Subgroups — C₁₉×#14308 #18020267

Order 4864.

1210 conjugacy classes of subgroups.

The subgroup lattice has 556 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×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1445	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1445	C₂	1	2	yes	maximal
6	C₁₉×#1443	C₂	1	2	yes	maximal
7	C₁₉×#1442	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1436	C₂	1	2	yes	maximal
10	C₁₉×#1436	C₂	1	2	yes	maximal
11	C₁₉×#1434	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
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×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#398	C₄	1	8	yes	complemented
20	C₁₉×#387	—	2	4	no	—
21	C₄×C₄⋊C₄×C₁₉	—	2	4	no	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#95	C₂²	1	2	yes	—
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
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	2	yes	—
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂×C₁₉×#95	C₂²	1	2	yes	—
35	C₂×C₁₉×#95	C₂²	1	2	yes	—
36	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#95	C₂²	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
62	C₂×C₄²×C₁₉	—	2	4	no	—
63	C₂×C₄²×C₁₉	—	2	4	no	—
64	C₂×C₄²×C₁₉	—	4	2	no	—
65	C₂×C₄²×C₁₉	—	4	2	no	—
66	C₂×C₄²×C₁₉	D₄	1	4	yes	—
67	C₁₉×#95	—	2	4	no	—
68	C₁₉×#95	—	2	2	no	—
69	C₁₉×#95	—	2	2	no	—
70	C₁₉×#95	—	2	2	no	—
71	C₁₉×#95	—	2	2	no	—
72	C₁₉×#95	—	2	4	no	—
73	C₁₉×#95	—	2	4	no	—
74	C₁₉×#95	—	2	4	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	4	2	no	—
77	C₁₉×#95	—	4	2	no	—
78	C₁₉×#95	—	4	2	no	—
79	C₁₉×#95	—	4	2	no	—
80	C₁₉×#95	—	4	2	no	—
81	C₁₉×#95	C₂×C₄	1	8	yes	—
82	C₁₉×#95	C₂×C₄	1	4	yes	—
83	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	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	1	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	1	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	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	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	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	#41	1	4	yes	—
147	C₂²×C₄×C₁₉	#41	1	2	yes	—
148	C₂²×C₄×C₁₉	#41	1	4	yes	—
149	C₄⋊C₄×C₁₉	—	2	8	no	—
150	C₄⋊C₄×C₁₉	—	2	8	no	—
151	C₄⋊C₄×C₁₉	—	2	8	no	—
152	C₄⋊C₄×C₁₉	—	4	8	no	—
153	C₄⋊C₄×C₁₉	—	4	4	no	—
154	C₄²×C₁₉	—	2	8	no	—
155	C₄²×C₁₉	—	4	8	no	—
156	#14308	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
158	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
159	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
160	C₂³×C₁₉	C₂×#41	1	2	yes	—
161	C₂³×C₁₉	C₂×#41	1	2	yes	—
162	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
166	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
167	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	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	1	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	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	1	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	1	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	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
232	C₂×C₄×C₁₉	#123	1	4	yes	—
233	C₂×#398	C₂×C₁₉	1	1	yes	characteristic
234	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
235	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
236	#1445	C₂×C₁₉	1	1	yes	characteristic
237	#1445	C₂×C₁₉	1	2	yes	—
238	#1443	C₂×C₁₉	1	2	yes	—
