Finite Group Databasebeta

← #14302451

Subgroups — #14302451

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5521C211yesmaximal, characteristic, complemented
2C2×#91304C211yesmaximal, characteristic
3#11751107C211yesmaximal, characteristic, complemented
4#11748428C211yesmaximal, characteristic, complemented
5#11748389C211yesmaximal, characteristic, complemented
6C3×#64753C211yesmaximal, characteristic, complemented
7#11745971C211yesmaximal, characteristic, complemented
8#10602444—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91815C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C5×#893—22no—
15C5×D3×C22⋊C4—22no—
16C4×C5×D12—22no—
17C2×C3×#681C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19C2×#6659C412yescomplemented
20#91304—22no—
21#91304—22no—
22C2×#6654C412yescomplemented
23#91090—22no—
24#90980—22no—
25#90967—22no—
26#69027—51nomaximal, Hall
27C5×#518—31no—
28C2×#4078—31no—
29#65504—31no—
30#65295—31no—
31#65294—31no—
32#64753D311yescharacteristic, complemented
33#64751—31no—
34C23×C5×D3—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×#1220—21no—
37#6817—21no—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41C2×D60C2×C411yescharacteristic, complemented
42C2×C4×D15—21no—
43C2×Dic30C2×C411yescharacteristic, complemented
44C2×C5×D12—21no—
45C2×C5×D12—21no—
46C2×C5×D12—21no—
47C2×C5×D12C2×C412yes—
48C2×C5×D12D412yes—
49C2×C5×D12D412yes—
50C2×C4×C5×D3—24no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C22⋊C4D412yes—
53C3×C42×C5—21no—
54#6719—21no—
55C4⋊Dic15—21no—
56C4×Dic15—21no—
57C5×#217—21no—
58C5×(C2×D3)⋊C4—24no—
59C5×C4⋊Dic3—21no—
60C4×C5×Dic3D412yes—
61C3×#681—21no—
62C3×#681—21no—
63C3×#681—21no—
64C3×#681—21no—
65C2×C3×#168—21no—
66C2×C3×#168C2×C412yescomplemented
67#6659—24no—
68#6654—24no—
69C2×#908—51no—
70#5521D511yescharacteristic, complemented
71#5139—51no—
72#5131—51no—
73#5006—51no—
74C3×#344—51no—
75#4557—51no—
76C22×C5×D4—31no—
77C2×#709—31no—
78C4×C5×D4—62no—
79C4×C5×D4—62no—
80C5×#117—31no—
81C5×#117C2×D311yescharacteristic
82C2×C5×C22⋊C4—62no—
83C2×#687—32no—
84#4078—62no—
85#4078—62no—
86C2×#686—32no—
87#4072—31no—
88C2×#681C2×D311yescharacteristic
89C2×#681C2×D311yescharacteristic
90#3964—62no—
91#3938—62no—
92#3937—62no—
93#1904—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C22×C5×D3—22no—
97C22×C5×D3—22no—
98C22×C5×D3—22no—
99C22×C5×D3—82no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107#1220—41no—
108#1220—41no—
109C2×Dic15—21no—
110C2×Dic15—41no—
111D60—21no—
112D60—21no—
113C4×D15—41no—
114C4×D15—41no—
115Dic30—21no—
116Dic30—21no—
117C2×C5×Dic3—22no—
118C5×D12—22no—
119C5×D12—22no—
120C5×D12—22no—
121C5×D12C22⋊C414yes—
122C4×C5×D3—84no—
123C3×#168—22no—
124C3×#168—41no—
125C2×#235—51no—
126C22×D12C2×D511yescharacteristic
127C2×C3×M16—51no—
128C2×C3×M16—51no—
129C3×#117C2×D511yescharacteristic
130#926—51no—
131#926C2×D511yescharacteristic
132#908—102no—
133#908—102no—
134C2×D24—52no—
135C2×#204—52no—
136#893—22no—
137D3×C22⋊C4—22no—
138C4×D12—22no—
139#825—102no—
140#821—102no—
141#806—102no—
142C24×C5—61no—
143C2×C5×D4—32no—
144C2×C5×D4—32no—
145C2×C5×D4—32no—
146C2×C5×D4—61no—
147C2×C5×D4—61no—
148C2×C5×D4—61no—
149C22×C4×C5—64no—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—61no—
152#709—61no—
153#709—61no—
154#709—61no—
155#709—61no—
156C2×D20—31no—
157C2×C4×D5—61no—
