Finite Group Databasebeta

← #14303055

Subgroups — #14303055

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
1#11756504C211yesmaximal, characteristic, complemented
2#11754602C211yesmaximal, characteristic
3C2×C3×#3955C211yesmaximal, characteristic, complemented
4#11748357C211yesmaximal, characteristic, complemented
5C2×#90958C211yesmaximal, characteristic, complemented
6C5×#4559C211yesmaximal, characteristic, complemented
7#11745988C211yesmaximal, characteristic, complemented
8#10599833—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13#91796—22no—
14M16×D15—22no—
15#91790—22no—
16C5×#926C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91564C414yes—
20#91465—22no—
21#91458—21no—
22#91364—21no—
23C3×#3955—22no—
24#90963—21no—
25#90960—21no—
26#90958—22no—
27#70089—51nomaximal, Hall
28#66079—31no—
29#65859—31no—
30#65421—31no—
31C2×#3955—31no—
32C2×#3955D311yescharacteristic, complemented
33C5×#344—31no—
34#64753—31no—
35C23×C3×D5C2×C412yes—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220C2×C412yes—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41#6817—21no—
42C2×D60D411yescharacteristic
43C2×C4×D15D412yes—
44C2×Dic30D411yescharacteristic
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20—21no—
51C2×#1202—24no—
52C3×C5×M16—21no—
53C3×C5×M16D412yescomplemented
54C2×C3×C5×C8—21no—
55#6710—21no—
56#6710D412yescomplemented
57C2×C3⋊#168—21no—
58#6705—24no—
59C8×D15—24no—
60C5×#217C2×C412yes—
61C5×C4⋊Dic3—21no—
62C4×C5×Dic3—21no—
63C5×#208—21no—
64C5×#208—21no—
65C2×C5×C3⋊C8—21no—
66C3×#681—21no—
67C3×#681—21no—
68C2×C3×#168—21no—
69#6665—24no—
70#5805—51no—
71#5745—51no—
72C2×C3×#100—51no—
73C2×#833—51no—
74#5132—51no—
75#4559D511yescharacteristic, complemented
76#4556—51no—
77C2×#709—31no—
78C22×D20C2×D311yescharacteristic
79C2×C5×M16—31no—
80C2×C5×M16C2×D311yescharacteristic
81C5×#117—31no—
82C2×#681—31no—
83C2×#681C2×D311yescharacteristic
84#4053—62no—
85D5×M16—62no—
86#4047—62no—
87#4041—62no—
88#4028—34no—
89#4021—61no—
90#4020—61no—
91#3956—61no—
92#3955—22no—
93#3955—61no—
94#3955—62no—
95#1914—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×D15C22⋊C412yes—
98C22×C3×D5—22no—
99C22×C3×D5—22no—
100C22×C3×D5—22no—
101C22×C3×D5—82no—
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108#1220—22no—
109#1220—22no—
110C2×Dic15C22⋊C412yes—
111D60—21no—
112D60—21no—
113C4×D15—22no—
114C4×D15—22no—
115Dic30—21no—
116Dic30—21no—
117C2×C5×Dic3—22no—
118C3×D20—41no—
119C3×D20—41no—
120C3×D20—41no—
121C3×D20—41no—
122#1202—84no—
123C3×C5×C8—22no—
124C3⋊#168—22no—
125C3×#168—41no—
126C5×C3⋊C8—41no—
127C22×C3×D4—51no—
128C2×#235—51no—
129C2×C3×M16—51no—
130C2×C3×M16C2×D511yescharacteristic
131#953—54no—
132#940—101no—
133#938—102no—
134#936—101no—
135#926C2×D511yescharacteristic
136C2×#208—51no—
137C2×#208C2×D511yescharacteristic
138#907—102no—
139D3×M16—102no—
140#901—102no—
141C3×#100—102no—
142#833—102no—
143#824—101no—
144#823—101no—
145C23×D5C4×D312yes—
146C22×C4×C5C22×D311yescharacteristic
147C2×C22⋊D5—32no—
148#709—61no—
149#709—61no—
150#709—61no—
151#709—61no—
152C2×D20—21no—
153C2×D20—21no—
154C2×D20—21no—
155C2×D20—21no—
156C2×D20—21no—
157C2×D20—21no—
158C2×D20—31no—
