Subgroups — C₁₉×#24859 #18030818

Order 4864.

736 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3080	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1907	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1907	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1816	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1815	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
20	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#479	—	2	1	no	—
23	C₁₉×#479	—	2	1	no	—
24	C₁₉×#478	—	2	1	no	—
25	C₁₉×#478	—	2	1	no	—
26	C₁₉×#478	—	2	1	no	—
27	C₁₉×#478	—	2	1	no	—
28	C₁₉×#478	—	2	1	no	—
29	C₁₉×#478	—	2	1	no	—
30	C₁₉×#442	—	2	1	no	—
31	C₁₉×#440	—	2	1	no	—
32	C₄×SD₁₆×C₁₉	—	2	1	no	—
33	C₄×D₈×C₁₉	—	2	1	no	—
34	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
36	C₁₉×#428	C₂²	1	1	yes	characteristic
37	C₁₉×#428	C₂²	1	1	yes	characteristic
38	C₁₉×#428	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
41	C₁₉×#424	—	2	1	no	—
42	C₁₉×#424	—	2	1	no	—
43	C₁₉×#424	C₂²	1	1	yes	characteristic
44	C₁₉×#424	C₂²	1	1	yes	characteristic
45	C₁₉×#423	—	2	1	no	—
46	C₁₉×#423	C₂²	1	1	yes	characteristic
47	C₁₉×#423	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
49	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₁₉×#418	C₂²	1	1	yes	characteristic
51	C₁₉×#417	C₂²	1	1	yes	characteristic
52	C₁₉×#417	C₂²	1	1	yes	characteristic
53	C₁₉×#417	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
58	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
59	C₁₉×#343	C₂²	1	1	yes	characteristic
60	C₁₉×#343	C₂²	1	1	yes	characteristic
61	C₁₉×#343	C₂²	1	1	yes	characteristic
62	C₁₉×#343	C₂²	1	1	yes	characteristic
63	C₁₉×#343	C₂²	1	1	yes	characteristic
64	C₁₉×#343	C₂²	1	1	yes	characteristic
65	C₁₉×#341	C₂²	1	1	yes	characteristic
66	C₁₉×#341	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	—	2	1	no	—
70	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
71	C₁₉×AGL(1,ℤ/8)	Q₈	1	4	yes	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×D₈×C₁₉	—	2	1	no	—
74	C₁₉×#131	—	2	2	no	—
75	C₁₉×#131	—	2	2	no	—
76	C₁₉×#131	—	4	1	no	—
77	C₁₉×#131	—	4	1	no	—
78	C₂×M₁₆×C₁₉	—	2	1	no	—
79	C₂×M₁₆×C₁₉	—	2	1	no	—
80	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₉	—	2	1	no	—
87	C₂²×C₈×C₁₉	—	2	1	no	—
88	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×#125	—	2	1	no	—
91	C₁₉×#125	—	2	1	no	—
92	C₁₉×#125	—	2	1	no	—
93	C₁₉×#125	—	2	1	no	—
94	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
103	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#108	—	4	1	no	—
115	C₁₉×#108	—	4	1	no	—
116	C₁₉×#107	—	2	1	no	—
117	C₁₉×#107	—	2	1	no	—
118	C₁₉×#107	—	2	1	no	—
119	C₁₉×#107	—	2	1	no	—
120	C₁₉×#107	—	2	1	no	—
121	C₁₉×#106	—	2	1	no	—
122	C₁₉×#106	—	2	1	no	—
123	C₁₉×#106	—	2	1	no	—
124	C₁₉×#106	—	2	1	no	—
125	C₁₉×#106	—	2	1	no	—
126	C₁₉×C₄⋊C₈	—	2	1	no	—
127	C₁₉×C₄⋊C₈	—	2	1	no	—
128	C₁₉×C₄⋊C₈	—	2	1	no	—
129	C₁₉×C₄⋊C₈	—	2	1	no	—
130	C₁₉×C₄⋊C₈	—	2	1	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×C₄⋊C₈	—	2	1	no	—
134	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
135	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
136	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
137	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
