Subgroups — C₁₉×#19535 #18025494

Order 4864.

562 conjugacy classes of subgroups.

The subgroup lattice has 412 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×#3249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3228	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×#1682	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1676	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×#1551	C₂	1	1	yes	maximal, characteristic
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×#486	C₂²	1	1	yes	characteristic
18	C₁₉×#486	C₂²	1	1	yes	characteristic
19	C₁₉×#482	—	2	2	no	—
20	C₁₉×#478	—	2	2	no	—
21	C₁₉×#477	—	2	1	no	—
22	C₁₉×#477	C₂²	1	2	yes	—
23	C₁₉×#477	C₂²	1	2	yes	—
24	C₁₉×#474	—	2	1	no	—
25	C₁₉×#468	—	2	2	no	—
26	C₁₉×#467	—	2	2	no	—
27	C₁₉×#462	—	2	1	no	—
28	C₁₉×#462	C₂²	1	2	yes	—
29	C₁₉×#461	—	2	1	no	—
30	C₁₉×#460	C₂²	1	2	yes	—
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×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#423	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₉×#335	C₂²	1	2	yes	—
40	C₁₉×#335	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	C₂×Q₁₆×C₁₉	—	2	2	no	—
47	C₂×SD₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
51	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
52	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
53	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₁₉×#127	C₂³	1	1	yes	characteristic
56	C₁₉×#125	—	2	1	no	—
57	C₁₉×#125	—	2	1	no	—
58	C₁₉×#124	—	2	1	no	—
59	C₁₉×C₂²⋊Q₈	—	2	1	no	—
60	C₁₉×C₂²⋊Q₈	—	2	1	no	—
61	C₁₉×C₂²⋊Q₈	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
63	C₁₉×#121	—	2	1	no	—
64	C₁₉×#121	—	2	1	no	—
65	C₄×Q₈×C₁₉	—	2	1	no	—
66	C₄×Q₈×C₁₉	—	2	1	no	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
69	C₄×D₄×C₁₉	—	2	1	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₁₉×#117	—	2	1	no	—
72	C₁₉×#117	—	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	—	2	2	no	—
79	C₁₉×C₄⋊C₈	—	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×#102	—	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	D₄	1	2	yes	—
94	C₁₉×#97	—	2	2	no	—
95	C₁₉×#97	—	2	1	no	—
96	C₄×C₈×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	4	1	no	—
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	SD₁₆×C₁₉	—	8	2	no	—
115	M₁₆×C₁₉	—	8	1	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	8	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	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	C₂×D₄	1	2	yes	—
136	C₂²⋊C₄×C₁₉	—	2	2	no	—
137	C₂²⋊C₄×C₁₉	—	4	1	no	—
138	C₂²⋊C₄×C₁₉	—	4	1	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	#19535	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	#121	1	1	yes	characteristic
149	Q₈×C₁₉	—	2	2	no	—
150	Q₈×C₁₉	—	2	2	no	—
151	Q₈×C₁₉	—	4	1	no	—
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	—	8	1	no	—
154	Q₈×C₁₉	—	8	1	no	—
155	Q₈×C₁₉	—	8	1	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	4	2	no	—
158	D₄×C₁₉	—	4	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	2	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	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	#3254	C₂×C₁₉	1	1	yes	characteristic
183	#3249	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#3228	C₂×C₁₉	1	1	yes	characteristic
185	#2985	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#1698	C₂×C₁₉	1	2	yes	complemented
187	#1692	C₂×C₁₉	1	2	yes	complemented
188	#1682	C₂×C₁₉	1	2	yes	complemented
189	#1676	C₂×C₁₉	1	2	yes	complemented
190	#1571	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#1551	C₂×C₁₉	1	1	yes	characteristic
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	8	1	no	—
197	C₂²×C₁₉	—	8	1	no	—
198	C₂²×C₁₉	—	8	1	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	—	4	2	no	—
206	C₄×C₁₉	—	8	1	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	—	8	1	no	—
209	C₄×C₁₉	#576	1	1	yes	characteristic
210	C₄×C₁₉	#578	1	2	yes	—
211	C₄×C₁₉	#578	1	1	yes	characteristic
212	#533	C₂²×C₁₉	1	1	yes	characteristic
213	#533	C₂²×C₁₉	1	1	yes	characteristic
214	#532	C₂²×C₁₉	1	1	yes	characteristic
215	#500	C₂²×C₁₉	1	1	yes	characteristic
216	#498	C₂²×C₁₉	1	1	yes	characteristic
217	#486	C₂²×C₁₉	1	1	yes	characteristic
218	#486	C₂²×C₁₉	1	1	yes	characteristic
219	#482	—	2	2	no	—
220	#478	—	2	2	no	—
221	#477	—	2	1	no	—
222	#477	C₂²×C₁₉	1	2	yes	—
223	#477	C₂²×C₁₉	1	2	yes	—
224	#474	—	2	1	no	—
