Subgroups — C₁₉×#26236 #18032195

Order 4864.

934 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#484	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2542	C₂	1	1	yes	maximal, characteristic
3	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2036	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2036	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1872	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₉	—	2	1	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#484	—	2	8	no	—
19	C₂×C₁₉×#107	C₂²	1	2	yes	—
20	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#103	C₂²	1	2	yes	—
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#399	—	2	2	no	—
31	C₁₉×#390	—	2	1	no	—
32	C₁₉×#389	—	2	1	no	—
33	C₁₉×#385	—	2	2	no	—
34	C₁₉×#384	—	2	1	no	—
35	C₁₉×#384	C₂²	1	1	yes	characteristic
36	C₁₉×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	—	2	2	no	—
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₁₉×C₂²⋊Q₈	—	2	4	no	—
52	C₁₉×C₂²⋊Q₈	—	2	4	no	—
53	C₁₉×C₂²⋊Q₈	—	4	2	no	—
54	C₁₉×C₂²⋊Q₈	—	4	2	no	—
55	C₄×D₄×C₁₉	—	2	2	no	—
56	C₄×D₄×C₁₉	—	2	2	no	—
57	C₄×D₄×C₁₉	—	4	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
67	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#107	—	2	4	no	—
81	C₁₉×#107	—	2	2	no	—
82	C₁₉×#107	D₄	1	4	yes	complemented
83	C₁₉×C₄⋊C₈	—	2	2	no	—
84	C₁₉×#103	—	2	4	no	—
85	C₁₉×#103	—	2	4	no	—
86	C₁₉×#103	—	4	2	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₁₉×C₂²⋊C₈	—	2	4	no	—
89	C₁₉×C₂²⋊C₈	—	4	2	no	—
90	C₄×C₈×C₁₉	—	2	2	no	—
91	C₁₉×#95	—	2	1	no	—
92	C₁₉×#95	—	2	1	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	Q₁₆	1	4	yes	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	4	4	no	—
117	C₂²×C₄×C₁₉	—	4	4	no	—
118	C₂²×C₄×C₁₉	—	8	2	no	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₁₉	—	2	1	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	1	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	4	4	no	—
141	C₄⋊C₄×C₁₉	—	4	4	no	—
142	C₄⋊C₄×C₁₉	—	4	4	no	—
143	C₄⋊C₄×C₁₉	—	4	2	no	—
144	C₄⋊C₄×C₁₉	—	4	2	no	—
145	C₄⋊C₄×C₁₉	—	4	2	no	—
146	C₄⋊C₄×C₁₉	—	8	1	no	—
147	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₁₉	#41	1	2	yes	—
150	C₂²⋊C₄×C₁₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₉	—	4	4	no	—
152	C₂²⋊C₄×C₁₉	—	4	4	no	—
153	C₂²⋊C₄×C₁₉	—	4	4	no	—
154	C₄²×C₁₉	—	4	2	no	—
155	C₄²×C₁₉	—	4	2	no	—
156	C₄²×C₁₉	#41	1	2	yes	—
157	C₄²×C₁₉	#41	1	2	yes	—
158	#26236	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	C₂×Q₁₆	1	4	yes	—
166	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₉	—	4	2	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	2	8	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	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	1	no	—
195	C₂×C₄×C₁₉	—	4	1	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	—	8	8	no	—
200	C₂×C₄×C₁₉	#123	1	2	yes	—
201	C₂×C₄×C₁₉	#123	1	2	yes	—
202	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
203	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
210	C₈×C₁₉	—	2	2	no	—
211	C₈×C₁₉	—	4	1	no	—
212	C₈×C₁₉	—	4	2	no	—
213	C₂×#484	C₂×C₁₉	1	2	yes	complemented
214	#2542	C₂×C₁₉	1	1	yes	characteristic
215	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
216	#2036	C₂×C₁₉	1	2	yes	complemented
217	#2036	C₂×C₁₉	1	2	yes	complemented
218	#1981	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#1956	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1954	C₂×C₁₉	1	1	yes	characteristic
221	#1947	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1872	C₂×C₁₉	1	2	yes	complemented
223	C₄×#107	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂²×C₁₉	—	2	4	no	—
225	C₂²×C₁₉	—	2	4	no	—
226	C₂²×C₁₉	—	2	4	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	—	4	2	no	—
231	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
232	C₂²×C₁₉	D₄²	1	1	yes	characteristic
233	C₂²×C₁₉	#546	1	1	yes	characteristic
234	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
235	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂²×C₁₉	#577	1	1	yes	characteristic
237	C₂²×C₁₉	#578	1	1	yes	characteristic
238	C₄×C₁₉	—	2	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	4	2	no	—
243	C₄×C₁₉	—	8	1	no	—
244	C₄×C₁₉	—	8	2	no	—
245	C₄×C₁₉	—	8	2	no	—
246	C₄×C₁₉	#484	1	4	yes	complemented
247	C₄×C₁₉	#532	1	1	yes	characteristic
248	C₄×C₁₉	#540	1	1	yes	characteristic
249	C₄×C₁₉	#550	1	1	yes	characteristic
250	C₄×C₁₉	#559	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
253	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
254	C₂×C₄×D₄	—	2	1	no	—
255	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
257	#484	—	2	8	no	—
258	C₂×#107	C₂²×C₁₉	1	2	yes	—
259	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×#103	C₂²×C₁₉	1	2	yes	—
