Finite Group Databasebeta

← #14297849

Subgroups — #14297849

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756281C211yesmaximal, characteristic
2C4×#6669C211yesmaximal, characteristic, complemented
3#11748437C211yesmaximal, characteristic, complemented
4C2×#90981C211yesmaximal, characteristic
5C2×#90980C211yesmaximal, characteristic
6C5×#4532C211yesmaximal, characteristic, complemented
7C3×#64752C211yesmaximal, characteristic, complemented
8#10599563—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12#91782C411yescharacteristic, complemented
13#91782C411yescharacteristic, complemented
14#91776C411yescharacteristic, complemented
15#91776C411yescharacteristic, complemented
16#91770—21no—
17#91770—21no—
18#91761—21no—
19C42×D15—21no—
20C2×C4×C5×Dic3C2211yescharacteristic
21C2×C5×#208C2211yescharacteristic
22C2×C3×C4×Dic5C2211yescharacteristic
23C2×C3×#681C2211yescharacteristic
24C2×#6669—21no—
25#90994—21no—
26#90983—21no—
27#90983—21no—
28#90981—22no—
29#90980—22no—
30#68770—51nomaximal, Hall
31#65856—31no—
32C2×#3957—31no—
33#65407—31no—
34C4×#683—31no—
35C2×#3937—31no—
36C5×#339—31no—
37#64752D311yescharacteristic, complemented
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C22×Dic15D411yescharacteristic
41C22×Dic15D411yescharacteristic
42#6817—21no—
43#6817—21no—
44#6817D412yes—
45#6817Q812yes—
46C2×D60C2×C411yescharacteristic
47C2×C4×D15—21no—
48C2×C4×D15—21no—
49C2×C4×D15—21no—
50C2×Dic30C2×C411yescharacteristic
51C22×C5×Dic3—21no—
52C22×C3×Dic5—21no—
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C3×C42×C5—21no—
57#6714—21no—
58#6714—21no—
59#6712—21no—
60#6712—21no—
61C4×Dic15—21no—
62C4×Dic15—21no—
63C4×Dic15C2×C411yescharacteristic
64C4×Dic15C2×C411yescharacteristic
65C4×Dic15D411yescharacteristic
66C4×Dic15D411yescharacteristic
67C4×C5×Dic3—21no—
68C4×C5×Dic3—21no—
69C5×#208—21no—
70C5×#208—21no—
71C2×C5×C3⋊C8—21no—
72C3×C4×Dic5—21no—
73C3×C4×Dic5—21no—
74C3×#681—21no—
75C3×#681—21no—
76C2×C3×#168—21no—
77#6669—24no—
78#5522—51no—
79C2×#825—51no—
80#5118—51no—
81C4×Dic3⋊C4—51no—
82C2×#805—51no—
83C3×#339—51no—
84#4532D511yescharacteristic, complemented
85C2×#709—31no—
86C2×C5×M16—31no—
87C5×#117C2×D311yescharacteristic
88C2×C42×C5—31no—
89C2×#683—61no—
90C2×C4×Dic5—31no—
91C2×C4×Dic5C2×D311yescharacteristic
92C2×#681C2×D311yescharacteristic
93#4039—31no—
94#4039—31no—
95#4033—31no—
96#4033—31no—
97#4027—61no—
98#4027—61no—
99#4018—61no—
100C42×D5—61no—
101#3963—61no—
102#3957—62no—
103#3946—61no—
104#3946—61no—
105#3937—62no—
106#1806—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×D15—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×Q811yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117#1220—22no—
118#1220—22no—
119C2×Dic15—21no—
120C2×Dic15—22no—
121C2×Dic15—41no—
122C2×Dic15C22⋊C411yescharacteristic
123C2×Dic15C22⋊C411yescharacteristic
124C2×Dic15C22⋊C411yescharacteristic
