Finite Group Databasebeta

← #14418151

Subgroups — #14418151

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#11753979C211yesmaximal, characteristic
2#11753953C212yesmaximal, complemented
3#11750808C211yesmaximal, characteristic, complemented
4C5×#4717C211yesmaximal, characteristic, complemented
5C3×#65006C211yesmaximal, characteristic, complemented
6#11748074C212yesmaximal, complemented
7#11748072C211yesmaximal, characteristic, complemented
8#11748070C211yesmaximal, characteristic, complemented
9#11748061C211yesmaximal, characteristic, complemented
10#11747112C212yesmaximal, complemented
11#11747107C212yesmaximal, complemented
12#10611629—31nomaximal, Hall
13#92016C2212yes—
14C2×#6705C2211yescharacteristic
15C2×#6705C2211yescharacteristic
16C42×D15C2211yescharacteristic
17C5×#904C2211yescharacteristic
18C5×#901C2212yescomplemented
19C3×#4050C2211yescharacteristic
20C3×#4047C2212yescomplemented
21#91297C2212yes—
22#91292C2212yes—
23#91288C2212yescomplemented
24#91284C2212yescomplemented
25#91280C412yescomplemented
26#91278C412yescomplemented
27#91267—22no—
28#91266—22no—
29#91258C412yescomplemented
30#91257C412yescomplemented
31D3×#676—22no—
32D5×ΓL(1,𝔽25)—22no—
33C3×C5×#97C2211yescharacteristic, complemented
34C8×Dic15C2211yescharacteristic, complemented
35C8×Dic15C2211yescharacteristic, complemented
36#91087C2211yescharacteristic, complemented
37C5×#819C2211yescharacteristic, complemented
38C5×#805C2212yescomplemented
39C3×#3951C2211yescharacteristic, complemented
40C3×#3937C2212yescomplemented
41#90992C2212yescomplemented
42#90978C2212yescomplemented
43#90976C2212yescomplemented
44#79898—51nomaximal, Hall
45#66102—31no—
46#66084—32no—
47C5×#444—31no—
48#65485—31no—
49#65433—32no—
50#65184—31no—
51#65182—31no—
52#65112—32no—
53D5×#104—32no—
54#65006D311yescharacteristic, complemented
55#64996—31no—
56C2×C4×D15—21no—
57C2×C4×D15C2311yescharacteristic
58C5×#235C2312yes—
59C3×#709C2312yes—
60#6790—22no—
61#6780—22no—
62#6777C2×C412yes—
63C4×D3×D5—22no—
64#6771—22no—
65D15⋊Q8C2×C412yes—
66#6768C2×C412yes—
67#6766C2×C412yes—
68C2×C3×C5×C8C2311yescharacteristic
69C2×C3×C5×C8C2311yescharacteristic
70C3×C42×C5C2311yescharacteristic
71C4×Dic15—21no—
72C4×Dic15C2311yescharacteristic
73C2×C3⋊#168C2311yescharacteristic
74C2×C3⋊#168C2311yescharacteristic
75#6705C2×C412yes—
76#6705C2×C412yes—
77#6705D412yes—
78#6705D412yes—
79C5×#208C2312yes—
80C5×Dic12C2×C411yescharacteristic, complemented
81C5×D24C2×C411yescharacteristic, complemented
82C5×#204C2×C412yescomplemented
83C5×ΓL(1,𝔽25)—22no—
84C5×D3×C8—22no—
85C3×#681C2312yes—
86C3×Dic20C2×C411yescharacteristic, complemented
87C3×D40C2×C411yescharacteristic, complemented
88C3×#677C2×C412yescomplemented
89C3×#676—22no—
90C3×C8×D5—22no—
91#6661C2×C412yescomplemented
92#6656C2×C412yescomplemented
93#6655C2×C412yescomplemented
94#6652C2×C412yescomplemented
95#6651—22no—
96#6650—22no—
97#6649—22no—
98#6648—22no—
99D3×#168—22no—
100D5×C3⋊C8—22no—
101#5768—51no—
102#5750—52no—
103C3×#444—51no—
104#5196—51no—
105#5144—52no—
106#4895—51no—
107#4893—51no—
108#4823—52no—
109D3×#104—52no—
110#4717D511yescharacteristic, complemented
111#4707—51no—
112D5×#41—32no—
113C5×#135—31no—
114C5×#131—32no—
115#4096—32no—
116#4094—32no—
