Finite Group Databasebeta

← #14417559

Subgroups — #14417559

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×Q16C211yesmaximal, characteristic
2#11755144C212yesmaximal
3Q16×Dic15C211yesmaximal, characteristic, complemented
4C3×Q16×Dic5C211yesmaximal, characteristic, complemented
5#11749266C212yesmaximal, complemented
6#11749247C212yesmaximal, complemented
7#11749213C212yesmaximal
8#11747886C211yesmaximal, characteristic, complemented
9Dic5×Dic12C211yesmaximal, characteristic, complemented
10#11747682C211yesmaximal, characteristic
11#11747653C211yesmaximal, characteristic
12#10615605—31nomaximal, Hall
13C2×C5×D3×Q8C2212yes—
14C2×C3×C5×Q16C2211yescharacteristic
15Q8×Dic15C2212yes—
16C2×C5×#216C2212yes—
17C5×D3×Q16C418yescomplemented
18C2×C5×Dic12C2211yescharacteristic
19C2×C5×D3×C8C2211yescharacteristic
20C3×Q8×Dic5C2212yes—
21#91371—22no—
22#91371C2211yescharacteristic
23#91344—22no—
24#91344C2212yes—
25#91338—22no—
26#91338C2212yes—
27Dic5×Dic6—22no—
28Dic5×Dic6C2212yes—
29C2×#6650C2211yescharacteristic
30#91119C2212yes—
31#91102C2211yescharacteristic
32C8×Dic15C2211yescharacteristic
33C3×#3967C2212yes—
34C3×#3950C2211yescharacteristic
35C3×C8×Dic5C2211yescharacteristic
36#90987C2212yes—
37#90973C2212yes—
38#90972C2212yes—
39#90954C2211yescharacteristic
40#90952C2211yescharacteristic
41#79720—51nomaximal, Hall
42C22×C5×Q16—31no—
43#66146—32no—
44#65514—32no—
45#65473—32no—
46#65473—32no—
47Q16×Dic5—31no—
48Q16×Dic5—31no—
49Q16×Dic5—31no—
50Q16×Dic5D311yescharacteristic, complemented
51#65395—31no—
52#65390—31no—
53C2×C3×C5×Q8C2312yes—
54C5×D3×Q8—24no—
55C5×D3×Q8C2×C418yes—
56C2×C4×C5×D3—22no—
57C2×C4×C5×D3C2311yescharacteristic
58C2×C5×Dic6—22no—
59C2×C5×Dic6C2312yes—
60C3×C5×Q16C2×C414yes—
61C2×C3×C5×C8C2311yescharacteristic
62C4⋊Dic15—22no—
63C4⋊Dic15C2312yes—
64C4×Dic15—22no—
65C4×Dic15C2311yescharacteristic
66C2×C3⋊#168C2311yescharacteristic
67C5×#216C2×C418yes—
68C2×C5×C3⋊C8C2311yescharacteristic
69C5×Dic12C2×C414yes—
70C5×D3×C8C2×C414yes—
71C3×C4⋊Dic5—22no—
72C3×C4⋊Dic5C2312yes—
73C3×C4×Dic5—22no—
74C3×C4×Dic5C2311yescharacteristic
75C2×C3×#168C2311yescharacteristic
76Dic3⋊Dic5—22no—
77Dic3⋊Dic5—22no—
78Dic3⋊Dic5D411yescharacteristic
79Dic3⋊Dic5D411yescharacteristic
80(C2×D3)⋊Dic5—22no—
81(C2×D3)⋊Dic5D411yescharacteristic
82(C2×D3)⋊Dic5D411yescharacteristic
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85Dic3×Dic5—22no—
86#6650—22no—
87C2×D3×Q16D511yescharacteristic
88#5572—52no—
89C3×C4×Q16—51no—
90Dic3×Q16—51no—
91#5030—52no—
92#4880—51no—
93#4873—51no—
94#4802—52no—
95#4789—52no—
96C4×Dic12—51no—
97#4689—51no—
98C22×C5×Q8—32no—
99C2×C5×Q16—32no—
100C2×C5×Q16—38no—
