Finite Group Databasebeta

← #14307367

Subgroups — #14307367

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#890C211yesmaximal, characteristic
2#11751860C211yesmaximal, characteristic
3#11751788C211yesmaximal, characteristic
4#11746745C211yesmaximal, characteristic
5C3×#64874C211yesmaximal, characteristic
6#11746530C211yesmaximal, characteristic
7#11746528C211yesmaximal, characteristic
8#10604591—31nomaximal, Hall
9C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
10C2×D5⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
12C2×C3×D5⋊C8C2211yescharacteristic
13C2×Dic3⋊AGL(1,𝔽5)—21no—
14C2×Dic3⋊AGL(1,𝔽5)—21no—
15#91779C411yescharacteristic, complemented
16C5×#890C411yescharacteristic, complemented
17C3×D5×C4⋊C4C2211yescharacteristic
18D5×C4⋊Dic3—21no—
19D5×C4⋊Dic3C2211yescharacteristic
20D5×Dic3⋊C4—21no—
21C4×D5×Dic3C2211yescharacteristic
22#91384C411yescharacteristic, complemented
23#91381C411yescharacteristic, complemented
24#91335—21no—
25#91334—21no—
26#91169—21no—
27#91169—21no—
28#68805—51nomaximal, Hall
29D5×#125—31no—
30#65688—31no—
31#65676—31no—
32#64874—31no—
33#64874—31no—
34#64874—31no—
35#64874D311yescharacteristic
36C22×ΓL(1,𝔽16)—21no—
37C22×C3×AGL(1,𝔽5)—21no—
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5C2311yescharacteristic
40C2×D5×Dic3—21no—
41C2×D5×Dic3D411yescharacteristic
42C2×D5×Dic3D411yescharacteristic
43C2×C3⋊#170—21no—
44C4⋊ΓL(1,𝔽16)—21no—
45C4⋊ΓL(1,𝔽16)—21no—
46D5⋊(C3⋊C8)—21no—
47D5⋊(C3⋊C8)Q812yes—
48C2×C3×#170—21no—
49C3×C4⋊AGL(1,𝔽5)—21no—
50C3×C4⋊AGL(1,𝔽5)—21no—
51C3×D5⋊C8—21no—
52C3×D5⋊C8Q812yes—
53Dic3⋊AGL(1,𝔽5)—42no—
54Dic3⋊AGL(1,𝔽5)—42no—
55C3×C5×C4⋊C4C2×C411yescharacteristic
56C4⋊Dic15—21no—
57C4⋊Dic15C2×C411yescharacteristic
58#6712—21no—
59C4×Dic15C2×C411yescharacteristic
60C5×C4⋊Dic3—21no—
61C5×C4⋊Dic3C2×C411yescharacteristic
62C5×Dic3⋊C4—21no—
63C4×C5×Dic3C2×C411yescharacteristic
64C3×C4⋊Dic5C2×C411yescharacteristic
65C3×#683—21no—
66Dic3⋊Dic5—21no—
67#6669—21no—
68#6668—21no—
69#6668—21no—
70#6668—21no—
71Dic3×Dic5D411yescharacteristic
72Dic3×Dic5D411yescharacteristic
73C2×#890—51no—
74C2×#815—51no—
75#4975—51no—
76C3×#340—51no—
77#4551—51no—
78#4529—51no—
79#4529—51no—
80C2×C4⋊AGL(1,𝔽5)—31no—
81C2×C4⋊AGL(1,𝔽5)—61no—
82C2×C4⋊AGL(1,𝔽5)—61no—
83C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
84C2×D5⋊C8—31no—
85C2×D5⋊C8C2×D311yescharacteristic
86C5×#125—31no—
87D5×C4⋊C4—31no—
88D5×C4⋊C4—61no—
89D5×C4⋊C4—61no—
90D5×C4⋊C4C2×D311yescharacteristic
91#4036—31no—
92#4036—31no—
93#4035—61no—
94#4035—61no—
95C42×D5—31no—
96#4016—31no—
97#4002—61no—
98#4002—61no—
99#1992—151noSylow
100C22×C3×D5C2×D411yescharacteristic
101C2×ΓL(1,𝔽16)—41no—
102C2×ΓL(1,𝔽16)—41no—
103C2×ΓL(1,𝔽16)—41no—
104C2×C3×AGL(1,𝔽5)—41no—
105C2×C3×AGL(1,𝔽5)—41no—
106C2×C3×AGL(1,𝔽5)—41no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×Dic15—21no—
110C2×Dic15C22⋊C411yescharacteristic
111C2×Dic15C22⋊C411yescharacteristic
