Finite Group Databasebeta

← #14307399

Subgroups — #14307399

Order 1920.

552 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
1D5×#888C211yesmaximal, characteristic
2#11751788C211yesmaximal, characteristic
3#11751751C211yesmaximal, characteristic
4#11746745C211yesmaximal, characteristic
5C3×#64874C211yesmaximal, characteristic
6#11746530C211yesmaximal, characteristic
7#11746528C211yesmaximal, characteristic
8#10604675—31nomaximal, Hall
9C2×D5×Dic6—21no—
10C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
11C2×D5⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
13C2×C3×D5⋊C8C2211yescharacteristic
14#91777C411yescharacteristic, complemented
15C5×#888C411yescharacteristic, complemented
16C3×D5×C4⋊C4C2211yescharacteristic
17#91470C411yescharacteristic, complemented
18#91469C411yescharacteristic, complemented
19D5×C4⋊Dic3C2211yescharacteristic
20D5×Dic3⋊C4—21no—
21C4×D5×Dic3C2211yescharacteristic
22#91329—21no—
23#91328—21no—
24#91169—21no—
25#91169—21no—
26(C2×AGL(1,𝔽5))⋊Dic3—21no—
27(C2×AGL(1,𝔽5))⋊Dic3—21no—
28#68806—51nomaximal, Hall
29D5×C4⋊Q8—31no—
30#65689—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×Dic30—21no—
39C2×C5×Dic6—21no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5C2311yescharacteristic
42C2×#1204—21no—
43C2×#1204—21no—
44C2×D5×Dic3—21no—
45C2×D5×Dic3D411yescharacteristic
46C2×D5×Dic3D411yescharacteristic
47D5×Dic6—42no—
48D5×Dic6—42no—
49C2×C3⋊#170—21no—
50C4⋊ΓL(1,𝔽16)—21no—
51C4⋊ΓL(1,𝔽16)—21no—
52D5⋊(C3⋊C8)—21no—
53D5⋊(C3⋊C8)Q812yescomplemented
54C2×C3×#170—21no—
55C3×C4⋊AGL(1,𝔽5)—21no—
56C3×C4⋊AGL(1,𝔽5)—21no—
57C3×D5⋊C8—21no—
58C3×D5⋊C8Q812yescomplemented
59C3×C5×C4⋊C4C2×C411yescharacteristic
60C4⋊Dic15C2×C411yescharacteristic
61#6712—21no—
62C4×Dic15C2×C411yescharacteristic
63C5×C4⋊Dic3C2×C411yescharacteristic
64C5×Dic3⋊C4—21no—
65C4×C5×Dic3C2×C411yescharacteristic
66C3×C4⋊Dic5C2×C411yescharacteristic
67C3×#683—21no—
68Dic3⋊Dic5—21no—
69#6669—21no—
70#6668—21no—
71Dic3×Dic5D411yescharacteristic
72Dic3×Dic5D411yescharacteristic
73C2×#888—51no—
74C2×#815—51no—
75#4977—51no—
76C3×#340—51no—
77#4551—51no—
78#4529—51no—
79#4529—51no—
80C2×Q8×D5—61no—
81C2×C4⋊AGL(1,𝔽5)—31no—
82C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
83C2×D5⋊C8—31no—
84C2×D5⋊C8C2×D311yescharacteristic
85C5×C4⋊Q8—31no—
86#4090—61no—
87D5×C4⋊C4—31no—
88D5×C4⋊C4—61no—
89D5×C4⋊C4C2×D311yescharacteristic
90#4034—31no—
91#4034—31no—
92#4034—61no—
93C42×D5—31no—
94#4015—31no—
95(C2×AGL(1,𝔽5))⋊C4—61no—
96(C2×AGL(1,𝔽5))⋊C4—61no—
97#4002—61no—
98#4002—61no—
99#1993—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
112Dic30—42no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3C22⋊C411yescharacteristic
115C2×C5×Dic3C22⋊C411yescharacteristic
116C5×Dic6—42no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5C2×D411yescharacteristic
119C3×C4×D5—41no—
120C3×C4×D5—41no—
121C3×C4×D5C2×Q811yescharacteristic
