Finite Group Databasebeta

← C4×#91228 #14295375

Subgroups — C4×#91228 #14295375

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D20C211yesmaximal, characteristic
2C4×#6763C212yesmaximal, complemented
3C2×#91228C212yesmaximal
4#11746788C212yesmaximal, complemented
5C4×#3999—31nomaximal, Hall
6C22×C3×D20C2211yescharacteristic
7C22×C3×C4×D5C411yescharacteristic, complemented
8C22×C3×C4×D5C2211yescharacteristic
9C2×#6763C2214yes—
10C2×C4×ΓL(1,𝔽16)—22no—
11C2×C3×C42×C5C411yescharacteristic, complemented
12C2×C3×#685C411yescharacteristic, complemented
13C2×C3×#685C2211yescharacteristic
14C2×C3×C4⋊Dic5C411yescharacteristic, complemented
15C3×C4×D20—22no—
16C3×C4×D20—22no—
17#91235—22no—
18#91228C418yesdirect product factor
19C4×#834—51nomaximal, Hall
20C2×C4×D20D311yescharacteristic
21C4×C22⋊AGL(1,𝔽5)—32no—
22C2×#3999—32no—
23#64917—32no—
24C23×C3×D5C2×C411yescharacteristic
25C23×C3×D5C2311yescharacteristic
26C22×ΓL(1,𝔽16)—24no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×Dic5C2×C411yescharacteristic
31C22×C3×Dic5C2×C411yescharacteristic
32C2×C3×D20—22no—
33C2×C3×D20—22no—
34C2×C3×D20C2×C414yes—
35C2×C3×C4×D5—21no—
36C2×C3×C4×D5—21no—
37C2×C3×C4×D5—42no—
38C2×C3×C4×D5—42no—
39C2×C3×C4×D5D412yes—
40C2×C3×C4×D5D412yes—
41#6763—24no—
42#6763C2×C418yescomplemented
43C4×ΓL(1,𝔽16)—44no—
44C3×C42×C5—21no—
45C3×C42×C5—21no—
46C3×#685—22no—
47C3×#685—22no—
48C3×C4⋊Dic5—22no—
49C2×C3×C4×D4—51no—
50C2×#834—52no—
51C4×#217—52no—
52#4526—52no—
53C22×D20C2×D311yescharacteristic
54C22×C4×D5Dic311yescharacteristic, complemented
55C22×C4×D5C2×D311yescharacteristic
56C2×C22⋊AGL(1,𝔽5)—34no—
57C2×C4×AGL(1,𝔽5)—62no—
58C2×C42×C5Dic311yescharacteristic, complemented
59C2×#685Dic311yescharacteristic, complemented
60C2×#685C2×D311yescharacteristic
61C2×C4⋊Dic5Dic311yescharacteristic, complemented
62C4×D20—22no—
63C4×D20—22no—
64(C2×AGL(1,𝔽5))⋊C4—62no—
65#3999—38no—
66C4×#99—151noSylow
67C23×C3×C5C22×C411yescharacteristic
68C22×C3×D5—21no—
69C22×C3×D5—21no—
70C22×C3×D5—41no—
71C22×C3×D5—41no—
72C22×C3×D5—41no—
73C22×C3×D5—41no—
74C22×C3×D5C4212yescomplemented
75C22×C3×D5C22×C412yes—
76C22×C3×D5C2×D412yes—
77C22×C3×D5#4112yes—
78C2×ΓL(1,𝔽16)—28no—
79C2×ΓL(1,𝔽16)—44no—
80C2×ΓL(1,𝔽16)—44no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C4212yescomplemented
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×Dic5—21no—
90C2×C3×Dic5—41no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5C22⋊C412yes—
93C3×D20—28no—
94C3×C4×D5—24no—
95C3×C4×D5—42no—
96C3×C4×D5—42no—
97C3×C4×D5—42no—
98C22×C3×D4—51no—
99C23×C3×C4—51no—
100C23×C3×C4—51no—
101C3×C4×D4—102no—