101C2×C5×Q16—31no—
102C2×C5×Q16C2×D311yescharacteristic
103C22×C5×C8—31no—
104Q8×Dic5—32no—
105Q8×Dic5—32no—
106Q8×Dic5—32no—
107Q8×Dic5—62no—
108Q8×Dic5—62no—
109Q8×Dic5C2×D312yes—
110#4072—31no—
111#4072—32no—
112#4072—62no—
113#4072—62no—
114C2×#681—31no—
115#3967—32no—
116#3967—32no—
117#3967—32no—
118#3967C2×D312yes—
119#3950—31no—
120#3950C2×D311yescharacteristic
121#3949—32no—
122#3947—31no—
123#3947—31no—
124C8×Dic5—31no—
125C8×Dic5C2×D311yescharacteristic
126#2950—151noSylow
127C22×C5×D3C2×D411yescharacteristic
128C3×C5×Q8—22no—
129C3×C5×Q8C22×C414yes—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133C2×Dic15C2×D411yescharacteristic
134C2×Dic15C2×D411yescharacteristic
135C2×C5×Dic3—22no—
136C2×C5×Dic3C2×D411yescharacteristic
137C4×C5×D3—28no—
138C4×C5×D3C22×C412yes—
139C4×C5×D3#4112yes—
140C5×Dic6—22no—
141C5×Dic6—28no—
142C5×Dic6C22×C414yes—
143C2×C3×Dic5—22no—
144C2×C3×Dic5C2×D411yescharacteristic
145C2×C3×Dic5C2×D411yescharacteristic
146C3×C5×C8C22×C412yes—
147C3⋊#168—21no—
148C3×#168—21no—
149C5×C3⋊C8C22×C412yes—
150C2×D3×Q8C2×D512yes—
151C2×C3×Q16C2×D511yescharacteristic
152C3×C4×Q8—52no—
153Q8×Dic3—52no—
154C2×#216C2×D512yes—
155D3×Q16Dic518yescomplemented
156C2×Dic12C2×D511yescharacteristic
157C2×ΓL(1,𝔽25)—51no—
158C2×D3×C8C2×D511yescharacteristic
159#892—52no—
160#892—102no—
161#887—52no—
162#887—102no—
163#872—51no—
164#872—102no—
165C4×Dic6—52no—
166C4×Dic6—102no—
167C3×#107—51no—
168C3×#103—52no—
169C3×C4×C8—51no—
170#835—52no—
171#818—51no—
172#816—52no—
173#815—51no—
174C8×Dic3—51no—
175#810—52no—
176#808—52no—
177#803—51no—
178C2×C5×Q8—38no—
179C2×C5×Q8—32no—
180C2×C5×Q8—62no—
181C2×C5×Q8—64no—
182C2×C5×Q8C22×D312yes—
183C22×C4×C5—31no—
184C22×C4×C5—62no—
185C5×Q16—38no—
186C5×Q16—34no—
187C5×Q16C4×D314yes—
188C2×C5×C8—31no—
189C2×C5×C8—34no—
190C2×C5×C8C22×D311yescharacteristic
191C22⋊Dic5—31no—
192C22⋊Dic5—31no—
193C22⋊Dic5—62no—
194C4⋊Dic5—22no—
195C4⋊Dic5—31no—
196C4⋊Dic5—31no—
197C4⋊Dic5—32no—
198C4⋊Dic5—62no—
199C4⋊Dic5—62no—
200C4⋊Dic5—62no—
201C4⋊Dic5C22×D312yes—
202C4×Dic5—22no—
203C4×Dic5—31no—
204C4×Dic5—62no—
205C4×Dic5—62no—
206C4×Dic5—62no—
207C4×Dic5—62no—
208C4×Dic5C22×D311yescharacteristic
209#681—62no—
210C2×#168—31no—
211C2×#168C22×D311yescharacteristic
212C22×Q16—31no—
213#519—152no—
214#441—152no—
215#441—152no—
216C4×Q16—51no—
217C4×Q16—151no—
218C4×Q16—151no—
219C4×Q16—151no—
220#427—151no—
221#419—152no—
222#405—151no—
223C22×C3×C5C22×D411yescharacteristic
224C2×C5×D3—21no—
225C2×C5×D3—21no—
226C2×C5×D3C4×D412yes—
227C3×C4×C5—24no—
228C3×C4×C5C23×C411yescharacteristic
229C3×C4×C5C2×#4111yescharacteristic
230Dic15—21no—
