Finite Group Databasebeta

← #14417530

Subgroups — #14417530

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×Q16×D15C211yesmaximal, characteristic
2#11756331C212yesmaximal
3C3×C4×C5×Q16C211yesmaximal, characteristic, complemented
4Q16×Dic15C211yesmaximal, characteristic, complemented
5#11751131C212yesmaximal, complemented
6#11750981C211yesmaximal, characteristic
7#11750974C211yesmaximal, characteristic, complemented
8#11750903C212yesmaximal
9#11750890C212yesmaximal, complemented
10C4×Dic60C211yesmaximal, characteristic, complemented
11#11750790C211yesmaximal, characteristic
12#10611451—31nomaximal, Hall
13C2×Q8×D15C2212yes—
14C2×C3×C5×Q16C2211yescharacteristic
15C3×C4×C5×Q8C2212yes—
16Q8×Dic15C2212yes—
17C2×#6718C2212yes—
18Q16×D15C418yescomplemented
19C2×Dic60C2211yescharacteristic
20C2×#6705C2211yescharacteristic
21C2×C8×D15C2211yescharacteristic
22#91781—22no—
23#91781C2212yes—
24#91776—22no—
25#91776C2212yes—
26#91761—22no—
27#91761C2211yescharacteristic
28C4×Dic30—22no—
29C4×Dic30C2212yes—
30C3×C5×#107C2211yescharacteristic
31C3×C5×#103C2212yes—
32C3×C4×C5×C8C2211yescharacteristic
33#91119C2212yes—
34#91102C2211yescharacteristic
35#91100C2212yes—
36#91099C2211yescharacteristic
37C8×Dic15C2211yescharacteristic
38#91094C2212yes—
39#91092C2212yes—
40#91087C2211yescharacteristic
41#79720—51nomaximal, Hall
42C2×D5×Q16—31no—
43#65906—32no—
44C4×C5×Q16D311yescharacteristic, complemented
45Q16×Dic5—31no—
46#65319—32no—
47#65169—31no—
48#65162—31no—
49#65091—32no—
50#65078—32no—
51C4×Dic20—31no—
52#64978—31no—
53C2×C3×C5×Q8C2312yes—
54Q8×D15—24no—
55Q8×D15C2×C418yes—
56C2×C4×D15—22no—
57C2×C4×D15C2311yescharacteristic
58C2×Dic30—22no—
59C2×Dic30C2312yes—
60C3×C5×Q16C2×C414yes—
61C2×C3×C5×C8C2311yescharacteristic
62C2×C3×C5×C8C2311yescharacteristic
63C3×C5×C4⋊C4—22no—
64C3×C5×C4⋊C4C2312yes—
65C3×C42×C5—22no—
66C3×C42×C5C2311yescharacteristic
67#6718C2×C418yes—
68#6714—22no—
69#6714D411yescharacteristic
70#6714D411yescharacteristic
71C4⋊Dic15—22no—
72C4⋊Dic15C2312yes—
73#6712—22no—
74#6712—22no—
75#6712D411yescharacteristic
76#6712D411yescharacteristic
77C4×Dic15—22no—
78C4×Dic15—22no—
79C4×Dic15—22no—
80C4×Dic15—22no—
81C4×Dic15C2311yescharacteristic
82C2×C3⋊#168C2311yescharacteristic
83C2×C3⋊#168C2311yescharacteristic
84Dic60C2×C414yes—
85#6705—22no—
86C8×D15C2×C414yes—
87C2×D3×Q16—51no—
88#5572—52no—
89C3×C4×Q16D511yescharacteristic, complemented
90Dic3×Q16—51no—
91#5030—52no—
92#4880—51no—
93#4873—51no—
94#4802—52no—
95#4789—52no—
96C4×Dic12—51no—
97#4689—51no—
98C2×Q8×D5—32no—
99C2×C5×Q16C2×D311yescharacteristic
100C4×C5×Q8C2×D312yes—
101Q8×Dic5—32no—
102C2×#689—32no—
103D5×Q16—38no—
104C2×Dic20—31no—
105C2×#676—31no—
106C2×C8×D5—31no—
107#4038—32no—
108#4038—62no—
109#4033—32no—
110#4033—62no—
111#4018—31no—
112#4018—62no—
113C4×Dic10—32no—
114C4×Dic10—62no—
115C5×#107C2×D311yescharacteristic
116C5×#103C2×D312yes—
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3950—31no—
120#3948—32no—
121#3947—31no—
122C8×Dic5—31no—
123#3942—32no—
124#3940—32no—
125#3935—31no—
126#2950—151noSylow
127C22×D15C2×D411yescharacteristic
128C3×C5×Q8—22no—
129C3×C5×Q8C22×C414yes—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15C2×D411yescharacteristic
138C2×Dic15C2×D411yescharacteristic
139C2×Dic15C2×D411yescharacteristic
140C4×D15—28no—
141C4×D15C22×C412yes—
