Finite Group Databasebeta

← #14418048

Subgroups — #14418048

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4053C211yesmaximal, characteristic, complemented
2#11754138C211yesmaximal, characteristic
3C2×#91286C211yesmaximal, characteristic, complemented
4#11751225C211yesmaximal, characteristic, complemented
5C5×#5139C211yesmaximal, characteristic, complemented
6#11748421C211yesmaximal, characteristic, complemented
7#11748323C211yesmaximal, characteristic, complemented
8#11748203C214yesmaximal, complemented
9#11748202C214yesmaximal, complemented
10#10610720—31nomaximal, Hall
11C2×C5×#235C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C5×#926C2211yescharacteristic
17C22×C3×#168C2211yescharacteristic
18C3×#4053—21no—
19C3×#4053—21no—
20C3×#4053C2212yescomplemented
21C3×#4053C2212yescomplemented
22C2×C3×#676—21no—
23C2×C3×C8×D5—21no—
24#91309C412yescomplemented
25#91307C412yescomplemented
26#91299C412yescomplemented
27#91298C412yescomplemented
28#91297C2214yes—
29C2×#6650—21no—
30#91286—21no—
31#91286—21no—
32#91286C2212yescomplemented
33#91286C2212yescomplemented
34C2×D3×#168—21no—
35#91106C2214yescomplemented
36C5×#825C2214yescomplemented
37#90977C2214yescomplemented
38#90953C2212yescomplemented
39Dic3×#168C2212yescomplemented
40#83792—51nomaximal, Hall
41#66156—31no—
42C2×#4094—31no—
43C2×#4053D311yescharacteristic, complemented
44C5×#421—31no—
45#65413—31no—
46#65294—31no—
47#65286—31no—
48#65113—34no—
49#65112—34no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×C5×#67—21no—
52C5×#235—21no—
53C5×#235—21no—
54C5×#235C2×C412yes—
55C5×#235C2312yes—
56C2×C5×D12C2×C411yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C5×Dic6C2×C411yescharacteristic
59C2×C3×C22⋊D5—21no—
60C3×#709—21no—
61C3×#709—21no—
62C3×#709C2×C412yes—
63C3×#709C2312yes—
64C2×C3×D20C2×C411yescharacteristic
65C2×C3×C4×D5—21no—
66C2×C3×Dic10C2×C411yescharacteristic
67C3×C5×M16—21no—
68C3×C5×M16C2312yes—
69C2×C3×C5×C8—21no—
70#6710—21no—
71#6710C2×C412yes—
72#6710C2×C412yes—
73#6710C2312yes—
74C2×C3⋊#168—21no—
75C2×C3⋊#168C2312yes—
76C5×#217—21no—
77C5×C4⋊Dic3—21no—
78C4×C5×Dic3C2312yes—
79C2×C3×#168D411yescharacteristic
80C2×C3×#168D411yescharacteristic
81C2×C3×#168D411yescharacteristic
82C2×C3×#168D411yescharacteristic
83C2×C3×#168C2311yescharacteristic
84C2×C3×#168C2311yescharacteristic
85C3×#676—22no—
86C3×#676—22no—
87C3×C8×D5—22no—
88C3×C8×D5—22no—
89#6661C2×C414yes—
90#6656C2×C414yes—
91#6655C2×C414yes—
92#6652C2×C414yes—
93#6650—22no—
94#6650—22no—
95D3×#168—22no—
96D3×#168—22no—
97C2×C3×#131—51no—
98#5822—51no—
99C2×#901—51no—
100#5236—51no—
101#5145—54no—
102#5144—54no—
103#5139D511yescharacteristic, complemented
104#5124—51no—
105#5101—51no—
106C2×C5×#41—31no—
107C2×#709C2×D311yescharacteristic
108C2×C5×M16C2×D311yescharacteristic
109C5×#117—31no—
110#4097—32no—
111#4096—34no—
112#4095—32no—
113#4094—32no—
114#4094—32no—
115#4094—61no—
116#4094—61no—
117#4088—32no—
118#4078—32no—
119C2×#681—31no—
120C2×#681—31no—
121C2×#681—61no—
122C22×#168—61no—
123C22×#168C2×D311yescharacteristic
124#4053—21no—
125#4053—21no—
126#4053C2×D312yescomplemented
127#4053C2×D312yescomplemented
128C2×#676—21no—
129C2×C8×D5—21no—
130C5×#104—34no—
131#3954—34no—
132#3937—34no—
133#3935—32no—
134C4×#168—32no—
135#2955—151noSylow
