Subgroups — C₁₉×#18015 #18023974

Order 4864.

640 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3106	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1590	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1586	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1585	C₂	1	2	yes	maximal, complemented
7	C₈×D₈×C₁₉	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#532	C₂²	1	1	yes	characteristic
13	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#482	C₄	1	2	yes	—
15	C₁₉×#477	C₄	1	1	yes	characteristic
16	C₁₉×#476	C₄	1	1	yes	characteristic
17	C₁₉×#460	C₄	1	1	yes	characteristic
18	C₁₉×#459	C₄	1	1	yes	characteristic
19	C₁₉×#449	C₄	1	2	yes	—
20	C₁₉×#446	C₂²	1	2	yes	—
21	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
22	C₄×D₈×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#436	—	2	1	no	—
24	C₁₉×#436	C₂²	1	2	yes	—
25	C₁₉×#435	—	2	2	no	—
26	C₈×D₄×C₁₉	—	2	1	no	—
27	C₈×D₄×C₁₉	C₂²	1	2	yes	—
28	C₈×D₄×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#432	—	2	1	no	—
30	C₁₉×#431	C₂²	1	1	yes	characteristic
31	C₁₉×#431	C₂²	1	1	yes	characteristic
32	C₁₉×#431	C₂²	1	1	yes	characteristic
33	C₁₉×#423	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×#408	—	2	2	no	—
36	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#335	C₂²	1	2	yes	—
38	C₁₉×#334	C₂²	1	2	yes	—
39	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
44	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₉×#322	C₂²	1	2	yes	—
46	C₈²×C₁₉	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₉	C₂×C₄	1	2	yes	—
50	C₂×D₈×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	2	no	—
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	2	no	—
55	C₂²×C₈×C₁₉	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
57	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
58	C₁₉×#124	—	2	1	no	—
59	C₁₉×#121	—	2	1	no	—
60	C₁₉×#121	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₉	—	2	1	no	—
64	C₄×D₄×C₁₉	—	2	1	no	—
65	C₄×D₄×C₁₉	—	2	1	no	—
66	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₁₉	C₂³	1	2	yes	—
69	C₁₉×#117	—	2	1	no	—
70	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#107	C₂×C₄	1	2	yes	—
74	C₁₉×#106	C₂×C₄	1	2	yes	—
75	C₁₉×C₄⋊C₈	—	2	2	no	—
76	C₁₉×C₄⋊C₈	—	2	1	no	—
77	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
80	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
81	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
82	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₉×#103	C₂×C₄	1	2	yes	—
85	C₁₉×#102	C₂×C₄	1	2	yes	—
86	C₁₉×#102	C₂×C₄	1	2	yes	—
87	C₁₉×#102	C₂×C₄	1	2	yes	—
88	C₁₉×C₂²⋊C₈	—	2	1	no	—
89	C₁₉×C₂²⋊C₈	—	2	2	no	—
90	C₁₉×C₂²⋊C₈	—	2	2	no	—
91	C₁₉×C₂²⋊C₈	—	2	2	no	—
92	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
94	C₁₉×#97	—	2	2	no	—
95	C₄×C₈×C₁₉	—	2	1	no	—
96	C₄×C₈×C₁₉	—	2	1	no	—
97	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₉	C₂³	1	2	yes	—
100	C₄×C₈×C₁₉	C₂³	1	2	yes	—
101	#41×C₁₉	—	2	2	no	—
102	#41×C₁₉	—	4	1	no	—
103	#41×C₁₉	—	8	1	no	—
104	#41×C₁₉	—	8	1	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
120	SD₁₆×C₁₉	—	4	2	no	—
121	D₈×C₁₉	—	2	4	no	—
122	M₁₆×C₁₉	—	8	2	no	—
123	M₁₆×C₁₉	—	8	1	no	—
124	C₂×C₈×C₁₉	—	2	4	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	—	2	1	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	—	2	1	no	—
130	C₂×C₈×C₁₉	—	8	2	no	—
131	C₂×C₈×C₁₉	—	8	2	no	—
132	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₁₉	—	2	1	no	—
143	C₂²⋊C₄×C₁₉	—	2	1	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	1	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	2	1	no	—