112C2×C5×Dic3—21no—
113C2×C5×Dic3C22⋊C411yescharacteristic
114C2×C5×Dic3C22⋊C411yescharacteristic
115C2×C3×Dic5—21no—
116C2×C3×Dic5C2×D411yescharacteristic
117C3×C4×D5—41no—
118C3×C4×D5—41no—
119C3×C4×D5C2×Q811yescharacteristic
120C3×C4×D5C2×Q811yescharacteristic
121C3×C4×D5#4111yescharacteristic
122C3×C4×D5#4111yescharacteristic
123D5×Dic3—21no—
124D5×Dic3—21no—
125D5×Dic3—21no—
126D5×Dic3—21no—
127D5×Dic3—41no—
128D5×Dic3—41no—
129C3⋊#170—22no—
130C3×#170—22no—
131C22×C3×C8—51no—
132C2×C3×C4⋊C4—51no—
133C2×C3×C4⋊C4—51no—
134C2×C4⋊Dic3—51no—
135C2×C4⋊Dic3—51no—
136C2×C4⋊Dic3—101no—
137C2×Dic3⋊C4—101no—
138C2×Dic3⋊C4—101no—
139C2×Dic3⋊C4—101no—
140C2×C4×Dic3—51no—
141C22×C3⋊C8—51no—
142#890—51no—
143#890—51no—
144#890—51no—
145#890—101no—
146#890—101no—
147#890AGL(1,𝔽5)11yescharacteristic, complemented
148#815—101no—
149#815—101no—
150C22×AGL(1,𝔽5)—21no—
151C22×AGL(1,𝔽5)—61no—
152C2×C4×D5—21no—
153C2×C4×D5—31no—
154C2×C4×D5—31no—
155C2×C4×D5—61no—
156C2×C4×D5C22×D311yescharacteristic
157C2×#170—21no—
158C2×#170—61no—
159C4⋊AGL(1,𝔽5)—21no—
160C4⋊AGL(1,𝔽5)—21no—
161C4⋊AGL(1,𝔽5)—61no—
162C4⋊AGL(1,𝔽5)—61no—
163C4⋊AGL(1,𝔽5)—122no—
164C4⋊AGL(1,𝔽5)—122no—
165D5⋊C8—21no—
166D5⋊C8—32no—
167D5⋊C8—61no—
168D5⋊C8Dic612yes—
169C5×C4⋊C4—31no—
170C5×C4⋊C4—61no—
171C5×C4⋊C4—61no—
172C5×C4⋊C4C4×D311yescharacteristic
173C42×C5—31no—
174C4⋊Dic5—31no—
175C4⋊Dic5—61no—
176C4⋊Dic5—61no—
177C4⋊Dic5C4×D311yescharacteristic
178#683—21no—
179#683—61no—
180#683—61no—
181#683—61no—
182#683—61no—
183#683—61no—
184C4×Dic5—31no—
185C4×Dic5—31no—
186C4×Dic5—31no—
187C2×#125—151no—
188C2×#97—151no—
189#384—151no—
190#340—51no—
191#340—151no—
192#340—151no—
193#340—151no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C2×C3×D5#12411yescharacteristic
196C2×C3×D5C4⋊Q811yescharacteristic
197C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
198C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
199C2×C3×D5#13711yescharacteristic
200C2×C3×D5#13711yescharacteristic
201ΓL(1,𝔽16)—81no—
202C3×AGL(1,𝔽5)—81no—
203C3×C4×C5—41no—
204C3×C4×C5C4×Q811yescharacteristic
205C3×C4×C5C4×Q811yescharacteristic
206Dic15—21no—
207Dic15—21no—
208Dic15—41no—
209C3×Dic5—41no—
210C3×Dic5C22⋊Q811yescharacteristic
211C3×Dic5C22⋊Q811yescharacteristic
212C5×Dic3—21no—
213C5×Dic3—21no—
214C5×Dic3—41no—
215C22×C3×C4—51no—
216C22×C3×C4—101no—
217C22×C3×C4—101no—
218C22×Dic3—51no—
219C22×Dic3—51no—
220C22×Dic3—101no—
221C22×Dic3—101no—
222C2×C3×C8—52no—
223C2×C3×C8—101no—
224C2×C3×C8—101no—
225C3×C4⋊C4—51no—
226C3×C4⋊C4—101no—
227C3×C4⋊C4—101no—
228C3×C4⋊C4—101no—
229C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
230C4⋊Dic3—21no—
231C4⋊Dic3—51no—
232C4⋊Dic3—101no—
233C4⋊Dic3—101no—
234C4⋊Dic3—101no—
235C4⋊Dic3—101no—
236C4⋊Dic3—101no—
237C4⋊Dic3—101no—
238C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
239Dic3⋊C4—21no—
240Dic3⋊C4—101no—
241Dic3⋊C4—101no—
