Finite Group Databasebeta

← C2×C19×#2045 #18029476

Subgroups — C2×C19×#2045 #18029476

Order 4864.

1586 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D8×C19C211yesmaximal, characteristic
2C2×C19×#424C211yesmaximal, characteristic, complemented
3C2×C19×#418C212yesmaximal, complemented
4C22×C19×#100C212yesmaximal, complemented
5C19×#2045C218yesmaximal, direct product factor
6C2×C19×#341C211yesmaximal, characteristic, complemented
7C23×D4×C19C2212yes—
8C22×D8×C19—28no—
9C22×D8×C19—22no—
10C22×D8×C19—22no—
11C22×D8×C19C2214yes—
12C22×M16×C19C2212yes—
13C22×M16×C19C2211yescharacteristic
14C23×C8×C19C2211yescharacteristic
15C2×C19×#117C2211yescharacteristic
16C19×#424—22no—
17C19×#424C2214yescomplemented
18C2×C19×C4⋊C8—22no—
19C19×#418—24no—
20C19×#418C2218yescomplemented
21C2×C19×#102—24no—
22C2×C19×#100—28no—
23C2×C19×#100C2218yescomplemented
24C19×#341C2214yescomplemented
25C25×C19—22no—
26C22×D4×C19—22no—
27C22×D4×C19—22no—
28C22×D4×C19—24no—
29C22×D4×C19—22no—
30C22×D4×C19—22no—
31C22×D4×C19—24no—
32C22×D4×C19—22no—
33C22×D4×C19—24no—
34C22×D4×C19D418yes—
35C22×D4×C19C2314yes—
36C23×C4×C19C2311yescharacteristic
37C2×D8×C19—216no—
38C2×D8×C19—216no—
39C2×D8×C19—216no—
40C2×D8×C19—28no—
41C2×M16×C19—22no—
42C2×M16×C19—21no—
43C2×M16×C19—24no—
44C2×M16×C19—24no—
45C2×M16×C19—24no—
46C2×M16×C19C2314yes—
47C2×M16×C19C2312yes—
48C22×C8×C19—24no—
49C22×C8×C19—22no—
50C22×C8×C19—21no—
51C22×C8×C19D412yes—
52C22×C8×C19D412yes—
53C22×C8×C19C2312yes—
54C19×#117—21no—
55C19×#117—21no—
56C19×#117D412yes—
57C19×#117C2312yes—
58C2×C4⋊C4×C19D412yes—
59C2×C22⋊C4×C19—21no—
60C2×C42×C19—21no—
61C19×C4⋊C8—28no—
62C19×#102—216no—
63C19×#100—216no—
64C24×C19—28no—
65C24×C19—24no—
66C24×C19—42no—
67C24×C19—42no—
68C24×C19—44no—
69C24×C19—88no—
70C24×C19#4111yescharacteristic
71C2×D4×C19—28no—
72C2×D4×C19—28no—
73C2×D4×C19—28no—
74C2×D4×C19—28no—
75C2×D4×C19—28no—
76C2×D4×C19—24no—
77C2×D4×C19—24no—
78C2×D4×C19—24no—
79C2×D4×C19—24no—
80C2×D4×C19—24no—
81C2×D4×C19—44no—
82C2×D4×C19—44no—
83C2×D4×C19—42no—
84C2×D4×C19—42no—
85C2×D4×C19—44no—
86C2×D4×C19—44no—
87C2×D4×C19—44no—
88C2×D4×C19C2×D418yes—
89C22×C4×C19—22no—
90C22×C4×C19C2×D414yes—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C22×C4×C19#4114yes—
97C22×C4×C19C2411yescharacteristic
98D8×C19—232no—
99M16×C19—24no—
100M16×C19—24no—
101M16×C19—24no—
102M16×C19—42no—
103M16×C19—44no—
104C2×C8×C19—24no—
105C2×C8×C19—24no—
106C2×C8×C19—24no—
107C2×C8×C19—24no—
108C2×C8×C19—22no—
109C2×C8×C19—42no—
110C2×C8×C19—44no—
111C2×C8×C19C2×D414yes—
112C4⋊C4×C19—22no—
113C4⋊C4×C19C2×D414yes—
114C22⋊C4×C19—22no—
115C22⋊C4×C19—22no—
116C42×C19—22no—
117C42×C19—22no—
118C2×#2045C1911yesmaximal, characteristic, direct product factor, Sylow
119C23×C19—24no—
120C23×C19—28no—
121C23×C19—44no—
122C23×C19—44no—
123C23×C19—48no—
124C23×C19—48no—
125C23×C19—88no—
126C23×C19—816no—
127C23×C19—88no—
128C23×C19—816no—
129C23×C19—88no—
130C23×C19#12111yescharacteristic
