Subgroups — C₁₉×#19239 #18025198

Order 4864.

658 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3152	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1690	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1686	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1670	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1666	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1540	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	—	2	1	no	—
13	C₂×C₁₉×#137	—	2	1	no	—
14	C₁₉×#533	C₂²	1	1	yes	characteristic
15	C₁₉×#532	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₁₉×#498	—	2	1	no	—
18	C₁₉×#497	—	2	2	no	—
19	C₁₉×#494	C₂²	1	2	yes	—
20	C₁₉×#492	C₂²	1	2	yes	—
21	C₁₉×#487	—	2	1	no	—
22	C₁₉×#483	—	2	2	no	—
23	C₁₉×#476	—	2	1	no	—
24	C₁₉×#475	C₂²	1	2	yes	—
25	C₁₉×#475	C₂²	1	2	yes	—
26	C₁₉×#475	C₂²	1	2	yes	—
27	C₁₉×#465	—	2	2	no	—
28	C₁₉×#461	—	2	1	no	—
29	C₁₉×#460	C₂²	1	2	yes	—
30	C₁₉×#446	—	2	2	no	—
31	C₁₉×#446	C₂²	1	2	yes	—
32	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#431	C₂²	1	1	yes	characteristic
34	C₁₉×#424	—	2	1	no	—
35	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₉×#405	—	2	1	no	—
38	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#335	C₂²	1	2	yes	—
40	C₁₉×#334	C₂²	1	2	yes	—
41	C₁₉×#332	C₂²	1	2	yes	—
42	C₁₉×#332	C₂²	1	1	yes	characteristic
43	C₁₉×#332	C₂²	1	2	yes	—
44	C₁₉×#332	C₂²	1	1	yes	characteristic
45	C₁₉×#331	C₂²	1	1	yes	characteristic
46	C₁₉×#331	C₂²	1	1	yes	characteristic
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₁₉×#137	—	4	4	no	—
50	C₁₉×#137	—	4	4	no	—
51	C₂×Q₁₆×C₁₉	—	2	2	no	—
52	C₂×Q₁₆×C₁₉	—	2	2	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	2	no	—
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
57	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₉×#127	C₂³	1	1	yes	characteristic
68	C₁₉×#125	—	2	1	no	—
69	C₁₉×#124	—	2	1	no	—
70	C₁₉×C₂²⋊Q₈	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
72	C₁₉×#121	—	2	1	no	—
73	C₁₉×#121	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
76	C₄×D₄×C₁₉	—	2	1	no	—
77	C₄×D₄×C₁₉	—	2	1	no	—
78	C₁₉×#117	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#106	—	2	2	no	—
83	C₁₉×#106	—	2	2	no	—
84	C₁₉×#106	—	2	2	no	—
85	C₁₉×C₄⋊C₈	—	2	2	no	—
86	C₁₉×C₄⋊C₈	—	2	2	no	—
87	C₁₉×C₄⋊C₈	—	2	1	no	—
88	C₁₉×C₄⋊C₈	—	2	1	no	—
89	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
92	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₁₉×#103	—	2	2	no	—
95	C₁₉×#103	—	2	2	no	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#102	—	2	2	no	—
98	C₁₉×C₂²⋊C₈	—	2	1	no	—
99	C₁₉×#97	—	2	2	no	—
100	C₁₉×#97	D₄	1	2	yes	—
101	C₄×C₈×C₁₉	—	2	2	no	—
102	C₄×C₈×C₁₉	—	2	1	no	—
103	C₄×C₈×C₁₉	C₂³	1	2	yes	—
104	#41×C₁₉	—	4	2	no	—
105	#41×C₁₉	—	4	2	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	4	1	no	—
110	C₂×Q₈×C₁₉	—	4	2	no	—
111	C₂×Q₈×C₁₉	—	4	2	no	—
112	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
122	Q₁₆×C₁₉	—	4	4	no	—
123	Q₁₆×C₁₉	—	4	4	no	—
124	SD₁₆×C₁₉	—	4	4	no	—
125	SD₁₆×C₁₉	—	4	4	no	—
126	SD₁₆×C₁₉	—	8	2	no	—
127	M₁₆×C₁₉	—	2	2	no	—
128	M₁₆×C₁₉	SD₁₆	1	4	yes	complemented
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	4	2	no	—
135	C₂×C₈×C₁₉	—	8	1	no	—
136	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²⋊C₄×C₁₉	—	2	2	no	—
151	C₂²⋊C₄×C₁₉	—	4	1	no	—
152	C₂²⋊C₄×C₁₉	—	4	1	no	—
153	C₄²×C₁₉	—	2	2	no	—
154	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₉	#41	1	1	yes	characteristic
