Finite Group Databasebeta

← #14459954

Subgroups — #14459954

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#11756310C211yesmaximal, characteristic
2#11756301C211yesmaximal, characteristic, complemented
3C3×C5×C8×D4C211yesmaximal, characteristic, complemented
4#11751217C212yesmaximal, complemented
5#11751214C212yesmaximal, complemented
6#11750950C211yesmaximal, characteristic, complemented
7#11750947C211yesmaximal, characteristic, complemented
8#11750834C212yesmaximal, complemented
9#11750824C212yesmaximal, complemented
10C4×#6706C211yesmaximal, characteristic, complemented
11#11750782C211yesmaximal, characteristic, complemented
12#10611173—31nomaximal, Hall
13C2×#6817C2212yes—
14C22×C3×C5×C8C2212yes—
15C3×C4×C5×D4C2211yescharacteristic
16#91827—21no—
17#91825—21no—
18#91815C2212yes—
19#91813C2212yes—
20#91813C2212yes—
21C2×Dic60C2212yes—
22C2×#6706C2211yescharacteristic
23C4⋊C4×D15—21no—
24#91776—21no—
25#91772—22no—
26#91768—22no—
27C4×D60C2211yescharacteristic
28#91758C2211yescharacteristic
29#91758C2211yescharacteristic
30C4×Dic30C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic
32C3×C5×C22⋊C8C2212yes—
33C3×C4×C5×C8C2211yescharacteristic
34#91105C2212yes—
35#91105C2211yescharacteristic
36#91102C2212yes—
37#91101C2211yescharacteristic
38#91100C2212yes—
39#91100C2212yes—
40#91100C2211yescharacteristic
41#91100C2212yes—
42#79442—51nomaximal, Hall
43#65885—31no—
44#65876—31no—
45C5×C8×D4D311yescharacteristic, complemented
46#65405—32no—
47#65402—32no—
48#65138—31no—
49#65135—31no—
50#65022—32no—
51#65012—32no—
52C4×#677—31no—
53#64970—31no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×#1220—22no—
57#6817—24no—
58#6817—42no—
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×C4×D15—22no—
62C2×Dic30—21no—
63C2×Dic30C2311yescharacteristic
64C2×Dic30C2312yes—
65C2×C3×C5×C8—42no—
66C2×C3×C5×C8C2311yescharacteristic
67C2×C3×C5×C8C2312yes—
68C2×C3×C5×C8C2311yescharacteristic
69C3×C5×C4⋊C4D411yescharacteristic
70C3×C5×C22⋊C4D412yes—
71C3×C42×C5C2311yescharacteristic
72#6719—22no—
73#6719—22no—
74#6719—22no—
75#6714—21no—
76C4⋊Dic15—21no—
77C4⋊Dic15—21no—
78C4⋊Dic15—21no—
79C4⋊Dic15C2311yescharacteristic
80C4⋊Dic15C2312yes—
81C4⋊Dic15C2311yescharacteristic
82#6712—21no—
83#6712—22no—
84#6712—22no—
85C4×Dic15—21no—
86C4×Dic15—22no—
87Dic60—42no—
88#6706—22no—
89#5551—51no—
90#5542—51no—
91C3×C8×D4D511yescharacteristic, complemented
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×#709—32no—
101C22×C5×C8C2×D312yes—
102C4×C5×D4C2×D311yescharacteristic
103#4084—61no—
104#4082—61no—
105#4072—32no—
106#4070—32no—
107#4070—32no—
108C2×Dic20—32no—
109C2×#677—31no—
110D5×C4⋊C4—61no—
111#4033—61no—
112#4029—62no—
113#4025—62no—
114C4×D20—31no—
115#4015—31no—
116#4015—31no—
117C4×Dic10—31no—
118C5×C4⋊C8C2×D311yescharacteristic
119C5×C22⋊C8C2×D312yes—
120C4×C5×C8C2×D311yescharacteristic
121#3953—32no—
122#3953—31no—
123#3950—32no—
124#3949—31no—
125#3948—32no—
126#3948—32no—
127#3948—31no—
128#3948—32no—
129#3302—151noSylow
130C23×C3×C5C2×D412yes—
131C22×D15—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
139#1220—44no—
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145D60—21no—
146D60#4112yes—
147C4×D15—44no—
148C4×D15—42no—
149Dic30—21no—
150Dic30—22no—
151Dic30—21no—
152Dic30—22no—
153Dic30—42no—
154C3×C5×C8—21no—
155C3×C5×C8—22no—
156C3×C5×C8—21no—
157C2×#235—52no—
158C22×C3×C8C2×D512yes—
159C3×C4×D4C2×D511yescharacteristic
160#938—101no—
161#936—101no—
162#926—52no—
163#924—52no—
164#924—52no—
165C2×Dic12—52no—
166C2×#204—51no—
167D3×C4⋊C4—101no—
168#887—101no—
169#883—102no—
170#879—102no—
