Finite Group Databasebeta

← #14303066

Subgroups — #14303066

Order 1920.

680 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65859C211yesmaximal, characteristic
2#11754120C211yesmaximal, characteristic, complemented
3#11748353C211yesmaximal, characteristic, complemented
4C2×#90958C211yesmaximal, characteristic, complemented
5C2×#90958C211yesmaximal, characteristic, complemented
6#11746354C211yesmaximal, characteristic, complemented
7C5×#4533C211yesmaximal, characteristic, complemented
8#10599833—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C3×#4041—22no—
17C3×#4028C414yes—
18C3×#4021—21no—
19C3×#4020—21no—
20#91284—22no—
21#91283—22no—
22D5×#208—22no—
23#90961—21no—
24#90958—21no—
25#90958—22no—
26#90958—22no—
27#71855—51nomaximal, Hall
28#66079—31no—
29#65859D311yescharacteristic
30#65421—31no—
31C2×#3955—31no—
32C2×#3955—31no—
33C5×#344—31no—
34#64753—31no—
35C23×C3×D5C2×C412yes—
36C22×C3×C4×C5C2311yescharacteristic
37C2×C3×C22⋊D5C2×C412yes—
38C3×#709—21no—
39C3×#709—21no—
40C3×#709—21no—
41C3×#709—21no—
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20—24no—
49C2×C3×D20D411yescharacteristic
50C2×C3×C4×D5D412yes—
51C2×C3×Dic10D411yescharacteristic
52C3×C5×C4⋊C4—21no—
53C3×C5×C22⋊C4C2×C412yes—
54C3×C42×C5—21no—
55#6710—21no—
56#6710—21no—
57#6710—21no—
58#6710D412yescomplemented
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61C5×#208—21no—
62C5×#208—21no—
63C5×#208—21no—
64C5×#208D412yescomplemented
65C2×C5×C3⋊C8—21no—
66C2×C5×C3⋊C8—21no—
67C3×#685—24no—
68#6649—24no—
69D5×C3⋊C8—24no—
70C3×#535—51no—
71#5819—51no—
72#5237—51no—
73C2×#833—51no—
74C2×#833—51no—
75#4533—51no—
76#4533D511yescharacteristic, complemented
77C2×#709C2×D311yescharacteristic
78C22×D20C2×D311yescharacteristic
79C2×C5×M16—31no—
80C2×C5×M16—31no—
81C5×#117C2×D311yescharacteristic
82C2×#681—31no—
83C2×#681—31no—
84#4053—62no—
85D5×M16—62no—
86#4047—62no—
87#4041—22no—
88#4028Dic314yes—
89#4021—21no—
90#4020—21no—
91#3956—61no—
92#3955—62no—
93#3955—62no—
94#3955—61no—
95#1914—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×C3×D5—22no—
98C22×C3×D5—22no—
99C22×C3×D5—22no—
100C22×C3×D5—82no—
101C22×C3×D5C22⋊C412yes—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C3×C22⋊D5—22no—
110C3×C22⋊D5—22no—
111C2×C3×Dic5C22⋊C412yes—
112C3×D20—21no—
113C3×D20—21no—
114C3×D20—41no—
115C3×D20—41no—
116C3×D20—41no—
117C3×D20—41no—
118C3×D20—84no—
119C3×C4×D5—22no—
120C3×C4×D5—22no—
121C3×Dic10—21no—
122C3×Dic10—21no—
123C3⋊#168—22no—
124C3⋊#168—41no—
125C5×C3⋊C8—22no—
126C5×C3⋊C8—41no—
127C2×C3×#41—51no—
128C22×C3×D4—51no—
129C3×#127—101no—
130C3×#124—101no—
131C3×#121—102no—
132C3×#120—54no—
133C3×#117C2×D511yescharacteristic
134#948—102no—
135#948—102no—
136C2×#208—51no—
137C2×#208—51no—
138C2×#208—102no—
139C2×#208C2×D511yescharacteristic
140C2×#208C2×D511yescharacteristic
141#836—101no—
142#833—102no—
143#833—101no—
144#833—102no—
145C23×D5C2×Dic312yes—
146C22×C4×C5C22×D311yescharacteristic
147C2×C22⋊D5C2×Dic312yes—
148#709—21no—
149#709—21no—
150#709—21no—
151#709—21no—
152C2×D20—21no—
153C2×D20—21no—
154C2×D20—21no—
155C2×D20—21no—
156C2×D20—21no—
157C2×D20—21no—
158C2×D20—24no—
159C2×D20#6711yescharacteristic
160C2×C4×D5#6712yes—
161C2×Dic10#6711yescharacteristic
