Finite Group Databasebeta

← #14417779

Subgroups — #14417779

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756263C211yesmaximal, characteristic, complemented
2#11754492C211yesmaximal, characteristic, complemented
3C2×#91303C211yesmaximal, characteristic
4C5×#4966C211yesmaximal, characteristic, complemented
5C2×C3×#3940C211yesmaximal, characteristic, complemented
6#11748413C211yesmaximal, characteristic, complemented
7#11748324C211yesmaximal, characteristic, complemented
8#11747281C212yesmaximal, complemented
9#11747279C212yesmaximal, complemented
10#11747236C212yesmaximal, complemented
11#11747234C212yesmaximal, complemented
12#10610600—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C4×#1220—22no—
17#91815C2211yescharacteristic
18#91782C2212yes—
19#91781—21no—
20C4⋊C4×D15—21no—
21#91776C2212yes—
22C2×C5×#208C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25Dic5×#67—22no—
26#91435C2212yes—
27D3×C4⋊Dic5—21no—
28#91344C2212yes—
29#91338—21no—
30C2×#6663C2211yescharacteristic
31C2×#6660C2211yescharacteristic
32C2×#6659C2211yescharacteristic
33#91303C418yescomplemented
34C2×#6654C2211yescharacteristic
35C5×#810C2212yes—
36C5×#809C2212yes—
37C3×#3940C2212yes—
38C3×#3940C2212yes—
39#90974C2212yes—
40#90968C2212yes—
41#90954C2212yes—
42#90951C2212yes—
43#79106—51nomaximal, Hall
44#66161—31no—
45C2×#4096—31no—
46#65838—31no—
47C5×#417—31no—
48#65422—31no—
49#65411—31no—
50C2×#3940D311yescharacteristic, complemented
51#65078—32no—
52#65077—32no—
53#65074—32no—
54#65047—32no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58#6817—22no—
59#6817C2×C414yescomplemented
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×C4×D15—22no—
63C2×Dic30C2311yescharacteristic
64C2×C5×#67—21no—
65C5×#235—22no—
66C5×#235C2×C414yescomplemented
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C5×Dic6C2311yescharacteristic
70C22×C3×Dic5—21no—
71C2×D3×Dic5—22no—
72C3×C5×C4⋊C4—21no—
73C3×C5×C4⋊C4C2312yes—
74#6719D412yes—
75#6714—22no—
76C4⋊Dic15D411yescharacteristic
77C4⋊Dic15D411yescharacteristic
78#6712—22no—
79C4×Dic15—22no—
80C4×Dic15C2312yes—
81C5×#208—22no—
82C2×C5×C3⋊C8C2312yes—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5C2312yes—
85C2×C3×#168C2×C414yescomplemented
86C2×C3×#168C2311yescharacteristic
87C2×C3×#168C2311yescharacteristic
88Dic3⋊Dic5—22no—
89(C2×D3)⋊Dic5—22no—
90Dic3×Dic5—22no—
91#6663C2×C414yescomplemented
92#6660C2×C414yescomplemented
93#6659C2×C414yescomplemented
94#6654C2×C414yescomplemented
95C2×#904—51no—
96#5504—51no—
97#5504—51no—
98C2×C3×#106—51no—
99#5101—51no—
100#4966—51no—
101#4966D511yescharacteristic, complemented
102#4869—52no—
103#4853—52no—
104#4852—52no—
105#4852—52no—
106C2×C5×#41—31no—
107C2×#709—31no—
108C2×C5×M16—31no—
109C2×C5×C4⋊C4C2×D311yescharacteristic
110#4096—38no—
111Q8×Dic5—32no—
112C2×#689—31no—
113C2×#688—31no—
114D4×Dic5—32no—
115D4×Dic5—62no—
116C2×#687—31no—
117C2×#686—31no—
118C4×C22⋊D5—62no—
119#4072—31no—
120#4072—61no—
121C2×C4⋊Dic5—61no—
122C2×C4⋊Dic5C2×D311yescharacteristic
123C22×#168C2×D311yescharacteristic
124#4039—32no—
125#4038—61no—
