Finite Group Databasebeta

← #14295549

Subgroups — #14295549

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91268C211yesmaximal, characteristic
2#11751818C211yesmaximal, characteristic
3#11751815C211yesmaximal, characteristic
4#11751696C211yesmaximal, characteristic, complemented
5#11751695C211yesmaximal, characteristic, complemented
6#11746765C211yesmaximal, characteristic, complemented
7C3×#64894C211yesmaximal, characteristic, complemented
8#10604764—31nomaximal, Hall
9C2×#6771C2211yescharacteristic
10#91989C2211yescharacteristic
11D5⋊#208C2211yescharacteristic
12C3×#4130C2211yescharacteristic
13C3×D5⋊M16C2211yescharacteristic
14C2×C8×D15C411yescharacteristic, complemented
15C2×C5×ΓL(1,𝔽25)C411yescharacteristic, complemented
16C2×C3×#676C2211yescharacteristic
17C2×#6651C411yescharacteristic, complemented
18C2×D3×#168C411yescharacteristic, complemented
19C2×D5×C3⋊C8C2211yescharacteristic
20#91268—21no—
21#91268—21no—
22#91268—21no—
23#91268—21no—
24#91175C412yescomplemented
25#91174C412yescomplemented
26#91173C412yes—
27#91172C412yes—
28#91150—21no—
29#91149—21no—
30ΓL(1,𝔽16)⋊C8—21no—
31AGL(1,𝔽5)×C3⋊C8—21no—
32#69014—51nomaximal, Hall
33C2×#4053—31no—
34#65761—31no—
35#65745—31no—
36#65718—31no—
37#65718—31no—
38#64894—31no—
39#64894D311yescharacteristic, complemented
40C2×C4×D15C2×C411yescharacteristic
41C2×C4×C5×D3C2×C411yescharacteristic
42C2×C3×C4×D5C2311yescharacteristic
43C2×#1204C2×C411yescharacteristic
44C2×#1203C2×C411yescharacteristic
45C2×#1202C2×C411yescharacteristic
46C2×#1201C2×C411yescharacteristic
47#6771—21no—
48#6771—21no—
49#6771—21no—
50#6771—21no—
51#6763C2×C412yes—
52#6762C2×C412yes—
53C4⋊ΓL(1,𝔽16)—21no—
54C4×ΓL(1,𝔽16)—21no—
55#6758—21no—
56D5⋊(C3⋊C8)—21no—
57C3×C22⋊AGL(1,𝔽5)C2×C412yes—
58C3×#704C2×C412yes—
59C3×C4⋊AGL(1,𝔽5)—21no—
60C3×C4×AGL(1,𝔽5)—21no—
61C3×#700—21no—
62C3×D5⋊C8—21no—
63C2×C3×C5×C8C2×C411yescharacteristic
64C2×C3⋊#168C2×C411yescharacteristic
65C8×D15—21no—
66C8×D15—21no—
67C2×C5×C3⋊C8C2×C411yescharacteristic
68C5×ΓL(1,𝔽25)—21no—
69C5×ΓL(1,𝔽25)—21no—
70C2×C3×#168C2×C411yescharacteristic
71C3×#676—21no—
72C3×#676—21no—
73#6651—21no—
74#6651—21no—
75D3×#168—21no—
76D3×#168—21no—
77D5×C3⋊C8D411yescharacteristic
78D5×C3⋊C8D411yescharacteristic
79D5×C3⋊C8D411yescharacteristic
80D5×C3⋊C8D411yescharacteristic
81C2×#907—51no—
82#5132—51no—
83#5122—51no—
84#5006—51no—
85#4997—51no—
86C3×#344—51no—
87#4556—51no—
88C2×#709—31no—
89#4130—31no—
90#4130C2×D311yescharacteristic
91D5⋊M16—31no—
92D5⋊M16C2×D311yescharacteristic
93C2×C5×M16—31no—
94C22×#168—31no—
95#4053—61no—
96#4053—61no—
97#4053—61no—
98#4053—61no—
99C2×#676—31no—
100C2×#676C2×D311yescharacteristic
101C2×C8×D5—31no—
102C2×C8×D5—31no—
103#4013—32no—
104#4011—32no—
105#4005—32no—
106#3999—32no—
107#3992—61no—
108#3992—61no—
109C8×AGL(1,𝔽5)—61no—
110C8×AGL(1,𝔽5)—61no—
111#1757—151noSylow
112C22×D15C4211yescharacteristic
