Finite Group Databasebeta

← #14297802

Subgroups — #14297802

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D5×Dic3C211yesmaximal, characteristic
2C2×#91238C211yesmaximal, characteristic
3C2×C3×#4009C211yesmaximal, characteristic
4D5⋊(Dic3⋊C8)C211yesmaximal, characteristic
5#11751751C211yesmaximal, characteristic
6#11746530C211yesmaximal, characteristic
7#11746528C211yesmaximal, characteristic
8#10604452—31nomaximal, Hall
9C2×C3×Q8×D5C2211yescharacteristic
10C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
11C2×D5⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
13C2×C3×D5⋊C8C2211yescharacteristic
14Q8×Dic15C411yescharacteristic, complemented
15C5×Q8×Dic3C411yescharacteristic, complemented
16D5×C4⋊Dic3—21no—
17D5×C4⋊Dic3C2211yescharacteristic
18C4×D5×Dic3—21no—
19C4×D5×Dic3C2211yescharacteristic
20#91331—21no—
21#91331C411yescharacteristic, complemented
22Dic3×Dic10—21no—
23Dic3×Dic10C411yescharacteristic, complemented
24#91238—22no—
25C3×#4009—22no—
26#91177—21no—
27Dic3⋊#170—21no—
28(C2×AGL(1,𝔽5))⋊Dic3—21no—
29(C2×AGL(1,𝔽5))⋊Dic3—21no—
30#70222—51nomaximal, Hall
31C4×Q8×D5—31no—
32C2×#4009—31no—
33C2×#4009D311yescharacteristic
34#65689—31no—
35D5⋊(C4⋊C8)—31no—
36#64874—31no—
37#64874—31no—
38C22×ΓL(1,𝔽16)—21no—
39C22×C3×AGL(1,𝔽5)—21no—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C3×Q8×D5—21no—
42C3×Q8×D5—21no—
43C3×Q8×D5D412yes—
44C3×Q8×D5Q812yes—
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5C2311yescharacteristic
47C2×C3×Dic10—21no—
48C2×C3×Dic10C2×C411yescharacteristic
49C2×D5×Dic3—21no—
50C2×D5×Dic3D411yescharacteristic
51C2×D5×Dic3D411yescharacteristic
52C2×C3⋊#170—21no—
53C4⋊ΓL(1,𝔽16)—21no—
54C4⋊ΓL(1,𝔽16)—21no—
55D5⋊(C3⋊C8)—21no—
56D5⋊(C3⋊C8)—21no—
57C2×C3×#170—21no—
58C3×C4⋊AGL(1,𝔽5)—21no—
59C3×C4⋊AGL(1,𝔽5)—21no—
60C3×D5⋊C8—21no—
61C3×D5⋊C8—21no—
62C4⋊Dic15—21no—
63C4⋊Dic15C2×C411yescharacteristic
64C4×Dic15—21no—
65C4×Dic15C2×C411yescharacteristic
66C5×C4⋊Dic3—21no—
67C5×C4⋊Dic3C2×C411yescharacteristic
68C4×C5×Dic3—21no—
69C4×C5×Dic3C2×C411yescharacteristic
70#6668—21no—
71#6668—21no—
72#6668—21no—
73Dic3×Dic5—21no—
74Dic3×Dic5—21no—
75Dic3×Dic5D411yescharacteristic
76Dic3×Dic5D411yescharacteristic
77C2×Q8×Dic3—51no—
78C2×C3×#103—51no—
79C2×#835—51no—
80C2×Dic3⋊C8—51no—
81#4977—51no—
82#4551—51no—
83#4529—51no—
84C2×Q8×D5C2×D311yescharacteristic
85C2×C4⋊AGL(1,𝔽5)—31no—
86C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
87C2×D5⋊C8—31no—
88C2×D5⋊C8C2×D311yescharacteristic
89C4×C5×Q8—31no—
90Q8×Dic5—31no—
91D5×C4⋊C4—31no—
92D5×C4⋊C4—61no—
93#4033—31no—
94#4033—61no—
95C42×D5—31no—
96C42×D5—61no—
