Finite Group Databasebeta

← #14438036

Subgroups — #14438036

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754616C211yesmaximal, characteristic, complemented
2#11754581C211yesmaximal, characteristic
3#11751214C211yesmaximal, characteristic, complemented
4C2×C5×#815C211yesmaximal, characteristic, complemented
5C3×#65402C211yesmaximal, characteristic, complemented
6#11748411C211yesmaximal, characteristic, complemented
7#11748365C211yesmaximal, characteristic, complemented
8#11748031C212yesmaximal, complemented
9#11748008C212yesmaximal, complemented
10#11747990C212yesmaximal, complemented
11#11747968C212yesmaximal, complemented
12#10610228—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16#91815C2211yescharacteristic
17C2×C4×C5×Dic3C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20#91575—22no—
21#91569—22no—
22#91469C2212yes—
23C4×#1204—22no—
24#91458C2211yescharacteristic
25C4×#1202—22no—
26#91389C2211yescharacteristic
27#91381C2212yes—
28#91374C2211yescharacteristic
29#91364C2211yescharacteristic
30#91105C2212yes—
31#91100C2212yes—
32C5×#815C2212yes—
33C5×#815C2212yes—
34C3×#3953C2212yes—
35C3×#3948C2212yes—
36#90974C2212yes—
37#90971C2212yes—
38#90968C2212yes—
39#90965C2212yes—
40#78826—51nomaximal, Hall
41#65811—31no—
42#65804—31no—
43C2×C5×#97—31no—
44#65402—31no—
45#65402—31no—
46#65402—31no—
47#65402D311yescharacteristic, complemented
48#65003—32no—
49#65003—32no—
50#65002—32no—
51#64992—32no—
52C22×C3×C4×C5C2311yescharacteristic
53C2×#1220—21no—
54#6817—22no—
55#6817—22no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×Dic30C2311yescharacteristic
59C22×C5×Dic3D412yes—
60C2×C3×C22⋊D5—21no—
61C3×#709—22no—
62C3×#709—22no—
63C2×C3×D20C2311yescharacteristic
64C2×C3×C4×D5—21no—
65C2×C3×Dic10C2311yescharacteristic
66C2×#1204—22no—
67C2×#1202—22no—
68C2×C3×C5×C8—22no—
69C2×C3×C5×C8C2312yes—
70#6719—21no—
71C4⋊Dic15C2312yes—
72C4×Dic15—21no—
73C4×C5×Dic3D412yes—
74C4×C5×Dic3C2311yescharacteristic
75C4×C5×Dic3C2311yescharacteristic
76C2×C5×C3⋊C8—22no—
77C2×C5×C3⋊C8C2312yes—
78C3×C22⋊Dic5—21no—
79C3×C4⋊Dic5C2312yes—
80C3×C4×Dic5—21no—
81Dic3⋊Dic5—22no—
82Dic3⋊Dic5—22no—
83#6669—22no—
84#6668—22no—
85#6667—22no—
86#6665—22no—
87#5832—51no—
88#5517—51no—
89C3×#416—51no—
90#5233—51no—
91#5113—51no—
92C2×#815D511yescharacteristic, complemented
93#5002—51no—
94#4797—52no—
95#4794—52no—
96#4765—52no—
97#4764—52no—
98C2×#709—31no—
99C2×#709C2×D311yescharacteristic
100C22×C5×C8—31no—
101C22×C5×C8C2×D311yescharacteristic
102C2×C42×C5—31no—
103#4076—62no—
104#4072—31no—
105#4072C2×D311yescharacteristic
106#4070—62no—
107#4021—31no—
108#4021—31no—
109#4020—31no—
110C4×D20—62no—
111#4016—32no—
112#4015—32no—
113#4015—31no—
