Subgroups — C₁₉×#19758 #18025717

Order 4864.

736 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3334	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3272	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1722	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1689	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1681	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1673	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1647	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1647	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1639	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂×C₁₉×#135	—	2	1	no	—
18	C₁₉×#547	C₂²	1	1	yes	characteristic
19	C₁₉×#547	C₂²	1	1	yes	characteristic
20	C₁₉×#547	C₂²	1	1	yes	characteristic, complemented
21	D₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#492	C₂²	1	1	yes	characteristic
26	C₁₉×#486	C₂²	1	1	yes	characteristic
27	C₁₉×#486	C₂²	1	1	yes	characteristic
28	C₁₉×#480	—	2	1	no	—
29	C₁₉×#480	—	2	1	no	—
30	C₁₉×#480	—	2	1	no	—
31	C₁₉×#474	C₂²	1	1	yes	characteristic
32	C₁₉×#474	C₂²	1	1	yes	characteristic
33	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#468	—	2	1	no	—
35	C₁₉×#467	—	2	1	no	—
36	C₁₉×#466	—	2	1	no	—
37	C₁₉×#466	—	2	1	no	—
38	C₁₉×#461	C₂²	1	1	yes	characteristic
39	C₁₉×#461	C₂²	1	1	yes	characteristic
40	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#459	C₂²	1	1	yes	characteristic
42	C₁₉×#459	C₂²	1	1	yes	characteristic
43	C₁₉×#452	—	2	1	no	—
44	C₁₉×#452	—	2	1	no	—
45	C₁₉×#450	—	2	1	no	—
46	C₁₉×#449	—	2	1	no	—
47	C₁₉×#447	—	2	1	no	—
48	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#436	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
53	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₉×#107	—	2	1	no	—
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×#332	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	—	2	1	no	—
69	C₂×#41×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
73	C₁₉×#135	—	4	4	no	—
74	C₂×Q₁₆×C₁₉	—	2	1	no	—
75	C₂×Q₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	—	2	1	no	—
77	C₂×SD₁₆×C₁₉	—	2	1	no	—
78	C₂×SD₁₆×C₁₉	—	2	1	no	—
79	C₂×SD₁₆×C₁₉	—	2	1	no	—
80	C₂×SD₁₆×C₁₉	—	2	1	no	—
81	C₂×D₈×C₁₉	—	2	1	no	—
82	C₂×D₈×C₁₉	—	2	1	no	—
83	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
84	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
85	C₂×M₁₆×C₁₉	—	2	1	no	—
86	C₂²×C₈×C₁₉	—	2	1	no	—
87	C₂²×C₈×C₁₉	—	2	1	no	—
88	C₂²×C₈×C₁₉	—	2	1	no	—
89	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₉×#127	C₂³	1	1	yes	characteristic
93	C₁₉×#123	—	4	1	no	—
94	C₁₉×#123	—	4	1	no	—
95	C₁₉×#123	—	4	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	—	2	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	—	2	1	no	—
104	C₁₉×#120	—	4	1	no	—
105	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₁₉×#107	—	2	1	no	—
113	C₁₉×#107	—	2	1	no	—
114	C₁₉×#107	—	2	1	no	—
115	C₁₉×#107	—	2	1	no	—
116	C₁₉×#107	—	2	1	no	—
117	C₁₉×#107	—	4	1	no	—
118	C₁₉×#107	D₄	1	1	yes	characteristic
119	C₁₉×#107	D₄	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	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	D₄	1	1	yes	characteristic
