Subgroups — C₁₉×#22148 #18028107

Order 4864.

820 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#462	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2295	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1981	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1969	C₂	1	2	yes	maximal
6	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1933	C₂	1	2	yes	maximal
8	C₁₉×#1878	C₂	1	2	yes	maximal
9	C₁₉×#1863	C₂	1	2	yes	maximal
10	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
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	C₁₉×#462	C₄	1	8	yes	complemented
17	C₂×C₁₉×#107	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₁₉×#103	C₂²	1	2	yes	—
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
25	C₁₉×#391	C₂²	1	2	yes	—
26	C₁₉×#391	C₂²	1	1	yes	characteristic
27	C₁₉×#391	C₂²	1	1	yes	characteristic
28	C₁₉×#389	—	2	1	no	—
29	C₁₉×#389	—	2	1	no	—
30	C₁₉×#389	C₂²	1	1	yes	characteristic
31	C₁₉×#389	C₂²	1	1	yes	characteristic
32	C₁₉×#387	—	2	1	no	—
33	C₁₉×#387	—	2	1	no	—
34	C₁₉×#384	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#376	—	2	1	no	—
40	C₄³×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
46	C₂×Q₁₆×C₁₉	—	4	2	no	—
47	C₂×Q₁₆×C₁₉	—	4	2	no	—
48	C₂×Q₁₆×C₁₉	C₂×C₄	1	8	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₁₉×C₄⋊Q₈	—	2	2	no	—
52	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
53	C₄×Q₈×C₁₉	—	2	2	no	—
54	C₄×Q₈×C₁₉	—	4	2	no	—
55	C₄×Q₈×C₁₉	—	4	2	no	—
56	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×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	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#107	—	4	2	no	—
80	C₁₉×C₄⋊C₈	—	2	2	no	—
81	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
82	C₁₉×#103	—	4	2	no	—
83	C₁₉×#103	—	4	2	no	—
84	C₁₉×#103	—	4	2	no	—
85	C₁₉×#103	C₂×C₄	1	8	yes	—
86	C₄×C₈×C₁₉	—	4	2	no	—
87	C₁₉×#95	—	2	1	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₁₉×#95	—	2	1	no	—
90	C₁₉×#95	—	2	1	no	—
91	C₁₉×#95	—	2	1	no	—
92	C₁₉×#95	—	2	1	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	—	2	2	no	—
95	C₁₉×#95	—	2	1	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
121	Q₁₆×C₁₉	—	4	8	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	4	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	4	2	no	—
139	C₄⋊C₄×C₁₉	—	4	2	no	—
140	C₄⋊C₄×C₁₉	—	4	4	no	—
141	C₄⋊C₄×C₁₉	—	4	2	no	—
142	C₄⋊C₄×C₁₉	—	4	2	no	—
143	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
144	C₄²×C₁₉	—	2	4	no	—
145	C₄²×C₁₉	—	2	2	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	2	1	no	—
148	C₄²×C₁₉	—	2	1	no	—
149	C₄²×C₁₉	—	2	1	no	—
150	C₄²×C₁₉	—	2	1	no	—
151	C₄²×C₁₉	—	4	1	no	—
152	C₄²×C₁₉	—	4	4	no	—
153	C₄²×C₁₉	—	4	2	no	—
154	C₄²×C₁₉	Q₁₆	1	4	yes	complemented
155	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
156	C₄²×C₁₉	#41	1	2	yes	—
157	#22148	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₁₉	—	2	2	no	—
160	Q₈×C₁₉	—	2	4	no	—
161	Q₈×C₁₉	—	2	4	no	—
162	Q₈×C₁₉	—	2	2	no	—
163	Q₈×C₁₉	—	4	1	no	—
164	Q₈×C₁₉	—	4	2	no	—
165	Q₈×C₁₉	—	4	1	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
199	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
200	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
201	C₂×C₄×C₁₉	#135	1	2	yes	—
202	C₂×C₄×C₁₉	#137	1	2	yes	—
203	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
209	C₈×C₁₉	—	2	4	no	—
210	C₈×C₁₉	—	4	2	no	—
211	C₂×#462	C₂×C₁₉	1	1	yes	characteristic
212	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
213	#2295	C₂×C₁₉	1	1	yes	characteristic
214	#1981	C₂×C₁₉	1	1	yes	characteristic
215	#1969	C₂×C₁₉	1	2	yes	—
216	#1947	C₂×C₁₉	1	1	yes	characteristic
217	#1933	C₂×C₁₉	1	2	yes	—
218	#1878	C₂×C₁₉	1	2	yes	—
219	#1863	C₂×C₁₉	1	2	yes	—
220	#1803	C₂×C₁₉	1	1	yes	characteristic
221	C₄×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic
222	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂²×C₁₉	#535	1	1	yes	characteristic
224	C₂²×C₁₉	#537	1	1	yes	characteristic
225	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
226	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
227	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
228	C₂²×C₁₉	#575	1	1	yes	characteristic
229	C₄×C₁₉	—	2	2	no	—
230	C₄×C₁₉	—	2	2	no	—
231	C₄×C₁₉	—	2	2	no	—
232	C₄×C₁₉	—	2	2	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	4	4	no	—
235	C₄×C₁₉	—	4	2	no	—
236	C₄×C₁₉	—	4	1	no	—
237	C₄×C₁₉	—	8	2	no	—
238	C₄×C₁₉	—	8	1	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	C₄×Q₁₆	1	4	yes	—
241	C₄×C₁₉	#518	1	1	yes	characteristic
242	C₄×C₁₉	#520	1	1	yes	characteristic
243	C₄×C₁₉	#540	1	1	yes	characteristic
244	C₄×C₁₉	#542	1	1	yes	characteristic
245	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
246	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
