Subgroups — C₁₉×#14836 #18020795

Order 4864.

2254 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#399	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#386	C₂	1	3	yes	maximal
3	C₂×C₁₉×#380	C₂	1	3	yes	maximal, complemented
4	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1445	C₂	1	3	yes	maximal, complemented
6	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1439	C₂	1	3	yes	maximal, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₉	C₂²	1	3	yes	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
15	C₁₉×#399	—	2	4	no	—
16	C₁₉×#386	—	2	12	no	—
17	C₁₉×#380	—	2	12	no	—
18	C₂×C₁₉×#95	—	2	4	no	—
19	C₂×C₁₉×#95	C₂²	1	3	yes	—
20	C₂×C₁₉×#95	C₂²	1	6	yes	—
21	C₂×C₁₉×#95	C₂²	1	3	yes	—
22	C₂×C₁₉×#95	C₂²	1	3	yes	—
23	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
24	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
25	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	—	2	6	no	—
27	C₂²×D₄×C₁₉	—	2	6	no	—
28	C₂²×D₄×C₁₉	Q₈	1	4	yes	—
29	C₂³×C₄×C₁₉	—	2	12	no	—
30	C₂³×C₄×C₁₉	—	2	6	no	—
31	C₂³×C₄×C₁₉	—	2	6	no	—
32	C₂³×C₄×C₁₉	—	4	6	no	—
33	C₂³×C₄×C₁₉	D₄	1	12	yes	—
34	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
36	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
39	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
43	C₂×C₄⋊C₄×C₁₉	—	4	6	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	4	6	no	—
51	C₁₉×#95	—	2	6	no	—
52	C₁₉×#95	—	2	12	no	—
53	C₁₉×#95	—	2	6	no	—
54	C₁₉×#95	—	2	6	no	—
55	C₁₉×#95	D₄	1	4	yes	complemented
56	C₂⁴×C₁₉	—	2	1	no	—
57	C₂⁴×C₁₉	—	2	3	no	—
58	C₂⁴×C₁₉	—	2	3	no	—
59	C₂⁴×C₁₉	—	2	1	no	—
60	C₂⁴×C₁₉	—	2	1	no	—
61	C₂⁴×C₁₉	—	2	3	no	—
62	C₂⁴×C₁₉	—	2	3	no	—
63	C₂⁴×C₁₉	—	2	3	no	—
64	C₂⁴×C₁₉	—	2	3	no	—
65	C₂⁴×C₁₉	—	2	1	no	—
66	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
67	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
68	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
69	C₂⁴×C₁₉	#41	1	6	yes	—
70	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
71	C₂×D₄×C₁₉	—	2	24	no	—
72	C₂×D₄×C₁₉	—	4	12	no	—
73	C₂×D₄×C₁₉	—	4	4	no	—
74	C₂²×C₄×C₁₉	—	2	6	no	—
75	C₂²×C₄×C₁₉	—	2	6	no	—
76	C₂²×C₄×C₁₉	—	2	24	no	—
77	C₂²×C₄×C₁₉	—	2	3	no	—
78	C₂²×C₄×C₁₉	—	2	3	no	—
79	C₂²×C₄×C₁₉	—	2	3	no	—
80	C₂²×C₄×C₁₉	—	2	6	no	—
81	C₂²×C₄×C₁₉	—	2	3	no	—
82	C₂²×C₄×C₁₉	—	2	6	no	—
83	C₂²×C₄×C₁₉	—	2	24	no	—
84	C₂²×C₄×C₁₉	—	2	3	no	—
85	C₂²×C₄×C₁₉	—	2	3	no	—
86	C₂²×C₄×C₁₉	—	2	3	no	—
87	C₂²×C₄×C₁₉	—	2	6	no	—
88	C₂²×C₄×C₁₉	—	2	6	no	—
89	C₂²×C₄×C₁₉	—	2	3	no	—
90	C₂²×C₄×C₁₉	—	2	6	no	—
