Finite Group Databasebeta

← #14417697

Subgroups — #14417697

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91275C211yesmaximal, characteristic
2#11753337C212yesmaximal, complemented
3#11750973C211yesmaximal, characteristic, complemented
4C5×D3×#107C211yesmaximal, characteristic, complemented
5C3×#65162C211yesmaximal, characteristic, complemented
6#11747883C211yesmaximal, characteristic, complemented
7#11747766C211yesmaximal, characteristic, complemented
8#11747653C211yesmaximal, characteristic, complemented
9#11747505C212yesmaximal, complemented
10#11747273C212yesmaximal, complemented
11#11747224C212yesmaximal, complemented
12#10610867—31nomaximal, Hall
13C2×#6769C2212yes—
14C2×D120C2211yescharacteristic
15#91782C2212yes—
16C2×C5×D3×C8C2211yescharacteristic
17C5×D3×C4⋊C4C2212yes—
18C2×C3×Dic20C2211yescharacteristic
19C3×#4033C2212yes—
20#91446—22no—
21C4×#1203—22no—
22#91418C2212yes—
23#91404—22no—
24#91402—22no—
25#91371C2211yescharacteristic
26#91331C2212yes—
27C2×#6658C2212yes—
28C2×#6650C2211yescharacteristic
29#91275C418yescomplemented
30C3×C5×#107C2211yescharacteristic
31C8×Dic15C2211yescharacteristic
32#91093C2212yes—
33C5×#818C2211yescharacteristic
34C5×#807C2212yes—
35C3×C8×Dic5C2211yescharacteristic
36C3×#3942C2212yes—
37#90970C2212yes—
38#90969C2212yes—
39#90954C2211yescharacteristic
40#90952C2211yescharacteristic
41#79721—51nomaximal, Hall
42C2×#4050—31no—
43#65838—32no—
44C2×C5×#107—31no—
45#65390—31no—
46#65255—32no—
47#65178—32no—
48#65178—32no—
49#65162—31no—
50#65162D311yescharacteristic, complemented
51#65161—31no—
52#65161—31no—
53C2×D60C2312yes—
54C2×C4×D15—22no—
55C2×C4×C5×D3—22no—
56C2×C4×C5×D3C2311yescharacteristic
57C2×C3×Dic10C2312yes—
58C2×#1203—22no—
59C2×#1200—22no—
60C2×#1200—22no—
61#6769—24no—
62#6769C2×C418yescomplemented
63C2×C3×C5×C8C2311yescharacteristic
64C3×C5×C4⋊C4C2312yes—
65#6714—22no—
66C4×Dic15C2311yescharacteristic
67C2×C3⋊#168C2311yescharacteristic
68D120C2×C414yescomplemented
69C5×C4⋊Dic3C2312yes—
70C5×Dic3⋊C4—22no—
71C2×C5×C3⋊C8C2311yescharacteristic
72C5×D3×C8C2×C414yescomplemented
73C3×#683—22no—
74C3×C4×Dic5—22no—
75C3×C4×Dic5C2311yescharacteristic
76C2×C3×#168C2311yescharacteristic
77C3×Dic20C2×C414yescomplemented
78Dic3⋊Dic5D411yescharacteristic
79Dic3⋊Dic5D411yescharacteristic
80#6668—22no—
81#6667—22no—
82(C2×D3)⋊Dic5D411yescharacteristic
83(C2×D3)⋊Dic5D411yescharacteristic
84Dic3×Dic5—22no—
85#6658C2×C418yescomplemented
86#6650—22no—
87C2×#919—51no—
88#5574—52no—
89C3×C4×Q16—51no—
90Dic3×Q16—51no—
91#5026—52no—
92D3×#107D511yescharacteristic, complemented
93#4872—51no—
94#4817—52no—
95#4803—52no—
96C4×D24—51no—
97#4689—51no—
98C2×#709—32no—
99C22×C5×C8—31no—
100C2×C5×C4⋊C4—32no—
101C4×C22⋊D5—62no—
102C4×C22⋊D5—62no—
103#4072—31no—
104C2×#681—31no—
105C2×Dic20C2×D311yescharacteristic
106#4050—38no—
