Finite Group Databasebeta

← #14411555

Subgroups — #14411555

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#907C211yesmaximal, characteristic
2Dic5×#235C211yesmaximal, characteristic
3C2×#91288C211yesmaximal, characteristic
4#11751223C211yesmaximal, characteristic, complemented
5C3×M16×Dic5C211yesmaximal, characteristic, complemented
6C2×#90952C211yesmaximal, characteristic, complemented
7#11748326C211yesmaximal, characteristic, complemented
8#11748052C212yesmaximal, complemented
9#11747653C212yesmaximal, complemented
10#11747602C212yesmaximal, complemented
11D3×#3947C212yesmaximal, complemented
12#10615513—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15#91815C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C22×C5×C3⋊C8C2211yescharacteristic
18C5×#907C418yescomplemented
19C2×C5×ΓL(1,𝔽25)C2212yes—
20C2×C5×D3×C8C2212yes—
21C2×C3×C4×Dic5C2211yescharacteristic
22C2×C3×#681C2211yescharacteristic
23Dic5×#67C414yes—
24Dic5×D12C412yes—
25C4×D3×Dic5C2212yes—
26#91371C2212yes—
27Dic5×Dic6C412yes—
28C2×#6650C2212yes—
29#91288C418yescomplemented
30C2×D3×#168C2212yes—
31#91099C2212yes—
32C8×Dic15C2212yes—
33C3×#3947C2212yes—
34C3×C8×Dic5C2212yes—
35#90954C2212yes—
36#90952C2211yescharacteristic
37#90952C2211yescharacteristic
38#90952C2211yescharacteristic
39#90952C2211yescharacteristic
40#90951C2212yes—
41#78516—51nomaximal, Hall
42C2×C5×#131—31no—
43#41×Dic5—31no—
44C2×#4094—31no—
45#65411—32no—
46#65411—31no—
47M16×Dic5—32no—
48M16×Dic5D311yescharacteristic, complemented
49#65390—31no—
50#65390—32no—
51C2×#3947—31no—
52C2×#3947—32no—
53C22×C3×C4×C5C2311yescharacteristic
54C2×C5×#67C2×C412yes—
55C5×#235C2×C414yes—
56C5×#235C2×C414yes—
57C2×C5×D12C2×C411yescharacteristic
58C2×C4×C5×D3C2312yes—
59C2×C5×Dic6C2×C411yescharacteristic
60C22×C3×Dic5C2×C412yes—
61C2×D3×Dic5C2×C414yes—
62C3×C5×M16C2×C414yescomplemented
63C2×C3×C5×C8C2312yes—
64#6719C2×C412yes—
65C4⋊Dic15C2×C412yes—
66C4×Dic15C2312yes—
67C2×C3⋊#168C2×C414yescomplemented
68C2×C3⋊#168C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C2×C5×C3⋊C8C2×C414yescomplemented
71C2×C5×C3⋊C8C2311yescharacteristic
72C2×C5×C3⋊C8C2311yescharacteristic
73C5×ΓL(1,𝔽25)C2×C418yescomplemented
74C5×D3×C8C2×C418yescomplemented
75C3×C4×Dic5C2×C412yes—
76C3×C4×Dic5C2311yescharacteristic
77C3×C4×Dic5C2311yescharacteristic
78C3×#681C2×C414yescomplemented
79C2×C3×#168C2312yes—
80Dic3⋊Dic5C2×C414yes—
81(C2×D3)⋊Dic5C2×C414yes—
82Dic3×Dic5C2×C414yes—
83#6650C2×C418yescomplemented
84D3×#168C2×C418yescomplemented
85C2×#907—51no—
86C2×#907D511yescharacteristic
87C4×#235—51no—
88C3×C4×M16—51no—
89#5122—51no—
90#5122—51no—
91C2×#803—51no—
92#4707—52no—
93D3×#97—52no—
94#4689—52no—
95#4689—52no—
96C2×C5×#41—31no—
97C5×#131—38no—
98C2×C5×M16—32no—
99C2×C5×M16C2×D311yescharacteristic
100C22×C5×C8—31no—
