Subgroups — C₁₉×#14238 #18020197

Order 4864.

1378 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#398	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	2	yes	maximal
3	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1441	C₂	1	2	yes	maximal
5	C₁₉×#1436	C₂	1	2	yes	maximal
6	C₁₉×#1436	C₂	1	2	yes	maximal
7	C₁₉×#1436	C₂	1	2	yes	maximal
8	C₁₉×#1436	C₂	1	2	yes	maximal
9	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#398	C₄	1	8	yes	complemented
20	C₄×C₄⋊C₄×C₁₉	—	2	8	no	—
21	C₂×C₁₉×#95	C₂²	1	2	yes	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	2	yes	—
24	C₂×C₁₉×#95	C₂²	1	2	yes	—
25	C₂×C₁₉×#95	C₂²	1	2	yes	—
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	2	yes	—
30	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#95	C₂²	1	2	yes	—
32	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
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	4	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₉	Q₈	1	8	yes	—
59	C₂×C₄²×C₁₉	—	2	4	no	—
60	C₂×C₄²×C₁₉	—	2	4	no	—
61	C₂×C₄²×C₁₉	—	2	4	no	—
62	C₂×C₄²×C₁₉	—	2	4	no	—
63	C₂×C₄²×C₁₉	—	4	1	no	—
64	C₂×C₄²×C₁₉	—	4	1	no	—
65	C₂×C₄²×C₁₉	—	4	2	no	—
66	C₂×C₄²×C₁₉	—	4	2	no	—
67	C₂×C₄²×C₁₉	D₄	1	4	yes	—
68	C₁₉×#95	—	2	4	no	—
69	C₁₉×#95	—	2	4	no	—
70	C₁₉×#95	—	2	4	no	—
71	C₁₉×#95	—	2	4	no	—
72	C₁₉×#95	—	2	4	no	—
73	C₁₉×#95	—	2	4	no	—
74	C₁₉×#95	—	2	4	no	—
75	C₁₉×#95	—	4	1	no	—
76	C₁₉×#95	—	4	2	no	—
77	C₁₉×#95	—	4	2	no	—
78	C₁₉×#95	C₂×C₄	1	8	yes	—
79	C₁₉×#95	C₂×C₄	1	4	yes	—
80	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	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	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
134	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
136	C₂²×C₄×C₁₉	#41	1	4	yes	—
137	C₂²×C₄×C₁₉	#41	1	2	yes	—
138	C₂²×C₄×C₁₉	#41	1	4	yes	—
139	C₂²×C₄×C₁₉	#41	1	4	yes	—
140	C₄⋊C₄×C₁₉	—	2	16	no	—
141	C₄⋊C₄×C₁₉	—	2	16	no	—
142	C₄⋊C₄×C₁₉	—	4	4	no	—
143	C₄⋊C₄×C₁₉	—	4	4	no	—
144	C₄⋊C₄×C₁₉	—	4	4	no	—
145	C₄⋊C₄×C₁₉	—	4	4	no	—
146	C₄²×C₁₉	—	2	16	no	—
147	C₄²×C₁₉	—	4	4	no	—
148	C₄²×C₁₉	—	4	8	no	—
149	#14238	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
151	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
152	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
153	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
154	C₂³×C₁₉	C₂×#41	1	2	yes	—
155	C₂³×C₁₉	C₂×#41	1	2	yes	—
156	C₂³×C₁₉	C₂×#41	1	2	yes	—
157	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	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	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
218	C₂×C₄×C₁₉	C₄×Q₈	1	8	yes	—
219	C₂×C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
220	C₂×#398	C₂×C₁₉	1	1	yes	characteristic
221	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	2	yes	—
222	#1441	C₂×C₁₉	1	1	yes	characteristic
223	#1441	C₂×C₁₉	1	2	yes	—
224	#1436	C₂×C₁₉	1	2	yes	—
225	#1436	C₂×C₁₉	1	2	yes	—
226	#1436	C₂×C₁₉	1	2	yes	—
227	#1436	C₂×C₁₉	1	2	yes	—
228	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic
229	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×C₄×Q₈	1	2	yes	—
231	C₂²×C₁₉	C₄×#41	1	2	yes	—
232	C₂²×C₁₉	#518	1	1	yes	characteristic
233	C₂²×C₁₉	#520	1	1	yes	characteristic
234	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
