Subgroups — C₁₉×#21865 #18027824

Order 4864.

1394 conjugacy classes of subgroups.

The subgroup lattice has 410 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	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1993	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1961	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1874	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1804	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	C₂²×C₄⋊C₄×C₁₉	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	C₁₉×#382	—	2	1	no	—
26	C₁₉×#382	—	2	1	no	—
27	C₁₉×#382	C₂²	1	2	yes	—
28	C₁₉×#382	C₂²	1	2	yes	—
29	C₂×C₁₉×#95	—	2	1	no	—
30	C₂×C₁₉×#95	—	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	—	2	2	no	—
41	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
45	C₁₉×C₄⋊Q₈	—	2	2	no	—
46	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
47	C₁₉×#127	—	2	2	no	—
48	C₁₉×#127	C₂×C₄	1	4	yes	complemented
49	C₁₉×#124	—	2	8	no	—
50	C₁₉×#121	—	2	8	no	—
51	C₁₉×#121	—	2	4	no	—
52	C₁₉×#121	C₂×C₄	1	8	yes	—
53	C₄×D₄×C₁₉	—	2	8	no	—
54	C₄×D₄×C₁₉	—	2	4	no	—
55	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	complemented
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	D₄	1	4	yes	—
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×C₄⋊C₈	—	2	4	no	—
70	C₁₉×#102	—	4	8	no	—
71	C₁₉×C₂²⋊C₈	—	2	4	no	—
72	C₁₉×#97	—	2	4	no	—
73	C₁₉×#95	—	2	2	no	—
74	C₁₉×#95	—	2	2	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	4	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	4	4	no	—
89	C₂×D₄×C₁₉	—	4	4	no	—
90	C₂×D₄×C₁₉	—	4	8	no	—
91	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	8	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	8	no	—
100	C₂²×C₄×C₁₉	—	4	4	no	—
101	C₂²×C₄×C₁₉	—	4	4	no	—
102	C₂²×C₄×C₁₉	—	4	4	no	—
103	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₁₉	—	2	4	no	—
114	C₂×C₈×C₁₉	—	2	4	no	—
115	C₂×C₈×C₁₉	—	2	4	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	8	no	—
119	C₄⋊C₄×C₁₉	—	4	4	no	—
120	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₁₉	—	2	8	no	—
122	C₂²⋊C₄×C₁₉	—	2	8	no	—
123	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
124	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
125	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
126	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
127	C₄²×C₁₉	C₂×D₄	1	2	yes	—
128	C₄²×C₁₉	C₂×D₄	1	2	yes	—
129	#21865	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	1	no	—
131	C₂³×C₁₉	—	2	1	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	4	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	4	no	—
137	C₂³×C₁₉	—	4	4	no	—
138	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
140	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₉	—	4	8	no	—
142	D₄×C₁₉	—	2	8	no	—
143	D₄×C₁₉	—	4	8	no	—
144	D₄×C₁₉	—	4	8	no	—
145	D₄×C₁₉	—	4	16	no	—
146	D₄×C₁₉	—	4	4	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	8	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	—	4	4	no	—
158	C₂×C₄×C₁₉	—	4	16	no	—
159	C₂×C₄×C₁₉	—	4	4	no	—
160	C₂×C₄×C₁₉	—	4	4	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	8	8	no	—
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
172	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
173	C₈×C₁₉	—	4	4	no	—
174	C₂×#532	C₂×C₁₉	1	1	yes	characteristic
175	C₂×#432	C₂×C₁₉	1	1	yes	characteristic, complemented
176	C₂×#382	C₂×C₁₉	1	1	yes	characteristic, complemented
177	#1993	C₂×C₁₉	1	2	yes	complemented
178	#1961	C₂×C₁₉	1	2	yes	complemented
179	#1874	C₂×C₁₉	1	4	yes	complemented
180	#1804	C₂×C₁₉	1	4	yes	complemented
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	2	4	no	—
185	C₂²×C₁₉	—	4	4	no	—
186	C₂²×C₁₉	—	4	4	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	8	4	no	—
189	C₂²×C₁₉	—	8	4	no	—
190	C₂²×C₁₉	#418	1	4	yes	—
191	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₁₉	#535	1	1	yes	characteristic
193	C₂²×C₁₉	#536	1	1	yes	characteristic
194	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
195	C₂²×C₁₉	#575	1	2	yes	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	2	2	no	—
201	C₄×C₁₉	—	4	4	no	—
202	C₄×C₁₉	—	8	4	no	—
203	C₄×C₁₉	#520	1	2	yes	—
204	C₄×C₁₉	#537	1	2	yes	—
205	C₂²×#41	—	2	1	no	—
206	#532	—	2	4	no	—
207	#532	C₄×C₁₉	1	8	yes	complemented
208	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×#124	—	2	1	no	—
211	C₂×#121	—	2	1	no	—
212	C₂×#121	C₂²×C₁₉	1	2	yes	—
213	C₂×C₄×D₄	—	2	1	no	—
214	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
216	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
