Finite Group Databasebeta

← #14295977

Subgroups — #14295977

Order 1920.

600 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5⋊#131C211yesmaximal, characteristic
2#11752453C211yesmaximal, characteristic
3Dic3×D5⋊C8C211yesmaximal, characteristic, complemented
4#11751694C211yesmaximal, characteristic, complemented
5D5×#837C211yesmaximal, characteristic
6#11746531C211yesmaximal, characteristic, complemented
7#11746525C211yesmaximal, characteristic, complemented
8#10604005—31nomaximal, Hall
9C3×D5×#41C2211yescharacteristic
10#91989C2211yescharacteristic
11C2×D5⋊(C3⋊C8)C2211yescharacteristic
12C3×#4133C412yescomplemented
13C3×#4131—22no—
14C3×#4131C412yescomplemented
15C3×D5⋊M16—21no—
16C3×D5⋊M16C2211yescharacteristic
17C2×C3×D5⋊C8—21no—
18C2×C3×D5⋊C8C2211yescharacteristic
19C4×D5×Dic3C2211yescharacteristic
20D5×#208C2211yescharacteristic
21#91238C412yescomplemented
22#91236C412yescomplemented
23Dic3×#170—22no—
24#91150—21no—
25ΓL(1,𝔽16)⋊C8—21no—
26#91121C411yescharacteristic, complemented
27C5×#837C411yescharacteristic, complemented
28#90977C411yescharacteristic, complemented
29#90976C411yescharacteristic, complemented
30#72008—51nomaximal, Hall
31D5⋊#131D311yescharacteristic
32#65794—31no—
33#65728—31no—
34C4×D5⋊C8—31no—
35D5×#104—31no—
36#64901—31no—
37#64862—31no—
38C3×C5×#41C2×C411yescharacteristic
39C3×#713C2×C411yescharacteristic
40C3×Q8×D5C2×C411yescharacteristic
41C3×#711—21no—
42C3×#711C2×C411yescharacteristic
43C3×D4×D5—21no—
44C3×D4×D5C2×C411yescharacteristic
45C3×#709—21no—
46C3×#709C2×C411yescharacteristic
47C2×C3×C4×D5—21no—
48C2×C3×C4×D5C2311yescharacteristic
49C2×D5×Dic3—21no—
50#6763—21no—
51C2×C3⋊#170—21no—
52C4⋊ΓL(1,𝔽16)C2×C412yes—
53C4×ΓL(1,𝔽16)—21no—
54D5⋊(C3⋊C8)—21no—
55D5⋊(C3⋊C8)C2×C412yes—
56C3×#704—21no—
57C3×#704—22no—
58C2×C3×#170—22no—
59C2×C3×#170D412yes—
60C3×#700—22no—
61C3×#700C2×C412yes—
62C3×D5⋊C8—21no—
63C3×D5⋊C8—22no—
64C3×D5⋊C8C2×C412yes—
65C3×D5⋊C8D411yescharacteristic
66C3×D5⋊C8D411yescharacteristic
67C4×Dic15C2×C411yescharacteristic
68#6710C2×C411yescharacteristic
69C4×C5×Dic3C2×C411yescharacteristic
70C5×#208C2×C411yescharacteristic
71Dic3×Dic5—21no—
72#6649—21no—
73D5×C3⋊C8—21no—
74C2×C3×#131—51no—
75C2×#837—51no—
76#5233—51no—
77#5101—51no—
78C2×C8×Dic3—51no—
79#4558—51no—
80#4555—51no—
81D5×#41C2×D311yescharacteristic
82#4133Dic312yescomplemented
83#4131—22no—
84#4131Dic312yescomplemented
85#4130—31no—
86D5⋊M16—21no—
87D5⋊M16C2×D311yescharacteristic
88C2×D5⋊C8—21no—
89C2×D5⋊C8—31no—
90C2×D5⋊C8C2×D311yescharacteristic
91D5×M16—31no—
92C42×D5—31no—
93#4009—32no—
94#4007—32no—
95C4×#170—62no—
96#3992—61no—
97C8×AGL(1,𝔽5)—61no—
98C5×#104—31no—
99#3969—31no—
100#3957—31no—
101#3937—31no—
102#1764—151noSylow
103C22×C3×D5—21no—
104C22×C3×D5#4111yescharacteristic
105C2×ΓL(1,𝔽16)—22no—
106C3×C5×Q8C4211yescharacteristic
107C3×C5×D4—21no—
