Finite Group Databasebeta

← #14471684

Subgroups — #14471684

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752641C211yesmaximal, characteristic, complemented
2#11752480C211yesmaximal, characteristic, complemented
3C8×Dic30C211yesmaximal, characteristic, complemented
4C4×C5×D24C211yesmaximal, characteristic
5C3×#64970C211yesmaximal, characteristic, complemented
6#11747979C212yesmaximal, complemented
7#11747878C212yesmaximal, complemented
8#11747787C212yesmaximal
9#11747737C212yesmaximal, complemented
10#11747070C211yesmaximal, characteristic, complemented
11#11746882C211yesmaximal, characteristic, complemented
12#10611299—31nomaximal, Hall
13C4×Dic30C2211yescharacteristic
14C2×C5×D24C2211yescharacteristic
15C4×C5×D12C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91435C2212yes—
20D3×C4⋊Dic5—21no—
21#91410—22no—
22#91384C2212yes—
23#91370C2212yes—
24#91365—21no—
25#91365—21no—
26#91341—22no—
27#91338—21no—
28#91331C2212yes—
29C2×#6656C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#821C2211yescharacteristic
35C5×#821C2211yescharacteristic
36C5×#818C2211yescharacteristic
37C3×#3948C2212yes—
38C3×#3948C2212yes—
39#90986C2212yes—
40#90970C2212yes—
41#90966C2212yes—
42#81621—51nomaximal, Hall
43#65877—31no—
44#65876—31no—
45C4×C5×D8—31no—
46#65442—32no—
47#65308—31no—
48#65297—31no—
49#65166—32no—
50#65057—32no—
51#65047—32no—
52#64970D311yescharacteristic, complemented
53C8×Dic10—31no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12C2311yescharacteristic
56C2×C5×D12C2311yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C4×C5×D3—21no—
59C2×C3×Dic10—21no—
60C2×C3×Dic10C2312yes—
61C2×D3×Dic5—22no—
62C2×C3×C5×C8C2311yescharacteristic
63C2×C3×C5×C8C2311yescharacteristic
64C3×C42×C5C2311yescharacteristic
65C4⋊Dic15D411yescharacteristic
66#6712D412yes—
67C4×Dic15C2312yes—
68C2×C3⋊#168C2312yes—
69C5×(C2×D3)⋊C4—21no—
70C5×(C2×D3)⋊C4—21no—
71C5×C4⋊Dic3C2311yescharacteristic
72C5×C4⋊Dic3C2311yescharacteristic
73C5×D24—22no—
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5C2312yes—
78Dic3⋊Dic5—22no—
79#6668—22no—
80#6668—22no—
81(C2×D3)⋊Dic5—22no—
82(C2×D3)⋊Dic5—22no—
83(C2×D3)⋊Dic5—22no—
84Dic3×Dic5—22no—
85#6656—24no—
86#5732—51no—
87#5730—51no—
88C3×#487—51no—
89#5084—51no—
90#5083—51no—
91#4819—52no—
92#4800—52no—
93#4796—52no—
94#4788—52no—
95C4×D24D511yescharacteristic
96C8×Dic6—51no—
97C2×C5×D8—31no—
98C4×C5×D4—31no—
99C4×C5×D4—31no—
100#4082—32no—
101D4×Dic5—32no—
102C2×#687—32no—
103#4072—61no—
104C2×C4⋊Dic5—61no—
105#4070—61no—
106#4070—61no—
107#4036—32no—
108#4033—32no—
109#4025—62no—
110#4024—62no—
111#4015C2×D311yescharacteristic
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C5×#107—31no—
115C5×#102—31no—
116C5×#102—31no—
117C4×C5×C8C2×D311yescharacteristic
118#3964—32no—
119#3948C2×D312yes—
120#3948C2×D312yes—
121#3946—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3940—32no—
125C4⋊#168—31no—
126#3360—151noSylow
127C22×C5×D3—21no—
128C22×C5×D3—21no—
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—
137C5×D12—21no—
138C5×D12—21no—
139C5×D12—21no—
140C5×D12#4112yes—
141C4×C5×D3—42no—
142C4×C5×D3—42no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C3×Dic10—22no—
146C3×Dic10—22no—
147C3×Dic10—81no—
148D3×Dic5—82no—
149C3×C5×C8—21no—
150C3×C5×C8—21no—
151C3⋊#168—22no—
152C3×C4⋊Q8—51no—
153C3×C4⋊Q8—51no—
154#947—52no—
155#946—102no—
156Q8×Dic3—52no—
157C2×#215—52no—
158C2×D24C2×D511yescharacteristic
