Subgroups — C₁₉×#14492 #18020451

Order 4864.

1918 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#391	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1439	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1438	C₂	1	2	yes	maximal
5	C₁₉×#1437	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1434	C₂	1	2	yes	maximal, complemented
7	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#124	—	2	8	no	—
10	C₂×C₁₉×#124	C₄	1	8	yes	complemented
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#391	—	2	8	no	—
19	C₂×C₁₉×#95	C₂²	1	4	yes	—
20	C₂×C₁₉×#95	C₂²	1	4	yes	—
21	C₂×C₁₉×#95	C₂²	1	4	yes	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	2	yes	—
24	C₂⁵×C₁₉	C₂³	1	2	yes	—
25	C₂²×Q₈×C₁₉	—	4	1	no	—
26	C₂²×Q₈×C₁₉	—	4	2	no	—
27	C₂²×Q₈×C₁₉	—	4	1	no	—
28	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
29	C₂²×Q₈×C₁₉	D₄	1	8	yes	—
30	C₂²×D₄×C₁₉	—	2	4	no	—
31	C₂²×D₄×C₁₉	—	4	2	no	—
32	C₂²×D₄×C₁₉	—	4	1	no	—
33	C₂²×D₄×C₁₉	—	4	1	no	—
34	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₁₉×#124	—	2	32	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
53	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
54	C₂×C₄²×C₁₉	—	2	4	no	—
55	C₂×C₄²×C₁₉	—	2	4	no	—
56	C₂×C₄²×C₁₉	—	4	2	no	—
57	C₂×C₄²×C₁₉	—	4	2	no	—
58	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
59	C₁₉×#95	—	2	8	no	—
60	C₁₉×#95	—	2	8	no	—
61	C₁₉×#95	—	2	8	no	—
62	C₁₉×#95	—	4	2	no	—
63	C₁₉×#95	—	4	2	no	—
64	C₂⁴×C₁₉	—	2	4	no	—
65	C₂⁴×C₁₉	—	2	4	no	—
66	C₂⁴×C₁₉	—	2	4	no	—
67	C₂⁴×C₁₉	—	2	4	no	—
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	—	2	4	no	—
72	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
73	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
74	C₂×Q₈×C₁₉	—	4	4	no	—
75	C₂×Q₈×C₁₉	—	4	4	no	—
76	C₂×Q₈×C₁₉	—	4	8	no	—
77	C₂×Q₈×C₁₉	—	4	8	no	—
78	C₂×Q₈×C₁₉	C₂²⋊C₄	1	16	yes	complemented
79	C₂×D₄×C₁₉	—	2	8	no	—
80	C₂×D₄×C₁₉	—	4	4	no	—
81	C₂×D₄×C₁₉	—	4	4	no	—
82	C₂×D₄×C₁₉	—	4	8	no	—
83	C₂×D₄×C₁₉	—	4	8	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	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₁₉	#41	1	8	yes	—
115	C₄⋊C₄×C₁₉	—	4	8	no	—
116	C₂²⋊C₄×C₁₉	—	2	32	no	—
117	C₂²⋊C₄×C₁₉	—	4	8	no	—
118	C₂²⋊C₄×C₁₉	—	4	16	no	—
119	C₂²⋊C₄×C₁₉	—	4	8	no	—
120	C₄²×C₁₉	—	2	8	no	—
121	C₄²×C₁₉	—	4	8	no	—
122	#14492	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₁₉	—	2	4	no	—
124	C₂³×C₁₉	—	2	8	no	—
125	C₂³×C₁₉	—	2	4	no	—
126	C₂³×C₁₉	—	2	4	no	—
127	C₂³×C₁₉	—	2	8	no	—
128	C₂³×C₁₉	—	4	4	no	—
129	C₂³×C₁₉	—	4	4	no	—
130	C₂³×C₁₉	—	4	4	no	—
131	C₂³×C₁₉	—	4	4	no	—
132	C₂³×C₁₉	—	4	4	no	—
133	C₂³×C₁₉	—	4	4	no	—
134	C₂³×C₁₉	—	4	4	no	—
135	C₂³×C₁₉	—	4	4	no	—
136	C₂³×C₁₉	—	4	4	no	—
137	C₂³×C₁₉	—	4	4	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	4	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
145	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
146	C₂³×C₁₉	C₂×#41	1	4	yes	—
147	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
148	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
150	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
151	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
152	Q₈×C₁₉	—	4	16	no	—
153	D₄×C₁₉	—	4	16	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	8	no	—
168	C₂×C₄×C₁₉	—	2	8	no	—
169	C₂×C₄×C₁₉	—	2	8	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	4	no	—
172	C₂×C₄×C₁₉	—	4	4	no	—
173	C₂×C₄×C₁₉	—	4	4	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	4	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	4	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
