Subgroups — C₁₉×#14128 #18020087

Order 4864.

2222 conjugacy classes of subgroups.

The subgroup lattice has 502 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×#385	C₂	1	2	yes	maximal
3	C₂×C₁₉×#381	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1444	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1442	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1436	C₂	1	4	yes	maximal, complemented
8	C₁₉×C₂²⋊#95	C₂	1	2	yes	maximal
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#117	—	2	4	no	—
13	C₂×C₁₉×#117	—	2	8	no	—
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	4	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#385	—	2	8	no	—
21	C₁₉×#381	C₄	1	8	yes	complemented
22	C₂×C₁₉×#95	—	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	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	4	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	2	yes	—
30	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	4	no	—
32	C₂³×C₄×C₁₉	—	2	4	no	—
33	C₂³×C₄×C₁₉	—	2	2	no	—
34	C₂³×C₄×C₁₉	—	2	2	no	—
35	C₂³×C₄×C₁₉	—	2	4	no	—
36	C₂³×C₄×C₁₉	—	2	4	no	—
37	C₂³×C₄×C₁₉	—	2	4	no	—
38	C₂³×C₄×C₁₉	—	2	4	no	—
39	C₂³×C₄×C₁₉	—	4	2	no	—
40	C₂³×C₄×C₁₉	—	4	2	no	—
41	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
42	C₂³×C₄×C₁₉	D₄	1	4	yes	—
43	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₁₉×#117	—	2	32	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
64	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
65	C₂×C₄²×C₁₉	—	2	4	no	—
66	C₂×C₄²×C₁₉	—	2	4	no	—
67	C₂×C₄²×C₁₉	—	2	4	no	—
68	C₁₉×#95	—	2	4	no	—
69	C₁₉×#95	—	2	4	no	—
70	C₁₉×#95	—	2	8	no	—
71	C₁₉×#95	—	2	8	no	—
72	C₁₉×#95	—	4	4	no	—
73	C₁₉×#95	C₂×C₄	1	8	yes	complemented
74	C₁₉×#95	C₂×C₄	1	8	yes	complemented
75	C₂⁴×C₁₉	—	2	2	no	—
76	C₂⁴×C₁₉	—	2	2	no	—
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂⁴×C₁₉	—	2	2	no	—
79	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
80	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
81	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
82	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
83	C₂⁴×C₁₉	#41	1	4	yes	—
84	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	—	2	16	no	—
86	C₂²×C₄×C₁₉	—	2	8	no	—
87	C₂²×C₄×C₁₉	—	2	16	no	—
88	C₂²×C₄×C₁₉	—	2	8	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	8	no	—
94	C₂²×C₄×C₁₉	—	2	8	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	4	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	4	16	no	—
118	C₂²×C₄×C₁₉	—	4	16	no	—
119	C₂²×C₄×C₁₉	—	4	4	no	—
120	C₂²×C₄×C₁₉	—	4	4	no	—
121	C₂²×C₄×C₁₉	—	4	4	no	—
122	C₂²×C₄×C₁₉	—	4	4	no	—
123	C₂²×C₄×C₁₉	C₄⋊C₄	1	16	yes	complemented
124	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
125	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₁₉	#41	1	4	yes	—
134	C₂²×C₄×C₁₉	#41	1	4	yes	—
135	C₄⋊C₄×C₁₉	—	2	8	no	—
136	C₄⋊C₄×C₁₉	—	2	8	no	—
137	C₄⋊C₄×C₁₉	—	4	16	no	—
138	C₂²⋊C₄×C₁₉	—	2	16	no	—
139	C₂²⋊C₄×C₁₉	—	2	16	no	—
140	C₄²×C₁₉	—	2	16	no	—
141	#14128	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₉	—	2	4	no	—
143	C₂³×C₁₉	—	2	4	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	4	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	2	4	no	—
150	C₂³×C₁₉	—	2	8	no	—
151	C₂³×C₁₉	—	2	8	no	—
152	C₂³×C₁₉	—	2	8	no	—
153	C₂³×C₁₉	—	2	8	no	—
154	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
155	C₂³×C₁₉	C₄×D₄	1	8	yes	—
156	C₂³×C₁₉	#120	1	4	yes	—
157	C₂³×C₁₉	C₂²⋊Q₈	1	8	yes	—
158	C₂³×C₁₉	#123	1	4	yes	—
159	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
160	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
161	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
162	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
163	C₂³×C₁₉	C₂×#41	1	2	yes	—
164	C₂³×C₁₉	C₂×#41	1	2	yes	—
165	C₂³×C₁₉	C₂×#41	1	2	yes	—
166	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
167	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	32	no	—
177	C₂×C₄×C₁₉	—	2	8	no	—
178	C₂×C₄×C₁₉	—	2	8	no	—
179	C₂×C₄×C₁₉	—	2	8	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	8	no	—
185	C₂×C₄×C₁₉	—	2	8	no	—
186	C₂×C₄×C₁₉	—	2	8	no	—
187	C₂×C₄×C₁₉	—	2	8	no	—
188	C₂×C₄×C₁₉	—	4	16	no	—
