Finite Group Databasebeta

← #14418182

Subgroups — #14418182

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#11754014C212yesmaximal, complemented
2#11753959C211yesmaximal, characteristic
3#11750996C211yesmaximal, characteristic, complemented
4C5×#4894C211yesmaximal, characteristic, complemented
5C3×#65182C211yesmaximal, characteristic, complemented
6D5×#825C212yesmaximal, complemented
7#11748208C212yesmaximal, complemented
8#11748177C212yesmaximal, complemented
9#11748072C211yesmaximal, characteristic, complemented
10#11748069C211yesmaximal, characteristic, complemented
11#11747601C211yesmaximal, characteristic, complemented
12#10611629—31nomaximal, Hall
13D5×#235C2212yes—
14#91796C2212yescomplemented
15#91793C2211yescharacteristic
16C5×#907C2212yescomplemented
17C5×#904C2211yescharacteristic
18C3×D5×M16C2212yes—
19C2×C3×#676C2211yescharacteristic
20C4×D5×Dic3C2211yescharacteristic
21#91303C2212yes—
22C2×#6649C2211yescharacteristic
23#91291C2212yescomplemented
24#91288C2212yescomplemented
25#91266—22no—
26#91265—22no—
27#91261C412yescomplemented
28#91260C412yescomplemented
29#91250C412yescomplemented
30#91249C412yescomplemented
31#91246—22no—
32D3×#676—22no—
33C3×C5×#108C2211yescharacteristic, complemented
34#91109C2212yescomplemented
35C8×Dic15C2211yescharacteristic, complemented
36C5×#825C2212yescomplemented
37C5×#815C2211yescharacteristic, complemented
38C3×#3954C2212yescomplemented
39C3×#3951C2211yescharacteristic, complemented
40#90980C2212yescomplemented
41#90978C2212yescomplemented
42#90953C2211yescharacteristic, complemented
43#90951C2211yescharacteristic, complemented
44#79258—51nomaximal, Hall
45#66102—31no—
46#66084—32no—
47C5×#444—31no—
48#65485—31no—
49#65433—32no—
50#65184—31no—
51#65182D311yescharacteristic, complemented
52#65112—32no—
53D5×#104—32no—
54#65006—31no—
55#64996—31no—
56#6817C2312yes—
57C5×#235C2312yes—
58C2×C3×C4×D5C2311yescharacteristic
59D5×#67—22no—
60#6782—22no—
61C2×D5×Dic3—21no—
62D5×D12C2×C412yes—
63C4×D3×D5—22no—
64#6773C2×C412yes—
65#6772C2×C412yes—
66#6771—22no—
67D5×Dic6C2×C412yes—
68C3×C5×M16C2312yes—
69C2×C3×C5×C8C2311yescharacteristic
70C4×Dic15C2311yescharacteristic
71C2×C3⋊#168C2311yescharacteristic
72Dic60C2×C411yescharacteristic, complemented
73D120C2×C411yescharacteristic, complemented
74#6706C2×C412yescomplemented
75#6705—22no—
76C8×D15—22no—
77C4×C5×Dic3C2311yescharacteristic
78C2×C5×C3⋊C8C2311yescharacteristic
79C5×Dic12C2×C411yescharacteristic, complemented
80C5×D24C2×C411yescharacteristic, complemented
81C5×#204C2×C412yescomplemented
82C5×ΓL(1,𝔽25)—22no—
83C5×D3×C8—22no—
84C3×#681C2312yes—
85C2×C3×#168C2311yescharacteristic
86C3×#676—22no—
87C3×#676C2×C412yes—
88C3×#676C2×C412yes—
89C3×C8×D5—22no—
90Dic3×Dic5—21no—
91#6663C2×C412yescomplemented
92#6660C2×C412yescomplemented
93#6659C2×C412yescomplemented
94#6654C2×C412yescomplemented
95#6651—22no—
96#6650—22no—
97#6649D412yes—
98#6649D412yes—
99#6648—22no—
100D3×#168—22no—
101#5748—51no—
102#5745—52no—
103C3×#430—51no—
104C2×#825—52no—
105Dic3×M16—51no—
106#4895—52no—
107#4895—51no—
108#4895—51no—
109#4894—52no—
110#4894—51no—
111#4894D511yescharacteristic, complemented
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—62no—
