Finite Group Databasebeta

← #14417658

Subgroups — #14417658

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91275C211yesmaximal, characteristic
2#11752527C212yesmaximal, complemented
3C4×D120C211yesmaximal, characteristic, complemented
4C5×#4689C211yesmaximal, characteristic, complemented
5C3×C4×Dic20C211yesmaximal, characteristic, complemented
6Dic3×Dic20C211yesmaximal, characteristic, complemented
7#11747793C211yesmaximal, characteristic, complemented
8#11747743C212yesmaximal, complemented
9D3×#3950C211yesmaximal, characteristic, complemented
10#11747608C212yesmaximal, complemented
11#11747054C212yesmaximal, complemented
12#10610293—31nomaximal, Hall
13C2×#6769C2212yes—
14C2×D120C2211yescharacteristic
15C4×D60C2212yes—
16C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
17C2×C5×D3×C8C2211yescharacteristic
18C5×#872C2211yescharacteristic
19C2×C3×Dic20C2211yescharacteristic
20C3×C4×Dic10C2212yes—
21#91428C2212yes—
22D3×C4⋊Dic5C2212yes—
23#91406—22no—
24#91405—22no—
25#91404—22no—
26#91402—22no—
27Dic3×Dic10C2212yes—
28C2×#6658C2212yes—
29#91275C418yescomplemented
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2212yes—
32#91102C2211yescharacteristic
33C5×#815C2211yescharacteristic
34C5×C8×Dic3C2211yescharacteristic
35C5×#803C2211yescharacteristic
36C3×#3950C2211yescharacteristic
37C3×#3948C2212yes—
38#90990C2212yes—
39#90971C2212yes—
40#90968C2212yes—
41#79721—51nomaximal, Hall
42C2×#4050—31no—
43#65857—32no—
44C5×#405—31no—
45#65422—32no—
46C2×#3950—31no—
47#64999—32no—
48#64999—32no—
49C4×Dic20—31no—
50C4×Dic20D311yescharacteristic, complemented
51C4×D40—31no—
52C4×D40—31no—
53C2×D60C2312yes—
54C2×C4×D15—22no—
55C2×C4×C5×D3C2311yescharacteristic
56C2×C3×Dic10C2312yes—
57C2×#1203—22no—
58C2×#1200—22no—
59C2×#1200—22no—
60C2×D3×Dic5—22no—
61#6769—24no—
62#6769C2×C418yescomplemented
63C2×C3×C5×C8C2311yescharacteristic
64C2×C3×C5×C8C2311yescharacteristic
65C3×C42×C5C2311yescharacteristic
66#6714—22no—
67C4⋊Dic15C2312yes—
68D120C2×C414yescomplemented
69C5×(C2×D3)⋊C4D411yescharacteristic
70C5×(C2×D3)⋊C4D411yescharacteristic
71C5×Dic3⋊C4D411yescharacteristic
72C5×Dic3⋊C4D411yescharacteristic
73C4×C5×Dic3C2311yescharacteristic
74C2×C5×C3⋊C8C2311yescharacteristic
75C2×C5×C3⋊C8C2311yescharacteristic
76C5×ΓL(1,𝔽25)—22no—
77C5×D3×C8C2×C414yescomplemented
78C3×C4⋊Dic5C2312yes—
79C3×#683—22no—
80C3×C4×Dic5—22no—
81C3×Dic20C2×C414yescomplemented
82Dic3⋊Dic5—22no—
83#6668—22no—
84#6667—22no—
85Dic3×Dic5—22no—
86#6658C2×C418yescomplemented
87C2×#919—51no—
88#5574—52no—
89C3×C4×Q16—51no—
90Dic3×Q16—51no—
91#5026—52no—
92D3×#107—51no—
93#4872—51no—
94#4817—52no—
95#4803—52no—
96C4×D24—51no—
97#4689D511yescharacteristic, complemented
98C2×#709—32no—
99C2×C5×M16—31no—
100C22×C5×C8—31no—
101C5×#117—31no—
102C2×C4⋊Dic5—32no—
103C2×Dic20C2×D311yescharacteristic
104#4050—38no—
105C2×D40—31no—
106C2×#677—32no—
107#4038—62no—
108D5×C4⋊C4—62no—
