Subgroups — C₁₉×#19816 #18025775

Order 4864.

564 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×#3385	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3381	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3338	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1723	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1692	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1683	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1676	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1676	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1644	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1633	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1632	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic
16	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#557	C₂²	1	1	yes	characteristic
18	C₁₉×#554	C₂²	1	1	yes	characteristic
19	C₁₉×#554	C₂²	1	1	yes	characteristic
20	C₁₉×#501	—	2	1	no	—
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#500	C₂²	1	1	yes	characteristic
23	C₁₉×#499	—	2	1	no	—
24	C₁₉×#498	C₂²	1	1	yes	characteristic
25	C₁₉×#494	C₂²	1	1	yes	characteristic
26	C₁₉×#487	—	2	1	no	—
27	C₁₉×#487	C₂²	1	1	yes	characteristic
28	C₁₉×#487	C₂²	1	1	yes	characteristic
29	C₁₉×#484	—	2	1	no	—
30	C₁₉×#484	—	2	1	no	—
31	C₁₉×#479	—	2	1	no	—
32	C₁₉×#479	—	2	1	no	—
33	C₁₉×#478	—	2	1	no	—
34	C₁₉×#477	—	2	1	no	—
35	C₁₉×#477	C₂²	1	1	yes	characteristic
36	C₁₉×#477	C₂²	1	1	yes	characteristic
37	C₁₉×#477	C₂²	1	1	yes	characteristic
38	C₁₉×#477	C₂²	1	1	yes	characteristic
39	C₁₉×#477	C₂²	1	1	yes	characteristic
40	C₁₉×#476	C₂²	1	1	yes	characteristic
41	C₁₉×#474	—	2	1	no	—
42	C₁₉×#474	C₂²	1	1	yes	characteristic
43	C₁₉×#467	—	2	1	no	—
44	C₁₉×#462	—	2	1	no	—
45	C₁₉×#462	C₂²	1	1	yes	characteristic
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×#107	—	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×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	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	C₂×Q₁₆×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	4	1	no	—
69	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	—	2	1	no	—
72	C₁₉×C₄⋊Q₈	—	2	1	no	—
73	C₁₉×C₄⋊Q₈	—	2	1	no	—
74	C₁₉×C₄⋊Q₈	—	2	1	no	—
75	C₁₉×C₄⋊Q₈	—	4	1	no	—
76	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#125	—	2	1	no	—
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	—	4	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	1	no	—
86	C₁₉×C₂²⋊Q₈	—	4	1	no	—
87	C₁₉×C₂²⋊Q₈	—	4	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	—	2	1	no	—
92	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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×#107	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#107	—	2	1	no	—
110	C₁₉×#107	D₄	1	1	yes	characteristic
111	C₁₉×#106	—	2	1	no	—
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	D₄	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
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	—	4	1	no	—
131	C₁₉×#103	D₄	1	1	yes	characteristic
132	C₁₉×#103	D₄	1	1	yes	characteristic
133	C₁₉×#103	D₄	1	1	yes	characteristic
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	4	1	no	—
155	C₂²×C₄×C₁₉	—	4	1	no	—
156	Q₁₆×C₁₉	—	4	1	no	—
157	Q₁₆×C₁₉	—	4	2	no	—
158	Q₁₆×C₁₉	—	8	2	no	—
159	SD₁₆×C₁₉	Q₁₆	1	4	yes	complemented
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	—	4	2	no	—
166	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	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	—	4	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	—	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	C₂×D₄	1	1	yes	characteristic
191	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₂²⋊C₄×C₁₉	—	4	1	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	2	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	4	1	no	—
201	C₄²×C₁₉	—	4	1	no	—
202	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
203	#19816	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂³×C₁₉	—	2	1	no	—
205	Q₈×C₁₉	—	2	1	no	—
