Finite Group Databasebeta

← #14438038

Subgroups — #14438038

Order 1920.

784 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
1C3×#65851C211yesmaximal, characteristic, complemented
2#11754572C211yesmaximal, characteristic
3#11751103C211yesmaximal, characteristic, complemented
4C5×#5002C211yesmaximal, characteristic, complemented
5#11748411C211yesmaximal, characteristic, complemented
6#11748382C211yesmaximal, characteristic, complemented
7C2×#90952C211yesmaximal, characteristic, complemented
8#11747401C212yesmaximal, complemented
9#11747369C212yesmaximal, complemented
10#11747159C212yesmaximal, complemented
11#11747156C212yesmaximal, complemented
12#10610557—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C22×C5×C3⋊C8C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20C3×#4036C2212yes—
21C3×#4034C2212yes—
22C3×#4024—22no—
23C3×C4×Dic10—22no—
24#91566—22no—
25#91451C2211yescharacteristic
26C4×#1203—22no—
27#91376C2211yescharacteristic
28#91375C2211yescharacteristic
29#91373C2211yescharacteristic
30#91094C2212yes—
31#91093C2212yes—
32C5×#810C2212yes—
33C5×#809C2212yes—
34#90974C2212yes—
35#90972C2212yes—
36#90968C2212yes—
37#90966C2212yes—
38#90952C2212yes—
39#90952C2212yes—
40#83335—51nomaximal, Hall
41#66166—31no—
42#65851D311yescharacteristic, complemented
43C5×#416—31no—
44#65522—31no—
45#65402—31no—
46C2×#3947—31no—
47#65291—31no—
48#65086—32no—
49#65084—32no—
50#65054—32no—
51#65053—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×C3×Dic10—22no—
67C2×#1203—22no—
68C3×C5×C4⋊C4C2312yes—
69C3×C5×C22⋊C4—21no—
70C3×C42×C5—21no—
71C2×C3⋊#168—22no—
72C2×C3⋊#168C2312yes—
73C2×C5×C3⋊C8—22no—
74C2×C5×C3⋊C8C2312yes—
75C3×C22⋊Dic5—21no—
76C3×C4⋊Dic5—22no—
77C3×C4⋊Dic5C2312yes—
78C3×#683—22no—
79C3×#683—22no—
80C3×C4×Dic5—21no—
81C3×C4×Dic5D412yes—
82C3×C4×Dic5C2311yescharacteristic
83C3×C4×Dic5C2311yescharacteristic
84#6668—22no—
85#6667—22no—
86(C2×D3)⋊Dic5—22no—
87C3×#533—51no—
88#5477—51no—
89#5089—52no—
90#5089—52no—
91#5069—52no—
92#5067—52no—
93#5002—51no—
94#5002—51no—
95#5002—51no—
96#5002D511yescharacteristic, complemented
97C2×#803—51no—
98C2×C5×#41—31no—
99C2×#709—31no—
100C22×C5×C8—31no—
101C5×#117C2×D311yescharacteristic
102#4093—31no—
103#4090—31no—
104#4086—31no—
105#4085—62no—
106#4082—31no—
107C4×C22⋊D5—62no—
108#4072C2×D311yescharacteristic
109C2×C4×Dic5C2×D311yescharacteristic
110C22×#168—31no—
111#4036C2×D312yes—
112#4034C2×D312yes—
113#4024—22no—
114C4×Dic10—22no—
115C5×#103—32no—
116C5×#102—32no—
117#3967—32no—
118#3964—32no—
119#3953—32no—
120#3948—32no—
121#3947—32no—
122#3947—32no—
123#3942—32no—
124#3941—32no—
125#3135—151noSylow
126C23×C3×C5C2×D411yescharacteristic
127C22×D15—21no—
128C22×C5×D3—21no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5#4112yes—
132C2×C3×C4×C5#4112yes—
133C2×C3×C4×C5C2411yescharacteristic
134#1220—42no—
135C2×Dic15—21no—
136D60—21no—
137D60—21no—
138C4×D15—42no—
139Dic30—21no—
140Dic30—21no—
141C5×#67—42no—
142C2×C5×Dic3—21no—
143C5×D12—21no—
144C5×D12—21no—
145C4×C5×D3—42no—
146C5×Dic6—21no—
147C5×Dic6—21no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—42no—
150C2×C3×Dic5C2×D412yes—
151C2×C3×Dic5C2×D412yes—
152C3×Dic10—44no—
153#1203—44no—
154C3⋊#168—22no—
155C5×C3⋊C8—22no—
156C2×#235—51no—
157C2×#235C2×D511yescharacteristic
158C3×C4⋊Q8—52no—
159C3×#125—52no—