113C22×C5×D3C4211yescharacteristic
114C22×C3×D5C22×C411yescharacteristic
115C2×ΓL(1,𝔽16)—22no—
116C2×C3×AGL(1,𝔽5)—22no—
117C2×C3×C4×C5C22×C411yescharacteristic
118C2×Dic15C4211yescharacteristic
119C4×D15—21no—
120C4×D15—21no—
121C2×C5×Dic3C4211yescharacteristic
122C4×C5×D3—21no—
123C4×C5×D3—21no—
124C2×C3×Dic5C22×C411yescharacteristic
125C3×C4×D5C2×D411yescharacteristic
126C3×C4×D5C2×D411yescharacteristic
127C3×C4×D5#4111yescharacteristic
128C3×C4×D5#4111yescharacteristic
129#1204—21no—
130#1204—21no—
131#1203—21no—
132#1203—21no—
133#1202—21no—
134#1202—21no—
135#1201—21no—
136#1201—21no—
137C3⋊#170—22no—
138C3×#170—22no—
139C3×C5×C8—21no—
140C3⋊#168C22⋊C411yescharacteristic
141C3⋊#168C22⋊C411yescharacteristic
142C3×#168—21no—
143C5×C3⋊C8C22⋊C411yescharacteristic
144C5×C3⋊C8C22⋊C411yescharacteristic
145C2×#235—51no—
146C2×C3×M16—51no—
147C2×C3×M16—51no—
148C3×#117—51no—
149#926—51no—
150C2×#208—51no—
151C22×C3⋊C8—51no—
152#907—101no—
153#907—101no—
154#907—101no—
155#907—101no—
156C2×ΓL(1,𝔽25)—51no—
157C2×ΓL(1,𝔽25)AGL(1,𝔽5)11yescharacteristic, complemented
158C2×D3×C8—51no—
159C2×D3×C8—51no—
160#824—52no—
161#823—52no—
162#815—101no—
163C8×Dic3—101no—
164#806—52no—
165#806—52no—
166#803—101no—
167C4×C3⋊C8—101no—
168C22×C4×C5—31no—
169C2×C22⋊D5—31no—
170C2×C22⋊D5—31no—
171#709—61no—
172#709—61no—
173#709—61no—
174#709—61no—
175C2×D20—31no—
176C2×C4×D5—31no—
177C2×C4×D5C22×D311yescharacteristic
178C2×Dic10—31no—
179C22⋊AGL(1,𝔽5)—32no—
180C22⋊AGL(1,𝔽5)C4×D312yes—
181#704—32no—
182#704C4×D312yes—
183C4⋊AGL(1,𝔽5)—21no—
184C4⋊AGL(1,𝔽5)—61no—
185C4×AGL(1,𝔽5)—21no—
186C4×AGL(1,𝔽5)—61no—
187#700—21no—
188#700—61no—
189D5⋊C8—21no—
190D5⋊C8—61no—
191C5×M16—61no—
192C5×M16—61no—
193C2×C5×C8—31no—
194C2×C5×C8C4×D311yescharacteristic
195C2×#168—31no—
196C2×#168—61no—
197C2×#168—61no—
198C2×#168C4×D311yescharacteristic
199#676—21no—
200#676—21no—
201#676—61no—
202#676—61no—
203C8×D5—31no—
204C8×D5—31no—
205C8×D5—31no—
206C8×D5—31no—
207C8×D5—61no—
208C8×D5—61no—
209C2×#131—151no—
210#413—151no—
211#410—151no—
212#405—151no—
213#405—151no—
214#344—51no—
215#344—151no—
216C22×C3×C5C2×C4211yescharacteristic
217C2×D15—21no—
218C2×D15—41no—
219C2×C5×D3—21no—
220C2×C5×D3—41no—
221C2×C3×D5—41no—
222C2×C3×D5C4×D411yescharacteristic
223C2×C3×D5C4×D411yescharacteristic
224ΓL(1,𝔽16)—42no—
225C3×AGL(1,𝔽5)—42no—
226C3×C4×C5C2×C22⋊C411yescharacteristic
227C3×C4×C5#11711yescharacteristic
228Dic15—21no—
229C3×Dic5C4×D411yescharacteristic
230C3×Dic5C4×D411yescharacteristic
231C5×Dic3—21no—
232C22×C3×C4—51no—
233C2×#67—51no—
234C2×#67—51no—
235#235—101no—
236#235—101no—
237#235—101no—
238#235—101no—
239C2×D12—51no—
240C2×C4×D3—51no—
241C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
242C2×Dic6—51no—
243C3×M16—52no—
244C3×M16—101no—
245C3×M16—101no—
246C3×M16—101no—
247C2×C3×C8—51no—
248C2×C3×C8—101no—
249C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
