Finite Group Databasebeta

← #14296017

Subgroups — #14296017

Order 1920.

584 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
1D5⋊#948C211yesmaximal, characteristic
2#11752453C211yesmaximal, characteristic
3#11752387C211yesmaximal, characteristic, complemented
4#11752335C211yesmaximal, characteristic, complemented
5C3×D5×#104C211yesmaximal, characteristic
6#11746772C211yesmaximal, characteristic, complemented
7#11746733C211yesmaximal, characteristic, complemented
8#10604006—31nomaximal, Hall
9C3×D5×#41C2211yescharacteristic
10#91992C412yescomplemented
11#91990—22no—
12#91990C412yescomplemented
13#91989C2211yescharacteristic
14D5⋊#208—21no—
15D5⋊#208C2211yescharacteristic
16C2×D5⋊(C3⋊C8)—21no—
17C2×D5⋊(C3⋊C8)C2211yescharacteristic
18C2×D5⋊(C3⋊C8)C2211yescharacteristic
19C3×D5×M16C2211yescharacteristic
20C3×C42×D5C2211yescharacteristic
21#91238C412yescomplemented
22#91236C412yescomplemented
23#91231—22no—
24#91221—21no—
25C8×ΓL(1,𝔽16)—21no—
26C3×C5×#104C411yescharacteristic, complemented
27C3×#3969C411yescharacteristic, complemented
28C3×#3957C411yescharacteristic, complemented
29C3×#3937C411yescharacteristic, complemented
30#70370—51nomaximal, Hall
31D5⋊#131—31no—
32#65794—31no—
33#65728—31no—
34#65676—31no—
35D5×#104D311yescharacteristic
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×D5—21no—
49C2×C3×C4×D5C2311yescharacteristic
50#6763—21no—
51#6762—21no—
52#6762—22no—
53C2×C3⋊#170—21no—
54C2×C3⋊#170—22no—
55C2×C3⋊#170D412yes—
56C4⋊ΓL(1,𝔽16)C2×C412yes—
57C4×ΓL(1,𝔽16)—21no—
58#6758—22no—
59#6758C2×C412yes—
60D5⋊(C3⋊C8)—21no—
61D5⋊(C3⋊C8)—21no—
62D5⋊(C3⋊C8)—22no—
63D5⋊(C3⋊C8)C2×C412yes—
64D5⋊(C3⋊C8)C2×C412yes—
65D5⋊(C3⋊C8)D411yescharacteristic
66D5⋊(C3⋊C8)D411yescharacteristic
67C3×C5×M16C2×C411yescharacteristic
68C3×C42×C5C2×C411yescharacteristic
69C3×C4×Dic5—21no—
70C3×C4×Dic5C2×C411yescharacteristic
71C3×#681C2×C411yescharacteristic
72C3×#676—21no—
73C3×C8×D5—21no—
74C2×#948—51no—
75C2×C3×#104—51no—
76#5233—51no—
77#5122—51no—
78C2×#803—51no—
79#4558—51no—
80#4523—51no—
81D5×#41C2×D311yescharacteristic
82#4133—32no—
83#4131—32no—
84#4131—62no—
85#4130—31no—
86D5⋊M16—31no—
87D5⋊M16—61no—
88C2×D5⋊C8—31no—
89C2×D5⋊C8—31no—
90C2×D5⋊C8—61no—
91D5×M16C2×D311yescharacteristic
92C42×D5C2×D311yescharacteristic
93#4009—32no—
94#4007—32no—
95#4002—62no—
96#3992—61no—
97C8×AGL(1,𝔽5)—61no—
98C5×#104Dic311yescharacteristic, complemented
99#3969Dic311yescharacteristic, complemented
100#3957Dic311yescharacteristic, complemented
101#3937Dic311yescharacteristic, complemented
102#1765—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×C5—21no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C3×C22⋊D5—21no—
113C3×C22⋊D5—21no—
114C3×C22⋊D5—21no—
115C2×C3×Dic5—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×D5—42no—
124C3×C4×D5C22×C411yescharacteristic
125C3×C4×D5C22×C411yescharacteristic
126C3×C4×D5C2×D411yescharacteristic
127C3×C4×D5#4111yescharacteristic
128C3×Dic10—21no—
129C3×Dic10C4211yescharacteristic
130C3⋊#170—22no—
131C3⋊#170—22no—
132C3⋊#170C22⋊C412yes—
133C3⋊#170C22⋊C412yes—
134C3×C5×C8—21no—
135C3×#168—21no—
136C2×C3×#41—51no—
137C2×C3×M16—51no—
138C2×C3×C42—51no—
139#948—52no—
140#948—52no—
141#948—102no—
142#926—51no—
143C2×#208—51no—
144C2×#208—101no—
145C22×C3⋊C8—51no—
146C22×C3⋊C8—51no—
147C22×C3⋊C8—101no—
148C3×#104—51no—
149C3×#104—51no—
150C3×#104—51no—
151C3×#104AGL(1,𝔽5)11yescharacteristic, complemented
152#835—52no—
153#832—52no—
154#815—101no—