109#4027—62no—
110#4027—62no—
111C4×D20—32no—
112C4×D20—32no—
113C4×Dic10—32no—
114C4×Dic10C2×D312yes—
115C5×#97—31no—
116C5×#97—31no—
117C4×C5×C8—31no—
118C4×C5×C8C2×D311yescharacteristic
119#3953—32no—
120#3953—32no—
121#3950—31no—
122#3950—32no—
123#3950C2×D311yescharacteristic
124#3948—32no—
125#3948C2×D312yes—
126#2951—151noSylow
127C22×D15—22no—
128C22×C5×D3C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133D60—22no—
134D60C22×C414yes—
135C4×D15—82no—
136C2×C5×Dic3C2×D411yescharacteristic
137C2×C5×Dic3C2×D411yescharacteristic
138C2×C5×Dic3C2×D411yescharacteristic
139C4×C5×D3C22×C412yes—
140C4×C5×D3#4112yes—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—22no—
143C3×Dic10—22no—
144C3×Dic10C22×C414yes—
145#1203—28no—
146#1200—28no—
147#1200—82no—
148D3×Dic5—82no—
149C3×C5×C8—21no—
150C3×C5×C8C22×C412yes—
151C5×C3⋊C8—21no—
152C5×C3⋊C8C22×C412yes—
153C2×#239—52no—
154C2×C3×Q16—51no—
155C3×C4×Q8—52no—
156Q8×Dic3—52no—
157C2×#215—52no—
158#919—58no—
159C2×D24—51no—
160C2×ΓL(1,𝔽25)C2×D511yescharacteristic
161C2×D3×C8C2×D511yescharacteristic
162#893—52no—
163#893—102no—
164D3×C4⋊C4—52no—
165D3×C4⋊C4—102no—
166C4×D12—52no—
167C4×D12—102no—
168#872—102no—
169#872C2×D511yescharacteristic
170C3×#107—51no—
171C3×#103—52no—
172C3×C4×C8C2×D511yescharacteristic
173#835—52no—
174#821—52no—
175#818—51no—
176#815C2×D511yescharacteristic
177C8×Dic3C2×D511yescharacteristic
178#809—52no—
179#807—52no—
180#803C2×D511yescharacteristic
181C22×C4×C5—31no—
182C2×C22⋊D5—62no—
183C22×Dic5—62no—
184#709—38no—
185#709—64no—
186C2×D20—32no—
187C2×C4×D5—62no—
188C2×C4×D5—62no—
189C2×C4×D5—62no—
190C2×Dic10C22×D312yes—
191C5×M16—62no—
192C2×C5×C8—31no—
193C2×C5×C8—34no—
194C2×C5×C8—31no—
195C2×C5×C8C22×D311yescharacteristic
196C2×C5×C8C22×D311yescharacteristic
197C5×C4⋊C4—31no—
198C5×C4⋊C4—31no—
199C5×C22⋊C4—31no—
200C5×C22⋊C4—31no—
201C42×C5—31no—
202C42×C5C22×D311yescharacteristic
203#685—62no—
204#685—62no—
205C4⋊Dic5—32no—
206C4⋊Dic5—62no—
207C4⋊Dic5C22×D312yes—
208#683—22no—
209#683—62no—
210C4×Dic5—22no—
211C4×Dic5—62no—
212Dic20C4×D314yescomplemented
213D40—34no—
214#677—38no—
215C2×#135—151no—
216#520—152no—
217#440—152no—
218#440—152no—
219C4×Q16—51no—
220C4×Q16—151no—
221C4×D8—151no—
222C4×D8—151no—
223C2×#107—151no—
224#417—152no—
225#405—31no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—24no—
228C2×D15—42no—
229C2×D15—42no—
230C2×C5×D3—21no—
231C2×C5×D3—21no—
232C2×C5×D3C4×D412yes—
233C3×C4×C5—21no—
234C3×C4×C5—21no—
235C3×C4×C5C23×C411yescharacteristic
236C3×C4×C5C2×#4111yescharacteristic
237Dic15—42no—
238C3×Dic5—24no—
239C3×Dic5—42no—
240C5×Dic3—21no—
241C5×Dic3—21no—
242C5×Dic3C4×D412yes—
243C2×C3×Q8—52no—
244#239—58no—
245#239—104no—
246C2×D12—52no—
247C2×D12—102no—
248C2×C4×D3—102no—
249C2×C4×D3—102no—
250C2×C4×D3—102no—
251C2×C4×D3—102no—
252C2×C4×D3C22×D511yescharacteristic
253C3×Q16—54no—
254C2×C3×C8C22×D511yescharacteristic
