Subgroups — C₁₉×#19478 #18025437

Order 4864.

558 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3231	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3104	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3078	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2984	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×#1574	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1554	C₂	1	1	yes	maximal, characteristic
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#500	C₂²	1	1	yes	characteristic
20	C₁₉×#498	C₂²	1	1	yes	characteristic
21	C₁₉×#487	C₂²	1	1	yes	characteristic
22	C₁₉×#487	C₂²	1	1	yes	characteristic
23	C₁₉×#485	—	2	1	no	—
24	C₁₉×#485	—	2	1	no	—
25	C₁₉×#484	—	2	1	no	—
26	C₁₉×#479	—	2	1	no	—
27	C₁₉×#479	—	2	1	no	—
28	C₁₉×#479	—	2	1	no	—
29	C₁₉×#479	—	2	1	no	—
30	C₁₉×#477	C₂²	1	1	yes	characteristic
31	C₁₉×#477	C₂²	1	1	yes	characteristic
32	C₁₉×#477	C₂²	1	1	yes	characteristic
33	C₁₉×#477	C₂²	1	1	yes	characteristic
34	C₁₉×#475	C₂²	1	1	yes	characteristic
35	C₁₉×#475	C₂²	1	1	yes	characteristic
36	C₁₉×#462	C₂²	1	1	yes	characteristic
37	C₁₉×#462	C₂²	1	1	yes	characteristic
38	C₁₉×#451	—	2	1	no	—
39	C₁₉×#446	—	2	1	no	—
40	C₁₉×#446	—	2	1	no	—
41	C₁₉×#446	C₂²	1	1	yes	characteristic
42	C₁₉×#446	C₂²	1	1	yes	characteristic
43	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
44	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₄×Q₁₆×C₁₉	—	2	1	no	—
46	C₄×Q₁₆×C₁₉	—	2	1	no	—
47	C₁₉×#432	—	2	1	no	—
48	C₁₉×#432	C₂²	1	1	yes	characteristic
49	C₁₉×#431	—	2	1	no	—
50	C₁₉×#431	C₂²	1	1	yes	characteristic
51	C₁₉×#431	C₂²	1	1	yes	characteristic
52	C₁₉×#428	—	2	1	no	—
53	C₁₉×#423	C₂²	1	1	yes	characteristic
54	C₁₉×#419	—	2	1	no	—
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	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×M₁₆×C₁₉	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	C₂³	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×#125	—	2	1	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	2	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	—	2	1	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	—	2	1	no	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
88	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×#117	—	2	1	no	—
92	C₁₉×#117	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	—	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	2	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	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	4	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
158	Q₁₆×C₁₉	—	4	2	no	—
159	Q₁₆×C₁₉	—	4	2	no	—
160	M₁₆×C₁₉	—	4	2	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	4	1	no	—
185	C₄⋊C₄×C₁₉	—	4	1	no	—
186	C₄⋊C₄×C₁₉	—	4	1	no	—
187	C₄⋊C₄×C₁₉	—	4	1	no	—
188	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	4	1	no	—
197	C₄²×C₁₉	—	4	1	no	—
198	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₉	#41	1	1	yes	characteristic
201	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
202	#19478	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂³×C₁₉	#121	1	1	yes	characteristic
204	Q₈×C₁₉	—	2	1	no	—
205	Q₈×C₁₉	—	2	1	no	—
206	Q₈×C₁₉	—	2	1	no	—
207	Q₈×C₁₉	—	4	2	no	—
208	Q₈×C₁₉	—	4	1	no	—
209	Q₈×C₁₉	—	4	1	no	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	Q₈×C₁₉	—	8	1	no	—
213	Q₈×C₁₉	—	8	1	no	—
214	Q₈×C₁₉	#137	1	2	yes	—
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	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
236	C₈×C₁₉	—	2	1	no	—
237	C₈×C₁₉	—	2	1	no	—
238	C₈×C₁₉	—	2	1	no	—
239	C₈×C₁₉	—	2	1	no	—
240	C₈×C₁₉	—	4	1	no	—
241	C₈×C₁₉	—	4	1	no	—
