Subgroups — C₁₉×#19574 #18025533

Order 4864.

534 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3249	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3237	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3231	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2986	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1696	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1692	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1684	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1676	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1573	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1554	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1542	C₂	1	1	yes	maximal, characteristic
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₁₉×#501	—	2	1	no	—
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#498	C₂²	1	1	yes	characteristic
22	C₁₉×#491	—	2	1	no	—
23	C₁₉×#487	C₂²	1	1	yes	characteristic
24	C₁₉×#487	C₂²	1	1	yes	characteristic
25	C₁₉×#485	—	2	1	no	—
26	C₁₉×#485	—	2	1	no	—
27	C₁₉×#485	—	2	1	no	—
28	C₁₉×#485	—	2	1	no	—
29	C₁₉×#479	—	2	1	no	—
30	C₁₉×#479	—	2	1	no	—
31	C₁₉×#477	—	2	1	no	—
32	C₁₉×#477	C₂²	1	1	yes	characteristic
33	C₁₉×#477	C₂²	1	1	yes	characteristic
34	C₁₉×#477	C₂²	1	1	yes	characteristic
35	C₁₉×#477	C₂²	1	1	yes	characteristic
36	C₁₉×#475	C₂²	1	1	yes	characteristic
37	C₁₉×#475	C₂²	1	1	yes	characteristic
38	C₁₉×#467	—	2	1	no	—
39	C₁₉×#467	—	2	1	no	—
40	C₁₉×#462	—	2	1	no	—
41	C₁₉×#462	C₂²	1	1	yes	characteristic
42	C₁₉×#462	C₂²	1	1	yes	characteristic
43	C₁₉×#446	—	2	1	no	—
44	C₁₉×#446	C₂²	1	1	yes	characteristic
45	C₁₉×#446	C₂²	1	1	yes	characteristic
46	C₈×Q₈×C₁₉	—	2	1	no	—
47	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#433	—	2	1	no	—
50	C₁₉×#433	—	2	1	no	—
51	C₁₉×#432	C₂²	1	1	yes	characteristic
52	C₁₉×#431	C₂²	1	1	yes	characteristic
53	C₁₉×#431	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₁₉×#335	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#334	C₂²	1	1	yes	characteristic
59	C₁₉×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	C₂²	1	1	yes	characteristic
61	C₁₉×#333	C₂²	1	1	yes	characteristic
62	C₁₉×#333	C₂²	1	1	yes	characteristic
63	C₁₉×#332	C₂²	1	1	yes	characteristic
64	C₁₉×#332	C₂²	1	1	yes	characteristic
65	C₁₉×#332	C₂²	1	1	yes	characteristic
66	C₁₉×#332	C₂²	1	1	yes	characteristic
67	C₂×Q₁₆×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂²×C₈×C₁₉	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
71	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
72	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
75	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
85	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×Q₈×C₁₉	—	2	1	no	—
91	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₁₉×#117	—	2	1	no	—
94	C₁₉×#117	—	2	1	no	—
95	C₁₉×#117	—	2	1	no	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₁₉×#107	—	2	1	no	—
98	C₁₉×#107	—	2	1	no	—
99	C₁₉×#107	—	2	1	no	—
100	C₁₉×#107	—	2	1	no	—
101	C₁₉×#107	—	2	1	no	—
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#106	—	2	1	no	—
104	C₁₉×#106	—	2	1	no	—
105	C₁₉×#106	—	2	1	no	—
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×C₄⋊C₈	—	2	1	no	—
108	C₁₉×C₄⋊C₈	—	2	1	no	—
109	C₁₉×C₄⋊C₈	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
114	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×#103	—	2	1	no	—
121	C₁₉×#103	—	2	1	no	—
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	—	2	1	no	—
131	C₁₉×#103	—	2	1	no	—
132	C₁₉×C₂²⋊C₈	—	2	1	no	—
133	C₁₉×C₂²⋊C₈	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
135	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
136	C₁₉×#97	—	2	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₁₉×#97	—	2	1	no	—
139	C₄×C₈×C₁₉	—	2	1	no	—
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
154	Q₁₆×C₁₉	—	8	1	no	—
155	Q₁₆×C₁₉	—	8	1	no	—
156	C₂×C₈×C₁₉	—	2	1	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	8	1	no	—
163	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	4	1	no	—
183	C₄⋊C₄×C₁₉	—	4	1	no	—
184	C₄⋊C₄×C₁₉	—	4	1	no	—
185	C₄⋊C₄×C₁₉	—	4	1	no	—
186	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²⋊C₄×C₁₉	—	2	1	no	—
