Finite Group Databasebeta

← #14411514

Subgroups — #14411514

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91916C211yesmaximal, characteristic
2C2×#91914C211yesmaximal, characteristic
3#11753403C211yesmaximal, characteristic
4#11752360C211yesmaximal, characteristic, complemented
5C3×#65701C211yesmaximal, characteristic, complemented
6#11751874C212yesmaximal, complemented
7#11751872C212yesmaximal, complemented
8C4×#6738C212yesmaximal, complemented
9Dic3×#700C211yesmaximal, characteristic, complemented
10Dic3×D5⋊C8C211yesmaximal, characteristic, complemented
11#11751756C212yesmaximal, complemented
12C4×#4133—31nomaximal, Hall
13C2×#6773C2211yescharacteristic
14C2×#6758C2211yescharacteristic
15C2×D5⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#700C2211yescharacteristic
17C2×C3×D5⋊C8C2211yescharacteristic
18C2×#6740C2212yes—
19C2×#6740C2212yes—
20C2×#6738C2212yes—
21C2×#6738C2212yes—
22#91916C418yescomplemented
23#91914C418yescomplemented
24#91782C411yescharacteristic
25C5×#887C411yescharacteristic
26C3×#4038C2211yescharacteristic
27#91428C411yescharacteristic
28#91402C2212yes—
29C4×#1200C2212yes—
30#91396C412yes—
31#91395C412yes—
32C4×D5×Dic3C2211yescharacteristic
33#91344C411yescharacteristic
34#91231C2212yes—
35C4×C3⋊#170C2212yes—
36C3×#4002C2212yes—
37C3×C4×#170C2212yes—
38#91169C2212yes—
39Dic3×#170C2211yescharacteristic
40Dic3×#170C2212yes—
41Dic3×#170C2211yescharacteristic
42Dic3×#170C2211yescharacteristic
43Dic3×#170C2211yescharacteristic
44#78549—51nomaximal, Hall
45C2×#4133—31no—
46C2×#4133—31no—
47C4×#713—31no—
48#65701—31no—
49#65701—32no—
50#65701—32no—
51#65701D311yescharacteristic, complemented
52C4×#700—32no—
53C4×#700—31no—
54C4×D5⋊C8—32no—
55C4×D5⋊C8—31no—
56C2×D60C2×C411yescharacteristic
57C2×C4×D15C2×C412yes—
58C2×C5×Dic6C2×C411yescharacteristic
59C2×C3×C4×D5C2311yescharacteristic
60C2×#1202C2×C412yes—
61C2×#1200C2×C412yes—
62C2×#1200C2312yes—
63C2×D5×Dic3C2×C411yescharacteristic
64C2×D5×Dic3C2×C411yescharacteristic
65#6773C2×C414yes—
66#6773C2×C414yes—
67C2×C3⋊#170C2311yescharacteristic
68C2×C3⋊#170C2312yes—
69C2×C3⋊#170C2311yescharacteristic
70#6758C2×C414yescomplemented
71D5⋊(C3⋊C8)C2×C414yescomplemented
72C2×C3×#170C2311yescharacteristic
73C2×C3×#170C2312yes—
74C2×C3×#170C2311yescharacteristic
75C3×#700C2×C414yescomplemented
76C3×D5⋊C8C2×C414yescomplemented
77#6740C2×C418yescomplemented
78#6740C2×C418yescomplemented
79#6738C2×C418yescomplemented
80#6738C2×C418yescomplemented
81C3×C5×C4⋊C4C2×C411yescharacteristic
82#6714C2×C412yes—