189	C₂×C₄×C₁₉	—	4	16	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	2	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	4	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	—	4	4	no	—
201	C₂×C₄×C₁₉	—	4	4	no	—
202	C₂×C₄×C₁₉	—	4	4	no	—
203	C₂×C₄×C₁₉	—	4	4	no	—
204	C₂×C₄×C₁₉	—	4	4	no	—
205	C₂×C₄×C₁₉	—	4	4	no	—
206	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
207	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
208	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic
209	C₂×#385	C₂×C₁₉	1	2	yes	—
210	C₂×#381	C₂×C₁₉	1	1	yes	characteristic
211	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic
212	#1444	C₂×C₁₉	1	2	yes	complemented
213	#1442	C₂×C₁₉	1	2	yes	complemented
214	#1436	C₂×C₁₉	1	4	yes	complemented
215	C₂²⋊#95	C₂×C₁₉	1	2	yes	—
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	2	16	no	—
218	C₂²×C₁₉	—	2	4	no	—
219	C₂²×C₁₉	—	2	4	no	—
220	C₂²×C₁₉	—	2	16	no	—
221	C₂²×C₁₉	—	2	4	no	—
222	C₂²×C₁₉	—	2	4	no	—
223	C₂²×C₁₉	—	2	4	no	—
224	C₂²×C₁₉	#385	1	8	yes	—
225	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
226	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
227	C₂²×C₁₉	C₄×#41	1	2	yes	—
228	C₂²×C₁₉	#520	1	2	yes	—
229	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
231	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
232	C₂²×C₁₉	#525	1	1	yes	characteristic
233	C₂²×C₁₉	#525	1	1	yes	characteristic
234	C₂²×C₁₉	#533	1	2	yes	—
235	C₂²×C₁₉	#535	1	1	yes	characteristic
236	C₂²×C₁₉	#536	1	1	yes	characteristic
237	C₂²×C₁₉	#544	1	2	yes	—
238	C₂²×C₁₉	#546	1	4	yes	—
239	C₂²×C₁₉	#547	1	4	yes	—
240	C₂²×C₁₉	#551	1	4	yes	—
241	C₂²×C₁₉	#552	1	4	yes	—
242	C₄×C₁₉	—	2	4	no	—
243	C₄×C₁₉	—	2	4	no	—
244	C₄×C₁₉	—	4	8	no	—
245	C₄×C₁₉	—	4	4	no	—
246	C₄×C₁₉	—	4	4	no	—
247	C₄×C₁₉	—	4	4	no	—
248	C₄×C₁₉	—	4	4	no	—
249	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
250	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
251	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#117	—	2	4	no	—
253	C₂×#117	—	2	8	no	—
254	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
257	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
258	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
259	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
260	#385	—	2	8	no	—
261	#381	C₄×C₁₉	1	8	yes	complemented
262	C₂×#95	—	2	4	no	—
263	C₂×#95	C₂²×C₁₉	1	4	yes	—
264	C₂×#95	C₂²×C₁₉	1	2	yes	—
265	C₂×#95	C₂²×C₁₉	1	4	yes	—
266	C₂×#95	C₂²×C₁₉	1	2	yes	—
267	C₂×#95	C₂²×C₁₉	1	4	yes	—
268	C₂×#95	C₂²×C₁₉	1	2	yes	—
269	C₂×#95	C₂²×C₁₉	1	2	yes	—
270	C₂×C₁₉	—	2	8	no	—
271	C₂×C₁₉	C₂×#385	1	1	yes	characteristic
272	C₂×C₁₉	#2296	1	1	yes	characteristic
273	C₂×C₁₉	#2317	1	1	yes	characteristic
274	C₂×C₁₉	#2359	1	4	yes	—
275	C₂×C₁₉	#2404	1	1	yes	characteristic
276	C₂×C₁₉	#2406	1	1	yes	characteristic
277	C₂×C₁₉	#2438	1	4	yes	—
278	C₂×C₁₉	#2482	1	1	yes	characteristic
279	C₂×C₁₉	#2484	1	1	yes	characteristic
280	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
281	C₂³×C₄	—	2	4	no	—
282	C₂³×C₄	—	2	4	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	—	2	4	no	—
286	C₂³×C₄	—	2	4	no	—
287	C₂³×C₄	—	2	4	no	—
288	C₂³×C₄	—	2	4	no	—
289	C₂³×C₄	—	4	2	no	—
290	C₂³×C₄	—	4	2	no	—
291	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
292	C₂³×C₄	D₄×C₁₉	1	4	yes	—
293	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
294	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
295	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
296	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
299	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
301	#117	—	2	32	no	—
302	C₂×C₄⋊C₄	—	2	4	no	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	8	no	—
307	C₂×C₄⋊C₄	—	2	8	no	—
308	C₂×C₄⋊C₄	—	4	4	no	—
309	C₂×C₂²⋊C₄	—	2	4	no	—
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₂²⋊C₄	—	2	4	no	—
313	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
314	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
315	C₂×C₄²	—	2	4	no	—
316	C₂×C₄²	—	2	4	no	—
317	C₂×C₄²	—	2	4	no	—
318	#95	—	2	4	no	—
319	#95	—	2	4	no	—
320	#95	—	2	8	no	—
321	#95	—	2	8	no	—
322	#95	—	4	4	no	—
323	#95	C₂×C₄×C₁₉	1	8	yes	complemented
324	#95	C₂×C₄×C₁₉	1	8	yes	complemented
325	C₁₉	#14128	1	1	yes	characteristic, direct product factor, Sylow
326	C₂⁴	—	2	2	no	—
327	C₂⁴	—	2	2	no	—
