Finite Group Databasebeta

← #14308907

Subgroups — #14308907

Order 1920.

564 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756278C211yesmaximal, characteristic, complemented
2#11751232C211yesmaximal, characteristic
3#11751102C211yesmaximal, characteristic
4#11751040C211yesmaximal, characteristic
5C3×C5×#339C211yesmaximal, characteristic, complemented
6#11746375C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10599556—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C2×#6714—22no—
14#91815C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17#91779—21no—
18#91777—21no—
19#91767—22no—
20#91759—21no—
21#91758—21no—
22#91105—21no—
23#91105—21no—
24#91093—21no—
25#91093—21no—
26#68763—51nomaximal, Hall
27#65853—31no—
28#65420—31no—
29#65290—31no—
30#65228—31no—
31C5×#339D311yescharacteristic, complemented
32#64774—31no—
33#64743—31no—
34C23×D15—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15D412yes—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60Q812yescomplemented
44C2×Dic30—22no—
45C3×C5×M16—21no—
46C3×C5×M16—21no—
47C2×C3×C5×C8—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C3×C42×C5—21no—
53C3×C42×C5—21no—
54#6719—21no—
55#6714—44no—
56C4⋊Dic15—22no—
57C4⋊Dic15—21no—
58C4⋊Dic15—21no—
59C4⋊Dic15D411yescharacteristic
60C4⋊Dic15D411yescharacteristic
61#6712—22no—
62#6712—22no—
63C4×Dic15—21no—
64#6710—21no—
65#6710—21no—
66C2×C3⋊#168—21no—
67#5519—51no—
68#5131—51no—
69#5001—51no—
70#4939—51no—
71C3×#339D511yescharacteristic, complemented
72#4554—51no—
73#4523—51no—
74C22×D20—31no—
75C2×C5×M16C2×D311yescharacteristic
76C5×#117C2×D311yescharacteristic
77C2×C42×C5C2×D311yescharacteristic
78C2×#685—62no—
79#4072—31no—
80C2×C4⋊Dic5—31no—
81C2×#681—31no—
82#4036—61no—
83#4034—61no—
84#4024—62no—
85#4016—61no—
86#4015—61no—
87#3953—61no—
88#3953—61no—
89#3941—61no—
90#3941—61no—
91#2027—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×D15—22no—
94C22×D15—42no—
95C22×D15—42no—
96C22×D15—41no—
97C22×D15—41no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×Q811yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×Dic15—21no—
110C2×Dic15—21no—
111C2×Dic15—22no—
112C2×Dic15—42no—
113D60—22no—
114D60—22no—
115D60—41no—
116D60—41no—
117Dic30—82no—
118C3×C5×C8—41no—
119C3⋊#168—41no—
120C22×D12—51no—
121C2×C3×M16C2×D511yescharacteristic
122C3×#117C2×D511yescharacteristic
123C2×C3×C42C2×D511yescharacteristic
124C2×(C2×D3)⋊C4—102no—
125#926—51no—
126C2×C4⋊Dic3—51no—
127C2×#208—51no—
128#890—101no—
129#888—101no—
130#878—102no—
131#870—101no—
132#869—101no—
133#821—101no—
134#821—101no—
135#809—101no—
136#809—101no—
137C23×D5—61no—
138C22×C4×C5—21no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—32no—
141C2×D20—32no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20—61no—
145C2×D20—61no—
146C2×D20—61no—
147C2×Dic10—62no—
148C5×M16—21no—
149C5×M16—21no—
150C2×C5×C8—21no—
151C5×C4⋊C4D1211yescharacteristic
152C5×C4⋊C4D1211yescharacteristic
153C5×C22⋊C4—21no—
154C42×C5—21no—
155C42×C5—21no—
156C42×C5—21no—
157C22⋊Dic5—61no—
158#685—124no—
159C4⋊Dic5—31no—
160C4⋊Dic5—31no—
161C4⋊Dic5—62no—
162C4⋊Dic5—61no—
163C4⋊Dic5—61no—
164#683—62no—
165#683—62no—
166C4×Dic5—61no—