155C8×Dic3—101no—
156#803—102no—
157C5×#41C2×Dic311yescharacteristic
158#713C4×D311yescharacteristic
159Q8×D5C4×D311yescharacteristic
160#711—21no—
161#711C4×D311yescharacteristic
162D4×D5—21no—
163D4×D5C4×D311yescharacteristic
164#709—21no—
165#709C2×Dic311yescharacteristic
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5C22×D311yescharacteristic
169C22⋊AGL(1,𝔽5)—61no—
170#704—62no—
171#704—61no—
172C2×#170—32no—
173C2×#170—62no—
174C2×#170—61no—
175C4⋊AGL(1,𝔽5)—32no—
176C4×AGL(1,𝔽5)—61no—
177#700—32no—
178#700—62no—
179D5⋊C8—32no—
180D5⋊C8—31no—
181D5⋊C8—31no—
182D5⋊C8—32no—
183D5⋊C8—62no—
184D5⋊C8—61no—
185D5⋊C8—61no—
186C5×M16C2×Dic311yescharacteristic
187C42×C5C2×Dic311yescharacteristic
188C4×Dic5—21no—
189C4×Dic5C2×Dic311yescharacteristic
190#681C2×Dic311yescharacteristic
191#676—21no—
192C8×D5—21no—
193C2×#131—151no—
194C2×#104—51no—
195#416—151no—
196#405—151no—
197C2×#97—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×C5—41no—
210C3×C4×C5C2×C4211yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×Dic5—21no—
213C3×Dic5—41no—
214C3×Dic5C2×C22⋊C411yescharacteristic
215C3×Dic5C4×D411yescharacteristic
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×C3×C4—101no—
228C3×M16—51no—
229C3×M16—101no—
230C3×M16C2×AGL(1,𝔽5)11yescharacteristic
231C2×C3×C8—101no—
232C3×C42—51no—
233C3×C42—101no—
234C3×C42C2×AGL(1,𝔽5)11yescharacteristic
235#217—101no—
236C4⋊Dic3—52no—
237C4×Dic3—101no—
238#208—52no—
239#208—102no—
240#208—102no—
241#208—101no—
242C2×C3⋊C8—52no—
243C2×C3⋊C8—51no—
244C2×C3⋊C8—51no—
245C2×C3⋊C8—52no—
246C2×C3⋊C8—52no—
247C2×C3⋊C8—102no—
248C2×C3⋊C8—102no—
249C2×C3⋊C8—101no—
250C2×C3⋊C8—101no—
251C2×C3⋊C8—101no—
252C22×D5—21no—
253C22×D5#23711yescharacteristic
254C2×AGL(1,𝔽5)—62no—
255C5×Q8C4×Dic311yescharacteristic
256C5×D4—21no—
257C5×D4C4×Dic311yescharacteristic
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5C22×Dic311yescharacteristic
261C22⋊D5—21no—
262C22⋊D5—21no—
263C22⋊D5—21no—
264C2×Dic5—21no—
265C2×Dic5—21no—
266C2×Dic5D3×D411yescharacteristic
267D20—21no—
268D20C4×Dic311yescharacteristic
269C4×D5—21no—
270C4×D5—21no—
271C4×D5—21no—
272C4×D5—42no—
273C4×D5C2×C4×D311yescharacteristic
274C4×D5C2×C4×D311yescharacteristic
275C4×D5D3×D411yescharacteristic
276C4×D5#23711yescharacteristic
277Dic10—21no—
278Dic10C4×Dic311yescharacteristic
279#170—32no—
280#170—32no—
281#170—62no—
282#170—62no—
283C5×C8—21no—
284#168—21no—
285C2×#41—51no—
286#131—152no—
287#131—152no—
288#131—302no—
289C2×M16—51no—
290C2×M16—151no—
291C2×M16—301no—
292C22×C8—151no—
293C22×C8—151no—
294C22×C8—301no—
295#117—151no—
296C2×C42—51no—
297#104—51no—
298#104—51no—
299#104—51no—
300#104ΓL(1,𝔽16)11yescharacteristic, complemented
301#103—152no—
302#102—152no—
303#97—302no—
304#97—301no—
305C4×C8—301no—
306C2×C3×C5—21no—
307C2×C3×C5—41no—
308C2×C3×C5C4×C22⋊C411yescharacteristic
309C3×D5—21no—
310C3×D5—41no—
311C3×D5#44412yes—
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—21no—
326C2×C3×C4—51no—
327C2×C3×C4—51no—
328C2×C3×C4—51no—
329C2×C3×C4—51no—
330C2×C3×C4—51no—
331C2×C3×C4—101no—
332C2×C3×C4—101no—
333C2×C3×C4—101no—
334C2×C3×C4—101no—
335C2×C3×C4—101no—
336C2×C3×C4—202no—
337C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
338C2×Dic3—102no—
339C3×C8—21no—
340C3×C8—101no—
341C3⋊C8—52no—
342C3⋊C8—52no—
343C3⋊C8—102no—
344C3⋊C8—102no—
345C22×C5—21no—
346C22×C5D4×Dic311yescharacteristic
347C2×D5—22no—
348C2×D5—21no—
349C2×D5—42no—
350C2×D5#87711yescharacteristic