131C23×C19#12111yescharacteristic
132C23×C19#12314yes—
133C23×C19C2×#4111yescharacteristic
134D4×C19—28no—
135D4×C19—28no—
136D4×C19—44no—
137D4×C19—44no—
138D4×C19—48no—
139D4×C19—48no—
140C2×C4×C19—24no—
141C2×C4×C19—44no—
142C2×C4×C19#12012yes—
143C2×C4×C19#12012yes—
144C2×C4×C19#12114yes—
145C2×C4×C19#12114yes—
146C2×C4×C19#12111yescharacteristic
147C2×C4×C19#12111yescharacteristic
148C2×C4×C19#12314yes—
149C2×C4×C19#12412yes—
150C2×C4×C19#12412yes—
151C2×C4×C19C22×D412yes—
152C2×C4×C19C22×D411yescharacteristic
153C2×C4×C19C22×D411yescharacteristic
154C2×C4×C19C2×#4112yes—
155C8×C19—24no—
156C8×C19—42no—
157C8×C19—44no—
158C23×D8C2×C1911yescharacteristic
159C2×#424C2×C1911yescharacteristic, complemented
160C2×#418C2×C1912yescomplemented
161C22×#100C2×C1912yescomplemented
162#2045C2×C1918yesdirect product factor
163C2×#341C2×C1911yescharacteristic, complemented
164C22×C19—22no—
165C22×C19—22no—
166C22×C19—28no—
167C22×C19—48no—
168C22×C19—88no—
169C22×C19—88no—
170C22×C19—816no—
171C22×C19—88no—
172C22×C19—816no—
173C22×C19#39412yes—
174C22×C19#39412yes—
175C22×C19#47214yes—
176C22×C19C2×#12111yescharacteristic
177C22×C19C2×#12312yes—
178C4×C19—44no—
179C4×C19#39412yes—
180C4×C19#39412yes—
181C4×C19C2×#12011yescharacteristic
182C4×C19C2×#12112yes—
183C4×C19C2×#12411yescharacteristic
184C23×D4C22×C1912yes—
185C22×D8—28no—
186C22×D8—22no—
187C22×D8—22no—
188C22×D8C22×C1914yes—
189C22×M16C22×C1911yescharacteristic
190C22×M16C22×C1912yes—
191C23×C8C22×C1911yescharacteristic
192C2×#117C22×C1911yescharacteristic
193#424—22no—
194#424C22×C1914yescomplemented
195C2×C4⋊C8—22no—
196#418—24no—
197#418C22×C1918yescomplemented
198C2×#102—24no—
199C2×#100—28no—
200C2×#100C22×C1918yescomplemented
201#341C22×C1914yescomplemented
202C2×C19—22no—
203C2×C19—22no—
204C2×C19—88no—
205C2×C19#204514yesdirect product factor
206C2×C19C2×#39411yescharacteristic
207C2×C19C2×#47212yes—
208C25—22no—
209C22×D4—24no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—24no—
215C22×D4—22no—
216C22×D4—24no—
217C22×D4D4×C1918yes—
218C22×D4C23×C1914yes—
219C23×C4C23×C1911yescharacteristic
220C2×D8—216no—
221C2×D8—216no—
222C2×D8—216no—
223C2×D8—28no—
224C2×M16—22no—
225C2×M16—21no—
226C2×M16—24no—
227C2×M16—24no—
228C2×M16—24no—
229C2×M16C23×C1914yes—
230C2×M16C23×C1912yes—
231C22×C8—24no—
232C22×C8—22no—
233C22×C8—21no—
234C22×C8D4×C1912yes—
235C22×C8D4×C1912yes—
236C22×C8C23×C1912yes—
237#117—21no—
238#117—21no—
239#117D4×C1912yes—
240#117C23×C1912yes—
241C2×C4⋊C4D4×C1912yes—
242C2×C22⋊C4—21no—
243C2×C42—21no—
244C4⋊C8—28no—
245#102—216no—
246#100—216no—
247C19C2×#204511yescharacteristic, direct product factor, Sylow
248C24—28no—
249C24—24no—
250C24—42no—
251C24—42no—
252C24—44no—
253C24—88no—
254C24#41×C1911yescharacteristic
255C2×D4—28no—
256C2×D4—28no—
257C2×D4—28no—
258C2×D4—28no—
259C2×D4—28no—
260C2×D4—24no—
261C2×D4—24no—
262C2×D4—24no—
263C2×D4—24no—