136C23×C3×C5#4111yescharacteristic
137C22×C5×D3—21no—
138C22×C3×D5—21no—
139C2×C3×C4×C5C22×C411yescharacteristic
140C2×C3×C4×C5C22×C411yescharacteristic
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5#4111yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145C5×#67—22no—
146C5×#67—22no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—22no—
149C5×D12—21no—
150C5×D12C22×C412yes—
151C4×C5×D3—22no—
152C4×C5×D3—22no—
153C5×Dic6—21no—
154C5×Dic6C22×C412yes—
155C3×C22⋊D5—22no—
156C3×C22⋊D5—22no—
157C2×C3×Dic5—21no—
158C3×D20—21no—
159C3×D20C22×C412yes—
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×Dic10—21no—
163C3×Dic10C22×C412yes—
164C3×C5×C8—22no—
165C3⋊#168—22no—
166C3⋊#168C22×C414yes—
167C3×#168C2×D411yescharacteristic
168C3×#168C2×D411yescharacteristic
169C3×#168C2×D411yescharacteristic
170C3×#168C2×D411yescharacteristic
171C2×C3×#41—51no—
172C2×#235C2×D511yescharacteristic
173C3×#131—52no—
174C3×#131—52no—
175C3×#131—101no—
176C3×#131—101no—
177C2×C3×M16—101no—
178C2×C3×M16C2×D511yescharacteristic
179C22×C3×C8—51no—
180C22×C3×C8—101no—
181#951—52no—
182#950—54no—
183#949—52no—
184#942—52no—
185#932—52no—
186#926C2×D511yescharacteristic
187C2×#208—51no—
188C2×#208—51no—
189#901—52no—
190#901—52no—
191#901—101no—
192#901—101no—
193C2×ΓL(1,𝔽25)—101no—
194C2×D3×C8—101no—
195#837—54no—
196#825C2×D514yescomplemented
197#822—54no—
198#815—52no—
199C8×Dic3—52no—
200C5×#41—32no—
201C5×#41—32no—
202C5×#41—61no—
203C5×#41—61no—
204C2×C5×Q8—31no—
205C2×C5×D4—31no—
206C2×C5×D4—61no—
207C22×C4×C5—61no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—21no—
210#709—21no—
211#709—21no—
212#709C4×D312yes—
213#709C22×D312yes—
214C2×D20C4×D311yescharacteristic
215C2×C4×D5—21no—
216C2×Dic10C4×D311yescharacteristic
217C5×M16—21no—
218C5×M16C22×D312yes—
219C2×C5×C8—21no—
220C5×C4⋊C4—61no—
221C5×C22⋊C4—61no—
222C42×C5—32no—
223#689—34no—
224#688—34no—
225#687—34no—
226#686—34no—
227#681—32no—
228#681—32no—
229#681—32no—
230#681—61no—
231#681—62no—
232#681—62no—
233C2×#168—32no—
234C2×#168—61no—
235C2×#168—62no—
236C2×#168—62no—
237C2×#168#6711yescharacteristic
238C2×#168#6711yescharacteristic
239C2×#168#6711yescharacteristic
240C2×#168#6711yescharacteristic
241C2×#168C22×D311yescharacteristic
242C2×#168C22×D311yescharacteristic
243#676—22no—
244#676—22no—
245C8×D5—22no—
246C8×D5—22no—
247#575—151no—
248C2×#131—51no—
249C2×#131—151no—
250#444—154no—
251#443—154no—
252#430—151no—
253#421—31no—
254#421—151no—
255#405—151no—
256C22×C3×C5—41no—
257C22×C3×C5C4×D411yescharacteristic
258C22×C3×C5C4×D411yescharacteristic
259C22×C3×C5C2×#4111yescharacteristic
260C2×C5×D3—22no—
261C2×C5×D3—42no—
262C2×C3×D5—22no—
263C2×C3×D5—42no—
264C3×C4×C5C4×D411yescharacteristic
265C3×C4×C5C4×D411yescharacteristic
266C3×C4×C5C23×C411yescharacteristic
267C3×C4×C5C22×D411yescharacteristic
268C3×Dic5—22no—
269C5×Dic3—22no—
270C5×Dic3—42no—
271C3×#41—52no—
272C3×#41—52no—
273C3×#41—101no—
274C3×#41—101no—
275C2×C3×Q8—51no—
276C2×C3×D4—51no—
277C2×C3×D4—101no—
278C22×C3×C4—101no—
279C22×C3×C4C22×D511yescharacteristic
280C2×#67—21no—
281#235—21no—
282#235—21no—
283#235C4×D512yes—
284#235C22×D512yes—
285C2×D12C4×D511yescharacteristic
286C2×C4×D3—21no—
287C2×Dic6C4×D511yescharacteristic
288C3×M16—21no—
289C3×M16—102no—
290C3×M16—102no—