97C4×Dic10—31no—
98C4×Dic10—61no—
99#4009—22no—
100#4009—62no—
101(C2×AGL(1,𝔽5))⋊C4—61no—
102(C2×AGL(1,𝔽5))⋊C4—61no—
103#4004—61no—
104C4⋊#170—61no—
105#1805—151noSylow
106C22×C3×D5C2×D411yescharacteristic
107C2×ΓL(1,𝔽16)—41no—
108C2×ΓL(1,𝔽16)—41no—
109C2×ΓL(1,𝔽16)—41no—
110C2×C3×AGL(1,𝔽5)—41no—
111C2×C3×AGL(1,𝔽5)—41no—
112C2×C3×AGL(1,𝔽5)—41no—
113C3×C5×Q8—21no—
114C3×C5×Q8C4⋊C412yes—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5C22×C411yescharacteristic
117C2×Dic15—21no—
118C2×Dic15C22⋊C411yescharacteristic
119C2×Dic15C22⋊C411yescharacteristic
120C2×C5×Dic3—21no—
121C2×C5×Dic3C22⋊C411yescharacteristic
122C2×C5×Dic3C22⋊C411yescharacteristic
123C2×C3×Dic5—21no—
124C2×C3×Dic5C2×D411yescharacteristic
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×C4×D5C2×D411yescharacteristic
128C3×C4×D5C2×Q811yescharacteristic
129C3×C4×D5#4111yescharacteristic
130C3×C4×D5#4111yescharacteristic
131C3×Dic10—21no—
132C3×Dic10—22no—
133C3×Dic10—22no—
134C3×Dic10C4⋊C412yes—
135D5×Dic3—21no—
136D5×Dic3—21no—
137D5×Dic3—21no—
138D5×Dic3—21no—
139D5×Dic3—41no—
140D5×Dic3—41no—
141C3⋊#170—41no—
142C3×#170—41no—
143C22×C3×Q8—51no—
144C22×C3×C8—51no—
145C2×C3×C4⋊C4—51no—
146Q8×Dic3—51no—
147Q8×Dic3—51no—
148Q8×Dic3—51no—
149Q8×Dic3—101no—
150Q8×Dic3—101no—
151Q8×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
152C2×C4⋊Dic3—51no—
153C2×C4⋊Dic3—51no—
154C2×C4⋊Dic3—101no—
155C2×C4×Dic3—51no—
156C2×C4×Dic3—101no—
157C22×C3⋊C8—51no—
158C3×#103—102no—
159#835—102no—
160C3⋊#95—101no—
161C3⋊#95—101no—
162Dic3⋊C8—101no—
163Dic3⋊C8—101no—
164C22×AGL(1,𝔽5)—21no—
165C22×AGL(1,𝔽5)—61no—
166C2×C5×Q8C4×D311yescharacteristic
167Q8×D5—21no—
168Q8×D5—21no—
169Q8×D5Dic612yes—
170Q8×D5#6712yes—
171C2×C4×D5—21no—
172C2×C4×D5—31no—
173C2×C4×D5—31no—
174C2×C4×D5—61no—
175C2×C4×D5C22×D311yescharacteristic
176C2×Dic10—21no—
177C2×Dic10C4×D311yescharacteristic
178C2×#170—21no—
179C2×#170—61no—
180C4⋊AGL(1,𝔽5)—21no—
181C4⋊AGL(1,𝔽5)—21no—
182C4⋊AGL(1,𝔽5)—61no—
183C4⋊AGL(1,𝔽5)—61no—
184D5⋊C8—21no—
185D5⋊C8—21no—
186D5⋊C8—61no—
187D5⋊C8—61no—
188C5×C4⋊C4—31no—
189C5×C4⋊C4—61no—
190C42×C5—31no—
191C42×C5—61no—
192C4⋊Dic5—31no—
193C4⋊Dic5—61no—
194#683—61no—
195#683—61no—
196#683—61no—
197C4×Dic5—31no—
198C4×Dic5—31no—
199C4×Dic5—31no—
200C4×Dic5—61no—
201C4×Dic5—61no—
202C4×Dic5—61no—
203C2×C4×Q8—151no—
204C2×C4⋊C8—151no—
205C2×#103—51no—
206C2×#103—151no—
207#382—151no—
208#340—151no—
209#340—151no—
210C22×C3×C5C2×C22⋊C411yescharacteristic
211C2×C3×D5#12111yescharacteristic
212C2×C3×D5C22⋊Q811yescharacteristic
213C2×C3×D5#13511yescharacteristic
214C2×C3×D5#13511yescharacteristic