102C3×C4×D4—102no—
103C2×C3×C4⋊C4—51no—
104C2×C3×C22⋊C4—51no—
105C2×C3×C22⋊C4—51no—
106C2×C3×C42AGL(1,𝔽5)11yescharacteristic, complemented
107C2×#217—54no—
108C2×C4×Dic3—102no—
109#834—58no—
110C3⋊#95—102no—
111C23×D5C2×Dic311yescharacteristic
112C23×D5C22×D311yescharacteristic
113C22×AGL(1,𝔽5)—64no—
114C22×C4×C5C2×Dic311yescharacteristic
115C22×C4×C5C2×Dic311yescharacteristic
116C22×C4×C5C2×Dic311yescharacteristic
117C22×Dic5C2×Dic311yescharacteristic
118C22×Dic5C2×Dic311yescharacteristic
119C2×D20—22no—
120C2×D20—22no—
121C2×D20C4×D314yes—
122C2×C4×D5—21no—
123C2×C4×D5—21no—
124C2×C4×D5—42no—
125C2×C4×D5—42no—
126C2×C4×D5#6712yes—
127C2×C4×D5#6712yes—
128C22⋊AGL(1,𝔽5)—38no—
129C22⋊AGL(1,𝔽5)—64no—
130C4×AGL(1,𝔽5)—124no—
131C42×C5—21no—
132C42×C5—21no—
133#685—22no—
134#685—22no—
135C4⋊Dic5—22no—
136C2×C4×D4—51no—
137C2×#99—152no—
138C4×C22⋊C4—152no—
139#342—152no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5C2×C4211yescharacteristic
143C22×C3×C5C2×C22⋊C411yescharacteristic
144C22×C3×C5#11711yescharacteristic
145C2×C3×D5—22no—
146C2×C3×D5—22no—
147C2×C3×D5—22no—
148C2×C3×D5—42no—
149C2×C3×D5—42no—
150C2×C3×D5—42no—
151C2×C3×D5—41no—
152C2×C3×D5—41no—
153C2×C3×D5—42no—
154C2×C3×D5C4×D414yes—
155ΓL(1,𝔽16)—48no—
156C3×C4×C5—22no—
157C3×C4×C5—21no—
158C3×C4×C5—41no—
159C3×C4×C5#9912yescomplemented
160C3×Dic5—22no—
161C3×Dic5—41no—
162C24×C3—51no—
163C24×C3—51no—
164C2×C3×D4—54no—
165C2×C3×D4—102no—
166C2×C3×D4—102no—
167C22×C3×C4—51no—
168C22×C3×C4—52no—
169C22×C3×C4—52no—
170C22×C3×C4—51no—
171C22×C3×C4—101no—
172C22×C3×C4—101no—
173C22×C3×C4—202no—
174C22×C3×C4—202no—
175C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
176C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
177C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
178C22×Dic3—104no—
179C3×C4⋊C4—102no—
180C3×C22⋊C4—102no—
181C3×C22⋊C4—102no—
182C3×C42—21no—
183C3×C42—21no—
184#217—58no—
185#217—104no—
186C4×Dic3—204no—
187C23×C5C22×Dic311yescharacteristic
188C22×D5—21no—
189C22×D5—21no—
190C22×D5—41no—
191C22×D5—41no—
192C22×D5—41no—
193C22×D5—41no—
194C22×D5C4×Dic312yescomplemented
195C22×D5C2×C4×D312yes—
196C22×D5#23512yes—
197C22×D5C2×#6712yes—
198C2×AGL(1,𝔽5)—68no—
199C2×AGL(1,𝔽5)—124no—
200C2×AGL(1,𝔽5)—124no—
201C2×C4×C5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—22no—
204C2×C4×C5—21no—
205C2×C4×C5—41no—
206C2×C4×C5C4×Dic312yescomplemented
207C2×C4×C5#21711yescharacteristic
208C2×C4×C5#21711yescharacteristic
209C2×Dic5—21no—
210C2×Dic5—41no—
211C2×Dic5—41no—
212C2×Dic5#21712yes—
213D20—28no—
214C4×D5—24no—
215C4×D5—42no—
216C4×D5—42no—
217C4×D5—42no—
218C22×D4—51no—
