Finite Group Databasebeta

← #14301351

Subgroups — #14301351

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
1C5×#5504C211yesmaximal, characteristic, complemented
2C2×#91298C211yesmaximal, characteristic
3C3×#65277C211yesmaximal, characteristic, complemented
4C2×#90979C211yesmaximal, characteristic, complemented
5#11748366C211yesmaximal, characteristic, complemented
6#11746351C211yesmaximal, characteristic, complemented
7#11745977C211yesmaximal, characteristic, complemented
8#10602460—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C4×C5×#67—22no—
15C5×#926C2211yescharacteristic
16C5×#893—21no—
17C5×#892—21no—
18C5×D3×C4⋊C4—21no—
19C5×#887—21no—
20C2×C3×#685—22no—
21C2×C3×C4×Dic5C2211yescharacteristic
22C2×#6655—21no—
23#91298—22no—
24#91298C414yescomplemented
25C2×#6652—21no—
26#90979—22no—
27#90964—21no—
28#90964—21no—
29#69663—51nomaximal, Hall
30C5×#520—31no—
31C2×#4095—31no—
32C2×#3969—31no—
33#65290—31no—
34#65277D311yescharacteristic, complemented
35#64752—31no—
36#64750—31no—
37C23×C3×D5—21no—
38C22×C3×C4×C5D412yes—
39C22×C3×C4×C5C2311yescharacteristic
40C2×C5×#67—21no—
41C5×#235—21no—
42C5×#235—21no—
43C5×#235C2×C412yes—
44C5×#235D412yes—
45C2×C5×D12D411yescharacteristic
46C2×C4×C5×D3—21no—
47C2×C4×C5×D3—22no—
48C2×C5×Dic6D411yescharacteristic
49C22×C3×Dic5—21no—
50C2×C3×D20—21no—
51C2×C3×D20—21no—
52C2×C3×D20—21no—
53C2×C3×D20—21no—
54C2×C3×D20—21no—
55C2×C3×D20C2×C412yescomplemented
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4—21no—
58#6710—21no—
59#6710—21no—
60#6710—21no—
61#6710C2×C412yescomplemented
62C2×C3⋊#168—21no—
63C2×C3⋊#168—21no—
64C5×#217—21no—
65C5×(C2×D3)⋊C4—22no—
66C5×C4⋊Dic3D411yescharacteristic
67C5×C4⋊Dic3D411yescharacteristic
68C5×Dic3⋊C4—22no—
69C4×C5×Dic3—22no—
70C4×C5×Dic3—21no—
71C3×#685—44no—
72C3×C4×Dic5—21no—
73C3×C4×Dic5—21no—
74#6655—24no—
75#6652—24no—
76C2×#932—51no—
77#5504D511yescharacteristic, complemented
78C3×#390—51no—
79#5215—51no—
80C2×#805—51no—
81#4530—51no—
82#4523—51no—
83C2×C5×#41—31no—
84C22×D20C2×D311yescharacteristic
85C4×C5×Q8—61no—
86C4×C5×D4—61no—
87C4×C5×D4—62no—
88C5×#117—31no—
89C5×#117—61no—
90C2×C5×C4⋊C4—61no—
91C2×C5×C4⋊C4C2×D311yescharacteristic
92#4095—34no—
93#4095—62no—
94C2×#688—61no—
95C2×#686—61no—
96C2×#685—22no—
97C2×C4×Dic5C2×D311yescharacteristic
98C2×#681—31no—
99C2×#681—31no—
100#3969—62no—
101#3941—61no—
102#3941—61no—
103#1883—151noSylow
104C23×C3×C5C2×D411yescharacteristic
105C22×C5×D3—21no—
106C22×C3×D5—22no—
107C22×C3×D5—42no—
108C22×C3×D5—42no—
109C22×C3×D5—41no—
110C22×C3×D5—41no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—42no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C5×#67—22no—
120C5×#67—22no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—21no—
124C5×D12—21no—
125C5×D12C22⋊C412yescomplemented
126C4×C5×D3—22no—
127C4×C5×D3—22no—
128C4×C5×D3—82no—
129C5×Dic6—21no—
130C5×Dic6C22⋊C412yescomplemented
131C2×C3×Dic5—22no—