91	C₂²×C₄×C₁₉	—	2	6	no	—
92	C₂²×C₄×C₁₉	—	2	3	no	—
93	C₂²×C₄×C₁₉	—	2	3	no	—
94	C₂²×C₄×C₁₉	—	4	12	no	—
95	C₂²×C₄×C₁₉	—	4	24	no	—
96	C₂²×C₄×C₁₉	—	4	24	no	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
100	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₁₉	#41	1	6	yes	—
102	C₄⋊C₄×C₁₉	—	4	12	no	—
103	C₄⋊C₄×C₁₉	—	4	12	no	—
104	C₂²⋊C₄×C₁₉	—	4	12	no	—
105	C₂²⋊C₄×C₁₉	—	4	12	no	—
106	C₂²⋊C₄×C₁₉	—	4	12	no	—
107	#14836	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₁₉	—	2	6	no	—
109	C₂³×C₁₉	—	2	6	no	—
110	C₂³×C₁₉	—	2	6	no	—
111	C₂³×C₁₉	—	2	6	no	—
112	C₂³×C₁₉	—	2	6	no	—
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	—	2	12	no	—
115	C₂³×C₁₉	—	2	6	no	—
116	C₂³×C₁₉	—	2	6	no	—
117	C₂³×C₁₉	—	2	6	no	—
118	C₂³×C₁₉	—	2	2	no	—
119	C₂³×C₁₉	—	2	6	no	—
120	C₂³×C₁₉	—	4	3	no	—
121	C₂³×C₁₉	—	4	3	no	—
122	C₂³×C₁₉	—	4	1	no	—
123	C₂³×C₁₉	—	4	3	no	—
124	C₂³×C₁₉	—	4	3	no	—
125	C₂³×C₁₉	—	4	3	no	—
126	C₂³×C₁₉	—	4	3	no	—
127	C₂³×C₁₉	—	4	6	no	—
128	C₂³×C₁₉	—	4	3	no	—
129	C₂³×C₁₉	C₂²⋊Q₈	1	12	yes	—
130	C₂³×C₁₉	#123	1	12	yes	—
131	C₂³×C₁₉	#127	1	4	yes	—
132	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
133	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
134	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
135	C₂³×C₁₉	C₂×#41	1	3	yes	—
136	C₂³×C₁₉	C₂×#41	1	3	yes	—
137	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
138	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
139	D₄×C₁₉	—	4	16	no	—
140	C₂×C₄×C₁₉	—	2	6	no	—
141	C₂×C₄×C₁₉	—	2	6	no	—
142	C₂×C₄×C₁₉	—	2	12	no	—
143	C₂×C₄×C₁₉	—	2	12	no	—
144	C₂×C₄×C₁₉	—	2	6	no	—
145	C₂×C₄×C₁₉	—	2	6	no	—
146	C₂×C₄×C₁₉	—	2	6	no	—
147	C₂×C₄×C₁₉	—	2	6	no	—
148	C₂×C₄×C₁₉	—	4	48	no	—
149	C₂×C₄×C₁₉	—	4	3	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	6	no	—
152	C₂×C₄×C₁₉	—	4	6	no	—
153	C₂×C₄×C₁₉	—	4	3	no	—
154	C₂×C₄×C₁₉	—	4	6	no	—
155	C₂×C₄×C₁₉	—	4	3	no	—
156	C₂×C₄×C₁₉	—	4	3	no	—
157	C₂×C₄×C₁₉	—	4	3	no	—
158	C₂×C₄×C₁₉	—	4	6	no	—
159	C₂×C₄×C₁₉	—	4	3	no	—
160	C₂×C₄×C₁₉	—	4	6	no	—
161	C₂×C₄×C₁₉	—	4	3	no	—
162	C₂×C₄×C₁₉	—	4	6	no	—
163	C₂×C₄×C₁₉	#121	1	12	yes	—
164	C₂×#399	C₂×C₁₉	1	1	yes	characteristic, complemented
165	C₂×#386	C₂×C₁₉	1	3	yes	—
166	C₂×#380	C₂×C₁₉	1	3	yes	complemented
167	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic, complemented
168	#1445	C₂×C₁₉	1	3	yes	complemented
169	#1444	C₂×C₁₉	1	1	yes	characteristic, complemented
170	#1439	C₂×C₁₉	1	3	yes	complemented
171	C₂²×C₁₉	—	2	12	no	—
172	C₂²×C₁₉	—	2	4	no	—
173	C₂²×C₁₉	—	2	4	no	—
174	C₂²×C₁₉	—	2	12	no	—
