Finite Group Databasebeta

← #14417698

Subgroups — #14417698

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×#91277C211yesmaximal, characteristic
2#11753401C212yesmaximal, complemented
3D15×#107C211yesmaximal, characteristic, complemented
4C5×#4873C211yesmaximal, characteristic, complemented
5C3×#65161C211yesmaximal, characteristic, complemented
6Dic5×Dic12C211yesmaximal, characteristic, complemented
7Dic3×D40C211yesmaximal, characteristic, complemented
8#11747657C211yesmaximal, characteristic, complemented
9#11747507C212yesmaximal, complemented
10#11747471C212yesmaximal, complemented
11#11747222C212yesmaximal, complemented
12#10611452—31nomaximal, Hall
13C2×#6766C2212yes—
14C2×C8×D15C2211yescharacteristic
15C4⋊C4×D15C2212yes—
16C2×C5×Dic12C2211yescharacteristic
17C5×#887C2212yes—
18C2×C3×D40C2211yescharacteristic
19C3×#4039C2212yes—
20C4×#1202—22no—
21Dic3×D20C2212yes—
22#91396—22no—
23#91393—22no—
24D5×Dic3⋊C4—22no—
25#91386C2211yescharacteristic
26Dic5×Dic6C2212yes—
27C2×#6655C2212yes—
28C2×#6651C2211yescharacteristic
29#91277C418yescomplemented
30C3×C5×#107C2211yescharacteristic
31#91102C2211yescharacteristic
32#91091C2212yes—
33C5×C8×Dic3C2211yescharacteristic
34C5×#810C2212yes—
35C3×C8×Dic5C2211yescharacteristic
36C3×#3941C2212yes—
37#90973C2212yes—
38#90965C2212yes—
39#90953C2211yescharacteristic
40#90952C2211yescharacteristic
41#79589—51nomaximal, Hall
42C2×#4065—31no—
43#65908—32no—
44C4×C5×Q16—31no—
45Q16×Dic5—31no—
46#65315—32no—
47D5×#107—31no—
48#65161D311yescharacteristic, complemented
49#65106—32no—
50#65092—32no—
51C4×D40—31no—
52#64978—31no—
53C2×C4×D15—22no—
54C2×C4×D15C2311yescharacteristic
55C2×C5×Dic6C2312yes—
56C2×C3×D20C2312yes—
57C2×C3×C4×D5—22no—
58C2×#1202—22no—
59C2×D5×Dic3—22no—
60C2×D5×Dic3—22no—
61#6766—24no—
62#6766C2×C418yescomplemented
63C2×C3×C5×C8C2311yescharacteristic
64C3×C5×C4⋊C4C2312yes—
65C4⋊Dic15C2312yes—
66#6712—22no—
67C2×C3⋊#168C2311yescharacteristic
68C8×D15C2×C414yescomplemented
69C5×Dic3⋊C4—22no—
70C4×C5×Dic3—22no—
71C4×C5×Dic3C2311yescharacteristic
72C2×C5×C3⋊C8C2311yescharacteristic
73C5×Dic12C2×C414yescomplemented
74C3×#685—22no—
75C3×C4×Dic5C2311yescharacteristic
76C2×C3×#168C2311yescharacteristic
77C3×D40C2×C414yescomplemented
78Dic3⋊Dic5—22no—
79#6669D411yescharacteristic
80#6669D411yescharacteristic
81#6667D411yescharacteristic
82#6667D411yescharacteristic
83#6665—22no—
84Dic3×Dic5—22no—
85#6655C2×C418yescomplemented
86#6651—22no—
87C2×#912—51no—
88#5546—52no—
89C3×C4×D8—51no—
90Dic3×D8—51no—
91#5018—52no—
92D3×#107—51no—
93#4873D511yescharacteristic, complemented
94#4771—52no—
95#4757—52no—
96C4×Dic12—51no—
97#4689—51no—
98C2×#713—32no—
99C2×C5×Q16—31no—
100C4×C5×Q8—32no—
101Q8×Dic5—32no—
102C2×#688—32no—
103#4065—38no—
104C2×D40C2×D311yescharacteristic
