Subgroups — C₁₉×#19573 #18025532

Order 4864.

572 conjugacy classes of subgroups.

The subgroup lattice has 420 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×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1698	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1696	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1678	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1676	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1543	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×#500	C₂²	1	2	yes	—
17	C₁₉×#487	—	2	1	no	—
18	C₁₉×#486	C₂²	1	2	yes	—
19	C₁₉×#484	—	2	2	no	—
20	C₁₉×#480	—	2	2	no	—
21	C₁₉×#477	C₂²	1	2	yes	—
22	C₁₉×#477	C₂²	1	2	yes	—
23	C₁₉×#477	C₂²	1	2	yes	—
24	C₁₉×#474	—	2	1	no	—
25	C₁₉×#474	—	2	1	no	—
26	C₁₉×#474	—	2	1	no	—
27	C₁₉×#468	—	2	2	no	—
28	C₁₉×#461	—	2	1	no	—
29	C₁₉×#460	C₂²	1	2	yes	—
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×#333	C₂²	1	1	yes	characteristic
42	C₁₉×#333	C₂²	1	2	yes	—
43	C₁₉×#333	C₂²	1	1	yes	characteristic
44	C₁₉×#333	C₂²	1	2	yes	—
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	C₂×SD₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₁₉×#127	C₂³	1	1	yes	characteristic
59	C₁₉×#125	—	2	1	no	—
60	C₁₉×#124	—	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	C₂³	1	2	yes	—
67	C₄×D₄×C₁₉	—	2	1	no	—
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₁₉×#117	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#107	—	2	2	no	—
74	C₁₉×#107	—	2	2	no	—
75	C₁₉×#107	—	2	2	no	—
76	C₁₉×#107	—	2	2	no	—
77	C₁₉×#107	—	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×#102	—	2	2	no	—
92	C₁₉×#102	—	2	2	no	—
93	C₁₉×#102	—	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	#41×C₁₉	—	8	2	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	2	no	—
108	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
118	SD₁₆×C₁₉	—	8	2	no	—
119	M₁₆×C₁₉	—	8	1	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	2	1	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
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	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	4	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₉	#41	1	1	yes	characteristic
146	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
147	#19573	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	#121	1	1	yes	characteristic
150	Q₈×C₁₉	—	2	2	no	—
151	Q₈×C₁₉	—	2	2	no	—
152	Q₈×C₁₉	—	4	2	no	—
153	Q₈×C₁₉	—	8	2	no	—
154	Q₈×C₁₉	—	8	1	no	—
155	Q₈×C₁₉	—	8	2	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	4	1	no	—
158	D₄×C₁₉	—	4	1	no	—
159	D₄×C₁₉	—	4	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	8	2	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	1	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	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	—	8	2	no	—
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
179	C₈×C₁₉	—	2	2	no	—
180	C₈×C₁₉	—	2	2	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	4	2	no	—
183	C₈×C₁₉	—	4	1	no	—
184	C₈×C₁₉	—	4	1	no	—
185	C₈×C₁₉	—	4	1	no	—
186	#3254	C₂×C₁₉	1	1	yes	characteristic
187	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#3226	C₂×C₁₉	1	1	yes	characteristic
189	#2986	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1698	C₂×C₁₉	1	2	yes	complemented
191	#1696	C₂×C₁₉	1	2	yes	complemented
192	#1678	C₂×C₁₉	1	2	yes	complemented
193	#1676	C₂×C₁₉	1	2	yes	complemented
194	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1548	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#1543	C₂×C₁₉	1	1	yes	characteristic
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	8	1	no	—
201	C₂²×C₁₉	—	8	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	8	1	no	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	#472	1	2	yes	—
212	C₄×C₁₉	#577	1	1	yes	characteristic
213	C₄×C₁₉	#578	1	1	yes	characteristic
214	C₄×C₁₉	#578	1	1	yes	characteristic
215	C₄×C₁₉	#578	1	1	yes	characteristic
216	#533	C₂²×C₁₉	1	1	yes	characteristic
217	#532	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
219	#500	—	2	1	no	—
220	#500	C₂²×C₁₉	1	2	yes	—
221	#487	—	2	1	no	—
222	#486	C₂²×C₁₉	1	2	yes	—
223	#484	—	2	2	no	—
224	#480	—	2	2	no	—
225	#477	C₂²×C₁₉	1	2	yes	—
226	#477	C₂²×C₁₉	1	2	yes	—
227	#477	C₂²×C₁₉	1	2	yes	—
228	#474	—	2	1	no	—
229	#474	—	2	1	no	—
230	#474	—	2	1	no	—
231	#468	—	2	2	no	—