124D5×M16C2×D312yes—
125#4050—31no—
126#4047—32no—
127#4047—62no—
128C2×#676—31no—
129C2×#676—62no—
130C2×#676C2×D311yescharacteristic
131C42×D5—31no—
132C5×#108C2×D311yescharacteristic, complemented
133C5×#104—32no—
134C5×#97—31no—
135#3969—32no—
136#3957—32no—
137#3954C2×D312yescomplemented
138#3951C2×D311yescharacteristic, complemented
139C8×Dic5—31no—
140C8×Dic5—31no—
141#3937—32no—
142#3935—31no—
143#2956—151noSylow
144C22×C3×D5#4111yescharacteristic
145C2×D3×D5—22no—
146C2×C3×C4×C5C2411yescharacteristic
147#1220—22no—
148C2×Dic15—21no—
149D60C22×C412yes—
150C4×D15—22no—
151Dic30C22×C412yes—
152C5×#67—22no—
153C2×C5×Dic3—21no—
154C5×D12C22×C412yes—
155C4×C5×D3—22no—
156C5×Dic6C22×C412yes—
157C2×C3×Dic5#4111yescharacteristic
158C3×C4×D5C22×C412yes—
159C3×C4×D5C2×D412yes—
160#1204—22no—
161#1203—22no—
162#1202—22no—
163#1201—22no—
164#1200—22no—
165D3×Dic5—22no—
166D5×Dic3—22no—
167D5×Dic3—42no—
168C3×C5×C8—22no—
169C3×C5×C8C22×C411yescharacteristic
170C3×C5×C8C22×C411yescharacteristic
171C3⋊#168C2×D411yescharacteristic
172C3⋊#168C2×D411yescharacteristic
173C3×#168—22no—
174C3×#168C22×C412yes—
175C5×C3⋊C8C2×D412yes—
176C2×#235—52no—
177C2×C3×M16—51no—
178C2×C3×M16—52no—
179C2×C4×Dic3—51no—
180C2×#208—51no—
181#909—52no—
182#909—52no—
183#908—52no—
184#908—52no—
185#907—52no—
186#907—52no—
187#907—52no—
188#907C2×D512yescomplemented
189D3×M16—102no—
190D3×M16—102no—
191#904—52no—
192#904—51no—
193#904C2×D511yescharacteristic
194#901—102no—
195#901—102no—
196C3×#108—52no—
197C3×#108—51no—
198C3×#108C2×D511yescharacteristic, complemented
199#825—52no—
200#825—52no—
201#825—52no—
202#825C2×D512yescomplemented
203#815—51no—
204#815C2×D511yescharacteristic, complemented
205C8×Dic3—51no—
206C8×Dic3—51no—
207C5×#41—32no—
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—62no—
217C2×C4×D5—61no—
218C2×C4×D5C22×D311yescharacteristic
219C5×Q16—31no—
220C5×SD16—32no—
221C5×D8—31no—
222C5×M16—62no—
223C5×M16C22×D312yes—
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—31no—
233C4×Dic5—61no—
234#681—62no—
235#681C22×D312yes—
236C2×#168—31no—
237C2×#168—62no—
238C2×#168C22×D311yescharacteristic
239Dic20—31no—
240D40—31no—
241#677—32no—
242#676—22no—
243#676—32no—
244#676—32no—
245#676—62no—
246#676—62no—
247#676C4×D312yes—
248#676C4×D312yes—
249C8×D5—22no—
250C8×D5—62no—
251C8×D5—62no—
252#575—151no—
253#568—152no—
254#444—31no—
255#444—151no—
256#444—152no—
257#443—152no—
258#443—151no—
259#443—151no—
260#430—51no—
261C2×#104—152no—
262C4×M16—151no—
263C22×C3×C5C2×#4111yescharacteristic
264C2×D15—22no—
265C2×C5×D3—22no—
266C2×C3×D5—41no—
267C2×C3×D5C4×D412yes—
268D3×D5—82no—
269C3×C4×C5C23×C411yescharacteristic
270C3×C4×C5C22×D411yescharacteristic
271Dic15—22no—
272Dic15—22no—
273C3×Dic5C4×D412yes—
274C5×Dic3—22no—
275C5×Dic3—41no—
276C22×C3×C4—51no—
277C2×#67—102no—
278C22×Dic3—101no—
279#235—52no—
280#235—52no—
281#235—52no—
282#235—102no—
283#235—102no—
284#235C22×D512yes—
285C2×D12—52no—
286C2×C4×D3—102no—
287C2×Dic6—52no—
288C3×M16—52no—
289C3×M16—52no—
290C3×M16—52no—
291C3×M16—102no—
292C3×M16C22×D512yes—
293C2×C3×C8—51no—
294C2×C3×C8—102no—
295C2×C3×C8C22×D511yescharacteristic
296C4×Dic3—51no—