160C3×C22⋊Q8—102no—
161C3×C4×Q8—102no—
162C3×#117—51no—
163C3×#117C2×D511yescharacteristic
164C2×C3×C42—51no—
165#930—102no—
166C22×C3⋊C8—51no—
167C22×C3⋊C8C2×D511yescharacteristic
168#875—51no—
169#875—51no—
170#874—51no—
171C4×D12—102no—
172#869—51no—
173#810—52no—
174#810—52no—
175#810—52no—
176#810C2×D512yes—
177#809—52no—
178#809—52no—
179#809—52no—
180#809C2×D512yes—
181#803—52no—
182#803—52no—
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×Dic5#6712yes—
193#709—62no—
194#709—62no—
195C2×D20—31no—
196C2×C4×D5—61no—
197C2×Dic10—22no—
198C2×Dic10—31no—
199C2×C5×C8—32no—
200C2×C5×C8—62no—
201C5×C4⋊C4C22×D312yes—
202C5×C22⋊C4—21no—
203C42×C5—21no—
204C22⋊Dic5—21no—
205C22⋊Dic5—62no—
206#685—62no—
207C4⋊Dic5—22no—
208C4⋊Dic5C22×D312yes—
209#683—22no—
210#683—22no—
211#683—62no—
212C4×Dic5—21no—
213C4×Dic5#6712yes—
214C4×Dic5C22×D311yescharacteristic
215C4×Dic5C22×D311yescharacteristic
216C2×#168—32no—
217C2×#168—62no—
218#533—51no—
219#532—151no—
220#491—152no—
221#490—152no—
222#489—152no—
223#489—152no—
224#416—31no—
225#416—151no—
226#416—151no—
227#416—151no—
228C2×#97—151no—
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—42no—
237C3×C4×C5#12412yes—
238C3×C4×C5C2×#4111yescharacteristic
239C3×C4×C5C2×#4111yescharacteristic
240Dic15—41no—
241C3×Dic5—22no—
242C3×Dic5—22no—
243C3×Dic5—42no—
244C5×Dic3—41no—
245C2×C3×Q8—102no—
246C22×C3×C4—52no—
247C22×C3×C4C22×D511yescharacteristic
248C2×#67—21no—
249C2×#67—101no—
250#235—22no—
251#235—22no—
252#235—102no—
253#235—102no—
254C2×D12—51no—
255C2×D12—102no—
256C2×D12C22×D511yescharacteristic
257C2×C4×D3—21no—
258C2×C4×D3—101no—
259C2×Dic6—51no—
260C2×Dic6C22×D511yescharacteristic
261C3×C4⋊C4—52no—
262C3×C4⋊C4—102no—
263C3×C4⋊C4—102no—
264C3×C4⋊C4—102no—
265C3×C4⋊C4C22×D512yes—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—101no—
268C3×C42—21no—
269C3×C42—52no—
270C3×C42—51no—
271C3×C42—51no—
272C3×C42—101no—
273(C2×D3)⋊C4—102no—
274(C2×D3)⋊C4—102no—
275C4⋊Dic3—102no—
276C2×C3⋊C8—22no—
277C2×C3⋊C8—52no—
278C2×C3⋊C8—102no—
279C2×C3⋊C8C22×D512yes—
280C23×C5—61no—
281C23×C5C2×#6711yescharacteristic
282C22×D5—61no—
283C5×Q8—61no—
284C5×Q8—61no—
285C5×D4—61no—
286C5×D4—61no—
287C5×D4—122no—
288C2×C4×C5—22no—
289C2×C4×C5—61no—
290C2×C4×C5—122no—
291C2×C4×C5#23912yes—
292C2×C4×C5#23912yes—
293C2×C4×C5C2×#6711yescharacteristic
294C2×C4×C5C23×D311yescharacteristic
295C22⋊D5—124no—
296C22⋊D5—122no—
297C2×Dic5—22no—
298C2×Dic5—42no—
299C2×Dic5—61no—
300C2×Dic5C2×#6712yes—
301C2×Dic5C2×#6712yes—
302D20—61no—
303D20—61no—
304C4×D5—122no—
305Dic10—44no—
306Dic10—61no—
307Dic10—61no—
308C5×C8—62no—
309#168—62no—
310C2×#41—31no—
311C2×#41—151no—
312C22×C8—31no—
313C22×C8—151no—
314C4⋊Q8—52no—
315C4⋊Q8—151no—
316#127—151no—
317#125—52no—
318#124—151no—
319#124—151no—
320C22⋊Q8—102no—
321#121—302no—
322C4×Q8—102no—
323C4×D4—302no—
324#117—51no—
325#117D3×D511yescharacteristic
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—
335#97—152no—
336#97—152no—
337C2×C3×C5—22no—
338C2×C3×C5C2×#12411yescharacteristic
339C2×C3×C5#57512yes—
340D15—81no—
341C5×D3—81no—
342C23×C3D4×D511yescharacteristic
343C22×D3—21no—
344C22×D3—101no—
345C3×Q8—204no—
346C2×C3×C4—22no—
347C2×C3×C4—52no—
348C2×C3×C4—52no—
349C2×C3×C4—102no—
350C2×C3×C4—202no—
351C2×C3×C4#70912yes—
