Finite Group Databasebeta

← C19×#20781 #18026740

Subgroups — C19×#20781 #18026740

Order 4864.

758 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C19×#117C211yesmaximal, characteristic
2C19×#1839C212yesmaximal, complemented
3C19×#1832C212yesmaximal, complemented
4C19×#1817C212yesmaximal
5C19×#1798C212yesmaximal
6C19×#1767C211yesmaximal, characteristic, complemented
7C4×C19×C4⋊C8C211yesmaximal, characteristic, complemented
8C19×#1750C212yesmaximal
9C19×#1746C212yesmaximal, complemented
10C2×C19×#117C2211yescharacteristic
11C2×C19×#117C2211yescharacteristic
12C22×C42×C19C2211yescharacteristic
13C2×C19×C4⋊C8C2212yes—
14C2×C19×C4⋊C8C2212yes—
15C2×C19×C22⋊C8C2214yes—
16C2×C19×#97C2212yes—
17C2×C4×C8×C19C2212yes—
18C4×C4⋊C4×C19C412yes—
19C4×C4⋊C4×C19C412yes—
20C4×C22⋊C4×C19C412yes—
21C4×C22⋊C4×C19C412yes—
22C19×#376C2211yescharacteristic
23C19×#376C2211yescharacteristic
24C43×C19C2211yescharacteristic
25C43×C19C2211yescharacteristic
26C19×#336C2214yes—
27C19×#336C2214yes—
28C19×#336C2214yes—
29C19×#336C2212yes—
30C19×#336C2212yes—
31C23×C4×C19C2×C412yes—
32C23×C4×C19C2311yescharacteristic
33C22×C8×C19C2314yes—
34C22×C8×C19C2314yes—
35C19×#117—22no—
36C19×#117—22no—
37C19×#117—24no—
38C2×C4⋊C4×C19C2×C412yes—
39C2×C4⋊C4×C19C2×C411yescharacteristic
40C2×C4⋊C4×C19C2×C411yescharacteristic
41C2×C22⋊C4×C19C2×C412yes—
42C2×C22⋊C4×C19C2×C411yescharacteristic
43C2×C22⋊C4×C19C2×C411yescharacteristic
44C2×C42×C19—24no—
45C2×C42×C19C2×C412yes—
46C2×C42×C19C2×C412yes—
47C2×C42×C19C2×C412yes—
48C2×C42×C19C2×C412yes—
49C2×C42×C19C2×C412yes—
50C2×C42×C19C2311yescharacteristic
51C2×C42×C19C2311yescharacteristic
52C2×C42×C19C2311yescharacteristic
53C2×C42×C19C2311yescharacteristic
54C2×C42×C19C2311yescharacteristic
55C2×C42×C19C2311yescharacteristic
56C19×C4⋊C8—24no—
57C19×C4⋊C8—24no—
58C19×C22⋊C8—28no—
59C19×#97—24no—
60C4×C8×C19—24no—
61C19×#95C2×C412yes—
62C19×#95C2×C412yes—
63C19×#95C2×C412yes—
64C19×#95C2×C412yes—
65C24×C19C22×C411yescharacteristic
66C22×C4×C19—22no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—24no—
70C22×C4×C19—24no—
71C22×C4×C19—42no—
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C22×C412yes—
74C22×C4×C19C22×C411yescharacteristic
75C22×C4×C19C22×C412yes—
76C22×C4×C19C22×C411yescharacteristic
77C22×C4×C19C22×C412yes—
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C22×C412yes—
81C22×C4×C19#4114yes—
82C22×C4×C19C2411yescharacteristic
83C2×C8×C19—24no—
84C2×C8×C19—24no—
85C2×C8×C19—24no—
86C2×C8×C19—24no—
87C2×C8×C19—24no—
88C2×C8×C19—24no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—24no—
92C22⋊C4×C19—22no—
93C22⋊C4×C19—22no—
94C22⋊C4×C19—24no—
95C42×C19—24no—
96C42×C19—24no—
97C42×C19—24no—
98C42×C19—22no—
99C42×C19—22no—
100C42×C19—22no—
101C42×C19—21no—
102C42×C19—21no—
103C42×C19—42no—
104C42×C19—42no—
105C42×C19#4112yes—
106C42×C19#4112yes—