235	C₂²×C₁₉	#525	1	2	yes	—
236	C₂²×C₁₉	#529	1	2	yes	—
237	C₂²×C₁₉	#533	1	2	yes	—
238	C₂²×C₁₉	#534	1	1	yes	characteristic
239	C₂²×C₁₉	#537	1	1	yes	characteristic
240	C₂²×C₁₉	#538	1	1	yes	characteristic
241	C₂²×C₁₉	#539	1	1	yes	characteristic
242	C₂²×C₁₉	#551	1	1	yes	characteristic
243	C₂²×C₁₉	#552	1	2	yes	—
244	C₂²×C₁₉	#553	1	2	yes	—
245	C₂²×C₁₉	#553	1	2	yes	—
246	C₂²×C₁₉	#554	1	2	yes	—
247	C₂²×C₁₉	#554	1	2	yes	—
248	C₂²×C₁₉	#555	1	1	yes	characteristic
249	C₂²×C₁₉	#557	1	2	yes	—
250	C₂²×C₁₉	Q₈²	1	1	yes	characteristic
251	C₂²×C₁₉	#559	1	1	yes	characteristic
252	C₄×C₁₉	—	2	8	no	—
253	C₄×C₁₉	—	2	4	no	—
254	C₄×C₁₉	—	2	8	no	—
255	C₄×C₁₉	—	4	4	no	—
256	C₄×C₁₉	—	4	4	no	—
257	C₄×C₁₉	—	4	4	no	—
258	C₄×C₁₉	—	4	2	no	—
259	C₄×C₁₉	—	4	2	no	—
260	C₄×C₁₉	—	8	2	no	—
261	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
263	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
264	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
267	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
268	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
269	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
270	#398	C₄×C₁₉	1	8	yes	complemented
271	C₄×C₄⋊C₄	—	2	8	no	—
272	C₂×#95	C₂²×C₁₉	1	2	yes	—
273	C₂×#95	C₂²×C₁₉	1	2	yes	—
274	C₂×#95	C₂²×C₁₉	1	2	yes	—
275	C₂×#95	C₂²×C₁₉	1	2	yes	—
276	C₂×#95	C₂²×C₁₉	1	2	yes	—
277	C₂×#95	C₂²×C₁₉	1	2	yes	—
278	C₂×#95	C₂²×C₁₉	1	2	yes	—
279	C₂×#95	C₂²×C₁₉	1	2	yes	—
280	C₂×#95	C₂²×C₁₉	1	2	yes	—
281	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
282	C₂×#95	C₂²×C₁₉	1	2	yes	—
283	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×C₁₉	C₄×C₂²⋊Q₈	1	2	yes	—
285	C₂×C₁₉	#2325	1	1	yes	characteristic
286	C₂×C₁₉	#2369	1	1	yes	characteristic
287	C₂×C₁₉	#2370	1	2	yes	—
288	C₂×C₁₉	#2374	1	1	yes	characteristic
289	C₂×C₁₉	#2579	1	2	yes	—
290	C₂×C₁₉	#2582	1	1	yes	characteristic
291	C₂×C₁₉	#2585	1	2	yes	—
292	C₂×C₁₉	#2586	1	1	yes	characteristic
293	C₂×C₁₉	#2593	1	1	yes	characteristic
294	C₂×C₁₉	#2609	1	1	yes	characteristic
295	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
296	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
299	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
301	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
303	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	—	2	4	no	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₄⋊C₄	—	2	4	no	—
308	C₂×C₄⋊C₄	—	2	4	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	4	1	no	—
311	C₂×C₄⋊C₄	—	4	1	no	—
312	C₂×C₄⋊C₄	—	4	1	no	—
313	C₂×C₄⋊C₄	—	4	1	no	—
314	C₂×C₄⋊C₄	—	4	1	no	—
315	C₂×C₄⋊C₄	—	4	1	no	—
316	C₂×C₄⋊C₄	—	4	1	no	—
317	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
318	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
319	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
320	C₂×C₄⋊C₄	Q₈×C₁₉	1	8	yes	—
321	C₂×C₄²	—	2	4	no	—
322	C₂×C₄²	—	2	4	no	—
323	C₂×C₄²	—	2	4	no	—
324	C₂×C₄²	—	2	4	no	—
325	C₂×C₄²	—	4	1	no	—
326	C₂×C₄²	—	4	1	no	—
327	C₂×C₄²	—	4	2	no	—
328	C₂×C₄²	—	4	2	no	—
329	C₂×C₄²	D₄×C₁₉	1	4	yes	—
330	#95	—	2	4	no	—
331	#95	—	2	4	no	—
332	#95	—	2	4	no	—
333	#95	—	2	4	no	—
334	#95	—	2	4	no	—
335	#95	—	2	4	no	—
336	#95	—	2	4	no	—
337	#95	—	4	1	no	—
338	#95	—	4	2	no	—
339	#95	—	4	2	no	—
340	#95	C₂×C₄×C₁₉	1	8	yes	—
341	#95	C₂×C₄×C₁₉	1	4	yes	—
