Finite Group Databasebeta

← #14417570

Subgroups — #14417570

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×#91264C211yesmaximal, characteristic
2#11752460C212yesmaximal
3#11750790C211yesmaximal, characteristic
4C4×C5×Dic12C211yesmaximal, characteristic, complemented
5C3×C4×Dic20C211yesmaximal, characteristic, complemented
6#11747886C211yesmaximal, characteristic, complemented
7#11747883C211yesmaximal, characteristic, complemented
8#11747829C212yesmaximal, complemented
9#11747690C211yesmaximal, characteristic
10#11747644C212yesmaximal
11#11747089C212yesmaximal, complemented
12#10611451—31nomaximal, Hall
13C2×D15⋊Q8C2212yes—
14C2×#6705C2211yescharacteristic
15C2×C8×D15C2211yescharacteristic
16#91761C2211yescharacteristic
17C2×C5×Dic12C2211yescharacteristic
18C4×C5×Dic6C2212yes—
19C2×C3×Dic20C2211yescharacteristic
20C3×C4×Dic10C2212yes—
21#91403—22no—
22#91402—22no—
23#91347C2212yes—
24#91344C2212yes—
25#91331C2212yes—
26#91324—22no—
27#91323—22no—
28C2×#6661C2212yes—
29#91264C418yescomplemented
30C3×C4×C5×C8C2211yescharacteristic
31#91099C2211yescharacteristic
32C8×Dic15C2211yescharacteristic
33#91087C2211yescharacteristic
34C5×#818C2211yescharacteristic
35C5×#816C2212yes—
36C3×#3950C2211yescharacteristic
37C3×#3948C2212yes—
38#90986C2212yes—
39#90972C2212yes—
40#90970C2212yes—
41#79720—51nomaximal, Hall
42C2×D5×Q16—31no—
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×Dic20D311yescharacteristic, complemented
52#64978—31no—
53C2×C4×D15C2311yescharacteristic
54C2×C5×Dic6C2312yes—
55C2×C3×Dic10C2312yes—
56C2×#1204—22no—
57C2×#1200—22no—
58D15⋊Q8—24no—
59D15⋊Q8C2×C418yes—
60C2×C3×C5×C8C2311yescharacteristic
61C2×C3×C5×C8C2311yescharacteristic
62C3×C42×C5C2311yescharacteristic
63#6714D411yescharacteristic
64#6714D411yescharacteristic
65#6712D411yescharacteristic
66#6712D411yescharacteristic
67C4×Dic15C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70#6705—22no—
71C8×D15C2×C414yes—
72C5×C4⋊Dic3C2312yes—
73C5×Dic3⋊C4—22no—
74C4×C5×Dic3—22no—
75C5×Dic12C2×C414yes—
76C3×C4⋊Dic5C2312yes—
77C3×#683—22no—
78C3×C4×Dic5—22no—
79C3×Dic20C2×C414yes—
80Dic3⋊Dic5—22no—
81#6668—22no—
82#6667—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85Dic3×Dic5—22no—
86#6661C2×C418yes—
87C2×D3×Q16—51no—
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×Dic12D511yescharacteristic, complemented
97#4689—51no—
98C2×Q8×D5—32no—
99C2×C5×Q16—31no—
100C4×C5×Q8—32no—
101Q8×Dic5—32no—
102C2×#689—32no—
103D5×Q16—38no—
104C2×Dic20C2×D311yescharacteristic
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—62no—
114C4×Dic10C2×D312yes—
115C5×#107—31no—
116C5×#103—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3950C2×D311yescharacteristic
120#3948C2×D312yes—
121#3947—31no—
122C8×Dic5—31no—
123#3942—32no—
124#3940—32no—
125#3935—31no—
126#2950—151noSylow
127C22×D15C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15C2×D411yescharacteristic
132C2×Dic15C2×D411yescharacteristic
133C2×Dic15C2×D411yescharacteristic
134C4×D15C22×C412yes—
135C4×D15#4112yes—
136C2×C5×Dic3—22no—
137C2×C5×Dic3—22no—
138C5×Dic6—22no—
139C5×Dic6C22×C414yes—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—22no—
