Finite Group Databasebeta

← #14301340

Subgroups — #14301340

Order 1920.

740 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
1C2×#91821C211yesmaximal, characteristic
2#11754506C211yesmaximal, characteristic, complemented
3C5×#5221C211yesmaximal, characteristic, complemented
4C3×#65504C211yesmaximal, characteristic, complemented
5C2×#90980C211yesmaximal, characteristic, complemented
6#11745986C211yesmaximal, characteristic, complemented
7#11745974C211yesmaximal, characteristic, complemented
8#10600456—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C2×#6716—21no—
12#91821—22no—
13#91821C414yescomplemented
14C2×#6715—21no—
15C2×#6710C2211yescharacteristic
16C2×C5×#217—22no—
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C4×C5×Dic3C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91556—22no—
22#91437—21no—
23#91418—21no—
24#91347—21no—
25#91333—21no—
26C3×#3964—21no—
27C3×#3964—21no—
28#90980—22no—
29#70328—51nomaximal, Hall
30C2×#4078—31no—
31#65838—31no—
32C5×#390—31no—
33#65504D311yescharacteristic, complemented
34C2×#3937—31no—
35#64750—31no—
36#64743—31no—
37C24×C3×C5—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4C2×C412yescomplemented
44C22×C3×C4×C5C2311yescharacteristic
45C2×#1220—21no—
46#6817—21no—
47#6817—21no—
48#6817C2×C412yes—
49#6817D412yes—
50C2×D60D411yescharacteristic
51C2×C4×D15—21no—
52C2×Dic30D411yescharacteristic
53C22×C5×Dic3—21no—
54C22×C5×Dic3D412yes—
55C2×#1200—22no—
56#6716—24no—
57#6715—24no—
58#6710—21no—
59#6710C2×C412yescomplemented
60C2×C3⋊#168—21no—
61C5×#217—44no—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3—21no—
64C4×C5×Dic3—21no—
65C4×C5×Dic3—21no—
66C3×C22⋊Dic5—21no—
67C3×C4⋊Dic5D411yescharacteristic
68C3×C4⋊Dic5D411yescharacteristic
69C3×C4×Dic5—21no—
70C3×#681—21no—
71C3×#681—21no—
72C2×C3×#168—21no—
73#6669—22no—
74#6667—22no—
75Dic3×Dic5—22no—
76C2×#932—51no—
77#5523—51no—
78C3×#418—51no—
79#5221D511yescharacteristic, complemented
80C2×#825—51no—
81#4554—51no—
82#4532—51no—
83C22×C5×D4C2×D311yescharacteristic
84C2×#709—31no—
85C2×C5×C4⋊C4—31no—
86C2×C5×C22⋊C4—62no—
87C2×C42×C5—31no—
88C2×#687—61no—
89#4078—34no—
90#4078—62no—
91C2×#686—61no—
92C4×C22⋊D5—62no—
93#4072C2×D311yescharacteristic
94C2×#681—31no—
95C2×#681C2×D311yescharacteristic
96#4039—61no—
97#4038—61no—
98D5×C4⋊C4—61no—
99#4033—61no—
100#3964—21no—
101#3964—21no—
102#3937—62no—
103#1883—151noSylow
104C23×C3×C5—22no—
105C23×C3×C5—42no—
106C23×C3×C5—42no—
107C23×C3×C5—41no—
108C23×C3×C5—41no—
109C23×C3×C5C2×D411yescharacteristic
110C22×D15—21no—
111C3×C5×D4—22no—
112C3×C5×D4—22no—
113C3×C5×D4—41no—
114C3×C5×D4—41no—
115C2×C3×C4×C5C22×C411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×C3×C4×C5#4111yescharacteristic
121#1220—22no—
122#1220—22no—
123C2×Dic15—21no—
124D60—21no—
125D60C22⋊C412yescomplemented
126C4×D15—22no—
127C4×D15—22no—
128Dic30—21no—
129Dic30C22⋊C412yescomplemented
130C2×C5×Dic3—22no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—41no—
133C2×C5×Dic3—41no—
134C2×C5×Dic3—42no—
135C2×C3×Dic5—21no—
136C2×C3×Dic5—21no—
137#1200—82no—
138C3⋊#168—22no—
139C3×#168—41no—
140C22×C3×D4C2×D511yescharacteristic
141C2×#235—51no—
142C2×C3×M16—51no—
143C3×#117—51no—
144C2×#217—22no—
145C2×#214—101no—
146#932—54no—
147#932—102no—
148C2×#213—101no—
149C2×C4⋊Dic3C2×D511yescharacteristic
150C2×C4×Dic3C2×D511yescharacteristic
151C2×#208—51no—
152#892—101no—
153D3×C4⋊C4—101no—
154#67⋊C4—102no—
155C4×D12—101no—
156C4×Dic6—101no—
157C3×#102—101no—
158C3×#102—101no—
159#825—102no—
160C24×C5—21no—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4C4×D312yescomplemented
167C22×C4×C5—32no—
168C22×C4×C5—61no—
169C22×C4×C5C22×D311yescharacteristic
170C2×C22⋊D5—61no—
171#709—32no—
172#709—32no—
173#709—61no—
174#709—61no—
175C2×D20—31no—
176C2×C4×D5—61no—
177C2×C4×D5—62no—
178C2×Dic10—31no—
179C5×C4⋊C4—61no—
180C5×C4⋊C4—61no—
