Finite Group Databasebeta

← #14301094

Subgroups — #14301094

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×#6716C211yesmaximal, characteristic
2C2×C4×Dic30C211yesmaximal, characteristic, complemented
3C3×C5×#390C211yesmaximal, characteristic
4C2×#91116C211yesmaximal, characteristic
5C2×#91094C211yesmaximal, characteristic, complemented
6#11746350C211yesmaximal, characteristic, complemented
7#11746345C211yesmaximal, characteristic, complemented
8#10600453—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×Dic30C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C5×C22⋊C4—21no—
13C2×C3×C5×C22⋊C4—21no—
14C2×C3×C42×C5C2211yescharacteristic
15C2×#6716—22no—
16C2×#6716—22no—
17C2×#6716C414yescomplemented
18C2×C4⋊Dic15C2211yescharacteristic
19C2×#6712—21no—
20C2×C4×Dic15—21no—
21C22×C3⋊#168C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C4×Dic30—22no—
24C4×Dic30—22no—
25#91116—22no—
26#91094—22no—
27#69660—51nomaximal, Hall
28C22×#687—31no—
29C2×C4×Dic10—31no—
30C5×#390D311yescharacteristic
31C2×#3964—31no—
32C2×#3942—31no—
33#64749—31no—
34#64744—31no—
35C24×C3×C5—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4C2×C412yes—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5D411yescharacteristic
44C22×C3×C4×C5D411yescharacteristic
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15—21no—
47C22×Dic15—21no—
48C2×Dic30—21no—
49C2×Dic30—21no—
50C2×Dic30—21no—
51C2×Dic30C2×C412yes—
52C2×Dic30D412yes—
53C2×Dic30D412yes—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C22⋊C4—42no—
57C3×C5×C22⋊C4—42no—
58C3×C42×C5—21no—
59C3×C42×C5—21no—
60#6716—28no—
61C4⋊Dic15—21no—
62C4⋊Dic15D412yes—
63#6712—24no—
64C4×Dic15—24no—
65C2×C3⋊#168—21no—
66C2×C3⋊#168—21no—
67C2×C3⋊#168—21no—
68C2×C3⋊#168—21no—
69C2×C3⋊#168—21no—
70C2×C3⋊#168C2×C412yes—
71C22×#214—51no—
72C2×C4×Dic6—51no—
73C3×#390D511yescharacteristic
74C2×#832—51no—
75C2×#810—51no—
76#4529—51no—
77#4524—51no—
78C22×C5×D4C2×D311yescharacteristic
79C22×Dic10—31no—
80C2×C5×C4⋊C4C2×D311yescharacteristic
81C2×C5×C22⋊C4—21no—
82C2×C5×C22⋊C4—21no—
83C2×C42×C5C2×D311yescharacteristic
84C2×#687—34no—
85C2×#687—62no—
86C2×#687—62no—
87C2×C4⋊Dic5—31no—
88C2×#683—61no—
89C2×C4×Dic5—61no—
90C22×#168—31no—
91C22×#168—31no—
92C4×Dic10—62no—
93C4×Dic10—62no—
94#3964—62no—
95#3942—62no—
96#1880—151noSylow
97C23×C3×C5—22no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C2×D411yescharacteristic
105C3×C5×D4—22no—
106C3×C5×D4—22no—
107C3×C5×D4—41no—
108C3×C5×D4—41no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5SD1612yescomplemented
118C2×C3×C4×C5C22×C411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5#4111yescharacteristic
123C2×C3×C4×C5#4111yescharacteristic
124C2×Dic15—22no—
125C2×Dic15—22no—
126C2×Dic15—22no—
127C2×Dic15—22no—
128C2×Dic15—41no—
129C2×Dic15—41no—
130Dic30—22no—
131Dic30—22no—
132Dic30—22no—
133Dic30C22⋊C414yescomplemented
134C3⋊#168—22no—
135C3⋊#168—41no—
136C22×C3×D4C2×D511yescharacteristic
137C22×Dic6—51no—
138C2×C3×C4⋊C4C2×D511yescharacteristic
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C42C2×D511yescharacteristic
142C2×#214—54no—
143C2×#214—102no—
144C2×#214—102no—
145C2×C4⋊Dic3—51no—
146C2×Dic3⋊C4—101no—
147C2×C4×Dic3—101no—
148C22×C3⋊C8—51no—
149C22×C3⋊C8—51no—
150C4×Dic6—102no—
151C4×Dic6—102no—
152#832—102no—
153#810—102no—
154C24×C5—21no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4C4×D312yes—
161C22×C4×C5—21no—
162C22×C4×C5#6711yescharacteristic
163C22×C4×C5#6711yescharacteristic
164C22×C4×C5C22×D311yescharacteristic
165C22×Dic5—61no—
166C22×Dic5—61no—
167C2×Dic10—32no—
168C2×Dic10—32no—
169C2×Dic10—32no—
170C2×Dic10—61no—
171C2×Dic10—61no—
172C2×Dic10—61no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C22⋊C4—42no—
176C5×C22⋊C4—42no—
177C42×C5—21no—
178C42×C5—21no—
179#687—68no—
180C4⋊Dic5—32no—
181C4⋊Dic5—61no—
182#683—64no—