159#898—102no—
160#897—101no—
161#897—101no—
162#893—52no—
163#892—101no—
164D3×C4⋊C4—101no—
165#890—52no—
166C4×D12C2×D511yescharacteristic
167C4×D12C2×D511yescharacteristic
168C4×Dic6—51no—
169C3×#103—52no—
170C3×#103—52no—
171C3×C4×C8C2×D511yescharacteristic
172#835—52no—
173#821C2×D511yescharacteristic
174#821C2×D511yescharacteristic
175#818C2×D511yescharacteristic
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—52no—
179#808—52no—
180C4⋊(C3⋊C8)—51no—
181C2×C5×D4—31no—
182C2×C5×D4—31no—
183C22×C4×C5—61no—
184C22×C4×C5—61no—
185C22×Dic5—62no—
186C2×Dic10—21no—
187C2×Dic10—31no—
188C2×Dic10C22×D312yes—
189C5×D8—62no—
190C2×C5×C8C22×D311yescharacteristic
191C2×C5×C8C22×D311yescharacteristic
192C5×C4⋊C4—31no—
193C5×C4⋊C4—31no—
194C5×C22⋊C4—61no—
195C5×C22⋊C4—61no—
196C42×C5C22×D311yescharacteristic
197C22⋊Dic5—62no—
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200#687—64no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5—31no—
205C4⋊Dic5—62no—
206C4⋊Dic5C22×D312yes—
207#683—32no—
208#683—62no—
209#683—62no—
210C4×Dic5—32no—
211C4×Dic5—62no—
212C2×#168—32no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487—51no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—151no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—31no—
224C22×C3×C5C22×D411yescharacteristic
225C2×C5×D3—22no—
226C2×C5×D3—41no—
227C2×C5×D3—41no—
228C2×C5×D3—41no—
229C2×C5×D3—41no—
230C2×C5×D3—41no—
231C3×C4×C5—21no—
232C3×C4×C5#13512yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—22no—
236Dic15—22no—
237C3×Dic5—42no—
238C3×Dic5—42no—
239C5×Dic3—41no—
240C5×Dic3—41no—
241C2×C3×Q8—52no—
242C2×C3×Q8—101no—
243C2×D12C22×D511yescharacteristic
244C2×D12C22×D511yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—102no—
248C2×Dic6—51no—
249C2×C3×C8C22×D511yescharacteristic
250C2×C3×C8C22×D511yescharacteristic
251C3×C4⋊C4—52no—
252C3×C4⋊C4—101no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4—101no—
255C3×C42C22×D511yescharacteristic
256#215—104no—
257(C2×D3)⋊C4—21no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—102no—
260(C2×D3)⋊C4—102no—
261(C2×D3)⋊C4—102no—
262C4⋊Dic3—51no—
263C4⋊Dic3—102no—
264C4⋊Dic3—102no—
265C4⋊Dic3C22×D511yescharacteristic
266C4⋊Dic3C22×D511yescharacteristic
267Dic3⋊C4—52no—
268Dic3⋊C4—102no—
269C4×Dic3—52no—
270C4×Dic3—102no—
271C2×C3⋊C8—52no—
272D24—22no—
273C23×C5—61no—
274C23×C5—61no—
275C5×D4—32no—
276C5×D4—61no—
277C5×D4—61no—
278C5×D4—61no—
279C2×C4×C5—61no—
280C2×C4×C5—61no—
281C2×C4×C5—122no—
282C2×C4×C5—122no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—32no—
289C2×Dic5—32no—
290C2×Dic5—242no—
291Dic10—22no—
292Dic10—22no—
293Dic10—62no—
294Dic10—81no—
295C5×C8—21no—
296C5×C8—21no—
297#168—62no—
298C2×SD16—152no—
299C2×D8—31no—
300C4⋊Q8—51no—
301C4⋊Q8—51no—
302#126—302no—
303#125—152no—
304#124—152no—
305C22⋊Q8—302no—
306C22⋊Q8—301no—
307C22⋊Q8—301no—
308C4×Q8—151no—
309C4×Q8—152no—
310C4×D4—31no—
311C4×D4—31no—
312C4×D4—152no—
313#117—301no—
314C2×C4⋊C4—301no—
315#107—31no—
316#106—152no—
317C4⋊C8—152no—
318C4⋊C8—151no—
319#103—52no—
320#103—52no—
321#103—152no—
322#102—31no—
323#102—31no—
324#102—152no—
325C4×C8—152no—
326C4×C8D3×D511yescharacteristic
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330C5×D3—42no—
331C5×D3—81no—
332C22×D3—21no—
333C22×D3—21no—
334C3×Q8—102no—
335C3×Q8—102no—
336C3×Q8—401no—
337C2×C3×C4—102no—
338C2×C3×C4—102no—
