Finite Group Databasebeta

← #14413505

Subgroups — #14413505

Order 1920.

952 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
1C2×#91796C211yesmaximal, characteristic
2#11756282C211yesmaximal, characteristic
3#11756263C211yesmaximal, characteristic
4C3×C5×#428C211yesmaximal, characteristic, complemented
5#11751222C211yesmaximal, characteristic, complemented
6#11751099C211yesmaximal, characteristic, complemented
7C2×#91091C211yesmaximal, characteristic, complemented
8#11750982C212yesmaximal, complemented
9D15×#107C212yesmaximal, complemented
10#11750962C212yesmaximal, complemented
11#11750961C212yesmaximal, complemented
12#10610941—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C4×#1220—22no—
18#91815C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21#91796C418yescomplemented
22C2×#6705C2212yes—
23C2×C8×D15C2212yes—
24#91782—21no—
25#91781C2212yes—
26#91781C2212yes—
27C4⋊C4×D15C2212yes—
28C4⋊C4×D15C2212yes—
29#91776—21no—
30#91770—22no—
31C4×D60—21no—
32C4×Dic30—21no—
33C3×C5×#107C2212yes—
34C3×C5×#106C2212yes—
35#91102C2212yes—
36#91101C2212yes—
37#91092C2211yescharacteristic
38#91092C2211yescharacteristic
39#91091C2211yescharacteristic
40#91091C2212yes—
41#91091C2212yes—
42#91091C2211yescharacteristic
43#79210—51nomaximal, Hall
44C2×#4053—31no—
45#65857—31no—
46#65838—31no—
47C5×#428D311yescharacteristic, complemented
48#65410—31no—
49#65287—31no—
50C2×#3939—31no—
51#65170—32no—
52D5×#107—32no—
53#65150—32no—
54#65149—32no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220D412yes—
58C22×Dic15—21no—
59#6817C2×C414yes—
60#6817Q814yes—
61C2×D60D411yescharacteristic
62C2×C4×D15—22no—
63C2×C4×D15—22no—
64C2×C4×D15C2312yes—
65C2×Dic30D411yescharacteristic
66C3×C5×M16C2×C414yescomplemented
67C2×C3×C5×C8C2312yes—
68C3×C5×C4⋊C4—21no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2312yes—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C22⋊C4—21no—
73C3×C42×C5—21no—
74#6719—21no—
75#6714—22no—
76#6714—22no—
77C4⋊Dic15—21no—
78C4⋊Dic15C2311yescharacteristic
79C4⋊Dic15C2312yes—
80C4⋊Dic15C2311yescharacteristic
81#6712—22no—
82#6712—22no—
83C4×Dic15—21no—
84C4×Dic15—22no—
85C4×Dic15—22no—
86C2×C3⋊#168C2×C414yescomplemented
87C2×C3⋊#168C2311yescharacteristic
88C2×C3⋊#168C2311yescharacteristic
89#6705C2×C418yescomplemented
90C8×D15C2×C418yescomplemented
91C2×#907—51no—
92#5523—51no—
93#5504—51no—
94C3×#428D511yescharacteristic, complemented
95#5121—51no—
96#4998—51no—
97C2×#807—51no—
98#4881—52no—
99D3×#107—52no—
100#4861—52no—
101#4860—52no—
102C2×#709—31no—
103C2×C5×M16C2×D311yescharacteristic
104C5×#117C2×D311yescharacteristic
105C2×C5×C4⋊C4C2×D311yescharacteristic
106C4×C22⋊D5—62no—
107#4072—31no—
108C2×C4⋊Dic5—31no—
109C22×#168—31no—
110#4053—38no—
111C2×#676—32no—
112C2×C8×D5—32no—
113#4039—61no—
114#4038—32no—
115#4038—32no—
116D5×C4⋊C4—32no—
117D5×C4⋊C4—32no—
118#4033—61no—
