Subgroups — C₁₉×#21393 #18027352

Order 4864.

1430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1988	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1982	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1875	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1762	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₉	—	2	1	no	—
9	C₁₉×#532	—	2	4	no	—
10	C₁₉×#532	C₄	1	8	yes	complemented
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#124	—	2	1	no	—
14	C₂×C₁₉×#121	—	2	1	no	—
15	C₂×C₁₉×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₁₉×#117	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#432	—	2	4	no	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×#102	C₂²	1	8	yes	—
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₉×#97	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
28	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₁₉×#376	—	2	1	no	—
30	C₄³×C₁₉	—	2	1	no	—
31	C₁₉×#340	C₂²	1	8	yes	—
32	C₂×#41×C₁₉	—	2	8	no	—
33	C₂×#41×C₁₉	—	4	8	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	—	2	2	no	—
40	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
44	C₁₉×C₄⋊Q₈	—	2	2	no	—
45	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
46	C₁₉×#127	—	2	2	no	—
47	C₁₉×#127	C₂×C₄	1	4	yes	—
48	C₁₉×#124	—	2	8	no	—
49	C₁₉×#121	—	2	8	no	—
50	C₁₉×#121	—	2	4	no	—
51	C₁₉×#121	C₂×C₄	1	8	yes	—
52	C₄×D₄×C₁₉	—	2	8	no	—
53	C₄×D₄×C₁₉	—	2	4	no	—
54	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
55	C₁₉×#117	—	2	8	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄²×C₁₉	—	2	2	no	—
63	C₂×C₄²×C₁₉	—	2	2	no	—
64	C₂×C₄²×C₁₉	—	2	2	no	—
65	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	D₄	1	4	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×C₄⋊C₈	—	2	4	no	—
72	C₁₉×#102	—	2	16	no	—
73	C₁₉×C₂²⋊C₈	—	2	4	no	—
74	C₁₉×#97	—	2	4	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	#41×C₁₉	—	4	32	no	—
80	C₂×Q₈×C₁₉	—	2	4	no	—
81	C₂×Q₈×C₁₉	—	4	4	no	—
82	C₂×D₄×C₁₉	—	2	8	no	—
83	C₂×D₄×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	8	no	—
87	C₂×D₄×C₁₉	—	4	4	no	—
88	C₂×D₄×C₁₉	—	4	8	no	—
89	C₂×D₄×C₁₉	—	4	4	no	—
90	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	8	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	8	no	—
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₉	—	2	4	no	—
109	C₂×C₈×C₁₉	—	2	8	no	—
110	C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
114	C₄⋊C₄×C₁₉	#41	1	8	yes	complemented
115	C₂²⋊C₄×C₁₉	—	2	8	no	—
116	C₂²⋊C₄×C₁₉	—	2	8	no	—
117	C₂²⋊C₄×C₁₉	—	2	8	no	—
118	C₄²×C₁₉	—	2	8	no	—
119	C₄²×C₁₉	—	4	4	no	—
120	C₄²×C₁₉	—	4	4	no	—
121	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
122	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
123	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
124	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
125	C₄²×C₁₉	C₂×D₄	1	2	yes	—
126	C₄²×C₁₉	C₂×D₄	1	2	yes	—
127	#21393	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₁₉	—	2	2	no	—
129	C₂³×C₁₉	—	2	2	no	—
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	4	no	—
132	C₂³×C₁₉	—	4	4	no	—
133	C₂³×C₁₉	—	4	4	no	—
134	C₂³×C₁₉	—	4	4	no	—
135	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₁₉	—	4	8	no	—
138	D₄×C₁₉	—	2	8	no	—
139	D₄×C₁₉	—	4	8	no	—
140	D₄×C₁₉	—	4	16	no	—
141	D₄×C₁₉	—	4	4	no	—
142	D₄×C₁₉	—	4	8	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	8	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	8	no	—
152	C₂×C₄×C₁₉	—	4	4	no	—
153	C₂×C₄×C₁₉	—	4	16	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	4	4	no	—
156	C₂×C₄×C₁₉	—	4	4	no	—
157	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
163	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
166	C₈×C₁₉	—	4	4	no	—
167	C₂×#532	C₂×C₁₉	1	1	yes	characteristic
168	C₂×#432	C₂×C₁₉	1	1	yes	characteristic, complemented
169	C₄×#117	C₂×C₁₉	1	1	yes	characteristic, complemented
170	#1988	C₂×C₁₉	1	2	yes	complemented
171	#1982	C₂×C₁₉	1	2	yes	complemented
172	#1875	C₂×C₁₉	1	4	yes	complemented
173	#1762	C₂×C₁₉	1	4	yes	complemented
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	4	4	no	—
178	C₂²×C₁₉	—	4	4	no	—
179	C₂²×C₁₉	—	4	4	no	—
180	C₂²×C₁₉	—	4	4	no	—
181	C₂²×C₁₉	—	8	8	no	—
182	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₁₉	#525	1	2	yes	—
184	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
185	C₂²×C₁₉	#575	1	2	yes	—
186	C₄×C₁₉	—	2	2	no	—
187	C₄×C₁₉	—	2	2	no	—
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	2	2	no	—
190	C₄×C₁₉	—	4	8	no	—
191	C₄×C₁₉	—	4	4	no	—
192	C₄×C₁₉	#418	1	4	yes	—
193	C₄×C₁₉	C₄×#41	1	2	yes	—
194	C₄×C₁₉	#532	1	2	yes	—
195	C₂²×#41	—	2	1	no	—
196	#532	—	2	4	no	—
197	#532	C₄×C₁₉	1	8	yes	complemented
198	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
