Finite Group Databasebeta

← #14417557

Subgroups — #14417557

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×C3×D5×Q16C211yesmaximal, characteristic
2#11755140C212yesmaximal
3Q16×Dic15C211yesmaximal, characteristic, complemented
4C5×Dic3×Q16C211yesmaximal, characteristic, complemented
5#11749264C212yesmaximal, complemented
6#11749256C212yesmaximal, complemented
7#11749208C212yesmaximal
8#11747883C211yesmaximal, characteristic, complemented
9Dic3×Dic20C211yesmaximal, characteristic, complemented
10#11747672C211yesmaximal, characteristic
11#11747645C211yesmaximal, characteristic
12#10611451—31nomaximal, Hall
13C2×C3×Q8×D5C2212yes—
14C2×C3×C5×Q16C2211yescharacteristic
15Q8×Dic15C2212yes—
16C5×Q8×Dic3C2212yes—
17C2×C3×#689C2212yes—
18C3×D5×Q16C418yescomplemented
19C2×C3×Dic20C2211yescharacteristic
20C2×C3×C8×D5C2211yescharacteristic
21#91358—22no—
22#91358C2212yes—
23#91357—22no—
24#91357C2211yescharacteristic
25#91331—22no—
26#91331C2212yes—
27Dic3×Dic10—22no—
28Dic3×Dic10C2212yes—
29C2×#6649C2211yescharacteristic
30#91119C2212yes—
31#91102C2211yescharacteristic
32C8×Dic15C2211yescharacteristic
33C5×#835C2212yes—
34C5×#818C2211yescharacteristic
35C5×C8×Dic3C2211yescharacteristic
36#90985C2212yes—
37#90971C2212yes—
38#90970C2212yes—
39#90954C2211yescharacteristic
40#90953C2211yescharacteristic
41#83874—51nomaximal, Hall
42C2×D5×Q16D311yescharacteristic
43#65906—32no—
44C4×C5×Q16—31no—
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—
54C3×Q8×D5—24no—
55C3×Q8×D5C2×C418yes—
56C2×C3×C4×D5—22no—
57C2×C3×C4×D5C2311yescharacteristic
58C2×C3×Dic10—22no—
59C2×C3×Dic10C2312yes—
60C3×C5×Q16C2×C414yes—
61C2×C3×C5×C8C2311yescharacteristic
62C4⋊Dic15—22no—
63C4⋊Dic15C2312yes—
64C4×Dic15—22no—
65C4×Dic15C2311yescharacteristic
66C2×C3⋊#168C2311yescharacteristic
67C5×C4⋊Dic3—22no—
68C5×C4⋊Dic3C2312yes—
69C4×C5×Dic3—22no—
70C4×C5×Dic3C2311yescharacteristic
71C2×C5×C3⋊C8C2311yescharacteristic
72C3×#689C2×C418yes—
73C2×C3×#168C2311yescharacteristic
74C3×Dic20C2×C414yes—
75C3×C8×D5C2×C414yes—
76#6668—22no—
77#6668—22no—
78#6668D411yescharacteristic
79#6668D411yescharacteristic
80#6665—22no—
81#6665D411yescharacteristic
82#6665D411yescharacteristic
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85Dic3×Dic5—22no—
86#6649—22no—
87C22×C3×Q16—51no—
88#5812—52no—
89#5225—52no—
90#5184—52no—
91#5184—52no—
92Dic3×Q16—51no—
93Dic3×Q16—51no—
94Dic3×Q16—51no—
95Dic3×Q16D511yescharacteristic, complemented
96#5106—51no—
97#5101—51no—
98C2×Q8×D5C2×D312yes—
99C2×C5×Q16C2×D311yescharacteristic
100C4×C5×Q8—32no—
101Q8×Dic5—32no—
102C2×#689C2×D312yes—
103D5×Q16Dic318yescomplemented
104C2×Dic20C2×D311yescharacteristic
105C2×#676—31no—
106C2×C8×D5C2×D311yescharacteristic
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×#107—31no—
116C5×#103—32no—
117C4×C5×C8—31no—
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×C3×D5C2×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
137C2×C5×Dic3C2×D411yescharacteristic
138C2×C3×Dic5—22no—
139C2×C3×Dic5C2×D411yescharacteristic
140C3×C4×D5—28no—
141C3×C4×D5C22×C412yes—
142C3×C4×D5#4112yes—
143C3×Dic10—22no—
144C3×Dic10—28no—
145C3×Dic10C22×C414yes—
146C3×C5×C8C22×C412yes—