215C2×C3×D5#13711yescharacteristic
216C2×C3×D5#13711yescharacteristic
217ΓL(1,𝔽16)—81no—
218C3×AGL(1,𝔽5)—81no—
219C3×C4×C5—22no—
220C3×C4×C5C2×C4⋊C411yescharacteristic
221C3×C4×C5#11711yescharacteristic
222Dic15—21no—
223Dic15—21no—
224Dic15—41no—
225C3×Dic5—22no—
226C3×Dic5#12111yescharacteristic
227C3×Dic5C22⋊Q811yescharacteristic
228C5×Dic3—21no—
229C5×Dic3—21no—
230C5×Dic3—41no—
231C2×C3×Q8—52no—
232C2×C3×Q8—52no—
233C2×C3×Q8—51no—
234C2×C3×Q8—101no—
235C2×C3×Q8—101no—
236C2×C3×Q8—101no—
237C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
238C22×C3×C4—51no—
239C22×C3×C4—101no—
240C22×C3×C4—101no—
241C22×Dic3—51no—
242C22×Dic3—51no—
243C22×Dic3—101no—
244C22×Dic3—101no—
245C2×C3×C8—101no—
246C2×C3×C8—101no—
247C2×C3×C8—101no—
248C3×C4⋊C4—101no—
249C3×C4⋊C4—101no—
250C4⋊Dic3—21no—
251C4⋊Dic3—51no—
252C4⋊Dic3—101no—
253C4⋊Dic3—101no—
254C4⋊Dic3—101no—
255C4⋊Dic3—101no—
256C4⋊Dic3—101no—
257C4⋊Dic3—101no—
258C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
259C4×Dic3—21no—
260C4×Dic3—51no—
261C4×Dic3—51no—
262C4×Dic3—51no—
263C4×Dic3—101no—
264C4×Dic3—101no—
265C4×Dic3—101no—
266C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
267C2×C3⋊C8—101no—
268C2×C3⋊C8—101no—
269C2×C3⋊C8—101no—
270C22×D5D3×D411yescharacteristic
271C2×AGL(1,𝔽5)—41no—
272C2×AGL(1,𝔽5)—41no—
273C2×AGL(1,𝔽5)—41no—
274C2×AGL(1,𝔽5)—121no—
275C2×AGL(1,𝔽5)—121no—
276C2×AGL(1,𝔽5)—121no—
277C5×Q8—21no—
278C5×Q8Dic3⋊C412yes—
279C2×C4×C5—21no—
280C2×C4×C5—31no—
281C2×C4×C5—31no—
282C2×C4×C5—61no—
283C2×C4×C5C2×C4×D311yescharacteristic
284C2×Dic5—21no—
285C2×Dic5—31no—
286C2×Dic5—31no—
287C2×Dic5—61no—
288C2×Dic5D3×D411yescharacteristic
289C4×D5—22no—
290C4×D5—22no—
291C4×D5—61no—
292C4×D5—61no—
293C4×D5—61no—
294C4×D5—61no—
295C4×D5—121no—
296C4×D5—121no—
297C4×D5C2×Dic611yescharacteristic
298C4×D5#23711yescharacteristic
299C4×D5#23711yescharacteristic
300C4×D5C2×#6711yescharacteristic
301Dic10—21no—
302Dic10—22no—
303Dic10—22no—
304Dic10Dic3⋊C412yes—
305#170—41no—
306#170—121no—
307C22×Q8—51no—
308C22×C8—51no—
309C22×C8—151no—
310C4×Q8—31no—
311C4×Q8—151no—
312C4×Q8—151no—
313C4×Q8—151no—
314C4×Q8—301no—
315C4×Q8—301no—
316C2×C4⋊C4—51no—
317C2×C4⋊C4—151no—
318C2×C4⋊C4—151no—
319C2×C4⋊C4—301no—
320C2×C42—151no—
321C2×C42—301no—
322C4⋊C8—301no—
323C4⋊C8—301no—
324#103—102no—
325#103—302no—
326#95—301no—
327#95—301no—
328C2×C3×C5#38011yescharacteristic
329C2×C3×C5#41611yescharacteristic
330C2×C3×C5#41911yescharacteristic
331C3×D5#46411yescharacteristic
332C3×D5#46411yescharacteristic
333C3×D5#47911yescharacteristic
334C3×D5#47911yescharacteristic
335C23×C3—51no—
336C3×Q8—21no—
