Subgroups — C₁₉×#14288 #18020247

Order 4864.

1934 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1446	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1439	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1438	C₂	1	2	yes	maximal
7	C₁₉×#1437	C₂	1	4	yes	maximal, complemented
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#124	—	2	4	no	—
11	C₂×C₁₉×#124	—	2	4	no	—
12	C₂×C₁₉×#124	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#383	—	2	4	no	—
20	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
21	C₂×C₁₉×#95	C₂²	1	2	yes	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	2	yes	—
24	C₂×C₁₉×#95	C₂²	1	2	yes	—
25	C₂×C₁₉×#95	C₂²	1	8	yes	—
26	C₂⁵×C₁₉	C₂³	1	2	yes	—
27	C₂²×Q₈×C₁₉	—	2	2	no	—
28	C₂²×Q₈×C₁₉	—	2	2	no	—
29	C₂²×Q₈×C₁₉	—	4	4	no	—
30	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
31	C₂²×D₄×C₁₉	—	2	2	no	—
32	C₂²×D₄×C₁₉	—	2	2	no	—
33	C₂²×D₄×C₁₉	—	4	4	no	—
34	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₁₉×#124	—	2	32	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
51	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
52	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
53	C₂×C₄²×C₁₉	—	2	4	no	—
54	C₂×C₄²×C₁₉	—	4	4	no	—
55	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
56	C₂×C₄²×C₁₉	D₄	1	4	yes	—
57	C₂×C₄²×C₁₉	D₄	1	4	yes	—
58	C₁₉×#95	—	2	4	no	—
59	C₁₉×#95	—	2	4	no	—
60	C₁₉×#95	—	2	4	no	—
61	C₁₉×#95	—	2	4	no	—
62	C₁₉×#95	—	4	8	no	—
63	C₂⁴×C₁₉	—	2	2	no	—
64	C₂⁴×C₁₉	—	2	2	no	—
65	C₂⁴×C₁₉	—	2	8	no	—
66	C₂⁴×C₁₉	—	2	4	no	—
67	C₂⁴×C₁₉	—	2	8	no	—
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
70	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
71	C₂×Q₈×C₁₉	—	2	8	no	—
72	C₂×Q₈×C₁₉	—	4	8	no	—
73	C₂×Q₈×C₁₉	—	4	8	no	—
74	C₂×Q₈×C₁₉	—	4	8	no	—
75	C₂×D₄×C₁₉	—	2	8	no	—
76	C₂×D₄×C₁₉	—	4	8	no	—
77	C₂×D₄×C₁₉	—	4	8	no	—
78	C₂×D₄×C₁₉	—	4	8	no	—
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	4	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	2	8	no	—
88	C₂²×C₄×C₁₉	—	2	8	no	—
89	C₂²×C₄×C₁₉	—	2	8	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	8	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	8	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	#41	1	8	yes	—
106	C₄⋊C₄×C₁₉	—	2	16	no	—
107	C₂²⋊C₄×C₁₉	—	2	16	no	—
108	C₂²⋊C₄×C₁₉	—	2	16	no	—
109	C₂²⋊C₄×C₁₉	—	4	32	no	—
110	C₄²×C₁₉	—	4	8	no	—
111	C₄²×C₁₉	C₂²⋊C₄	1	16	yes	complemented
112	#14288	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₁₉	—	2	4	no	—
114	C₂³×C₁₉	—	2	8	no	—
115	C₂³×C₁₉	—	2	8	no	—
116	C₂³×C₁₉	—	2	8	no	—
117	C₂³×C₁₉	—	4	4	no	—
118	C₂³×C₁₉	—	4	4	no	—
119	C₂³×C₁₉	—	4	4	no	—
120	C₂³×C₁₉	—	4	4	no	—
121	C₂³×C₁₉	—	4	2	no	—
122	C₂³×C₁₉	—	4	2	no	—
123	C₂³×C₁₉	—	4	4	no	—
124	C₂³×C₁₉	—	4	8	no	—
125	C₂³×C₁₉	—	4	8	no	—
126	C₂³×C₁₉	—	4	16	no	—
127	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
128	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
129	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
130	C₂³×C₁₉	C₂×#41	1	4	yes	—
131	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
132	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
133	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
134	Q₈×C₁₉	—	4	16	no	—
135	D₄×C₁₉	—	4	16	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	4	no	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	2	4	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	4	no	—
