Finite Group Databasebeta

← #14413457

Subgroups — #14413457

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91265C211yesmaximal, characteristic
2#11753669C212yesmaximal
3D15×#106C211yesmaximal, characteristic, complemented
4C5×D3×#106C211yesmaximal, characteristic, complemented
5C3×#65149C211yesmaximal, characteristic, complemented
6#11747687C211yesmaximal, characteristic, complemented
7#11747679C211yesmaximal, characteristic, complemented
8D5×#817C211yesmaximal, characteristic, complemented
9#11747457C212yesmaximal, complemented
10#11747454C212yesmaximal, complemented
11#11747189C212yesmaximal, complemented
12#10610847—31nomaximal, Hall
13C2×#6771C2211yescharacteristic
14C2×C8×D15C2211yescharacteristic
15C4⋊C4×D15C2212yes—
16C2×C5×D3×C8C2211yescharacteristic
17C5×D3×C4⋊C4C2212yes—
18C2×C3×C8×D5C2211yescharacteristic
19C3×#4038C2212yes—
20C4×#1203—22no—
21#91441—22no—
22D5×C4⋊Dic3C2212yes—
23#91396—22no—
24#91347C2212yes—
25#91338C2212yes—
26#91323—22no—
27C2×#6651C2211yescharacteristic
28C2×#6650C2211yescharacteristic
29C2×#6649C2211yescharacteristic
30#91265C418yescomplemented
31C3×C5×#106C2211yescharacteristic
32#91101C2211yescharacteristic
33#91092C2212yes—
34C5×#817C2211yescharacteristic
35C5×#808C2212yes—
36C3×#3949C2211yescharacteristic
37C3×#3939C2212yes—
38#90990C2212yes—
39#90989C2212yes—
40#90985C2212yes—
41#79178—51nomaximal, Hall
42C2×#4047—31no—
43#65838—32no—
44C2×C5×#106—31no—
45#65395—31no—
46#65253—32no—
47#65150—32no—
48#65150—32no—
49#65149—31no—
50#65149D311yescharacteristic, complemented
51D5×#106—31no—
52D5×#106—31no—
53C2×C4×D15—22no—
54C2×C4×D15C2311yescharacteristic
55C2×C4×C5×D3—22no—
56C2×C4×C5×D3C2311yescharacteristic
57C2×C3×C4×D5C2311yescharacteristic
58C2×#1204D411yescharacteristic
59C2×#1203D411yescharacteristic
60C2×#1202D411yescharacteristic
61C2×#1201D411yescharacteristic
62C2×D5×Dic3—22no—
63#6771C2×C414yes—
64#6771Q814yes—
65C2×C3×C5×C8C2311yescharacteristic
66C3×C5×C4⋊C4C2312yes—
67C4⋊Dic15C2312yes—
68#6712—22no—
69C2×C3⋊#168C2311yescharacteristic
70C8×D15C2×C414yescomplemented
71C5×C4⋊Dic3C2312yes—
72C5×Dic3⋊C4—22no—
73C2×C5×C3⋊C8C2311yescharacteristic
74C5×D3×C8C2×C414yescomplemented
75C3×#685—22no—
76C3×C4⋊Dic5C2312yes—
77C3×C4×Dic5—22no—
78C2×C3×#168C2311yescharacteristic
79C3×C8×D5C2×C414yescomplemented
80#6668—22no—
81#6667—22no—
82(C2×D3)⋊Dic5—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6651C2×C414yescomplemented
86#6650C2×C414yescomplemented
87#6649C2×C414yescomplemented
88C2×#901—51no—
89#5523—52no—
90C3×#427—51no—
91C2×#817—51no—
92#4995—52no—
93#4881—52no—
94#4881—52no—
95#4860—51no—
96#4860—51no—
97D3×#106—51no—