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4—52no—
257C3×C4⋊C4—102no—
258C3×C42—102no—
259C3×C42C22×D511yescharacteristic
260#215—58no—
261(C2×D3)⋊C4—102no—
262(C2×D3)⋊C4—102no—
263(C2×D3)⋊C4D2011yescharacteristic
264(C2×D3)⋊C4D2011yescharacteristic
265C4⋊Dic3—52no—
266C4⋊Dic3—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4D2011yescharacteristic
269Dic3⋊C4D2011yescharacteristic
270C4×Dic3—102no—
271C4×Dic3C22×D511yescharacteristic
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D511yescharacteristic
274D24—54no—
275ΓL(1,𝔽25)—22no—
276D3×C8C4×D514yescomplemented
277C23×C5—31no—
278C22×D5—62no—
279C2×C4×C5—31no—
280C2×C4×C5—32no—
281C2×C4×C5—32no—
282C2×C4×C5—31no—
283C2×C4×C5—31no—
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5C23×D311yescharacteristic
287C22⋊D5—68no—
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—62no—
291C2×Dic5—242no—
292D20—34no—
293D20—62no—
294C4×D5—68no—
295C4×D5—242no—
296C4×D5—242no—
297Dic10—22no—
298Dic10C2×C4×D314yes—
299C5×C8—21no—
300C5×C8—32no—
301C5×C8—61no—
302C5×C8C2×C4×D312yes—
303C2×#41—152no—
304#135—158no—
305C2×Q16—51no—
306C2×SD16—152no—
307C2×D8—151no—
308C2×M16—31no—
309C22×C8—31no—
310C4×Q8—52no—
311C4×Q8—152no—
312C4×D4—152no—
313C4×D4—152no—
314C4×D4—302no—
315C4×D4—302no—
316#117—31no—
317#117—302no—
318C2×C4⋊C4—152no—
319C2×C4⋊C4—302no—
320#107—51no—
321#107—152no—
322#107—151no—
323#103—52no—
324#103—152no—
325#102—152no—
326#102—152no—
327#97—31no—
328#97—31no—
329C4×C8—31no—
330C4×C8D3×D511yescharacteristic
331C2×C3×C5C2×C4×D411yescharacteristic
332C2×C3×C5#57611yescharacteristic
333C2×C3×C5#57811yescharacteristic
334D15—44no—
335C5×D3—22no—
336C22×D3—102no—
337C22×D3C2×D2011yescharacteristic
338C3×Q8—54no—
339C3×Q8—102no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4C2×D2011yescharacteristic
343C2×C3×C4C2×D2011yescharacteristic
344C2×C3×C4C23×D511yescharacteristic
345C2×Dic3—102no—
346C2×Dic3C2×D2011yescharacteristic
347C2×Dic3C2×D2011yescharacteristic
348C2×Dic3C2×D2011yescharacteristic
349D12—54no—
350D12—108no—
351D12—102no—
352C4×D3—108no—
353C4×D3—402no—
354C4×D3—402no—
355C4×D3—402no—
356C4×D3C2×C4×D512yes—
357C4×D3#70912yes—
358C3×C8—21no—
359C3×C8C2×C4×D512yes—
360C3⋊C8—21no—
361C3⋊C8C2×C4×D512yes—
362C22×C5—32no—
363C22×C5—61no—
364C22×C5—61no—
365C22×C5C2×D3×D411yescharacteristic
366C2×D5—64no—
367C2×D5—122no—
368C2×D5—122no—
369C4×C5—21no—
370C4×C5—21no—
371C4×C5—32no—
372C4×C5—61no—
373C4×C5—61no—
374C4×C5C22×C4×D311yescharacteristic
375C4×C5D3×#4111yescharacteristic
376Dic5—24no—
377Dic5—42no—
378Dic5—122no—
379#41—158no—
380#41—304no—
381C2×Q8—52no—
382C2×D4—152no—
383C2×D4—302no—
384C22×C4—31no—
385C22×C4—302no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—302no—
389Q16—54no—
390SD16—158no—
391D8—154no—
392M16—62no—
393C2×C8—31no—
394C2×C8—34no—
395C2×C8—31no—
396C2×C8C2×D3×D511yescharacteristic
