Finite Group Databasebeta

← #14438037

Subgroups — #14438037

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
1#11756276C211yesmaximal, characteristic, complemented
2#11754586C211yesmaximal, characteristic
3C5×#5002C211yesmaximal, characteristic, complemented
4C3×#65291C211yesmaximal, characteristic, complemented
5#11748388C211yesmaximal, characteristic, complemented
6#11748365C211yesmaximal, characteristic, complemented
7C2×#90954C211yesmaximal, characteristic, complemented
8#11747429C212yesmaximal, complemented
9#11747409C212yesmaximal, complemented
10#11747388C212yesmaximal, complemented
11#11747384C212yesmaximal, complemented
12#10610557—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16#91815C2211yescharacteristic
17C2×C4×Dic15C2211yescharacteristic
18#91779C2212yes—
19#91777C2212yes—
20#91767—22no—
21C4×Dic30—22no—
22C22×C5×C3⋊C8C2211yescharacteristic
23C22×C3×#168C2211yescharacteristic
24#91571—22no—
25#91463C2211yescharacteristic
26C4×#1201—22no—
27#91385C2211yescharacteristic
28#91370C2211yescharacteristic
29#91368C2211yescharacteristic
30C5×#810C2212yes—
31C5×#809C2212yes—
32C3×#3942C2212yes—
33C3×#3941C2212yes—
34#90973C2212yes—
35#90971C2212yes—
36#90967C2212yes—
37#90965C2212yes—
38#90954C2212yes—
39#90954C2212yes—
40#78826—51nomaximal, Hall
41#66166—31no—
42#65851—31no—
43C5×#416—31no—
44#65522—31no—
45#65402—31no—
46C2×#3947—31no—
47#65291D311yescharacteristic, complemented
48#65086—32no—
49#65084—32no—
50#65054—32no—
51#65053—32no—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15D412yes—
54C2×Dic30—22no—
55C2×C5×#67—21no—
56C5×#235—22no—
57C5×#235—22no—
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C5×Dic6C2311yescharacteristic
61C2×C3×C22⋊D5—21no—
62C3×#709—22no—
63C3×#709—22no—
64C2×C3×D20C2311yescharacteristic
65C2×C3×C4×D5—21no—
66C2×C3×Dic10C2311yescharacteristic
67C2×#1201—22no—
68C3×C5×C4⋊C4C2312yes—
69C3×C5×C22⋊C4—21no—
70C3×C42×C5—21no—
71#6719—21no—
72C4⋊Dic15—22no—
73C4⋊Dic15C2312yes—
74#6712—22no—
75#6712—22no—
76C4×Dic15—21no—
77C4×Dic15D412yes—
78C4×Dic15C2311yescharacteristic
79C4×Dic15C2311yescharacteristic
80C2×C5×C3⋊C8—22no—
81C2×C5×C3⋊C8C2312yes—
82C2×C3×#168—22no—
83C2×C3×#168C2312yes—
84#6669—22no—
85(C2×D3)⋊Dic5—22no—
86#6665—22no—
87#5832—51no—
88#5517—51no—
89C3×#416—51no—
90#5233—51no—
91#5113—51no—
92C2×#815—51no—
93#5002D511yescharacteristic, complemented
94#4797—52no—
95#4794—52no—
96#4765—52no—
97#4764—52no—
98C2×C5×#41—31no—
99C2×#709C2×D311yescharacteristic
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#4072—31no—
109C2×C4×Dic5—31no—
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—
121#3947—32no—
122#3947—32no—
123#3942C2×D312yes—
124#3941C2×D312yes—
125#3135—151noSylow
126C23×C3×C5C2×D411yescharacteristic
127C22×C5×D3—21no—
128C22×C3×D5—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
134C2×Dic15—22no—
135C2×Dic15—42no—
136C2×Dic15C2×D412yes—
137C2×Dic15C2×D412yes—
138Dic30—44no—
139C5×#67—42no—
140C2×C5×Dic3—21no—
141C5×D12—21no—
142C5×D12—21no—
143C4×C5×D3—42no—
144C5×Dic6—21no—
145C5×Dic6—21no—
146C3×C22⋊D5—42no—
147C2×C3×Dic5—21no—
148C3×D20—21no—
149C3×D20—21no—
150C3×C4×D5—42no—
151C3×Dic10—21no—
152C3×Dic10—21no—
153#1201—44no—
154C3×#168—22no—
155C5×C3⋊C8—22no—
156C2×C3×#41—51no—
157C2×#235C2×D511yescharacteristic
158C22×C3×C8—51no—
159C3×#117C2×D511yescharacteristic
160#947—51no—
161#944—51no—
162#940—51no—
