Subgroups — C₁₉×#11072 #18017031

Order 4864.

934 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#421	C₂	1	2	yes	maximal
2	C₁₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#117	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#421	—	2	4	no	—
12	C₁₉×#421	—	2	4	no	—
13	C₂×C₁₉×#104	—	2	4	no	—
14	C₁₉×#391	C₄	1	2	yes	complemented
15	C₁₉×#390	C₄	1	2	yes	complemented
16	C₁₉×#389	—	2	4	no	—
17	C₁₉×#386	—	2	2	no	—
18	C₁₉×#380	—	2	2	no	—
19	C₁₉×#380	—	2	2	no	—
20	C₁₉×#343	—	2	2	no	—
21	C₁₉×H(3,ℤ/4)	—	2	4	no	—
22	C₂×#41×C₁₉	—	2	1	no	—
23	C₂×#41×C₁₉	—	2	1	no	—
24	C₂×#41×C₁₉	—	2	2	no	—
25	C₂×#41×C₁₉	—	2	2	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	D₄	1	2	yes	—
29	C₂×#41×C₁₉	Q₈	1	2	yes	—
30	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂³×C₄×C₁₉	D₄	1	2	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	—	2	2	no	—
37	C₂×M₁₆×C₁₉	—	2	2	no	—
38	C₂×M₁₆×C₁₉	—	2	2	no	—
39	C₂×M₁₆×C₁₉	—	2	2	no	—
40	C₂×M₁₆×C₁₉	—	2	2	no	—
41	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
42	C₂²×C₈×C₁₉	—	2	2	no	—
43	C₁₉×#117	—	2	2	no	—
44	C₁₉×#117	—	2	2	no	—
45	C₁₉×#117	—	2	2	no	—
46	C₁₉×#117	—	2	2	no	—
47	C₁₉×#117	—	2	2	no	—
48	C₁₉×#117	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₁₉	D₄	1	4	yes	—
61	C₁₉×#104	—	2	16	no	—
62	C₁₉×#95	—	2	4	no	—
63	C₁₉×#95	—	2	4	no	—
64	C₂⁴×C₁₉	—	2	1	no	—
65	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
66	#41×C₁₉	—	2	4	no	—
67	#41×C₁₉	—	2	4	no	—
68	#41×C₁₉	—	2	4	no	—
69	#41×C₁₉	—	2	4	no	—
70	#41×C₁₉	—	4	2	no	—
71	#41×C₁₉	—	4	2	no	—
72	#41×C₁₉	—	4	2	no	—
73	#41×C₁₉	—	4	2	no	—
74	C₂×Q₈×C₁₉	—	2	1	no	—
75	C₂×Q₈×C₁₉	—	2	2	no	—
76	C₂×Q₈×C₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	complemented
78	C₂×D₄×C₁₉	—	2	2	no	—
79	C₂×D₄×C₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	2	1	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	C₄⋊C₄	1	2	yes	complemented
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	8	2	no	—
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	2	yes	—
108	C₂²×C₄×C₁₉	#41	1	2	yes	—
109	M₁₆×C₁₉	—	2	4	no	—
110	M₁₆×C₁₉	—	2	4	no	—
111	M₁₆×C₁₉	—	4	2	no	—
112	M₁₆×C₁₉	—	4	2	no	—
113	C₂×C₈×C₁₉	—	2	4	no	—
114	C₂×C₈×C₁₉	—	4	2	no	—
115	C₂×C₈×C₁₉	—	4	2	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	4	no	—
118	C₄⋊C₄×C₁₉	—	4	2	no	—
119	C₄⋊C₄×C₁₉	—	4	2	no	—
120	C₄⋊C₄×C₁₉	—	4	2	no	—
121	C₄⋊C₄×C₁₉	—	8	4	no	—
122	C₂²⋊C₄×C₁₉	—	4	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₂²⋊C₄×C₁₉	—	4	2	no	—
126	C₂²⋊C₄×C₁₉	—	8	4	no	—
127	C₄²×C₁₉	—	2	4	no	—
128	C₄²×C₁₉	—	2	4	no	—
129	C₄²×C₁₉	—	2	4	no	—
130	#11072	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₁₉	#120	1	1	yes	characteristic
140	C₂³×C₁₉	#121	1	1	yes	characteristic
141	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂³×C₁₉	#123	1	1	yes	characteristic
143	C₂³×C₁₉	#124	1	1	yes	characteristic
144	C₂³×C₁₉	#127	1	1	yes	characteristic
145	Q₈×C₁₉	—	2	4	no	—
146	Q₈×C₁₉	—	4	2	no	—
147	D₄×C₁₉	—	2	4	no	—
148	D₄×C₁₉	—	4	2	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	4	4	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	—	4	4	no	—
