Subgroups — C₁₉×#13782 #18019741

Order 4864.

2102 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#385	C₂	1	2	yes	maximal
2	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1436	C₂	1	4	yes	maximal, complemented
6	C₁₉×C₄⋊#95	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1434	C₂	1	2	yes	maximal, complemented
8	C₁₉×C₂²⋊#95	C₂	1	2	yes	maximal
9	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
17	C₁₉×#385	C₄	1	16	yes	complemented
18	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
19	C₄×C₂²⋊C₄×C₁₉	C₄	1	8	yes	complemented
20	C₂×C₁₉×#95	—	2	4	no	—
21	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
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	4	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	4	no	—
31	C₂³×C₄×C₁₉	—	2	4	no	—
32	C₂³×C₄×C₁₉	—	4	4	no	—
33	C₂³×C₄×C₁₉	—	4	4	no	—
34	C₂³×C₄×C₁₉	—	4	4	no	—
35	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	—
36	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₉	D₄	1	4	yes	—
38	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
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	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
47	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	complemented
49	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
53	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
54	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
55	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
56	C₂×C₄²×C₁₉	—	2	4	no	—
57	C₂×C₄²×C₁₉	—	4	4	no	—
58	C₂×C₄²×C₁₉	—	4	4	no	—
59	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	complemented
60	C₁₉×#95	—	2	4	no	—
61	C₁₉×#95	—	2	4	no	—
62	C₁₉×#95	—	2	2	no	—
63	C₁₉×#95	—	2	2	no	—
64	C₁₉×#95	—	4	4	no	—
65	C₁₉×#95	—	4	4	no	—
66	C₁₉×#95	C₂×C₄	1	8	yes	complemented
67	C₁₉×#95	C₂×C₄	1	16	yes	complemented
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
72	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
73	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
74	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
75	C₂⁴×C₁₉	#41	1	4	yes	—
76	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	4	no	—
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	16	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	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	4	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	4	8	no	—
102	C₂²×C₄×C₁₉	—	4	16	no	—
103	C₂²×C₄×C₁₉	—	4	8	no	—
104	C₂²×C₄×C₁₉	—	4	8	no	—
105	C₂²×C₄×C₁₉	—	4	8	no	—
106	C₂²×C₄×C₁₉	—	4	8	no	—
107	C₂²×C₄×C₁₉	—	4	16	no	—
108	C₂²×C₄×C₁₉	C₄⋊C₄	1	16	yes	complemented
109	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
113	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
114	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
115	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
121	C₄⋊C₄×C₁₉	—	4	16	no	—
122	C₂²⋊C₄×C₁₉	—	2	8	no	—
123	C₂²⋊C₄×C₁₉	—	2	16	no	—
124	C₂²⋊C₄×C₁₉	C₄²	1	16	yes	complemented
125	C₄²×C₁₉	—	4	8	no	—
126	C₄²×C₁₉	—	4	8	no	—
127	#13782	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₁₉	—	2	4	no	—
129	C₂³×C₁₉	—	2	8	no	—
130	C₂³×C₁₉	—	2	4	no	—
131	C₂³×C₁₉	—	2	8	no	—
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	8	no	—
136	C₂³×C₁₉	—	2	8	no	—
137	C₂³×C₁₉	—	2	4	no	—
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	C₂×C₄²	1	4	yes	—
140	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
141	C₂³×C₁₉	#117	1	4	yes	—
142	C₂³×C₁₉	C₄×D₄	1	8	yes	—
143	C₂³×C₁₉	C₄×Q₈	1	8	yes	—
144	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
145	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
146	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
148	C₂³×C₁₉	C₂×#41	1	2	yes	—
149	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
150	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
151	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	8	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	8	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	8	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	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	8	no	—
172	C₂×C₄×C₁₉	—	4	16	no	—
173	C₂×C₄×C₁₉	—	4	32	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	4	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	4	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	C₂×C₄²	1	8	yes	—