239	#1442	C₂×C₁₉	1	1	yes	characteristic
240	#1441	C₂×C₁₉	1	1	yes	characteristic
241	#1436	C₂×C₁₉	1	2	yes	—
242	#1436	C₂×C₁₉	1	2	yes	—
243	#1434	C₂×C₁₉	1	1	yes	characteristic
244	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₁₉	C₄×#41	1	2	yes	—
246	C₂²×C₁₉	#518	1	1	yes	characteristic
247	C₂²×C₁₉	#519	1	2	yes	—
248	C₂²×C₁₉	#520	1	1	yes	characteristic
249	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
250	C₂²×C₁₉	#525	1	1	yes	characteristic
251	C₂²×C₁₉	#529	1	2	yes	—
252	C₂²×C₁₉	#535	1	1	yes	characteristic
253	C₂²×C₁₉	#536	1	1	yes	characteristic
254	C₂²×C₁₉	#536	1	1	yes	characteristic
255	C₂²×C₁₉	#537	1	1	yes	characteristic
256	C₂²×C₁₉	#539	1	2	yes	—
257	C₂²×C₁₉	#539	1	2	yes	—
258	C₂²×C₁₉	#539	1	2	yes	—
259	C₂²×C₁₉	#539	1	2	yes	—
260	C₂²×C₁₉	#540	1	1	yes	characteristic
261	C₂²×C₁₉	#541	1	2	yes	—
262	C₂²×C₁₉	#541	1	2	yes	—
263	C₂²×C₁₉	#541	1	2	yes	—
264	C₂²×C₁₉	#542	1	1	yes	characteristic
265	C₂²×C₁₉	#542	1	2	yes	—
266	C₂²×C₁₉	#542	1	2	yes	—
267	C₄×C₁₉	—	2	4	no	—
268	C₄×C₁₉	—	2	4	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	4	4	no	—
271	C₄×C₁₉	—	4	4	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	4	4	no	—
274	C₄×C₁₉	—	4	2	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	—	8	2	no	—
278	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
280	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
283	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
284	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
285	#398	C₄×C₁₉	1	8	yes	complemented
286	#387	—	2	4	no	—
287	C₄×C₄⋊C₄	—	2	4	no	—
288	C₂×#95	C₂²×C₁₉	1	2	yes	—
289	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×#95	C₂²×C₁₉	1	2	yes	—
292	C₂×#95	C₂²×C₁₉	1	2	yes	—
293	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#95	C₂²×C₁₉	1	2	yes	—
296	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#95	C₂²×C₁₉	1	2	yes	—
298	C₂×#95	C₂²×C₁₉	1	2	yes	—
299	C₂×#95	C₂²×C₁₉	1	2	yes	—
300	C₂×#95	C₂²×C₁₉	1	2	yes	—
301	C₂×#95	C₂²×C₁₉	1	2	yes	—
302	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×#95	C₂²×C₁₉	1	2	yes	—
304	C₂×C₁₉	C₄×#123	1	1	yes	characteristic
305	C₂×C₁₉	#2324	1	1	yes	characteristic
306	C₂×C₁₉	#2327	1	1	yes	characteristic
307	C₂×C₁₉	#2332	1	2	yes	—
308	C₂×C₁₉	#2336	1	2	yes	—
309	C₂×C₁₉	#2623	1	1	yes	characteristic
310	C₂×C₁₉	#2625	1	1	yes	characteristic
311	C₂×C₁₉	#2633	1	1	yes	characteristic
312	C₂×C₁₉	#2637	1	1	yes	characteristic
313	C₂×C₁₉	#2654	1	2	yes	—
314	C₂×C₁₉	#2655	1	2	yes	—
315	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
318	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
322	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
324	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	4	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	—	4	2	no	—
335	C₂×C₄⋊C₄	—	4	2	no	—
336	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
337	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
338	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
339	C₂×C₄²	—	2	4	no	—
340	C₂×C₄²	—	2	4	no	—
341	C₂×C₄²	—	4	2	no	—
342	C₂×C₄²	—	4	2	no	—
343	C₂×C₄²	D₄×C₁₉	1	4	yes	—
344	#95	—	2	4	no	—
345	#95	—	2	2	no	—
346	#95	—	2	2	no	—
347	#95	—	2	2	no	—
348	#95	—	2	2	no	—
349	#95	—	2	4	no	—
350	#95	—	2	4	no	—
351	#95	—	2	4	no	—
352	#95	—	2	2	no	—
353	#95	—	4	2	no	—
354	#95	—	4	2	no	—
355	#95	—	4	2	no	—