108C3×C5×D4C4211yescharacteristic
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5C22×C411yescharacteristic
111C2×Dic15—21no—
112C2×C5×Dic3—21no—
113C3×C22⋊D5—21no—
114C3×C22⋊D5—21no—
115C3×C22⋊D5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5C2×D411yescharacteristic
118C3×D20—21no—
119C3×D20C4211yescharacteristic
120C3×C4×D5—21no—
121C3×C4×D5—21no—
122C3×C4×D5—21no—
123C3×C4×D5C22×C411yescharacteristic
124C3×C4×D5C22×C411yescharacteristic
125C3×C4×D5C2×D411yescharacteristic
126C3×C4×D5#4111yescharacteristic
127C3×Dic10—21no—
128C3×Dic10C4211yescharacteristic
129D5×Dic3—24no—
130C3⋊#170—22no—
131C3×#170—22no—
132C3×#170C22⋊C412yes—
133C3×#170C22⋊C412yes—
134C3⋊#168—21no—
135C5×C3⋊C8—21no—
136C2×C3×#41—51no—
137C3×#131—52no—
138C3×#131—52no—
139C3×#131—102no—
140C2×C3×M16—51no—
141C2×C3×M16—101no—
142C22×C3×C8—51no—
143C22×C3×C8—101no—
144#926—51no—
145C2×C4×Dic3—51no—
146C2×#208—51no—
147C22×C3⋊C8—51no—
148#837—51no—
149#837—51no—
150#837—51no—
151#837AGL(1,𝔽5)11yescharacteristic, complemented
152#835—52no—
153#832—52no—
154#815—101no—
155C8×Dic3—101no—
156C8×Dic3—102no—
157C5×#41C4×D311yescharacteristic
158#713C2×Dic311yescharacteristic
159Q8×D5C4×D311yescharacteristic
160#711—21no—
161#711C2×Dic311yescharacteristic
162D4×D5—21no—
163D4×D5C4×D311yescharacteristic
164#709—21no—
165#709C4×D311yescharacteristic
166C2×C4×D5—21no—
167C2×C4×D5—61no—
168C2×C4×D5C22×D311yescharacteristic
169C22⋊AGL(1,𝔽5)—61no—
170#704—21no—
171#704—22no—
172C2×#170—22no—
173C2×#170—61no—
174C2×#170#6712yes—
175C4⋊AGL(1,𝔽5)—32no—
176C4×AGL(1,𝔽5)—61no—
177#700—22no—
178#700C2×Dic312yes—
179D5⋊C8—21no—
180D5⋊C8—22no—
181D5⋊C8—32no—
182D5⋊C8—61no—
183D5⋊C8C2×Dic312yes—
184D5⋊C8#6711yescharacteristic
185D5⋊C8#6711yescharacteristic
186C5×M16—31no—
187C42×C5—31no—
188C4×Dic5—31no—
189C4×Dic5—61no—
190#681—31no—
191#676—61no—
192C8×D5—61no—
193C2×#131—51no—
194C2×#104—151no—
195#416—151no—
196#405—151no—
197C2×C4×C8—151no—
198#341—151no—
199#339—151no—
200C22×C3×C5—21no—
201C22×C3×C5C4×D411yescharacteristic
202C2×C3×D5—22no—
203C2×C3×D5—21no—
204C2×C3×D5—42no—
205C2×C3×D5#11711yescharacteristic
206C2×C3×D5C4×D411yescharacteristic
207ΓL(1,𝔽16)—42no—
208C3×C4×C5—21no—
209C3×C4×C5C2×C4211yescharacteristic
210C3×C4×C5C4×D411yescharacteristic
211Dic15—22no—
212C3×Dic5—21no—
213C3×Dic5C2×C22⋊C411yescharacteristic
214C3×Dic5C4×D411yescharacteristic
215C5×Dic3—22no—
216C3×#41—51no—
217C3×#41—51no—
218C3×#41—51no—
219C3×#41—101no—
220C3×#41—101no—
221C3×#41C2×AGL(1,𝔽5)11yescharacteristic
222C2×C3×Q8—51no—
223C2×C3×D4—51no—
224C2×C3×D4—101no—
225C22×C3×C4—51no—
226C22×C3×C4—101no—
227C22×Dic3—101no—
228C3×M16—52no—
229C3×M16—102no—
230C3×M16—102no—
231C3×M16—101no—
232C2×C3×C8—51no—
233C2×C3×C8—52no—
234C2×C3×C8—51no—
235C2×C3×C8—52no—
236C2×C3×C8—102no—
237C2×C3×C8—102no—
238C2×C3×C8—101no—
239#217—101no—