101C22×C5×C8—32no—
102#4094—38no—
103Q8×Dic5—32no—
104D4×Dic5—34no—
105D4×Dic5—32no—
106#4072—31no—
107#4072—32no—
108C2×C4×Dic5—32no—
109C2×C4×Dic5C2×D311yescharacteristic
110C2×#681—32no—
111C2×#681C2×D311yescharacteristic
112C22×#168—31no—
113C22×#168—32no—
114#3947—32no—
115#3947—31no—
116#3947—31no—
117#3947—31no—
118#3947—31no—
119#3947—32no—
120#3947C2×D312yes—
121C8×Dic5—32no—
122C8×Dic5—32no—
123C8×Dic5C2×D312yes—
124#2875—151noSylow
125C23×C3×C5C22×C411yescharacteristic
126C22×C5×D3C22×C412yes—
127C2×C3×C4×C5C22×C411yescharacteristic
128C2×C3×C4×C5C22×C412yes—
129C2×C3×C4×C5C22×C412yes—
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15C22×C414yes—
132C5×#67C4218yes—
133C2×C5×Dic3C22×C412yes—
134C5×D12C4214yes—
135C4×C5×D3C22×C414yes—
136C4×C5×D3C22×C414yes—
137C5×Dic6C4214yes—
138C2×C3×Dic5—42no—
139C2×C3×Dic5C22×C412yes—
140C2×C3×Dic5C22×C412yes—
141D3×Dic5—44no—
142C3×C5×C8C22×C414yes—
143C3⋊#168C22×C412yes—
144C3⋊#168C22×C412yes—
145C3×#168C22×C414yes—
146C5×C3⋊C8C22×C412yes—
147C5×C3⋊C8C22×C412yes—
148C2×#235C2×D511yescharacteristic
149C2×C3×M16—51no—
150C2×C3×M16C2×D511yescharacteristic
151C2×C3×C42—51no—
152C4×#67—54no—
153#926—51no—
154C22×C3⋊C8—51no—
155C22×C3⋊C8C2×D511yescharacteristic
156#907—58no—
157#907Dic518yescomplemented
158C2×ΓL(1,𝔽25)—52no—
159C2×ΓL(1,𝔽25)C2×D512yes—
160C2×D3×C8—52no—
161C2×D3×C8C2×D512yes—
162C4×D12—52no—
163#872—52no—
164C42×D3—52no—
165C4×Dic6—52no—
166C3×#97—52no—
167C3×C4×C8—52no—
168#815—52no—
169#815—52no—
170C8×Dic3—52no—
171C8×Dic3—52no—
172#803—51no—
173#803—51no—
174#803—51no—
175#803—51no—
176C5×#41—34no—
177C5×#41—34no—
178C2×C5×Q8—31no—
179C2×C5×D4—32no—
180C2×C5×D4—31no—
181C22×C4×C5—32no—
182C22×C4×C5C22×D311yescharacteristic
183C22×Dic5—34no—
184C22×Dic5C4×D312yes—
185C5×M16—38no—
186C5×M16C4×D314yescomplemented
187C2×C5×C8—34no—
188C2×C5×C8—31no—
189C2×C5×C8—31no—
190C2×C5×C8—38no—
191C2×C5×C8C22×D312yes—
192C22⋊Dic5—32no—
193C22⋊Dic5—34no—
194C4⋊Dic5—32no—
195C4⋊Dic5—34no—
196C4×Dic5—32no—
197C4×Dic5—34no—
198C4×Dic5C4×D312yes—
199C4×Dic5C22×D311yescharacteristic
200C4×Dic5C22×D311yescharacteristic
201#681—38no—
202#681C4×D314yescomplemented
203C2×#168—34no—
204C2×#168—31no—
205C2×#168—31no—
206C2×#168—38no—
207C2×#168C22×D312yes—
208C2×#131—31no—
209C2×#131—151no—
210C4×#41—151no—
211#405—152no—
212#405—152no—
213#405—151no—
214#405—151no—
215C4×M16—51no—
216C4×M16—152no—
217C2×#97—152no—
218C2×#97—151no—
219C22×C3×C5—22no—
220C22×C3×C5C2×C4212yes—
221C22×C3×C5C23×C411yescharacteristic
222C2×C5×D3—24no—
223C2×C5×D3C2×C4214yes—
224C3×C4×C5C2×C4212yes—
225C3×C4×C5C23×C411yescharacteristic
226C3×C4×C5C23×C411yescharacteristic
227Dic15—24no—
228C3×Dic5—22no—
229C3×Dic5—22no—
230C5×Dic3C2×C4214yes—
231C22×C3×C4—52no—
232C22×C3×C4C22×D511yescharacteristic
233C2×#67C4×D512yes—
