Finite Group Databasebeta

← #14418136

Subgroups — #14418136

Order 1920.

916 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756527C211yesmaximal, characteristic
2#11755300C212yesmaximal, complemented
3C5×#5197C211yesmaximal, characteristic, complemented
4C3×#65485C211yesmaximal, characteristic, complemented
5#11749438C212yesmaximal, complemented
6#11749435C212yesmaximal, complemented
7#11749430C212yesmaximal, complemented
8#11748069C211yesmaximal, characteristic, complemented
9#11748064C211yesmaximal, characteristic, complemented
10#11748061C211yesmaximal, characteristic, complemented
11#11747592C211yesmaximal, characteristic, complemented
12#10611629—31nomaximal, Hall
13#41×D15C2212yes—
14C3×C5×#135C2211yescharacteristic
15#91839C2212yes—
16#91807C412yescomplemented
17#91804C412yescomplemented
18#91803C412yescomplemented
19#91800C412yescomplemented
20#91793C2211yescharacteristic
21C2×#6705C2211yescharacteristic
22C5×#948C2212yescomplemented
23C3×#4094C2212yescomplemented
24C4×#1200C2211yescharacteristic
25C2×#6651—22no—
26C2×#6651C2211yescharacteristic
27#91292—22no—
28#91292C2212yes—
29#91291—22no—
30#91291C2212yescomplemented
31#91290—22no—
32#91290C2212yescomplemented
33C5×#837C2212yescomplemented
34C5×#819C2211yescharacteristic, complemented
35C5×#815C2211yescharacteristic, complemented
36C3×#3969C2212yescomplemented
37C3×#3951C2211yescharacteristic, complemented
38C3×C8×Dic5C2211yescharacteristic, complemented
39#90992C2212yescomplemented
40#90981C2212yescomplemented
41#90980C2212yescomplemented
42#90953C2211yescharacteristic, complemented
43Dic5×C3⋊C8C2211yescharacteristic, complemented
44#79889—51nomaximal, Hall
45#66102—31no—
46#66084—32no—
47C5×#444—31no—
48#65485D311yescharacteristic, complemented
49#65433—32no—
50#65184—31no—
51#65182—31no—
52#65112—32no—
53D5×#104—32no—
54#65006—31no—
55#64996—31no—
56C3×C5×#41C2312yes—
57#6821C2×C412yes—
58Q8×D15C2×C412yes—
59#6819—22no—
60#6819C2×C412yes—
61D4×D15—22no—
62D4×D15C2×C412yes—
63#6817—22no—
64#6817C2312yes—
65C2×C4×D15—22no—
66C2×C4×D15C2311yescharacteristic
67C2×#1200—21no—
68C3×C5×Q16C2×C411yescharacteristic, complemented
69C3×C5×SD16C2×C412yescomplemented
70C3×C5×D8C2×C411yescharacteristic, complemented
71C2×C3×C5×C8C2311yescharacteristic
72#6718C2×C412yescomplemented
73#6717C2×C412yescomplemented
74#6716C2×C412yescomplemented
75#6715C2×C412yescomplemented
76C2×C3⋊#168C2311yescharacteristic
77Dic60C2×C411yescharacteristic, complemented
78D120C2×C411yescharacteristic, complemented
79#6706C2×C412yescomplemented
80#6705C2×C412yes—
81#6705C2×C412yes—
82C4×C5×Dic3C2311yescharacteristic
83C5×#208—22no—
84C5×#208C2312yes—
85C2×C5×C3⋊C8—22no—
86C2×C5×C3⋊C8C2311yescharacteristic
