Subgroups — D₁₉×#1301 #18072761

Order 4864.

666 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	D₁₉×#431	C₂	1	1	yes	maximal, characteristic
2	D₁₉×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
4	#14561532	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561531	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561530	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1301	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₁₉	—	2	1	no	—
9	C₂²×C₈×D₁₉	—	2	1	no	—
10	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
11	#11926597	C₂²	1	1	yes	characteristic
12	#11926596	—	2	1	no	—
13	#11926595	—	2	1	no	—
14	#11926594	C₄	1	2	yes	—
15	#11926568	C₂²	1	1	yes	characteristic
16	#11926567	—	2	1	no	—
17	#11926566	—	2	1	no	—
18	#11926566	C₄	1	2	yes	—
19	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×Dic₁₉⋊C₈	—	2	1	no	—
21	C₄⋊C₈×D₁₉	—	2	1	no	—
22	C₄⋊C₈×D₁₉	—	2	1	no	—
23	C₄⋊C₈×D₁₉	—	2	1	no	—
24	C₄⋊C₈×D₁₉	—	2	1	no	—
25	C₄⋊C₈×D₁₉	C₄	1	2	yes	—
26	C₄⋊C₈×D₁₉	C₄	1	2	yes	—
27	C₄⋊C₈×D₁₉	C₄	1	2	yes	—
28	C₂²⋊C₈×D₁₉	C₄	1	2	yes	—
29	C₄×C₈×D₁₉	—	2	1	no	—
30	C₁₉×#431	C₂²	1	1	yes	characteristic
31	C₁₉×#423	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₁₉	Q₈	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄×Dic₁₉	Q₈	1	1	yes	characteristic
42	C₂×#64520	—	2	1	no	—
43	C₂²×C₁₉⋊C₈	—	2	1	no	—
44	M₁₆×D₁₉	—	4	2	no	—
45	M₁₆×D₁₉	—	4	2	no	—
46	C₂×#64515	—	2	2	no	—
47	C₂×C₈×D₁₉	—	2	2	no	—
48	C₂×C₈×D₁₉	—	2	2	no	—
49	C₂×C₈×D₁₉	—	2	2	no	—
50	C₂×C₈×D₁₉	—	2	2	no	—
51	C₂×C₈×D₁₉	—	4	2	no	—
52	C₂×C₈×D₁₉	—	4	2	no	—
53	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₉	D₄	1	1	yes	characteristic
58	C₄²×D₁₉	D₄	1	1	yes	characteristic
59	C₄²×D₁₉	D₄	1	1	yes	characteristic
60	C₄²×D₁₉	D₄	1	1	yes	characteristic
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
65	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
66	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₁₉	—	2	1	no	—
68	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
69	(C₂×D₁₉)⋊C₈	—	2	2	no	—
70	Dic₁₉⋊C₈	—	2	2	no	—
71	Dic₁₉⋊C₈	—	2	2	no	—
72	Dic₁₉⋊C₈	—	2	2	no	—
73	Dic₁₉⋊C₈	—	2	2	no	—
74	Dic₁₉⋊C₈	—	2	2	no	—
75	C₈×Dic₁₉	—	2	2	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
79	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
80	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
81	C₄×C₁₉⋊C₈	—	2	1	no	—
82	C₂³×D₁₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
86	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₁₉	—	2	4	no	—
90	C₂×C₄×D₁₉	—	4	2	no	—
91	C₂×C₄×D₁₉	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₁₉	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₉	D₈	1	2	yes	—
104	C₂×C₄×D₁₉	SD₁₆	1	2	yes	—
105	C₂×C₄×D₁₉	SD₁₆	1	2	yes	—
106	C₂×C₄×D₁₉	Q₁₆	1	2	yes	—
107	M₁₆×C₁₉	—	4	1	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₄×Dic₁₉	C₄²	1	1	yes	characteristic
119	C₄×Dic₁₉	C₄²	1	1	yes	characteristic
120	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
130	#64520	—	4	1	no	—
