Finite Group Databasebeta

← #14460009

Subgroups — #14460009

Order 1920.

772 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
1C5×#5542C211yesmaximal, characteristic, complemented
2C3×#65885C211yesmaximal, characteristic
3D4×C3⋊#168C211yesmaximal, characteristic, complemented
4#11748562C212yesmaximal, complemented
5#11748528C212yesmaximal, complemented
6#11748402C212yesmaximal, complemented
7#11748364C212yesmaximal, complemented
8#11747099C211yesmaximal, characteristic, complemented
9C4×#6655C211yesmaximal, characteristic, complemented
10#11746924C211yesmaximal, characteristic, complemented
11#11746886C211yesmaximal, characteristic, complemented
12#10615395—31nomaximal, Hall
13C2×C3×#709C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15C22×C3⋊#168C2212yes—
16C5×#936—21no—
17C5×#926C2212yes—
18C5×#924C2212yes—
19C5×#887—21no—
20C5×#879—22no—
21C5×#869C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C3×#4084—21no—
24C3×#4070C2212yes—
25C3×D5×C4⋊C4—21no—
26C3×#4029—22no—
27C3×C4×D20C2211yescharacteristic
28C3×#4015C2211yescharacteristic
29C2×#6661C2212yes—
30C2×#6655C2211yescharacteristic
31#91114C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34#90989C2212yes—
35#90986C2211yescharacteristic
36#90972C2211yescharacteristic
37#90970C2212yes—
38#90970C2212yes—
39#90970C2212yes—
40#90964C2211yescharacteristic
41#90964C2212yes—
42#83510—51nomaximal, Hall
43C5×#556—31no—
44#65885D311yescharacteristic
45#65382—31no—
46#65376—31no—
47#65340—32no—
48#65336—32no—
49#65320—31no—
50C4×#688—31no—
51D4×#168—31no—
52#65291—32no—
53#65285—32no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×C5×Dic6—21no—
57C2×C5×Dic6C2311yescharacteristic
58C2×C3×C22⋊D5—22no—
59C3×#709—24no—
60C3×#709—42no—
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×C4×D5—22no—
64C2×C3×Dic10C2312yes—
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C22⋊C4D412yes—
67C3×C42×C5C2311yescharacteristic
68C2×C3⋊#168—42no—
69C2×C3⋊#168C2311yescharacteristic
70C2×C3⋊#168C2312yes—
71C2×C3⋊#168C2311yescharacteristic
72C5×#217—22no—
73C5×#217—22no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×C4⋊Dic3C2312yes—
77C5×Dic3⋊C4—21no—
78C5×Dic3⋊C4—22no—
79C4×C5×Dic3—21no—
80C4×C5×Dic3—22no—
81C3×C22⋊Dic5—22no—
82C3×#685—21no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×#683—22no—
87#6661—42no—
88#6655—22no—
89C3×#547—51no—
90#5542D511yescharacteristic, complemented
91#5239—52no—
92#5233—52no—
93#5090—51no—
94#5079—51no—
95#5051—52no—
96#5045—52no—
97C4×#214—51no—
98D4×C3⋊C8—51no—
99#5007—51no—
100C2×#709C2×D312yes—
101C5×C4⋊Q8—31no—
102C5×#126—62no—
103C5×#124—61no—
104C5×C22⋊Q8—32no—
105C4×C5×Q8—31no—
106C4×C5×Q8—61no—
107C4×C5×D4C2×D311yescharacteristic
108C5×#117—32no—
109C2×#689—32no—
110C2×#688—31no—
111#4084—21no—
112#4070C2×D312yes—
113C22×#168—32no—
114D5×C4⋊C4—21no—
115#4029—22no—
116C4×D20C2×D311yescharacteristic
117#4015C2×D311yescharacteristic
118#3967—31no—
119C22⋊#168—32no—
120#3942—32no—
121#3942—32no—
122#3942—32no—
123#3941—31no—
124#3941—32no—
125#3940—31no—
126#3939—32no—
127C4⋊#168—31no—
128C4×#168—31no—
129#3302—151noSylow
130C23×C3×C5C2×D412yes—
131C22×C3×D5—21no—
132C3×C5×D4—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×C5×Dic3—21no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—22no—
142C5×Dic6—21no—
143C5×Dic6—21no—
144C5×Dic6—42no—
145C3×C22⋊D5—44no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—22no—
148C3×D20—21no—
149C3×D20#4112yes—
150C3×C4×D5—44no—
151C3×C4×D5—42no—
152C3×Dic10—22no—
153C3×Dic10—22no—
154C3⋊#168—21no—
155C3⋊#168—22no—
156C3⋊#168—21no—
157C2×C3×#41—52no—
158C3×C4⋊Q8—51no—
159C3×#123—102no—