189	C₂²⋊C₄×C₁₉	—	2	1	no	—
190	C₂²⋊C₄×C₁₉	—	4	1	no	—
191	C₂²⋊C₄×C₁₉	—	4	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	4	1	no	—
195	C₄²×C₁₉	—	4	1	no	—
196	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₉	#41	1	1	yes	characteristic
199	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
200	#19574	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂³×C₁₉	#121	1	1	yes	characteristic
202	Q₈×C₁₉	—	2	1	no	—
203	Q₈×C₁₉	—	2	1	no	—
204	Q₈×C₁₉	—	2	1	no	—
205	Q₈×C₁₉	—	2	1	no	—
206	Q₈×C₁₉	—	4	2	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	Q₈×C₁₉	—	4	1	no	—
209	Q₈×C₁₉	—	4	1	no	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	8	1	no	—
212	Q₈×C₁₉	—	8	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
232	C₈×C₁₉	—	2	1	no	—
233	C₈×C₁₉	—	2	1	no	—
234	C₈×C₁₉	—	2	1	no	—
235	C₈×C₁₉	—	2	1	no	—
236	C₈×C₁₉	—	4	1	no	—
237	C₈×C₁₉	—	4	1	no	—
238	C₈×C₁₉	—	4	1	no	—
239	C₈×C₁₉	—	4	1	no	—
240	C₈×C₁₉	—	4	1	no	—
241	C₈×C₁₉	—	4	1	no	—
242	#3249	C₂×C₁₉	1	1	yes	characteristic
243	#3237	C₂×C₁₉	1	1	yes	characteristic
244	#3231	C₂×C₁₉	1	1	yes	characteristic
245	#2986	C₂×C₁₉	1	1	yes	characteristic
246	#1704	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#1696	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1676	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1573	C₂×C₁₉	1	1	yes	characteristic
255	#1554	C₂×C₁₉	1	1	yes	characteristic
256	#1542	C₂×C₁₉	1	1	yes	characteristic
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	2	1	no	—
264	C₄×C₁₉	—	2	1	no	—
265	C₄×C₁₉	—	4	1	no	—
266	C₄×C₁₉	—	4	1	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	8	1	no	—
270	C₄×C₁₉	—	8	1	no	—
271	C₄×C₁₉	—	8	1	no	—
272	C₄×C₁₉	—	8	1	no	—
273	C₄×C₁₉	#577	1	1	yes	characteristic
274	C₄×C₁₉	#578	1	1	yes	characteristic
275	C₄×C₁₉	#578	1	1	yes	characteristic
276	C₄×C₁₉	#578	1	1	yes	characteristic
277	#533	C₂²×C₁₉	1	1	yes	characteristic
278	#533	C₂²×C₁₉	1	1	yes	characteristic
279	#533	C₂²×C₁₉	1	1	yes	characteristic
280	#501	—	2	1	no	—
281	#500	C₂²×C₁₉	1	1	yes	characteristic
282	#498	C₂²×C₁₉	1	1	yes	characteristic
283	#491	—	2	1	no	—
284	#487	C₂²×C₁₉	1	1	yes	characteristic
285	#487	C₂²×C₁₉	1	1	yes	characteristic
286	#485	—	2	1	no	—
287	#485	—	2	1	no	—
288	#485	—	2	1	no	—
289	#485	—	2	1	no	—
290	#479	—	2	1	no	—
291	#479	—	2	1	no	—
292	#477	—	2	1	no	—
293	#477	C₂²×C₁₉	1	1	yes	characteristic
294	#477	C₂²×C₁₉	1	1	yes	characteristic
295	#477	C₂²×C₁₉	1	1	yes	characteristic
296	#477	C₂²×C₁₉	1	1	yes	characteristic
297	#475	C₂²×C₁₉	1	1	yes	characteristic
298	#475	C₂²×C₁₉	1	1	yes	characteristic
299	#467	—	2	1	no	—
300	#467	—	2	1	no	—
301	#462	—	2	1	no	—
302	#462	C₂²×C₁₉	1	1	yes	characteristic
303	#462	C₂²×C₁₉	1	1	yes	characteristic
304	#446	—	2	1	no	—
305	#446	C₂²×C₁₉	1	1	yes	characteristic
306	#446	C₂²×C₁₉	1	1	yes	characteristic
307	C₈×Q₈	—	2	1	no	—
308	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
309	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
310	#433	—	2	1	no	—
311	#433	—	2	1	no	—
312	#432	C₂²×C₁₉	1	1	yes	characteristic
313	#431	C₂²×C₁₉	1	1	yes	characteristic
314	#431	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
316	#335	C₂²×C₁₉	1	1	yes	characteristic
317	#335	C₂²×C₁₉	1	1	yes	characteristic
318	#334	C₂²×C₁₉	1	1	yes	characteristic
319	#334	C₂²×C₁₉	1	1	yes	characteristic
320	#333	C₂²×C₁₉	1	1	yes	characteristic
321	#333	C₂²×C₁₉	1	1	yes	characteristic
322	#333	C₂²×C₁₉	1	1	yes	characteristic
323	#333	C₂²×C₁₉	1	1	yes	characteristic
324	#332	C₂²×C₁₉	1	1	yes	characteristic
325	#332	C₂²×C₁₉	1	1	yes	characteristic
326	#332	C₂²×C₁₉	1	1	yes	characteristic
327	#332	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×C₁₉	—	4	1	no	—
329	C₂×C₁₉	#3044	1	1	yes	characteristic
330	C₂×C₁₉	#3063	1	1	yes	characteristic
331	C₂×C₁₉	#3067	1	1	yes	characteristic
332	C₂×Q₁₆	—	2	1	no	—
333	C₂×Q₁₆	—	2	1	no	—
334	C₂²×C₈	—	2	1	no	—
335	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
336	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
337	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
341	#125	—	2	1	no	—
342	#125	—	2	1	no	—
343	#125	—	2	1	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	—	2	1	no	—
