Subgroups — C₁₉×#32959 #18038918

Order 4864.

1720 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#478	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1864	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1862	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1804	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	—	2	1	no	—
14	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₄×D₄×C₁₉	—	2	8	no	—
16	C₂×C₄×D₄×C₁₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₉	—	2	1	no	—
18	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#478	—	2	8	no	—
24	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
27	C₂×C₁₉×#102	C₂²	1	2	yes	—
28	C₂×C₁₉×#102	C₂²	1	2	yes	—
29	C₂×C₁₉×#102	C₂²	1	2	yes	—
30	C₂×C₁₉×#102	C₂²	1	2	yes	—
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₉×#389	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#389	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#387	—	2	1	no	—
36	C₁₉×#387	—	2	1	no	—
37	C₁₉×#385	—	2	1	no	—
38	C₁₉×#385	—	2	1	no	—
39	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#380	C₂²	1	1	yes	characteristic
41	C₁₉×#380	C₂²	1	1	yes	characteristic
42	C₁₉×#340	C₂²	1	2	yes	complemented
43	C₁₉×#340	C₂²	1	2	yes	complemented
44	C₁₉×#336	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	4	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	Q₈	1	4	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₉	—	2	8	no	—
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	—	2	2	no	—
55	C₂³×C₄×C₁₉	—	2	2	no	—
56	C₂³×C₄×C₁₉	—	4	4	no	—
57	C₂³×C₄×C₁₉	—	4	4	no	—
58	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₁₉×#125	—	2	4	no	—
64	C₄×D₄×C₁₉	—	2	8	no	—
65	C₄×D₄×C₁₉	—	2	8	no	—
66	C₄×D₄×C₁₉	—	2	4	no	—
67	C₄×D₄×C₁₉	—	2	4	no	—
68	C₄×D₄×C₁₉	—	2	4	no	—
69	C₄×D₄×C₁₉	D₄	1	8	yes	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	—	2	4	no	—
87	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×#107	—	2	4	no	—
92	C₁₉×#106	—	2	4	no	—
93	C₁₉×C₄⋊C₈	—	2	4	no	—
94	C₁₉×#102	—	2	4	no	—
95	C₁₉×#102	—	2	4	no	—
96	C₁₉×#102	—	2	4	no	—
97	C₁₉×#102	—	2	4	no	—
98	C₁₉×C₂²⋊C₈	—	2	2	no	—
99	C₁₉×C₂²⋊C₈	—	2	2	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	—	2	1	no	—
104	C₁₉×#95	—	2	1	no	—
105	C₁₉×#95	—	2	1	no	—
106	C₂⁴×C₁₉	—	2	4	no	—
107	C₂⁴×C₁₉	—	2	4	no	—
108	C₂⁴×C₁₉	—	2	4	no	—
109	C₂⁴×C₁₉	—	2	2	no	—
110	C₂⁴×C₁₉	—	4	2	no	—
111	C₂⁴×C₁₉	—	4	2	no	—
112	C₂⁴×C₁₉	—	4	2	no	—
113	C₂⁴×C₁₉	—	4	2	no	—
114	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	16	no	—
118	C₂×D₄×C₁₉	—	2	16	no	—
119	C₂×D₄×C₁₉	—	2	4	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
124	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	—
125	C₂×D₄×C₁₉	#41	1	4	yes	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	4	no	—
132	C₂²×C₄×C₁₉	—	2	8	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	8	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	4	1	no	—
142	C₂²×C₄×C₁₉	—	4	32	no	—
143	C₂²×C₄×C₁₉	—	4	4	no	—
144	C₂²×C₄×C₁₉	—	4	4	no	—
145	C₂²×C₄×C₁₉	—	4	4	no	—
146	C₂²×C₄×C₁₉	—	4	2	no	—
147	C₂²×C₄×C₁₉	—	4	2	no	—
148	C₂²×C₄×C₁₉	—	4	4	no	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
155	C₂²×C₄×C₁₉	#41	1	2	yes	—
156	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	4	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₄⋊C₄×C₁₉	—	4	2	no	—
171	C₄⋊C₄×C₁₉	—	4	2	no	—
172	C₄⋊C₄×C₁₉	—	4	2	no	—
173	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
174	C₂²⋊C₄×C₁₉	—	2	8	no	—
175	C₂²⋊C₄×C₁₉	—	2	8	no	—
176	C₂²⋊C₄×C₁₉	—	4	2	no	—