126D5×C4⋊C4—61no—
127#4033—32no—
128C5×#103—32no—
129C5×#102—32no—
130#3953—32no—
131#3948—32no—
132#3947—32no—
133C8×Dic5—32no—
134#3940C2×D312yes—
135#3940C2×D312yes—
136#2952—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C22×C5×D3—21no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—81no—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146#1220—24no—
147C2×Dic15—21no—
148C2×Dic15C2×D412yes—
149C2×Dic15C2×D412yes—
150D60—21no—
151D60C22×C412yes—
152C4×D15—24no—
153C4×D15—82no—
154Dic30—21no—
155Dic30C22×C412yes—
156C5×#67—24no—
157C2×C5×Dic3—21no—
158C5×D12—21no—
159C5×D12C22×C412yes—
160C4×C5×D3—24no—
161C5×Dic6—21no—
162C5×Dic6C22×C412yes—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—81no—
165D3×Dic5—82no—
166C3×#168C22×C412yes—
167C3×#168C22×C412yes—
168C5×C3⋊C8—22no—
169C2×#235—51no—
170C2×#235C2×D511yescharacteristic
171C22×C3×C8—51no—
172C2×C3×C4⋊C4—51no—
173C2×C3×C4⋊C4C2×D511yescharacteristic
174C4×#67—102no—
175C4×#67—102no—
176#926—51no—
177C2×#208C2×D511yescharacteristic
178C2×Dic12—51no—
179#904—58no—
180C2×D24—51no—
181C2×#204—51no—
182C2×#204—51no—
183#893—52no—
184#893—52no—
185#892—101no—
186#892—101no—
187D3×C4⋊C4—101no—
188D3×C4⋊C4—101no—
189#887—52no—
190#887—52no—
191C3×#106—52no—
192C3×#106—52no—
193#815—52no—
194C8×Dic3—52no—
195#810—52no—
196#810C2×D512yes—
197#809—52no—
198#809C2×D512yes—
199C5×#41—34no—
200C5×#41—62no—
201C2×C5×Q8—31no—
202C2×C5×D4—31no—
203C2×C5×D4—61no—
204C22×C4×C5—21no—
205C22×C4×C5—61no—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—61no—
208C22×Dic5—21no—
209C22×Dic5—62no—
210#709—34no—
211#709—62no—
212C2×D20—31no—
213C2×C4×D5—61no—
214C2×C4×D5—62no—
215C2×Dic10—31no—
216C5×M16—62no—
217C2×C5×C8—32no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4C22×D312yes—
220C22⋊Dic5—32no—
221C22⋊Dic5—62no—
222#689—34no—
223#688—34no—
224#687—34no—
225#686—34no—
226#685—62no—
227C4⋊Dic5—21no—
228C4⋊Dic5—31no—
229C4⋊Dic5—31no—
230C4⋊Dic5—62no—
231C4⋊Dic5C22×D312yes—
232#683—62no—
233C4×Dic5—32no—
234C4×Dic5—62no—
235C4×Dic5—62no—
236C2×#168C4×D314yescomplemented
237C2×#168C22×D311yescharacteristic
238C2×#168C22×D311yescharacteristic
239C2×#135—151no—
240#520—151no—
241#520—151no—
242#442—152no—
243#441—152no—
244C4×SD16—152no—
245C4×SD16—152no—
246C2×#106—51no—
247#417—31no—
248#417—151no—
249#405—151no—
250C22×C3×C5—21no—
251C22×C3×C5—21no—
252C22×C3×C5C4×D412yes—
253C22×C3×C5C22×D411yescharacteristic
254C2×D15—22no—
255C2×D15—41no—
256C2×D15—41no—
257C2×C5×D3—22no—
258C2×C5×D3—41no—
259C2×C5×D3—41no—
260C3×C4×C5—42no—
261C3×C4×C5C4×D412yes—
262C3×C4×C5C23×C411yescharacteristic
263C3×C4×C5C2×#4111yescharacteristic
264Dic15—22no—
265Dic15—22no—
266Dic15—22no—
267C3×Dic5—42no—
268C5×Dic3—22no—
269C22×C3×C4—21no—
270C22×C3×C4—101no—
271C22×C3×C4C22×D511yescharacteristic
272C2×#67—21no—
273C2×#67—101no—
274#235—22no—
275#235—54no—
276#235—102no—
277#235C4×D514yescomplemented
278C2×D12—51no—
279C2×D12C22×D511yescharacteristic
280C2×C4×D3—21no—
281C2×C4×D3—101no—
282C2×C4×D3—102no—
283C2×C4×D3—102no—
284C2×Dic6—51no—
285C2×Dic6C22×D511yescharacteristic
