Subgroups — C₁₉×#22971 #18028930

Order 4864.

782 conjugacy classes of subgroups.

The subgroup lattice has 432 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	C₁₉×#2369	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1943	C₂	1	2	yes	maximal
7	C₁₉×#1918	C₂	1	2	yes	maximal
8	C₁₉×#1865	C₂	1	2	yes	maximal
9	C₁₉×#1770	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1763	C₂	1	2	yes	maximal
11	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#477	C₄	1	8	yes	complemented
16	C₂×C₁₉×#107	C₂²	1	2	yes	—
17	C₂×C₁₉×#106	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#391	—	2	2	no	—
25	C₁₉×#389	—	2	2	no	—
26	C₁₉×#389	—	2	1	no	—
27	C₁₉×#389	C₂²	1	2	yes	—
28	C₁₉×#389	C₂²	1	2	yes	—
29	C₁₉×#384	—	2	1	no	—
30	C₁₉×#384	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#340	C₂²	1	1	yes	characteristic
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	1	yes	characteristic
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
49	C₄×Q₈×C₁₉	—	2	2	no	—
50	C₄×Q₈×C₁₉	—	2	4	no	—
51	C₄×Q₈×C₁₉	—	4	2	no	—
52	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	—	2	2	no	—
71	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#107	C₂×C₄	1	8	yes	—
74	C₁₉×#106	—	4	2	no	—
75	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
76	C₁₉×#103	—	2	2	no	—
77	C₁₉×#103	C₂×C₄	1	8	yes	—
78	C₁₉×#103	Q₈	1	4	yes	complemented
79	C₁₉×#97	—	4	2	no	—
80	C₄×C₈×C₁₉	—	2	2	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	D₄	1	2	yes	—
86	C₂×Q₈×C₁₉	—	2	4	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×Q₈×C₁₉	—	8	1	no	—
91	C₂×Q₈×C₁₉	—	8	1	no	—
92	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
93	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
94	C₂×Q₈×C₁₉	#41	1	2	yes	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
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×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	1	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	C₂×C₈×C₁₉	—	2	1	no	—
113	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
114	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
115	C₄⋊C₄×C₁₉	—	2	4	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	4	4	no	—
127	C₄⋊C₄×C₁₉	—	4	2	no	—
128	C₄⋊C₄×C₁₉	—	8	1	no	—
129	C₄⋊C₄×C₁₉	—	8	2	no	—
130	C₄⋊C₄×C₁₉	—	8	2	no	—
131	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
132	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
134	C₄²×C₁₉	—	2	4	no	—
135	C₄²×C₁₉	—	2	2	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	4	4	no	—
138	C₄²×C₁₉	—	4	2	no	—
139	C₄²×C₁₉	—	8	2	no	—
140	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
141	C₄²×C₁₉	#41	1	2	yes	—
142	#22971	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₁₉	—	2	2	no	—
145	Q₈×C₁₉	—	2	2	no	—
146	Q₈×C₁₉	—	2	2	no	—
147	Q₈×C₁₉	—	8	4	no	—
148	Q₈×C₁₉	C₄×Q₈	1	4	yes	—
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	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
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	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₉	#137	1	2	yes	—
178	C₂×C₄×C₁₉	#137	1	2	yes	—
179	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
185	C₈×C₁₉	—	2	4	no	—
186	C₈×C₁₉	—	2	2	no	—
187	C₈×C₁₉	—	4	1	no	—
188	C₂×#477	C₂×C₁₉	1	1	yes	characteristic
189	#2369	C₂×C₁₉	1	1	yes	characteristic
190	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
191	#1990	C₂×C₁₉	1	1	yes	characteristic
192	#1948	C₂×C₁₉	1	1	yes	characteristic
193	#1943	C₂×C₁₉	1	2	yes	—
194	#1918	C₂×C₁₉	1	2	yes	—
195	#1865	C₂×C₁₉	1	2	yes	—
196	#1770	C₂×C₁₉	1	1	yes	characteristic
197	#1763	C₂×C₁₉	1	2	yes	—
198	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
199	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂²×C₁₉	#546	1	1	yes	characteristic
201	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
204	C₂²×C₁₉	#576	1	1	yes	characteristic
205	C₂²×C₁₉	#577	1	1	yes	characteristic
206	C₄×C₁₉	—	2	4	no	—
207	C₄×C₁₉	—	2	2	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	4	2	no	—
212	C₄×C₁₉	—	4	4	no	—
213	C₄×C₁₉	—	8	1	no	—
214	C₄×C₁₉	—	8	2	no	—
215	C₄×C₁₉	#441	1	4	yes	—
216	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
217	C₄×C₁₉	#520	1	1	yes	characteristic
218	C₄×C₁₉	#552	1	1	yes	characteristic
219	C₄×C₁₉	#554	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
222	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
223	#477	C₄×C₁₉	1	8	yes	complemented
224	C₂×#107	C₂²×C₁₉	1	2	yes	—
225	C₂×#106	C₂²×C₁₉	1	2	yes	—
