Finite Group Databasebeta

← #14413511

Subgroups — #14413511

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91265C211yesmaximal, characteristic
2#11753667C212yesmaximal
3#11750981C211yesmaximal, characteristic, complemented
4C5×D3×#107C211yesmaximal, characteristic, complemented
5C3×D5×#107C211yesmaximal, characteristic, complemented
6#11747682C211yesmaximal, characteristic, complemented
7#11747672C211yesmaximal, characteristic, complemented
8#11747636C211yesmaximal, characteristic, complemented
9#11747456C212yesmaximal, complemented
10#11747454C212yesmaximal, complemented
11#11747452C212yesmaximal, complemented
12#10610877—31nomaximal, Hall
13C2×#6771C2211yescharacteristic
14C2×C8×D15C2211yescharacteristic
15#91781C2212yes—
16C2×C5×D3×C8C2211yescharacteristic
17C5×D3×C4⋊C4C2212yes—
18C2×C3×C8×D5C2211yescharacteristic
19C3×D5×C4⋊C4C2212yes—
20#91446—22no—
21#91444—22no—
22C4×#1201—22no—
23#91437C2212yes—
24#91358C2212yes—
25#91338C2212yes—
26#91325—22no—
27C2×#6651C2211yescharacteristic
28C2×#6650C2211yescharacteristic
29C2×#6649C2211yescharacteristic
30#91265C418yescomplemented
31C3×C5×#107C2211yescharacteristic
32#91102C2211yescharacteristic
33#91092C2212yes—
34C5×#818C2211yescharacteristic
35C5×#807C2212yes—
36C3×#3950C2211yescharacteristic
37C3×#3939C2212yes—
38#90989C2212yes—
39#90987C2212yes—
40#90985C2212yes—
41#79146—51nomaximal, Hall
42C2×#4047—31no—
43#65838—32no—
44C2×C5×#107—31no—
45#65395—31no—
46#65253—32no—
47#65170—32no—
48#65170—32no—
49#65169—31no—
50#65169—31no—
51D5×#107—31no—
52D5×#107D311yescharacteristic, complemented
53C2×C4×D15C2311yescharacteristic
54C2×C4×C5×D3—22no—
55C2×C4×C5×D3C2311yescharacteristic
56C2×C3×C4×D5—22no—
57C2×C3×C4×D5C2311yescharacteristic
58C2×#1204D411yescharacteristic
59C2×#1203D411yescharacteristic
60C2×#1202D411yescharacteristic
61C2×#1201D411yescharacteristic
62C2×#1200—22no—
63#6771C2×C414yes—
64#6771Q814yes—
65C2×C3×C5×C8C2311yescharacteristic
66C3×C5×C4⋊C4C2312yes—
67#6714—22no—
68C4⋊Dic15C2312yes—
69C4×Dic15—22no—
70C2×C3⋊#168C2311yescharacteristic
71C8×D15C2×C414yescomplemented
72C5×C4⋊Dic3C2312yes—
73C5×Dic3⋊C4—22no—
74C2×C5×C3⋊C8C2311yescharacteristic
75C5×D3×C8C2×C414yescomplemented
76C3×C4⋊Dic5C2312yes—
77C3×#683—22no—
78C2×C3×#168C2311yescharacteristic
79C3×C8×D5C2×C414yescomplemented
80#6669—22no—
81(C2×D3)⋊Dic5—22no—
82#6665—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6651C2×C414yescomplemented
86#6650C2×C414yescomplemented
87#6649C2×C414yescomplemented
88C2×#901—51no—
89#5504—52no—
90C2×C3×#107—51no—
91#5106—51no—
92#4964—52no—
93#4881—52no—
94#4881—52no—
95#4880—51no—
96#4880—51no—
97D3×#107—51no—
98D3×#107D511yescharacteristic, complemented
99C2×#709—31no—
100C22×C5×C8—31no—
101C2×C5×C4⋊C4—32no—
102C4×C22⋊D5—62no—
103C4×C22⋊D5—62no—
104#4072—32no—
105C2×#681—31no—
106#4047—38no—
107C2×#676—31no—
108C2×#676—31no—
109C2×C8×D5—31no—
110C2×C8×D5C2×D311yescharacteristic
111#4039—62no—
112#4038—32no—