138	C₁₉×#103	—	2	1	no	—
139	C₁₉×#103	—	2	1	no	—
140	C₁₉×#103	—	2	1	no	—
141	C₁₉×#102	—	2	1	no	—
142	C₁₉×#102	—	2	1	no	—
143	C₁₉×#102	—	2	1	no	—
144	C₁₉×#102	—	2	1	no	—
145	C₁₉×#102	—	2	1	no	—
146	C₁₉×#102	—	2	1	no	—
147	C₁₉×#102	—	2	1	no	—
148	C₁₉×#102	—	2	1	no	—
149	C₁₉×#102	—	2	1	no	—
150	C₁₉×#100	—	4	1	no	—
151	C₁₉×#100	—	4	1	no	—
152	C₁₉×#97	—	2	1	no	—
153	C₄×C₈×C₁₉	—	2	1	no	—
154	C₂⁴×C₁₉	—	2	1	no	—
155	#41×C₁₉	—	2	1	no	—
156	#41×C₁₉	—	2	1	no	—
157	#41×C₁₉	C₂×Q₈	1	2	yes	—
158	#41×C₁₉	#41	1	2	yes	—
159	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	—	2	1	no	—
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	4	1	no	—
175	C₂²×C₄×C₁₉	—	4	1	no	—
176	C₂²×C₄×C₁₉	—	8	2	no	—
177	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	SD₁₆×C₁₉	—	2	4	no	—
181	D₈×C₁₉	—	2	4	no	—
182	M₁₆×C₁₉	—	2	1	no	—
183	M₁₆×C₁₉	—	2	1	no	—
184	M₁₆×C₁₉	—	2	1	no	—
185	M₁₆×C₁₉	—	2	1	no	—
186	M₁₆×C₁₉	—	2	1	no	—
187	M₁₆×C₁₉	—	2	1	no	—
188	M₁₆×C₁₉	—	2	1	no	—
189	M₁₆×C₁₉	—	2	1	no	—
190	M₁₆×C₁₉	—	2	1	no	—
191	M₁₆×C₁₉	—	2	1	no	—
192	M₁₆×C₁₉	—	2	1	no	—
193	M₁₆×C₁₉	—	4	2	no	—
194	M₁₆×C₁₉	—	4	2	no	—
195	M₁₆×C₁₉	C₂×Q₈	1	2	yes	—
196	C₂×C₈×C₁₉	—	2	1	no	—
197	C₂×C₈×C₁₉	—	2	1	no	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₂×C₈×C₁₉	—	2	1	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	2	1	no	—
204	C₂×C₈×C₁₉	—	2	1	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	—	4	2	no	—
207	C₂×C₈×C₁₉	—	4	2	no	—
208	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	2	1	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	2	1	no	—
220	C₄⋊C₄×C₁₉	—	4	1	no	—
221	C₄⋊C₄×C₁₉	—	4	1	no	—
222	C₄⋊C₄×C₁₉	—	4	1	no	—
223	C₄⋊C₄×C₁₉	—	4	1	no	—
224	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₂²⋊C₄×C₁₉	—	2	1	no	—
229	C₂²⋊C₄×C₁₉	—	4	1	no	—
230	C₂²⋊C₄×C₁₉	—	4	1	no	—
231	C₄²×C₁₉	—	2	1	no	—
232	C₄²×C₁₉	—	2	1	no	—
233	C₄²×C₁₉	—	2	1	no	—
234	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
238	#24859	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₁₉	—	2	1	no	—
240	C₂³×C₁₉	—	2	2	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	—	4	1	no	—
243	C₂³×C₁₉	—	8	1	no	—
244	C₂³×C₁₉	—	8	1	no	—
245	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
246	Q₈×C₁₉	—	2	1	no	—
247	Q₈×C₁₉	C₂²⋊Q₈	1	2	yes	—
248	D₄×C₁₉	—	2	2	no	—
249	D₄×C₁₉	—	2	2	no	—
250	D₄×C₁₉	—	2	2	no	—
251	D₄×C₁₉	—	2	1	no	—
252	D₄×C₁₉	—	2	2	no	—
253	D₄×C₁₉	—	4	1	no	—
254	D₄×C₁₉	—	4	1	no	—
255	D₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	8	1	no	—
268	C₂×C₄×C₁₉	—	8	2	no	—
269	C₂×C₄×C₁₉	—	8	2	no	—
270	C₂×C₄×C₁₉	—	8	1	no	—
271	C₂×C₄×C₁₉	—	8	1	no	—
272	C₂×C₄×C₁₉	—	8	1	no	—
273	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
274	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
275	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
276	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
280	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
282	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
283	C₈×C₁₉	—	2	2	no	—
284	C₈×C₁₉	—	2	1	no	—
285	C₈×C₁₉	—	2	1	no	—
286	C₈×C₁₉	—	2	1	no	—
287	C₈×C₁₉	—	2	1	no	—
288	C₈×C₁₉	—	4	1	no	—
289	C₈×C₁₉	—	4	1	no	—
290	C₈×C₁₉	—	4	1	no	—
291	C₈×C₁₉	—	4	1	no	—
292	C₈×C₁₉	—	4	1	no	—
293	#3080	C₂×C₁₉	1	1	yes	characteristic, complemented
