Subgroups — C₁₉×#14150 #18020109

Order 4864.

1486 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#389	C₂	1	2	yes	maximal
2	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1444	C₂	1	2	yes	maximal
6	C₁₉×#1442	C₂	1	2	yes	maximal
7	C₁₉×#1436	C₂	1	4	yes	maximal
8	C₁₉×C₄⋊#95	C₂	1	2	yes	maximal
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#389	—	2	8	no	—
19	C₁₉×#382	C₄	1	8	yes	complemented
20	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
21	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
22	C₂×C₁₉×#95	C₂²	1	4	yes	—
23	C₂×C₁₉×#95	C₂²	1	2	yes	—
24	C₂×C₁₉×#95	C₂²	1	4	yes	—
25	C₂×C₁₉×#95	C₂²	1	2	yes	—
26	C₂×C₁₉×#95	C₂²	1	4	yes	—
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
30	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
49	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
51	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	—
53	C₂×C₄²×C₁₉	—	2	4	no	—
54	C₂×C₄²×C₁₉	—	2	4	no	—
55	C₂×C₄²×C₁₉	—	2	4	no	—
56	C₂×C₄²×C₁₉	—	2	4	no	—
57	C₂×C₄²×C₁₉	—	4	4	no	—
58	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
59	C₂×C₄²×C₁₉	D₄	1	4	yes	—
60	C₂×C₄²×C₁₉	Q₈	1	4	yes	—
61	C₁₉×#95	—	2	4	no	—
62	C₁₉×#95	—	2	4	no	—
63	C₁₉×#95	—	2	8	no	—
64	C₁₉×#95	—	2	8	no	—
65	C₁₉×#95	—	4	4	no	—
66	C₁₉×#95	C₂×C₄	1	8	yes	—
67	C₁₉×#95	C₂×C₄	1	8	yes	—
68	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	2	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	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
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	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₁₉	#41	1	4	yes	—
114	C₂²×C₄×C₁₉	#41	1	4	yes	—
115	C₂²×C₄×C₁₉	#41	1	2	yes	—
116	C₂²×C₄×C₁₉	#41	1	2	yes	—
117	C₄⋊C₄×C₁₉	—	2	8	no	—
118	C₄⋊C₄×C₁₉	—	2	8	no	—
119	C₄⋊C₄×C₁₉	—	2	16	no	—
120	C₄⋊C₄×C₁₉	—	2	8	no	—
121	C₄⋊C₄×C₁₉	—	2	8	no	—
122	C₄⋊C₄×C₁₉	—	4	16	no	—
123	C₄²×C₁₉	—	4	8	no	—
124	C₄²×C₁₉	—	4	8	no	—
125	C₄²×C₁₉	C₄⋊C₄	1	16	yes	complemented
126	#14150	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	C₂²×Q₈	1	1	yes	characteristic
131	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
132	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
133	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
134	C₂³×C₁₉	C₂×#41	1	2	yes	—
135	C₂³×C₁₉	C₂×#41	1	2	yes	—
136	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
137	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	4	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	8	no	—
147	C₂×C₄×C₁₉	—	2	8	no	—
148	C₂×C₄×C₁₉	—	2	8	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	8	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	8	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	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	4	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
178	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
179	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
180	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
181	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
182	C₂×C₄×C₁₉	#121	1	4	yes	—
183	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
184	C₂×C₄×C₁₉	#125	1	4	yes	—
185	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
186	C₂×#389	C₂×C₁₉	1	2	yes	—
187	C₂×#382	C₂×C₁₉	1	1	yes	characteristic
188	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
189	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
190	#1444	C₂×C₁₉	1	2	yes	—
191	#1442	C₂×C₁₉	1	2	yes	—
192	#1436	C₂×C₁₉	1	4	yes	—
193	C₄⋊#95	C₂×C₁₉	1	2	yes	—
