Subgroups — C₁₉×#13219 #18019178

Order 4864.

624 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	C₁₉×#2534	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#352	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×AΣL(1,𝔽₁₆)	C₂	1	2	yes	maximal
4	C₁₉×#1799	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#120	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
10	C₂×C₁₉×#100	C₂²	1	2	yes	—
11	C₂×C₁₉×#99	C₂²	1	2	yes	—
12	C₄×M₁₆×C₁₉	—	2	1	no	—
13	C₁₉×#396	—	2	1	no	—
14	C₁₉×#394	—	2	1	no	—
15	C₁₉×#388	—	2	1	no	—
16	C₁₉×#386	—	2	1	no	—
17	C₁₉×#381	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#380	—	2	1	no	—
19	C₁₉×#380	C₄	1	1	yes	characteristic, complemented
20	C₁₉×#379	C₄	1	1	yes	characteristic, complemented
21	C₁₉×#352	—	2	4	no	—
22	C₁₉×AΣL(1,𝔽₁₆)	—	2	4	no	—
23	C₁₉×#343	—	2	1	no	—
24	C₁₉×#342	—	2	1	no	—
25	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	—	2	1	no	—
27	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂×M₁₆×C₁₉	—	2	2	no	—
32	C₁₉×#123	—	2	2	no	—
33	C₁₉×#123	—	2	2	no	—
34	C₁₉×#120	—	2	2	no	—
35	C₁₉×#120	—	2	2	no	—
36	C₄×D₄×C₁₉	—	4	1	no	—
37	C₄×D₄×C₁₉	—	4	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
41	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
51	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
56	C₁₉×#100	—	2	2	no	—
57	C₁₉×#100	D₄	1	4	yes	—
58	C₁₉×#99	—	2	2	no	—
59	C₁₉×#99	—	2	2	no	—
60	C₁₉×#97	—	4	1	no	—
61	C₄×C₈×C₁₉	—	4	1	no	—
62	C₁₉×#95	—	2	1	no	—
63	C₁₉×#95	—	2	1	no	—
64	C₁₉×#95	—	2	1	no	—
65	C₁₉×#95	—	4	1	no	—
66	C₂⁴×C₁₉	—	2	1	no	—
67	C₂⁴×C₁₉	—	2	2	no	—
68	C₂⁴×C₁₉	—	4	1	no	—
69	C₂⁴×C₁₉	—	4	2	no	—
70	C₂⁴×C₁₉	—	4	1	no	—
71	C₂⁴×C₁₉	—	8	1	no	—
72	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂×D₄×C₁₉	—	4	1	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	2	no	—
77	C₂×D₄×C₁₉	—	4	1	no	—
78	C₂×D₄×C₁₉	—	4	1	no	—
79	C₂×D₄×C₁₉	—	8	1	no	—
80	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
81	C₂×D₄×C₁₉	#41	1	2	yes	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	8	1	no	—
94	C₂²×C₄×C₁₉	—	8	1	no	—
95	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	M₁₆×C₁₉	—	2	4	no	—
101	M₁₆×C₁₉	—	4	2	no	—
102	C₂×C₈×C₁₉	—	4	2	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	—	4	2	no	—
105	C₄⋊C₄×C₁₉	—	8	1	no	—
106	C₄⋊C₄×C₁₉	—	8	2	no	—
107	C₂²⋊C₄×C₁₉	—	2	2	no	—
108	C₂²⋊C₄×C₁₉	—	2	2	no	—
109	C₂²⋊C₄×C₁₉	—	4	1	no	—
110	C₂²⋊C₄×C₁₉	—	4	1	no	—
111	C₂²⋊C₄×C₁₉	—	4	2	no	—
112	C₂²⋊C₄×C₁₉	—	4	2	no	—
113	C₂²⋊C₄×C₁₉	—	4	1	no	—
114	C₂²⋊C₄×C₁₉	—	4	1	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₂²⋊C₄×C₁₉	—	4	1	no	—
117	C₂²⋊C₄×C₁₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₉	—	4	2	no	—
119	C₂²⋊C₄×C₁₉	—	4	2	no	—
120	C₂²⋊C₄×C₁₉	—	8	1	no	—
121	C₄²×C₁₉	—	2	1	no	—
122	C₄²×C₁₉	—	2	1	no	—
123	#13219	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	—	2	1	no	—
128	C₂³×C₁₉	—	2	2	no	—
129	C₂³×C₁₉	—	4	1	no	—
130	C₂³×C₁₉	—	4	1	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	8	2	no	—
142	C₂³×C₁₉	—	8	4	no	—
143	C₂³×C₁₉	—	8	4	no	—
144	C₂³×C₁₉	—	8	2	no	—
145	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₁₉	C₄×D₄	1	2	yes	—
147	C₂³×C₁₉	#124	1	1	yes	characteristic
148	C₂³×C₁₉	#127	1	1	yes	characteristic
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	8	2	no	—
152	D₄×C₁₉	—	8	2	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	2	no	—
176	C₂×C₄×C₁₉	—	8	2	no	—
177	C₂×C₄×C₁₉	—	8	2	no	—
178	C₂×C₄×C₁₉	—	8	2	no	—
179	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	2	yes	—
182	C₈×C₁₉	—	4	4	no	—
183	#2534	C₂×C₁₉	1	1	yes	characteristic
184	C₂×#352	C₂×C₁₉	1	2	yes	complemented
185	C₂×AΣL(1,𝔽₁₆)	C₂×C₁₉	1	2	yes	—
186	#1799	C₂×C₁₉	1	1	yes	characteristic, complemented
187	C₄×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	2	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	4	1	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	4	1	no	—
201	C₂²×C₁₉	—	4	1	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	4	2	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	4	no	—
208	C₂²×C₁₉	—	8	4	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	#390	1	1	yes	characteristic
212	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
213	C₂²×C₁₉	#410	1	1	yes	characteristic
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	4	1	no	—
218	C₄×C₁₉	—	4	1	no	—
219	C₄×C₁₉	—	4	1	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	—	8	1	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	—	16	2	no	—