107C42×C19#4114yes—
108#20781C1911yesmaximal, characteristic, direct product factor, Sylow
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—22no—
112C23×C19—22no—
113C23×C19#11712yes—
114C23×C19C23×C411yescharacteristic
115C2×C4×C19—22no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—24no—
124C2×C4×C19—24no—
125C2×C4×C19—22no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—22no—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
133C2×C4×C19—22no—
134C2×C4×C19—22no—
135C2×C4×C19—48no—
136C2×C4×C19#11712yes—
137C2×C4×C19#11712yes—
138C2×C4×C19#11712yes—
139C2×C4×C19#11714yes—
140C2×C4×C19#13114yes—
141C2×C4×C19C2×#4112yes—
142C2×C4×C19C2×#4112yes—
143C2×C4×C19C2×#4111yescharacteristic
144C2×C4×C19C2×#4111yescharacteristic
145C8×C19—44no—
146C8×C19—44no—
147C4×#117C2×C1911yescharacteristic
148#1839C2×C1912yescomplemented
149#1832C2×C1912yescomplemented
150#1817C2×C1912yes—
151#1798C2×C1912yes—
152#1767C2×C1911yescharacteristic, complemented
153C4×C4⋊C8C2×C1911yescharacteristic, complemented
154#1750C2×C1912yes—
155#1746C2×C1912yescomplemented
156C22×C19—24no—
157C22×C19—22no—
158C22×C19—41no—
159C22×C19—41no—
160C22×C19—42no—
161C22×C19C2×#11711yescharacteristic
162C22×C19C2×#11711yescharacteristic
163C22×C19C2×#11711yescharacteristic
164C22×C19C2×#13112yes—
165C22×C19#56812yes—
166C4×C19—22no—
167C4×C19—22no—
168C4×C19—24no—
169C4×C19—24no—
170C4×C19—22no—
171C4×C19—41no—
172C4×C19—41no—
173C4×C19—42no—
174C4×C19—42no—
175C4×C19#52912yes—
176C4×C19#52912yes—
177C2×#117C22×C1911yescharacteristic
178C2×#117C22×C1911yescharacteristic
179C22×C42C22×C1911yescharacteristic
180C2×C4⋊C8C22×C1912yes—
181C2×C4⋊C8C22×C1912yes—
182C2×C22⋊C8C22×C1914yes—
183C2×#97C22×C1912yes—
184C2×C4×C8C22×C1912yes—
185C4×C4⋊C4C4×C1912yes—
186C4×C4⋊C4C4×C1912yes—
187C4×C22⋊C4C4×C1912yes—
188C4×C22⋊C4C4×C1912yes—
189#376C22×C1911yescharacteristic
190#376C22×C1911yescharacteristic
191C43C22×C1911yescharacteristic
192C43C22×C1911yescharacteristic
193#336C22×C1914yes—
194#336C22×C1914yes—
195#336C22×C1912yes—
196#336C22×C1912yes—
197#336C22×C1914yes—
198C2×C19—42no—
199C2×C19#228311yescharacteristic
200C2×C19#292211yescharacteristic
201C2×C19#292311yescharacteristic
202C2×C19#292412yes—
203C2×C19#292512yes—
204C23×C4C2×C4×C1912yes—
205C23×C4C23×C1911yescharacteristic
206C22×C8C23×C1914yes—
207C22×C8C23×C1914yes—
208#117—22no—
209#117—22no—
210#117—24no—
211C2×C4⋊C4C2×C4×C1911yescharacteristic
212C2×C4⋊C4C2×C4×C1911yescharacteristic
213C2×C4⋊C4C2×C4×C1912yes—
214C2×C22⋊C4C2×C4×C1911yescharacteristic
215C2×C22⋊C4C2×C4×C1911yescharacteristic
216C2×C22⋊C4C2×C4×C1912yes—
217C2×C42—24no—
218C2×C42C2×C4×C1912yes—
219C2×C42C2×C4×C1912yes—
220C2×C42C2×C4×C1912yes—
221C2×C42C2×C4×C1912yes—
222C2×C42C2×C4×C1912yes—
223C2×C42C23×C1911yescharacteristic
224C2×C42C23×C1911yescharacteristic
