Subgroups — C₁₉×#9712 #18015671

Order 4864.

856 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#327	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#127	C₄	1	1	yes	characteristic, complemented
6	C₂×C₁₉×#121	—	2	1	no	—
7	C₂×C₁₉×#121	—	2	1	no	—
8	C₂×C₁₉×#121	C₂²	1	2	yes	—
9	C₂²×C₄²×C₁₉	—	2	1	no	—
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₁₉×#390	—	2	1	no	—
14	C₁₉×#390	—	2	1	no	—
15	C₁₉×#390	C₄	1	2	yes	complemented
16	C₁₉×#384	C₄	1	1	yes	characteristic, complemented
17	C₂×C₁₉×#95	—	2	1	no	—
18	C₂×C₁₉×#95	C₂²	1	2	yes	—
19	C₁₉×#336	—	2	1	no	—
20	C₁₉×#327	—	2	8	no	—
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×D₄×C₁₉	—	2	1	no	—
23	C₂²×D₄×C₁₉	—	2	1	no	—
24	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₉	—	2	2	no	—
26	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	—	2	2	no	—
30	C₁₉×#127	—	4	2	no	—
31	C₁₉×#121	—	2	4	no	—
32	C₁₉×#121	—	2	4	no	—
33	C₁₉×#121	—	4	4	no	—
34	C₁₉×#121	—	4	2	no	—
35	C₁₉×#121	—	4	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄²×C₁₉	—	2	4	no	—
43	C₂×C₄²×C₁₉	—	4	2	no	—
44	C₂×C₄²×C₁₉	—	4	2	no	—
45	C₂×C₄²×C₁₉	—	4	2	no	—
46	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₁₉×C₄⋊C₈	—	4	2	no	—
51	C₁₉×C₂²⋊C₈	—	2	4	no	—
52	C₁₉×#95	—	2	4	no	—
53	C₁₉×#95	—	2	2	no	—
54	C₁₉×#95	D₄	1	4	yes	complemented
55	C₂⁴×C₁₉	—	2	2	no	—
56	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×D₄×C₁₉	—	2	4	no	—
58	C₂×D₄×C₁₉	—	4	2	no	—
59	C₂×D₄×C₁₉	—	4	2	no	—
60	C₂×D₄×C₁₉	—	4	2	no	—
61	C₂×D₄×C₁₉	—	4	2	no	—
62	C₂×D₄×C₁₉	—	4	4	no	—
63	C₂×D₄×C₁₉	—	4	2	no	—
64	C₂×D₄×C₁₉	—	4	2	no	—
65	C₂×D₄×C₁₉	—	4	4	no	—
66	C₂×D₄×C₁₉	—	4	2	no	—
67	C₂×D₄×C₁₉	—	4	2	no	—
68	C₂×D₄×C₁₉	—	4	2	no	—
69	C₂×D₄×C₁₉	—	4	2	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	4	no	—
73	C₂²×C₄×C₁₉	—	2	4	no	—
74	C₂²×C₄×C₁₉	—	2	4	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	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	2	no	—
82	C₂²×C₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	—	4	2	no	—
84	C₂²×C₄×C₁₉	—	4	2	no	—
85	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	D₈	1	2	yes	—
90	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₉	#41	1	2	yes	—
95	C₂×C₈×C₁₉	—	4	2	no	—
96	C₂×C₈×C₁₉	—	4	2	no	—
97	C₂×C₈×C₁₉	—	4	2	no	—
98	C₄⋊C₄×C₁₉	—	2	4	no	—
99	C₄⋊C₄×C₁₉	—	4	2	no	—
100	C₄⋊C₄×C₁₉	—	4	2	no	—
101	C₂²⋊C₄×C₁₉	—	4	4	no	—
102	C₂²⋊C₄×C₁₉	—	4	4	no	—
103	C₂²⋊C₄×C₁₉	—	4	2	no	—
104	C₂²⋊C₄×C₁₉	—	4	2	no	—
105	C₄²×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	—	2	2	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	—	4	1	no	—
109	C₄²×C₁₉	—	4	8	no	—
110	#9712	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	—	2	1	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	4	2	no	—
116	C₂³×C₁₉	—	4	2	no	—
117	C₂³×C₁₉	—	4	2	no	—
118	C₂³×C₁₉	—	4	2	no	—
119	C₂³×C₁₉	—	4	2	no	—
120	C₂³×C₁₉	—	4	2	no	—
121	C₂³×C₁₉	—	4	2	no	—
122	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂³×C₁₉	#121	1	2	yes	—
124	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