194	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
195	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
197	C₂²×C₁₉	C₄×#41	1	2	yes	—
198	C₂²×C₁₉	#520	1	2	yes	—
199	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
200	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
201	C₂²×C₁₉	#525	1	1	yes	characteristic
202	C₂²×C₁₉	#525	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×#125	1	1	yes	characteristic
204	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
205	C₂²×C₁₉	#533	1	2	yes	—
206	C₂²×C₁₉	#535	1	1	yes	characteristic
207	C₂²×C₁₉	#536	1	1	yes	characteristic
208	C₂²×C₁₉	#544	1	2	yes	—
209	C₂²×C₁₉	#546	1	2	yes	—
210	C₂²×C₁₉	#548	1	2	yes	—
211	C₂²×C₁₉	#552	1	2	yes	—
212	C₂²×C₁₉	#553	1	2	yes	—
213	C₂²×C₁₉	#554	1	2	yes	—
214	C₂²×C₁₉	#556	1	2	yes	—
215	C₂²×C₁₉	#557	1	2	yes	—
216	C₂²×C₁₉	#559	1	2	yes	—
217	C₄×C₁₉	—	2	4	no	—
218	C₄×C₁₉	—	2	4	no	—
219	C₄×C₁₉	—	4	4	no	—
220	C₄×C₁₉	—	4	8	no	—
221	C₄×C₁₉	—	4	4	no	—
222	C₄×C₁₉	—	4	4	no	—
223	C₄×C₁₉	—	4	4	no	—
224	C₄×C₁₉	#389	1	8	yes	—
225	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
228	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
231	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
232	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
233	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
234	#389	—	2	8	no	—
235	#382	C₄×C₁₉	1	8	yes	complemented
236	C₄×C₄⋊C₄	—	2	4	no	—
237	C₄×C₄⋊C₄	—	2	4	no	—
238	C₂×#95	C₂²×C₁₉	1	4	yes	—
239	C₂×#95	C₂²×C₁₉	1	2	yes	—
240	C₂×#95	C₂²×C₁₉	1	4	yes	—
241	C₂×#95	C₂²×C₁₉	1	2	yes	—
242	C₂×#95	C₂²×C₁₉	1	4	yes	—
243	C₂×#95	C₂²×C₁₉	1	2	yes	—
244	C₂×#95	C₂²×C₁₉	1	2	yes	—
245	C₂×C₁₉	C₂×#389	1	1	yes	characteristic
246	C₂×C₁₉	#2296	1	1	yes	characteristic
247	C₂×C₁₉	#2317	1	1	yes	characteristic
248	C₂×C₁₉	#2367	1	2	yes	—
249	C₂×C₁₉	#2370	1	2	yes	—
250	C₂×C₁₉	#2535	1	1	yes	characteristic
251	C₂×C₁₉	#2536	1	1	yes	characteristic
252	C₂×C₁₉	#2550	1	2	yes	—
253	C₂×C₁₉	#2570	1	2	yes	—
254	C₂×C₁₉	#2580	1	1	yes	characteristic
255	C₂×C₁₉	#2581	1	1	yes	characteristic
256	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
257	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
258	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
259	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
260	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
261	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	4	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	8	no	—
275	C₂×C₄⋊C₄	—	2	8	no	—
276	C₂×C₄⋊C₄	—	4	4	no	—
277	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
278	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
279	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	—
280	C₂×C₄²	—	2	4	no	—
281	C₂×C₄²	—	2	4	no	—
282	C₂×C₄²	—	2	4	no	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	—	4	4	no	—
285	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
286	C₂×C₄²	D₄×C₁₉	1	4	yes	—
287	C₂×C₄²	Q₈×C₁₉	1	4	yes	—
288	#95	—	2	4	no	—
289	#95	—	2	4	no	—
290	#95	—	2	8	no	—
291	#95	—	2	8	no	—
292	#95	—	4	4	no	—
293	#95	C₂×C₄×C₁₉	1	8	yes	—
294	#95	C₂×C₄×C₁₉	1	8	yes	—
295	C₁₉	#14150	1	1	yes	characteristic, direct product factor, Sylow
296	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
328	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
329	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
336	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
337	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