264C2×D4—24no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—44no—
268C2×D4—44no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4C2×D4×C1918yes—
273C22×C4—22no—
274C22×C4C2×D4×C1914yes—
275C22×C4C2×D4×C1911yescharacteristic
276C22×C4C2×D4×C1911yescharacteristic
277C22×C4C2×D4×C1911yescharacteristic
278C22×C4C2×D4×C1911yescharacteristic
279C22×C4#41×C1911yescharacteristic
280C22×C4#41×C1914yes—
281C22×C4C24×C1911yescharacteristic
282D8—232no—
283M16—24no—
284M16—24no—
285M16—24no—
286M16—42no—
287M16—44no—
288C2×C8—24no—
289C2×C8—24no—
290C2×C8—24no—
291C2×C8—24no—
292C2×C8—22no—
293C2×C8—42no—
294C2×C8—44no—
295C2×C8C2×D4×C1914yes—
296C4⋊C4—22no—
297C4⋊C4C2×D4×C1914yes—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C42—22no—
301C42—22no—
302C23—24no—
303C23—28no—
304C23—48no—
305C23—48no—
306C23—44no—
307C23—44no—
308C23—88no—
309C23—816no—
310C23—88no—
311C23—816no—
312C23—88no—
313C23C19×#12111yescharacteristic
314C23C19×#12111yescharacteristic
315C23C19×#12314yes—
316C23C2×#41×C1911yescharacteristic
317D4—28no—
318D4—28no—
319D4—48no—
320D4—48no—
321D4—44no—
322D4—44no—
323C2×C4—24no—
324C2×C4—44no—
325C2×C4C19×#12012yes—
326C2×C4C19×#12012yes—
327C2×C4C19×#12111yescharacteristic
328C2×C4C19×#12111yescharacteristic
329C2×C4C19×#12114yes—
330C2×C4C19×#12114yes—
331C2×C4C19×#12314yes—
332C2×C4C19×#12412yes—
333C2×C4C19×#12412yes—
334C2×C4C22×D4×C1912yes—
335C2×C4C22×D4×C1911yescharacteristic
336C2×C4C22×D4×C1911yescharacteristic
337C2×C4C2×#41×C1912yes—
338C8—24no—
339C8—42no—
340C8—44no—
341C22—22no—
342C22—22no—
343C22—28no—
344C22—48no—
345C22—88no—
346C22—816no—
347C22—88no—
348C22—88no—
349C22—816no—
350C22C19×#39412yes—
351C22C19×#39412yes—
352C22C19×#47214yes—
353C22C2×C19×#12111yescharacteristic
354C22C2×C19×#12312yes—
355C4—44no—
356C4C19×#39412yes—
357C4C19×#39412yes—
358C4C2×C19×#12011yescharacteristic
359C4C2×C19×#12112yes—
360C4C2×C19×#12411yescharacteristic
361C2—22no—
362C2—22no—
363C2—88no—
364C2C19×#204514yesdirect product factor
365C2C2×C19×#39411yescharacteristic
366C2C2×C19×#47212yes—
subgroupG/H
center, socleC23×C19#121
commutator, Frattini, cosocleC22×C4C24×C19
prime radicalC23×D8×C19C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C19×#424C2semidirect
3. C2×C19×#418C2semidirect
4. C22×C19×#100C2semidirect
5. C19×#2045C2direct (N × H)
6. C2×C19×#341C2semidirect
17. C19×#424C22semidirect
20. C19×#418C22semidirect
23. C2×C19×#100C22semidirect
24. C19×#341C22semidirect
118. C2×#2045C19direct (N × H)
159. C2×#424C2×C19semidirect
160. C2×#418C2×C19semidirect
161. C22×#100C2×C19semidirect
162. #2045C2×C19direct (N × H)
163. C2×#341C2×C19semidirect
194. #424C22×C19semidirect
197. #418C22×C19semidirect
200. C2×#100C22×C19semidirect
201. #341C22×C19semidirect
205. C2×C19#2045direct (N × H)
247. C19C2×#2045direct (N × H)
364. C2C19×#2045direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D8×C192
C2×C19×#4242
C2×C19×#4182
C22×C19×#1002
C19×#20452
C2×C19×#3412
C2×#204519