Finite Group Databasebeta

← #14460012

Subgroups — #14460012

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
1#11756301C211yesmaximal, characteristic, complemented
2C5×#5551C211yesmaximal, characteristic
3C3×D4×#168C211yesmaximal, characteristic, complemented
4#11748557C212yesmaximal, complemented
5#11748466C212yesmaximal, complemented
6#11748388C212yesmaximal, complemented
7#11748361C212yesmaximal, complemented
8#11747105C211yesmaximal, characteristic, complemented
9C4×#6659C211yesmaximal, characteristic, complemented
10#11746964C211yesmaximal, characteristic, complemented
11#11746929C211yesmaximal, characteristic, complemented
12#10615241—31nomaximal, Hall
13C2×C5×#235C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91825—21no—
16#91815C2212yes—
17#91813C2212yes—
18#91776—21no—
19#91768—22no—
20#91758C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C5×#938—21no—
23C5×#924C2212yes—
24C5×D3×C4⋊C4—21no—
25C5×#883—22no—
26C4×C5×D12C2211yescharacteristic
27C5×#869C2211yescharacteristic
28C22×C3×#168C2212yes—
29C2×#6663C2212yes—
30C2×#6659C2211yescharacteristic
31C3×C22⋊#168C2212yes—
32C3×C4⋊#168C2211yescharacteristic
33C3×C4×#168C2211yescharacteristic
34#90988C2212yes—
35#90985C2211yescharacteristic
36#90975C2211yescharacteristic
37#90973C2212yes—
38#90973C2212yes—
39#90973C2212yes—
40#90967C2212yes—
41#90967C2211yescharacteristic
42#79442—51nomaximal, Hall
43C5×#547—31no—
44#65876—31no—
45#65528—32no—
46#65522—32no—
47#65379—31no—
48#65370—31no—
49#65340—32no—
50#65334—32no—
51C4×#687—31no—
52D4×#168D311yescharacteristic, complemented
53#65296—31no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×Dic30—21no—
57C2×Dic30C2311yescharacteristic
58C2×C5×#67—22no—
59C5×#235—24no—
60C5×#235—42no—
61C2×C5×D12C2311yescharacteristic
62C2×C4×C5×D3—21no—
63C2×C4×C5×D3—22no—
64C2×C5×Dic6C2312yes—
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C22⋊C4D412yes—
67C3×C42×C5C2311yescharacteristic
68#6719—22no—
69#6719—22no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2311yescharacteristic
72C4⋊Dic15C2312yes—
73#6712—21no—
74#6712—22no—
75C4×Dic15—21no—
76C4×Dic15—22no—
77C5×#217—22no—
78C5×(C2×D3)⋊C4—21no—
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3—21no—
81C5×C4⋊Dic3C2311yescharacteristic
82C5×Dic3⋊C4—22no—
83C2×C3×#168—42no—
84C2×C3×#168C2311yescharacteristic
85C2×C3×#168C2312yes—
86C2×C3×#168C2311yescharacteristic
87#6663—42no—
88#6659—22no—
89#5551D511yescharacteristic
90#5542—51no—
91C3×C8×D4—51no—
92#5116—52no—
93#5113—52no—
94#4849—51no—
95#4846—51no—
96#4733—52no—
97#4723—52no—
98C4×#204—51no—
99#4681—51no—
100C2×C5×#41—32no—
101C5×C4⋊Q8—31no—
102C5×#123—62no—
103C5×C22⋊Q8—32no—
104C5×#121—61no—
105C4×C5×D4—31no—
106C4×C5×D4C2×D311yescharacteristic
107C2×C5×C4⋊C4—61no—
108C2×#689—32no—
109#4082—61no—
110C2×#687—31no—
111#4072—32no—
112#4070—32no—
113C22×#168C2×D312yes—
114#4033—61no—
115#4025—62no—
116#4015—31no—
117C4×Dic10—31no—
118#3967—32no—
119#3967—32no—
120#3967—32no—
121#3964—32no—
122#3964—31no—
123C22⋊#168C2×D312yes—
124#3942—31no—
125#3940—31no—
126#3939—32no—
127C4⋊#168C2×D311yescharacteristic
128C4×#168C2×D311yescharacteristic
129#3302—151noSylow
130C23×C3×C5C2×D412yes—
131C22×C5×D3—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×Dic15—21no—
140C2×Dic15—21no—
141C2×Dic15—22no—
142Dic30—21no—
143Dic30—21no—
144Dic30—42no—
145C5×#67—44no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—22no—
148C5×D12—21no—
149C5×D12#4112yes—
150C4×C5×D3—44no—
151C4×C5×D3—42no—
152C5×Dic6—22no—
153C5×Dic6—22no—
154C3×#168—21no—
155C3×#168—22no—
156C3×#168—21no—
157C2×#235C2×D512yes—