184	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
185	C₂²×#124	C₂×C₁₉	1	1	yes	characteristic
186	C₂×#391	C₂×C₁₉	1	2	yes	complemented
187	#1439	C₂×C₁₉	1	4	yes	complemented
188	#1438	C₂×C₁₉	1	2	yes	—
189	#1437	C₂×C₁₉	1	4	yes	complemented
190	#1434	C₂×C₁₉	1	2	yes	complemented
191	C₂²×C₁₉	—	4	4	no	—
192	C₂²×C₁₉	—	4	8	no	—
193	C₂²×C₁₉	—	4	8	no	—
194	C₂²×C₁₉	—	4	4	no	—
195	C₂²×C₁₉	—	4	4	no	—
196	C₂²×C₁₉	—	8	4	no	—
197	C₂²×C₁₉	—	8	4	no	—
198	C₂²×C₁₉	—	8	4	no	—
199	C₂²×C₁₉	—	8	4	no	—
200	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₁₉	C₄×#41	1	2	yes	—
202	C₂²×C₁₉	#518	1	1	yes	characteristic
203	C₂²×C₁₉	#518	1	1	yes	characteristic
204	C₂²×C₁₉	#520	1	2	yes	—
205	C₂²×C₁₉	#534	1	2	yes	—
206	C₂²×C₁₉	#534	1	2	yes	—
207	C₂²×C₁₉	#538	1	4	yes	—
208	C₂²×C₁₉	#542	1	4	yes	—
209	C₂²×C₁₉	#548	1	4	yes	—
210	C₂²×C₁₉	#550	1	4	yes	—
211	C₂²×C₁₉	#551	1	2	yes	—
212	C₂²×C₁₉	#555	1	2	yes	—
213	C₂²×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
214	C₂²×C₁₉	#562	1	2	yes	—
215	C₂²×C₁₉	#563	1	1	yes	characteristic
216	C₄×C₁₉	—	2	4	no	—
217	C₄×C₁₉	—	2	8	no	—
218	C₄×C₁₉	—	4	4	no	—
219	C₄×C₁₉	—	4	8	no	—
220	C₄×C₁₉	—	8	4	no	—
221	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
222	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×#124	—	2	8	no	—
224	C₂×#124	C₄×C₁₉	1	8	yes	complemented
225	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
226	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
227	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
228	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
229	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
230	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
231	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
232	#391	—	2	8	no	—
233	C₂×#95	C₂²×C₁₉	1	4	yes	—
234	C₂×#95	C₂²×C₁₉	1	4	yes	—
235	C₂×#95	C₂²×C₁₉	1	4	yes	—
236	C₂×#95	C₂²×C₁₉	1	2	yes	—
237	C₂×#95	C₂²×C₁₉	1	2	yes	—
238	C₂×C₁₉	—	8	4	no	—
239	C₂×C₁₉	#2308	1	1	yes	characteristic
240	C₂×C₁₉	#2337	1	2	yes	—
241	C₂×C₁₉	#2341	1	2	yes	—
242	C₂×C₁₉	#2372	1	1	yes	characteristic
243	C₂×C₁₉	#2379	1	1	yes	characteristic
244	C₂×C₁₉	#2730	1	4	yes	—
245	C₂×C₁₉	#2731	1	2	yes	—
246	C₂×C₁₉	#2733	1	2	yes	—
247	C₂⁵	C₂³×C₁₉	1	2	yes	—
248	C₂²×Q₈	—	4	1	no	—
249	C₂²×Q₈	—	4	2	no	—
250	C₂²×Q₈	—	4	1	no	—
251	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
252	C₂²×Q₈	D₄×C₁₉	1	8	yes	—
253	C₂²×D₄	—	2	4	no	—
254	C₂²×D₄	—	4	2	no	—
255	C₂²×D₄	—	4	1	no	—
256	C₂²×D₄	—	4	1	no	—
257	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
258	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
259	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
260	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
261	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
262	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
263	#124	—	2	32	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	4	2	no	—
266	C₂×C₄⋊C₄	—	4	2	no	—
267	C₂×C₂²⋊C₄	—	2	8	no	—
268	C₂×C₂²⋊C₄	—	2	8	no	—
269	C₂×C₂²⋊C₄	—	2	8	no	—
270	C₂×C₂²⋊C₄	—	2	8	no	—
271	C₂×C₂²⋊C₄	—	4	2	no	—
272	C₂×C₂²⋊C₄	—	4	4	no	—
273	C₂×C₂²⋊C₄	—	4	4	no	—
274	C₂×C₂²⋊C₄	—	4	4	no	—
275	C₂×C₂²⋊C₄	—	4	2	no	—
276	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
277	C₂×C₄²	—	2	4	no	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	—	4	2	no	—
280	C₂×C₄²	—	4	2	no	—
281	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
282	#95	—	2	8	no	—
283	#95	—	2	8	no	—
284	#95	—	2	8	no	—
285	#95	—	4	2	no	—