143	C₂×C₄×C₁₉	—	2	4	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	2	8	no	—
148	C₂×C₄×C₁₉	—	2	8	no	—
149	C₂×C₄×C₁₉	—	2	16	no	—
150	C₂×C₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	—	4	4	no	—
152	C₂×C₄×C₁₉	—	4	4	no	—
153	C₂×C₄×C₁₉	—	4	4	no	—
154	C₂×C₄×C₁₉	—	4	8	no	—
155	C₂×C₄×C₁₉	—	4	4	no	—
156	C₂×C₄×C₁₉	—	4	4	no	—
157	C₂×C₄×C₁₉	—	4	4	no	—
158	C₂×C₄×C₁₉	—	4	8	no	—
159	C₂×C₄×C₁₉	—	4	8	no	—
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
163	C₂²×#124	C₂×C₁₉	1	1	yes	characteristic
164	C₂×#383	C₂×C₁₉	1	1	yes	characteristic, complemented
165	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
166	#1446	C₂×C₁₉	1	2	yes	complemented
167	#1439	C₂×C₁₉	1	4	yes	complemented
168	#1438	C₂×C₁₉	1	2	yes	—
169	#1437	C₂×C₁₉	1	4	yes	complemented
170	C₂²×C₁₉	—	4	4	no	—
171	C₂²×C₁₉	—	4	4	no	—
172	C₂²×C₁₉	—	4	16	no	—
173	C₂²×C₁₉	—	4	4	no	—
174	C₂²×C₁₉	—	8	4	no	—
175	C₂²×C₁₉	—	8	4	no	—
176	C₂²×C₁₉	—	8	8	no	—
177	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₁₉	C₄×#41	1	2	yes	—
179	C₂²×C₁₉	#518	1	2	yes	—
180	C₂²×C₁₉	#520	1	2	yes	—
181	C₂²×C₁₉	#525	1	2	yes	—
182	C₂²×C₁₉	#532	1	2	yes	—
183	C₂²×C₁₉	#535	1	2	yes	—
184	C₂²×C₁₉	#535	1	2	yes	—
185	C₂²×C₁₉	#535	1	1	yes	characteristic
186	C₂²×C₁₉	#536	1	1	yes	characteristic
187	C₂²×C₁₉	#537	1	2	yes	—
188	C₂²×C₁₉	#538	1	8	yes	—
189	C₂²×C₁₉	#542	1	8	yes	—
190	C₄×C₁₉	—	2	4	no	—
191	C₄×C₁₉	—	2	4	no	—
192	C₄×C₁₉	—	2	4	no	—
193	C₄×C₁₉	—	4	4	no	—
194	C₄×C₁₉	—	4	8	no	—
195	C₄×C₁₉	—	8	4	no	—
196	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
197	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
198	C₂×#124	—	2	4	no	—
199	C₂×#124	—	2	4	no	—
200	C₂×#124	C₄×C₁₉	1	8	yes	complemented
201	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
202	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
203	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
204	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
205	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
206	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
207	#383	—	2	4	no	—
208	C₄×C₄⋊C₄	—	2	4	no	—
209	C₂×#95	C₂²×C₁₉	1	2	yes	—
210	C₂×#95	C₂²×C₁₉	1	2	yes	—
211	C₂×#95	C₂²×C₁₉	1	2	yes	—
212	C₂×#95	C₂²×C₁₉	1	2	yes	—
213	C₂×#95	C₂²×C₁₉	1	8	yes	—
214	C₂×C₁₉	—	8	4	no	—
215	C₂×C₁₉	#2297	1	1	yes	characteristic
216	C₂×C₁₉	#2309	1	1	yes	characteristic
217	C₂×C₁₉	#2311	1	1	yes	characteristic
218	C₂×C₁₉	#2337	1	4	yes	—
219	C₂×C₁₉	#2631	1	2	yes	—
220	C₂×C₁₉	#2632	1	2	yes	—
221	C₂×C₁₉	#2662	1	4	yes	—
222	C₂⁵	C₂³×C₁₉	1	2	yes	—
223	C₂²×Q₈	—	2	2	no	—
224	C₂²×Q₈	—	2	2	no	—
225	C₂²×Q₈	—	4	4	no	—
226	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	—	4	4	no	—
230	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
231	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
232	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
233	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
234	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
237	#124	—	2	32	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	8	no	—
240	C₂×C₂²⋊C₄	—	2	4	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	—	2	4	no	—
244	C₂×C₂²⋊C₄	—	2	16	no	—
245	C₂×C₂²⋊C₄	—	4	8	no	—
246	C₂×C₂²⋊C₄	—	4	8	no	—
247	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
248	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
249	C₂×C₄²	—	2	4	no	—
250	C₂×C₄²	—	4	4	no	—
251	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
252	C₂×C₄²	D₄×C₁₉	1	4	yes	—
