Finite Group Databasebeta

← #14460013

Subgroups — #14460013

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
2C3×#65876C211yesmaximal, characteristic, complemented
3C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#11748560C212yesmaximal, complemented
5#11748552C212yesmaximal, complemented
6#11748412C212yesmaximal, complemented
7#11748411C212yesmaximal, complemented
8#11747095C211yesmaximal, characteristic, complemented
9C4×#6658C211yesmaximal, characteristic, complemented
10#11746971C211yesmaximal, characteristic, complemented
11#11746921C211yesmaximal, characteristic, complemented
12#10611173—31nomaximal, Hall
13C2×#6817C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91827—21no—
16#91813C2212yes—
17C4⋊C4×D15—21no—
18#91772—22no—
19C4×D60C2211yescharacteristic
20#91758C2211yescharacteristic
21C22×C5×C3⋊C8C2212yes—
22C3×#4082—21no—
23C3×#4072C2212yes—
24C3×#4070C2212yes—
25C3×#4033—21no—
26C3×#4025—22no—
27C3×#4015C2211yescharacteristic
28C3×C4×Dic10C2211yescharacteristic
29C2×#6662C2212yes—
30C2×#6658C2211yescharacteristic
31C5×#830C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C4×C5×C3⋊C8C2211yescharacteristic
34#90990C2212yes—
35#90987C2211yescharacteristic
36#90974C2212yes—
37#90974C2212yes—
38#90974C2212yes—
39#90971C2211yescharacteristic
40#90968C2211yescharacteristic
41#90968C2212yes—
42#83664—51nomaximal, Hall
43#65885—31no—
44#65876D311yescharacteristic, complemented
45C5×C8×D4—31no—
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×Dic30C2312yes—
63C2×C3×Dic10—21no—
64C2×C3×Dic10C2311yescharacteristic
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C22⋊C4D412yes—
67C3×C42×C5C2311yescharacteristic
68#6719—22no—
69#6714—21no—
70C4⋊Dic15—21no—
71C4⋊Dic15—21no—
72C4⋊Dic15C2311yescharacteristic
73#6712—22no—
74C2×C5×C3⋊C8—42no—
75C2×C5×C3⋊C8C2311yescharacteristic
76C2×C5×C3⋊C8C2312yes—
77C2×C5×C3⋊C8C2311yescharacteristic
78C3×C22⋊Dic5—22no—
79C3×C22⋊Dic5—22no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2312yes—
83C3×#683—21no—
84C3×#683—22no—
85C3×C4×Dic5—21no—
86C3×C4×Dic5—22no—
87#6662—42no—
88#6658—22no—
89C3×#556—51no—
90#5551—51no—
91#5093—51no—
92#5087—51no—
93#5051—52no—
94#5047—52no—
95#5031—51no—
96C4×#215—51no—
97D4×C3⋊C8D511yescharacteristic, complemented
98#5002—52no—
99#4996—52no—
100C2×#709—32no—
101C22×C5×C8—32no—
102C4×C5×D4C2×D311yescharacteristic
103#4084—61no—
104#4082—21no—
105#4072C2×D312yes—
106#4070—32no—
107#4070C2×D312yes—
108C2×Dic20—32no—
109C2×#677—31no—
110D5×C4⋊C4—61no—
111#4033—21no—
112#4029—62no—
113#4025—22no—
114C4×D20—31no—
115#4015—31no—
116#4015C2×D311yescharacteristic
117C4×Dic10C2×D311yescharacteristic
118C5×C4⋊C8—31no—
119C5×C22⋊C8—32no—
120C4×C5×C8—31no—
121#3953—32no—
122#3953—31no—
123#3950—32no—
124#3949—31no—
125#3948—31no—
126#3948—32no—
127#3948—32no—
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—22no—
142D60—21no—
143D60#4112yes—
144C4×D15—44no—
145C4×D15—42no—
146Dic30—22no—
147Dic30—22no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—22no—
151C3×Dic10—21no—
152C3×Dic10—21no—
153C3×Dic10—42no—
154C5×C3⋊C8—21no—
155C5×C3⋊C8—22no—
156C5×C3⋊C8—21no—
157C2×#235—52no—
158C3×C4⋊Q8—51no—
159C3×#126—102no—
160C3×#124—101no—
161C3×C22⋊Q8—52no—
162C3×C4×Q8—51no—
163C3×C4×Q8—101no—