250C3×C4⋊C4—101no—
251C3×C22⋊C4—52no—
252C3×C42—101no—
253#217—52no—
254C4⋊Dic3—101no—
255C4×Dic3—101no—
256#208—52no—
257#208—101no—
258C2×C3⋊C8—51no—
259C2×C3⋊C8—51no—
260C2×C3⋊C8—51no—
261C2×C3⋊C8—51no—
262C2×C3⋊C8—51no—
263C2×C3⋊C8—101no—
264C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
265ΓL(1,𝔽25)—21no—
266ΓL(1,𝔽25)—21no—
267ΓL(1,𝔽25)—101no—
268ΓL(1,𝔽25)—101no—
269D3×C8—101no—
270D3×C8—101no—
271D3×C8—101no—
272D3×C8—101no—
273C23×C5—31no—
274C22×D5—31no—
275C22×D5C2×C4×D311yescharacteristic
276C2×AGL(1,𝔽5)—22no—
277C2×AGL(1,𝔽5)—62no—
278C2×C4×C5—31no—
279C2×C4×C5—61no—
280C2×C4×C5—61no—
281C2×C4×C5C2×C4×D311yescharacteristic
282C22⋊D5—61no—
283C22⋊D5—61no—
284C22⋊D5—61no—
285C22⋊D5—61no—
286C2×Dic5—31no—
287C2×Dic5C2×C4×D311yescharacteristic
288D20—61no—
289D20—61no—
290C4×D5—61no—
291C4×D5—61no—
292C4×D5D3×D411yescharacteristic
293C4×D5D3×D411yescharacteristic
294C4×D5#23711yescharacteristic
295C4×D5#23911yescharacteristic
296Dic10—61no—
297Dic10—61no—
298#170—22no—
299#170—62no—
300C5×C8—21no—
301C5×C8—31no—
302C5×C8—31no—
303#168—21no—
304#168—31no—
305#168—31no—
306C2×#41—151no—
307#131—301no—
308#131—301no—
309#131—301no—
310#131—301no—
311C2×M16—31no—
312C2×M16—51no—
313C2×M16—51no—
314C2×M16—151no—
315C2×M16—151no—
316C22×C8—151no—
317C22×C8—151no—
318C22×C8—151no—
319#117—51no—
320#117—151no—
321#101—152no—
322#100—152no—
323#99—152no—
324#99—152no—
325#97—301no—
326#97—301no—
327C4×C8—301no—
328C4×C8—301no—
329C2×C3×C5—21no—
330C2×C3×C5C4×C22⋊C411yescharacteristic
331D15—41no—
332C3×D5—21no—
333C3×D5—21no—
334C5×D3—41no—
335C23×C3—51no—
336C22×D3—51no—
337C22×D3C4×AGL(1,𝔽5)11yescharacteristic
338C2×C3×C4—51no—
339C2×C3×C4—51no—
340C2×C3×C4—51no—
341C2×C3×C4—51no—
342C2×C3×C4—51no—
343C2×C3×C4—102no—
344C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
345#67—101no—
346#67—101no—
347#67—101no—
348#67—101no—
349C2×Dic3—51no—
350C2×Dic3—102no—
351C2×Dic3C4×AGL(1,𝔽5)11yescharacteristic
352D12—101no—
353D12—101no—
354C4×D3—21no—
355C4×D3—21no—
356C4×D3—101no—
357C4×D3—101no—
358Dic6—101no—
359Dic6—101no—
360C3×C8—21no—
361C3×C8—102no—
362C3×C8—101no—
363C3⋊C8—51no—
364C3⋊C8—51no—
365C3⋊C8—102no—
366C3⋊C8C22⋊AGL(1,𝔽5)11yescharacteristic
367C3⋊C8C22⋊AGL(1,𝔽5)11yescharacteristic
368C22×C5—61no—
369C22×C5—121no—
370C22×C5C42×D311yescharacteristic
371C2×D5—41no—
372C2×D5—61no—
373C2×D5—121no—
374C2×D5#67⋊C411yescharacteristic
375C2×D5#89311yescharacteristic
376AGL(1,𝔽5)—42no—
377AGL(1,𝔽5)—122no—
378C4×C5—61no—
379C4×C5D3×C22⋊C411yescharacteristic
380C4×C5#89211yescharacteristic
381Dic5—61no—
382Dic5#67⋊C411yescharacteristic
383Dic5#89311yescharacteristic
384#41—301no—
385#41—301no—
386#41—301no—
387#41—301no—
388C2×Q8—151no—
389C2×D4—151no—
390C2×D4—151no—
391C2×D4—151no—
392C22×C4—31no—
393C22×C4—51no—
394C22×C4—151no—
395M16—52no—
396M16—61no—
397M16—61no—
398M16—101no—
399M16—101no—
