Subgroups — C₁₉×#10192 #18016151

Order 4864.

678 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₁₉×#532	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
12	C₁₉×#496	—	2	2	no	—
13	C₁₉×#493	—	2	1	no	—
14	C₁₉×#493	—	2	1	no	—
15	C₁₉×#492	—	2	1	no	—
16	C₁₉×#486	—	2	1	no	—
17	C₁₉×#474	—	2	1	no	—
18	C₁₉×#474	—	2	1	no	—
19	C₁₉×#466	—	2	2	no	—
20	C₁₉×#459	—	2	2	no	—
21	C₁₉×#459	—	2	1	no	—
22	C₁₉×#459	—	2	1	no	—
23	C₁₉×#447	—	2	2	no	—
24	C₁₉×#431	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#104	—	2	2	no	—
27	C₂×C₁₉×#102	—	2	2	no	—
28	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#327	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
37	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
38	C₂×SD₁₆×C₁₉	—	2	4	no	—
39	C₂×D₈×C₁₉	—	2	4	no	—
40	C₂×D₈×C₁₉	—	2	4	no	—
41	C₂×D₈×C₁₉	—	2	2	no	—
42	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
43	C₂²×C₈×C₁₉	D₄	1	2	yes	—
44	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
45	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
46	C₁₉×#127	—	2	1	no	—
47	C₁₉×#127	—	2	1	no	—
48	C₁₉×#127	—	2	1	no	—
49	C₁₉×#127	D₄	1	1	yes	characteristic
50	C₁₉×#127	D₄	1	1	yes	characteristic
51	C₁₉×#127	D₄	1	2	yes	—
52	C₁₉×#124	—	2	1	no	—
53	C₁₉×#124	—	2	1	no	—
54	C₁₉×#121	—	2	1	no	—
55	C₁₉×#121	—	2	1	no	—
56	C₁₉×#121	—	2	1	no	—
57	C₁₉×#121	—	2	1	no	—
58	C₄×D₄×C₁₉	—	2	1	no	—
59	C₄×D₄×C₁₉	—	2	1	no	—
60	C₄×D₄×C₁₉	—	2	1	no	—
61	C₄×D₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×#107	—	2	2	no	—
66	C₁₉×C₄⋊C₈	—	2	1	no	—
67	C₁₉×C₄⋊C₈	—	2	1	no	—
68	C₁₉×C₄⋊C₈	—	2	1	no	—
69	C₁₉×#104	—	4	4	no	—
70	C₁₉×#102	—	2	4	no	—
71	C₁₉×#102	—	2	2	no	—
72	C₁₉×#102	—	2	2	no	—
73	C₁₉×#102	—	4	4	no	—
74	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
75	C₁₉×#97	—	2	1	no	—
76	C₄×C₈×C₁₉	—	2	1	no	—
77	C₄×C₈×C₁₉	—	2	1	no	—
78	C₁₉×#95	—	2	1	no	—
79	C₂⁴×C₁₉	—	4	1	no	—
80	#41×C₁₉	—	4	2	no	—
81	#41×C₁₉	—	4	2	no	—
82	#41×C₁₉	—	4	2	no	—
83	#41×C₁₉	—	4	2	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	2	1	no	—
87	C₂×D₄×C₁₉	—	2	1	no	—
88	C₂×D₄×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	4	2	no	—
96	C₂×D₄×C₁₉	—	4	2	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	—	4	1	no	—
101	C₂×D₄×C₁₉	—	4	1	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	8	2	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	SD₁₆×C₁₉	—	4	8	no	—
112	D₈×C₁₉	—	4	8	no	—
113	D₈×C₁₉	—	8	4	no	—
114	D₈×C₁₉	—	8	2	no	—
115	M₁₆×C₁₉	—	2	2	no	—
116	M₁₆×C₁₉	D₈	1	4	yes	complemented
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	—	4	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
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	1	no	—
126	C₄⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	1	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₄²×C₁₉	—	4	2	no	—
132	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₉	#41	1	1	yes	characteristic
136	#10192	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	8	2	no	—
141	C₂³×C₁₉	—	8	2	no	—
142	C₂³×C₁₉	—	8	1	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	#127	1	1	yes	characteristic
145	Q₈×C₁₉	—	4	2	no	—
146	Q₈×C₁₉	—	4	2	no	—
147	D₄×C₁₉	—	4	2	no	—
148	D₄×C₁₉	—	4	4	no	—
149	D₄×C₁₉	—	4	4	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	4	4	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	4	1	no	—