114C4×Dic10—62no—
115C5×#97—32no—
116C5×#97—32no—
117#3953—32no—
118#3953—32no—
119#3953—32no—
120#3953C2×D312yes—
121#3948—32no—
122#3948—32no—
123#3948—32no—
124#3948C2×D312yes—
125#3135—151noSylow
126C23×C3×C5C2×D411yescharacteristic
127C22×D15—21no—
128C22×C3×D5—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5#4112yes—
131C2×C3×C4×C5#4112yes—
132C2×C3×C4×C5C2411yescharacteristic
133#1220—42no—
134C2×Dic15—21no—
135C2×Dic15—22no—
136D60—21no—
137D60—21no—
138C4×D15—42no—
139Dic30—21no—
140Dic30—21no—
141C2×C5×Dic3—42no—
142C2×C5×Dic3C2×D412yes—
143C2×C5×Dic3C2×D412yes—
144C3×C22⋊D5—42no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—22no—
147C3×D20—21no—
148C3×D20—21no—
149C3×C4×D5—42no—
150C3×Dic10—21no—
151C3×Dic10—21no—
152#1204—44no—
153#1202—44no—
154C3×C5×C8—22no—
155C5×C3⋊C8—22no—
156C2×C3×#41—51no—
157C2×#235—51no—
158C22×C3×C8C2×D511yescharacteristic
159C3×#117—51no—
160#947—51no—
161#944—51no—
162#940—51no—
163#939—102no—
164#936—51no—
165C4×#67—102no—
166#926—51no—
167C2×C4×Dic3C2×D511yescharacteristic
168C22×C3⋊C8C2×D511yescharacteristic
169#890—52no—
170#888—52no—
171#878—102no—
172C4×Dic6—102no—
173C3×#103—52no—
174C3×#102—52no—
175#835—52no—
176#832—52no—
177#821—52no—
178#816—52no—
179#815C2×D512yes—
180#815C2×D512yes—
181#810—52no—
182#809—52no—
183C22×C4×C5—32no—
184C22×C4×C5C22×D311yescharacteristic
185C2×C22⋊D5—21no—
186C2×C22⋊D5—61no—
187#709—22no—
188#709—22no—
189#709—62no—
190#709—62no—
191C2×D20—31no—
192C2×D20—62no—
193C2×D20C22×D311yescharacteristic
194C2×C4×D5—21no—
195C2×C4×D5—61no—
196C2×Dic10—31no—
197C2×Dic10—62no—
198C2×Dic10C22×D311yescharacteristic
199C2×C5×C8—22no—
200C2×C5×C8—32no—
201C2×C5×C8—62no—
202C2×C5×C8C22×D312yes—
203C42×C5—32no—
204C42×C5—31no—
205C42×C5—31no—
206C22⋊Dic5—21no—
207C22⋊Dic5—61no—
208#685—62no—
209#685—62no—
210C4⋊Dic5—32no—
211C4⋊Dic5—62no—
212C4⋊Dic5—62no—
213C4⋊Dic5C22×D312yes—
214#683—62no—
215#683—62no—
216C4×Dic5—21no—
217C4×Dic5—61no—
218#533—151no—
219#532—151no—
220#491—152no—
221#490—152no—
222#489—152no—
223#489—152no—
224#416—51no—
225#416—151no—
226#416—151no—
227#416—151no—
228C2×#97—31no—
229C22×C3×C5—22no—
230C22×C3×C5#12412yes—
231C22×C3×C5C22×D411yescharacteristic
232C2×D15—41no—
233C2×D15—42no—
234C2×C3×D5—41no—
235C2×C3×D5—42no—
236C3×C4×C5#12412yes—
237C3×C4×C5C2×#4111yescharacteristic
238C3×C4×C5C2×#4111yescharacteristic
239Dic15—41no—
240Dic15—42no—
241C3×Dic5—41no—
242C3×Dic5—42no—
243C5×Dic3—22no—
244C5×Dic3—22no—
245C3×#41—102no—
246C3×#41—102no—
247C2×C3×Q8—51no—
248C2×C3×D4—51no—
249C2×C3×D4—101no—
250C22×C3×C4—101no—
251C22×C3×C4C22×D511yescharacteristic
252C2×#67—101no—
253C2×#67—102no—
254C22×Dic3D2012yes—
255#235—102no—