240C4⋊Dic3—52no—
241C4×Dic3—51no—
242C4×Dic3—101no—
243C4×Dic3—101no—
244C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
245#208—51no—
246#208—101no—
247#208C2×AGL(1,𝔽5)11yescharacteristic
248C2×C3⋊C8—52no—
249C2×C3⋊C8—101no—
250C2×C3⋊C8—101no—
251C2×C3⋊C8—101no—
252C22×D5—21no—
253C22×D5#23511yescharacteristic
254C2×AGL(1,𝔽5)—62no—
255C5×Q8C4×Dic311yescharacteristic
256C5×D4—21no—
257C5×D4C4×Dic311yescharacteristic
258C2×C4×C5—21no—
259C2×C4×C5—61no—
260C2×C4×C5C2×C4×D311yescharacteristic
261C22⋊D5—21no—
262C22⋊D5—21no—
263C22⋊D5—21no—
264C2×Dic5—21no—
265C2×Dic5—61no—
266C2×Dic5C2×#6711yescharacteristic
267D20—21no—
268D20C4×Dic311yescharacteristic
269C4×D5—21no—
270C4×D5—21no—
271C4×D5—21no—
272C4×D5—64no—
273C4×D5C2×C4×D311yescharacteristic
274C4×D5#23511yescharacteristic
275C4×D5C22×Dic311yescharacteristic
276C4×D5C2×#6711yescharacteristic
277Dic10—21no—
278Dic10C4×Dic311yescharacteristic
279#170—22no—
280#170—62no—
281#170#21712yes—
282#170#21712yes—
283C5×C8—61no—
284#168—61no—
285C2×#41—51no—
286#131—52no—
287#131—52no—
288#131—102no—
289C2×M16—51no—
290C2×M16—101no—
291C2×M16—151no—
292C22×C8—51no—
293C22×C8—101no—
294C22×C8—151no—
295#117—151no—
296C2×C42—151no—
297#104—31no—
298#104—151no—
299#104—151no—
300#104—151no—
301#103—152no—
302#102—152no—
303#97—301no—
304C4×C8—302no—
305C4×C8—301no—
306C2×C3×C5—21no—
307C2×C3×C5—41no—
308C2×C3×C5C4×C22⋊C411yescharacteristic
309C3×D5—21no—
310C3×D5—41no—
311C3×D5#44312yes—
312C23×C3—51no—
313C23×C3—101no—
314C3×Q8—51no—
315C3×Q8—101no—
316C3×Q8C4×AGL(1,𝔽5)11yescharacteristic
317C3×D4—21no—
318C3×D4—51no—
319C3×D4—101no—
320C3×D4—101no—
321C3×D4—101no—
322C3×D4—101no—
323C3×D4C4×AGL(1,𝔽5)11yescharacteristic
324C2×C3×C4—21no—
325C2×C3×C4—51no—
326C2×C3×C4—51no—
327C2×C3×C4—51no—
328C2×C3×C4—51no—
329C2×C3×C4—51no—
330C2×C3×C4—101no—
331C2×C3×C4—101no—
332C2×C3×C4—101no—
333C2×C3×C4—101no—
334C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
335C2×Dic3—21no—
336C2×Dic3—104no—
337C2×Dic3—101no—
338C2×Dic3—102no—
339C3×C8—52no—
340C3×C8—52no—
341C3×C8—102no—
342C3⋊C8—21no—
343C3⋊C8—102no—
344C3⋊C8—101no—
345C22×C5—21no—
346C22×C5C4×#6711yescharacteristic
347C2×D5—22no—
348C2×D5—21no—
349C2×D5—42no—
350C2×D5#92611yescharacteristic
351C2×D5C4×#6711yescharacteristic
352AGL(1,𝔽5)—122no—
353C4×C5—21no—
354C4×C5—62no—
355C4×C5C2×C4×Dic311yescharacteristic
356C4×C5C4×#6711yescharacteristic
357Dic5—21no—
358Dic5—62no—
359Dic5C4×#6711yescharacteristic
360Dic5C2×#21711yescharacteristic
361#41—51no—
362#41—51no—
363#41—51no—
364#41—101no—
365#41—101no—
366#41D3×AGL(1,𝔽5)11yescharacteristic
367C2×Q8—51no—
368C2×D4—51no—
369C2×D4—101no—
370C22×C4—51no—
371C22×C4—101no—
372C22×C4—301no—
373M16—31no—
374M16—52no—
375M16—102no—
376M16—102no—
377M16—101no—
378M16—151no—
379M16—301no—
380C2×C8—51no—
381C2×C8—52no—
382C2×C8—51no—
