Finite Group Databasebeta

← #14322697

Subgroups — #14322697

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×Dic3⋊C4C211yesmaximal, characteristic
2#11752424C211yesmaximal, characteristic
3C3×#65765C211yesmaximal, characteristic
4Dic3×C22⋊AGL(1,𝔽5)C212yesmaximal
5#11751984C212yesmaximal
6#11751845C214yesmaximal, complemented
7#11751835C214yesmaximal, complemented
8#10617101—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×D5×Dic3C2211yescharacteristic
11C22×D5×Dic3C2211yescharacteristic
12C2×#6763C2212yes—
13C2×C4⋊ΓL(1,𝔽16)C2212yes—
14C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
15C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
16C2×Dic3×AGL(1,𝔽5)C2214yes—
17C2×#6712C411yescharacteristic, complemented
18C2×C5×Dic3⋊C4C411yescharacteristic, complemented
19C2×Dic3⋊Dic5C411yescharacteristic, complemented
20C2×#6669C411yescharacteristic, complemented
21D5×Dic3⋊C4C412yescomplemented
22D5×Dic3⋊C4C412yescomplemented
23D5×Dic3⋊C4C2212yes—
24D5×Dic3⋊C4C2212yes—
25#91235C2212yes—
26C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
27(C2×AGL(1,𝔽5))⋊Dic3C2218yes—
28(C2×AGL(1,𝔽5))⋊Dic3C2214yes—
29#73867—51nomaximal, Hall
30C2×D5×C4⋊C4—31no—
31#65765—31no—
32#65765D311yescharacteristic
33#65764—32no—
34C4×C22⋊AGL(1,𝔽5)—32no—
35#65711—34no—
36#65711—34no—
37C23×C3×D5C2311yescharacteristic
38C22×ΓL(1,𝔽16)C2314yes—
39C22×C3×AGL(1,𝔽5)C2314yes—
40C22×C3×C4×C5C2×C411yescharacteristic
41C22×Dic15C2×C411yescharacteristic
42C22×Dic15C2×C411yescharacteristic
43C22×C5×Dic3C2×C411yescharacteristic
44C22×C5×Dic3C2×C411yescharacteristic
45C22×C3×Dic5C2×C411yescharacteristic
46C2×C3×C4×D5—42no—
47C2×C3×C4×D5C2×C411yescharacteristic
48C2×C3×C4×D5C2×C411yescharacteristic
49C2×C3×C4×D5C2311yescharacteristic
50C2×C3×C4×D5C2311yescharacteristic
51C2×D5×Dic3—22no—
52C2×D5×Dic3—22no—
53C2×D5×Dic3—42no—
54C2×D5×Dic3C2×C412yes—
55C2×D5×Dic3C2×C412yes—
56C2×D5×Dic3C2312yes—
57C2×D5×Dic3C2312yes—
58#6763—24no—
59C4⋊ΓL(1,𝔽16)—42no—
60C3×C22⋊AGL(1,𝔽5)—24no—
61C3×C4⋊AGL(1,𝔽5)—42no—
62Dic3×AGL(1,𝔽5)—44no—
63#6712C2×C412yes—
64#6712C2×C412yes—
65C5×Dic3⋊C4C2×C412yes—
66C5×Dic3⋊C4C2×C412yes—
67Dic3⋊Dic5C2×C412yes—
68Dic3⋊Dic5C2×C412yes—
69#6669C2×C412yes—
70#6669C2×C412yes—
71C22×Dic3⋊C4—51no—
72C3×#380—51no—
73#5212—51no—
74#4978—54no—
75#4943—52no—
76Dic3×C22⋊C4—52no—
77#4655—54no—
78C22×C4×D5—31no—
79C22×C4×D5—31no—
80C22×C4×D5C2×D311yescharacteristic
81C2×C22⋊AGL(1,𝔽5)—32no—
82C2×C22⋊AGL(1,𝔽5)C2×D312yes—
83C2×C4⋊AGL(1,𝔽5)—32no—
84C2×C4⋊AGL(1,𝔽5)C2×D312yes—
85C2×C4×AGL(1,𝔽5)—34no—
86C2×C5×C4⋊C4—31no—
87C2×C4⋊Dic5—31no—
88C2×#683—31no—
89C2×#683—31no—
90D5×C4⋊C4—32no—
91D5×C4⋊C4—32no—
92D5×C4⋊C4—32no—
93D5×C4⋊C4—32no—
94(C2×AGL(1,𝔽5))⋊C4—34no—
95(C2×AGL(1,𝔽5))⋊C4—38no—
96(C2×AGL(1,𝔽5))⋊C4—32no—
97(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
98#2313—151noSylow
99C23×C3×C5C22×C411yescharacteristic
100C22×C3×D5—22no—
101C22×C3×D5—22no—
102C22×C3×D5C22×C411yescharacteristic
103C22×C3×D5#4112yes—
104C22×C3×D5#4112yes—