107C2×D40—31no—
108C2×#677—32no—
109#4039—32no—
110#4039—32no—
111#4038—62no—
112D5×C4⋊C4—62no—
113#4033—32no—
114#4033C2×D312yes—
115C5×#107—31no—
116C5×#107—32no—
117C5×#107C2×D311yescharacteristic
118#3947—31no—
119#3947—31no—
120C8×Dic5—31no—
121C8×Dic5C2×D311yescharacteristic
122#3942—32no—
123#3942C2×D312yes—
124#3941—32no—
125#3941—32no—
126#2951—151noSylow
127C22×D15—22no—
128C22×C5×D3C2×D411yescharacteristic
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15C2×D411yescharacteristic
132C2×Dic15C2×D411yescharacteristic
133D60—22no—
134D60C22×C414yes—
135C4×D15—82no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3C2×D411yescharacteristic
138C4×C5×D3—82no—
139C4×C5×D3C22×C412yes—
140C4×C5×D3#4112yes—
141C2×C3×Dic5—22no—
142C2×C3×Dic5C2×D411yescharacteristic
143C2×C3×Dic5C2×D411yescharacteristic
144C3×Dic10—22no—
145C3×Dic10C22×C414yes—
146#1203—28no—
147#1200—28no—
148#1200—82no—
149C3×C5×C8C22×C412yes—
150C3⋊#168—21no—
151C3×#168—21no—
152C5×C3⋊C8C22×C412yes—
153C2×#239—52no—
154C2×C3×Q16—51no—
155C3×C4×Q8—52no—
156Q8×Dic3—52no—
157C2×#215—52no—
158#919—58no—
159C2×D24—51no—
160C2×ΓL(1,𝔽25)—51no—
161C2×D3×C8C2×D511yescharacteristic
162#893—52no—
163#893—102no—
164D3×C4⋊C4—102no—
165D3×C4⋊C4C2×D512yes—
166C4×D12—52no—
167C4×D12—102no—
168#872—51no—
169#872—102no—
170C3×#107C2×D511yescharacteristic
171C3×#103—52no—
172C3×C4×C8—51no—
173#835—52no—
174#821—52no—
175#818C2×D511yescharacteristic
176#815—51no—
177C8×Dic3—51no—
178#809—52no—
179#807C2×D512yes—
180#803—51no—
181C22×C4×C5—31no—
182C22×C4×C5—62no—
183C2×C22⋊D5—62no—
184#709—38no—
185#709—64no—
186C2×D20—32no—
187C2×C4×D5—62no—
188C2×C4×D5—62no—
189C2×C4×D5—62no—
190C2×Dic10C22×D312yes—
191C2×C5×C8—31no—
192C2×C5×C8—34no—
193C2×C5×C8C22×D311yescharacteristic
194C5×C4⋊C4—32no—
195C5×C4⋊C4—62no—
196C5×C4⋊C4C22×D312yes—
197C22⋊Dic5—31no—
198C22⋊Dic5—31no—
199#685—62no—
200#685—62no—
201C4⋊Dic5—31no—
202C4⋊Dic5—31no—
203#683—22no—
204#683—62no—
205C4×Dic5—22no—
206C4×Dic5—31no—
207C4×Dic5—62no—
208C4×Dic5C22×D311yescharacteristic
209#681—62no—
210C2×#168—31no—
211C2×#168C22×D311yescharacteristic
212Dic20C4×D314yescomplemented
213D40—34no—
214#677—38no—
215C2×#135—151no—
216#520—152no—
217#440—152no—
218#440—152no—
219C4×Q16—51no—
220C4×Q16—151no—
221C4×D8—151no—
222C4×D8—151no—
223C2×#107—31no—
224#417—152no—
225#405—151no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—24no—
228C2×D15—42no—
229C2×D15—42no—
230C2×C5×D3—21no—
231C2×C5×D3—21no—
232C2×C5×D3C4×D412yes—
233C3×C4×C5—42no—
234C3×C4×C5C23×C411yescharacteristic
235C3×C4×C5C2×#4111yescharacteristic
236Dic15—21no—
237Dic15—21no—
238C3×Dic5—24no—
239C3×Dic5—21no—
240C3×Dic5—21no—
241C5×Dic3—42no—
242C5×Dic3C4×D412yes—
243C2×C3×Q8—52no—
244#239—58no—
245#239—104no—
246C2×D12—52no—
247C2×D12—102no—
248C2×C4×D3—22no—
249C2×C4×D3—102no—
