Finite Group Databasebeta

← #14301352

Subgroups — #14301352

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
1#11756263C211yesmaximal, characteristic, complemented
2C2×#91304C211yesmaximal, characteristic
3C5×#4988C211yesmaximal, characteristic, complemented
4C2×#90980C211yesmaximal, characteristic, complemented
5#11748389C211yesmaximal, characteristic, complemented
6C3×#64750C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10600456—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C4×#1220—22no—
13#91815C2211yescharacteristic
14#91782—21no—
15#91781—21no—
16C4⋊C4×D15—21no—
17#91776—21no—
18C2×C5×(C2×D3)⋊C4—22no—
19C2×C4×C5×Dic3C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C2×C3×#681C2211yescharacteristic
22C2×#6659—21no—
23#91304—22no—
24#91304C414yescomplemented
25C2×#6654—21no—
26#90980—22no—
27#90967—21no—
28#90967—21no—
29#69005—51nomaximal, Hall
30C2×#4078—31no—
31#65838—31no—
32C5×#390—31no—
33#65504—31no—
34C2×#3937—31no—
35#64750D311yescharacteristic, complemented
36#64743—31no—
37C23×C5×D3—21no—
38C22×C3×C4×C5D412yes—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41#6817—21no—
42#6817—21no—
43#6817C2×C412yes—
44#6817D412yes—
45C2×D60D411yescharacteristic
46C2×C4×D15—21no—
47C2×C4×D15—22no—
48C2×Dic30D411yescharacteristic
49C22×C5×Dic3—21no—
50C2×C5×D12—21no—
51C2×C5×D12—21no—
52C2×C5×D12—21no—
53C2×C5×D12—21no—
54C2×C5×D12—21no—
55C2×C5×D12C2×C412yescomplemented
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4—21no—
58#6719—21no—
59#6714—22no—
60C4⋊Dic15D411yescharacteristic
61C4⋊Dic15D411yescharacteristic
62#6712—22no—
63C4×Dic15—22no—
64C4×Dic15—21no—
65C5×(C2×D3)⋊C4—44no—
66C4×C5×Dic3—21no—
67C4×C5×Dic3—21no—
68C3×#681—21no—
69C3×#681—21no—
70C3×#681—21no—
71C3×#681C2×C412yescomplemented
72C2×C3×#168—21no—
73C2×C3×#168—21no—
74#6659—24no—
75#6654—24no—
76C2×#908—51no—
77#5504—51no—
78C2×#825—51no—
79#5131—51no—
80#4988D511yescharacteristic, complemented
81C3×#343—51no—
82#4555—51no—
83C22×C5×D4—31no—
84C2×#709—31no—
85C2×C5×C4⋊C4C2×D311yescharacteristic
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#4072—31no—
94C2×#681C2×D311yescharacteristic
95C2×#681C2×D311yescharacteristic
96#4039—61no—
97#4038—61no—
98D5×C4⋊C4—61no—
99#4033—61no—
100#3964—61no—
101#3964—61no—
102#3937—62no—
103#1883—151noSylow
104C23×C3×C5C2×D411yescharacteristic
105C22×D15—21no—
106C22×C5×D3—22no—
107C22×C5×D3—42no—
108C22×C5×D3—42no—
109C22×C5×D3—41no—
110C22×C5×D3—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
119#1220—22no—
120#1220—22no—
121C2×Dic15—21no—
122C2×Dic15—21no—
123C2×Dic15—21no—
124D60—21no—
125D60C22⋊C412yescomplemented
126C4×D15—22no—
127C4×D15—22no—
128C4×D15—82no—
129Dic30—21no—
130Dic30C22⋊C412yescomplemented
131C2×C5×Dic3—22no—
132C2×C5×Dic3—41no—
133C2×C5×Dic3—41no—
134C5×D12—22no—
135C5×D12—22no—
136C5×D12—41no—
137C5×D12—41no—
138C3×#168—22no—
139C3×#168—41no—
140C2×#235—51no—
141C22×D12C2×D511yescharacteristic
142C2×C3×M16—51no—
143C2×C3×M16—51no—
144C2×C3×C4⋊C4C2×D511yescharacteristic
145C4×#67—102no—
146C2×(C2×D3)⋊C4—22no—
147#926—51no—
148C2×C4×Dic3C2×D511yescharacteristic
149#908—54no—
150#908—102no—
151C2×D24—101no—
152C2×#204—101no—
153#893—101no—
154#892—101no—
155D3×C4⋊C4—101no—
156#887—101no—
157#825—102no—
158#821—101no—
159#821—101no—
160C24×C5—61no—
161C2×C5×D4—32no—
162C2×C5×D4—61no—
163C2×C5×D4—61no—
164C2×C5×D4—61no—
165C2×C5×D4—61no—
166C2×C5×D4—61no—
167C22×C4×C5—61no—
168C22×C4×C5D1212yes—
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—21no—
180C5×C4⋊C4—21no—
181C5×C22⋊C4—124no—
182C42×C5—61no—
183C42×C5—61no—
184C22⋊Dic5—61no—
185#687—64no—
