Subgroups — C₁₉×#9299 #18015258

Order 4864.

632 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1963	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1517	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1286	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1274	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#532	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	—	2	1	no	—
11	C₁₉×#493	C₄	1	2	yes	complemented
12	C₁₉×#486	C₄	1	2	yes	complemented
13	C₁₉×#459	—	2	2	no	—
14	C₁₉×#447	—	2	2	no	—
15	C₁₉×#431	C₂²	1	1	yes	characteristic
16	C₁₉×#431	C₂²	1	1	yes	characteristic
17	C₁₉×#423	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#104	—	2	1	no	—
19	C₂×C₁₉×#104	—	2	1	no	—
20	C₁₉×#390	—	2	1	no	—
21	C₁₉×#386	—	2	2	no	—
22	C₁₉×#386	—	2	2	no	—
23	C₁₉×#382	C₂²	1	1	yes	characteristic
24	C₁₉×#376	C₂²	1	1	yes	characteristic
25	C₁₉×#331	—	2	2	no	—
26	C₁₉×#327	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	D₄	1	2	yes	—
31	C₂³×C₄×C₁₉	—	2	2	no	—
32	C₂×D₈×C₁₉	—	2	4	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
35	C₁₉×#127	—	2	1	no	—
36	C₁₉×#127	—	2	1	no	—
37	C₁₉×#127	C₂×C₄	1	2	yes	—
38	C₁₉×#127	C₂×C₄	1	1	yes	characteristic, complemented
39	C₁₉×#127	D₄	1	2	yes	—
40	C₁₉×#124	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₁₉×#121	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	4	2	no	—
46	C₄×D₄×C₁₉	—	4	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	1	no	—
58	C₁₉×#104	—	4	2	no	—
59	C₁₉×#104	—	4	2	no	—
60	C₁₉×#102	—	2	4	no	—
61	C₁₉×C₂²⋊C₈	—	2	1	no	—
62	C₁₉×C₂²⋊C₈	—	2	1	no	—
63	C₄×C₈×C₁₉	—	2	1	no	—
64	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	complemented
65	C₁₉×#95	—	2	1	no	—
66	C₁₉×#95	—	2	1	no	—
67	C₁₉×#95	—	2	1	no	—
68	C₁₉×#95	D₄	1	2	yes	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	#41×C₁₉	—	4	1	no	—
71	#41×C₁₉	—	4	1	no	—
72	#41×C₁₉	—	4	1	no	—
73	#41×C₁₉	—	4	1	no	—
74	C₂×Q₈×C₁₉	—	2	1	no	—
75	C₂×D₄×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	2	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	2	2	no	—
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	2	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	8	2	no	—
89	C₂×D₄×C₁₉	—	8	2	no	—
90	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	4	4	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	8	2	no	—
97	C₂²×C₄×C₁₉	—	8	2	no	—
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×D₄	1	1	yes	characteristic
101	D₈×C₁₉	—	8	4	no	—
102	M₁₆×C₁₉	—	4	1	no	—
103	M₁₆×C₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₂²⋊C₄×C₁₉	—	4	4	no	—
112	C₂²⋊C₄×C₁₉	—	4	1	no	—
113	C₂²⋊C₄×C₁₉	—	4	1	no	—
114	C₂²⋊C₄×C₁₉	—	8	2	no	—
115	C₂²⋊C₄×C₁₉	—	8	2	no	—
116	C₄²×C₁₉	—	2	1	no	—
117	C₄²×C₁₉	—	2	1	no	—
118	C₄²×C₁₉	—	2	1	no	—
119	C₄²×C₁₉	D₈	1	2	yes	complemented
120	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	#41	1	1	yes	characteristic
123	C₄²×C₁₉	#41	1	1	yes	characteristic
124	#9299	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₁₉	—	2	4	no	—
126	C₂³×C₁₉	—	4	2	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	#120	1	1	yes	characteristic
134	Q₈×C₁₉	—	4	1	no	—
135	Q₈×C₁₉	—	4	1	no	—
136	D₄×C₁₉	—	4	4	no	—
137	D₄×C₁₉	—	4	2	no	—
138	D₄×C₁₉	—	4	2	no	—
139	D₄×C₁₉	—	4	1	no	—
140	D₄×C₁₉	—	4	2	no	—