175	C₂²×C₁₉	—	2	12	no	—
176	C₂²×C₁₉	—	2	12	no	—
177	C₂²×C₁₉	—	4	6	no	—
178	C₂²×C₁₉	—	4	2	no	—
179	C₂²×C₁₉	—	4	6	no	—
180	C₂²×C₁₉	—	8	1	no	—
181	C₂²×C₁₉	—	8	1	no	—
182	C₂²×C₁₉	—	8	3	no	—
183	C₂²×C₁₉	—	8	3	no	—
184	C₂²×C₁₉	#399	1	8	yes	complemented
185	C₂²×C₁₉	C₂×#121	1	3	yes	—
186	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	3	yes	—
187	C₂²×C₁₉	C₂×#123	1	3	yes	—
188	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
189	C₂²×C₁₉	#532	1	3	yes	—
190	C₂²×C₁₉	#534	1	3	yes	—
191	C₂²×C₁₉	#537	1	3	yes	—
192	C₂²×C₁₉	#546	1	3	yes	—
193	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
194	C₂²×C₁₉	#551	1	6	yes	—
195	C₂²×C₁₉	#552	1	3	yes	—
196	C₂²×C₁₉	#554	1	3	yes	—
197	C₄×C₁₉	—	2	12	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	—	4	6	no	—
200	C₄×C₁₉	—	8	3	no	—
201	C₄×C₁₉	—	8	3	no	—
202	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
203	C₂⁴×C₄	C₂²×C₁₉	1	3	yes	—
204	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
206	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
207	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
208	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
209	#399	—	2	4	no	—
210	#386	—	2	12	no	—
211	#380	—	2	12	no	—
212	C₂×#95	—	2	4	no	—
213	C₂×#95	C₂²×C₁₉	1	3	yes	—
214	C₂×#95	C₂²×C₁₉	1	6	yes	—
215	C₂×#95	C₂²×C₁₉	1	3	yes	—
216	C₂×#95	C₂²×C₁₉	1	3	yes	—
217	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×C₁₉	—	2	8	no	—
219	C₂×C₁₉	—	8	2	no	—
220	C₂×C₁₉	C₂×#399	1	1	yes	characteristic
221	C₂×C₁₉	#2412	1	3	yes	—
222	C₂×C₁₉	#2417	1	3	yes	—
223	C₂×C₁₉	#2498	1	3	yes	—
224	C₂×C₁₉	#2564	1	3	yes	—
225	C₂×C₁₉	#2656	1	1	yes	characteristic
226	C₂×C₁₉	#2856	1	1	yes	characteristic
227	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
228	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
229	C₂²×D₄	—	2	6	no	—
230	C₂²×D₄	—	2	6	no	—
231	C₂²×D₄	Q₈×C₁₉	1	4	yes	—
232	C₂³×C₄	—	2	12	no	—
233	C₂³×C₄	—	2	6	no	—
234	C₂³×C₄	—	2	6	no	—
235	C₂³×C₄	—	4	6	no	—
236	C₂³×C₄	D₄×C₁₉	1	12	yes	—
237	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
238	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
239	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
240	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
242	C₂×C₄⋊C₄	—	2	6	no	—
243	C₂×C₄⋊C₄	—	2	6	no	—
244	C₂×C₄⋊C₄	—	2	6	no	—
245	C₂×C₄⋊C₄	—	2	6	no	—
246	C₂×C₄⋊C₄	—	4	6	no	—
247	C₂×C₂²⋊C₄	—	2	12	no	—
248	C₂×C₂²⋊C₄	—	2	6	no	—
249	C₂×C₂²⋊C₄	—	2	6	no	—
250	C₂×C₂²⋊C₄	—	2	6	no	—
251	C₂×C₂²⋊C₄	—	2	6	no	—
252	C₂×C₂²⋊C₄	—	2	6	no	—