122C3×C4×D5C2×Q811yescharacteristic
123C3×C4×D5#4111yescharacteristic
124C3×C4×D5#4111yescharacteristic
125#1204—42no—
126#1204—42no—
127D5×Dic3—21no—
128D5×Dic3—21no—
129D5×Dic3—21no—
130D5×Dic3—21no—
131D5×Dic3—41no—
132D5×Dic3—41no—
133C3⋊#170—22no—
134C3×#170—22no—
135C22×Dic6—101no—
136C22×C3×C8—51no—
137C2×C3×C4⋊C4—51no—
138C2×C3×C4⋊C4—51no—
139C2×C4⋊Dic3—51no—
140C2×C4⋊Dic3—51no—
141C2×Dic3⋊C4—101no—
142C2×C4×Dic3—51no—
143C22×C3⋊C8—51no—
144#888—51no—
145#888—51no—
146#888—51no—
147#888—101no—
148#888—101no—
149#888AGL(1,𝔽5)11yescharacteristic, complemented
150C3⋊#95—101no—
151C3⋊#95—101no—
152#815—101no—
153#815—101no—
154C22×AGL(1,𝔽5)—21no—
155C22×AGL(1,𝔽5)—61no—
156C2×C5×Q8—61no—
157Q8×D5—122no—
158Q8×D5—122no—
159C2×C4×D5—21no—
160C2×C4×D5—31no—
161C2×C4×D5—31no—
162C2×C4×D5—61no—
163C2×C4×D5C22×D311yescharacteristic
164C2×Dic10—61no—
165C2×Dic10—61no—
166C2×Dic10—61no—
167C2×#170—21no—
168C2×#170—61no—
169C4⋊AGL(1,𝔽5)—21no—
170C4⋊AGL(1,𝔽5)—21no—
171C4⋊AGL(1,𝔽5)—61no—
172C4⋊AGL(1,𝔽5)—61no—
173D5⋊C8—21no—
174D5⋊C8—32no—
175D5⋊C8—61no—
176D5⋊C8Dic612yescomplemented
177C5×C4⋊C4—31no—
178C5×C4⋊C4—61no—
179C5×C4⋊C4C4×D311yescharacteristic
180C42×C5—31no—
181C4⋊Dic5—31no—
182C4⋊Dic5—61no—
183C4⋊Dic5C4×D311yescharacteristic
184#683—21no—
185#683—61no—
186#683—61no—
187#683—61no—
188C4×Dic5—31no—
189C4×Dic5—31no—
190C4×Dic5—31no—
191C2×C4⋊Q8—151no—
192C2×#97—151no—
193#382—151no—
194#340—51no—
195#340—151no—
196#340—151no—
197#340—151no—
198C22×C3×C5C2×C22⋊C411yescharacteristic
199C2×C3×D5#12411yescharacteristic
200C2×C3×D5C4⋊Q811yescharacteristic
201C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
202C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
203C2×C3×D5#13711yescharacteristic
204C2×C3×D5#13711yescharacteristic
205ΓL(1,𝔽16)—81no—
206C3×AGL(1,𝔽5)—81no—
207C3×C4×C5—41no—
208C3×C4×C5C4×Q811yescharacteristic
209C3×C4×C5C4×Q811yescharacteristic
210Dic15—21no—
211Dic15—21no—
212Dic15—41no—
213C3×Dic5—41no—
214C3×Dic5C22⋊Q811yescharacteristic
215C3×Dic5C22⋊Q811yescharacteristic
216C5×Dic3—21no—
217C5×Dic3—21no—
218C5×Dic3—41no—
219C22×C3×C4—51no—
220C22×C3×C4—101no—
221C22×C3×C4—101no—
222C22×Dic3—51no—
223C22×Dic3—51no—
224C22×Dic3—101no—
225C22×Dic3—101no—
226C2×Dic6—21no—
227C2×Dic6—101no—
228C2×Dic6—101no—
229C2×Dic6—101no—
230C2×Dic6—202no—
231C2×Dic6—202no—
232C2×C3×C8—52no—
233C2×C3×C8—101no—
234C2×C3×C8—101no—
235C3×C4⋊C4—51no—
236C3×C4⋊C4—101no—
237C3×C4⋊C4—101no—
238C3×C4⋊C4—101no—
239C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
240C4⋊Dic3—51no—
241C4⋊Dic3—101no—
242C4⋊Dic3—101no—
243C4⋊Dic3—101no—
244C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
245Dic3⋊C4—21no—
246Dic3⋊C4—101no—
247Dic3⋊C4—101no—
248Dic3⋊C4—101no—
249C4×Dic3—51no—
250C4×Dic3—51no—
251C4×Dic3—51no—
252C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
253C2×C3⋊C8—52no—
254C2×C3⋊C8—101no—
255C2×C3⋊C8—101no—
