Subgroups — C₁₉×#19844 #18025803

Order 4864.

590 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3362	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3304	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1719	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1684	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1675	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1638	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1631	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1623	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, complemented
16	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
17	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#556	C₂²	1	1	yes	characteristic
19	C₁₉×#550	C₂²	1	1	yes	characteristic
20	C₁₉×#500	—	2	1	no	—
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#492	C₂²	1	1	yes	characteristic
23	C₁₉×#489	—	2	1	no	—
24	C₁₉×#487	C₂²	1	1	yes	characteristic
25	C₁₉×#487	C₂²	1	1	yes	characteristic
26	C₁₉×#486	—	2	1	no	—
27	C₁₉×#486	C₂²	1	1	yes	characteristic
28	C₁₉×#486	C₂²	1	1	yes	characteristic
29	C₁₉×#482	—	2	1	no	—
30	C₁₉×#477	—	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×#476	—	2	1	no	—
35	C₁₉×#476	C₂²	1	1	yes	characteristic
36	C₁₉×#476	C₂²	1	1	yes	characteristic
37	C₁₉×#475	—	2	1	no	—
38	C₁₉×#475	C₂²	1	1	yes	characteristic
39	C₁₉×#465	—	2	1	no	—
40	C₁₉×#464	—	2	1	no	—
41	C₁₉×#462	C₂²	1	1	yes	characteristic
42	C₁₉×#460	—	2	1	no	—
43	C₁₉×#460	C₂²	1	1	yes	characteristic
44	C₁₉×#460	C₂²	1	1	yes	characteristic
45	C₁₉×#452	—	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×#441	—	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	C₁₉×#416	—	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×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#331	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×#41×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	—	4	1	no	—
73	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	—	2	1	no	—
75	C₁₉×C₄⋊Q₈	—	2	1	no	—
76	C₁₉×C₄⋊Q₈	—	2	1	no	—
77	C₁₉×C₄⋊Q₈	—	2	1	no	—
78	C₁₉×C₄⋊Q₈	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	—	4	1	no	—
80	C₁₉×C₄⋊Q₈	—	4	1	no	—
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×#127	—	2	1	no	—
85	C₁₉×#127	C₂³	1	1	yes	characteristic
86	C₁₉×#126	—	4	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×#121	—	2	1	no	—
90	C₁₉×#121	—	4	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	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#117	—	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	D₄	1	1	yes	characteristic
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	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	—	4	1	no	—
125	C₁₉×#103	D₄	1	1	yes	characteristic
126	C₁₉×#103	D₄	1	1	yes	characteristic
127	C₁₉×#103	D₄	1	1	yes	characteristic
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
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	#41×C₁₉	—	4	2	no	—
145	#41×C₁₉	—	8	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	—	4	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	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	4	1	no	—
158	C₂×D₄×C₁₉	—	4	1	no	—
159	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	4	1	no	—
162	Q₁₆×C₁₉	—	2	2	no	—
163	Q₁₆×C₁₉	—	4	2	no	—
164	SD₁₆×C₁₉	—	2	2	no	—
165	SD₁₆×C₁₉	—	4	2	no	—
166	SD₁₆×C₁₉	—	8	1	no	—
167	SD₁₆×C₁₉	—	8	2	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	8	1	no	—
174	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	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	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₂²⋊C₄×C₁₉	—	4	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	—	4	1	no	—
206	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
207	#19844	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	4	1	no	—