163#939—102no—
164#936—51no—
165C4×#67—102no—
166#926—51no—
167C2×C4×Dic3—51no—
168C22×C3⋊C8C2×D511yescharacteristic
169#890—52no—
170#888—52no—
171#878—102no—
172C4×Dic6—102no—
173C3×#103—52no—
174C3×#102—52no—
175#835—52no—
176#832—52no—
177#821—52no—
178#816—52no—
179#815—52no—
180#815—52no—
181#810C2×D512yes—
182#809C2×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—21no—
191C2×C22⋊D5—62no—
192C22×Dic5—32no—
193#709—22no—
194#709—22no—
195C2×D20C22×D311yescharacteristic
196C2×C4×D5—21no—
197C2×Dic10—62no—
198C2×Dic10C22×D311yescharacteristic
199C2×C5×C8—32no—
200C2×C5×C8—62no—
201C5×C4⋊C4C22×D312yes—
202C5×C22⋊C4—21no—
203C42×C5—21no—
204C22⋊Dic5—62no—
205C22⋊Dic5—61no—
206#685—62no—
207C4⋊Dic5—32no—
208C4⋊Dic5—62no—
209#683—62no—
210#683—62no—
211#683—62no—
212C4×Dic5—32no—
213C4×Dic5—31no—
214C4×Dic5—31no—
215C4×Dic5—61no—
216C2×#168—22no—
217C2×#168C22×D312yes—
218#533—151no—
219#532—151no—
220#491—152no—
221#490—152no—
222#489—152no—
223#489—152no—
224#416—31no—
225#416—51no—
226#416—151no—
227#416—151no—
228C2×#97—151no—
229C22×C3×C5—22no—
230C22×C3×C5#12412yes—
231C22×C3×C5C22×D411yescharacteristic
232C2×C5×D3—41no—
233C2×C5×D3—42no—
234C2×C3×D5—41no—
235C2×C3×D5—42no—
236C3×C4×C5—42no—
237C3×C4×C5#12412yes—
238C3×C4×C5C2×#4111yescharacteristic
239C3×C4×C5C2×#4111yescharacteristic
240Dic15—22no—
241Dic15—22no—
242Dic15—42no—
243C3×Dic5—41no—
244C5×Dic3—41no—
245C3×#41—102no—
246C3×#41—102no—
247C2×C3×Q8—51no—
248C2×C3×D4—51no—
249C2×C3×D4—101no—
250C22×C3×C4—101no—
251C22×C3×C4C22×D511yescharacteristic
252C2×#67—21no—
253C2×#67—102no—
254C22×Dic3—52no—
255#235—22no—
256#235—22no—
257C2×D12C22×D511yescharacteristic
258C2×C4×D3—21no—
259C2×Dic6—102no—
260C2×Dic6C22×D511yescharacteristic
261C2×C3×C8—52no—
262C2×C3×C8—102no—
263C3×C4⋊C4C22×D512yes—
264C3×C22⋊C4—21no—
265C3×C42—21no—
266#217—102no—
267#217—101no—
268(C2×D3)⋊C4—102no—
269C4⋊Dic3—52no—
270C4⋊Dic3—102no—
271Dic3⋊C4—102no—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274C4×Dic3—52no—
275C4×Dic3—51no—
276C4×Dic3—51no—
277C4×Dic3—101no—
278C2×C3⋊C8—22no—
279C2×C3⋊C8C22×D512yes—
280C23×C5—61no—
281C23×C5D3×D411yescharacteristic
282C22×D5—21no—
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#23512yes—
292C2×C4×C5D3×D411yescharacteristic
293C2×C4×C5#23712yes—
294C2×C4×C5C23×D311yescharacteristic
295C22⋊D5—42no—
296C22⋊D5—124no—
297C2×Dic5—21no—
298C2×Dic5—32no—
299C2×Dic5—32no—
300C2×Dic5—62no—
301C2×Dic5—122no—
302D20—21no—
303D20—21no—
304C4×D5—42no—
305Dic10—21no—
306Dic10—21no—
307Dic10—124no—
308C5×C8—62no—
309#168—22no—
310C2×#41—31no—
311C2×#41—51no—
312C22×C8—31no—
313C22×C8—51no—
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—151no—
325#117D3×D511yescharacteristic
326C2×C42—151no—
327#103—32no—
328#103—52no—
329#103—152no—
330#103—152no—
331#102—32no—
332#102—52no—
333#102—152no—
334#102—152no—
335#97—152no—
336#97—152no—
337C2×C3×C5—22no—
338C2×C3×C5C2×#12411yescharacteristic
339C2×C3×C5#57512yes—
340C3×D5—81no—
341C5×D3—81no—
342C23×C3—101no—
343C23×C3D4×D511yescharacteristic
344C22×D3—21no—
345C3×Q8—101no—
346C3×Q8—101no—
347C3×D4—101no—
348C3×D4—101no—
349C3×D4—202no—
350C2×C3×C4—22no—
351C2×C3×C4—101no—
352C2×C3×C4—202no—
353C2×C3×C4#70912yes—
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4#71112yes—
356C2×C3×C4C23×D511yescharacteristic
357#67—42no—
358#67—204no—
359C2×Dic3—21no—
360C2×Dic3—52no—