232	#461	—	2	1	no	—
233	#460	C₂²×C₁₉	1	2	yes	—
234	#446	—	2	1	no	—
235	#446	C₂²×C₁₉	1	2	yes	—
236	C₈×Q₈	—	2	1	no	—
237	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
238	#433	—	2	2	no	—
239	#431	C₂²×C₁₉	1	1	yes	characteristic
240	#431	C₂²×C₁₉	1	1	yes	characteristic
241	#431	C₂²×C₁₉	1	1	yes	characteristic
242	#423	C₂²×C₁₉	1	1	yes	characteristic
243	#335	C₂²×C₁₉	1	2	yes	—
244	#334	C₂²×C₁₉	1	2	yes	—
245	#333	C₂²×C₁₉	1	1	yes	characteristic
246	#333	C₂²×C₁₉	1	1	yes	characteristic
247	#333	C₂²×C₁₉	1	2	yes	—
248	#333	C₂²×C₁₉	1	2	yes	—
249	#331	C₂²×C₁₉	1	1	yes	characteristic
250	#331	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×C₁₉	—	4	1	no	—
252	C₂×C₁₉	—	16	1	no	—
253	C₂×C₁₉	#3044	1	1	yes	characteristic
254	C₂×C₁₉	#3063	1	1	yes	characteristic
255	C₂×C₁₉	C₂×#472	1	1	yes	characteristic
256	C₂×#41	—	2	1	no	—
257	C₂²×Q₈	—	2	1	no	—
258	C₂×SD₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
264	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
265	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
266	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
267	#127	C₂³×C₁₉	1	1	yes	characteristic
268	#125	—	2	1	no	—
269	#124	—	2	1	no	—
270	C₂²⋊Q₈	—	2	1	no	—
271	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
272	#121	—	2	1	no	—
273	#121	—	2	1	no	—
274	C₄×Q₈	—	2	1	no	—
275	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	#117	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
282	#107	—	2	2	no	—
283	#107	—	2	2	no	—
284	#107	—	2	2	no	—
285	#107	—	2	2	no	—
286	#107	—	2	2	no	—
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
291	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
292	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
293	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
294	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
295	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	#103	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	2	2	no	—
302	#102	—	2	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
306	#97	—	2	2	no	—
307	C₄×C₈	—	2	2	no	—
308	C₄×C₈	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	C₂³×C₁₉	1	2	yes	—
311	C₁₉	#19573	1	1	yes	characteristic, direct product factor, Sylow
312	#41	—	8	2	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	4	1	no	—
317	C₂×Q₈	—	8	2	no	—
318	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
327	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
328	SD₁₆	—	8	2	no	—
329	M₁₆	—	8	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
336	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₄²	—	2	2	no	—
353	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
355	C₄²	#41×C₁₉	1	1	yes	characteristic
356	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
357	C₂³	—	4	1	no	—
358	C₂³	C₁₉×#121	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	8	2	no	—
363	Q₈	—	8	1	no	—
364	Q₈	—	8	2	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	8	1	no	—
370	D₄	—	8	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
383	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
384	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	2	no	—
409	C₄	C₁₉×#472	1	2	yes	—
410	C₄	C₁₉×#577	1	1	yes	characteristic
411	C₄	C₁₉×#578	1	1	yes	characteristic
412	C₄	C₁₉×#578	1	1	yes	characteristic
413	C₄	C₁₉×#578	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	16	1	no	—
416	C₂	C₁₉×#3044	1	1	yes	characteristic
417	C₂	C₁₉×#3063	1	1	yes	characteristic
418	C₂	C₂×C₁₉×#472	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×#3230	C₂	semidirect
4. C₁₉×#2986	C₂	semidirect
5. C₁₉×#1698	C₂	semidirect
6. C₁₉×#1696	C₂	semidirect
7. C₁₉×#1678	C₂	semidirect
8. C₁₉×#1676	C₂	semidirect
9. C₁₉×#1574	C₂	semidirect
10. C₁₉×#1548	C₂	semidirect
147. #19573	C₁₉	direct (N × H)
187. #3230	C₂×C₁₉	semidirect
189. #2986	C₂×C₁₉	semidirect
190. #1698	C₂×C₁₉	semidirect
191. #1696	C₂×C₁₉	semidirect
192. #1678	C₂×C₁₉	semidirect
193. #1676	C₂×C₁₉	semidirect
194. #1574	C₂×C₁₉	semidirect
195. #1548	C₂×C₁₉	semidirect
311. C₁₉	#19573	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×#3230	2
C₁₉×#3226	2
C₁₉×#2986	2
C₁₉×#1698	2
C₁₉×#1696	2
C₁₉×#1678	2
C₁₉×#1676	2
C₁₉×#1574	2
C₁₉×#1548	2
C₁₉×#1543	2
#19573	19

Subgroups — C19×#19573 #18025532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19573 #18025532