Finite Group Databasebeta

← #14471843

Subgroups — #14471843

Order 1920.

724 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
1#11752641C211yesmaximal, characteristic, complemented
2#11752636C211yesmaximal, characteristic, complemented
3C8×Dic30C211yesmaximal, characteristic, complemented
4C4×C5×#204C211yesmaximal, characteristic, complemented
5C3×#64983C211yesmaximal, characteristic, complemented
6#11747978C212yesmaximal, complemented
7#11747805C212yesmaximal, complemented
8#11747785C212yesmaximal, complemented
9#11747733C212yesmaximal, complemented
10#11747033C211yesmaximal, characteristic
11#11746959C211yesmaximal, characteristic, complemented
12#10611352—31nomaximal, Hall
13C4×Dic30C2211yescharacteristic
14C2×C5×#204C2211yescharacteristic
15C4×C5×D12C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4020C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91435C2212yes—
20#91434C2212yes—
21D3×C4⋊Dic5—21no—
22Dic3×D20—21no—
23#91410—22no—
24#91407—22no—
25#91384C2212yes—
26#91368C2212yes—
27#91365—21no—
28#91364—21no—
29C2×#6652C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#821C2211yescharacteristic
35C5×#817C2211yescharacteristic
36C5×#816C2211yescharacteristic
37C3×#3953C2212yes—
38C3×#3953C2212yes—
39#90989C2212yes—
40#90972C2212yes—
41#90964C2212yes—
42#81585—51nomaximal, Hall
43#65919—31no—
44#65877—31no—
45C4×C5×SD16—31no—
46#65454—32no—
47#65310—31no—
48#65304—31no—
49#65160—32no—
50#65089—32no—
51#65045—32no—
52#64983D311yescharacteristic, complemented
53C8×Dic10—31no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12C2311yescharacteristic
56C2×C4×C5×D3—21no—
57C2×C5×Dic6C2311yescharacteristic
58C2×C3×D20—21no—
59C2×C3×D20—21no—
60C2×C3×D20C2312yes—
61C2×C3×Dic10—21no—
62C2×D3×Dic5—22no—
63C2×D5×Dic3—22no—
64C2×C3×C5×C8C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C3×C42×C5C2311yescharacteristic
67C4⋊Dic15D411yescharacteristic
68#6712D412yes—
69C4×Dic15C2312yes—
70C2×C3⋊#168C2312yes—
71C5×(C2×D3)⋊C4—21no—
72C5×C4⋊Dic3C2311yescharacteristic
73C5×C4⋊Dic3C2311yescharacteristic
74C5×Dic3⋊C4—21no—
75C4×C5×Dic3—21no—
76C5×#204—22no—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5C2312yes—
79Dic3⋊Dic5—22no—
80#6668—22no—
81(C2×D3)⋊Dic5—22no—
82#6665—22no—
83#6665—22no—
84#6665—22no—
85#6652—24no—
86#5730—51no—
87#5713—51no—
88C3×#486—51no—
89#5091—51no—
90#5072—51no—
91#4787—52no—
92#4768—52no—
93#4763—52no—
94#4756—52no—
95C4×#204D511yescharacteristic, complemented
96C8×Dic6—51no—
97C2×C5×SD16—31no—
98C4×C5×Q8—31no—
99C4×C5×D4—31no—
100#4093—32no—
101D4×Dic5—32no—
102C2×#686—32no—
103C2×C4⋊Dic5—61no—
104#4070—61no—
105#4040—62no—
106#4039—32no—
107#4036—32no—
108#4024—62no—
109#4021—61no—
110#4020C2×D311yescharacteristic
111C4×D20—61no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C5×#106—31no—
115C5×#103—31no—
116C5×#102—31no—
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3953C2×D312yes—
120#3953C2×D312yes—
121#3946—32no—
122C8×Dic5—32no—
123#3941—32no—
124#3939—32no—
125C4⋊#168—31no—
126#3361—151noSylow
127C22×C5×D3—21no—
128C22×C3×D5—22no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15C2×D412yes—
133C2×Dic15C2×D412yes—
134Dic30—22no—
135C2×C5×Dic3—21no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3—21no—
138C5×D12—21no—
139C5×D12#4112yes—
140C4×C5×D3—42no—
141C5×Dic6—21no—
142C5×Dic6—21no—
143C2×C3×Dic5—22no—
144C3×D20—22no—
145C3×D20—22no—
146C3×D20—42no—
147C3×D20—81no—
