Subgroups — C₁₉×#21416 #18027375

Order 4864.

1170 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3444	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1995	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1963	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1897	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₉×#104	C₂	1	4	yes	maximal, complemented
8	C₁₉×#533	C₄	1	2	yes	complemented
9	C₁₉×#533	C₂²	1	1	yes	characteristic
10	C₁₉×#532	C₄	1	2	yes	complemented
11	C₁₉×#532	C₂²	1	1	yes	characteristic
12	C₁₉×#529	—	2	2	no	—
13	C₁₉×#529	—	2	2	no	—
14	C₁₉×#529	C₄	1	4	yes	complemented
15	C₁₉×#525	—	2	2	no	—
16	C₁₉×#525	C₂²	1	2	yes	—
17	C₄×#41×C₁₉	—	2	2	no	—
18	C₄×#41×C₁₉	C₂²	1	2	yes	—
19	C₂×C₁₉×#117	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#432	—	2	2	no	—
22	C₁₉×#431	—	2	2	no	—
23	C₁₉×#423	C₂²	1	2	yes	—
24	C₂×C₁₉×#104	C₂²	1	8	yes	—
25	C₁₉×#407	C₂²	1	2	yes	—
26	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
29	C₁₉×#376	C₂²	1	2	yes	—
30	C₄³×C₁₉	C₂²	1	2	yes	—
31	C₁₉×#339	C₂²	1	8	yes	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₉	D₄	1	2	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
37	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
38	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
39	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
40	C₁₉×#126	—	2	4	no	—
41	C₁₉×#125	—	2	2	no	—
42	C₁₉×#125	C₂×C₄	1	2	yes	—
43	C₁₉×#124	—	2	2	no	—
44	C₁₉×#124	C₂×C₄	1	2	yes	—
45	C₁₉×#123	—	2	4	no	—
46	C₁₉×#123	—	2	2	no	—
47	C₁₉×C₂²⋊Q₈	—	2	2	no	—
48	C₁₉×C₂²⋊Q₈	—	2	2	no	—
49	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
50	C₁₉×#121	—	2	2	no	—
51	C₁₉×#121	—	2	2	no	—
52	C₁₉×#121	C₂×C₄	1	4	yes	—
53	C₁₉×#120	—	2	2	no	—
54	C₄×Q₈×C₁₉	—	2	2	no	—
55	C₄×Q₈×C₁₉	—	2	2	no	—
56	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
57	C₄×D₄×C₁₉	—	2	4	no	—
58	C₄×D₄×C₁₉	—	2	4	no	—
59	C₄×D₄×C₁₉	—	2	4	no	—
60	C₄×D₄×C₁₉	—	2	2	no	—
61	C₄×D₄×C₁₉	—	2	2	no	—
62	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
63	C₁₉×#117	—	2	2	no	—
64	C₁₉×#117	—	2	4	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	—	2	8	no	—
67	C₁₉×#117	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	—	2	2	no	—
71	C₂×C₄²×C₁₉	—	2	4	no	—
72	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₁₉	D₄	1	2	yes	—
75	C₂×C₄²×C₁₉	D₄	1	2	yes	—
76	C₂×C₄²×C₁₉	D₄	1	2	yes	—
77	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊C₈	—	2	4	no	—
81	C₁₉×#104	—	2	16	no	—
82	C₁₉×C₂²⋊C₈	—	2	4	no	—
83	C₁₉×#97	—	2	2	no	—
84	C₄×C₈×C₁₉	—	2	2	no	—
85	C₁₉×#95	—	2	4	no	—
86	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
87	#41×C₁₉	—	2	8	no	—
88	#41×C₁₉	—	4	8	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	4	4	no	—
100	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₁₉	—	2	8	no	—
111	C₂×C₈×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	8	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	4	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	4	no	—
118	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
119	C₂²⋊C₄×C₁₉	—	2	8	no	—
120	C₂²⋊C₄×C₁₉	—	2	4	no	—
121	C₂²⋊C₄×C₁₉	—	2	2	no	—
122	C₂²⋊C₄×C₁₉	—	2	4	no	—
123	C₂²⋊C₄×C₁₉	—	2	4	no	—
124	C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₄²×C₁₉	—	2	4	no	—
126	C₄²×C₁₉	—	2	2	no	—
127	C₄²×C₁₉	—	2	4	no	—
128	C₄²×C₁₉	—	4	8	no	—
129	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
131	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
134	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₉	C₂×D₄	1	2	yes	—
138	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₉	#41	1	8	yes	complemented
140	#21416	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₁₉	—	2	4	no	—
147	Q₈×C₁₉	—	4	4	no	—
148	D₄×C₁₉	—	2	4	no	—
149	D₄×C₁₉	—	4	4	no	—
150	D₄×C₁₉	—	4	8	no	—
151	D₄×C₁₉	—	4	4	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	8	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	8	no	—
167	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
175	C₈×C₁₉	—	4	4	no	—
176	#3444	C₂×C₁₉	1	1	yes	characteristic
177	#2920	C₂×C₁₉	1	1	yes	characteristic, complemented
178	C₄×#117	C₂×C₁₉	1	1	yes	characteristic, complemented
179	#1995	C₂×C₁₉	1	2	yes	complemented
180	#1963	C₂×C₁₉	1	2	yes	complemented
181	#1897	C₂×C₁₉	1	4	yes	complemented
182	C₄×#104	C₂×C₁₉	1	4	yes	complemented
183	C₂²×C₁₉	—	2	2	no	—
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₁₉	#525	1	2	yes	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	2	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	4	8	no	—
197	C₄×C₁₉	—	4	4	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	#421	1	4	yes	—
200	C₄×C₁₉	C₄×#41	1	2	yes	—
201	C₄×C₁₉	#532	1	2	yes	—
202	#533	C₄×C₁₉	1	2	yes	complemented
203	#533	C₂²×C₁₉	1	1	yes	characteristic
204	#532	C₄×C₁₉	1	2	yes	complemented
205	#532	C₂²×C₁₉	1	1	yes	characteristic
206	#529	—	2	2	no	—
207	#529	—	2	2	no	—
208	#529	C₄×C₁₉	1	4	yes	complemented