294	C₂×#478	C₂×C₁₉	1	1	yes	characteristic, complemented
295	C₄×AGL(1,ℤ/8)	C₂×C₁₉	1	1	yes	characteristic
296	#2906	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#2090	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#2089	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#2063	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#2063	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1998	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1950	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1907	C₂×C₁₉	1	1	yes	characteristic
304	#1907	C₂×C₁₉	1	1	yes	characteristic
305	#1816	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#1815	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	1	no	—
310	C₂²×C₁₉	—	2	2	no	—
311	C₂²×C₁₉	—	4	1	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	4	2	no	—
314	C₂²×C₁₉	—	8	2	no	—
315	C₂²×C₁₉	—	8	2	no	—
316	C₂²×C₁₉	—	8	1	no	—
317	C₂²×C₁₉	—	8	1	no	—
318	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
319	C₂²×C₁₉	#552	1	1	yes	characteristic
320	C₂²×C₁₉	#554	1	1	yes	characteristic
321	C₄×C₁₉	—	2	2	no	—
322	C₄×C₁₉	—	2	1	no	—
323	C₄×C₁₉	—	2	1	no	—
324	C₄×C₁₉	—	2	1	no	—
325	C₄×C₁₉	—	2	1	no	—
326	C₄×C₁₉	—	4	1	no	—
327	C₄×C₁₉	—	4	1	no	—
328	C₄×C₁₉	—	8	1	no	—
329	C₄×C₁₉	—	8	1	no	—
330	C₄×C₁₉	—	8	1	no	—
331	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
332	C₄×C₁₉	#537	1	1	yes	characteristic
333	C₄×C₁₉	#546	1	1	yes	characteristic
334	C₄×C₁₉	D₄×Q₈	1	1	yes	characteristic
335	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
339	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
341	#479	—	2	1	no	—
342	#479	—	2	1	no	—
343	#478	—	2	1	no	—
344	#478	—	2	1	no	—
345	#478	—	2	1	no	—
346	#478	—	2	1	no	—
347	#478	—	2	1	no	—
348	#478	—	2	1	no	—
349	#442	—	2	1	no	—
350	#440	—	2	1	no	—
351	C₄×SD₁₆	—	2	1	no	—
352	C₄×D₈	—	2	1	no	—
353	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
354	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
355	#428	C₂²×C₁₉	1	1	yes	characteristic
356	#428	C₂²×C₁₉	1	1	yes	characteristic
357	#428	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
360	#424	—	2	1	no	—
361	#424	—	2	1	no	—
362	#424	C₂²×C₁₉	1	1	yes	characteristic
363	#424	C₂²×C₁₉	1	1	yes	characteristic
364	#423	—	2	1	no	—
365	#423	C₂²×C₁₉	1	1	yes	characteristic
366	#423	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×C₄⋊C₈	—	2	1	no	—
368	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
369	#418	C₂²×C₁₉	1	1	yes	characteristic
370	#417	C₂²×C₁₉	1	1	yes	characteristic
371	#417	C₂²×C₁₉	1	1	yes	characteristic
372	#417	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
377	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
378	#343	C₂²×C₁₉	1	1	yes	characteristic
379	#343	C₂²×C₁₉	1	1	yes	characteristic
380	#343	C₂²×C₁₉	1	1	yes	characteristic
381	#343	C₂²×C₁₉	1	1	yes	characteristic
382	#343	C₂²×C₁₉	1	1	yes	characteristic
383	#343	C₂²×C₁₉	1	1	yes	characteristic
384	#341	C₂²×C₁₉	1	1	yes	characteristic
385	#341	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×C₁₉	—	2	1	no	—
387	C₂×C₁₉	—	2	1	no	—
388	C₂×C₁₉	—	4	2	no	—
389	C₂×C₁₉	—	8	2	no	—
390	C₂×C₁₉	#2417	1	1	yes	characteristic
391	C₂×C₁₉	#3067	1	1	yes	characteristic