167#681—61no—
168#681—61no—
169C2×#168—61no—
170#544—151no—
171#418—151no—
172#418—151no—
173#390—151no—
174#343—151no—
175#339—151no—
176#339D1511yescharacteristic, complemented
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5#12011yescharacteristic
180C22×C3×C5C22⋊Q811yescharacteristic
181C22×C3×C5#12411yescharacteristic
182C2×D15—44no—
183C2×D15—42no—
184C2×D15—82no—
185C2×D15—81no—
186C2×D15—81no—
187C3×C4×C5—42no—
188C3×C4×C5—41no—
189C3×C4×C5—41no—
190C3×C4×C5C22⋊Q811yescharacteristic
191C3×C4×C5C22⋊Q811yescharacteristic
192C3×C4×C5#12411yescharacteristic
193C3×C4×C5#12411yescharacteristic
194Dic15—41no—
195Dic15—42no—
196Dic15—41no—
197C23×D3—101no—
198C22×C3×C4—21no—
199C22×C3×C4C22×D511yescharacteristic
200C22×Dic3—52no—
201C2×D12—52no—
202C2×D12—101no—
203C2×D12—101no—
204C2×D12—101no—
205C2×D12—101no—
206C2×D12—101no—
207C2×Dic6—102no—
208C3×M16—21no—
209C3×M16—21no—
210C2×C3×C8—21no—
211C3×C4⋊C4D2011yescharacteristic
212C3×C4⋊C4D2011yescharacteristic
213C3×C22⋊C4—21no—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42—21no—
217#217—101no—
218(C2×D3)⋊C4—204no—
219C4⋊Dic3—51no—
220C4⋊Dic3—51no—
221C4⋊Dic3—102no—
222C4⋊Dic3—101no—
223C4⋊Dic3—101no—
224Dic3⋊C4—102no—
225Dic3⋊C4—102no—
226C4×Dic3—101no—
227#208—101no—
228#208—101no—
229C2×C3⋊C8—101no—
230C23×C5D3×D411yescharacteristic
231C22×D5—62no—
232C22×D5—122no—
233C22×D5—122no—
234C22×D5—121no—
235C22×D5—121no—
236C2×C4×C5—22no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5C2×D1211yescharacteristic
242C2×C4×C5#23511yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5D3×Q811yescharacteristic
247C2×Dic5—61no—
248C2×Dic5—61no—
249C2×Dic5—62no—
250C2×Dic5—122no—
251D20—62no—
252D20—62no—
253D20—121no—
254D20—121no—
255Dic10—242no—
256C5×C8—41no—
257#168—121no—
258C22×D4—151no—
259C2×M16—151no—
260C2×M16C2×D1511yescharacteristic
261C4⋊Q8—301no—
262C4⋊Q8—301no—
263#125—301no—
264#125—301no—
265C22⋊Q8—302no—
266#117—151no—
267#117C2×D1511yescharacteristic
268C2×C4⋊C4—151no—
269C2×C22⋊C4—302no—
270C2×C42C2×D1511yescharacteristic
271#102—301no—
272#102—301no—
273#102—301no—
274#102—301no—
275C2×C3×C5—21no—
276C2×C3×C5—21no—
277C2×C3×C5#39311yescharacteristic
278C2×C3×C5#45311yescharacteristic
279C2×C3×C5#45411yescharacteristic
280D15—82no—
281C23×C3D4×D511yescharacteristic
282C22×D3—102no—
283C22×D3—202no—
284C22×D3—202no—
285C22×D3—201no—
286C22×D3—201no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4C2×D2011yescharacteristic
293C2×C3×C4#70911yescharacteristic
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4#71111yescharacteristic
297C2×C3×C4Q8×D511yescharacteristic
298C2×Dic3—101no—
299C2×Dic3—101no—
300C2×Dic3—102no—
301C2×Dic3—202no—
302D12—102no—
303D12—102no—
304D12—201no—
305D12—201no—
306Dic6—402no—
307C3×C8—41no—
308C3⋊C8—201no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5#88211yescharacteristic
312C22×C5#88511yescharacteristic
313C22×C5#89611yescharacteristic
314C2×D5—124no—
315C2×D5—122no—
316C2×D5—242no—
317C2×D5—241no—
318C2×D5—241no—
319C4×C5—42no—
320C4×C5—41no—
321C4×C5—41no—
322C4×C5#87511yescharacteristic
323C4×C5#88511yescharacteristic
324C4×C5#89611yescharacteristic
325C4×C5#89711yescharacteristic