383C2×C8—52no—
384C2×C8—102no—
385C2×C8—102no—
386C2×C8—101no—
387C2×C8—152no—
388C2×C8—301no—
389C2×C8—301no—
390C2×C8—301no—
391C4⋊C4—152no—
392C22⋊C4—301no—
393C42—31no—
394C42—151no—
395C42—301no—
396C42—301no—
397C3×C5#176411yescharacteristic, complemented, Hall
398C22×C3—21no—
399C22×C3—51no—
400C22×C3—51no—
401C22×C3—102no—
402C22×C3—101no—
403C22×C3—202no—
404C22×C3D4×AGL(1,𝔽5)11yescharacteristic
405C3×C4—21no—
406C3×C4—51no—
407C3×C4—51no—
408C3×C4—101no—
409C3×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
410C3×C4D4×AGL(1,𝔽5)11yescharacteristic
411Dic3—22no—
412Dic3—102no—
413Dic3—202no—
414C2×C5—21no—
415C2×C5—41no—
416C2×C5C4×#21711yescharacteristic
417D5—21no—
418D5—41no—
419D5#514412yes—
420C23—51no—
421C23—101no—
422Q8—51no—
423Q8—101no—
424Q8Dic3×AGL(1,𝔽5)11yescharacteristic
425D4—21no—
426D4—51no—
427D4—101no—
428D4—101no—
429D4—101no—
430D4—101no—
431D4Dic3×AGL(1,𝔽5)11yescharacteristic
432C2×C4—21no—
433C2×C4—51no—
434C2×C4—51no—
435C2×C4—51no—
436C2×C4—51no—
437C2×C4—51no—
438C2×C4—61no—
439C2×C4—101no—
440C2×C4—101no—
441C2×C4—101no—
442C2×C4—101no—
443C2×C4—304no—
444C2×C4—301no—
445C2×C4—302no—
446C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
447C8—52no—
448C8—52no—
449C8—61no—
450C8—102no—
451C8—302no—
452C8—301no—
453C2×C3—21no—
454C2×C3—41no—
455C2×C3—52no—
456C2×C3—101no—
457C2×C3—201no—
458C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
459C5#7200811yescharacteristic, complemented, Sylow
460C22—21no—
461C22—51no—
462C22—51no—
463C22—102no—
464C22—101no—
465C22—202no—
466C22AGL(1,𝔽5)×#6711yescharacteristic
467C4—21no—
468C4—51no—
469C4—51no—
470C4—62no—
471C4—101no—
472C4—302no—
473C4—602no—
474C4C2×Dic3×AGL(1,𝔽5)11yescharacteristic
475C4AGL(1,𝔽5)×#6711yescharacteristic
476C3#1060400511yescharacteristic, complemented, Sylow
477C2—21no—
478C2—41no—
479C2—52no—
480C2—101no—
481C2—201no—
482C2AGL(1,𝔽5)×#21711yescharacteristic
subgroupG/H
centerC4AGL(1,𝔽5)×#67
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×#41C2×C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC3×D5×#41C22
cosocleC2×C3×C4×D5C23
hypercenter#41D3×AGL(1,𝔽5)
hypocenterC3×C5#1764
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
3. Dic3×D5⋊C8C2semidirect
4. #11751694C2semidirect
6. #11746531C2semidirect
7. #11746525C2semidirect
12. C3×#4133C4semidirect
14. C3×#4131C4semidirect
21. #91238C4semidirect
22. #91236C4semidirect
26. #91121C4semidirect
27. C5×#837C4semidirect
28. #90977C4semidirect
29. #90976C4semidirect
82. #4133Dic3semidirect
84. #4131Dic3semidirect
151. #837AGL(1,𝔽5)semidirect
397. C3×C5#1764semidirect
459. C5#72008semidirect
476. C3#10604005semidirect

Maximal subgroups

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

subgroupindex
C3×D5⋊#1312
#117524532
Dic3×D5⋊C82
#117516942
D5×#8372
#117465312
#117465252
#106040053
#720085