147C3⋊#168—21no—
148C3×#168C22×C412yes—
149C5×C3⋊C8—21no—
150C22×C3×Q8—52no—
151C2×C3×Q16—52no—
152C2×C3×Q16—58no—
153C2×C3×Q16—51no—
154C2×C3×Q16C2×D511yescharacteristic
155C22×C3×C8—51no—
156Q8×Dic3—52no—
157Q8×Dic3—52no—
158Q8×Dic3—52no—
159Q8×Dic3—102no—
160Q8×Dic3—102no—
161Q8×Dic3C2×D512yes—
162#926—51no—
163#926—52no—
164#926—102no—
165#926—102no—
166C2×#208—51no—
167#835—52no—
168#835—52no—
169#835—52no—
170#835C2×D512yes—
171#818—51no—
172#818C2×D511yescharacteristic
173#817—52no—
174#815—51no—
175#815—51no—
176C8×Dic3—51no—
177C8×Dic3C2×D511yescharacteristic
178C2×C5×Q8C22×D312yes—
179Q8×D5—24no—
180Q8×D5C2×Dic318yes—
181C2×C4×D5—22no—
182C2×C4×D5C22×D311yescharacteristic
183C2×Dic10—22no—
184C2×Dic10C22×D312yes—
185C5×Q16C2×Dic314yes—
186C2×C5×C8—31no—
187C2×C5×C8C22×D311yescharacteristic
188C5×C4⋊C4—32no—
189C5×C4⋊C4—62no—
190C42×C5—31no—
191C42×C5—62no—
192#689C2×Dic318yes—
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×#168C22×D311yescharacteristic
209Dic20C2×Dic314yes—
210#676—62no—
211C8×D5C2×Dic314yes—
212C22×Q16—51no—
213#519—152no—
214#441—152no—
215#441—152no—
216C4×Q16—31no—
217C4×Q16—151no—
218C4×Q16—151no—
219C4×Q16—151no—
220#427—151no—
221#419—152no—
222#405—151no—
223C22×C3×C5C22×D411yescharacteristic
224C2×C3×D5—21no—
225C2×C3×D5—21no—
226C2×C3×D5C4×D412yes—
227C3×C4×C5—24no—
228C3×C4×C5C23×C411yescharacteristic
229C3×C4×C5C2×#4111yescharacteristic
230Dic15—21no—
231Dic15—21no—
232Dic15—42no—
233C3×Dic5—24no—
234C3×Dic5C4×D412yes—
235C5×Dic3—21no—
236C5×Dic3—21no—
237C5×Dic3—42no—
238C2×C3×Q8—58no—
239C2×C3×Q8—52no—
240C2×C3×Q8—102no—
241C2×C3×Q8—104no—
242C2×C3×Q8C22×D512yes—
243C22×C3×C4—51no—
244C22×C3×C4—102no—
245C3×Q16—58no—
246C3×Q16—54no—
247C3×Q16C4×D514yes—
248C2×C3×C8—51no—
249C2×C3×C8—54no—
250C2×C3×C8C22×D511yescharacteristic
251#217—51no—
252#217—51no—
253#217—102no—
254C4⋊Dic3—22no—
255C4⋊Dic3—51no—
256C4⋊Dic3—51no—
257C4⋊Dic3—52no—
258C4⋊Dic3—102no—
259C4⋊Dic3—102no—
260C4⋊Dic3—102no—
261C4⋊Dic3C22×D512yes—
262C4×Dic3—22no—
263C4×Dic3—51no—
264C4×Dic3—102no—
265C4×Dic3—102no—
266C4×Dic3—102no—
267C4×Dic3—102no—
268C4×Dic3C22×D511yescharacteristic
269#208—102no—
270C2×C3⋊C8—51no—
271C2×C3⋊C8C22×D511yescharacteristic
272C22×D5D3×D411yescharacteristic
273C5×Q8—22no—
274C5×Q8C22×Dic314yes—
275C2×C4×C5—22no—
276C2×C4×C5—31no—
277C2×C4×C5—31no—
278C2×C4×C5—62no—
279C2×C4×C5C23×D311yescharacteristic
280C2×Dic5—22no—
281C2×Dic5—31no—
282C2×Dic5—31no—
283C2×Dic5—62no—
284C2×Dic5D3×D411yescharacteristic
285C4×D5—28no—
286C4×D5#23712yes—
287C4×D5C22×Dic312yes—
288Dic10—22no—
289Dic10—28no—
290Dic10C22×Dic314yes—
291C5×C8—61no—
292C5×C8C22×Dic312yes—
293#168—61no—
294#168C22×Dic312yes—
295C22×Q8—52no—
296C2×Q16—52no—
297C2×Q16—58no—
298C2×Q16—51no—
299C2×Q16D3×D511yescharacteristic
300C2×M16—151no—
301C22×C8—51no—
302C4×Q8—32no—
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—31no—
313#107—151no—
314#106—152no—
315#103—32no—
316#103—152no—
317#103—152no—
318#103—152no—
319#97—151no—
320#97—151no—
321C4×C8—31no—
322C4×C8—151no—
323C2×C3×C5C2×C4×D411yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C2×C3×C5#57811yescharacteristic
326C3×D5—22no—
327C23×C3—51no—
