Subgroups — C₁₉×#19838 #18025797

Order 4864.

574 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3383	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3372	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3359	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3299	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1718	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1684	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1684	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1673	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1651	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1643	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic
16	C₁₉×#557	C₂²	1	1	yes	characteristic
17	C₁₉×#557	C₂²	1	1	yes	characteristic
18	C₁₉×#554	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#499	—	2	1	no	—
22	C₁₉×#498	C₂²	1	1	yes	characteristic
23	C₁₉×#491	—	2	1	no	—
24	C₁₉×#487	—	2	1	no	—
25	C₁₉×#487	C₂²	1	1	yes	characteristic
26	C₁₉×#487	C₂²	1	1	yes	characteristic
27	C₁₉×#487	C₂²	1	1	yes	characteristic
28	C₁₉×#487	C₂²	1	1	yes	characteristic
29	C₁₉×#484	—	2	1	no	—
30	C₁₉×#479	—	2	1	no	—
31	C₁₉×#479	—	2	1	no	—
32	C₁₉×#479	—	2	1	no	—
33	C₁₉×#477	C₂²	1	1	yes	characteristic
34	C₁₉×#477	C₂²	1	1	yes	characteristic
35	C₁₉×#475	—	2	1	no	—
36	C₁₉×#475	C₂²	1	1	yes	characteristic
37	C₁₉×#475	C₂²	1	1	yes	characteristic
38	C₁₉×#475	C₂²	1	1	yes	characteristic
39	C₁₉×#467	—	2	1	no	—
40	C₁₉×#462	C₂²	1	1	yes	characteristic
41	C₁₉×#461	—	2	1	no	—
42	C₁₉×#461	—	2	1	no	—
43	C₁₉×#461	C₂²	1	1	yes	characteristic
44	C₁₉×#461	C₂²	1	1	yes	characteristic
45	C₁₉×#451	—	2	1	no	—
46	C₁₉×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#440	—	2	1	no	—
50	C₄×Q₁₆×C₁₉	—	2	1	no	—
51	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×SD₁₆×C₁₉	—	2	1	no	—
53	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#103	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#335	C₂²	1	1	yes	characteristic
58	C₁₉×#333	C₂²	1	1	yes	characteristic
59	C₁₉×#332	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#332	C₂²	1	1	yes	characteristic
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×#322	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	—	2	1	no	—
74	C₁₉×C₄⋊Q₈	—	2	1	no	—
75	C₁₉×C₄⋊Q₈	—	2	1	no	—
76	C₁₉×C₄⋊Q₈	—	2	1	no	—
77	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#125	—	4	1	no	—
85	C₁₉×#125	—	4	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	4	1	no	—
89	C₁₉×C₂²⋊Q₈	—	4	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	—	2	1	no	—
94	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	—	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×#107	D₄	1	1	yes	characteristic
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	4	1	no	—
110	C₁₉×#106	D₄	1	1	yes	characteristic
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	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×#103	—	2	1	no	—
119	C₁₉×#103	—	2	1	no	—
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×#103	—	4	1	no	—
133	C₁₉×#103	D₄	1	1	yes	characteristic
134	C₁₉×#103	D₄	1	1	yes	characteristic
135	C₁₉×#103	D₄	1	1	yes	characteristic
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	—	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	C₂³	1	1	yes	characteristic
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	—	4	1	no	—
149	C₂×Q₈×C₁₉	—	4	2	no	—
150	C₂×Q₈×C₁₉	—	8	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	4	1	no	—
157	C₂²×C₄×C₁₉	—	4	1	no	—
158	Q₁₆×C₁₉	—	2	2	no	—
159	Q₁₆×C₁₉	—	8	1	no	—
160	SD₁₆×C₁₉	—	2	2	no	—
161	SD₁₆×C₁₉	—	4	2	no	—
162	SD₁₆×C₁₉	—	4	2	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	—	2	1	no	—
168	C₂×C₈×C₁₉	—	8	1	no	—
169	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	—	4	1	no	—
191	C₄⋊C₄×C₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	—	4	1	no	—