159C2×D20—64no—
160C2×C4×D5—32no—
161C2×Dic10—31no—
162C5×M16—21no—
163C5×M16—61no—
164C5×M16—61no—
165C5×M16#6712yescomplemented
166C2×C5×C8—21no—
167C2×C5×C8—61no—
168C5×C4⋊C4—61no—
169C5×C22⋊C4—32no—
170C42×C5—61no—
171#685—64no—
172#681—21no—
173#681—21no—
174#681—32no—
175#681—61no—
176C2×#168—21no—
177C2×#168—61no—
178#676—64no—
179C8×D5—64no—
180#568—151no—
181#535—151no—
182#413—151no—
183C2×#100—51no—
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×D15—22no—
192C2×D15—42no—
193C2×C3×D5—44no—
194C2×C3×D5—42no—
195C2×C3×D5—82no—
196C2×C3×D5—82no—
197C3×C4×C5#12011yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12311yescharacteristic
201Dic15—22no—
202C5×Dic3—42no—
203C24×C3—52no—
204C2×C3×D4—101no—
205C2×C3×D4—101no—
206C2×C3×D4—101no—
207C2×C3×D4—101no—
208C2×C3×D4—101no—
209C2×C3×D4—101no—
210C22×C3×C4C22×D511yescharacteristic
211C2×#67—52no—
212C2×#67—104no—
213#235—101no—
214#235—101no—
215#235—101no—
216#235—101no—
217C2×D12—51no—
218C2×C4×D3—52no—
219C2×Dic6—51no—
220C3×M16—21no—
221C3×M16—101no—
222C3×M16—101no—
223C3×M16D2012yescomplemented
224C2×C3×C8—21no—
225C2×C3×C8—101no—
226#217—104no—
227#217C4×D512yes—
228C4⋊Dic3—21no—
229C4×Dic3—21no—
230#208—21no—
231#208—21no—
232#208—52no—
233#208—101no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—101no—
236ΓL(1,𝔽25)—104no—
237D3×C8—104no—
238C23×C5C2×C4×D311yescharacteristic
239C22×D5—22no—
240C22×D5—22no—
241C22×D5—22no—
242C22×D5—32no—
243C22×D5—82no—
244C2×C4×C5—62no—
245C2×C4×C5#23511yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5#23711yescharacteristic
250C2×C4×C5C2×#6711yescharacteristic
251C22⋊D5—62no—
252C22⋊D5—62no—
253C2×Dic5—32no—
254D20—41no—
255D20—41no—
256D20—41no—
257D20—41no—
258D20—61no—
259D20—61no—
260D20—244no—
261C4×D5—62no—
262C4×D5—62no—
263Dic10—61no—
264Dic10—61no—
265C5×C8—22no—
266C5×C8—121no—
267#168—41no—
268#168—62no—
269C2×#41—151no—
270C22×D4—51no—
271#131—302no—
272#131—302no—
273C2×M16—31no—
274C2×M16—51no—
275C2×M16—151no—
276C2×M16—302no—
277C2×M16D3×D511yescharacteristic
278#127—301no—
279#124—301no—
280#121—302no—
281#120—154no—
282#117—31no—
283#101—301no—
284#100—102no—
285#100—301no—
286#100—302no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291D15—42no—
292C3×D5—82no—
293C23×C3—102no—
294C23×C3—102no—
295C23×C3—102no—
296C23×C3—402no—
297C23×C3C2×C4×D511yescharacteristic
298C22×D3—52no—
299C3×D4—201no—
300C3×D4—201no—
301C3×D4—201no—
302C3×D4—201no—
303C2×C3×C4C2×D2011yescharacteristic
304C2×C3×C4#70911yescharacteristic
305C2×C3×C4D4×D511yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307C2×C3×C4D4×D511yescharacteristic
308C2×C3×C4#71311yescharacteristic
309#67—102no—
310#67—102no—
311#67—404no—
312C2×Dic3—22no—
313C2×Dic3—52no—
314D12—101no—
315D12—101no—
316C4×D3—102no—
317C4×D3—102no—
318Dic6—101no—
319Dic6—101no—
320C3×C8—22no—
321C3×C8—201no—
322C3⋊C8—41no—
323C3⋊C8—102no—
324C22×C5—41no—
325C22×C5D3×C22⋊C411yescharacteristic
326C22×C5#67⋊C411yescharacteristic
327C22×C5C4×#6711yescharacteristic
328C2×D5—44no—
329C2×D5—42no—
330C2×D5—62no—
331C2×D5—82no—
332C2×D5—82no—
333C2×D5—122no—
334C4×C5—122no—
335C4×C5#88311yescharacteristic
336C4×C5#88411yescharacteristic