131	#64520	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	2	2	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	2	2	no	—
135	C₂×C₁₉⋊C₈	—	4	1	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	#64515	—	4	4	no	—
138	C₈×D₁₉	—	4	4	no	—
139	C₈×D₁₉	—	4	4	no	—
140	C₈×D₁₉	—	4	4	no	—
141	C₈×D₁₉	—	4	4	no	—
142	C₂×#1301	—	19	1	no	maximal, Sylow
143	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂²×D₁₉	—	2	2	no	—
145	C₂²×D₁₉	—	2	2	no	—
146	C₂²×D₁₉	#95	1	1	yes	characteristic
147	C₂²×D₁₉	#95	1	1	yes	characteristic
148	C₂²×D₁₉	#106	1	2	yes	—
149	C₂²×D₁₉	#107	1	2	yes	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
162	C₂×Dic₁₉	—	2	2	no	—
163	C₂×Dic₁₉	—	4	1	no	—
164	C₂×Dic₁₉	#95	1	1	yes	characteristic
165	C₂×Dic₁₉	#95	1	1	yes	characteristic
166	C₂×Dic₁₉	#95	1	1	yes	characteristic
167	C₂×Dic₁₉	#95	1	1	yes	characteristic
168	C₂×Dic₁₉	#95	1	1	yes	characteristic
169	C₂×Dic₁₉	#95	1	1	yes	characteristic
170	C₂×Dic₁₉	#106	1	2	yes	—
171	C₂×Dic₁₉	#107	1	2	yes	—
172	C₄×D₁₉	—	2	2	no	—
173	C₄×D₁₉	—	2	2	no	—
174	C₄×D₁₉	—	2	2	no	—
175	C₄×D₁₉	—	2	2	no	—
176	C₄×D₁₉	—	2	2	no	—
177	C₄×D₁₉	—	4	1	no	—
178	C₄×D₁₉	—	4	1	no	—
179	C₄×D₁₉	#102	1	2	yes	—
180	C₄×D₁₉	#102	1	2	yes	—
181	C₄×D₁₉	#102	1	2	yes	—
182	C₄×D₁₉	#102	1	2	yes	—
183	C₄×D₁₉	#103	1	2	yes	—
184	C₄×D₁₉	#103	1	2	yes	—
185	C₄×D₁₉	#103	1	2	yes	—
186	C₄×D₁₉	#103	1	2	yes	—
187	C₄×D₁₉	#108	1	4	yes	—
188	C₈×C₁₉	—	4	2	no	—
189	C₈×C₁₉	—	4	2	no	—
190	C₈×C₁₉	—	4	2	no	—
191	C₁₉⋊C₈	—	4	2	no	—
192	C₁₉⋊C₈	—	4	2	no	—
193	C₁₉⋊C₈	—	4	2	no	—
194	C₂×#431	—	19	1	no	—
195	C₂×#423	—	19	1	no	—
196	C₂²×C₄⋊C₈	—	19	1	no	—
197	#1301	—	19	1	no	—
198	#1301	—	19	1	no	—
199	#1301	—	19	1	no	—
200	#1301	D₁₉	1	1	yes	characteristic, direct product factor
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
204	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
205	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
206	C₂×D₁₉	—	2	1	no	—
207	C₂×D₁₉	—	2	1	no	—
208	C₂×D₁₉	—	2	4	no	—
209	C₂×D₁₉	—	2	4	no	—
210	C₂×D₁₉	#340	1	2	yes	—
211	C₂×D₁₉	#340	1	2	yes	—
212	C₂×D₁₉	#341	1	2	yes	—
213	C₂×D₁₉	#344	1	2	yes	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
218	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
219	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
220	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
221	C₄×C₁₉	C₂×#108	1	2	yes	—
222	Dic₁₉	—	2	1	no	—
223	Dic₁₉	—	2	1	no	—
224	Dic₁₉	—	2	1	no	—
225	Dic₁₉	#340	1	2	yes	—
226	Dic₁₉	#340	1	2	yes	—
227	Dic₁₉	#341	1	2	yes	—
228	C₂²×M₁₆	—	38	1	no	—
229	C₂³×C₈	—	38	1	no	—
230	C₂²×C₄²	—	19	1	no	—
231	#431	—	19	1	no	—
232	#431	—	19	2	no	—
233	#431	—	38	1	no	—
234	#431	—	38	1	no	—
235	#431	C₂×D₁₉	1	1	yes	characteristic
236	#423	—	19	1	no	—
237	#423	—	19	2	no	—
238	#423	—	38	1	no	—
239	#423	—	38	1	no	—
240	#423	C₂×D₁₉	1	1	yes	characteristic
241	C₂×C₄⋊C₈	—	19	1	no	—
242	C₂×C₄⋊C₈	—	19	2	no	—
243	C₂×C₄⋊C₈	—	19	2	no	—
244	C₂×C₄⋊C₈	—	19	2	no	—
245	C₂×C₄⋊C₈	—	38	1	no	—
246	C₂×C₄⋊C₈	—	38	1	no	—
247	C₂×C₄⋊C₈	—	38	1	no	—
248	C₂×C₄⋊C₈	—	38	1	no	—
249	C₂×C₄⋊C₈	—	38	1	no	—
250	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	—	19	2	no	—
