Subgroups — C₁₉×#19572 #18025531

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×#3255	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3209	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2986	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1700	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1694	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1680	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1674	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1544	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#500	C₂²	1	2	yes	—
16	C₁₉×#494	—	2	1	no	—
17	C₁₉×#487	—	2	1	no	—
18	C₁₉×#487	C₂²	1	2	yes	—
19	C₁₉×#484	—	2	2	no	—
20	C₁₉×#477	—	2	1	no	—
21	C₁₉×#477	—	2	1	no	—
22	C₁₉×#475	—	2	1	no	—
23	C₁₉×#475	C₂²	1	2	yes	—
24	C₁₉×#470	—	2	2	no	—
25	C₁₉×#462	—	2	1	no	—
26	C₁₉×#462	C₂²	1	2	yes	—
27	C₁₉×#462	C₂²	1	2	yes	—
28	C₁₉×#462	C₂²	1	2	yes	—
29	C₁₉×#451	—	2	2	no	—
30	C₁₉×#446	—	2	1	no	—
31	C₁₉×#446	C₂²	1	2	yes	—
32	C₈×Q₈×C₁₉	—	2	1	no	—
33	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#433	—	2	2	no	—
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#423	C₂²	1	1	yes	characteristic
39	C₁₉×#335	C₂²	1	2	yes	—
40	C₁₉×#334	C₂²	1	2	yes	—
41	C₁₉×#332	C₂²	1	1	yes	characteristic
42	C₁₉×#332	C₂²	1	2	yes	—
43	C₁₉×#332	C₂²	1	1	yes	characteristic
44	C₁₉×#332	C₂²	1	1	yes	characteristic
45	C₁₉×#332	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂×Q₁₆×C₁₉	—	2	2	no	—
49	C₂×Q₁₆×C₁₉	—	2	2	no	—
50	C₂×Q₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×#125	—	2	1	no	—
61	C₁₉×#125	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	1	no	—
65	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
66	C₄×Q₈×C₁₉	—	2	1	no	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
70	C₁₉×#117	—	2	1	no	—
71	C₁₉×#117	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
82	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₉×#103	—	2	2	no	—
89	C₁₉×#103	—	2	2	no	—
90	C₁₉×#103	—	2	2	no	—
91	C₁₉×#103	—	2	2	no	—
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	1	no	—
95	C₁₉×C₂²⋊C₈	—	2	1	no	—
96	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
97	C₁₉×#97	—	2	2	no	—
98	C₄×C₈×C₁₉	—	2	2	no	—
99	C₄×C₈×C₁₉	—	2	1	no	—
100	C₄×C₈×C₁₉	—	2	1	no	—
101	C₄×C₈×C₁₉	C₂³	1	2	yes	—
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	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	4	1	no	—
107	C₂×Q₈×C₁₉	—	8	1	no	—
108	C₂×Q₈×C₁₉	—	8	1	no	—
109	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
114	Q₁₆×C₁₉	—	8	2	no	—
115	Q₁₆×C₁₉	—	8	2	no	—
116	Q₁₆×C₁₉	—	8	2	no	—
117	M₁₆×C₁₉	—	8	1	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	2	1	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	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₄⋊C₄×C₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	—	4	1	no	—
140	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	4	1	no	—
145	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₉	#41	1	1	yes	characteristic
148	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
149	#19572	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	#121	1	1	yes	characteristic
151	Q₈×C₁₉	—	2	2	no	—
152	Q₈×C₁₉	—	2	2	no	—
153	Q₈×C₁₉	—	4	2	no	—
154	Q₈×C₁₉	—	4	1	no	—
155	Q₈×C₁₉	—	4	2	no	—
156	Q₈×C₁₉	—	4	2	no	—
157	Q₈×C₁₉	—	4	1	no	—
158	Q₈×C₁₉	—	4	1	no	—
159	Q₈×C₁₉	—	4	1	no	—
160	Q₈×C₁₉	—	8	2	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	8	2	no	—
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
178	C₈×C₁₉	—	2	2	no	—
179	C₈×C₁₉	—	2	2	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	4	1	no	—
183	C₈×C₁₉	—	4	1	no	—
184	C₈×C₁₉	—	4	1	no	—
185	#3255	C₂×C₁₉	1	1	yes	characteristic
186	#3230	C₂×C₁₉	1	1	yes	characteristic
187	#3209	C₂×C₁₉	1	1	yes	characteristic
188	#2986	C₂×C₁₉	1	1	yes	characteristic
189	#1700	C₂×C₁₉	1	2	yes	complemented
190	#1694	C₂×C₁₉	1	2	yes	complemented
191	#1680	C₂×C₁₉	1	2	yes	complemented
192	#1674	C₂×C₁₉	1	2	yes	complemented
193	#1574	C₂×C₁₉	1	1	yes	characteristic
194	#1546	C₂×C₁₉	1	1	yes	characteristic
195	#1544	C₂×C₁₉	1	1	yes	characteristic
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	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	—	4	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	—	8	2	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	#473	1	2	yes	—
209	C₄×C₁₉	#576	1	1	yes	characteristic
210	C₄×C₁₉	#577	1	1	yes	characteristic
211	C₄×C₁₉	#578	1	1	yes	characteristic
212	C₄×C₁₉	#578	1	1	yes	characteristic
213	#533	C₂²×C₁₉	1	1	yes	characteristic
214	#533	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
216	#500	C₂²×C₁₉	1	2	yes	—
217	#494	—	2	1	no	—
218	#487	—	2	1	no	—