148C3×Dic10—81no—
149D3×Dic5—82no—
150D5×Dic3—82no—
151C3×C5×C8—21no—
152C3×C5×C8—21no—
153C3⋊#168—22no—
154C3×C4⋊Q8—51no—
155C3×#127—51no—
156#946—102no—
157#936—52no—
158#936—101no—
159#935—102no—
160D4×Dic3—52no—
161D4×Dic3—101no—
162C2×#213—52no—
163C2×#204C2×D511yescharacteristic
164#897—101no—
165#893—52no—
166D3×C4⋊C4—101no—
167#890—52no—
168C4×D12C2×D511yescharacteristic
169C4×Dic6—51no—
170C4×Dic6C2×D511yescharacteristic
171C3×#102—52no—
172C3×#102—52no—
173C3×C4×C8C2×D511yescharacteristic
174#832—52no—
175#821C2×D511yescharacteristic
176#817C2×D511yescharacteristic
177#816C2×D511yescharacteristic
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180#810—52no—
181#807—52no—
182C4⋊(C3⋊C8)—51no—
183C2×C5×Q8—31no—
184C2×C5×D4—31no—
185C22×C4×C5—61no—
186C22×Dic5—62no—
187C2×D20—21no—
188C2×D20—21no—
189C2×D20C22×D312yes—
190C2×C4×D5—62no—
191C2×Dic10—21no—
192C2×Dic10—31no—
193C5×SD16—62no—
194C2×C5×C8C22×D311yescharacteristic
195C2×C5×C8C22×D311yescharacteristic
196C5×C4⋊C4—31no—
197C5×C4⋊C4—31no—
198C5×C4⋊C4—61no—
199C5×C22⋊C4—61no—
200C42×C5—61no—
201C42×C5C22×D311yescharacteristic
202C22⋊Dic5—62no—
203#686—64no—
204#685—62no—
205#685—62no—
206#685—62no—
207C4⋊Dic5—21no—
208C4⋊Dic5—31no—
209C4⋊Dic5—62no—
210C4⋊Dic5C22×D312yes—
211#683—32no—
212#683—62no—
213C4×Dic5—32no—
214C2×#168—32no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—51no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—31no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C5×D3—22no—
228C2×C5×D3—41no—
229C2×C5×D3—41no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5—42no—
233C3×C4×C5—21no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—22no—
238Dic15—22no—
239C3×Dic5—42no—
240C5×Dic3—41no—
241C5×Dic3—41no—
242C5×Dic3—41no—
243C2×C3×Q8—101no—
244C2×C3×D4—52no—
245C2×C3×D4—101no—
246C2×C3×D4—101no—
247C22×Dic3—102no—
248C2×D12C22×D511yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—102no—
251C2×Dic6—51no—
252C2×Dic6C22×D511yescharacteristic
253C2×C3×C8C22×D511yescharacteristic
254C2×C3×C8C22×D511yescharacteristic
255C3×C4⋊C4—52no—
256C3×C4⋊C4—101no—
257C3×C42C22×D511yescharacteristic
258#217—102no—
259#217—102no—
260#217—102no—
261#213—104no—
262(C2×D3)⋊C4—21no—
263(C2×D3)⋊C4—102no—
264C4⋊Dic3—51no—
265C4⋊Dic3—102no—
266C4⋊Dic3C22×D511yescharacteristic
267C4⋊Dic3C22×D511yescharacteristic
268Dic3⋊C4—21no—
269Dic3⋊C4—52no—
270Dic3⋊C4—102no—
271C4×Dic3—21no—
272C4×Dic3—52no—
273C2×C3⋊C8—52no—
274#204—22no—
275C23×C5—61no—
276C22×D5—22no—
277C5×Q8—61no—
278C5×Q8—61no—
279C5×D4—32no—
280C5×D4—61no—
281C2×C4×C5—61no—
282C2×C4×C5—61no—
283C2×C4×C5—61no—
284C2×C4×C5—122no—
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—22no—
289C2×Dic5—32no—
290C2×Dic5—32no—
291C2×Dic5—242no—
292D20—22no—
293D20—22no—
294D20—42no—
295D20—81no—
296C4×D5—242no—
297Dic10—62no—
298Dic10—81no—
299C5×C8—21no—
300C5×C8—21no—
301#168—62no—
302C2×SD16—31no—
303C2×D8—152no—
304C4⋊Q8—51no—
305#127—51no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—31no—
313C4×Q8—151no—
314C4×D4—31no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—31no—
321C4⋊C8—152no—
322C4⋊C8—151no—
323#103—31no—
324#103—152no—
325#102—31no—
326#102—52no—
327#102—52no—
328#102—152no—
329C4×C8—152no—
330C4×C8D3×D511yescharacteristic
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334C3×D5—82no—
335C5×D3—42no—
336C23×C3—102no—
337C22×D3—21no—
338C3×Q8—401no—
339C3×D4—102no—
340C3×D4—102no—