199	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
200	C₂×#124	—	2	1	no	—
201	C₂×#121	—	2	1	no	—
202	C₂×#121	C₂²×C₁₉	1	2	yes	—
203	C₂×C₄×D₄	—	2	1	no	—
204	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
205	C₂×#117	C₂²×C₁₉	1	2	yes	—
206	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
207	#432	—	2	4	no	—
208	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
209	C₂×#102	C₂²×C₁₉	1	8	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
211	C₂×#97	C₂²×C₁₉	1	2	yes	—
212	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
213	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
214	C₄×C₂²⋊C₄	—	2	1	no	—
215	C₄×C₂²⋊C₄	—	2	1	no	—
216	#376	—	2	1	no	—
217	C₄³	—	2	1	no	—
218	#340	C₂²×C₁₉	1	8	yes	—
219	C₂×C₁₉	—	4	2	no	—
220	C₂×C₁₉	—	8	4	no	—
221	C₂×C₁₉	#2297	1	1	yes	characteristic
222	C₂×C₁₉	C₂×#418	1	1	yes	characteristic
223	C₂×C₁₉	#2896	1	1	yes	characteristic
224	C₂×C₁₉	#3115	1	4	yes	—
225	C₂×#41	—	2	8	no	—
226	C₂×#41	—	4	8	no	—
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
239	#127	—	2	2	no	—
240	#127	C₂×C₄×C₁₉	1	4	yes	—
241	#124	—	2	8	no	—
242	#121	—	2	8	no	—
243	#121	—	2	4	no	—
244	#121	C₂×C₄×C₁₉	1	8	yes	—
245	C₄×D₄	—	2	8	no	—
246	C₄×D₄	—	2	4	no	—
247	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
248	#117	—	2	8	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
259	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄²	D₄×C₁₉	1	4	yes	—
262	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
264	C₄⋊C₈	—	2	4	no	—
265	#102	—	2	16	no	—
266	C₂²⋊C₈	—	2	4	no	—
267	#97	—	2	4	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	C₁₉	#21393	1	1	yes	characteristic, direct product factor, Sylow
271	C₂⁴	—	2	2	no	—
272	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
273	#41	—	4	32	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	4	4	no	—
276	C₂×D₄	—	2	8	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	8	no	—
281	C₂×D₄	—	4	4	no	—
282	C₂×D₄	—	4	8	no	—
283	C₂×D₄	—	4	4	no	—
284	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	8	no	—
292	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
293	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	8	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
308	C₄⋊C₄	#41×C₁₉	1	8	yes	complemented
309	C₂²⋊C₄	—	2	8	no	—
310	C₂²⋊C₄	—	2	8	no	—
311	C₂²⋊C₄	—	2	8	no	—
312	C₄²	—	2	8	no	—
313	C₄²	—	4	4	no	—
314	C₄²	—	4	4	no	—
315	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
316	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
317	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
318	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
319	C₄²	C₂×D₄×C₁₉	1	2	yes	—
320	C₄²	C₂×D₄×C₁₉	1	2	yes	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	4	4	no	—
328	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
329	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
330	Q₈	—	4	8	no	—
331	D₄	—	2	8	no	—
332	D₄	—	4	8	no	—
333	D₄	—	4	16	no	—
334	D₄	—	4	8	no	—
335	D₄	—	4	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	16	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
351	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
355	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
356	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
357	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
359	C₈	—	4	4	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	8	8	no	—
368	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
369	C₂²	C₁₉×#525	1	2	yes	—
370	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
371	C₂²	C₁₉×#575	1	2	yes	—
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	8	no	—
377	C₄	—	4	4	no	—
378	C₄	C₁₉×#418	1	4	yes	—
379	C₄	C₄×#41×C₁₉	1	2	yes	—
380	C₄	C₁₉×#532	1	2	yes	—
381	C₂	—	4	2	no	—
382	C₂	—	8	4	no	—
383	C₂	C₁₉×#2297	1	1	yes	characteristic
384	C₂	C₂×C₁₉×#418	1	1	yes	characteristic
385	C₂	C₁₉×#2896	1	1	yes	characteristic
386	C₂	C₁₉×#3115	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#432	C₂	semidirect
3. C₄×C₁₉×#117	C₂	semidirect
4. C₁₉×#1988	C₂	semidirect
5. C₁₉×#1982	C₂	semidirect
6. C₁₉×#1875	C₂	semidirect
7. C₁₉×#1762	C₂	semidirect
10. C₁₉×#532	C₄	semidirect
114. C₄⋊C₄×C₁₉	#41	semidirect
127. #21393	C₁₉	direct (N × H)
168. C₂×#432	C₂×C₁₉	semidirect
169. C₄×#117	C₂×C₁₉	semidirect
170. #1988	C₂×C₁₉	semidirect
171. #1982	C₂×C₁₉	semidirect
172. #1875	C₂×C₁₉	semidirect
173. #1762	C₂×C₁₉	semidirect
197. #532	C₄×C₁₉	semidirect
270. C₁₉	#21393	direct (N × H)
308. C₄⋊C₄	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#532	2
C₂×C₁₉×#432	2
C₄×C₁₉×#117	2
C₁₉×#1988	2
C₁₉×#1982	2
C₁₉×#1875	2
C₁₉×#1762	2
#21393	19

Subgroups — C19×#21393 #18027352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21393 #18027352