Finite Group Databasebeta

← #14302136

Subgroups — #14302136

Order 1920.

780 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91827C211yesmaximal, characteristic
2C2×M16×D15C211yesmaximal, characteristic, complemented
3C2×C3×C5×#100C211yesmaximal, characteristic, complemented
4C2×#91117C211yesmaximal, characteristic, complemented
5#11751227C211yesmaximal, characteristic, complemented
6#11746375C211yesmaximal, characteristic, complemented
7#11746375C211yesmaximal, characteristic, complemented
8#10600874—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220C412yes—
11C22×C4×D15C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×#6719C412yes—
15#91827—21no—
16#91827—21no—
17#91827—21no—
18#91827—21no—
19C2×C4⋊Dic15C2211yescharacteristic
20C2×#6710C2211yescharacteristic
21C2×#6710C2211yescharacteristic
22M16×D15—22no—
23M16×D15—22no—
24C2×#6705—21no—
25C2×C8×D15—21no—
26C3×C5×#100—22no—
27#91117—22no—
28#91104—21no—
29#91104—21no—
30#70081—51nomaximal, Hall
31C2×#4084—31no—
32C2×D5×M16—31no—
33C2×C5×#100D311yescharacteristic, complemented
34C2×#3965—31no—
35#65415—31no—
36#64774—31no—
37#64774—31no—
38C24×C3×C5C2×C412yes—
39C23×D15C2×C411yescharacteristic
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×#1220—22no—
48C2×#1220—22no—
49C2×#1220—44no—
50C22×Dic15C2×C411yescharacteristic
51C22×Dic15C2×C412yes—
52C2×C4×D15—21no—
53C2×C4×D15—21no—
54C2×C4×D15—21no—
55C2×C4×D15—21no—
56C2×C4×D15D411yescharacteristic
57C2×C4×D15D411yescharacteristic
58C2×C4×D15D411yescharacteristic
59C2×C4×D15D411yescharacteristic
60C3×C5×M16—21no—
61C3×C5×M16—21no—
62C3×C5×M16—21no—
63C3×C5×M16D412yescomplemented
64C2×C3×C5×C8—21no—
65C2×C3×C5×C8—21no—
66#6719—22no—
67#6719—22no—
68C4⋊Dic15—21no—
69C4⋊Dic15—21no—
70#6710—21no—
71#6710—21no—
72#6710—21no—
73#6710D412yescomplemented
74C2×C3⋊#168—21no—
75C2×C3⋊#168—21no—
76#6705—24no—
77C8×D15—24no—
78C2×#938—51no—
79C2×D3×M16—51no—
80C2×C3×#100D511yescharacteristic, complemented
81C2×#833—51no—
82#5126—51no—
83#4554—51no—
84#4554—51no—
85C22×C5×D4C2×D311yescharacteristic
86C22×C22⋊D5—32no—
87C22×C4×D5—31no—
88C2×C5×M16C2×D311yescharacteristic
89C2×C5×M16C2×D311yescharacteristic
90C2×C22⋊Dic5—32no—
91#4084—61no—
92#4084—61no—
93#4084—61no—
94#4084—61no—
95C2×C4⋊Dic5—31no—
96C2×#681—31no—
97C2×#681—31no—
98D5×M16—62no—
99D5×M16—62no—
100C2×#676—61no—
101C2×C8×D5—61no—
102C5×#100—22no—
103#3965—62no—
104#3952—61no—
105#3952—61no—
106#1900—151noSylow
107C23×C3×C5—22no—
108C23×C3×C5—22no—
109C23×C3×C5—22no—
110C23×C3×C5—42no—
111C23×C3×C5—42no—
112C23×C3×C5C22×C411yescharacteristic
113C22×D15—21no—
114C22×D15—21no—
115C22×D15—22no—
116C22×D15—41no—
117C22×D15C22⋊C411yescharacteristic
118C22×D15C22⋊C411yescharacteristic
119C3×C5×D4—41no—
120C3×C5×D4—41no—
121C3×C5×D4—41no—
122C3×C5×D4—41no—
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5#4111yescharacteristic
128C2×C3×C4×C5#4111yescharacteristic
129#1220—44no—
130#1220—44no—
131C2×Dic15—21no—
132C2×Dic15—21no—
133C2×Dic15—22no—
134C2×Dic15—42no—
135C2×Dic15C22⋊C411yescharacteristic
136C2×Dic15C22⋊C411yescharacteristic
137C4×D15—21no—
138C4×D15—21no—