225	#468	—	2	2	no	—
226	#467	—	2	2	no	—
227	#462	—	2	1	no	—
228	#462	C₂²×C₁₉	1	2	yes	—
229	#461	—	2	1	no	—
230	#460	C₂²×C₁₉	1	2	yes	—
231	#446	—	2	2	no	—
232	#446	C₂²×C₁₉	1	2	yes	—
233	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
234	#433	—	2	2	no	—
235	#432	C₂²×C₁₉	1	1	yes	characteristic
236	#431	C₂²×C₁₉	1	1	yes	characteristic
237	#423	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
239	#335	C₂²×C₁₉	1	2	yes	—
240	#335	C₂²×C₁₉	1	2	yes	—
241	#333	C₂²×C₁₉	1	2	yes	—
242	#333	C₂²×C₁₉	1	2	yes	—
243	#332	C₂²×C₁₉	1	2	yes	—
244	#331	C₂²×C₁₉	1	2	yes	—
245	C₂×C₁₉	—	4	1	no	—
246	C₂×C₁₉	—	16	1	no	—
247	C₂×C₁₉	#3044	1	1	yes	characteristic
248	C₂×C₁₉	#3061	1	1	yes	characteristic
249	C₂×C₁₉	#3068	1	1	yes	characteristic
250	C₂×#41	—	2	1	no	—
251	C₂×Q₁₆	—	2	2	no	—
252	C₂×SD₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
256	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
257	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
258	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
259	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
260	#127	C₂³×C₁₉	1	1	yes	characteristic
261	#125	—	2	1	no	—
262	#125	—	2	1	no	—
263	#124	—	2	1	no	—
264	C₂²⋊Q₈	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	—	2	1	no	—
267	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
268	#121	—	2	1	no	—
269	#121	—	2	1	no	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×Q₈	—	2	1	no	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	#117	—	2	1	no	—
277	#117	—	2	1	no	—
278	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
279	#107	—	2	2	no	—
280	#107	—	2	2	no	—
281	#107	—	2	2	no	—
282	#106	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
288	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
289	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
290	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
291	#103	—	2	2	no	—
292	#103	—	2	2	no	—
293	#103	—	2	2	no	—
294	#102	—	2	2	no	—
295	#102	—	2	2	no	—
296	#102	—	2	2	no	—
297	C₂²⋊C₈	—	2	1	no	—
298	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
299	#97	—	2	2	no	—
300	#97	—	2	1	no	—
301	C₄×C₈	—	2	2	no	—
302	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
303	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
304	C₁₉	#19535	1	1	yes	characteristic, direct product factor, Sylow
305	#41	—	8	2	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	C₂×D₄×C₁₉	1	2	yes	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	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	M₁₆	—	8	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	8	1	no	—
326	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	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	C₂×D₄×C₁₉	1	2	yes	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₄²	—	2	2	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	—	4	1	no	—
353	C₂³	C₁₉×#121	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	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	2	no	—
363	D₄	—	4	1	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
377	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
380	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	—	8	1	no	—
392	C₂²	—	8	1	no	—
393	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	C₁₉×#576	1	1	yes	characteristic
404	C₄	C₁₉×#578	1	2	yes	—
405	C₄	C₁₉×#578	1	1	yes	characteristic
406	C₂	—	4	1	no	—
407	C₂	—	16	1	no	—
408	C₂	C₁₉×#3044	1	1	yes	characteristic
409	C₂	C₁₉×#3061	1	1	yes	characteristic
410	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
2. C₁₉×#3249	C₂	semidirect
4. C₁₉×#2985	C₂	semidirect
5. C₁₉×#1698	C₂	semidirect
6. C₁₉×#1692	C₂	semidirect
7. C₁₉×#1682	C₂	semidirect
8. C₁₉×#1676	C₂	semidirect
9. C₁₉×#1571	C₂	semidirect
10. C₁₉×#1559	C₂	semidirect
146. #19535	C₁₉	direct (N × H)
183. #3249	C₂×C₁₉	semidirect
185. #2985	C₂×C₁₉	semidirect
186. #1698	C₂×C₁₉	semidirect
187. #1692	C₂×C₁₉	semidirect
188. #1682	C₂×C₁₉	semidirect
189. #1676	C₂×C₁₉	semidirect
190. #1571	C₂×C₁₉	semidirect
191. #1559	C₂×C₁₉	semidirect
304. C₁₉	#19535	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×#3249	2
C₁₉×#3228	2
C₁₉×#2985	2
C₁₉×#1698	2
C₁₉×#1692	2
C₁₉×#1682	2
C₁₉×#1676	2
C₁₉×#1571	2
C₁₉×#1559	2
C₁₉×#1551	2
#19535	19

Subgroups — C19×#19535 #18025494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19535 #18025494