256#235—102no—
257C2×D12—51no—
258C2×C4×D3—101no—
259C2×Dic6—51no—
260C2×Dic6—102no—
261C2×C3×C8—22no—
262C2×C3×C8C22×D512yes—
263C3×C4⋊C4—52no—
264C3×C22⋊C4—101no—
265C3×C42—101no—
266#217—101no—
267#217—102no—
268(C2×D3)⋊C4—102no—
269C4⋊Dic3—52no—
270C4⋊Dic3—102no—
271Dic3⋊C4—102no—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274C4×Dic3—101no—
275C4×Dic3D2012yes—
276C4×Dic3C22×D511yescharacteristic
277C4×Dic3C22×D511yescharacteristic
278C2×C3⋊C8—22no—
279C2×C3⋊C8C22×D512yes—
280C23×C5D3×D411yescharacteristic
281C22×D5—21no—
282C22×D5—61no—
283C2×C4×C5—32no—
284C2×C4×C5—32no—
285C2×C4×C5—122no—
286C2×C4×C5#23512yes—
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5#23712yes—
289C2×C4×C5C23×D311yescharacteristic
290C22⋊D5—42no—
291C22⋊D5—122no—
292C2×Dic5—22no—
293C2×Dic5—21no—
294C2×Dic5—62no—
295C2×Dic5—61no—
296D20—21no—
297D20—21no—
298D20—61no—
299D20—61no—
300D20—124no—
301C4×D5—42no—
302C4×D5—122no—
303Dic10—21no—
304Dic10—21no—
305Dic10—61no—
306Dic10—61no—
307Dic10—124no—
308C5×C8—22no—
309C5×C8—62no—
310C2×#41—51no—
311C2×#41—151no—
312C22×C8—31no—
313C22×C8D3×D511yescharacteristic
314C4⋊Q8—152no—
315C4⋊Q8—151no—
316#127—151no—
317#125—152no—
318#124—151no—
319#124—151no—
320C22⋊Q8—302no—
321#121—302no—
322C4×Q8—302no—
323C4×D4—302no—
324#117—51no—
325#117—151no—
326C2×C42—31no—
327#103—52no—
328#103—152no—
329#103—152no—
330#103—152no—
331#102—52no—
332#102—152no—
333#102—152no—
334#102—152no—
335#97—32no—
336#97—32no—
337C2×C3×C5—22no—
338C2×C3×C5C2×#12411yescharacteristic
339C2×C3×C5#57512yes—
340D15—81no—
341C3×D5—81no—
342C23×C3—101no—
343C23×C3C2×D2011yescharacteristic
344C22×D3—101no—
345C3×Q8—101no—
346C3×Q8—101no—
347C3×D4—101no—
348C3×D4—101no—
349C3×D4—202no—
350C2×C3×C4—102no—
351C2×C3×C4—101no—
352C2×C3×C4—202no—
353C2×C3×C4C2×D2011yescharacteristic
354C2×C3×C4#70912yes—
355C2×C3×C4#70912yes—
356C2×C3×C4C23×D511yescharacteristic
357#67—204no—
358#67—202no—
359C2×Dic3—42no—
360C2×Dic3—102no—
361C2×Dic3—101no—
362C2×Dic3C2×D2012yes—
363C2×Dic3C2×D2012yes—
364D12—101no—
365D12—101no—
366C4×D3—202no—
367Dic6—101no—
368Dic6—101no—
369Dic6—204no—
370C3×C8—22no—
371C3⋊C8—22no—
372C22×C5—22no—
373C22×C5#88512yes—
374C22×C5C2×D3×D411yescharacteristic
375C2×D5—41no—
376C2×D5—42no—
377C2×D5—121no—
378C2×D5—122no—
379C4×C5—62no—
380C4×C5—62no—
381C4×C5#88512yes—
382C4×C5C2×#23511yescharacteristic
383C4×C5C2×#23711yescharacteristic
384Dic5—41no—
385Dic5—42no—
386Dic5—121no—
387Dic5—122no—
388#41—102no—
389#41—102no—
390#41—302no—
391#41—302no—
392C2×Q8—51no—
393C2×Q8—151no—
394C2×Q8—302no—
395C2×D4—51no—
396C2×D4—101no—
397C2×D4—151no—
398C2×D4—302no—
399C2×D4—301no—
400C22×C4—32no—
