Subgroups — C₁₉×#10242 #18016201

Order 4864.

658 conjugacy classes of subgroups.

The subgroup lattice has 454 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×#3037	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#137	—	2	1	no	—
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#124	—	2	1	no	—
12	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#493	—	2	1	no	—
14	C₁₉×#486	—	2	1	no	—
15	C₁₉×#464	—	2	2	no	—
16	C₁₉×#462	—	2	1	no	—
17	C₁₉×#460	—	2	1	no	—
18	C₁₉×#459	—	2	2	no	—
19	C₁₉×#447	—	2	2	no	—
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#423	C₂²	1	1	yes	characteristic
23	C₁₉×#417	—	2	1	no	—
24	C₁₉×#394	—	2	2	no	—
25	C₁₉×#390	—	2	2	no	—
26	C₁₉×#390	—	2	1	no	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#331	—	2	2	no	—
29	C₁₉×#327	—	2	2	no	—
30	C₁₉×Q₈⋊C₈	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	D₄	1	2	yes	—
36	C₁₉×#137	—	4	2	no	—
37	C₁₉×#137	—	4	2	no	—
38	C₂×Q₁₆×C₁₉	—	2	2	no	—
39	C₂×SD₁₆×C₁₉	—	2	2	no	—
40	C₂×D₈×C₁₉	—	2	4	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
43	C₁₉×#127	—	2	1	no	—
44	C₁₉×#127	—	2	1	no	—
45	C₁₉×#127	—	2	1	no	—
46	C₁₉×#127	—	2	1	no	—
47	C₁₉×#127	D₄	1	1	yes	characteristic
48	C₁₉×#124	—	2	1	no	—
49	C₁₉×#124	—	4	2	no	—
50	C₁₉×#124	—	4	2	no	—
51	C₁₉×#121	—	2	1	no	—
52	C₁₉×#121	—	2	1	no	—
53	C₄×Q₈×C₁₉	—	2	1	no	—
54	C₄×Q₈×C₁₉	—	2	1	no	—
55	C₄×Q₈×C₁₉	—	2	1	no	—
56	C₄×Q₈×C₁₉	—	2	1	no	—
57	C₄×D₄×C₁₉	—	2	1	no	—
58	C₄×D₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊C₈	—	2	1	no	—
68	C₁₉×C₄⋊C₈	—	2	1	no	—
69	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
70	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
71	C₁₉×#103	—	2	2	no	—
72	C₁₉×#102	—	2	2	no	—
73	C₁₉×#102	—	2	4	no	—
74	C₁₉×C₂²⋊C₈	—	2	1	no	—
75	C₁₉×C₂²⋊C₈	—	2	1	no	—
76	C₄×C₈×C₁₉	—	2	1	no	—
77	C₄×C₈×C₁₉	—	2	1	no	—
78	C₁₉×#95	D₄	1	2	yes	—
79	C₂⁴×C₁₉	—	2	2	no	—
80	#41×C₁₉	—	4	1	no	—
81	#41×C₁₉	—	4	1	no	—
82	#41×C₁₉	—	4	1	no	—
83	#41×C₁₉	—	4	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×Q₈×C₁₉	D₈	1	2	yes	complemented
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	4	4	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	—	4	1	no	—
101	C₂×D₄×C₁₉	—	4	1	no	—
102	C₂×D₄×C₁₉	—	4	1	no	—
103	C₂×D₄×C₁₉	—	4	1	no	—
104	C₂×D₄×C₁₉	—	4	1	no	—
105	C₂×D₄×C₁₉	—	4	1	no	—
106	C₂×D₄×C₁₉	—	8	2	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	Q₁₆×C₁₉	—	4	4	no	—
115	SD₁₆×C₁₉	—	4	4	no	—
116	D₈×C₁₉	—	8	4	no	—
117	M₁₆×C₁₉	—	4	1	no	—
118	M₁₆×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	4	2	no	—
127	C₄⋊C₄×C₁₉	—	4	1	no	—
128	C₄⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	8	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₂²⋊C₄×C₁₉	—	4	1	no	—
132	C₂²⋊C₄×C₁₉	—	8	4	no	—
133	C₄²×C₁₉	—	4	1	no	—
134	C₄²×C₁₉	—	4	1	no	—
135	C₄²×C₁₉	—	4	1	no	—
136	C₄²×C₁₉	—	4	1	no	—
137	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₉	#41	1	1	yes	characteristic
141	#10242	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₉	—	4	4	no	—
143	C₂³×C₁₉	—	4	4	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	#120	1	1	yes	characteristic
149	Q₈×C₁₉	—	2	2	no	—
150	Q₈×C₁₉	—	2	2	no	—
151	Q₈×C₁₉	—	4	1	no	—
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	—	4	1	no	—
154	Q₈×C₁₉	—	4	1	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	4	2	no	—
158	D₄×C₁₉	—	4	4	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	2	no	—
161	D₄×C₁₉	—	8	2	no	—
162	D₄×C₁₉	—	8	2	no	—
163	D₄×C₁₉	—	8	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	—	8	1	no	—
166	D₄×C₁₉	—	8	1	no	—
167	D₄×C₁₉	—	8	1	no	—
168	D₄×C₁₉	—	8	1	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	8	1	no	—
181	C₂×C₄×C₁₉	—	8	1	no	—
182	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
190	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₈×C₁₉	—	4	2	no	—
193	C₈×C₁₉	—	4	2	no	—
194	C₈×C₁₉	—	8	1	no	—
195	#3205	C₂×C₁₉	1	1	yes	characteristic
196	#3037	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#2548	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#1545	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#1502	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#1479	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#1303	C₂×C₁₉	1	1	yes	characteristic, complemented
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	8	4	no	—
205	C₂²×C₁₉	—	8	4	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	2	no	—
208	C₂²×C₁₉	—	8	2	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	2	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	#392	1	1	yes	characteristic
213	C₂²×C₁₉	#447	1	1	yes	characteristic
214	C₂²×C₁₉	#449	1	1	yes	characteristic
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	8	2	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	—	8	1	no	—
222	C₄×C₁₉	#447	1	1	yes	characteristic
223	C₄×C₁₉	#449	1	1	yes	characteristic
224	C₄×C₁₉	#455	1	2	yes	—
225	C₄×C₁₉	#466	1	1	yes	characteristic
226	C₄×C₁₉	#469	1	1	yes	characteristic
227	C₂×#137	—	2	1	no	—