263	C₂×#103	C₂²×C₁₉	1	2	yes	—
264	C₂×#103	C₂²×C₁₉	1	2	yes	—
265	C₂×#103	C₂²×C₁₉	1	2	yes	—
266	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
267	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
268	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
269	#399	—	2	2	no	—
270	#390	—	2	1	no	—
271	#389	—	2	1	no	—
272	#385	—	2	2	no	—
273	#384	—	2	1	no	—
274	#384	C₂²×C₁₉	1	1	yes	characteristic
275	#380	C₂²×C₁₉	1	2	yes	—
276	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
277	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
278	#340	C₂²×C₁₉	1	1	yes	characteristic
279	#340	C₂²×C₁₉	1	2	yes	—
280	#340	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×C₁₉	—	4	4	no	—
282	C₂×C₁₉	#2445	1	1	yes	characteristic
283	C₂×C₁₉	C₂×#484	1	1	yes	characteristic
284	C₂×C₁₉	#3097	1	1	yes	characteristic
285	C₂×C₁₉	#3272	1	1	yes	characteristic
286	C₂×C₁₉	D₄×Q₁₆	1	1	yes	characteristic
287	C₂×C₁₉	#3299	1	1	yes	characteristic
288	C₂×C₁₉	#3330	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
290	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
291	C₂³×C₄	—	2	2	no	—
292	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
293	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
295	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	—	4	2	no	—
301	C₂²⋊Q₈	—	4	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	4	4	no	—
305	C₂×C₄⋊C₄	—	2	4	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	4	2	no	—
314	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
327	#107	—	2	4	no	—
328	#107	—	2	2	no	—
329	#107	D₄×C₁₉	1	4	yes	complemented
330	C₄⋊C₈	—	2	2	no	—
331	#103	—	2	4	no	—
332	#103	—	2	4	no	—
333	#103	—	4	2	no	—
334	#103	—	4	2	no	—
335	C₂²⋊C₈	—	2	4	no	—
336	C₂²⋊C₈	—	4	2	no	—
337	C₄×C₈	—	2	2	no	—
338	#95	—	2	1	no	—
339	#95	—	2	1	no	—
340	#95	—	2	2	no	—
341	C₁₉	#26236	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	Q₁₆×C₁₉	1	4	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	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	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	8	2	no	—
367	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	8	1	no	—
395	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
396	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
397	C₄⋊C₄	#41×C₁₉	1	2	yes	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₄²	—	4	2	no	—
403	C₄²	—	4	2	no	—
404	C₄²	#41×C₁₉	1	2	yes	—
405	C₄²	#41×C₁₉	1	2	yes	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	C₂×Q₁₆×C₁₉	1	4	yes	—
413	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	4	2	no	—
418	D₄	—	2	8	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	8	8	no	—
447	C₂×C₄	C₁₉×#123	1	2	yes	—
448	C₂×C₄	C₁₉×#123	1	2	yes	—
449	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
450	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
455	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
468	C₂²	D₄²×C₁₉	1	1	yes	characteristic
469	C₂²	C₁₉×#546	1	1	yes	characteristic
470	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
471	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
472	C₂²	C₁₉×#577	1	1	yes	characteristic
473	C₂²	C₁₉×#578	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	2	no	—
481	C₄	—	8	1	no	—
482	C₄	C₁₉×#484	1	4	yes	complemented
483	C₄	C₁₉×#532	1	1	yes	characteristic
484	C₄	C₁₉×#540	1	1	yes	characteristic
485	C₄	C₁₉×#550	1	1	yes	characteristic
486	C₄	C₁₉×#559	1	1	yes	characteristic
487	C₂	—	4	4	no	—
488	C₂	C₁₉×#2445	1	1	yes	characteristic
489	C₂	C₂×C₁₉×#484	1	1	yes	characteristic
490	C₂	C₁₉×#3097	1	1	yes	characteristic
491	C₂	C₁₉×#3272	1	1	yes	characteristic
492	C₂	D₄×Q₁₆×C₁₉	1	1	yes	characteristic
493	C₂	C₁₉×#3299	1	1	yes	characteristic
494	C₂	C₁₉×#3330	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#484	C₂	semidirect
4. C₁₉×#2036	C₂	semidirect
5. C₁₉×#2036	C₂	semidirect
6. C₁₉×#1981	C₂	semidirect
7. C₁₉×#1956	C₂	semidirect
9. C₁₉×#1947	C₂	semidirect
10. C₁₉×#1872	C₂	semidirect
11. C₄×C₁₉×#107	C₂	semidirect
82. C₁₉×#107	D₄	semidirect
158. #26236	C₁₉	direct (N × H)
213. C₂×#484	C₂×C₁₉	semidirect
216. #2036	C₂×C₁₉	semidirect
217. #2036	C₂×C₁₉	semidirect
218. #1981	C₂×C₁₉	semidirect
219. #1956	C₂×C₁₉	semidirect
221. #1947	C₂×C₁₉	semidirect
222. #1872	C₂×C₁₉	semidirect
223. C₄×#107	C₂×C₁₉	semidirect
246. C₄×C₁₉	#484	semidirect
329. #107	D₄×C₁₉	semidirect
341. C₁₉	#26236	direct (N × H)
482. C₄	C₁₉×#484	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#484	2
C₁₉×#2542	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2036	2
C₁₉×#1981	2
C₁₉×#1956	2
C₁₉×#1954	2
C₁₉×#1947	2
C₁₉×#1872	2
C₄×C₁₉×#107	2
#26236	19

Subgroups — C19×#26236 #18032195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26236 #18032195