183C4×Dic5—64no—
184C2×#168—32no—
185C2×#168—61no—
186C2×#168—61no—
187C2×#168—61no—
188C2×#168—61no—
189C2×#168—61no—
190C22×SD16—151no—
191C2×C4×Q8—151no—
192C2×#103—151no—
193C2×#102—151no—
194#390D1511yescharacteristic
195#340—151no—
196#336—151no—
197C22×C3×C5—42no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—81no—
201C22×C3×C5—81no—
202C22×C3×C5—81no—
203C22×C3×C5—81no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5C2×SD1611yescharacteristic
208C22×C3×C5#13511yescharacteristic
209C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
210C22×C3×C5#13711yescharacteristic
211C3×C4×C5—22no—
212C3×C4×C5—41no—
213C3×C4×C5—81no—
214C3×C4×C5C2×C22⋊C411yescharacteristic
215C3×C4×C5C4×D411yescharacteristic
216C3×C4×C5#12111yescharacteristic
217C3×C4×C5#12311yescharacteristic
218Dic15—24no—
219Dic15—42no—
220C24×C3—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4C4×D512yes—
227C22×C3×C4—21no—
228C22×C3×C4C22⋊D511yescharacteristic
229C22×C3×C4C22⋊D511yescharacteristic
230C22×C3×C4C22×D511yescharacteristic
231C22×Dic3—101no—
232C22×Dic3—101no—
233C2×Dic6—52no—
234C2×Dic6—52no—
235C2×Dic6—52no—
236C2×Dic6—101no—
237C2×Dic6—101no—
238C2×Dic6—101no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C22⋊C4—42no—
242C3×C22⋊C4—42no—
243C3×C42—21no—
244C3×C42—21no—
245#214—108no—
246C4⋊Dic3—52no—
247C4⋊Dic3—101no—
248Dic3⋊C4—104no—
249C4×Dic3—104no—
250C2×C3⋊C8—52no—
251C2×C3⋊C8—101no—
252C2×C3⋊C8—101no—
253C2×C3⋊C8—101no—
254C2×C3⋊C8—101no—
255C2×C3⋊C8—101no—
256C23×C5—22no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5C2×#6711yescharacteristic
264C5×D4—22no—
265C5×D4—22no—
266C5×D4—41no—
267C5×D4—41no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5#21412yescomplemented
277C2×C4×C5C2×C4×D311yescharacteristic
278C2×C4×C5#23511yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5#23711yescharacteristic
283C2×Dic5—62no—
284C2×Dic5—62no—
285C2×Dic5—62no—
286C2×Dic5—62no—
287C2×Dic5—121no—
288C2×Dic5—121no—
289Dic10—34no—
290Dic10—62no—
291Dic10—62no—
292Dic10—62no—
293#168—62no—
294#168—121no—
295C22×Q8—151no—
296C22×D4C2×D1511yescharacteristic
297C2×SD16—154no—
298C2×SD16—302no—
299C2×SD16—302no—
300C22×C8—151no—
301C22×C8—151no—
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—151no—
305C2×C4⋊C4—301no—
306C2×C4⋊C4C2×D1511yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C42—301no—
310C2×C42C2×D1511yescharacteristic
311#103—302no—
312#102—302no—
313C2×C3×C5—82no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5C4×SD1611yescharacteristic
316C2×C3×C5#44011yescharacteristic
317C2×C3×C5#44811yescharacteristic
318C2×C3×C5#44911yescharacteristic
319C2×C3×C5#46011yescharacteristic
320C2×C3×C5#46411yescharacteristic
321C23×C3—22no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3C2×C22⋊D511yescharacteristic
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—41no—
332C3×D4—41no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4#68712yescomplemented
342C2×C3×C4C2×C4×D511yescharacteristic
343C2×C3×C4#70911yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4D4×D511yescharacteristic
347C2×C3×C4#71111yescharacteristic
348C2×Dic3—102no—
349C2×Dic3—102no—
350C2×Dic3—102no—
351C2×Dic3—102no—
352C2×Dic3—201no—
353C2×Dic3—201no—
354Dic6—54no—
355Dic6—102no—
356Dic6—102no—
357Dic6—102no—
358C3⋊C8—102no—
359C3⋊C8—201no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—81no—
366C22×C5—81no—
367C22×C5C4×#6711yescharacteristic
368C22×C5#93211yescharacteristic
369C22×C5C2×#21411yescharacteristic
370C22×C5#93711yescharacteristic
371C22×C5#93811yescharacteristic
372C22×C5#95011yescharacteristic
373C22×C5#95111yescharacteristic
374C4×C5—22no—
375C4×C5—41no—
376C4×C5—81no—
377C4×C5D3×C22⋊C411yescharacteristic
378C4×C5#67⋊C411yescharacteristic
379C4×C5#88311yescharacteristic
380C4×C5#88411yescharacteristic
381Dic5—64no—