164C3×C4×D4C2×D511yescharacteristic
165C3×#117—52no—
166C2×#216—52no—
167C2×#215—51no—
168#938—101no—
169#924—52no—
170C22×C3⋊C8C2×D512yes—
171D3×C4⋊C4—101no—
172#883—102no—
173C4×D12—51no—
174#869—51no—
175#835—51no—
176#830C2×D512yes—
177#810—52no—
178#810—52no—
179#810—52no—
180#809—51no—
181#809—52no—
182#808—51no—
183#807—52no—
184C4⋊(C3⋊C8)C2×D511yescharacteristic
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×D4#6711yescharacteristic
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—21no—
195C2×Dic10—32no—
196C2×Dic10C22×D311yescharacteristic
197C2×C5×C8—31no—
198C2×C5×C8—32no—
199C2×C5×C8—31no—
200C2×C5×C8—122no—
201C5×C4⋊C4#6711yescharacteristic
202C5×C22⋊C4#6712yes—
203C42×C5C22×D311yescharacteristic
204C22⋊Dic5—22no—
205C22⋊Dic5—22no—
206C22⋊Dic5—62no—
207#685—61no—
208C4⋊Dic5—21no—
209C4⋊Dic5—31no—
210C4⋊Dic5—61no—
211C4⋊Dic5—61no—
212C4⋊Dic5C22×D311yescharacteristic
213C4⋊Dic5C22×D312yes—
214#683—21no—
215#683—22no—
216#683—62no—
217C4×Dic5—21no—
218C4×Dic5—22no—
219Dic20—122no—
220#677—62no—
221#556—51no—
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×D4—31no—
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—
246C3×Dic5—41no—
247C3×Dic5—42no—
248C3×Dic5—41no—
249C2×C3×Q8—51no—
250C2×C3×Q8—101no—
251C2×C3×D4D2011yescharacteristic
252C22×C3×C4C22×D512yes—
253C2×#67—102no—
254#235—104no—
255#235—202no—
256C2×D12—51no—
257C2×C4×D3—101no—
258C2×C4×D3—102no—
259C2×Dic6—52no—
260C3×C4⋊C4—52no—
261C3×C4⋊C4—51no—
262C3×C4⋊C4—101no—
263C3×C4⋊C4—102no—
264C3×C4⋊C4—101no—
265C3×C4⋊C4D2011yescharacteristic
266C3×C22⋊C4—102no—
267C3×C22⋊C4—102no—
268C3×C22⋊C4D2012yes—
269C3×C42—102no—
270C3×C42—101no—
271C3×C42C22×D511yescharacteristic
272#217—102no—
273#216—202no—
274#215—102no—
275(C2×D3)⋊C4—101no—
276C4⋊Dic3—51no—
277C4⋊Dic3—101no—
278C4⋊Dic3—101no—
279Dic3⋊C4—102no—
280C2×C3⋊C8—42no—
281C2×C3⋊C8C22×D511yescharacteristic
282C2×C3⋊C8C22×D511yescharacteristic
283C2×C3⋊C8C22×D512yes—
284C23×C5C2×#6712yes—
285C22×D5—61no—
286C5×D4—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5C2×#6712yes—
290C2×C4×C5C2×#6711yescharacteristic
291C2×C4×C5C2×#6711yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—22no—
297C2×Dic5—61no—
298C2×Dic5—62no—
299D20—32no—
300D20—61no—
301C4×D5—124no—
302C4×D5—122no—
303Dic10—21no—
304Dic10—21no—
305Dic10—42no—
306Dic10—62no—
307Dic10—62no—
308C5×C8—61no—
309C5×C8—62no—
310C5×C8—61no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—32no—
315C4⋊Q8—51no—
316C4⋊Q8—151no—
317#126—102no—
318#124—101no—
319#123—302no—
320C22⋊Q8—52no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—51no—
324C4×Q8—101no—
325C4×D4—151no—
326C4×D4D3×D511yescharacteristic
327#117—52no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—151no—
331C4⋊C8—31no—
332#103—152no—
333#103—152no—
334#103—152no—
335#103—151no—
336#102—151no—
337#102—152no—
338C22⋊C8—32no—
339C4×C8—31no—
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×Q8—101no—
348C3×Q8—101no—
349C3×Q8—202no—
350C3×D4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—101no—
354C2×C3×C4—102no—
355C2×C3×C4—101no—
356C2×C3×C4C2×D2012yes—
357C2×C3×C4C2×D2011yescharacteristic
358C2×C3×C4C2×D2011yescharacteristic
359C2×C3×C4C23×D511yescharacteristic
360#67—204no—
361C2×Dic3—101no—
362C2×Dic3—102no—