328C3×Q8—22no—
329C3×Q8—54no—
330C3×Q8—108no—
331C3×Q8—102no—
332C3×Q8C2×C4×D514yes—
333C2×C3×C4—22no—
334C2×C3×C4—51no—
335C2×C3×C4—52no—
336C2×C3×C4—52no—
337C2×C3×C4—108no—
338C2×C3×C4—102no—
339C2×C3×C4C23×D511yescharacteristic
340C2×Dic3—22no—
341C2×Dic3—51no—
342C2×Dic3—51no—
343C2×Dic3—102no—
344C2×Dic3D4×D511yescharacteristic
345C2×Dic3D4×D511yescharacteristic
346C3×C8—52no—
347C3×C8C2×C4×D512yes—
348C3⋊C8—21no—
349C3⋊C8—101no—
350C22×C5C2×D3×D411yescharacteristic
351C2×D5—21no—
352C2×D5—21no—
353C2×D5D4×Dic312yes—
354C4×C5—24no—
355C4×C5—61no—
356C4×C5—61no—
357C4×C5—122no—
358C4×C5C2×#23711yescharacteristic
359C4×C5C23×Dic311yescharacteristic
360Dic5—24no—
361Dic5—61no—
362Dic5—61no—
363Dic5—122no—
364Dic5D4×Dic312yes—
365C2×Q8—58no—
366C2×Q8—52no—
367C2×Q8—102no—
368C2×Q8—104no—
369C2×Q8C2×D3×D512yes—
370C22×C4—51no—
371C22×C4—102no—
372Q16—58no—
373Q16—54no—
374Q16D5×Dic314yes—
375M16—302no—
376C2×C8—31no—
377C2×C8—51no—
378C2×C8—54no—
379C2×C8—151no—
380C2×C8C2×D3×D511yescharacteristic
381C4⋊C4—32no—
382C4⋊C4—62no—
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—31no—
393C42—62no—
394C42—151no—
395C42—302no—
396C42—302no—
397C42—302no—
398C42—302no—
399C3×C5#295011yescharacteristic, complemented, Hall
400C22×C3—52no—
401C22×C3—101no—
402C22×C3—101no—
403C22×C3C2×D4×D511yescharacteristic
404C3×C4—24no—
405C3×C4—52no—
406C3×C4—104no—
407C3×C4C22×C4×D511yescharacteristic
408C3×C4D5×#4111yescharacteristic
409Dic3—21no—
410Dic3—21no—
411Dic3—42no—
412Dic3—101no—
413Dic3—101no—
414Dic3—202no—
415C2×C5#576611yescharacteristic
416C2×C5#576611yescharacteristic
417C2×C5C2×D4×Dic311yescharacteristic
418D5—22no—
419C23—51no—
420Q8—22no—
421Q8—54no—
422Q8—108no—
423Q8—102no—
424Q8C2×D5×Dic314yes—
425C2×C4—22no—
426C2×C4—31no—
427C2×C4—31no—
428C2×C4—51no—
429C2×C4—52no—
430C2×C4—52no—
431C2×C4—62no—
432C2×C4—108no—
433C2×C4—102no—
434C2×C4—151no—
435C2×C4—151no—
436C2×C4—302no—
437C2×C4C22×D3×D511yescharacteristic
438C8—52no—
439C8—61no—
440C8—301no—
441C8C2×D5×Dic312yes—
442C2×C3—102no—
443C2×C3C4×D4×D511yescharacteristic
444C2×C3#6610011yescharacteristic
445C2×C3#6610511yescharacteristic
446C5#8387411yescharacteristic, complemented, Sylow
447C22—52no—
448C22—101no—
449C22—101no—
450C22D3×D4×D511yescharacteristic
451C4—24no—
452C4—52no—
453C4—61no—
454C4—61no—
455C4—104no—
456C4—122no—
457C4—301no—
458C4—301no—
459C4—602no—
460C4D5×#23711yescharacteristic
461C4C22×D5×Dic311yescharacteristic
462C3#1061145111yescharacteristic, complemented, Sylow
463C2—102no—
464C2#1175410611yescharacteristic
465C2#1175411011yescharacteristic
466C2D4×D5×Dic311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×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. C5×Dic3×Q16C2semidirect
5. #11749264C2semidirect
6. #11749256C2semidirect
8. #11747883C2semidirect
9. Dic3×Dic20C2semidirect
18. C3×D5×Q16C4semidirect
95. Dic3×Q16D5semidirect
103. D5×Q16Dic3semidirect
399. C3×C5#2950semidirect
446. C5#83874semidirect
462. C3#10611451semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×Q162
#117551402
Q16×Dic152
C5×Dic3×Q162
#117492642
#117492562
#117492082
#117478832
Dic3×Dic202
#117476722
#117476452
#106114513
#838745