125C2×Dic15C22⋊C411yescharacteristic
126D60—21no—
127D60C4⋊C412yescomplemented
128C4×D15—22no—
129C4×D15—22no—
130C4×D15—42no—
131C4×D15—42no—
132Dic30—21no—
133Dic30C4⋊C412yescomplemented
134C2×C5×Dic3—22no—
135C2×C5×Dic3—41no—
136C2×C5×Dic3—41no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—41no—
139C2×C3×Dic5—41no—
140C3×#168—41no—
141C5×C3⋊C8—41no—
142C2×#235—51no—
143C2×C3×M16—51no—
144C3×#117C2×D511yescharacteristic
145C2×C3×C42—51no—
146C2×Dic3⋊C4—101no—
147C2×C4×Dic3—51no—
148C2×C4×Dic3C2×D511yescharacteristic
149C2×#208C2×D511yescharacteristic
150#893—51no—
151#893—51no—
152#887—51no—
153#887—51no—
154#67⋊C4—101no—
155#67⋊C4—101no—
156#872—101no—
157C42×D3—101no—
158C3⋊#95—101no—
159#825—102no—
160Dic3⋊C8—101no—
161Dic3⋊C8—101no—
162#805—102no—
163C22×C4×C5—61no—
164C22×C4×C5C22×D311yescharacteristic
165C2×C22⋊D5—61no—
166C22×Dic5—21no—
167C22×Dic5—31no—
168C22×Dic5—31no—
169#709—32no—
170#709—32no—
171#709—61no—
172#709—61no—
173C2×D20—31no—
174C2×C4×D5—61no—
175C2×C4×D5—61no—
176C2×C4×D5—61no—
177C2×Dic10—31no—
178C5×M16—61no—
179C5×M16—61no—
180C2×C5×C8—61no—
181C5×C4⋊C4C4×D311yescharacteristic
182C5×C4⋊C4C4×D311yescharacteristic
183C5×C22⋊C4—21no—
184C42×C5—21no—
185C42×C5—61no—
186C42×C5—61no—
187#685—61no—
188#685—61no—
189#683—64no—
190#683—61no—
191#683—61no—
192C4×Dic5—21no—
193C4×Dic5—21no—
194C4×Dic5—31no—
195C4×Dic5—31no—
196C4×Dic5—31no—
197C4×Dic5—31no—
198C4×Dic5—61no—
199C4×Dic5—61no—
200#681—21no—
201#681—21no—
202C2×#168—21no—
203C4×#41—151no—
204#423—151no—
205C2×#104—151no—
206C2×#104—151no—
207C4×C4⋊C4—151no—
208#339—31no—
209#339—51no—
210C22×C3×C5—21no—
211C22×C3×C5—21no—
212C22×C3×C5C2×C22⋊C411yescharacteristic
213C22×C3×C5#12111yescharacteristic
214C22×C3×C5C22⋊Q811yescharacteristic
215C2×D15—22no—
216C2×D15—41no—
217C2×D15—41no—
218C3×C4×C5—41no—
219C3×C4×C5—41no—
220C3×C4×C5C2×C4⋊C411yescharacteristic
221C3×C4×C5#11711yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5C22⋊Q811yescharacteristic
224Dic15—22no—
225Dic15—21no—
226Dic15—21no—
227Dic15—21no—
228Dic15#10412yescomplemented
229C3×Dic5—42no—
230C5×Dic3—42no—
231C22×C3×C4—101no—
232C22×C3×C4C22×D511yescharacteristic
233C2×#67—101no—
234C22×Dic3—21no—
235C22×Dic3—51no—
236C22×Dic3—51no—
237#235—52no—
238#235—52no—
239#235—101no—
240#235—101no—
241C2×D12—51no—
242C2×C4×D3—101no—
243C2×C4×D3—101no—
244C2×C4×D3—101no—
245C2×Dic6—51no—
246C3×M16—101no—
247C3×M16—101no—
248C2×C3×C8—101no—
249C3×C4⋊C4C4×D511yescharacteristic
250C3×C4⋊C4C4×D511yescharacteristic
251C3×C22⋊C4—21no—
252C3×C42—21no—
253C3×C42—101no—
254C3×C42—101no—
255(C2×D3)⋊C4—101no—
256(C2×D3)⋊C4—101no—
257Dic3⋊C4—104no—
258Dic3⋊C4—101no—
259Dic3⋊C4—101no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—51no—
263C4×Dic3—51no—
264C4×Dic3—51no—
265C4×Dic3—51no—
266C4×Dic3—101no—
267C4×Dic3—101no—
268#208—21no—
269#208—21no—
270C2×C3⋊C8—21no—