157	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
158	#19239	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	#121	1	1	yes	characteristic
161	Q₈×C₁₉	—	2	2	no	—
162	Q₈×C₁₉	—	2	2	no	—
163	Q₈×C₁₉	—	4	2	no	—
164	Q₈×C₁₉	—	4	1	no	—
165	Q₈×C₁₉	—	4	2	no	—
166	Q₈×C₁₉	—	4	1	no	—
167	Q₈×C₁₉	—	8	1	no	—
168	Q₈×C₁₉	—	8	2	no	—
169	D₄×C₁₉	—	4	1	no	—
170	D₄×C₁₉	—	4	1	no	—
171	D₄×C₁₉	—	4	1	no	—
172	D₄×C₁₉	—	4	1	no	—
173	D₄×C₁₉	—	8	1	no	—
174	D₄×C₁₉	—	8	2	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	8	2	no	—
183	C₂×C₄×C₁₉	—	8	2	no	—
184	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
188	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
192	C₈×C₁₉	—	2	2	no	—
193	C₈×C₁₉	—	4	1	no	—
194	C₈×C₁₉	—	4	1	no	—
195	C₈×C₁₉	—	4	1	no	—
196	C₈×C₁₉	—	4	2	no	—
197	C₈×C₁₉	—	4	1	no	—
198	C₈×C₁₉	C₂×SD₁₆	1	4	yes	—
199	#3246	C₂×C₁₉	1	1	yes	characteristic
200	#3229	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#3152	C₂×C₁₉	1	1	yes	characteristic
202	#2962	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#1690	C₂×C₁₉	1	2	yes	complemented
204	#1686	C₂×C₁₉	1	2	yes	complemented
205	#1670	C₂×C₁₉	1	2	yes	complemented
206	#1666	C₂×C₁₉	1	2	yes	complemented
207	#1565	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1540	C₂×C₁₉	1	1	yes	characteristic
209	C₂×#332	C₂×C₁₉	1	1	yes	characteristic, complemented
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	8	1	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	#460	1	2	yes	—
216	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	4	2	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	—	8	2	no	—
224	C₄×C₁₉	#460	1	2	yes	—
225	C₄×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
226	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₄×C₁₉	#577	1	1	yes	characteristic
228	C₄×C₁₉	#578	1	1	yes	characteristic
229	C₂×#137	—	2	1	no	—
230	C₂×#137	—	2	1	no	—
231	#533	C₂²×C₁₉	1	1	yes	characteristic
232	#532	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	#498	—	2	1	no	—
235	#497	—	2	2	no	—
236	#494	C₂²×C₁₉	1	2	yes	—
237	#492	C₂²×C₁₉	1	2	yes	—
238	#487	—	2	1	no	—
239	#483	—	2	2	no	—
240	#476	—	2	1	no	—
241	#475	C₂²×C₁₉	1	2	yes	—
242	#475	C₂²×C₁₉	1	2	yes	—
243	#475	C₂²×C₁₉	1	2	yes	—
244	#465	—	2	2	no	—
245	#461	—	2	1	no	—
246	#460	C₂²×C₁₉	1	2	yes	—
247	#446	—	2	2	no	—
248	#446	C₂²×C₁₉	1	2	yes	—
249	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
250	#431	C₂²×C₁₉	1	1	yes	characteristic
251	#424	—	2	1	no	—
252	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
254	#405	—	2	1	no	—
255	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
256	#335	C₂²×C₁₉	1	2	yes	—
257	#334	C₂²×C₁₉	1	2	yes	—
258	#332	C₂²×C₁₉	1	2	yes	—
259	#332	C₂²×C₁₉	1	2	yes	—
260	#332	C₂²×C₁₉	1	1	yes	characteristic
261	#332	C₂²×C₁₉	1	1	yes	characteristic
262	#331	C₂²×C₁₉	1	1	yes	characteristic
263	#331	C₂²×C₁₉	1	1	yes	characteristic
264	C₂×C₁₉	—	2	2	no	—
265	C₂×C₁₉	—	16	1	no	—
266	C₂×C₁₉	C₂×#460	1	1	yes	characteristic
267	C₂×C₁₉	#3063	1	1	yes	characteristic
268	C₂×C₁₉	#3069	1	1	yes	characteristic
269	C₂×#41	—	2	1	no	—
270	C₂²×Q₈	—	2	1	no	—
271	#137	—	4	4	no	—
272	#137	—	4	4	no	—
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×Q₁₆	—	2	2	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
279	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
286	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