83C4×Dic15C2×C411yescharacteristic
84C5×Dic3⋊C4C2×C412yes—
85C4×C5×Dic3C2×C412yes—
86C4×C5×Dic3C2×C411yescharacteristic
87C3×#685C2×C412yes—
88C3×C4⋊Dic5C2×C411yescharacteristic
89C3×C4×Dic5C2312yes—
90Dic3⋊Dic5C2×C412yes—
91#6667C2×C412yes—
92Dic3×Dic5C2×C412yes—
93Dic3×Dic5C2311yescharacteristic
94Dic3×Dic5C2311yescharacteristic
95C2×#907—51no—
96C2×#901—51no—
97#5522—51no—
98C3×#405—51no—
99Dic3×M16—51no—
100C2×C8×Dic3—51no—
101#4997—51no—
102#4708—52no—
103#4707—52no—
104#4689—52no—
105C4×D3×C8—52no—
106C2×#713—31no—
107#4133—38no—
108#4133—38no—
109C2×#700—31no—
110C2×#700—32no—
111C2×#700—32no—
112C2×#700C2×D311yescharacteristic
113C2×D5⋊C8—31no—
114C2×D5⋊C8—32no—
115C2×D5⋊C8—32no—
116C2×D5⋊C8C2×D311yescharacteristic
117C4×C5×Q8—31no—
118Q8×Dic5—31no—
119#4039—31no—
120#4039—32no—
121#4038—32no—
122#4038C2×D311yescharacteristic
123C4×D20—32no—
124C4×D20—31no—
125C42×D5—31no—
126C42×D5—32no—
127#4002—32no—
128#4002—32no—
129#4002C2×D312yes—
130C4×#170—31no—
131C4×#170—32no—
132C4×#170—31no—
133C4×#170—31no—
134C4×#170—31no—
135C4×#170—32no—
136C4×#170C2×D312yes—
137C4×#131—151noSylow
138C22×D15C22×C412yes—
139C22×C3×D5C22×C411yescharacteristic
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C22×C411yescharacteristic
142C2×Dic15C22×C411yescharacteristic
143C2×Dic15C22×C411yescharacteristic
144D60C4214yes—
145C4×D15—24no—
146C2×C5×Dic3C22×C411yescharacteristic
147C2×C5×Dic3C22×C412yes—
148C2×C5×Dic3C22×C411yescharacteristic
149C5×Dic6C4214yes—
150C2×C3×Dic5C22×C412yes—
151C2×C3×Dic5C2411yescharacteristic
152C3×C4×D5C22×C412yes—
153C3×C4×D5C22×C412yes—
154#1202C4218yes—
155#1200—24no—
156#1200C22×C414yes—
157#1200C22×C414yes—
158D5×Dic3—22no—
159D5×Dic3—22no—
160C3⋊#170C22×C412yes—
161C3⋊#170C22×C414yes—
162C3⋊#170C22×C412yes—
163C3×#170C22×C412yes—
164C3×#170C22×C414yes—
165C3×#170C22×C412yes—
166C2×#235—51no—
167C2×C3×M16—51no—
168C22×C3×C8—51no—
169C3×#117—51no—
170C2×C4×Dic3—51no—
171C2×#208—51no—
172C22×C3⋊C8—51no—
173#907—58no—
174#901—58no—
175C2×ΓL(1,𝔽25)—52no—
176C2×ΓL(1,𝔽25)—52no—
177C2×D3×C8—52no—
178C2×D3×C8—52no—
179#893—51no—
180#893—51no—
181#887—51no—
182#887AGL(1,𝔽5)11yescharacteristic
183#67⋊C4—52no—
184#67⋊C4—52no—
185#872—52no—
186C42×D3—52no—
187C3×#97—52no—
188C3×C4×C8—52no—
189#815—52no—
190C8×Dic3—51no—
191C8×Dic3—52no—
192C8×Dic3—51no—
193C8×Dic3—51no—
194C8×Dic3—51no—
195#803—52no—
196C4×C3⋊C8—52no—
197C2×C5×Q8—31no—
198#713—34no—
199#713—34no—
200C2×D20—32no—
201C2×D20—31no—
202C2×C4×D5—32no—
203C2×C4×D5—31no—
204C2×C4×D5—31no—
