Finite Group Databasebeta

← #14301120

Subgroups — #14301120

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×C3×#687C211yesmaximal, characteristic
2C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
3C2×#91116C211yesmaximal, characteristic
4C5×#5221C211yesmaximal, characteristic
5C2×#90970C211yesmaximal, characteristic, complemented
6#11745981C211yesmaximal, characteristic, complemented
7#11745967C211yesmaximal, characteristic, complemented
8#10600453—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×#217—21no—
14C2×C5×#217—21no—
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C2×C4×C5×Dic3C2211yescharacteristic
17C2×C3×#687—22no—
18C2×C3×#687—22no—
19C2×C3×#687C414yescomplemented
20C22×C3×#168C2211yescharacteristic
21C2×#6668—21no—
22C2×Dic3×Dic5—21no—
23Dic3×Dic10—22no—
24Dic3×Dic10—22no—
25#91116—22no—
26#90970—22no—
27#72048—51nomaximal, Hall
28C22×#687D311yescharacteristic
29C2×C4×Dic10—31no—
30C5×#390—31no—
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×C5C2311yescharacteristic
43C22×Dic15—21no—
44C22×C5×Dic3—21no—
45C22×C5×Dic3D411yescharacteristic
46C22×C5×Dic3D411yescharacteristic
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—
54C4⋊Dic15—21no—
55C4⋊Dic15D412yes—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C5×#217—42no—
60C5×#217—42no—
61C5×C4⋊Dic3—21no—
62C5×C4⋊Dic3—21no—
63C4×C5×Dic3—21no—
64C4×C5×Dic3—21no—
65C3×#687—28no—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68C2×C3×#168C2×C412yes—
69#6668—24no—
70Dic3×Dic5—24no—
71C22×C3×SD16—51no—
72C2×Q8×Dic3—51no—
73C2×#835—51no—
74#5221D511yescharacteristic
75C2×#832—51no—
76#4551—51no—
77#4550—51no—
78C22×C5×D4C2×D311yescharacteristic
79C22×Dic10C2×D311yescharacteristic
80C2×C5×C4⋊C4—31no—
81C2×C5×C22⋊C4—61no—
82C2×C5×C22⋊C4—61no—
83C2×C42×C5—31no—
84C2×#687—22no—
85C2×#687—22no—
86C2×#687Dic314yescomplemented
87C2×C4⋊Dic5—31no—
88C2×#683—61no—
89C2×C4×Dic5—61no—
90C22×#168—31no—
91C22×#168C2×D311yescharacteristic
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×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—22no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×C5×Dic3—21no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—41no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3—41no—
126C2×C5×Dic3SD1612yescomplemented
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—
135C3×#168—22no—
136C22×C3×Q8—51no—
137C22×C3×D4C2×D511yescharacteristic
138C2×C3×SD16—54no—
139C2×C3×SD16—102no—
140C2×C3×SD16—102no—
141C22×C3×C8—51no—
142C2×#217—21no—
143C2×#217—21no—
144Q8×Dic3—102no—
145Q8×Dic3—102no—
146C2×C4⋊Dic3—51no—
147C2×C4⋊Dic3—101no—
148C2×C4⋊Dic3C2×D511yescharacteristic
149C2×C4×Dic3—101no—
150C2×C4×Dic3C2×D511yescharacteristic
151C22×C3⋊C8—51no—
152#835—102no—
153#832—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×D4C2×Dic312yes—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—61no—
164C22×C4×C5C22×D311yescharacteristic
165C22×Dic5—21no—
166C22×Dic5—61no—
167C2×Dic10—21no—
168C2×Dic10—21no—
169C2×Dic10—21no—
170C2×Dic10C2×Dic312yes—
171C2×Dic10#6712yes—
172C2×Dic10#6712yes—
173C5×C4⋊C4—61no—
174C5×C4⋊C4—61no—
175C5×C22⋊C4—122no—
