Subgroups — C₁₉×#22115 #18028074

Order 4864.

720 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#479	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2295	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1949	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1942	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1941	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1927	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#479	C₄	1	8	yes	complemented
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#391	C₂²	1	1	yes	characteristic
32	C₁₉×#391	C₂²	1	1	yes	characteristic
33	C₁₉×#389	C₂²	1	1	yes	characteristic
34	C₁₉×#389	C₂²	1	1	yes	characteristic
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#389	C₂²	1	1	yes	characteristic
37	C₁₉×#387	—	2	1	no	—
38	C₁₉×#387	—	2	1	no	—
39	C₁₉×#387	—	2	1	no	—
40	C₁₉×#387	—	2	1	no	—
41	C₁₉×#382	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₁₉×#376	—	2	1	no	—
49	C₄³×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	C₂×C₄	1	4	yes	—
67	C₄×Q₈×C₁₉	—	2	2	no	—
68	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₂×C₄²×C₁₉	—	2	1	no	—
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×#107	—	4	1	no	—
95	C₁₉×#107	C₂×C₄	1	4	yes	—
96	C₁₉×#106	—	4	1	no	—
97	C₁₉×#106	C₂×C₄	1	4	yes	—
98	C₁₉×C₄⋊C₈	—	2	2	no	—
99	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
100	C₁₉×#103	—	4	1	no	—
101	C₁₉×#103	—	4	1	no	—
102	C₁₉×#103	C₂×C₄	1	4	yes	—
103	C₁₉×#103	C₂×C₄	1	4	yes	—
104	C₄×C₈×C₁₉	—	4	1	no	—
105	C₄×C₈×C₁₉	—	4	1	no	—
106	C₁₉×#95	—	2	1	no	—
107	C₁₉×#95	—	2	1	no	—
108	C₁₉×#95	—	2	1	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	4	2	no	—
167	C₄⋊C₄×C₁₉	—	4	2	no	—
168	C₄⋊C₄×C₁₉	—	4	2	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
172	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
173	C₄²×C₁₉	—	2	4	no	—
174	C₄²×C₁₉	—	2	2	no	—
175	C₄²×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	—	2	2	no	—
177	C₄²×C₁₉	—	2	1	no	—
178	C₄²×C₁₉	—	2	1	no	—
179	C₄²×C₁₉	—	2	1	no	—
180	C₄²×C₁₉	—	2	1	no	—
181	C₄²×C₁₉	—	4	1	no	—
182	C₄²×C₁₉	—	4	2	no	—
183	C₄²×C₁₉	—	4	2	no	—
184	C₄²×C₁₉	—	4	2	no	—
185	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
186	C₄²×C₁₉	#41	1	2	yes	—
187	#22115	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₁₉	—	2	2	no	—
190	Q₈×C₁₉	—	2	2	no	—
191	Q₈×C₁₉	—	4	1	no	—
192	Q₈×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
231	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
232	C₂×C₄×C₁₉	#135	1	2	yes	—
233	C₂×C₄×C₁₉	#135	1	2	yes	—
234	C₂×C₄×C₁₉	#137	1	2	yes	—
235	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
241	C₈×C₁₉	—	2	2	no	—
242	C₈×C₁₉	—	2	2	no	—
243	C₈×C₁₉	—	4	1	no	—
244	C₈×C₁₉	—	4	1	no	—
245	C₂×#479	C₂×C₁₉	1	1	yes	characteristic
246	C₄×#125	C₂×C₁₉	1	1	yes	characteristic
247	#2295	C₂×C₁₉	1	1	yes	characteristic
248	#1989	C₂×C₁₉	1	1	yes	characteristic
249	#1949	C₂×C₁₉	1	1	yes	characteristic
250	#1942	C₂×C₁₉	1	1	yes	characteristic
251	#1941	C₂×C₁₉	1	1	yes	characteristic
252	#1933	C₂×C₁₉	1	1	yes	characteristic
253	#1933	C₂×C₁₉	1	1	yes	characteristic
254	#1928	C₂×C₁₉	1	1	yes	characteristic
255	#1927	C₂×C₁₉	1	1	yes	characteristic
256	#1919	C₂×C₁₉	1	1	yes	characteristic
257	#1918	C₂×C₁₉	1	1	yes	characteristic
258	#1805	C₂×C₁₉	1	1	yes	characteristic
259	C₄×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic
260	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
261	C₂²×C₁₉	#536	1	1	yes	characteristic
262	C₂²×C₁₉	#537	1	1	yes	characteristic
263	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
264	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
265	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
266	C₂²×C₁₉	#575	1	1	yes	characteristic
267	C₄×C₁₉	—	2	2	no	—
268	C₄×C₁₉	—	2	2	no	—
269	C₄×C₁₉	—	2	2	no	—
270	C₄×C₁₉	—	2	2	no	—
271	C₄×C₁₉	—	2	2	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	4	2	no	—
275	C₄×C₁₉	—	4	2	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	—	8	1	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	—	8	1	no	—
281	C₄×C₁₉	#519	1	1	yes	characteristic
282	C₄×C₁₉	#520	1	1	yes	characteristic
283	C₄×C₁₉	#541	1	1	yes	characteristic
284	C₄×C₁₉	#542	1	1	yes	characteristic
285	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
287	#479	C₄×C₁₉	1	8	yes	complemented
288	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
300	#391	C₂²×C₁₉	1	1	yes	characteristic
301	#391	C₂²×C₁₉	1	1	yes	characteristic
302	#389	C₂²×C₁₉	1	1	yes	characteristic
303	#389	C₂²×C₁₉	1	1	yes	characteristic