139C4×D15—21no—
140C4×D15—21no—
141C4×D15—21no—
142C4×D15—21no—
143C4×D15—21no—
144C4×D15—21no—
145C3×C5×C8—22no—
146C3×C5×C8—41no—
147C3⋊#168—22no—
148C3⋊#168—41no—
149C22×C3×D4C2×D511yescharacteristic
150C22×#67—52no—
151C22×C4×D3—51no—
152C2×C3×M16C2×D511yescharacteristic
153C2×C3×M16C2×D511yescharacteristic
154C2×#217—52no—
155#938—101no—
156#938—101no—
157#938—101no—
158#938—101no—
159C2×C4⋊Dic3—51no—
160C2×#208—51no—
161C2×#208—51no—
162D3×M16—102no—
163D3×M16—102no—
164C2×ΓL(1,𝔽25)—101no—
165C2×D3×C8—101no—
166C3×#100—22no—
167#833—102no—
168(C2×D3)⋊C8—101no—
169(C2×D3)⋊C8—101no—
170C24×C5C4×D312yes—
171C23×D5—31no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—21no—
177C2×C5×D4—21no—
178C22×C4×C5C22×D311yescharacteristic
179C2×C22⋊D5—62no—
180C2×C22⋊D5—62no—
181C2×C22⋊D5—124no—
182C22×Dic5—31no—
183C22×Dic5—32no—
184C2×C4×D5—31no—
185C2×C4×D5—31no—
186C2×C4×D5—31no—
187C2×C4×D5—31no—
188C2×C4×D5—61no—
189C2×C4×D5—61no—
190C2×C4×D5—61no—
191C2×C4×D5—61no—
192C5×M16—21no—
193C5×M16—21no—
194C5×M16—21no—
195C5×M16#6712yescomplemented
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200C4⋊Dic5—61no—
201C4⋊Dic5—61no—
202#681—32no—
203#681—61no—
204#681—61no—
205#681—61no—
206C2×#168—61no—
207C2×#168—61no—
208#676—64no—
209C8×D5—64no—
210C22×M16—151no—
211C2×#121—151no—
212C2×#100—151no—
213C2×#100D1511yescharacteristic, complemented
214#407—151no—
215#343—151no—
216#343—151no—
217C22×C3×C5—21no—
218C22×C3×C5—21no—
219C22×C3×C5—42no—
220C22×C3×C5—42no—
221C22×C3×C5—42no—
222C22×C3×C5—82no—
223C22×C3×C5—82no—
224C22×C3×C5C2×C22⋊C411yescharacteristic
225C22×C3×C5C4×D411yescharacteristic
226C22×C3×C5C4×D411yescharacteristic
227C2×D15—21no—
228C2×D15—21no—
229C2×D15—21no—
230C2×D15—21no—
231C2×D15—21no—
232C2×D15—42no—
233C2×D15—42no—
234C2×D15#10012yescomplemented
235C3×C4×C5#12011yescharacteristic
236C3×C4×C5#12111yescharacteristic
237C3×C4×C5#12111yescharacteristic
238C3×C4×C5#12311yescharacteristic
239Dic15—21no—
240Dic15—21no—
241Dic15—42no—
242C24×C3C4×D512yes—
243C23×D3—51no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C22×C3×C4C22×D511yescharacteristic
251C2×#67—102no—
252C2×#67—102no—
253C2×#67—204no—
254C22×Dic3—51no—
255C22×Dic3—52no—
256C2×C4×D3—51no—
257C2×C4×D3—51no—
258C2×C4×D3—51no—
259C2×C4×D3—51no—
260C2×C4×D3—101no—
261C2×C4×D3—101no—
262C2×C4×D3—101no—
263C2×C4×D3—101no—
264C3×M16—21no—
265C3×M16—21no—
266C3×M16—21no—
267C3×M16C22⋊D512yescomplemented
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270#217—102no—
271#217—102no—
272C4⋊Dic3—101no—
273C4⋊Dic3—101no—
274#208—52no—
275#208—101no—
276#208—101no—
277#208—101no—
278C2×C3⋊C8—101no—
279C2×C3⋊C8—101no—
280ΓL(1,𝔽25)—104no—
281D3×C8—104no—
282C23×C5—22no—
283C23×C5—22no—
284C23×C5—22no—
285C23×C5—42no—
286C23×C5—42no—
287C23×C5C2×C4×D311yescharacteristic
288C22×D5—31no—
289C22×D5—31no—
290C22×D5—62no—
291C22×D5—61no—
292C22×D5—61no—
293C22×D5—121no—
294C5×D4—41no—
295C5×D4—41no—
296C5×D4—41no—
297C5×D4—41no—
298C2×C4×C5#23511yescharacteristic
299C2×C4×C5D3×D411yescharacteristic
300C2×C4×C5D3×D411yescharacteristic
301C2×C4×C5D3×D411yescharacteristic
