Subgroups — C₁₉×#19585 #18025544

Order 4864.

550 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3252	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3233	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3231	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2994	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1695	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1692	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1683	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×#1671	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₁₉×#529	C₂²	1	1	yes	characteristic
19	C₁₉×#500	C₂²	1	1	yes	characteristic
20	C₁₉×#499	—	2	1	no	—
21	C₁₉×#498	C₂²	1	1	yes	characteristic
22	C₁₉×#488	—	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×#482	—	2	1	no	—
29	C₁₉×#479	—	2	1	no	—
30	C₁₉×#479	—	2	1	no	—
31	C₁₉×#479	—	2	1	no	—
32	C₁₉×#477	C₂²	1	1	yes	characteristic
33	C₁₉×#477	C₂²	1	1	yes	characteristic
34	C₁₉×#476	C₂²	1	1	yes	characteristic
35	C₁₉×#476	C₂²	1	1	yes	characteristic
36	C₁₉×#475	C₂²	1	1	yes	characteristic
37	C₁₉×#474	C₂²	1	1	yes	characteristic
38	C₁₉×#470	—	2	1	no	—
39	C₁₉×#468	—	2	1	no	—
40	C₁₉×#464	—	2	1	no	—
41	C₁₉×#462	C₂²	1	1	yes	characteristic
42	C₁₉×#461	C₂²	1	1	yes	characteristic
43	C₁₉×#446	C₂²	1	1	yes	characteristic
44	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#436	C₂²	1	1	yes	characteristic
46	C₁₉×#435	—	2	1	no	—
47	C₈×D₄×C₁₉	—	2	1	no	—
48	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#433	—	2	1	no	—
50	C₁₉×#431	C₂²	1	1	yes	characteristic
51	C₁₉×#431	C₂²	1	1	yes	characteristic
52	C₁₉×#424	—	2	1	no	—
53	C₁₉×#423	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×SD₁₆×C₁₉	—	2	1	no	—
69	C₂×M₁₆×C₁₉	—	2	1	no	—
70	C₂×M₁₆×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	—	2	1	no	—
72	C₂²×C₈×C₁₉	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₉×#126	—	2	1	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×#125	—	2	1	no	—
80	C₁₉×#125	D₄	1	1	yes	characteristic
81	C₁₉×#124	D₄	1	1	yes	characteristic
82	C₁₉×#123	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
88	C₁₉×#121	D₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×Q₈×C₁₉	—	2	1	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×#117	—	2	1	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	—	2	1	no	—
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₁₉×#107	—	2	1	no	—
101	C₁₉×#107	—	2	1	no	—
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#107	—	2	1	no	—
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#106	—	2	1	no	—
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	D₄	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×C₂²⋊C₈	—	2	1	no	—
136	C₁₉×C₂²⋊C₈	—	2	1	no	—
137	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
139	C₁₉×#97	—	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	C₂×D₄	1	1	yes	characteristic
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
155	Q₁₆×C₁₉	—	8	1	no	—
156	SD₁₆×C₁₉	—	8	1	no	—
157	M₁₆×C₁₉	—	8	1	no	—
158	M₁₆×C₁₉	—	8	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	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	8	1	no	—
166	C₂×C₈×C₁₉	—	8	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	—	4	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	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²⋊C₄×C₁₉	—	2	1	no	—
190	C₂²⋊C₄×C₁₉	—	2	1	no	—
191	C₂²⋊C₄×C₁₉	—	2	1	no	—
192	C₂²⋊C₄×C₁₉	—	2	1	no	—
193	C₂²⋊C₄×C₁₉	—	2	1	no	—
194	C₂²⋊C₄×C₁₉	—	4	1	no	—
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	4	1	no	—
198	C₄²×C₁₉	—	4	1	no	—
199	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₁₉	#41	1	1	yes	characteristic
202	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
203	#19585	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	#121	1	1	yes	characteristic
206	Q₈×C₁₉	—	2	1	no	—