187	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
188	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
189	C₂×#385	C₂×C₁₉	1	2	yes	—
190	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
191	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
192	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic
193	#1436	C₂×C₁₉	1	4	yes	complemented
194	C₄⋊#95	C₂×C₁₉	1	2	yes	complemented
195	#1434	C₂×C₁₉	1	2	yes	complemented
196	C₂²⋊#95	C₂×C₁₉	1	2	yes	—
197	C₂²×C₁₉	—	2	4	no	—
198	C₂²×C₁₉	—	2	4	no	—
199	C₂²×C₁₉	—	2	8	no	—
200	C₂²×C₁₉	—	2	8	no	—
201	C₂²×C₁₉	—	2	8	no	—
202	C₂²×C₁₉	—	2	16	no	—
203	C₂²×C₁₉	—	2	8	no	—
204	C₂²×C₁₉	C₄×C₄⋊C₄	1	8	yes	—
205	C₂²×C₁₉	C₂²×C₄²	1	1	yes	characteristic
206	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
207	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
208	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
209	C₂²×C₁₉	C₂×C₄×Q₈	1	2	yes	—
210	C₂²×C₁₉	#518	1	2	yes	—
211	C₂²×C₁₉	#518	1	4	yes	—
212	C₂²×C₁₉	#520	1	2	yes	—
213	C₂²×C₁₉	#520	1	4	yes	—
214	C₂²×C₁₉	#534	1	2	yes	—
215	C₂²×C₁₉	#535	1	1	yes	characteristic
216	C₂²×C₁₉	#536	1	1	yes	characteristic
217	C₂²×C₁₉	#538	1	4	yes	—
218	C₂²×C₁₉	#539	1	4	yes	—
219	C₂²×C₁₉	#543	1	2	yes	—
220	C₂²×C₁₉	#544	1	2	yes	—
221	C₄×C₁₉	—	2	4	no	—
222	C₄×C₁₉	—	2	4	no	—
223	C₄×C₁₉	—	2	8	no	—
224	C₄×C₁₉	—	4	4	no	—
225	C₄×C₁₉	—	4	4	no	—
226	C₄×C₁₉	—	4	8	no	—
227	C₄×C₁₉	—	4	4	no	—
228	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
229	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
231	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
232	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
234	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
235	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
236	#385	C₄×C₁₉	1	16	yes	complemented
237	C₄×C₂²⋊C₄	—	2	4	no	—
238	C₄×C₂²⋊C₄	C₄×C₁₉	1	8	yes	complemented
239	C₂×#95	—	2	4	no	—
240	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×#95	C₂²×C₁₉	1	2	yes	—
242	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×#95	C₂²×C₁₉	1	2	yes	—
244	C₂×#95	C₂²×C₁₉	1	4	yes	—
245	C₂×#95	C₂²×C₁₉	1	4	yes	—
246	C₂×#95	C₂²×C₁₉	1	4	yes	—
247	C₂×#95	C₂²×C₁₉	1	2	yes	—
248	C₂×C₁₉	—	2	8	no	—
249	C₂×C₁₉	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
250	C₂×C₁₉	#2275	1	2	yes	—
251	C₂×C₁₉	#2315	1	1	yes	characteristic
252	C₂×C₁₉	#2317	1	1	yes	characteristic
253	C₂×C₁₉	#2318	1	2	yes	—
254	C₂×C₁₉	#2321	1	2	yes	—
255	C₂×C₁₉	#2322	1	2	yes	—
256	C₂×C₁₉	#2329	1	4	yes	—
257	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
258	C₂³×C₄	—	2	4	no	—
259	C₂³×C₄	—	2	4	no	—
260	C₂³×C₄	—	4	4	no	—
261	C₂³×C₄	—	4	4	no	—
262	C₂³×C₄	—	4	4	no	—
263	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	—
264	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
265	C₂³×C₄	D₄×C₁₉	1	4	yes	—
266	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
267	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
268	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
269	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
270	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
271	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
272	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	—	4	4	no	—
275	C₂×C₄⋊C₄	—	4	4	no	—
276	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	complemented
277	C₂×C₂²⋊C₄	—	2	4	no	—
278	C₂×C₂²⋊C₄	—	2	4	no	—
279	C₂×C₂²⋊C₄	—	2	4	no	—
280	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
281	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
282	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
283	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
284	C₂×C₄²	—	2	4	no	—
285	C₂×C₄²	—	4	4	no	—
286	C₂×C₄²	—	4	4	no	—
287	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	complemented
288	#95	—	2	4	no	—
289	#95	—	2	4	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	4	4	no	—
293	#95	—	4	4	no	—
294	#95	C₂×C₄×C₁₉	1	8	yes	complemented
295	#95	C₂×C₄×C₁₉	1	16	yes	complemented
296	C₁₉	#13782	1	1	yes	characteristic, direct product factor, Sylow
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	2	2	no	—
299	C₂⁴	—	2	2	no	—
300	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
301	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
302	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
