Finite Group Databasebeta

← #14307335

Subgroups — #14307335

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#890C211yesmaximal, characteristic
2Dic3×D5⋊C8C211yesmaximal, characteristic
3#11751751C211yesmaximal, characteristic
4#11746745C211yesmaximal, characteristic
5C3×#64874C211yesmaximal, characteristic
6#11746530C211yesmaximal, characteristic
7#11746528C211yesmaximal, characteristic
8#10604590—31nomaximal, Hall
9C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
10C2×D5⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
12C2×C3×D5⋊C8C2211yescharacteristic
13#91779C411yescharacteristic, complemented
14C5×#890C411yescharacteristic, complemented
15C3×D5×C4⋊C4C2211yescharacteristic
16D5×C4⋊Dic3—21no—
17D5×C4⋊Dic3C2211yescharacteristic
18D5×Dic3⋊C4—21no—
19C4×D5×Dic3C2211yescharacteristic
20#91384C411yescharacteristic, complemented
21#91381C411yescharacteristic, complemented
22#91335—21no—
23#91334—21no—
24Dic3×#170—21no—
25Dic3×#170—21no—
26(C2×AGL(1,𝔽5))⋊Dic3—21no—
27(C2×AGL(1,𝔽5))⋊Dic3—21no—
28#68804—51nomaximal, Hall
29D5×#125—31no—
30#65689—31no—
31C4×D5⋊C8—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—
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C4⋊Dic15—21no—
55C4⋊Dic15C2×C411yescharacteristic
56#6712—21no—
57C4×Dic15C2×C411yescharacteristic
58C5×C4⋊Dic3—21no—
59C5×C4⋊Dic3C2×C411yescharacteristic
60C5×Dic3⋊C4—21no—
61C4×C5×Dic3C2×C411yescharacteristic
62C3×C4⋊Dic5C2×C411yescharacteristic
63C3×#683—21no—
64Dic3⋊Dic5—21no—
65#6669—21no—
66#6668—21no—
67#6668—21no—
68#6668—21no—
69Dic3×Dic5D411yescharacteristic
70Dic3×Dic5D411yescharacteristic
71C2×#890—51no—
72C2×C8×Dic3—51no—
73#4977—51no—
74C3×#340—51no—
75#4551—51no—
76#4529—51no—
77#4529—51no—
78C2×C4⋊AGL(1,𝔽5)—31no—
79C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
80C2×D5⋊C8—31no—
81C2×D5⋊C8C2×D311yescharacteristic
82C5×#125—31no—
83D5×C4⋊C4—31no—
84D5×C4⋊C4—61no—
85D5×C4⋊C4—61no—
86D5×C4⋊C4C2×D311yescharacteristic
87#4036—31no—
88#4036—31no—
89#4035—61no—
90#4035—61no—
91C42×D5—31no—
92#4016—31no—
93(C2×AGL(1,𝔽5))⋊C4—61no—
94(C2×AGL(1,𝔽5))⋊C4—61no—
95C4×#170—61no—
96C4×#170—61no—
97#1991—151noSylow
98C22×C3×D5C2×D411yescharacteristic
99C2×ΓL(1,𝔽16)—41no—
100C2×ΓL(1,𝔽16)—41no—
101C2×ΓL(1,𝔽16)—41no—
102C2×C3×AGL(1,𝔽5)—41no—
103C2×C3×AGL(1,𝔽5)—41no—
104C2×C3×AGL(1,𝔽5)—41no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×Dic15—21no—
108C2×Dic15C22⋊C411yescharacteristic
109C2×Dic15C22⋊C411yescharacteristic
110C2×C5×Dic3—21no—
111C2×C5×Dic3C22⋊C411yescharacteristic
112C2×C5×Dic3C22⋊C411yescharacteristic
113C2×C3×Dic5—21no—
114C2×C3×Dic5C2×D411yescharacteristic
115C3×C4×D5—41no—
116C3×C4×D5—41no—
117C3×C4×D5C2×Q811yescharacteristic
118C3×C4×D5C2×Q811yescharacteristic
