689	C₂×C₁₉	1	2	yes	complemented
188	#1683	C₂×C₁₉	1	2	yes	complemented
189	#1669	C₂×C₁₉	1	2	yes	complemented
190	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#1554	C₂×C₁₉	1	1	yes	characteristic, complemented
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	C₂×#121	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	—	2	1	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	—	8	1	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	—	8	1	no	—
209	C₄×C₁₉	#576	1	2	yes	—
210	C₄×C₁₉	#578	1	2	yes	—
211	#533	C₂²×C₁₉	1	1	yes	characteristic
212	#532	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
214	#501	—	2	1	no	—
215	#500	—	2	1	no	—
216	#494	C₂²×C₁₉	1	1	yes	characteristic
217	#494	C₂²×C₁₉	1	1	yes	characteristic
218	#490	—	2	1	no	—
219	#487	C₂²×C₁₉	1	1	yes	characteristic
220	#487	C₂²×C₁₉	1	1	yes	characteristic
221	#486	—	2	1	no	—
222	#482	—	2	2	no	—
223	#480	—	2	2	no	—
224	#476	C₂²×C₁₉	1	2	yes	—
225	#474	C₂²×C₁₉	1	2	yes	—
226	#474	C₂²×C₁₉	1	2	yes	—
227	#474	C₂²×C₁₉	1	2	yes	—
228	#462	—	2	2	no	—
229	#451	—	2	2	no	—
230	#436	C₂²×C₁₉	1	2	yes	—
231	#435	—	2	2	no	—
232	C₈×D₄	C₂²×C₁₉	1	2	yes	—
233	#432	C₂²×C₁₉	1	1	yes	characteristic
234	#432	C₂²×C₁₉	1	1	yes	characteristic
235	#431	C₂²×C₁₉	1	1	yes	characteristic
236	#431	C₂²×C₁₉	1	1	yes	characteristic
237	#408	—	2	2	no	—
238	#335	C₂²×C₁₉	1	2	yes	—
239	#334	C₂²×C₁₉	1	2	yes	—
240	#333	C₂²×C₁₉	1	2	yes	—
241	#332	C₂²×C₁₉	1	2	yes	—
242	#332	C₂²×C₁₉	1	2	yes	—
243	#332	C₂²×C₁₉	1	2	yes	—
244	C₂×C₁₉	—	4	1	no	—
245	C₂×C₁₉	—	8	2	no	—
246	C₂×C₁₉	#3041	1	1	yes	characteristic
247	C₂×C₁₉	#3059	1	1	yes	characteristic
248	C₂×C₁₉	#3069	1	1	yes	characteristic
249	C₂×#41	—	2	1	no	—
250	C₂²×Q₈	—	2	1	no	—
251	C₂×Q₁₆	—	2	2	no	—
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
259	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
260	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
261	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
262	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
263	#127	D₄×C₁₉	1	1	yes	characteristic
264	#125	—	2	1	no	—
265	#124	—	2	1	no	—
266	C₂²⋊Q₈	—	2	1	no	—
267	C₂²⋊Q₈	—	2	1	no	—
268	#121	—	2	1	no	—
269	#121	D₄×C₁₉	1	2	yes	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×Q₈	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	C₂³×C₁₉	1	2	yes	—
274	#117	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
278	#107	—	2	2	no	—
279	#107	—	2	2	no	—
280	#107	—	2	2	no	—
281	#106	—	2	2	no	—
282	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
283	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
284	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
285	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
286	#103	—	2	2	no	—
287	#103	—	2	2	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
298	#97	—	2	1	no	—
299	#97	—	2	1	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
302	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
303	C₁₉	#19507	1	1	yes	characteristic, direct product factor, Sylow
304	#41	—	8	2	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	4	1	no	—
311	C₂×Q₈	—	8	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
321	Q₁₆	—	8	2	no	—
322	Q₁₆	—	8	2	no	—
323	M₁₆	—	8	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	8	2	no	—
328	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
329	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₄²	—	4	1	no	—
348	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₄²	#41×C₁₉	1	1	yes	characteristic
351	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
352	C₂³	—	2	2	no	—
353	C₂³	C₁₉×#121	1	1	yes	characteristic
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	8	1	no	—
358	Q₈	—	8	1	no	—
359	Q₈	—	8	2	no	—
360	D₄	—	2	4	no	—
361	D₄	—	8	1	no	—
362	D₄	—	8	1	no	—
363	D₄	—	8	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
376	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
377	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	4	2	no	—
398	C₄	—	8	1	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	1	no	—
402	C₄	C₁₉×#576	1	2	yes	—
403	C₄	C₁₉×#578	1	2	yes	—
404	C₂	—	4	1	no	—
405	C₂	—	8	2	no	—
406	C₂	C₁₉×#3041	1	1	yes	characteristic
407	C₂	C₁₉×#3059	1	1	yes	characteristic
408	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×#3209	C₂	semidirect
5. C₁₉×#1703	C₂	semidirect
6. C₁₉×#1689	C₂	semidirect
7. C₁₉×#1683	C₂	semidirect
8. C₁₉×#1669	C₂	semidirect
9. C₁₉×#1572	C₂	semidirect
10. C₁₉×#1556	C₂	semidirect
11. C₁₉×#1554	C₂	semidirect
147. #19507	C₁₉	direct (N × H)
184. #3209	C₂×C₁₉	semidirect
186. #1703	C₂×C₁₉	semidirect
187. #1689	C₂×C₁₉	semidirect
188. #1683	C₂×C₁₉	semidirect
189. #1669	C₂×C₁₉	semidirect
190. #1572	C₂×C₁₉	semidirect
191. #1556	C₂×C₁₉	semidirect
192. #1554	C₂×C₁₉	semidirect
303. C₁₉	#19507	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×#3235	2
C₁₉×#3226	2
C₁₉×#3209	2
C₁₉×#2981	2
C₁₉×#1703	2
C₁₉×#1689	2
C₁₉×#1683	2
C₁₉×#1669	2
C₁₉×#1572	2
C₁₉×#1556	2
C₁₉×#1554	2
#19507	19

Subgroups — C19×#19507 #18025466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19507 #18025466