249	#462	C₄×C₁₉	1	8	yes	complemented
250	C₂×#107	C₂²×C₁₉	1	2	yes	—
251	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×#103	C₂²×C₁₉	1	2	yes	—
254	C₂×#103	C₂²×C₁₉	1	2	yes	—
255	C₂×#103	C₂²×C₁₉	1	2	yes	—
256	C₂×#103	C₂²×C₁₉	1	2	yes	—
257	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
258	#391	C₂²×C₁₉	1	2	yes	—
259	#391	C₂²×C₁₉	1	1	yes	characteristic
260	#391	C₂²×C₁₉	1	1	yes	characteristic
261	#389	—	2	1	no	—
262	#389	—	2	1	no	—
263	#389	C₂²×C₁₉	1	1	yes	characteristic
264	#389	C₂²×C₁₉	1	1	yes	characteristic
265	#387	—	2	1	no	—
266	#387	—	2	1	no	—
267	#384	C₂²×C₁₉	1	1	yes	characteristic
268	C₄×C₄⋊C₄	—	2	1	no	—
269	C₄×C₄⋊C₄	—	2	1	no	—
270	C₄×C₄⋊C₄	—	2	1	no	—
271	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
272	#376	—	2	1	no	—
273	C₄³	C₂²×C₁₉	1	1	yes	characteristic
274	#340	C₂²×C₁₉	1	2	yes	—
275	#340	C₂²×C₁₉	1	2	yes	—
276	#336	C₂²×C₁₉	1	2	yes	—
277	C₂×C₁₉	#2324	1	1	yes	characteristic
278	C₂×C₁₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
279	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
280	C₂×C₁₉	#3209	1	1	yes	characteristic
281	C₂×C₁₉	#3212	1	1	yes	characteristic
282	C₂×C₁₉	#3248	1	1	yes	characteristic
283	C₂×C₁₉	#3249	1	1	yes	characteristic
284	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
285	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
286	C₂×Q₁₆	—	4	2	no	—
287	C₂×Q₁₆	—	4	2	no	—
288	C₂×Q₁₆	C₂×C₄×C₁₉	1	8	yes	—
289	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
290	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	4	2	no	—
295	C₄×Q₈	—	4	2	no	—
296	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
313	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
314	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
319	#107	—	4	2	no	—
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
322	#103	—	4	2	no	—
323	#103	—	4	2	no	—
324	#103	—	4	2	no	—
325	#103	C₂×C₄×C₁₉	1	8	yes	—
326	C₄×C₈	—	4	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	1	no	—
329	#95	—	2	1	no	—
330	#95	—	2	1	no	—
331	#95	—	2	1	no	—
332	#95	—	2	1	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	1	no	—
336	C₁₉	#22148	1	1	yes	characteristic, direct product factor, Sylow
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
348	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
362	Q₁₆	—	4	8	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	4	1	no	—
393	C₄²	—	4	4	no	—
394	C₄²	—	4	2	no	—
395	C₄²	Q₁₆×C₁₉	1	4	yes	complemented
396	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
397	C₄²	#41×C₁₉	1	2	yes	—
398	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
399	Q₈	—	2	2	no	—
400	Q₈	—	2	4	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	2	4	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
437	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
438	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
439	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
440	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
441	C₂×C₄	C₁₉×#135	1	2	yes	—
442	C₂×C₄	C₁₉×#137	1	2	yes	—
443	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
445	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
449	C₈	—	2	4	no	—
450	C₈	—	4	2	no	—
451	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
452	C₂²	C₁₉×#535	1	1	yes	characteristic
453	C₂²	C₁₉×#537	1	1	yes	characteristic
454	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
455	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
456	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
457	C₂²	C₁₉×#575	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	4	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	1	no	—
468	C₄	—	8	1	no	—
469	C₄	C₄×Q₁₆×C₁₉	1	4	yes	—
470	C₄	C₁₉×#518	1	1	yes	characteristic
471	C₄	C₁₉×#520	1	1	yes	characteristic
472	C₄	C₁₉×#540	1	1	yes	characteristic
473	C₄	C₁₉×#542	1	1	yes	characteristic
474	C₂	C₁₉×#2324	1	1	yes	characteristic
475	C₂	C₂×C₄×Q₁₆×C₁₉	1	1	yes	characteristic
476	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
477	C₂	C₁₉×#3209	1	1	yes	characteristic
478	C₂	C₁₉×#3212	1	1	yes	characteristic
479	C₂	C₁₉×#3248	1	1	yes	characteristic
480	C₂	C₁₉×#3249	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₁₉×#462	C₄	semidirect
154. C₄²×C₁₉	Q₁₆	semidirect
157. #22148	C₁₉	direct (N × H)
249. #462	C₄×C₁₉	semidirect
336. C₁₉	#22148	direct (N × H)
395. C₄²	Q₁₆×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×#462	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#2295	2
C₁₉×#1981	2
C₁₉×#1969	2
C₁₉×#1947	2
C₁₉×#1933	2
C₁₉×#1878	2
C₁₉×#1863	2
C₁₉×#1803	2
C₄×C₁₉×C₄⋊C₈	2
#22148	19

Subgroups — C19×#22148 #18028107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22148 #18028107