Subgroups — C₁₉×#26026 #18031985

Order 4864.

710 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2551	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2068	C₂	1	2	yes	maximal
4	C₁₉×#2024	C₂	1	2	yes	maximal
5	C₁₉×#1987	C₂	1	2	yes	maximal
6	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1939	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1921	C₂	1	2	yes	maximal
9	C₁₉×#1834	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#107	C₂²	1	2	yes	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#395	—	2	2	no	—
23	C₁₉×#391	C₂²	1	2	yes	—
24	C₁₉×#389	—	2	1	no	—
25	C₁₉×#389	C₂²	1	2	yes	—
26	C₁₉×#387	—	2	2	no	—
27	C₁₉×#384	C₂²	1	1	yes	characteristic
28	C₁₉×#384	C₂²	1	1	yes	characteristic
29	C₁₉×#382	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	1	yes	characteristic
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₉	—	2	2	no	—
42	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₁₉×C₄⋊Q₈	—	2	4	no	—
47	C₁₉×C₄⋊Q₈	—	4	2	no	—
48	C₁₉×C₄⋊Q₈	—	4	4	no	—
49	C₄×Q₈×C₁₉	—	2	2	no	—
50	C₄×Q₈×C₁₉	Q₈	1	4	yes	complemented
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×#107	—	2	4	no	—
71	C₁₉×C₄⋊C₈	—	2	2	no	—
72	C₁₉×C₄⋊C₈	—	4	2	no	—
73	C₁₉×#103	—	2	2	no	—
74	C₁₉×#103	—	2	2	no	—
75	C₁₉×#103	—	4	2	no	—
76	C₄×C₈×C₁₉	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	1	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	D₄	1	2	yes	—
83	C₂×Q₈×C₁₉	—	2	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	—	4	4	no	—
89	C₂×Q₈×C₁₉	—	4	4	no	—
90	C₂×Q₈×C₁₉	—	8	2	no	—
91	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₁₉	—	2	1	no	—
104	C₂×C₈×C₁₉	—	2	1	no	—
105	C₂×C₈×C₁₉	—	2	1	no	—
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	4	4	no	—
122	C₄⋊C₄×C₁₉	—	4	4	no	—
123	C₄⋊C₄×C₁₉	—	4	2	no	—
124	C₄⋊C₄×C₁₉	—	4	2	no	—
125	C₄⋊C₄×C₁₉	—	8	1	no	—
126	C₄⋊C₄×C₁₉	—	8	1	no	—
127	C₄⋊C₄×C₁₉	Q₁₆	1	4	yes	—
128	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
129	C₄⋊C₄×C₁₉	#41	1	2	yes	—
130	C₄⋊C₄×C₁₉	#41	1	2	yes	—
131	C₄²×C₁₉	—	2	4	no	—
132	C₄²×C₁₉	—	2	2	no	—
133	C₄²×C₁₉	—	2	2	no	—
134	C₄²×C₁₉	—	4	2	no	—
135	C₄²×C₁₉	—	8	2	no	—
136	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
137	C₄²×C₁₉	#41	1	2	yes	—
138	#26026	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₁₉	—	2	2	no	—
141	Q₈×C₁₉	—	2	2	no	—
142	Q₈×C₁₉	—	4	1	no	—
143	Q₈×C₁₉	—	4	1	no	—
144	Q₈×C₁₉	—	8	8	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
173	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	4	2	no	—
183	C₈×C₁₉	—	4	1	no	—
184	#2551	C₂×C₁₉	1	1	yes	characteristic
185	#2355	C₂×C₁₉	1	1	yes	characteristic
186	#2068	C₂×C₁₉	1	2	yes	—
187	#2024	C₂×C₁₉	1	2	yes	—
188	#1987	C₂×C₁₉	1	2	yes	—
189	#1947	C₂×C₁₉	1	1	yes	characteristic
190	#1939	C₂×C₁₉	1	1	yes	characteristic
191	#1921	C₂×C₁₉	1	2	yes	—
192	#1834	C₂×C₁₉	1	1	yes	characteristic
193	#1803	C₂×C₁₉	1	1	yes	characteristic
194	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
195	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
196	C₂²×C₁₉	#546	1	1	yes	characteristic
197	C₂²×C₁₉	#548	1	1	yes	characteristic
198	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
199	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₂²×C₁₉	#577	1	1	yes	characteristic
201	C₂²×C₁₉	#577	1	1	yes	characteristic
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	4	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	4	2	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	8	2	no	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	#477	1	4	yes	—
212	C₄×C₁₉	#533	1	1	yes	characteristic
213	C₄×C₁₉	#544	1	1	yes	characteristic
214	C₄×C₁₉	#555	1	1	yes	characteristic
215	C₄×C₁₉	#556	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	—	2	1	no	—
217	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
218	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
219	C₂×#107	C₂²×C₁₉	1	2	yes	—
220	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
222	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#103	C₂²×C₁₉	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