142C3×Dic10—22no—
143C3×Dic10C22×C414yes—
144#1204—28no—
145#1200—28no—
146C3×C5×C8—21no—
147C3×C5×C8C22×C412yes—
148C3⋊#168—21no—
149C3⋊#168C22×C412yes—
150C2×D3×Q8—52no—
151C2×C3×Q16—51no—
152C3×C4×Q8—52no—
153Q8×Dic3—52no—
154C2×#216—52no—
155D3×Q16—58no—
156C2×Dic12C2×D511yescharacteristic
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—102no—
166C4×Dic6C2×D512yes—
167C3×#107—51no—
168C3×#103—52no—
169C3×C4×C8C2×D511yescharacteristic
170#835—52no—
171#818C2×D511yescharacteristic
172#816C2×D512yes—
173#815—51no—
174C8×Dic3—51no—
175#810—52no—
176#808—52no—
177#803—51no—
178C2×C5×Q8—32no—
179Q8×D5—38no—
180Q8×D5—64no—
181C2×C4×D5—31no—
182C2×C4×D5—62no—
183C2×Dic10—62no—
184C2×Dic10C22×D312yes—
185C5×Q16—34no—
186C2×C5×C8C22×D311yescharacteristic
187C2×C5×C8C22×D311yescharacteristic
188C5×C4⋊C4—32no—
189C5×C4⋊C4—62no—
190C42×C5—62no—
191C42×C5C22×D311yescharacteristic
192#689—38no—
193#685—31no—
194#685—31no—
195#685—62no—
196C4⋊Dic5—62no—
197C4⋊Dic5C22×D312yes—
198#683—22no—
199#683—31no—
200#683—31no—
201#683—62no—
202C4×Dic5—22no—
203C4×Dic5—31no—
204C4×Dic5—62no—
205C4×Dic5—62no—
206C4×Dic5—62no—
207C2×#168—31no—
208C2×#168—31no—
209Dic20C4×D314yes—
210#676—62no—
211C8×D5—34no—
212C22×Q16—151no—
213#519—152no—
214#441—152no—
215#441—152no—
216C4×Q16—31no—
217C4×Q16—51no—
218C4×Q16—151no—
219C4×Q16—151no—
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—21no—
228C3×C4×C5—21no—
229C3×C4×C5C23×C411yescharacteristic
230C3×C4×C5C2×#4111yescharacteristic
231Dic15—21no—
232Dic15—21no—
233Dic15C4×D412yes—
234C3×Dic5—24no—
235C3×Dic5—42no—
236C5×Dic3—24no—
237C5×Dic3—42no—
238C2×C3×Q8—52no—
239D3×Q8—58no—
240D3×Q8—104no—
241C2×C4×D3—51no—
242C2×C4×D3—102no—
243C2×Dic6—102no—
244C2×Dic6C22×D512yes—
245C3×Q16—54no—
246C2×C3×C8C22×D511yescharacteristic
247C2×C3×C8C22×D511yescharacteristic
248C3×C4⋊C4—52no—
249C3×C4⋊C4—102no—
250C3×C42—102no—
251C3×C42C22×D511yescharacteristic
252#216—58no—
253(C2×D3)⋊C4—51no—
254(C2×D3)⋊C4—51no—
255(C2×D3)⋊C4—102no—
256C4⋊Dic3—102no—
257C4⋊Dic3C22×D512yes—
258Dic3⋊C4—22no—
259Dic3⋊C4—51no—
260Dic3⋊C4—51no—
261Dic3⋊C4—102no—
262C4×Dic3—22no—
263C4×Dic3—51no—
264C4×Dic3—102no—
265C4×Dic3—102no—
266C4×Dic3—102no—
267C2×C3⋊C8—51no—
268C2×C3⋊C8—51no—
269Dic12C4×D514yes—
270ΓL(1,𝔽25)—102no—
271D3×C8—54no—
272C22×D5—31no—
273C5×Q8—34no—
274C5×Q8—62no—
275C2×C4×C5—62no—
276C2×C4×C5—62no—
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5C23×D311yescharacteristic
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—31no—
283C2×Dic5—31no—
284C2×Dic5—31no—
285C4×D5—32no—
286C4×D5—32no—
287C4×D5—68no—
288Dic10—22no—
289Dic10—68no—
290Dic10C2×C4×D314yes—
291C5×C8—21no—
292C5×C8C2×C4×D312yes—
293#168—32no—
294#168—61no—
295C22×Q8—152no—
296C2×Q16—31no—
297C2×Q16—51no—
298C2×Q16—158no—
299C2×Q16—152no—
300C2×M16—151no—
301C22×C8—151no—
302C4×Q8—32no—
303C4×Q8—52no—
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—51no—
314#106—152no—
315#103—32no—
316#103—52no—
317#103—152no—
318#103—152no—
319#97—151no—
320#97—151no—
321C4×C8—151no—
322C4×C8D3×D511yescharacteristic