206	Q₈×C₁₉	—	2	1	no	—
207	Q₈×C₁₉	—	2	1	no	—
208	Q₈×C₁₉	—	2	1	no	—
209	Q₈×C₁₉	—	2	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	—	8	1	no	—
215	Q₈×C₁₉	—	16	1	no	—
216	Q₈×C₁₉	C₂×Q₁₆	1	2	yes	—
217	D₄×C₁₉	—	2	1	no	—
218	D₄×C₁₉	C₂×Q₁₆	1	2	yes	—
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	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
232	C₂×C₄×C₁₉	—	16	1	no	—
233	C₂×C₄×C₁₉	—	16	1	no	—
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	H(5,𝔽₂)	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	—	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	C₂×Q₁₆	1	2	yes	—
246	#3385	C₂×C₁₉	1	1	yes	characteristic
247	#3381	C₂×C₁₉	1	1	yes	characteristic
248	#3363	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#3338	C₂×C₁₉	1	1	yes	characteristic
250	#1723	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1683	C₂×C₁₉	1	1	yes	characteristic
253	#1676	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1676	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1644	C₂×C₁₉	1	1	yes	characteristic
256	#1636	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1633	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1632	C₂×C₁₉	1	1	yes	characteristic
259	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
260	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic
261	C₂²×C₁₉	—	2	2	no	—
262	C₂²×C₁₉	—	4	1	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	D₄²	1	1	yes	characteristic
265	C₄×C₁₉	—	2	2	no	—
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	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	C₂²×Q₁₆	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	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
282	#557	C₂²×C₁₉	1	1	yes	characteristic
283	#554	C₂²×C₁₉	1	1	yes	characteristic
284	#554	C₂²×C₁₉	1	1	yes	characteristic
285	#501	—	2	1	no	—
286	#500	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	#494	C₂²×C₁₉	1	1	yes	characteristic
291	#487	—	2	1	no	—
292	#487	C₂²×C₁₉	1	1	yes	characteristic
293	#487	C₂²×C₁₉	1	1	yes	characteristic
294	#484	—	2	1	no	—
295	#484	—	2	1	no	—
296	#479	—	2	1	no	—
297	#479	—	2	1	no	—
298	#478	—	2	1	no	—
299	#477	—	2	1	no	—
300	#477	C₂²×C₁₉	1	1	yes	characteristic
301	#477	C₂²×C₁₉	1	1	yes	characteristic
302	#477	C₂²×C₁₉	1	1	yes	characteristic
303	#477	C₂²×C₁₉	1	1	yes	characteristic
304	#477	C₂²×C₁₉	1	1	yes	characteristic
305	#476	C₂²×C₁₉	1	1	yes	characteristic
306	#474	—	2	1	no	—
307	#474	C₂²×C₁₉	1	1	yes	characteristic
308	#467	—	2	1	no	—
309	#462	—	2	1	no	—
310	#462	C₂²×C₁₉	1	1	yes	characteristic
311	#446	C₂²×C₁₉	1	1	yes	characteristic
312	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
313	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
314	#440	—	2	1	no	—
315	C₄×Q₁₆	—	2	1	no	—
316	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
317	C₄×SD₁₆	—	2	1	no	—
318	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
319	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#107	—	2	1	no	—
321	#335	C₂²×C₁₉	1	1	yes	characteristic
322	#335	C₂²×C₁₉	1	1	yes	characteristic
323	#333	C₂²×C₁₉	1	1	yes	characteristic
324	#333	C₂²×C₁₉	1	1	yes	characteristic
325	#333	C₂²×C₁₉	1	1	yes	characteristic
326	#332	C₂²×C₁₉	1	1	yes	characteristic
327	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
328	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
329	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
330	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
331	#322	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×C₁₉	—	4	2	no	—
333	C₂×C₁₉	#3269	1	1	yes	characteristic
334	C₂×C₁₉	D₄×Q₁₆	1	1	yes	characteristic
335	C₂×C₁₉	#3288	1	1	yes	characteristic
336	C₂×Q₁₆	—	2	1	no	—
337	C₂×Q₁₆	—	4	1	no	—
338	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
339	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	—	2	1	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	4	1	no	—
345	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
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	#125	—	2	1	no	—
