Subgroups — C₁₉×#24832 #18030791

Order 4864.

776 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#477	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#441	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2568	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2351	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2085	C₂	1	2	yes	maximal
6	C₁₉×#2068	C₂	1	2	yes	maximal
7	C₁₉×#1993	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1940	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1878	C₂	1	2	yes	maximal
10	C₁₉×#1805	C₂	1	2	yes	maximal
11	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#477	—	2	4	no	—
18	C₁₉×#441	—	2	4	no	—
19	C₂×C₁₉×#107	C₂²	1	2	yes	—
20	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	2	yes	—
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
28	C₁₉×#400	—	2	1	no	—
29	C₁₉×#400	—	2	1	no	—
30	C₁₉×#391	—	2	2	no	—
31	C₁₉×#391	C₂²	1	2	yes	—
32	C₁₉×#389	—	2	2	no	—
33	C₁₉×#389	C₂²	1	2	yes	—
34	C₁₉×#382	—	2	1	no	—
35	C₁₉×#382	C₂²	1	1	yes	characteristic
36	C₁₉×#382	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₁₉	—	2	2	no	—
47	C₂×Q₁₆×C₁₉	—	2	2	no	—
48	C₂×Q₁₆×C₁₉	Q₈	1	4	yes	complemented
49	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₁₉×C₄⋊Q₈	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₄×Q₈×C₁₉	—	2	2	no	—
55	C₄×Q₈×C₁₉	—	2	4	no	—
56	C₄×Q₈×C₁₉	—	2	2	no	—
57	C₄×Q₈×C₁₉	—	2	2	no	—
58	C₄×Q₈×C₁₉	—	4	2	no	—
59	C₄×Q₈×C₁₉	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#107	—	2	4	no	—
76	C₁₉×#106	—	2	2	no	—
77	C₁₉×C₄⋊C₈	—	2	2	no	—
78	C₁₉×C₄⋊C₈	—	4	2	no	—
79	C₁₉×#103	—	2	2	no	—
80	C₁₉×#103	—	2	4	no	—
81	C₁₉×#103	—	2	2	no	—
82	C₁₉×#103	—	4	2	no	—
83	C₁₉×#97	—	2	2	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₁₉×#95	—	2	2	no	—
88	C₁₉×#95	—	2	2	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	D₄	1	1	yes	characteristic
92	C₁₉×#95	D₄	1	1	yes	characteristic
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	1	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	2	1	no	—
99	C₂×Q₈×C₁₉	—	2	1	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	4	4	no	—
102	C₂×Q₈×C₁₉	—	4	2	no	—
103	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
105	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
106	C₂×Q₈×C₁₉	#41	1	2	yes	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₁₉	—	2	8	no	—
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	4	2	no	—
137	C₄⋊C₄×C₁₉	—	4	4	no	—
138	C₄⋊C₄×C₁₉	—	4	4	no	—
139	C₄⋊C₄×C₁₉	—	4	2	no	—
140	C₄⋊C₄×C₁₉	—	4	2	no	—
141	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₄²×C₁₉	—	2	4	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	—	4	4	no	—
146	C₄²×C₁₉	—	4	2	no	—
147	C₄²×C₁₉	C₂×D₄	1	2	yes	—
148	C₄²×C₁₉	#41	1	2	yes	—
149	#24832	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₉	—	2	2	no	—
152	Q₈×C₁₉	—	2	2	no	—
153	Q₈×C₁₉	—	2	2	no	—
154	Q₈×C₁₉	—	2	2	no	—
155	Q₈×C₁₉	—	2	2	no	—
156	Q₈×C₁₉	—	4	1	no	—
157	Q₈×C₁₉	—	4	1	no	—
158	Q₈×C₁₉	—	8	4	no	—
159	Q₈×C₁₉	C₂²⋊Q₈	1	4	yes	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	#121	1	2	yes	—
184	C₂×C₄×C₁₉	#121	1	2	yes	—
185	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
191	C₈×C₁₉	—	2	2	no	—
192	C₈×C₁₉	—	4	1	no	—
193	C₈×C₁₉	—	4	2	no	—
194	C₂×#477	C₂×C₁₉	1	1	yes	characteristic
195	C₂×#441	C₂×C₁₉	1	1	yes	characteristic
196	#2568	C₂×C₁₉	1	1	yes	characteristic
197	#2351	C₂×C₁₉	1	1	yes	characteristic
198	#2085	C₂×C₁₉	1	2	yes	—
199	#2068	C₂×C₁₉	1	2	yes	—
200	#1993	C₂×C₁₉	1	1	yes	characteristic
201	#1940	C₂×C₁₉	1	1	yes	characteristic
202	#1878	C₂×C₁₉	1	2	yes	—
203	#1805	C₂×C₁₉	1	1	yes	characteristic
204	#1805	C₂×C₁₉	1	2	yes	—
205	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
206	C₂²×C₁₉	#546	1	1	yes	characteristic
207	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
208	C₂²×C₁₉	#575	1	2	yes	—
209	C₂²×C₁₉	#578	1	2	yes	—
210	C₄×C₁₉	—	2	4	no	—
211	C₄×C₁₉	—	2	2	no	—
212	C₄×C₁₉	—	2	2	no	—
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	4	2	no	—
215	C₄×C₁₉	—	4	2	no	—
216	C₄×C₁₉	—	4	2	no	—
217	C₄×C₁₉	—	8	2	no	—
218	C₄×C₁₉	—	8	1	no	—
