Subgroups — C₁₉×#19886 #18025845

Order 4864.

738 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3358	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1709	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1689	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1687	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1681	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1641	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1639	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1627	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1589	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	—	2	1	no	—
17	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
18	C₁₉×#550	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₁₉×#547	C₂²	1	1	yes	characteristic
21	D₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#493	C₂²	1	1	yes	characteristic
24	C₁₉×#486	—	2	1	no	—
25	C₁₉×#486	C₂²	1	1	yes	characteristic
26	C₁₉×#486	C₂²	1	1	yes	characteristic
27	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#480	—	2	1	no	—
30	C₁₉×#474	—	2	1	no	—
31	C₁₉×#474	C₂²	1	1	yes	characteristic
32	C₁₉×#474	C₂²	1	1	yes	characteristic
33	C₁₉×#470	—	2	1	no	—
34	C₁₉×#469	—	2	1	no	—
35	C₁₉×#466	—	2	1	no	—
36	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#461	C₂²	1	1	yes	characteristic
38	C₁₉×#460	C₂²	1	1	yes	characteristic
39	C₁₉×#459	—	2	1	no	—
40	C₁₉×#459	C₂²	1	1	yes	characteristic
41	C₁₉×#459	C₂²	1	1	yes	characteristic
42	C₁₉×#459	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#452	—	2	1	no	—
44	C₁₉×#451	—	2	1	no	—
45	C₁₉×#449	—	2	1	no	—
46	C₁₉×#447	—	2	1	no	—
47	C₁₉×#447	—	2	1	no	—
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
49	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
50	C₄×D₈×C₁₉	—	2	1	no	—
51	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
52	C₁₉×#436	C₂²	1	1	yes	characteristic
53	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
54	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#102	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#331	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	—	2	1	no	—
69	C₂²×Q₈×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₁₉×#137	—	4	4	no	—
73	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
74	C₂×Q₁₆×C₁₉	—	2	1	no	—
75	C₂×Q₁₆×C₁₉	—	2	1	no	—
76	C₂×Q₁₆×C₁₉	—	2	1	no	—
77	C₂×SD₁₆×C₁₉	—	2	1	no	—
78	C₂×SD₁₆×C₁₉	—	2	1	no	—
79	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
80	C₂×D₈×C₁₉	—	2	1	no	—
81	C₂×D₈×C₁₉	—	2	1	no	—
82	C₂×D₈×C₁₉	—	2	1	no	—
83	C₂×D₈×C₁₉	—	2	1	no	—
84	C₂×D₈×C₁₉	—	2	1	no	—
85	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
86	C₂×M₁₆×C₁₉	—	2	1	no	—
87	C₂×M₁₆×C₁₉	—	2	1	no	—
88	C₂²×C₈×C₁₉	—	2	1	no	—
89	C₁₉×C₄⋊Q₈	—	2	1	no	—
90	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₉×#127	—	2	1	no	—
93	C₁₉×#127	C₂³	1	1	yes	characteristic
94	C₁₉×#127	C₂³	1	1	yes	characteristic