98D3×#106D511yescharacteristic, 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#4038C2×D312yes—
114D5×C4⋊C4—32no—
115D5×C4⋊C4—32no—
116#4033—62no—
117C5×#106—31no—
118C5×#106—32no—
119C5×#106C2×D311yescharacteristic
120#3950—32no—
121#3949—31no—
122#3949C2×D311yescharacteristic
123#3940—32no—
124#3940—32no—
125#3939—32no—
126#3939C2×D312yes—
127#2912—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×D15—82no—
136C4×D15C22×C412yes—
137C4×D15C2×Q812yes—
138C2×C5×Dic3—22no—
139C2×C5×Dic3C2×D411yescharacteristic
140C4×C5×D3—82no—
141C4×C5×D3C22×C412yes—
142C4×C5×D3C2×Q812yes—
143C2×C3×Dic5—22no—
144C2×C3×Dic5C2×D411yescharacteristic
145C3×C4×D5C22×C412yes—
146C3×C4×D5C2×Q812yes—
147#1204C4⋊C414yes—
148#1203C4⋊C414yes—
149#1202C4⋊C414yes—
150#1201C4⋊C414yes—
151D5×Dic3—82no—
152C3×C5×C8C22×C412yes—
153C3⋊#168C22×C412yes—
154C3×#168C22×C412yes—
155C5×C3⋊C8C22×C412yes—
156C2×#235—51no—
157C22×C3×C8—51no—
158C3×#117—52no—
159C2×C4⋊Dic3—52no—
160C2×#208—51no—
161#901—58no—
162C2×ΓL(1,𝔽25)—51no—
163C2×ΓL(1,𝔽25)—51no—
164C2×D3×C8—51no—
165C2×D3×C8C2×D511yescharacteristic
166#892—52no—
167#892—52no—
168D3×C4⋊C4—52no—
169D3×C4⋊C4C2×D512yes—
170#67⋊C4—102no—
171#67⋊C4—102no—
172C4×D12—102no—
173C4×Dic6—102no—
174C3×#107—52no—
175C3×#106—51no—
176C3×#106C2×D511yescharacteristic
177#817—51no—
178#817—52no—
179#817C2×D511yescharacteristic
180#808—52no—
181#808C2×D512yes—
182#807—52no—
183#807—52no—
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—31no—
192C2×C4×D5—62no—
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—22no—
204#685—62no—
205C4⋊Dic5—32no—
206C4⋊Dic5C22×D312yes—
207#683—62no—
208#683—62no—
209C4×Dic5—22no—
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—51no—
225#427—151no—
226#427—151no—
227C2×#106—31no—
228C2×#106—151no—
229C2×#106—151no—
230C22×C3×C5C22×D411yescharacteristic
231C2×D15—22no—
232C2×D15C2×C4⋊C412yes—
233C2×C5×D3—22no—
234C2×C5×D3C2×C4⋊C412yes—
235C2×C3×D5—22no—
236C2×C3×D5C2×C4⋊C412yes—
237C3×C4×C5—42no—
238C3×C4×C5C23×C411yescharacteristic
239C3×C4×C5C22×Q811yescharacteristic
240Dic15—42no—
241Dic15C2×C4⋊C412yes—
242C3×Dic5—42no—
243C3×Dic5C2×C4⋊C412yes—
244C5×Dic3—42no—
245C5×Dic3C2×C4⋊C412yes—
246C22×C3×C4—51no—
247C2×#67—51no—
248C2×#67—51no—
249C22×Dic3—102no—
250#235—54no—
251#235—54no—
252C2×D12—51no—
253C2×C4×D3—22no—
254C2×C4×D3—51no—
255C2×C4×D3—102no—
256C2×C4×D3C22×D511yescharacteristic
257C2×Dic6—51no—
258C2×C3×C8—51no—
259C2×C3×C8—54no—
260C2×C3×C8C22×D511yescharacteristic
261C3×C4⋊C4—52no—
262C3×C4⋊C4C22×D512yes—
263C3×C22⋊C4—102no—
264C3×C42—102no—
265(C2×D3)⋊C4—102no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—52no—
268C4⋊Dic3—102no—
