Finite Group Databasebeta

← #14301121

Subgroups — #14301121

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91331C211yesmaximal, characteristic, complemented
2C22×#6658C211yesmaximal, characteristic
3#11751089C211yesmaximal, characteristic
4C2×C3×#3942C211yesmaximal, characteristic, complemented
5C2×#90969C211yesmaximal, characteristic
6C5×#4529C211yesmaximal, characteristic, complemented
7#11745968C211yesmaximal, characteristic, complemented
8#10599702—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×#6714—21no—
13C2×#6714—21no—
14C2×C4×Dic15C2211yescharacteristic
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C22×C5×C3⋊C8C2211yescharacteristic
17C22×C3×#168C2211yescharacteristic
18C2×#6668—21no—
19C2×Dic3×Dic5—21no—
20#91331—22no—
21#91331—22no—
22C2×#6658—22no—
23C2×#6658—22no—
24C2×#6658C414yescomplemented
25C3×#3942—22no—
26#90969—22no—
27#70240—51nomaximal, Hall
28C22×#677—31no—
29C2×#4033—31no—
30#65277—31no—
31C2×#3942D311yescharacteristic, complemented
32C2×#3941—31no—
33C5×#340—31no—
34#64770—31no—
35C23×D15—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15D411yescharacteristic
39C22×Dic15D411yescharacteristic
40C2×D60—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60C2×C412yes—
46C22×C5×Dic3—21no—
47C22×C3×Dic5—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10C2×C412yes—
52C2×C3×Dic10D412yes—
53C2×C3×Dic10D412yes—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56#6714—42no—
57#6714—42no—
58C4×Dic15—21no—
59C4×Dic15—21no—
60C5×C4⋊Dic3—21no—
61C5×C4⋊Dic3D412yes—
62C2×C5×C3⋊C8—21no—
63C2×C5×C3⋊C8—21no—
64C2×C5×C3⋊C8C2×C412yes—
65C2×C3×#168—21no—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68#6668—24no—
69Dic3×Dic5—24no—
70#6658—28no—
71C2×Q8×Dic3—51no—
72C22×#215—51no—
73C2×C3×#103—51no—
74C2×#821—51no—
75#4988—51no—
76#4550—51no—
77#4529D511yescharacteristic, complemented
78C22×D20—31no—
79C22×Dic10C2×D311yescharacteristic
80C22×C5×C8—31no—
81C2×C5×C4⋊C4—31no—
82C2×C5×C4⋊C4C2×D311yescharacteristic
83C2×#685—61no—
84C2×#685—61no—
85C2×#683—61no—
86C2×C4×Dic5—31no—
87C2×C4×Dic5—61no—
88C22×#168C2×D311yescharacteristic
89C2×#677—34no—
90C2×#677—62no—
91C2×#677—62no—
92#4033—62no—
93#4033—62no—
94#3942—22no—
95#3941—62no—
96#1880—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×D15—22no—
99C22×D15—41no—
100C22×D15—41no—
101C22×D15—41no—
102C22×D15—41no—
103C22×D15—41no—
104C22×D15—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×Dic15—21no—
115C2×Dic15—21no—
116C2×Dic15—21no—
117C2×Dic15—21no—
118C2×Dic15—21no—
119C2×Dic15SD1612yescomplemented
120D60—22no—
121D60—22no—
122D60—41no—
123D60—41no—
124C2×C5×Dic3—22no—
125C2×C5×Dic3—41no—
126C2×C5×Dic3—41no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—22no—
129C2×C3×Dic5—22no—
130C3×Dic10—22no—
131C3×Dic10—22no—
132C3×Dic10—22no—
133C3×Dic10C22⋊C414yescomplemented
134C3×#168—41no—
135C5×C3⋊C8—22no—
136C22×C3×Q8—51no—
137C22×D12—51no—
138C22×C3×C8—51no—
139C2×C3×C4⋊C4C2×D511yescharacteristic
