Finite Group Databasebeta

← #14301088

Subgroups — #14301088

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
1C22×#6706C211yesmaximal, characteristic
2C2×#91776C211yesmaximal, characteristic, complemented
3#11751089C211yesmaximal, characteristic
4C2×#91094C211yesmaximal, characteristic, complemented
5C2×#91093C211yesmaximal, characteristic
6C3×C5×#340C211yesmaximal, characteristic, complemented
7#11746371C211yesmaximal, characteristic, complemented
8#10599702—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C22×Dic30C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×#6714—21no—
15C2×#6714—21no—
16C2×#6712—21no—
17C2×C4×Dic15—21no—
18C2×C4×Dic15C2211yescharacteristic
19C22×C3⋊#168C2211yescharacteristic
20C2×#6706—22no—
21C2×#6706—22no—
22C2×#6706C414yescomplemented
23#91776—22no—
24#91776—22no—
25#91094—22no—
26#91093—22no—
27#68909—51nomaximal, Hall
28C22×#677—31no—
29C2×#4033—31no—
30#65277—31no—
31C2×#3942—31no—
32C2×#3941—31no—
33C5×#340D311yescharacteristic, complemented
34#64770—31no—
35C23×D15—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15D411yescharacteristic
41C22×Dic15D411yescharacteristic
42C2×D60—21no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60C2×C412yes—
48C2×Dic30—21no—
49C2×Dic30—21no—
50C2×Dic30—21no—
51C2×Dic30C2×C412yes—
52C2×Dic30D412yes—
53C2×Dic30D412yes—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8C2×C412yes—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C4⋊C4—21no—
60C3×C5×C4⋊C4D412yes—
61#6714—42no—
62#6714—42no—
63#6712—24no—
64C4×Dic15—24no—
65C4×Dic15—21no—
66C4×Dic15—21no—
67C2×C3⋊#168—21no—
68C2×C3⋊#168—21no—
69C2×C3⋊#168—21no—
70#6706—28no—
71C22×#204—51no—
72C2×#887—51no—
73#4988—51no—
74C2×#810—51no—
75C2×#809—51no—
76C3×#340D511yescharacteristic, complemented
77#4550—51no—
78C22×D20—31no—
79C22×Dic10—31no—
80C22×C5×C8C2×D311yescharacteristic
81C2×C5×C4⋊C4C2×D311yescharacteristic
82C2×C5×C4⋊C4C2×D311yescharacteristic
83C2×#685—61no—
84C2×#685—61no—
85C2×#683—61no—
86C2×C4×Dic5—31no—
87C2×C4×Dic5—61no—
88C22×#168—31no—
89C2×#677—34no—
90C2×#677—62no—
91C2×#677—62no—
92#4033—62no—
93#4033—62no—
94#3942—62no—
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—22no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×Dic15—22no—
118C2×Dic15—21no—
119C2×Dic15—22no—
120C2×Dic15—22no—
121C2×Dic15—21no—
122C2×Dic15—21no—
123C2×Dic15—21no—
124C2×Dic15—21no—
125C2×Dic15SD1612yescomplemented
126D60—22no—
127D60—22no—
128D60—41no—
129D60—41no—
130Dic30—22no—
131Dic30—22no—
132Dic30—22no—
133Dic30C22⋊C414yescomplemented
134C3×C5×C8—22no—
135C3⋊#168—41no—
136C22×D12—51no—
137C22×Dic6—51no—
138C22×C3×C8C2×D511yescharacteristic
139C2×C3×C4⋊C4C2×D511yescharacteristic
140C2×C3×C4⋊C4C2×D511yescharacteristic
141C2×(C2×D3)⋊C4—101no—
142C2×(C2×D3)⋊C4—101no—
143C2×Dic3⋊C4—101no—
144C2×C4×Dic3—51no—
145C2×C4×Dic3—101no—
146C22×C3⋊C8—51no—
147C2×#204—54no—
148C2×#204—102no—
149C2×#204—102no—
150#887—102no—
151#887—102no—
152#810—102no—
153#809—102no—
154C23×D5—61no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5C22×D311yescharacteristic
158C22×Dic5—31no—
159C22×Dic5—31no—
160C22×Dic5—61no—
161C2×D20—32no—
162C2×D20—61no—
163C2×D20—61no—
164C2×D20—61no—
165C2×D20—61no—
166C2×D20—61no—
167C2×Dic10—32no—
168C2×Dic10—32no—
169C2×Dic10—32no—
170C2×Dic10—61no—
171C2×Dic10—61no—
172C2×Dic10—61no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8C4×D312yes—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4D1212yes—