158C2×Dic10—31no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—61no—
161C5×C22⋊C4—64no—
162C5×C22⋊C4—61no—
163C5×C22⋊C4D1212yes—
164C42×C5—21no—
165C42×C5—32no—
166C22⋊Dic5—61no—
167#687—64no—
168#686—64no—
169C4⋊Dic5—61no—
170C4×Dic5—61no—
171#681—21no—
172#681—21no—
173#681—21no—
174#681—21no—
175C2×#168—21no—
176C2×#168C4×D312yescomplemented
177C2×AGL(1,ℤ/8)—151no—
178#518—31no—
179#421—151no—
180#418—151no—
181#410—151no—
182#344—51no—
183H(3,ℤ/4)—151no—
184C22×C3×C5—41no—
185C22×C3×C5C4×D411yescharacteristic
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#12111yescharacteristic
188C2×D15—41no—
189C2×D15—81no—
190C2×C5×D3—24no—
191C2×C5×D3—44no—
192C2×C5×D3—82no—
193C2×C5×D3—82no—
194C3×C4×C5—42no—
195C3×C4×C5C2×C22⋊C411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5#12111yescharacteristic
198C3×C4×C5#12311yescharacteristic
199Dic15—41no—
200Dic15—81no—
201C5×Dic3—42no—
202C23×D3—21no—
203C22×C3×C4C22×D511yescharacteristic
204C2×#67—101no—
205#235—101no—
206#235—101no—
207#235—101no—
208#235—101no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—51no—
213C2×D12C4×D512yes—
214C2×D12D2012yes—
215C2×D12C22⋊D512yes—
216C2×C4×D3—24no—
217C2×C4×D3—101no—
218C2×Dic6—51no—
219C3×M16—101no—
220C3×M16—101no—
221C3×M16—101no—
222C3×M16—101no—
223C2×C3×C8—52no—
224C2×C3×C8—101no—
225C3×C4⋊C4—21no—
226C3×C22⋊C4C22⋊D512yes—
227C3×C42—21no—
228#217—21no—
229#217—101no—
230(C2×D3)⋊C4—24no—
231C4⋊Dic3—21no—
232C4⋊Dic3—101no—
233C4×Dic3—101no—
234C4×Dic3C22⋊D512yes—
235D24—104no—
236#204—104no—
237C23×C5—62no—
238C23×C5—62no—
239C23×C5—62no—
240C23×C5—242no—
241C23×C5C2×D1211yescharacteristic
242C22×D5—61no—
243C5×D4—34no—
244C5×D4—62no—
245C5×D4—62no—
246C5×D4—62no—
247C2×C4×C5—22no—
248C2×C4×C5—62no—
249C2×C4×C5—244no—
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×C4×C5#23511yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5D3×D411yescharacteristic
254C2×C4×C5D3×D411yescharacteristic
255C2×C4×C5#23911yescharacteristic
256C22⋊D5—121no—
257C22⋊D5—121no—
258C2×Dic5—61no—
259C2×Dic5—121no—
260D20—61no—
261D20—61no—
262C4×D5—121no—
263C4×D5—121no—
264Dic10—61no—
265Dic10—61no—
266#168—22no—
267#168—41no—
268C2×#41—151no—
269C22×D4—31no—
270AGL(1,ℤ/8)—302no—
271AGL(1,ℤ/8)—302no—
272C2×SD16—152no—
273C2×D8—152no—
274C2×M16—51no—
275C2×M16—51no—
276C4×D4—62no—
277C4×D4—62no—
278#117—31no—
279#117—151no—
280#117D3×D511yescharacteristic
281C2×C22⋊C4—62no—
282#104—302no—
283#102—302no—
284#99—302no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5#38611yescharacteristic
289D15—81no—
290C5×D3—44no—
291C23×C3C2×C22⋊D511yescharacteristic
292C22×D3—22no—
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—82no—
296C22×D3—101no—
297C2×C3×C4—22no—
298C2×C3×C4C2×C4×D511yescharacteristic
299C2×C3×C4C2×D2011yescharacteristic
300C2×C3×C4#70911yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4C2×C22⋊D511yescharacteristic
303C2×C3×C4C2×C22⋊D511yescharacteristic
304#67—201no—
305#67—201no—
306C2×Dic3—22no—
307C2×Dic3—101no—
308C2×Dic3—201no—
309D12—22no—
310D12—22no—
311D12—22no—
312D12—101no—
313D12—101no—
314D12#68514yes—
315C4×D3—84no—
316C4×D3—201no—
317C4×D3—201no—
318Dic6—101no—
319Dic6—101no—
320C3×C8—102no—
321C3×C8—201no—
322C22×C5—41no—
323C22×C5—64no—
324C22×C5—124no—
325C22×C5—242no—
326C22×C5—242no—
327C22×C5C4×D1211yescharacteristic
328C22×C5#88211yescharacteristic
329C22×C5#89511yescharacteristic
330C2×D5—121no—