87C3×C4×Dic5C2311yescharacteristic
88C3×#681—22no—
89C3×#681C2312yes—
90C2×C3×#168—22no—
91C2×C3×#168C2311yescharacteristic
92Dic3×Dic5—21no—
93#6651—22no—
94#6651—22no—
95#6651—22no—
96#6651D412yes—
97#6651D412yes—
98#6648—22no—
99#6648—22no—
100#6648—22no—
101#5768—51no—
102#5750—52no—
103C3×#443—51no—
104#5197D511yescharacteristic, complemented
105#5145—52no—
106#4894—51no—
107#4893—51no—
108#4824—52no—
109D3×#104—52no—
110#4700—51no—
111C4×ΓL(1,𝔽25)—51no—
112D5×#41—32no—
113C5×#135C2×D311yescharacteristic
114C5×#131—32no—
115#4096—32no—
116#4094C2×D312yescomplemented
117#4064—32no—
118#4061—32no—
119#4060—32no—
120#4057—32no—
121#4053—32no—
122#4053—62no—
123D5×M16—32no—
124D5×M16—62no—
125#4050—31no—
126#4047—32no—
127#4047—62no—
128C2×#676—31no—
129C2×#676—31no—
130C2×#676—62no—
131C42×D5—31no—
132C5×#108—31no—
133C5×#104—32no—
134C5×#97—31no—
135#3969C2×D312yescomplemented
136#3957—32no—
137#3954—32no—
138#3951C2×D311yescharacteristic, complemented
139C8×Dic5—31no—
140C8×Dic5C2×D311yescharacteristic, complemented
141#3937—32no—
142#3935—31no—
143#2956—151noSylow
144C22×D15—22no—
145C22×D15#4111yescharacteristic
146C3×C5×Q8C22×C412yes—
147C3×C5×D4—22no—
148C3×C5×D4C22×C412yes—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C2411yescharacteristic
151#1220—22no—
152#1220—22no—
153#1220—22no—
154C2×Dic15—22no—
155C2×Dic15#4111yescharacteristic
156D60—22no—
157D60C22×C412yes—
158C4×D15—22no—
159C4×D15—22no—
160C4×D15—22no—
161C4×D15C22×C412yes—
162C4×D15C2×D412yes—
163Dic30—22no—
164Dic30C22×C412yes—
165C2×C5×Dic3—21no—
166C2×C3×Dic5—21no—
167#1200—42no—
168C3×C5×C8C22×C411yescharacteristic
169C3×C5×C8C22×C411yescharacteristic
170C3⋊#168C22×C412yes—
171C3×#168—22no—
172C3×#168C2×D411yescharacteristic
173C3×#168C2×D411yescharacteristic
174C5×C3⋊C8—22no—
175C5×C3⋊C8C2×D412yes—
176D3×#41—52no—
177C3×#135C2×D511yescharacteristic
178C3×#131—52no—
179#950—52no—
180#948C2×D512yescomplemented
181#918—52no—
182#915—52no—
183#914—52no—
184#911—52no—
185#907—52no—
186#907—102no—
187D3×M16—52no—
188D3×M16—102no—
189#904—51no—
190#901—52no—
191#901—102no—
192C2×ΓL(1,𝔽25)—51no—
193C2×ΓL(1,𝔽25)—51no—
194C2×ΓL(1,𝔽25)—102no—
195C42×D3—51no—
196C3×#108—51no—
197C3×#104—52no—
198C3×C4×C8—51no—
199#837C2×D512yescomplemented
200#825—52no—
201#822—52no—
202#819C2×D511yescharacteristic, complemented
203#815—51no—
204#815C2×D511yescharacteristic, complemented
205#805—52no—
206C4×C3⋊C8—51no—
207C5×#41C22×D312yes—
208#713—32no—
209Q8×D5—32no—
210#711—32no—
211#711—62no—
212D4×D5—32no—
213D4×D5—62no—
214#709—32no—
215#709—62no—
216C2×C4×D5—31no—
217C2×C4×D5—62no—
218C2×C4×D5—61no—
219C5×Q16C4×D311yescharacteristic, complemented
220C5×SD16C4×D312yescomplemented
221C5×D8C4×D311yescharacteristic, complemented