392	C₂×C₁₉	#3068	1	1	yes	characteristic
393	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
394	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
395	C₂³×C₄	—	2	1	no	—
396	AGL(1,ℤ/8)	—	2	2	no	—
397	AGL(1,ℤ/8)	Q₈×C₁₉	1	4	yes	—
398	C₂×SD₁₆	—	2	1	no	—
399	C₂×D₈	—	2	1	no	—
400	#131	—	2	2	no	—
401	#131	—	2	2	no	—
402	#131	—	4	1	no	—
403	#131	—	4	1	no	—
404	C₂×M₁₆	—	2	1	no	—
405	C₂×M₁₆	—	2	1	no	—
406	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
407	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
408	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
409	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
410	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
411	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
412	C₂²×C₈	—	2	1	no	—
413	C₂²×C₈	—	2	1	no	—
414	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
416	#125	—	2	1	no	—
417	#125	—	2	1	no	—
418	#125	—	2	1	no	—
419	#125	—	2	1	no	—
420	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
421	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	—	2	1	no	—
426	C₄×D₄	—	2	1	no	—
427	C₄×D₄	—	2	1	no	—
428	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
429	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
430	#117	—	2	1	no	—
431	#117	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
440	#108	—	4	1	no	—
441	#108	—	4	1	no	—
442	#107	—	2	1	no	—
443	#107	—	2	1	no	—
444	#107	—	2	1	no	—
445	#107	—	2	1	no	—
446	#107	—	2	1	no	—
447	#106	—	2	1	no	—
448	#106	—	2	1	no	—
449	#106	—	2	1	no	—
450	#106	—	2	1	no	—
451	#106	—	2	1	no	—
452	C₄⋊C₈	—	2	1	no	—
453	C₄⋊C₈	—	2	1	no	—
454	C₄⋊C₈	—	2	1	no	—
455	C₄⋊C₈	—	2	1	no	—
456	C₄⋊C₈	—	2	1	no	—
457	C₄⋊C₈	—	2	1	no	—
458	C₄⋊C₈	—	2	1	no	—
459	C₄⋊C₈	—	2	1	no	—
460	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
461	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
462	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
463	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
464	#103	—	2	1	no	—
465	#103	—	2	1	no	—
466	#103	—	2	1	no	—
467	#102	—	2	1	no	—
468	#102	—	2	1	no	—
469	#102	—	2	1	no	—
470	#102	—	2	1	no	—
471	#102	—	2	1	no	—
472	#102	—	2	1	no	—
473	#102	—	2	1	no	—
474	#102	—	2	1	no	—
475	#102	—	2	1	no	—
476	#100	—	4	1	no	—
477	#100	—	4	1	no	—
478	#97	—	2	1	no	—
479	C₄×C₈	—	2	1	no	—
480	C₁₉	#24859	1	1	yes	characteristic, direct product factor, Sylow
481	C₂⁴	—	2	1	no	—
482	#41	—	2	1	no	—
483	#41	—	2	1	no	—
484	#41	C₂×Q₈×C₁₉	1	2	yes	—
485	#41	#41×C₁₉	1	2	yes	—
486	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	—	8	2	no	—
504	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
505	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
507	SD₁₆	—	2	4	no	—
508	D₈	—	2	4	no	—
509	M₁₆	—	2	1	no	—
510	M₁₆	—	2	1	no	—
511	M₁₆	—	2	1	no	—
512	M₁₆	—	2	1	no	—
513	M₁₆	—	2	1	no	—
514	M₁₆	—	2	1	no	—
515	M₁₆	—	2	1	no	—
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	4	2	no	—
521	M₁₆	—	4	2	no	—
522	M₁₆	C₂×Q₈×C₁₉	1	2	yes	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	4	2	no	—
534	C₂×C₈	—	4	2	no	—
535	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
536	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
537	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	4	1	no	—