250C2×C4×D3—102no—
251C2×C4×D3—102no—
252C2×C4×D3C22×D511yescharacteristic
253C3×Q16—54no—
254C2×C3×C8—51no—
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4—102no—
257C3×C4⋊C4C22×D512yes—
258C3×C42—51no—
259C3×C42—102no—
260#215—58no—
261(C2×D3)⋊C4—51no—
262(C2×D3)⋊C4—51no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—102no—
266C4⋊Dic3C22×D512yes—
267Dic3⋊C4—22no—
268Dic3⋊C4—51no—
269Dic3⋊C4—51no—
270C4×Dic3—51no—
271C4×Dic3—102no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8C22×D511yescharacteristic
274D24—54no—
275ΓL(1,𝔽25)—102no—
276D3×C8C4×D514yescomplemented
277C23×C5—31no—
278C22×D5—62no—
279C2×C4×C5—22no—
280C2×C4×C5—31no—
281C2×C4×C5—32no—
282C2×C4×C5—32no—
283C2×C4×C5—62no—
284C2×C4×C5—242no—
285C2×C4×C5C23×D311yescharacteristic
286C22⋊D5—68no—
287C2×Dic5—22no—
288C2×Dic5—31no—
289C2×Dic5—31no—
290C2×Dic5D3×D411yescharacteristic
291C2×Dic5D3×D411yescharacteristic
292D20—34no—
293D20—62no—
294C4×D5—68no—
295C4×D5—242no—
296C4×D5—242no—
297Dic10—22no—
298Dic10C2×C4×D314yes—
299C5×C8—32no—
300C5×C8C2×C4×D312yes—
301#168—21no—
302#168—61no—
303C2×#41—152no—
304#135—158no—
305C2×Q16—51no—
306C2×SD16—152no—
307C2×D8—151no—
308C2×M16—151no—
309C22×C8—31no—
310C4×Q8—52no—
311C4×Q8—152no—
312C4×D4—152no—
313C4×D4—152no—
314C4×D4—302no—
315C4×D4—302no—
316#117—151no—
317#117—302no—
318C2×C4⋊C4—32no—
319C2×C4⋊C4—302no—
320#107—31no—
321#107—32no—
322#107D3×D511yescharacteristic
323#103—52no—
324#103—152no—
325#102—152no—
326#102—152no—
327#97—151no—
328#97—151no—
329C4×C8—51no—
330C4×C8—151no—
331C2×C3×C5C2×C4×D411yescharacteristic
332C2×C3×C5#57611yescharacteristic
333C2×C3×C5#57811yescharacteristic
334D15—44no—
335C5×D3—22no—
336C22×D3—102no—
337C22×D3D4×D511yescharacteristic
338C3×Q8—54no—
339C3×Q8—102no—
340C2×C3×C4—22no—
341C2×C3×C4—51no—
342C2×C3×C4—51no—
343C2×C3×C4—102no—
344C2×C3×C4C23×D511yescharacteristic
345C2×Dic3—22no—
346C2×Dic3—51no—
347C2×Dic3—51no—
348C2×Dic3D4×D511yescharacteristic
349D12—54no—
350D12—108no—
351D12—102no—
352C4×D3—82no—
353C4×D3—108no—
354C4×D3—402no—
355C4×D3—402no—
356C4×D3C2×C4×D512yes—
357C4×D3#71312yes—
358C3×C8—101no—
359C3×C8C2×C4×D512yes—
360C3⋊C8—101no—
361C3⋊C8C2×C4×D512yes—
362C22×C5—32no—
363C22×C5—61no—
364C22×C5—61no—
365C22×C5C2×D3×D411yescharacteristic
366C2×D5—64no—
367C2×D5—122no—
368C2×D5—122no—
369C4×C5—32no—
370C4×C5—42no—
371C4×C5—122no—
372C4×C5C22×C4×D311yescharacteristic
373C4×C5D3×#4111yescharacteristic
374Dic5—21no—
375Dic5—21no—
376Dic5—24no—
377Dic5—61no—
378Dic5—61no—
379#41—158no—
380#41—304no—
381C2×Q8—52no—
382C2×D4—152no—
383C2×D4—302no—
384C22×C4—31no—
385C22×C4—62no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—302no—
389Q16—54no—
390SD16—158no—
391D8—154no—
392M16—302no—
393C2×C8—31no—
394C2×C8—34no—
395C2×C8—51no—
396C2×C8—151no—
397C2×C8C2×D3×D511yescharacteristic