363D12—52no—
364D12—101no—
365C4×D3—204no—
366C4×D3—202no—
367Dic6—102no—
368Dic6—102no—
369C3⋊C8—21no—
370C3⋊C8—22no—
371C3⋊C8—21no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5C22×#6711yescharacteristic
376C2×D5—62no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—22no—
380C4×C5—21no—
381C4×C5#95012yes—
382C4×C5D3×#4111yescharacteristic
383C4×C5#100911yescharacteristic
384Dic5—42no—
385Dic5—41no—
386Dic5—41no—
387Dic5—121no—
388Dic5—122no—
389#41—304no—
390#41—602no—
391C2×Q8—51no—
392C2×Q8—101no—
393C2×Q8—152no—
394C2×D4—151no—
395C2×D4—302no—
396C2×D4#120211yescharacteristic
397C22×C4—301no—
398C22×C4—302no—
399C22×C4C2×D3×D512yes—
400Q16—602no—
401SD16—302no—
402C2×C8—31no—
403C2×C8—31no—
404C2×C8—32no—
405C2×C8—122no—
406C4⋊C4—51no—
407C4⋊C4—52no—
408C4⋊C4—101no—
409C4⋊C4—102no—
410C4⋊C4—101no—
411C4⋊C4—151no—
412C4⋊C4—301no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4#120211yescharacteristic
416C22⋊C4—102no—
417C22⋊C4—102no—
418C22⋊C4—302no—
419C22⋊C4—301no—
420C22⋊C4#120212yes—
421C42—102no—
422C42—101no—
423C42C2×D3×D511yescharacteristic
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—202no—
435C3×C4—201no—
436C3×C4—201no—
437C3×C4#405012yes—
438C3×C4#414411yescharacteristic
439C3×C4D5×#4111yescharacteristic
440Dic3—201no—
441Dic3—202no—
442C2×C5—42no—
443C2×C5C2×#95011yescharacteristic
444C2×C5#582911yescharacteristic
445C2×C5#583811yescharacteristic
446D5—122no—
447C23—301no—
448C23C2×#120212yes—
449Q8—101no—
450Q8—101no—
451Q8—202no—
452Q8—302no—
453Q8—302no—
454D4—22no—
455D4—152no—
456D4—301no—
457D4—604no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—101no—
461C2×C4—102no—
462C2×C4—101no—
463C2×C4—301no—
464C2×C4—302no—
465C2×C4—604no—
466C2×C4—602no—
467C2×C4C2×#120212yes—
468C2×C4C2×#120211yescharacteristic
469C2×C4C2×#120211yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—61no—
472C8—61no—
473C8—62no—
474C2×C3—42no—
475C2×C3#6588811yescharacteristic
476C2×C3C2×#405011yescharacteristic
477C2×C3#6608711yescharacteristic
478D3—202no—
479C5#8366411yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—22no—
483C22—302no—
484C22—601no—
485C22—601no—
486C22C22×#120211yescharacteristic
487C4—21no—
488C4—22no—
489C4—201no—
490C4—202no—
491C4—201no—
492C4—601no—
493C4—602no—
494C4#9131112yes—
495C4#9202411yescharacteristic
496C4#9202711yescharacteristic
497C3#1061117311yescharacteristic, complemented, Sylow
498C2—42no—
499C2—602no—
500C2C2×#9131111yescharacteristic
501C2#1175498011yescharacteristic
502C2#1175531211yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radical#11756310C2
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
2. C3×#65876C2semidirect
3. C5×D4×C3⋊C8C2semidirect
4. #11748560C2semidirect
5. #11748552C2semidirect
6. #11748412C2semidirect
7. #11748411C2semidirect
8. #11747095C2semidirect
9. C4×#6658C2semidirect
10. #11746971C2semidirect
11. #11746921C2semidirect
44. #65876D3semidirect
97. D4×C3⋊C8D5semidirect
424. C3×C5#3302semidirect
479. C5#83664semidirect
497. C3#10611173semidirect

Maximal subgroups

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

subgroupindex
#117563102
C3×#658762
C5×D4×C3⋊C82
#117485602
#117485522
#117484122
#117484112
#117470952
C4×#66582
#117469712
#117469212
#106111733
#836645