Finite Group Databasebeta

← #14437818

Subgroups — #14437818

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754615C211yesmaximal, characteristic, complemented
2#11754572C211yesmaximal, characteristic
3#11751214C211yesmaximal, characteristic, complemented
4C5×#5113C211yesmaximal, characteristic, complemented
5C2×C3×C8×Dic5C211yesmaximal, characteristic, complemented
6#11748393C211yesmaximal, characteristic, complemented
7#11748388C211yesmaximal, characteristic, complemented
8#11748017C212yesmaximal, complemented
9#11747995C212yesmaximal, complemented
10#11747985C212yesmaximal, complemented
11#11747963C212yesmaximal, complemented
12#10610556—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16#91815C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C3×C4×Dic5C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20#91574—22no—
21#91566—22no—
22#91468C2212yes—
23C4×#1204—22no—
24#91451C2211yescharacteristic
25C4×#1203—22no—
26#91388C2212yes—
27#91376C2211yescharacteristic
28#91375C2211yescharacteristic
29#91373C2211yescharacteristic
30#91105C2212yes—
31#91100C2212yes—
32C5×#821C2212yes—
33C5×#816C2212yes—
34C3×C8×Dic5C2212yes—
35C3×C8×Dic5C2212yes—
36#90975C2212yes—
37#90973C2212yes—
38#90969C2212yes—
39#90967C2212yes—
40#78463—51nomaximal, Hall
41#66166—31no—
42#65851—31no—
43C5×#416—31no—
44#65522—31no—
45#65402—31no—
46C2×C8×Dic5D311yescharacteristic, complemented
47#65291—31no—
48#65089—32no—
49#65081—32no—
50#65057—32no—
51#65049—32no—
52C22×C3×C4×C5C2311yescharacteristic
53C2×#1220—21no—
54#6817—22no—
55#6817—22no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×Dic30C2311yescharacteristic
59C2×C5×#67—21no—
60C5×#235—22no—
61C5×#235—22no—
62C2×C5×D12C2311yescharacteristic
63C2×C4×C5×D3—21no—
64C2×C5×Dic6C2311yescharacteristic
65C22×C3×Dic5D412yes—
66C2×#1204—22no—
67C2×#1203—22no—
68C2×C3×C5×C8—22no—
69C2×C3×C5×C8C2312yes—
70#6719—21no—
71C4⋊Dic15C2312yes—
72C4×Dic15—21no—
73C5×#217—21no—
74C5×C4⋊Dic3C2312yes—
75C4×C5×Dic3—21no—
76C3×C4×Dic5D412yes—
77C3×C4×Dic5C2311yescharacteristic
78C3×C4×Dic5C2311yescharacteristic
79C2×C3×#168—22no—
80C2×C3×#168C2312yes—
81Dic3⋊Dic5—22no—
82#6669—22no—
83#6668—22no—
84#6668—22no—
85#6667—22no—
86(C2×D3)⋊Dic5—22no—
87#5477—51no—
88#5470—51no—
89C2×C3×C4×C8—51no—
90#5113—51no—
91#5113—51no—
92#5113—51no—
93#5113D511yescharacteristic, complemented
94#4697—52no—
95#4697—52no—
96#4694—52no—
97#4681—52no—
98C2×C5×#41—31no—
99C2×#709—31no—
100C22×C5×C8C2×D311yescharacteristic
101C5×#117—31no—
102#4093—31no—
103#4090—31no—
104#4086—31no—
105#4085—62no—
106#4082—31no—
107C4×C22⋊D5—62no—
108#4072—31no—
109C2×C4×Dic5C2×D311yescharacteristic
110C22×#168C2×D311yescharacteristic
111#4036—32no—