207	Q₈×C₁₉	—	2	1	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	D₄×C₁₉	—	2	1	no	—
215	D₄×C₁₉	—	2	1	no	—
216	D₄×C₁₉	—	4	2	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	—	2	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	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	—	4	1	no	—
231	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
237	C₈×C₁₉	—	2	1	no	—
238	C₈×C₁₉	—	2	1	no	—
239	C₈×C₁₉	—	2	1	no	—
240	C₈×C₁₉	—	2	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	C₈×C₁₉	—	4	1	no	—
247	#3252	C₂×C₁₉	1	1	yes	characteristic
248	#3233	C₂×C₁₉	1	1	yes	characteristic
249	#3231	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#2994	C₂×C₁₉	1	1	yes	characteristic
251	#1704	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1699	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1695	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1683	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1676	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1550	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1542	C₂×C₁₉	1	1	yes	characteristic, complemented
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	4	1	no	—
268	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	2	1	no	—
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	—	8	1	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	#577	1	1	yes	characteristic
281	C₄×C₁₉	#577	1	1	yes	characteristic
282	C₄×C₁₉	#578	1	1	yes	characteristic
283	C₄×C₁₉	#578	1	1	yes	characteristic
284	#533	C₂²×C₁₉	1	1	yes	characteristic
285	#533	C₂²×C₁₉	1	1	yes	characteristic
286	#529	C₂²×C₁₉	1	1	yes	characteristic
287	#500	C₂²×C₁₉	1	1	yes	characteristic
288	#499	—	2	1	no	—
289	#498	C₂²×C₁₉	1	1	yes	characteristic
290	#488	—	2	1	no	—
291	#487	C₂²×C₁₉	1	1	yes	characteristic
292	#487	C₂²×C₁₉	1	1	yes	characteristic
293	#485	—	2	1	no	—
294	#485	—	2	1	no	—
295	#485	—	2	1	no	—
296	#482	—	2	1	no	—
297	#479	—	2	1	no	—
298	#479	—	2	1	no	—
299	#479	—	2	1	no	—
300	#477	C₂²×C₁₉	1	1	yes	characteristic
301	#477	C₂²×C₁₉	1	1	yes	characteristic
302	#476	C₂²×C₁₉	1	1	yes	characteristic
303	#476	C₂²×C₁₉	1	1	yes	characteristic
304	#475	C₂²×C₁₉	1	1	yes	characteristic
305	#474	C₂²×C₁₉	1	1	yes	characteristic
306	#470	—	2	1	no	—
307	#468	—	2	1	no	—
308	#464	—	2	1	no	—
309	#462	C₂²×C₁₉	1	1	yes	characteristic
310	#461	C₂²×C₁₉	1	1	yes	characteristic
311	#446	C₂²×C₁₉	1	1	yes	characteristic
312	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
313	#436	C₂²×C₁₉	1	1	yes	characteristic
314	#435	—	2	1	no	—
315	C₈×D₄	—	2	1	no	—
316	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
317	#433	—	2	1	no	—
318	#431	C₂²×C₁₉	1	1	yes	characteristic
319	#431	C₂²×C₁₉	1	1	yes	characteristic
320	#424	—	2	1	no	—
321	#423	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
323	#335	C₂²×C₁₉	1	1	yes	characteristic
324	#335	C₂²×C₁₉	1	1	yes	characteristic
325	#334	C₂²×C₁₉	1	1	yes	characteristic
326	#334	C₂²×C₁₉	1	1	yes	characteristic
327	#333	C₂²×C₁₉	1	1	yes	characteristic
328	#333	C₂²×C₁₉	1	1	yes	characteristic
329	#333	C₂²×C₁₉	1	1	yes	characteristic
330	#333	C₂²×C₁₉	1	1	yes	characteristic
331	#332	C₂²×C₁₉	1	1	yes	characteristic
332	#332	C₂²×C₁₉	1	1	yes	characteristic
333	#332	C₂²×C₁₉	1	1	yes	characteristic
334	#332	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₁₉	—	4	1	no	—
336	C₂×C₁₉	—	8	1	no	—
337	C₂×C₁₉	#3046	1	1	yes	characteristic
338	C₂×C₁₉	#3063	1	1	yes	characteristic
339	C₂×C₁₉	#3067	1	1	yes	characteristic
340	C₂×Q₁₆	—	2	1	no	—
341	C₂×SD₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂²×C₈	—	2	1	no	—
345	C₂²×C₈	—	2	1	no	—
346	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
347	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
348	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
349	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
350	#126	—	2	1	no	—
351	#125	—	2	1	no	—
352	#125	—	2	1	no	—