401C22×C4—101no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404C2×C8—22no—
405C2×C8—32no—
406C2×C8—62no—
407C2×C8C2×D3×D512yes—
408C4⋊C4—52no—
409C4⋊C4—152no—
410C4⋊C4—302no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C22⋊C4—101no—
415C22⋊C4—302no—
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—32no—
419C42—31no—
420C42—31no—
421C42—101no—
422C42—301no—
423C3×C5#313511yescharacteristic, complemented, Hall
424C22×C3—22no—
425C22×C3—201no—
426C22×C3—202no—
427C22×C3#402112yes—
428C22×C3C22×D2011yescharacteristic
429C2×D3—201no—
430C2×D3—202no—
431C3×C4—201no—
432C3×C4—202no—
433C3×C4#402112yes—
434C3×C4C2×#70911yescharacteristic
435C3×C4C2×#70911yescharacteristic
436Dic3—22no—
437Dic3—22no—
438Dic3—201no—
439Dic3—202no—
440C2×C5—22no—
441C2×C5C2×#88511yescharacteristic
442C2×C5#576812yes—
443D5—81no—
444D5—241no—
445C23—101no—
446C23—301no—
447C23D3×D2011yescharacteristic
448Q8—101no—
449Q8—101no—
450Q8—301no—
451Q8—301no—
452Q8—604no—
453D4—101no—
454D4—101no—
455D4—202no—
456D4—301no—
457D4—301no—
458D4—604no—
459D4—602no—
460C2×C4—32no—
461C2×C4—32no—
462C2×C4—102no—
463C2×C4—101no—
464C2×C4—122no—
465C2×C4—202no—
466C2×C4—302no—
467C2×C4—301no—
468C2×C4—602no—
469C2×C4#677112yes—
470C2×C4D3×D2011yescharacteristic
471C2×C4#677912yes—
472C2×C4C22×D3×D511yescharacteristic
473C8—22no—
474C8—62no—
475C2×C3—22no—
476C2×C3—401no—
477C2×C3C2×#402111yescharacteristic
478C2×C3#6608212yes—
479D3—401no—
480C5#7882611yescharacteristic, complemented, Sylow
481C22—22no—
482C22—201no—
483C22—202no—
484C22—601no—
485C22—602no—
486C22#9135312yes—
487C22C2×D3×D2011yescharacteristic
488C4—62no—
489C4—62no—
490C4—201no—
491C4—202no—
492C4—601no—
493C4—602no—
494C4#9135312yes—
495C4C2×#677111yescharacteristic
496C4C2×#677911yescharacteristic
497C3#1061022811yescharacteristic, complemented, Sylow
498C2—22no—
499C2—401no—
500C2—1201no—
501C2#1175396912yes—
502C2C2×#9135311yescharacteristic
subgroupG/H
centerC2×C4D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11754581C2
hypercenterC22×C8D3×D5
hypocenterC3×C5#3135
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #11754616C2semidirect
3. #11751214C2semidirect
4. C2×C5×#815C2semidirect
5. C3×#65402C2semidirect
6. #11748411C2semidirect
7. #11748365C2semidirect
8. #11748031C2semidirect
9. #11748008C2semidirect
10. #11747990C2semidirect
11. #11747968C2semidirect
47. #65402D3semidirect
92. C2×#815D5semidirect
423. C3×C5#3135semidirect
480. C5#78826semidirect
497. C3#10610228semidirect

Maximal subgroups

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

subgroupindex
#117546162
#117545812
#117512142
C2×C5×#8152
C3×#654022
#117484112
#117483652
#117480312
#117480082
#117479902
#117479682
#106102283
#788265