105C22×C3×D5C2411yescharacteristic
106C2×ΓL(1,𝔽16)—24no—
107C2×ΓL(1,𝔽16)—24no—
108C2×ΓL(1,𝔽16)—24no—
109C2×C3×AGL(1,𝔽5)—24no—
110C2×C3×AGL(1,𝔽5)—24no—
111C2×C3×AGL(1,𝔽5)—24no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×Dic15—22no—
116C2×Dic15—41no—
117C2×Dic15C22×C412yes—
118C2×Dic15C22×C412yes—
119C2×C5×Dic3—22no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3C22×C412yes—
122C2×C5×Dic3C22×C412yes—
123C2×C3×Dic5—41no—
124C2×C3×Dic5C22×C411yescharacteristic
125C2×C3×Dic5C22×C411yescharacteristic
126C3×C4×D5—22no—
127C3×C4×D5—22no—
128C3×C4×D5—41no—
129C3×C4×D5—41no—
130D5×Dic3—24no—
131D5×Dic3—22no—
132D5×Dic3—22no—
133D5×Dic3—24no—
134D5×Dic3—42no—
135C23×C3×C4—51no—
136C23×Dic3—51no—
137C23×Dic3—51no—
138C2×C3×C4⋊C4—52no—
139C2×C3×C22⋊C4—52no—
140C2×#217—52no—
141C2×C4⋊Dic3—52no—
142C2×Dic3⋊C4—51no—
143C2×Dic3⋊C4—51no—
144C2×Dic3⋊C4—51no—
145C2×Dic3⋊C4—52no—
146C2×Dic3⋊C4—52no—
147C2×Dic3⋊C4—52no—
148C2×Dic3⋊C4—52no—
149C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
150C2×C4×Dic3—54no—
151C3×#95—52no—
152C3⋊#95—54no—
153C3⋊#95—58no—
154C3⋊#95—52no—
155C23×D5C22×D311yescharacteristic
156C22×AGL(1,𝔽5)—34no—
157C22×AGL(1,𝔽5)C22×D314yes—
158C22×C4×C5—31no—
159C22×C4×C5—31no—
160C22×C4×C5C4×D311yescharacteristic
161C22×Dic5—31no—
162C22×Dic5—31no—
163C22×Dic5C4×D311yescharacteristic
164C2×C4×D5—32no—
165C2×C4×D5—32no—
166C2×C4×D5—32no—
167C2×C4×D5—32no—
168C2×C4×D5—42no—
169C2×C4×D5—62no—
170C2×C4×D5—62no—
171C2×C4×D5—122no—
172C2×C4×D5C4×D311yescharacteristic
173C2×C4×D5C4×D311yescharacteristic
174C2×C4×D5C22×D311yescharacteristic
175C2×C4×D5C22×D311yescharacteristic
176C22⋊AGL(1,𝔽5)—24no—
177C22⋊AGL(1,𝔽5)—64no—
178C4⋊AGL(1,𝔽5)—42no—
179C4⋊AGL(1,𝔽5)—122no—
180C4×AGL(1,𝔽5)—124no—
181C5×C4⋊C4—32no—
182C5×C4⋊C4—32no—
183C4⋊Dic5—32no—
184C4⋊Dic5—32no—
185#683—32no—
186#683—32no—
187#683—32no—
188#683—32no—
189C22×C4⋊C4—151no—
190#387—154no—
191#387—154no—
192#381—152no—
193#380—51no—
194#380—151no—
195C4×C22⋊C4—152no—
196C22×C3×C5—21no—
197C22×C3×C5—21no—
198C22×C3×C5#11712yes—
199C22×C3×C5C23×C411yescharacteristic
200C2×C3×D5—21no—
201C2×C3×D5—21no—
202C2×C3×D5—24no—
203C2×C3×D5—24no—
204C2×C3×D5#11712yes—
205C2×C3×D5C2×#4111yescharacteristic
206C2×C3×D5C2×#4111yescharacteristic
207C2×C3×D5H(5,𝔽2)12yes—
208C2×C3×D52−1+412yes—
209ΓL(1,𝔽16)—44no—
210C3×AGL(1,𝔽5)—44no—
211C3×C4×C5—21no—
212C3×C4×C5—21no—
213Dic15—22no—
214Dic15—22no—
215C3×Dic5—21no—
216C3×Dic5—21no—
217C5×Dic3—22no—
218C5×Dic3—22no—
219C24×C3—51no—
220C22×C3×C4—51no—
221C22×C3×C4—51no—
222C22×C3×C4—51no—
223C22×C3×C4—51no—
224C22×C3×C4—51no—
225C22×C3×C4—54no—
226C22×C3×C4—202no—
227C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
228C22×Dic3—51no—
229C22×Dic3—51no—
230C22×Dic3—52no—
231C22×Dic3—52no—
232C22×Dic3—52no—
233C22×Dic3—52no—
234C22×Dic3—54no—
235C22×Dic3—102no—
236C22×Dic3—102no—
237C22×Dic3—202no—
238C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
239C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
240C3×C4⋊C4—202no—
