Subgroups — C₁₉×#14129 #18020088

Order 4864.

2006 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#389	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1439	C₂	1	4	yes	maximal
6	C₁₉×#1436	C₂	1	4	yes	maximal, complemented
7	C₁₉×C₄⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#117	—	2	4	no	—
10	C₂×C₁₉×#117	—	2	8	no	—
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#389	—	2	8	no	—
21	C₁₉×#380	C₄	1	8	yes	complemented
22	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
23	C₂×C₁₉×#95	C₂²	1	4	yes	—
24	C₂×C₁₉×#95	C₂²	1	2	yes	—
25	C₂×C₁₉×#95	C₂²	1	4	yes	—
26	C₂×C₁₉×#95	C₂²	1	4	yes	—
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	—	2	4	no	—
30	C₂³×C₄×C₁₉	—	2	4	no	—
31	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₉	D₄	1	4	yes	—
33	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
34	C₂³×C₄×C₁₉	C₂³	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	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₁₉×#117	—	2	32	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
47	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
49	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
56	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
57	C₂×C₄²×C₁₉	—	2	8	no	—
58	C₂×C₄²×C₁₉	—	2	4	no	—
59	C₂×C₄²×C₁₉	—	2	2	no	—
60	C₂×C₄²×C₁₉	—	2	2	no	—
61	C₂×C₄²×C₁₉	—	2	4	no	—
62	C₂×C₄²×C₁₉	—	2	4	no	—
63	C₁₉×#95	—	2	4	no	—
64	C₁₉×#95	—	2	8	no	—
65	C₁₉×#95	—	2	8	no	—
66	C₁₉×#95	—	4	4	no	—
67	C₁₉×#95	C₂×C₄	1	8	yes	—
68	C₂⁴×C₁₉	—	2	2	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	—	2	2	no	—
72	C₂⁴×C₁₉	—	2	2	no	—
73	C₂⁴×C₁₉	—	2	2	no	—
74	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
75	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
76	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
77	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	16	no	—
81	C₂²×C₄×C₁₉	—	2	8	no	—
82	C₂²×C₄×C₁₉	—	2	16	no	—
83	C₂²×C₄×C₁₉	—	2	8	no	—
84	C₂²×C₄×C₁₉	—	2	4	no	—
85	C₂²×C₄×C₁₉	—	2	4	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	2	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	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	4	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	C₄⋊C₄	1	16	yes	complemented
109	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₉	#41	1	4	yes	—
119	C₂²×C₄×C₁₉	#41	1	4	yes	—
120	C₂²×C₄×C₁₉	#41	1	4	yes	—
121	C₄⋊C₄×C₁₉	—	2	16	no	—
122	C₄⋊C₄×C₁₉	—	2	16	no	—
123	C₄⋊C₄×C₁₉	—	4	16	no	—
124	C₂²⋊C₄×C₁₉	—	2	16	no	—
125	C₂²⋊C₄×C₁₉	—	2	16	no	—
126	C₂²⋊C₄×C₁₉	—	4	8	no	—
127	C₄²×C₁₉	—	2	16	no	—
128	C₄²×C₁₉	—	4	4	no	—
129	C₄²×C₁₉	—	4	4	no	—
130	#14129	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₁₉	—	2	4	no	—
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	4	no	—
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	4	no	—
142	C₂³×C₁₉	—	2	4	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	—	4	2	no	—
149	C₂³×C₁₉	—	4	2	no	—
150	C₂³×C₁₉	—	4	2	no	—
151	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
152	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
153	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
154	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
155	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
156	C₂³×C₁₉	C₂×#41	1	2	yes	—
157	C₂³×C₁₉	C₂×#41	1	2	yes	—
158	C₂³×C₁₉	C₂×#41	1	2	yes	—
159	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
160	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	32	no	—
166	C₂×C₄×C₁₉	—	2	8	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	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	8	no	—
174	C₂×C₄×C₁₉	—	2	8	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	4	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
195	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
196	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
197	C₂×C₄×C₁₉	#120	1	4	yes	—
198	C₂×C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