95	C₁₉×#123	—	4	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	—	4	1	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	2	1	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	4	1	no	—
104	C₁₉×#120	—	4	1	no	—
105	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₁₉×#107	—	2	1	no	—
113	C₁₉×#107	—	2	1	no	—
114	C₁₉×#107	D₄	1	1	yes	characteristic
115	C₁₉×#106	D₄	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	—	2	1	no	—
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×#103	—	2	1	no	—
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	D₄	1	1	yes	characteristic
124	C₁₉×#102	—	2	1	no	—
125	C₁₉×#102	—	2	1	no	—
126	C₁₉×#102	—	2	1	no	—
127	C₁₉×#102	—	2	1	no	—
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	—	4	1	no	—
135	C₁₉×#102	—	4	1	no	—
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×#102	D₄	1	1	yes	characteristic
138	C₁₉×#102	D₄	1	1	yes	characteristic
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₄×C₈×C₁₉	—	2	1	no	—
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
146	C₂⁴×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	4	2	no	—
148	#41×C₁₉	—	4	2	no	—
149	#41×C₁₉	—	8	1	no	—
150	#41×C₁₉	—	8	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	4	1	no	—
154	C₂×Q₈×C₁₉	—	4	2	no	—
155	C₂×Q₈×C₁₉	—	8	1	no	—
156	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	4	1	no	—
164	C₂×D₄×C₁₉	—	4	1	no	—
165	C₂×D₄×C₁₉	—	4	1	no	—
166	C₂×D₄×C₁₉	—	4	1	no	—
167	C₂×D₄×C₁₉	—	4	2	no	—
168	C₂×D₄×C₁₉	—	4	2	no	—
169	C₂×D₄×C₁₉	—	4	1	no	—
170	C₂×D₄×C₁₉	—	8	1	no	—
171	C₂×D₄×C₁₉	—	8	1	no	—
172	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	4	1	no	—
179	C₂²×C₄×C₁₉	—	4	1	no	—
180	C₂²×C₄×C₁₉	—	4	1	no	—
181	Q₁₆×C₁₉	—	4	2	no	—
182	Q₁₆×C₁₉	—	4	2	no	—
183	Q₁₆×C₁₉	—	8	1	no	—
184	SD₁₆×C₁₉	—	4	2	no	—
185	SD₁₆×C₁₉	—	4	2	no	—
186	SD₁₆×C₁₉	D₈	1	4	yes	complemented
187	D₈×C₁₉	—	4	1	no	—
188	D₈×C₁₉	—	4	2	no	—
189	D₈×C₁₉	—	4	2	no	—
190	D₈×C₁₉	—	4	2	no	—
191	D₈×C₁₉	—	8	1	no	—
192	D₈×C₁₉	—	8	1	no	—
193	M₁₆×C₁₉	—	4	2	no	—
194	M₁₆×C₁₉	—	4	2	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	2	1	no	—
197	C₂×C₈×C₁₉	—	2	1	no	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	8	1	no	—
201	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	4	1	no	—
211	C₄⋊C₄×C₁₉	—	4	1	no	—
212	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	4	1	no	—
220	C₂²⋊C₄×C₁₉	—	4	1	no	—
221	C₂²⋊C₄×C₁₉	—	4	1	no	—
222	C₂²⋊C₄×C₁₉	—	4	1	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
225	#19886	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	8	2	no	—
232	C₂³×C₁₉	—	8	2	no	—
233	C₂³×C₁₉	—	16	1	no	—
234	Q₈×C₁₉	—	2	1	no	—
235	Q₈×C₁₉	—	4	1	no	—
236	Q₈×C₁₉	—	4	1	no	—
237	Q₈×C₁₉	—	4	1	no	—
238	Q₈×C₁₉	—	4	1	no	—
239	Q₈×C₁₉	—	8	2	no	—
240	Q₈×C₁₉	C₂×D₈	1	2	yes	—
241	D₄×C₁₉	—	2	1	no	—
242	D₄×C₁₉	—	2	1	no	—
243	D₄×C₁₉	—	2	1	no	—
244	D₄×C₁₉	—	2	1	no	—
245	D₄×C₁₉	—	2	1	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	1	no	—
250	D₄×C₁₉	—	4	1	no	—
251	D₄×C₁₉	—	4	1	no	—
252	D₄×C₁₉	—	4	1	no	—
253	D₄×C₁₉	—	4	1	no	—
254	D₄×C₁₉	—	8	2	no	—