217	#432	—	2	4	no	—
218	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
219	C₂×#102	C₂²×C₁₉	1	8	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
221	C₂×#97	C₂²×C₁₉	1	2	yes	—
222	#382	—	2	1	no	—
223	#382	—	2	1	no	—
224	#382	C₂²×C₁₉	1	2	yes	—
225	#382	C₂²×C₁₉	1	2	yes	—
226	C₂×#95	—	2	1	no	—
227	C₂×#95	—	2	1	no	—
228	#340	C₂²×C₁₉	1	8	yes	—
229	C₂×C₁₉	—	2	4	no	—
230	C₂×C₁₉	—	8	4	no	—
231	C₂×C₁₉	#2311	1	1	yes	characteristic
232	C₂×C₁₉	C₂×#418	1	1	yes	characteristic
233	C₂×C₁₉	#2896	1	1	yes	characteristic
234	C₂×C₁₉	#3213	1	2	yes	—
235	C₂×C₁₉	#3234	1	2	yes	—
236	C₂×#41	—	2	8	no	—
237	C₂×#41	—	4	8	no	—
238	C₂²×Q₈	—	2	1	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
243	C₂³×C₄	—	2	2	no	—
244	C₂³×C₄	—	2	2	no	—
245	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
249	C₄⋊Q₈	—	2	2	no	—
250	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
251	#127	—	2	2	no	—
252	#127	C₂×C₄×C₁₉	1	4	yes	complemented
253	#124	—	2	8	no	—
254	#121	—	2	8	no	—
255	#121	—	2	4	no	—
256	#121	C₂×C₄×C₁₉	1	8	yes	—
257	C₄×D₄	—	2	8	no	—
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	complemented
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	4	4	no	—
263	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
268	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
269	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₁₉	1	4	yes	—
271	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
273	C₄⋊C₈	—	2	4	no	—
274	#102	—	4	8	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	#97	—	2	4	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	C₁₉	#21865	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁴	—	2	2	no	—
283	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
284	#41	—	4	32	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	8	no	—
296	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	8	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
309	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
329	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
330	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
331	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
332	C₄²	C₂×D₄×C₁₉	1	2	yes	—
333	C₄²	C₂×D₄×C₁₉	1	2	yes	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
343	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
344	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
345	Q₈	—	4	8	no	—
346	D₄	—	2	8	no	—
347	D₄	—	4	8	no	—
348	D₄	—	4	8	no	—
349	D₄	—	4	16	no	—
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	16	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	8	8	no	—
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	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
373	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
376	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
377	C₈	—	4	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	4	no	—
386	C₂²	—	8	4	no	—
387	C₂²	C₁₉×#418	1	4	yes	—
388	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
389	C₂²	C₁₉×#535	1	1	yes	characteristic
390	C₂²	C₁₉×#536	1	1	yes	characteristic
391	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
392	C₂²	C₁₉×#575	1	2	yes	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	4	no	—
400	C₄	C₁₉×#520	1	2	yes	—
401	C₄	C₁₉×#537	1	2	yes	—
402	C₂	—	2	4	no	—
403	C₂	—	8	4	no	—
404	C₂	C₁₉×#2311	1	1	yes	characteristic
405	C₂	C₂×C₁₉×#418	1	1	yes	characteristic
406	C₂	C₁₉×#2896	1	1	yes	characteristic
407	C₂	C₁₉×#3213	1	2	yes	—
408	C₂	C₁₉×#3234	1	2	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. C₂×C₁₉×#382	C₂	semidirect
4. C₁₉×#1993	C₂	semidirect
5. C₁₉×#1961	C₂	semidirect
6. C₁₉×#1874	C₂	semidirect
7. C₁₉×#1804	C₂	semidirect
10. C₁₉×#532	C₄	semidirect
46. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
48. C₁₉×#127	C₂×C₄	semidirect
55. C₄×D₄×C₁₉	C₂×C₄	semidirect
129. #21865	C₁₉	direct (N × H)
175. C₂×#432	C₂×C₁₉	semidirect
176. C₂×#382	C₂×C₁₉	semidirect
177. #1993	C₂×C₁₉	semidirect
178. #1961	C₂×C₁₉	semidirect
179. #1874	C₂×C₁₉	semidirect
180. #1804	C₂×C₁₉	semidirect
207. #532	C₄×C₁₉	semidirect
250. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
252. #127	C₂×C₄×C₁₉	semidirect
259. C₄×D₄	C₂×C₄×C₁₉	semidirect
281. C₁₉	#21865	direct (N × H)

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
C₂×C₁₉×#382	2
C₁₉×#1993	2
C₁₉×#1961	2
C₁₉×#1874	2
C₁₉×#1804	2
#21865	19

Subgroups — C19×#21865 #18027824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21865 #18027824