291C3×M16C22×D512yes—
292C2×C3×C8—21no—
293C2×C3×C8—51no—
294C2×C3×C8—51no—
295C2×C3×C8—51no—
296C2×C3×C8—51no—
297C2×C3×C8—51no—
298C2×C3×C8—51no—
299C2×C3×C8—102no—
300C2×C3×C8—102no—
301#217—21no—
302#216—54no—
303#215—54no—
304#214—54no—
305#213—54no—
306C4⋊Dic3—21no—
307C4×Dic3C22×D512yes—
308#208—52no—
309#208—52no—
310#208—52no—
311#208—101no—
312C2×C3⋊C8—52no—
313C2×C3⋊C8—101no—
314ΓL(1,𝔽25)—102no—
315ΓL(1,𝔽25)—102no—
316D3×C8—102no—
317D3×C8—102no—
318C23×C5—61no—
319C23×C5#23511yescharacteristic
320C22×D5—21no—
321C5×Q8—32no—
322C5×Q8—61no—
323C5×D4—32no—
324C5×D4—62no—
325C5×D4—62no—
326C5×D4—61no—
327C2×C4×C5—61no—
328C2×C4×C5—62no—
329C2×C4×C5—62no—
330C2×C4×C5—62no—
331C2×C4×C5C2×C4×D311yescharacteristic
332C2×C4×C5C2×C4×D311yescharacteristic
333C2×C4×C5#23511yescharacteristic
334C2×C4×C5C2×#6711yescharacteristic
335C2×C4×C5C2×#6711yescharacteristic
336C2×C4×C5C23×D311yescharacteristic
337C22⋊D5—22no—
338C22⋊D5—22no—
339C2×Dic5—21no—
340D20—21no—
341D20C2×C4×D312yes—
342C4×D5—22no—
343C4×D5—22no—
344Dic10—21no—
345Dic10C2×C4×D312yes—
346C5×C8—22no—
347#168—34no—
348#168—62no—
349#168C2×#6711yescharacteristic
350#168C2×#6711yescharacteristic
351#168C2×#6711yescharacteristic
352#168C2×#6711yescharacteristic
353C2×#41—31no—
354C2×#41—51no—
355#137—152no—
356#137—152no—
357AGL(1,ℤ/8)—152no—
358AGL(1,ℤ/8)—152no—
359#135—154no—
360#131—52no—
361#131—52no—
362#131—101no—
363#131—101no—
364#131—152no—
365#131—152no—
366#131—301no—
367#131—301no—
368C2×M16—101no—
369C2×M16—151no—
370C2×M16—151no—
371C2×M16—301no—
372C2×M16D3×D511yescharacteristic
373C22×C8—51no—
374C22×C8—101no—
375C22×C8—301no—
376#117—31no—
377#108—154no—
378#104—34no—
379#104—154no—
380#97—152no—
381C4×C8—152no—
382C2×C3×C5—21no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5C2×C4×D411yescharacteristic
386C3×D5—42no—
387C5×D3—42no—
388C23×C3—101no—
389C23×C3#71111yescharacteristic
390C22×D3—21no—
391C3×Q8—52no—
392C3×Q8—101no—
393C3×D4—52no—
394C3×D4—102no—
395C3×D4—102no—
396C3×D4—101no—
397C2×C3×C4—101no—
398C2×C3×C4—102no—
399C2×C3×C4—102no—
400C2×C3×C4C2×C4×D511yescharacteristic
401C2×C3×C4C2×C4×D511yescharacteristic
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4D4×D511yescharacteristic
404C2×C3×C4#71111yescharacteristic
405C2×C3×C4C23×D511yescharacteristic
406#67—22no—
407#67—22no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410D12—21no—
411D12C2×C4×D512yes—
412C4×D3—22no—
413C4×D3—22no—
414Dic6—21no—
415Dic6C2×C4×D512yes—
416C3×C8—22no—
417C3×C8—51no—
418C3×C8—51no—
419C3×C8—51no—
420C3×C8—51no—
421C3⋊C8—54no—
422C3⋊C8—102no—
423C22×C5—41no—
424C22×C5—62no—
425C22×C5—122no—
426C22×C5C4×#6711yescharacteristic
427C22×C5C4×#6711yescharacteristic
428C22×C5C2×#23511yescharacteristic
429C2×D5—22no—
430C2×D5—42no—
431C4×C5—62no—
432C4×C5—122no—
433C4×C5C4×#6711yescharacteristic
434C4×C5C4×#6711yescharacteristic
435C4×C5C22×C4×D311yescharacteristic
436C4×C5C22×#6711yescharacteristic
437Dic5—22no—
438#41—32no—
439#41—32no—
440#41—52no—
441#41—52no—
442#41—61no—
443#41—61no—
444#41—101no—
445#41—101no—
446C2×Q8—31no—
447C2×Q8—51no—
448C2×D4—31no—
449C2×D4—51no—
450C2×D4—61no—
451C2×D4—101no—
452C22×C4—61no—
453C22×C4—101no—
454C22×C4C2×D3×D511yescharacteristic
455Q16—154no—
456SD16—154no—
457SD16—154no—
458D8—154no—
