Finite Group Databasebeta

← #14297843

Subgroups — #14297843

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#11754436C211yesmaximal, characteristic
2C2×#91089C211yesmaximal, characteristic
3C4×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#11748440C211yesmaximal, characteristic, complemented
5C2×#90980C211yesmaximal, characteristic
6C3×#64743C211yesmaximal, characteristic, complemented
7#11745974C211yesmaximal, characteristic, complemented
8#10600287—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×C5×Dic3⋊C4—21no—
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17#91556—21no—
18#91556—21no—
19#91428C411yescharacteristic, complemented
20#91428C411yescharacteristic, complemented
21C4×#1200—21no—
22#91386—21no—
23#91340C411yescharacteristic, complemented
24#91340C411yescharacteristic, complemented
25#91089—22no—
26C5×C3⋊#95—21no—
27Dic3⋊#168—21no—
28Dic3⋊#168—21no—
29#90980—22no—
30#68770—51nomaximal, Hall
31C4×#709—31no—
32C4×C5×C4⋊C4—31no—
33C2×#3937—31no—
34C2×#3937—31no—
35#65213—31no—
36#64743—31no—
37#64743D311yescharacteristic, complemented
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41#6817—21no—
42#6817—21no—
43#6817D412yes—
44#6817Q812yes—
45C2×D60C2×C411yescharacteristic
46C2×C4×D15—21no—
47C2×Dic30C2×C411yescharacteristic
48C22×C5×Dic3—21no—
49C22×C5×Dic3D411yescharacteristic
50C22×C5×Dic3D411yescharacteristic
51C2×#1200—21no—
52C2×#1200—21no—
53C3×C42×C5—21no—
54C3×C42×C5—21no—
55#6710—21no—
56#6710—21no—
57C2×C3⋊#168—21no—
58C5×Dic3⋊C4—24no—
59C4×C5×Dic3—21no—
60C4×C5×Dic3—21no—
61C4×C5×Dic3C2×C411yescharacteristic
62C4×C5×Dic3C2×C411yescharacteristic
63C4×C5×Dic3D411yescharacteristic
64C4×C5×Dic3D411yescharacteristic
65C3×C22⋊Dic5—21no—
66C3×C4⋊Dic5C2×C411yescharacteristic
67C3×C4⋊Dic5C2×C411yescharacteristic
68C3×C4×Dic5—21no—
69C3×#681—21no—
70C3×#681—21no—
71C2×C3×#168—21no—
72#6669—21no—
73#6669—21no—
74#6667—21no—
75#6667—21no—
76Dic3×Dic5—21no—
77Dic3×Dic5—21no—
78#5522—51no—
79C2×#825—51no—
80#5118—51no—
81C4×Dic3⋊C4D511yescharacteristic, complemented
82C2×#805—51no—
83C3×#339—51no—
84#4532—51no—
85C2×#709—31no—
86C2×C5×C4⋊C4—61no—
87C2×C42×C5—31no—
88C2×C42×C5—31no—
89C2×C42×C5C2×D311yescharacteristic
90C4×C22⋊D5—61no—
91C4×C22⋊D5—61no—
92#4072C2×D311yescharacteristic
93C2×#681—31no—
94C2×#681C2×D311yescharacteristic
95C4×D20—31no—
96C4×D20—31no—
97#4018—61no—
98C42×D5—61no—
99C4×Dic10—31no—
100C4×Dic10—31no—
101C5×#95—61no—
102#3937—62no—
103#3937—62no—
104C4⋊#168—61no—
105C4⋊#168—61no—
106#1806—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×D15—21no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×Q811yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118#1220—22no—
119#1220—22no—
120C2×Dic15—21no—
121D60—21no—
122D60C4⋊C412yescomplemented
123C4×D15—22no—
124C4×D15—22no—
125Dic30—21no—
126Dic30C4⋊C412yescomplemented
127C2×C5×Dic3—22no—
128C2×C5×Dic3—22no—
129C2×C5×Dic3—41no—
130C2×C5×Dic3—41no—
131C2×C5×Dic3—41no—
132C2×C5×Dic3C22⋊C411yescharacteristic
133C2×C5×Dic3C22⋊C411yescharacteristic
134C2×C5×Dic3C22⋊C411yescharacteristic
135C2×C5×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic5—21no—
137C2×C3×Dic5—21no—
138#1200—42no—
139#1200—42no—
140C3⋊#168—41no—
141C3×#168—41no—
142C2×#235—51no—
143C2×C3×M16—51no—
144C3×#117—51no—
145C2×C3×C42C2×D511yescharacteristic
146C2×Dic3⋊C4—21no—
147C2×C4×Dic3C2×D511yescharacteristic
148C2×C4×Dic3C2×D511yescharacteristic
149C2×#208—51no—
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—21no—
159#825—102no—
160Dic3⋊C8—101no—
161Dic3⋊C8—101no—
162#805—102no—
163C22×C4×C5—21no—
164C22×C4×C5—31no—
165C22×C4×C5—31no—
166C22×C4×C5—61no—
167C22×C4×C5C22×D311yescharacteristic