112#4034—32no—
113#4024—62no—
114C4×Dic10—62no—
115C5×#103—32no—
116C5×#102—32no—
117#3967—32no—
118#3964—32no—
119#3953—32no—
120#3948—32no—
121C8×Dic5C2×D312yes—
122C8×Dic5C2×D312yes—
123#3942—32no—
124#3941—32no—
125#3131—151noSylow
126C23×C3×C5C2×D411yescharacteristic
127C22×D15—21no—
128C22×C5×D3—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5#4112yes—
131C2×C3×C4×C5#4112yes—
132C2×C3×C4×C5C2411yescharacteristic
133#1220—42no—
134C2×Dic15—21no—
135C2×Dic15—22no—
136D60—21no—
137D60—21no—
138C4×D15—42no—
139Dic30—21no—
140Dic30—21no—
141C5×#67—42no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—22no—
144C5×D12—21no—
145C5×D12—21no—
146C4×C5×D3—42no—
147C5×Dic6—21no—
148C5×Dic6—21no—
149C2×C3×Dic5—24no—
150C2×C3×Dic5C2×D412yes—
151C2×C3×Dic5C2×D412yes—
152#1204—44no—
153#1203—44no—
154C3×C5×C8—22no—
155C3×#168—22no—
156C2×#235—51no—
157C2×#235C2×D511yescharacteristic
158C22×C3×C8—51no—
159C22×C3×C8C2×D511yescharacteristic
160C2×C3×C42—51no—
161#930—102no—
162#926—51no—
163#926C2×D511yescharacteristic
164#924—102no—
165#875—51no—
166#875—51no—
167#874—51no—
168C4×D12—102no—
169#870—52no—
170#869—52no—
171#869—51no—
172C4×Dic6—102no—
173C3×C4×C8—52no—
174C3×C4×C8—52no—
175#821—52no—
176#821—52no—
177#821—52no—
178#821C2×D512yes—
179#816—52no—
180#816—52no—
181#816—52no—
182#816C2×D512yes—
183C5×#41—62no—
184C5×#41—62no—
185C2×C5×Q8—31no—
186C2×C5×D4—31no—
187C2×C5×D4—61no—
188C22×C4×C5—61no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—61no—
191C2×C22⋊D5—62no—
192C22×Dic5D1212yes—
193#709—62no—
194#709—62no—
195C2×D20—31no—
196C2×C4×D5—61no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C2×C5×C8—22no—
200C2×C5×C8C22×D312yes—
201C5×C4⋊C4—32no—
202C5×C22⋊C4—61no—
203C42×C5—61no—
204C22⋊Dic5—61no—
205C22⋊Dic5—62no—
206#685—62no—
207C4⋊Dic5—32no—
208C4⋊Dic5—62no—
209#683—62no—
210#683—62no—
211#683—62no—
212C4×Dic5—61no—
213C4×Dic5D1212yes—
214C4×Dic5C22×D311yescharacteristic
215C4×Dic5C22×D311yescharacteristic
216C2×#168—22no—
217C2×#168C22×D312yes—
218#533—151no—
219#532—151no—
220#488—152no—
221#488—152no—
222#487—152no—
223#486—152no—
224#416—31no—
225#416—151no—
226#416—151no—
227#416—151no—
228C2×C4×C8—51no—
229C22×C3×C5—22no—
230C22×C3×C5#12412yes—
231C22×C3×C5C22×D411yescharacteristic
232C2×D15—41no—
233C2×D15—42no—
234C2×C5×D3—41no—
235C2×C5×D3—42no—
236C3×C4×C5#12412yes—
237C3×C4×C5C2×#4111yescharacteristic
238C3×C4×C5C2×#4111yescharacteristic
239Dic15—41no—
240Dic15—42no—
241C3×Dic5—22no—
242C3×Dic5#13514yes—
243C5×Dic3—41no—
244C5×Dic3—42no—
245C22×C3×C4—52no—
246C22×C3×C4C22×D511yescharacteristic
247C2×#67—21no—
248C2×#67—101no—
249#235—22no—
250#235—22no—
251#235—102no—
252#235—102no—