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#4050C2×D311yescharacteristic
126#4047—62no—
127#4047C2×D312yescomplemented
128C2×#676—31no—
129C2×#676—31no—
130C2×#676—62no—
131C42×D5—31no—
132C5×#108—31no—
133C5×#104—32no—
134C5×#97C2×D311yescharacteristic, complemented
135#3969—32no—
136#3957—32no—
137#3954—32no—
138#3951C2×D311yescharacteristic, complemented
139C8×Dic5—31no—
140C8×Dic5—31no—
141#3937C2×D312yescomplemented
142#3935—31no—
143#2956—151noSylow
144C22×D15#4111yescharacteristic
145C2×D3×D5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—21no—
149C2×Dic15#4111yescharacteristic
150C4×D15—42no—
151C4×D15C22×C412yes—
152C4×D15C2×D412yes—
153C5×#67—22no—
154C5×D12C22×C412yes—
155C4×C5×D3—22no—
156C5×Dic6C22×C412yes—
157C3×C22⋊D5—22no—
158C3×D20C22×C412yes—
159C3×C4×D5—22no—
160C3×Dic10C22×C412yes—
161#1204—22no—
162#1203—22no—
163#1202—22no—
164#1201—22no—
165#1200—22no—
166D3×Dic5—22no—
167D5×Dic3—22no—
168C3×C5×C8C22×C411yescharacteristic
169C3×C5×C8C22×C411yescharacteristic
170C3×C5×C8C2×D412yes—
171C3⋊#168C22×C412yes—
172C3⋊#168C2×D411yescharacteristic
173C3⋊#168C2×D411yescharacteristic
174C3×#168—22no—
175C5×C3⋊C8—22no—
176D3×#41—52no—
177C3×#135—51no—
178C3×#131—52no—
179#950—52no—
180#948—52no—
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#904C2×D511yescharacteristic
190#901—102no—
191#901C2×D512yescomplemented
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×#97C2×D511yescharacteristic, complemented
199#837—52no—
200#825—52no—
201#822—52no—
202#819C2×D511yescharacteristic, complemented
203C8×Dic3—51no—
204C8×Dic3—51no—
205#805C2×D512yescomplemented
206#803—51no—
207C5×#41—32no—
208#713—32no—
209Q8×D5—32no—
210#711—32no—
211#711—62no—
212D4×D5—32no—
213D4×D5—62no—
214#709—62no—
215#709C22×D312yes—
216C2×C4×D5—31no—
217C2×C4×D5—62no—
218C2×C4×D5—61no—
219C5×Q16—31no—
220C5×SD16—32no—
221C5×D8—31no—
222C5×M16—32no—
223C5×M16—62no—
224C2×C5×C8—62no—
225C2×C5×C8C22×D311yescharacteristic
226C2×C5×C8C22×D311yescharacteristic
227C42×C5C22×D311yescharacteristic
228#689—32no—
229#688—32no—
230#687—32no—
231#686—32no—
232C4×Dic5—31no—
233C4×Dic5—61no—
234#681—62no—
235#681C22×D312yes—
236C2×#168—31no—
237C2×#168—31no—
238C2×#168—62no—
239Dic20C4×D311yescharacteristic, complemented
240D40C4×D311yescharacteristic, complemented
241#677C4×D312yescomplemented
242#676—22no—
243#676—32no—
244#676—32no—
245#676—32no—
246#676—32no—
247#676—62no—
248#676—62no—
249C8×D5—22no—
250C8×D5—62no—
251C8×D5—62no—
252#575—151no—
253#568—152no—
254#444—31no—
255#444—51no—
256#444—152no—
257#443—151no—
258#443—151no—
259#443—152no—
260#430—151no—
261C2×#104—152no—
262C4×M16—151no—
263C22×C3×C5C2×#4111yescharacteristic
264C2×D15—41no—
265C2×D15C4×D412yes—
266C2×C5×D3—22no—
267C2×C3×D5—22no—
268D3×D5—82no—
269C3×C4×C5—41no—
270C3×C4×C5C23×C411yescharacteristic
271C3×C4×C5C22×D411yescharacteristic
272Dic15—22no—
273Dic15C4×D412yes—
274C3×Dic5—22no—
275C5×Dic3—22no—
276C3×#41—52no—
277#239—52no—
278D3×Q8—52no—
279#237—52no—
280#237—102no—
281D3×D4—52no—
282D3×D4—102no—
283#235—102no—
284#235C22×D512yes—
285C2×C4×D3—51no—
286C2×C4×D3—102no—
287C2×C4×D3—101no—
288C3×Q16—51no—
289C3×SD16—52no—
290C3×D8—51no—
291C3×M16—52no—
292C3×M16—102no—
293C2×C3×C8—102no—
294C2×C3×C8C22×D511yescharacteristic