142C4×D15#4112yes—
143Dic30—22no—
144Dic30—28no—
145Dic30C22×C414yes—
146C3×C5×C8—21no—
147C3×C5×C8C22×C412yes—
148C3⋊#168—21no—
149C3⋊#168C22×C412yes—
150C2×D3×Q8—52no—
151C2×C3×Q16C2×D511yescharacteristic
152C3×C4×Q8C2×D512yes—
153Q8×Dic3—52no—
154C2×#216—52no—
155D3×Q16—58no—
156C2×Dic12—51no—
157C2×ΓL(1,𝔽25)—51no—
158C2×D3×C8—51no—
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×#107C2×D511yescharacteristic
168C3×#103C2×D512yes—
169C3×C4×C8C2×D511yescharacteristic
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×Q8C22×D312yes—
179Q8×D5—38no—
180Q8×D5—64no—
181C2×C4×D5—31no—
182C2×C4×D5—62no—
183C2×Dic10—32no—
184C2×Dic10—62no—
185C5×Q16C4×D314yes—
186C2×C5×C8C22×D311yescharacteristic
187C2×C5×C8C22×D311yescharacteristic
188C5×C4⋊C4—22no—
189C5×C4⋊C4C22×D312yes—
190C42×C5—22no—
191C42×C5C22×D311yescharacteristic
192#689—38no—
193#685—31no—
194#685—31no—
195#685—62no—
196C4⋊Dic5—32no—
197C4⋊Dic5—62no—
198#683—31no—
199#683—31no—
200#683—62no—
201#683—62no—
202C4×Dic5—31no—
203C4×Dic5—62no—
204C4×Dic5—62no—
205C4×Dic5—62no—
206C4×Dic5—62no—
207C2×#168—31no—
208C2×#168—31no—
209Dic20—34no—
210#676—62no—
211C8×D5—34no—
212C22×Q16—151no—
213#519—152no—
214#441—152no—
215#441—152no—
216C4×Q16—151no—
217C4×Q16—151no—
218C4×Q16—151no—
219C4×Q16D1511yescharacteristic, complemented
220#427—151no—
221#419—152no—
222#405—151no—
223C22×C3×C5C22×D411yescharacteristic
224C2×D15—21no—
225C2×D15—21no—
226C2×D15C4×D412yes—
227C3×C4×C5—24no—
228C3×C4×C5—21no—
229C3×C4×C5—21no—
230C3×C4×C5—42no—
231C3×C4×C5C23×C411yescharacteristic
232C3×C4×C5C2×#4111yescharacteristic
233Dic15—24no—
234Dic15—21no—
235Dic15—21no—
236Dic15—42no—
237Dic15C4×D412yes—
238C2×C3×Q8C22×D512yes—
239D3×Q8—58no—
240D3×Q8—104no—
241C2×C4×D3—51no—
242C2×C4×D3—102no—
243C2×Dic6—52no—
244C2×Dic6—102no—
245C3×Q16C4×D514yes—
246C2×C3×C8C22×D511yescharacteristic
247C2×C3×C8C22×D511yescharacteristic
248C3×C4⋊C4—22no—
249C3×C4⋊C4C22×D512yes—
250C3×C42—22no—
251C3×C42C22×D511yescharacteristic
252#216—58no—
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⋊C8—51no—
269Dic12—54no—
270ΓL(1,𝔽25)—102no—
271D3×C8—54no—
272C22×D5—31no—
273C5×Q8—22no—
274C5×Q8C2×C4×D314yes—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5C23×D311yescharacteristic
280C2×Dic5—31no—
281C2×Dic5—31no—
282C2×Dic5—31no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285C4×D5—32no—
286C4×D5—32no—
287C4×D5—68no—
288Dic10—34no—
289Dic10—68no—
290Dic10—62no—
291C5×C8—21no—
292C5×C8C2×C4×D312yes—
293#168—32no—
294#168—61no—
295C22×Q8—152no—
296C2×Q16—152no—
297C2×Q16—158no—
298C2×Q16—151no—
299C2×Q16C2×D1511yescharacteristic
300C2×M16—151no—
301C22×C8—151no—
302C4×Q8—152no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—302no—
306C4×Q8—302no—
307C4×Q8C2×D1512yes—
308#117—151no—
309#117—152no—
310#117—302no—
311#117—302no—
312#107—151no—
313#107C2×D1511yescharacteristic
314#106—152no—
315#103—152no—
316#103—152no—
317#103—152no—
318#103C2×D1512yes—
319#97—151no—
320#97—151no—
321C4×C8—151no—
322C4×C8C2×D1511yescharacteristic
323C2×C3×C5C2×C4×D411yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C2×C3×C5#57811yescharacteristic
326D15—22no—
327C22×D3—51no—
328C3×Q8—22no—
329C3×Q8C2×C4×D514yes—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4C23×D511yescharacteristic
335C2×Dic3—51no—
336C2×Dic3—51no—