160C3×C22⋊Q8—52no—
161C3×#121—101no—
162C3×C4×D4—51no—
163C3×C4×D4C2×D511yescharacteristic
164C2×C3×C4⋊C4—101no—
165C2×#216—52no—
166#936—21no—
167C2×#214—51no—
168#926C2×D512yes—
169#924C2×D512yes—
170C22×C3⋊C8—52no—
171#887—21no—
172#879—22no—
173#869C2×D511yescharacteristic
174C4×Dic6C2×D511yescharacteristic
175#835—52no—
176#835—52no—
177#835—52no—
178#832—51no—
179#832—52no—
180#830—52no—
181#810—51no—
182#808—51no—
183#807—52no—
184C4⋊(C3⋊C8)—51no—
185C4×C3⋊C8—51no—
186C2×C5×Q8—31no—
187C2×C5×Q8—61no—
188C2×C5×D4#6711yescharacteristic
189C22×C4×C5C22×D312yes—
190C2×C22⋊D5—22no—
191#709—24no—
192#709—42no—
193C2×D20C22×D311yescharacteristic
194C2×C4×D5—22no—
195C2×C4×D5—21no—
196C2×Dic10C22×D312yes—
197C5×C4⋊C4—31no—
198C5×C4⋊C4—32no—
199C5×C4⋊C4—61no—
200C5×C4⋊C4—62no—
201C5×C4⋊C4—61no—
202C5×C4⋊C4#6711yescharacteristic
203C5×C22⋊C4—62no—
204C5×C22⋊C4—62no—
205C5×C22⋊C4#6712yes—
206C42×C5—62no—
207C42×C5—61no—
208C42×C5C22×D311yescharacteristic
209C22⋊Dic5—22no—
210#689—122no—
211#688—62no—
212#685—21no—
213C4⋊Dic5—21no—
214C4⋊Dic5—21no—
215C4⋊Dic5C22×D311yescharacteristic
216#683—22no—
217C2×#168—31no—
218C2×#168—31no—
219C2×#168—32no—
220C2×#168—122no—
221#556—31no—
222#547—51no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—151no—
231#416—152no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—22no—
235C22×C3×C5C22×D411yescharacteristic
236C2×C3×D5—22no—
237C2×C3×D5—41no—
238C2×C3×D5—41no—
239C3×C4×C5—22no—
240C3×C4×C5—21no—
241C3×C4×C5#13512yes—
242C3×C4×C5C2×#4111yescharacteristic
243C3×C4×C5H(5,𝔽2)11yescharacteristic
244C3×Dic5—42no—
245C3×Dic5—41no—
246C5×Dic3—41no—
247C5×Dic3—42no—
248C5×Dic3—41no—
249C3×#41—104no—
250C3×#41—202no—
251C2×C3×Q8—52no—
252C2×C3×D4—51no—
253C2×C3×D4—102no—
254C2×C3×D4C22⋊D511yescharacteristic
255C22×C3×C4—101no—
256C22×C3×C4—102no—
257C22×C3×C4C22×D512yes—
258C2×Dic6—21no—
259C2×Dic6C22×D511yescharacteristic
260C3×C4⋊C4—51no—
261C3×C4⋊C4—102no—
262C3×C4⋊C4—101no—
263C3×C4⋊C4—101no—
264C3×C4⋊C4C22⋊D511yescharacteristic
265C3×C22⋊C4—102no—
266C3×C22⋊C4—101no—
267C3×C22⋊C4C22⋊D512yes—
268C3×C42C22×D511yescharacteristic
269#217—22no—
270#217—22no—
271#216—202no—
272#214—102no—
273C4⋊Dic3—21no—
274C4⋊Dic3C22×D512yes—
275C4⋊Dic3C22×D511yescharacteristic
276Dic3⋊C4—21no—
277Dic3⋊C4—22no—
278C4×Dic3—21no—
279C4×Dic3—22no—
280C2×C3⋊C8—51no—
281C2×C3⋊C8—51no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—202no—
284C23×C5C2×#6712yes—
285C22×D5—21no—
286C5×Q8—61no—
287C5×Q8—61no—
288C5×Q8—122no—
289C5×D4—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—61no—
293C2×C4×C5—62no—
294C2×C4×C5—61no—
295C2×C4×C5C2×#6712yes—
296C2×C4×C5C2×#6711yescharacteristic
297C2×C4×C5C2×#6711yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C22⋊D5—44no—
300C2×Dic5—21no—
301C2×Dic5—22no—
302D20—21no—
303D20#23712yes—
304C4×D5—44no—
305C4×D5—42no—
306Dic10—22no—
307Dic10—22no—
308#168—61no—
309#168—61no—
310#168—62no—
311C2×#41—52no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—152no—
315C4⋊Q8—31no—
316C4⋊Q8—51no—
317#126—62no—
318#124—61no—
319#123—102no—
320C22⋊Q8—32no—
321C22⋊Q8—52no—
322#121—101no—
323C4×Q8—31no—
324C4×Q8—61no—
325C4×D4—51no—
326C4×D4D3×D511yescharacteristic
327#117—32no—
328C2×C4⋊C4—101no—
329#107—152no—
330#106—151no—
331C4⋊C8—151no—
332#103—152no—
333#103—152no—
334#103—152no—
335#103—151no—
336#102—151no—
337#102—152no—
338C22⋊C8—152no—
339C4×C8—151no—
340C2×C3×C5—42no—
341C2×C3×C5#54611yescharacteristic
342C2×C3×C5C2×#13511yescharacteristic
343C2×C3×C5#57811yescharacteristic
344C3×D5—42no—
345C23×C3—101no—
346C23×C3C2×C22⋊D512yes—
347C3×Q8—102no—
348C3×Q8—102no—