219C23×C4—51no—
220C23×C4—51no—
221C4×D4—102no—
222C4×D4—102no—
223C2×C4⋊C4—51no—
224C2×C22⋊C4—51no—
225C2×C22⋊C4—51no—
226C2×C22⋊C4—154no—
227C2×C42—302no—
228C2×C42ΓL(1,𝔽16)11yescharacteristic, complemented
229#99—158no—
230#95—302no—
231C2×C3×C5—21no—
232C2×C3×C5—21no—
233C2×C3×C5C4×C22⋊C411yescharacteristic
234C2×C3×C5C2×#9911yescharacteristic
235C2×C3×C5#41011yescharacteristic
236C3×D5—24no—
237C3×D5—42no—
238C23×C3—52no—
239C23×C3—52no—
240C23×C3—52no—
241C23×C3—52no—
242C23×C3—101no—
243C23×C3—101no—
244C23×C3—201no—
245C23×C3—201no—
246C23×C3—201no—
247C23×C3—201no—
248C23×C3C22×AGL(1,𝔽5)11yescharacteristic
249C3×D4—108no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—41no—
255C2×C3×C4—52no—
256C2×C3×C4—104no—
257C2×C3×C4—101no—
258C2×C3×C4—202no—
259C2×C3×C4—202no—
260C2×C3×C4—201no—
261C2×C3×C4—202no—
262C2×C3×C4—201no—
263C2×C3×C4C4×AGL(1,𝔽5)12yescomplemented
264C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
265C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
266C2×Dic3—108no—
267C2×Dic3—204no—
268C2×Dic3—204no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5C2×C4×Dic311yescharacteristic
272C22×C5#92611yescharacteristic
273C22×C5C2×#21711yescharacteristic
274C2×D5—22no—
275C2×D5—22no—
276C2×D5—22no—
277C2×D5—42no—
278C2×D5—42no—
279C2×D5—42no—
280C2×D5—41no—
281C2×D5—41no—
282C2×D5—42no—
283C2×D5C4×#6714yes—
284AGL(1,𝔽5)—128no—
285C4×C5—22no—
286C4×C5—21no—
287C4×C5—41no—
288C4×C5#83412yescomplemented
289Dic5—22no—
290Dic5—41no—
291C24—51no—
292C24—51no—
293C2×D4—54no—
294C2×D4—102no—
295C2×D4—102no—
296C22×C4—51no—
297C22×C4—52no—
298C22×C4—52no—
299C22×C4—51no—
300C22×C4—101no—
301C22×C4—101no—
302C22×C4—202no—
303C22×C4—202no—
304C22×C4—304no—
305C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
306C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
307C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
308C4⋊C4—102no—
309C22⋊C4—102no—
310C22⋊C4—102no—
311C22⋊C4—158no—
312C22⋊C4—304no—
313C42—21no—
314C42—21no—
315C42—604no—
316C3×C5C4×#9911yescharacteristic, complemented, Hall
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—54no—
320C22×C3—102no—
321C22×C3—102no—
322C22×C3—102no—
323C22×C3—202no—
324C22×C3—202no—
325C22×C3—202no—
326C22×C3—202no—
327C22×C3—201no—
328C22×C3—201no—
329C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
330C22×C3#413011yescharacteristic
331C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
332C3×C4—21no—
333C3×C4—22no—
334C3×C4—41no—
335C3×C4—102no—
336C3×C4—201no—
337C3×C4#399912yescomplemented
338Dic3—208no—
339C2×C5—21no—
340C2×C5—21no—