231Dic15—21no—
232Dic15—42no—
233C3×Dic5—21no—
234C3×Dic5—21no—
235C3×Dic5—42no—
236C5×Dic3—24no—
237C5×Dic3C4×D412yes—
238C2×C3×Q8C22×D512yes—
239D3×Q8—24no—
240D3×Q8C2×Dic518yes—
241C2×C4×D3—22no—
242C2×C4×D3C22×D511yescharacteristic
243C2×Dic6—22no—
244C2×Dic6C22×D512yes—
245C3×Q16C2×Dic514yes—
246C2×C3×C8—51no—
247C2×C3×C8C22×D511yescharacteristic
248C3×C4⋊C4—52no—
249C3×C4⋊C4—102no—
250C3×C42—51no—
251C3×C42—102no—
252#216C2×Dic518yes—
253(C2×D3)⋊C4—51no—
254(C2×D3)⋊C4—51no—
255(C2×D3)⋊C4—102no—
256C4⋊Dic3—52no—
257C4⋊Dic3—102no—
258Dic3⋊C4—51no—
259Dic3⋊C4—51no—
260Dic3⋊C4—102no—
261Dic3⋊C4—102no—
262C4×Dic3—51no—
263C4×Dic3—102no—
264C4×Dic3—102no—
265C4×Dic3—102no—
266C4×Dic3—102no—
267C2×C3⋊C8—51no—
268C2×C3⋊C8C22×D511yescharacteristic
269Dic12C2×Dic514yes—
270ΓL(1,𝔽25)—102no—
271D3×C8C2×Dic514yes—
272C23×C5—31no—
273C5×Q8—22no—
274C5×Q8—34no—
275C5×Q8—68no—
276C5×Q8—62no—
277C5×Q8C2×C4×D314yes—
278C2×C4×C5—22no—
279C2×C4×C5—31no—
280C2×C4×C5—32no—
281C2×C4×C5—32no—
282C2×C4×C5—68no—
283C2×C4×C5—62no—
284C2×C4×C5C23×D311yescharacteristic
285C2×Dic5—22no—
286C2×Dic5—31no—
287C2×Dic5—31no—
288C2×Dic5—62no—
289C2×Dic5D3×D411yescharacteristic
290C2×Dic5D3×D411yescharacteristic
291C5×C8—32no—
292C5×C8C2×C4×D312yes—
293#168—21no—
294#168—61no—
295C22×Q8—32no—
296C2×Q16—32no—
297C2×Q16—38no—
298C2×Q16—31no—
299C2×Q16D3×D511yescharacteristic
300C2×M16—151no—
301C22×C8—31no—
302C4×Q8—52no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—152no—
306C4×Q8—302no—
307C4×Q8—302no—
308#117—151no—
309#117—152no—
310#117—302no—
311#117—302no—
312#107—51no—
313#107—151no—
314#106—152no—
315#103—52no—
316#103—152no—
317#103—152no—
318#103—152no—
319#97—151no—
320#97—151no—
321C4×C8—51no—
322C4×C8—151no—
323C2×C3×C5C2×C4×D411yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C2×C3×C5#57811yescharacteristic
326C5×D3—22no—
327C22×D3D4×D511yescharacteristic
328C3×Q8—22no—
329C3×Q8C22×Dic514yes—
330C2×C3×C4—22no—
331C2×C3×C4—51no—
332C2×C3×C4—51no—
333C2×C3×C4—102no—
334C2×C3×C4C23×D511yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—51no—
337C2×Dic3—51no—
338C2×Dic3—102no—
339C2×Dic3D4×D511yescharacteristic
340C4×D3—28no—
341C4×D3#71112yes—
342C4×D3C22×Dic512yes—
343Dic6—22no—
344Dic6—28no—
345Dic6C22×Dic514yes—
346C3×C8—101no—
347C3×C8C22×Dic512yes—
348C3⋊C8—101no—
349C3⋊C8C22×Dic512yes—
350C22×C5—32no—
351C22×C5—61no—
352C22×C5—61no—
353C22×C5C2×D3×D411yescharacteristic
354C4×C5—24no—
355C4×C5—32no—
356C4×C5—64no—
357C4×C5C22×C4×D311yescharacteristic
358C4×C5D3×#4111yescharacteristic
359Dic5—21no—
360Dic5—21no—
361Dic5—42no—
362Dic5—61no—
363Dic5—61no—
364Dic5—122no—
365C2×Q8—38no—