338	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
339	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
340	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
341	C₂²×C₄	#41×C₁₉	1	4	yes	—
342	C₂²×C₄	#41×C₁₉	1	4	yes	—
343	C₂²×C₄	#41×C₁₉	1	2	yes	—
344	C₂²×C₄	#41×C₁₉	1	2	yes	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	16	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	4	16	no	—
351	C₄²	—	4	8	no	—
352	C₄²	—	4	8	no	—
353	C₄²	C₄⋊C₄×C₁₉	1	16	yes	complemented
354	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
355	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
356	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
357	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
358	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
359	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
360	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
361	C₂³	C₂×#41×C₁₉	1	2	yes	—
362	C₂³	C₂×#41×C₁₉	1	2	yes	—
363	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
364	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
405	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
406	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
407	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
408	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
409	C₂×C₄	C₁₉×#121	1	4	yes	—
410	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
411	C₂×C₄	C₁₉×#125	1	4	yes	—
412	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
413	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
414	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
415	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
416	C₂²	C₄×#41×C₁₉	1	2	yes	—
417	C₂²	C₁₉×#520	1	2	yes	—
418	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
419	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
420	C₂²	C₁₉×#525	1	1	yes	characteristic
421	C₂²	C₁₉×#525	1	1	yes	characteristic
422	C₂²	C₂×C₁₉×#125	1	1	yes	characteristic
423	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
424	C₂²	C₁₉×#533	1	2	yes	—
425	C₂²	C₁₉×#535	1	1	yes	characteristic
426	C₂²	C₁₉×#536	1	1	yes	characteristic
427	C₂²	C₁₉×#544	1	2	yes	—
428	C₂²	C₁₉×#546	1	2	yes	—
429	C₂²	C₁₉×#548	1	2	yes	—
430	C₂²	C₁₉×#552	1	2	yes	—
431	C₂²	C₁₉×#553	1	2	yes	—
432	C₂²	C₁₉×#554	1	2	yes	—
433	C₂²	C₁₉×#556	1	2	yes	—
434	C₂²	C₁₉×#557	1	2	yes	—
435	C₂²	C₁₉×#559	1	2	yes	—
436	C₄	—	2	4	no	—
437	C₄	—	2	4	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	4	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	8	no	—
443	C₄	C₁₉×#389	1	8	yes	—
444	C₂	C₂×C₁₉×#389	1	1	yes	characteristic
445	C₂	C₁₉×#2296	1	1	yes	characteristic
446	C₂	C₁₉×#2317	1	1	yes	characteristic
447	C₂	C₁₉×#2367	1	2	yes	—
448	C₂	C₁₉×#2370	1	2	yes	—
449	C₂	C₁₉×#2535	1	1	yes	characteristic
450	C₂	C₁₉×#2536	1	1	yes	characteristic
451	C₂	C₁₉×#2550	1	2	yes	—
452	C₂	C₁₉×#2570	1	2	yes	—
453	C₂	C₁₉×#2580	1	1	yes	characteristic
454	C₂	C₁₉×#2581	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
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
19. C₁₉×#382	C₄	semidirect
125. C₄²×C₁₉	C₄⋊C₄	semidirect
126. #14150	C₁₉	direct (N × H)
235. #382	C₄×C₁₉	semidirect
295. C₁₉	#14150	direct (N × H)
353. C₄²	C₄⋊C₄×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×#389	2
C₂×C₁₉×#382	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1444	2
C₁₉×#1442	2
C₁₉×#1436	2
C₁₉×C₄⋊#95	2
#14150	19

Subgroups — C19×#14150 #18020109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14150 #18020109