Finite Group Databasebeta

← #14417601

Subgroups — #14417601

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×D3×Dic20C211yesmaximal, characteristic
2#11753405C212yesmaximal
3#11750974C211yesmaximal, characteristic, complemented
4C5×#4880C211yesmaximal, characteristic
5C3×#65162C211yesmaximal, characteristic, complemented
6#11747883C211yesmaximal, characteristic, complemented
7#11747851C211yesmaximal, characteristic, complemented
8#11747653C211yesmaximal, characteristic
9#11747489C212yesmaximal
10#11747274C212yesmaximal, complemented
11#11747269C212yesmaximal, complemented
12#10610900—31nomaximal, Hall
13C2×D3×Dic10C2212yes—
14C2×Dic60C2211yescharacteristic
15#91776C2212yes—
16C2×C5×D3×C8C2211yescharacteristic
17C5×#892C2212yes—
18C2×C3×Dic20C2211yescharacteristic
19C3×#4033C2212yes—
20C4×#1204—22no—
21#91400—22no—
22#91398—22no—
23#91371C2211yescharacteristic
24#91333C2212yes—
25#91331C2212yes—
26#91324—22no—
27C2×#6662C2212yes—
28C2×#6650C2211yescharacteristic
29D3×Dic20C418yescomplemented
30C3×C5×#107C2211yescharacteristic
31C8×Dic15C2211yescharacteristic
32#91094C2212yes—
33C5×#818C2211yescharacteristic
34C5×#808C2212yes—
35C3×C8×Dic5C2211yescharacteristic
36C3×#3942C2212yes—
37#90975C2212yes—
38#90970C2212yes—
39#90954C2211yescharacteristic
40#90952C2211yescharacteristic
41#79720—51nomaximal, Hall
42C22×Dic20—31no—
43#65850—32no—
44C5×#427—31no—
45#65390—31no—
46#65293—32no—
47#65162—31no—
48#65162—31no—
49#65162—31no—
50#65162D311yescharacteristic, complemented
51#65142—32no—
52#65142—32no—
53C2×Dic30C2312yes—
54C2×C4×C5×D3C2311yescharacteristic
55C2×C3×Dic10C2312yes—
56C2×#1204—22no—
57C2×D3×Dic5—22no—
58D3×Dic10—24no—
59D3×Dic10C2×C418yes—
60C2×C3×C5×C8C2311yescharacteristic
61C3×C5×C4⋊C4C2312yes—
62#6712—22no—
63C4×Dic15—22no—
64C4×Dic15C2311yescharacteristic
65C2×C3⋊#168C2311yescharacteristic
66Dic60C2×C414yes—
67C5×(C2×D3)⋊C4—22no—
68C5×C4⋊Dic3C2312yes—
69C4×C5×Dic3—22no—
70C2×C5×C3⋊C8C2311yescharacteristic
71C5×D3×C8C2×C414yes—
72C3×#683—22no—
73C3×C4×Dic5—22no—
74C3×C4×Dic5C2311yescharacteristic
75C2×C3×#168C2311yescharacteristic
76C3×Dic20C2×C414yes—
77Dic3⋊Dic5D411yescharacteristic
78Dic3⋊Dic5D411yescharacteristic
79#6669—22no—
80#6668—22no—
81(C2×D3)⋊Dic5D411yescharacteristic
82(C2×D3)⋊Dic5D411yescharacteristic
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6662C2×C418yes—
86#6650—22no—
87C2×D3×Q16—51no—
88#5572—52no—
89C3×C4×Q16—51no—
90Dic3×Q16—51no—
91#5030—52no—
92#4880D511yescharacteristic
93#4873—51no—
94#4802—52no—
95#4789—52no—
96C4×Dic12—51no—
97#4689—51no—
98C22×Dic10—32no—
99C22×C5×C8—31no—
100C5×#117—32no—
101#4072—31no—
102C2×#681—31no—
103C2×Dic20—32no—
104C2×Dic20—31no—
105C2×Dic20—38no—
106C2×Dic20C2×D311yescharacteristic
107#4033—32no—
108#4033—32no—
109#4033—32no—
110#4033C2×D312yes—
111#4023—62no—
112#4023—62no—
113C4×Dic10—62no—
114C4×Dic10—62no—
115C5×#107—31no—
116C5×#107C2×D311yescharacteristic
117C5×#106—32no—
118#3947—31no—
119#3947—31no—
120C8×Dic5—31no—
121C8×Dic5C2×D311yescharacteristic
122#3942—32no—
123#3942—32no—
124#3942—32no—
125#3942C2×D312yes—
126#2950—151noSylow
127C22×C5×D3C2×D411yescharacteristic
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5C2411yescharacteristic
130C2×Dic15—22no—
131C2×Dic15C2×D411yescharacteristic