176C5×C22⋊C4—122no—
177C42×C5—61no—
178C42×C5—61no—
179#687—28no—
180C4⋊Dic5—32no—
181C4⋊Dic5—61no—
182#683—64no—
183C4×Dic5—64no—
184C2×#168—21no—
185C2×#168—21no—
186C2×#168—61no—
187C2×#168—61no—
188C2×#168—61no—
189C2×#168C2×Dic312yes—
190C22×SD16—51no—
191C2×C4×Q8—151no—
192C2×#103—151no—
193C2×#102—151no—
194#390—31no—
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×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215Dic15—42no—
216C3×Dic5—24no—
217C5×Dic3—22no—
218C5×Dic3—41no—
219C5×Dic3—81no—
220C24×C3—21no—
221C2×C3×Q8—52no—
222C2×C3×Q8—52no—
223C2×C3×Q8—52no—
224C2×C3×Q8—101no—
225C2×C3×Q8—101no—
226C2×C3×Q8—101no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4C4×D512yes—
233C22×C3×C4—101no—
234C22×C3×C4C22×D511yescharacteristic
235C22×Dic3—21no—
236C22×Dic3—101no—
237C22×Dic3C22⋊D511yescharacteristic
238C22×Dic3C22⋊D511yescharacteristic
239C3×SD16—108no—
240C2×C3×C8—52no—
241C2×C3×C8—101no—
242C2×C3×C8—101no—
243#217—42no—
244#217—42no—
245C4⋊Dic3—21no—
246C4⋊Dic3—21no—
247C4⋊Dic3—52no—
248C4⋊Dic3—104no—
249C4⋊Dic3—101no—
250C4×Dic3—21no—
251C4×Dic3—21no—
252C4×Dic3—104no—
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×C5D3×D411yescharacteristic
264C5×D4—22no—
265C5×D4—22no—
266C5×D4—41no—
267C5×D4—41no—
268C2×C4×C5—32no—
269C2×C4×C5—61no—
270C2×C4×C5—61no—
271C2×C4×C5—61no—
272C2×C4×C5—61no—
273C2×C4×C5—61no—
274C2×C4×C5—121no—
275C2×C4×C5—121no—
276C2×C4×C5—121no—
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5#23711yescharacteristic
279C2×C4×C5#23711yescharacteristic
280C2×C4×C5C22×Dic311yescharacteristic
281C2×C4×C5C2×#6711yescharacteristic
282C2×C4×C5C2×#6711yescharacteristic
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—62no—
287C2×Dic5—121no—
288C2×Dic5—121no—
289Dic10—22no—
290Dic10—22no—
291Dic10—22no—
292Dic10#21714yescomplemented
293#168—22no—
294#168—121no—
295C22×Q8—51no—
296C22×D4D3×D511yescharacteristic
297C2×SD16—54no—
298C2×SD16—102no—
299C2×SD16—102no—
300C22×C8—51no—
301C22×C8—151no—
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—151no—
306C2×C4⋊C4—301no—
307C2×C22⋊C4—61no—
308C2×C22⋊C4—61no—
309C2×C42—31no—
310C2×C42—301no—
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×Q8—54no—
330C3×Q8—102no—
331C3×Q8—102no—
332C3×Q8—102no—
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—41no—
336C3×D4—41no—
337C2×C3×C4—102no—
338C2×C3×C4—102no—
339C2×C3×C4—102no—
340C2×C3×C4C2×C4×D511yescharacteristic
341C2×C3×C4#70911yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4#71111yescharacteristic
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—102no—
355C2×Dic3—201no—
356C2×Dic3—201no—
357C2×Dic3#68712yescomplemented
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×C5D3×SD1611yescharacteristic
368C22×C5#91411yescharacteristic
369C22×C5#91511yescharacteristic
370C22×C5#91611yescharacteristic
371C22×C5D4×Dic311yescharacteristic
372C22×C5#93711yescharacteristic
373C22×C5#93911yescharacteristic
374C4×C5—62no—
375C4×C5—121no—
376C4×C5—241no—
377C4×C5D4×Dic311yescharacteristic
378C4×C5#93511yescharacteristic
379C4×C5#93911yescharacteristic
380C4×C5C2×#21711yescharacteristic
381Dic5—24no—