548	C₄⋊C₄	—	4	1	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	—	4	1	no	—
551	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	1	no	—
555	C₂²⋊C₄	—	2	1	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	4	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
562	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
563	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
564	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₂³	—	2	1	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	8	1	no	—
570	C₂³	—	8	1	no	—
571	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
572	Q₈	—	2	1	no	—
573	Q₈	C₁₉×C₂²⋊Q₈	1	2	yes	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	2	1	no	—
578	D₄	—	2	2	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	8	1	no	—
594	C₂×C₄	—	8	2	no	—
595	C₂×C₄	—	8	2	no	—
596	C₂×C₄	—	8	1	no	—
597	C₂×C₄	—	8	1	no	—
598	C₂×C₄	—	8	1	no	—
599	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
600	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
601	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
602	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
603	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
605	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
606	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
607	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
609	C₈	—	2	2	no	—
610	C₈	—	2	1	no	—
611	C₈	—	2	1	no	—
612	C₈	—	2	1	no	—
613	C₈	—	2	1	no	—
614	C₈	—	4	1	no	—
615	C₈	—	4	1	no	—
616	C₈	—	4	1	no	—
617	C₈	—	4	1	no	—
618	C₈	—	4	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	8	2	no	—
626	C₂²	—	8	2	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
630	C₂²	C₁₉×#552	1	1	yes	characteristic
631	C₂²	C₁₉×#554	1	1	yes	characteristic
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
643	C₄	C₁₉×#537	1	1	yes	characteristic
644	C₄	C₁₉×#546	1	1	yes	characteristic
645	C₄	D₄×Q₈×C₁₉	1	1	yes	characteristic
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	4	2	no	—
649	C₂	—	8	2	no	—
650	C₂	C₁₉×#2417	1	1	yes	characteristic
651	C₂	C₁₉×#3067	1	1	yes	characteristic
652	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3080	C₂	semidirect
2. C₂×C₁₉×#478	C₂	semidirect
4. C₁₉×#2906	C₂	semidirect
5. C₁₉×#2090	C₂	semidirect
6. C₁₉×#2089	C₂	semidirect
7. C₁₉×#2063	C₂	semidirect
8. C₁₉×#2063	C₂	semidirect
9. C₁₉×#1998	C₂	semidirect
10. C₁₉×#1950	C₂	semidirect
13. C₁₉×#1816	C₂	semidirect
14. C₁₉×#1815	C₂	semidirect
15. C₁₉×#1800	C₂	semidirect
238. #24859	C₁₉	direct (N × H)
293. #3080	C₂×C₁₉	semidirect
294. C₂×#478	C₂×C₁₉	semidirect
296. #2906	C₂×C₁₉	semidirect
297. #2090	C₂×C₁₉	semidirect
298. #2089	C₂×C₁₉	semidirect
299. #2063	C₂×C₁₉	semidirect
300. #2063	C₂×C₁₉	semidirect
301. #1998	C₂×C₁₉	semidirect
302. #1950	C₂×C₁₉	semidirect
305. #1816	C₂×C₁₉	semidirect
306. #1815	C₂×C₁₉	semidirect
307. #1800	C₂×C₁₉	semidirect
480. C₁₉	#24859	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3080	2
C₂×C₁₉×#478	2
C₄×C₁₉×AGL(1,ℤ/8)	2
C₁₉×#2906	2
C₁₉×#2090	2
C₁₉×#2089	2
C₁₉×#2063	2
C₁₉×#1998	2
C₁₉×#1950	2
C₁₉×#1907	2
C₁₉×#1816	2
C₁₉×#1815	2
C₁₉×#1800	2
#24859	19

Subgroups — C19×#24859 #18030818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24859 #18030818