224	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#120	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
227	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
228	C₂×#100	C₂²×C₁₉	1	2	yes	—
229	C₂×#99	C₂²×C₁₉	1	2	yes	—
230	C₄×M₁₆	—	2	1	no	—
231	#396	—	2	1	no	—
232	#394	—	2	1	no	—
233	#388	—	2	1	no	—
234	#386	—	2	1	no	—
235	#381	C₄×C₁₉	1	1	yes	characteristic, complemented
236	#380	—	2	1	no	—
237	#380	C₄×C₁₉	1	1	yes	characteristic, complemented
238	#379	C₄×C₁₉	1	1	yes	characteristic, complemented
239	#352	—	2	4	no	—
240	AΣL(1,𝔽₁₆)	—	2	4	no	—
241	#343	—	2	1	no	—
242	#342	—	2	1	no	—
243	C₂×C₁₉	—	2	1	no	—
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	4	1	no	—
246	C₂×C₁₉	—	4	2	no	—
247	C₂×C₁₉	—	4	1	no	—
248	C₂×C₁₉	—	8	2	no	—
249	C₂×C₁₉	#1964	1	1	yes	characteristic
250	C₂×C₁₉	#2120	1	1	yes	characteristic
251	C₂×C₁₉	#2121	1	1	yes	characteristic
252	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
255	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
256	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
257	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
258	C₂×M₁₆	—	2	2	no	—
259	#123	—	2	2	no	—
260	#123	—	2	2	no	—
261	#120	—	2	2	no	—
262	#120	—	2	2	no	—
263	C₄×D₄	—	4	1	no	—
264	C₄×D₄	—	4	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	4	1	no	—
268	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	4	1	no	—
277	C₂×C₂²⋊C₄	—	4	1	no	—
278	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
283	#100	—	2	2	no	—
284	#100	D₄×C₁₉	1	4	yes	—
285	#99	—	2	2	no	—
286	#99	—	2	2	no	—
287	#97	—	4	1	no	—
288	C₄×C₈	—	4	1	no	—
289	#95	—	2	1	no	—
290	#95	—	2	1	no	—
291	#95	—	2	1	no	—
292	#95	—	4	1	no	—
293	C₁₉	#13219	1	1	yes	characteristic, direct product factor, Sylow
294	C₂⁴	—	2	1	no	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	4	1	no	—
297	C₂⁴	—	4	2	no	—
298	C₂⁴	—	4	1	no	—
299	C₂⁴	—	8	1	no	—
300	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
301	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	8	1	no	—
308	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂×D₄	#41×C₁₉	1	2	yes	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	8	1	no	—
322	C₂²×C₄	—	8	1	no	—
323	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
328	M₁₆	—	2	4	no	—
329	M₁₆	—	4	2	no	—
330	C₂×C₈	—	4	2	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	8	1	no	—
334	C₄⋊C₄	—	8	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	8	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	8	2	no	—
369	C₂³	—	8	4	no	—
370	C₂³	—	8	4	no	—
371	C₂³	—	8	2	no	—
372	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
373	C₂³	C₄×D₄×C₁₉	1	2	yes	—
374	C₂³	C₁₉×#124	1	1	yes	characteristic
375	C₂³	C₁₉×#127	1	1	yes	characteristic
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	2	no	—
379	D₄	—	8	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	8	1	no	—
400	C₂×C₄	—	8	1	no	—
401	C₂×C₄	—	8	1	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
407	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
408	C₂×C₄	C₁₉×#121	1	2	yes	—
409	C₈	—	4	4	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	8	4	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	C₁₉×#390	1	1	yes	characteristic
434	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
435	C₂²	C₁₉×#410	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	1	no	—
445	C₄	—	16	2	no	—
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	4	1	no	—
449	C₂	—	4	2	no	—
450	C₂	—	4	1	no	—
451	C₂	—	8	2	no	—
452	C₂	C₁₉×#1964	1	1	yes	characteristic
453	C₂	C₁₉×#2120	1	1	yes	characteristic
454	C₂	C₁₉×#2121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#120	C₂²
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#352	C₂	semidirect
4. C₁₉×#1799	C₂	semidirect
5. C₄×C₁₉×#100	C₂	semidirect
9. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
17. C₁₉×#381	C₄	semidirect
19. C₁₉×#380	C₄	semidirect
20. C₁₉×#379	C₄	semidirect
123. #13219	C₁₉	direct (N × H)
184. C₂×#352	C₂×C₁₉	semidirect
186. #1799	C₂×C₁₉	semidirect
187. C₄×#100	C₂×C₁₉	semidirect
227. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
235. #381	C₄×C₁₉	semidirect
237. #380	C₄×C₁₉	semidirect
238. #379	C₄×C₁₉	semidirect
293. C₁₉	#13219	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2534	2
C₂×C₁₉×#352	2
C₂×C₁₉×AΣL(1,𝔽₁₆)	2
C₁₉×#1799	2
C₄×C₁₉×#100	2
#13219	19

Subgroups — C19×#13219 #18019178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13219 #18019178