199	C₂×C₄×C₁₉	#123	1	4	yes	—
200	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic
201	C₂×#389	C₂×C₁₉	1	2	yes	complemented
202	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
203	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
204	#1439	C₂×C₁₉	1	4	yes	—
205	#1436	C₂×C₁₉	1	4	yes	complemented
206	C₄⋊#95	C₂×C₁₉	1	2	yes	complemented
207	C₂²×C₁₉	—	2	4	no	—
208	C₂²×C₁₉	—	2	4	no	—
209	C₂²×C₁₉	—	2	4	no	—
210	C₂²×C₁₉	—	4	4	no	—
211	C₂²×C₁₉	—	4	4	no	—
212	C₂²×C₁₉	—	4	4	no	—
213	C₂²×C₁₉	—	4	4	no	—
214	C₂²×C₁₉	—	4	4	no	—
215	C₂²×C₁₉	—	4	4	no	—
216	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
218	C₂²×C₁₉	C₄×#41	1	2	yes	—
219	C₂²×C₁₉	#518	1	1	yes	characteristic
220	C₂²×C₁₉	#519	1	1	yes	characteristic
221	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
222	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
223	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
224	C₂²×C₁₉	#525	1	2	yes	—
225	C₂²×C₁₉	#533	1	1	yes	characteristic
226	C₂²×C₁₉	#533	1	1	yes	characteristic
227	C₂²×C₁₉	#537	1	2	yes	—
228	C₂²×C₁₉	#544	1	2	yes	—
229	C₂²×C₁₉	#546	1	2	yes	—
230	C₂²×C₁₉	#547	1	2	yes	—
231	C₂²×C₁₉	#548	1	2	yes	—
232	C₂²×C₁₉	#550	1	2	yes	—
233	C₂²×C₁₉	#552	1	2	yes	—
234	C₂²×C₁₉	#553	1	2	yes	—
235	C₂²×C₁₉	#555	1	2	yes	—
236	C₂²×C₁₉	#556	1	2	yes	—
237	C₄×C₁₉	—	2	4	no	—
238	C₄×C₁₉	—	4	8	no	—
239	C₄×C₁₉	—	4	8	no	—
240	C₄×C₁₉	—	4	4	no	—
241	C₄×C₁₉	—	4	4	no	—
242	C₄×C₁₉	#385	1	8	yes	—
243	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×#117	—	2	4	no	—
245	C₂×#117	—	2	8	no	—
246	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
247	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
248	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
249	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
250	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
251	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
252	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
253	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
254	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
255	#389	—	2	8	no	—
256	#380	C₄×C₁₉	1	8	yes	complemented
257	C₄×C₂²⋊C₄	—	2	4	no	—
258	C₂×#95	C₂²×C₁₉	1	4	yes	—
259	C₂×#95	C₂²×C₁₉	1	2	yes	—
260	C₂×#95	C₂²×C₁₉	1	4	yes	—
261	C₂×#95	C₂²×C₁₉	1	4	yes	—
262	C₂×#95	C₂²×C₁₉	1	2	yes	—
263	C₂×C₁₉	—	4	4	no	—
264	C₂×C₁₉	C₂×#385	1	1	yes	characteristic
265	C₂×C₁₉	#2296	1	1	yes	characteristic
266	C₂×C₁₉	#2316	1	1	yes	characteristic
267	C₂×C₁₉	#2362	1	2	yes	—
268	C₂×C₁₉	#2363	1	2	yes	—
269	C₂×C₁₉	#2407	1	2	yes	—
270	C₂×C₁₉	#2439	1	2	yes	—
271	C₂×C₁₉	#2441	1	2	yes	—
272	C₂×C₁₉	#2485	1	2	yes	—
273	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	—	2	4	no	—
276	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
277	C₂³×C₄	D₄×C₁₉	1	4	yes	—
278	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
279	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
280	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
281	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
282	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
283	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
285	#117	—	2	32	no	—
286	C₂×C₄⋊C₄	—	2	4	no	—
287	C₂×C₄⋊C₄	—	2	4	no	—
288	C₂×C₄⋊C₄	—	2	4	no	—
289	C₂×C₄⋊C₄	—	2	4	no	—
290	C₂×C₄⋊C₄	—	2	8	no	—
291	C₂×C₄⋊C₄	—	2	8	no	—
292	C₂×C₄⋊C₄	—	4	4	no	—
293	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
294	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	—
295	C₂×C₂²⋊C₄	—	2	4	no	—
296	C₂×C₂²⋊C₄	—	2	4	no	—
297	C₂×C₂²⋊C₄	—	2	8	no	—
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₂²⋊C₄	—	2	4	no	—
300	C₂×C₂²⋊C₄	—	4	4	no	—
301	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
302	C₂×C₄²	—	2	8	no	—
303	C₂×C₄²	—	2	4	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	4	no	—
307	C₂×C₄²	—	2	4	no	—
308	#95	—	2	4	no	—
309	#95	—	2	8	no	—
310	#95	—	2	8	no	—
311	#95	—	4	4	no	—