132C2×Dic15C2×D411yescharacteristic
133Dic30—22no—
134Dic30C22×C414yes—
135C2×C5×Dic3—22no—
136C2×C5×Dic3C2×D411yescharacteristic
137C4×C5×D3C22×C412yes—
138C4×C5×D3#4112yes—
139C2×C3×Dic5—22no—
140C2×C3×Dic5C2×D411yescharacteristic
141C2×C3×Dic5C2×D411yescharacteristic
142C3×Dic10—22no—
143C3×Dic10C22×C414yes—
144#1204—28no—
145D3×Dic5—28no—
146C3×C5×C8C22×C412yes—
147C3⋊#168—21no—
148C3×#168—21no—
149C5×C3⋊C8C22×C412yes—
150C2×D3×Q8—52no—
151C2×C3×Q16—51no—
152C3×C4×Q8—52no—
153Q8×Dic3—52no—
154C2×#216—52no—
155D3×Q16—58no—
156C2×Dic12—51no—
157C2×ΓL(1,𝔽25)—51no—
158C2×D3×C8C2×D511yescharacteristic
159#892—102no—
160#892C2×D512yes—
161#887—52no—
162#887—102no—
163#872—51no—
164#872—102no—
165C4×Dic6—52no—
166C4×Dic6—102no—
167C3×#107C2×D511yescharacteristic
168C3×#103—52no—
169C3×C4×C8—51no—
170#835—52no—
171#818C2×D511yescharacteristic
172#816—52no—
173#815—51no—
174C8×Dic3—51no—
175#810—52no—
176#808C2×D512yes—
177#803—51no—
178C22×C4×C5—31no—
179C22×Dic5—62no—
180C2×Dic10—32no—
181C2×Dic10—38no—
182C2×Dic10—64no—
183C2×Dic10—62no—
184C2×Dic10C22×D312yes—
185C2×C5×C8—31no—
186C2×C5×C8—34no—
187C2×C5×C8C22×D311yescharacteristic
188C5×C4⋊C4—32no—
189C5×C4⋊C4C22×D312yes—
190C5×C22⋊C4—62no—
191C42×C5—62no—
192C22⋊Dic5—31no—
193C22⋊Dic5—31no—
194C4⋊Dic5—31no—
195C4⋊Dic5—31no—
196#683—22no—
197#683—62no—
198#683—62no—
199#683—62no—
200C4×Dic5—22no—
201C4×Dic5—31no—
202C4×Dic5—62no—
203C4×Dic5—62no—
204C4×Dic5—62no—
205C4×Dic5C22×D311yescharacteristic
206#681—62no—
207C2×#168—31no—
208C2×#168C22×D311yescharacteristic
209Dic20—38no—
210Dic20—34no—
211Dic20C4×D314yes—
212C22×Q16—151no—
213#519—152no—
214#441—152no—
215#441—152no—
216C4×Q16—51no—
217C4×Q16—151no—
218C4×Q16—151no—
219C4×Q16—151no—
220#427—31no—
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—42no—
228C3×C4×C5C23×C411yescharacteristic
229C3×C4×C5C2×#4111yescharacteristic
230Dic15—24no—
231Dic15—21no—
232Dic15—21no—
233C3×Dic5—24no—
234C3×Dic5—21no—
235C3×Dic5—21no—
236C5×Dic3—42no—
237C5×Dic3C4×D412yes—
238C2×C3×Q8—52no—
239D3×Q8—58no—
240D3×Q8—104no—
241C2×C4×D3—102no—
242C2×C4×D3C22×D511yescharacteristic
243C2×Dic6—52no—
244C2×Dic6—102no—
245C3×Q16—54no—
246C2×C3×C8—51no—
247C2×C3×C8C22×D511yescharacteristic
248C3×C4⋊C4—102no—
249C3×C4⋊C4C22×D512yes—
250C3×C42—51no—
251C3×C42—102no—
252#216—58no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—51no—
255(C2×D3)⋊C4—51no—
256C4⋊Dic3—102no—
257C4⋊Dic3C22×D512yes—
258Dic3⋊C4—51no—
259Dic3⋊C4—51no—
260Dic3⋊C4—102no—
261Dic3⋊C4—102no—
262C4×Dic3—22no—
263C4×Dic3—51no—
264C4×Dic3—102no—
265C4×Dic3—102no—
266C4×Dic3—102no—
267C2×C3⋊C8—51no—
268C2×C3⋊C8C22×D511yescharacteristic
269Dic12—54no—
270ΓL(1,𝔽25)—102no—
271D3×C8C4×D514yes—
272C23×C5—31no—
273C2×C4×C5—22no—
274C2×C4×C5—31no—
275C2×C4×C5—32no—
276C2×C4×C5—32no—
277C2×C4×C5—62no—
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—22no—
280C2×Dic5—31no—
281C2×Dic5—31no—
282C2×Dic5—68no—
283C2×Dic5—62no—
284C2×Dic5D3×D411yescharacteristic
285C2×Dic5D3×D411yescharacteristic
286Dic10—22no—
287Dic10—34no—
288Dic10—68no—
289Dic10—62no—
290Dic10C2×C4×D314yes—
291C5×C8—32no—
292C5×C8C2×C4×D312yes—
293#168—21no—
294#168—61no—
295C22×Q8—152no—
296C2×Q16—51no—
297C2×Q16—158no—
298C2×Q16—152no—
299C2×Q16—151no—
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—32no—