193	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₁₉	—	2	1	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	4	1	no	—
204	C₄²×C₁₉	—	4	1	no	—
205	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
206	#19838	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	1	no	—
208	Q₈×C₁₉	—	2	1	no	—
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	8	2	no	—
220	Q₈×C₁₉	—	8	1	no	—
221	Q₈×C₁₉	#137	1	2	yes	—
222	D₄×C₁₉	—	2	1	no	—
223	D₄×C₁₉	#135	1	2	yes	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	8	2	no	—
238	C₂×C₄×C₁₉	—	16	1	no	—
239	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
242	C₈×C₁₉	—	2	1	no	—
243	C₈×C₁₉	—	2	1	no	—
244	C₈×C₁₉	—	2	1	no	—
245	C₈×C₁₉	—	2	1	no	—
246	C₈×C₁₉	—	4	1	no	—
247	C₈×C₁₉	—	4	1	no	—
248	C₈×C₁₉	—	4	1	no	—
249	C₈×C₁₉	—	4	1	no	—
250	C₈×C₁₉	—	4	1	no	—
251	#3383	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#3372	C₂×C₁₉	1	1	yes	characteristic
253	#3359	C₂×C₁₉	1	1	yes	characteristic
254	#3299	C₂×C₁₉	1	1	yes	characteristic
255	#1718	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1673	C₂×C₁₉	1	1	yes	characteristic
260	#1653	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1651	C₂×C₁₉	1	1	yes	characteristic
262	#1643	C₂×C₁₉	1	1	yes	characteristic
263	#1636	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
265	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	4	1	no	—
268	C₂²×C₁₉	—	4	1	no	—
269	C₂²×C₁₉	D₄²	1	1	yes	characteristic
270	C₄×C₁₉	—	2	2	no	—
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	8	1	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	—	8	1	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
283	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
284	C₄×C₁₉	#577	1	1	yes	characteristic
285	C₄×C₁₉	#578	1	1	yes	characteristic
286	#557	C₂²×C₁₉	1	1	yes	characteristic
287	#557	C₂²×C₁₉	1	1	yes	characteristic
288	#554	C₂²×C₁₉	1	1	yes	characteristic
289	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
290	#500	C₂²×C₁₉	1	1	yes	characteristic
291	#499	—	2	1	no	—
292	#498	C₂²×C₁₉	1	1	yes	characteristic
293	#491	—	2	1	no	—
294	#487	—	2	1	no	—
295	#487	C₂²×C₁₉	1	1	yes	characteristic
296	#487	C₂²×C₁₉	1	1	yes	characteristic
297	#487	C₂²×C₁₉	1	1	yes	characteristic
298	#487	C₂²×C₁₉	1	1	yes	characteristic
299	#484	—	2	1	no	—
300	#479	—	2	1	no	—
301	#479	—	2	1	no	—
302	#479	—	2	1	no	—
303	#477	C₂²×C₁₉	1	1	yes	characteristic
304	#477	C₂²×C₁₉	1	1	yes	characteristic
305	#475	—	2	1	no	—
306	#475	C₂²×C₁₉	1	1	yes	characteristic
307	#475	C₂²×C₁₉	1	1	yes	characteristic
308	#475	C₂²×C₁₉	1	1	yes	characteristic
309	#467	—	2	1	no	—
310	#462	C₂²×C₁₉	1	1	yes	characteristic
311	#461	—	2	1	no	—
312	#461	—	2	1	no	—
313	#461	C₂²×C₁₉	1	1	yes	characteristic
314	#461	C₂²×C₁₉	1	1	yes	characteristic
315	#451	—	2	1	no	—
316	#446	C₂²×C₁₉	1	1	yes	characteristic
317	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
319	#440	—	2	1	no	—
320	C₄×Q₁₆	—	2	1	no	—
321	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
322	C₄×SD₁₆	—	2	1	no	—
323	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
324	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×#103	—	2	1	no	—
326	#335	C₂²×C₁₉	1	1	yes	characteristic
327	#335	C₂²×C₁₉	1	1	yes	characteristic
328	#333	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	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
333	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
334	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
335	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
336	#322	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×C₁₉	—	4	2	no	—
338	C₂×C₁₉	#3266	1	1	yes	characteristic
339	C₂×C₁₉	#3285	1	1	yes	characteristic
340	C₂×C₁₉	#3289	1	1	yes	characteristic
341	C₂²×Q₈	—	2	1	no	—
342	C₂×Q₁₆	—	2	1	no	—