168C2×C22⋊D5—61no—
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×C4⋊C4—64no—
179C42×C5—21no—
180C42×C5—21no—
181C42×C5—31no—
182C42×C5—31no—
183C42×C5—31no—
184C42×C5—31no—
185C42×C5—61no—
186C42×C5—61no—
187C22⋊Dic5—21no—
188#685—61no—
189#685—61no—
190C4⋊Dic5C4×D311yescharacteristic
191C4⋊Dic5C4×D311yescharacteristic
192#683—61no—
193#683—61no—
194C4×Dic5—21no—
195C4×Dic5—61no—
196C4×Dic5—61no—
197#681—21no—
198#681—21no—
199#681—61no—
200#681—61no—
201C2×#168—21no—
202C2×#168—61no—
203C4×#41—151no—
204#423—151no—
205C2×#104—151no—
206C2×#104—151no—
207C4×C4⋊C4—31no—
208#339—51no—
209#339—151no—
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—42no—
219C3×C4×C5C2×C4⋊C411yescharacteristic
220C3×C4×C5#11711yescharacteristic
221C3×C4×C5#12111yescharacteristic
222C3×C4×C5C22⋊Q811yescharacteristic
223Dic15—22no—
224C3×Dic5—41no—
225C3×Dic5—41no—
226C5×Dic3—21no—
227C5×Dic3—21no—
228C5×Dic3—21no—
229C5×Dic3—42no—
230C5×Dic3#10412yescomplemented
231C22×C3×C4—21no—
232C22×C3×C4C22×D511yescharacteristic
233C2×#67—101no—
234C22×Dic3—21no—
235C22×Dic3C22⋊D511yescharacteristic
236C22×Dic3C22⋊D511yescharacteristic
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⋊C4—51no—
250C3×C4⋊C4—51no—
251C3×C22⋊C4—101no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—101no—
255(C2×D3)⋊C4—101no—
256(C2×D3)⋊C4—101no—
257Dic3⋊C4—24no—
258Dic3⋊C4—101no—
259Dic3⋊C4—101no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—101no—
263C4×Dic3—101no—
264C4×Dic3C4×D511yescharacteristic
265C4×Dic3C4×D511yescharacteristic
266C4×Dic3D2011yescharacteristic
267C4×Dic3D2011yescharacteristic
268#208—101no—
269#208—101no—
270C2×C3⋊C8—101no—
271C23×C5D3×D411yescharacteristic
272C22×D5—61no—
273C2×C4×C5—22no—
274C2×C4×C5—31no—
275C2×C4×C5—31no—
276C2×C4×C5—31no—
277C2×C4×C5—31no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—62no—
281C2×C4×C5—62no—
282C2×C4×C5—121no—
283C2×C4×C5—121no—
284C2×C4×C5—121no—
285C2×C4×C5C2×C4×D311yescharacteristic
286C2×C4×C5#23511yescharacteristic
287C2×C4×C5#23511yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5D3×Q811yescharacteristic
291C22⋊D5—62no—
292C22⋊D5—62no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—61no—
296D20—32no—
297D20—61no—
298C4×D5—62no—
299C4×D5—62no—
300C4×D5—122no—
301C4×D5—122no—
302Dic10—32no—
303Dic10—61no—
304#168—41no—
305#168—121no—
306C2×#41—151no—
307C2×M16—51no—
308C2×M16—151no—
309C4×Q8—151no—
310C4×Q8—151no—
311C4×D4—151no—
312C4×D4—151no—
313C4×D4—301no—
314C4×D4—301no—
315#117—51no—
316#117—301no—
317C2×C4⋊C4—61no—
318C2×C42—31no—
319C2×C42—31no—
320C2×C42—301no—
321C2×C42D3×D511yescharacteristic
322C4⋊C8—301no—
323C4⋊C8—301no—
324#104—302no—
325#104—302no—
326#95—61no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5#38011yescharacteristic
330C2×C3×C5C2×#10411yescharacteristic
331C2×C3×C5#42111yescharacteristic
332D15—42no—
333C23×C3C2×C22⋊D511yescharacteristic
334C22×D3—101no—
335C2×C3×C4—22no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—101no—
339C2×C3×C4—101no—
340C2×C3×C4C2×C4×D511yescharacteristic
341C2×C3×C4C2×D2011yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4#71111yescharacteristic
344C2×C3×C4Q8×D511yescharacteristic
345C2×C3×C4#71311yescharacteristic
346#67—102no—
347#67—102no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—101no—
354C2×Dic3#68511yescharacteristic
355C2×Dic3#68511yescharacteristic
356C2×Dic3#68511yescharacteristic
357C2×Dic3#68511yescharacteristic
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—201no—
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—32no—
377C4×C5—42no—
378C4×C5—61no—
379C4×C5—61no—
380C4×C5—61no—
381C4×C5—122no—