400M16—101no—
401M16—152no—
402M16—301no—
403M16—301no—
404M16—301no—
405C2×C8—31no—
406C2×C8—51no—
407C2×C8—101no—
408C2×C8—151no—
409C2×C8—151no—
410C2×C8—151no—
411C2×C8—151no—
412C2×C8—151no—
413C2×C8—301no—
414C2×C8—301no—
415C2×C8—301no—
416C2×C8—301no—
417C2×C8—301no—
418C2×C8D3×AGL(1,𝔽5)11yescharacteristic
419C4⋊C4—101no—
420C4⋊C4—301no—
421C22⋊C4—52no—
422C22⋊C4—152no—
423C42—101no—
424C42—301no—
425C3×C5#175711yescharacteristic, complemented, Hall
426C22×C3—51no—
427C22×C3—51no—
428C22×C3—201no—
429C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
430C2×D3—21no—
431C2×D3—41no—
432C2×D3—101no—
433C2×D3—201no—
434C3×C4—51no—
435C3×C4—51no—
436C3×C4—202no—
437C3×C4#413011yescharacteristic
438C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
439Dic3—21no—
440Dic3—101no—
441Dic3—202no—
442C2×C5—21no—
443C2×C5—121no—
444C2×C5#466611yescharacteristic
445D5—21no—
446D5—21no—
447D5—121no—
448C23—31no—
449C23—51no—
450C23—151no—
451Q8—301no—
452Q8—301no—
453D4—301no—
454D4—301no—
455D4—301no—
456D4—301no—
457D4—301no—
458D4—301no—
459C2×C4—31no—
460C2×C4—51no—
461C2×C4—51no—
462C2×C4—51no—
463C2×C4—51no—
464C2×C4—51no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—102no—
468C2×C4—151no—
469C2×C4—301no—
470C2×C4—301no—
471C2×C4—302no—
472C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
473C8—21no—
474C8—31no—
475C8—31no—
476C8—102no—
477C8—101no—
478C8—151no—
479C8—151no—
480C8—302no—
481C2×C3—21no—
482C2×C3—101no—
483C2×C3—101no—
484C2×C3C4×C22⋊AGL(1,𝔽5)11yescharacteristic
485D3—41no—
486D3—201no—
487C5#6901411yescharacteristic, complemented, Sylow
488C22—51no—
489C22—51no—
490C22—61no—
491C22—121no—
492C22—201no—
493C22—301no—
494C22—601no—
495C22C4×D3×AGL(1,𝔽5)11yescharacteristic
496C4—51no—
497C4—51no—
498C4—61no—
499C4—202no—
500C4—301no—
501C4—602no—
502C4#9190711yescharacteristic
503C4D3×C22⋊AGL(1,𝔽5)11yescharacteristic
504C3#1060476411yescharacteristic, complemented, Sylow
505C2—21no—
506C2—101no—
507C2—101no—
508C2—121no—
509C2—601no—
510C2#1175184811yescharacteristic
subgroupG/H
centerC4D3×C22⋊AGL(1,𝔽5)
commutatorC22×C3×C5C2×C42
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC2×#6771C22
cosocleC2×C3×C4×D5C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5#1757
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. #11751696C2semidirect
5. #11751695C2semidirect
6. #11746765C2semidirect
7. C3×#64894C2semidirect
14. C2×C8×D15C4semidirect
15. C2×C5×ΓL(1,𝔽25)C4semidirect
17. C2×#6651C4semidirect
18. C2×D3×#168C4semidirect
24. #91175C4semidirect
25. #91174C4semidirect
39. #64894D3semidirect
157. C2×ΓL(1,𝔽25)AGL(1,𝔽5)semidirect
425. C3×C5#1757semidirect
487. C5#69014semidirect
504. C3#10604764semidirect

Maximal subgroups

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

subgroupindex
C2×#912682
#117518182
#117518152
#117516962
#117516952
#117467652
C3×#648942
#106047643
#690145