119C3×C4×D5#4111yescharacteristic
120C3×C4×D5#4111yescharacteristic
121D5×Dic3—21no—
122D5×Dic3—21no—
123D5×Dic3—21no—
124D5×Dic3—21no—
125D5×Dic3—41no—
126D5×Dic3—41no—
127C3⋊#170—22no—
128C3×#170—22no—
129C22×C3×C8—51no—
130C2×C3×C4⋊C4—51no—
131C2×C3×C4⋊C4—51no—
132C2×C4⋊Dic3—51no—
133C2×C4⋊Dic3—51no—
134C2×C4⋊Dic3—101no—
135C2×Dic3⋊C4—101no—
136C2×C4×Dic3—51no—
137C22×C3⋊C8—51no—
138#890—51no—
139#890—51no—
140#890—51no—
141#890—101no—
142#890—101no—
143#890AGL(1,𝔽5)11yescharacteristic, complemented
144C3⋊#95—101no—
145C3⋊#95—101no—
146C8×Dic3—101no—
147C8×Dic3—101no—
148C22×AGL(1,𝔽5)—21no—
149C22×AGL(1,𝔽5)—61no—
150C2×C4×D5—21no—
151C2×C4×D5—31no—
152C2×C4×D5—31no—
153C2×C4×D5—61no—
154C2×C4×D5C22×D311yescharacteristic
155C2×#170—21no—
156C2×#170—61no—
157C4⋊AGL(1,𝔽5)—21no—
158C4⋊AGL(1,𝔽5)—21no—
159C4⋊AGL(1,𝔽5)—61no—
160C4⋊AGL(1,𝔽5)—61no—
161D5⋊C8—21no—
162D5⋊C8—32no—
163D5⋊C8—61no—
164D5⋊C8Dic612yes—
165C5×C4⋊C4—31no—
166C5×C4⋊C4—61no—
167C5×C4⋊C4—61no—
168C5×C4⋊C4C4×D311yescharacteristic
169C42×C5—31no—
170C4⋊Dic5—31no—
171C4⋊Dic5—61no—
172C4⋊Dic5—61no—
173C4⋊Dic5C4×D311yescharacteristic
174#683—21no—
175#683—61no—
176#683—61no—
177#683—61no—
178#683—61no—
179#683—61no—
180C4×Dic5—31no—
181C4×Dic5—31no—
182C4×Dic5—31no—
183C2×#125—151no—
184C2×C4×C8—151no—
185#382—151no—
186#340—51no—
187#340—151no—
188#340—151no—
189#340—151no—
190C22×C3×C5C2×C22⋊C411yescharacteristic
191C2×C3×D5#12411yescharacteristic
192C2×C3×D5C4⋊Q811yescharacteristic
193C2×C3×D5#13511yescharacteristic
194C2×C3×D5#13511yescharacteristic
195C2×C3×D5#13511yescharacteristic
196C2×C3×D5#13511yescharacteristic
197ΓL(1,𝔽16)—81no—
198C3×AGL(1,𝔽5)—81no—
199C3×C4×C5—41no—
200C3×C4×C5C4×Q811yescharacteristic
201C3×C4×C5C4×Q811yescharacteristic
202Dic15—21no—
203Dic15—21no—
204Dic15—41no—
205C3×Dic5—41no—
206C3×Dic5C22⋊Q811yescharacteristic
207C3×Dic5C22⋊Q811yescharacteristic
208C5×Dic3—21no—
209C5×Dic3—21no—
210C5×Dic3—41no—
211C22×C3×C4—51no—
212C22×C3×C4—101no—
213C22×C3×C4—101no—
214C22×Dic3—51no—
215C22×Dic3—51no—
216C22×Dic3—101no—
217C22×Dic3—101no—
218C2×C3×C8—52no—
219C2×C3×C8—101no—
220C2×C3×C8—101no—
221C3×C4⋊C4—51no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
226C4⋊Dic3—21no—
227C4⋊Dic3—51no—
228C4⋊Dic3—101no—
229C4⋊Dic3—101no—
230C4⋊Dic3—101no—
231C4⋊Dic3—101no—
232C4⋊Dic3—101no—
233C4⋊Dic3—101no—
234C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
235Dic3⋊C4—21no—
236Dic3⋊C4—101no—
237Dic3⋊C4—101no—
238Dic3⋊C4—101no—
239C4×Dic3—51no—
240C4×Dic3—51no—
241C4×Dic3—51no—
242C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
243C2×C3⋊C8—52no—
244C2×C3⋊C8—101no—
245C2×C3⋊C8—101no—
246C22×D5D3×D411yescharacteristic
247C2×AGL(1,𝔽5)—41no—
248C2×AGL(1,𝔽5)—41no—
249C2×AGL(1,𝔽5)—41no—