141	D₄×C₁₉	—	4	1	no	—
142	D₄×C₁₉	—	4	2	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	8	2	no	—
145	D₄×C₁₉	—	8	2	no	—
146	D₄×C₁₉	—	8	2	no	—
147	D₄×C₁₉	—	8	1	no	—
148	D₄×C₁₉	—	8	1	no	—
149	D₄×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	8	8	no	—
163	C₂×C₄×C₁₉	—	8	1	no	—
164	C₂×C₄×C₁₉	—	8	1	no	—
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
173	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₈×C₁₉	—	4	2	no	—
176	C₈×C₁₉	—	8	1	no	—
177	C₈×C₁₉	—	8	1	no	—
178	#3205	C₂×C₁₉	1	1	yes	characteristic
179	#2328	C₂×C₁₉	1	1	yes	characteristic, complemented
180	#1963	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#1545	C₂×C₁₉	1	1	yes	characteristic, complemented
182	#1517	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1286	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#1274	C₂×C₁₉	1	1	yes	characteristic, complemented
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	—	4	4	no	—
190	C₂²×C₁₉	—	8	2	no	—
191	C₂²×C₁₉	—	8	2	no	—
192	C₂²×C₁₉	—	8	2	no	—
193	C₂²×C₁₉	—	8	2	no	—
194	C₂²×C₁₉	—	8	1	no	—
195	C₂²×C₁₉	—	8	1	no	—
196	C₂²×C₁₉	—	8	1	no	—
197	C₂²×C₁₉	#386	1	1	yes	characteristic
198	C₂²×C₁₉	#447	1	1	yes	characteristic
199	C₂²×C₁₉	#449	1	1	yes	characteristic
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	—	8	2	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
209	C₄×C₁₉	#442	1	1	yes	characteristic
210	C₄×C₁₉	#459	1	1	yes	characteristic
211	C₄×C₁₉	#463	1	1	yes	characteristic
212	#532	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×C₄×D₄	—	2	1	no	—
215	#493	C₄×C₁₉	1	2	yes	complemented
216	#486	C₄×C₁₉	1	2	yes	complemented
217	#459	—	2	2	no	—
218	#447	—	2	2	no	—
219	#431	C₂²×C₁₉	1	1	yes	characteristic
220	#431	C₂²×C₁₉	1	1	yes	characteristic
221	#423	C₂²×C₁₉	1	1	yes	characteristic
222	C₂×#104	—	2	1	no	—
223	C₂×#104	—	2	1	no	—
224	#390	—	2	1	no	—
225	#386	—	2	2	no	—
226	#386	—	2	2	no	—
227	#382	C₂²×C₁₉	1	1	yes	characteristic
228	#376	C₂²×C₁₉	1	1	yes	characteristic
229	#331	—	2	2	no	—
230	#327	—	2	2	no	—
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	—	8	4	no	—
234	C₂×C₁₉	—	16	1	no	—
235	C₂×C₁₉	#1879	1	1	yes	characteristic
236	C₂×C₁₉	#1904	1	1	yes	characteristic
237	C₂×C₁₉	#1911	1	1	yes	characteristic
238	C₂×#41	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	D₄×C₁₉	1	2	yes	—
242	C₂³×C₄	—	2	2	no	—
243	C₂×D₈	—	2	4	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
246	#127	—	2	1	no	—
247	#127	—	2	1	no	—
248	#127	C₂×C₄×C₁₉	1	2	yes	—
249	#127	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
250	#127	D₄×C₁₉	1	2	yes	—
251	#124	—	2	1	no	—
252	#121	—	2	1	no	—
253	#121	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	4	2	no	—
257	C₄×D₄	—	4	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	1	no	—
269	#104	—	4	2	no	—
270	#104	—	4	2	no	—
271	#102	—	2	4	no	—
272	C₂²⋊C₈	—	2	1	no	—
273	C₂²⋊C₈	—	2	1	no	—
274	C₄×C₈	—	2	1	no	—
275	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	complemented
276	#95	—	2	1	no	—
277	#95	—	2	1	no	—
278	#95	—	2	1	no	—
279	#95	D₄×C₁₉	1	2	yes	—
280	C₁₉	#9299	1	1	yes	characteristic, direct product factor, Sylow
281	C₂⁴	—	2	2	no	—
282	#41	—	4	1	no	—
283	#41	—	4	1	no	—
284	#41	—	4	1	no	—
285	#41	—	4	1	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	8	2	no	—