154	D₄×C₁₉	—	4	1	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	8	2	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	8	1	no	—
162	D₄×C₁₉	—	8	1	no	—
163	D₄×C₁₉	—	8	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	—	8	2	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	4	1	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	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	—	8	2	no	—
175	C₂×C₄×C₁₉	—	8	2	no	—
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
183	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
184	C₈×C₁₉	—	2	4	no	—
185	C₈×C₁₉	—	4	2	no	—
186	C₈×C₁₉	—	4	2	no	—
187	#3245	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#3205	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#3151	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1982	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1980	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#1502	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#1283	C₂×C₁₉	1	1	yes	characteristic, complemented
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	—	8	1	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	1	no	—
201	C₂²×C₁₉	—	8	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	2	no	—
205	C₂²×C₁₉	—	16	2	no	—
206	C₂²×C₁₉	—	16	2	no	—
207	C₂²×C₁₉	#392	1	1	yes	characteristic
208	C₂²×C₁₉	#493	1	1	yes	characteristic
209	C₂²×C₁₉	#496	1	1	yes	characteristic
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	8	2	no	—
214	C₄×C₁₉	—	8	1	no	—
215	C₄×C₁₉	—	8	1	no	—
216	C₄×C₁₉	#447	1	2	yes	—
217	C₄×C₁₉	#453	1	1	yes	characteristic
218	C₄×C₁₉	#454	1	1	yes	characteristic
219	C₄×C₁₉	#459	1	2	yes	—
220	C₂×AGL(1,ℤ/8)	—	2	2	no	—
221	#532	C₂²×C₁₉	1	1	yes	characteristic
222	#532	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
224	#496	—	2	2	no	—
225	#493	—	2	1	no	—
226	#493	—	2	1	no	—
227	#492	—	2	1	no	—
228	#486	—	2	1	no	—
229	#474	—	2	1	no	—
230	#474	—	2	1	no	—
231	#466	—	2	2	no	—
232	#459	—	2	2	no	—
233	#459	—	2	1	no	—
234	#459	—	2	1	no	—
235	#447	—	2	2	no	—
236	#431	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#104	—	2	2	no	—
239	C₂×#102	—	2	2	no	—
240	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
241	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
242	#327	—	2	2	no	—
243	C₂×C₁₉	—	2	1	no	—
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	16	1	no	—
246	C₂×C₁₉	—	16	1	no	—
247	C₂×C₁₉	—	16	2	no	—
248	C₂×C₁₉	#2006	1	1	yes	characteristic
249	C₂×C₁₉	#2008	1	1	yes	characteristic
250	C₂×C₁₉	#2011	1	1	yes	characteristic
251	C₂×#41	—	2	1	no	—
252	C₂×#41	—	2	1	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	AGL(1,ℤ/8)	—	4	4	no	—
257	AGL(1,ℤ/8)	—	4	4	no	—
258	C₂×SD₁₆	—	2	4	no	—
259	C₂×D₈	—	2	4	no	—
260	C₂×D₈	—	2	4	no	—
261	C₂×D₈	—	2	2	no	—
262	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
263	C₂²×C₈	D₄×C₁₉	1	2	yes	—
264	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
265	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
266	#127	—	2	1	no	—
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#127	D₄×C₁₉	1	2	yes	—
270	#127	D₄×C₁₉	1	1	yes	characteristic
271	#127	D₄×C₁₉	1	1	yes	characteristic
272	#124	—	2	1	no	—
273	#124	—	2	1	no	—
274	#121	—	2	1	no	—
275	#121	—	2	1	no	—
276	#121	—	2	1	no	—
277	#121	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
285	#107	—	2	2	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	#104	—	4	4	no	—