353	#125	D₄×C₁₉	1	1	yes	characteristic
354	#124	D₄×C₁₉	1	1	yes	characteristic
355	#123	—	2	1	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
361	#121	D₄×C₁₉	1	1	yes	characteristic
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
373	#107	—	2	1	no	—
374	#107	—	2	1	no	—
375	#107	—	2	1	no	—
376	#107	—	2	1	no	—
377	#107	—	2	1	no	—
378	#106	—	2	1	no	—
379	#106	—	2	1	no	—
380	#106	—	2	1	no	—
381	#106	—	2	1	no	—
382	#106	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
388	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
390	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
391	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
392	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
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	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#102	—	2	1	no	—
405	#102	—	2	1	no	—
406	#102	—	2	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
411	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
412	#97	—	2	1	no	—
413	C₄×C₈	—	2	1	no	—
414	C₄×C₈	—	2	1	no	—
415	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₁₉	#19585	1	1	yes	characteristic, direct product factor, Sylow
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
429	Q₁₆	—	8	1	no	—
430	SD₁₆	—	8	1	no	—
431	M₁₆	—	8	1	no	—
432	M₁₆	—	8	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	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	8	1	no	—
440	C₂×C₈	—	8	1	no	—
441	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	4	1	no	—
472	C₄²	—	4	1	no	—
473	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₄²	#41×C₁₉	1	1	yes	characteristic
476	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
477	C₂³	—	2	1	no	—
478	C₂³	C₁₉×#121	1	1	yes	characteristic
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	4	1	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	4	1	no	—
484	Q₈	—	4	1	no	—
485	Q₈	—	8	1	no	—
486	Q₈	—	8	1	no	—
487	D₄	—	2	1	no	—
488	D₄	—	2	1	no	—
489	D₄	—	4	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
505	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
506	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
509	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	4	1	no	—
515	C₈	—	4	1	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	8	1	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	—	8	1	no	—
538	C₄	C₁₉×#577	1	1	yes	characteristic
539	C₄	C₁₉×#577	1	1	yes	characteristic
540	C₄	C₁₉×#578	1	1	yes	characteristic
541	C₄	C₁₉×#578	1	1	yes	characteristic
542	C₂	—	4	1	no	—
543	C₂	—	8	1	no	—
544	C₂	C₁₉×#3046	1	1	yes	characteristic
545	C₂	C₁₉×#3063	1	1	yes	characteristic
546	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#121	D₄
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
3. C₁₉×#3231	C₂	semidirect
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1699	C₂	semidirect
7. C₁₉×#1695	C₂	semidirect
8. C₁₉×#1692	C₂	semidirect
9. C₁₉×#1683	C₂	semidirect
10. C₁₉×#1680	C₂	semidirect
11. C₁₉×#1676	C₂	semidirect
12. C₁₉×#1671	C₂	semidirect
13. C₁₉×#1574	C₂	semidirect
14. C₁₉×#1550	C₂	semidirect
15. C₁₉×#1542	C₂	semidirect
203. #19585	C₁₉	direct (N × H)
249. #3231	C₂×C₁₉	semidirect
251. #1704	C₂×C₁₉	semidirect
252. #1699	C₂×C₁₉	semidirect
253. #1695	C₂×C₁₉	semidirect
254. #1692	C₂×C₁₉	semidirect
255. #1683	C₂×C₁₉	semidirect
256. #1680	C₂×C₁₉	semidirect
257. #1676	C₂×C₁₉	semidirect
258. #1671	C₂×C₁₉	semidirect
259. #1574	C₂×C₁₉	semidirect
260. #1550	C₂×C₁₉	semidirect
261. #1542	C₂×C₁₉	semidirect
417. C₁₉	#19585	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×#3252	2
C₁₉×#3233	2
C₁₉×#3231	2
C₁₉×#2994	2
C₁₉×#1704	2
C₁₉×#1699	2
C₁₉×#1695	2
C₁₉×#1692	2
C₁₉×#1683	2
C₁₉×#1680	2
C₁₉×#1676	2
C₁₉×#1671	2
C₁₉×#1574	2
C₁₉×#1550	2
C₁₉×#1542	2
#19585	19

Subgroups — C19×#19585 #18025544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19585 #18025544