Subgroups — C₁₉×#19892 #18025851

Order 4864.

720 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3386	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3274	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1706	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1693	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1688	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1642	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×#1626	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂²×SD₁₆×C₁₉	—	2	1	no	—
18	C₁₉×#557	C₂²	1	1	yes	characteristic, complemented
19	C₁₉×#550	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	D₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#501	—	2	1	no	—
23	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#493	C₂²	1	1	yes	characteristic
25	C₁₉×#492	—	2	1	no	—
26	C₁₉×#492	C₂²	1	1	yes	characteristic
27	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#486	C₂²	1	1	yes	characteristic
29	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#478	—	2	1	no	—
31	C₁₉×#477	—	2	1	no	—
32	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#474	C₂²	1	1	yes	characteristic
34	C₁₉×#469	—	2	1	no	—
35	C₁₉×#465	—	2	1	no	—
36	C₁₉×#461	—	2	1	no	—
37	C₁₉×#461	C₂²	1	1	yes	characteristic
38	C₁₉×#461	C₂²	1	1	yes	characteristic
39	C₁₉×#460	—	2	1	no	—
40	C₁₉×#460	C₂²	1	1	yes	characteristic
41	C₁₉×#460	C₂²	1	1	yes	characteristic
42	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#459	C₂²	1	1	yes	characteristic
44	C₁₉×#450	—	2	1	no	—
45	C₁₉×#449	—	2	1	no	—
46	C₁₉×#448	—	2	1	no	—
47	C₁₉×#447	—	2	1	no	—
48	C₁₉×#446	C₂²	1	1	yes	characteristic, complemented
49	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#440	—	2	1	no	—
51	C₄×SD₁₆×C₁₉	—	2	1	no	—
52	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
54	C₁₉×#436	C₂²	1	1	yes	characteristic
55	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
56	C₁₉×#334	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×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×Q₈×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×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×SD₁₆×C₁₉	—	4	4	no	—
82	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
83	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
84	C₂×D₈×C₁₉	—	2	1	no	—
85	C₂×D₈×C₁₉	—	2	1	no	—
86	C₂×D₈×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	—	2	1	no	—
91	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₁₉×#127	—	2	1	no	—
94	C₁₉×#127	C₂³	1	1	yes	characteristic
95	C₁₉×#127	C₂³	1	1	yes	characteristic
96	C₁₉×#125	—	2	1	no	—
97	C₁₉×#125	—	4	1	no	—
98	C₁₉×C₂²⋊Q₈	—	2	1	no	—
99	C₁₉×C₂²⋊Q₈	—	4	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	—	2	1	no	—
106	C₄×Q₈×C₁₉	—	2	1	no	—
107	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
108	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₄×D₄×C₁₉	—	2	1	no	—
110	C₄×D₄×C₁₉	—	2	1	no	—
111	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₁₉×#107	—	2	1	no	—
114	C₁₉×#107	—	2	1	no	—
115	C₁₉×#107	—	2	1	no	—
116	C₁₉×#106	—	2	1	no	—
117	C₁₉×#106	D₄	1	1	yes	characteristic
118	C₁₉×#106	D₄	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	D₄	1	1	yes	characteristic
129	C₁₉×#103	D₄	1	1	yes	characteristic
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	—	4	1	no	—
136	C₁₉×#102	—	4	1	no	—