181C5×C22⋊C4—124no—
182C42×C5—61no—
183C42×C5—61no—
184C22⋊Dic5—21no—
185#687—64no—
186#686—64no—
187#685—62no—
188C4⋊Dic5#6711yescharacteristic
189C4⋊Dic5#6711yescharacteristic
190#683—62no—
191C4×Dic5—21no—
192C4×Dic5—62no—
193#681—21no—
194#681—21no—
195#681—32no—
196#681—61no—
197C2×#168—21no—
198C2×#168—61no—
199C2×AGL(1,ℤ/8)—151no—
200#520—151no—
201C2×#104—151no—
202#418—51no—
203#390—31no—
204#343—151no—
205#339—151no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5—44no—
209C22×C3×C5—42no—
210C22×C3×C5—82no—
211C22×C3×C5—81no—
212C22×C3×C5—81no—
213C22×C3×C5C4×D411yescharacteristic
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5#12111yescharacteristic
216C2×D15—22no—
217C2×D15—41no—
218C2×D15—41no—
219C3×C4×C5C2×C22⋊C411yescharacteristic
220C3×C4×C5C4×D411yescharacteristic
221C3×C4×C5#12111yescharacteristic
222C3×C4×C5#12311yescharacteristic
223Dic15—22no—
224C3×Dic5—41no—
225C3×Dic5—41no—
226C5×Dic3—42no—
227C5×Dic3—42no—
228C24×C3—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4C4×D512yescomplemented
235C22×C3×C4C22×D511yescharacteristic
236C2×#67—101no—
237C22×Dic3—21no—
238C22×Dic3C22⋊D512yes—
239#235—52no—
240#235—52no—
241#235—101no—
242#235—101no—
243C2×D12—51no—
244C2×C4×D3—101no—
245C2×C4×D3—102no—
246C2×Dic6—51no—
247C3×M16—101no—
248C3×M16—101no—
249C2×C3×C8—101no—
250C3×C4⋊C4—51no—
251C3×C4⋊C4—51no—
252C3×C22⋊C4—101no—
253C3×C42—101no—
254#217—44no—
255#214—104no—
256#213—104no—
257(C2×D3)⋊C4—102no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260Dic3⋊C4—102no—
261C4×Dic3—21no—
262C4×Dic3—21no—
263C4×Dic3—102no—
264#208—52no—
265#208—101no—
266C2×C3⋊C8—101no—
267C23×C5—22no—
268C23×C5—42no—
269C23×C5—42no—
270C23×C5—41no—
271C23×C5—41no—
272C23×C5D3×D411yescharacteristic
273C22×D5—61no—
274C5×D4—22no—
275C5×D4—22no—
276C5×D4—41no—
277C5×D4—41no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5—121no—
281C2×C4×C5—121no—
282C2×C4×C5—122no—
283C2×C4×C5C2×C4×D311yescharacteristic
284C2×C4×C5#23511yescharacteristic
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5#23711yescharacteristic
288C2×C4×C5C2×#6711yescharacteristic
289C22⋊D5—62no—
290C22⋊D5—62no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—61no—
294D20—32no—
295D20—61no—
296C4×D5—62no—
297C4×D5—62no—
298C4×D5—242no—
299Dic10—32no—
300Dic10—61no—
301#168—41no—
302#168—62no—
303C2×#41—151no—
304C22×D4D3×D511yescharacteristic
305AGL(1,ℤ/8)—154no—
306AGL(1,ℤ/8)—302no—
307C2×SD16—301no—
308C2×D8—301no—
309C2×M16—51no—
310C2×M16—151no—
311C4×Q8—301no—
312C4×D4—301no—
313C4×D4—302no—
314#117—51no—
315#117—301no—
316C2×C4⋊C4—31no—
317C2×C4⋊C4—301no—
318C2×C22⋊C4—62no—
319C2×C42—31no—
320#104—302no—
321#102—101no—
322#102—101no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5—82no—
326C2×C3×C5#38611yescharacteristic
327C2×C3×C5#45311yescharacteristic
328C2×C3×C5#45411yescharacteristic
329D15—42no—
330C23×C3—22no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3C2×C22⋊D511yescharacteristic
336C22×D3—101no—
337C3×D4—22no—
338C3×D4—22no—
339C3×D4—41no—
340C3×D4—41no—
341C2×C3×C4—101no—
342C2×C3×C4—101no—
343C2×C3×C4C2×C4×D511yescharacteristic
344C2×C3×C4#70911yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4D4×D511yescharacteristic
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4#71111yescharacteristic
349#67—102no—
350#67—102no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—42no—
356C2×Dic3—101no—
357D12—52no—
358D12—101no—
359C4×D3—102no—
360C4×D3—102no—
361C4×D3—402no—
362Dic6—52no—
363Dic6—101no—
364C3×C8—201no—
365C3⋊C8—102no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—44no—
369C22×C5—42no—
370C22×C5—82no—
371C22×C5—81no—
372C22×C5—81no—
373C22×C5#67⋊C411yescharacteristic
374C22×C5#88411yescharacteristic
375C22×C5#93711yescharacteristic
376C2×D5—62no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—122no—