125	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
126	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
127	D₄×C₁₉	—	8	4	no	—
128	D₄×C₁₉	—	8	4	no	—
129	D₄×C₁₉	—	8	4	no	—
130	D₄×C₁₉	—	8	4	no	—
131	D₄×C₁₉	—	8	4	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	4	no	—
141	C₂×C₄×C₁₉	—	2	4	no	—
142	C₂×C₄×C₁₉	—	2	8	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	—	4	4	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	4	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	#99	1	2	yes	—
159	C₂×C₄×C₁₉	#102	1	2	yes	—
160	C₂×C₄×C₁₉	#102	1	2	yes	—
161	C₂×C₄×C₁₉	#104	1	2	yes	—
162	C₂×C₄×C₁₉	#104	1	2	yes	—
163	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
166	C₈×C₁₉	—	8	2	no	—
167	#2856	C₂×C₁₉	1	1	yes	characteristic
168	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
169	C₂×#327	C₂×C₁₉	1	4	yes	complemented
170	C₄×#95	C₂×C₁₉	1	1	yes	characteristic, complemented
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	2	no	—
179	C₂²×C₁₉	—	8	2	no	—
180	C₂²×C₁₉	—	8	2	no	—
181	C₂²×C₁₉	—	8	2	no	—
182	C₂²×C₁₉	—	8	2	no	—
183	C₂²×C₁₉	—	8	2	no	—
184	C₂²×C₁₉	—	8	2	no	—
185	C₂²×C₁₉	—	8	2	no	—
186	C₂²×C₁₉	#390	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
188	C₂²×C₁₉	#410	1	1	yes	characteristic
189	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
190	C₂²×C₁₉	#418	1	1	yes	characteristic
191	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
193	C₂²×C₁₉	#459	1	2	yes	—
194	C₂²×C₁₉	#460	1	2	yes	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	4	8	no	—
201	C₄×C₁₉	—	4	1	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	#327	1	4	yes	complemented
204	C₂×#127	C₄×C₁₉	1	1	yes	characteristic, complemented
205	C₂×#121	—	2	1	no	—
206	C₂×#121	—	2	1	no	—
207	C₂×#121	C₂²×C₁₉	1	2	yes	—
208	C₂²×C₄²	—	2	1	no	—
209	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×C₄⋊C₈	—	2	1	no	—
211	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
212	#390	—	2	1	no	—
213	#390	—	2	1	no	—
214	#390	C₄×C₁₉	1	2	yes	complemented
215	#384	C₄×C₁₉	1	1	yes	characteristic, complemented
216	C₂×#95	—	2	1	no	—
217	C₂×#95	C₂²×C₁₉	1	2	yes	—
218	#336	—	2	1	no	—
219	#327	—	2	8	no	—
220	C₂×C₁₉	—	2	2	no	—
221	C₂×C₁₉	—	2	2	no	—
222	C₂×C₁₉	—	16	2	no	—
223	C₂×C₁₉	C₂×#327	1	1	yes	characteristic
224	C₂×C₁₉	#1502	1	1	yes	characteristic
225	C₂×C₁₉	#1505	1	1	yes	characteristic
226	C₂×C₁₉	#1507	1	1	yes	characteristic
227	C₂×C₁₉	#1962	1	1	yes	characteristic
228	C₂×C₁₉	#1964	1	1	yes	characteristic
229	C₂×C₁₉	#1982	1	1	yes	characteristic
230	C₂²×D₄	—	2	2	no	—
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
238	C₂²×C₈	—	2	2	no	—
239	#127	—	4	2	no	—
240	#121	—	2	4	no	—
241	#121	—	2	4	no	—
242	#121	—	4	4	no	—
243	#121	—	4	2	no	—
244	#121	—	4	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₄²	—	2	4	no	—
252	C₂×C₄²	—	4	2	no	—
253	C₂×C₄²	—	4	2	no	—
254	C₂×C₄²	—	4	2	no	—
255	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
256	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
259	C₄⋊C₈	—	4	2	no	—
260	C₂²⋊C₈	—	2	4	no	—
261	#95	—	2	4	no	—
262	#95	—	2	2	no	—