222C5×M16—32no—
223C5×M16—62no—
224C2×C5×C8—31no—
225C2×C5×C8—62no—
226C2×C5×C8C22×D311yescharacteristic
227C42×C5—31no—
228#689—32no—
229#688—32no—
230#687—32no—
231#686—32no—
232C4×Dic5—61no—
233C4×Dic5C22×D311yescharacteristic
234#681—22no—
235#681C22×D312yes—
236C2×#168—22no—
237C2×#168—31no—
238C2×#168C22×D311yescharacteristic
239Dic20—31no—
240D40—31no—
241#677—32no—
242#676—32no—
243#676—32no—
244#676—32no—
245#676—32no—
246#676—62no—
247#676—62no—
248#676—62no—
249C8×D5—62no—
250C8×D5—62no—
251C8×D5—62no—
252#575—151no—
253#568—152no—
254#444—31no—
255#444—151no—
256#444—152no—
257#443—51no—
258#443—151no—
259#443—152no—
260#430—151no—
261C2×#104—152no—
262C4×M16—151no—
263C22×C3×C5—22no—
264C22×C3×C5C2×#4111yescharacteristic
265C2×D15—22no—
266C2×D15—41no—
267C2×D15—82no—
268C2×D15C4×D412yes—
269C3×C4×C5—22no—
270C3×C4×C5C23×C411yescharacteristic
271C3×C4×C5C22×D411yescharacteristic
272Dic15—22no—
273Dic15C4×D412yes—
274C3×Dic5—22no—
275C5×Dic3—41no—
276C3×#41C22×D512yes—
277#239—52no—
278D3×Q8—52no—
279#237—52no—
280#237—102no—
281D3×D4—52no—
282D3×D4—102no—
283#235—52no—
284#235—102no—
285C2×C4×D3—51no—
286C2×C4×D3—102no—
287C2×C4×D3—101no—
288C3×Q16C4×D511yescharacteristic, complemented
289C3×SD16C4×D512yescomplemented
290C3×D8C4×D511yescharacteristic, complemented
291C3×M16—52no—
292C3×M16—102no—
293C2×C3×C8—51no—
294C2×C3×C8—102no—
295C2×C3×C8C22×D511yescharacteristic
296C3×C42—51no—
297#216—52no—
298#215—52no—
299#214—52no—
300#213—52no—
301C4×Dic3—101no—
302C4×Dic3C22×D511yescharacteristic
303#208—22no—
304#208C22×D512yes—
305C2×C3⋊C8—22no—
306C2×C3⋊C8—51no—
307C2×C3⋊C8C22×D511yescharacteristic
308Dic12—51no—
309D24—51no—
310#204—52no—
311ΓL(1,𝔽25)—52no—
312ΓL(1,𝔽25)—52no—
313ΓL(1,𝔽25)—52no—
314ΓL(1,𝔽25)—52no—
315ΓL(1,𝔽25)—102no—
316ΓL(1,𝔽25)—102no—
317ΓL(1,𝔽25)—102no—
318D3×C8—102no—
319D3×C8—102no—
320D3×C8—102no—
321C22×D5—31no—
322C22×D5—62no—
323C5×Q8C2×C4×D312yes—
324C5×D4—22no—
325C5×D4C2×C4×D312yes—
326C2×C4×C5—22no—
327C2×C4×C5—61no—
328C2×C4×C5C23×D311yescharacteristic
329C22⋊D5—62no—
330C22⋊D5—62no—
331C22⋊D5—62no—
332C2×Dic5—21no—
333C2×Dic5—31no—
334C2×Dic5—62no—
335D20—32no—
336D20—62no—
337C4×D5—32no—
338C4×D5—32no—
339C4×D5—62no—
340C4×D5—62no—
341C4×D5—62no—
342C4×D5—122no—
343Dic10—32no—
344Dic10—62no—
345C5×C8—32no—
346C5×C8—62no—
347C5×C8C2×C4×D311yescharacteristic
348C5×C8C2×C4×D311yescharacteristic
349#168—22no—
350#168—32no—
351#168D3×D411yescharacteristic
352#168D3×D411yescharacteristic
353C2×#41—152no—
354#137—152no—
355#137—152no—
356AGL(1,ℤ/8)—152no—
357AGL(1,ℤ/8)—152no—
358#135—152no—
359#135—151no—
360#135D3×D511yescharacteristic
361#131—32no—
362#131—52no—
363#131—152no—
364#131—152no—
365#131—302no—