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×#97	—	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	—	8	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	4	1	no	—
152	C₂×Q₈×C₁₉	—	4	2	no	—
153	C₂×Q₈×C₁₉	—	8	1	no	—
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	4	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	2	no	—
167	C₂×D₄×C₁₉	—	4	2	no	—
168	C₂×D₄×C₁₉	—	8	1	no	—
169	C₂×D₄×C₁₉	—	8	1	no	—
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	—	4	1	no	—
175	C₂²×C₄×C₁₉	—	4	1	no	—
176	SD₁₆×C₁₉	—	2	2	no	—
177	SD₁₆×C₁₉	—	4	2	no	—
178	SD₁₆×C₁₉	—	4	2	no	—
179	SD₁₆×C₁₉	—	4	2	no	—
180	SD₁₆×C₁₉	—	4	2	no	—
181	SD₁₆×C₁₉	—	4	2	no	—
182	SD₁₆×C₁₉	—	8	1	no	—
183	SD₁₆×C₁₉	—	8	1	no	—
184	SD₁₆×C₁₉	—	8	1	no	—
185	SD₁₆×C₁₉	—	8	1	no	—
186	SD₁₆×C₁₉	SD₁₆	1	4	yes	complemented
187	D₈×C₁₉	—	4	2	no	—
188	D₈×C₁₉	—	4	2	no	—
189	D₈×C₁₉	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
208	C₄⋊C₄×C₁₉	—	4	1	no	—
209	C₄⋊C₄×C₁₉	—	4	1	no	—
210	C₄⋊C₄×C₁₉	—	4	1	no	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	4	1	no	—
218	C₂²⋊C₄×C₁₉	—	4	1	no	—
219	C₂²⋊C₄×C₁₉	—	4	1	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	—	4	1	no	—
223	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
224	#19892	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂³×C₁₉	—	2	1	no	—
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	8	2	no	—
230	C₂³×C₁₉	—	8	2	no	—
231	C₂³×C₁₉	—	16	1	no	—
232	Q₈×C₁₉	—	2	1	no	—
233	Q₈×C₁₉	—	2	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×SD₁₆	1	2	yes	complemented
241	D₄×C₁₉	—	2	1	no	—
242	D₄×C₁₉	—	2	1	no	—
243	D₄×C₁₉	—	2	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	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	—	8	2	no	—
253	D₄×C₁₉	—	8	1	no	—
254	D₄×C₁₉	—	8	1	no	—
255	D₄×C₁₉	—	8	2	no	—
256	D₄×C₁₉	—	8	2	no	—
257	D₄×C₁₉	—	16	1	no	—
258	D₄×C₁₉	C₂×SD₁₆	1	2	yes	—
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	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	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	—	8	2	no	—
272	C₂×C₄×C₁₉	—	8	2	no	—
273	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
276	C₈×C₁₉	—	2	1	no	—
277	C₈×C₁₉	—	2	1	no	—
278	C₈×C₁₉	—	4	1	no	—
279	C₈×C₁₉	—	4	1	no	—
280	C₈×C₁₉	—	4	1	no	—
281	C₈×C₁₉	—	4	1	no	—
282	C₈×C₁₉	—	4	1	no	—
283	C₈×C₁₉	C₂×SD₁₆	1	2	yes	complemented
284	C₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	complemented
285	#3392	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3386	C₂×C₁₉	1	1	yes	characteristic, complemented
287	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#3274	C₂×C₁₉	1	1	yes	characteristic
289	#1706	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1693	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1688	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1666	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1665	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1642	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1639	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1627	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1626	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1590	C₂×C₁₉	1	1	yes	characteristic, complemented
299	C₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