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4C23×D511yescharacteristic
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—52no—
345C2×Dic3—52no—
346D12—21no—
347D12—21no—
348D12—21no—
349D12#70912yes—
350C4×D3—42no—
351C4×D3—42no—
352C4×D3—402no—
353Dic6—102no—
354C3×C8—21no—
355C3×C8—21no—
356C3⋊C8—102no—
357C22×C5—62no—
358C22×C5—121no—
359C22×C5—121no—
360C22×C5—121no—
361C22×C5—121no—
362C22×C5—121no—
363C22×C5C2×D3×D411yescharacteristic
364C4×C5—21no—
365C4×C5—121no—
366C4×C5—121no—
367C4×C5#91912yes—
368C4×C5D3×#4111yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—42no—
371Dic5—42no—
372Dic5—62no—
373Dic5—62no—
374C2×Q8—52no—
375C2×Q8—101no—
376C2×Q8—151no—
377C2×D4—31no—
378C2×D4—31no—
379C22×C4—61no—
380C22×C4—61no—
381C22×C4—302no—
382SD16—304no—
383D8—62no—
384C2×C8—152no—
385C2×C8C2×D3×D511yescharacteristic
386C2×C8C2×D3×D511yescharacteristic
387C4⋊C4—31no—
388C4⋊C4—31no—
389C4⋊C4—52no—
390C4⋊C4—101no—
391C4⋊C4—101no—
392C4⋊C4—101no—
393C4⋊C4—151no—
394C4⋊C4—152no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C22⋊C4—61no—
399C22⋊C4—61no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C22⋊C4—302no—
403C42—152no—
404C42—302no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3C2×D4×D511yescharacteristic
408C2×D3—22no—
409C2×D3—41no—
410C2×D3—41no—
411C2×D3—41no—
412C2×D3—41no—
413C2×D3—41no—
414C3×C4—21no—
415C3×C4—202no—
416C3×C4—202no—
417C3×C4#405812yes—
418C3×C4C2×#70911yescharacteristic
419C3×C4#415011yescharacteristic
420Dic3—41no—
421Dic3—41no—
422Dic3—102no—
423Dic3—102no—
424C2×C5—122no—
425C2×C5—241no—
426C2×C5#567711yescharacteristic
427C2×C5#576211yescharacteristic
428C2×C5C2×#91911yescharacteristic
429C23—61no—
430C23—61no—
431Q8—102no—
432Q8—102no—
433Q8—302no—
434Q8—401no—
435D4—32no—
436D4—61no—
437D4—61no—
438D4—61no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—102no—
442C2×C4—102no—
443C2×C4—122no—
444C2×C4—122no—
445C2×C4—152no—
446C2×C4—152no—
447C2×C4—1202no—
448C2×C4#677711yescharacteristic
449C2×C4#677711yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—21no—
452C8—21no—
453C8—302no—
454C2×C3#6588611yescharacteristic
455C2×C3C2×#405811yescharacteristic
456C2×C3#6610411yescharacteristic
457D3—42no—
458D3—81no—
459C5#8162111yescharacteristic, complemented, Sylow
460C22—62no—
461C22—121no—
462C22—121no—
463C22—121no—
464C22—121no—
465C22—121no—
466C22C2×#677711yescharacteristic
467C4—21no—
468C4—121no—
469C4—121no—
470C4—202no—
471C4—202no—
472C4—302no—
473C4—302no—
474C4#9127912yes—
475C4#9200111yescharacteristic
476C4D3×#70911yescharacteristic
477C3#1061129911yescharacteristic, complemented, Sylow
478C2—122no—
479C2—241no—
480C2#1175255511yescharacteristic
481C2#1175398011yescharacteristic
482C2C2×#9127911yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D24C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#3360
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. #11752480C2semidirect
3. C8×Dic30C2semidirect
5. C3×#64970C2semidirect
6. #11747979C2semidirect
7. #11747878C2semidirect
9. #11747737C2semidirect
10. #11747070C2semidirect
11. #11746882C2semidirect
52. #64970D3semidirect
406. C3×C5#3360semidirect
459. C5#81621semidirect
477. C3#10611299semidirect

Maximal subgroups

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

subgroupindex
#117526412
#117524802
C8×Dic302
C4×C5×D242
C3×#649702
#117479792
#117478782
#117477872
#117477372
#117470702
#117468822
#106112993
#816215