Subgroups — C₁₉×#19310 #18025269

Order 4864.

654 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3184	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3112	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1702	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1692	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1688	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1678	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1668	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1560	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	—	2	1	no	—
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#498	C₂²	1	1	yes	characteristic
21	C₁₉×#493	C₂²	1	1	yes	characteristic
22	C₁₉×#486	C₂²	1	1	yes	characteristic
23	C₁₉×#486	C₂²	1	1	yes	characteristic
24	C₁₉×#480	—	2	1	no	—
25	C₁₉×#477	C₂²	1	1	yes	characteristic
26	C₁₉×#477	C₂²	1	1	yes	characteristic
27	C₁₉×#469	—	2	1	no	—
28	C₁₉×#469	—	2	1	no	—
29	C₁₉×#464	—	2	1	no	—
30	C₁₉×#464	—	2	1	no	—
31	C₁₉×#462	C₂²	1	1	yes	characteristic
32	C₁₉×#462	C₂²	1	1	yes	characteristic
33	C₁₉×#460	C₂²	1	1	yes	characteristic
34	C₁₉×#460	C₂²	1	1	yes	characteristic
35	C₁₉×#460	C₂²	1	1	yes	characteristic
36	C₁₉×#460	C₂²	1	1	yes	characteristic
37	C₁₉×#448	—	2	1	no	—
38	C₁₉×#446	—	2	1	no	—
39	C₁₉×#446	—	2	1	no	—
40	C₁₉×#446	C₂²	1	1	yes	characteristic
41	C₁₉×#446	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
44	C₁₉×#442	—	2	1	no	—
45	C₁₉×#442	—	2	1	no	—
46	C₁₉×#440	—	2	1	no	—
47	C₁₉×#440	—	2	1	no	—
48	C₁₉×#432	C₂²	1	1	yes	characteristic
49	C₁₉×#423	—	2	1	no	—
50	C₁₉×#423	C₂²	1	1	yes	characteristic
51	C₁₉×#423	C₂²	1	1	yes	characteristic
52	C₁₉×#417	—	2	1	no	—
53	C₄×M₁₆×C₁₉	—	2	1	no	—
54	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#335	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#334	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×#332	C₂²	1	1	yes	characteristic
63	C₁₉×#331	C₂²	1	1	yes	characteristic
64	C₁₉×#331	C₂²	1	1	yes	characteristic
65	C₁₉×#331	C₂²	1	1	yes	characteristic
66	C₁₉×#331	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	—	2	1	no	—
69	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
70	C₁₉×#137	—	4	4	no	—
71	C₂×Q₁₆×C₁₉	—	2	1	no	—
72	C₂×Q₁₆×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×D₈×C₁₉	—	2	1	no	—
78	C₂×D₈×C₁₉	—	2	1	no	—
79	C₂×M₁₆×C₁₉	—	2	1	no	—
80	C₂×M₁₆×C₁₉	—	2	1	no	—
81	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
82	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×#127	C₂³	1	1	yes	characteristic
86	C₁₉×#127	C₂³	1	1	yes	characteristic
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×#121	—	2	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	D₄	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	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#107	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×#106	—	2	1	no	—
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	—	2	1	no	—
115	C₁₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#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	—	2	1	no	—
135	C₁₉×C₂²⋊C₈	—	2	1	no	—
136	C₁₉×#97	—	2	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₁₉×#97	—	2	1	no	—
139	C₁₉×#97	D₄	1	1	yes	characteristic
140	C₁₉×#97	D₄	1	1	yes	characteristic
141	C₄×C₈×C₁₉	—	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	#41×C₁₉	—	4	2	no	—