382Dic5—122no—
383C24—21no—
384C2×Q8—52no—
385C2×Q8—52no—
386C2×Q8—52no—
387C2×Q8—101no—
388C2×Q8—101no—
389C2×Q8—101no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4D5×Dic312yes—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—61no—
399C22×C4—101no—
400C22×C4—301no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—108no—
403C2×C8—52no—
404C2×C8—101no—
405C2×C8—101no—
406C2×C8—301no—
407C2×C8—301no—
408C2×C8—301no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—152no—
412C4⋊C4—304no—
413C4⋊C4—301no—
414C22⋊C4—122no—
415C22⋊C4—122no—
416C42—61no—
417C42—61no—
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—104no—
435C3×C4D5×C22⋊C411yescharacteristic
436C3×C4#402711yescharacteristic
437C3×C4#402911yescharacteristic
438C3×C4#403011yescharacteristic
439Dic3—22no—
440Dic3—41no—
441Dic3—81no—
442Dic3—202no—
443C2×C5—82no—
444C2×C5Dic3×SD1611yescharacteristic
445C2×C5#516311yescharacteristic
446C2×C5#516411yescharacteristic
447C2×C5#516611yescharacteristic
448C2×C5#517011yescharacteristic
449C2×C5#517211yescharacteristic
450C2×C5#522011yescharacteristic
451C23—22no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23D3×C22⋊D511yescharacteristic
459Q8—54no—
460Q8—102no—
461Q8—102no—
462Q8—102no—
463D4—22no—
464D4—22no—
465D4—41no—
466D4—41no—
467C2×C4—32no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—102no—
474C2×C4—102no—
475C2×C4—102no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—302no—
480C2×C4—601no—
481C2×C4—601no—
482C2×C4C2×D5×Dic311yescharacteristic
483C2×C4#677911yescharacteristic
484C2×C4#678011yescharacteristic
485C2×C4D5×#6711yescharacteristic
486C2×C4D5×#6711yescharacteristic
487C2×C4#679011yescharacteristic
488C8—102no—
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#7204811yescharacteristic, complemented, Sylow
499C22—42no—
500C22—42no—
501C22—42no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22D3×#68711yescharacteristic
507C22#9148611yescharacteristic
508C22#9149511yescharacteristic
509C22#9149611yescharacteristic
510C22#9154911yescharacteristic
511C22Dic3×C22⋊D511yescharacteristic
512C22#9157711yescharacteristic
513C4—62no—
514C4—104no—
515C4—121no—
516C4—241no—
517C4—602no—
518C4D5×#21711yescharacteristic
519C4#9154811yescharacteristic
520C4#9155011yescharacteristic
521C4#9155911yescharacteristic
522C3#1060045311yescharacteristic, complemented, Sylow
523C2—82no—
524C2#1174900511yescharacteristic
525C2#1174900611yescharacteristic
526C2Dic3×#68711yescharacteristic
527C2#1174901011yescharacteristic
528C2#1174915511yescharacteristic
529C2#1174916211yescharacteristic
530C2#1174951811yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×Dic10C2semidirect
5. C2×#90970C2semidirect
6. #11745981C2semidirect
7. #11745967C2semidirect
19. C2×C3×#687C4semidirect
86. C2×#687Dic3semidirect
126. C2×C5×Dic3SD16semidirect
133. C3×Dic10C22⋊C4semidirect
292. Dic10#217semidirect
357. C2×Dic3#687semidirect
419. C3×C5#1880semidirect
498. C5#72048semidirect
522. C3#10600453semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6872
C2×Dic3×Dic102
C2×#911162
C5×#52212
C2×#909702
#117459812
#117459672
#106004533
#720485