234#235C4×D514yes—
235#235C2×Dic514yes—
236C2×D12C4×D511yescharacteristic
237C2×C4×D3—54no—
238C2×C4×D3C22×D512yes—
239C2×Dic6C4×D511yescharacteristic
240C3×M16—54no—
241C3×M16C2×Dic514yescomplemented
242C2×C3×C8—52no—
243C2×C3×C8C22×D512yes—
244C3×C42—52no—
245C3×C42—51no—
246C3×C42—51no—
247#217—52no—
248(C2×D3)⋊C4—54no—
249C4⋊Dic3—52no—
250Dic3⋊C4—54no—
251C4×Dic3—52no—
252C4×Dic3—54no—
253C2×C3⋊C8—54no—
254C2×C3⋊C8—51no—
255C2×C3⋊C8—51no—
256C2×C3⋊C8C2×Dic514yescomplemented
257C2×C3⋊C8C22×D511yescharacteristic
258C2×C3⋊C8C22×D511yescharacteristic
259ΓL(1,𝔽25)—58no—
260ΓL(1,𝔽25)C2×Dic518yescomplemented
261D3×C8—58no—
262D3×C8C2×Dic518yescomplemented
263C23×C5—32no—
264C23×C5C2×C4×D311yescharacteristic
265C5×Q8—34no—
266C5×D4—38no—
267C5×D4—34no—
268C2×C4×C5—32no—
269C2×C4×C5—34no—
270C2×C4×C5—34no—
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×C4×C5C2×C4×D312yes—
273C2×C4×C5C2×C4×D312yes—
274C2×C4×C5C23×D311yescharacteristic
275C2×Dic5—34no—
276C2×Dic5—42no—
277C2×Dic5—124no—
278C2×Dic5C2×C4×D312yes—
279C2×Dic5C2×C4×D312yes—
280C5×C8—32no—
281C5×C8—32no—
282C5×C8C2×C4×D314yes—
283#168—32no—
284#168—32no—
285#168C2×C4×D314yes—
286C2×#41—31no—
287#131—38no—
288#131—158no—
289C2×M16—32no—
290C2×M16—51no—
291C2×M16—152no—
292C2×M16D3×D511yescharacteristic
293C22×C8—31no—
294C22×C8—32no—
295C22×C8—152no—
296C22×C8—151no—
297C4×Q8—152no—
298C4×D4—152no—
299C4×D4—154no—
300#117—152no—
301#117—151no—
302C2×C42—51no—
303C2×C42—152no—
304#97—52no—
305#97—151no—
306#97—151no—
307#97—151no—
308#97—151no—
309#97—152no—
310#97—152no—
311C4×C8—52no—
312C4×C8—152no—
313C4×C8—152no—
314C2×C3×C5—22no—
315C2×C3×C5C22×C4211yescharacteristic
316C2×C3×C5#56812yes—
317C5×D3—24no—
318C23×C3C2×C4×D511yescharacteristic
319C22×D3C2×C4×D512yes—
320C2×C3×C4—52no—
321C2×C3×C4—52no—
322C2×C3×C4—202no—
323C2×C3×C4C2×C4×D512yes—
324C2×C3×C4C2×C4×D511yescharacteristic
325C2×C3×C4C22×Dic512yes—
326C2×C3×C4C23×D511yescharacteristic
327#67C4×Dic518yes—
328C2×Dic3—54no—
329C2×Dic3C2×C4×D512yes—
330D12C4×Dic514yes—
331C4×D3—204no—
332C4×D3C2×C4×D514yes—
333C4×D3C22×Dic514yes—
334Dic6C4×Dic514yes—
335C3×C8—54no—
336C3×C8C22×Dic514yes—
337C3⋊C8—52no—
338C3⋊C8—52no—
339C3⋊C8C22×Dic512yes—
340C3⋊C8C22×Dic512yes—
341C22×C5—22no—
342C22×C5—34no—
343C22×C5—64no—
344C22×C5C42×D312yes—
345C22×C5C22×C4×D311yescharacteristic
346C4×C5—34no—
347C4×C5C42×D312yes—
348C4×C5C22×C4×D311yescharacteristic
349C4×C5C22×C4×D311yescharacteristic
350Dic5—22no—
351Dic5—22no—
352Dic5—64no—
353#41—34no—
354#41—34no—
355C2×Q8—31no—
356C2×D4—32no—
357C2×D4—31no—
358C22×C4—32no—
359C22×C4—52no—
360C22×C4—154no—
361C22×C4C2×D3×D511yescharacteristic
362M16—38no—
363M16—54no—
364M16—158no—
365M16D3×Dic514yescomplemented
366C2×C8—34no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—38no—