366C2×Q8—32no—
367C2×Q8—62no—
368C2×Q8—64no—
369C2×Q8C2×D3×D512yes—
370C22×C4—31no—
371C22×C4—62no—
372Q16—38no—
373Q16—34no—
374Q16D3×Dic514yes—
375M16—302no—
376C2×C8—31no—
377C2×C8—34no—
378C2×C8—51no—
379C2×C8—151no—
380C2×C8C2×D3×D511yescharacteristic
381C4⋊C4—52no—
382C4⋊C4—102no—
383C4⋊C4—151no—
384C4⋊C4—151no—
385C4⋊C4—152no—
386C4⋊C4—302no—
387C4⋊C4—302no—
388C4⋊C4—302no—
389C22⋊C4—151no—
390C22⋊C4—151no—
391C22⋊C4—302no—
392C42—51no—
393C42—102no—
394C42—151no—
395C42—302no—
396C42—302no—
397C42—302no—
398C42—302no—
399C3×C5#295011yescharacteristic, complemented, Hall
400C22×C3C2×D4×D511yescharacteristic
401C2×D3—21no—
402C2×D3—21no—
403C2×D3D4×Dic512yes—
404C3×C4—24no—
405C3×C4—101no—
406C3×C4—101no—
407C3×C4—202no—
408C3×C4C2×#71111yescharacteristic
409C3×C4C23×Dic511yescharacteristic
410Dic3—24no—
411Dic3—101no—
412Dic3—101no—
413Dic3—202no—
414Dic3D4×Dic512yes—
415C2×C5—62no—
416C2×C5C4×D3×D411yescharacteristic
417C2×C5#576611yescharacteristic
418C2×C5#577111yescharacteristic
419C23—31no—
420Q8—22no—
421Q8—34no—
422Q8—68no—
423Q8—62no—
424Q8C2×D3×Dic514yes—
425C2×C4—22no—
426C2×C4—31no—
427C2×C4—32no—
428C2×C4—32no—
429C2×C4—51no—
430C2×C4—51no—
431C2×C4—68no—
432C2×C4—62no—
433C2×C4—102no—
434C2×C4—151no—
435C2×C4—151no—
436C2×C4—302no—
437C2×C4C22×D3×D511yescharacteristic
438C8—32no—
439C8—101no—
440C8—301no—
441C8C2×D3×Dic512yes—
442C2×C3#6610011yescharacteristic
443C2×C3#6610011yescharacteristic
444C2×C3C2×D4×Dic511yescharacteristic
445D3—22no—
446C5#7972011yescharacteristic, complemented, Sylow
447C22—32no—
448C22—61no—
449C22—61no—
450C22D3×D4×D511yescharacteristic
451C4—24no—
452C4—32no—
453C4—64no—
454C4—101no—
455C4—101no—
456C4—202no—
457C4—301no—
458C4—301no—
459C4—602no—
460C4D3×#71111yescharacteristic
461C4C22×D3×Dic511yescharacteristic
462C3#1061560511yescharacteristic, complemented, Sylow
463C2—62no—
464C2#1175410611yescharacteristic
465C2#1175411311yescharacteristic
466C2D3×D4×Dic511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
cosocleC2×C3×C4×C5C24
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2950
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. Q16×Dic15C2semidirect
4. C3×Q16×Dic5C2semidirect
5. #11749266C2semidirect
6. #11749247C2semidirect
8. #11747886C2semidirect
9. Dic5×Dic12C2semidirect
17. C5×D3×Q16C4semidirect
50. Q16×Dic5D3semidirect
155. D3×Q16Dic5semidirect
399. C3×C5#2950semidirect
446. C5#79720semidirect
462. C3#10615605semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×Q162
#117551442
Q16×Dic152
C3×Q16×Dic52
#117492662
#117492472
#117492132
#117478862
Dic5×Dic122
#117476822
#117476532
#106156053
#797205