304	#389	C₂²×C₁₉	1	1	yes	characteristic
305	#389	C₂²×C₁₉	1	1	yes	characteristic
306	#387	—	2	1	no	—
307	#387	—	2	1	no	—
308	#387	—	2	1	no	—
309	#387	—	2	1	no	—
310	#382	C₂²×C₁₉	1	1	yes	characteristic
311	C₄×C₄⋊C₄	—	2	1	no	—
312	C₄×C₄⋊C₄	—	2	1	no	—
313	C₄×C₄⋊C₄	—	2	1	no	—
314	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
315	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
316	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
317	#376	—	2	1	no	—
318	C₄³	C₂²×C₁₉	1	1	yes	characteristic
319	#340	C₂²×C₁₉	1	1	yes	characteristic
320	#340	C₂²×C₁₉	1	1	yes	characteristic
321	#340	C₂²×C₁₉	1	1	yes	characteristic
322	#340	C₂²×C₁₉	1	1	yes	characteristic
323	#340	C₂²×C₁₉	1	1	yes	characteristic
324	#340	C₂²×C₁₉	1	1	yes	characteristic
325	#340	C₂²×C₁₉	1	1	yes	characteristic
326	#340	C₂²×C₁₉	1	1	yes	characteristic
327	#336	C₂²×C₁₉	1	1	yes	characteristic
328	#336	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×C₁₉	#2323	1	1	yes	characteristic
330	C₂×C₁₉	C₄×#135	1	1	yes	characteristic
331	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
332	C₂×C₁₉	#3231	1	1	yes	characteristic
333	C₂×C₁₉	#3232	1	1	yes	characteristic
334	C₂×C₁₉	#3248	1	1	yes	characteristic
335	C₂×C₁₉	#3250	1	1	yes	characteristic
336	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
341	#125	—	2	2	no	—
342	#125	C₂×C₄×C₁₉	1	4	yes	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
364	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
365	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
366	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
370	#107	—	4	1	no	—
371	#107	C₂×C₄×C₁₉	1	4	yes	—
372	#106	—	4	1	no	—
373	#106	C₂×C₄×C₁₉	1	4	yes	—
374	C₄⋊C₈	—	2	2	no	—
375	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
376	#103	—	4	1	no	—
377	#103	—	4	1	no	—
378	#103	C₂×C₄×C₁₉	1	4	yes	—
379	#103	C₂×C₄×C₁₉	1	4	yes	—
380	C₄×C₈	—	4	1	no	—
381	C₄×C₈	—	4	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	C₁₉	#22115	1	1	yes	characteristic, direct product factor, Sylow
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
428	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	4	2	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
448	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
449	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	4	1	no	—
459	C₄²	—	4	2	no	—
460	C₄²	—	4	2	no	—
461	C₄²	—	4	2	no	—
462	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
463	C₄²	#41×C₁₉	1	2	yes	—
464	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
465	Q₈	—	2	2	no	—
466	Q₈	—	2	2	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	4	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
507	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
508	C₂×C₄	C₁₉×#135	1	2	yes	—
509	C₂×C₄	C₁₉×#135	1	2	yes	—
510	C₂×C₄	C₁₉×#137	1	2	yes	—
511	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
515	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
516	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
517	C₈	—	2	2	no	—
518	C₈	—	2	2	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	1	no	—
521	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
522	C₂²	C₁₉×#536	1	1	yes	characteristic
523	C₂²	C₁₉×#537	1	1	yes	characteristic
524	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
525	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
526	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
527	C₂²	C₁₉×#575	1	1	yes	characteristic
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	2	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₄	—	8	1	no	—
542	C₄	C₁₉×#519	1	1	yes	characteristic
543	C₄	C₁₉×#520	1	1	yes	characteristic
544	C₄	C₁₉×#541	1	1	yes	characteristic
545	C₄	C₁₉×#542	1	1	yes	characteristic
546	C₂	C₁₉×#2323	1	1	yes	characteristic
547	C₂	C₄×C₁₉×#135	1	1	yes	characteristic
548	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
549	C₂	C₁₉×#3231	1	1	yes	characteristic
550	C₂	C₁₉×#3232	1	1	yes	characteristic
551	C₂	C₁₉×#3248	1	1	yes	characteristic
552	C₂	C₁₉×#3250	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
18. C₁₉×#479	C₄	semidirect
187. #22115	C₁₉	direct (N × H)
287. #479	C₄×C₁₉	semidirect
395. C₁₉	#22115	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×#479	2
C₄×C₁₉×#125	2
C₁₉×#2295	2
C₁₉×#1989	2
C₁₉×#1949	2
C₁₉×#1942	2
C₁₉×#1941	2
C₁₉×#1933	2
C₁₉×#1928	2
C₁₉×#1927	2
C₁₉×#1919	2
C₁₉×#1918	2
C₁₉×#1805	2
C₄×C₁₉×C₄⋊C₈	2
#22115	19

Subgroups — C19×#22115 #18028074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22115 #18028074