162C5×M16—32no—
163C5×M16—61no—
164C5×M16—61no—
165C5×M16—61no—
166C2×C5×C8—61no—
167C2×C5×C8—61no—
168C5×C4⋊C4—21no—
169C5×C22⋊C4C2×Dic312yes—
170C42×C5—21no—
171#685—24no—
172#681—32no—
173#681—61no—
174#681—61no—
175#681—61no—
176C2×#168—61no—
177C2×#168—61no—
178#676—64no—
179C8×D5—64no—
180#568—151no—
181#535—51no—
182#413—151no—
183C2×#100—151no—
184C2×#100—151no—
185#344—31no—
186#344—151no—
187C22×C3×C5—41no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5C4×D411yescharacteristic
190C22×C3×C5C4×D411yescharacteristic
191C2×C3×D5—22no—
192C2×C3×D5—42no—
193C2×C3×D5—44no—
194C2×C3×D5—42no—
195C2×C3×D5—82no—
196C2×C3×D5—82no—
197C3×C4×C5—42no—
198C3×C4×C5#12011yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12111yescharacteristic
201C3×C4×C5#12311yescharacteristic
202C3×Dic5—22no—
203C24×C3—52no—
204C3×#41—101no—
205C3×#41—101no—
206C3×#41—101no—
207C3×#41—101no—
208C2×C3×Q8—51no—
209C2×C3×D4—52no—
210C2×C3×D4—51no—
211C2×C3×D4—104no—
212C2×C3×D4—101no—
213C2×C3×D4—101no—
214C2×C3×D4—101no—
215C2×C3×D4—101no—
216C2×C3×D4—101no—
217C2×C3×D4—101no—
218C22×C3×C4—52no—
219C22×C3×C4C22×D511yescharacteristic
220C3×C4⋊C4—21no—
221C3×C22⋊C4—104no—
222C3×C22⋊C4C4×D512yes—
223C3×C42—21no—
224#208—21no—
225#208—21no—
226#208—21no—
227#208—52no—
228#208—104no—
229#208—101no—
230#208—101no—
231#208—101no—
232#208D2012yescomplemented
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—104no—
236C2×C3⋊C8—101no—
237C2×C3⋊C8—101no—
238C23×C5C22×Dic311yescharacteristic
239C22×D5—22no—
240C22×D5—22no—
241C22×D5—22no—
242C22×D5—82no—
243C22×D5#21712yes—
244C2×C4×C5—22no—
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×C4×C5#23711yescharacteristic
249C2×C4×C5C2×#6711yescharacteristic
250C2×C4×C5C2×#6711yescharacteristic
251C22⋊D5—22no—
252C22⋊D5—22no—
253C2×Dic5#21712yes—
254D20—21no—
255D20—21no—
256D20—41no—
257D20—41no—
258D20—41no—
259D20—41no—
260D20—84no—
261C4×D5—22no—
262C4×D5—22no—
263Dic10—21no—
264Dic10—21no—
265C5×C8—62no—
266C5×C8—121no—
267#168—62no—
268#168—121no—
269C2×#41—51no—
270C22×D4—51no—
271#131—302no—
272#131—302no—
273C2×M16—31no—
274C2×M16—31no—
275C2×M16—151no—
276C2×M16—151no—
277C2×M16—302no—
278#127—101no—
279#124—101no—
280#121—102no—
281#120—54no—
282#117D3×D511yescharacteristic
283#101—301no—
284#100—302no—
285#100—302no—
286#100—301no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291C3×D5—42no—
292C3×D5—82no—
293C23×C3—52no—
294C23×C3—102no—
295C23×C3—102no—
296C23×C3—102no—
297C23×C3—402no—
298C23×C3C2×C4×D511yescharacteristic
299C3×Q8—101no—
300C3×Q8—101no—
301C3×D4—102no—
302C3×D4—102no—
303C3×D4—101no—
304C3×D4—101no—
305C3×D4—201no—
306C3×D4—201no—
307C3×D4—201no—
308C3×D4—201no—
309C3×D4—404no—
310C2×C3×C4—22no—
311C2×C3×C4—52no—
312C2×C3×C4—102no—
313C2×C3×C4—102no—
314C2×C3×C4C2×D2011yescharacteristic
315C2×C3×C4#70911yescharacteristic
316C2×C3×C4D4×D511yescharacteristic
317C2×C3×C4D4×D511yescharacteristic
318C2×C3×C4D4×D511yescharacteristic
319C2×C3×C4#71311yescharacteristic
320C3⋊C8—22no—
321C3⋊C8—41no—
322C3⋊C8—102no—
323C3⋊C8—201no—
324C22×C5—41no—
325C22×C5D4×Dic311yescharacteristic
326C22×C5D4×Dic311yescharacteristic
327C22×C5C2×#21711yescharacteristic
328C2×D5—22no—
329C2×D5—42no—
330C2×D5—44no—