177	C₂²⋊C₄×C₁₉	—	4	2	no	—
178	C₄²×C₁₉	—	2	2	no	—
179	C₄²×C₁₉	—	2	2	no	—
180	C₄²×C₁₉	—	2	2	no	—
181	C₄²×C₁₉	C₂×D₄	1	4	yes	—
182	#32959	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₁₉	—	2	1	no	—
184	C₂³×C₁₉	—	2	1	no	—
185	C₂³×C₁₉	—	2	1	no	—
186	C₂³×C₁₉	—	2	1	no	—
187	C₂³×C₁₉	—	2	16	no	—
188	C₂³×C₁₉	—	2	4	no	—
189	C₂³×C₁₉	—	2	4	no	—
190	C₂³×C₁₉	—	2	4	no	—
191	C₂³×C₁₉	—	4	8	no	—
192	C₂³×C₁₉	—	4	8	no	—
193	C₂³×C₁₉	—	4	8	no	—
194	C₂³×C₁₉	—	4	8	no	—
195	C₂³×C₁₉	—	4	8	no	—
196	C₂³×C₁₉	—	4	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	—	4	8	no	—
201	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
202	C₂³×C₁₉	#135	1	2	yes	—
203	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
204	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
205	D₄×C₁₉	—	2	16	no	—
206	D₄×C₁₉	—	2	4	no	—
207	D₄×C₁₉	—	2	4	no	—
208	D₄×C₁₉	—	2	4	no	—
209	D₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
210	C₂×C₄×C₁₉	—	2	8	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	4	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	4	4	no	—
226	C₂×C₄×C₁₉	—	4	16	no	—
227	C₂×C₄×C₁₉	—	4	16	no	—
228	C₂×C₄×C₁₉	—	4	8	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	#120	1	2	yes	—
244	C₂×C₄×C₁₉	#120	1	2	yes	—
245	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
246	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
247	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
250	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
251	C₈×C₁₉	—	4	2	no	—
252	C₈×C₁₉	—	4	2	no	—
253	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic
254	C₂×#478	C₂×C₁₉	1	2	yes	complemented
255	#2851	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1864	C₂×C₁₉	1	2	yes	complemented
257	#1862	C₂×C₁₉	1	2	yes	complemented
258	#1853	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1852	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1804	C₂×C₁₉	1	2	yes	complemented
261	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1786	C₂×C₁₉	1	1	yes	characteristic
263	#1786	C₂×C₁₉	1	1	yes	characteristic
264	C₂²×C₁₉	—	2	2	no	—
265	C₂²×C₁₉	—	2	2	no	—
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	2	no	—
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	2	2	no	—
270	C₂²×C₁₉	—	2	8	no	—
271	C₂²×C₁₉	—	4	32	no	—
272	C₂²×C₁₉	—	4	4	no	—
273	C₂²×C₁₉	—	4	4	no	—
274	C₂²×C₁₉	—	4	4	no	—
275	C₂²×C₁₉	—	4	4	no	—
276	C₂²×C₁₉	—	4	4	no	—
277	C₂²×C₁₉	—	4	4	no	—
278	C₂²×C₁₉	#478	1	4	yes	complemented
279	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
280	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
281	C₂²×C₁₉	#525	1	1	yes	characteristic
282	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
283	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₂²×C₁₉	#575	1	1	yes	characteristic
286	C₄×C₁₉	—	2	2	no	—
287	C₄×C₁₉	—	2	2	no	—
288	C₄×C₁₉	—	2	2	no	—
289	C₄×C₁₉	—	2	2	no	—
290	C₄×C₁₉	—	4	1	no	—
291	C₄×C₁₉	—	4	4	no	—
292	C₄×C₁₉	—	8	1	no	—
293	C₄×C₁₉	—	8	1	no	—
294	C₄×C₁₉	—	8	1	no	—
295	C₄×C₁₉	—	8	1	no	—
296	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
297	C₄×C₁₉	#525	1	2	yes	—
298	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
299	C₂⁴×C₄	—	2	1	no	—
300	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic, complemented
301	C₂×C₄×D₄	—	2	8	no	—
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×C₄×D₄	—	2	1	no	—
304	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
305	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