361C2×Dic3—52no—
362C2×Dic3—102no—
363C2×Dic3—202no—
364D12—21no—
365D12—21no—
366C4×D3—42no—
367Dic6—21no—
368Dic6—21no—
369Dic6—204no—
370C3×C8—102no—
371C3⋊C8—22no—
372C22×C5—22no—
373C22×C5—121no—
374C22×C5—122no—
375C22×C5#88512yes—
376C22×C5C2×D3×D411yescharacteristic
377C2×D5—41no—
378C2×D5—42no—
379C4×C5—42no—
380C4×C5—121no—
381C4×C5#88512yes—
382C4×C5C2×#23511yescharacteristic
383C4×C5C2×#23711yescharacteristic
384Dic5—41no—
385Dic5—62no—
386Dic5—62no—
387Dic5—122no—
388#41—62no—
389#41—62no—
390#41—102no—
391#41—102no—
392C2×Q8—31no—
393C2×Q8—51no—
394C2×Q8—302no—
395C2×D4—31no—
396C2×D4—51no—
397C2×D4—61no—
398C2×D4—101no—
399C2×D4—302no—
400C22×C4—61no—
401C22×C4—101no—
402C22×C4—152no—
403C22×C4C2×D3×D511yescharacteristic
404C2×C8—32no—
405C2×C8—52no—
406C2×C8—62no—
407C2×C8—102no—
408C4⋊C4—152no—
409C4⋊C4—302no—
410C4⋊C4—302no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4C2×D3×D512yes—
414C22⋊C4—21no—
415C22⋊C4—302no—
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—21no—
419C42—152no—
420C42—151no—
421C42—151no—
422C42—301no—
423C3×C5#313511yescharacteristic, complemented, Hall
424C22×C3—22no—
425C22×C3—201no—
426C22×C3—202no—
427C22×C3#403112yes—
428C22×C3C2×D4×D511yescharacteristic
429C2×D3—41no—
430C2×D3—42no—
431C3×C4—42no—
432C3×C4—201no—
433C3×C4#403112yes—
434C3×C4C2×#70911yescharacteristic
435C3×C4C2×#71111yescharacteristic
436Dic3—41no—
437Dic3—102no—
438Dic3—102no—
439Dic3—202no—
440C2×C5—22no—
441C2×C5—241no—
442C2×C5C2×#88511yescharacteristic
443C2×C5#576812yes—
444D5—81no—
445C23—61no—
446C23—101no—
447C23#679011yescharacteristic
448Q8—61no—
449Q8—61no—
450Q8—101no—
451Q8—101no—
452Q8—604no—
453D4—61no—
454D4—61no—
455D4—101no—
456D4—101no—
457D4—122no—
458D4—202no—
459D4—604no—
460C2×C4—22no—
461C2×C4—61no—
462C2×C4—101no—
463C2×C4—122no—
464C2×C4—152no—
465C2×C4—152no—
466C2×C4—202no—
467C2×C4—302no—
468C2×C4—602no—
469C2×C4#676512yes—
470C2×C4#677212yes—
471C2×C4#679011yescharacteristic
472C2×C4C22×D3×D511yescharacteristic
473C8—62no—
474C8—102no—
475C2×C3—22no—
476C2×C3—401no—
477C2×C3C2×#403111yescharacteristic
478C2×C3#6610212yes—
479D3—81no—
480C5#7882611yescharacteristic, complemented, Sylow
481C22—22no—
482C22—121no—
483C22—122no—
484C22—201no—
485C22—202no—
486C22#9146212yes—
487C22C2×#679011yescharacteristic
488C4—42no—
489C4—121no—
490C4—201no—
491C4—302no—
492C4—302no—
493C4—602no—
494C4#9146212yes—
495C4C2×#676511yescharacteristic
496C4C2×#677211yescharacteristic
497C3#1061055711yescharacteristic, complemented, Sylow
498C2—22no—
499C2—241no—
500C2—401no—
501C2C2×#9146211yescharacteristic
502C2#1175532912yes—
subgroupG/H
centerC2×C4#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radical#11754586C2
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. #11756276C2semidirect
3. C5×#5002C2semidirect
4. C3×#65291C2semidirect
5. #11748388C2semidirect
6. #11748365C2semidirect
7. C2×#90954C2semidirect
8. #11747429C2semidirect
9. #11747409C2semidirect
10. #11747388C2semidirect
11. #11747384C2semidirect
47. #65291D3semidirect
93. #5002D5semidirect
423. C3×C5#3135semidirect
480. C5#78826semidirect
497. C3#10610557semidirect

Maximal subgroups

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

subgroupindex
#117562762
#117545862
C5×#50022
C3×#652912
#117483882
#117483652
C2×#909542
#117474292
#117474092
#117473882
#117473842
#106105573
#788265