350	#125	—	2	1	no	—
351	#125	—	2	1	no	—
352	#125	—	4	1	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	—	2	1	no	—
355	C₂²⋊Q₈	—	4	1	no	—
356	C₂²⋊Q₈	—	4	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
362	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
363	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	#107	—	2	1	no	—
370	#107	—	2	1	no	—
371	#107	—	2	1	no	—
372	#107	—	2	1	no	—
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	#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	D₄×C₁₉	1	1	yes	characteristic
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
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	#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	—	4	1	no	—
400	#103	D₄×C₁₉	1	1	yes	characteristic
401	#103	D₄×C₁₉	1	1	yes	characteristic
402	#103	D₄×C₁₉	1	1	yes	characteristic
403	#102	—	2	1	no	—
404	#102	—	2	1	no	—
405	#102	D₄×C₁₉	1	1	yes	characteristic
406	C₂²⋊C₈	—	2	1	no	—
407	#97	—	2	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	2	1	no	—
410	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₁₉	#19816	1	1	yes	characteristic, direct product factor, Sylow
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	4	1	no	—
419	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
421	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	—	4	1	no	—
426	Q₁₆	—	4	1	no	—
427	Q₁₆	—	4	2	no	—
428	Q₁₆	—	8	2	no	—
429	SD₁₆	Q₁₆×C₁₉	1	4	yes	complemented
430	C₂×C₈	—	2	1	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	—	4	2	no	—
436	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	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	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	—	4	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	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	4	1	no	—
471	C₄²	—	4	1	no	—
472	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
473	C₂³	—	2	1	no	—
474	Q₈	—	2	1	no	—
475	Q₈	—	2	1	no	—
476	Q₈	—	2	1	no	—
477	Q₈	—	2	1	no	—
478	Q₈	—	2	1	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	4	1	no	—
481	Q₈	—	8	1	no	—
482	Q₈	—	8	1	no	—
483	Q₈	—	8	1	no	—
484	Q₈	—	16	1	no	—
485	Q₈	C₂×Q₁₆×C₁₉	1	2	yes	—
486	D₄	—	2	1	no	—
487	D₄	C₂×Q₁₆×C₁₉	1	2	yes	—
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	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	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	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	16	1	no	—
502	C₂×C₄	—	16	1	no	—
503	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
505	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
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	C₂×Q₁₆×C₁₉	1	2	yes	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	D₄²×C₁₉	1	1	yes	characteristic
519	C₄	—	2	2	no	—
520	C₄	—	2	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	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	C₂²×Q₁₆×C₁₉	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	2	no	—
536	C₂	C₁₉×#3269	1	1	yes	characteristic
537	C₂	D₄×Q₁₆×C₁₉	1	1	yes	characteristic
538	C₂	C₁₉×#3288	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
3. C₁₉×#3363	C₂	semidirect
5. C₁₉×#1723	C₂	semidirect
6. C₁₉×#1692	C₂	semidirect
8. C₁₉×#1676	C₂	semidirect
9. C₁₉×#1676	C₂	semidirect
11. C₁₉×#1636	C₂	semidirect
12. C₁₉×#1633	C₂	semidirect
14. C₁₉×#1584	C₂	semidirect
159. SD₁₆×C₁₉	Q₁₆	semidirect
203. #19816	C₁₉	direct (N × H)
248. #3363	C₂×C₁₉	semidirect
250. #1723	C₂×C₁₉	semidirect
251. #1692	C₂×C₁₉	semidirect
253. #1676	C₂×C₁₉	semidirect
254. #1676	C₂×C₁₉	semidirect
256. #1636	C₂×C₁₉	semidirect
257. #1633	C₂×C₁₉	semidirect
259. #1584	C₂×C₁₉	semidirect
413. C₁₉	#19816	direct (N × H)
429. SD₁₆	Q₁₆×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3385	2
C₁₉×#3381	2
C₁₉×#3363	2
C₁₉×#3338	2
C₁₉×#1723	2
C₁₉×#1692	2
C₁₉×#1683	2
C₁₉×#1676	2
C₁₉×#1644	2
C₁₉×#1636	2
C₁₉×#1633	2
C₁₉×#1632	2
C₁₉×#1584	2
C₁₉×SD₁₆⋊C₈	2
#19816	19

Subgroups — C19×#19816 #18025775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19816 #18025775