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	2	1	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	8	1	no	—
217	Q₈×C₁₉	—	8	1	no	—
218	Q₈×C₁₉	—	16	1	no	—
219	Q₈×C₁₉	—	16	1	no	—
220	Q₈×C₁₉	#135	1	2	yes	—
221	Q₈×C₁₉	#137	1	2	yes	—
222	D₄×C₁₉	—	2	1	no	—
223	D₄×C₁₉	—	2	1	no	—
224	D₄×C₁₉	—	4	1	no	—
225	D₄×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	8	2	no	—
229	D₄×C₁₉	—	8	1	no	—
230	D₄×C₁₉	—	16	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	8	2	no	—
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
247	C₈×C₁₉	—	2	1	no	—
248	C₈×C₁₉	—	2	1	no	—
249	C₈×C₁₉	—	2	1	no	—
250	C₈×C₁₉	—	2	1	no	—
251	C₈×C₁₉	—	4	1	no	—
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	—	4	1	no	—
254	C₈×C₁₉	—	4	1	no	—
255	C₈×C₁₉	—	4	1	no	—
256	Q₈×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#3369	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#3362	C₂×C₁₉	1	1	yes	characteristic
259	#3304	C₂×C₁₉	1	1	yes	characteristic
260	#1719	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1698	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1675	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1645	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1638	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1631	C₂×C₁₉	1	1	yes	characteristic
268	#1623	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
270	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	1	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	8	1	no	—
275	C₂²×C₁₉	—	8	1	no	—
276	C₂²×C₁₉	—	8	1	no	—
277	C₂²×C₁₉	D₄²	1	1	yes	characteristic
278	C₄×C₁₉	—	2	2	no	—
279	C₄×C₁₉	—	2	2	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	8	1	no	—
287	C₄×C₁₉	—	8	1	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
290	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
291	C₄×C₁₉	#577	1	1	yes	characteristic
292	C₄×C₁₉	#578	1	1	yes	characteristic
293	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
294	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
295	#556	C₂²×C₁₉	1	1	yes	characteristic
296	#550	C₂²×C₁₉	1	1	yes	characteristic
297	#500	—	2	1	no	—
298	#500	C₂²×C₁₉	1	1	yes	characteristic
299	#492	C₂²×C₁₉	1	1	yes	characteristic
300	#489	—	2	1	no	—
301	#487	C₂²×C₁₉	1	1	yes	characteristic
302	#487	C₂²×C₁₉	1	1	yes	characteristic
303	#486	—	2	1	no	—
304	#486	C₂²×C₁₉	1	1	yes	characteristic
305	#486	C₂²×C₁₉	1	1	yes	characteristic
306	#482	—	2	1	no	—
307	#477	—	2	1	no	—
308	#477	—	2	1	no	—
309	#477	C₂²×C₁₉	1	1	yes	characteristic
310	#477	C₂²×C₁₉	1	1	yes	characteristic
311	#476	—	2	1	no	—
312	#476	C₂²×C₁₉	1	1	yes	characteristic
313	#476	C₂²×C₁₉	1	1	yes	characteristic
314	#475	—	2	1	no	—
315	#475	C₂²×C₁₉	1	1	yes	characteristic
316	#465	—	2	1	no	—
317	#464	—	2	1	no	—
318	#462	C₂²×C₁₉	1	1	yes	characteristic
319	#460	—	2	1	no	—
320	#460	C₂²×C₁₉	1	1	yes	characteristic
321	#460	C₂²×C₁₉	1	1	yes	characteristic
322	#452	—	2	1	no	—
323	#446	C₂²×C₁₉	1	1	yes	characteristic
324	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
325	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
326	#441	—	2	1	no	—
327	C₄×Q₁₆	—	2	1	no	—
328	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
329	C₄×SD₁₆	—	2	1	no	—
330	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
331	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
332	#416	—	2	1	no	—
333	#335	C₂²×C₁₉	1	1	yes	characteristic
334	#335	C₂²×C₁₉	1	1	yes	characteristic
335	#333	C₂²×C₁₉	1	1	yes	characteristic
336	#333	C₂²×C₁₉	1	1	yes	characteristic
337	#332	C₂²×C₁₉	1	1	yes	characteristic
338	#331	C₂²×C₁₉	1	1	yes	characteristic
339	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
340	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
341	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
342	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
343	#322	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×C₁₉	—	8	1	no	—