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	C₁₉×C₂²⋊C₈	—	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	—	4	2	no	—
150	#41×C₁₉	—	8	1	no	—
151	#41×C₁₉	—	8	1	no	—
152	#41×C₁₉	—	8	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	4	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	2	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	—	8	1	no	—
167	C₂×D₄×C₁₉	—	8	1	no	—
168	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	4	1	no	—
177	C₂²×C₄×C₁₉	—	4	1	no	—
178	C₂²×C₄×C₁₉	—	4	1	no	—
179	Q₁₆×C₁₉	—	4	2	no	—
180	Q₁₆×C₁₉	—	8	1	no	—
181	SD₁₆×C₁₉	—	4	2	no	—
182	SD₁₆×C₁₉	—	4	2	no	—
183	SD₁₆×C₁₉	—	4	2	no	—
184	SD₁₆×C₁₉	—	4	2	no	—
185	SD₁₆×C₁₉	—	8	1	no	—
186	D₈×C₁₉	—	4	1	no	—
187	D₈×C₁₉	—	4	2	no	—
188	D₈×C₁₉	—	8	1	no	—
189	D₈×C₁₉	D₈	1	4	yes	complemented
190	M₁₆×C₁₉	—	4	2	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	4	2	no	—
197	C₂×C₈×C₁₉	—	4	2	no	—
198	C₂×C₈×C₁₉	—	8	1	no	—
199	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	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	—	2	1	no	—
220	C₂²⋊C₄×C₁₉	—	4	1	no	—
221	C₂²⋊C₄×C₁₉	—	4	1	no	—
222	C₂²⋊C₄×C₁₉	—	4	1	no	—
223	C₂²⋊C₄×C₁₉	—	4	1	no	—
224	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
225	#19758	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	—	2	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	—	4	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	—	4	1	no	—
240	D₄×C₁₉	—	2	1	no	—
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	—	8	1	no	—
251	D₄×C₁₉	—	8	2	no	—
252	D₄×C₁₉	—	8	2	no	—
253	D₄×C₁₉	—	8	2	no	—
254	D₄×C₁₉	—	8	2	no	—
255	D₄×C₁₉	—	8	2	no	—
256	D₄×C₁₉	C₂×D₈	1	2	yes	—
257	D₄×C₁₉	C₂×D₈	1	2	yes	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	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	—	8	2	no	—
274	C₂×C₄×C₁₉	—	8	2	no	—
275	C₂×C₄×C₁₉	—	8	2	no	—
276	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
279	C₈×C₁₉	—	2	1	no	—
280	C₈×C₁₉	—	2	1	no	—
281	C₈×C₁₉	—	2	1	no	—
282	C₈×C₁₉	—	4	1	no	—
283	C₈×C₁₉	—	4	1	no	—
284	C₈×C₁₉	—	4	1	no	—
285	C₈×C₁₉	—	4	1	no	—
286	C₈×C₁₉	—	4	1	no	—
287	C₈×C₁₉	C₂×D₈	1	2	yes	—
288	#3334	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#3294	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#3283	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#3272	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1722	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1689	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1681	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1673	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1665	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1647	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1647	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#1639	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1625	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1580	C₂×C₁₉	1	1	yes	characteristic, complemented
303	C₂²×C₁₉	—	2	2	no	—
304	C₂²×C₁₉	—	2	2	no	—
305	C₂²×C₁₉	—	4	1	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	—	4	1	no	—
315	C₂²×C₁₉	—	8	1	no	—
316	C₂²×C₁₉	—	8	1	no	—
317	C₂²×C₁₉	—	8	1	no	—
318	C₂²×C₁₉	—	16	4	no	—
319	C₂²×C₁₉	D₄²	1	1	yes	characteristic
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	4	1	no	—