263	#95	D₄×C₁₉	1	4	yes	complemented
264	C₁₉	#9712	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	—	2	2	no	—
266	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
296	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
299	C₂²×C₄	D₈×C₁₉	1	2	yes	—
300	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
304	C₂²×C₄	#41×C₁₉	1	2	yes	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	4	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	4	8	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
332	C₂³	C₁₉×#121	1	2	yes	—
333	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
334	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
335	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
336	D₄	—	8	4	no	—
337	D₄	—	8	4	no	—
338	D₄	—	8	4	no	—
339	D₄	—	8	4	no	—
340	D₄	—	8	4	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	C₁₉×#99	1	2	yes	—
368	C₂×C₄	C₁₉×#102	1	2	yes	—
369	C₂×C₄	C₁₉×#102	1	2	yes	—
370	C₂×C₄	C₁₉×#104	1	2	yes	—
371	C₂×C₄	C₁₉×#104	1	2	yes	—
372	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
373	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
374	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
375	C₈	—	8	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	C₁₉×#390	1	1	yes	characteristic
392	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
393	C₂²	C₁₉×#410	1	1	yes	characteristic
394	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
395	C₂²	C₁₉×#418	1	1	yes	characteristic
396	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
397	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
398	C₂²	C₁₉×#459	1	2	yes	—
399	C₂²	C₁₉×#460	1	2	yes	—
400	C₄	—	2	1	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	8	no	—
406	C₄	—	4	1	no	—
407	C₄	—	8	2	no	—
408	C₄	C₁₉×#327	1	4	yes	complemented
409	C₂	—	2	2	no	—
410	C₂	—	2	2	no	—
411	C₂	—	16	2	no	—
412	C₂	C₂×C₁₉×#327	1	1	yes	characteristic
413	C₂	C₁₉×#1502	1	1	yes	characteristic
414	C₂	C₁₉×#1505	1	1	yes	characteristic
415	C₂	C₁₉×#1507	1	1	yes	characteristic
416	C₂	C₁₉×#1962	1	1	yes	characteristic
417	C₂	C₁₉×#1964	1	1	yes	characteristic
418	C₂	C₁₉×#1982	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₁₉×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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. C₁₉×#1797	C₂	semidirect
3. C₂×C₁₉×#327	C₂	semidirect
4. C₄×C₁₉×#95	C₂	semidirect
5. C₂×C₁₉×#127	C₄	semidirect
15. C₁₉×#390	C₄	semidirect
16. C₁₉×#384	C₄	semidirect
54. C₁₉×#95	D₄	semidirect
110. #9712	C₁₉	direct (N × H)
168. #1797	C₂×C₁₉	semidirect
169. C₂×#327	C₂×C₁₉	semidirect
170. C₄×#95	C₂×C₁₉	semidirect
203. C₄×C₁₉	#327	semidirect
204. C₂×#127	C₄×C₁₉	semidirect
214. #390	C₄×C₁₉	semidirect
215. #384	C₄×C₁₉	semidirect
263. #95	D₄×C₁₉	semidirect
264. C₁₉	#9712	direct (N × H)
408. C₄	C₁₉×#327	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#2856	2
C₁₉×#1797	2
C₂×C₁₉×#327	2
C₄×C₁₉×#95	2
#9712	19

Subgroups — C19×#9712 #18015671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9712 #18015671