Finite Group Databasebeta

← #14295643

Subgroups — #14295643

Order 1920.

640 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#711C211yesmaximal, characteristic
2C2×#91237C212yesmaximal
3#11752345C211yesmaximal, characteristic, complemented
4C4×#6758C211yesmaximal, characteristic, complemented
5#11746746C212yesmaximal, complemented
6#10604416—31nomaximal, Hall
7C2×C3×#711C2211yescharacteristic
8C2×C4×ΓL(1,𝔽16)C2212yes—
9C2×#6758C2212yes—
10C3×C4×C5×D4C411yescharacteristic, complemented
11C3×D4×Dic5C411yescharacteristic, complemented
12C3×C4×C22⋊D5—21no—
13C2×C3×C4×Dic5—21no—
14C3×#4038C2211yescharacteristic
15C3×#4033C411yescharacteristic, complemented
16C3×#4027—21no—
17C3×#4023—21no—
18C3×C42×D5C2211yescharacteristic
19C3×C4×Dic10C411yescharacteristic, complemented
20#91237C418yescomplemented
21#91235—21no—
22#91235—21no—
23#91231—21no—
24C4×C3⋊#170—21no—
25#71643—51nomaximal, Hall
26C4×#711D311yescharacteristic
27C2×#4008—32no—
28#65686—31no—
29C4×#700—31no—
30#64875—32no—
31C22×ΓL(1,𝔽16)—22no—
32C2×C3×C5×D4C2×C411yescharacteristic
33C22×C3×C4×C5—21no—
34C2×C3×C22⋊D5—21no—
35C22×C3×Dic5—21no—
36C22×C3×Dic5—21no—
37C3×#711—22no—
38C3×#711C2×C414yes—
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5C2311yescharacteristic
42C2×C3×Dic10C2×C411yescharacteristic
43C2×C3⋊#170—22no—
44C4×ΓL(1,𝔽16)—22no—
45C4×ΓL(1,𝔽16)C2×C414yescomplemented
46#6758—22no—
47#6758C2×C414yescomplemented
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×C5×C22⋊C4—21no—
50C3×C42×C5C2×C411yescharacteristic
51C3×C22⋊Dic5—21no—
52C3×#685—21no—
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×#683—21no—
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5C2×C411yescharacteristic
60C3×C4×Dic5D411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×#41—51no—
63C2×#837—52no—
64#4932—51no—
65C4×#208—51no—
66#4532—52no—
67C2×#711C2×D311yescharacteristic
68C2×C4×AGL(1,𝔽5)—32no—
69C2×#700—32no—
70C4×C5×D4Dic311yescharacteristic, complemented
71D4×Dic5Dic311yescharacteristic, complemented
72C4×C22⋊D5—21no—
73C2×C4×Dic5—21no—
74#4038C2×D311yescharacteristic
75#4033Dic311yescharacteristic, complemented
76#4027—21no—
77#4023—21no—
78C42×D5C2×D311yescharacteristic
79C4×Dic10Dic311yescharacteristic, complemented
80#4008—38no—
81(C2×AGL(1,𝔽5))⋊C4—61no—
82(C2×AGL(1,𝔽5))⋊C4—61no—
83#4002—61no—
84C4×#170—61no—
85#1759—151noSylow
86C23×C3×C5—21no—
87C22×C3×D5C2×D411yescharacteristic
88C2×ΓL(1,𝔽16)—24no—
89C2×ΓL(1,𝔽16)—42no—
90C2×ΓL(1,𝔽16)—42no—
91C3×C5×D4—21no—
92C3×C5×D4C4212yes—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—42no—
95C2×C3×C4×C5C22⋊C411yescharacteristic
96C2×C3×C4×C5C22⋊C411yescharacteristic
97C2×C3×C4×C5C22×C411yescharacteristic
98C3×C22⋊D5—24no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—24no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—42no—
103C2×C3×Dic5C22⋊C411yescharacteristic
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C2×D411yescharacteristic
106C3×C4×D5—41no—
107C3×C4×D5—41no—
108C3×C4×D5C22×C412yes—
109C3×C4×D5#4112yes—
110C3×Dic10—21no—
111C3×Dic10C4212yes—
112C3⋊#170—24no—
113C2×C3×#41—51no—
114C3×C4×Q8—51no—
115C3×C4×Q8—51no—
116C3×C4×D4—51no—
117C3×C4×D4—101no—
118C3×C4×D4—101no—
119C3×C4×D4AGL(1,𝔽5)11yescharacteristic, complemented
120C3×#117—51no—
121C3×#117—101no—
122C2×C3×C42—51no—
123C2×C3×C42—101no—
124C2×C4×Dic3—52no—
125C2×#208—52no—
126#837—58no—
127C3⋊#95—101no—
128C3⋊#95—101no—
129#803—101no—
130C4×C3⋊C8—101no—
131C22×AGL(1,𝔽5)—62no—
132C2×C5×D4C2×Dic311yescharacteristic