322	C₄×C₁₉	—	4	1	no	—
323	C₄×C₁₉	—	4	1	no	—
324	C₄×C₁₉	—	4	1	no	—
325	C₄×C₁₉	—	8	1	no	—
326	C₄×C₁₉	—	8	1	no	—
327	C₄×C₁₉	—	8	1	no	—
328	C₄×C₁₉	C₂²×D₈	1	1	yes	characteristic
329	C₄×C₁₉	#575	1	1	yes	characteristic
330	C₄×C₁₉	#576	1	1	yes	characteristic
331	C₄×C₁₉	#577	1	1	yes	characteristic
332	C₂×AGL(1,ℤ/8)	—	2	1	no	—
333	C₂×#135	—	2	1	no	—
334	#547	C₂²×C₁₉	1	1	yes	characteristic
335	#547	C₂²×C₁₉	1	1	yes	characteristic
336	#547	C₂²×C₁₉	1	1	yes	characteristic, complemented
337	D₄²	C₂²×C₁₉	1	1	yes	characteristic
338	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
340	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	#492	C₂²×C₁₉	1	1	yes	characteristic
342	#486	C₂²×C₁₉	1	1	yes	characteristic
343	#486	C₂²×C₁₉	1	1	yes	characteristic
344	#480	—	2	1	no	—
345	#480	—	2	1	no	—
346	#480	—	2	1	no	—
347	#474	C₂²×C₁₉	1	1	yes	characteristic
348	#474	C₂²×C₁₉	1	1	yes	characteristic
349	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
350	#468	—	2	1	no	—
351	#467	—	2	1	no	—
352	#466	—	2	1	no	—
353	#466	—	2	1	no	—
354	#461	C₂²×C₁₉	1	1	yes	characteristic
355	#461	C₂²×C₁₉	1	1	yes	characteristic
356	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#459	C₂²×C₁₉	1	1	yes	characteristic
358	#459	C₂²×C₁₉	1	1	yes	characteristic
359	#452	—	2	1	no	—
360	#452	—	2	1	no	—
361	#450	—	2	1	no	—
362	#449	—	2	1	no	—
363	#447	—	2	1	no	—
364	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
365	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
366	#436	C₂²×C₁₉	1	1	yes	characteristic
367	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
368	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	C₂×#107	—	2	1	no	—
371	C₂×#102	—	2	1	no	—
372	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
375	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
376	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
377	#331	C₂²×C₁₉	1	1	yes	characteristic
378	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
379	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
380	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
381	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
382	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
383	C₂×C₁₉	—	4	2	no	—
384	C₂×C₁₉	—	4	2	no	—
385	C₂×C₁₉	—	8	1	no	—
386	C₂×C₁₉	—	8	1	no	—
387	C₂×C₁₉	—	16	1	no	—
388	C₂×C₁₉	#3267	1	1	yes	characteristic
389	C₂×C₁₉	D₄×D₈	1	1	yes	characteristic
390	C₂×C₁₉	#3289	1	1	yes	characteristic
391	C₂×#41	—	2	1	no	—
392	C₂×#41	—	2	1	no	—
393	C₂×#41	—	2	1	no	—
394	C₂²×D₄	—	2	1	no	—
395	C₂²×D₄	—	2	1	no	—
396	AGL(1,ℤ/8)	—	4	4	no	—
397	#135	—	4	4	no	—
398	C₂×Q₁₆	—	2	1	no	—
399	C₂×Q₁₆	—	2	1	no	—
400	C₂×SD₁₆	—	2	1	no	—
401	C₂×SD₁₆	—	2	1	no	—
402	C₂×SD₁₆	—	2	1	no	—
403	C₂×SD₁₆	—	2	1	no	—
404	C₂×SD₁₆	—	2	1	no	—
405	C₂×D₈	—	2	1	no	—
406	C₂×D₈	—	2	1	no	—
407	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
408	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
409	C₂×M₁₆	—	2	1	no	—
410	C₂²×C₈	—	2	1	no	—
411	C₂²×C₈	—	2	1	no	—
412	C₂²×C₈	—	2	1	no	—
413	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
416	#127	C₂³×C₁₉	1	1	yes	characteristic
417	#123	—	4	1	no	—
418	#123	—	4	1	no	—
419	#123	—	4	1	no	—
420	C₂²⋊Q₈	—	2	1	no	—