342	C₁₉	#14238	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
390	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
391	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
392	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
393	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
394	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
395	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
396	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
397	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
398	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
399	C₂²×C₄	#41×C₁₉	1	4	yes	—
400	C₂²×C₄	#41×C₁₉	1	2	yes	—
401	C₂²×C₄	#41×C₁₉	1	4	yes	—
402	C₂²×C₄	#41×C₁₉	1	4	yes	—
403	C₄⋊C₄	—	2	16	no	—
404	C₄⋊C₄	—	2	16	no	—
405	C₄⋊C₄	—	4	4	no	—
406	C₄⋊C₄	—	4	4	no	—
407	C₄⋊C₄	—	4	4	no	—
408	C₄⋊C₄	—	4	4	no	—
409	C₄²	—	2	16	no	—
410	C₄²	—	4	4	no	—
411	C₄²	—	4	8	no	—
412	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
413	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
414	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
415	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
416	C₂³	C₂×#41×C₁₉	1	2	yes	—
417	C₂³	C₂×#41×C₁₉	1	2	yes	—
418	C₂³	C₂×#41×C₁₉	1	2	yes	—
419	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
422	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
480	C₂×C₄	C₄×Q₈×C₁₉	1	8	yes	—
481	C₂×C₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
482	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
483	C₂²	C₂×C₄×Q₈×C₁₉	1	2	yes	—
484	C₂²	C₄×#41×C₁₉	1	2	yes	—
485	C₂²	C₁₉×#518	1	1	yes	characteristic
486	C₂²	C₁₉×#520	1	1	yes	characteristic
487	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
488	C₂²	C₁₉×#525	1	2	yes	—
489	C₂²	C₁₉×#529	1	2	yes	—
490	C₂²	C₁₉×#533	1	2	yes	—
491	C₂²	C₁₉×#534	1	1	yes	characteristic
492	C₂²	C₁₉×#537	1	1	yes	characteristic
493	C₂²	C₁₉×#538	1	1	yes	characteristic
494	C₂²	C₁₉×#539	1	1	yes	characteristic
495	C₂²	C₁₉×#551	1	1	yes	characteristic
496	C₂²	C₁₉×#552	1	2	yes	—
497	C₂²	C₁₉×#553	1	2	yes	—
498	C₂²	C₁₉×#553	1	2	yes	—
499	C₂²	C₁₉×#554	1	2	yes	—
500	C₂²	C₁₉×#554	1	2	yes	—
501	C₂²	C₁₉×#555	1	1	yes	characteristic
502	C₂²	C₁₉×#557	1	2	yes	—
503	C₂²	Q₈²×C₁₉	1	1	yes	characteristic
504	C₂²	C₁₉×#559	1	1	yes	characteristic
505	C₄	—	2	8	no	—
506	C₄	—	2	8	no	—
507	C₄	—	2	4	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	8	2	no	—
514	C₂	C₄×C₁₉×C₂²⋊Q₈	1	2	yes	—
515	C₂	C₁₉×#2325	1	1	yes	characteristic
516	C₂	C₁₉×#2369	1	1	yes	characteristic
517	C₂	C₁₉×#2370	1	2	yes	—
518	C₂	C₁₉×#2374	1	1	yes	characteristic
519	C₂	C₁₉×#2579	1	2	yes	—
520	C₂	C₁₉×#2582	1	1	yes	characteristic
521	C₂	C₁₉×#2585	1	2	yes	—
522	C₂	C₁₉×#2586	1	1	yes	characteristic
523	C₂	C₁₉×#2593	1	1	yes	characteristic
524	C₂	C₁₉×#2609	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
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
19. C₁₉×#398	C₄	semidirect
149. #14238	C₁₉	direct (N × H)
270. #398	C₄×C₁₉	semidirect
342. C₁₉	#14238	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×#398	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1441	2
C₁₉×#1436	2
C₁₉×C₄⋊#95	2
#14238	19

Subgroups — C19×#14238 #18020197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14238 #18020197