Subgroups — C₁₉×#22838 #18028797

Order 4864.

732 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2293	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1955	C₂	1	2	yes	maximal
3	C₁₉×#1924	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1923	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1818	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1771	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1750	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#117	C₂²	1	2	yes	—
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₉×#97	C₂²	1	2	yes	—
19	C₂×C₁₉×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
21	C₁₉×#390	C₄	1	1	yes	characteristic
22	C₁₉×#390	C₄	1	1	yes	characteristic
23	C₁₉×#389	C₄	1	1	yes	characteristic
24	C₁₉×#389	C₄	1	1	yes	characteristic
25	C₁₉×#388	C₄	1	2	yes	—
26	C₁₉×#388	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₄³×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#336	C₂²	1	1	yes	characteristic
31	C₁₉×#336	C₂²	1	2	yes	—
32	C₁₉×#336	C₂²	1	1	yes	characteristic
33	C₁₉×#336	C₂²	1	2	yes	—
34	C₁₉×#336	C₂²	1	1	yes	characteristic
35	C₁₉×#336	C₂²	1	2	yes	—
36	C₁₉×#336	C₂²	1	1	yes	characteristic
37	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
43	C₄×D₄×C₁₉	—	2	2	no	—
44	C₄×D₄×C₁₉	—	2	2	no	—
45	C₁₉×#117	—	4	2	no	—
46	C₁₉×#117	—	4	2	no	—
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×C₄⋊C₈	—	2	4	no	—
66	C₁₉×C₄⋊C₈	—	2	4	no	—
67	C₁₉×C₂²⋊C₈	—	2	4	no	—
68	C₁₉×C₂²⋊C₈	—	2	4	no	—
69	C₁₉×C₂²⋊C₈	—	4	2	no	—
70	C₁₉×C₂²⋊C₈	—	4	2	no	—
71	C₁₉×#97	—	2	4	no	—
72	C₁₉×#97	—	4	2	no	—
73	C₄×C₈×C₁₉	—	4	2	no	—
74	C₁₉×#95	C₂×C₄	1	2	yes	—
75	C₁₉×#95	C₂×C₄	1	2	yes	—
76	C₁₉×#95	C₂×C₄	1	2	yes	—
77	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
78	C₂×D₄×C₁₉	—	2	2	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	#41	1	4	yes	—
109	C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	4	2	no	—
113	C₄⋊C₄×C₁₉	—	4	2	no	—
114	C₂²⋊C₄×C₁₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₉	—	2	4	no	—
116	C₂²⋊C₄×C₁₉	—	4	2	no	—
117	C₂²⋊C₄×C₁₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₉	—	4	2	no	—
119	C₄²×C₁₉	—	2	2	no	—
120	C₄²×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	C₄²×C₁₉	—	2	2	no	—
123	C₄²×C₁₉	—	2	2	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	—	4	1	no	—
126	C₄²×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	#41	1	2	yes	—
128	C₄²×C₁₉	#41	1	2	yes	—
129	#22838	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
138	D₄×C₁₉	—	4	4	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	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	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	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	2	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	#117	1	2	yes	—
168	C₂×C₄×C₁₉	#117	1	2	yes	—
169	C₂×C₄×C₁₉	#131	1	2	yes	—
170	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
174	C₈×C₁₉	—	2	4	no	—
175	C₈×C₁₉	—	4	2	no	—
176	C₈×C₁₉	—	4	2	no	—
177	C₈×C₁₉	—	4	2	no	—
178	#2293	C₂×C₁₉	1	1	yes	characteristic
179	#1955	C₂×C₁₉	1	2	yes	—
180	#1924	C₂×C₁₉	1	2	yes	complemented
181	#1923	C₂×C₁₉	1	2	yes	complemented
182	#1831	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1818	C₂×C₁₉	1	2	yes	complemented
184	#1771	C₂×C₁₉	1	2	yes	complemented
185	#1767	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#1750	C₂×C₁₉	1	2	yes	complemented
187	C₂²×C₁₉	—	4	2	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	—	4	2	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
195	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
196	C₂²×C₁₉	#518	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
198	C₂²×C₁₉	#568	1	1	yes	characteristic
199	C₂²×C₁₉	#568	1	1	yes	characteristic
200	C₂²×C₁₉	#568	1	1	yes	characteristic
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	4	1	no	—
206	C₄×C₁₉	—	4	1	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	1	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	#553	1	2	yes	—
211	C₄×C₁₉	#559	1	2	yes	—
212	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×#117	C₂²×C₁₉	1	2	yes	—
214	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
215	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