421	C₂²⋊Q₈	—	2	1	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	#121	—	2	1	no	—
424	#121	—	2	1	no	—
425	#121	—	2	1	no	—
426	#121	—	2	1	no	—
427	#121	—	2	1	no	—
428	#120	—	4	1	no	—
429	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
430	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
431	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
432	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	#107	—	2	1	no	—
437	#107	—	2	1	no	—
438	#107	—	2	1	no	—
439	#107	—	2	1	no	—
440	#107	—	2	1	no	—
441	#107	—	4	1	no	—
442	#107	D₄×C₁₉	1	1	yes	characteristic
443	#107	D₄×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	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
448	#103	—	2	1	no	—
449	#103	—	2	1	no	—
450	#103	—	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	—	4	1	no	—
459	#102	D₄×C₁₉	1	1	yes	characteristic
460	#102	D₄×C₁₉	1	1	yes	characteristic
461	#102	D₄×C₁₉	1	1	yes	characteristic
462	#102	D₄×C₁₉	1	1	yes	characteristic
463	C₂²⋊C₈	—	2	1	no	—
464	C₂²⋊C₈	—	2	1	no	—
465	C₂²⋊C₈	—	2	1	no	—
466	C₂²⋊C₈	—	2	1	no	—
467	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
468	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
469	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
470	C₁₉	#19758	1	1	yes	characteristic, direct product factor, Sylow
471	C₂⁴	—	4	1	no	—
472	#41	—	4	2	no	—
473	#41	—	4	2	no	—
474	#41	—	4	2	no	—
475	#41	—	8	1	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	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	4	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	—	4	2	no	—
488	C₂×D₄	—	4	1	no	—
489	C₂×D₄	—	4	1	no	—
490	C₂×D₄	—	4	1	no	—
491	C₂×D₄	—	8	1	no	—
492	C₂×D₄	—	8	1	no	—
493	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	—	4	1	no	—
504	Q₁₆	—	4	2	no	—
505	Q₁₆	—	8	1	no	—
506	SD₁₆	—	4	2	no	—
507	SD₁₆	—	4	2	no	—
508	SD₁₆	—	4	2	no	—
509	SD₁₆	—	4	2	no	—
510	SD₁₆	—	8	1	no	—
511	D₈	—	4	1	no	—
512	D₈	—	4	2	no	—
513	D₈	—	8	1	no	—
514	D₈	D₈×C₁₉	1	4	yes	complemented
515	M₁₆	—	4	2	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	4	2	no	—
522	C₂×C₈	—	4	2	no	—
523	C₂×C₈	—	8	1	no	—
524	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	4	1	no	—
535	C₄⋊C₄	—	4	1	no	—
536	C₄⋊C₄	—	4	1	no	—
537	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
540	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₂²⋊C₄	—	2	1	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	4	1	no	—
546	C₂²⋊C₄	—	4	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	1	no	—
549	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	8	2	no	—
556	C₂³	—	8	2	no	—
557	C₂³	—	16	1	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	4	1	no	—
560	Q₈	—	4	1	no	—
561	Q₈	—	4	1	no	—
562	Q₈	—	4	1	no	—
563	Q₈	—	4	1	no	—
564	D₄	—	2	1	no	—
565	D₄	—	2	1	no	—
566	D₄	—	2	1	no	—
567	D₄	—	2	1	no	—
568	D₄	—	2	1	no	—
569	D₄	—	2	1	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	1	no	—
574	D₄	—	8	1	no	—
575	D₄	—	8	2	no	—
576	D₄	—	8	2	no	—
577	D₄	—	8	2	no	—
578	D₄	—	8	2	no	—
579	D₄	—	8	2	no	—
580	D₄	C₂×D₈×C₁₉	1	2	yes	—
581	D₄	C₂×D₈×C₁₉	1	2	yes	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	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	—	8	2	no	—