105C2×#676—31no—
106C2×C8×D5—31no—
107#4039—62no—
108#4039C2×D312yes—
109D5×C4⋊C4—32no—
110D5×C4⋊C4—62no—
111C4×D20—32no—
112C4×D20—62no—
113#4018—31no—
114#4018—62no—
115C5×#107C2×D311yescharacteristic
116C5×#103—32no—
117C4×C5×C8—31no—
118#3967—32no—
119#3953—32no—
120#3950—31no—
121#3947—31no—
122C8×Dic5C2×D311yescharacteristic
123#3941C2×D312yes—
124#3939—32no—
125#3935—31no—
126#2951—151noSylow
127C22×D15C2×D411yescharacteristic
128C22×C3×D5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—22no—
132C2×Dic15C2×D411yescharacteristic
133C4×D15—82no—
134C4×D15C22×C412yes—
135C4×D15#4112yes—
136C2×C5×Dic3—22no—
137C2×C5×Dic3C2×D411yescharacteristic
138C2×C5×Dic3C2×D411yescharacteristic
139C5×Dic6—22no—
140C5×Dic6C22×C414yes—
141C2×C3×Dic5C2×D411yescharacteristic
142C2×C3×Dic5C2×D411yescharacteristic
143C3×D20—22no—
144C3×D20C22×C414yes—
145C3×C4×D5—82no—
146#1202—28no—
147D5×Dic3—28no—
148D5×Dic3—82no—
149C3×C5×C8C22×C412yes—
150C3⋊#168C22×C412yes—
151C3×#168—21no—
152C5×C3⋊C8—21no—
153C2×#237—52no—
154C2×C3×D8—51no—
155C3×C4×D4—52no—
156D4×Dic3—52no—
157C2×#214—52no—
158C4×#67—102no—
159C2×Dic3⋊C4—102no—
160#912—58no—
161C2×Dic12C2×D511yescharacteristic
162C2×ΓL(1,𝔽25)—51no—
163C2×D3×C8—51no—
164D3×C4⋊C4—52no—
165#887C2×D512yes—
166#67⋊C4—102no—
167#877—102no—
168#872—51no—
169C4×Dic6—52no—
170C3×#107C2×D511yescharacteristic
171C3×#102—52no—
172C3×C4×C8—51no—
173#832—52no—
174#818—51no—
175#816—52no—
176#815—51no—
177C8×Dic3C2×D511yescharacteristic
178#810C2×D512yes—
179#807—52no—
180#803—51no—
181C2×C5×Q8—32no—
182#713—38no—
183#713—64no—
184C2×D20—62no—
185C2×D20C22×D312yes—
186C2×C4×D5—22no—
187C2×C4×D5—31no—
188C2×C4×D5—62no—
189C2×C4×D5—62no—
190C2×C4×D5—62no—
191C5×Q16—34no—
192C2×C5×C8—31no—
193C2×C5×C8C22×D311yescharacteristic
194C5×C4⋊C4—62no—
195C5×C4⋊C4C22×D312yes—
196C42×C5—31no—
197C42×C5—62no—
198#688—38no—
199#685—22no—
200#685—31no—
201#685—31no—
202#685—62no—
203C4⋊Dic5—32no—
204C4⋊Dic5—62no—
205#683—31no—
206#683—31no—
207#683—62no—
208C4×Dic5—62no—
209C4×Dic5C22×D311yescharacteristic
210C2×#168—31no—
211C2×#168C22×D311yescharacteristic
212D40C4×D314yescomplemented
213#676—62no—
214C8×D5—34no—
215C2×#135—151no—
216#520—152no—
217#440—152no—
218#440—152no—
219C4×Q16—31no—
220C4×Q16—151no—
221C4×D8—51no—
222C4×D8—151no—
223C2×#107—151no—
224#417—152no—
225#405—151no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—21no—
228C2×D15—21no—
229C2×D15C4×D412yes—
230C2×C3×D5—24no—
231C2×C3×D5—42no—
232C2×C3×D5—42no—
233C3×C4×C5—42no—
234C3×C4×C5C23×C411yescharacteristic
235C3×C4×C5C2×#4111yescharacteristic
236Dic15—42no—
237Dic15C4×D412yes—
238C3×Dic5—21no—
239C3×Dic5—21no—
240C5×Dic3—24no—
241C5×Dic3—21no—
242C5×Dic3—21no—
243C2×C3×D4—52no—
244C22×C3×C4—102no—
245C2×#67—102no—
246C22×Dic3—102no—