171C4×D12—51no—
172#869—51no—
173#869—51no—
174C4×Dic6—51no—
175C3×C4⋊C8C2×D511yescharacteristic
176C3×C22⋊C8C2×D512yes—
177C3×C4×C8C2×D511yescharacteristic
178#821—51no—
179#821—52no—
180#818—52no—
181#817—51no—
182#816—52no—
183#816—52no—
184#816—51no—
185#816—52no—
186C2×C5×D4D1211yescharacteristic
187C22×C4×C5C22×D312yes—
188C2×C22⋊D5—62no—
189#709—64no—
190#709—122no—
191C2×D20—31no—
192C2×C4×D5—62no—
193C2×C4×D5—61no—
194C2×Dic10—32no—
195C2×Dic10—31no—
196C2×Dic10—61no—
197C2×C5×C8—42no—
198C2×C5×C8C22×D311yescharacteristic
199C2×C5×C8C22×D312yes—
200C2×C5×C8C22×D311yescharacteristic
201C5×C4⋊C4D1211yescharacteristic
202C5×C22⋊C4D1212yes—
203C42×C5C22×D311yescharacteristic
204C22⋊Dic5—62no—
205C22⋊Dic5—62no—
206C22⋊Dic5—62no—
207#685—61no—
208C4⋊Dic5—31no—
209C4⋊Dic5—32no—
210C4⋊Dic5—31no—
211C4⋊Dic5—61no—
212C4⋊Dic5—61no—
213C4⋊Dic5—61no—
214#683—61no—
215#683—62no—
216#683—62no—
217C4×Dic5—61no—
218C4×Dic5—62no—
219Dic20—122no—
220#677—62no—
221#556—151no—
222#547—151no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4D1511yescharacteristic, complemented
231#416—152no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—22no—
235C22×C3×C5C22×D411yescharacteristic
236C2×D15—22no—
237C2×D15—41no—
238C2×D15—41no—
239C3×C4×C5—22no—
240C3×C4×C5—21no—
241C3×C4×C5#13512yes—
242C3×C4×C5C2×#4111yescharacteristic
243C3×C4×C5H(5,𝔽2)11yescharacteristic
244Dic15—42no—
245Dic15—41no—
246Dic15—42no—
247Dic15—41no—
248Dic15—41no—
249C2×C3×D4D2011yescharacteristic
250C22×C3×C4C22×D512yes—
251C2×#67—102no—
252#235—104no—
253#235—202no—
254C2×D12—51no—
255C2×C4×D3—101no—
256C2×C4×D3—102no—
257C2×Dic6—52no—
258C2×Dic6—51no—
259C2×Dic6—101no—
260C2×C3×C8—42no—
261C2×C3×C8C22×D511yescharacteristic
262C2×C3×C8C22×D511yescharacteristic
263C2×C3×C8C22×D512yes—
264C3×C4⋊C4D2011yescharacteristic
265C3×C22⋊C4D2012yes—
266C3×C42C22×D511yescharacteristic
267#217—102no—
268#217—102no—
269#217—102no—
270(C2×D3)⋊C4—101no—
271C4⋊Dic3—51no—
272C4⋊Dic3—52no—
273C4⋊Dic3—51no—
274C4⋊Dic3—101no—
275C4⋊Dic3—101no—
276C4⋊Dic3—101no—
277Dic3⋊C4—101no—
278Dic3⋊C4—102no—
279Dic3⋊C4—102no—
280C4×Dic3—101no—
281C4×Dic3—102no—
282Dic12—202no—
283#204—102no—
284C23×C5C2×D1212yes—
285C22×D5—61no—
286C5×D4—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5C2×D1212yes—
290C2×C4×C5C2×D1211yescharacteristic
291C2×C4×C5C2×D1211yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C2×Dic5—61no—
295C2×Dic5—61no—
296C2×Dic5—62no—
297C2×Dic5—61no—
298C2×Dic5—62no—
299D20—32no—
300D20—61no—
301C4×D5—124no—
302C4×D5—122no—
303Dic10—61no—
304Dic10—62no—
305Dic10—61no—
306Dic10—62no—
307Dic10—122no—
308C5×C8—22no—
309C5×C8—21no—
310C5×C8—21no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8C2×D1512yes—
315C4⋊Q8—151no—
316C4⋊Q8—151no—
317#126—302no—
318#124—301no—
319#123—302no—
320C22⋊Q8—152no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—151no—
324C4×Q8—301no—
325C4×D4—151no—
326C4×D4C2×D1511yescharacteristic
327#117—152no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—151no—
331C4⋊C8C2×D1511yescharacteristic
332#103—152no—
333#103—152no—
334#103—151no—
335#103—152no—
336#102—151no—
337#102—152no—
338C22⋊C8C2×D1512yes—
339C4×C8C2×D1511yescharacteristic
340C2×C3×C5—42no—
341C2×C3×C5#54611yescharacteristic
342C2×C3×C5C2×#13511yescharacteristic
343C2×C3×C5#57811yescharacteristic
344D15—42no—
345C23×C3C2×D2012yes—
346C22×D3—101no—
347C3×D4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4C2×D2012yes—
351C2×C3×C4C2×D2011yescharacteristic
352C2×C3×C4C2×D2011yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355C2×Dic3—101no—
356C2×Dic3—101no—