242	C₈×C₁₉	—	4	1	no	—
243	C₈×C₁₉	—	4	1	no	—
244	C₈×C₁₉	—	4	1	no	—
245	C₈×C₁₉	—	4	1	no	—
246	#3231	C₂×C₁₉	1	1	yes	characteristic
247	#3104	C₂×C₁₉	1	1	yes	characteristic
248	#3078	C₂×C₁₉	1	1	yes	characteristic
249	#2984	C₂×C₁₉	1	1	yes	characteristic
250	#1704	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1696	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1676	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1574	C₂×C₁₉	1	1	yes	characteristic
259	#1559	C₂×C₁₉	1	1	yes	characteristic
260	#1554	C₂×C₁₉	1	1	yes	characteristic
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
265	C₄×C₁₉	—	2	1	no	—
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	2	2	no	—
268	C₄×C₁₉	—	2	1	no	—
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	4	1	no	—
271	C₄×C₁₉	—	4	1	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	8	1	no	—
274	C₄×C₁₉	—	8	1	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
278	C₄×C₁₉	#575	1	1	yes	characteristic
279	C₄×C₁₉	#578	1	1	yes	characteristic
280	C₄×C₁₉	#578	1	1	yes	characteristic
281	#533	C₂²×C₁₉	1	1	yes	characteristic
282	#533	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
284	#500	C₂²×C₁₉	1	1	yes	characteristic
285	#498	C₂²×C₁₉	1	1	yes	characteristic
286	#487	C₂²×C₁₉	1	1	yes	characteristic
287	#487	C₂²×C₁₉	1	1	yes	characteristic
288	#485	—	2	1	no	—
289	#485	—	2	1	no	—
290	#484	—	2	1	no	—
291	#479	—	2	1	no	—
292	#479	—	2	1	no	—
293	#479	—	2	1	no	—
294	#479	—	2	1	no	—
295	#477	C₂²×C₁₉	1	1	yes	characteristic
296	#477	C₂²×C₁₉	1	1	yes	characteristic
297	#477	C₂²×C₁₉	1	1	yes	characteristic
298	#477	C₂²×C₁₉	1	1	yes	characteristic
299	#475	C₂²×C₁₉	1	1	yes	characteristic
300	#475	C₂²×C₁₉	1	1	yes	characteristic
301	#462	C₂²×C₁₉	1	1	yes	characteristic
302	#462	C₂²×C₁₉	1	1	yes	characteristic
303	#451	—	2	1	no	—
304	#446	—	2	1	no	—
305	#446	—	2	1	no	—
306	#446	C₂²×C₁₉	1	1	yes	characteristic
307	#446	C₂²×C₁₉	1	1	yes	characteristic
308	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
309	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
310	C₄×Q₁₆	—	2	1	no	—
311	C₄×Q₁₆	—	2	1	no	—
312	#432	—	2	1	no	—
313	#432	C₂²×C₁₉	1	1	yes	characteristic
314	#431	—	2	1	no	—
315	#431	C₂²×C₁₉	1	1	yes	characteristic
316	#431	C₂²×C₁₉	1	1	yes	characteristic
317	#428	—	2	1	no	—
318	#423	C₂²×C₁₉	1	1	yes	characteristic
319	#419	—	2	1	no	—
320	#335	C₂²×C₁₉	1	1	yes	characteristic
321	#335	C₂²×C₁₉	1	1	yes	characteristic
322	#334	C₂²×C₁₉	1	1	yes	characteristic
323	#334	C₂²×C₁₉	1	1	yes	characteristic
324	#333	C₂²×C₁₉	1	1	yes	characteristic
325	#333	C₂²×C₁₉	1	1	yes	characteristic
326	#333	C₂²×C₁₉	1	1	yes	characteristic
327	#333	C₂²×C₁₉	1	1	yes	characteristic
328	#332	C₂²×C₁₉	1	1	yes	characteristic
329	#332	C₂²×C₁₉	1	1	yes	characteristic
330	#332	C₂²×C₁₉	1	1	yes	characteristic
331	#332	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×C₁₉	—	4	1	no	—
333	C₂×C₁₉	#3044	1	1	yes	characteristic
334	C₂×C₁₉	#3056	1	1	yes	characteristic
335	C₂×C₁₉	#3067	1	1	yes	characteristic
336	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
337	C₂×Q₁₆	—	2	1	no	—
338	C₂×Q₁₆	—	2	1	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
341	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
342	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
343	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
344	#125	—	2	1	no	—
345	#125	—	2	1	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	—	2	1	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₄×Q₈	—	2	1	no	—
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	D₄×C₁₉	1	1	yes	characteristic