397C2×C8C2×D3×D511yescharacteristic
398C4⋊C4—31no—
399C4⋊C4—31no—
400C4⋊C4—52no—
401C4⋊C4—102no—
402C4⋊C4—152no—
403C4⋊C4—302no—
404C4⋊C4—302no—
405C22⋊C4—31no—
406C22⋊C4—31no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—31no—
410C42—102no—
411C42—302no—
412C42C2×D3×D511yescharacteristic
413C3×C5#295111yescharacteristic, complemented, Hall
414C22×C3C22×D2011yescharacteristic
415C2×D3—21no—
416C2×D3—21no—
417C2×D3—104no—
418C2×D3—202no—
419C2×D3—202no—
420C2×D3C4×D2012yes—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—104no—
424C3×C4—202no—
425C3×C4C22×C4×D511yescharacteristic
426C3×C4C2×#70911yescharacteristic
427Dic3—21no—
428Dic3—21no—
429Dic3—202no—
430Dic3C4×D2012yes—
431C2×C5—62no—
432C2×C5C4×D3×D411yescharacteristic
433C2×C5#576611yescharacteristic
434C2×C5#576911yescharacteristic
435D5—124no—
436C23—31no—
437C23—302no—
438Q8—54no—
439Q8—102no—
440D4—154no—
441D4—308no—
442D4—302no—
443C2×C4—31no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—31no—
447C2×C4—31no—
448C2×C4—102no—
449C2×C4—102no—
450C2×C4—308no—
451C2×C4—302no—
452C2×C4—1202no—
453C2×C4—1202no—
454C2×C4—1202no—
455C2×C4D3×D2011yescharacteristic
456C2×C4D3×D2011yescharacteristic
457C2×C4C22×D3×D511yescharacteristic
458C8—21no—
459C8—32no—
460C8—61no—
461C8C4×D3×D512yes—
462C2×C3C2×C4×D2011yescharacteristic
463C2×C3#6608611yescharacteristic
464C2×C3#6608711yescharacteristic
465D3—22no—
466D3—204no—
467C5#7972111yescharacteristic, complemented, Sylow
468C22—32no—
469C22—61no—
470C22—61no—
471C22—304no—
472C22—602no—
473C22—602no—
474C22C2×D3×D2011yescharacteristic
475C4—21no—
476C4—21no—
477C4—32no—
478C4—61no—
479C4—61no—
480C4—104no—
481C4—202no—
482C4—602no—
483C4C2×C4×D3×D511yescharacteristic
484C4D3×#70911yescharacteristic
485C3#1061029311yescharacteristic, complemented, Sylow
486C2—62no—
487C2—604no—
488C2C4×D3×D2011yescharacteristic
489C2#1175397311yescharacteristic
490C2#1175399111yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91275C2
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5#2951
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #11752527C2semidirect
3. C4×D120C2semidirect
4. C5×#4689C2semidirect
5. C3×C4×Dic20C2semidirect
6. Dic3×Dic20C2semidirect
7. #11747793C2semidirect
8. #11747743C2semidirect
9. D3×#3950C2semidirect
10. #11747608C2semidirect
11. #11747054C2semidirect
29. #91275C4semidirect
50. C4×Dic20D3semidirect
62. #6769C2×C4semidirect
68. D120C2×C4semidirect
77. C5×D3×C8C2×C4semidirect
81. C3×Dic20C2×C4semidirect
86. #6658C2×C4semidirect
97. #4689D5semidirect
212. Dic20C4×D3semidirect
276. D3×C8C4×D5semidirect
413. C3×C5#2951semidirect
467. C5#79721semidirect
485. C3#10610293semidirect

Maximal subgroups

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

subgroupindex
C2×#912752
#117525272
C4×D1202
C5×#46892
C3×C4×Dic202
Dic3×Dic202
#117477932
#117477432
D3×#39502
#117476082
#117470542
#106102933
#797215