119#4027—62no—
120C4×D20—61no—
121C4×Dic10—61no—
122C5×#107C2×D312yes—
123C5×#106C2×D312yes—
124#3950—32no—
125#3949—32no—
126#3940—31no—
127#3940—31no—
128#3939—31no—
129#3939—31no—
130#3939—32no—
131#3939—32no—
132#2913—151noSylow
133C23×C3×C5C2×D411yescharacteristic
134C22×D15C2×D412yes—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—81no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×Q812yes—
142C2×C3×C4×C5C2411yescharacteristic
143#1220C4⋊C418yes—
144C2×Dic15—21no—
145C2×Dic15—21no—
146C2×Dic15—22no—
147C2×Dic15—81no—
148C2×Dic15C2×D412yes—
149D60C4⋊C414yes—
150C4×D15—82no—
151C4×D15—82no—
152C4×D15C22×C414yes—
153C4×D15C2×Q814yes—
154Dic30C4⋊C414yes—
155C3×C5×C8C22×C414yes—
156C3⋊#168C22×C412yes—
157C3⋊#168C22×C412yes—
158C2×#235—51no—
159C2×C3×M16C2×D511yescharacteristic
160C3×#117C2×D511yescharacteristic
161C2×C3×C4⋊C4C2×D511yescharacteristic
162C4×#67—102no—
163#926—51no—
164C2×C4⋊Dic3—51no—
165C22×C3⋊C8—51no—
166#907—58no—
167C2×ΓL(1,𝔽25)—52no—
168C2×D3×C8—52no—
169#893—101no—
170#892—52no—
171#892—52no—
172D3×C4⋊C4—52no—
173D3×C4⋊C4—52no—
174#887—101no—
175#67⋊C4—102no—
176C4×D12—101no—
177C4×Dic6—101no—
178C3×#107C2×D512yes—
179C3×#106C2×D512yes—
180#818—52no—
181#817—52no—
182#808—51no—
183#808—51no—
184#807—51no—
185#807—52no—
186#807—52no—
187#807—51no—
188C22×C4×C5—21no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—32no—
191C22×Dic5—61no—
192#709—34no—
193#709—34no—
194C2×D20—31no—
195C2×C4×D5—32no—
196C2×C4×D5—62no—
197C2×C4×D5—62no—
198C2×Dic10—31no—
199C5×M16C4×D314yescomplemented
200C2×C5×C8C22×D312yes—
201C5×C4⋊C4—21no—
202C5×C4⋊C4C22×D312yes—
203C5×C4⋊C4C22×D311yescharacteristic
204C5×C4⋊C4C22×D311yescharacteristic
205C5×C22⋊C4—21no—
206C42×C5—21no—
207C22⋊Dic5—61no—
208#685—62no—
209#685—62no—
210C4⋊Dic5—32no—
211C4⋊Dic5—31no—
212C4⋊Dic5—31no—
213C4⋊Dic5—61no—
214#683—62no—
215#683—62no—
216C4×Dic5—62no—
217C4×Dic5—62no—
218C4×Dic5—61no—
219C2×#168—34no—
220C2×#168—31no—
221C2×#168—31no—
222#676—38no—
223C8×D5—38no—
224C2×#131—151no—
225#520—151no—
226#520—151no—
227#428—151no—
228#428—152no—
229#428—152no—
230#428D1511yescharacteristic, complemented
231#427—151no—
232#427—152no—
233C2×#107—151no—
234C2×#107—152no—
235C22×C3×C5—21no—
236C22×C3×C5—21no—
237C22×C3×C5C2×C4⋊C412yes—
238C22×C3×C5C22×D411yescharacteristic
239C2×D15—22no—
240C2×D15—22no—
241C2×D15C2×C4⋊C414yes—
242C3×C4×C5—41no—
243C3×C4×C5—42no—
244C3×C4×C5—41no—
245C3×C4×C5C2×C4⋊C412yes—
246C3×C4×C5C23×C411yescharacteristic
247C3×C4×C5C22×Q811yescharacteristic
248Dic15—41no—
249Dic15—42no—
250Dic15—41no—
251Dic15C2×C4⋊C414yes—
252C22×C3×C4—21no—
253C22×C3×C4C22×D511yescharacteristic
254C2×#67—52no—
255C22×Dic3—101no—
256#235—54no—
257#235—54no—
258C2×D12—51no—
259C2×C4×D3—52no—
260C2×C4×D3—102no—
261C2×C4×D3—102no—
262C2×Dic6—51no—
263C3×M16C4×D514yescomplemented
264C2×C3×C8C22×D512yes—
265C3×C4⋊C4—21no—