300	C₂²×C₁₉	—	2	2	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	1	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	8	1	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	8	1	no	—
311	C₂²×C₁₉	—	8	1	no	—
312	C₂²×C₁₉	—	16	4	no	—
313	C₂²×C₁₉	D₄²	1	1	yes	characteristic
314	C₄×C₁₉	—	2	2	no	—
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	8	1	no	—
322	C₄×C₁₉	—	8	1	no	—
323	C₄×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
324	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
325	C₄×C₁₉	#576	1	1	yes	characteristic
326	C₄×C₁₉	#577	1	1	yes	characteristic
327	C₂×AGL(1,ℤ/8)	—	2	1	no	—
328	C₂²×SD₁₆	—	2	1	no	—
329	#557	C₂²×C₁₉	1	1	yes	characteristic, complemented
330	#550	C₂²×C₁₉	1	1	yes	characteristic
331	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
332	D₄²	C₂²×C₁₉	1	1	yes	characteristic
333	#501	—	2	1	no	—
334	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
335	#493	C₂²×C₁₉	1	1	yes	characteristic
336	#492	—	2	1	no	—
337	#492	C₂²×C₁₉	1	1	yes	characteristic
338	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#486	C₂²×C₁₉	1	1	yes	characteristic
340	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	#478	—	2	1	no	—
342	#477	—	2	1	no	—
343	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
344	#474	C₂²×C₁₉	1	1	yes	characteristic
345	#469	—	2	1	no	—
346	#465	—	2	1	no	—
347	#461	—	2	1	no	—
348	#461	C₂²×C₁₉	1	1	yes	characteristic
349	#461	C₂²×C₁₉	1	1	yes	characteristic
350	#460	—	2	1	no	—
351	#460	C₂²×C₁₉	1	1	yes	characteristic
352	#460	C₂²×C₁₉	1	1	yes	characteristic
353	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#459	C₂²×C₁₉	1	1	yes	characteristic
355	#450	—	2	1	no	—
356	#449	—	2	1	no	—
357	#448	—	2	1	no	—
358	#447	—	2	1	no	—
359	#446	C₂²×C₁₉	1	1	yes	characteristic, complemented
360	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#440	—	2	1	no	—
362	C₄×SD₁₆	—	2	1	no	—
363	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
364	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
365	#436	C₂²×C₁₉	1	1	yes	characteristic
366	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
367	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
368	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
370	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	#331	C₂²×C₁₉	1	1	yes	characteristic
372	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
374	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
375	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
376	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
377	C₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
378	C₂×C₁₉	—	4	2	no	—
379	C₂×C₁₉	—	8	1	no	—
380	C₂×C₁₉	—	16	1	no	—
381	C₂×C₁₉	—	16	1	no	—
382	C₂×C₁₉	#3274	1	1	yes	characteristic
383	C₂×C₁₉	D₄×SD₁₆	1	1	yes	characteristic
384	C₂×C₁₉	#3290	1	1	yes	characteristic
385	C₂×#41	—	2	1	no	—
386	C₂²×Q₈	—	2	1	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	AGL(1,ℤ/8)	—	4	4	no	—
390	C₂×SD₁₆	—	2	1	no	—
391	C₂×SD₁₆	—	2	1	no	—
392	C₂×SD₁₆	—	2	1	no	—
393	C₂×SD₁₆	—	2	1	no	—
394	C₂×SD₁₆	—	2	1	no	—
395	C₂×SD₁₆	—	2	1	no	—
396	C₂×SD₁₆	—	2	1	no	—
397	C₂×SD₁₆	—	2	1	no	—
398	C₂×SD₁₆	—	2	1	no	—
399	C₂×SD₁₆	—	4	4	no	—
400	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
401	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
402	C₂×D₈	—	2	1	no	—
403	C₂×D₈	—	2	1	no	—
404	C₂×D₈	—	2	1	no	—
405	C₂×M₁₆	—	2	1	no	—
406	C₂²×C₈	—	2	1	no	—
407	C₄⋊Q₈	—	2	1	no	—
