Finite Group Databasebeta

← C19×#8720 #18014679

Subgroups — C19×#8720 #18014679

Order 4864.

482 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#2283C211yesmaximal, characteristic
2C19×#1749C211yesmaximal, characteristic
3C19×#1749C211yesmaximal, characteristic
4C19×#1295C212yesmaximal, complemented
5C19×#1295C212yesmaximal, complemented
6C22×C42×C19C2211yescharacteristic
7C2×C19×C22⋊C8—21no—
8C2×C19×C22⋊C8—21no—
9C2×C19×#97C2212yes—
10C2×C19×#97C2212yes—
11C19×#383—21no—
12C19×#382C2211yescharacteristic
13C19×#382C2211yescharacteristic
14C19×#381—21no—
15C19×#380C411yescharacteristic
16C19×#380C411yescharacteristic
17C4×C4⋊C4×C19C411yescharacteristic
18C4×C4⋊C4×C19C411yescharacteristic
19C4×C22⋊C4×C19—21no—
20C19×#376—21no—
21C19×#336—21no—
22C19×#336—21no—
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C22×C8×C19—22no—
27C22×C8×C19—22no—
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C42×C19—24no—
35C2×C42×C19—21no—
36C2×C42×C19—21no—
37C2×C42×C19C2×C411yescharacteristic
38C2×C42×C19D411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19C2311yescharacteristic
41C19×C22⋊C8—24no—
42C19×C22⋊C8—24no—
43C19×#97—24no—
44C19×#97—24no—
45C19×#95—21no—
46C19×#95—21no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C24×C19C22⋊C411yescharacteristic
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
65C22×C4×C19—41no—
66C22×C4×C19—41no—
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C2×C8×C19—24no—
74C2×C8×C19—24no—
75C2×C8×C19—42no—
76C2×C8×C19—42no—
77C2×C8×C19—42no—
78C2×C8×C19—42no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83C22⋊C4×C19—42no—
84C22⋊C4×C19—42no—
85C42×C19—22no—
86C42×C19—22no—
87C42×C19—22no—
88C42×C19—42no—
89C42×C19—42no—
90C42×C19#4114yes—
91#8720C1911yesmaximal, characteristic, direct product factor, Sylow
92C23×C19—21no—
93C23×C19—21no—
94C23×C19—21no—
95C23×C19—21no—
96C23×C19—21no—
97C23×C19—21no—
98C23×C19#10412yes—
99C23×C19C2×C22⋊C411yescharacteristic
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—44no—
115C2×C4×C19—44no—
116C2×C4×C19—44no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19#10412yes—
130C2×C4×C19#11712yes—
131C2×C4×C19#12312yes—
132C2×C4×C19#12312yes—
133C8×C19—44no—
134C8×C19—44no—
135#2283C2×C1911yescharacteristic
136#1749C2×C1911yescharacteristic
137#1749C2×C1911yescharacteristic
138#1295C2×C1912yescomplemented
139#1295C2×C1912yescomplemented
140C22×C19—22no—
141C22×C19—22no—
142C22×C19—22no—
143C22×C19—41no—
144C22×C19—41no—
145C22×C19—41no—
146C22×C19—41no—
147C22×C19#38111yescharacteristic
148C22×C19#41311yescharacteristic
149C22×C19#41311yescharacteristic
150C22×C19C2×#10411yescharacteristic
151C22×C19C2×#10411yescharacteristic
152C22×C19#42111yescharacteristic
153C22×C19#42111yescharacteristic
154C4×C19—22no—
155C4×C19—22no—
156C4×C19—22no—
157C4×C19—22no—
158C4×C19—41no—
159C4×C19—41no—
160C4×C19—81no—
161C4×C19—81no—
162C4×C19—81no—
163C4×C19—81no—
164C22×C42C22×C1911yescharacteristic
165C2×C22⋊C8—21no—
166C2×C22⋊C8—21no—
167C2×#97C22×C1912yes—
168C2×#97C22×C1912yes—
169#383—21no—
170#382C22×C1911yescharacteristic
171#382C22×C1911yescharacteristic
172#381—21no—
173#380C4×C1911yescharacteristic
174#380C4×C1911yescharacteristic
175C4×C4⋊C4C4×C1911yescharacteristic
176C4×C4⋊C4C4×C1911yescharacteristic
177C4×C22⋊C4—21no—
178#376—21no—
179#336—21no—
180#336—21no—
181C2×C19—42no—
182C2×C19#152411yescharacteristic
183C2×C19#152911yescharacteristic
184C2×C19#153211yescharacteristic
185C2×C19#153511yescharacteristic
186C2×C19#182211yescharacteristic
187C2×C19#182611yescharacteristic
188C2×C19#182611yescharacteristic
189C23×C4C2×C4×C1911yescharacteristic
190C23×C4D4×C1911yescharacteristic
191C23×C4D4×C1911yescharacteristic
192C22×C8—22no—
193C22×C8—22no—
194C2×C4⋊C4C2×C4×C1911yescharacteristic
195C2×C4⋊C4C2×C4×C1911yescharacteristic
196C2×C4⋊C4C2×C4×C1911yescharacteristic
197C2×C4⋊C4C2×C4×C1911yescharacteristic
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C42—24no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42C2×C4×C1911yescharacteristic
204C2×C42D4×C1911yescharacteristic
205C2×C42D4×C1911yescharacteristic
206C2×C42C23×C1911yescharacteristic
207C22⋊C8—24no—
208C22⋊C8—24no—
209#97—24no—
210#97—24no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219C19#872011yescharacteristic, direct product factor, Sylow
220C24C22⋊C4×C1911yescharacteristic
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4C22⋊C4×C1911yescharacteristic
235C22×C4C22⋊C4×C1911yescharacteristic
236C22×C4C22⋊C4×C1911yescharacteristic
237C22×C4C22×C4×C1911yescharacteristic
238C22×C4C2×D4×C1911yescharacteristic
239C22×C4C2×D4×C1911yescharacteristic
240C2×C8—24no—
241C2×C8—24no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C42—22no—
253C42—22no—
254C42—22no—
255C42—42no—
256C42—42no—
257C42#41×C1914yes—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23C19×#10412yes—
265C23C2×C22⋊C4×C1911yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4C19×#10412yes—
296C2×C4C19×#11712yes—
297C2×C4C19×#12312yes—
298C2×C4C19×#12312yes—
299C8—44no—
300C8—44no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22C19×#38111yescharacteristic
309C22C19×#41311yescharacteristic
310C22C19×#41311yescharacteristic
311C22C2×C19×#10411yescharacteristic
312C22C2×C19×#10411yescharacteristic
313C22C19×#42111yescharacteristic
314C22C19×#42111yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—41no—
320C4—41no—
321C4—81no—
322C4—81no—
323C4—81no—
324C4—81no—
325C2—42no—
326C2C19×#152411yescharacteristic
327C2C19×#152911yescharacteristic
328C2C19×#153211yescharacteristic
329C2C19×#153511yescharacteristic
330C2C19×#182211yescharacteristic
331C2C19×#182611yescharacteristic
332C2C19×#182611yescharacteristic
subgroupG/H
center, socleC23×C19C2×C22⋊C4
commutatorC22×C4C22×C4×C19
Frattini, cosocleC2×C42C23×C19
prime radicalC24×C19C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C19 ◁ C22×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
4. C19×#1295C2semidirect
5. C19×#1295C2semidirect
91. #8720C19direct (N × H)
138. #1295C2×C19semidirect
139. #1295C2×C19semidirect
219. C19#8720direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#22832
C19×#17492
C19×#12952
#872019