186#686—64no—
187#685—62no—
188C4⋊Dic5—31no—
189C4⋊Dic5—31no—
190#683—62no—
191C4×Dic5—62no—
192C4×Dic5—61no—
193#681—21no—
194#681—21no—
195#681—21no—
196#681C4×D312yescomplemented
197C2×#168—21no—
198C2×#168—21no—
199C2×AGL(1,ℤ/8)—151no—
200#520—151no—
201C2×#104—151no—
202#418—151no—
203#390—31no—
204#343—51no—
205#339—151no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5C4×D411yescharacteristic
209C22×C3×C5#12011yescharacteristic
210C22×C3×C5#12111yescharacteristic
211C2×D15—22no—
212C2×D15—41no—
213C2×D15—41no—
214C2×C5×D3—44no—
215C2×C5×D3—42no—
216C2×C5×D3—82no—
217C2×C5×D3—81no—
218C2×C5×D3—81no—
219C3×C4×C5—42no—
220C3×C4×C5C2×C22⋊C411yescharacteristic
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5#12311yescharacteristic
224Dic15—22no—
225Dic15—41no—
226Dic15—41no—
227C5×Dic3—42no—
228C23×D3—21no—
229C22×C3×C4C22⋊D512yes—
230C22×C3×C4C22×D511yescharacteristic
231C2×#67—101no—
232C22×Dic3—21no—
233#235—52no—
234#235—52no—
235#235—101no—
236#235—101no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—51no—
243C2×D12C4×D512yescomplemented
244C2×C4×D3—101no—
245C2×C4×D3—102no—
246C2×Dic6—51no—
247C3×M16—52no—
248C3×M16—101no—
249C3×M16—101no—
250C3×M16—101no—
251C2×C3×C8—101no—
252C2×C3×C8—101no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255#217—101no—
256(C2×D3)⋊C4—44no—
257(C2×D3)⋊C4—102no—
258C4⋊Dic3—51no—
259C4⋊Dic3—51no—
260Dic3⋊C4—102no—
261C4×Dic3—21no—
262C4×Dic3—21no—
263C4×Dic3—102no—
264C4×Dic3—101no—
265D24—104no—
266#204—104no—
267C23×C5—62no—
268C23×C5—122no—
269C23×C5—122no—
270C23×C5—121no—
271C23×C5—121no—
272C23×C5C2×D1211yescharacteristic
273C22×D5—61no—
274C5×D4—62no—
275C5×D4—62no—
276C5×D4—121no—
277C5×D4—121no—
278C2×C4×C5—22no—
279C2×C4×C5—42no—
280C2×C4×C5—62no—
281C2×C4×C5—121no—
282C2×C4×C5—121no—
283C2×C4×C5C2×C4×D311yescharacteristic
284C2×C4×C5#23511yescharacteristic
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5#23911yescharacteristic
289C22⋊D5—62no—
290C22⋊D5—62no—
291C2×Dic5—61no—
292C2×Dic5—61no—
293C2×Dic5—61no—
294D20—32no—
295D20—61no—
296C4×D5—62no—
297C4×D5—62no—
298C4×D5—242no—
299Dic10—32no—
300Dic10—61no—
301#168—22no—
302#168—41no—
303C2×#41—151no—
304C22×D4—31no—
305AGL(1,ℤ/8)—154no—
306AGL(1,ℤ/8)—302no—
307C2×SD16—301no—
308C2×D8—301no—
309C2×M16—51no—
310C2×M16—51no—
311C4×Q8—301no—
312C4×D4—301no—
313C4×D4—302no—
314#117—151no—
315#117—301no—
316C2×C4⋊C4—301no—
317C2×C4⋊C4D3×D511yescharacteristic
318C2×C22⋊C4—62no—
319C2×C42—31no—
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
328D15—42no—
329C5×D3—82no—
330C23×C3C2×C22⋊D511yescharacteristic
331C22×D3—22no—
332C22×D3—42no—
333C22×D3—42no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—101no—
337C2×C3×C4—22no—
338C2×C3×C4—42no—
339C2×C3×C4C2×C4×D511yescharacteristic
340C2×C3×C4#70911yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4#71111yescharacteristic
345#67—102no—
346#67—102no—
347C2×Dic3—22no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—101no—
351C2×Dic3—101no—
352C2×Dic3—101no—
353D12—22no—
354D12—22no—
355D12—41no—
356D12—41no—
357D12—52no—
358D12—101no—
359C4×D3—102no—
360C4×D3—102no—
361C4×D3—402no—
362Dic6—52no—
363Dic6—101no—
364C3×C8—102no—
365C3×C8—201no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—124no—
369C22×C5—122no—
370C22×C5—242no—
371C22×C5—241no—
372C22×C5—241no—
373C22×C5C4×D1211yescharacteristic
374C22×C5#88211yescharacteristic
375C22×C5#89511yescharacteristic
376C2×D5—62no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—42no—
380C4×C5—122no—
381C4×C5D3×C22⋊C411yescharacteristic
382C4×C5#88411yescharacteristic
383C4×C5#89311yescharacteristic