323C2×C3×C5C2×C4×D411yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C2×C3×C5#57811yescharacteristic
326D15—22no—
327C22×D3—51no—
328C3×Q8—54no—
329C3×Q8—102no—
330C2×C3×C4—102no—
331C2×C3×C4—102no—
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4C23×D511yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—51no—
338C2×Dic3—51no—
339C2×Dic3—51no—
340C4×D3—52no—
341C4×D3—52no—
342C4×D3—108no—
343Dic6—22no—
344Dic6—108no—
345Dic6C2×C4×D514yes—
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—64no—
357C4×C5—122no—
358C4×C5C22×C4×D311yescharacteristic
359C4×C5D3×#4111yescharacteristic
360Dic5—24no—
361Dic5—32no—
362Dic5—42no—
363Dic5—61no—
364Dic5—61no—
365C2×Q8—32no—
366C2×Q8—52no—
367C2×Q8—158no—
368C2×Q8—302no—
369C2×Q8—304no—
370C22×C4—151no—
371C22×C4—302no—
372Q16—34no—
373Q16—54no—
374Q16—158no—
375M16—302no—
376C2×C8—151no—
377C2×C8—154no—
378C2×C8—151no—
379C2×C8C2×D3×D511yescharacteristic
380C2×C8C2×D3×D511yescharacteristic
381C4⋊C4—32no—
382C4⋊C4—52no—
383C4⋊C4—62no—
384C4⋊C4—102no—
385C4⋊C4—151no—
386C4⋊C4—151no—
387C4⋊C4—302no—
388C4⋊C4—302no—
389C22⋊C4—151no—
390C22⋊C4—151no—
391C22⋊C4—302no—
392C42—62no—
393C42—102no—
394C42—151no—
395C42—302no—
396C42—302no—
397C42—302no—
398C42C2×D3×D511yescharacteristic
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—104no—
407C3×C4—202no—
408C3×C4C22×C4×D511yescharacteristic
409C3×C4D5×#4111yescharacteristic
410Dic3—24no—
411Dic3—42no—
412Dic3—52no—
413Dic3—101no—
414Dic3—101no—
415C2×C5C4×D3×D411yescharacteristic
416C2×C5#576611yescharacteristic
417C2×C5#577111yescharacteristic
418D5—62no—
419C23—151no—
420Q8—34no—
421Q8—54no—
422Q8—62no—
423Q8—102no—
424Q8—308no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—102no—
428C2×C4—102no—
429C2×C4—151no—
430C2×C4—152no—
431C2×C4—152no—
432C2×C4—151no—
433C2×C4—151no—
434C2×C4—308no—
435C2×C4#677711yescharacteristic
436C2×C4#677711yescharacteristic
437C2×C4C22×D3×D511yescharacteristic
438C8—21no—
439C8—152no—
440C8—301no—
441C8C4×D3×D512yes—
442C2×C3C4×D4×D511yescharacteristic
443C2×C3#6610011yescharacteristic
444C2×C3#6610511yescharacteristic
445D3—102no—
446C5#7972011yescharacteristic, complemented, Sylow
447C22—152no—
448C22—301no—
449C22—301no—
450C22C2×#677711yescharacteristic
451C4—21no—
452C4—21no—
453C4—64no—
454C4—104no—
455C4—122no—
456C4—152no—
457C4—202no—
458C4—301no—
459C4—301no—
460C4C2×C4×D3×D511yescharacteristic
461C4#9201611yescharacteristic
462C3#1061145111yescharacteristic, complemented, Sylow
463C2—302no—
464C2C4×#677711yescharacteristic
465C2#1175400811yescharacteristic
466C2#1175401111yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5#2950
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
4. C4×C5×Dic12C2semidirect
5. C3×C4×Dic20C2semidirect
6. #11747886C2semidirect
7. #11747883C2semidirect
8. #11747829C2semidirect
11. #11747089C2semidirect
29. #91264C4semidirect
51. C4×Dic20D3semidirect
96. C4×Dic12D5semidirect
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×#912642
#117524602
#117507902
C4×C5×Dic122
C3×C4×Dic202
#117478862
#117478832
#117478292
#117476902
#117476442
#117470892
#106114513
#797205