343	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
344	C₂×SD₁₆	—	2	1	no	—
345	C₂×SD₁₆	—	2	1	no	—
346	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	—	2	1	no	—
350	C₄⋊Q₈	—	2	1	no	—
351	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
354	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
355	#125	—	2	1	no	—
356	#125	—	2	1	no	—
357	#125	—	2	1	no	—
358	#125	—	4	1	no	—
359	#125	—	4	1	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	—	2	1	no	—
362	C₂²⋊Q₈	—	4	1	no	—
363	C₂²⋊Q₈	—	4	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
369	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
374	C₂×C₄⋊C₄	—	2	1	no	—
375	#107	—	2	1	no	—
376	#107	—	2	1	no	—
377	#107	—	2	1	no	—
378	#107	—	2	1	no	—
379	#107	D₄×C₁₉	1	1	yes	characteristic
380	#106	—	2	1	no	—
381	#106	—	2	1	no	—
382	#106	—	2	1	no	—
383	#106	—	4	1	no	—
384	#106	D₄×C₁₉	1	1	yes	characteristic
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	C₂³×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	#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	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	4	1	no	—
407	#103	D₄×C₁₉	1	1	yes	characteristic
408	#103	D₄×C₁₉	1	1	yes	characteristic
409	#103	D₄×C₁₉	1	1	yes	characteristic
410	#102	D₄×C₁₉	1	1	yes	characteristic
411	C₂²⋊C₈	—	2	1	no	—
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	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₁₉	#19838	1	1	yes	characteristic, direct product factor, Sylow
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	4	2	no	—
425	C₂×Q₈	—	8	1	no	—
426	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	Q₁₆	—	2	2	no	—
434	Q₁₆	—	8	1	no	—
435	SD₁₆	—	2	2	no	—
436	SD₁₆	—	4	2	no	—
437	SD₁₆	—	4	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	8	1	no	—
444	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	4	1	no	—
479	C₄²	—	4	1	no	—
480	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
481	C₂³	—	2	1	no	—
482	Q₈	—	2	1	no	—
483	Q₈	—	2	1	no	—
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	4	1	no	—
488	Q₈	—	4	1	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	8	2	no	—
494	Q₈	—	8	1	no	—
495	Q₈	C₁₉×#137	1	2	yes	—
496	D₄	—	2	1	no	—
497	D₄	C₁₉×#135	1	2	yes	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	8	2	no	—
512	C₂×C₄	—	16	1	no	—
513	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
515	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	D₄²×C₁₉	1	1	yes	characteristic
529	C₄	—	2	2	no	—
530	C₄	—	2	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	8	1	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
542	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
543	C₄	C₁₉×#577	1	1	yes	characteristic
544	C₄	C₁₉×#578	1	1	yes	characteristic
545	C₂	—	4	2	no	—
546	C₂	C₁₉×#3266	1	1	yes	characteristic
547	C₂	C₁₉×#3285	1	1	yes	characteristic
548	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×D₄×C₁₉	C₂×D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉×#3383	C₂	semidirect
5. C₁₉×#1718	C₂	semidirect
6. C₁₉×#1700	C₂	semidirect
7. C₁₉×#1684	C₂	semidirect
8. C₁₉×#1684	C₂	semidirect
10. C₁₉×#1653	C₂	semidirect
13. C₁₉×#1636	C₂	semidirect
14. C₁₉×#1584	C₂	semidirect
206. #19838	C₁₉	direct (N × H)
251. #3383	C₂×C₁₉	semidirect
255. #1718	C₂×C₁₉	semidirect
256. #1700	C₂×C₁₉	semidirect
257. #1684	C₂×C₁₉	semidirect
258. #1684	C₂×C₁₉	semidirect
260. #1653	C₂×C₁₉	semidirect
263. #1636	C₂×C₁₉	semidirect
264. #1584	C₂×C₁₉	semidirect
418. C₁₉	#19838	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×#3383	2
C₁₉×#3372	2
C₁₉×#3359	2
C₁₉×#3299	2
C₁₉×#1718	2
C₁₉×#1700	2
C₁₉×#1684	2
C₁₉×#1673	2
C₁₉×#1653	2
C₁₉×#1651	2
C₁₉×#1643	2
C₁₉×#1636	2
C₁₉×#1584	2
C₁₉×SD₁₆⋊C₈	2
#19838	19

Subgroups — C19×#19838 #18025797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19838 #18025797