255	D₄×C₁₉	—	8	1	no	—
256	D₄×C₁₉	—	8	1	no	—
257	D₄×C₁₉	—	8	2	no	—
258	D₄×C₁₉	—	8	2	no	—
259	D₄×C₁₉	—	8	2	no	—
260	D₄×C₁₉	—	16	1	no	—
261	D₄×C₁₉	C₂×D₈	1	2	yes	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	8	2	no	—
276	C₂×C₄×C₁₉	—	8	2	no	—
277	C₂×C₄×C₁₉	—	8	2	no	—
278	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
281	C₈×C₁₉	—	2	1	no	—
282	C₈×C₁₉	—	2	1	no	—
283	C₈×C₁₉	—	2	1	no	—
284	C₈×C₁₉	—	4	1	no	—
285	C₈×C₁₉	—	4	1	no	—
286	C₈×C₁₉	—	4	1	no	—
287	C₈×C₁₉	—	4	1	no	—
288	C₈×C₁₉	—	4	1	no	—
289	C₈×C₁₉	C₂×D₈	1	2	yes	—
290	#3358	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#3294	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#3276	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#3274	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1709	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1689	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1687	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1681	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1641	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1639	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1627	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1625	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1589	C₂×C₁₉	1	1	yes	characteristic, complemented
304	C₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
305	C₂²×C₁₉	—	2	2	no	—
306	C₂²×C₁₉	—	4	1	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	—	4	1	no	—
310	C₂²×C₁₉	—	4	1	no	—
311	C₂²×C₁₉	—	4	1	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	4	1	no	—
314	C₂²×C₁₉	—	8	1	no	—
315	C₂²×C₁₉	—	8	1	no	—
316	C₂²×C₁₉	—	8	1	no	—
317	C₂²×C₁₉	—	8	1	no	—
318	C₂²×C₁₉	—	8	1	no	—
319	C₂²×C₁₉	—	8	1	no	—
320	C₂²×C₁₉	—	16	4	no	—
321	C₂²×C₁₉	D₄²	1	1	yes	characteristic
322	C₄×C₁₉	—	2	2	no	—
323	C₄×C₁₉	—	2	1	no	—
324	C₄×C₁₉	—	4	1	no	—
325	C₄×C₁₉	—	4	1	no	—
326	C₄×C₁₉	—	4	1	no	—
327	C₄×C₁₉	—	4	1	no	—
328	C₄×C₁₉	—	8	1	no	—
329	C₄×C₁₉	—	8	1	no	—
330	C₄×C₁₉	C₂²×D₈	1	1	yes	characteristic
331	C₄×C₁₉	#575	1	1	yes	characteristic
332	C₄×C₁₉	#576	1	1	yes	characteristic
333	C₄×C₁₉	#577	1	1	yes	characteristic
334	C₂×#137	—	2	1	no	—
335	C₂×AGL(1,ℤ/8)	—	2	1	no	—
336	#550	C₂²×C₁₉	1	1	yes	characteristic
337	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	#547	C₂²×C₁₉	1	1	yes	characteristic
339	D₄²	C₂²×C₁₉	1	1	yes	characteristic
340	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	#493	C₂²×C₁₉	1	1	yes	characteristic
342	#486	—	2	1	no	—
343	#486	C₂²×C₁₉	1	1	yes	characteristic
344	#486	C₂²×C₁₉	1	1	yes	characteristic
345	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
346	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
347	#480	—	2	1	no	—
348	#474	—	2	1	no	—
349	#474	C₂²×C₁₉	1	1	yes	characteristic
350	#474	C₂²×C₁₉	1	1	yes	characteristic
351	#470	—	2	1	no	—
352	#469	—	2	1	no	—
353	#466	—	2	1	no	—
354	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
355	#461	C₂²×C₁₉	1	1	yes	characteristic
356	#460	C₂²×C₁₉	1	1	yes	characteristic