253	C₂×C₄²	D₄×C₁₉	1	4	yes	—
254	#95	—	2	4	no	—
255	#95	—	2	4	no	—
256	#95	—	2	4	no	—
257	#95	—	2	4	no	—
258	#95	—	4	8	no	—
259	C₁₉	#14288	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	—	2	2	no	—
261	C₂⁴	—	2	2	no	—
262	C₂⁴	—	2	8	no	—
263	C₂⁴	—	2	4	no	—
264	C₂⁴	—	2	8	no	—
265	C₂⁴	—	2	4	no	—
266	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
267	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
268	C₂×Q₈	—	2	8	no	—
269	C₂×Q₈	—	4	8	no	—
270	C₂×Q₈	—	4	8	no	—
271	C₂×Q₈	—	4	8	no	—
272	C₂×D₄	—	2	8	no	—
273	C₂×D₄	—	4	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	—	4	8	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	2	8	no	—
286	C₂²×C₄	—	2	8	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
302	C₂²×C₄	#41×C₁₉	1	8	yes	—
303	C₄⋊C₄	—	2	16	no	—
304	C₂²⋊C₄	—	2	16	no	—
305	C₂²⋊C₄	—	2	16	no	—
306	C₂²⋊C₄	—	4	32	no	—
307	C₄²	—	4	8	no	—
308	C₄²	C₂²⋊C₄×C₁₉	1	16	yes	complemented
309	C₂³	—	2	4	no	—
310	C₂³	—	2	8	no	—
311	C₂³	—	2	8	no	—
312	C₂³	—	2	8	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	4	8	no	—
321	C₂³	—	4	8	no	—
322	C₂³	—	4	16	no	—
323	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
324	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
325	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
326	C₂³	C₂×#41×C₁₉	1	4	yes	—
327	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
328	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
329	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
330	Q₈	—	4	16	no	—
331	D₄	—	4	16	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	16	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
357	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
359	C₂²	—	4	4	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	4	16	no	—
363	C₂²	—	8	8	no	—
364	C₂²	—	8	4	no	—
365	C₂²	—	8	4	no	—
366	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
367	C₂²	C₄×#41×C₁₉	1	2	yes	—
368	C₂²	C₁₉×#518	1	2	yes	—
369	C₂²	C₁₉×#520	1	2	yes	—
370	C₂²	C₁₉×#525	1	2	yes	—
371	C₂²	C₁₉×#532	1	2	yes	—
372	C₂²	C₁₉×#535	1	2	yes	—
373	C₂²	C₁₉×#535	1	2	yes	—
374	C₂²	C₁₉×#535	1	1	yes	characteristic
375	C₂²	C₁₉×#536	1	1	yes	characteristic
376	C₂²	C₁₉×#537	1	2	yes	—
377	C₂²	C₁₉×#538	1	8	yes	—
378	C₂²	C₁₉×#542	1	8	yes	—
379	C₄	—	2	4	no	—
380	C₄	—	2	4	no	—
381	C₄	—	2	4	no	—
382	C₄	—	4	4	no	—
383	C₄	—	4	8	no	—
384	C₄	—	8	4	no	—
385	C₂	—	8	4	no	—
386	C₂	C₁₉×#2297	1	1	yes	characteristic
387	C₂	C₁₉×#2309	1	1	yes	characteristic
388	C₂	C₁₉×#2311	1	1	yes	characteristic
389	C₂	C₁₉×#2337	1	4	yes	—
390	C₂	C₁₉×#2631	1	2	yes	—
391	C₂	C₁₉×#2632	1	2	yes	—
392	C₂	C₁₉×#2662	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#383	C₂	semidirect
3. C₂×C₄×C₄⋊C₄×C₁₉	C₂	semidirect
4. C₁₉×#1446	C₂	semidirect
5. C₁₉×#1439	C₂	semidirect
7. C₁₉×#1437	C₂	semidirect
12. C₂×C₁₉×#124	C₄	semidirect
111. C₄²×C₁₉	C₂²⋊C₄	semidirect
112. #14288	C₁₉	direct (N × H)
164. C₂×#383	C₂×C₁₉	semidirect
165. C₂×C₄×C₄⋊C₄	C₂×C₁₉	semidirect
166. #1446	C₂×C₁₉	semidirect
167. #1439	C₂×C₁₉	semidirect
169. #1437	C₂×C₁₉	semidirect
200. C₂×#124	C₄×C₁₉	semidirect
259. C₁₉	#14288	direct (N × H)
308. C₄²	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#124	2
C₂×C₁₉×#383	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1446	2
C₁₉×#1439	2
C₁₉×#1438	2
C₁₉×#1437	2
#14288	19

Subgroups — C19×#14288 #18020247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14288 #18020247