219	#487	C₂²×C₁₉	1	2	yes	—
220	#484	—	2	2	no	—
221	#477	—	2	1	no	—
222	#477	—	2	1	no	—
223	#475	—	2	1	no	—
224	#475	C₂²×C₁₉	1	2	yes	—
225	#470	—	2	2	no	—
226	#462	—	2	1	no	—
227	#462	C₂²×C₁₉	1	2	yes	—
228	#462	C₂²×C₁₉	1	2	yes	—
229	#462	C₂²×C₁₉	1	2	yes	—
230	#451	—	2	2	no	—
231	#446	—	2	1	no	—
232	#446	C₂²×C₁₉	1	2	yes	—
233	C₈×Q₈	—	2	1	no	—
234	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
235	#433	—	2	2	no	—
236	#431	C₂²×C₁₉	1	1	yes	characteristic
237	#431	C₂²×C₁₉	1	1	yes	characteristic
238	#431	C₂²×C₁₉	1	1	yes	characteristic
239	#423	C₂²×C₁₉	1	1	yes	characteristic
240	#335	C₂²×C₁₉	1	2	yes	—
241	#334	C₂²×C₁₉	1	2	yes	—
242	#332	C₂²×C₁₉	1	1	yes	characteristic
243	#332	C₂²×C₁₉	1	1	yes	characteristic
244	#332	C₂²×C₁₉	1	1	yes	characteristic
245	#332	C₂²×C₁₉	1	1	yes	characteristic
246	#332	C₂²×C₁₉	1	2	yes	—
247	#332	C₂²×C₁₉	1	2	yes	—
248	C₂×C₁₉	—	4	1	no	—
249	C₂×C₁₉	#3044	1	1	yes	characteristic
250	C₂×C₁₉	#3062	1	1	yes	characteristic
251	C₂×C₁₉	C₂×#473	1	1	yes	characteristic
252	C₂²×Q₈	—	2	1	no	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×Q₁₆	—	2	2	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
261	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
262	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
263	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
264	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
265	#125	—	2	1	no	—
266	#125	—	2	1	no	—
267	C₂²⋊Q₈	—	2	1	no	—
268	C₂²⋊Q₈	—	2	1	no	—
269	C₂²⋊Q₈	—	2	1	no	—
270	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
271	C₄×Q₈	—	2	1	no	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
275	#117	—	2	1	no	—
276	#117	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
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	D₄×C₁₉	1	1	yes	characteristic
287	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
288	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
289	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
290	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
291	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
292	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
293	#103	—	2	2	no	—
294	#103	—	2	2	no	—
295	#103	—	2	2	no	—
296	#103	—	2	2	no	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	C₂²⋊C₈	—	2	1	no	—
300	C₂²⋊C₈	—	2	1	no	—
301	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
302	#97	—	2	2	no	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	C₂³×C₁₉	1	2	yes	—
307	C₁₉	#19572	1	1	yes	characteristic, direct product factor, Sylow
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	8	1	no	—
314	C₂×Q₈	—	8	1	no	—
315	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
320	Q₁₆	—	8	2	no	—
321	Q₁₆	—	8	2	no	—
322	Q₁₆	—	8	2	no	—
323	M₁₆	—	8	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	4	1	no	—
351	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₄²	#41×C₁₉	1	1	yes	characteristic
354	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
355	C₂³	C₁₉×#121	1	1	yes	characteristic
356	Q₈	—	2	2	no	—
357	Q₈	—	2	2	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	1	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	8	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	8	2	no	—
377	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
379	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
380	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	2	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	1	no	—
387	C₈	—	4	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	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	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	1	no	—
402	C₄	C₁₉×#473	1	2	yes	—
403	C₄	C₁₉×#576	1	1	yes	characteristic
404	C₄	C₁₉×#577	1	1	yes	characteristic
405	C₄	C₁₉×#578	1	1	yes	characteristic
406	C₄	C₁₉×#578	1	1	yes	characteristic
407	C₂	—	4	1	no	—
408	C₂	C₁₉×#3044	1	1	yes	characteristic
409	C₂	C₁₉×#3062	1	1	yes	characteristic
410	C₂	C₂×C₁₉×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#121
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
5. C₁₉×#1700	C₂	semidirect
6. C₁₉×#1694	C₂	semidirect
7. C₁₉×#1680	C₂	semidirect
8. C₁₉×#1674	C₂	semidirect
149. #19572	C₁₉	direct (N × H)
189. #1700	C₂×C₁₉	semidirect
190. #1694	C₂×C₁₉	semidirect
191. #1680	C₂×C₁₉	semidirect
192. #1674	C₂×C₁₉	semidirect
307. C₁₉	#19572	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×#3255	2
C₁₉×#3230	2
C₁₉×#3209	2
C₁₉×#2986	2
C₁₉×#1700	2
C₁₉×#1694	2
C₁₉×#1680	2
C₁₉×#1674	2
C₁₉×#1574	2
C₁₉×#1546	2
C₁₉×#1544	2
#19572	19

Subgroups — C19×#19572 #18025531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19572 #18025531