228	#532	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#124	—	2	1	no	—
231	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
232	#493	—	2	1	no	—
233	#486	—	2	1	no	—
234	#464	—	2	2	no	—
235	#462	—	2	1	no	—
236	#460	—	2	1	no	—
237	#459	—	2	2	no	—
238	#447	—	2	2	no	—
239	#431	C₂²×C₁₉	1	1	yes	characteristic
240	#431	C₂²×C₁₉	1	1	yes	characteristic
241	#423	C₂²×C₁₉	1	1	yes	characteristic
242	#417	—	2	1	no	—
243	#394	—	2	2	no	—
244	#390	—	2	2	no	—
245	#390	—	2	1	no	—
246	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
247	#331	—	2	2	no	—
248	#327	—	2	2	no	—
249	Q₈⋊C₈	—	2	2	no	—
250	C₂×C₁₉	—	2	1	no	—
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	—	16	1	no	—
253	C₂×C₁₉	—	16	2	no	—
254	C₂×C₁₉	#1999	1	1	yes	characteristic
255	C₂×C₁₉	#2004	1	1	yes	characteristic
256	C₂×C₁₉	#2008	1	1	yes	characteristic
257	C₂×#41	—	2	1	no	—
258	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	D₄×C₁₉	1	2	yes	—
262	#137	—	4	2	no	—
263	#137	—	4	2	no	—
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×SD₁₆	—	2	2	no	—
266	C₂×D₈	—	2	4	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
269	#127	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	D₄×C₁₉	1	1	yes	characteristic
274	#124	—	2	1	no	—
275	#124	—	4	2	no	—
276	#124	—	4	2	no	—
277	#121	—	2	1	no	—
278	#121	—	2	1	no	—
279	C₄×Q₈	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	—	2	4	no	—
289	C₂×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
296	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
297	#103	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	4	no	—
300	C₂²⋊C₈	—	2	1	no	—
301	C₂²⋊C₈	—	2	1	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	2	1	no	—
304	#95	D₄×C₁₉	1	2	yes	—
305	C₁₉	#10242	1	1	yes	characteristic, direct product factor, Sylow
306	C₂⁴	—	2	2	no	—
307	#41	—	4	1	no	—
308	#41	—	4	1	no	—
309	#41	—	4	1	no	—
310	#41	—	4	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	D₈×C₁₉	1	2	yes	complemented
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	8	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
341	Q₁₆	—	4	4	no	—
342	SD₁₆	—	4	4	no	—
343	D₈	—	8	4	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	—	4	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	4	8	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	8	4	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	—	4	1	no	—
364	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
366	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₄²	#41×C₁₉	1	1	yes	characteristic
368	C₂³	—	4	4	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	C₁₉×#120	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	4	1	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	D₄	—	4	1	no	—
382	D₄	—	4	1	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	1	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	1	no	—
390	D₄	—	8	1	no	—
391	D₄	—	8	1	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
409	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
410	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
411	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
412	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
413	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
414	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
415	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
416	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
417	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	8	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	8	4	no	—
424	C₂²	—	8	4	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	1	no	—
431	C₂²	C₁₉×#392	1	1	yes	characteristic
432	C₂²	C₁₉×#447	1	1	yes	characteristic
433	C₂²	C₁₉×#449	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	2	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	1	no	—
441	C₄	C₁₉×#447	1	1	yes	characteristic
442	C₄	C₁₉×#449	1	1	yes	characteristic
443	C₄	C₁₉×#455	1	2	yes	—
444	C₄	C₁₉×#466	1	1	yes	characteristic
445	C₄	C₁₉×#469	1	1	yes	characteristic
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	16	2	no	—
449	C₂	—	16	1	no	—
450	C₂	C₁₉×#1999	1	1	yes	characteristic
451	C₂	C₁₉×#2004	1	1	yes	characteristic
452	C₂	C₁₉×#2008	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3205	C₂
LCS	G ▷ C₂×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×#3037	C₂	semidirect
3. C₁₉×#2548	C₂	semidirect
4. C₁₉×#1545	C₂	semidirect
5. C₁₉×#1502	C₂	semidirect
6. C₁₉×#1479	C₂	semidirect
7. C₁₉×#1303	C₂	semidirect
90. C₂×Q₈×C₁₉	D₈	semidirect
141. #10242	C₁₉	direct (N × H)
196. #3037	C₂×C₁₉	semidirect
197. #2548	C₂×C₁₉	semidirect
198. #1545	C₂×C₁₉	semidirect
199. #1502	C₂×C₁₉	semidirect
200. #1479	C₂×C₁₉	semidirect
201. #1303	C₂×C₁₉	semidirect
305. C₁₉	#10242	direct (N × H)
317. C₂×Q₈	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×#3037	2
C₁₉×#2548	2
C₁₉×#1545	2
C₁₉×#1502	2
C₁₉×#1479	2
C₁₉×#1303	2
#10242	19

Subgroups — C19×#10242 #18016201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10242 #18016201