Subgroups — C₁₉×#19529 #18025488

Order 4864.

570 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3227	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3216	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1698	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1692	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1678	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1672	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1558	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1553	C₂	1	1	yes	maximal, characteristic
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×#500	—	2	1	no	—
16	C₁₉×#498	C₂²	1	1	yes	characteristic
17	C₁₉×#498	C₂²	1	1	yes	characteristic
18	C₁₉×#497	—	2	1	no	—
19	C₁₉×#489	—	2	1	no	—
20	C₁₉×#487	—	2	1	no	—
21	C₁₉×#486	C₂²	1	1	yes	characteristic
22	C₁₉×#486	C₂²	1	1	yes	characteristic
23	C₁₉×#484	—	2	2	no	—
24	C₁₉×#481	—	2	2	no	—
25	C₁₉×#477	C₂²	1	2	yes	—
26	C₁₉×#477	C₂²	1	2	yes	—
27	C₁₉×#476	—	2	2	no	—
28	C₁₉×#462	C₂²	1	2	yes	—
29	C₁₉×#460	C₂²	1	2	yes	—
30	C₁₉×#452	—	2	2	no	—
31	C₁₉×#446	—	2	2	no	—
32	C₁₉×#446	C₂²	1	2	yes	—
33	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#433	—	2	2	no	—
35	C₁₉×#432	C₂²	1	1	yes	characteristic
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#431	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	2	yes	—
44	C₁₉×#331	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×SD₁₆×C₁₉	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	—	2	1	no	—
50	C₁₉×C₄⋊Q₈	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
53	C₁₉×C₄⋊Q₈	D₄	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	C₂³	1	1	yes	characteristic
58	C₁₉×#125	—	2	1	no	—
59	C₁₉×#124	—	2	1	no	—
60	C₁₉×C₂²⋊Q₈	—	2	1	no	—
61	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
62	C₁₉×#121	—	2	1	no	—
63	C₁₉×#121	—	2	1	no	—
64	C₄×Q₈×C₁₉	—	2	1	no	—
65	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
66	C₄×D₄×C₁₉	—	2	1	no	—
67	C₄×D₄×C₁₉	—	2	1	no	—
68	C₁₉×#117	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×#107	—	2	2	no	—
73	C₁₉×#107	—	2	2	no	—
74	C₁₉×#106	—	2	2	no	—
75	C₁₉×#106	—	2	2	no	—
76	C₁₉×C₄⋊C₈	—	2	2	no	—
77	C₁₉×C₄⋊C₈	—	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×#103	—	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	D₄	1	2	yes	—
92	C₁₉×#97	—	2	2	no	—
93	C₁₉×#97	—	2	1	no	—
94	C₁₉×#97	—	2	1	no	—
95	C₄×C₈×C₁₉	—	2	2	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	—	4	1	no	—
105	C₂×Q₈×C₁₉	—	8	2	no	—
106	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	4	1	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	SD₁₆×C₁₉	—	8	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	4	1	no	—
139	C₂²⋊C₄×C₁₉	—	4	1	no	—
140	C₄²×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₁₉	#41	1	1	yes	characteristic
144	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
145	#19529	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂³×C₁₉	—	4	1	no	—
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	—	8	1	no	—
152	Q₈×C₁₉	—	8	1	no	—
153	Q₈×C₁₉	—	8	1	no	—
154	Q₈×C₁₉	—	8	2	no	—
155	D₄×C₁₉	—	4	2	no	—
156	D₄×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	8	2	no	—
159	C₂×C₄×C₁₉	—	2	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	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	—	8	2	no	—
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
175	C₈×C₁₉	—	2	2	no	—
176	C₈×C₁₉	—	2	2	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₈×C₁₉	—	4	2	no	—
179	C₈×C₁₉	—	4	2	no	—
180	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#3227	C₂×C₁₉	1	1	yes	characteristic
182	#3216	C₂×C₁₉	1	1	yes	characteristic
183	#2985	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#1698	C₂×C₁₉	1	2	yes	complemented
185	#1692	C₂×C₁₉	1	2	yes	complemented
186	#1678	C₂×C₁₉	1	2	yes	complemented
187	#1672	C₂×C₁₉	1	2	yes	complemented
188	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1558	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1553	C₂×C₁₉	1	1	yes	characteristic
191	C₂²×C₁₉	—	2	1	no	—
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	C₂×#121	1	1	yes	characteristic
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	8	1	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	—	8	1	no	—
207	C₄×C₁₉	#577	1	2	yes	—
208	C₄×C₁₉	#578	1	2	yes	—
209	#533	C₂²×C₁₉	1	1	yes	characteristic
