Subgroups — C₁₉×#21944 #18027903

Order 4864.

1162 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#407	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1854	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1853	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1852	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1809	C₂	1	4	yes	maximal, complemented
8	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₂×C₁₉×#117	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
13	C₂×C₁₉×#107	C₂²	1	4	yes	complemented
14	C₂×C₁₉×#106	C₂²	1	4	yes	complemented
15	C₁₉×#407	C₄	1	8	yes	complemented
16	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₁₉×#381	—	2	1	no	—
19	C₁₉×#380	—	2	1	no	—
20	C₁₉×#380	—	2	1	no	—
21	C₁₉×#380	C₂²	1	2	yes	—
22	C₁₉×#380	C₂²	1	2	yes	—
23	C₁₉×#380	C₂²	1	2	yes	—
24	C₁₉×#380	C₂²	1	1	yes	characteristic
25	C₁₉×#380	C₂²	1	1	yes	characteristic
26	C₁₉×#379	—	2	1	no	—
27	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
28	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₁₉×#95	—	2	1	no	—
30	C₁₉×#340	C₂²	1	4	yes	complemented
31	C₁₉×#340	C₂²	1	4	yes	complemented
32	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	—	2	2	no	—
34	C₂³×C₄×C₁₉	—	4	4	no	—
35	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₁₉	—	4	4	no	—
44	C₂×M₁₆×C₁₉	C₂×C₄	1	8	yes	complemented
45	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
46	C₁₉×#117	—	4	4	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
49	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
59	C₂×C₄²×C₁₉	—	2	2	no	—
60	C₁₉×#107	—	4	4	no	—
61	C₁₉×#106	—	4	4	no	—
62	C₁₉×C₂²⋊C₈	C₂×C₄	1	8	yes	—
63	C₁₉×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
64	C₁₉×#95	—	2	2	no	—
65	C₁₉×#95	—	2	2	no	—
66	C₁₉×#95	—	2	1	no	—
67	C₁₉×#95	—	2	1	no	—
68	C₁₉×#95	—	2	2	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	—	4	2	no	—
72	C₂⁴×C₁₉	—	4	2	no	—
73	C₂⁴×C₁₉	C₄⋊C₄	1	4	yes	—
74	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	4	no	—
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	4	no	—
83	C₂²×C₄×C₁₉	—	4	8	no	—
84	C₂²×C₄×C₁₉	—	4	8	no	—
85	C₂²×C₄×C₁₉	—	4	2	no	—
86	C₂²×C₄×C₁₉	—	4	2	no	—
87	C₂²×C₄×C₁₉	—	4	2	no	—
88	C₂²×C₄×C₁₉	—	4	4	no	—
89	C₂²×C₄×C₁₉	—	4	4	no	—
90	C₂²×C₄×C₁₉	—	4	4	no	—
91	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
92	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
93	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
104	M₁₆×C₁₉	—	4	8	no	—
105	C₂×C₈×C₁₉	—	2	4	no	—
106	C₂×C₈×C₁₉	—	2	4	no	—
107	C₂×C₈×C₁₉	C₂²×C₄	1	8	yes	—
108	C₄⋊C₄×C₁₉	—	2	4	no	—
109	C₄⋊C₄×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	4	4	no	—
113	C₂²⋊C₄×C₁₉	—	4	4	no	—
114	C₂²⋊C₄×C₁₉	—	4	4	no	—
115	C₂²⋊C₄×C₁₉	—	4	4	no	—
116	C₂²⋊C₄×C₁₉	—	4	4	no	—
117	C₂²⋊C₄×C₁₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₉	—	4	2	no	—
119	C₄²×C₁₉	—	4	4	no	—
120	#21944	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	—	2	1	no	—
128	C₂³×C₁₉	—	2	1	no	—
129	C₂³×C₁₉	—	2	2	no	—
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	8	no	—
132	C₂³×C₁₉	—	4	4	no	—
133	C₂³×C₁₉	—	4	4	no	—
134	C₂³×C₁₉	—	4	8	no	—
135	C₂³×C₁₉	—	4	8	no	—
136	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
137	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
138	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
139	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
140	C₂³×C₁₉	#137	1	2	yes	—
141	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	2	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	4	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	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	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	4	no	—
157	C₂×C₄×C₁₉	—	4	4	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	8	8	no	—
164	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
170	C₈×C₁₉	—	2	8	no	—
171	C₂×#407	C₂×C₁₉	1	1	yes	characteristic
172	#2280	C₂×C₁₉	1	1	yes	characteristic
173	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
174	#1854	C₂×C₁₉	1	4	yes	complemented
175	#1853	C₂×C₁₉	1	2	yes	complemented
176	#1852	C₂×C₁₉	1	2	yes	complemented
177	#1809	C₂×C₁₉	1	4	yes	complemented
178	C₂²×C₁₉	—	2	2	no	—
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	2	4	no	—
181	C₂²×C₁₉	—	2	4	no	—
182	C₂²×C₁₉	—	2	2	no	—
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	—	2	2	no	—
188	C₂²×C₁₉	—	4	16	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	—	4	2	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	#428	1	4	yes	—
194	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
195	C₂²×C₁₉	#534	1	2	yes	—
196	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
198	C₂²×C₁₉	#575	1	2	yes	—
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	2	2	no	—
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	—	8	4	no	—
204	C₄×C₁₉	—	8	2	no	—
205	C₄×C₁₉	#518	1	2	yes	—
206	C₄×C₁₉	#543	1	2	yes	—
207	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
209	C₂×#117	C₂²×C₁₉	1	2	yes	—
210	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
211	C₂²×C₂²⋊C₄	—	2	1	no	—
212	C₂×#107	C₂²×C₁₉	1	4	yes	complemented
213	C₂×#106	C₂²×C₁₉	1	4	yes	complemented
214	#407	C₄×C₁₉	1	8	yes	complemented
215	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
216	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
217	#381	—	2	1	no	—