357	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
358	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
359	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
360	#117	—	2	1	no	—
361	#117	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
366	#107	—	2	1	no	—
367	#107	—	2	1	no	—
368	#107	—	2	1	no	—
369	#107	—	2	1	no	—
370	#107	—	2	1	no	—
371	#107	—	2	1	no	—
372	#106	—	2	1	no	—
373	#106	—	2	1	no	—
374	#106	—	2	1	no	—
375	#106	—	2	1	no	—
376	C₄⋊C₈	—	2	1	no	—
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
382	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
383	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
384	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
386	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
388	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
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	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	C₂²⋊C₈	—	2	1	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
404	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
405	#97	—	2	1	no	—
406	#97	—	2	1	no	—
407	#97	—	2	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	2	1	no	—
410	C₄×C₈	—	2	1	no	—
411	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₁₉	#19478	1	1	yes	characteristic, direct product factor, Sylow
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	4	1	no	—
421	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
428	Q₁₆	—	4	2	no	—
429	Q₁₆	—	4	2	no	—
430	M₁₆	—	4	2	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂²⋊C₄	—	4	1	no	—
461	C₂²⋊C₄	—	4	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	4	1	no	—
467	C₄²	—	4	1	no	—
468	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₄²	#41×C₁₉	1	1	yes	characteristic
471	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
472	C₂³	C₁₉×#121	1	1	yes	characteristic
473	Q₈	—	2	1	no	—
474	Q₈	—	2	1	no	—
475	Q₈	—	2	1	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	1	no	—
478	Q₈	—	4	1	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	4	1	no	—
481	Q₈	—	8	1	no	—
482	Q₈	—	8	1	no	—
483	Q₈	C₁₉×#137	1	2	yes	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
500	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
501	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
505	C₈	—	2	1	no	—
506	C₈	—	2	1	no	—
507	C₈	—	2	1	no	—
508	C₈	—	2	1	no	—
509	C₈	—	4	1	no	—
510	C₈	—	4	1	no	—
511	C₈	—	4	1	no	—
512	C₈	—	4	1	no	—
513	C₈	—	4	1	no	—
514	C₈	—	4	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	1	no	—
518	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	8	1	no	—
528	C₄	—	8	1	no	—
529	C₄	—	8	1	no	—
530	C₄	—	8	1	no	—
531	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
532	C₄	C₁₉×#575	1	1	yes	characteristic
533	C₄	C₁₉×#578	1	1	yes	characteristic
534	C₄	C₁₉×#578	1	1	yes	characteristic
535	C₂	—	4	1	no	—
536	C₂	C₁₉×#3044	1	1	yes	characteristic
537	C₂	C₁₉×#3056	1	1	yes	characteristic
538	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
202. #19478	C₁₉	direct (N × H)
250. #1704	C₂×C₁₉	semidirect
251. #1700	C₂×C₁₉	semidirect
252. #1696	C₂×C₁₉	semidirect
253. #1692	C₂×C₁₉	semidirect
254. #1684	C₂×C₁₉	semidirect
255. #1680	C₂×C₁₉	semidirect
256. #1676	C₂×C₁₉	semidirect
257. #1672	C₂×C₁₉	semidirect
413. C₁₉	#19478	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×#3231	2
C₁₉×#3104	2
C₁₉×#3078	2
C₁₉×#2984	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×#1574	2
C₁₉×#1559	2
C₁₉×#1554	2
#19478	19

Subgroups — C19×#19478 #18025437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19478 #18025437