148	C₄²×C₁₉	—	2	1	no	—
149	C₄²×C₁₉	—	2	1	no	—
150	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₉	#41	1	1	yes	characteristic
153	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
154	#18015	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₉	—	2	1	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
158	Q₈×C₁₉	—	2	1	no	—
159	Q₈×C₁₉	—	2	1	no	—
160	Q₈×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	2	2	no	—
162	D₄×C₁₉	—	2	1	no	—
163	D₄×C₁₉	—	2	2	no	—
164	D₄×C₁₉	—	4	2	no	—
165	D₄×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	8	1	no	—
167	D₄×C₁₉	—	8	2	no	—
168	D₄×C₁₉	#131	1	2	yes	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
190	C₈×C₁₉	—	2	2	no	—
191	C₈×C₁₉	—	2	2	no	—
192	C₈×C₁₉	—	2	2	no	—
193	C₈×C₁₉	—	2	2	no	—
194	C₈×C₁₉	—	2	2	no	—
195	C₈×C₁₉	—	2	2	no	—
196	C₈×C₁₉	—	4	1	no	—
197	C₈×C₁₉	—	4	2	no	—
198	C₈×C₁₉	—	4	1	no	—
199	#3106	C₂×C₁₉	1	1	yes	characteristic
200	#2990	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#2979	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#1590	C₂×C₁₉	1	2	yes	complemented
203	#1586	C₂×C₁₉	1	2	yes	complemented
204	#1585	C₂×C₁₉	1	2	yes	complemented
205	C₈×D₈	C₂×C₁₉	1	2	yes	complemented
206	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#1492	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1476	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#1450	C₂×C₁₉	1	1	yes	characteristic, complemented
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	4	1	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	4	1	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	#443	1	2	yes	—
228	C₄×C₁₉	C₂×#131	1	1	yes	characteristic
229	C₄×C₁₉	#568	1	1	yes	characteristic
230	C₄×C₁₉	#576	1	1	yes	characteristic
231	C₄×C₁₉	#577	1	1	yes	characteristic
232	#532	C₂²×C₁₉	1	1	yes	characteristic
233	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
234	#482	C₄×C₁₉	1	2	yes	—
235	#477	C₄×C₁₉	1	1	yes	characteristic
236	#476	C₄×C₁₉	1	1	yes	characteristic
237	#460	C₄×C₁₉	1	1	yes	characteristic
238	#459	C₄×C₁₉	1	1	yes	characteristic
239	#449	C₄×C₁₉	1	2	yes	—
240	#446	C₂²×C₁₉	1	2	yes	—
241	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
242	C₄×D₈	C₂²×C₁₉	1	2	yes	—
243	#436	—	2	1	no	—
244	#436	C₂²×C₁₉	1	2	yes	—
245	#435	—	2	2	no	—
246	C₈×D₄	—	2	1	no	—
247	C₈×D₄	C₂²×C₁₉	1	2	yes	—
248	C₈×D₄	C₂²×C₁₉	1	2	yes	—
249	#432	—	2	1	no	—
250	#431	C₂²×C₁₉	1	1	yes	characteristic
251	#431	C₂²×C₁₉	1	1	yes	characteristic
252	#431	C₂²×C₁₉	1	1	yes	characteristic
253	#423	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×C₄⋊C₈	—	2	1	no	—
255	#408	—	2	2	no	—
256	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
257	#335	C₂²×C₁₉	1	2	yes	—
258	#334	C₂²×C₁₉	1	2	yes	—
259	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
260	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
261	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
262	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
263	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
264	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
265	#322	C₂²×C₁₉	1	2	yes	—
266	C₈²	C₂²×C₁₉	1	2	yes	—
267	C₂×C₁₉	—	4	1	no	—
268	C₂×C₁₉	—	4	2	no	—
269	C₂×C₁₉	—	8	2	no	—
270	C₂×C₁₉	#2933	1	1	yes	characteristic
271	C₂×C₁₉	#2946	1	1	yes	characteristic
272	C₂×C₁₉	C₂×#443	1	1	yes	characteristic
273	C₂×#41	—	2	1	no	—
274	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
275	C₂×SD₁₆	C₂×C₄×C₁₉	1	2	yes	—
276	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