366#131—302no—
367C2×M16—151no—
368C2×M16—151no—
369C2×M16—152no—
370C2×M16—302no—
371C2×M16—302no—
372C2×C42—151no—
373#108—31no—
374#108—51no—
375#108—152no—
376#104—32no—
377#104—52no—
378#104—152no—
379#104—152no—
380#97—31no—
381#97—151no—
382C4×C8—51no—
383C4×C8—151no—
384C2×C3×C5—21no—
385C2×C3×C5—42no—
386C2×C3×C5C2×C4×D411yescharacteristic
387D15—22no—
388D15—42no—
389C22×D3—51no—
390C22×D3—102no—
391C3×Q8C2×C4×D512yes—
392C3×D4—22no—
393C3×D4C2×C4×D512yes—
394C2×C3×C4—22no—
395C2×C3×C4—101no—
396C2×C3×C4C23×D511yescharacteristic
397#67—102no—
398#67—102no—
399#67—102no—
400C2×Dic3—21no—
401C2×Dic3—51no—
402C2×Dic3—102no—
403D12—52no—
404D12—102no—
405C4×D3—52no—
406C4×D3—52no—
407C4×D3—102no—
408C4×D3—102no—
409C4×D3—102no—
410C4×D3—202no—
411Dic6—52no—
412Dic6—102no—
413C3×C8—51no—
414C3×C8—51no—
415C3×C8—102no—
416C3×C8C2×C4×D511yescharacteristic
417C3×C8C2×C4×D511yescharacteristic
418C3⋊C8—22no—
419C3⋊C8—52no—
420C3⋊C8D4×D512yes—
421C22×C5—22no—
422C22×C5D3×#4111yescharacteristic
423C2×D5—32no—
424C2×D5—62no—
425C2×D5—121no—
426C2×D5—242no—
427C4×C5—22no—
428C4×C5—121no—
429C4×C5C22×C4×D311yescharacteristic
430C4×C5C2×D3×D411yescharacteristic
431Dic5—22no—
432Dic5—32no—
433Dic5—62no—
434#41—152no—
435#41—152no—
436#41—152no—
437#41—302no—
438#41—302no—
439#41C2×D3×D512yes—
440C2×Q8—152no—
441C2×D4—152no—
442C2×D4—302no—
443C22×C4—151no—
444C22×C4—302no—
445C22×C4—301no—
446Q16—152no—
447Q16—151no—
448Q16#120011yescharacteristic, complemented
449SD16—152no—
450SD16—152no—
451SD16—152no—
452SD16#120012yescomplemented
453D8—152no—
454D8—151no—
455D8#120011yescharacteristic, complemented
456M16—32no—
457M16—52no—
458M16—62no—
459M16—102no—
460M16—152no—
461M16—152no—
462M16—152no—
463M16—152no—
464M16—302no—
465M16—302no—
466M16—302no—
467C2×C8—31no—
468C2×C8—51no—
469C2×C8—62no—
470C2×C8—102no—
471C2×C8—151no—
472C2×C8—302no—
473C2×C8—302no—
474C2×C8—302no—
475C2×C8C2×D3×D511yescharacteristic
476C42—31no—
477C42—51no—
478C42—301no—
479C3×C5#295611yescharacteristic, complemented, Hall
480C22×C3—22no—
481C22×C3D5×#4111yescharacteristic
482C2×D3—52no—
483C2×D3—102no—
484C2×D3—201no—
485C2×D3—402no—
486C3×C4—22no—
487C3×C4—102no—
488C3×C4C22×C4×D511yescharacteristic
489C3×C4C2×D4×D511yescharacteristic
490Dic3—41no—
491Dic3—52no—
492Dic3—102no—
493C2×C5—21no—
494C2×C5—42no—
495C2×C5C4×D3×D411yescharacteristic
496D5—62no—
497D5—122no—
498C23—151no—
499C23—302no—
500Q8—152no—
501Q8—302no—
502Q8C2×#120012yes—
503D4—22no—
504D4—152no—
505D4—302no—
506D4—302no—
507D4—302no—
508D4—302no—
509D4C2×#120012yes—
510C2×C4—22no—
511C2×C4—61no—
512C2×C4—101no—
513C2×C4—151no—
514C2×C4—152no—
515C2×C4—152no—
516C2×C4—302no—
517C2×C4—302no—
518C2×C4—302no—