351C2×D5#67⋊C411yescharacteristic
352AGL(1,𝔽5)—122no—
353C4×C5—21no—
354C4×C5—41no—
355C4×C5C2×C4×Dic311yescharacteristic
356C4×C5D4×Dic311yescharacteristic
357Dic5—21no—
358Dic5—41no—
359Dic5D3×C22⋊C411yescharacteristic
360Dic5#67⋊C411yescharacteristic
361#41—51no—
362#41—51no—
363#41—51no—
364#41—101no—
365#41—101no—
366#41C2×ΓL(1,𝔽16)11yescharacteristic
367C2×Q8—51no—
368C2×D4—51no—
369C2×D4—101no—
370C22×C4—51no—
371C22×C4—101no—
372C22×C4—101no—
373M16—51no—
374M16—101no—
375M16—152no—
376M16—302no—
377M16—302no—
378M16—301no—
379M16C2×ΓL(1,𝔽16)11yescharacteristic
380C2×C8—101no—
381C2×C8—151no—
382C2×C8—151no—
383C2×C8—152no—
384C2×C8—152no—
385C2×C8—152no—
386C2×C8—302no—
387C2×C8—302no—
388C2×C8—301no—
389C2×C8—301no—
390C2×C8—301no—
391C4⋊C4—152no—
392C22⋊C4—301no—
393C42—51no—
394C42—101no—
395C42—301no—
396C42C2×ΓL(1,𝔽16)11yescharacteristic
397C3×C5#176511yescharacteristic, 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—41no—
407C3×C4—51no—
408C3×C4—51no—
409C3×C4—101no—
410C3×C4—201no—
411C3×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
412C3×C4D4×AGL(1,𝔽5)11yescharacteristic
413Dic3—202no—
414C2×C5—21no—
415C2×C5—41no—
416C2×C5Dic3×C22⋊C411yescharacteristic
417D5—21no—
418D5—41no—
419D5#482312yes—
420C23—51no—
421C23—101no—
422Q8—51no—
423Q8—101no—
424Q8C4×ΓL(1,𝔽16)11yescharacteristic
425D4—21no—
426D4—51no—
427D4—101no—
428D4—101no—
429D4—101no—
430D4—101no—
431D4C4×ΓL(1,𝔽16)11yescharacteristic
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—51no—
435C2×C4—51no—
436C2×C4—51no—
437C2×C4—51no—
438C2×C4—51no—
439C2×C4—101no—
440C2×C4—101no—
441C2×C4—101no—
442C2×C4—101no—
443C2×C4—101no—
444C2×C4—202no—
445C2×C4—302no—
446C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
447C8—21no—
448C8—101no—
449C8—152no—
450C8—152no—
451C8—302no—
452C8—302no—
453C2×C3—21no—
454C2×C3—41no—
455C2×C3—52no—
456C2×C3—101no—
457C2×C3—201no—
458C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
459C5#7037011yescharacteristic, complemented, Sylow
460C22—21no—
461C22—51no—
462C22—51no—
463C22—102no—
464C22—101no—
465C22—202no—
466C22D4×ΓL(1,𝔽16)11yescharacteristic
467C4—21no—
468C4—41no—
469C4—51no—
470C4—51no—
471C4—101no—
472C4—201no—
473C4—602no—
474C4C2×C4×ΓL(1,𝔽16)11yescharacteristic
475C4D4×ΓL(1,𝔽16)11yescharacteristic
476C3#1060400611yescharacteristic, complemented, Sylow
477C2—21no—
478C2—41no—
479C2—52no—
480C2—101no—
481C2—201no—
482C2C22⋊C4×ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
centerC4D4×ΓL(1,𝔽16)
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#104C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC3×D5×#41C22
cosocleC2×C3×C4×D5C23
hypercenter#104ΓL(1,𝔽16)
hypocenterC3×C5#1765
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
3. #11752387C2semidirect
4. #11752335C2semidirect
6. #11746772C2semidirect
7. #11746733C2semidirect
10. #91992C4semidirect
12. #91990C4semidirect
21. #91238C4semidirect
22. #91236C4semidirect
26. C3×C5×#104C4semidirect
27. C3×#3969C4semidirect
28. C3×#3957C4semidirect
29. C3×#3937C4semidirect
98. C5×#104Dic3semidirect
99. #3969Dic3semidirect
100. #3957Dic3semidirect
101. #3937Dic3semidirect
151. C3×#104AGL(1,𝔽5)semidirect
300. #104ΓL(1,𝔽16)semidirect
397. C3×C5#1765semidirect
459. C5#70370semidirect
476. C3#10604006semidirect

Maximal subgroups

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

subgroupindex
D5⋊#9482
#117524532
#117523872
#117523352
C3×D5×#1042
#117467722
#117467332
#106040063
#703705