326Dic5—121no—
327Dic5—122no—
328Dic5—121no—
329C24—301no—
330C2×Q8—302no—
331C2×D4—152no—
332C2×D4—301no—
333C2×D4—301no—
334C2×D4—301no—
335C2×D4—301no—
336C2×D4—301no—
337C22×C4—21no—
338C22×C4—152no—
339C22×C4C22×D1511yescharacteristic
340M16—21no—
341M16—21no—
342M16—301no—
343M16—301no—
344C2×C8—21no—
345C2×C8—301no—
346C4⋊C4—151no—
347C4⋊C4—151no—
348C4⋊C4—302no—
349C4⋊C4—302no—
350C4⋊C4—302no—
351C4⋊C4—301no—
352C4⋊C4—301no—
353C4⋊C4D6011yescharacteristic
354C4⋊C4D6011yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—301no—
357C22⋊C4—604no—
358C42—21no—
359C42—21no—
360C42—21no—
361C42—301no—
362C3×C5#202711yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3#402811yescharacteristic
366C22×C3#403111yescharacteristic
367C22×C3#404211yescharacteristic
368C2×D3—204no—
369C2×D3—202no—
370C2×D3—402no—
371C2×D3—401no—
372C2×D3—401no—
373C3×C4—42no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4#402111yescharacteristic
377C3×C4#403111yescharacteristic
378C3×C4#404211yescharacteristic
379C3×C4#404311yescharacteristic
380Dic3—201no—
381Dic3—202no—
382Dic3—201no—
383C2×C5—21no—
384C2×C5—21no—
385C2×C5#467311yescharacteristic
386C2×C5#482211yescharacteristic
387C2×C5#482711yescharacteristic
388D5—242no—
389C23—302no—
390C23—602no—
391C23—602no—
392C23—601no—
393C23—601no—
394C23D4×D1511yescharacteristic
395Q8—1202no—
396D4—302no—
397D4—302no—
398D4—601no—
399D4—601no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—301no—
406C2×C4—301no—
407C2×C4—302no—
408C2×C4—602no—
409C2×C4C2×D6011yescharacteristic
410C2×C4#681711yescharacteristic
411C2×C4#681711yescharacteristic
412C2×C4D4×D1511yescharacteristic
413C2×C4#681911yescharacteristic
414C2×C4Q8×D1511yescharacteristic
415C8—41no—
416C8—601no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3#6496211yescharacteristic
420C2×C3#6511111yescharacteristic
421C2×C3#6511611yescharacteristic
422D3—402no—
423C5#6876311yescharacteristic, complemented, Sylow
424C22—21no—
425C22—21no—
426C22—604no—
427C22—602no—
428C22—1202no—
429C22—1201no—
430C22—1201no—
431C22#9177111yescharacteristic
432C22#9177411yescharacteristic
433C22#9178511yescharacteristic
434C4—42no—
435C4—41no—
436C4—41no—
437C4—602no—
438C4—601no—
439C4—601no—
440C4#9176411yescharacteristic
441C4#9177411yescharacteristic
442C4#9178511yescharacteristic
443C4#9178611yescharacteristic
444C3#1059955611yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—1202no—
448C2#1175077411yescharacteristic
449C2#1175092311yescharacteristic
450C2#1175092811yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#339C2
socleC22×C3×C5#120
prime radicalC22×D60C22
hypercenter#339D15
hypocenterC3×C5#2027
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #11756278C2semidirect
5. C3×C5×#339C2semidirect
6. #11746375C2semidirect
7. #11746344C2semidirect
31. C5×#339D3semidirect
43. C2×D60Q8semidirect
71. C3×#339D5semidirect
176. #339D15semidirect
362. C3×C5#2027semidirect
423. C5#68763semidirect
444. C3#10599556semidirect

Maximal subgroups

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

subgroupindex
#117562782
#117512322
#117511022
#117510402
C3×C5×#3392
#117463752
#117463442
#105995563
#687635