253C2×D12—51no—
254C2×D12—102no—
255C2×D12C22×D511yescharacteristic
256C2×C4×D3—21no—
257C2×C4×D3—101no—
258C2×Dic6—51no—
259C2×Dic6—102no—
260C2×Dic6C22×D511yescharacteristic
261C2×C3×C8—22no—
262C2×C3×C8—52no—
263C2×C3×C8—102no—
264C2×C3×C8C22×D512yes—
265C3×C42—52no—
266C3×C42—51no—
267C3×C42—51no—
268#217—21no—
269#217—101no—
270(C2×D3)⋊C4—102no—
271(C2×D3)⋊C4—102no—
272C4⋊Dic3—52no—
273C4⋊Dic3—102no—
274C4⋊Dic3—102no—
275C4⋊Dic3C22×D512yes—
276Dic3⋊C4—102no—
277Dic3⋊C4—102no—
278C4×Dic3—21no—
279C4×Dic3—101no—
280C23×C5—61no—
281C23×C5C2×D1211yescharacteristic
282C22×D5—61no—
283C5×Q8—61no—
284C5×Q8—61no—
285C5×D4—61no—
286C5×D4—61no—
287C5×D4—122no—
288C2×C4×C5—62no—
289C2×C4×C5—61no—
290C2×C4×C5—122no—
291C2×C4×C5C2×D1211yescharacteristic
292C2×C4×C5#23512yes—
293C2×C4×C5#23512yes—
294C2×C4×C5C23×D311yescharacteristic
295C22⋊D5—122no—
296C22⋊D5—124no—
297C2×Dic5—24no—
298C2×Dic5—62no—
299C2×Dic5—61no—
300C2×Dic5C2×D1212yes—
301C2×Dic5C2×D1212yes—
302D20—61no—
303D20—61no—
304C4×D5—122no—
305Dic10—61no—
306Dic10—61no—
307Dic10—124no—
308C5×C8—22no—
309#168—22no—
310C2×#41—31no—
311C2×#41—151no—
312C22×C8—51no—
313C22×C8D3×D511yescharacteristic
314C4⋊Q8—152no—
315C4⋊Q8—151no—
316#127—151no—
317#125—152no—
318#124—151no—
319#124—151no—
320C22⋊Q8—302no—
321#121—302no—
322C4×Q8—302no—
323C4×D4—302no—
324#117—31no—
325#117—151no—
326C2×C42—51no—
327#103—32no—
328#103—152no—
329#103—152no—
330#103—152no—
331#102—32no—
332#102—152no—
333#102—152no—
334#102—152no—
335C4×C8—52no—
336C4×C8—52no—
337C2×C3×C5—22no—
338C2×C3×C5C2×#12411yescharacteristic
339C2×C3×C5C2×#13512yes—
340D15—81no—
341C5×D3—81no—
342C23×C3D4×D511yescharacteristic
343C22×D3—21no—
344C22×D3—101no—
345C2×C3×C4—52no—
346C2×C3×C4—52no—
347C2×C3×C4—104no—
348C2×C3×C4#70912yes—
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4#71112yes—
351C2×C3×C4C23×D511yescharacteristic
352#67—42no—
353#67—202no—
354C2×Dic3—22no—
355C2×Dic3—21no—
356C2×Dic3—102no—
357C2×Dic3—101no—
358D12—21no—
359D12—21no—
360D12—101no—
361D12—101no—
362D12—204no—
363C4×D3—42no—
364C4×D3—202no—
365Dic6—21no—
366Dic6—21no—
367Dic6—101no—
368Dic6—101no—
369Dic6—204no—
370C3×C8—22no—
371C3×C8—102no—
372C22×C5—22no—
373C22×C5—121no—
374C22×C5—122no—
375C22×C5#87512yes—
376C22×C5C22×D1211yescharacteristic
377C2×D5—121no—
378C2×D5—122no—
379C4×C5—121no—
380C4×C5—122no—
381C4×C5#87512yes—
382C4×C5C2×#23511yescharacteristic
383C4×C5C2×#23511yescharacteristic
384Dic5—22no—
385Dic5—121no—
386Dic5—122no—
387Dic5#90414yes—
388#41—62no—
389#41—62no—
390#41—302no—
391#41—302no—
392C2×Q8—31no—
393C2×Q8—151no—
394C2×Q8—302no—
395C2×D4—31no—
396C2×D4—61no—
397C2×D4—151no—
398C2×D4—302no—
399C2×D4—301no—
400C22×C4—52no—