113#4038—32no—
114D5×C4⋊C4—32no—
115D5×C4⋊C4C2×D312yes—
116#4033—62no—
117C5×#107—31no—
118C5×#107—32no—
119C5×#107C2×D311yescharacteristic
120#3950—31no—
121#3950C2×D311yescharacteristic
122#3949—32no—
123#3940—32no—
124#3940—32no—
125#3939—32no—
126#3939C2×D312yes—
127#2913—151noSylow
128C22×D15C2×D411yescharacteristic
129C22×C5×D3C2×D411yescharacteristic
130C22×C3×D5C2×D411yescharacteristic
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15—22no—
134C2×Dic15C2×D411yescharacteristic
135C4×D15C22×C412yes—
136C4×D15C2×Q812yes—
137C2×C5×Dic3—22no—
138C2×C5×Dic3C2×D411yescharacteristic
139C4×C5×D3—82no—
140C4×C5×D3C22×C412yes—
141C4×C5×D3C2×Q812yes—
142C2×C3×Dic5—22no—
143C2×C3×Dic5C2×D411yescharacteristic
144C3×C4×D5—82no—
145C3×C4×D5C22×C412yes—
146C3×C4×D5C2×Q812yes—
147#1204C4⋊C414yes—
148#1203C4⋊C414yes—
149#1202C4⋊C414yes—
150#1201C4⋊C414yes—
151#1200—82no—
152C3×C5×C8C22×C412yes—
153C3⋊#168C22×C412yes—
154C3×#168C22×C412yes—
155C5×C3⋊C8C22×C412yes—
156C2×#235—51no—
157C22×C3×C8—51no—
158C2×C3×C4⋊C4—52no—
159C4×#67—102no—
160C4×#67—102no—
161#926—52no—
162C2×#208—51no—
163#901—58no—
164C2×ΓL(1,𝔽25)—51no—
165C2×ΓL(1,𝔽25)—51no—
166C2×D3×C8—51no—
167C2×D3×C8C2×D511yescharacteristic
168#893—102no—
169#892—52no—
170#892—52no—
171D3×C4⋊C4—52no—
172D3×C4⋊C4C2×D512yes—
173#887—102no—
174C3×#107—51no—
175C3×#107—52no—
176C3×#107C2×D511yescharacteristic
177#818—51no—
178#818C2×D511yescharacteristic
179#817—52no—
180#808—52no—
181#808—52no—
182#807—52no—
183#807C2×D512yes—
184C22×C4×C5—31no—
185C22×C4×C5—62no—
186C2×C22⋊D5—31no—
187C2×C22⋊D5—31no—
188#709—34no—
189#709—34no—
190C2×D20—31no—
191C2×C4×D5—22no—
192C2×C4×D5—31no—
193C2×C4×D5—62no—
194C2×C4×D5C22×D311yescharacteristic
195C2×Dic10—31no—
196C2×C5×C8—31no—
197C2×C5×C8—34no—
198C2×C5×C8C22×D311yescharacteristic
199C5×C4⋊C4—32no—
200C5×C4⋊C4—62no—
201C5×C4⋊C4C22×D312yes—
202C22⋊Dic5—62no—
203#685—62no—
204#685—62no—
205C4⋊Dic5—32no—
206C4⋊Dic5C22×D312yes—
207#683—22no—
208#683—62no—
209C4×Dic5—62no—
210C4×Dic5—62no—
211C4×Dic5—62no—
212#681—34no—
213C2×#168—31no—
214C2×#168C22×D311yescharacteristic
215#676—34no—
216#676—34no—
217C8×D5—34no—
218C8×D5C4×D314yescomplemented
219C2×#131—151no—
220#520—152no—
221#428—152no—
222#428—152no—
223#428—152no—
224#427—151no—
225#427—151no—
226#427—151no—
227C2×#107—31no—
228C2×#107—51no—
229C2×#107—151no—
230C22×C3×C5C22×D411yescharacteristic
231C2×D15—21no—
232C2×D15—21no—
233C2×D15C2×C4⋊C412yes—
234C2×C5×D3—21no—
235C2×C5×D3—21no—
236C2×C5×D3C2×C4⋊C412yes—
237C2×C3×D5—21no—
238C2×C3×D5—21no—
239C2×C3×D5C2×C4⋊C412yes—
240C3×C4×C5—42no—
241C3×C4×C5C23×C411yescharacteristic
242C3×C4×C5C22×Q811yescharacteristic
243Dic15—42no—
244Dic15C2×C4⋊C412yes—
245C3×Dic5—42no—
246C3×Dic5C2×C4⋊C412yes—
247C5×Dic3—42no—
248C5×Dic3C2×C4⋊C412yes—
249C22×C3×C4—51no—
250C22×C3×C4—102no—
251C2×#67—51no—
252C2×#67—51no—
253#235—54no—
254#235—54no—
255C2×D12—51no—
256C2×C4×D3—22no—
257C2×C4×D3—51no—
258C2×C4×D3—102no—