160	C₂×C₄×C₁₉	—	4	4	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₁₉	#120	1	2	yes	—
173	C₂×C₄×C₁₉	#121	1	2	yes	—
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	2	yes	—
176	C₂×C₄×C₁₉	#121	1	2	yes	—
177	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#123	1	2	yes	—
181	C₂×C₄×C₁₉	#123	1	2	yes	—
182	C₂×C₄×C₁₉	#124	1	2	yes	—
183	C₂×C₄×C₁₉	#126	1	2	yes	—
184	C₈×C₁₉	—	4	4	no	—
185	C₂×#421	C₂×C₁₉	1	2	yes	—
186	#2316	C₂×C₁₉	1	1	yes	characteristic, complemented
187	#2311	C₂×C₁₉	1	1	yes	characteristic
188	C₂×#343	C₂×C₁₉	1	1	yes	characteristic, complemented
189	C₂×H(3,ℤ/4)	C₂×C₁₉	1	2	yes	complemented
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	4	4	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	8	2	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	#380	1	1	yes	characteristic
206	C₂²×C₁₉	#386	1	1	yes	characteristic
207	C₂²×C₁₉	#390	1	1	yes	characteristic
208	C₂²×C₁₉	#392	1	1	yes	characteristic
209	C₂²×C₁₉	#393	1	1	yes	characteristic
210	C₂²×C₁₉	#397	1	1	yes	characteristic
211	C₂²×C₁₉	#399	1	1	yes	characteristic
212	C₄×C₁₉	—	4	4	no	—
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	8	4	no	—
215	C₄×C₁₉	—	8	2	no	—
216	C₄×C₁₉	#385	1	2	yes	—
217	C₄×C₁₉	#388	1	2	yes	—
218	C₄×C₁₉	#394	1	2	yes	—
219	C₄×C₁₉	#396	1	2	yes	—
220	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
221	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
222	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×#117	C₂²×C₁₉	1	2	yes	—
224	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
225	#421	—	2	4	no	—
226	#421	—	2	4	no	—
227	C₂×#104	—	2	4	no	—
228	#391	C₄×C₁₉	1	2	yes	complemented
229	#390	C₄×C₁₉	1	2	yes	complemented
230	#389	—	2	4	no	—
231	#386	—	2	2	no	—
232	#380	—	2	2	no	—
233	#380	—	2	2	no	—
234	#343	—	2	2	no	—
235	H(3,ℤ/4)	—	2	4	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	2	1	no	—
242	C₂×C₁₉	—	8	2	no	—
243	C₂×C₁₉	#1439	1	1	yes	characteristic
244	C₂×C₁₉	#1911	1	1	yes	characteristic
245	C₂×C₁₉	#1912	1	1	yes	characteristic
246	C₂×#41	—	2	1	no	—
247	C₂×#41	—	2	1	no	—
248	C₂×#41	—	2	2	no	—
249	C₂×#41	—	2	2	no	—
250	C₂×#41	—	2	2	no	—
251	C₂×#41	—	2	2	no	—
252	C₂×#41	D₄×C₁₉	1	2	yes	—
253	C₂×#41	Q₈×C₁₉	1	2	yes	—
254	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	D₄×C₁₉	1	2	yes	—
259	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
266	C₂²×C₈	—	2	2	no	—
267	#117	—	2	2	no	—
268	#117	—	2	2	no	—
269	#117	—	2	2	no	—
270	#117	—	2	2	no	—
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
279	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
284	C₂×C₄²	D₄×C₁₉	1	4	yes	—
285	#104	—	2	16	no	—
286	#95	—	2	4	no	—
287	#95	—	2	4	no	—
288	C₁₉	#11072	1	1	yes	characteristic, direct product factor, Sylow
289	C₂⁴	—	2	1	no	—
290	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	#41	—	2	4	no	—
294	#41	—	2	4	no	—
295	#41	—	4	2	no	—
296	#41	—	4	2	no	—
297	#41	—	4	2	no	—
298	#41	—	4	2	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	C₄⋊C₄×C₁₉	1	2	yes	complemented
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	complemented