328	C₂⁴	—	2	2	no	—
329	C₂⁴	—	2	2	no	—
330	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
331	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
332	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
333	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
334	C₂⁴	#41×C₁₉	1	4	yes	—
335	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	—	2	16	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	16	no	—
339	C₂²×C₄	—	2	8	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	4	16	no	—
369	C₂²×C₄	—	4	16	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	C₄⋊C₄×C₁₉	1	16	yes	complemented
375	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
376	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
377	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
379	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
382	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
383	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
384	C₂²×C₄	#41×C₁₉	1	4	yes	—
385	C₂²×C₄	#41×C₁₉	1	4	yes	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	4	16	no	—
389	C₂²⋊C₄	—	2	16	no	—
390	C₂²⋊C₄	—	2	16	no	—
391	C₄²	—	2	16	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	2	8	no	—
401	C₂³	—	2	8	no	—
402	C₂³	—	2	8	no	—
403	C₂³	—	2	8	no	—
404	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
405	C₂³	C₄×D₄×C₁₉	1	8	yes	—
406	C₂³	C₁₉×#120	1	4	yes	—
407	C₂³	C₁₉×C₂²⋊Q₈	1	8	yes	—
408	C₂³	C₁₉×#123	1	4	yes	—
409	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
410	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
411	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
412	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
413	C₂³	C₂×#41×C₁₉	1	2	yes	—
414	C₂³	C₂×#41×C₁₉	1	2	yes	—
415	C₂³	C₂×#41×C₁₉	1	2	yes	—
416	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
417	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
418	C₂×C₄	—	2	32	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
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	8	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	4	16	no	—
439	C₂×C₄	—	4	16	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
457	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	16	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	16	no	—
466	C₂²	C₁₉×#385	1	8	yes	—
467	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
468	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
469	C₂²	C₄×#41×C₁₉	1	2	yes	—
470	C₂²	C₁₉×#520	1	2	yes	—
471	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
472	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
473	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
474	C₂²	C₁₉×#525	1	1	yes	characteristic
475	C₂²	C₁₉×#525	1	1	yes	characteristic
476	C₂²	C₁₉×#533	1	2	yes	—
477	C₂²	C₁₉×#535	1	1	yes	characteristic
478	C₂²	C₁₉×#536	1	1	yes	characteristic
479	C₂²	C₁₉×#544	1	2	yes	—
480	C₂²	C₁₉×#546	1	4	yes	—
481	C₂²	C₁₉×#547	1	4	yes	—
482	C₂²	C₁₉×#551	1	4	yes	—
483	C₂²	C₁₉×#552	1	4	yes	—
484	C₄	—	2	4	no	—
485	C₄	—	2	4	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	8	no	—
491	C₂	—	2	8	no	—
492	C₂	C₂×C₁₉×#385	1	1	yes	characteristic
493	C₂	C₁₉×#2296	1	1	yes	characteristic
494	C₂	C₁₉×#2317	1	1	yes	characteristic
495	C₂	C₁₉×#2359	1	4	yes	—
496	C₂	C₁₉×#2404	1	1	yes	characteristic
497	C₂	C₁₉×#2406	1	1	yes	characteristic
498	C₂	C₁₉×#2438	1	4	yes	—
499	C₂	C₁₉×#2482	1	1	yes	characteristic
500	C₂	C₁₉×#2484	1	1	yes	characteristic

	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
5. C₁₉×#1444	C₂	semidirect
6. C₁₉×#1442	C₂	semidirect
7. C₁₉×#1436	C₂	semidirect
21. C₁₉×#381	C₄	semidirect
73. C₁₉×#95	C₂×C₄	semidirect
74. C₁₉×#95	C₂×C₄	semidirect
123. C₂²×C₄×C₁₉	C₄⋊C₄	semidirect
141. #14128	C₁₉	direct (N × H)
212. #1444	C₂×C₁₉	semidirect
213. #1442	C₂×C₁₉	semidirect
214. #1436	C₂×C₁₉	semidirect
261. #381	C₄×C₁₉	semidirect
323. #95	C₂×C₄×C₁₉	semidirect
324. #95	C₂×C₄×C₁₉	semidirect
325. C₁₉	#14128	direct (N × H)
374. 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×#385	2
C₂×C₁₉×#381	2
C₂²×C₁₉×#95	2
C₁₉×#1444	2
C₁₉×#1442	2
C₁₉×#1436	2
C₁₉×C₂²⋊#95	2
#14128	19

Subgroups — C19×#14128 #18020087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14128 #18020087