132C2×C3×Dic5—41no—
133C2×C3×Dic5—41no—
134C3×D20—22no—
135C3×D20—22no—
136C3×D20—41no—
137C3×D20—41no—
138C3⋊#168—22no—
139C3⋊#168—41no—
140C22×C3×D4—51no—
141C2×#235C2×D511yescharacteristic
142C2×C3×C4⋊C4C2×D511yescharacteristic
143C2×C3×C22⋊C4—102no—
144C2×C3×C42—51no—
145C2×#214—101no—
146#932—54no—
147#932—102no—
148C2×#213—101no—
149C4×#67—22no—
150#926C2×D511yescharacteristic
151C2×#208—51no—
152C2×#208—51no—
153#893—21no—
154#892—21no—
155D3×C4⋊C4—21no—
156#887—21no—
157#832—101no—
158#832—101no—
159#805—102no—
160C23×D5—21no—
161C5×#41—32no—
162C5×#41—32no—
163C5×#41—61no—
164C5×#41—61no—
165C2×C5×Q8—31no—
166C2×C5×D4—31no—
167C2×C5×D4—61no—
168C22×C4×C5—62no—
169C22×C4×C5—61no—
170C22×C4×C5#6712yes—
171C22×C4×C5C22×D311yescharacteristic
172C22×Dic5—21no—
173C2×D20—21no—
174C2×D20—21no—
175C2×D20—21no—
176C2×D20—21no—
177C2×D20—21no—
178C2×D20C4×D312yescomplemented
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—31no—
182C5×C4⋊C4—31no—
183C5×C4⋊C4—62no—
184C5×C22⋊C4—62no—
185C5×C22⋊C4—61no—
186C42×C5—62no—
187C42×C5—61no—
188#688—64no—
189#686—64no—
190#685—44no—
191C4×Dic5—21no—
192C4×Dic5—21no—
193#681—32no—
194#681—61no—
195#681—61no—
196#681—61no—
197C2×#168—61no—
198C2×#168—61no—
199C2×AGL(1,ℤ/8)—151no—
200#520—31no—
201C2×#104—151no—
202#418—151no—
203#390—51no—
204#343—151no—
205#339—151no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5C4×D411yescharacteristic
209C22×C3×C5#12011yescharacteristic
210C22×C3×C5#12111yescharacteristic
211C2×C5×D3—22no—
212C2×C5×D3—41no—
213C2×C5×D3—41no—
214C2×C3×D5—44no—
215C2×C3×D5—42no—
216C2×C3×D5—82no—
217C2×C3×D5—81no—
218C2×C3×D5—81no—
219C3×C4×C5—42no—
220C3×C4×C5C2×C22⋊C411yescharacteristic
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5#12311yescharacteristic
224C3×Dic5—42no—
225C5×Dic3—22no—
226C5×Dic3—41no—
227C5×Dic3—41no—
228C24×C3—101no—
229C2×C3×D4—52no—
230C2×C3×D4—101no—
231C2×C3×D4—101no—
232C2×C3×D4—101no—
233C2×C3×D4—101no—
234C2×C3×D4—101no—
235C22×C3×C4—101no—
236C22×C3×C4C22⋊D512yes—
237C22×C3×C4C22×D511yescharacteristic
238C2×#67—21no—
239#235—21no—
240#235—21no—
241#235C4×D512yes—
242#235D2012yes—
243C2×D12C22⋊D511yescharacteristic
244C2×C4×D3—21no—
245C2×C4×D3—22no—
246C2×Dic6C22⋊D511yescharacteristic
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C22⋊C4—204no—
250C3×C42—101no—
251C3×C42—101no—
252#217—21no—
253#214—104no—
254#213—104no—
255(C2×D3)⋊C4—22no—
256C4⋊Dic3C22⋊D511yescharacteristic
257C4⋊Dic3C22⋊D511yescharacteristic
258Dic3⋊C4—22no—
259C4×Dic3—22no—
260C4×Dic3—21no—
261#208—52no—
262#208—101no—
263#208—101no—
264#208—101no—
265C2×C3⋊C8—101no—
266C2×C3⋊C8—101no—
267C23×C5—61no—
268C23×C5C2×#6711yescharacteristic
269C22×D5—22no—
270C22×D5—42no—
271C22×D5—42no—
272C22×D5—41no—
273C22×D5—41no—
274C5×Q8—32no—
275C5×Q8—61no—
276C5×D4—32no—
277C5×D4—62no—
278C5×D4—62no—
279C5×D4—61no—
280C2×C4×C5—22no—
281C2×C4×C5—42no—
282C2×C4×C5—61no—