146	#41×C₁₉	—	4	2	no	—
147	#41×C₁₉	—	8	2	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	2	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	4	1	no	—
153	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×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	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	4	1	no	—
162	C₂×D₄×C₁₉	—	4	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	4	1	no	—
166	C₂²×C₄×C₁₉	—	4	1	no	—
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
170	Q₁₆×C₁₉	—	4	2	no	—
171	Q₁₆×C₁₉	—	4	2	no	—
172	SD₁₆×C₁₉	—	4	2	no	—
173	SD₁₆×C₁₉	—	4	2	no	—
174	SD₁₆×C₁₉	—	4	2	no	—
175	SD₁₆×C₁₉	—	4	2	no	—
176	D₈×C₁₉	—	4	2	no	—
177	D₈×C₁₉	—	4	2	no	—
178	M₁₆×C₁₉	—	2	2	no	—
179	M₁₆×C₁₉	—	4	1	no	—
180	M₁₆×C₁₉	—	4	2	no	—
181	M₁₆×C₁₉	—	4	2	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₂²⋊C₄×C₁₉	—	4	1	no	—
205	C₂²⋊C₄×C₁₉	—	4	1	no	—
206	C₂²⋊C₄×C₁₉	—	4	1	no	—
207	C₄²×C₁₉	—	2	1	no	—
208	C₄²×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	—	2	1	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₉	#41	1	1	yes	characteristic
214	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
215	#19310	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₁₉	—	4	1	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	C₂³×C₁₉	#121	1	1	yes	characteristic
219	Q₈×C₁₉	—	2	1	no	—
220	Q₈×C₁₉	—	2	1	no	—
221	Q₈×C₁₉	—	2	1	no	—
222	Q₈×C₁₉	—	4	2	no	—
223	Q₈×C₁₉	—	4	1	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	8	1	no	—
226	Q₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	1	no	—
235	D₄×C₁₉	—	8	1	no	—
236	D₄×C₁₉	—	8	1	no	—
237	D₄×C₁₉	—	8	2	no	—
238	D₄×C₁₉	—	8	2	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	8	2	no	—
252	C₂×C₄×C₁₉	—	8	2	no	—
253	C₂×C₄×C₁₉	—	8	1	no	—
254	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
260	C₈×C₁₉	—	2	1	no	—
261	C₈×C₁₉	—	2	1	no	—
262	C₈×C₁₉	—	2	1	no	—
263	C₈×C₁₉	—	4	1	no	—
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	—	4	1	no	—
267	C₈×C₁₉	—	4	1	no	—
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	#137	1	2	yes	complemented
270	#3184	C₂×C₁₉	1	1	yes	characteristic
271	#3112	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#3037	C₂×C₁₉	1	1	yes	characteristic, complemented
273	Q₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1702	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1698	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1688	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1678	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1668	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1560	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1557	C₂×C₁₉	1	1	yes	characteristic, complemented
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	8	1	no	—
289	C₂²×C₁₉	—	8	1	no	—
290	C₂²×C₁₉	—	8	1	no	—
291	C₂²×C₁₉	—	8	1	no	—
292	C₂²×C₁₉	—	8	1	no	—
293	C₂²×C₁₉	—	8	1	no	—
294	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	2	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	8	1	no	—
304	C₄×C₁₉	—	8	1	no	—
305	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
307	C₄×C₁₉	#575	1	1	yes	characteristic
308	C₄×C₁₉	#575	1	1	yes	characteristic
309	C₂×#137	—	2	1	no	—
310	#532	C₂²×C₁₉	1	1	yes	characteristic
311	#532	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