250C2×AGL(1,𝔽5)—121no—
251C2×AGL(1,𝔽5)—121no—
252C2×AGL(1,𝔽5)—121no—
253C2×C4×C5—21no—
254C2×C4×C5—31no—
255C2×C4×C5—31no—
256C2×C4×C5—61no—
257C2×C4×C5C2×C4×D311yescharacteristic
258C2×Dic5—21no—
259C2×Dic5—31no—
260C2×Dic5—31no—
261C2×Dic5—61no—
262C2×Dic5D3×D411yescharacteristic
263C4×D5—41no—
264C4×D5—41no—
265C4×D5—61no—
266C4×D5—61no—
267C4×D5—61no—
268C4×D5—61no—
269C4×D5—121no—
270C4×D5—121no—
271C4×D5C2×Dic611yescharacteristic
272C4×D5#23511yescharacteristic
273C4×D5#23711yescharacteristic
274C4×D5D3×Q811yescharacteristic
275#170—22no—
276#170—62no—
277C22×C8—51no—
278C22×C8—151no—
279#125—31no—
280#125—151no—
281#125—151no—
282#125—151no—
283#125—301no—
284#125—301no—
285C2×C4⋊C4—51no—
286C2×C4⋊C4—51no—
287C2×C4⋊C4—151no—
288C2×C4⋊C4—151no—
289C2×C4⋊C4—301no—
290C2×C4⋊C4—301no—
291C2×C42—151no—
292C4×C8—301no—
293C4×C8—301no—
294#95—301no—
295#95—301no—
296C2×C3×C5#39111yescharacteristic
297C2×C3×C5#41611yescharacteristic
298C2×C3×C5#41611yescharacteristic
299C3×D5#48811yescharacteristic
300C3×D5#48811yescharacteristic
301C3×D5#49911yescharacteristic
302C3×D5#49911yescharacteristic
303C23×C3—51no—
304C2×C3×C4—21no—
305C2×C3×C4—51no—
306C2×C3×C4—51no—
307C2×C3×C4—51no—
308C2×C3×C4—51no—
309C2×C3×C4—51no—
310C2×C3×C4—101no—
311C2×C3×C4—201no—
312C2×C3×C4—201no—
313C2×C3×C4—201no—
314C2×C3×C4—201no—
315C2×C3×C4—201no—
316C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
317C2×Dic3—21no—
318C2×Dic3—51no—
319C2×Dic3—51no—
320C2×Dic3—101no—
321C2×Dic3—101no—
322C2×Dic3—101no—
323C2×Dic3—101no—
324C2×Dic3—101no—
325C2×Dic3—201no—
326C2×Dic3—201no—
327C2×Dic3—201no—
328C2×Dic3—201no—
329C2×Dic3—201no—
330C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
331C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
332C3×C8—102no—
333C3⋊C8—102no—
334C22×C5D3×C22⋊C411yescharacteristic
335C2×D5#88511yescharacteristic
336C2×D5#88811yescharacteristic
337C2×D5#91211yescharacteristic
338C2×D5#91611yescharacteristic
339C2×D5#91611yescharacteristic
340C2×D5#91911yescharacteristic
341AGL(1,𝔽5)—81no—
342AGL(1,𝔽5)—241no—
343C4×C5—41no—
344C4×C5—61no—
345C4×C5—61no—
346C4×C5—121no—
347C4×C5C4×Dic611yescharacteristic
348C4×C5#88711yescharacteristic
349Dic5—41no—
350Dic5—61no—
351Dic5—61no—
352Dic5—121no—
353Dic5#87811yescharacteristic
354Dic5#89611yescharacteristic
355C22×C4—51no—
356C22×C4—101no—
357C22×C4—101no—
358C22×C4—151no—
359C22×C4—151no—
360C22×C4—301no—
361C22×C4—301no—
362C2×C8—52no—
363C2×C8—101no—
364C2×C8—101no—
365C2×C8—152no—
366C2×C8—301no—
367C2×C8—301no—
368C4⋊C4—31no—
369C4⋊C4—51no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C4⋊C4—101no—
373C4⋊C4—101no—
374C4⋊C4—101no—
375C4⋊C4—151no—
376C4⋊C4—301no—
377C4⋊C4—301no—
378C4⋊C4—301no—
379C4⋊C4—301no—