283	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
284	#124	—	2	1	no	—
285	#121	—	2	1	no	—
286	#121	C₂×C₄×C₁₉	1	2	yes	—
287	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
288	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
293	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
294	C₄×D₄	C₂³×C₁₉	1	2	yes	—
295	#117	—	2	1	no	—
296	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
299	#107	C₂×C₄×C₁₉	1	2	yes	—
300	#106	C₂×C₄×C₁₉	1	2	yes	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
304	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
305	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
306	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
307	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
308	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
309	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
310	#103	C₂×C₄×C₁₉	1	2	yes	—
311	#102	C₂×C₄×C₁₉	1	2	yes	—
312	#102	C₂×C₄×C₁₉	1	2	yes	—
313	#102	C₂×C₄×C₁₉	1	2	yes	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
319	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
320	#97	—	2	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
324	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
325	C₄×C₈	C₂³×C₁₉	1	2	yes	—
326	C₄×C₈	C₂³×C₁₉	1	2	yes	—
327	C₁₉	#18015	1	1	yes	characteristic, direct product factor, Sylow
328	#41	—	2	2	no	—
329	#41	—	4	1	no	—
330	#41	—	8	1	no	—
331	#41	—	8	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
339	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
347	SD₁₆	—	4	2	no	—
348	D₈	—	2	4	no	—
349	M₁₆	—	8	2	no	—
350	M₁₆	—	8	1	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	8	2	no	—
358	C₂×C₈	—	8	2	no	—
359	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
360	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
367	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₄²	#41×C₁₉	1	1	yes	characteristic
380	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	8	1	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	2	no	—
394	D₄	C₁₉×#131	1	2	yes	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	C₁₉×#443	1	2	yes	—
443	C₄	C₂×C₁₉×#131	1	1	yes	characteristic
444	C₄	C₁₉×#568	1	1	yes	characteristic
445	C₄	C₁₉×#576	1	1	yes	characteristic
446	C₄	C₁₉×#577	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	4	2	no	—
449	C₂	—	8	2	no	—
450	C₂	C₁₉×#2933	1	1	yes	characteristic
451	C₂	C₁₉×#2946	1	1	yes	characteristic
452	C₂	C₂×C₁₉×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄×D₄
prime radical	C₁₉×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2990	C₂	semidirect
3. C₁₉×#2979	C₂	semidirect
4. C₁₉×#1590	C₂	semidirect
5. C₁₉×#1586	C₂	semidirect
6. C₁₉×#1585	C₂	semidirect
7. C₈×D₈×C₁₉	C₂	semidirect
8. C₁₉×#1574	C₂	semidirect
9. C₁₉×#1492	C₂	semidirect
10. C₁₉×#1476	C₂	semidirect
11. C₁₉×#1450	C₂	semidirect
154. #18015	C₁₉	direct (N × H)
200. #2990	C₂×C₁₉	semidirect
201. #2979	C₂×C₁₉	semidirect
202. #1590	C₂×C₁₉	semidirect
203. #1586	C₂×C₁₉	semidirect
204. #1585	C₂×C₁₉	semidirect
205. C₈×D₈	C₂×C₁₉	semidirect
206. #1574	C₂×C₁₉	semidirect
207. #1492	C₂×C₁₉	semidirect
208. #1476	C₂×C₁₉	semidirect
209. #1450	C₂×C₁₉	semidirect
327. C₁₉	#18015	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3106	2
C₁₉×#2990	2
C₁₉×#2979	2
C₁₉×#1590	2
C₁₉×#1586	2
C₁₉×#1585	2
C₈×D₈×C₁₉	2
C₁₉×#1574	2
C₁₉×#1492	2
C₁₉×#1476	2
C₁₉×#1450	2
#18015	19

Subgroups — C19×#18015 #18023974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18015 #18023974