256C22×D5D3×D411yescharacteristic
257C2×AGL(1,𝔽5)—41no—
258C2×AGL(1,𝔽5)—41no—
259C2×AGL(1,𝔽5)—41no—
260C2×AGL(1,𝔽5)—121no—
261C2×AGL(1,𝔽5)—121no—
262C2×AGL(1,𝔽5)—121no—
263C5×Q8—122no—
264C2×C4×C5—21no—
265C2×C4×C5—31no—
266C2×C4×C5—31no—
267C2×C4×C5—61no—
268C2×C4×C5C2×C4×D311yescharacteristic
269C2×Dic5—21no—
270C2×Dic5—31no—
271C2×Dic5—31no—
272C2×Dic5—61no—
273C2×Dic5D3×D411yescharacteristic
274C4×D5—41no—
275C4×D5—41no—
276C4×D5—61no—
277C4×D5—61no—
278C4×D5—61no—
279C4×D5—61no—
280C4×D5—121no—
281C4×D5—121no—
282C4×D5C2×Dic611yescharacteristic
283C4×D5#23511yescharacteristic
284C4×D5#23711yescharacteristic
285C4×D5D3×Q811yescharacteristic
286Dic10—122no—
287Dic10—122no—
288Dic10—122no—
289#170—22no—
290#170—62no—
291C22×Q8—301no—
292C22×C8—51no—
293C22×C8—151no—
294C4⋊Q8—31no—
295C4⋊Q8—151no—
296C4⋊Q8—151no—
297C4⋊Q8—151no—
298C4⋊Q8—301no—
299C4⋊Q8—301no—
300C2×C4⋊C4—51no—
301C2×C4⋊C4—51no—
302C2×C4⋊C4—151no—
303C2×C4⋊C4—151no—
304C2×C4⋊C4—301no—
305C2×C42—151no—
306#97—301no—
307#97—301no—
308#95—301no—
309#95—301no—
310C2×C3×C5#39111yescharacteristic
311C2×C3×C5#41811yescharacteristic
312C2×C3×C5#41911yescharacteristic
313C3×D5#48911yescharacteristic
314C3×D5#48911yescharacteristic
315C3×D5#50111yescharacteristic
316C3×D5#50111yescharacteristic
317C23×C3—51no—
318C2×C3×C4—21no—
319C2×C3×C4—51no—
320C2×C3×C4—51no—
321C2×C3×C4—51no—
322C2×C3×C4—51no—
323C2×C3×C4—51no—
324C2×C3×C4—101no—
325C2×C3×C4—201no—
326C2×C3×C4—201no—
327C2×C3×C4—201no—
328C2×C3×C4—201no—
329C2×C3×C4—201no—
330C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
331C2×Dic3—21no—
332C2×Dic3—51no—
333C2×Dic3—51no—
334C2×Dic3—101no—
335C2×Dic3—101no—
336C2×Dic3—101no—
337C2×Dic3—101no—
338C2×Dic3—101no—
339C2×Dic3—201no—
340C2×Dic3—201no—
341C2×Dic3—201no—
342C2×Dic3—201no—
343C2×Dic3—201no—
344C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
345C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
346Dic6—42no—
347Dic6—202no—
348Dic6—202no—
349Dic6—202no—
350C3×C8—102no—
351C3⋊C8—102no—
352C22×C5D3×C22⋊C411yescharacteristic
353C2×D5#88511yescharacteristic
354C2×D5#88811yescharacteristic
355C2×D5#91111yescharacteristic
356C2×D5#91411yescharacteristic
357C2×D5#91511yescharacteristic
358C2×D5#91811yescharacteristic
359AGL(1,𝔽5)—81no—
360AGL(1,𝔽5)—241no—
361C4×C5—41no—
362C4×C5—61no—
363C4×C5—61no—
364C4×C5—121no—
365C4×C5C4×Dic611yescharacteristic
366C4×C5#88711yescharacteristic
367Dic5—41no—
368Dic5—61no—
369Dic5—61no—
370Dic5—121no—
371Dic5#87811yescharacteristic
372Dic5#89611yescharacteristic
373C2×Q8—61no—
374C2×Q8—301no—
375C2×Q8—301no—
376C2×Q8—301no—
377C2×Q8—602no—
378C2×Q8—602no—
379C22×C4—51no—
380C22×C4—101no—
381C22×C4—101no—
382C22×C4—151no—
383C22×C4—151no—
384C22×C4—301no—
385C22×C4—301no—
386C2×C8—52no—
387C2×C8—101no—
388C2×C8—101no—
389C2×C8—152no—
390C2×C8—301no—
391C2×C8—301no—
392C4⋊C4—31no—
393C4⋊C4—51no—
394C4⋊C4—61no—
395C4⋊C4—101no—
396C4⋊C4—101no—