140Q8×Dic3—102no—
141Q8×Dic3—102no—
142C2×#215—54no—
143C2×#215—102no—
144C2×#215—102no—
145C2×(C2×D3)⋊C4—101no—
146C2×(C2×D3)⋊C4—101no—
147C2×C4⋊Dic3—101no—
148C2×C4⋊Dic3C2×D511yescharacteristic
149C2×C4×Dic3—51no—
150C2×C4×Dic3—101no—
151C22×C3⋊C8C2×D511yescharacteristic
152C3×#103—102no—
153#821—102no—
154C23×D5—61no—
155C22×C4×C5—21no—
156C22×C4×C5—61no—
157C22×C4×C5C22×D311yescharacteristic
158C22×Dic5—21no—
159C22×Dic5—31no—
160C22×Dic5—31no—
161C2×D20—32no—
162C2×D20—61no—
163C2×D20—61no—
164C2×D20—61no—
165C2×D20—61no—
166C2×D20—61no—
167C2×Dic10—21no—
168C2×Dic10—21no—
169C2×Dic10—21no—
170C2×Dic10C4×D312yes—
171C2×Dic10D1212yes—
172C2×Dic10#6712yes—
173C2×C5×C8—32no—
174C2×C5×C8—61no—
175C2×C5×C8—61no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—32no—
179C5×C4⋊C4—61no—
180#685—122no—
181#685—122no—
182#683—64no—
183C4×Dic5—64no—
184C4×Dic5—61no—
185C4×Dic5—61no—
186C2×#168—21no—
187C2×#168—21no—
188C2×#168—21no—
189#677—68no—
190C22×SD16—151no—
191C2×C4×Q8—151no—
192C2×#103—51no—
193C2×#102—151no—
194#390—151no—
195#340—31no—
196#336—151no—
197C22×C3×C5C4×D411yescharacteristic
198C22×C3×C5#12011yescharacteristic
199C22×C3×C5#12111yescharacteristic
200C22×C3×C5C2×SD1611yescharacteristic
201C22×C3×C5#13511yescharacteristic
202C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
203C22×C3×C5#13711yescharacteristic
204C2×D15—42no—
205C2×D15—42no—
206C2×D15—42no—
207C2×D15—81no—
208C2×D15—81no—
209C2×D15—81no—
210C2×D15—81no—
211C3×C4×C5—81no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—22no—
217Dic15—41no—
218C3×Dic5—24no—
219C5×Dic3—42no—
220C23×D3—101no—
221C2×C3×Q8—52no—
222C2×C3×Q8—52no—
223C2×C3×Q8—52no—
224C2×C3×Q8—101no—
225C2×C3×Q8—101no—
226C2×C3×Q8—101no—
227C22×C3×C4—21no—
228C22×C3×C4—101no—
229C22×C3×C4C22×D511yescharacteristic
230C22×Dic3—21no—
231C22×Dic3—51no—
232C22×Dic3—51no—
233C2×D12—52no—
234C2×D12—101no—
235C2×D12—101no—
236C2×D12—101no—
237C2×D12—101no—
238C2×D12—101no—
239C2×C3×C8—101no—
240C2×C3×C8—101no—
241C2×C3×C8—101no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244#215—108no—
245(C2×D3)⋊C4—202no—
246(C2×D3)⋊C4—202no—
247C4⋊Dic3—21no—
248C4⋊Dic3—104no—
249C4⋊Dic3D2012yes—
250C4×Dic3—104no—
251C4×Dic3—101no—
252C4×Dic3—101no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8C4×D512yes—
256C23×C5D3×D411yescharacteristic
257C22×D5—62no—
258C22×D5—121no—
259C22×D5—121no—
260C22×D5—121no—
261C22×D5—121no—
262C22×D5—121no—
263C22×D5—121no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—62no—
268C2×C4×C5—121no—
269C2×C4×C5—121no—
270C2×C4×C5C2×C4×D311yescharacteristic
271C2×C4×C5C2×D1211yescharacteristic
272C2×C4×C5D3×D411yescharacteristic
273C2×C4×C5#23711yescharacteristic
274C2×C4×C5#23711yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C2×Dic5—22no—
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—32no—
280C2×Dic5—61no—
281C2×Dic5—61no—
282C2×Dic5—61no—
283C2×Dic5—61no—
284C2×Dic5—61no—
285D20—62no—
286D20—62no—