408	C₄⋊Q₈	—	2	1	no	—
409	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
411	#127	—	2	1	no	—
412	#127	C₂³×C₁₉	1	1	yes	characteristic
413	#127	C₂³×C₁₉	1	1	yes	characteristic
414	#125	—	2	1	no	—
415	#125	—	4	1	no	—
416	C₂²⋊Q₈	—	2	1	no	—
417	C₂²⋊Q₈	—	4	1	no	—
418	#121	—	2	1	no	—
419	#121	—	2	1	no	—
420	#121	—	2	1	no	—
421	#121	—	4	1	no	—
422	#120	—	4	1	no	—
423	C₄×Q₈	—	2	1	no	—
424	C₄×Q₈	—	2	1	no	—
425	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₄×D₄	—	2	1	no	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
430	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
431	#107	—	2	1	no	—
432	#107	—	2	1	no	—
433	#107	—	2	1	no	—
434	#106	—	2	1	no	—
435	#106	D₄×C₁₉	1	1	yes	characteristic
436	#106	D₄×C₁₉	1	1	yes	characteristic
437	C₄⋊C₈	—	2	1	no	—
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
440	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
441	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
442	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
443	#103	—	2	1	no	—
444	#103	—	2	1	no	—
445	#103	—	2	1	no	—
446	#103	D₄×C₁₉	1	1	yes	characteristic
447	#103	D₄×C₁₉	1	1	yes	characteristic
448	#102	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	4	1	no	—
454	#102	—	4	1	no	—
455	#102	D₄×C₁₉	1	1	yes	characteristic
456	#102	D₄×C₁₉	1	1	yes	characteristic
457	C₂²⋊C₈	—	2	1	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	#97	—	2	1	no	—
460	C₄×C₈	—	2	1	no	—
461	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
462	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
463	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
464	C₁₉	#19892	1	1	yes	characteristic, direct product factor, Sylow
465	C₂⁴	—	4	1	no	—
466	#41	—	4	2	no	—
467	#41	—	8	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	4	1	no	—
471	C₂×Q₈	—	4	2	no	—
472	C₂×Q₈	—	8	1	no	—
473	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	—	4	1	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	—	8	1	no	—
488	C₂×D₄	—	8	1	no	—
489	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	4	1	no	—
494	C₂²×C₄	—	4	1	no	—
495	SD₁₆	—	2	2	no	—
496	SD₁₆	—	4	2	no	—
497	SD₁₆	—	4	2	no	—
498	SD₁₆	—	4	2	no	—
499	SD₁₆	—	4	2	no	—
500	SD₁₆	—	4	2	no	—
501	SD₁₆	—	8	1	no	—
502	SD₁₆	—	8	1	no	—
503	SD₁₆	—	8	1	no	—
504	SD₁₆	—	8	1	no	—
505	SD₁₆	SD₁₆×C₁₉	1	4	yes	complemented
506	D₈	—	4	2	no	—
507	D₈	—	4	2	no	—
508	D₈	—	8	1	no	—
509	M₁₆	—	4	2	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	4	2	no	—
516	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	4	1	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
533	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	4	1	no	—
542	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	8	2	no	—
548	C₂³	—	8	2	no	—
549	C₂³	—	16	1	no	—
550	Q₈	—	2	1	no	—
551	Q₈	—	2	1	no	—
552	Q₈	—	2	1	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	4	1	no	—
555	Q₈	—	4	1	no	—
556	Q₈	—	4	1	no	—
557	Q₈	—	8	2	no	—
558	Q₈	C₂×SD₁₆×C₁₉	1	2	yes	complemented
559	D₄	—	2	1	no	—
560	D₄	—	2	1	no	—
561	D₄	—	2	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	D₄	—	8	2	no	—
571	D₄	—	8	1	no	—
572	D₄	—	8	1	no	—
573	D₄	—	8	2	no	—
574	D₄	—	8	2	no	—
575	D₄	—	16	1	no	—
576	D₄	C₂×SD₁₆×C₁₉	1	2	yes	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	8	2	no	—
590	C₂×C₄	—	8	2	no	—
591	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