380C4×C5—122no—
381C4×C5D3×C22⋊C411yescharacteristic
382C4×C5#88311yescharacteristic
383C4×C5C4×#6711yescharacteristic
384C4×C5#93811yescharacteristic
385Dic5—41no—
386Dic5—41no—
387Dic5—62no—
388C24—21no—
389#41—152no—
390#41—152no—
391#41—301no—
392#41—301no—
393C2×Q8—151no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—151no—
400C2×D4—301no—
401C2×D4#120012yescomplemented
402C22×C4—32no—
403C22×C4—61no—
404C22×C4—302no—
405C22×C4—301no—
406C22×C4C2×D3×D511yescharacteristic
407SD16—304no—
408D8—304no—
409M16—101no—
410M16—101no—
411M16—152no—
412M16—301no—
413C2×C8—101no—
414C2×C8—301no—
415C4⋊C4—51no—
416C4⋊C4—51no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—302no—
420C22⋊C4—101no—
421C22⋊C4—124no—
422C22⋊C4—302no—
423C42—61no—
424C42—61no—
425C42—101no—
426C42—302no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—44no—
431C22×C3—42no—
432C22×C3—82no—
433C22×C3—81no—
434C22×C3—81no—
435C22×C3C4×C22⋊D511yescharacteristic
436C22×C3#408311yescharacteristic
437C22×C3#408411yescharacteristic
438C2×D3—102no—
439C2×D3—201no—
440C2×D3—201no—
441C3×C4—201no—
442C3×C4—201no—
443C3×C4D5×C22⋊C411yescharacteristic
444C3×C4#402711yescharacteristic
445C3×C4#402911yescharacteristic
446C3×C4#403011yescharacteristic
447Dic3—42no—
448Dic3—42no—
449Dic3—102no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—82no—
453C2×C5#495611yescharacteristic
454C2×C5#519811yescharacteristic
455C2×C5#520111yescharacteristic
456D5—122no—
457C23—22no—
458C23—42no—
459C23—42no—
460C23—41no—
461C23—41no—
462C23—301no—
463C23D3×C22⋊D511yescharacteristic
464Q8—152no—
465Q8—301no—
466D4—22no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—152no—
471D4—302no—
472D4—302no—
473D4—301no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—101no—
477C2×C4—101no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—122no—
481C2×C4—301no—
482C2×C4—302no—
483C2×C4—302no—
484C2×C4—1202no—
485C2×C4#677911yescharacteristic
486C2×C4#678211yescharacteristic
487C2×C4C2×#120011yescharacteristic
488C2×C4D5×#6711yescharacteristic
489C2×C4#679011yescharacteristic
490C2×C4#679011yescharacteristic
491C8—201no—
492C8—302no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—82no—
496C2×C3#6524511yescharacteristic
497C2×C3#6535111yescharacteristic
498C2×C3#6536611yescharacteristic
499D3—202no—
500C5#7032811yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—44no—
504C22—42no—
505C22—82no—
506C22—81no—
507C22—81no—
508C22—302no—
509C22—601no—
510C22—601no—
511C22#9155611yescharacteristic
512C22#9155711yescharacteristic
513C22#9157711yescharacteristic
514C4—122no—
515C4—122no—
516C4—201no—
517C4—201no—
518C4—302no—
519C4#9153311yescharacteristic
520C4#9155211yescharacteristic
521C4#9156111yescharacteristic
522C4#9156211yescharacteristic
523C3#1060045611yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—82no—
527C2—602no—
528C2#1174916511yescharacteristic
529C2#1174916711yescharacteristic
530C2#1174952011yescharacteristic
subgroupG/H
centerC22#91577
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5#120
prime radicalC2×#91821C2
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1883
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11754506C2semidirect
3. C5×#5221C2semidirect
4. C3×#65504C2semidirect
5. C2×#90980C2semidirect
6. #11745986C2semidirect
7. #11745974C2semidirect
13. #91821C4semidirect
33. #65504D3semidirect
43. C2×C3×C5×D4C2×C4semidirect
59. #6710C2×C4semidirect
79. #5221D5semidirect
125. D60C22⋊C4semidirect
129. Dic30C22⋊C4semidirect
166. C2×C5×D4C4×D3semidirect
234. C2×C3×D4C4×D5semidirect
401. C2×D4#1200semidirect
427. C3×C5#1883semidirect
500. C5#70328semidirect
523. C3#10600456semidirect

Maximal subgroups

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

subgroupindex
C2×#918212
#117545062
C5×#52212
C3×#655042
C2×#909802
#117459862
#117459742
#106004563
#703285