303	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
304	C₂⁴	#41×C₁₉	1	4	yes	—
305	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	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	4	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	2	no	—
330	C₂²×C₄	—	4	8	no	—
331	C₂²×C₄	—	4	16	no	—
332	C₂²×C₄	—	4	8	no	—
333	C₂²×C₄	—	4	8	no	—
334	C₂²×C₄	—	4	8	no	—
335	C₂²×C₄	—	4	8	no	—
336	C₂²×C₄	—	4	16	no	—
337	C₂²×C₄	C₄⋊C₄×C₁₉	1	16	yes	complemented
338	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
339	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
341	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
342	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
343	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
344	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
345	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
350	C₄⋊C₄	—	4	16	no	—
351	C₂²⋊C₄	—	2	8	no	—
352	C₂²⋊C₄	—	2	16	no	—
353	C₂²⋊C₄	C₄²×C₁₉	1	16	yes	complemented
354	C₄²	—	4	8	no	—
355	C₄²	—	4	8	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	8	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	4	no	—
367	C₂³	C₂×C₄²×C₁₉	1	4	yes	—
368	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
369	C₂³	C₁₉×#117	1	4	yes	—
370	C₂³	C₄×D₄×C₁₉	1	8	yes	—
371	C₂³	C₄×Q₈×C₁₉	1	8	yes	—
372	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
373	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
374	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
375	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
376	C₂³	C₂×#41×C₁₉	1	2	yes	—
377	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
378	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
379	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	8	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	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	4	16	no	—
401	C₂×C₄	—	4	32	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	C₂×C₄²×C₁₉	1	8	yes	—
415	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
416	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
417	C₂²	—	2	8	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	2	16	no	—
424	C₂²	C₄×C₄⋊C₄×C₁₉	1	8	yes	—
425	C₂²	C₂²×C₄²×C₁₉	1	1	yes	characteristic
426	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
427	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
428	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
429	C₂²	C₂×C₄×Q₈×C₁₉	1	2	yes	—
430	C₂²	C₁₉×#518	1	2	yes	—
431	C₂²	C₁₉×#518	1	4	yes	—
432	C₂²	C₁₉×#520	1	2	yes	—
433	C₂²	C₁₉×#520	1	4	yes	—
434	C₂²	C₁₉×#534	1	2	yes	—
435	C₂²	C₁₉×#535	1	1	yes	characteristic
436	C₂²	C₁₉×#536	1	1	yes	characteristic
437	C₂²	C₁₉×#538	1	4	yes	—
438	C₂²	C₁₉×#539	1	4	yes	—
439	C₂²	C₁₉×#543	1	2	yes	—
440	C₂²	C₁₉×#544	1	2	yes	—
441	C₄	—	2	8	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	4	no	—
444	C₄	—	4	4	no	—
445	C₄	—	4	8	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₂	—	2	8	no	—
449	C₂	C₂×C₄×C₄⋊C₄×C₁₉	1	1	yes	characteristic
450	C₂	C₁₉×#2275	1	2	yes	—
451	C₂	C₁₉×#2315	1	1	yes	characteristic
452	C₂	C₁₉×#2317	1	1	yes	characteristic
453	C₂	C₁₉×#2318	1	2	yes	—
454	C₂	C₁₉×#2321	1	2	yes	—
455	C₂	C₁₉×#2322	1	2	yes	—
456	C₂	C₁₉×#2329	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#1436	C₂	semidirect
6. C₁₉×C₄⋊#95	C₂	semidirect
7. C₁₉×#1434	C₂	semidirect
17. C₁₉×#385	C₄	semidirect
19. C₄×C₂²⋊C₄×C₁₉	C₄	semidirect
48. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
59. C₂×C₄²×C₁₉	C₂×C₄	semidirect
66. C₁₉×#95	C₂×C₄	semidirect
67. C₁₉×#95	C₂×C₄	semidirect
108. C₂²×C₄×C₁₉	C₄⋊C₄	semidirect
124. C₂²⋊C₄×C₁₉	C₄²	semidirect
127. #13782	C₁₉	direct (N × H)
193. #1436	C₂×C₁₉	semidirect
194. C₄⋊#95	C₂×C₁₉	semidirect
195. #1434	C₂×C₁₉	semidirect
236. #385	C₄×C₁₉	semidirect
238. C₄×C₂²⋊C₄	C₄×C₁₉	semidirect
276. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
287. C₂×C₄²	C₂×C₄×C₁₉	semidirect
294. #95	C₂×C₄×C₁₉	semidirect
295. #95	C₂×C₄×C₁₉	semidirect
296. C₁₉	#13782	direct (N × H)
337. C₂²×C₄	C₄⋊C₄×C₁₉	semidirect
353. C₂²⋊C₄	C₄²×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#385	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₂²×C₁₉×#95	2
C₁₉×#1436	2
C₁₉×C₄⋊#95	2
C₁₉×#1434	2
C₁₉×C₂²⋊#95	2
#13782	19

Subgroups — C19×#13782 #18019741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13782 #18019741