180#685—122no—
181#685—122no—
182#683—64no—
183C4×Dic5—64no—
184C4×Dic5—61no—
185C4×Dic5—61no—
186C2×#168—61no—
187C2×#168—61no—
188C2×#168—61no—
189#677—68no—
190C22×SD16—151no—
191C2×C4×Q8—151no—
192C2×#103—151no—
193C2×#102—151no—
194#390—151no—
195#340D1511yescharacteristic, complemented
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—42no—
212C3×C4×C5—81no—
213C3×C4×C5C2×C22⋊C411yescharacteristic
214C3×C4×C5C4×D411yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12311yescharacteristic
217Dic15—24no—
218Dic15—22no—
219Dic15—41no—
220C23×D3—101no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4C22×D511yescharacteristic
224C22×Dic3—51no—
225C22×Dic3—51no—
226C22×Dic3—101no—
227C2×D12—52no—
228C2×D12—101no—
229C2×D12—101no—
230C2×D12—101no—
231C2×D12—101no—
232C2×D12—101no—
233C2×Dic6—52no—
234C2×Dic6—52no—
235C2×Dic6—52no—
236C2×Dic6—101no—
237C2×Dic6—101no—
238C2×Dic6—101no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8C4×D512yes—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4D2012yes—
246(C2×D3)⋊C4—202no—
247(C2×D3)⋊C4—202no—
248Dic3⋊C4—104no—
249C4×Dic3—104no—
250C4×Dic3—101no—
251C4×Dic3—101no—
252C2×C3⋊C8—101no—
253C2×C3⋊C8—101no—
254C2×C3⋊C8—101no—
255#204—108no—
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—22no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5C2×C4×D311yescharacteristic
271C2×C4×C5C2×D1211yescharacteristic
272C2×C4×C5#23511yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5#23911yescharacteristic
276C2×Dic5—32no—
277C2×Dic5—61no—
278C2×Dic5—62no—
279C2×Dic5—62no—
280C2×Dic5—62no—
281C2×Dic5—61no—
282C2×Dic5—61no—
283C2×Dic5—61no—
284C2×Dic5—61no—
285D20—62no—
286D20—62no—
287D20—121no—
288D20—121no—
289Dic10—34no—
290Dic10—62no—
291Dic10—62no—
292Dic10—62no—
293C5×C8—22no—
294#168—121no—
295C22×Q8—151no—
296C22×D4—151no—
297C2×SD16—154no—
298C2×SD16—302no—
299C2×SD16—302no—
300C22×C8—151no—
301C22×C8C2×D1511yescharacteristic
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—301no—
305C2×C4⋊C4C2×D1511yescharacteristic
306C2×C4⋊C4C2×D1511yescharacteristic
307C2×C22⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—151no—
310C2×C42—301no—
311#103—302no—
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—
329C2×C3×C4—22no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4C2×C4×D511yescharacteristic
336C2×C3×C4C2×D2011yescharacteristic
337C2×C3×C4#70911yescharacteristic
338C2×C3×C4D4×D511yescharacteristic
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4#71311yescharacteristic
341C2×Dic3—52no—
342C2×Dic3—101no—
343C2×Dic3—102no—
344C2×Dic3—102no—
345C2×Dic3—102no—
346C2×Dic3—101no—
347C2×Dic3—101no—
348C2×Dic3—101no—
349C2×Dic3—101no—
350D12—102no—
351D12—102no—
352D12—201no—
353D12—201no—
354Dic6—54no—
355Dic6—102no—
356Dic6—102no—
357Dic6—102no—
358C3×C8—22no—
359C3⋊C8—201no—
360C22×C5#88211yescharacteristic
361C22×C5#88411yescharacteristic
362C22×C5#89311yescharacteristic
363C22×C5#91111yescharacteristic
364C22×C5D3×SD1611yescharacteristic
365C22×C5#91611yescharacteristic
366C22×C5#91811yescharacteristic
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C2×D5—241no—
371C2×D5—241no—
372C2×D5—241no—
373C2×D5—241no—
374C4×C5—42no—
375C4×C5—81no—
376C4×C5C4×D1211yescharacteristic
377C4×C5D3×C22⋊C411yescharacteristic
378C4×C5#89411yescharacteristic
379C4×C5#89511yescharacteristic
380Dic5—64no—
381Dic5—62no—
382Dic5—121no—
383C24—301no—
384C2×Q8—152no—
385C2×Q8—152no—
386C2×Q8—152no—