459M16—21no—
460M16—102no—
461M16—102no—
462M16—152no—
463M16—152no—
464M16—152no—
465M16—302no—
466M16—302no—
467M16—301no—
468M16C2×D3×D512yes—
469C2×C8—21no—
470C2×C8—51no—
471C2×C8—51no—
472C2×C8—51no—
473C2×C8—51no—
474C2×C8—51no—
475C2×C8—51no—
476C2×C8—102no—
477C2×C8—102no—
478C2×C8—152no—
479C2×C8—302no—
480C2×C8—302no—
481C2×C8—301no—
482C4⋊C4—61no—
483C22⋊C4—61no—
484C42—32no—
485C3×C5#295511yescharacteristic, complemented, Hall
486C22×C3—41no—
487C22×C3—102no—
488C22×C3—202no—
489C22×C3#402711yescharacteristic
490C22×C3#402711yescharacteristic
491C22×C3C2×#71111yescharacteristic
492C2×D3—22no—
493C2×D3—42no—
494C3×C4—102no—
495C3×C4#402711yescharacteristic
496C3×C4#402711yescharacteristic
497C3×C4C22×C4×D511yescharacteristic
498C3×C4C2×D4×D511yescharacteristic
499Dic3—22no—
500Dic3—42no—
501C2×C5—21no—
502C2×C5—21no—
503C2×C5—21no—
504C2×C5—122no—
505C2×C5C2×C4×#6711yescharacteristic
506D5—42no—
507C23—61no—
508C23—101no—
509C23#677211yescharacteristic
510Q8—32no—
511Q8—52no—
512Q8—61no—
513Q8—101no—
514D4—32no—
515D4—52no—
516D4—62no—
517D4—62no—
518D4—61no—
519D4—102no—
520D4—102no—
521D4—101no—
522C2×C4—61no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—101no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4#677211yescharacteristic
530C2×C4C4×D3×D511yescharacteristic
531C2×C4C4×D3×D511yescharacteristic
532C2×C4D5×#6711yescharacteristic
533C2×C4D5×#6711yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—22no—
536C8—51no—
537C8—51no—
538C8—51no—
539C8—51no—
540C8—154no—
541C8—302no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—202no—
546C2×C3C2×#402711yescharacteristic
547D3—42no—
548C5#8379211yescharacteristic, complemented, Sylow
549C22—41no—
550C22—62no—
551C22—102no—
552C22—122no—
553C22—202no—
554C22#9144011yescharacteristic
555C22#9144011yescharacteristic
556C22C2×#677211yescharacteristic
557C4—62no—
558C4—102no—
559C4—122no—
560C4#9144011yescharacteristic
561C4#9144011yescharacteristic
562C4C2×C4×D3×D511yescharacteristic
563C4C2×D5×#6711yescharacteristic
564C3#1061072011yescharacteristic, complemented, Sylow
565C2—21no—
566C2—21no—
567C2—21no—
568C2—122no—
569C2—202no—
570C2C2×#9144011yescharacteristic
subgroupG/H
centerC4C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5C2×C4×D4
prime radical#11754138C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2955
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4053C2semidirect
3. C2×#91286C2semidirect
4. #11751225C2semidirect
5. C5×#5139C2semidirect
6. #11748421C2semidirect
7. #11748323C2semidirect
8. #11748203C2semidirect
9. #11748202C2semidirect
20. C3×#4053C22semidirect
21. C3×#4053C22semidirect
24. #91309C4semidirect
25. #91307C4semidirect
26. #91299C4semidirect
27. #91298C4semidirect
32. #91286C22semidirect
33. #91286C22semidirect
35. #91106C22semidirect
36. C5×#825C22semidirect
37. #90977C22semidirect
38. #90953C22semidirect
39. Dic3×#168C22semidirect
43. C2×#4053D3semidirect
103. #5139D5semidirect
126. #4053C2×D3semidirect
127. #4053C2×D3semidirect
196. #825C2×D5semidirect
485. C3×C5#2955semidirect
548. C5#83792semidirect
564. C3#10610720semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40532
#117541382
C2×#912862
#117512252
C5×#51392
#117484212
#117483232
#117482032
#117482022
#106107203
#837925