309#117—151no—
310#117—302no—
311#117—302no—
312#107—31no—
313#107D3×D511yescharacteristic
314#106—32no—
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—54no—
329C3×Q8—102no—
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—108no—
341C4×D3C2×C4×D512yes—
342C4×D3#71312yes—
343Dic6—54no—
344Dic6—102no—
345Dic6—108no—
346C3×C8—101no—
347C3×C8C2×C4×D512yes—
348C3⋊C8—101no—
349C3⋊C8C2×C4×D512yes—
350C22×C5—32no—
351C22×C5—61no—
352C22×C5—61no—
353C22×C5C2×D3×D411yescharacteristic
354C4×C5—32no—
355C4×C5—42no—
356C4×C5—122no—
357C4×C5C22×C4×D311yescharacteristic
358C4×C5D3×#4111yescharacteristic
359Dic5—21no—
360Dic5—21no—
361Dic5—24no—
362Dic5—61no—
363Dic5—61no—
364Dic5—64no—
365C2×Q8—52no—
366C2×Q8—158no—
367C2×Q8—152no—
368C2×Q8—302no—
369C2×Q8—304no—
370C22×C4—31no—
371C22×C4—302no—
372Q16—54no—
373Q16—158no—
374Q16—154no—
375M16—302no—
376C2×C8—31no—
377C2×C8—34no—
378C2×C8—51no—
379C2×C8—151no—
380C2×C8C2×D3×D511yescharacteristic
381C4⋊C4—32no—
382C4⋊C4—102no—
383C4⋊C4—151no—
384C4⋊C4—151no—
385C4⋊C4—302no—
386C4⋊C4—302no—
387C4⋊C4—302no—
388C4⋊C4C2×D3×D512yes—
389C22⋊C4—62no—
390C22⋊C4—151no—
391C22⋊C4—151no—
392C42—51no—
393C42—62no—
394C42—102no—
395C42—151no—
396C42—302no—
397C42—302no—
398C42—302no—
399C3×C5#295011yescharacteristic, complemented, Hall
400C22×C3C2×D4×D511yescharacteristic
401C2×D3—21no—
402C2×D3—21no—
403C2×D3#403912yes—
404C3×C4—42no—
405C3×C4—104no—
406C3×C4—101no—
407C3×C4—101no—
408C3×C4C22×C4×D511yescharacteristic
409C3×C4C2×#71311yescharacteristic
410Dic3—42no—
411Dic3—104no—
412Dic3—101no—
413Dic3—101no—
414Dic3#403912yes—
415C2×C5—62no—
416C2×C5C4×D3×D411yescharacteristic
417C2×C5#576611yescharacteristic
418C2×C5#577111yescharacteristic
419C23—31no—
420Q8—54no—
421Q8—102no—
422Q8—154no—
423Q8—308no—
424Q8—302no—
425C2×C4—22no—
426C2×C4—31no—
427C2×C4—32no—
428C2×C4—32no—
429C2×C4—51no—
430C2×C4—51no—
431C2×C4—62no—
432C2×C4—102no—
433C2×C4—151no—
434C2×C4—151no—
435C2×C4—308no—
436C2×C4—302no—
437C2×C4C22×D3×D511yescharacteristic
438C8—32no—
439C8—101no—
440C8—301no—
441C8C4×D3×D512yes—
442C2×C3C2×#403911yescharacteristic
443C2×C3#6610511yescharacteristic
444C2×C3#6610511yescharacteristic
445D3—22no—
446C5#7972011yescharacteristic, complemented, Sylow
447C22—32no—
448C22—61no—
449C22—61no—
450C22D3×D4×D511yescharacteristic
451C4—32no—
452C4—42no—
453C4—101no—
454C4—104no—
455C4—101no—
456C4—122no—
457C4—301no—
458C4—304no—
459C4—301no—
460C4C2×C4×D3×D511yescharacteristic
461C4D3×#71311yescharacteristic
462C3#1061090011yescharacteristic, complemented, Sylow
463C2—62no—
464C2D3×#403911yescharacteristic
465C2#1175406311yescharacteristic
466C2#1175411011yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
cosocleC2×C3×C4×C5C24
hypercenter#107D3×D5
hypocenterC3×C5#2950
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #11750974C2semidirect
5. C3×#65162C2semidirect
6. #11747883C2semidirect
7. #11747851C2semidirect
10. #11747274C2semidirect
11. #11747269C2semidirect
29. D3×Dic20C4semidirect
50. #65162D3semidirect
399. C3×C5#2950semidirect
446. C5#79720semidirect
462. C3#10610900semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic202
#117534052
#117509742
C5×#48802
C3×#651622
#117478832
#117478512
#117476532
#117474892
#117472742
#117472692
#106109003
#797205