253	C₂×C₂²⋊C₄	—	4	6	no	—
254	#95	—	2	6	no	—
255	#95	—	2	12	no	—
256	#95	—	2	6	no	—
257	#95	—	2	6	no	—
258	#95	D₄×C₁₉	1	4	yes	complemented
259	C₁₉	#14836	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	—	2	1	no	—
261	C₂⁴	—	2	3	no	—
262	C₂⁴	—	2	3	no	—
263	C₂⁴	—	2	1	no	—
264	C₂⁴	—	2	1	no	—
265	C₂⁴	—	2	3	no	—
266	C₂⁴	—	2	3	no	—
267	C₂⁴	—	2	3	no	—
268	C₂⁴	—	2	3	no	—
269	C₂⁴	—	2	1	no	—
270	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
271	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
272	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
273	C₂⁴	#41×C₁₉	1	6	yes	—
274	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
275	C₂×D₄	—	2	24	no	—
276	C₂×D₄	—	4	12	no	—
277	C₂×D₄	—	4	4	no	—
278	C₂²×C₄	—	2	6	no	—
279	C₂²×C₄	—	2	6	no	—
280	C₂²×C₄	—	2	24	no	—
281	C₂²×C₄	—	2	3	no	—
282	C₂²×C₄	—	2	3	no	—
283	C₂²×C₄	—	2	3	no	—
284	C₂²×C₄	—	2	6	no	—
285	C₂²×C₄	—	2	3	no	—
286	C₂²×C₄	—	2	6	no	—
287	C₂²×C₄	—	2	24	no	—
288	C₂²×C₄	—	2	3	no	—
289	C₂²×C₄	—	2	3	no	—
290	C₂²×C₄	—	2	6	no	—
291	C₂²×C₄	—	2	6	no	—
292	C₂²×C₄	—	2	3	no	—
293	C₂²×C₄	—	2	3	no	—
294	C₂²×C₄	—	2	6	no	—
295	C₂²×C₄	—	2	6	no	—
296	C₂²×C₄	—	2	3	no	—
297	C₂²×C₄	—	2	3	no	—
298	C₂²×C₄	—	4	12	no	—
299	C₂²×C₄	—	4	24	no	—
300	C₂²×C₄	—	4	24	no	—
301	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
302	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
303	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
304	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
305	C₂²×C₄	#41×C₁₉	1	6	yes	—
306	C₄⋊C₄	—	4	12	no	—
307	C₄⋊C₄	—	4	12	no	—
308	C₂²⋊C₄	—	4	12	no	—
309	C₂²⋊C₄	—	4	12	no	—
310	C₂²⋊C₄	—	4	12	no	—
311	C₂³	—	2	6	no	—
312	C₂³	—	2	6	no	—
313	C₂³	—	2	6	no	—
314	C₂³	—	2	6	no	—
315	C₂³	—	2	6	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	12	no	—
318	C₂³	—	2	6	no	—
319	C₂³	—	2	6	no	—
320	C₂³	—	2	6	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	6	no	—
323	C₂³	—	4	3	no	—
324	C₂³	—	4	3	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	3	no	—
327	C₂³	—	4	3	no	—
328	C₂³	—	4	3	no	—
329	C₂³	—	4	3	no	—
330	C₂³	—	4	6	no	—
331	C₂³	—	4	3	no	—
332	C₂³	C₁₉×C₂²⋊Q₈	1	12	yes	—
333	C₂³	C₁₉×#123	1	12	yes	—
334	C₂³	C₁₉×#127	1	4	yes	—
335	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
336	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
337	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
338	C₂³	C₂×#41×C₁₉	1	3	yes	—
339	C₂³	C₂×#41×C₁₉	1	3	yes	—
340	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
341	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