286	#95	—	4	2	no	—
287	C₁₉	#14492	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁴	—	2	4	no	—
289	C₂⁴	—	2	4	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	2	no	—
294	C₂⁴	—	2	2	no	—
295	C₂⁴	—	2	4	no	—
296	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
297	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
298	C₂×Q₈	—	4	4	no	—
299	C₂×Q₈	—	4	4	no	—
300	C₂×Q₈	—	4	8	no	—
301	C₂×Q₈	—	4	8	no	—
302	C₂×Q₈	C₂²⋊C₄×C₁₉	1	16	yes	complemented
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	8	no	—
307	C₂×D₄	—	4	8	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
333	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
334	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
336	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
337	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
338	C₂²×C₄	#41×C₁₉	1	8	yes	—
339	C₄⋊C₄	—	4	8	no	—
340	C₂²⋊C₄	—	2	32	no	—
341	C₂²⋊C₄	—	4	8	no	—
342	C₂²⋊C₄	—	4	16	no	—
343	C₂²⋊C₄	—	4	8	no	—
344	C₄²	—	2	8	no	—
345	C₄²	—	4	8	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	8	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	8	no	—
351	C₂³	—	4	4	no	—
352	C₂³	—	4	4	no	—
353	C₂³	—	4	4	no	—
354	C₂³	—	4	4	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	—	4	4	no	—
359	C₂³	—	4	4	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	4	2	no	—
367	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
368	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
369	C₂³	C₂×#41×C₁₉	1	4	yes	—
370	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
371	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
374	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
375	Q₈	—	4	16	no	—
376	D₄	—	4	16	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	8	no	—
410	C₂²	—	4	8	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	8	4	no	—
414	C₂²	—	8	4	no	—
415	C₂²	—	8	4	no	—
416	C₂²	—	8	4	no	—
417	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
418	C₂²	C₄×#41×C₁₉	1	2	yes	—
419	C₂²	C₁₉×#518	1	1	yes	characteristic
420	C₂²	C₁₉×#518	1	1	yes	characteristic
421	C₂²	C₁₉×#520	1	2	yes	—
422	C₂²	C₁₉×#534	1	2	yes	—
423	C₂²	C₁₉×#534	1	2	yes	—
424	C₂²	C₁₉×#538	1	4	yes	—
425	C₂²	C₁₉×#542	1	4	yes	—
426	C₂²	C₁₉×#548	1	4	yes	—
427	C₂²	C₁₉×#550	1	4	yes	—
428	C₂²	C₁₉×#551	1	2	yes	—
429	C₂²	C₁₉×#555	1	2	yes	—
430	C₂²	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
431	C₂²	C₁₉×#562	1	2	yes	—
432	C₂²	C₁₉×#563	1	1	yes	characteristic
433	C₄	—	2	4	no	—
434	C₄	—	2	8	no	—
435	C₄	—	4	8	no	—
436	C₄	—	4	4	no	—
437	C₄	—	8	4	no	—
438	C₂	—	8	4	no	—
439	C₂	C₁₉×#2308	1	1	yes	characteristic
440	C₂	C₁₉×#2337	1	2	yes	—
441	C₂	C₁₉×#2341	1	2	yes	—
442	C₂	C₁₉×#2372	1	1	yes	characteristic
443	C₂	C₁₉×#2379	1	1	yes	characteristic
444	C₂	C₁₉×#2730	1	4	yes	—
445	C₂	C₁₉×#2731	1	2	yes	—
446	C₂	C₁₉×#2733	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#391	C₂	semidirect
3. C₁₉×#1439	C₂	semidirect
5. C₁₉×#1437	C₂	semidirect
6. C₁₉×#1434	C₂	semidirect
10. C₂×C₁₉×#124	C₄	semidirect
78. C₂×Q₈×C₁₉	C₂²⋊C₄	semidirect
122. #14492	C₁₉	direct (N × H)
186. C₂×#391	C₂×C₁₉	semidirect
187. #1439	C₂×C₁₉	semidirect
189. #1437	C₂×C₁₉	semidirect
190. #1434	C₂×C₁₉	semidirect
224. C₂×#124	C₄×C₁₉	semidirect
287. C₁₉	#14492	direct (N × H)
302. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#124	2
C₂×C₁₉×#391	2
C₁₉×#1439	2
C₁₉×#1438	2
C₁₉×#1437	2
C₁₉×#1434	2
#14492	19

Subgroups — C19×#14492 #18020451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14492 #18020451