337C4×C5#93711yescharacteristic
338C4×C5#93811yescharacteristic
339Dic5—62no—
340C24—52no—
341#41—301no—
342#41—301no—
343#41—301no—
344#41—301no—
345C2×Q8—151no—
346C2×D4—101no—
347C2×D4—101no—
348C2×D4—101no—
349C2×D4—101no—
350C2×D4—101no—
351C2×D4—101no—
352C2×D4—152no—
353C2×D4—151no—
354C2×D4—304no—
355C22×C4—152no—
356C22×C4C2×D3×D511yescharacteristic
357M16—21no—
358M16—61no—
359M16—61no—
360M16—101no—
361M16—101no—
362M16—152no—
363M16—304no—
364M16—301no—
365M16#120212yescomplemented
366C2×C8—21no—
367C2×C8—61no—
368C2×C8—101no—
369C2×C8—304no—
370C2×C8—301no—
371C4⋊C4—61no—
372C22⋊C4—32no—
373C22⋊C4—304no—
374C42—61no—
375C3×C5#191411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—204no—
378C22×C3—202no—
379C22×C3—402no—
380C22×C3—402no—
381C22×C3C4×D2011yescharacteristic
382C22×C3D5×C22⋊C411yescharacteristic
383C22×C3#403911yescharacteristic
384C2×D3—102no—
385C2×D3—202no—
386C3×C4#402811yescharacteristic
387C3×C4#403011yescharacteristic
388C3×C4#404011yescharacteristic
389C3×C4#404111yescharacteristic
390Dic3—42no—
391Dic3—102no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—21no—
395C2×C5#495611yescharacteristic
396D5—82no—
397D5—122no—
398C23—102no—
399C23—102no—
400C23—102no—
401C23—152no—
402C23—402no—
403C23C4×D3×D511yescharacteristic
404Q8—301no—
405Q8—301no—
406D4—201no—
407D4—201no—
408D4—201no—
409D4—201no—
410D4—302no—
411D4—302no—
412D4—301no—
413D4—301no—
414D4—1204no—
415C2×C4—62no—
416C2×C4—152no—
417C2×C4—302no—
418C2×C4—302no—
419C2×C4#676611yescharacteristic
420C2×C4#677111yescharacteristic
421C2×C4#677711yescharacteristic
422C2×C4C2×#120211yescharacteristic
423C2×C4#679011yescharacteristic
424C2×C4#679011yescharacteristic
425C8—22no—
426C8—121no—
427C8—201no—
428C8—302no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—402no—
433C2×C3#6495411yescharacteristic
434D3—202no—
435C5#7008911yescharacteristic, complemented, Sylow
436C22—41no—
437C22—204no—
438C22—202no—
439C22—302no—
440C22—402no—
441C22—402no—
442C22—602no—
443C22#9139611yescharacteristic
444C22C4×#120211yescharacteristic
445C22#9147311yescharacteristic
446C4—122no—
447C4—302no—
448C4#9135411yescharacteristic
449C4#9146111yescharacteristic
450C4#9146511yescharacteristic
451C4#9157211yescharacteristic
452C3#1059983311yescharacteristic, complemented, Sylow
453C2—21no—
454C2—21no—
455C2—21no—
456C2—402no—
457C2—602no—
458C2#1174891711yescharacteristic
subgroupG/H
centerC2#11748917
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754602C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1914
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #11756504C2semidirect
3. C2×C3×#3955C2semidirect
4. #11748357C2semidirect
5. C2×#90958C2semidirect
6. C5×#4559C2semidirect
7. #11745988C2semidirect
32. C2×#3955D3semidirect
53. C3×C5×M16D4semidirect
56. #6710D4semidirect
75. #4559D5semidirect
165. C5×M16#67semidirect
223. C3×M16D20semidirect
365. M16#1202semidirect
375. C3×C5#1914semidirect
435. C5#70089semidirect
452. C3#10599833semidirect

Maximal subgroups

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

subgroupindex
#117565042
#117546022
C2×C3×#39552
#117483572
C2×#909582
C5×#45592
#117459882
#105998333
#700895