266C3×C4⋊C4C22×D512yes—
267C3×C4⋊C4C22×D511yescharacteristic
268C3×C4⋊C4C22×D511yescharacteristic
269C3×C22⋊C4—21no—
270C3×C42—21no—
271#217—101no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4—102no—
274C4⋊Dic3—52no—
275C4⋊Dic3—51no—
276C4⋊Dic3—51no—
277C4⋊Dic3—101no—
278Dic3⋊C4—102no—
279Dic3⋊C4—102no—
280C4×Dic3—102no—
281C4×Dic3—102no—
282C4×Dic3—101no—
283C2×C3⋊C8—54no—
284C2×C3⋊C8—51no—
285C2×C3⋊C8—51no—
286ΓL(1,𝔽25)—58no—
287D3×C8—58no—
288C23×C5D3×D411yescharacteristic
289C22×D5—32no—
290C2×C4×C5—21no—
291C2×C4×C5—22no—
292C2×C4×C5—21no—
293C2×C4×C5—81no—
294C2×C4×C5C2×C4×D312yes—
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5D3×Q812yes—
297C2×C4×C5C23×D311yescharacteristic
298C22⋊D5—38no—
299C2×Dic5—32no—
300C2×Dic5—61no—
301C2×Dic5—61no—
302C2×Dic5—62no—
303C2×Dic5—241no—
304D20—34no—
305C4×D5—34no—
306C4×D5—34no—
307C4×D5—242no—
308C4×D5—242no—
309Dic10—34no—
310C5×C8C2×C4×D314yes—
311#168—32no—
312#168—32no—
313C2×#41—151no—
314#131—158no—
315C2×M16—152no—
316C2×M16C2×D1511yescharacteristic
317C22×C8—151no—
318C22×C8—152no—
319C4×Q8—301no—
320C4×Q8—301no—
321C4×D4—301no—
322C4×D4—302no—
323C4×D4—301no—
324C4×D4—302no—
325#117—151no—
326#117—152no—
327#117—152no—
328#117C2×D1511yescharacteristic
329C2×C4⋊C4—151no—
330C2×C4⋊C4—152no—
331C2×C4⋊C4—152no—
332C2×C4⋊C4C2×D1511yescharacteristic
333#107—152no—
334#107—151no—
335#107—152no—
336#107—152no—
337#107—151no—
338#107C2×D1512yes—
339#106—152no—
340#106—151no—
341#106—151no—
342#106C2×D1512yes—
343C2×C3×C5—22no—
344C2×C3×C5C22×C4⋊C411yescharacteristic
345C2×C3×C5#57611yescharacteristic
346C2×C3×C5#57811yescharacteristic
347D15—24no—
348C23×C3D4×D511yescharacteristic
349C22×D3—52no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—81no—
354C2×C3×C4C2×C4×D512yes—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4Q8×D512yes—
357C2×C3×C4C23×D511yescharacteristic
358#67—58no—
359C2×Dic3—52no—
360C2×Dic3—101no—
361C2×Dic3—101no—
362C2×Dic3—102no—
363C2×Dic3—401no—
364D12—54no—
365C4×D3—54no—
366C4×D3—54no—
367C4×D3—402no—
368C4×D3—402no—
369Dic6—54no—
370C3×C8C2×C4×D514yes—
371C3⋊C8—52no—
372C3⋊C8—52no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5D3×C4⋊C412yes—
376C22×C5C2×D3×D411yescharacteristic
377C2×D5—34no—
378C2×D5—62no—
379C2×D5—62no—
380C4×C5—41no—
381C4×C5—42no—
382C4×C5—41no—
383C4×C5D3×C4⋊C412yes—
384C4×C5C22×C4×D311yescharacteristic
385C4×C5C2×D3×Q811yescharacteristic
386Dic5—34no—
387Dic5—121no—
388Dic5—122no—
389Dic5—121no—
390#41—154no—
391#41—154no—
392C2×Q8—151no—
393C2×D4—152no—
394C2×D4—151no—
395C22×C4—21no—
396C22×C4—152no—
397C22×C4—302no—
398C22×C4—302no—
399C22×C4—301no—
400C22×C4C22×D1511yescharacteristic
401M16—158no—
402M16C4×D1514yescomplemented
403C2×C8—154no—
404C2×C8—151no—
405C2×C8—151no—
406C2×C8—158no—
407C2×C8C22×D1512yes—
408C4⋊C4—21no—
409C4⋊C4—151no—
410C4⋊C4—152no—