218	#380	—	2	1	no	—
219	#380	—	2	1	no	—
220	#380	C₂²×C₁₉	1	2	yes	—
221	#380	C₂²×C₁₉	1	2	yes	—
222	#380	C₂²×C₁₉	1	1	yes	characteristic
223	#380	C₂²×C₁₉	1	1	yes	characteristic
224	#380	C₂²×C₁₉	1	2	yes	—
225	#379	—	2	1	no	—
226	C₄×C₂²⋊C₄	—	2	1	no	—
227	C₄×C₂²⋊C₄	—	2	1	no	—
228	C₂×#95	—	2	1	no	—
229	#340	C₂²×C₁₉	1	4	yes	complemented
230	#340	C₂²×C₁₉	1	4	yes	complemented
231	C₂×C₁₉	—	2	4	no	—
232	C₂×C₁₉	—	4	2	no	—
233	C₂×C₁₉	—	4	2	no	—
234	C₂×C₁₉	#2315	1	1	yes	characteristic
235	C₂×C₁₉	C₂×#428	1	1	yes	characteristic
236	C₂×C₁₉	#2911	1	1	yes	characteristic
237	C₂×C₁₉	#3194	1	2	yes	—
238	C₂×C₁₉	#3196	1	2	yes	—
239	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
240	C₂³×C₄	—	2	2	no	—
241	C₂³×C₄	—	4	4	no	—
242	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
243	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
244	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
246	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
247	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₂×M₁₆	—	4	4	no	—
251	C₂×M₁₆	C₂×C₄×C₁₉	1	8	yes	complemented
252	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
253	#117	—	4	4	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	4	4	no	—
256	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	4	4	no	—
266	C₂×C₄²	—	2	2	no	—
267	#107	—	4	4	no	—
268	#106	—	4	4	no	—
269	C₂²⋊C₈	C₂×C₄×C₁₉	1	8	yes	—
270	C₂²⋊C₈	C₂×C₄×C₁₉	1	8	yes	complemented
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	1	no	—
275	#95	—	2	1	no	—
276	C₁₉	#21944	1	1	yes	characteristic, direct product factor, Sylow
277	C₂⁴	—	2	2	no	—
278	C₂⁴	—	2	2	no	—
279	C₂⁴	—	4	2	no	—
280	C₂⁴	—	4	2	no	—
281	C₂⁴	C₄⋊C₄×C₁₉	1	4	yes	—
282	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
283	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
284	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
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	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	8	no	—
292	C₂²×C₄	—	4	8	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
300	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
301	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	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	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
310	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
312	M₁₆	—	4	8	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	C₂²×C₄×C₁₉	1	8	yes	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	4	4	no	—
323	C₂²⋊C₄	—	4	4	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₄²	—	4	4	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	8	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	8	no	—
342	C₂³	—	4	8	no	—
343	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
344	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
345	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
346	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
347	C₂³	C₁₉×#137	1	2	yes	—
348	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	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	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	8	8	no	—
371	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
372	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
373	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
374	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
376	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
377	C₈	—	2	8	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	16	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	C₁₉×#428	1	4	yes	—
394	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
395	C₂²	C₁₉×#534	1	2	yes	—
396	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
398	C₂²	C₁₉×#575	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	8	4	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	C₁₉×#518	1	2	yes	—
406	C₄	C₁₉×#543	1	2	yes	—
407	C₂	—	2	4	no	—
408	C₂	—	4	2	no	—
409	C₂	—	4	2	no	—
410	C₂	C₁₉×#2315	1	1	yes	characteristic
411	C₂	C₂×C₁₉×#428	1	1	yes	characteristic
412	C₂	C₁₉×#2911	1	1	yes	characteristic
413	C₂	C₁₉×#3194	1	2	yes	—
414	C₂	C₁₉×#3196	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	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1854	C₂	semidirect
5. C₁₉×#1853	C₂	semidirect
6. C₁₉×#1852	C₂	semidirect
7. C₁₉×#1809	C₂	semidirect
13. C₂×C₁₉×#107	C₂²	semidirect
14. C₂×C₁₉×#106	C₂²	semidirect
15. C₁₉×#407	C₄	semidirect
30. C₁₉×#340	C₂²	semidirect
31. C₁₉×#340	C₂²	semidirect
44. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
63. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
120. #21944	C₁₉	direct (N × H)
174. #1854	C₂×C₁₉	semidirect
175. #1853	C₂×C₁₉	semidirect
176. #1852	C₂×C₁₉	semidirect
177. #1809	C₂×C₁₉	semidirect
212. C₂×#107	C₂²×C₁₉	semidirect
213. C₂×#106	C₂²×C₁₉	semidirect
214. #407	C₄×C₁₉	semidirect
229. #340	C₂²×C₁₉	semidirect
230. #340	C₂²×C₁₉	semidirect
251. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
270. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
276. C₁₉	#21944	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×#407	2
C₁₉×#2280	2
C₂×C₁₉×#380	2
C₁₉×#1854	2
C₁₉×#1853	2
C₁₉×#1852	2
C₁₉×#1809	2
#21944	19

Subgroups — C19×#21944 #18027903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21944 #18027903