Finite Group Databasebeta

← #14301410

Subgroups — #14301410

Order 1920.

664 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
1C3×#65811C211yesmaximal, characteristic
2#11754120C211yesmaximal, characteristic, complemented
3#11748624C211yesmaximal, characteristic, complemented
4#11748421C211yesmaximal, characteristic, complemented
5#11748420C211yesmaximal, characteristic, complemented
6#11746344C211yesmaximal, characteristic, complemented
7C5×#4523C211yesmaximal, characteristic, complemented
8#10599570—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C3×#4076—22no—
17C3×#4021C411yescharacteristic, complemented
18C3×#4021C411yescharacteristic, complemented
19C3×#4020C411yescharacteristic, complemented
20C3×C4×D20—22no—
21C3×#4015C411yescharacteristic, complemented
22#91284—22no—
23#91283—22no—
24D5×#208—22no—
25#90995—22no—
26#90977—22no—
27#90976—22no—
28#71817—51nomaximal, Hall
29#66079—31no—
30#65811D311yescharacteristic
31#65428—31no—
32#65295—31no—
33#65294—31no—
34C5×#339—31no—
35#64743—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×C3×C22⋊D5—21no—
39C2×C3×C22⋊D5D412yes—
40C3×#709—21no—
41C3×#709—21no—
42C3×#709—21no—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C3×#709—21no—
48C2×C3×D20—22no—
49C2×C3×D20C2×C411yescharacteristic
50C2×C3×D20C2×C411yescharacteristic
51C2×C3×C4×D5—21no—
52C2×C3×C4×D5D412yes—
53C2×C3×Dic10C2×C411yescharacteristic
54C2×C3×Dic10C2×C411yescharacteristic
55C3×C42×C5—21no—
56C3×C42×C5C2×C411yescharacteristic
57C3×C42×C5C2×C411yescharacteristic
58#6719—21no—
59C4⋊Dic15—21no—
60C4×Dic15—21no—
61#6710—21no—
62#6710D412yescomplemented
63C2×C3⋊#168—21no—
64C5×#217—21no—
65C5×C4⋊Dic3—21no—
66C4×C5×Dic3—21no—
67C5×#208—21no—
68C5×#208D412yescomplemented
69C2×C5×C3⋊C8—21no—
70C3×#685—22no—
71C3×#685—22no—
72C3×C4⋊Dic5—22no—
73#6649—24no—
74D5×C3⋊C8—24no—
75C3×#532—51no—
76#5819—51no—
77#5240—51no—
78#5236—51no—
79#5236—51no—
80#4523—51no—
81#4523D511yescharacteristic, complemented
82C2×#709C2×D311yescharacteristic
83C2×#709C2×D311yescharacteristic
84C2×C5×M16—31no—
85C5×#117—31no—
86C2×C42×C5C2×D311yescharacteristic
87#4076—22no—
88#4072—31no—
89C2×#681—31no—
90#4053—62no—
91D5×M16—62no—
92#4047—62no—
93#4021Dic311yescharacteristic, complemented
94#4021Dic311yescharacteristic, complemented
95#4020Dic311yescharacteristic, complemented
96C4×D20—22no—
97#4015Dic311yescharacteristic, complemented
98#3957—62no—
99#3938—62no—
100#3937—62no—
101#1884—151noSylow
102C23×C3×C5C2×D411yescharacteristic
103C22×C3×D5—21no—
104C22×C3×D5C22⋊C412yes—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×Dic15—41no—
115C2×C5×Dic3—41no—
116C3×C22⋊D5—22no—
117C3×C22⋊D5—22no—
118C3×C22⋊D5—41no—
119C3×C22⋊D5—41no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5C22⋊C412yes—
122C3×D20—21no—