225C2×C42C23×C1911yescharacteristic
226C2×C42C23×C1911yescharacteristic
227C2×C42C23×C1911yescharacteristic
228C2×C42C23×C1911yescharacteristic
229C4⋊C8—24no—
230C4⋊C8—24no—
231C22⋊C8—28no—
232#97—24no—
233C4×C8—24no—
234#95C2×C4×C1912yes—
235#95C2×C4×C1912yes—
236#95C2×C4×C1912yes—
237#95C2×C4×C1912yes—
238C19#2078111yescharacteristic, direct product factor, Sylow
239C24C22×C4×C1911yescharacteristic
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—42no—
246C22×C4C22×C4×C1912yes—
247C22×C4C22×C4×C1911yescharacteristic
248C22×C4C22×C4×C1912yes—
249C22×C4C22×C4×C1911yescharacteristic
250C22×C4C22×C4×C1911yescharacteristic
251C22×C4C22×C4×C1912yes—
252C22×C4C22×C4×C1911yescharacteristic
253C22×C4C22×C4×C1911yescharacteristic
254C22×C4C22×C4×C1912yes—
255C22×C4#41×C1914yes—
256C22×C4C24×C1911yescharacteristic
257C2×C8—24no—
258C2×C8—24no—
259C2×C8—24no—
260C2×C8—24no—
261C2×C8—24no—
262C2×C8—24no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—24no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—24no—
269C42—24no—
270C42—24no—
271C42—24no—
272C42—22no—
273C42—22no—
274C42—22no—
275C42—21no—
276C42—21no—
277C42—42no—
278C42—42no—
279C42#41×C1912yes—
280C42#41×C1912yes—
281C42#41×C1914yes—
282C23—21no—
283C23—21no—
284C23—22no—
285C23—22no—
286C23C19×#11712yes—
287C23C23×C4×C1911yescharacteristic
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—48no—
309C2×C4C19×#11712yes—
310C2×C4C19×#11712yes—
311C2×C4C19×#11712yes—
312C2×C4C19×#11714yes—
313C2×C4C19×#13114yes—
314C2×C4C2×#41×C1912yes—
315C2×C4C2×#41×C1912yes—
316C2×C4C2×#41×C1911yescharacteristic
317C2×C4C2×#41×C1911yescharacteristic
318C8—44no—
319C8—44no—
320C22—24no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—42no—
325C22C2×C19×#11711yescharacteristic
326C22C2×C19×#11711yescharacteristic
327C22C2×C19×#11711yescharacteristic
328C22C2×C19×#13112yes—
329C22C19×#56812yes—
330C4—22no—
331C4—22no—
332C4—24no—
333C4—24no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—42no—
338C4—42no—
339C4C19×#52912yes—
340C4C19×#52912yes—
341C2—42no—
342C2C19×#228311yescharacteristic
343C2C19×#292211yescharacteristic
344C2C19×#292311yescharacteristic
345C2C19×#292412yes—
346C2C19×#292512yes—
subgroupG/H
centerC22×C4×C19C24
commutatorC23C23×C4×C19
Frattini, cosocleC22×C4C24×C19
socleC23×C19C23×C4
prime radicalC24×C19C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#1839C2semidirect
3. C19×#1832C2semidirect
6. C19×#1767C2semidirect
7. C4×C19×C4⋊C8C2semidirect
9. C19×#1746C2semidirect
108. #20781C19direct (N × H)
148. #1839C2×C19semidirect
149. #1832C2×C19semidirect
152. #1767C2×C19semidirect
153. C4×C4⋊C8C2×C19semidirect
155. #1746C2×C19semidirect
238. C19#20781direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C19×#1172
C19×#18392
C19×#18322
C19×#18172
C19×#17982
C19×#17672
C4×C19×C4⋊C82
C19×#17502
C19×#17462
#2078119