158C22×C3×C8—52no—
159C3×C4×D4C2×D511yescharacteristic
160#938—21no—
161#936—101no—
162#926—52no—
163#924—52no—
164#924C2×D512yes—
165C2×Dic12—52no—
166C2×#204—51no—
167D3×C4⋊C4—21no—
168#887—101no—
169#883—22no—
170#879—102no—
171C4×D12C2×D511yescharacteristic
172#869—51no—
173#869C2×D511yescharacteristic
174C4×Dic6—51no—
175C3×C4⋊C8—51no—
176C3×C22⋊C8—52no—
177C3×C4×C8—51no—
178#821—51no—
179#821—52no—
180#818—52no—
181#817—51no—
182#816—52no—
183#816—52no—
184#816—52no—
185#816—51no—
186C5×#41—64no—
187C5×#41—122no—
188C2×C5×Q8—32no—
189C2×C5×D4—31no—
190C2×C5×D4—62no—
191C2×C5×D4D1211yescharacteristic
192C22×C4×C5—61no—
193C22×C4×C5—62no—
194C22×C4×C5C22×D312yes—
195C2×Dic10—31no—
196C2×Dic10—61no—
197C5×C4⋊C4—31no—
198C5×C4⋊C4—61no—
199C5×C4⋊C4—62no—
200C5×C4⋊C4—61no—
201C5×C4⋊C4D1211yescharacteristic
202C5×C22⋊C4—62no—
203C5×C22⋊C4—61no—
204C5×C22⋊C4D1212yes—
205C42×C5C22×D311yescharacteristic
206C22⋊Dic5—62no—
207C22⋊Dic5—62no—
208#689—122no—
209#687—62no—
210C4⋊Dic5—32no—
211C4⋊Dic5—31no—
212C4⋊Dic5—61no—
213#683—61no—
214#683—62no—
215C4×Dic5—61no—
216C4×Dic5—62no—
217C2×#168—42no—
218C2×#168C22×D311yescharacteristic
219C2×#168C22×D311yescharacteristic
220C2×#168C22×D312yes—
221#556—151no—
222#547—31no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—51no—
231#416—152no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—22no—
235C22×C3×C5C22×D411yescharacteristic
236C2×C5×D3—22no—
237C2×C5×D3—41no—
238C2×C5×D3—41no—
239C3×C4×C5—22no—
240C3×C4×C5—21no—
241C3×C4×C5#13512yes—
242C3×C4×C5C2×#4111yescharacteristic
243C3×C4×C5H(5,𝔽2)11yescharacteristic
244Dic15—41no—
245Dic15—42no—
246Dic15—41no—
247C5×Dic3—42no—
248C5×Dic3—41no—
249C2×C3×D4C22⋊D511yescharacteristic
250C22×C3×C4C22×D512yes—
251C2×#67—22no—
252#235—24no—
253#235—42no—
254C2×D12C22×D511yescharacteristic
255C2×C4×D3—21no—
256C2×C4×D3—22no—
257C2×Dic6—51no—
258C2×Dic6—101no—
259C2×Dic6C22×D512yes—
260C2×C3×C8—51no—
261C2×C3×C8—51no—
262C2×C3×C8—52no—
263C2×C3×C8—202no—
264C3×C4⋊C4C22⋊D511yescharacteristic
265C3×C22⋊C4C22⋊D512yes—
266C3×C42C22×D511yescharacteristic
267#217—22no—
268#217—102no—
269#217—102no—
270(C2×D3)⋊C4—21no—
271C4⋊Dic3—21no—
272C4⋊Dic3—21no—
273C4⋊Dic3—51no—
274C4⋊Dic3—52no—
275C4⋊Dic3—101no—
276C4⋊Dic3C22×D511yescharacteristic
277Dic3⋊C4—22no—
278Dic3⋊C4—101no—
279Dic3⋊C4—102no—
280C4×Dic3—101no—
281C4×Dic3—102no—
282Dic12—202no—
283#204—102no—
284C23×C5—61no—
285C23×C5C2×D1212yes—
286C5×Q8—62no—
287C5×Q8—62no—
288C5×D4—22no—
289C5×D4—32no—
290C5×D4—61no—
291C5×D4—124no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—61no—
295C2×C4×C5—62no—
296C2×C4×C5—124no—
297C2×C4×C5—122no—
298C2×C4×C5C2×D1212yes—
299C2×C4×C5C2×D1211yescharacteristic
300C2×C4×C5C2×D1211yescharacteristic
301C2×C4×C5C23×D311yescharacteristic
302C2×Dic5—61no—
303C2×Dic5—61no—
304C2×Dic5—62no—
305Dic10—61no—
306Dic10—61no—
307Dic10—122no—
308#168—21no—
309#168—22no—
310#168—21no—
311C2×#41—32no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—52no—
315C4⋊Q8—31no—
316C4⋊Q8—151no—
317#126—302no—
318#124—301no—
319#123—62no—
320C22⋊Q8—32no—
321C22⋊Q8—152no—
322#121—61no—
323C4×Q8—151no—
324C4×Q8—301no—
325C4×D4—31no—
326C4×D4D3×D511yescharacteristic
327#117—152no—
328C2×C4⋊C4—61no—
329#107—152no—
330#106—151no—
331C4⋊C8—51no—
332#103—151no—
333#103—152no—
334#103—152no—
335#103—152no—
336#102—151no—
337#102—152no—
338C22⋊C8—52no—
339C4×C8—51no—
340C2×C3×C5—42no—
341C2×C3×C5#54611yescharacteristic
342C2×C3×C5C2×#13511yescharacteristic
343C2×C3×C5#57811yescharacteristic
344C5×D3—42no—
345C23×C3C2×C22⋊D512yes—
346C22×D3—21no—