259C2×C4×D3C22×D511yescharacteristic
260C2×Dic6—51no—
261C2×C3×C8—51no—
262C2×C3×C8—54no—
263C2×C3×C8C22×D511yescharacteristic
264C3×C4⋊C4—52no—
265C3×C4⋊C4—102no—
266C3×C4⋊C4C22×D512yes—
267#217—102no—
268(C2×D3)⋊C4—102no—
269(C2×D3)⋊C4—102no—
270C4⋊Dic3—52no—
271C4⋊Dic3C22×D512yes—
272Dic3⋊C4—22no—
273Dic3⋊C4—102no—
274C4×Dic3—102no—
275C4×Dic3—102no—
276C4×Dic3—102no—
277#208—54no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8C22×D511yescharacteristic
280ΓL(1,𝔽25)—54no—
281ΓL(1,𝔽25)—54no—
282D3×C8—54no—
283D3×C8C4×D514yescomplemented
284C23×C5—31no—
285C22×D5—31no—
286C22×D5D3×D411yescharacteristic
287C2×C4×C5—22no—
288C2×C4×C5—31no—
289C2×C4×C5—32no—
290C2×C4×C5—32no—
291C2×C4×C5—62no—
292C2×C4×C5—242no—
293C2×C4×C5C23×D311yescharacteristic
294C22⋊D5—34no—
295C22⋊D5—34no—
296C2×Dic5—22no—
297C2×Dic5—31no—
298C2×Dic5—62no—
299C2×Dic5D3×D411yescharacteristic
300D20—34no—
301C4×D5—32no—
302C4×D5—32no—
303C4×D5—82no—
304C4×D5—242no—
305C4×D5C2×C4×D312yes—
306C4×D5D3×Q812yes—
307Dic10—34no—
308C5×C8—32no—
309C5×C8C2×C4×D312yes—
310#168—32no—
311#168C2×C4×D312yes—
312C2×#41—151no—
313#131—158no—
314C2×M16—151no—
315C2×M16—151no—
316C2×M16—151no—
317C22×C8—31no—
318C22×C8—51no—
319C22×C8—151no—
320C4×Q8—302no—
321C4×D4—302no—
322C4×D4—302no—
323C4×D4—302no—
324#117—152no—
325#117—152no—
326#117—152no—
327C2×C4⋊C4—32no—
328C2×C4⋊C4—52no—
329C2×C4⋊C4—152no—
330#107—31no—
331#107—32no—
332#107—51no—
333#107—52no—
334#107—152no—
335#107—151no—
336#107D3×D511yescharacteristic
337#106—152no—
338#106—152no—
339#106—152no—
340C2×C3×C5C22×C4⋊C411yescharacteristic
341C2×C3×C5#57611yescharacteristic
342C2×C3×C5#57811yescharacteristic
343D15—22no—
344C3×D5—22no—
345C5×D3—22no—
346C23×C3—51no—
347C22×D3—51no—
348C22×D3D4×D511yescharacteristic
349C2×C3×C4—22no—
350C2×C3×C4—51no—
351C2×C3×C4—52no—
352C2×C3×C4—52no—
353C2×C3×C4—102no—
354C2×C3×C4—402no—
355C2×C3×C4C23×D511yescharacteristic
356#67—54no—
357#67—54no—
358C2×Dic3—22no—
359C2×Dic3—51no—
360C2×Dic3—102no—
361C2×Dic3D4×D511yescharacteristic
362D12—54no—
363C4×D3—52no—
364C4×D3—52no—
365C4×D3—82no—
366C4×D3—402no—
367C4×D3C2×C4×D512yes—
368C4×D3Q8×D512yes—
369Dic6—54no—
370C3×C8—52no—
371C3×C8C2×C4×D512yes—
372C3⋊C8—52no—
373C3⋊C8C2×C4×D512yes—
374C22×C5—32no—
375C22×C5—61no—
376C22×C5—61no—
377C22×C5C2×D3×D411yescharacteristic
378C2×D5—21no—
379C2×D5—21no—
380C2×D5—32no—
381C2×D5—61no—
382C2×D5—61no—
383C2×D5D3×C4⋊C412yes—
384C4×C5—32no—
385C4×C5—42no—
386C4×C5—122no—
387C4×C5C22×C4×D311yescharacteristic
388C4×C5C2×D3×Q811yescharacteristic
389Dic5—32no—
390Dic5—42no—
391Dic5—122no—
392Dic5D3×C4⋊C412yes—
393#41—154no—
394#41—154no—
395C2×Q8—151no—
396C2×D4—151no—
397C2×D4—151no—
398C2×D4—151no—
399C22×C4—31no—
400C22×C4—51no—
401C22×C4—62no—
402C22×C4—102no—
403C22×C4—151no—
404C22×C4—302no—
405M16—154no—
406M16—154no—
407M16—154no—
408C2×C8—31no—
409C2×C8—34no—
410C2×C8—51no—
411C2×C8—54no—
412C2×C8—151no—
413C2×C8—154no—