297C4×Dic3—101no—
298C4×Dic3C22×D511yescharacteristic
299#208—52no—
300#208—52no—
301C2×C3⋊C8—51no—
302C2×C3⋊C8C22×D511yescharacteristic
303Dic12—52no—
304Dic12—51no—
305Dic12C4×D511yescharacteristic, complemented
306D24—52no—
307D24—51no—
308D24C4×D511yescharacteristic, complemented
309#204—52no—
310#204—52no—
311#204—52no—
312#204C4×D512yescomplemented
313ΓL(1,𝔽25)—22no—
314ΓL(1,𝔽25)—102no—
315ΓL(1,𝔽25)—102no—
316ΓL(1,𝔽25)—102no—
317D3×C8—22no—
318D3×C8—102no—
319D3×C8—102no—
320D3×C8—102no—
321C22×D5—62no—
322C22×D5#23911yescharacteristic
323C5×Q8—32no—
324C5×D4—32no—
325C5×D4—62no—
326C2×C4×C5—62no—
327C2×C4×C5—61no—
328C2×C4×C5C23×D311yescharacteristic
329C22⋊D5—62no—
330C22⋊D5—62no—
331C22⋊D5—62no—
332C2×Dic5—61no—
333C2×Dic5—62no—
334C2×Dic5#23911yescharacteristic
335D20—32no—
336D20—62no—
337C4×D5—62no—
338C4×D5—62no—
339C4×D5—62no—
340C4×D5—122no—
341C4×D5C2×C4×D312yes—
342C4×D5D3×D412yes—
343Dic10—32no—
344Dic10—62no—
345C5×C8—22no—
346C5×C8—32no—
347C5×C8C2×C4×D311yescharacteristic
348C5×C8C2×C4×D311yescharacteristic
349#168—22no—
350#168—31no—
351#168—31no—
352#168C2×C4×D312yes—
353C2×#41—152no—
354#137—152no—
355#137—152no—
356AGL(1,ℤ/8)—152no—
357AGL(1,ℤ/8)—152no—
358#135—31no—
359#135—152no—
360#135—151no—
361#131—32no—
362#131—152no—
363#131—152no—
364#131—152no—
365#131—302no—
366#131—302no—
367C2×M16—51no—
368C2×M16—52no—
369C2×M16—151no—
370C2×M16—302no—
371C2×M16—302no—
372C2×C42—151no—
373#108—52no—
374#108—51no—
375#108D3×D511yescharacteristic, complemented
376#104—32no—
377#104—152no—
378#104—152no—
379#104—152no—
380#97—31no—
381#97—151no—
382C4×C8—151no—
383C4×C8—151no—
384C2×C3×C5—21no—
385C2×C3×C5C2×C4×D411yescharacteristic
386D15—42no—
387C3×D5—22no—
388C5×D3—42no—
389C23×C3—51no—
390C22×D3—102no—
391C2×C3×C4—51no—
392C2×C3×C4—52no—
393C2×C3×C4—52no—
394C2×C3×C4C23×D511yescharacteristic
395#67—22no—
396#67—102no—
397#67—102no—
398#67—102no—
399C2×Dic3—21no—
400C2×Dic3—102no—
401C2×Dic3—101no—
402C2×Dic3—202no—
403D12—52no—
404D12—102no—
405D12C2×C4×D512yes—
406C4×D3—22no—
407C4×D3—102no—
408C4×D3—102no—
409C4×D3—102no—
410Dic6—52no—
411Dic6—102no—
412Dic6C2×C4×D512yes—
413C3×C8—22no—
414C3×C8—52no—
415C3×C8—102no—
416C3×C8C2×C4×D511yescharacteristic
417C3×C8C2×C4×D511yescharacteristic
418C3⋊C8—51no—
419C3⋊C8—51no—
420C3⋊C8D4×D512yes—
421C22×C5—62no—
422C22×C5C2×#23911yescharacteristic
423C2×D5—41no—
424C2×D5—62no—
425C2×D5—242no—
426C2×D5#89312yes—
427C4×C5—62no—
428C4×C5—121no—
429C4×C5C22×C4×D311yescharacteristic
430C4×C5C2×D3×D411yescharacteristic
431Dic5—62no—
432Dic5—62no—
433Dic5#89312yes—
434#41—32no—
435#41—152no—
436#41—152no—
437#41—152no—
438#41—302no—
439#41—302no—
440C2×Q8—152no—
441C2×D4—152no—
442C2×D4—302no—
443C22×C4—51no—
444C22×C4—302no—
445C22×C4—301no—
446Q16—31no—
447Q16—152no—
448Q16—151no—
449SD16—32no—
450SD16—152no—
451SD16—152no—
452SD16—152no—
453D8—31no—
454D8—152no—
455D8—151no—
456M16—52no—
457M16—52no—
458M16—52no—
459M16—62no—
460M16—102no—
461M16—152no—
462M16—152no—
463M16—302no—
464M16—302no—
465M16—302no—
466M16C2×D3×D512yes—
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—151no—
478C42—301no—
479C3×C5#295611yescharacteristic, complemented, Hall
480C22×C3—52no—