209	#525	—	2	2	no	—
210	#525	C₂²×C₁₉	1	2	yes	—
211	C₄×#41	—	2	2	no	—
212	C₄×#41	C₂²×C₁₉	1	2	yes	—
213	C₂×#117	C₂²×C₁₉	1	2	yes	—
214	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
215	#432	—	2	2	no	—
216	#431	—	2	2	no	—
217	#423	C₂²×C₁₉	1	2	yes	—
218	C₂×#104	C₂²×C₁₉	1	8	yes	—
219	#407	C₂²×C₁₉	1	2	yes	—
220	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
221	C₄×C₄⋊C₄	—	2	2	no	—
222	C₄×C₂²⋊C₄	—	2	2	no	—
223	#376	C₂²×C₁₉	1	2	yes	—
224	C₄³	C₂²×C₁₉	1	2	yes	—
225	#339	C₂²×C₁₉	1	8	yes	—
226	C₂×C₁₉	—	2	2	no	—
227	C₂×C₁₉	—	4	2	no	—
228	C₂×C₁₉	—	8	2	no	—
229	C₂×C₁₉	#2297	1	1	yes	characteristic
230	C₂×C₁₉	C₂×#421	1	2	yes	—
231	C₂×#41	—	2	2	no	—
232	C₂×#41	C₂³×C₁₉	1	2	yes	—
233	C₂³×C₄	D₄×C₁₉	1	2	yes	—
234	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
235	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
236	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
237	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
238	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
239	#126	—	2	4	no	—
240	#125	—	2	2	no	—
241	#125	C₂×C₄×C₁₉	1	2	yes	—
242	#124	—	2	2	no	—
243	#124	C₂×C₄×C₁₉	1	2	yes	—
244	#123	—	2	4	no	—
245	#123	—	2	2	no	—
246	C₂²⋊Q₈	—	2	2	no	—
247	C₂²⋊Q₈	—	2	2	no	—
248	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
249	#121	—	2	2	no	—
250	#121	—	2	2	no	—
251	#121	C₂×C₄×C₁₉	1	4	yes	—
252	#120	—	2	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
262	#117	—	2	2	no	—
263	#117	—	2	4	no	—
264	#117	—	2	2	no	—
265	#117	—	2	8	no	—
266	#117	C₂³×C₁₉	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	4	no	—
271	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
272	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
273	C₂×C₄²	D₄×C₁₉	1	2	yes	—
274	C₂×C₄²	D₄×C₁₉	1	2	yes	—
275	C₂×C₄²	D₄×C₁₉	1	2	yes	—
276	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
277	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
279	C₄⋊C₈	—	2	4	no	—
280	#104	—	2	16	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	#95	—	2	4	no	—
285	C₁₉	#21416	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
287	#41	—	2	8	no	—
288	#41	—	4	8	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
301	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
302	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
303	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
310	M₁₆	—	2	8	no	—
311	C₂×C₈	—	2	4	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
319	C₂²⋊C₄	—	2	8	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	4	no	—
328	C₄²	—	4	8	no	—
329	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
330	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
331	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
332	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
333	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
334	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
335	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
336	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₄²	C₂×D₄×C₁₉	1	2	yes	—
338	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₄²	#41×C₁₉	1	8	yes	complemented
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
344	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
345	Q₈	—	2	4	no	—
346	Q₈	—	4	4	no	—
347	D₄	—	2	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	8	no	—
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
371	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
374	C₈	—	4	4	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
383	C₂²	C₁₉×#525	1	2	yes	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	4	8	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	4	no	—
391	C₄	C₁₉×#421	1	4	yes	—
392	C₄	C₄×#41×C₁₉	1	2	yes	—
393	C₄	C₁₉×#532	1	2	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	4	2	no	—
396	C₂	—	8	2	no	—
397	C₂	C₁₉×#2297	1	1	yes	characteristic
398	C₂	C₂×C₁₉×#421	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₁₉×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2920	C₂	semidirect
3. C₄×C₁₉×#117	C₂	semidirect
4. C₁₉×#1995	C₂	semidirect
5. C₁₉×#1963	C₂	semidirect
6. C₁₉×#1897	C₂	semidirect
7. C₄×C₁₉×#104	C₂	semidirect
8. C₁₉×#533	C₄	semidirect
10. C₁₉×#532	C₄	semidirect
14. C₁₉×#529	C₄	semidirect
139. C₄²×C₁₉	#41	semidirect
140. #21416	C₁₉	direct (N × H)
177. #2920	C₂×C₁₉	semidirect
178. C₄×#117	C₂×C₁₉	semidirect
179. #1995	C₂×C₁₉	semidirect
180. #1963	C₂×C₁₉	semidirect
181. #1897	C₂×C₁₉	semidirect
182. C₄×#104	C₂×C₁₉	semidirect
202. #533	C₄×C₁₉	semidirect
204. #532	C₄×C₁₉	semidirect
208. #529	C₄×C₁₉	semidirect
285. C₁₉	#21416	direct (N × H)
339. C₄²	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3444	2
C₁₉×#2920	2
C₄×C₁₉×#117	2
C₁₉×#1995	2
C₁₉×#1963	2
C₁₉×#1897	2
C₄×C₁₉×#104	2
#21416	19

Subgroups — C19×#21416 #18027375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21416 #18027375