301	C₂×D₄	—	8	2	no	—
302	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	8	2	no	—
309	C₂²×C₄	—	8	2	no	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
313	D₈	—	8	4	no	—
314	M₁₆	—	4	1	no	—
315	M₁₆	—	4	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	4	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	—	8	2	no	—
327	C₂²⋊C₄	—	8	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	D₈×C₁₉	1	2	yes	complemented
332	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₄²	#41×C₁₉	1	1	yes	characteristic
335	C₄²	#41×C₁₉	1	1	yes	characteristic
336	C₂³	—	2	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	C₁₉×#120	1	1	yes	characteristic
345	Q₈	—	4	1	no	—
346	Q₈	—	4	1	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	8	2	no	—
356	D₄	—	8	2	no	—
357	D₄	—	8	2	no	—
358	D₄	—	8	1	no	—
359	D₄	—	8	1	no	—
360	D₄	—	8	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	8	8	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	—	8	1	no	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
377	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
378	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
379	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
380	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
381	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
382	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
383	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
384	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	—	8	1	no	—
388	C₈	—	8	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₁₉×#386	1	1	yes	characteristic
402	C₂²	C₁₉×#447	1	1	yes	characteristic
403	C₂²	C₁₉×#449	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	1	no	—
412	C₄	C₄×D₈×C₁₉	1	1	yes	characteristic
413	C₄	C₁₉×#442	1	1	yes	characteristic
414	C₄	C₁₉×#459	1	1	yes	characteristic
415	C₄	C₁₉×#463	1	1	yes	characteristic
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	8	4	no	—
419	C₂	—	16	1	no	—
420	C₂	C₁₉×#1879	1	1	yes	characteristic
421	C₂	C₁₉×#1904	1	1	yes	characteristic
422	C₂	C₁₉×#1911	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3205	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2328	C₂	semidirect
3. C₁₉×#1963	C₂	semidirect
4. C₁₉×#1545	C₂	semidirect
5. C₁₉×#1517	C₂	semidirect
6. C₁₉×#1286	C₂	semidirect
7. C₁₉×#1274	C₂	semidirect
11. C₁₉×#493	C₄	semidirect
12. C₁₉×#486	C₄	semidirect
34. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
38. C₁₉×#127	C₂×C₄	semidirect
64. C₄×C₈×C₁₉	C₂×C₄	semidirect
119. C₄²×C₁₉	D₈	semidirect
124. #9299	C₁₉	direct (N × H)
179. #2328	C₂×C₁₉	semidirect
180. #1963	C₂×C₁₉	semidirect
181. #1545	C₂×C₁₉	semidirect
182. #1517	C₂×C₁₉	semidirect
183. #1286	C₂×C₁₉	semidirect
184. #1274	C₂×C₁₉	semidirect
215. #493	C₄×C₁₉	semidirect
216. #486	C₄×C₁₉	semidirect
245. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
249. #127	C₂×C₄×C₁₉	semidirect
275. C₄×C₈	C₂×C₄×C₁₉	semidirect
280. C₁₉	#9299	direct (N × H)
331. C₄²	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3205	2
C₁₉×#2328	2
C₁₉×#1963	2
C₁₉×#1545	2
C₁₉×#1517	2
C₁₉×#1286	2
C₁₉×#1274	2
#9299	19

Subgroups — C19×#9299 #18015258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9299 #18015258