313	#498	C₂²×C₁₉	1	1	yes	characteristic
314	#493	C₂²×C₁₉	1	1	yes	characteristic
315	#486	C₂²×C₁₉	1	1	yes	characteristic
316	#486	C₂²×C₁₉	1	1	yes	characteristic
317	#480	—	2	1	no	—
318	#477	C₂²×C₁₉	1	1	yes	characteristic
319	#477	C₂²×C₁₉	1	1	yes	characteristic
320	#469	—	2	1	no	—
321	#469	—	2	1	no	—
322	#464	—	2	1	no	—
323	#464	—	2	1	no	—
324	#462	C₂²×C₁₉	1	1	yes	characteristic
325	#462	C₂²×C₁₉	1	1	yes	characteristic
326	#460	C₂²×C₁₉	1	1	yes	characteristic
327	#460	C₂²×C₁₉	1	1	yes	characteristic
328	#460	C₂²×C₁₉	1	1	yes	characteristic
329	#460	C₂²×C₁₉	1	1	yes	characteristic
330	#448	—	2	1	no	—
331	#446	—	2	1	no	—
332	#446	—	2	1	no	—
333	#446	C₂²×C₁₉	1	1	yes	characteristic
334	#446	C₂²×C₁₉	1	1	yes	characteristic
335	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
337	#442	—	2	1	no	—
338	#442	—	2	1	no	—
339	#440	—	2	1	no	—
340	#440	—	2	1	no	—
341	#432	C₂²×C₁₉	1	1	yes	characteristic
342	#423	—	2	1	no	—
343	#423	C₂²×C₁₉	1	1	yes	characteristic
344	#423	C₂²×C₁₉	1	1	yes	characteristic
345	#417	—	2	1	no	—
346	C₄×M₁₆	—	2	1	no	—
347	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
348	#335	C₂²×C₁₉	1	1	yes	characteristic
349	#335	C₂²×C₁₉	1	1	yes	characteristic
350	#334	C₂²×C₁₉	1	1	yes	characteristic
351	#334	C₂²×C₁₉	1	1	yes	characteristic
352	#333	C₂²×C₁₉	1	1	yes	characteristic
353	#333	C₂²×C₁₉	1	1	yes	characteristic
354	#332	C₂²×C₁₉	1	1	yes	characteristic
355	#332	C₂²×C₁₉	1	1	yes	characteristic
356	#331	C₂²×C₁₉	1	1	yes	characteristic
357	#331	C₂²×C₁₉	1	1	yes	characteristic
358	#331	C₂²×C₁₉	1	1	yes	characteristic
359	#331	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×C₁₉	—	4	1	no	—
361	C₂×C₁₉	—	16	1	no	—
362	C₂×C₁₉	—	16	1	no	—
363	C₂×C₁₉	#3037	1	1	yes	characteristic
364	C₂×C₁₉	#3055	1	1	yes	characteristic
365	C₂×C₁₉	#3068	1	1	yes	characteristic
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
369	#137	—	4	4	no	—
370	C₂×Q₁₆	—	2	1	no	—
371	C₂×Q₁₆	—	2	1	no	—
372	C₂×SD₁₆	—	2	1	no	—
373	C₂×SD₁₆	—	2	1	no	—
374	C₂×SD₁₆	—	2	1	no	—
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×D₈	—	2	1	no	—
377	C₂×D₈	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
381	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
382	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
384	#127	C₂³×C₁₉	1	1	yes	characteristic
385	#127	C₂³×C₁₉	1	1	yes	characteristic
386	#124	—	2	1	no	—
387	#124	—	2	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	—	2	1	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
395	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
396	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
406	#107	—	2	1	no	—
407	#107	—	2	1	no	—
408	#106	—	2	1	no	—
409	#106	—	2	1	no	—
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	—	2	1	no	—
413	C₄⋊C₈	—	2	1	no	—
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	—	2	1	no	—
416	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
420	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
421	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
422	#103	—	2	1	no	—
423	#103	—	2	1	no	—
424	#103	—	2	1	no	—
425	#103	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	#97	—	2	1	no	—
436	#97	—	2	1	no	—
437	#97	—	2	1	no	—
438	#97	D₄×C₁₉	1	1	yes	characteristic
439	#97	D₄×C₁₉	1	1	yes	characteristic