337C2×Dic3—51no—
338C2×Dic3—102no—
339C2×Dic3—102no—
340C4×D3—52no—
341C4×D3—52no—
342C4×D3—108no—
343Dic6—54no—
344Dic6—108no—
345Dic6—102no—
346C3×C8—21no—
347C3×C8C2×C4×D512yes—
348C3⋊C8—52no—
349C3⋊C8—101no—
350C22×C5C2×D3×D411yescharacteristic
351C2×D5—32no—
352C2×D5—61no—
353C2×D5—61no—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5—24no—
357C4×C5—42no—
358C4×C5C22×C4×D311yescharacteristic
359C4×C5D3×#4111yescharacteristic
360Dic5—32no—
361Dic5—61no—
362Dic5—61no—
363Dic5—64no—
364Dic5—122no—
365C2×Q8—158no—
366C2×Q8—152no—
367C2×Q8—302no—
368C2×Q8—304no—
369C2×Q8C22×D1512yes—
370C22×C4—151no—
371C22×C4—302no—
372Q16—158no—
373Q16—154no—
374Q16C4×D1514yes—
375M16—302no—
376C2×C8—151no—
377C2×C8—154no—
378C2×C8—151no—
379C2×C8C22×D1511yescharacteristic
380C2×C8C22×D1511yescharacteristic
381C4⋊C4—22no—
382C4⋊C4—151no—
383C4⋊C4—151no—
384C4⋊C4—152no—
385C4⋊C4—302no—
386C4⋊C4—302no—
387C4⋊C4—302no—
388C4⋊C4C22×D1512yes—
389C22⋊C4—151no—
390C22⋊C4—151no—
391C22⋊C4—302no—
392C42—22no—
393C42—151no—
394C42—302no—
395C42—302no—
396C42—302no—
397C42—302no—
398C42C22×D1511yescharacteristic
399C3×C5#295011yescharacteristic, complemented, Hall
400C22×C3C2×D4×D511yescharacteristic
401C2×D3—52no—
402C2×D3—101no—
403C2×D3—101no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—24no—
407C3×C4—42no—
408C3×C4C22×C4×D511yescharacteristic
409C3×C4D5×#4111yescharacteristic
410Dic3—52no—
411Dic3—101no—
412Dic3—101no—
413Dic3—104no—
414Dic3—202no—
415C2×C5C4×D3×D411yescharacteristic
416C2×C5#576611yescharacteristic
417C2×C5#577111yescharacteristic
418D5—62no—
419C23—151no—
420Q8—22no—
421Q8—154no—
422Q8—308no—
423Q8—302no—
424Q8C2×C4×D1514yes—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—151no—
428C2×C4—152no—
429C2×C4—152no—
430C2×C4—151no—
431C2×C4—151no—
432C2×C4—308no—
433C2×C4—302no—
434C2×C4—302no—
435C2×C4D4×D1511yescharacteristic
436C2×C4D4×D1511yescharacteristic
437C2×C4C23×D1511yescharacteristic
438C8—21no—
439C8—152no—
440C8—301no—
441C8C2×C4×D1512yes—
442C2×C3C4×D4×D511yescharacteristic
443C2×C3#6610011yescharacteristic
444C2×C3#6610511yescharacteristic
445D3—102no—
446C5#7972011yescharacteristic, complemented, Sylow
447C22—152no—
448C22—301no—
449C22—301no—
450C22C2×D4×D1511yescharacteristic
451C4—24no—
452C4—21no—
453C4—21no—
454C4—42no—
455C4—152no—
456C4—304no—
457C4—301no—
458C4—301no—
459C4—602no—
460C4C22×C4×D1511yescharacteristic
461C4#41×D1511yescharacteristic
462C3#1061145111yescharacteristic, complemented, Sylow
463C2—302no—
464C2C4×D4×D1511yescharacteristic
465C2#1175652511yescharacteristic
466C2#1175653011yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C4×C5×Q16C2
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
cosocleC2×C3×C4×C5C24
hypercenterC4×Q16D15
hypocenterC3×C5#2950
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C3×C4×C5×Q16C2semidirect
4. Q16×Dic15C2semidirect
5. #11751131C2semidirect
7. #11750974C2semidirect
9. #11750890C2semidirect
10. C4×Dic60C2semidirect
18. Q16×D15C4semidirect
44. C4×C5×Q16D3semidirect
89. C3×C4×Q16D5semidirect
219. C4×Q16D15semidirect
399. C3×C5#2950semidirect
446. C5#79720semidirect
462. C3#10611451semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D152
#117563312
C3×C4×C5×Q162
Q16×Dic152
#117511312
#117509812
#117509742
#117509032
#117508902
C4×Dic602
#117507902
#106114513
#797205