342	D₄	—	4	16	no	—
343	C₂×C₄	—	2	6	no	—
344	C₂×C₄	—	2	6	no	—
345	C₂×C₄	—	2	12	no	—
346	C₂×C₄	—	2	12	no	—
347	C₂×C₄	—	2	6	no	—
348	C₂×C₄	—	2	6	no	—
349	C₂×C₄	—	2	6	no	—
350	C₂×C₄	—	2	6	no	—
351	C₂×C₄	—	4	48	no	—
352	C₂×C₄	—	4	3	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	6	no	—
355	C₂×C₄	—	4	6	no	—
356	C₂×C₄	—	4	3	no	—
357	C₂×C₄	—	4	6	no	—
358	C₂×C₄	—	4	3	no	—
359	C₂×C₄	—	4	3	no	—
360	C₂×C₄	—	4	3	no	—
361	C₂×C₄	—	4	6	no	—
362	C₂×C₄	—	4	3	no	—
363	C₂×C₄	—	4	6	no	—
364	C₂×C₄	—	4	3	no	—
365	C₂×C₄	—	4	6	no	—
366	C₂×C₄	C₁₉×#121	1	12	yes	—
367	C₂²	—	2	4	no	—
368	C₂²	—	2	12	no	—
369	C₂²	—	2	12	no	—
370	C₂²	—	2	12	no	—
371	C₂²	—	2	12	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	4	6	no	—
374	C₂²	—	4	6	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	3	no	—
378	C₂²	—	8	3	no	—
379	C₂²	—	8	1	no	—
380	C₂²	C₁₉×#399	1	8	yes	complemented
381	C₂²	C₂×C₁₉×#121	1	3	yes	—
382	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	3	yes	—
383	C₂²	C₂×C₁₉×#123	1	3	yes	—
384	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
385	C₂²	C₁₉×#532	1	3	yes	—
386	C₂²	C₁₉×#534	1	3	yes	—
387	C₂²	C₁₉×#537	1	3	yes	—
388	C₂²	C₁₉×#546	1	3	yes	—
389	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
390	C₂²	C₁₉×#551	1	6	yes	—
391	C₂²	C₁₉×#552	1	3	yes	—
392	C₂²	C₁₉×#554	1	3	yes	—
393	C₄	—	2	12	no	—
394	C₄	—	4	6	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	3	no	—
397	C₄	—	8	3	no	—
398	C₂	—	2	8	no	—
399	C₂	—	8	2	no	—
400	C₂	C₂×C₁₉×#399	1	1	yes	characteristic
401	C₂	C₁₉×#2412	1	3	yes	—
402	C₂	C₁₉×#2417	1	3	yes	—
403	C₂	C₁₉×#2498	1	3	yes	—
404	C₂	C₁₉×#2564	1	3	yes	—
405	C₂	C₁₉×#2656	1	1	yes	characteristic
406	C₂	C₁₉×#2856	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#399	C₂	semidirect
3. C₂×C₁₉×#380	C₂	semidirect
4. C₂²×C₁₉×#95	C₂	semidirect
5. C₁₉×#1445	C₂	semidirect
6. C₁₉×#1444	C₂	semidirect
7. C₁₉×#1439	C₂	semidirect
55. C₁₉×#95	D₄	semidirect
107. #14836	C₁₉	direct (N × H)
164. C₂×#399	C₂×C₁₉	semidirect
166. C₂×#380	C₂×C₁₉	semidirect
167. C₂²×#95	C₂×C₁₉	semidirect
168. #1445	C₂×C₁₉	semidirect
169. #1444	C₂×C₁₉	semidirect
170. #1439	C₂×C₁₉	semidirect
184. C₂²×C₁₉	#399	semidirect
258. #95	D₄×C₁₉	semidirect
259. C₁₉	#14836	direct (N × H)
380. C₂²	C₁₉×#399	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#399	2
C₂×C₁₉×#386	2
C₂×C₁₉×#380	2
C₂²×C₁₉×#95	2
C₁₉×#1445	2
C₁₉×#1444	2
C₁₉×#1439	2
#14836	19

Subgroups — C19×#14836 #18020795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14836 #18020795