247C22×Dic3—102no—
248#237—58no—
249#237—104no—
250C2×C4×D3—51no—
251C2×C4×D3—102no—
252C2×Dic6C22×D512yes—
253C3×D8—54no—
254C2×C3×C8—51no—
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4C22×D512yes—
257C3×C22⋊C4—102no—
258C3×C42—51no—
259#217—102no—
260#214—58no—
261(C2×D3)⋊C4—51no—
262(C2×D3)⋊C4—51no—
263C4⋊Dic3—52no—
264Dic3⋊C4—22no—
265Dic3⋊C4—51no—
266Dic3⋊C4—51no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269C4×Dic3—22no—
270C4×Dic3—102no—
271C4×Dic3C22×D511yescharacteristic
272C2×C3⋊C8—51no—
273C2×C3⋊C8C22×D511yescharacteristic
274Dic12C4×D514yescomplemented
275ΓL(1,𝔽25)—102no—
276D3×C8—54no—
277C22×D5—22no—
278C22×D5—31no—
279C5×Q8—34no—
280C5×Q8—62no—
281C2×C4×C5—22no—
282C2×C4×C5—31no—
283C2×C4×C5—31no—
284C2×C4×C5—62no—
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—31no—
287C2×Dic5—62no—
288C2×Dic5D3×D411yescharacteristic
289C2×Dic5D3×D411yescharacteristic
290D20—22no—
291D20—68no—
292D20C2×C4×D314yes—
293C4×D5—32no—
294C4×D5—32no—
295C4×D5—68no—
296C4×D5—82no—
297C4×D5—242no—
298C4×D5—242no—
299C5×C8—61no—
300C5×C8C2×C4×D312yes—
301#168—21no—
302#168—32no—
303C2×#41—152no—
304#135—158no—
305C2×Q16—31no—
306C2×SD16—152no—
307C2×D8—51no—
308C2×M16—151no—
309C22×C8—151no—
310C4×Q8—32no—
311C4×Q8—152no—
312C4×D4—52no—
313C4×D4—152no—
314C4×D4—302no—
315C4×D4—302no—
316#117—151no—
317#117—302no—
318C2×C4⋊C4—152no—
319C2×C4⋊C4—302no—
320#107—151no—
321#107—152no—
322#107D3×D511yescharacteristic
323#103—32no—
324#103—152no—
325#102—52no—
326#102—152no—
327#97—151no—
328#97—151no—
329C4×C8—31no—
330C4×C8—51no—
331C2×C3×C5C2×C4×D411yescharacteristic
332C2×C3×C5#57611yescharacteristic
333C2×C3×C5#57811yescharacteristic
334D15—22no—
335C3×D5—44no—
336C23×C3—102no—
337C22×D3—51no—
338C3×D4—54no—
339C3×D4—102no—
340C2×C3×C4—22no—
341C2×C3×C4—51no—
342C2×C3×C4—51no—
343C2×C3×C4—402no—
344C2×C3×C4C23×D511yescharacteristic
345#67—108no—
346C2×Dic3—22no—
347C2×Dic3—51no—
348C2×Dic3—108no—
349C2×Dic3—102no—
350C2×Dic3—402no—
351C2×Dic3D4×D511yescharacteristic
352C2×Dic3D4×D511yescharacteristic
353C4×D3—52no—
354C4×D3—52no—
355C4×D3—402no—
356Dic6—22no—
357Dic6C2×C4×D514yes—
358C3×C8—101no—
359C3×C8C2×C4×D512yes—
360C3⋊C8—21no—
361C3⋊C8—52no—
362C22×C5C2×D3×D411yescharacteristic
363C2×D5—24no—
364C2×D5—32no—
365C2×D5—42no—
366C2×D5—42no—
367C2×D5—61no—
368C2×D5—61no—
369C4×C5—42no—
370C4×C5—61no—
371C4×C5—61no—
372C4×C5—64no—
373C4×C5C22×C4×D311yescharacteristic
374C4×C5D3×#4111yescharacteristic
375Dic5—21no—
376Dic5—21no—
377Dic5—32no—
378Dic5—122no—
379#41—158no—
380#41—304no—
381C2×Q8—32no—
382C2×D4—52no—
383C2×D4—302no—
384C22×C4—102no—
385C22×C4—151no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—302no—
389Q16—34no—
390SD16—158no—
391D8—54no—
392M16—302no—
393C2×C8—31no—
394C2×C8—51no—