357C2×Dic3—102no—
358C2×Dic3—101no—
359C2×Dic3—102no—
360D12—52no—
361D12—101no—
362C4×D3—204no—
363C4×D3—202no—
364Dic6—101no—
365Dic6—102no—
366Dic6—101no—
367Dic6—102no—
368Dic6—202no—
369C3×C8—22no—
370C3×C8—21no—
371C3×C8—21no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5C22×D1211yescharacteristic
376C2×D5—62no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—22no—
381C4×C5#90412yes—
382C4×C5#100411yescharacteristic
383C4×C5D3×#4111yescharacteristic
384Dic5—122no—
385Dic5—121no—
386Dic5—121no—
387Dic5—122no—
388Dic5—121no—
389#41—304no—
390#41—602no—
391C2×Q8—152no—
392C2×Q8—151no—
393C2×Q8—301no—
394C2×D4—151no—
395C2×D4—302no—
396C2×D4D6011yescharacteristic
397C22×C4—301no—
398C22×C4—302no—
399C22×C4C22×D1512yes—
400Q16—602no—
401SD16—302no—
402C2×C8—42no—
403C2×C8C22×D1511yescharacteristic
404C2×C8C22×D1511yescharacteristic
405C2×C8C22×D1512yes—
406C4⋊C4—151no—
407C4⋊C4—152no—
408C4⋊C4—151no—
409C4⋊C4—301no—
410C4⋊C4—302no—
411C4⋊C4—301no—
412C4⋊C4—302no—
413C4⋊C4—301no—
414C4⋊C4—301no—
415C4⋊C4D6011yescharacteristic
416C22⋊C4—302no—
417C22⋊C4—302no—
418C22⋊C4—302no—
419C22⋊C4—301no—
420C22⋊C4D6012yes—
421C42—302no—
422C42—301no—
423C42C22×D1511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3C22×D2011yescharacteristic
429C2×D3—102no—
430C2×D3—201no—
431C2×D3—201no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4#405012yes—
435C3×C4#414411yescharacteristic
436C3×C4D5×#4111yescharacteristic
437Dic3—202no—
438Dic3—201no—
439Dic3—201no—
440Dic3—202no—
441Dic3—201no—
442C2×C5—42no—
443C2×C5#555411yescharacteristic
444C2×C5C2×#90411yescharacteristic
445C2×C5#575311yescharacteristic
446D5—122no—
447C23—301no—
448C23C2×D6012yes—
449Q8—301no—
450Q8—302no—
451Q8—301no—
452Q8—302no—
453Q8—602no—
454D4—22no—
455D4—152no—
456D4—301no—
457D4—604no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—301no—
461C2×C4—302no—
462C2×C4—301no—
463C2×C4—301no—
464C2×C4—302no—
465C2×C4—604no—
466C2×C4—602no—
467C2×C4C2×D6012yes—
468C2×C4C2×D6011yescharacteristic
469C2×C4C2×D6011yescharacteristic
470C2×C4C23×D1511yescharacteristic
471C8—21no—
472C8—22no—
473C8—21no—
474C2×C3—42no—
475C2×C3#6588811yescharacteristic
476C2×C3C2×#405011yescharacteristic
477C2×C3#6608711yescharacteristic
478D3—202no—
479C5#7944211yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—22no—
483C22—302no—
484C22—601no—
485C22—601no—
486C22C22×D6011yescharacteristic
487C4—22no—
488C4—21no—
489C4—602no—
490C4—601no—
491C4—601no—
492C4—602no—
493C4—601no—
494C4#9179312yes—
495C4#9209511yescharacteristic
496C4#41×D1511yescharacteristic
497C3#1061117311yescharacteristic, complemented, Sylow
498C2—42no—
499C2—602no—
500C2#1175631311yescharacteristic
501C2C2×#9179311yescharacteristic
502C2#1175651211yescharacteristic
subgroupG/H
centerC22C22×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×C8×D4C2
socleC22×C3×C5C22×D4
prime radical#11756310C2
hypercenterC8×D4D15
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #11756301C2semidirect
3. C3×C5×C8×D4C2semidirect
4. #11751217C2semidirect
5. #11751214C2semidirect
6. #11750950C2semidirect
7. #11750947C2semidirect
8. #11750834C2semidirect
9. #11750824C2semidirect
10. C4×#6706C2semidirect
11. #11750782C2semidirect
45. C5×C8×D4D3semidirect
91. C3×C8×D4D5semidirect
230. C8×D4D15semidirect
424. C3×C5#3302semidirect
479. C5#79442semidirect
497. C3#10611173semidirect

Maximal subgroups

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

subgroupindex
#117563102
#117563012
C3×C5×C8×D42
#117512172
#117512142
#117509502
#117509472
#117508342
#117508242
C4×#67062
#117507822
#106111733
#794425