306	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
307	C₂²×C₂²⋊C₄	—	2	1	no	—
308	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
309	#478	—	2	8	no	—
310	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
311	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
312	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
313	C₂×#102	C₂²×C₁₉	1	2	yes	—
314	C₂×#102	C₂²×C₁₉	1	2	yes	—
315	C₂×#102	C₂²×C₁₉	1	2	yes	—
316	C₂×#102	C₂²×C₁₉	1	2	yes	—
317	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
319	#389	C₂²×C₁₉	1	1	yes	characteristic, complemented
320	#389	C₂²×C₁₉	1	1	yes	characteristic, complemented
321	#387	—	2	1	no	—
322	#387	—	2	1	no	—
323	#385	—	2	1	no	—
324	#385	—	2	1	no	—
325	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
326	#380	C₂²×C₁₉	1	1	yes	characteristic
327	#380	C₂²×C₁₉	1	1	yes	characteristic
328	#340	C₂²×C₁₉	1	2	yes	complemented
329	#340	C₂²×C₁₉	1	2	yes	complemented
330	#336	C₂²×C₁₉	1	2	yes	complemented
331	C₂×C₁₉	—	2	4	no	—
332	C₂×C₁₉	—	4	8	no	—
333	C₂×C₁₉	#2848	1	1	yes	characteristic
334	C₂×C₁₉	#3002	1	1	yes	characteristic
335	C₂×C₁₉	#3003	1	1	yes	characteristic
336	C₂×C₁₉	C₂×#478	1	1	yes	characteristic
337	C₂×C₁₉	#3077	1	1	yes	characteristic
338	C₂×C₁₉	#3105	1	1	yes	characteristic
339	C₂×C₁₉	#3114	1	1	yes	characteristic
340	C₂⁵	—	2	1	no	—
341	C₂²×D₄	—	2	4	no	—
342	C₂²×D₄	—	2	4	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	Q₈×C₁₉	1	4	yes	—
346	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
347	C₂³×C₄	—	2	8	no	—
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	—	2	2	no	—
350	C₂³×C₄	—	2	2	no	—
351	C₂³×C₄	—	4	4	no	—
352	C₂³×C₄	—	4	4	no	—
353	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
354	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
357	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
358	#125	—	2	4	no	—
359	C₄×D₄	—	2	8	no	—
360	C₄×D₄	—	2	8	no	—
361	C₄×D₄	—	2	4	no	—
362	C₄×D₄	—	2	4	no	—
363	C₄×D₄	—	2	4	no	—
364	C₄×D₄	D₄×C₁₉	1	8	yes	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	4	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
376	C₂×C₂²⋊C₄	—	2	8	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₄²	—	2	4	no	—
382	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
383	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
386	#107	—	2	4	no	—
387	#106	—	2	4	no	—
388	C₄⋊C₈	—	2	4	no	—
389	#102	—	2	4	no	—
390	#102	—	2	4	no	—
391	#102	—	2	4	no	—
392	#102	—	2	4	no	—
393	C₂²⋊C₈	—	2	2	no	—
394	C₂²⋊C₈	—	2	2	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	C₁₉	#32959	1	1	yes	characteristic, direct product factor, Sylow
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	4	no	—
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	4	2	no	—
407	C₂⁴	—	4	2	no	—
408	C₂⁴	—	4	2	no	—
409	C₂⁴	—	4	2	no	—
410	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	16	no	—
414	C₂×D₄	—	2	16	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
420	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	—
421	C₂×D₄	#41×C₁₉	1	4	yes	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	8	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	8	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	4	32	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	—	4	4	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
451	C₂²×C₄	#41×C₁₉	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	2	2	no	—
477	C₄²	C₂×D₄×C₁₉	1	4	yes	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	16	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	8	no	—