302C2×C4×C5#23711yescharacteristic
303C2×C4×C5C2×#6711yescharacteristic
304C22⋊D5—124no—
305C22⋊D5—124no—
306C2×Dic5—31no—
307C2×Dic5—31no—
308C2×Dic5—61no—
309C2×Dic5—61no—
310C2×Dic5—62no—
311C2×Dic5—122no—
312C4×D5—61no—
313C4×D5—61no—
314C4×D5—61no—
315C4×D5—61no—
316C4×D5—61no—
317C4×D5—61no—
318C4×D5—61no—
319C4×D5—61no—
320C5×C8—22no—
321C5×C8—41no—
322#168—62no—
323#168—121no—
324C22×D4—152no—
325C22×D4C2×D1511yescharacteristic
326C23×C4—151no—
327C2×M16—151no—
328C2×M16—151no—
329C2×M16—301no—
330C2×M16—302no—
331C2×M16—302no—
332C2×M16C2×D1511yescharacteristic
333C2×M16C2×D1511yescharacteristic
334C22×C8—301no—
335#121—301no—
336#121—301no—
337#121—301no—
338#121—301no—
339C2×C4⋊C4—151no—
340C2×C22⋊C4—152no—
341#100—22no—
342#100—302no—
343C22⋊C8—301no—
344C22⋊C8—301no—
345C2×C3×C5—21no—
346C2×C3×C5—21no—
347C2×C3×C5—82no—
348C2×C3×C5#38611yescharacteristic
349C2×C3×C5C2×#10011yescharacteristic
350C2×C3×C5#41311yescharacteristic
351D15—22no—
352D15—41no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3C2×C4×D511yescharacteristic
359C22×D3—51no—
360C22×D3—51no—
361C22×D3—102no—
362C22×D3—101no—
363C22×D3—101no—
364C22×D3—201no—
365C3×D4—41no—
366C3×D4—41no—
367C3×D4—41no—
368C3×D4—41no—
369C2×C3×C4#70911yescharacteristic
370C2×C3×C4D4×D511yescharacteristic
371C2×C3×C4D4×D511yescharacteristic
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4#71111yescharacteristic
374C2×C3×C4C2×C22⋊D511yescharacteristic
375#67—204no—
376#67—204no—
377C2×Dic3—51no—
378C2×Dic3—51no—
379C2×Dic3—101no—
380C2×Dic3—101no—
381C2×Dic3—102no—
382C2×Dic3—202no—
383C4×D3—101no—
384C4×D3—101no—
385C4×D3—101no—
386C4×D3—101no—
387C4×D3—101no—
388C4×D3—101no—
389C4×D3—101no—
390C4×D3—101no—
391C3×C8—22no—
392C3×C8—41no—
393C3⋊C8—102no—
394C3⋊C8—201no—
395C22×C5—21no—
396C22×C5—21no—
397C22×C5—42no—
398C22×C5—42no—
399C22×C5—42no—
400C22×C5—82no—
401C22×C5—82no—
402C22×C5D3×C22⋊C411yescharacteristic
403C22×C5#67⋊C411yescharacteristic
404C22×C5C4×#6711yescharacteristic
405C2×D5—32no—
406C2×D5—61no—
407C2×D5—61no—
408C2×D5—61no—
409C2×D5—61no—
410C2×D5—61no—
411C2×D5—122no—
412C2×D5—122no—
413C4×C5#88311yescharacteristic
414C4×C5#88411yescharacteristic
415C4×C5#93711yescharacteristic
416C4×C5#93811yescharacteristic
417Dic5—61no—
418Dic5—61no—
419Dic5—122no—
420C24—151no—
421C24C4×D1512yes—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—302no—
429C2×D4—302no—
430C2×D4—604no—
431C22×C4—151no—
432C22×C4—151no—
433C22×C4—151no—
434C22×C4—151no—
435C22×C4—151no—
436C22×C4—152no—
437C22×C4—301no—
438C22×C4—301no—
439C22×C4—301no—
440C22×C4—301no—
441C22×C4C22×D1511yescharacteristic
442M16—21no—
443M16—21no—
444M16—21no—
445M16—152no—
446M16—304no—
447M16—301no—
448M16—301no—
449M16—301no—
450M16#122012yescomplemented
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—304no—
454C2×C8—301no—
455C2×C8—301no—
456C4⋊C4—301no—
457C4⋊C4—301no—
458C22⋊C4—302no—
459C22⋊C4—302no—
460C3×C5#190011yescharacteristic, complemented, Hall
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—82no—
467C22×C3—82no—
468C22×C3D5×C22⋊C411yescharacteristic