357	#459	—	2	1	no	—
358	#459	C₂²×C₁₉	1	1	yes	characteristic
359	#459	C₂²×C₁₉	1	1	yes	characteristic
360	#459	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#452	—	2	1	no	—
362	#451	—	2	1	no	—
363	#449	—	2	1	no	—
364	#447	—	2	1	no	—
365	#447	—	2	1	no	—
366	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
368	C₄×D₈	—	2	1	no	—
369	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
370	#436	C₂²×C₁₉	1	1	yes	characteristic
371	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
372	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#102	—	2	1	no	—
374	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
375	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
376	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
377	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
378	#331	C₂²×C₁₉	1	1	yes	characteristic
379	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
380	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
381	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
382	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
383	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
384	C₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
385	C₂×C₁₉	—	4	2	no	—
386	C₂×C₁₉	—	8	1	no	—
387	C₂×C₁₉	—	8	1	no	—
388	C₂×C₁₉	—	16	1	no	—
389	C₂×C₁₉	—	16	1	no	—
390	C₂×C₁₉	#3275	1	1	yes	characteristic
391	C₂×C₁₉	D₄×D₈	1	1	yes	characteristic
392	C₂×C₁₉	#3290	1	1	yes	characteristic
393	C₂×#41	—	2	1	no	—
394	C₂×#41	—	2	1	no	—
395	C₂²×Q₈	—	2	1	no	—
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	—	2	1	no	—
398	#137	—	4	4	no	—
399	AGL(1,ℤ/8)	—	4	4	no	—
400	C₂×Q₁₆	—	2	1	no	—
401	C₂×Q₁₆	—	2	1	no	—
402	C₂×Q₁₆	—	2	1	no	—
403	C₂×SD₁₆	—	2	1	no	—
404	C₂×SD₁₆	—	2	1	no	—
405	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
406	C₂×D₈	—	2	1	no	—
407	C₂×D₈	—	2	1	no	—
408	C₂×D₈	—	2	1	no	—
409	C₂×D₈	—	2	1	no	—
410	C₂×D₈	—	2	1	no	—
411	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
412	C₂×M₁₆	—	2	1	no	—
413	C₂×M₁₆	—	2	1	no	—
414	C₂²×C₈	—	2	1	no	—
415	C₄⋊Q₈	—	2	1	no	—
416	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
418	#127	—	2	1	no	—
419	#127	C₂³×C₁₉	1	1	yes	characteristic
420	#127	C₂³×C₁₉	1	1	yes	characteristic
421	#123	—	4	1	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	C₂²⋊Q₈	—	2	1	no	—
424	C₂²⋊Q₈	—	4	1	no	—
425	#121	—	2	1	no	—
426	#121	—	2	1	no	—
427	#121	—	2	1	no	—
428	#121	—	2	1	no	—
429	#121	—	4	1	no	—
430	#120	—	4	1	no	—
431	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
435	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
436	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	—	2	1	no	—
438	#107	—	2	1	no	—
439	#107	—	2	1	no	—
440	#107	D₄×C₁₉	1	1	yes	characteristic
441	#106	D₄×C₁₉	1	1	yes	characteristic
442	C₄⋊C₈	—	2	1	no	—
443	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
445	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
446	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