283C2×C4×C5—62no—
284C2×C4×C5—62no—
285C2×C4×C5—61no—
286C2×C4×C5—61no—
287C2×C4×C5—242no—
288C2×C4×C5C2×C4×D311yescharacteristic
289C2×C4×C5#23511yescharacteristic
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5D3×D411yescharacteristic
293C2×C4×C5#23711yescharacteristic
294C2×Dic5—22no—
295C2×Dic5—41no—
296C2×Dic5—41no—
297D20—22no—
298D20—22no—
299D20—41no—
300D20—41no—
301#168—62no—
302#168—121no—
303C2×#41—31no—
304C22×D4—51no—
305AGL(1,ℤ/8)—154no—
306AGL(1,ℤ/8)—302no—
307C2×SD16—301no—
308C2×D8—301no—
309C2×M16—151no—
310C2×M16—151no—
311C4×Q8—61no—
312C4×D4—61no—
313C4×D4—62no—
314#117—31no—
315#117—61no—
316C2×C4⋊C4—61no—
317C2×C4⋊C4D3×D511yescharacteristic
318C2×C22⋊C4—102no—
319C2×C42—51no—
320#104—302no—
321#102—301no—
322#102—301no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5#38611yescharacteristic
326C2×C3×C5#45311yescharacteristic
327C2×C3×C5#45411yescharacteristic
328C3×D5—82no—
329C5×D3—42no—
330C23×C3—102no—
331C23×C3—202no—
332C23×C3—202no—
333C23×C3—201no—
334C23×C3—201no—
335C23×C3C2×C22⋊D511yescharacteristic
336C22×D3—21no—
337C3×D4—102no—
338C3×D4—102no—
339C3×D4—201no—
340C3×D4—201no—
341C2×C3×C4—22no—
342C2×C3×C4—42no—
343C2×C3×C4—102no—
344C2×C3×C4—201no—
345C2×C3×C4—201no—
346C2×C3×C4C2×C4×D511yescharacteristic
347C2×C3×C4C2×D2011yescharacteristic
348C2×C3×C4#70911yescharacteristic
349C2×C3×C4#70911yescharacteristic
350C2×C3×C4C2×C22⋊D511yescharacteristic
351C2×C3×C4C2×C22⋊D511yescharacteristic
352#67—22no—
353#67—22no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357D12—21no—
358D12#68512yescomplemented
359C4×D3—22no—
360C4×D3—22no—
361C4×D3—82no—
362Dic6—21no—
363Dic6#68512yescomplemented
364C3⋊C8—102no—
365C3⋊C8—201no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—62no—
369C22×C5—121no—
370C22×C5—121no—
371C22×C5C4×#6711yescharacteristic
372C22×C5#93711yescharacteristic
373C22×C5#93811yescharacteristic
374C2×D5—44no—
375C2×D5—42no—
376C2×D5—82no—
377C2×D5—81no—
378C2×D5—81no—
379C4×C5—42no—
380C4×C5—62no—
381C4×C5—121no—
382C4×C5—121no—
383C4×C5D3×C22⋊C411yescharacteristic
384C4×C5#67⋊C411yescharacteristic
385C4×C5#88311yescharacteristic
386C4×C5#88411yescharacteristic
387Dic5—42no—
388C24—101no—
389#41—32no—
390#41—32no—
391#41—61no—
392#41—61no—
393C2×Q8—31no—
394C2×D4—31no—
395C2×D4—52no—
396C2×D4—61no—
397C2×D4—101no—
398C2×D4—101no—
399C2×D4—101no—
400C2×D4—101no—
401C2×D4—101no—
402C22×C4—62no—
403C22×C4—61no—
404C22×C4—101no—
405C22×C4#120112yes—
406C22×C4C2×D3×D511yescharacteristic
407SD16—304no—
408D8—304no—
409M16—152no—
410M16—301no—
411M16—301no—
412M16—301no—
413C2×C8—301no—
414C2×C8—301no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—31no—
418C4⋊C4—31no—
419C4⋊C4—62no—
420C22⋊C4—62no—
421C22⋊C4—61no—
422C22⋊C4—204no—
423C42—62no—
424C42—61no—
425C42—101no—
426C42—101no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—204no—
431C22×C3—202no—
432C22×C3—402no—