489	C₂³	—	4	8	no	—
490	C₂³	—	4	8	no	—
491	C₂³	—	4	8	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
497	C₂³	C₁₉×#135	1	2	yes	—
498	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
499	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
500	D₄	—	2	16	no	—
501	D₄	—	2	4	no	—
502	D₄	—	2	4	no	—
503	D₄	—	2	4	no	—
504	D₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
505	C₂×C₄	—	2	8	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	16	no	—
522	C₂×C₄	—	4	16	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	C₁₉×#120	1	2	yes	—
539	C₂×C₄	C₁₉×#120	1	2	yes	—
540	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
541	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
543	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
544	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
545	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
546	C₈	—	4	2	no	—
547	C₈	—	4	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	8	no	—
555	C₂²	—	4	32	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	4	no	—
562	C₂²	C₁₉×#478	1	4	yes	complemented
563	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
564	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
565	C₂²	C₁₉×#525	1	1	yes	characteristic
566	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
567	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
568	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
569	C₂²	C₁₉×#575	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	4	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
581	C₄	C₁₉×#525	1	2	yes	—
582	C₂	—	2	4	no	—
583	C₂	—	4	8	no	—
584	C₂	C₁₉×#2848	1	1	yes	characteristic
585	C₂	C₁₉×#3002	1	1	yes	characteristic
586	C₂	C₁₉×#3003	1	1	yes	characteristic
587	C₂	C₂×C₁₉×#478	1	1	yes	characteristic
588	C₂	C₁₉×#3077	1	1	yes	characteristic
589	C₂	C₁₉×#3105	1	1	yes	characteristic
590	C₂	C₁₉×#3114	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#478	C₂	semidirect
3. C₁₉×#2851	C₂	semidirect
4. C₁₉×#1864	C₂	semidirect
5. C₁₉×#1862	C₂	semidirect
6. C₁₉×#1853	C₂	semidirect
7. C₁₉×#1852	C₂	semidirect
8. C₁₉×#1804	C₂	semidirect
9. C₁₉×#1797	C₂	semidirect
14. C₂×C₁₉×#125	C₂²	semidirect
24. C₂×C₁₉×#107	C₂²	semidirect
25. C₂×C₁₉×#106	C₂²	semidirect
26. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
33. C₁₉×#389	C₂²	semidirect
34. C₁₉×#389	C₂²	semidirect
39. C₁₉×#382	C₂²	semidirect
42. C₁₉×#340	C₂²	semidirect
43. C₁₉×#340	C₂²	semidirect
44. C₁₉×#336	C₂²	semidirect
182. #32959	C₁₉	direct (N × H)
254. C₂×#478	C₂×C₁₉	semidirect
255. #2851	C₂×C₁₉	semidirect
256. #1864	C₂×C₁₉	semidirect
257. #1862	C₂×C₁₉	semidirect
258. #1853	C₂×C₁₉	semidirect
259. #1852	C₂×C₁₉	semidirect
260. #1804	C₂×C₁₉	semidirect
261. #1797	C₂×C₁₉	semidirect
278. C₂²×C₁₉	#478	semidirect
300. C₂×#125	C₂²×C₁₉	semidirect
310. C₂×#107	C₂²×C₁₉	semidirect
311. C₂×#106	C₂²×C₁₉	semidirect
312. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
319. #389	C₂²×C₁₉	semidirect
320. #389	C₂²×C₁₉	semidirect
325. #382	C₂²×C₁₉	semidirect
328. #340	C₂²×C₁₉	semidirect
329. #340	C₂²×C₁₉	semidirect
330. #336	C₂²×C₁₉	semidirect
401. C₁₉	#32959	direct (N × H)
562. C₂²	C₁₉×#478	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₉	2
C₂×C₁₉×#478	2
C₁₉×#2851	2
C₁₉×#1864	2
C₁₉×#1862	2
C₁₉×#1853	2
C₁₉×#1852	2
C₁₉×#1804	2
C₁₉×#1797	2
C₁₉×#1786	2
#32959	19

Subgroups — C19×#32959 #18038918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32959 #18038918