242Dic3⋊C4—101no—
243Dic3⋊C4—202no—
244Dic3⋊C4—202no—
245C4×Dic3—51no—
246C4×Dic3—51no—
247C4×Dic3—51no—
248C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
249C2×C3⋊C8—52no—
250C2×C3⋊C8—101no—
251C2×C3⋊C8—101no—
252C22×D5D3×D411yescharacteristic
253C2×AGL(1,𝔽5)—41no—
254C2×AGL(1,𝔽5)—41no—
255C2×AGL(1,𝔽5)—41no—
256C2×AGL(1,𝔽5)—121no—
257C2×AGL(1,𝔽5)—121no—
258C2×AGL(1,𝔽5)—121no—
259C2×C4×C5—21no—
260C2×C4×C5—31no—
261C2×C4×C5—31no—
262C2×C4×C5—61no—
263C2×C4×C5C2×C4×D311yescharacteristic
264C2×Dic5—21no—
265C2×Dic5—31no—
266C2×Dic5—31no—
267C2×Dic5—61no—
268C2×Dic5D3×D411yescharacteristic
269C4×D5—41no—
270C4×D5—41no—
271C4×D5—61no—
272C4×D5—61no—
273C4×D5—61no—
274C4×D5—61no—
275C4×D5—121no—
276C4×D5—121no—
277C4×D5C2×Dic611yescharacteristic
278C4×D5#23511yescharacteristic
279C4×D5#23711yescharacteristic
280C4×D5D3×Q811yescharacteristic
281#170—22no—
282#170—62no—
283C22×C8—51no—
284C22×C8—151no—
285#125—31no—
286#125—151no—
287#125—151no—
288#125—151no—
289#125—301no—
290#125—301no—
291C2×C4⋊C4—51no—
292C2×C4⋊C4—51no—
293C2×C4⋊C4—151no—
294C2×C4⋊C4—151no—
295C2×C4⋊C4—301no—
296C2×C4⋊C4—301no—
297C2×C4⋊C4—301no—
298C2×C4⋊C4—301no—
299C2×C42—151no—
300#97—301no—
301#97—301no—
302C2×C3×C5#39111yescharacteristic
303C2×C3×C5#41711yescharacteristic
304C2×C3×C5#41711yescharacteristic
305C3×D5#49011yescharacteristic
306C3×D5#49111yescharacteristic
307C3×D5#50111yescharacteristic
308C3×D5#50111yescharacteristic
309C23×C3—51no—
310C2×C3×C4—21no—
311C2×C3×C4—51no—
312C2×C3×C4—51no—
313C2×C3×C4—51no—
314C2×C3×C4—51no—
315C2×C3×C4—51no—
316C2×C3×C4—101no—
317C2×C3×C4—201no—
318C2×C3×C4—201no—
319C2×C3×C4—201no—
320C2×C3×C4—201no—
321C2×C3×C4—201no—
322C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
323C2×Dic3—21no—
324C2×Dic3—51no—
325C2×Dic3—51no—
326C2×Dic3—101no—
327C2×Dic3—101no—
328C2×Dic3—101no—
329C2×Dic3—101no—
330C2×Dic3—101no—
331C2×Dic3—201no—
332C2×Dic3—201no—
333C2×Dic3—201no—
334C2×Dic3—201no—
335C2×Dic3—201no—
336C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
337C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
338C3×C8—102no—
339C3⋊C8—102no—
340C22×C5D3×C22⋊C411yescharacteristic
341C2×D5#88511yescharacteristic
342C2×D5#88811yescharacteristic
343C2×D5#91111yescharacteristic
344C2×D5#91411yescharacteristic
345C2×D5#91511yescharacteristic
346C2×D5#91811yescharacteristic
347AGL(1,𝔽5)—81no—
348AGL(1,𝔽5)—241no—
349C4×C5—41no—
350C4×C5—61no—
351C4×C5—61no—
352C4×C5—121no—
353C4×C5C4×Dic611yescharacteristic
354C4×C5#88711yescharacteristic
355Dic5—41no—
356Dic5—61no—
357Dic5—61no—
358Dic5—121no—
359Dic5#87811yescharacteristic
360Dic5#89611yescharacteristic
361C22×C4—51no—
362C22×C4—101no—
363C22×C4—101no—
364C22×C4—151no—
365C22×C4—151no—
366C22×C4—301no—
367C22×C4—301no—
368C2×C8—52no—
369C2×C8—101no—
370C2×C8—101no—
371C2×C8—152no—
372C2×C8—301no—
373C2×C8—301no—
374C4⋊C4—31no—
375C4⋊C4—51no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—101no—