252	C₂×C₄×C₈	—	38	1	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	C₂×#340	1	1	yes	characteristic
256	C₂×C₁₉	C₂×#341	1	1	yes	characteristic
257	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
258	D₁₉	—	2	2	no	—
259	D₁₉	#1301	1	4	yes	direct product factor
260	C₂³×C₄	—	19	1	no	—
261	C₂³×C₄	—	19	1	no	—
262	C₂³×C₄	—	19	1	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	38	2	no	—
265	C₂×M₁₆	—	38	1	no	—
266	C₂×M₁₆	—	76	2	no	—
267	C₂×M₁₆	—	76	2	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	38	2	no	—
270	C₂²×C₈	—	38	2	no	—
271	C₂²×C₈	—	38	2	no	—
272	C₂²×C₈	—	38	2	no	—
273	C₂²×C₈	—	38	1	no	—
274	C₂²×C₈	—	76	2	no	—
275	C₂²×C₈	—	76	2	no	—
276	C₂×C₄²	—	19	1	no	—
277	C₂×C₄²	—	19	1	no	—
278	C₂×C₄²	—	19	1	no	—
279	C₂×C₄²	—	19	1	no	—
280	C₂×C₄²	—	19	1	no	—
281	C₂×C₄²	—	19	1	no	—
282	C₂×C₄²	—	19	1	no	—
283	C₂×C₄²	—	19	1	no	—
284	C₂×C₄²	—	19	1	no	—
285	C₂×C₄²	—	19	1	no	—
286	C₂×C₄²	—	19	1	no	—
287	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	19	2	no	—
292	C₄⋊C₈	—	19	2	no	—
293	C₄⋊C₈	—	38	2	no	—
294	C₄⋊C₈	—	38	2	no	—
295	C₄⋊C₈	—	38	2	no	—
296	C₄⋊C₈	—	38	2	no	—
297	C₄⋊C₈	—	38	2	no	—
298	C₄⋊C₈	—	38	1	no	—
299	C₄⋊C₈	—	38	1	no	—
300	C₄⋊C₈	—	38	1	no	—
301	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
302	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
303	C₂²⋊C₈	—	19	2	no	—
304	C₂²⋊C₈	—	38	2	no	—
305	C₂²⋊C₈	C₄×D₁₉	1	2	yes	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	—	38	2	no	—
308	C₄×C₈	—	38	1	no	—
309	C₁₉	C₂×#1301	1	1	yes	characteristic, complemented, Sylow
310	C₂⁴	—	19	1	no	—
311	C₂²×C₄	—	19	1	no	—
312	C₂²×C₄	—	19	1	no	—
313	C₂²×C₄	—	19	1	no	—
314	C₂²×C₄	—	19	1	no	—
315	C₂²×C₄	—	19	1	no	—
316	C₂²×C₄	—	19	1	no	—
317	C₂²×C₄	—	19	2	no	—
318	C₂²×C₄	—	19	2	no	—
319	C₂²×C₄	—	19	2	no	—
320	C₂²×C₄	—	19	2	no	—
321	C₂²×C₄	—	19	1	no	—
322	C₂²×C₄	—	19	1	no	—
323	C₂²×C₄	—	19	1	no	—
324	C₂²×C₄	—	19	1	no	—
325	C₂²×C₄	—	19	1	no	—
326	C₂²×C₄	—	19	1	no	—
327	C₂²×C₄	—	19	1	no	—
328	C₂²×C₄	—	19	1	no	—
329	C₂²×C₄	—	19	1	no	—
330	C₂²×C₄	—	38	4	no	—
331	C₂²×C₄	—	76	2	no	—
332	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
333	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
334	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
335	M₁₆	—	4	1	no	—
336	M₁₆	—	4	1	no	—
337	M₁₆	—	76	4	no	—
338	M₁₆	—	76	1	no	—
339	M₁₆	—	76	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	38	2	no	—
346	C₂×C₈	—	38	2	no	—
347	C₂×C₈	—	38	2	no	—
348	C₂×C₈	—	76	4	no	—
349	C₂×C₈	—	76	4	no	—
350	C₂×C₈	—	76	4	no	—
351	C₂×C₈	—	76	4	no	—
352	C₂×C₈	—	76	1	no	—
353	C₂×C₈	—	76	1	no	—
354	C₄²	—	19	1	no	—
355	C₄²	—	19	1	no	—
356	C₄²	—	19	1	no	—
357	C₄²	—	19	1	no	—
358	C₄²	—	19	1	no	—
359	C₄²	—	19	1	no	—
360	C₄²	—	19	1	no	—
361	C₄²	—	19	1	no	—
362	C₄²	—	19	1	no	—
363	C₄²	—	19	1	no	—
364	C₄²	—	19	1	no	—
365	C₄²	—	19	1	no	—
366	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
367	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
368	C₄²	D₄×D₁₉	1	1	yes	characteristic
369	C₄²	D₄×D₁₉	1	1	yes	characteristic
370	C₂³	—	19	1	no	—