370C2×C8—52no—
371C2×C8—158no—
372C2×C8—154no—
373C2×C8—151no—
374C2×C8—151no—
375C2×C8C2×D3×D512yes—
376C4⋊C4—154no—
377C4⋊C4—152no—
378C22⋊C4—154no—
379C22⋊C4—152no—
380C42—52no—
381C42—51no—
382C42—51no—
383C42—154no—
384C42—152no—
385C3×C5#287511yescharacteristic, complemented, Hall
386C22×C3—22no—
387C22×C3C2×C4×Dic512yes—
388C22×C3C22×C4×D511yescharacteristic
389C2×D3—24no—
390C2×D3C2×C4×Dic514yes—
391C3×C4—102no—
392C3×C4—102no—
393C3×C4C2×C4×Dic512yes—
394C3×C4C22×C4×D511yescharacteristic
395C3×C4C23×Dic511yescharacteristic
396Dic3—104no—
397Dic3C2×C4×Dic514yes—
398C2×C5—22no—
399C2×C5—64no—
400C2×C5C2×C42×D311yescharacteristic
401C2×C5#574512yes—
402C23—32no—
403C23C4×D3×D511yescharacteristic
404Q8—34no—
405D4—38no—
406D4—34no—
407C2×C4—32no—
408C2×C4—34no—
409C2×C4—34no—
410C2×C4—52no—
411C2×C4—52no—
412C2×C4—154no—
413C2×C4—202no—
414C2×C4—604no—
415C2×C4C4×D3×D511yescharacteristic
416C2×C4C4×D3×D512yes—
417C2×C4C2×D3×Dic512yes—
418C2×C4C22×D3×D511yescharacteristic
419C8—32no—
420C8—32no—
421C8—54no—
422C8—152no—
423C8—152no—
424C8C2×D3×Dic514yes—
425C2×C3—22no—
426C2×C3#6608412yes—
427C2×C3C22×C4×Dic511yescharacteristic
428D3—24no—
429C5#7851611yescharacteristic, complemented, Sylow
430C22—22no—
431C22—34no—
432C22—64no—
433C22C4×D3×Dic512yes—
434C22C2×C4×D3×D511yescharacteristic
435C4—34no—
436C4—102no—
437C4—102no—
438C4—304no—
439C4C4×D3×Dic512yes—
440C4C2×C4×D3×D511yescharacteristic
441C4C22×D3×Dic511yescharacteristic
442C3#1061551311yescharacteristic, complemented, Sylow
443C2—22no—
444C2—64no—
445C2#1175401412yes—
446C2C2×C4×D3×Dic511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC2×C3×C5×M16C22
socleC22×C3×C5C23×C4
prime radicalC2×C5×#235C22
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2875
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #11751223C2semidirect
5. C3×M16×Dic5C2semidirect
6. C2×#90952C2semidirect
7. #11748326C2semidirect
8. #11748052C2semidirect
9. #11747653C2semidirect
10. #11747602C2semidirect
11. D3×#3947C2semidirect
18. C5×#907C4semidirect
29. #91288C4semidirect
48. M16×Dic5D3semidirect
62. C3×C5×M16C2×C4semidirect
67. C2×C3⋊#168C2×C4semidirect
70. C2×C5×C3⋊C8C2×C4semidirect
73. C5×ΓL(1,𝔽25)C2×C4semidirect
74. C5×D3×C8C2×C4semidirect
78. C3×#681C2×C4semidirect
83. #6650C2×C4semidirect
84. D3×#168C2×C4semidirect
157. #907Dic5semidirect
186. C5×M16C4×D3semidirect
202. #681C4×D3semidirect
241. C3×M16C2×Dic5semidirect
256. C2×C3⋊C8C2×Dic5semidirect
260. ΓL(1,𝔽25)C2×Dic5semidirect
262. D3×C8C2×Dic5semidirect
365. M16D3×Dic5semidirect
385. C3×C5#2875semidirect
429. C5#78516semidirect
442. C3#10615513semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9072
Dic5×#2352
C2×#912882
#117512232
C3×M16×Dic52
C2×#909522
#117483262
#117480522
#117476532
#117476022
D3×#39472
#106155133
#785165