592	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
593	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
594	C₈	—	2	1	no	—
595	C₈	—	2	1	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	C₂×SD₁₆×C₁₉	1	2	yes	complemented
602	C₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	complemented
603	C₂²	—	2	2	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	16	4	no	—
616	C₂²	D₄²×C₁₉	1	1	yes	characteristic
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	8	1	no	—
625	C₄	—	8	1	no	—
626	C₄	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
627	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
628	C₄	C₁₉×#576	1	1	yes	characteristic
629	C₄	C₁₉×#577	1	1	yes	characteristic
630	C₂	—	4	2	no	—
631	C₂	—	8	1	no	—
632	C₂	—	16	1	no	—
633	C₂	—	16	1	no	—
634	C₂	C₁₉×#3274	1	1	yes	characteristic
635	C₂	D₄×SD₁₆×C₁₉	1	1	yes	characteristic
636	C₂	C₁₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3274	C₂
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×#3392	C₂	semidirect
2. C₁₉×#3386	C₂	semidirect
3. D₄×SD₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1706	C₂	semidirect
6. C₁₉×#1693	C₂	semidirect
7. C₁₉×#1688	C₂	semidirect
8. C₁₉×#1666	C₂	semidirect
9. C₁₉×#1665	C₂	semidirect
10. C₁₉×#1642	C₂	semidirect
11. C₁₉×#1639	C₂	semidirect
12. C₁₉×#1627	C₂	semidirect
13. C₁₉×#1626	C₂	semidirect
14. C₁₉×#1590	C₂	semidirect
15. C₈×SD₁₆×C₁₉	C₂	semidirect
18. C₁₉×#557	C₂²	semidirect
23. C₁₉×#500	C₂²	semidirect
27. C₁₉×#492	C₂²	semidirect
29. C₁₉×#486	C₂²	semidirect
32. C₁₉×#475	C₂²	semidirect
42. C₁₉×#460	C₂²	semidirect
48. C₁₉×#446	C₂²	semidirect
49. C₈×Q₈×C₁₉	C₂²	semidirect
56. C₁₉×#334	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
63. C₁₉×Q₈⋊C₈	C₂²	semidirect
66. C₈²×C₁₉	C₂²	semidirect
186. SD₁₆×C₁₉	SD₁₆	semidirect
224. #19892	C₁₉	direct (N × H)
240. Q₈×C₁₉	C₂×SD₁₆	semidirect
283. C₈×C₁₉	C₂×SD₁₆	semidirect
284. C₈×C₁₉	AGL(1,ℤ/8)	semidirect
285. #3392	C₂×C₁₉	semidirect
286. #3386	C₂×C₁₉	semidirect
287. D₄×SD₁₆	C₂×C₁₉	semidirect
289. #1706	C₂×C₁₉	semidirect
290. #1693	C₂×C₁₉	semidirect
291. #1688	C₂×C₁₉	semidirect
292. #1666	C₂×C₁₉	semidirect
293. #1665	C₂×C₁₉	semidirect
294. #1642	C₂×C₁₉	semidirect
295. #1639	C₂×C₁₉	semidirect
296. #1627	C₂×C₁₉	semidirect
297. #1626	C₂×C₁₉	semidirect
298. #1590	C₂×C₁₉	semidirect
299. C₈×SD₁₆	C₂×C₁₉	semidirect
329. #557	C₂²×C₁₉	semidirect
334. #500	C₂²×C₁₉	semidirect
338. #492	C₂²×C₁₉	semidirect
340. #486	C₂²×C₁₉	semidirect
343. #475	C₂²×C₁₉	semidirect
353. #460	C₂²×C₁₉	semidirect
359. #446	C₂²×C₁₉	semidirect
360. C₈×Q₈	C₂²×C₁₉	semidirect
367. #334	C₂²×C₁₉	semidirect
368. #334	C₂²×C₁₉	semidirect
369. #332	C₂²×C₁₉	semidirect
370. #332	C₂²×C₁₉	semidirect
372. #331	C₂²×C₁₉	semidirect
373. Q₈⋊C₈	C₂²×C₁₉	semidirect
374. Q₈⋊C₈	C₂²×C₁₉	semidirect
377. C₈²	C₂²×C₁₉	semidirect
464. C₁₉	#19892	direct (N × H)
505. SD₁₆	SD₁₆×C₁₉	semidirect
558. Q₈	C₂×SD₁₆×C₁₉	semidirect
601. C₈	C₂×SD₁₆×C₁₉	semidirect
602. C₈	C₁₉×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3392	2
C₁₉×#3386	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3274	2
C₁₉×#1706	2
C₁₉×#1693	2
C₁₉×#1688	2
C₁₉×#1666	2
C₁₉×#1665	2
C₁₉×#1642	2
C₁₉×#1639	2
C₁₉×#1627	2
C₁₉×#1626	2
C₁₉×#1590	2
C₈×SD₁₆×C₁₉	2
#19892	19

Subgroups — C19×#19892 #18025851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19892 #18025851