598	C₂×C₄	—	8	2	no	—
599	C₂×C₄	—	8	2	no	—
600	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
602	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
603	C₈	—	2	1	no	—
604	C₈	—	2	1	no	—
605	C₈	—	2	1	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₈	—	4	1	no	—
611	C₈	C₂×D₈×C₁₉	1	2	yes	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	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	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	16	4	no	—
628	C₂²	D₄²×C₁₉	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	8	1	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	C₂²×D₈×C₁₉	1	1	yes	characteristic
638	C₄	C₁₉×#575	1	1	yes	characteristic
639	C₄	C₁₉×#576	1	1	yes	characteristic
640	C₄	C₁₉×#577	1	1	yes	characteristic
641	C₂	—	4	2	no	—
642	C₂	—	4	2	no	—
643	C₂	—	8	1	no	—
644	C₂	—	8	1	no	—
645	C₂	—	16	1	no	—
646	C₂	C₁₉×#3267	1	1	yes	characteristic
647	C₂	D₄×D₈×C₁₉	1	1	yes	characteristic
648	C₂	C₁₉×#3289	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×#3334	C₂	semidirect
2. C₁₉×#3294	C₂	semidirect
3. C₁₉×#3283	C₂	semidirect
4. C₁₉×#3272	C₂	semidirect
5. C₁₉×#1722	C₂	semidirect
6. C₁₉×#1689	C₂	semidirect
7. C₁₉×#1681	C₂	semidirect
8. C₁₉×#1673	C₂	semidirect
9. C₁₉×#1665	C₂	semidirect
10. C₁₉×#1647	C₂	semidirect
11. C₁₉×#1647	C₂	semidirect
12. C₁₉×#1639	C₂	semidirect
13. C₁₉×#1625	C₂	semidirect
14. C₁₉×#1581	C₂	semidirect
15. C₁₉×#1580	C₂	semidirect
20. C₁₉×#547	C₂²	semidirect
22. C₁₉×#500	C₂²	semidirect
23. C₁₉×#500	C₂²	semidirect
24. C₁₉×#494	C₂²	semidirect
33. C₁₉×#474	C₂²	semidirect
40. C₁₉×#461	C₂²	semidirect
52. C₈×D₄×C₁₉	C₂²	semidirect
53. C₈×D₄×C₁₉	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#332	C₂²	semidirect
59. C₁₉×#332	C₂²	semidirect
60. C₁₉×#332	C₂²	semidirect
64. C₁₉×D₄⋊C₈	C₂²	semidirect
65. C₁₉×D₄⋊C₈	C₂²	semidirect
66. C₁₉×#322	C₂²	semidirect
189. D₈×C₁₉	D₈	semidirect
225. #19758	C₁₉	direct (N × H)
288. #3334	C₂×C₁₉	semidirect
289. #3294	C₂×C₁₉	semidirect
290. #3283	C₂×C₁₉	semidirect
291. #3272	C₂×C₁₉	semidirect
292. #1722	C₂×C₁₉	semidirect
293. #1689	C₂×C₁₉	semidirect
294. #1681	C₂×C₁₉	semidirect
295. #1673	C₂×C₁₉	semidirect
296. #1665	C₂×C₁₉	semidirect
297. #1647	C₂×C₁₉	semidirect
298. #1647	C₂×C₁₉	semidirect
299. #1639	C₂×C₁₉	semidirect
300. #1625	C₂×C₁₉	semidirect
301. #1581	C₂×C₁₉	semidirect
302. #1580	C₂×C₁₉	semidirect
336. #547	C₂²×C₁₉	semidirect
338. #500	C₂²×C₁₉	semidirect
339. #500	C₂²×C₁₉	semidirect
340. #494	C₂²×C₁₉	semidirect
349. #474	C₂²×C₁₉	semidirect
356. #461	C₂²×C₁₉	semidirect
368. C₈×D₄	C₂²×C₁₉	semidirect
369. C₈×D₄	C₂²×C₁₉	semidirect
372. #335	C₂²×C₁₉	semidirect
373. #334	C₂²×C₁₉	semidirect
374. #332	C₂²×C₁₉	semidirect
375. #332	C₂²×C₁₉	semidirect
376. #332	C₂²×C₁₉	semidirect
380. D₄⋊C₈	C₂²×C₁₉	semidirect
381. D₄⋊C₈	C₂²×C₁₉	semidirect
382. #322	C₂²×C₁₉	semidirect
470. C₁₉	#19758	direct (N × H)
514. D₈	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×#3334	2
C₁₉×#3294	2
C₁₉×#3283	2
C₁₉×#3272	2
C₁₉×#1722	2
C₁₉×#1689	2
C₁₉×#1681	2
C₁₉×#1673	2
C₁₉×#1665	2
C₁₉×#1647	2
C₁₉×#1639	2
C₁₉×#1625	2
C₁₉×#1581	2
C₁₉×#1580	2
#19758	19

Subgroups — C19×#19758 #18025717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19758 #18025717