205C2×C4×D5—32no—
206C2×C4×D5—32no—
207C2×C4×D5C22×D311yescharacteristic
208C2×#170—31no—
209C2×#170—31no—
210C2×#170—32no—
211C2×#170C22×D311yescharacteristic
212C2×#170C22×D312yes—
213C2×#170C22×D311yescharacteristic
214#700—34no—
215#700—38no—
216#700—38no—
217#700C4×D314yescomplemented
218D5⋊C8—34no—
219D5⋊C8—38no—
220D5⋊C8—38no—
221D5⋊C8C4×D314yescomplemented
222C5×C4⋊C4—32no—
223C5×C4⋊C4C4×D311yescharacteristic
224C42×C5—32no—
225C42×C5—31no—
226#685—32no—
227#685—32no—
228#685C4×D312yes—
229C4⋊Dic5—32no—
230C4⋊Dic5C4×D311yescharacteristic
231C4×Dic5—31no—
232C4×Dic5—32no—
233C4×Dic5—31no—
234C4×Dic5—31no—
235C4×Dic5C22×D312yes—
236C2×#131—151no—
237C2×#131—151no—
238C4×#41—151no—
239#405—51no—
240#405—152no—
241#405—152no—
242#405—151no—
243C4×M16—152no—
244C4×M16—151no—
245C2×C4×C8—152no—
246C2×C4×C8—151no—
247C22×C3×C5C23×C411yescharacteristic
248C2×D15—22no—
249C2×D15—22no—
250C2×D15C2×C4214yes—
251C2×C3×D5—21no—
252C2×C3×D5—21no—
253C2×C3×D5C2×C4212yes—
254C3×C4×C5—22no—
255C3×C4×C5C2×C4212yes—
256Dic15—21no—
257Dic15#13112yescomplemented
258C3×Dic5—22no—
259C3×Dic5C23×C411yescharacteristic
260C3×Dic5C23×C411yescharacteristic
261C5×Dic3—21no—
262C5×Dic3C2×C4214yes—
263C5×Dic3#13112yescomplemented
264C22×C3×C4—51no—
265C2×#67—52no—
266C22×Dic3—51no—
267C22×Dic3—51no—
268#235—54no—
269#235—54no—
270C2×D12—51no—
271C2×C4×D3—52no—
272C2×C4×D3—52no—
273C2×C4×D3—52no—
274C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
275C3×M16—54no—
276C2×C3×C8—51no—
277C2×C3×C8—51no—
278C2×C3×C8—52no—
279C2×C3×C8—54no—
280C3×C4⋊C4—51no—
281C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
282C3×C22⋊C4—52no—
283C3×C42—52no—
284(C2×D3)⋊C4—52no—
285(C2×D3)⋊C4—52no—
286Dic3⋊C4—52no—
287Dic3⋊C4C2×AGL(1,𝔽5)12yes—
288C4×Dic3—51no—
289C4×Dic3—52no—
290C4×Dic3—51no—
291C4×Dic3—51no—
292C4×Dic3C2×AGL(1,𝔽5)12yes—
293C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
294#208—54no—
295C2×C3⋊C8—51no—
296C2×C3⋊C8—52no—
297C2×C3⋊C8—51no—
298C2×C3⋊C8—54no—
299ΓL(1,𝔽25)—58no—
300ΓL(1,𝔽25)—58no—
301D3×C8—58no—
302D3×C8—58no—
303C22×D5—32no—
304C22×D5C2×C4×D311yescharacteristic
305C5×Q8—34no—
306C2×C4×C5—32no—
307C2×C4×C5—31no—
308C2×C4×C5—31no—
309C2×C4×C5C2×C4×D312yes—
310C2×C4×C5C2×C4×D311yescharacteristic
311C2×Dic5—31no—
312C2×Dic5—31no—
313C2×Dic5C2×C4×D312yes—
314C2×Dic5C23×D311yescharacteristic
315D20—38no—
316D20—34no—
317C4×D5—34no—
318C4×D5—34no—
319C4×D5—64no—
320C4×D5—64no—
321C4×D5—62no—
322C4×D5—62no—
323C4×D5C2×C4×D312yes—
324C4×D5C2×C4×D312yes—
325#170—32no—
326#170—34no—