123C3×D20—21no—
124C3×D20—21no—
125C3×D20—21no—
126C3×D20—44no—
127C3×C4×D5—22no—
128C3×C4×D5—22no—
129C3×C4×D5—41no—
130C3×C4×D5—41no—
131C3×Dic10—21no—
132C3×Dic10—21no—
133C3×Dic10—21no—
134C3×Dic10—21no—
135C3⋊#168—22no—
136C5×C3⋊C8—22no—
137C2×C3×#41—51no—
138C2×C3×#41—51no—
139C3×C4⋊Q8—51no—
140C3×#127—51no—
141C3×#124—51no—
142C3×#124—51no—
143C3×#121—102no—
144C3×C4×D4—102no—
145C2×C3×C42C2×D511yescharacteristic
146#948—102no—
147#948—102no—
148#926—51no—
149#926C2×D511yescharacteristic
150C2×#208—51no—
151C2×#208—102no—
152C2×#208C2×D511yescharacteristic
153#837—102no—
154#837—102no—
155#834—102no—
156C22×C4×C5—21no—
157C22×C4×C5C22×D311yescharacteristic
158C2×C22⋊D5—21no—
159C2×C22⋊D5#6712yes—
160#709—21no—
161#709—21no—
162#709—21no—
163#709—21no—
164#709—21no—
165#709—21no—
166#709—21no—
167#709—21no—
168C2×D20—22no—
169C2×D20C2×Dic311yescharacteristic
170C2×D20C2×Dic311yescharacteristic
171C2×C4×D5—21no—
172C2×C4×D5#6712yes—
173C2×Dic10C2×Dic311yescharacteristic
174C2×Dic10C2×Dic311yescharacteristic
175C5×M16—32no—
176C5×M16—61no—
177C2×C5×C8—61no—
178C5×C4⋊C4—61no—
179C5×C22⋊C4—61no—
180C42×C5—21no—
181C42×C5—61no—
182C42×C5C2×Dic311yescharacteristic
183C42×C5C2×Dic311yescharacteristic
184C22⋊Dic5—61no—
185#685—22no—
186#685—22no—
187C4⋊Dic5—22no—
188C4⋊Dic5—61no—
189C4×Dic5—61no—
190#681—32no—
191#681—61no—
192C2×#168—61no—
193#676—64no—
194C8×D5—64no—
195#568—151no—
196#532—51no—
197#421—151no—
198#421—151no—
199#410—151no—
200#339—31no—
201#339—151no—
202C22×C3×C5—41no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5#12111yescharacteristic
205C22×C3×C5#12111yescharacteristic
206C2×C3×D5—22no—
207C2×C3×D5—42no—
208C2×C3×D5—42no—
209C2×C3×D5—41no—
210C3×C4×C5—22no—
211C3×C4×C5—41no—
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12011yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—81no—
217C3×Dic5—22no—
218C3×Dic5—41no—
219C5×Dic3—81no—
220C3×#41—101no—
221C3×#41—101no—
222C3×#41—101no—
223C3×#41—101no—
224C3×#41—101no—
225C3×#41—101no—
226C3×#41—101no—
227C3×#41—101no—
228C2×C3×Q8—51no—
229C2×C3×Q8—51no—
230C2×C3×D4—52no—
231C2×C3×D4—51no—
232C2×C3×D4—51no—
233C2×C3×D4—102no—
234C2×C3×D4—101no—
235C22×C3×C4—21no—
236C22×C3×C4—52no—
237C22×C3×C4—101no—
238C22×C3×C4C22×D511yescharacteristic
239C3×C4⋊C4—102no—
240C3×C22⋊C4—102no—
241C3×C22⋊C4—102no—
242C3×C42—21no—
243C3×C42C4×D511yescharacteristic
244C3×C42C4×D511yescharacteristic
245#217—21no—
246#217—101no—
247C4⋊Dic3—21no—
248C4⋊Dic3—101no—
249C4×Dic3—21no—
250C4×Dic3—101no—
251#208—21no—
252#208—52no—
253#208—104no—
254#208—101no—
255#208D2012yescomplemented
256C2×C3⋊C8—21no—
257C2×C3⋊C8—104no—
258C2×C3⋊C8—101no—
259C23×C5C2×#6711yescharacteristic
260C22×D5—21no—
261C22×D5#21712yes—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—42no—