271C23×C5D3×D411yescharacteristic
272C22×D5—61no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—62no—
276C2×C4×C5—121no—
277C2×C4×C5—121no—
278C2×C4×C5C2×C4×D311yescharacteristic
279C2×C4×C5#23511yescharacteristic
280C2×C4×C5#23511yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5D3×Q811yescharacteristic
284C22⋊D5—62no—
285C22⋊D5—62no—
286C2×Dic5—22no—
287C2×Dic5—31no—
288C2×Dic5—31no—
289C2×Dic5—31no—
290C2×Dic5—31no—
291C2×Dic5—41no—
292C2×Dic5—41no—
293C2×Dic5—62no—
294C2×Dic5—61no—
295C2×Dic5—121no—
296D20—32no—
297D20—61no—
298C4×D5—62no—
299C4×D5—62no—
300C4×D5—122no—
301C4×D5—122no—
302Dic10—32no—
303Dic10—61no—
304C5×C8—121no—
305#168—41no—
306C2×#41—151no—
307C2×M16—31no—
308C2×M16—51no—
309C4×Q8—151no—
310C4×Q8—151no—
311C4×D4—151no—
312C4×D4—151no—
313C4×D4—301no—
314C4×D4—301no—
315#117—301no—
316#117D3×D511yescharacteristic
317C2×C4⋊C4—301no—
318C2×C42—31no—
319C2×C42—51no—
320C2×C42—151no—
321C2×C42—301no—
322C4⋊C8—301no—
323C4⋊C8—301no—
324#104—302no—
325#104—302no—
326#95—301no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5#38011yescharacteristic
330C2×C3×C5C2×#10411yescharacteristic
331C2×C3×C5#42111yescharacteristic
332D15—42no—
333C23×C3D4×D511yescharacteristic
334C22×D3—101no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—102no—
338C2×C3×C4—201no—
339C2×C3×C4—201no—
340C2×C3×C4C2×C4×D511yescharacteristic
341C2×C3×C4#70911yescharacteristic
342C2×C3×C4#70911yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4Q8×D511yescharacteristic
346#67—102no—
347#67—102no—
348C2×Dic3—22no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—51no—
352C2×Dic3—51no—
353C2×Dic3—51no—
354C2×Dic3—51no—
355C2×Dic3—102no—
356C2×Dic3—101no—
357C2×Dic3—201no—
358D12—52no—
359D12—101no—
360C4×D3—102no—
361C4×D3—102no—
362C4×D3—202no—
363C4×D3—202no—
364Dic6—52no—
365Dic6—101no—
366C3×C8—201no—
367C3⋊C8—41no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5D3×C22⋊C411yescharacteristic
371C22×C5#88411yescharacteristic
372C22×C5#89611yescharacteristic
373C2×D5—62no—
374C2×D5—121no—
375C2×D5—121no—
376C4×C5—41no—
377C4×C5—41no—
378C4×C5—122no—
379C4×C5#87211yescharacteristic
380C4×C5#88411yescharacteristic
381C4×C5D3×C4⋊C411yescharacteristic
382C4×C5#89611yescharacteristic
383Dic5—32no—
384Dic5—42no—
385Dic5—62no—
386Dic5—61no—
387Dic5—61no—
388Dic5—61no—
389#41—152no—
390#41—152no—
391#41—301no—
392#41—301no—
393C2×Q8—151no—
394C2×D4—151no—
395C2×D4—301no—
396C22×C4—61no—
397C22×C4—101no—
398C22×C4—151no—
399C22×C4—151no—
400C22×C4—301no—
401C22×C4—301no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404M16—61no—
405M16—61no—
406M16—101no—
407M16—101no—
408C2×C8—61no—
409C2×C8—101no—
410C4⋊C4—301no—
411C4⋊C4—301no—
412C4⋊C4—304no—
413C4⋊C4#120011yescharacteristic
414C4⋊C4#120011yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C42—21no—
419C42—61no—
420C42—61no—
421C42—101no—
422C42—101no—
423C42—151no—