519C2×C4—302no—
520C2×C4—602no—
521C2×C4C22×D3×D511yescharacteristic
522C8—32no—
523C8—51no—
524C8—51no—
525C8—62no—
526C8—102no—
527C8—152no—
528C8C2×#120011yescharacteristic
529C8C2×#120011yescharacteristic
530C2×C3—21no—
531C2×C3—42no—
532C2×C3C4×D4×D511yescharacteristic
533D3—102no—
534D3—202no—
535C5#7988911yescharacteristic, complemented, Sylow
536C22—22no—
537C22—152no—
538C22—302no—
539C22—601no—
540C22—1202no—
541C22#9202411yescharacteristic
542C4—22no—
543C4—102no—
544C4—121no—
545C4—152no—
546C4—302no—
547C4D3×D4×D511yescharacteristic
548C4C22×#120011yescharacteristic
549C3#1061162911yescharacteristic, complemented, Sylow
550C2—21no—
551C2—42no—
552C2—302no—
553C2—602no—
554C2D4×#120011yescharacteristic
subgroupG/H
centerC4D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#135C22
socleC2×C3×C5C2×C4×D4
prime radical#11756527C2
cosocleC2×C3×C4×C5C24
hypercenter#135D3×D5
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
2. #11755300C2semidirect
3. C5×#5197C2semidirect
4. C3×#65485C2semidirect
5. #11749438C2semidirect
6. #11749435C2semidirect
7. #11749430C2semidirect
8. #11748069C2semidirect
9. #11748064C2semidirect
10. #11748061C2semidirect
11. #11747592C2semidirect
16. #91807C4semidirect
17. #91804C4semidirect
18. #91803C4semidirect
19. #91800C4semidirect
22. C5×#948C22semidirect
23. C3×#4094C22semidirect
30. #91291C22semidirect
32. #91290C22semidirect
33. C5×#837C22semidirect
34. C5×#819C22semidirect
35. C5×#815C22semidirect
36. C3×#3969C22semidirect
37. C3×#3951C22semidirect
38. C3×C8×Dic5C22semidirect
39. #90992C22semidirect
40. #90981C22semidirect
41. #90980C22semidirect
42. #90953C22semidirect
43. Dic5×C3⋊C8C22semidirect
48. #65485D3semidirect
68. C3×C5×Q16C2×C4semidirect
69. C3×C5×SD16C2×C4semidirect
70. C3×C5×D8C2×C4semidirect
72. #6718C2×C4semidirect
73. #6717C2×C4semidirect
74. #6716C2×C4semidirect
75. #6715C2×C4semidirect
77. Dic60C2×C4semidirect
78. D120C2×C4semidirect
79. #6706C2×C4semidirect
104. #5197D5semidirect
116. #4094C2×D3semidirect
135. #3969C2×D3semidirect
138. #3951C2×D3semidirect
140. C8×Dic5C2×D3semidirect
180. #948C2×D5semidirect
199. #837C2×D5semidirect
202. #819C2×D5semidirect
204. #815C2×D5semidirect
219. C5×Q16C4×D3semidirect
220. C5×SD16C4×D3semidirect
221. C5×D8C4×D3semidirect
288. C3×Q16C4×D5semidirect
289. C3×SD16C4×D5semidirect
290. C3×D8C4×D5semidirect
448. Q16#1200semidirect
452. SD16#1200semidirect
455. D8#1200semidirect
479. C3×C5#2956semidirect
535. C5#79889semidirect
549. C3#10611629semidirect

Maximal subgroups

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

subgroupindex
#117565272
#117553002
C5×#51972
C3×#654852
#117494382
#117494352
#117494302
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