265C2×C4×C5—121no—
266C2×C4×C5D3×D411yescharacteristic
267C2×C4×C5D3×D411yescharacteristic
268C2×C4×C5#23711yescharacteristic
269C2×C4×C5#23711yescharacteristic
270C2×C4×C5C22×Dic311yescharacteristic
271C2×C4×C5C2×#6711yescharacteristic
272C22⋊D5—22no—
273C22⋊D5—22no—
274C22⋊D5—41no—
275C22⋊D5—41no—
276C2×Dic5—21no—
277C2×Dic5—121no—
278C2×Dic5#21712yes—
279D20—21no—
280D20—21no—
281D20—21no—
282D20—21no—
283D20—44no—
284C4×D5—22no—
285C4×D5—22no—
286C4×D5—41no—
287C4×D5—41no—
288Dic10—21no—
289Dic10—21no—
290Dic10—21no—
291Dic10—21no—
292C5×C8—62no—
293#168—62no—
294C2×#41—51no—
295C2×#41—51no—
296#131—302no—
297#131—302no—
298C2×M16—31no—
299C2×M16—151no—
300C2×M16—302no—
301C4⋊Q8—51no—
302#127—51no—
303#124—51no—
304#124—51no—
305#121—102no—
306C4×D4—102no—
307#117—31no—
308#117—151no—
309C2×C42D3×D511yescharacteristic
310#104—302no—
311#104—302no—
312#99—302no—
313C2×C3×C5—21no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#38611yescharacteristic
317C3×D5—42no—
318C3×D5—81no—
319C23×C3—52no—
320C23×C3—101no—
321C23×C3D4×D511yescharacteristic
322C3×Q8—101no—
323C3×Q8—101no—
324C3×Q8—101no—
325C3×Q8—101no—
326C3×D4—102no—
327C3×D4—102no—
328C3×D4—101no—
329C3×D4—101no—
330C3×D4—101no—
331C3×D4—101no—
332C3×D4—204no—
333C3×D4—201no—
334C3×D4—201no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—42no—
338C2×C3×C4—52no—
339C2×C3×C4—102no—
340C2×C3×C4—102no—
341C2×C3×C4—101no—
342C2×C3×C4—201no—
343C2×C3×C4—201no—
344C2×C3×C4C2×C4×D511yescharacteristic
345C2×C3×C4C2×D2011yescharacteristic
346C2×C3×C4#70911yescharacteristic
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4#71311yescharacteristic
350C2×Dic3—41no—
351C2×Dic3—201no—
352C3⋊C8—22no—
353C3⋊C8—102no—
354C22×C5—41no—
355C22×C5#93911yescharacteristic
356C22×C5#93911yescharacteristic
357C22×C5C2×#21711yescharacteristic
358C2×D5—22no—
359C2×D5—42no—
360C2×D5—42no—
361C2×D5—41no—
362C4×C5—22no—
363C4×C5—41no—
364C4×C5—241no—
365C4×C5D4×Dic311yescharacteristic
366C4×C5D4×Dic311yescharacteristic
367C4×C5#93511yescharacteristic
368C4×C5#93711yescharacteristic
369Dic5—22no—
370Dic5—41no—
371Dic5—241no—
372#41—101no—
373#41—101no—
374#41—101no—
375#41—101no—
376#41—101no—
377#41—101no—
378#41—101no—
379#41—101no—
380C2×Q8—51no—
381C2×Q8—51no—
382C2×D4—52no—
383C2×D4—51no—
384C2×D4—51no—
385C2×D4—102no—
386C2×D4—101no—
387C22×C4—21no—
388C22×C4—52no—
389C22×C4—101no—
390C22×C4C2×D3×D511yescharacteristic
391M16—32no—
392M16—61no—
393M16—152no—
394M16—304no—
395M16—301no—
396C2×C8—61no—
397C2×C8—304no—
398C2×C8—301no—
399C4⋊C4—61no—
400C4⋊C4—102no—
401C4⋊C4—301no—
402C22⋊C4—61no—
403C22⋊C4—102no—
404C22⋊C4—102no—
405C22⋊C4—301no—
406C42—21no—
407C42—61no—
408C42—301no—
409C42D5×Dic311yescharacteristic
410C42D5×Dic311yescharacteristic