133C22×C4×C5—21no—
134C2×C22⋊D5—21no—
135C22×Dic5—21no—
136C22×Dic5—21no—
137#711—22no—
138#711C4×D314yes—
139C2×C4×D5#6711yescharacteristic
140C2×C4×D5#6711yescharacteristic
141C2×C4×D5C22×D311yescharacteristic
142C2×Dic10C2×Dic311yescharacteristic
143C2×#170—62no—
144C4×AGL(1,𝔽5)—34no—
145C4×AGL(1,𝔽5)—62no—
146#700—34no—
147#700—62no—
148C5×C4⋊C4C2×Dic311yescharacteristic
149C5×C22⋊C4—21no—
150C42×C5C2×Dic311yescharacteristic
151C22⋊Dic5—21no—
152#685—21no—
153C4⋊Dic5C2×Dic311yescharacteristic
154#683—21no—
155#683—21no—
156C4×Dic5—21no—
157C4×Dic5—21no—
158C4×Dic5—21no—
159C4×Dic5C2×Dic311yescharacteristic
160C4×Dic5#6711yescharacteristic
161C4×Dic5#6711yescharacteristic
162C4×#41—51no—
163C2×#104—152no—
164C4×M16—151no—
165#376—151no—
166#339—152no—
167C22×C3×C5—22no—
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C2×C3×D5C4×D412yes—
174ΓL(1,𝔽16)—44no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177C3×C4×C5—41no—
178C3×C4×C5C2×C4211yescharacteristic
179C3×C4×C5#11711yescharacteristic
180C3×Dic5—22no—
181C3×Dic5—21no—
182C3×Dic5—21no—
183C3×Dic5—41no—
184C3×Dic5C4×D412yes—
185C3×#41—54no—
186C3×#41—102no—
187C2×C3×Q8—51no—
188C2×C3×D4—101no—
189C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
190C22×C3×C4—21no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—101no—
195C22×C3×C4—101no—
196C22×Dic3—102no—
197C3×C4⋊C4—51no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4—101no—
200C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
201C3×C22⋊C4—21no—
202C3×C22⋊C4—101no—
203C3×C22⋊C4—101no—
204C3×C42—51no—
205C3×C42—51no—
206C3×C42—51no—
207C3×C42—101no—
208C3×C42—101no—
209C3×C42—101no—
210C3×C42C2×AGL(1,𝔽5)11yescharacteristic
211C4×Dic3—54no—
212C4×Dic3—102no—
213#208—54no—
214#208—102no—
215C2×C3⋊C8—102no—
216C23×C5—21no—
217C22×D5C2×#6711yescharacteristic
218C2×AGL(1,𝔽5)—64no—
219C2×AGL(1,𝔽5)—122no—
220C2×AGL(1,𝔽5)—122no—
221C5×D4—21no—
222C5×D4C4×Dic312yes—
223C2×C4×C5—21no—
224C2×C4×C5—42no—
225C2×C4×C5#21711yescharacteristic
226C2×C4×C5#21711yescharacteristic
227C2×C4×C5C22×Dic311yescharacteristic
228C22⋊D5—24no—
229C2×Dic5—21no—
230C2×Dic5—24no—
231C2×Dic5—21no—
232C2×Dic5—42no—
233C2×Dic5#21711yescharacteristic
234C2×Dic5#21711yescharacteristic
235C2×Dic5C2×#6711yescharacteristic
236C4×D5—41no—
237C4×D5—41no—
238C4×D5C2×C4×D312yes—
239C4×D5#23512yes—
240Dic10—21no—
241Dic10C4×Dic312yes—
242#170—64no—
243C2×#41—51no—
244C2×M16—152no—
245C4×Q8—51no—
246C4×Q8—51no—
247C4×D4—51no—
248C4×D4—101no—
249C4×D4—101no—
250C4×D4ΓL(1,𝔽16)11yescharacteristic, complemented
251#117—51no—
252#117—101no—
253C2×C42—51no—
254C2×C42—101no—
255C2×C42—152no—
256#104—158no—
257#97—301no—
258C4×C8—301no—
259#95—301no—
260#95—301no—
261C2×C3×C5—42no—
262C2×C3×C5C4×C22⋊C411yescharacteristic
263C2×C3×C5#42111yescharacteristic
264C2×C3×C5#42111yescharacteristic
265C3×D5—22no—
266C23×C3—21no—
267C23×C3—51no—
268C3×Q8—52no—
269C3×Q8—101no—
270C3×D4—21no—
271C3×D4—104no—
272C3×D4C4×AGL(1,𝔽5)12yes—
273C2×C3×C4—21no—
274C2×C3×C4—42no—
275C2×C3×C4—51no—
276C2×C3×C4—52no—
277C2×C3×C4—52no—
278C2×C3×C4—51no—
279C2×C3×C4—51no—
280C2×C3×C4—104no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—201no—
284C2×C3×C4—201no—
285C2×C3×C4—202no—
286C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
287C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
288C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
289C2×Dic3—104no—
290C2×Dic3—202no—
291C2×Dic3—202no—
292C3⋊C8—104no—