341C2×C5C4×#21711yescharacteristic
342C2×C5C2×#83411yescharacteristic
343C2×C5#524011yescharacteristic
344D5—24no—
345D5—42no—
346C23—52no—
347C23—52no—
348C23—52no—
349C23—52no—
350C23—101no—
351C23—101no—
352C23—201no—
353C23—201no—
354C23—201no—
355C23—201no—
356C23C22×ΓL(1,𝔽16)11yescharacteristic
357D4—108no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—52no—
364C2×C4—104no—
365C2×C4—101no—
366C2×C4—202no—
367C2×C4—202no—
368C2×C4—201no—
369C2×C4—202no—
370C2×C4—201no—
371C2×C4—308no—
372C2×C4—604no—
373C2×C4—604no—
374C2×C4C4×ΓL(1,𝔽16)12yescomplemented
375C2×C4#676311yescharacteristic
376C2×C4#676311yescharacteristic
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—104no—
380C2×C3—202no—
381C2×C3C2×#399911yescharacteristic
382C2×C3#6574511yescharacteristic
383C2×C3C4×C22⋊AGL(1,𝔽5)11yescharacteristic
384C5C4×#83411yescharacteristic, complemented, Sylow
385C22—21no—
386C22—21no—
387C22—54no—
388C22—102no—
389C22—102no—
390C22—102no—
391C22—202no—
392C22—202no—
393C22—202no—
394C22—202no—
395C22—201no—
396C22—201no—
397C22C2×C4×ΓL(1,𝔽16)11yescharacteristic
398C22#9198911yescharacteristic
399C22C2×#676311yescharacteristic
400C4—21no—
401C4—22no—
402C4—41no—
403C4—102no—
404C4—201no—
405C4—608no—
406C4#9122812yesdirect product factor
407C3C4×#399911yescharacteristic, complemented, Sylow
408C2—21no—
409C2—21no—
410C2—104no—
411C2—202no—
412C2C2×#9122811yescharacteristic
413C2#1175240411yescharacteristic
414C2C4×#676311yescharacteristic
subgroupG/H
centerC2×C4#6763
commutatorC22×C3×C5C2×C42
FrattiniC23C22×ΓL(1,𝔽16)
FittingC2×C3×C42×C5C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D20C22
cosocleC23×C3×D5C23
hypercenterC2×C42ΓL(1,𝔽16)
hypocenterC3×C5C4×#99
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#6763C2semidirect
4. #11746788C2semidirect
7. C22×C3×C4×D5C4semidirect
11. C2×C3×C42×C5C4semidirect
12. C2×C3×#685C4semidirect
14. C2×C3×C4⋊Dic5C4semidirect
18. #91228C4direct (N × H)
42. #6763C2×C4semidirect
54. C22×C4×D5Dic3semidirect
58. C2×C42×C5Dic3semidirect
59. C2×#685Dic3semidirect
61. C2×C4⋊Dic5Dic3semidirect
74. C22×C3×D5C42semidirect
86. C2×C3×C4×C5C42semidirect
106. C2×C3×C42AGL(1,𝔽5)semidirect
159. C3×C4×C5#99semidirect
194. C22×D5C4×Dic3semidirect
206. C2×C4×C5C4×Dic3semidirect
228. C2×C42ΓL(1,𝔽16)semidirect
263. C2×C3×C4C4×AGL(1,𝔽5)semidirect
288. C4×C5#834semidirect
316. C3×C5C4×#99semidirect
337. C3×C4#3999semidirect
374. C2×C4C4×ΓL(1,𝔽16)semidirect
384. C5C4×#834semidirect
406. C4#91228direct (N × H)
407. C3C4×#3999semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D202
C4×#67632
C2×#912282
#117467882
C4×#39993
C4×#8345