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4#71112yes—
354C2×C3×C4C23×D511yescharacteristic
355#67—42no—
356#67—202no—
357C2×Dic3—21no—
358C2×Dic3—101no—
359D12—21no—
360D12—21no—
361D12—101no—
362D12—101no—
363D12—204no—
364C4×D3—42no—
365C4×D3—202no—
366Dic6—21no—
367Dic6—21no—
368Dic6—101no—
369Dic6—101no—
370C3⋊C8—22no—
371C3⋊C8—102no—
372C22×C5—22no—
373C22×C5—121no—
374C22×C5—122no—
375C22×C5#94712yes—
376C22×C5C22×#6711yescharacteristic
377C2×D5—121no—
378C2×D5—122no—
379C4×C5—42no—
380C4×C5—121no—
381C4×C5#94712yes—
382C4×C5C2×#23911yescharacteristic
383C4×C5C2×#23911yescharacteristic
384Dic5—22no—
385Dic5—22no—
386Dic5—42no—
387Dic5—121no—
388#41—62no—
389#41—62no—
390#41—302no—
391#41—302no—
392C2×Q8—31no—
393C2×Q8—102no—
394C2×Q8—151no—
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—32no—
405C2×C8—62no—
406C2×C8—152no—
407C2×C8—302no—
408C4⋊C4—52no—
409C4⋊C4—102no—
410C4⋊C4—102no—
411C4⋊C4—102no—
412C4⋊C4—302no—
413C4⋊C4C2×D3×D512yes—
414C22⋊C4—21no—
415C22⋊C4—101no—
416C22⋊C4—302no—
417C22⋊C4—302no—
418C42—21no—
419C42—52no—
420C42—51no—
421C42—51no—
422C42—101no—
423C3×C5#313511yescharacteristic, 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—42no—
432C3×C4—102no—
433C3×C4—102no—
434C3×C4—202no—
435C3×C4#403112yes—
436C3×C4C2×#70911yescharacteristic
437C3×C4C2×#71111yescharacteristic
438Dic3—41no—
439Dic3—201no—
440C2×C5—22no—
441C2×C5—241no—
442C2×C5C2×#94711yescharacteristic
443C2×C5#582212yes—
444D5—241no—
445C23—61no—
446C23—301no—
447C23D5×#6711yescharacteristic
448Q8—61no—
449Q8—61no—
450Q8—204no—
451Q8—301no—
452Q8—301no—
453D4—61no—
454D4—61no—
455D4—122no—
456D4—301no—
457D4—301no—
458D4—604no—
459D4—602no—
460C2×C4—22no—
461C2×C4—52no—
462C2×C4—52no—
463C2×C4—61no—
464C2×C4—102no—
465C2×C4—122no—
466C2×C4—202no—
467C2×C4—301no—
468C2×C4—602no—
469C2×C4#676812yes—
470C2×C4#676912yes—
471C2×C4D5×#6711yescharacteristic
472C2×C4C22×D3×D511yescharacteristic
473C8—62no—
474C8—302no—
475C2×C3—22no—
476C2×C3C2×#403111yescharacteristic
477C2×C3#6610212yes—
478D3—81no—
479D3—401no—
480C5#8333511yescharacteristic, complemented, Sylow
481C22—22no—
482C22—122no—
483C22—121no—
484C22—602no—
485C22—601no—
486C22#9132612yes—
487C22C2×D5×#6711yescharacteristic
488C4—42no—
489C4—102no—
490C4—102no—
491C4—121no—
492C4—202no—
493C4—601no—
494C4#9132612yes—
495C4C2×#676811yescharacteristic
496C4C2×#676911yescharacteristic
497C3#1061055711yescharacteristic, complemented, Sylow
498C2—22no—
499C2—241no—
500C2—1201no—
501C2C2×#9132611yescharacteristic
502C2#1175531512yes—
subgroupG/H
centerC2×C4D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radical#11754572C2
hypercenter#117D3×D5
hypocenterC3×C5#3135
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#65851C2semidirect
3. #11751103C2semidirect
4. C5×#5002C2semidirect
5. #11748411C2semidirect
6. #11748382C2semidirect
7. C2×#90952C2semidirect
8. #11747401C2semidirect
9. #11747369C2semidirect
10. #11747159C2semidirect
11. #11747156C2semidirect
42. #65851D3semidirect
96. #5002D5semidirect
423. C3×C5#3135semidirect
480. C5#83335semidirect
497. C3#10610557semidirect

Maximal subgroups

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

subgroupindex
C3×#658512
#117545722
#117511032
C5×#50022
#117484112
#117483822
C2×#909522
#117474012
#117473692
#117471592
#117471562
#106105573
#833355