210	#532	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	1	yes	characteristic
214	#498	C₂²×C₁₉	1	1	yes	characteristic
215	#497	—	2	1	no	—
216	#489	—	2	1	no	—
217	#487	—	2	1	no	—
218	#486	C₂²×C₁₉	1	1	yes	characteristic
219	#486	C₂²×C₁₉	1	1	yes	characteristic
220	#484	—	2	2	no	—
221	#481	—	2	2	no	—
222	#477	C₂²×C₁₉	1	2	yes	—
223	#477	C₂²×C₁₉	1	2	yes	—
224	#476	—	2	2	no	—
225	#462	C₂²×C₁₉	1	2	yes	—
226	#460	C₂²×C₁₉	1	2	yes	—
227	#452	—	2	2	no	—
228	#446	—	2	2	no	—
229	#446	C₂²×C₁₉	1	2	yes	—
230	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
231	#433	—	2	2	no	—
232	#432	C₂²×C₁₉	1	1	yes	characteristic
233	#432	C₂²×C₁₉	1	1	yes	characteristic
234	#431	C₂²×C₁₉	1	1	yes	characteristic
235	#431	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	2	yes	—
241	#331	C₂²×C₁₉	1	2	yes	—
242	C₂×C₁₉	—	4	1	no	—
243	C₂×C₁₉	—	16	1	no	—
244	C₂×C₁₉	#3044	1	1	yes	characteristic
245	C₂×C₁₉	#3057	1	1	yes	characteristic
246	C₂×C₁₉	#3068	1	1	yes	characteristic
247	C₂×#41	—	2	1	no	—
248	C₂²×Q₈	—	2	1	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	2	2	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	1	yes	characteristic
257	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
258	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
259	#127	C₂³×C₁₉	1	1	yes	characteristic
260	#125	—	2	1	no	—
261	#124	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
264	#121	—	2	1	no	—
265	#121	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	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	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
281	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
282	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
283	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
284	#103	—	2	2	no	—
285	#103	—	2	2	no	—
286	#103	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
294	#97	—	2	2	no	—
295	#97	—	2	1	no	—
296	#97	—	2	1	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
300	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
301	C₁₉	#19529	1	1	yes	characteristic, direct product factor, Sylow
302	#41	—	8	2	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×Q₈	—	8	2	no	—
309	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
319	Q₁₆	—	8	2	no	—
320	SD₁₆	—	8	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	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	—	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	C₂²⋊C₄	—	4	1	no	—
343	C₄²	—	2	2	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	—	4	1	no	—
349	C₂³	C₁₉×#121	1	1	yes	characteristic
350	Q₈	—	2	2	no	—
351	Q₈	—	2	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	8	1	no	—
354	Q₈	—	8	1	no	—
355	Q₈	—	8	1	no	—
356	Q₈	—	8	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	1	no	—
360	D₄	—	8	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	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	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	8	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
372	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
373	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	8	1	no	—
386	C₂²	—	8	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	1	no	—
397	C₄	—	8	1	no	—
398	C₄	C₁₉×#577	1	2	yes	—
399	C₄	C₁₉×#578	1	2	yes	—
400	C₂	—	4	1	no	—
401	C₂	—	16	1	no	—
402	C₂	C₁₉×#3044	1	1	yes	characteristic
403	C₂	C₁₉×#3057	1	1	yes	characteristic
404	C₂	C₁₉×#3068	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
1. C₁₉×#3230	C₂	semidirect
4. C₁₉×#2985	C₂	semidirect
5. C₁₉×#1698	C₂	semidirect
6. C₁₉×#1692	C₂	semidirect
7. C₁₉×#1678	C₂	semidirect
8. C₁₉×#1672	C₂	semidirect
9. C₁₉×#1572	C₂	semidirect
10. C₁₉×#1558	C₂	semidirect
145. #19529	C₁₉	direct (N × H)
180. #3230	C₂×C₁₉	semidirect
183. #2985	C₂×C₁₉	semidirect
184. #1698	C₂×C₁₉	semidirect
185. #1692	C₂×C₁₉	semidirect
186. #1678	C₂×C₁₉	semidirect
187. #1672	C₂×C₁₉	semidirect
188. #1572	C₂×C₁₉	semidirect
189. #1558	C₂×C₁₉	semidirect
301. C₁₉	#19529	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×#3230	2
C₁₉×#3227	2
C₁₉×#3216	2
C₁₉×#2985	2
C₁₉×#1698	2
C₁₉×#1692	2
C₁₉×#1678	2
C₁₉×#1672	2
C₁₉×#1572	2
C₁₉×#1558	2
C₁₉×#1553	2
#19529	19

Subgroups — C19×#19529 #18025488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19529 #18025488