433C22×C3—401no—
434C22×C3—401no—
435C22×C3C4×C22⋊D511yescharacteristic
436C22×C3#407611yescharacteristic
437C22×C3#409911yescharacteristic
438C2×D3—22no—
439C2×D3—41no—
440C2×D3—41no—
441C3×C4—42no—
442C3×C4—202no—
443C3×C4C2×#68511yescharacteristic
444C3×C4C4×C22⋊D511yescharacteristic
445C3×C4#407511yescharacteristic
446C3×C4#407611yescharacteristic
447Dic3—22no—
448Dic3—41no—
449Dic3—41no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—122no—
453C2×C5#495611yescharacteristic
454C2×C5#506211yescharacteristic
455C2×C5#507711yescharacteristic
456D5—82no—
457C23—61no—
458C23—102no—
459C23—202no—
460C23—202no—
461C23—201no—
462C23—201no—
463C23C2×#120111yescharacteristic
464Q8—32no—
465Q8—61no—
466D4—32no—
467D4—62no—
468D4—62no—
469D4—61no—
470D4—102no—
471D4—102no—
472D4—201no—
473D4—201no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—61no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—102no—
482C2×C4—201no—
483C2×C4—201no—
484C2×C4—242no—
485C2×C4#676511yescharacteristic
486C2×C4#677111yescharacteristic
487C2×C4C4×D3×D511yescharacteristic
488C2×C4D3×D2011yescharacteristic
489C2×C4D3×C22⋊D511yescharacteristic
490C2×C4D3×C22⋊D511yescharacteristic
491C8—302no—
492C8—601no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—402no—
496C2×C3#6550211yescharacteristic
497C2×C3#6553011yescharacteristic
498C2×C3#6553411yescharacteristic
499D3—42no—
500C5#6966311yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—62no—
504C22—121no—
505C22—121no—
506C22—204no—
507C22—202no—
508C22—402no—
509C22—401no—
510C22—401no—
511C22C4×#120111yescharacteristic
512C22#9145611yescharacteristic
513C22#9156811yescharacteristic
514C4—42no—
515C4—62no—
516C4—121no—
517C4—121no—
518C4—202no—
519C4#9144111yescharacteristic
520C4#9145211yescharacteristic
521C4#9145411yescharacteristic
522C4D3×#68511yescharacteristic
523C3#1060246011yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—122no—
527C2—402no—
528C2#1174891011yescharacteristic
529C2#1174914011yescharacteristic
530C2#1174938611yescharacteristic
subgroupG/H
centerC22#91568
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC2×#91298C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1883
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C5×#5504C2semidirect
3. C3×#65277C2semidirect
4. C2×#90979C2semidirect
5. #11748366C2semidirect
6. #11746351C2semidirect
7. #11745977C2semidirect
24. #91298C4semidirect
34. #65277D3semidirect
55. C2×C3×D20C2×C4semidirect
61. #6710C2×C4semidirect
77. #5504D5semidirect
125. C5×D12C22⋊C4semidirect
130. C5×Dic6C22⋊C4semidirect
178. C2×D20C4×D3semidirect
358. D12#685semidirect
363. Dic6#685semidirect
427. C3×C5#1883semidirect
500. C5#69663semidirect
523. C3#10602460semidirect

Maximal subgroups

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

subgroupindex
C5×#55042
C2×#912982
C3×#652772
C2×#909792
#117483662
#117463512
#117459772
#106024603
#696635