447	#103	—	2	1	no	—
448	#103	—	2	1	no	—
449	#103	D₄×C₁₉	1	1	yes	characteristic
450	#102	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	—	2	1	no	—
455	#102	—	2	1	no	—
456	#102	—	2	1	no	—
457	#102	—	2	1	no	—
458	#102	—	2	1	no	—
459	#102	—	2	1	no	—
460	#102	—	4	1	no	—
461	#102	—	4	1	no	—
462	#102	D₄×C₁₉	1	1	yes	characteristic
463	#102	D₄×C₁₉	1	1	yes	characteristic
464	#102	D₄×C₁₉	1	1	yes	characteristic
465	C₂²⋊C₈	—	2	1	no	—
466	C₂²⋊C₈	—	2	1	no	—
467	C₂²⋊C₈	—	2	1	no	—
468	C₄×C₈	—	2	1	no	—
469	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
470	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
471	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
472	C₁₉	#19886	1	1	yes	characteristic, direct product factor, Sylow
473	C₂⁴	—	4	1	no	—
474	#41	—	4	2	no	—
475	#41	—	4	2	no	—
476	#41	—	8	1	no	—
477	#41	—	8	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	4	1	no	—
481	C₂×Q₈	—	4	2	no	—
482	C₂×Q₈	—	8	1	no	—
483	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	4	1	no	—
491	C₂×D₄	—	4	1	no	—
492	C₂×D₄	—	4	1	no	—
493	C₂×D₄	—	4	1	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	4	1	no	—
497	C₂×D₄	—	8	1	no	—
498	C₂×D₄	—	8	1	no	—
499	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
501	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	4	1	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	1	no	—
508	Q₁₆	—	4	2	no	—
509	Q₁₆	—	4	2	no	—
510	Q₁₆	—	8	1	no	—
511	SD₁₆	—	4	2	no	—
512	SD₁₆	—	4	2	no	—
513	SD₁₆	D₈×C₁₉	1	4	yes	complemented
514	D₈	—	4	1	no	—
515	D₈	—	4	2	no	—
516	D₈	—	4	2	no	—
517	D₈	—	4	2	no	—
518	D₈	—	8	1	no	—
519	D₈	—	8	1	no	—
520	M₁₆	—	4	2	no	—
521	M₁₆	—	4	2	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	8	1	no	—
528	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	4	1	no	—
538	C₄⋊C₄	—	4	1	no	—
539	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
540	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	4	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	1	no	—
549	C₂²⋊C₄	—	4	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	8	2	no	—
558	C₂³	—	8	2	no	—
559	C₂³	—	16	1	no	—
560	Q₈	—	2	1	no	—
561	Q₈	—	4	1	no	—
562	Q₈	—	4	1	no	—
563	Q₈	—	4	1	no	—
564	Q₈	—	4	1	no	—
565	Q₈	—	8	2	no	—
566	Q₈	C₂×D₈×C₁₉	1	2	yes	—
567	D₄	—	2	1	no	—
568	D₄	—	2	1	no	—
569	D₄	—	2	1	no	—
570	D₄	—	2	1	no	—
571	D₄	—	2	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	1	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	1	no	—
576	D₄	—	4	1	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	1	no	—
580	D₄	—	8	2	no	—
581	D₄	—	8	1	no	—
582	D₄	—	8	1	no	—
583	D₄	—	8	2	no	—
584	D₄	—	8	2	no	—
585	D₄	—	8	2	no	—
586	D₄	—	16	1	no	—
587	D₄	C₂×D₈×C₁₉	1	2	yes	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	8	2	no	—
602	C₂×C₄	—	8	2	no	—
603	C₂×C₄	—	8	2	no	—
604	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
606	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
607	C₈	—	2	1	no	—
608	C₈	—	2	1	no	—
609	C₈	—	2	1	no	—
610	C₈	—	4	1	no	—