397C4⋊C4—101no—
398C4⋊C4—151no—
399C4⋊C4—301no—
400C4⋊C4—301no—
401C4⋊C4—301no—
402C4⋊C4—301no—
403C4⋊C4—301no—
404C4⋊C4—301no—
405C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
406C42—31no—
407C42—151no—
408C42—151no—
409C42—151no—
410C3×C5#199311yescharacteristic, complemented, Hall
411C22×C3—51no—
412C22×C3—51no—
413C22×C3—51no—
414C22×C3—51no—
415C22×C3—51no—
416C22×C3—51no—
417C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
418C3×C4—41no—
419C3×C4—51no—
420C3×C4—51no—
421C3×C4—201no—
422C3×C4—401no—
423C3×C4Q8×AGL(1,𝔽5)11yescharacteristic
424C3×C4Q8×AGL(1,𝔽5)11yescharacteristic
425Dic3—21no—
426Dic3—21no—
427Dic3—41no—
428Dic3—101no—
429Dic3—101no—
430Dic3—201no—
431Dic3—401no—
432C2×C5#464611yescharacteristic
433C2×C5#477011yescharacteristic
434C2×C5#480211yescharacteristic
435D5#476511yescharacteristic
436D5#479411yescharacteristic
437D5#485611yescharacteristic
438D5#487611yescharacteristic
439C23—51no—
440Q8—122no—
441Q8—602no—
442Q8—602no—
443Q8—602no—
444C2×C4—21no—
445C2×C4—31no—
446C2×C4—31no—
447C2×C4—51no—
448C2×C4—51no—
449C2×C4—51no—
450C2×C4—51no—
451C2×C4—51no—
452C2×C4—61no—
453C2×C4—101no—
454C2×C4—151no—
455C2×C4—151no—
456C2×C4—201no—
457C2×C4—201no—
458C2×C4—201no—
459C2×C4—201no—
460C2×C4—201no—
461C2×C4—301no—
462C2×C4—301no—
463C2×C4—301no—
464C2×C4—301no—
465C2×C4—301no—
466C2×C4—601no—
467C2×C4—601no—
468C2×C4—601no—
469C2×C4—601no—
470C2×C4—601no—
471C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
472C8—102no—
473C8—302no—
474C2×C3—51no—
475C2×C3—51no—
476C2×C3—51no—
477C2×C3—51no—
478C2×C3#6576711yescharacteristic
479C2×C3#6578211yescharacteristic
480C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
481C5#6880611yescharacteristic, complemented, Sylow
482C22—51no—
483C22—51no—
484C22—51no—
485C22—51no—
486C22—51no—
487C22—51no—
488C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
489C4—41no—
490C4—51no—
491C4—51no—
492C4—61no—
493C4—61no—
494C4—121no—
495C4—201no—
496C4—301no—
497C4—301no—
498C4—401no—
499C4—601no—
500C4—1201no—
501C4AGL(1,𝔽5)×Dic611yescharacteristic
502C4ΓL(1,𝔽16)⋊Q811yescharacteristic
503C3#1060467511yescharacteristic, complemented, Sylow
504C2—51no—
505C2—51no—
506C2—51no—
507C2—51no—
508C2#1175184211yescharacteristic
509C2#1175193811yescharacteristic
510C2#1175196211yescharacteristic
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#1993
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
14. #91777C4semidirect
15. C5×#888C4semidirect
17. #91470C4semidirect
18. #91469C4semidirect
53. D5⋊(C3⋊C8)Q8semidirect
58. C3×D5⋊C8Q8semidirect
149. #888AGL(1,𝔽5)semidirect
176. D5⋊C8Dic6semidirect
410. C3×C5#1993semidirect
481. C5#68806semidirect
503. C3#10604675semidirect

Maximal subgroups

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

subgroupindex
D5×#8882
#117517882
#117517512
#117467452
C3×#648742
#117465302
#117465282
#106046753
#688065