286C2×C3×C8—54no—
287C2×C3×C8—51no—
288C2×C3×C8—51no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—52no—
291C3×C4⋊C4—101no—
292C3×C4⋊C4C22×D512yes—
293#217—52no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—102no—
296C4⋊Dic3—51no—
297C4⋊Dic3—51no—
298Dic3⋊C4—102no—
299Dic3⋊C4—102no—
300C4×Dic3—52no—
301C4×Dic3—102no—
302C4×Dic3—102no—
303#208—22no—
304C2×C3⋊C8C22×D512yes—
305Dic12—54no—
306D24—54no—
307#204—54no—
308#204—54no—
309C23×C5—61no—
310C23×C5D3×D411yescharacteristic
311C22×D5—61no—
312C5×Q8—32no—
313C5×Q8—61no—
314C5×D4—32no—
315C5×D4—64no—
316C5×D4—61no—
317C2×C4×C5—22no—
318C2×C4×C5—61no—
319C2×C4×C5—64no—
320C2×C4×C5—81no—
321C2×C4×C5C2×C4×D312yes—
322C2×C4×C5D3×D411yescharacteristic
323C2×C4×C5#23912yes—
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—64no—
326C2×Dic5—22no—
327C2×Dic5—32no—
328C2×Dic5—32no—
329C2×Dic5—61no—
330C2×Dic5—81no—
331C2×Dic5—242no—
332D20—32no—
333D20—61no—
334C4×D5—64no—
335C4×D5—242no—
336Dic10—32no—
337Dic10—61no—
338C5×C8—62no—
339#168C2×C4×D312yes—
340#168C2×C4×D312yes—
341C2×#41—31no—
342C2×#41—151no—
343#135—158no—
344C2×Q16—151no—
345C2×SD16—151no—
346C2×SD16—151no—
347C2×D8—151no—
348C2×M16—31no—
349C22×C8—51no—
350C4×Q8—152no—
351C4×Q8—152no—
352C4×D4—152no—
353C4×D4—152no—
354C4×D4—302no—
355C4×D4—302no—
356#117—151no—
357#117—301no—
358#117—301no—
359C2×C4⋊C4—51no—
360C2×C4⋊C4—301no—
361C2×C4⋊C4—301no—
362C2×C4⋊C4D3×D511yescharacteristic
363#106—52no—
364#106—52no—
365#103—32no—
366#103—152no—
367#102—32no—
368#102—152no—
369#97—152no—
370C4×C8—152no—
371C2×C3×C5—22no—
372C2×C3×C5C2×C4×D411yescharacteristic
373C2×C3×C5#57711yescharacteristic
374C2×C3×C5#57711yescharacteristic
375D15—42no—
376C5×D3—42no—
377C23×C3D4×D511yescharacteristic
378C22×D3—21no—
379C22×D3—101no—
380C2×C3×C4—22no—
381C2×C3×C4—81no—
382C2×C3×C4—102no—
383C2×C3×C4—401no—
384C2×C3×C4C2×C4×D512yes—
385C2×C3×C4D4×D511yescharacteristic
386C2×C3×C4#71112yes—
387C2×C3×C4C23×D511yescharacteristic
388#67—24no—
389#67—104no—
390C2×Dic3—21no—
391C2×Dic3—52no—
392C2×Dic3—52no—
393C2×Dic3—101no—
394D12—21no—
395D12—52no—
396D12—101no—
397D12C2×C4×D512yes—
398C4×D3—24no—
399C4×D3—104no—
400C4×D3—402no—
401C4×D3—402no—
402Dic6—21no—
403Dic6—52no—
404Dic6—101no—
405Dic6C2×C4×D512yes—
406C3×C8—52no—
407C3×C8—52no—
408C3⋊C8—22no—
409C22×C5—21no—
410C22×C5—21no—
411C22×C5—62no—
412C22×C5—121no—
413C22×C5—121no—
414C22×C5#89312yes—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—62no—
417C2×D5—121no—
418C2×D5—121no—
419C4×C5—42no—
420C4×C5—62no—
421C4×C5#89312yes—
422C4×C5C22×C4×D311yescharacteristic
423C4×C5C2×#23911yescharacteristic
424Dic5—42no—
425Dic5—62no—
426Dic5—62no—
427Dic5—62no—
428#41—34no—
429#41—62no—
430#41—154no—
431#41—302no—
432C2×Q8—31no—
433C2×Q8—151no—
434C2×D4—31no—
435C2×D4—61no—
436C2×D4—151no—
437C2×D4—301no—
438C22×C4—21no—
439C22×C4—61no—
440C22×C4—101no—
441C22×C4—302no—
442C22×C4—302no—
443C22×C4—301no—
444C22×C4C2×D3×D511yescharacteristic
445Q16—154no—
446SD16—154no—
447SD16—154no—
448D8—154no—
449M16—62no—
450C2×C8—32no—
451C2×C8—54no—