440	C₄×C₈	—	2	1	no	—
441	C₄×C₈	—	2	1	no	—
442	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
443	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
444	C₁₉	#19310	1	1	yes	characteristic, direct product factor, Sylow
445	#41	—	4	2	no	—
446	#41	—	4	2	no	—
447	#41	—	8	2	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	4	1	no	—
453	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
470	Q₁₆	—	4	2	no	—
471	Q₁₆	—	4	2	no	—
472	SD₁₆	—	4	2	no	—
473	SD₁₆	—	4	2	no	—
474	SD₁₆	—	4	2	no	—
475	SD₁₆	—	4	2	no	—
476	D₈	—	4	2	no	—
477	D₈	—	4	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	4	1	no	—
480	M₁₆	—	4	2	no	—
481	M₁₆	—	4	2	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂²⋊C₄	—	4	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₄²	#41×C₁₉	1	1	yes	characteristic
514	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	C₁₉×#121	1	1	yes	characteristic
518	Q₈	—	2	1	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	8	1	no	—
525	Q₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	8	1	no	—
535	D₄	—	8	1	no	—
536	D₄	—	8	2	no	—
537	D₄	—	8	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	8	2	no	—
551	C₂×C₄	—	8	2	no	—
552	C₂×C₄	—	8	1	no	—
553	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
554	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
555	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
556	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
557	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
558	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	C₁₉×#137	1	2	yes	complemented
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
590	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
591	C₄	C₁₉×#575	1	1	yes	characteristic
592	C₄	C₁₉×#575	1	1	yes	characteristic
593	C₂	—	4	1	no	—
594	C₂	—	16	1	no	—
595	C₂	—	16	1	no	—
596	C₂	C₁₉×#3037	1	1	yes	characteristic
597	C₂	C₁₉×#3055	1	1	yes	characteristic
598	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3184	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₉×#3112	C₂	semidirect
3. C₁₉×#3037	C₂	semidirect
4. Q₈×M₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1702	C₂	semidirect
6. C₁₉×#1698	C₂	semidirect
7. C₁₉×#1692	C₂	semidirect
8. C₁₉×#1688	C₂	semidirect
9. C₁₉×#1682	C₂	semidirect
10. C₁₉×#1678	C₂	semidirect
11. C₁₉×#1672	C₂	semidirect
12. C₁₉×#1668	C₂	semidirect
13. C₁₉×#1569	C₂	semidirect
14. C₁₉×#1560	C₂	semidirect
15. C₁₉×#1557	C₂	semidirect
215. #19310	C₁₉	direct (N × H)
269. C₈×C₁₉	#137	semidirect
271. #3112	C₂×C₁₉	semidirect
272. #3037	C₂×C₁₉	semidirect
273. Q₈×M₁₆	C₂×C₁₉	semidirect
274. #1702	C₂×C₁₉	semidirect
275. #1698	C₂×C₁₉	semidirect
276. #1692	C₂×C₁₉	semidirect
277. #1688	C₂×C₁₉	semidirect
278. #1682	C₂×C₁₉	semidirect
279. #1678	C₂×C₁₉	semidirect
280. #1672	C₂×C₁₉	semidirect
281. #1668	C₂×C₁₉	semidirect
282. #1569	C₂×C₁₉	semidirect
283. #1560	C₂×C₁₉	semidirect
284. #1557	C₂×C₁₉	semidirect
444. C₁₉	#19310	direct (N × H)
568. C₈	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3184	2
C₁₉×#3112	2
C₁₉×#3037	2
Q₈×M₁₆×C₁₉	2
C₁₉×#1702	2
C₁₉×#1698	2
C₁₉×#1692	2
C₁₉×#1688	2
C₁₉×#1682	2
C₁₉×#1678	2
C₁₉×#1672	2
C₁₉×#1668	2
C₁₉×#1569	2
C₁₉×#1560	2
C₁₉×#1557	2
#19310	19

Subgroups — C19×#19310 #18025269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19310 #18025269