371	C₂³	—	19	2	no	—
372	C₂³	—	19	2	no	—
373	C₂³	—	19	1	no	—
374	C₂³	—	38	2	no	—
375	C₂³	—	38	2	no	—
376	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	19	2	no	—
380	C₂×C₄	—	19	2	no	—
381	C₂×C₄	—	19	1	no	—
382	C₂×C₄	—	19	1	no	—
383	C₂×C₄	—	19	1	no	—
384	C₂×C₄	—	19	2	no	—
385	C₂×C₄	—	19	2	no	—
386	C₂×C₄	—	19	2	no	—
387	C₂×C₄	—	19	2	no	—
388	C₂×C₄	—	19	2	no	—
389	C₂×C₄	—	19	2	no	—
390	C₂×C₄	—	19	2	no	—
391	C₂×C₄	—	19	2	no	—
392	C₂×C₄	—	19	4	no	—
393	C₂×C₄	—	19	1	no	—
394	C₂×C₄	—	19	1	no	—
395	C₂×C₄	—	19	1	no	—
396	C₂×C₄	—	38	2	no	—
397	C₂×C₄	—	38	2	no	—
398	C₂×C₄	—	38	2	no	—
399	C₂×C₄	—	38	2	no	—
400	C₂×C₄	—	38	2	no	—
401	C₂×C₄	—	38	2	no	—
402	C₂×C₄	—	76	1	no	—
403	C₂×C₄	—	76	1	no	—
404	C₂×C₄	—	76	1	no	—
405	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
406	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
407	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
408	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
409	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
410	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
411	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
412	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
413	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
414	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	76	2	no	—
419	C₈	—	76	2	no	—
420	C₈	—	76	2	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	19	2	no	—
424	C₂²	—	19	2	no	—
425	C₂²	—	19	2	no	—
426	C₂²	—	19	2	no	—
427	C₂²	—	38	4	no	—
428	C₂²	—	38	4	no	—
429	C₂²	—	38	1	no	—
430	C₂²	—	38	1	no	—
431	C₂²	#95×D₁₉	1	1	yes	characteristic
432	C₂²	#106×D₁₉	1	1	yes	characteristic
433	C₂²	#107×D₁₉	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	19	2	no	—
438	C₄	—	19	2	no	—
439	C₄	—	19	2	no	—
440	C₄	—	38	1	no	—
441	C₄	—	38	1	no	—
442	C₄	—	38	1	no	—
443	C₄	#102×D₁₉	1	1	yes	characteristic
444	C₄	#102×D₁₉	1	1	yes	characteristic
445	C₄	#103×D₁₉	1	1	yes	characteristic
446	C₄	#103×D₁₉	1	1	yes	characteristic
447	C₄	#108×D₁₉	1	2	yes	—
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	19	4	no	—
451	C₂	—	38	2	no	—
452	C₂	D₁₉×#340	1	1	yes	characteristic
453	C₂	D₁₉×#341	1	1	yes	characteristic
454	C₂	D₁₉×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1301	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂³×D₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1301	D₁₉
hypocenter	C₁₉	C₂×#1301
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

Complements

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

N	H ≅ G/N	type
4. #14561532	C₂	semidirect
5. #14561531	C₂	semidirect
6. #14561530	C₂	semidirect
7. C₁₉×#1301	C₂	semidirect
200. #1301	D₁₉	direct (N × H)
259. D₁₉	#1301	direct (N × H)
309. C₁₉	C₂×#1301	semidirect

Maximal subgroups

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

subgroup	index
D₁₉×#431	2
D₁₉×#423	2
C₂×C₄⋊C₈×D₁₉	2
#14561532	2
#14561531	2
#14561530	2
C₁₉×#1301	2
C₂×#1301	19

Subgroups — D19×#1301 #18072761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×#1301 #18072761