295C2×C3×C8C22×D511yescharacteristic
296C3×C42C22×D511yescharacteristic
297#216—52no—
298#215—52no—
299#214—52no—
300#213—52no—
301C4×Dic3—51no—
302C4×Dic3—101no—
303#208—102no—
304#208C22×D512yes—
305C2×C3⋊C8—51no—
306C2×C3⋊C8—51no—
307C2×C3⋊C8—102no—
308Dic12C4×D511yescharacteristic, complemented
309D24C4×D511yescharacteristic, complemented
310#204C4×D512yescomplemented
311ΓL(1,𝔽25)—22no—
312ΓL(1,𝔽25)—52no—
313ΓL(1,𝔽25)—52no—
314ΓL(1,𝔽25)—52no—
315ΓL(1,𝔽25)—52no—
316ΓL(1,𝔽25)—102no—
317ΓL(1,𝔽25)—102no—
318D3×C8—22no—
319D3×C8—102no—
320D3×C8—102no—
321C22×D5—31no—
322C22×D5—62no—
323C5×Q8—32no—
324C5×D4—32no—
325C5×D4—62no—
326C2×C4×C5—21no—
327C2×C4×C5—62no—
328C2×C4×C5C23×D311yescharacteristic
329C22⋊D5—22no—
330C22⋊D5—62no—
331C22⋊D5—62no—
332C2×Dic5—31no—
333C2×Dic5—62no—
334C2×Dic5—61no—
335D20—62no—
336D20C2×C4×D312yes—
337C4×D5—22no—
338C4×D5—32no—
339C4×D5—32no—
340C4×D5—62no—
341C4×D5—62no—
342C4×D5—122no—
343Dic10—62no—
344Dic10C2×C4×D312yes—
345C5×C8—62no—
346C5×C8C2×C4×D311yescharacteristic
347C5×C8C2×C4×D311yescharacteristic
348C5×C8D3×D412yes—
349#168—22no—
350#168—32no—
351#168—31no—
352#168—31no—
353C2×#41—152no—
354#137—152no—
355#137—152no—
356AGL(1,ℤ/8)—152no—
357AGL(1,ℤ/8)—152no—
358#135—31no—
359#135—51no—
360#135—152no—
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—151no—
381#97D3×D511yescharacteristic, complemented
382C4×C8—151no—
383C4×C8—151no—
384C2×C3×C5—21no—
385C2×C3×C5C2×C4×D411yescharacteristic
386D15—22no—
387C3×D5—42no—
388C5×D3—42no—
389C22×D3—51no—
390C22×D3—102no—
391C3×Q8—52no—
392C3×D4—52no—
393C3×D4—102no—
394C2×C3×C4—21no—
395C2×C3×C4—102no—
396C2×C3×C4C23×D511yescharacteristic
397#67—22no—
398#67—102no—
399#67—102no—
400C2×Dic3—51no—
401C2×Dic3—102no—
402C2×Dic3—101no—
403D12—102no—
404D12C2×C4×D512yes—
405C4×D3—22no—
406C4×D3—52no—
407C4×D3—52no—
408C4×D3—102no—
409C4×D3—102no—
410C4×D3—202no—
411Dic6—102no—
412Dic6C2×C4×D512yes—
413C3×C8—102no—
414C3×C8C2×C4×D511yescharacteristic
415C3×C8C2×C4×D511yescharacteristic
416C3×C8D4×D512yes—
417C3⋊C8—22no—
418C3⋊C8—52no—
419C3⋊C8—51no—
420C3⋊C8—51no—
421C22×C5—62no—
422C22×C5D3×#4111yescharacteristic
423C2×D5—22no—
424C2×D5—32no—
425C2×D5—121no—
426C2×D5—242no—
427C4×C5—41no—
428C4×C5—62no—
429C4×C5C22×C4×D311yescharacteristic
430C4×C5C2×D3×D411yescharacteristic
431Dic5—22no—
432Dic5—32no—
433Dic5—62no—
434#41—32no—
435#41—52no—
436#41—152no—
437#41—152no—
438#41—302no—
439#41—302no—
440C2×Q8—152no—
441C2×D4—152no—
442C2×D4—302no—
443C22×C4—151no—
444C22×C4—301no—
445C22×C4—302no—
446Q16—31no—
447Q16—51no—
448Q16—152no—
449SD16—32no—
450SD16—52no—
451SD16—152no—
452SD16—152no—
453D8—31no—
454D8—51no—
455D8—152no—
456M16—32no—
457M16—52no—
458M16—62no—
459M16—102no—
460M16—152no—
461M16—152no—
462M16—152no—
463M16—152no—
464M16—302no—
465M16—302no—
466M16—302no—
467C2×C8—62no—
468C2×C8—102no—
469C2×C8—151no—
470C2×C8—151no—
471C2×C8—302no—
472C2×C8—302no—
473C2×C8—302no—
474C2×C8C2×D3×D511yescharacteristic
475C2×C8C2×D3×D511yescharacteristic
476C42—151no—
477C42—301no—
478C42C2×D3×D511yescharacteristic
479C3×C5#295611yescharacteristic, complemented, Hall
480C22×C3—102no—
481C22×C3D5×#4111yescharacteristic
482C2×D3—22no—
483C2×D3—52no—
484C2×D3—201no—
485C2×D3—402no—
486C3×C4—41no—