241C3×C22⋊C4—104no—
242#217—104no—
243C4⋊Dic3—202no—
244Dic3⋊C4—52no—
245Dic3⋊C4—52no—
246Dic3⋊C4—52no—
247Dic3⋊C4—52no—
248Dic3⋊C4—52no—
249Dic3⋊C4—52no—
250Dic3⋊C4C2×AGL(1,𝔽5)12yes—
251Dic3⋊C4C2×AGL(1,𝔽5)12yes—
252C4×Dic3—204no—
253C23×C5C2×C4×D311yescharacteristic
254C22×D5—22no—
255C22×D5—22no—
256C22×D5C2×C4×D311yescharacteristic
257C22×D5#23712yes—
258C22×D5#23912yes—
259C22×D5C23×D311yescharacteristic
260C2×AGL(1,𝔽5)—24no—
261C2×AGL(1,𝔽5)—24no—
262C2×AGL(1,𝔽5)—24no—
263C2×AGL(1,𝔽5)—64no—
264C2×AGL(1,𝔽5)—64no—
265C2×AGL(1,𝔽5)—64no—
266C2×C4×C5—32no—
267C2×C4×C5—32no—
268C2×C4×C5—41no—
269C2×C4×C5—62no—
270C2×C4×C5—121no—
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×Dic5—32no—
274C2×Dic5—32no—
275C2×Dic5—41no—
276C2×Dic5—62no—
277C2×Dic5—121no—
278C2×Dic5C2×C4×D311yescharacteristic
279C2×Dic5C2×C4×D311yescharacteristic
280C4×D5—22no—
281C4×D5—22no—
282C4×D5—41no—
283C4×D5—41no—
284C4×D5—64no—
285C4×D5—62no—
286C4×D5—64no—
287C4×D5—62no—
288C4×D5—122no—
289C23×C4—51no—
290C23×C4—151no—
291C23×C4—151no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—52no—
294C2×C4⋊C4—152no—
295C2×C4⋊C4—152no—
296C2×C4⋊C4—152no—
297C2×C4⋊C4—152no—
298C2×C4⋊C4—151no—
299C2×C4⋊C4—151no—
300C2×C4⋊C4—151no—
301C2×C4⋊C4—152no—
302C2×C22⋊C4—52no—
303C2×C22⋊C4—152no—
304C2×C42—154no—
305#95—52no—
306#95—154no—
307#95—152no—
308#95—158no—
309C2×C3×C5—22no—
310C2×C3×C5C2×#11711yescharacteristic
311C2×C3×C5#51811yescharacteristic
312C2×C3×C5#51911yescharacteristic
313C3×D5—22no—
314C3×D5#53912yes—
315C3×D5#53912yes—
316C23×C3—51no—
317C23×C3—52no—
318C23×C3—52no—
319C23×C3—51no—
320C23×C3—102no—
321C23×C3—102no—
322C23×C3C22×AGL(1,𝔽5)11yescharacteristic
323C2×C3×C4—41no—
324C2×C3×C4—51no—
325C2×C3×C4—51no—
326C2×C3×C4—102no—
327C2×C3×C4—102no—
328C2×C3×C4—104no—
329C2×C3×C4—104no—
330C2×C3×C4—104no—
331C2×C3×C4—201no—
332C2×C3×C4—201no—
333C2×C3×C4—201no—
334C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
335C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
336C2×Dic3—22no—
337C2×Dic3—41no—
338C2×Dic3—52no—
339C2×Dic3—52no—
340C2×Dic3—104no—
341C2×Dic3—102no—
342C2×Dic3—102no—
343C2×Dic3—104no—
344C2×Dic3—102no—
345C2×Dic3—104no—
346C2×Dic3—104no—
347C2×Dic3—104no—
348C2×Dic3—202no—
349C2×Dic3—201no—
350C2×Dic3C22×AGL(1,𝔽5)12yes—
351C2×Dic3C22×AGL(1,𝔽5)12yes—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5#89212yes—
355C22×C5C22×C4×D311yescharacteristic
356C2×D5—21no—
357C2×D5—21no—
358C2×D5—24no—
359C2×D5—24no—
360C2×D5#89212yes—
361C2×D5C2×#23711yescharacteristic
362C2×D5#100412yes—
363C2×D5C2×#23911yescharacteristic
364C2×D5#101012yes—
365AGL(1,𝔽5)—44no—
366AGL(1,𝔽5)—124no—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—62no—
370C4×C5—62no—
371Dic5—21no—
372Dic5—21no—
373Dic5—62no—
374Dic5—62no—
375C24—51no—
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—51no—
379C22×C4—51no—
380C22×C4—51no—
381C22×C4—51no—
382C22×C4—51no—
383C22×C4—54no—
384C22×C4—152no—
385C22×C4—152no—
386C22×C4—152no—
387C22×C4—152no—