216	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
218	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
219	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
220	C₂×#97	C₂²×C₁₉	1	2	yes	—
221	C₂×#97	C₂²×C₁₉	1	2	yes	—
222	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
223	#390	C₄×C₁₉	1	1	yes	characteristic
224	#390	C₄×C₁₉	1	1	yes	characteristic
225	#389	C₄×C₁₉	1	1	yes	characteristic
226	#389	C₄×C₁₉	1	1	yes	characteristic
227	#388	C₄×C₁₉	1	2	yes	—
228	#388	C₄×C₁₉	1	2	yes	—
229	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
230	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
231	C₄³	C₂²×C₁₉	1	1	yes	characteristic
232	#336	C₂²×C₁₉	1	1	yes	characteristic
233	#336	C₂²×C₁₉	1	2	yes	—
234	#336	C₂²×C₁₉	1	2	yes	—
235	#336	C₂²×C₁₉	1	2	yes	—
236	#336	C₂²×C₁₉	1	1	yes	characteristic
237	#336	C₂²×C₁₉	1	1	yes	characteristic
238	#336	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×C₁₉	—	8	2	no	—
240	C₂×C₁₉	#2357	1	1	yes	characteristic
241	C₂×C₁₉	#2921	1	1	yes	characteristic
242	C₂×C₁₉	#2925	1	1	yes	characteristic
243	C₂×C₁₉	#2967	1	1	yes	characteristic
244	C₂×C₁₉	#2968	1	1	yes	characteristic
245	C₂×C₁₉	#2980	1	1	yes	characteristic
246	C₂×C₁₉	#2981	1	1	yes	characteristic
247	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
249	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
251	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
252	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	#117	—	4	2	no	—
256	#117	—	4	2	no	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
267	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
268	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
269	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
270	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
275	C₄⋊C₈	—	2	4	no	—
276	C₄⋊C₈	—	2	4	no	—
277	C₂²⋊C₈	—	2	4	no	—
278	C₂²⋊C₈	—	2	4	no	—
279	C₂²⋊C₈	—	4	2	no	—
280	C₂²⋊C₈	—	4	2	no	—
281	#97	—	2	4	no	—
282	#97	—	4	2	no	—
283	C₄×C₈	—	4	2	no	—
284	#95	C₂×C₄×C₁₉	1	2	yes	—
285	#95	C₂×C₄×C₁₉	1	2	yes	—
286	#95	C₂×C₄×C₁₉	1	2	yes	—
287	C₁₉	#22838	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	#41×C₁₉	1	4	yes	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	4	1	no	—
338	C₄²	#41×C₁₉	1	2	yes	—
339	C₄²	#41×C₁₉	1	2	yes	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
348	D₄	—	4	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	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	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	C₁₉×#117	1	2	yes	—
378	C₂×C₄	C₁₉×#117	1	2	yes	—
379	C₂×C₄	C₁₉×#131	1	2	yes	—
380	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
382	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
383	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
384	C₈	—	2	4	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
396	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
397	C₂²	C₁₉×#518	1	1	yes	characteristic
398	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
399	C₂²	C₁₉×#568	1	1	yes	characteristic
400	C₂²	C₁₉×#568	1	1	yes	characteristic
401	C₂²	C₁₉×#568	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	C₁₉×#553	1	2	yes	—
412	C₄	C₁₉×#559	1	2	yes	—
413	C₂	—	8	2	no	—
414	C₂	C₁₉×#2357	1	1	yes	characteristic
415	C₂	C₁₉×#2921	1	1	yes	characteristic
416	C₂	C₁₉×#2925	1	1	yes	characteristic
417	C₂	C₁₉×#2967	1	1	yes	characteristic
418	C₂	C₁₉×#2968	1	1	yes	characteristic
419	C₂	C₁₉×#2980	1	1	yes	characteristic
420	C₂	C₁₉×#2981	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1924	C₂	semidirect
4. C₁₉×#1923	C₂	semidirect
5. C₁₉×#1831	C₂	semidirect
6. C₁₉×#1818	C₂	semidirect
7. C₁₉×#1771	C₂	semidirect
8. C₁₉×#1767	C₂	semidirect
9. C₁₉×#1750	C₂	semidirect
129. #22838	C₁₉	direct (N × H)
180. #1924	C₂×C₁₉	semidirect
181. #1923	C₂×C₁₉	semidirect
182. #1831	C₂×C₁₉	semidirect
183. #1818	C₂×C₁₉	semidirect
184. #1771	C₂×C₁₉	semidirect
185. #1767	C₂×C₁₉	semidirect
186. #1750	C₂×C₁₉	semidirect
287. C₁₉	#22838	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×#2293	2
C₁₉×#1955	2
C₁₉×#1924	2
C₁₉×#1923	2
C₁₉×#1831	2
C₁₉×#1818	2
C₁₉×#1771	2
C₁₉×#1767	2
C₁₉×#1750	2
#22838	19

Subgroups — C19×#22838 #18028797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22838 #18028797