341C3×D4—202no—
342C3×D4—401no—
343C2×C3×C4—102no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—52no—
351C2×Dic3—52no—
352C2×Dic3—402no—
353D12—21no—
354D12#70912yes—
355C4×D3—42no—
356C4×D3—402no—
357Dic6—21no—
358Dic6—21no—
359Dic6—102no—
360C3×C8—21no—
361C3×C8—21no—
362C3⋊C8—102no—
363C22×C5—62no—
364C22×C5—121no—
365C22×C5—121no—
366C22×C5C2×D3×D411yescharacteristic
367C2×D5—42no—
368C2×D5—42no—
369C2×D5—42no—
370C4×C5—21no—
371C4×C5—121no—
372C4×C5—121no—
373C4×C5—121no—
374C4×C5#91612yes—
375C4×C5D3×#4111yescharacteristic
376C4×C5#101011yescharacteristic
377Dic5—42no—
378Dic5—62no—
379Dic5—62no—
380C2×Q8—31no—
381C2×Q8—101no—
382C2×Q8—151no—
383C2×D4—31no—
384C2×D4—52no—
385C2×D4—101no—
386C2×D4—101no—
387C22×C4—61no—
388C22×C4—302no—
389C22×C4—302no—
390SD16—62no—
391D8—304no—
392C2×C8—152no—
393C2×C8C2×D3×D511yescharacteristic
394C2×C8C2×D3×D511yescharacteristic
395C4⋊C4—31no—
396C4⋊C4—31no—
397C4⋊C4—52no—
398C4⋊C4—61no—
399C4⋊C4—101no—
400C4⋊C4—151no—
401C4⋊C4—152no—
402C4⋊C4—302no—
403C4⋊C4—302no—
404C22⋊C4—61no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—61no—
410C42—152no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—202no—
414C22×C3—202no—
415C22×C3—202no—
416C22×C3C2×D4×D511yescharacteristic
417C2×D3—22no—
418C2×D3—41no—
419C2×D3—41no—
420C3×C4—21no—
421C3×C4—202no—
422C3×C4#406212yes—
423C3×C4C2×#70911yescharacteristic
424C3×C4#415011yescharacteristic
425Dic3—41no—
426Dic3—41no—
427Dic3—41no—
428Dic3—102no—
429Dic3—102no—
430C2×C5—122no—
431C2×C5#567711yescharacteristic
432C2×C5#575711yescharacteristic
433C2×C5C2×#91611yescharacteristic
434D5—82no—
435C23—61no—
436C23—102no—
437Q8—61no—
438Q8—61no—
439Q8—302no—
440Q8—401no—
441D4—32no—
442D4—61no—
443D4—102no—
444D4—102no—
445D4—202no—
446D4—401no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—102no—
451C2×C4—122no—
452C2×C4—152no—
453C2×C4—152no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4#677711yescharacteristic
457C2×C4#677711yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—21no—
460C8—21no—
461C8—302no—
462C2×C3—402no—
463C2×C3#6588611yescharacteristic
464C2×C3C2×#406211yescharacteristic
465C2×C3#6610311yescharacteristic
466D3—42no—
467C5#8158511yescharacteristic, complemented, Sylow
468C22—62no—
469C22—121no—
470C22—121no—
471C22—202no—
472C22—202no—
473C22—202no—
474C22C2×#677711yescharacteristic
475C4—21no—
476C4—121no—
477C4—121no—
478C4—121no—
479C4—202no—
480C4—302no—
481C4—302no—
482C4#9127612yes—
483C4#9200111yescharacteristic
484C4D3×#70911yescharacteristic
485C3#1061135211yescharacteristic, complemented, Sylow
486C2—122no—
487C2—402no—
488C2#1175255511yescharacteristic
489C2#1175398111yescharacteristic
490C2C2×#9127611yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11747033C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11752641C2semidirect
2. #11752636C2semidirect
3. C8×Dic30C2semidirect
4. C4×C5×#204C2semidirect
5. C3×#64983C2semidirect
6. #11747978C2semidirect
7. #11747805C2semidirect
8. #11747785C2semidirect
9. #11747733C2semidirect
11. #11746959C2semidirect
52. #64983D3semidirect
95. C4×#204D5semidirect
412. C3×C5#3361semidirect
467. C5#81585semidirect
485. C3#10611352semidirect

Maximal subgroups

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

subgroupindex
#117526412
#117526362
C8×Dic302
C4×C5×#2042
C3×#649832
#117479782
#117478052
#117477852
#117477332
#117470332
#117469592
#106113523
#815855