382Dic5—122no—
383C24—21no—
384C2×Q8—152no—
385C2×Q8—152no—
386C2×Q8—152no—
387C2×Q8—301no—
388C2×Q8—301no—
389C2×Q8—301no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4C4×D1512yes—
396C22×C4—21no—
397C22×C4—301no—
398C22×C4—301no—
399C22×C4#122011yescharacteristic
400C22×C4#122011yescharacteristic
401C22×C4C22×D1511yescharacteristic
402SD16—308no—
403C2×C8—152no—
404C2×C8—301no—
405C2×C8—301no—
406C2×C8—301no—
407C2×C8—301no—
408C2×C8—301no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—152no—
412C4⋊C4—304no—
413C4⋊C4—301no—
414C22⋊C4—42no—
415C22⋊C4—42no—
416C42—21no—
417C42—21no—
418C42—304no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3C4×C22⋊D511yescharacteristic
428C22×C3#407811yescharacteristic
429C22×C3C2×#68711yescharacteristic
430C22×C3#408311yescharacteristic
431C22×C3#408411yescharacteristic
432C22×C3#409611yescharacteristic
433C22×C3#409711yescharacteristic
434C3×C4—22no—
435C3×C4—41no—
436C3×C4—81no—
437C3×C4D5×C22⋊C411yescharacteristic
438C3×C4#402711yescharacteristic
439C3×C4#402911yescharacteristic
440C3×C4#403011yescharacteristic
441Dic3—104no—
442Dic3—202no—
443C2×C5—82no—
444C2×C5#495611yescharacteristic
445C2×C5C4×#21411yescharacteristic
446C2×C5#501811yescharacteristic
447C2×C5#503711yescharacteristic
448C2×C5#504011yescharacteristic
449C2×C5#505411yescharacteristic
450C2×C5#507511yescharacteristic
451C23—22no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23C2×#122011yescharacteristic
459Q8—154no—
460Q8—302no—
461Q8—302no—
462Q8—302no—
463D4—22no—
464D4—22no—
465D4—41no—
466D4—41no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—302no—
476C2×C4—302no—
477C2×C4—302no—
478C2×C4—302no—
479C2×C4—601no—
480C2×C4—601no—
481C2×C4#671612yescomplemented
482C2×C4C2×C4×D1511yescharacteristic
483C2×C4#681711yescharacteristic
484C2×C4D4×D1511yescharacteristic
485C2×C4D4×D1511yescharacteristic
486C2×C4D4×D1511yescharacteristic
487C2×C4#681911yescharacteristic
488C8—302no—
489C8—601no—
490C2×C3—82no—
491C2×C3#6524511yescharacteristic
492C2×C3C4×#68711yescharacteristic
493C2×C3#6530711yescharacteristic
494C2×C3#6532611yescharacteristic
495C2×C3#6532911yescharacteristic
496C2×C3#6534311yescharacteristic
497C2×C3#6536411yescharacteristic
498C5#6966011yescharacteristic, complemented, Sylow
499C22—42no—
500C22—42no—
501C22—42no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22C4×#122011yescharacteristic
507C22#9182111yescharacteristic
508C22C2×#671611yescharacteristic
509C22#9182611yescharacteristic
510C22#9182711yescharacteristic
511C22#9183911yescharacteristic
512C22#9184011yescharacteristic
513C4—22no—
514C4—41no—
515C4—81no—
516C4—304no—
517C4—602no—
518C4C22⋊C4×D1511yescharacteristic
519C4#9177011yescharacteristic
520C4#9177211yescharacteristic
521C4#9177311yescharacteristic
522C3#1060045311yescharacteristic, complemented, Sylow
523C2—82no—
524C2#1175105711yescharacteristic
525C2C4×#671611yescharacteristic
526C2#1175111911yescharacteristic
527C2#1175113811yescharacteristic
528C2#1175114111yescharacteristic
529C2#1175115511yescharacteristic
530C2#1175117611yescharacteristic
subgroupG/H
centerC23C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#390C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
cosocleC22×C3×C4×C5C23
hypercenter#390D15
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic30C2semidirect
5. C2×#91094C2semidirect
6. #11746350C2semidirect
7. #11746345C2semidirect
17. C2×#6716C4semidirect
117. C2×C3×C4×C5SD16semidirect
133. Dic30C22⋊C4semidirect
276. C2×C4×C5#214semidirect
341. C2×C3×C4#687semidirect
419. C3×C5#1880semidirect
481. C2×C4#6716semidirect
498. C5#69660semidirect
522. C3#10600453semidirect

Maximal subgroups

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

subgroupindex
C22×#67162
C2×C4×Dic302
C3×C5×#3902
C2×#911162
C2×#910942
#117463502
#117463452
#106004533
#696605