387C2×Q8—301no—
388C2×Q8—301no—
389C2×Q8—301no—
390C2×D4—152no—
391C2×D4—301no—
392C2×D4—301no—
393C2×D4—301no—
394C2×D4—301no—
395C2×D4—301no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—151no—
399C22×C4—151no—
400C22×C4—301no—
401C22×C4C22×D1511yescharacteristic
402SD16—308no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—301no—
406C2×C8—301no—
407C2×C8—301no—
408C2×C8C4×D1512yes—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—304no—
413C4⋊C4D6012yes—
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—42no—
435C3×C4—81no—
436C3×C4C4×D2011yescharacteristic
437C3×C4D5×C22⋊C411yescharacteristic
438C3×C4#404011yescharacteristic
439C3×C4#404111yescharacteristic
440Dic3—102no—
441Dic3—104no—
442Dic3—201no—
443C2×C5#466511yescharacteristic
444C2×C5#476211yescharacteristic
445C2×C5#478111yescharacteristic
446C2×C5#479811yescharacteristic
447C2×C5#480611yescharacteristic
448C2×C5#485211yescharacteristic
449C2×C5#488911yescharacteristic
450D5—242no—
451C23—302no—
452C23—601no—
453C23—601no—
454C23—601no—
455C23—601no—
456C23—601no—
457C23—601no—
458C23D4×D1511yescharacteristic
459Q8—154no—
460Q8—302no—
461Q8—302no—
462Q8—302no—
463D4—302no—
464D4—302no—
465D4—601no—
466D4—601no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—152no—
474C2×C4—301no—
475C2×C4—302no—
476C2×C4—302no—
477C2×C4—302no—
478C2×C4—301no—
479C2×C4—301no—
480C2×C4—301no—
481C2×C4—301no—
482C2×C4C2×C4×D1511yescharacteristic
483C2×C4C2×D6011yescharacteristic
484C2×C4#681711yescharacteristic
485C2×C4D4×D1511yescharacteristic
486C2×C4D4×D1511yescharacteristic
487C2×C4#682111yescharacteristic
488C8—22no—
489C8—601no—
490C2×C3#6495411yescharacteristic
491C2×C3#6505111yescharacteristic
492C2×C3#6507011yescharacteristic
493C2×C3#6508711yescharacteristic
494C2×C3#6509511yescharacteristic
495C2×C3#6514111yescharacteristic
496C2×C3#6517811yescharacteristic
497D3—402no—
498C5#6890911yescharacteristic, complemented, Sylow
499C22—602no—
500C22—602no—
501C22—602no—
502C22—1201no—
503C22—1201no—
504C22—1201no—
505C22—1201no—
506C22#9177111yescharacteristic
507C22#9177311yescharacteristic
508C22#9178211yescharacteristic
509C22#9180011yescharacteristic
510C22SD16×D1511yescharacteristic
511C22#9180511yescharacteristic
512C22#9180711yescharacteristic
513C4—42no—
514C4—81no—
515C4—304no—
516C4—302no—
517C4—601no—
518C4C4×D6011yescharacteristic
519C4C22⋊C4×D1511yescharacteristic
520C4#9178311yescharacteristic
521C4#9178411yescharacteristic
522C3#1059970211yescharacteristic, complemented, Sylow
523C2—1202no—
524C2#1175076611yescharacteristic
525C2#1175086311yescharacteristic
526C2#1175088211yescharacteristic
527C2#1175089911yescharacteristic
528C2#1175090711yescharacteristic
529C2#1175095311yescharacteristic
530C2#1175099011yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#340C2
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenter#340D15
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#91776C2semidirect
4. C2×#91094C2semidirect
6. C3×C5×#340C2semidirect
7. #11746371C2semidirect
22. C2×#6706C4semidirect
33. C5×#340D3semidirect
76. C3×#340D5semidirect
125. C2×Dic15SD16semidirect
133. Dic30C22⋊C4semidirect
195. #340D15semidirect
419. C3×C5#1880semidirect
498. C5#68909semidirect
522. C3#10599702semidirect

Maximal subgroups

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

subgroupindex
C22×#67062
C2×#917762
#117510892
C2×#910942
C2×#910932
C3×C5×#3402
#117463712
#105997023
#689095