395C2×C8—151no—
396C2×C8—154no—
397C2×C8C2×D3×D511yescharacteristic
398C4⋊C4—62no—
399C4⋊C4—151no—
400C4⋊C4—151no—
401C4⋊C4—152no—
402C4⋊C4—302no—
403C4⋊C4—302no—
404C4⋊C4C2×D3×D512yes—
405C22⋊C4—102no—
406C22⋊C4—151no—
407C22⋊C4—151no—
408C22⋊C4—302no—
409C42—31no—
410C42—51no—
411C42—62no—
412C42—302no—
413C3×C5#295111yescharacteristic, complemented, Hall
414C22×C3—104no—
415C22×C3—202no—
416C22×C3—202no—
417C22×C3C2×D4×D511yescharacteristic
418C2×D3—52no—
419C2×D3—101no—
420C2×D3—101no—
421C3×C4—42no—
422C3×C4—101no—
423C3×C4—101no—
424C3×C4C22×C4×D511yescharacteristic
425C3×C4D5×#4111yescharacteristic
426Dic3—21no—
427Dic3—21no—
428Dic3—24no—
429Dic3—52no—
430Dic3—202no—
431C2×C5C4×D3×D411yescharacteristic
432C2×C5#575711yescharacteristic
433C2×C5#577111yescharacteristic
434D5—44no—
435D5—62no—
436C23—102no—
437C23—151no—
438Q8—34no—
439Q8—62no—
440D4—54no—
441D4—102no—
442D4—308no—
443C2×C4—22no—
444C2×C4—31no—
445C2×C4—31no—
446C2×C4—51no—
447C2×C4—51no—
448C2×C4—62no—
449C2×C4—151no—
450C2×C4—152no—
451C2×C4—152no—
452C2×C4—308no—
453C2×C4—302no—
454C2×C4—402no—
455C2×C4—1202no—
456C2×C4—1202no—
457C2×C4C22×D3×D511yescharacteristic
458C8—61no—
459C8—101no—
460C8—152no—
461C8C4×D3×D512yes—
462C2×C3—204no—
463C2×C3C4×D4×D511yescharacteristic
464C2×C3#6610011yescharacteristic
465C2×C3#6610311yescharacteristic
466D3—102no—
467C5#7958911yescharacteristic, complemented, Sylow
468C22—104no—
469C22—152no—
470C22—202no—
471C22—202no—
472C22—301no—
473C22—301no—
474C22D3×D4×D511yescharacteristic
475C4—42no—
476C4—61no—
477C4—64no—
478C4—61no—
479C4—101no—
480C4—101no—
481C4—152no—
482C4—602no—
483C4C2×C4×D3×D511yescharacteristic
484C4#9203411yescharacteristic
485C3#1061145211yescharacteristic, complemented, Sylow
486C2—204no—
487C2—302no—
488C2#1175384011yescharacteristic
489C2#1175405811yescharacteristic
490C2#1175411311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC2×#91277C2
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. #11753401C2semidirect
3. D15×#107C2semidirect
4. C5×#4873C2semidirect
5. C3×#65161C2semidirect
6. Dic5×Dic12C2semidirect
7. Dic3×D40C2semidirect
8. #11747657C2semidirect
9. #11747507C2semidirect
10. #11747471C2semidirect
11. #11747222C2semidirect
29. #91277C4semidirect
48. #65161D3semidirect
62. #6766C2×C4semidirect
68. C8×D15C2×C4semidirect
73. C5×Dic12C2×C4semidirect
77. C3×D40C2×C4semidirect
85. #6655C2×C4semidirect
93. #4873D5semidirect
212. D40C4×D3semidirect
274. Dic12C4×D5semidirect
413. C3×C5#2951semidirect
467. C5#79589semidirect
485. C3#10611452semidirect

Maximal subgroups

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

subgroupindex
C2×#912772
#117534012
D15×#1072
C5×#48732
C3×#651612
Dic5×Dic122
Dic3×D402
#117476572
#117475072
#117474712
#117472222
#106114523
#795895