356	#95	—	4	2	no	—
357	#95	—	4	2	no	—
358	#95	C₂×C₄×C₁₉	1	8	yes	—
359	#95	C₂×C₄×C₁₉	1	4	yes	—
360	C₁₉	#14308	1	1	yes	characteristic, direct product factor, Sylow
361	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	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	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
417	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
418	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
419	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
420	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
421	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
422	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
424	C₂²×C₄	#41×C₁₉	1	4	yes	—
425	C₂²×C₄	#41×C₁₉	1	2	yes	—
426	C₂²×C₄	#41×C₁₉	1	4	yes	—
427	C₄⋊C₄	—	2	8	no	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	4	8	no	—
431	C₄⋊C₄	—	4	4	no	—
432	C₄²	—	2	8	no	—
433	C₄²	—	4	8	no	—
434	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
435	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
436	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
437	C₂³	C₂×#41×C₁₉	1	2	yes	—
438	C₂³	C₂×#41×C₁₉	1	2	yes	—
439	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
443	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
444	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	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	1	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
509	C₂×C₄	C₁₉×#123	1	4	yes	—
510	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
511	C₂²	C₄×#41×C₁₉	1	2	yes	—
512	C₂²	C₁₉×#518	1	1	yes	characteristic
513	C₂²	C₁₉×#519	1	2	yes	—
514	C₂²	C₁₉×#520	1	1	yes	characteristic
515	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
516	C₂²	C₁₉×#525	1	1	yes	characteristic
517	C₂²	C₁₉×#529	1	2	yes	—
518	C₂²	C₁₉×#535	1	1	yes	characteristic
519	C₂²	C₁₉×#536	1	1	yes	characteristic
520	C₂²	C₁₉×#536	1	1	yes	characteristic
521	C₂²	C₁₉×#537	1	1	yes	characteristic
522	C₂²	C₁₉×#539	1	2	yes	—
523	C₂²	C₁₉×#539	1	2	yes	—
524	C₂²	C₁₉×#539	1	2	yes	—
525	C₂²	C₁₉×#539	1	2	yes	—
526	C₂²	C₁₉×#540	1	1	yes	characteristic
527	C₂²	C₁₉×#541	1	2	yes	—
528	C₂²	C₁₉×#541	1	2	yes	—
529	C₂²	C₁₉×#541	1	2	yes	—
530	C₂²	C₁₉×#542	1	1	yes	characteristic
531	C₂²	C₁₉×#542	1	2	yes	—
532	C₂²	C₁₉×#542	1	2	yes	—
533	C₄	—	2	4	no	—
534	C₄	—	2	4	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	4	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	4	no	—
541	C₄	—	8	1	no	—
542	C₄	—	8	1	no	—
543	C₄	—	8	2	no	—
544	C₂	C₄×C₁₉×#123	1	1	yes	characteristic
545	C₂	C₁₉×#2324	1	1	yes	characteristic
546	C₂	C₁₉×#2327	1	1	yes	characteristic
547	C₂	C₁₉×#2332	1	2	yes	—
548	C₂	C₁₉×#2336	1	2	yes	—
549	C₂	C₁₉×#2623	1	1	yes	characteristic
550	C₂	C₁₉×#2625	1	1	yes	characteristic
551	C₂	C₁₉×#2633	1	1	yes	characteristic
552	C₂	C₁₉×#2637	1	1	yes	characteristic
553	C₂	C₁₉×#2654	1	2	yes	—
554	C₂	C₁₉×#2655	1	2	yes	—

	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
156. #14308	C₁₉	direct (N × H)
285. #398	C₄×C₁₉	semidirect
360. C₁₉	#14308	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×C₁₉×#387	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1445	2
C₁₉×#1443	2
C₁₉×#1442	2
C₁₉×#1441	2
C₁₉×#1436	2
C₁₉×#1434	2
#14308	19

Subgroups — C19×#14308 #18020267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14308 #18020267