226	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#103	C₂²×C₁₉	1	2	yes	—
229	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#97	C₂²×C₁₉	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
232	#391	—	2	2	no	—
233	#389	—	2	1	no	—
234	#389	—	2	2	no	—
235	#389	C₂²×C₁₉	1	2	yes	—
236	#389	C₂²×C₁₉	1	2	yes	—
237	#384	—	2	1	no	—
238	#384	C₂²×C₁₉	1	1	yes	characteristic
239	C₄×C₄⋊C₄	—	2	1	no	—
240	C₄×C₄⋊C₄	—	2	1	no	—
241	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
242	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
243	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
244	#340	C₂²×C₁₉	1	2	yes	—
245	#340	C₂²×C₁₉	1	1	yes	characteristic
246	#340	C₂²×C₁₉	1	2	yes	—
247	#340	C₂²×C₁₉	1	1	yes	characteristic
248	#340	C₂²×C₁₉	1	2	yes	—
249	#336	C₂²×C₁₉	1	2	yes	—
250	C₂×C₁₉	#2360	1	1	yes	characteristic
251	C₂×C₁₉	C₂×#441	1	1	yes	characteristic
252	C₂×C₁₉	#2946	1	1	yes	characteristic
253	C₂×C₁₉	#3329	1	1	yes	characteristic
254	C₂×C₁₉	#3333	1	1	yes	characteristic
255	C₂×C₁₉	#3385	1	1	yes	characteristic
256	C₂×C₁₉	#3387	1	1	yes	characteristic
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
264	C₄×Q₈	—	2	2	no	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	4	2	no	—
267	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
287	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
288	#107	C₂×C₄×C₁₉	1	8	yes	—
289	#106	—	4	2	no	—
290	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
291	#103	—	2	2	no	—
292	#103	C₂×C₄×C₁₉	1	8	yes	—
293	#103	Q₈×C₁₉	1	4	yes	complemented
294	#97	—	4	2	no	—
295	C₄×C₈	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	1	no	—
300	#95	D₄×C₁₉	1	2	yes	—
301	C₁₉	#22971	1	1	yes	characteristic, direct product factor, Sylow
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	8	1	no	—
307	C₂×Q₈	—	8	1	no	—
308	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
309	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
310	C₂×Q₈	#41×C₁₉	1	2	yes	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
330	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	8	1	no	—
345	C₄⋊C₄	—	8	2	no	—
346	C₄⋊C₄	—	8	2	no	—
347	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
348	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
349	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
350	C₄²	—	2	4	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	4	4	no	—
354	C₄²	—	4	2	no	—
355	C₄²	—	8	2	no	—
356	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
357	C₄²	#41×C₁₉	1	2	yes	—
358	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	8	4	no	—
363	Q₈	C₄×Q₈×C₁₉	1	4	yes	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
391	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
392	C₂×C₄	C₁₉×#137	1	2	yes	—
393	C₂×C₄	C₁₉×#137	1	2	yes	—
394	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
398	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
400	C₈	—	2	4	no	—
401	C₈	—	2	2	no	—
402	C₈	—	4	1	no	—
403	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
404	C₂²	C₁₉×#546	1	1	yes	characteristic
405	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
406	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
407	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
408	C₂²	C₁₉×#576	1	1	yes	characteristic
409	C₂²	C₁₉×#577	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	4	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	2	no	—
419	C₄	C₁₉×#441	1	4	yes	—
420	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
421	C₄	C₁₉×#520	1	1	yes	characteristic
422	C₄	C₁₉×#552	1	1	yes	characteristic
423	C₄	C₁₉×#554	1	1	yes	characteristic
424	C₂	C₁₉×#2360	1	1	yes	characteristic
425	C₂	C₂×C₁₉×#441	1	1	yes	characteristic
426	C₂	C₁₉×#2946	1	1	yes	characteristic
427	C₂	C₁₉×#3329	1	1	yes	characteristic
428	C₂	C₁₉×#3333	1	1	yes	characteristic
429	C₂	C₁₉×#3385	1	1	yes	characteristic
430	C₂	C₁₉×#3387	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 ◁ C₄×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₉×#477	C₄	semidirect
78. C₁₉×#103	Q₈	semidirect
142. #22971	C₁₉	direct (N × H)
223. #477	C₄×C₁₉	semidirect
293. #103	Q₈×C₁₉	semidirect
301. C₁₉	#22971	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
C₁₉×#2369	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#1990	2
C₁₉×#1948	2
C₁₉×#1943	2
C₁₉×#1918	2
C₁₉×#1865	2
C₁₉×#1770	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
#22971	19

Subgroups — C19×#22971 #18028930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22971 #18028930