327#170—32no—
328#170C2×C4×D312yes—
329#170C2×C4×D314yes—
330#170C2×C4×D312yes—
331C2×#41—151no—
332#131—158no—
333#131—158no—
334C2×M16—51no—
335C2×M16—152no—
336C2×M16—152no—
337C2×M16—151no—
338C22×C8—51no—
339C22×C8—152no—
340C22×C8—152no—
341C22×C8—151no—
342C4×Q8—31no—
343C4×Q8—151no—
344C4×D4—152no—
345C4×D4—151no—
346C4×D4—152no—
347C4×D4—151no—
348#117—51no—
349#117—152no—
350C2×C42—152no—
351C2×C42—151no—
352#97—52no—
353#97—152no—
354#97—152no—
355C4×C8—52no—
356C4×C8—152no—
357C4×C8—151no—
358C4×C8—152no—
359C4×C8—151no—
360C4×C8—151no—
361C4×C8—151no—
362C2×C3×C5C22×C4211yescharacteristic
363C2×C3×C5C2×#13111yescharacteristic
364C2×C3×C5C2×#13111yescharacteristic
365D15—24no—
366C3×D5—22no—
367C23×C3—51no—
368C22×D3—52no—
369C2×C3×C4—51no—
370C2×C3×C4—52no—
371C2×C3×C4—52no—
372C2×C3×C4—52no—
373C2×C3×C4C22×AGL(1,𝔽5)12yes—
374C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
375#67—58no—
376C2×Dic3—51no—
377C2×Dic3—51no—
378C2×Dic3—102no—
379C2×Dic3—102no—
380C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
381C2×Dic3C22×AGL(1,𝔽5)12yes—
382C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
383D12—54no—
384C4×D3—54no—
385C4×D3—54no—
386C4×D3—104no—
387C4×D3—104no—
388Dic6C4×AGL(1,𝔽5)14yes—
389C3×C8—52no—
390C3×C8—54no—
391C3×C8—52no—
392C3⋊C8—52no—
393C3⋊C8—54no—
394C3⋊C8—52no—
395C22×C5C22×C4×D311yescharacteristic
396C2×D5—21no—
397C2×D5—21no—
398C2×D5—34no—
399C2×D5—62no—
400C2×D5—62no—
401C2×D5C42×D312yes—
402C4×C5—22no—
403C4×C5—34no—
404C4×C5—32no—
405C4×C5—61no—
406C4×C5C42×D312yes—
407Dic5—22no—
408Dic5—32no—
409Dic5—61no—
410Dic5C22×C4×D311yescharacteristic
411Dic5C22×C4×D311yescharacteristic
412#41—154no—
413#41—154no—
414C2×Q8—31no—
415C2×D4—152no—
416C2×D4—151no—
417C22×C4—51no—
418C22×C4—152no—
419C22×C4—152no—
420C22×C4—151no—
421C22×C4—151no—
422C22×C4—152no—
423M16—54no—
424M16—158no—
425M16—158no—
426M16—154no—
427C2×C8—51no—
428C2×C8—52no—
429C2×C8—51no—
430C2×C8—54no—
431C2×C8—158no—
432C2×C8—158no—
433C2×C8—151no—
434C2×C8—152no—
435C2×C8—151no—
436C2×C8—154no—
437C4⋊C4—32no—
438C4⋊C4—51no—
439C4⋊C4—152no—
440C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
441C22⋊C4—52no—
442C22⋊C4—152no—
443C22⋊C4—152no—
444C42—32no—
445C42—31no—
446C42—52no—
447C42—151no—
448C42—151no—
449C42—152no—
450C42—151no—
451C3×C5C4×#13111yescharacteristic, complemented, Hall
452C22×C3—52no—
453C22×C3—101no—
454C22×C3—101no—
455C22×C3C23×AGL(1,𝔽5)11yescharacteristic
456C2×D3—54no—
457C2×D3—102no—
458C2×D3—102no—
459C3×C4—22no—
460C3×C4—51no—