411C4⋊C4—151no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C22×D1511yescharacteristic
416C4⋊C4C22×D1511yescharacteristic
417C4⋊C4C22×D1512yes—
418C22⋊C4—21no—
419C22⋊C4—302no—
420C22⋊C4—302no—
421C22⋊C4—301no—
422C42—21no—
423C42—302no—
424C42—302no—
425C42—301no—
426C3×C5#291311yescharacteristic, complemented, Hall
427C22×C3—21no—
428C22×C3—21no—
429C22×C3D5×C4⋊C412yes—
430C22×C3C2×D4×D511yescharacteristic
431C2×D3—54no—
432C2×D3—102no—
433C2×D3—102no—
434C3×C4—41no—
435C3×C4—42no—
436C3×C4—41no—
437C3×C4D5×C4⋊C412yes—
438C3×C4C22×C4×D511yescharacteristic
439C3×C4C2×Q8×D511yescharacteristic
440Dic3—54no—
441Dic3—201no—
442Dic3—202no—
443Dic3—201no—
444C2×C5—22no—
445C2×C5C2×D3×C4⋊C411yescharacteristic
446C2×C5#577411yescharacteristic
447C2×C5#577911yescharacteristic
448D5—64no—
449C23—152no—
450C23D4×D1511yescharacteristic
451Q8—154no—
452D4—158no—
453D4—154no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—81no—
458C2×C4—152no—
459C2×C4—154no—
460C2×C4—154no—
461C2×C4—301no—
462C2×C4—302no—
463C2×C4—301no—
464C2×C4—1202no—
465C2×C4—1202no—
466C2×C4—1201no—
467C2×C4C2×C4×D1512yes—
468C2×C4D4×D1511yescharacteristic
469C2×C4Q8×D1512yes—
470C2×C4C23×D1511yescharacteristic
471C8—152no—
472C8—152no—
473C8C2×C4×D1514yes—
474C2×C3—22no—
475C2×C3C2×D5×C4⋊C411yescharacteristic
476C2×C3#6610811yescharacteristic
477C2×C3#6611311yescharacteristic
478D3—104no—
479C5#7921011yescharacteristic, complemented, Sylow
480C22—21no—
481C22—21no—
482C22—154no—
483C22—302no—
484C22—302no—
485C22C4⋊C4×D1512yes—
486C22C2×D4×D1511yescharacteristic
487C4—42no—
488C4—41no—
489C4—41no—
490C4—154no—
491C4—601no—
492C4—602no—
493C4—601no—
494C4C4⋊C4×D1512yes—
495C4C22×C4×D1511yescharacteristic
496C4C2×Q8×D1511yescharacteristic
497C3#1061094111yescharacteristic, complemented, Sylow
498C2—22no—
499C2—304no—
500C2C2×C4⋊C4×D1511yescharacteristic
501C2#1175653311yescharacteristic
502C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#428C2
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenter#428D15
hypocenterC3×C5#2913
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
4. C3×C5×#428C2semidirect
5. #11751222C2semidirect
6. #11751099C2semidirect
7. C2×#91091C2semidirect
8. #11750982C2semidirect
9. D15×#107C2semidirect
10. #11750962C2semidirect
11. #11750961C2semidirect
21. #91796C4semidirect
47. C5×#428D3semidirect
66. C3×C5×M16C2×C4semidirect
86. C2×C3⋊#168C2×C4semidirect
89. #6705C2×C4semidirect
90. C8×D15C2×C4semidirect
94. C3×#428D5semidirect
199. C5×M16C4×D3semidirect
230. #428D15semidirect
263. C3×M16C4×D5semidirect
402. M16C4×D15semidirect
426. C3×C5#2913semidirect
479. C5#79210semidirect
497. C3#10610941semidirect

Maximal subgroups

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

subgroupindex
C2×#917962
#117562822
#117562632
C3×C5×#4282
#117512222
#117510992
C2×#910912
#117509822
D15×#1072
#117509622
#117509612
#106109413
#792105