293C22×C5—22no—
294C22×C5—41no—
295C22×C5—41no—
296C22×C5C2×#21711yescharacteristic
297C2×D5—21no—
298C2×D5—21no—
299C2×D5C4×#6712yes—
300AGL(1,𝔽5)—124no—
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—41no—
304C4×C5C2×C4×Dic311yescharacteristic
305C4×C5#92611yescharacteristic
306Dic5—22no—
307Dic5—21no—
308Dic5—21no—
309Dic5—41no—
310Dic5C4×#6712yes—
311#41—54no—
312#41—102no—
313C2×Q8—51no—
314C2×D4—101no—
315C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
316C22×C4—21no—
317C22×C4—51no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—101no—
321C22×C4—101no—
322C22×C4—302no—
323M16—154no—
324M16—302no—
325C2×C8—302no—
326C4⋊C4—51no—
327C4⋊C4—101no—
328C4⋊C4—101no—
329C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—101no—
332C22⋊C4—101no—
333C42—51no—
334C42—51no—
335C42—51no—
336C42—101no—
337C42—101no—
338C42—101no—
339C42—154no—
340C42—302no—
341C42C2×ΓL(1,𝔽16)11yescharacteristic
342C3×C5#175911yescharacteristic, complemented, Hall
343C22×C3—22no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—52no—
347C22×C3—101no—
348C22×C3—101no—
349C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—52no—
354C3×C4—101no—
355C3×C4—102no—
356C3×C4—101no—
357C3×C4—201no—
358C3×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
359C3×C4#413011yescharacteristic
360Dic3—204no—
361C2×C5—42no—
362C2×C5C4×#21711yescharacteristic
363C2×C5#523611yescharacteristic
364C2×C5#523611yescharacteristic
365D5—22no—
366C23—21no—
367C23—51no—
368Q8—52no—
369Q8—101no—
370D4—21no—
371D4—104no—
372D4C4×ΓL(1,𝔽16)12yes—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—51no—
376C2×C4—52no—
377C2×C4—52no—
378C2×C4—51no—
379C2×C4—51no—
380C2×C4—104no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—201no—
384C2×C4—201no—
385C2×C4—202no—
386C2×C4—304no—
387C2×C4—602no—
388C2×C4—602no—
389C2×C4#676311yescharacteristic
390C2×C4#676311yescharacteristic
391C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
392C8—304no—
393C2×C3—42no—
394C2×C3—102no—
395C2×C3C4×C22⋊AGL(1,𝔽5)11yescharacteristic
396C2×C3#6576911yescharacteristic
397C2×C3#6579511yescharacteristic
398C5#7164311yescharacteristic, complemented, Sylow
399C22—22no—
400C22—41no—
401C22—41no—
402C22—52no—
403C22—101no—
404C22—101no—
405C22C2×#676311yescharacteristic
406C4—21no—
407C4—21no—
408C4—41no—
409C4—52no—
410C4—101no—
411C4—102no—
412C4—101no—
413C4—201no—
414C4—604no—
415C4C2×C4×ΓL(1,𝔽16)11yescharacteristic
416C4#9198911yescharacteristic
417C3#1060441611yescharacteristic, complemented, Sylow
418C2—42no—
419C2—102no—
420C2C4×#676311yescharacteristic
421C2#1175242811yescharacteristic
422C2#1175245411yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C4×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#711C22
cosocleC2×C3×C4×D5C23
hypercenterC4×D4ΓL(1,𝔽16)
hypocenterC3×C5#1759
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #11752345C2semidirect
4. C4×#6758C2semidirect
5. #11746746C2semidirect
10. C3×C4×C5×D4C4semidirect
11. C3×D4×Dic5C4semidirect
15. C3×#4033C4semidirect
19. C3×C4×Dic10C4semidirect
20. #91237C4semidirect
45. C4×ΓL(1,𝔽16)C2×C4semidirect
47. #6758C2×C4semidirect
70. C4×C5×D4Dic3semidirect
71. D4×Dic5Dic3semidirect
75. #4033Dic3semidirect
79. C4×Dic10Dic3semidirect
119. C3×C4×D4AGL(1,𝔽5)semidirect
250. C4×D4ΓL(1,𝔽16)semidirect
342. C3×C5#1759semidirect
398. C5#71643semidirect
417. C3#10604416semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#7112
C2×#912372
#117523452
C4×#67582
#117467462
#106044163
#716435