461C3×C4—51no—
462C3×C4—102no—
463C3×C4C2×C4×AGL(1,𝔽5)12yes—
464Dic3—21no—
465Dic3—52no—
466Dic3—101no—
467Dic3C2×C4×AGL(1,𝔽5)14yes—
468Dic3#413312yescomplemented
469C2×C5C2×C42×D311yescharacteristic
470C2×C5D3×#13111yescharacteristic
471C2×C5D3×#13111yescharacteristic
472D5—22no—
473D5—64no—
474C23—51no—
475C23—152no—
476Q8—34no—
477D4—158no—
478D4—154no—
479C2×C4—31no—
480C2×C4—32no—
481C2×C4—31no—
482C2×C4—51no—
483C2×C4—52no—
484C2×C4—52no—
485C2×C4—52no—
486C2×C4—154no—
487C2×C4—154no—
488C2×C4—151no—
489C2×C4—151no—
490C2×C4—304no—
491C2×C4—304no—
492C2×C4—302no—
493C2×C4—302no—
494C2×C4C2×D3×AGL(1,𝔽5)12yes—
495C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
496C8—52no—
497C8—52no—
498C8—54no—
499C8—152no—
500C8—154no—
501C8—152no—
502C2×C3—102no—
503C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
504C2×C3C2×#413311yescharacteristic
505C2×C3D5⋊#13111yescharacteristic
506D3—104no—
507C5#7854911yescharacteristic, complemented, Sylow
508C22—52no—
509C22—101no—
510C22—101no—
511C22—154no—
512C22—302no—
513C22—302no—
514C22C22×D3×AGL(1,𝔽5)11yescharacteristic
515C4—22no—
516C4—34no—
517C4—32no—
518C4—51no—
519C4—51no—
520C4—61no—
521C4—102no—
522C4—152no—
523C4—301no—
524C4C4×D3×AGL(1,𝔽5)12yes—
525C3C4×#413311yescharacteristic, complemented, Sylow
526C2—102no—
527C2—304no—
528C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
529C2#1175684011yescharacteristic
530C2D3×#413311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×#6773C22
cosocleC2×C3×Dic5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#131
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11752360C2semidirect
5. C3×#65701C2semidirect
6. #11751874C2semidirect
7. #11751872C2semidirect
8. C4×#6738C2semidirect
9. Dic3×#700C2semidirect
10. Dic3×D5⋊C8C2semidirect
11. #11751756C2semidirect
22. #91916C4semidirect
23. #91914C4semidirect
51. #65701D3semidirect
70. #6758C2×C4semidirect
71. D5⋊(C3⋊C8)C2×C4semidirect
75. C3×#700C2×C4semidirect
76. C3×D5⋊C8C2×C4semidirect
77. #6740C2×C4semidirect
78. #6740C2×C4semidirect
79. #6738C2×C4semidirect
80. #6738C2×C4semidirect
217. #700C4×D3semidirect
221. D5⋊C8C4×D3semidirect
257. Dic15#131semidirect
263. C5×Dic3#131semidirect
451. C3×C5C4×#131semidirect
468. Dic3#4133semidirect
507. C5#78549semidirect
525. C3C4×#4133semidirect

Maximal subgroups

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

subgroupindex
C2×#919162
C2×#919142
#117534032
#117523602
C3×#657012
#117518742
#117518722
C4×#67382
Dic3×#7002
Dic3×D5⋊C82
#117517562
C4×#41333
#785495