349C3×D4—22no—
350C3×D4—52no—
351C3×D4—101no—
352C3×D4—204no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—101no—
356C2×C3×C4—102no—
357C2×C3×C4—204no—
358C2×C3×C4—202no—
359C2×C3×C4C2×C22⋊D512yes—
360C2×C3×C4C2×C22⋊D511yescharacteristic
361C2×C3×C4C2×C22⋊D511yescharacteristic
362C2×C3×C4C23×D511yescharacteristic
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366Dic6—21no—
367Dic6—21no—
368Dic6—42no—
369C3⋊C8—101no—
370C3⋊C8—101no—
371C3⋊C8—102no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5C22×#6711yescharacteristic
376C2×D5—22no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—22no—
380C4×C5—21no—
381C4×C5—121no—
382C4×C5—122no—
383C4×C5—121no—
384C4×C5#95012yes—
385C4×C5C2×#23711yescharacteristic
386C4×C5#100411yescharacteristic
387Dic5—42no—
388Dic5—41no—
389#41—104no—
390#41—202no—
391C2×Q8—31no—
392C2×Q8—52no—
393C2×Q8—61no—
394C2×D4—51no—
395C2×D4—102no—
396C2×D4#120111yescharacteristic
397C22×C4—101no—
398C22×C4—102no—
399C22×C4C2×D3×D512yes—
400Q16—602no—
401SD16—302no—
402C2×C8—151no—
403C2×C8—151no—
404C2×C8—152no—
405C2×C8—602no—
406C4⋊C4—31no—
407C4⋊C4—32no—
408C4⋊C4—51no—
409C4⋊C4—61no—
410C4⋊C4—62no—
411C4⋊C4—61no—
412C4⋊C4—101no—
413C4⋊C4—102no—
414C4⋊C4—101no—
415C4⋊C4#120111yescharacteristic
416C22⋊C4—62no—
417C22⋊C4—62no—
418C22⋊C4—102no—
419C22⋊C4—101no—
420C22⋊C4#120112yes—
421C42—62no—
422C42—61no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—102no—
429C22×C3—201no—
430C22×C3—201no—
431C22×C3C22×C22⋊D511yescharacteristic
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—201no—
435C3×C4—202no—
436C3×C4#409612yes—
437C3×C4D5×#4111yescharacteristic
438C3×C4#414911yescharacteristic
439Dic3—42no—
440Dic3—41no—
441Dic3—41no—
442C2×C5—42no—
443C2×C5#580611yescharacteristic
444C2×C5C2×#95011yescharacteristic
445C2×C5#583811yescharacteristic
446D5—42no—
447C23—101no—
448C23C2×#120112yes—
449Q8—61no—
450Q8—61no—
451Q8—102no—
452Q8—102no—
453Q8—122no—
454D4—22no—
455D4—52no—
456D4—101no—
457D4—204no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—61no—
461C2×C4—62no—
462C2×C4—61no—
463C2×C4—101no—
464C2×C4—102no—
465C2×C4—204no—
466C2×C4—202no—
467C2×C4C2×#120112yes—
468C2×C4C2×#120111yescharacteristic
469C2×C4C2×#120111yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—301no—
472C8—301no—
473C8—302no—
474C2×C3—42no—
475C2×C3—202no—
476C2×C3C2×#409611yescharacteristic
477C2×C3#6616311yescharacteristic
478C2×C3#6617211yescharacteristic
479C5#8351011yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—22no—
483C22—102no—
484C22—201no—
485C22—201no—
486C22C22×#120111yescharacteristic
487C4—21no—
488C4—22no—
489C4—121no—
490C4—122no—
491C4—121no—
492C4—201no—
493C4—202no—
494C4#9129712yes—
495C4D5×#23711yescharacteristic
496C4#9202611yescharacteristic
497C3#1061539511yescharacteristic, complemented, Sylow
498C2—42no—
499C2—202no—
500C2C2×#9129711yescharacteristic
501C2#1175496111yescharacteristic
502C2#1175530211yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC3×#65885C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5542C2semidirect
3. D4×C3⋊#168C2semidirect
4. #11748562C2semidirect
5. #11748528C2semidirect
6. #11748402C2semidirect
7. #11748364C2semidirect
8. #11747099C2semidirect
9. C4×#6655C2semidirect
10. #11746924C2semidirect
11. #11746886C2semidirect
90. #5542D5semidirect
424. C3×C5#3302semidirect
479. C5#83510semidirect
497. C3#10615395semidirect

Maximal subgroups

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

subgroupindex
C5×#55422
C3×#658852
D4×C3⋊#1682
#117485622
#117485282
#117484022
#117483642
#117470992
C4×#66552
#117469242
#117468862
#106153953
#835105