469C22×C3#402711yescharacteristic
470C22×C3C4×C22⋊D511yescharacteristic
471C2×D3—52no—
472C2×D3—101no—
473C2×D3—101no—
474C2×D3—101no—
475C2×D3—101no—
476C2×D3—101no—
477C2×D3—202no—
478C2×D3—202no—
479C3×C4#402911yescharacteristic
480C3×C4#403011yescharacteristic
481C3×C4#408311yescharacteristic
482C3×C4#408411yescharacteristic
483Dic3—101no—
484Dic3—101no—
485Dic3—202no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5—82no—
489C2×C5D3×#10011yescharacteristic
490C2×C5#474511yescharacteristic
491C2×C5#495611yescharacteristic
492D5—62no—
493D5—121no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—42no—
498C23—42no—
499C23—151no—
500C23—151no—
501C23—302no—
502C23—301no—
503C23—301no—
504C23—601no—
505C23C2×C4×D1511yescharacteristic
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—604no—
511D4—604no—
512C2×C4—151no—
513C2×C4—151no—
514C2×C4—301no—
515C2×C4—301no—
516C2×C4—301no—
517C2×C4—301no—
518C2×C4—301no—
519C2×C4—301no—
520C2×C4—301no—
521C2×C4—301no—
522C2×C4—301no—
523C2×C4—301no—
524C2×C4—302no—
525C2×C4—602no—
526C2×C4#681711yescharacteristic
527C2×C4D4×D1511yescharacteristic
528C2×C4D4×D1511yescharacteristic
529C2×C4D4×D1511yescharacteristic
530C2×C4#681911yescharacteristic
531C2×C4C2×#122011yescharacteristic
532C8—22no—
533C8—41no—
534C8—302no—
535C8—601no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—82no—
539C2×C3D5×#10011yescharacteristic
540C2×C3#6503411yescharacteristic
541C2×C3#6524511yescharacteristic
542D3—102no—
543D3—201no—
544C5#7008111yescharacteristic, complemented, Sylow
545C22—21no—
546C22—21no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—82no—
551C22—82no—
552C22—152no—
553C22—301no—
554C22—301no—
555C22—301no—
556C22—301no—
557C22—301no—
558C22—602no—
559C22—602no—
560C22C22⋊C4×D1511yescharacteristic
561C22#9177011yescharacteristic
562C22C4×#122011yescharacteristic
563C4—301no—
564C4—301no—
565C4—602no—
566C4#9177211yescharacteristic
567C4#9177311yescharacteristic
568C4#9182611yescharacteristic
569C4#9182711yescharacteristic
570C3#1060087411yescharacteristic, complemented, Sylow
571C2—21no—
572C2—21no—
573C2—82no—
574C2—302no—
575C2—601no—
576C2D15×#10011yescharacteristic
577C2#1175084611yescharacteristic
578C2#1175105711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#100C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91827C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#100D15
hypocenterC3×C5#1900
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×M16×D15C2semidirect
3. C2×C3×C5×#100C2semidirect
4. C2×#91117C2semidirect
5. #11751227C2semidirect
6. #11746375C2semidirect
7. #11746375C2semidirect
33. C2×C5×#100D3semidirect
63. C3×C5×M16D4semidirect
73. #6710D4semidirect
80. C2×C3×#100D5semidirect
195. C5×M16#67semidirect
213. C2×#100D15semidirect
234. C2×D15#100semidirect
267. C3×M16C22⋊D5semidirect
450. M16#1220semidirect
460. C3×C5#1900semidirect
544. C5#70081semidirect
570. C3#10600874semidirect

Maximal subgroups

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

subgroupindex
C2×#918272
C2×M16×D152
C2×C3×C5×#1002
C2×#911172
#117512272
#117463752
#106008743
#700815