313	C₂²×C₄	—	2	1	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	2	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	8	2	no	—
323	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
324	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	#41×C₁₉	1	2	yes	—
333	C₂²×C₄	#41×C₁₉	1	2	yes	—
334	M₁₆	—	2	4	no	—
335	M₁₆	—	2	4	no	—
336	M₁₆	—	4	2	no	—
337	M₁₆	—	4	2	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	4	2	no	—
340	C₂×C₈	—	4	2	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	8	4	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	8	4	no	—
352	C₄²	—	2	4	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	4	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
363	C₂³	C₁₉×#120	1	1	yes	characteristic
364	C₂³	C₁₉×#121	1	1	yes	characteristic
365	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
366	C₂³	C₁₉×#123	1	1	yes	characteristic
367	C₂³	C₁₉×#124	1	1	yes	characteristic
368	C₂³	C₁₉×#127	1	1	yes	characteristic
369	Q₈	—	2	4	no	—
370	Q₈	—	4	2	no	—
371	D₄	—	2	4	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
394	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
395	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
396	C₂×C₄	C₁₉×#120	1	2	yes	—
397	C₂×C₄	C₁₉×#121	1	2	yes	—
398	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
399	C₂×C₄	C₁₉×#121	1	2	yes	—
400	C₂×C₄	C₁₉×#121	1	2	yes	—
401	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
402	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
403	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
404	C₂×C₄	C₁₉×#123	1	2	yes	—
405	C₂×C₄	C₁₉×#123	1	2	yes	—
406	C₂×C₄	C₁₉×#124	1	2	yes	—
407	C₂×C₄	C₁₉×#126	1	2	yes	—
408	C₈	—	4	4	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	C₁₉×#380	1	1	yes	characteristic
425	C₂²	C₁₉×#386	1	1	yes	characteristic
426	C₂²	C₁₉×#390	1	1	yes	characteristic
427	C₂²	C₁₉×#392	1	1	yes	characteristic
428	C₂²	C₁₉×#393	1	1	yes	characteristic
429	C₂²	C₁₉×#397	1	1	yes	characteristic
430	C₂²	C₁₉×#399	1	1	yes	characteristic
431	C₄	—	4	4	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	4	no	—
434	C₄	—	8	2	no	—
435	C₄	C₁₉×#385	1	2	yes	—
436	C₄	C₁₉×#388	1	2	yes	—
437	C₄	C₁₉×#394	1	2	yes	—
438	C₄	C₁₉×#396	1	2	yes	—
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	8	2	no	—
446	C₂	C₁₉×#1439	1	1	yes	characteristic
447	C₂	C₁₉×#1911	1	1	yes	characteristic
448	C₂	C₁₉×#1912	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2316	C₂	semidirect
4. C₂×C₁₉×#343	C₂	semidirect
5. C₂×C₁₉×H(3,ℤ/4)	C₂	semidirect
14. C₁₉×#391	C₄	semidirect
15. C₁₉×#390	C₄	semidirect
77. C₂×Q₈×C₁₉	C₄⋊C₄	semidirect
87. C₂×D₄×C₁₉	C₄⋊C₄	semidirect
130. #11072	C₁₉	direct (N × H)
186. #2316	C₂×C₁₉	semidirect
188. C₂×#343	C₂×C₁₉	semidirect
189. C₂×H(3,ℤ/4)	C₂×C₁₉	semidirect
228. #391	C₄×C₁₉	semidirect
229. #390	C₄×C₁₉	semidirect
288. C₁₉	#11072	direct (N × H)
302. C₂×Q₈	C₄⋊C₄×C₁₉	semidirect
312. C₂×D₄	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×#421	2
C₁₉×#2316	2
C₁₉×#2311	2
C₂×C₁₉×#343	2
C₂×C₁₉×H(3,ℤ/4)	2
#11072	19

Subgroups — C19×#11072 #18017031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11072 #18017031