379C4⋊C4—101no—
380C4⋊C4—101no—
381C4⋊C4—151no—
382C4⋊C4—301no—
383C4⋊C4—301no—
384C4⋊C4—301no—
385C4⋊C4—301no—
386C4⋊C4—301no—
387C4⋊C4—301no—
388C4⋊C4—301no—
389C4⋊C4—301no—
390C4⋊C4—301no—
391C4⋊C4—602no—
392C4⋊C4—602no—
393C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
394C42—31no—
395C42—151no—
396C42—151no—
397C42—151no—
398C3×C5#199211yescharacteristic, complemented, Hall
399C22×C3—51no—
400C22×C3—51no—
401C22×C3—51no—
402C22×C3—51no—
403C22×C3—51no—
404C22×C3—51no—
405C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
406C3×C4—41no—
407C3×C4—51no—
408C3×C4—51no—
409C3×C4—201no—
410C3×C4—401no—
411C3×C4Q8×AGL(1,𝔽5)11yescharacteristic
412C3×C4Q8×AGL(1,𝔽5)11yescharacteristic
413Dic3—21no—
414Dic3—21no—
415Dic3—41no—
416Dic3—101no—
417Dic3—101no—
418Dic3—201no—
419Dic3—401no—
420C2×C5#464611yescharacteristic
421C2×C5#477111yescharacteristic
422C2×C5#480311yescharacteristic
423D5#476411yescharacteristic
424D5#479711yescharacteristic
425D5#485611yescharacteristic
426D5#487611yescharacteristic
427C23—51no—
428C2×C4—21no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—51no—
432C2×C4—51no—
433C2×C4—51no—
434C2×C4—51no—
435C2×C4—51no—
436C2×C4—61no—
437C2×C4—101no—
438C2×C4—151no—
439C2×C4—151no—
440C2×C4—201no—
441C2×C4—201no—
442C2×C4—201no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4—301no—
446C2×C4—301no—
447C2×C4—301no—
448C2×C4—301no—
449C2×C4—301no—
450C2×C4—601no—
451C2×C4—601no—
452C2×C4—601no—
453C2×C4—601no—
454C2×C4—601no—
455C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
456C8—102no—
457C8—302no—
458C2×C3—51no—
459C2×C3—51no—
460C2×C3—51no—
461C2×C3—51no—
462C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
463C2×C3#6579311yescharacteristic
464C2×C3#6579311yescharacteristic
465C5#6880511yescharacteristic, complemented, Sylow
466C22—51no—
467C22—51no—
468C22—51no—
469C22—51no—
470C22—51no—
471C22—51no—
472C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
473C4—41no—
474C4—51no—
475C4—51no—
476C4—61no—
477C4—61no—
478C4—121no—
479C4—201no—
480C4—301no—
481C4—301no—
482C4—401no—
483C4—601no—
484C4—1201no—
485C4AGL(1,𝔽5)×Dic611yescharacteristic
486C4ΓL(1,𝔽16)⋊Q811yescharacteristic
487C3#1060459111yescharacteristic, complemented, Sylow
488C2—51no—
489C2—51no—
490C2—51no—
491C2—51no—
492C2#1175184211yescharacteristic
493C2#1175193711yescharacteristic
494C2#1175196111yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1992
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
15. #91779C4semidirect
16. C5×#890C4semidirect
22. #91384C4semidirect
23. #91381C4semidirect
147. #890AGL(1,𝔽5)semidirect
398. C3×C5#1992semidirect
465. C5#68805semidirect
487. C3#10604591semidirect

Maximal subgroups

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

subgroupindex
D5×#8902
#117518602
#117517882
#117467452
C3×#648742
#117465302
#117465282
#106045913
#688055