345	C₂×C₁₉	—	16	1	no	—
346	C₂×C₁₉	#3266	1	1	yes	characteristic
347	C₂×C₁₉	#3285	1	1	yes	characteristic
348	C₂×C₁₉	#3288	1	1	yes	characteristic
349	C₂×#41	—	2	1	no	—
350	C₂×Q₁₆	—	2	1	no	—
351	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	4	1	no	—
355	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₈	—	2	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	—	4	1	no	—
362	C₄⋊Q₈	—	4	1	no	—
363	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
366	#127	—	2	1	no	—
367	#127	C₂³×C₁₉	1	1	yes	characteristic
368	#126	—	4	1	no	—
369	#124	—	2	1	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	#121	—	2	1	no	—
372	#121	—	4	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	—	2	1	no	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
379	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#107	—	2	1	no	—
385	#107	—	2	1	no	—
386	#107	—	2	1	no	—
387	#107	—	2	1	no	—
388	#107	D₄×C₁₉	1	1	yes	characteristic
389	#106	—	2	1	no	—
390	#106	—	2	1	no	—
391	#106	—	2	1	no	—
392	#106	D₄×C₁₉	1	1	yes	characteristic
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	D₄×C₁₉	1	1	yes	characteristic
419	C₂²⋊C₈	—	2	1	no	—
420	#97	—	2	1	no	—
421	C₄×C₈	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₁₉	#19844	1	1	yes	characteristic, direct product factor, Sylow
427	#41	—	4	2	no	—
428	#41	—	8	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	4	1	no	—
433	C₂×Q₈	—	4	1	no	—
434	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	Q₁₆	—	2	2	no	—
446	Q₁₆	—	4	2	no	—
447	SD₁₆	—	2	2	no	—
448	SD₁₆	—	4	2	no	—
449	SD₁₆	—	8	1	no	—
450	SD₁₆	—	8	2	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	8	1	no	—
457	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	4	1	no	—
487	C₄²	—	4	1	no	—
488	C₄²	—	4	1	no	—
489	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
490	C₂³	—	2	1	no	—
491	C₂³	—	4	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	8	1	no	—
499	Q₈	—	8	1	no	—
500	Q₈	—	16	1	no	—
501	Q₈	—	16	1	no	—
502	Q₈	C₁₉×#135	1	2	yes	—
503	Q₈	C₁₉×#137	1	2	yes	—
504	D₄	—	2	1	no	—
505	D₄	—	2	1	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	1	no	—
512	D₄	—	16	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
528	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	D₄²×C₁₉	1	1	yes	characteristic
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
557	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
558	C₄	C₁₉×#577	1	1	yes	characteristic
559	C₄	C₁₉×#578	1	1	yes	characteristic
560	C₂	—	8	1	no	—
561	C₂	—	16	1	no	—
562	C₂	C₁₉×#3266	1	1	yes	characteristic
563	C₂	C₁₉×#3285	1	1	yes	characteristic
564	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#550	C₂²
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. Q₈×Q₁₆×C₁₉	C₂	semidirect
2. C₁₉×#3369	C₂	semidirect
5. C₁₉×#1719	C₂	semidirect
6. C₁₉×#1698	C₂	semidirect
7. C₁₉×#1684	C₂	semidirect
8. C₁₉×#1682	C₂	semidirect
9. C₁₉×#1675	C₂	semidirect
10. C₁₉×#1645	C₂	semidirect
11. C₁₉×#1638	C₂	semidirect
13. C₁₉×#1623	C₂	semidirect
14. C₁₉×#1584	C₂	semidirect
15. C₁₉×SD₁₆⋊C₈	C₂	semidirect
207. #19844	C₁₉	direct (N × H)
256. Q₈×Q₁₆	C₂×C₁₉	semidirect
257. #3369	C₂×C₁₉	semidirect
260. #1719	C₂×C₁₉	semidirect
261. #1698	C₂×C₁₉	semidirect
262. #1684	C₂×C₁₉	semidirect
263. #1682	C₂×C₁₉	semidirect
264. #1675	C₂×C₁₉	semidirect
265. #1645	C₂×C₁₉	semidirect
266. #1638	C₂×C₁₉	semidirect
268. #1623	C₂×C₁₉	semidirect
269. #1584	C₂×C₁₉	semidirect
270. SD₁₆⋊C₈	C₂×C₁₉	semidirect
426. C₁₉	#19844	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×Q₁₆×C₁₉	2
C₁₉×#3369	2
C₁₉×#3362	2
C₁₉×#3304	2
C₁₉×#1719	2
C₁₉×#1698	2
C₁₉×#1684	2
C₁₉×#1682	2
C₁₉×#1675	2
C₁₉×#1645	2
C₁₉×#1638	2
C₁₉×#1631	2
C₁₉×#1623	2
C₁₉×#1584	2
C₁₉×SD₁₆⋊C₈	2
#19844	19

Subgroups — C19×#19844 #18025803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19844 #18025803