219	C₄×C₁₉	—	8	2	no	—
220	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
221	C₄×C₁₉	#537	1	1	yes	characteristic
222	C₄×C₁₉	#552	1	1	yes	characteristic
223	C₄×C₁₉	#554	1	1	yes	characteristic
224	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
228	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
229	#477	—	2	4	no	—
230	#441	—	2	4	no	—
231	C₂×#107	C₂²×C₁₉	1	2	yes	—
232	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
235	C₂×#103	C₂²×C₁₉	1	2	yes	—
236	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#103	C₂²×C₁₉	1	2	yes	—
239	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
240	#400	—	2	1	no	—
241	#400	—	2	1	no	—
242	#391	—	2	2	no	—
243	#391	C₂²×C₁₉	1	2	yes	—
244	#389	—	2	2	no	—
245	#389	C₂²×C₁₉	1	2	yes	—
246	#382	—	2	1	no	—
247	#382	C₂²×C₁₉	1	2	yes	—
248	#382	C₂²×C₁₉	1	1	yes	characteristic
249	C₄×C₄⋊C₄	—	2	1	no	—
250	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
251	#340	C₂²×C₁₉	1	2	yes	—
252	#340	C₂²×C₁₉	1	2	yes	—
253	#340	C₂²×C₁₉	1	2	yes	—
254	#336	C₂²×C₁₉	1	2	yes	—
255	C₂×C₁₉	#2417	1	1	yes	characteristic
256	C₂×C₁₉	#3040	1	1	yes	characteristic
257	C₂×C₁₉	#3044	1	1	yes	characteristic
258	C₂×C₁₉	#3313	1	2	yes	—
259	C₂×C₁₉	#3390	1	2	yes	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
262	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	Q₈×C₁₉	1	4	yes	complemented
266	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
267	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	—	2	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	4	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	4	2	no	—
276	C₄×Q₈	D₄×C₁₉	1	4	yes	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
292	#107	—	2	4	no	—
293	#106	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	4	2	no	—
296	#103	—	2	2	no	—
297	#103	—	2	4	no	—
298	#103	—	2	2	no	—
299	#103	—	4	2	no	—
300	#97	—	2	2	no	—
301	#95	—	2	1	no	—
302	#95	—	2	2	no	—
303	#95	—	2	1	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	D₄×C₁₉	1	1	yes	characteristic
309	#95	D₄×C₁₉	1	1	yes	characteristic
310	C₁₉	#24832	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
322	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
323	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
324	C₂×Q₈	#41×C₁₉	1	2	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
336	Q₁₆	—	2	8	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	4	no	—
364	C₄²	—	4	2	no	—
365	C₄²	C₂×D₄×C₁₉	1	2	yes	—
366	C₄²	#41×C₁₉	1	2	yes	—
367	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	2	2	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	Q₈	—	4	1	no	—
374	Q₈	—	4	1	no	—
375	Q₈	—	8	4	no	—
376	Q₈	C₁₉×C₂²⋊Q₈	1	4	yes	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	C₁₉×#121	1	2	yes	—
401	C₂×C₄	C₁₉×#121	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
404	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
406	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	2	no	—
411	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
412	C₂²	C₁₉×#546	1	1	yes	characteristic
413	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
414	C₂²	C₁₉×#575	1	2	yes	—
415	C₂²	C₁₉×#578	1	2	yes	—
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	1	no	—
425	C₄	—	8	2	no	—
426	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
427	C₄	C₁₉×#537	1	1	yes	characteristic
428	C₄	C₁₉×#552	1	1	yes	characteristic
429	C₄	C₁₉×#554	1	1	yes	characteristic
430	C₂	C₁₉×#2417	1	1	yes	characteristic
431	C₂	C₁₉×#3040	1	1	yes	characteristic
432	C₂	C₁₉×#3044	1	1	yes	characteristic
433	C₂	C₁₉×#3313	1	2	yes	—
434	C₂	C₁₉×#3390	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
48. C₂×Q₁₆×C₁₉	Q₈	semidirect
149. #24832	C₁₉	direct (N × H)
265. C₂×Q₁₆	Q₈×C₁₉	semidirect
310. C₁₉	#24832	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#477	2
C₂×C₁₉×#441	2
C₁₉×#2568	2
C₁₉×#2351	2
C₁₉×#2085	2
C₁₉×#2068	2
C₁₉×#1993	2
C₁₉×#1940	2
C₁₉×#1878	2
C₁₉×#1805	2
#24832	19

Subgroups — C19×#24832 #18030791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24832 #18030791