290	#102	—	2	4	no	—
291	#102	—	2	2	no	—
292	#102	—	2	2	no	—
293	#102	—	4	4	no	—
294	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
295	#97	—	2	1	no	—
296	C₄×C₈	—	2	1	no	—
297	C₄×C₈	—	2	1	no	—
298	#95	—	2	1	no	—
299	C₁₉	#10192	1	1	yes	characteristic, direct product factor, Sylow
300	C₂⁴	—	4	1	no	—
301	#41	—	4	2	no	—
302	#41	—	4	2	no	—
303	#41	—	4	2	no	—
304	#41	—	4	2	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	8	2	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	SD₁₆	—	4	8	no	—
333	D₈	—	4	8	no	—
334	D₈	—	8	4	no	—
335	D₈	—	8	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	D₈×C₁₉	1	4	yes	complemented
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	4	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₄²	—	4	2	no	—
353	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₄²	#41×C₁₉	1	1	yes	characteristic
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	—	8	2	no	—
362	C₂³	—	8	1	no	—
363	C₂³	—	8	1	no	—
364	C₂³	C₁₉×#127	1	1	yes	characteristic
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	4	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	1	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	2	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	2	no	—
379	D₄	—	8	1	no	—
380	D₄	—	8	1	no	—
381	D₄	—	8	1	no	—
382	D₄	—	8	1	no	—
383	D₄	—	8	1	no	—
384	D₄	—	8	1	no	—
385	D₄	—	8	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
397	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
398	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
399	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
400	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
401	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
402	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
403	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
404	C₈	—	2	4	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	16	2	no	—
419	C₂²	—	16	2	no	—
420	C₂²	C₁₉×#392	1	1	yes	characteristic
421	C₂²	C₁₉×#493	1	1	yes	characteristic
422	C₂²	C₁₉×#496	1	1	yes	characteristic
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	8	2	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	1	no	—
429	C₄	C₁₉×#447	1	2	yes	—
430	C₄	C₁₉×#453	1	1	yes	characteristic
431	C₄	C₁₉×#454	1	1	yes	characteristic
432	C₄	C₁₉×#459	1	2	yes	—
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	16	2	no	—
436	C₂	—	16	1	no	—
437	C₂	—	16	1	no	—
438	C₂	C₁₉×#2006	1	1	yes	characteristic
439	C₂	C₁₉×#2008	1	1	yes	characteristic
440	C₂	C₁₉×#2011	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂×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×#3245	C₂	semidirect
2. C₁₉×#3205	C₂	semidirect
3. C₁₉×#3151	C₂	semidirect
4. C₁₉×#1982	C₂	semidirect
5. C₁₉×#1980	C₂	semidirect
6. C₁₉×#1502	C₂	semidirect
7. C₁₉×#1283	C₂	semidirect
116. M₁₆×C₁₉	D₈	semidirect
136. #10192	C₁₉	direct (N × H)
187. #3245	C₂×C₁₉	semidirect
188. #3205	C₂×C₁₉	semidirect
189. #3151	C₂×C₁₉	semidirect
190. #1982	C₂×C₁₉	semidirect
191. #1980	C₂×C₁₉	semidirect
192. #1502	C₂×C₁₉	semidirect
193. #1283	C₂×C₁₉	semidirect
299. C₁₉	#10192	direct (N × H)
337. M₁₆	D₈×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3245	2
C₁₉×#3205	2
C₁₉×#3151	2
C₁₉×#1982	2
C₁₉×#1980	2
C₁₉×#1502	2
C₁₉×#1283	2
#10192	19

Subgroups — C19×#10192 #18016151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10192 #18016151