487C3×C4—102no—
488C3×C4C22×C4×D511yescharacteristic
489C3×C4C2×D4×D511yescharacteristic
490Dic3—22no—
491Dic3—52no—
492Dic3—102no—
493C2×C5—21no—
494C2×C5—122no—
495C2×C5C4×D3×D411yescharacteristic
496D5—42no—
497D5—62no—
498C23—151no—
499C23—302no—
500Q8—32no—
501Q8—52no—
502Q8—302no—
503D4—32no—
504D4—52no—
505D4—62no—
506D4—102no—
507D4—302no—
508D4—302no—
509D4—302no—
510C2×C4—21no—
511C2×C4—62no—
512C2×C4—102no—
513C2×C4—151no—
514C2×C4—152no—
515C2×C4—152no—
516C2×C4—302no—
517C2×C4—302no—
518C2×C4—302no—
519C2×C4—301no—
520C2×C4—602no—
521C2×C4C22×D3×D511yescharacteristic
522C8—62no—
523C8—102no—
524C8—152no—
525C8—151no—
526C8—151no—
527C8C4×D3×D511yescharacteristic
528C8C4×D3×D511yescharacteristic
529C8#677712yes—
530C2×C3—21no—
531C2×C3—202no—
532C2×C3C4×D4×D511yescharacteristic
533D3—42no—
534D3—102no—
535C5#7989811yescharacteristic, complemented, Sylow
536C22—62no—
537C22—102no—
538C22—152no—
539C22—601no—
540C22—1202no—
541C22#9201611yescharacteristic
542C4—41no—
543C4—62no—
544C4—102no—
545C4—152no—
546C4—302no—
547C4C2×C4×D3×D511yescharacteristic
548C4C2×#677711yescharacteristic
549C3#1061162911yescharacteristic, complemented, Sylow
550C2—21no—
551C2—122no—
552C2—202no—
553C2—302no—
554C2C4×#677711yescharacteristic
subgroupG/H
centerC4C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC2×C3×C5C2×C4×D4
prime radical#11753979C2
cosocleC2×C3×C4×C5C24
hypercenter#97D3×D5
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C8 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #11753953C2semidirect
3. #11750808C2semidirect
4. C5×#4717C2semidirect
5. C3×#65006C2semidirect
6. #11748074C2semidirect
7. #11748072C2semidirect
8. #11748070C2semidirect
9. #11748061C2semidirect
10. #11747112C2semidirect
11. #11747107C2semidirect
18. C5×#901C22semidirect
20. C3×#4047C22semidirect
23. #91288C22semidirect
24. #91284C22semidirect
25. #91280C4semidirect
26. #91278C4semidirect
29. #91258C4semidirect
30. #91257C4semidirect
33. C3×C5×#97C22semidirect
34. C8×Dic15C22semidirect
35. C8×Dic15C22semidirect
36. #91087C22semidirect
37. C5×#819C22semidirect
38. C5×#805C22semidirect
39. C3×#3951C22semidirect
40. C3×#3937C22semidirect
41. #90992C22semidirect
42. #90978C22semidirect
43. #90976C22semidirect
54. #65006D3semidirect
80. C5×Dic12C2×C4semidirect
81. C5×D24C2×C4semidirect
82. C5×#204C2×C4semidirect
86. C3×Dic20C2×C4semidirect
87. C3×D40C2×C4semidirect
88. C3×#677C2×C4semidirect
91. #6661C2×C4semidirect
92. #6656C2×C4semidirect
93. #6655C2×C4semidirect
94. #6652C2×C4semidirect
110. #4717D5semidirect
127. #4047C2×D3semidirect
134. C5×#97C2×D3semidirect
138. #3951C2×D3semidirect
141. #3937C2×D3semidirect
191. #901C2×D5semidirect
198. C3×#97C2×D5semidirect
202. #819C2×D5semidirect
205. #805C2×D5semidirect
239. Dic20C4×D3semidirect
240. D40C4×D3semidirect
241. #677C4×D3semidirect
308. Dic12C4×D5semidirect
309. D24C4×D5semidirect
310. #204C4×D5semidirect
381. #97D3×D5semidirect
479. C3×C5#2956semidirect
535. C5#79898semidirect
549. C3#10611629semidirect

Maximal subgroups

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

subgroupindex
#117539792
#117539532
#117508082
C5×#47172
C3×#650062
#117480742
#117480722
#117480702
#117480612
#117471122
#117471072
#106116293
#798985