287	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
288	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
289	#127	C₂³×C₁₉	1	1	yes	characteristic
290	#125	—	2	1	no	—
291	#124	—	2	1	no	—
292	C₂²⋊Q₈	—	2	1	no	—
293	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
294	#121	—	2	1	no	—
295	#121	—	2	1	no	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	#117	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
304	#106	—	2	2	no	—
305	#106	—	2	2	no	—
306	#106	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
314	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
316	#103	—	2	2	no	—
317	#103	—	2	2	no	—
318	#103	—	2	2	no	—
319	#102	—	2	2	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	#97	—	2	2	no	—
322	#97	D₄×C₁₉	1	2	yes	—
323	C₄×C₈	—	2	2	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	C₂³×C₁₉	1	2	yes	—
326	C₁₉	#19239	1	1	yes	characteristic, direct product factor, Sylow
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	4	1	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
345	Q₁₆	—	4	4	no	—
346	Q₁₆	—	4	4	no	—
347	SD₁₆	—	4	4	no	—
348	SD₁₆	—	4	4	no	—
349	SD₁₆	—	8	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	SD₁₆×C₁₉	1	4	yes	complemented
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	8	1	no	—
359	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₄²	#41×C₁₉	1	1	yes	characteristic
380	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
381	C₂³	—	4	1	no	—
382	C₂³	C₁₉×#121	1	1	yes	characteristic
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	1	no	—
389	Q₈	—	8	1	no	—
390	Q₈	—	8	2	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	8	1	no	—
396	D₄	—	8	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
407	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
408	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
409	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
410	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	C₂×SD₁₆×C₁₉	1	4	yes	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	C₁₉×#460	1	2	yes	—
427	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₁₉×#460	1	2	yes	—
436	C₄	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
437	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
438	C₄	C₁₉×#577	1	1	yes	characteristic
439	C₄	C₁₉×#578	1	1	yes	characteristic
440	C₂	—	2	2	no	—
441	C₂	—	16	1	no	—
442	C₂	C₂×C₁₉×#460	1	1	yes	characteristic
443	C₂	C₁₉×#3063	1	1	yes	characteristic
444	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
2. C₁₉×#3229	C₂	semidirect
4. C₁₉×#2962	C₂	semidirect
5. C₁₉×#1690	C₂	semidirect
6. C₁₉×#1686	C₂	semidirect
7. C₁₉×#1670	C₂	semidirect
8. C₁₉×#1666	C₂	semidirect
9. C₁₉×#1565	C₂	semidirect
11. C₂×C₁₉×#332	C₂	semidirect
128. M₁₆×C₁₉	SD₁₆	semidirect
158. #19239	C₁₉	direct (N × H)
200. #3229	C₂×C₁₉	semidirect
202. #2962	C₂×C₁₉	semidirect
203. #1690	C₂×C₁₉	semidirect
204. #1686	C₂×C₁₉	semidirect
205. #1670	C₂×C₁₉	semidirect
206. #1666	C₂×C₁₉	semidirect
207. #1565	C₂×C₁₉	semidirect
209. C₂×#332	C₂×C₁₉	semidirect
326. C₁₉	#19239	direct (N × H)
351. M₁₆	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3246	2
C₁₉×#3229	2
C₁₉×#3152	2
C₁₉×#2962	2
C₁₉×#1690	2
C₁₉×#1686	2
C₁₉×#1670	2
C₁₉×#1666	2
C₁₉×#1565	2
C₁₉×#1540	2
C₂×C₁₉×#332	2
#19239	19

Subgroups — C19×#19239 #18025198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19239 #18025198