388C22×C4—151no—
389C22×C4—151no—
390C22×C4—154no—
391C22×C4—202no—
392C22×C4—302no—
393C22×C4—302no—
394C22×C4—602no—
395C22×C4D3×AGL(1,𝔽5)11yescharacteristic
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—152no—
399C4⋊C4—152no—
400C4⋊C4—152no—
401C4⋊C4—152no—
402C4⋊C4—152no—
403C4⋊C4—152no—
404C4⋊C4—202no—
405C4⋊C4—602no—
406C22⋊C4—104no—
407C22⋊C4—304no—
408C42—604no—
409C3×C5#231311yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—51no—
413C22×C3—51no—
414C22×C3—52no—
415C22×C3—52no—
416C22×C3—52no—
417C22×C3—104no—
418C22×C3—104no—
419C22×C3—101no—
420C22×C3—101no—
421C22×C3#413012yes—
422C22×C3C23×AGL(1,𝔽5)11yescharacteristic
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—101no—
426C3×C4—101no—
427C3×C4—204no—
428Dic3—22no—
429Dic3—22no—
430Dic3—102no—
431Dic3—102no—
432Dic3—204no—
433C2×C5—22no—
434C2×C5#548611yescharacteristic
435C2×C5C2×#89211yescharacteristic
436C2×C5#551611yescharacteristic
437D5—22no—
438D5#560212yes—
439D5#564512yes—
440C23—51no—
441C23—52no—
442C23—52no—
443C23—51no—
444C23—102no—
445C23—102no—
446C23C2×D3×AGL(1,𝔽5)11yescharacteristic
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—41no—
450C2×C4—51no—
451C2×C4—51no—
452C2×C4—62no—
453C2×C4—102no—
454C2×C4—102no—
455C2×C4—104no—
456C2×C4—104no—
457C2×C4—104no—
458C2×C4—121no—
459C2×C4—152no—
460C2×C4—152no—
461C2×C4—201no—
462C2×C4—201no—
463C2×C4—201no—
464C2×C4—304no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—304no—
468C2×C4—302no—
469C2×C4—304no—
470C2×C4—304no—
471C2×C4—304no—
472C2×C4—602no—
473C2×C4—601no—
474C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
475C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
476C2×C3—22no—
477C2×C3—52no—
478C2×C3—52no—
479C2×C3—102no—
480C2×C3C2×#413011yescharacteristic
481C2×C3#6625811yescharacteristic
482C2×C3#6626211yescharacteristic
483C5#7386711yescharacteristic, complemented, Sylow
484C22—21no—
485C22—21no—
486C22—51no—
487C22—51no—
488C22—52no—
489C22—52no—
490C22—52no—
491C22—104no—
492C22—104no—
493C22—101no—
494C22—101no—
495C22#9190712yes—
496C22C22×D3×AGL(1,𝔽5)11yescharacteristic
497C4—21no—
498C4—21no—
499C4—62no—
500C4—62no—
501C4—101no—
502C4—101no—
503C4—204no—
504C4—302no—
505C4—302no—
506C4—604no—
507C3#1061710111yescharacteristic, complemented, Sylow
508C2—22no—
509C2—52no—
510C2—52no—
511C2—102no—
512C2C2×#9190711yescharacteristic
513C2#1175681211yescharacteristic
514C2#1175687111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2313
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #11751845C2semidirect
7. #11751835C2semidirect
17. C2×#6712C4semidirect
18. C2×C5×Dic3⋊C4C4semidirect
19. C2×Dic3⋊Dic5C4semidirect
20. C2×#6669C4semidirect
21. D5×Dic3⋊C4C4semidirect
22. D5×Dic3⋊C4C4semidirect
149. C2×Dic3⋊C4AGL(1,𝔽5)semidirect
409. C3×C5#2313semidirect
483. C5#73867semidirect
507. C3#10617101semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic3⋊C42
#117524242
C3×#657652
Dic3×C22⋊AGL(1,𝔽5)2
#117519842
#117518452
#117518352
#106171013
#738675