380C4⋊C4—301no—
381C4⋊C4—301no—
382C4⋊C4—301no—
383C4⋊C4—301no—
384C4⋊C4—301no—
385C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
386C42—31no—
387C42—151no—
388C42—151no—
389C42—151no—
390C3×C5#199111yescharacteristic, complemented, Hall
391C22×C3—51no—
392C22×C3—51no—
393C22×C3—51no—
394C22×C3—51no—
395C22×C3—51no—
396C22×C3—51no—
397C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
398C3×C4—41no—
399C3×C4—51no—
400C3×C4—51no—
401C3×C4—201no—
402C3×C4—401no—
403C3×C4Q8×AGL(1,𝔽5)11yescharacteristic
404C3×C4Q8×AGL(1,𝔽5)11yescharacteristic
405Dic3—21no—
406Dic3—21no—
407Dic3—41no—
408Dic3—101no—
409Dic3—101no—
410Dic3—201no—
411Dic3—401no—
412C2×C5#464611yescharacteristic
413C2×C5#477211yescharacteristic
414C2×C5#480411yescharacteristic
415D5#476811yescharacteristic
416D5#480011yescharacteristic
417D5#485811yescharacteristic
418D5#487811yescharacteristic
419C23—51no—
420C2×C4—21no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—51no—
424C2×C4—51no—
425C2×C4—51no—
426C2×C4—51no—
427C2×C4—51no—
428C2×C4—61no—
429C2×C4—101no—
430C2×C4—151no—
431C2×C4—151no—
432C2×C4—201no—
433C2×C4—201no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4—201no—
437C2×C4—301no—
438C2×C4—301no—
439C2×C4—301no—
440C2×C4—301no—
441C2×C4—301no—
442C2×C4—601no—
443C2×C4—601no—
444C2×C4—601no—
445C2×C4—601no—
446C2×C4—601no—
447C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
448C8—102no—
449C8—302no—
450C2×C3—51no—
451C2×C3—51no—
452C2×C3—51no—
453C2×C3—51no—
454C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
455C2×C3#6579411yescharacteristic
456C2×C3#6579411yescharacteristic
457C5#6880411yescharacteristic, complemented, Sylow
458C22—51no—
459C22—51no—
460C22—51no—
461C22—51no—
462C22—51no—
463C22—51no—
464C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
465C4—41no—
466C4—51no—
467C4—51no—
468C4—61no—
469C4—61no—
470C4—121no—
471C4—201no—
472C4—301no—
473C4—301no—
474C4—401no—
475C4—601no—
476C4—1201no—
477C4AGL(1,𝔽5)×Dic611yescharacteristic
478C4ΓL(1,𝔽16)⋊Q811yescharacteristic
479C3#1060459011yescharacteristic, complemented, Sylow
480C2—51no—
481C2—51no—
482C2—51no—
483C2—51no—
484C2#1175184211yescharacteristic
485C2#1175194711yescharacteristic
486C2#1175197111yescharacteristic
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#1991
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
13. #91779C4semidirect
14. C5×#890C4semidirect
20. #91384C4semidirect
21. #91381C4semidirect
143. #890AGL(1,𝔽5)semidirect
390. C3×C5#1991semidirect
457. C5#68804semidirect
479. C3#10604590semidirect

Maximal subgroups

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

subgroupindex
D5×#8902
Dic3×D5⋊C82
#117517512
#117467452
C3×#648742
#117465302
#117465282
#106045903
#688045