611	C₈	—	4	1	no	—
612	C₈	—	4	1	no	—
613	C₈	—	4	1	no	—
614	C₈	—	4	1	no	—
615	C₈	C₂×D₈×C₁₉	1	2	yes	—
616	C₂²	—	2	2	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	—	8	1	no	—
631	C₂²	—	16	4	no	—
632	C₂²	D₄²×C₁₉	1	1	yes	characteristic
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	C₂²×D₈×C₁₉	1	1	yes	characteristic
642	C₄	C₁₉×#575	1	1	yes	characteristic
643	C₄	C₁₉×#576	1	1	yes	characteristic
644	C₄	C₁₉×#577	1	1	yes	characteristic
645	C₂	—	4	2	no	—
646	C₂	—	8	1	no	—
647	C₂	—	8	1	no	—
648	C₂	—	16	1	no	—
649	C₂	—	16	1	no	—
650	C₂	C₁₉×#3275	1	1	yes	characteristic
651	C₂	D₄×D₈×C₁₉	1	1	yes	characteristic
652	C₂	C₁₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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×#3358	C₂	semidirect
2. C₁₉×#3294	C₂	semidirect
3. C₁₉×#3276	C₂	semidirect
4. C₁₉×#3274	C₂	semidirect
5. C₁₉×#1709	C₂	semidirect
6. C₁₉×#1689	C₂	semidirect
7. C₁₉×#1687	C₂	semidirect
8. C₁₉×#1682	C₂	semidirect
9. C₁₉×#1681	C₂	semidirect
10. C₁₉×#1641	C₂	semidirect
11. C₁₉×#1639	C₂	semidirect
12. C₁₉×#1627	C₂	semidirect
13. C₁₉×#1625	C₂	semidirect
14. C₁₉×#1589	C₂	semidirect
15. C₈×SD₁₆×C₁₉	C₂	semidirect
19. D₄×Q₈×C₁₉	C₂²	semidirect
22. C₁₉×#494	C₂²	semidirect
27. C₁₉×#486	C₂²	semidirect
28. C₁₉×#486	C₂²	semidirect
36. C₁₉×#462	C₂²	semidirect
42. C₁₉×#459	C₂²	semidirect
48. C₈×Q₈×C₁₉	C₂²	semidirect
53. C₁₉×#436	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#332	C₂²	semidirect
59. C₁₉×#332	C₂²	semidirect
61. C₁₉×#331	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
65. C₁₉×D₄⋊C₈	C₂²	semidirect
66. C₈²×C₁₉	C₂²	semidirect
186. SD₁₆×C₁₉	D₈	semidirect
225. #19886	C₁₉	direct (N × H)
290. #3358	C₂×C₁₉	semidirect
291. #3294	C₂×C₁₉	semidirect
292. #3276	C₂×C₁₉	semidirect
293. #3274	C₂×C₁₉	semidirect
294. #1709	C₂×C₁₉	semidirect
295. #1689	C₂×C₁₉	semidirect
296. #1687	C₂×C₁₉	semidirect
297. #1682	C₂×C₁₉	semidirect
298. #1681	C₂×C₁₉	semidirect
299. #1641	C₂×C₁₉	semidirect
300. #1639	C₂×C₁₉	semidirect
301. #1627	C₂×C₁₉	semidirect
302. #1625	C₂×C₁₉	semidirect
303. #1589	C₂×C₁₉	semidirect
304. C₈×SD₁₆	C₂×C₁₉	semidirect
337. D₄×Q₈	C₂²×C₁₉	semidirect
340. #494	C₂²×C₁₉	semidirect
345. #486	C₂²×C₁₉	semidirect
346. #486	C₂²×C₁₉	semidirect
354. #462	C₂²×C₁₉	semidirect
360. #459	C₂²×C₁₉	semidirect
366. C₈×Q₈	C₂²×C₁₉	semidirect
371. #436	C₂²×C₁₉	semidirect
374. #335	C₂²×C₁₉	semidirect
375. #334	C₂²×C₁₉	semidirect
376. #332	C₂²×C₁₉	semidirect
377. #332	C₂²×C₁₉	semidirect
379. #331	C₂²×C₁₉	semidirect
380. Q₈⋊C₈	C₂²×C₁₉	semidirect
383. D₄⋊C₈	C₂²×C₁₉	semidirect
384. C₈²	C₂²×C₁₉	semidirect
472. C₁₉	#19886	direct (N × H)
513. SD₁₆	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3358	2
C₁₉×#3294	2
C₁₉×#3276	2
C₁₉×#3274	2
C₁₉×#1709	2
C₁₉×#1689	2
C₁₉×#1687	2
C₁₉×#1682	2
C₁₉×#1681	2
C₁₉×#1641	2
C₁₉×#1639	2
C₁₉×#1627	2
C₁₉×#1625	2
C₁₉×#1589	2
C₈×SD₁₆×C₁₉	2
#19886	19

Subgroups — C19×#19886 #18025845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19886 #18025845