452C2×C8—51no—
453C2×C8—51no—
454C4⋊C4—21no—
455C4⋊C4—52no—
456C4⋊C4—101no—
457C4⋊C4—151no—
458C4⋊C4—151no—
459C4⋊C4—302no—
460C4⋊C4—302no—
461C4⋊C4C2×D3×D512yes—
462C22⋊C4—152no—
463C22⋊C4—302no—
464C22⋊C4—302no—
465C42—152no—
466C42—302no—
467C42—302no—
468C3×C5#295211yescharacteristic, complemented, Hall
469C22×C3—21no—
470C22×C3—21no—
471C22×C3#402712yes—
472C22×C3C2×D4×D511yescharacteristic
473C2×D3—22no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—102no—
477C2×D3—201no—
478C2×D3—201no—
479C3×C4—42no—
480C3×C4—202no—
481C3×C4#402712yes—
482C3×C4C22×C4×D511yescharacteristic
483C3×C4C2×#71111yescharacteristic
484Dic3—22no—
485Dic3—102no—
486Dic3—102no—
487Dic3—102no—
488C2×C5—22no—
489C2×C5—122no—
490C2×C5C2×#89311yescharacteristic
491C2×C5#576211yescharacteristic
492C2×C5#576211yescharacteristic
493D5—122no—
494C23—61no—
495C23—301no—
496C23#679011yescharacteristic
497Q8—32no—
498Q8—61no—
499Q8—152no—
500Q8—301no—
501D4—32no—
502D4—64no—
503D4—61no—
504D4—152no—
505D4—304no—
506D4—301no—
507C2×C4—22no—
508C2×C4—61no—
509C2×C4—64no—
510C2×C4—81no—
511C2×C4—102no—
512C2×C4—152no—
513C2×C4—152no—
514C2×C4—301no—
515C2×C4—304no—
516C2×C4—401no—
517C2×C4—1202no—
518C2×C4—1202no—
519C2×C4#676812yes—
520C2×C4C4×D3×D512yes—
521C2×C4#679011yescharacteristic
522C2×C4C22×D3×D511yescharacteristic
523C8—52no—
524C8—52no—
525C8—62no—
526C2×C3—22no—
527C2×C3C2×#402711yescharacteristic
528C2×C3#6610911yescharacteristic
529C2×C3#6611211yescharacteristic
530D3—42no—
531D3—202no—
532C5#7910611yescharacteristic, complemented, Sylow
533C22—21no—
534C22—21no—
535C22—62no—
536C22—121no—
537C22—121no—
538C22—302no—
539C22—601no—
540C22—601no—
541C22#9140612yes—
542C22C2×#679011yescharacteristic
543C4—42no—
544C4—62no—
545C4—202no—
546C4—302no—
547C4—302no—
548C4—302no—
549C4#9140612yes—
550C4C2×#676811yescharacteristic
551C4C2×C4×D3×D511yescharacteristic
552C3#1061060011yescharacteristic, complemented, Sylow
553C2—22no—
554C2—122no—
555C2—602no—
556C2C2×#9140611yescharacteristic
557C2#1175472811yescharacteristic
558C2#1175509711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91303C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2952
LCSG ▷ 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
2. #11754492C2semidirect
4. C5×#4966C2semidirect
5. C2×C3×#3940C2semidirect
6. #11748413C2semidirect
7. #11748324C2semidirect
8. #11747281C2semidirect
9. #11747279C2semidirect
10. #11747236C2semidirect
11. #11747234C2semidirect
33. #91303C4semidirect
50. C2×#3940D3semidirect
59. #6817C2×C4semidirect
66. C5×#235C2×C4semidirect
85. C2×C3×#168C2×C4semidirect
91. #6663C2×C4semidirect
92. #6660C2×C4semidirect
93. #6659C2×C4semidirect
94. #6654C2×C4semidirect
101. #4966D5semidirect
236. C2×#168C4×D3semidirect
277. #235C4×D5semidirect
468. C3×C5#2952semidirect
532. C5#79106semidirect
552. C3#10610600semidirect

Maximal subgroups

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

subgroupindex
#117562632
#117544922
C2×#913032
C5×#49662
C2×C3×#39402
#117484132
#117483242
#117472812
#117472792
#117472362
#117472342
#106106003
#791065