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3—102no—
414C22×C3—202no—
415C22×C3—202no—
416C22×C3—201no—
417C22×C3D5×C22⋊C411yescharacteristic
418C22×C3#403011yescharacteristic
419C22×C3#404111yescharacteristic
420C3×C4—22no—
421C3×C4—41no—
422C3×C4—102no—
423C3×C4—201no—
424C3×C4C4×D2011yescharacteristic
425C3×C4#402811yescharacteristic
426C3×C4#403911yescharacteristic
427C3×C4#404011yescharacteristic
428Dic3—81no—
429Dic3—401no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5#522011yescharacteristic
434D5—42no—
435D5—81no—
436C23—52no—
437C23—101no—
438C23D5×#6711yescharacteristic
439Q8—101no—
440Q8—101no—
441Q8—101no—
442Q8—101no—
443D4—102no—
444D4—102no—
445D4—101no—
446D4—101no—
447D4—101no—
448D4—101no—
449D4—204no—
450D4—201no—
451D4—201no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—42no—
455C2×C4—52no—
456C2×C4—102no—
457C2×C4—102no—
458C2×C4—101no—
459C2×C4—121no—
460C2×C4—201no—
461C2×C4—201no—
462C2×C4—601no—
463C2×C4#676511yescharacteristic
464C2×C4#676611yescharacteristic
465C2×C4D3×D2011yescharacteristic
466C2×C4#677711yescharacteristic
467C2×C4C2×D5×Dic311yescharacteristic
468C2×C4D5×#6711yescharacteristic
469C8—62no—
470C8—302no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—202no—
475C2×C3—401no—
476C2×C3#6495411yescharacteristic
477C5#7181711yescharacteristic, complemented, Sylow
478C22—41no—
479C22—102no—
480C22—202no—
481C22—202no—
482C22—201no—
483C22#9140811yescharacteristic
484C22#9140911yescharacteristic
485C22D5×#21711yescharacteristic
486C4—22no—
487C4—41no—
488C4—102no—
489C4—201no—
490C4—241no—
491C4—1201no—
492C4#9140711yescharacteristic
493C4Dic3×D2011yescharacteristic
494C4#9143411yescharacteristic
495C4#9147411yescharacteristic
496C3#1059957011yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—202no—
501C2—401no—
502C2#1174889611yescharacteristic
subgroupG/H
centerC4#91474
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC2×C3×C5#386
prime radicalC3×#65811C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1884
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11754120C2semidirect
3. #11748624C2semidirect
4. #11748421C2semidirect
5. #11748420C2semidirect
6. #11746344C2semidirect
7. C5×#4523C2semidirect
17. C3×#4021C4semidirect
18. C3×#4021C4semidirect
19. C3×#4020C4semidirect
21. C3×#4015C4semidirect
62. #6710D4semidirect
68. C5×#208D4semidirect
81. #4523D5semidirect
93. #4021Dic3semidirect
94. #4021Dic3semidirect
95. #4020Dic3semidirect
97. #4015Dic3semidirect
255. #208D20semidirect
411. C3×C5#1884semidirect
477. C5#71817semidirect
496. C3#10599570semidirect

Maximal subgroups

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

subgroupindex
C3×#658112
#117541202
#117486242
#117484212
#117484202
#117463442
C5×#45232
#105995703
#718175