269C4⋊Dic3C22×D512yes—
270Dic3⋊C4—22no—
271Dic3⋊C4—102no—
272C4×Dic3—102no—
273C4×Dic3—102no—
274#208—54no—
275C2×C3⋊C8—51no—
276C2×C3⋊C8C22×D511yescharacteristic
277ΓL(1,𝔽25)—54no—
278ΓL(1,𝔽25)—54no—
279D3×C8—54no—
280D3×C8C4×D514yescomplemented
281C23×C5—31no—
282C22×D5—31no—
283C22×D5D3×D411yescharacteristic
284C2×C4×C5—22no—
285C2×C4×C5—31no—
286C2×C4×C5—32no—
287C2×C4×C5—32no—
288C2×C4×C5—62no—
289C2×C4×C5—242no—
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—34no—
292C22⋊D5—34no—
293C2×Dic5—22no—
294C2×Dic5—31no—
295C2×Dic5—62no—
296C2×Dic5D3×D411yescharacteristic
297D20—34no—
298C4×D5—32no—
299C4×D5—32no—
300C4×D5—242no—
301C4×D5—242no—
302C4×D5C2×C4×D312yes—
303C4×D5D3×Q812yes—
304Dic10—34no—
305C5×C8—32no—
306C5×C8C2×C4×D312yes—
307#168—32no—
308#168C2×C4×D312yes—
309C2×#41—151no—
310#131—158no—
311C2×M16—151no—
312C2×M16—151no—
313C2×M16—151no—
314C22×C8—31no—
315C22×C8—51no—
316C22×C8—151no—
317C4×Q8—302no—
318C4×D4—302no—
319C4×D4—302no—
320C4×D4—302no—
321#117—52no—
322#117—152no—
323#117—152no—
324C2×C4⋊C4—32no—
325C2×C4⋊C4—152no—
326C2×C4⋊C4—152no—
327#107—52no—
328#107—152no—
329#107—152no—
330#106—31no—
331#106—32no—
332#106—51no—
333#106—152no—
334#106—151no—
335#106—152no—
336#106D3×D511yescharacteristic
337C2×C3×C5C22×C4⋊C411yescharacteristic
338C2×C3×C5#57712yes—
339D15—22no—
340C3×D5—22no—
341C5×D3—22no—
342C23×C3—51no—
343C22×D3—51no—
344C22×D3D4×D511yescharacteristic
345C2×C3×C4—22no—
346C2×C3×C4—51no—
347C2×C3×C4—52no—
348C2×C3×C4—52no—
349C2×C3×C4—102no—
350C2×C3×C4C23×D511yescharacteristic
351#67—54no—
352#67—54no—
353C2×Dic3—22no—
354C2×Dic3—51no—
355C2×Dic3—102no—
356C2×Dic3—402no—
357C2×Dic3D4×D511yescharacteristic
358D12—54no—
359C4×D3—52no—
360C4×D3—52no—
361C4×D3—82no—
362C4×D3—402no—
363C4×D3C2×C4×D512yes—
364C4×D3Q8×D512yes—
365Dic6—54no—
366C3×C8—52no—
367C3×C8C2×C4×D512yes—
368C3⋊C8—52no—
369C3⋊C8C2×C4×D512yes—
370C22×C5—32no—
371C22×C5—62no—
372C22×C5C2×D3×D411yescharacteristic
373C2×D5—22no—
374C2×D5—32no—
375C2×D5—62no—
376C2×D5D3×C4⋊C412yes—
377C4×C5—32no—
378C4×C5—42no—
379C4×C5—122no—
380C4×C5C22×C4×D311yescharacteristic
381C4×C5C2×D3×Q811yescharacteristic
382Dic5—32no—
383Dic5—42no—
384Dic5—122no—
385Dic5D3×C4⋊C412yes—
386#41—154no—
387#41—154no—
388C2×Q8—151no—
389C2×D4—151no—
390C2×D4—151no—
391C2×D4—151no—
392C22×C4—31no—
393C22×C4—51no—
394C22×C4—62no—
395C22×C4—151no—
396C22×C4—302no—
397C22×C4—302no—
398M16—154no—
399M16—154no—
400M16—154no—
401C2×C8—31no—
402C2×C8—34no—
403C2×C8—51no—
404C2×C8—54no—
405C2×C8—151no—
406C2×C8—154no—
407C2×C8C2×D3×D511yescharacteristic
408C4⋊C4—32no—
409C4⋊C4—52no—
410C4⋊C4—62no—