287D20—121no—
288D20—121no—
289Dic10—22no—
290Dic10—22no—
291Dic10—22no—
292Dic10(C2×D3)⋊C414yescomplemented
293C5×C8—62no—
294#168—41no—
295C22×Q8—51no—
296C22×D4—151no—
297C2×SD16—154no—
298C2×SD16—302no—
299C2×SD16—302no—
300C22×C8—31no—
301C22×C8—51no—
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—301no—
306C2×C4⋊C4D3×D511yescharacteristic
307C2×C22⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—151no—
310C2×C42—301no—
311#103—102no—
312#102—302no—
313C2×C3×C5#38611yescharacteristic
314C2×C3×C5C4×SD1611yescharacteristic
315C2×C3×C5#44011yescharacteristic
316C2×C3×C5#44811yescharacteristic
317C2×C3×C5#44911yescharacteristic
318C2×C3×C5#46011yescharacteristic
319C2×C3×C5#46411yescharacteristic
320D15—82no—
321C23×C3D4×D511yescharacteristic
322C22×D3—102no—
323C22×D3—201no—
324C22×D3—201no—
325C22×D3—201no—
326C22×D3—201no—
327C22×D3—201no—
328C22×D3—201no—
329C3×Q8—54no—
330C3×Q8—102no—
331C3×Q8—102no—
332C3×Q8—102no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—102no—
337C2×C3×C4—102no—
338C2×C3×C4—102no—
339C2×C3×C4C2×C4×D511yescharacteristic
340C2×C3×C4C2×D2011yescharacteristic
341C2×C3×C4#70911yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4#71311yescharacteristic
345C2×Dic3—22no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—52no—
349C2×Dic3—101no—
350C2×Dic3—101no—
351C2×Dic3—101no—
352C2×Dic3—101no—
353C2×Dic3—101no—
354D12—102no—
355D12—102no—
356D12—201no—
357D12—201no—
358C3×C8—201no—
359C3⋊C8—22no—
360C22×C5#67⋊C411yescharacteristic
361C22×C5#88211yescharacteristic
362C22×C5D3×SD1611yescharacteristic
363C22×C5#91411yescharacteristic
364C22×C5#91811yescharacteristic
365C22×C5#91911yescharacteristic
366C22×C5#93911yescharacteristic
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C2×D5—241no—
371C2×D5—241no—
372C2×D5—241no—
373C2×D5—241no—
374C4×C5—81no—
375C4×C5—122no—
376C4×C5#67⋊C411yescharacteristic
377C4×C5#88611yescharacteristic
378C4×C5C2×(C2×D3)⋊C411yescharacteristic
379C4×C5#93911yescharacteristic
380Dic5—24no—
381Dic5—62no—
382Dic5—121no—
383C24—301no—
384C2×Q8—52no—
385C2×Q8—52no—
386C2×Q8—52no—
387C2×Q8—101no—
388C2×Q8—101no—
389C2×Q8—101no—
390C2×D4—152no—
391C2×D4—301no—
392C2×D4—301no—
393C2×D4—301no—
394C2×D4—301no—
395C2×D4—301no—
396C22×C4—21no—
397C22×C4—61no—
398C22×C4—101no—
399C22×C4—151no—
400C22×C4—151no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—308no—
403C2×C8—32no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—101no—
407C2×C8—101no—
408C2×C8—101no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—32no—
412C4⋊C4—61no—
413C4⋊C4—304no—
414C22⋊C4—602no—
415C22⋊C4—602no—
416C42—304no—
417C42—301no—
418C42—301no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3#402811yescharacteristic
421C22×C3#403011yescharacteristic
422C22×C3#403911yescharacteristic
423C22×C3#405711yescharacteristic
424C22×C3D5×SD1611yescharacteristic
425C22×C3#406211yescharacteristic
426C22×C3#406411yescharacteristic
427C2×D3—202no—