349	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
350	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	—	2	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
357	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
358	#117	—	2	1	no	—
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
362	#107	—	2	1	no	—
363	#107	—	2	1	no	—
364	#107	—	2	1	no	—
365	#107	—	2	1	no	—
366	#107	—	2	1	no	—
367	#107	—	2	1	no	—
368	#106	—	2	1	no	—
369	#106	—	2	1	no	—
370	#106	—	2	1	no	—
371	#106	—	2	1	no	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	2	1	no	—
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	2	1	no	—
377	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
378	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
379	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
381	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
382	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
384	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
385	#103	—	2	1	no	—
386	#103	—	2	1	no	—
387	#103	—	2	1	no	—
388	#103	—	2	1	no	—
389	#103	—	2	1	no	—
390	#103	—	2	1	no	—
391	#103	—	2	1	no	—
392	#103	—	2	1	no	—
393	#103	—	2	1	no	—
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
397	C₂²⋊C₈	—	2	1	no	—
398	C₂²⋊C₈	—	2	1	no	—
399	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
400	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
401	#97	—	2	1	no	—
402	#97	—	2	1	no	—
403	#97	—	2	1	no	—
404	C₄×C₈	—	2	1	no	—
405	C₄×C₈	—	2	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
408	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
409	C₁₉	#19574	1	1	yes	characteristic, direct product factor, Sylow
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
420	Q₁₆	—	8	1	no	—
421	Q₁₆	—	8	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	8	1	no	—
429	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	4	1	no	—
457	C₂²⋊C₄	—	4	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	4	1	no	—
461	C₄²	—	4	1	no	—
462	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₄²	#41×C₁₉	1	1	yes	characteristic
465	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
466	C₂³	C₁₉×#121	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	2	1	no	—
469	Q₈	—	2	1	no	—
470	Q₈	—	2	1	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	4	1	no	—
473	Q₈	—	4	1	no	—
474	Q₈	—	4	1	no	—
475	Q₈	—	4	1	no	—
476	Q₈	—	8	1	no	—
477	Q₈	—	8	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
492	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
493	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
496	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
497	C₈	—	2	1	no	—
498	C₈	—	2	1	no	—
499	C₈	—	2	1	no	—
500	C₈	—	2	1	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	1	no	—
503	C₈	—	4	1	no	—
504	C₈	—	4	1	no	—
505	C₈	—	4	1	no	—
506	C₈	—	4	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	8	1	no	—
520	C₄	—	8	1	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	1	no	—
523	C₄	C₁₉×#577	1	1	yes	characteristic
524	C₄	C₁₉×#578	1	1	yes	characteristic
525	C₄	C₁₉×#578	1	1	yes	characteristic
526	C₄	C₁₉×#578	1	1	yes	characteristic
527	C₂	—	4	1	no	—
528	C₂	C₁₉×#3044	1	1	yes	characteristic
529	C₂	C₁₉×#3063	1	1	yes	characteristic
530	C₂	C₁₉×#3067	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×#1704	C₂	semidirect
6. C₁₉×#1700	C₂	semidirect
7. C₁₉×#1696	C₂	semidirect
8. C₁₉×#1692	C₂	semidirect
9. C₁₉×#1684	C₂	semidirect
10. C₁₉×#1680	C₂	semidirect
11. C₁₉×#1676	C₂	semidirect
12. C₁₉×#1672	C₂	semidirect
200. #19574	C₁₉	direct (N × H)
246. #1704	C₂×C₁₉	semidirect
247. #1700	C₂×C₁₉	semidirect
248. #1696	C₂×C₁₉	semidirect
249. #1692	C₂×C₁₉	semidirect
250. #1684	C₂×C₁₉	semidirect
251. #1680	C₂×C₁₉	semidirect
252. #1676	C₂×C₁₉	semidirect
253. #1672	C₂×C₁₉	semidirect
409. C₁₉	#19574	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×#3249	2
C₁₉×#3237	2
C₁₉×#3231	2
C₁₉×#2986	2
C₁₉×#1704	2
C₁₉×#1700	2
C₁₉×#1696	2
C₁₉×#1692	2
C₁₉×#1684	2
C₁₉×#1680	2
C₁₉×#1676	2
C₁₉×#1672	2
C₁₉×#1573	2
C₁₉×#1554	2
C₁₉×#1542	2
#19574	19

Subgroups — C19×#19574 #18025533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19574 #18025533