481C22×C3—201no—
482C22×C3D5×#4111yescharacteristic
483C2×D3—22no—
484C2×D3—102no—
485C2×D3—402no—
486C3×C4—52no—
487C3×C4C22×C4×D511yescharacteristic
488C3×C4C2×D4×D511yescharacteristic
489Dic3—22no—
490Dic3—41no—
491Dic3—102no—
492Dic3—102no—
493C2×C5—21no—
494C2×C5—122no—
495C2×C5C2×#89311yescharacteristic
496D5—22no—
497D5—122no—
498C23—51no—
499C23—302no—
500Q8—32no—
501Q8—152no—
502Q8—302no—
503D4—32no—
504D4—62no—
505D4—152no—
506D4—302no—
507D4—302no—
508D4—302no—
509D4—302no—
510C2×C4—51no—
511C2×C4—52no—
512C2×C4—52no—
513C2×C4—62no—
514C2×C4—61no—
515C2×C4—302no—
516C2×C4—302no—
517C2×C4—302no—
518C2×C4—301no—
519C2×C4—302no—
520C2×C4—602no—
521C2×C4C22×D3×D511yescharacteristic
522C8—22no—
523C8—32no—
524C8—52no—
525C8—102no—
526C8—151no—
527C8—151no—
528C8C4×D3×D511yescharacteristic
529C8C4×D3×D511yescharacteristic
530C2×C3—21no—
531C2×C3—102no—
532C2×C3C4×D4×D511yescharacteristic
533D3—42no—
534D3—202no—
535C5#7925811yescharacteristic, complemented, Sylow
536C22—52no—
537C22—62no—
538C22—201no—
539C22—302no—
540C22—1202no—
541C22D5×#23911yescharacteristic
542C4—52no—
543C4—62no—
544C4—121no—
545C4—302no—
546C4—302no—
547C4C2×C4×D3×D511yescharacteristic
548C4D3×D4×D511yescharacteristic
549C3#1061162911yescharacteristic, complemented, Sylow
550C2—21no—
551C2—102no—
552C2—122no—
553C2—602no—
554C2D5×#89311yescharacteristic
subgroupG/H
centerC4D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#108C22
socleC2×C3×C5C2×C4×D4
prime radical#11753959C2
cosocleC2×C3×C4×C5C24
hypercenter#108D3×D5
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #11754014C2semidirect
3. #11750996C2semidirect
4. C5×#4894C2semidirect
5. C3×#65182C2semidirect
6. D5×#825C2semidirect
7. #11748208C2semidirect
8. #11748177C2semidirect
9. #11748072C2semidirect
10. #11748069C2semidirect
11. #11747601C2semidirect
14. #91796C22semidirect
16. C5×#907C22semidirect
23. #91291C22semidirect
24. #91288C22semidirect
27. #91261C4semidirect
28. #91260C4semidirect
29. #91250C4semidirect
30. #91249C4semidirect
33. C3×C5×#108C22semidirect
34. #91109C22semidirect
35. C8×Dic15C22semidirect
36. C5×#825C22semidirect
37. C5×#815C22semidirect
38. C3×#3954C22semidirect
39. C3×#3951C22semidirect
40. #90980C22semidirect
41. #90978C22semidirect
42. #90953C22semidirect
43. #90951C22semidirect
51. #65182D3semidirect
72. Dic60C2×C4semidirect
73. D120C2×C4semidirect
74. #6706C2×C4semidirect
79. C5×Dic12C2×C4semidirect
80. C5×D24C2×C4semidirect
81. C5×#204C2×C4semidirect
91. #6663C2×C4semidirect
92. #6660C2×C4semidirect
93. #6659C2×C4semidirect
94. #6654C2×C4semidirect
111. #4894D5semidirect
132. C5×#108C2×D3semidirect
137. #3954C2×D3semidirect
138. #3951C2×D3semidirect
188. #907C2×D5semidirect
198. C3×#108C2×D5semidirect
202. #825C2×D5semidirect
204. #815C2×D5semidirect
305. Dic12C4×D5semidirect
308. D24C4×D5semidirect
312. #204C4×D5semidirect
375. #108D3×D5semidirect
479. C3×C5#2956semidirect
535. C5#79258semidirect
549. C3#10611629semidirect

Maximal subgroups

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

subgroupindex
#117540142
#117539592
#117509962
C5×#48942
C3×#651822
D5×#8252
#117482082
#117481772
#117480722
#117480692
#117476012
#106116293
#792585