428C2×D3—202no—
429C2×D3—202no—
430C2×D3—401no—
431C2×D3—401no—
432C2×D3—401no—
433C2×D3—401no—
434C3×C4—81no—
435C3×C4—104no—
436C3×C4C4×D2011yescharacteristic
437C3×C4D5×C22⋊C411yescharacteristic
438C3×C4#404011yescharacteristic
439C3×C4#404111yescharacteristic
440Dic3—42no—
441Dic3—102no—
442Dic3—201no—
443C2×C5#478811yescharacteristic
444C2×C5#480611yescharacteristic
445C2×C5#481011yescharacteristic
446C2×C5#481711yescharacteristic
447C2×C5#495811yescharacteristic
448C2×C5#516311yescharacteristic
449C2×C5#518511yescharacteristic
450D5—242no—
451C23—302no—
452C23—601no—
453C23—601no—
454C23—601no—
455C23—601no—
456C23—601no—
457C23—601no—
458C23#679011yescharacteristic
459Q8—54no—
460Q8—102no—
461Q8—102no—
462Q8—102no—
463D4—302no—
464D4—302no—
465D4—601no—
466D4—601no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—62no—
471C2×C4—102no—
472C2×C4—102no—
473C2×C4—102no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—152no—
477C2×C4—301no—
478C2×C4—301no—
479C2×C4—301no—
480C2×C4—301no—
481C2×C4—301no—
482C2×C4#676611yescharacteristic
483C2×C4C4×D3×D511yescharacteristic
484C2×C4D5×D1211yescharacteristic
485C2×C4D3×D2011yescharacteristic
486C2×C4#677911yescharacteristic
487C2×C4D5×#6711yescharacteristic
488C8—62no—
489C8—201no—
490C2×C3#6495411yescharacteristic
491C2×C3#6505111yescharacteristic
492C2×C3#6507011yescharacteristic
493C2×C3#6508711yescharacteristic
494C2×C3#6509511yescharacteristic
495C2×C3#6514111yescharacteristic
496C2×C3#6517811yescharacteristic
497D3—402no—
498C5#7024011yescharacteristic, complemented, Sylow
499C22—602no—
500C22—602no—
501C22—602no—
502C22—1201no—
503C22—1201no—
504C22—1201no—
505C22—1201no—
506C22#9139611yescharacteristic
507C22#9147611yescharacteristic
508C22#9148711yescharacteristic
509C22#9150011yescharacteristic
510C22#9151211yescharacteristic
511C22#9152311yescharacteristic
512C22#9155011yescharacteristic
513C4—81no—
514C4—104no—
515C4—122no—
516C4—302no—
517C4—601no—
518C4#9139511yescharacteristic
519C4#9140911yescharacteristic
520C4#9141311yescharacteristic
521C4D5×(C2×D3)⋊C411yescharacteristic
522C3#1059970211yescharacteristic, complemented, Sylow
523C2—1202no—
524C2#1174727211yescharacteristic
525C2#1174727311yescharacteristic
526C2#1174749711yescharacteristic
527C2#1174752011yescharacteristic
528C2#1174887211yescharacteristic
529C2#1174900811yescharacteristic
530C2#1174925311yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91331C2semidirect
4. C2×C3×#3942C2semidirect
6. C5×#4529C2semidirect
7. #11745968C2semidirect
24. C2×#6658C4semidirect
31. C2×#3942D3semidirect
77. #4529D5semidirect
119. C2×Dic15SD16semidirect
133. C3×Dic10C22⋊C4semidirect
292. Dic10(C2×D3)⋊C4semidirect
419. C3×C5#1880semidirect
498. C5#70240semidirect
522. C3#10599702semidirect

Maximal subgroups

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

subgroupindex
C2×#913312
C22×#66582
#117510892
C2×C3×#39422
C2×#909692
C5×#45292
#117459682
#105997023
#702405