411C4⋊C4—152no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4C2×D3×D512yes—
415C22⋊C4—102no—
416C22⋊C4—302no—
417C22⋊C4—302no—
418C42—102no—
419C42—302no—
420C42—302no—
421C3×C5#291211yescharacteristic, complemented, Hall
422C22×C3—52no—
423C22×C3—102no—
424C22×C3C2×D4×D511yescharacteristic
425C2×D3—22no—
426C2×D3—52no—
427C2×D3—102no—
428C2×D3D5×C4⋊C412yes—
429C3×C4—42no—
430C3×C4—52no—
431C3×C4—202no—
432C3×C4C22×C4×D511yescharacteristic
433C3×C4C2×Q8×D511yescharacteristic
434Dic3—42no—
435Dic3—52no—
436Dic3—202no—
437Dic3D5×C4⋊C412yes—
438C2×C5—62no—
439C2×C5C2×D3×C4⋊C411yescharacteristic
440C2×C5#577012yes—
441D5—22no—
442D5—62no—
443C23—31no—
444C23—51no—
445C23—151no—
446Q8—154no—
447D4—154no—
448D4—154no—
449D4—154no—
450C2×C4—22no—
451C2×C4—31no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—51no—
455C2×C4—52no—
456C2×C4—52no—
457C2×C4—62no—
458C2×C4—102no—
459C2×C4—151no—
460C2×C4—152no—
461C2×C4—152no—
462C2×C4—242no—
463C2×C4—302no—
464C2×C4—1202no—
465C2×C4—1202no—
466C2×C4C22×D3×D511yescharacteristic
467C8—32no—
468C8—52no—
469C8—152no—
470C8C4×D3×D512yes—
471C2×C3—102no—
472C2×C3C2×D5×C4⋊C411yescharacteristic
473C2×C3#6609612yes—
474D3—22no—
475D3—102no—
476C5#7917811yescharacteristic, complemented, Sylow
477C22—32no—
478C22—52no—
479C22—62no—
480C22—102no—
481C22—152no—
482C22—302no—
483C22D3×D4×D511yescharacteristic
484C4—32no—
485C4—42no—
486C4—52no—
487C4—122no—
488C4—152no—
489C4—202no—
490C4—602no—
491C4C2×C4×D3×D511yescharacteristic
492C4D3×Q8×D511yescharacteristic
493C3#1061084711yescharacteristic, complemented, Sylow
494C2—62no—
495C2—102no—
496C2—302no—
497C2D3×D5×C4⋊C411yescharacteristic
498C2#1175409212yes—
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radicalC2×#6771C22
cosocleC2×C3×C4×C5C24
hypercenter#106D3×D5
hypocenterC3×C5#2912
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. D15×#106C2semidirect
4. C5×D3×#106C2semidirect
5. C3×#65149C2semidirect
6. #11747687C2semidirect
7. #11747679C2semidirect
8. D5×#817C2semidirect
9. #11747457C2semidirect
10. #11747454C2semidirect
11. #11747189C2semidirect
30. #91265C4semidirect
50. #65149D3semidirect
70. C8×D15C2×C4semidirect
74. C5×D3×C8C2×C4semidirect
79. C3×C8×D5C2×C4semidirect
85. #6651C2×C4semidirect
86. #6650C2×C4semidirect
87. #6649C2×C4semidirect
98. D3×#106D5semidirect
218. C8×D5C4×D3semidirect
280. D3×C8C4×D5semidirect
421. C3×C5#2912semidirect
476. C5#79178semidirect
493. C3#10610847semidirect

Maximal subgroups

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

subgroupindex
C2×#912652
#117536692
D15×#1062
C5×D3×#1062
C3×#651492
#117476872
#117476792
D5×#8172
#117474572
#117474542
#117471892
#106108473
#791785