424C42—151no—
425C42—151no—
426C42—151no—
427C42—301no—
428C42—301no—
429C3×C5#180611yescharacteristic, complemented, Hall
430C22×C3—21no—
431C22×C3—21no—
432C22×C3D5×C22⋊C411yescharacteristic
433C22×C3#403011yescharacteristic
434C22×C3#404211yescharacteristic
435C2×D3—102no—
436C2×D3—201no—
437C2×D3—201no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—202no—
441C3×C4#401811yescharacteristic
442C3×C4#403011yescharacteristic
443C3×C4D5×C4⋊C411yescharacteristic
444C3×C4#404211yescharacteristic
445Dic3—42no—
446Dic3—52no—
447Dic3—101no—
448Dic3—101no—
449Dic3—101no—
450Dic3—102no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5#466711yescharacteristic
454C2×C5D3×#10411yescharacteristic
455C2×C5#482111yescharacteristic
456D5—122no—
457C23—301no—
458C23#679011yescharacteristic
459Q8—152no—
460Q8—301no—
461D4—152no—
462D4—302no—
463D4—302no—
464D4—301no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—62no—
468C2×C4—102no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—151no—
472C2×C4—151no—
473C2×C4—151no—
474C2×C4—151no—
475C2×C4—201no—
476C2×C4—201no—
477C2×C4—302no—
478C2×C4—301no—
479C2×C4—302no—
480C2×C4—302no—
481C2×C4—602no—
482C2×C4—602no—
483C2×C4—601no—
484C2×C4D15⋊Q811yescharacteristic
485C2×C4#677111yescharacteristic
486C2×C4#677111yescharacteristic
487C2×C4#677711yescharacteristic
488C2×C4C2×#120011yescharacteristic
489C2×C4#679011yescharacteristic
490C8—121no—
491C8—201no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3#6495611yescharacteristic
495C2×C3D5×#10411yescharacteristic
496C2×C3#6511011yescharacteristic
497D3—202no—
498C5#6877011yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—302no—
502C22—601no—
503C22—601no—
504C22#9137711yescharacteristic
505C22#9146111yescharacteristic
506C22#9156111yescharacteristic
507C4—41no—
508C4—41no—
509C4—122no—
510C4—152no—
511C4—202no—
512C4—301no—
513C4—301no—
514C4—301no—
515C4—302no—
516C4#9137711yescharacteristic
517C4#9138611yescharacteristic
518C4#9143711yescharacteristic
519C4#9146111yescharacteristic
520C3#1059956311yescharacteristic, complemented, Sylow
521C2—21no—
522C2—21no—
523C2—602no—
524C2#1174886311yescharacteristic
525C2#1174943011yescharacteristic
526C2#1174943111yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1806
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C4×#6669C2semidirect
3. #11748437C2semidirect
6. C5×#4532C2semidirect
7. C3×#64752C2semidirect
12. #91782C4semidirect
13. #91782C4semidirect
14. #91776C4semidirect
15. #91776C4semidirect
37. #64752D3semidirect
84. #4532D5semidirect
127. D60C4⋊C4semidirect
133. Dic30C4⋊C4semidirect
228. Dic15#104semidirect
429. C3×C5#1806semidirect
498. C5#68770semidirect
520. C3#10599563semidirect

Maximal subgroups

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

subgroupindex
#117562812
C4×#66692
#117484372
C2×#909812
C2×#909802
C5×#45322
C3×#647522
#105995633
#687705