347C3×D4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4C2×C22⋊D512yes—
351C2×C3×C4C2×C22⋊D511yescharacteristic
352C2×C3×C4C2×C22⋊D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—44no—
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—101no—
358C2×Dic3—101no—
359C2×Dic3—102no—
360D12—21no—
361D12#71112yes—
362C4×D3—44no—
363C4×D3—42no—
364Dic6—22no—
365Dic6—22no—
366Dic6—101no—
367Dic6—101no—
368Dic6—202no—
369C3×C8—101no—
370C3×C8—102no—
371C3×C8—101no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5—62no—
376C22×C5—121no—
377C22×C5—121no—
378C22×C5C22×D1211yescharacteristic
379C4×C5—21no—
380C4×C5—22no—
381C4×C5—121no—
382C4×C5—122no—
383C4×C5#90412yes—
384C4×C5#100411yescharacteristic
385C4×C5D3×#4111yescharacteristic
386Dic5—122no—
387Dic5—121no—
388Dic5—121no—
389#41—64no—
390#41—122no—
391C2×Q8—32no—
392C2×Q8—151no—
393C2×Q8—301no—
394C2×D4—31no—
395C2×D4—62no—
396C2×D4#120311yescharacteristic
397C22×C4—61no—
398C22×C4—62no—
399C22×C4C2×D3×D512yes—
400Q16—602no—
401SD16—302no—
402C2×C8—51no—
403C2×C8—51no—
404C2×C8—52no—
405C2×C8—202no—
406C4⋊C4—31no—
407C4⋊C4—61no—
408C4⋊C4—62no—
409C4⋊C4—61no—
410C4⋊C4—151no—
411C4⋊C4—152no—
412C4⋊C4—301no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4#120311yescharacteristic
416C22⋊C4—62no—
417C22⋊C4—61no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4#120312yes—
421C42—302no—
422C42—301no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3C22×C22⋊D511yescharacteristic
429C2×D3—22no—
430C2×D3—41no—
431C2×D3—41no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4#409612yes—
435C3×C4C2×#71111yescharacteristic
436C3×C4#414411yescharacteristic
437Dic3—42no—
438Dic3—41no—
439Dic3—201no—
440Dic3—202no—
441Dic3—201no—
442C2×C5—42no—
443C2×C5—122no—
444C2×C5#555411yescharacteristic
445C2×C5C2×#90411yescharacteristic
446C2×C5#575311yescharacteristic
447C23—61no—
448C23C2×#120312yes—
449Q8—62no—
450Q8—62no—
451Q8—301no—
452Q8—301no—
453Q8—602no—
454D4—22no—
455D4—32no—
456D4—61no—
457D4—124no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—61no—
461C2×C4—62no—
462C2×C4—124no—
463C2×C4—122no—
464C2×C4—301no—
465C2×C4—302no—
466C2×C4—301no—
467C2×C4C2×#120312yes—
468C2×C4C2×#120311yescharacteristic
469C2×C4C2×#120311yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—101no—
472C8—101no—
473C8—102no—
474C2×C3—42no—
475C2×C3#6614011yescharacteristic
476C2×C3C2×#409611yescharacteristic
477C2×C3#6617211yescharacteristic
478D3—42no—
479C5#7944211yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—22no—
483C22—62no—
484C22—121no—
485C22—121no—
486C22C22×#120311yescharacteristic
487C4—21no—
488C4—22no—
489C4—121no—
490C4—122no—
491C4—601no—
492C4—602no—
493C4—601no—
494C4#9130312yes—
495C4D3×#71111yescharacteristic
496C4#9202511yescharacteristic
497C3#1061524111yescharacteristic, complemented, Sylow
498C2—42no—
499C2—122no—
500C2C2×#9130311yescharacteristic
501C2#1175497511yescharacteristic
502C2#1175530611yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5551C2
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. #11756301C2semidirect
3. C3×D4×#168C2semidirect
4. #11748557C2semidirect
5. #11748466C2semidirect
6. #11748388C2semidirect
7. #11748361C2semidirect
8. #11747105C2semidirect
9. C4×#6659C2semidirect
10. #11746964C2semidirect
11. #11746929C2semidirect
52. D4×#168D3semidirect
424. C3×C5#3302semidirect
479. C5#79442semidirect
497. C3#10615241semidirect

Maximal subgroups

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

subgroupindex
#117563012
C5×#55512
C3×D4×#1682
#117485572
#117484662
#117483882
#117483612
#117471052
C4×#66592
#117469642
#117469292
#106152413
#794425