382C4×C5#87211yescharacteristic
383C4×C5#88411yescharacteristic
384C4×C5D3×C4⋊C411yescharacteristic
385C4×C5#89611yescharacteristic
386Dic5—41no—
387Dic5—41no—
388Dic5—62no—
389#41—152no—
390#41—152no—
391#41—301no—
392#41—301no—
393C2×Q8—151no—
394C2×D4—151no—
395C2×D4—301no—
396C22×C4—21no—
397C22×C4—31no—
398C22×C4—31no—
399C22×C4—61no—
400C22×C4—301no—
401C22×C4—301no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404M16—101no—
405M16—101no—
406M16—301no—
407M16—301no—
408C2×C8—101no—
409C2×C8—301no—
410C4⋊C4—51no—
411C4⋊C4—51no—
412C4⋊C4—64no—
413C4⋊C4—301no—
414C4⋊C4—301no—
415C22⋊C4—101no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C42—21no—
419C42—21no—
420C42—31no—
421C42—31no—
422C42—31no—
423C42—31no—
424C42—61no—
425C42—61no—
426C42—101no—
427C42—301no—
428C42—301no—
429C3×C5#180611yescharacteristic, complemented, Hall
430C22×C3—21no—
431C22×C3—21no—
432C22×C3C2×#68511yescharacteristic
433C22×C3#408411yescharacteristic
434C22×C3#409211yescharacteristic
435C2×D3—102no—
436C2×D3—201no—
437C2×D3—201no—
438C3×C4—42no—
439C3×C4—201no—
440C3×C4—201no—
441C3×C4D5×C4⋊C411yescharacteristic
442C3×C4#403811yescharacteristic
443C3×C4#404111yescharacteristic
444C3×C4#404311yescharacteristic
445Dic3—21no—
446Dic3—21no—
447Dic3—21no—
448Dic3—42no—
449Dic3—102no—
450Dic3#393712yescomplemented
451C2×C5—21no—
452C2×C5—21no—
453C2×C5#466711yescharacteristic
454C2×C5D3×#10411yescharacteristic
455C2×C5#482111yescharacteristic
456D5—122no—
457C23—301no—
458C23D3×C22⋊D511yescharacteristic
459Q8—152no—
460Q8—301no—
461D4—152no—
462D4—302no—
463D4—302no—
464D4—301no—
465C2×C4—22no—
466C2×C4—31no—
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—31no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—101no—
475C2×C4—101no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—301no—
480C2×C4—302no—
481C2×C4—302no—
482C2×C4—602no—
483C2×C4—602no—
484C2×C4D15⋊Q811yescharacteristic
485C2×C4#677311yescharacteristic
486C2×C4C4×D3×D511yescharacteristic
487C2×C4D3×D2011yescharacteristic
488C2×C4#678211yescharacteristic
489C2×C4#679011yescharacteristic
490C8—201no—
491C8—601no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3C2×#393711yescharacteristic
495C2×C3#6527611yescharacteristic
496C2×C3#6529411yescharacteristic
497D3—202no—
498C5#6877011yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—302no—
502C22—601no—
503C22—601no—
504C22#9142411yescharacteristic
505C22D3×#68511yescharacteristic
506C22#9155711yescharacteristic
507C4—32no—
508C4—42no—
509C4—61no—
510C4—61no—
511C4—61no—
512C4—122no—
513C4—201no—
514C4—201no—
515C4—302no—
516C4#9140211yescharacteristic
517C4#9140411yescharacteristic
518C4#9142911yescharacteristic
519C4#9145911yescharacteristic
520C3#1060028711yescharacteristic, complemented, Sylow
521C2—21no—
522C2—21no—
523C2—602no—
524C2D3×#393711yescharacteristic
525C2#1174711111yescharacteristic
526C2#1174888211yescharacteristic
subgroupG/H
centerC2×C4D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1806
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C4×C5×Dic3⋊C4C2semidirect
4. #11748440C2semidirect
6. C3×#64743C2semidirect
7. #11745974C2semidirect
19. #91428C4semidirect
20. #91428C4semidirect
23. #91340C4semidirect
24. #91340C4semidirect
37. #64743D3semidirect
81. C4×Dic3⋊C4D5semidirect
122. D60C4⋊C4semidirect
126. Dic30C4⋊C4semidirect
230. C5×Dic3#104semidirect
429. C3×C5#1806semidirect
450. Dic3#3937semidirect
498. C5#68770semidirect
520. C3#10600287semidirect

Maximal subgroups

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

subgroupindex
#117544362
C2×#910892
C4×C5×Dic3⋊C42
#117484402
C2×#909802
C3×#647432
#117459742
#106002873
#687705