331C2×D5—241no—
332C4×C5—42no—
333C4×C5—122no—
334C4×C5D3×C22⋊C411yescharacteristic
335C4×C5#88411yescharacteristic
336C4×C5#89311yescharacteristic
337C4×C5#89411yescharacteristic
338Dic5—121no—
339Dic5—241no—
340C24—61no—
341#41—301no—
342#41—301no—
343#41—301no—
344#41—301no—
345C2×Q8—151no—
346C2×D4—32no—
347C2×D4—32no—
348C2×D4—32no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—151no—
353C2×D4—301no—
354C22×C4—64no—
355C22×C4—301no—
356C22×C4C2×D3×D511yescharacteristic
357SD16—304no—
358D8—304no—
359M16—101no—
360M16—101no—
361M16—101no—
362M16—101no—
363C2×C8—52no—
364C2×C8—101no—
365C4⋊C4—21no—
366C4⋊C4—61no—
367C4⋊C4—301no—
368C22⋊C4—64no—
369C22⋊C4—61no—
370C22⋊C4—301no—
371C22⋊C4#120312yes—
372C42—21no—
373C42—32no—
374C42—301no—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3C4×C22⋊D511yescharacteristic
378C22×C3#407611yescharacteristic
379C22×C3#409911yescharacteristic
380C2×D3—24no—
381C2×D3—44no—
382C2×D3—82no—
383C2×D3—82no—
384C2×D3—201no—
385C2×D3—401no—
386C3×C4—42no—
387C3×C4C2×#68511yescharacteristic
388C3×C4C4×C22⋊D511yescharacteristic
389C3×C4#407511yescharacteristic
390C3×C4#407611yescharacteristic
391Dic3—42no—
392Dic3—201no—
393Dic3—401no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—124no—
398C2×C5#466511yescharacteristic
399D5—241no—
400C23—62no—
401C23—62no—
402C23—62no—
403C23—242no—
404C23—301no—
405C23C2×#120311yescharacteristic
406Q8—301no—
407Q8—301no—
408D4—34no—
409D4—62no—
410D4—62no—
411D4—62no—
412D4—301no—
413D4—301no—
414D4—601no—
415D4—601no—
416C2×C4—22no—
417C2×C4—62no—
418C2×C4—244no—
419C2×C4—301no—
420C2×C4—601no—
421C2×C4—601no—
422C2×C4—601no—
423C2×C4#676911yescharacteristic
424C2×C4#677111yescharacteristic
425C2×C4C4×D3×D511yescharacteristic
426C2×C4D3×D2011yescharacteristic
427C2×C4D3×C22⋊D511yescharacteristic
428C2×C4D3×C22⋊D511yescharacteristic
429C8—102no—
430C8—201no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3#6550211yescharacteristic
435D3—44no—
436D3—401no—
437C5#6902711yescharacteristic, complemented, Sylow
438C22—41no—
439C22—64no—
440C22—124no—
441C22—242no—
442C22—242no—
443C22—601no—
444C22—1201no—
445C22C4×#120311yescharacteristic
446C22#9146011yescharacteristic
447C22#9157011yescharacteristic
448C4—42no—
449C4—122no—
450C4—601no—
451C4—1201no—
452C4#9135111yescharacteristic
453C4#9144611yescharacteristic
454C4#9145411yescharacteristic
455C4D3×#68511yescharacteristic
456C3#1060244411yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—124no—
461C2—1201no—
462C2#1174891411yescharacteristic
subgroupG/H
centerC2#11748914
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×#91304C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1904
LCSG ▷ C2×C3×C4×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
1. C5×#5521C2semidirect
3. #11751107C2semidirect
4. #11748428C2semidirect
5. #11748389C2semidirect
6. C3×#64753C2semidirect
7. #11745971C2semidirect
19. C2×#6659C4semidirect
22. C2×#6654C4semidirect
32. #64753D3semidirect
41. C2×D60C2×C4semidirect
43. C2×Dic30C2×C4semidirect
66. C2×C3×#168C2×C4semidirect
70. #5521D5semidirect
176. C2×#168C4×D3semidirect
375. C3×C5#1904semidirect
437. C5#69027semidirect
456. C3#10602444semidirect

Maximal subgroups

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

subgroupindex
C5×#55212
C2×#913042
#117511072
#117484282
#117483892
C3×#647532
#117459712
#106024443
#690275