398C4⋊C4—32no—
399C4⋊C4—62no—
400C4⋊C4—102no—
401C4⋊C4—151no—
402C4⋊C4—151no—
403C4⋊C4—302no—
404C4⋊C4C2×D3×D512yes—
405C22⋊C4—151no—
406C22⋊C4—151no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—51no—
410C42—102no—
411C42—151no—
412C42—302no—
413C3×C5#295111yescharacteristic, complemented, Hall
414C22×C3C2×D4×D511yescharacteristic
415C2×D3—21no—
416C2×D3—21no—
417C2×D3—104no—
418C2×D3—202no—
419C2×D3—202no—
420C2×D3#403912yes—
421C3×C4—42no—
422C3×C4—101no—
423C3×C4—104no—
424C3×C4—101no—
425C3×C4C22×C4×D511yescharacteristic
426C3×C4C2×#71311yescharacteristic
427Dic3—42no—
428Dic3—101no—
429Dic3—101no—
430Dic3#403912yes—
431C2×C5—62no—
432C2×C5C4×D3×D411yescharacteristic
433C2×C5#576611yescharacteristic
434C2×C5#576911yescharacteristic
435D5—124no—
436C23—31no—
437C23—302no—
438Q8—54no—
439Q8—102no—
440D4—154no—
441D4—308no—
442D4—302no—
443C2×C4—22no—
444C2×C4—31no—
445C2×C4—32no—
446C2×C4—32no—
447C2×C4—51no—
448C2×C4—51no—
449C2×C4—62no—
450C2×C4—102no—
451C2×C4—151no—
452C2×C4—151no—
453C2×C4—242no—
454C2×C4—308no—
455C2×C4—1202no—
456C2×C4—1202no—
457C2×C4C22×D3×D511yescharacteristic
458C8—32no—
459C8—101no—
460C8—301no—
461C8C4×D3×D512yes—
462C2×C3C2×#403911yescharacteristic
463C2×C3#6609111yescharacteristic
464C2×C3#6610011yescharacteristic
465D3—22no—
466D3—204no—
467C5#7972111yescharacteristic, complemented, Sylow
468C22—32no—
469C22—61no—
470C22—61no—
471C22—304no—
472C22—602no—
473C22—602no—
474C22D3×D4×D511yescharacteristic
475C4—32no—
476C4—42no—
477C4—101no—
478C4—104no—
479C4—101no—
480C4—122no—
481C4—301no—
482C4—301no—
483C4C2×C4×D3×D511yescharacteristic
484C4D3×#71311yescharacteristic
485C3#1061086711yescharacteristic, complemented, Sylow
486C2—62no—
487C2—604no—
488C2D3×#403911yescharacteristic
489C2#1175406111yescharacteristic
490C2#1175410611yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC2×#91275C2
cosocleC2×C3×C4×C5C24
hypercenter#107D3×D5
hypocenterC3×C5#2951
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
2. #11753337C2semidirect
3. #11750973C2semidirect
4. C5×D3×#107C2semidirect
5. C3×#65162C2semidirect
6. #11747883C2semidirect
7. #11747766C2semidirect
8. #11747653C2semidirect
9. #11747505C2semidirect
10. #11747273C2semidirect
11. #11747224C2semidirect
29. #91275C4semidirect
50. #65162D3semidirect
62. #6769C2×C4semidirect
68. D120C2×C4semidirect
72. C5×D3×C8C2×C4semidirect
77. C3×Dic20C2×C4semidirect
85. #6658C2×C4semidirect
92. D3×#107D5semidirect
212. Dic20C4×D3semidirect
276. D3×C8C4×D5semidirect
413. C3×C5#2951semidirect
467. C5#79721semidirect
485. C3#10610867semidirect

Maximal subgroups

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

subgroupindex
C2×#912752
#117533372
#117509732
C5×D3×#1072
C3×#651622
#117478832
#117477662
#117476532
#117475052
#117472732
#117472242
#106108673
#797215