226	#395	—	2	2	no	—
227	#391	C₂²×C₁₉	1	2	yes	—
228	#389	—	2	1	no	—
229	#389	C₂²×C₁₉	1	2	yes	—
230	#387	—	2	2	no	—
231	#384	C₂²×C₁₉	1	1	yes	characteristic
232	#384	C₂²×C₁₉	1	1	yes	characteristic
233	#382	—	2	1	no	—
234	C₄×C₄⋊C₄	—	2	1	no	—
235	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
236	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
238	#340	C₂²×C₁₉	1	2	yes	—
239	#340	C₂²×C₁₉	1	2	yes	—
240	#340	C₂²×C₁₉	1	2	yes	—
241	#340	C₂²×C₁₉	1	1	yes	characteristic
242	#340	C₂²×C₁₉	1	2	yes	—
243	#340	C₂²×C₁₉	1	1	yes	characteristic
244	#336	C₂²×C₁₉	1	2	yes	—
245	C₂×C₁₉	#2439	1	1	yes	characteristic
246	C₂×C₁₉	C₂×#477	1	1	yes	characteristic
247	C₂×C₁₉	#3084	1	1	yes	characteristic
248	C₂×C₁₉	#3299	1	1	yes	characteristic
249	C₂×C₁₉	#3324	1	1	yes	characteristic
250	C₂×C₁₉	#3363	1	1	yes	characteristic
251	C₂×C₁₉	#3373	1	1	yes	characteristic
252	C₂²×Q₈	—	2	2	no	—
253	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
257	C₄⋊Q₈	—	2	4	no	—
258	C₄⋊Q₈	—	4	2	no	—
259	C₄⋊Q₈	—	4	4	no	—
260	C₄×Q₈	—	2	2	no	—
261	C₄×Q₈	Q₈×C₁₉	1	4	yes	complemented
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
270	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
280	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
281	#107	—	2	4	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	4	2	no	—
284	#103	—	2	2	no	—
285	#103	—	2	2	no	—
286	#103	—	4	2	no	—
287	C₄×C₈	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	1	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	D₄×C₁₉	1	2	yes	—
294	C₁₉	#26026	1	1	yes	characteristic, direct product factor, Sylow
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	4	4	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×Q₈	—	8	2	no	—
303	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	8	1	no	—
338	C₄⋊C₄	—	8	1	no	—
339	C₄⋊C₄	Q₁₆×C₁₉	1	4	yes	—
340	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
341	C₄⋊C₄	#41×C₁₉	1	2	yes	—
342	C₄⋊C₄	#41×C₁₉	1	2	yes	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	4	2	no	—
347	C₄²	—	8	2	no	—
348	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
349	C₄²	#41×C₁₉	1	2	yes	—
350	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	Q₈	—	2	2	no	—
353	Q₈	—	4	1	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	8	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
382	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
383	C₂×C₄	C₂×Q₁₆×C₁₉	1	4	yes	—
384	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
385	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
386	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
388	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	1	no	—
395	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
396	C₂²	C₁₉×#546	1	1	yes	characteristic
397	C₂²	C₁₉×#548	1	1	yes	characteristic
398	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
399	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂²	C₁₉×#577	1	1	yes	characteristic
401	C₂²	C₁₉×#577	1	1	yes	characteristic
402	C₄	—	2	4	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₁₉×#477	1	4	yes	—
412	C₄	C₁₉×#533	1	1	yes	characteristic
413	C₄	C₁₉×#544	1	1	yes	characteristic
414	C₄	C₁₉×#555	1	1	yes	characteristic
415	C₄	C₁₉×#556	1	1	yes	characteristic
416	C₂	C₁₉×#2439	1	1	yes	characteristic
417	C₂	C₂×C₁₉×#477	1	1	yes	characteristic
418	C₂	C₁₉×#3084	1	1	yes	characteristic
419	C₂	C₁₉×#3299	1	1	yes	characteristic
420	C₂	C₁₉×#3324	1	1	yes	characteristic
421	C₂	C₁₉×#3363	1	1	yes	characteristic
422	C₂	C₁₉×#3373	1	1	yes	characteristic

	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
50. C₄×Q₈×C₁₉	Q₈	semidirect
138. #26026	C₁₉	direct (N × H)
261. C₄×Q₈	Q₈×C₁₉	semidirect
294. C₁₉	#26026	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2551	2
C₁₉×#2355	2
C₁₉×#2068	2
C₁₉×#2024	2
C₁₉×#1987	2
C₁₉×#1947	2
C₁₉×#1939	2
C₁₉×#1921	2
C₁₉×#1834	2
C₁₉×#1803	2
C₄×C₁₉×#103	2
#26026	19

Subgroups — C19×#26026 #18031985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26026 #18031985