331C2×D5—42no—
332C2×D5—82no—
333C2×D5—82no—
334C4×C5—42no—
335C4×C5#93511yescharacteristic
336C4×C5#93711yescharacteristic
337C4×C5#93911yescharacteristic
338C4×C5#93911yescharacteristic
339Dic5—22no—
340C24—52no—
341#41—101no—
342#41—101no—
343#41—101no—
344#41—101no—
345C2×Q8—51no—
346C2×D4—52no—
347C2×D4—51no—
348C2×D4—104no—
349C2×D4—101no—
350C2×D4—101no—
351C2×D4—101no—
352C2×D4—101no—
353C2×D4—101no—
354C2×D4—101no—
355C22×C4—52no—
356C22×C4C2×D3×D511yescharacteristic
357M16—32no—
358M16—61no—
359M16—61no—
360M16—61no—
361M16—152no—
362M16—304no—
363M16—301no—
364M16—301no—
365M16—301no—
366C2×C8—61no—
367C2×C8—61no—
368C2×C8—304no—
369C2×C8—301no—
370C2×C8—301no—
371C4⋊C4—21no—
372C22⋊C4—104no—
373C22⋊C4D5×Dic312yes—
374C42—21no—
375C3×C5#191411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—102no—
378C22×C3—202no—
379C22×C3—204no—
380C22×C3—202no—
381C22×C3—402no—
382C22×C3—402no—
383C22×C3C4×D2011yescharacteristic
384C22×C3D5×C22⋊C411yescharacteristic
385C22×C3#403911yescharacteristic
386C3×C4—42no—
387C3×C4—102no—
388C3×C4#402811yescharacteristic
389C3×C4#403011yescharacteristic
390C3×C4#404011yescharacteristic
391C3×C4#404111yescharacteristic
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—21no—
395C2×C5#522011yescharacteristic
396D5—42no—
397D5—82no—
398C23—52no—
399C23—102no—
400C23—102no—
401C23—102no—
402C23—402no—
403C23C2×D5×Dic311yescharacteristic
404Q8—101no—
405Q8—101no—
406D4—102no—
407D4—102no—
408D4—101no—
409D4—101no—
410D4—201no—
411D4—201no—
412D4—201no—
413D4—201no—
414D4—404no—
415C2×C4—22no—
416C2×C4—52no—
417C2×C4—102no—
418C2×C4—102no—
419C2×C4#676511yescharacteristic
420C2×C4#676611yescharacteristic
421C2×C4D3×D2011yescharacteristic
422C2×C4#677711yescharacteristic
423C2×C4D5×#6711yescharacteristic
424C2×C4D5×#6711yescharacteristic
425C8—62no—
426C8—121no—
427C8—302no—
428C8—601no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—202no—
433C2×C3—402no—
434C2×C3#6495411yescharacteristic
435C5#7185511yescharacteristic, complemented, Sylow
436C22—41no—
437C22—102no—
438C22—202no—
439C22—204no—
440C22—202no—
441C22—402no—
442C22—402no—
443C22Dic3×D2011yescharacteristic
444C22#9143411yescharacteristic
445C22D5×#21711yescharacteristic
446C4—42no—
447C4—102no—
448C4#9140711yescharacteristic
449C4#9140811yescharacteristic
450C4#9140911yescharacteristic
451C4#9147411yescharacteristic
452C3#1059983311yescharacteristic, complemented, Sylow
453C2—21no—
454C2—21no—
455C2—21no—
456C2—202no—
457C2—402no—
458C2#1174889611yescharacteristic
subgroupG/H
centerC2#11748896
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC3×#65859C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1914
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11754120C2semidirect
3. #11748353C2semidirect
4. C2×#90958C2semidirect
5. C2×#90958C2semidirect
6. #11746354C2semidirect
7. C5×#4533C2semidirect
58. #6710D4semidirect
64. C5×#208D4semidirect
76. #4533D5semidirect
232. #208D20semidirect
375. C3×C5#1914semidirect
435. C5#71855semidirect
452. C3#10599833semidirect

Maximal subgroups

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

subgroupindex
C3×#658592
#117541202
#117483532
C2×#909582
#117463542
C5×#45332
#105998333
#718555