312	#95	C₂×C₄×C₁₉	1	8	yes	—
313	C₁₉	#14129	1	1	yes	characteristic, direct product factor, Sylow
314	C₂⁴	—	2	2	no	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	—	2	2	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	2	2	no	—
320	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
321	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
322	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
323	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	16	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	16	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	C₄⋊C₄×C₁₉	1	16	yes	complemented
355	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
362	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
363	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
364	C₂²×C₄	#41×C₁₉	1	4	yes	—
365	C₂²×C₄	#41×C₁₉	1	4	yes	—
366	C₂²×C₄	#41×C₁₉	1	4	yes	—
367	C₄⋊C₄	—	2	16	no	—
368	C₄⋊C₄	—	2	16	no	—
369	C₄⋊C₄	—	4	16	no	—
370	C₂²⋊C₄	—	2	16	no	—
371	C₂²⋊C₄	—	2	16	no	—
372	C₂²⋊C₄	—	4	8	no	—
373	C₄²	—	2	16	no	—
374	C₄²	—	4	4	no	—
375	C₄²	—	4	4	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
397	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
398	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
399	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
400	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
401	C₂³	C₂×#41×C₁₉	1	2	yes	—
402	C₂³	C₂×#41×C₁₉	1	2	yes	—
403	C₂³	C₂×#41×C₁₉	1	2	yes	—
404	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
405	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	32	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
440	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
441	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
442	C₂×C₄	C₁₉×#120	1	4	yes	—
443	C₂×C₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
444	C₂×C₄	C₁₉×#123	1	4	yes	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	4	4	no	—
454	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
455	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
456	C₂²	C₄×#41×C₁₉	1	2	yes	—
457	C₂²	C₁₉×#518	1	1	yes	characteristic
458	C₂²	C₁₉×#519	1	1	yes	characteristic
459	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
460	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
461	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
462	C₂²	C₁₉×#525	1	2	yes	—
463	C₂²	C₁₉×#533	1	1	yes	characteristic
464	C₂²	C₁₉×#533	1	1	yes	characteristic
465	C₂²	C₁₉×#537	1	2	yes	—
466	C₂²	C₁₉×#544	1	2	yes	—
467	C₂²	C₁₉×#546	1	2	yes	—
468	C₂²	C₁₉×#547	1	2	yes	—
469	C₂²	C₁₉×#548	1	2	yes	—
470	C₂²	C₁₉×#550	1	2	yes	—
471	C₂²	C₁₉×#552	1	2	yes	—
472	C₂²	C₁₉×#553	1	2	yes	—
473	C₂²	C₁₉×#555	1	2	yes	—
474	C₂²	C₁₉×#556	1	2	yes	—
475	C₄	—	2	4	no	—
476	C₄	—	4	8	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	8	no	—
480	C₄	C₁₉×#385	1	8	yes	—
481	C₂	—	4	4	no	—
482	C₂	C₂×C₁₉×#385	1	1	yes	characteristic
483	C₂	C₁₉×#2296	1	1	yes	characteristic
484	C₂	C₁₉×#2316	1	1	yes	characteristic
485	C₂	C₁₉×#2362	1	2	yes	—
486	C₂	C₁₉×#2363	1	2	yes	—
487	C₂	C₁₉×#2407	1	2	yes	—
488	C₂	C₁₉×#2439	1	2	yes	—
489	C₂	C₁₉×#2441	1	2	yes	—
490	C₂	C₁₉×#2485	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
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×#389	C₂	semidirect
6. C₁₉×#1436	C₂	semidirect
7. C₁₉×C₄⋊#95	C₂	semidirect
21. C₁₉×#380	C₄	semidirect
108. C₂²×C₄×C₁₉	C₄⋊C₄	semidirect
130. #14129	C₁₉	direct (N × H)
201. C₂×#389	C₂×C₁₉	semidirect
205. #1436	C₂×C₁₉	semidirect
206. C₄⋊#95	C₂×C₁₉	semidirect
256. #380	C₄×C₁₉	semidirect
313. C₁₉	#14129	direct (N × H)
354. C₂²×C₄	C₄⋊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×#117	2
C₂×C₁₉×#389	2
C₂×C₁₉×#380	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1439	2
C₁₉×#1436	2
C₁₉×C₄⋊#95	2
#14129	19

Subgroups — C19×#14129 #18020088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14129 #18020088