401C22×C4—61no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404C2×C8—22no—
405C2×C8—52no—
406C2×C8—102no—
407C2×C8C2×D3×D512yes—
408C4⋊C4—32no—
409C4⋊C4—152no—
410C4⋊C4—302no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C22⋊C4—61no—
415C22⋊C4—302no—
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—52no—
419C42—51no—
420C42—51no—
421C42—61no—
422C42—301no—
423C3×C5#313111yescharacteristic, complemented, Hall
424C22×C3—22no—
425C22×C3#403112yes—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—41no—
428C2×D3—42no—
429C2×D3—201no—
430C2×D3—202no—
431C3×C4—54no—
432C3×C4—102no—
433C3×C4#403112yes—
434C3×C4C2×#70911yescharacteristic
435C3×C4C2×#71111yescharacteristic
436Dic3—41no—
437Dic3—42no—
438Dic3—201no—
439Dic3—202no—
440C2×C5—22no—
441C2×C5—241no—
442C2×C5C2×#87511yescharacteristic
443C2×C5C2×#90412yes—
444D5—241no—
445C23—61no—
446C23—301no—
447C23D5×D1211yescharacteristic
448Q8—61no—
449Q8—61no—
450Q8—301no—
451Q8—301no—
452Q8—604no—
453D4—61no—
454D4—61no—
455D4—122no—
456D4—301no—
457D4—301no—
458D4—604no—
459D4—602no—
460C2×C4—52no—
461C2×C4—52no—
462C2×C4—62no—
463C2×C4—61no—
464C2×C4—104no—
465C2×C4—122no—
466C2×C4—302no—
467C2×C4—301no—
468C2×C4—602no—
469C2×C4#677112yes—
470C2×C4D5×D1211yescharacteristic
471C2×C4#678212yes—
472C2×C4C22×D3×D511yescharacteristic
473C8—22no—
474C8—102no—
475C2×C3—22no—
476C2×C3C2×#403111yescharacteristic
477C2×C3D5×#13512yes—
478D3—81no—
479D3—401no—
480C5#7846311yescharacteristic, complemented, Sylow
481C22—22no—
482C22—122no—
483C22—121no—
484C22—602no—
485C22—601no—
486C22#9135012yes—
487C22C2×D5×D1211yescharacteristic
488C4—54no—
489C4—102no—
490C4—122no—
491C4—121no—
492C4—602no—
493C4—601no—
494C4#9135012yes—
495C4C2×#677111yescharacteristic
496C4C2×#678211yescharacteristic
497C3#1061055611yescharacteristic, complemented, Sylow
498C2—22no—
499C2—241no—
500C2—1201no—
501C2D5×#90412yes—
502C2C2×#9135011yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11754572C2
hypercenterC22×C8D3×D5
hypocenterC3×C5#3131
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #11754615C2semidirect
3. #11751214C2semidirect
4. C5×#5113C2semidirect
5. C2×C3×C8×Dic5C2semidirect
6. #11748393C2semidirect
7. #11748388C2semidirect
8. #11748017C2semidirect
9. #11747995C2semidirect
10. #11747985C2semidirect
11. #11747963C2semidirect
46. C2×C8×Dic5D3semidirect
93. #5113D5semidirect
423. C3×C5#3131semidirect
480. C5#78463semidirect
497. C3#10610556semidirect

Maximal subgroups

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

subgroupindex
#117546152
#117545722
#117512142
C5×#51132
C2×C3×C8×Dic52
#117483932
#117483882
#117480172
#117479952
#117479852
#117479632
#106105563
#784635