414C2×C8C2×D3×D511yescharacteristic
415C4⋊C4—32no—
416C4⋊C4—52no—
417C4⋊C4—62no—
418C4⋊C4—102no—
419C4⋊C4—152no—
420C4⋊C4—302no—
421C4⋊C4C2×D3×D512yes—
422C22⋊C4—302no—
423C22⋊C4—302no—
424C22⋊C4—302no—
425C42—302no—
426C42—302no—
427C42—302no—
428C3×C5#291311yescharacteristic, complemented, Hall
429C22×C3—52no—
430C22×C3—101no—
431C22×C3—101no—
432C22×C3C2×D4×D511yescharacteristic
433C2×D3—21no—
434C2×D3—21no—
435C2×D3—52no—
436C2×D3—101no—
437C2×D3—101no—
438C2×D3D5×C4⋊C412yes—
439C3×C4—42no—
440C3×C4—52no—
441C3×C4—202no—
442C3×C4C22×C4×D511yescharacteristic
443C3×C4C2×Q8×D511yescharacteristic
444Dic3—42no—
445Dic3—52no—
446Dic3—202no—
447Dic3D5×C4⋊C412yes—
448C2×C5—62no—
449C2×C5C2×D3×C4⋊C411yescharacteristic
450C2×C5#575711yescharacteristic
451C2×C5#576611yescharacteristic
452D5—22no—
453D5—62no—
454C23—31no—
455C23—51no—
456C23—151no—
457Q8—154no—
458D4—154no—
459D4—154no—
460D4—154no—
461C2×C4—22no—
462C2×C4—31no—
463C2×C4—32no—
464C2×C4—32no—
465C2×C4—51no—
466C2×C4—52no—
467C2×C4—52no—
468C2×C4—62no—
469C2×C4—102no—
470C2×C4—151no—
471C2×C4—152no—
472C2×C4—152no—
473C2×C4—242no—
474C2×C4—302no—
475C2×C4—402no—
476C2×C4—1202no—
477C2×C4C22×D3×D511yescharacteristic
478C8—32no—
479C8—52no—
480C8—152no—
481C8C4×D3×D512yes—
482C2×C3—102no—
483C2×C3C2×D5×C4⋊C411yescharacteristic
484C2×C3#6609111yescharacteristic
485C2×C3#6610011yescharacteristic
486D3—22no—
487D3—102no—
488C5#7914611yescharacteristic, complemented, Sylow
489C22—32no—
490C22—52no—
491C22—61no—
492C22—61no—
493C22—101no—
494C22—101no—
495C22—152no—
496C22—301no—
497C22—301no—
498C22D3×D4×D511yescharacteristic
499C4—32no—
500C4—42no—
501C4—52no—
502C4—122no—
503C4—152no—
504C4—202no—
505C4—602no—
506C4C2×C4×D3×D511yescharacteristic
507C4D3×Q8×D511yescharacteristic
508C3#1061087711yescharacteristic, complemented, Sylow
509C2—62no—
510C2—102no—
511C2—302no—
512C2D3×D5×C4⋊C411yescharacteristic
513C2#1175405411yescharacteristic
514C2#1175410611yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC2×#6771C22
cosocleC2×C3×C4×C5C24
hypercenter#107D3×D5
hypocenterC3×C5#2913
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #11750981C2semidirect
4. C5×D3×#107C2semidirect
5. C3×D5×#107C2semidirect
6. #11747682C2semidirect
7. #11747672C2semidirect
8. #11747636C2semidirect
9. #11747456C2semidirect
10. #11747454C2semidirect
11. #11747452C2semidirect
30. #91265C4semidirect
52. D5×#107D3semidirect
71. C8×D15C2×C4semidirect
75. C5×D3×C8C2×C4semidirect
79. C3×C8×D5C2×C4semidirect
85. #6651C2×C4semidirect
86. #6650C2×C4semidirect
87. #6649C2×C4semidirect
98. D3×#107D5semidirect
218. C8×D5C4×D3semidirect
283. D3×C8C4×D5semidirect
428. C3×C5#2913semidirect
488. C5#79146semidirect
508. C3#10610877semidirect

Maximal subgroups

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

subgroupindex
C2×#912652
#117536672
#117509812
C5×D3×#1072
C3×D5×#1072
#117476822
#117476722
#117476362
#117474562
#117474542
#117474522
#106108773
#791465