384C4×C5#89411yescharacteristic
385Dic5—62no—
386Dic5—121no—
387Dic5—121no—
388C24—61no—
389#41—152no—
390#41—152no—
391#41—301no—
392#41—301no—
393C2×Q8—151no—
394C2×D4—32no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—151no—
401C2×D4—301no—
402C22×C4—61no—
403C22×C4—302no—
404C22×C4—301no—
405C22×C4#120312yes—
406C22×C4C2×D3×D511yescharacteristic
407SD16—304no—
408D8—304no—
409M16—52no—
410M16—101no—
411M16—101no—
412M16—101no—
413C2×C8—101no—
414C2×C8—101no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—151no—
418C4⋊C4—151no—
419C4⋊C4—302no—
420C22⋊C4—124no—
421C22⋊C4—302no—
422C22⋊C4—301no—
423C42—61no—
424C42—61no—
425C42—302no—
426C42—301no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3C4×C22⋊D511yescharacteristic
431C22×C3#408311yescharacteristic
432C22×C3#408411yescharacteristic
433C2×D3—44no—
434C2×D3—42no—
435C2×D3—82no—
436C2×D3—81no—
437C2×D3—81no—
438C2×D3—102no—
439C2×D3—201no—
440C2×D3—201no—
441C3×C4—42no—
442C3×C4D5×C22⋊C411yescharacteristic
443C3×C4#402711yescharacteristic
444C3×C4#402911yescharacteristic
445C3×C4#403011yescharacteristic
446Dic3—42no—
447Dic3—102no—
448Dic3—201no—
449Dic3—201no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—242no—
453C2×C5#466511yescharacteristic
454C2×C5#474711yescharacteristic
455C2×C5#475311yescharacteristic
456D5—122no—
457C23—62no—
458C23—122no—
459C23—122no—
460C23—121no—
461C23—121no—
462C23—301no—
463C23C2×#120311yescharacteristic
464Q8—152no—
465Q8—301no—
466D4—62no—
467D4—62no—
468D4—121no—
469D4—121no—
470D4—152no—
471D4—302no—
472D4—302no—
473D4—301no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—62no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—301no—
480C2×C4—302no—
481C2×C4—302no—
482C2×C4—301no—
483C2×C4—301no—
484C2×C4—1202no—
485C2×C4#676811yescharacteristic
486C2×C4#677111yescharacteristic
487C2×C4C4×D3×D511yescharacteristic
488C2×C4#677711yescharacteristic
489C2×C4#679011yescharacteristic
490C2×C4#679011yescharacteristic
491C8—102no—
492C8—201no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3#6524511yescharacteristic
496C2×C3#6535111yescharacteristic
497C2×C3#6536611yescharacteristic
498D3—82no—
499D3—202no—
500C5#6900511yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—124no—
504C22—122no—
505C22—242no—
506C22—241no—
507C22—241no—
508C22—302no—
509C22—601no—
510C22—601no—
511C22C4×#120311yescharacteristic
512C22#9146611yescharacteristic
513C22#9157311yescharacteristic
514C4—42no—
515C4—122no—
516C4—302no—
517C4—601no—
518C4—601no—
519C4#9135511yescharacteristic
520C4#9140611yescharacteristic
521C4#9146111yescharacteristic
522C4#9147311yescharacteristic
523C3#1060045611yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—242no—
527C2—602no—
528C2#1174891811yescharacteristic
529C2#1174914311yescharacteristic
530C2#1174938911yescharacteristic
subgroupG/H
centerC22#91573
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC2×#91304C2
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. #11756263C2semidirect
3. C5×#4988C2semidirect
4. C2×#90980C2semidirect
5. #11748389C2semidirect
6. C3×#64750C2semidirect
7. #11745976C2semidirect
24. #91304C4semidirect
35. #64750D3semidirect
55. C2×C5×D12C2×C4semidirect
71. C3×#681C2×C4semidirect
80. #4988D5semidirect
125. D60C22⋊C4semidirect
130. Dic30C22⋊C4semidirect
196. #681C4×D3semidirect
243. C2×D12C4×D5semidirect
427. C3×C5#1883semidirect
500. C5#69005semidirect
523. C3#10600456semidirect

Maximal subgroups

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

subgroupindex
#117562632
C2×#913042
C5×#49882
C2×#909802
#117483892
C3×#647502
#117459762
#106004563
#690055