337C3×Q8—52no—
338C3×Q8—102no—
339C3×Q8—102no—
340C3×Q8—101no—
341C3×Q8C4⋊AGL(1,𝔽5)12yes—
342C2×C3×C4—21no—
343C2×C3×C4—51no—
344C2×C3×C4—51no—
345C2×C3×C4—51no—
346C2×C3×C4—51no—
347C2×C3×C4—51no—
348C2×C3×C4—102no—
349C2×C3×C4—102no—
350C2×C3×C4—101no—
351C2×C3×C4—201no—
352C2×C3×C4—201no—
353C2×C3×C4—201no—
354C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—51no—
357C2×Dic3—51no—
358C2×Dic3—101no—
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3—101no—
362C2×Dic3—101no—
363C2×Dic3—201no—
364C2×Dic3—201no—
365C2×Dic3—201no—
366C2×Dic3—201no—
367C2×Dic3—201no—
368C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
369C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
370C3×C8—201no—
371C3⋊C8—201no—
372C22×C5D3×C22⋊C411yescharacteristic
373C2×D5#87811yescharacteristic
374C2×D5#91511yescharacteristic
375C2×D5#91611yescharacteristic
376C2×D5#91811yescharacteristic
377C2×D5#91911yescharacteristic
378C2×D5#93911yescharacteristic
379AGL(1,𝔽5)—81no—
380AGL(1,𝔽5)—241no—
381C4×C5—22no—
382C4×C5—61no—
383C4×C5—61no—
384C4×C5—121no—
385C4×C5#87711yescharacteristic
386C4×C5C2×Dic3⋊C411yescharacteristic
387Dic5—22no—
388Dic5—61no—
389Dic5—61no—
390Dic5—121no—
391Dic5#87811yescharacteristic
392Dic5#93911yescharacteristic
393C2×Q8—52no—
394C2×Q8—52no—
395C2×Q8—51no—
396C2×Q8—101no—
397C2×Q8—101no—
398C2×Q8—101no—
399C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
400C22×C4—51no—
401C22×C4—101no—
402C22×C4—101no—
403C22×C4—151no—
404C22×C4—151no—
405C22×C4—301no—
406C22×C4—301no—
407C2×C8—101no—
408C2×C8—101no—
409C2×C8—101no—
410C2×C8—301no—
411C2×C8—301no—
412C2×C8—301no—
413C4⋊C4—31no—
414C4⋊C4—61no—
415C4⋊C4—101no—
416C4⋊C4—101no—
417C4⋊C4—151no—
418C4⋊C4—301no—
419C4⋊C4—301no—
420C4⋊C4—301no—
421C4⋊C4—301no—
422C4⋊C4—301no—
423C4⋊C4—301no—
424C42—31no—
425C42—61no—
426C42—151no—
427C42—151no—
428C42—151no—
429C42—301no—
430C42—301no—
431C42—301no—
432C3×C5#180511yescharacteristic, complemented, Hall
433C22×C3—51no—
434C22×C3—51no—
435C22×C3—51no—
436C22×C3—51no—
437C22×C3—51no—
438C22×C3—51no—
439C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
440C3×C4—22no—
441C3×C4—51no—
442C3×C4—51no—
443C3×C4—102no—
444C3×C4—401no—
445C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
446C3×C4#413011yescharacteristic
447Dic3—21no—
448Dic3—21no—
449Dic3—41no—
450Dic3—101no—
451Dic3—101no—
452Dic3—201no—
453Dic3—401no—
454C2×C5#480211yescharacteristic
455C2×C5#480411yescharacteristic
456C2×C5#494211yescharacteristic
457D5#479611yescharacteristic
458D5#479911yescharacteristic
459D5#516611yescharacteristic
460D5#518511yescharacteristic
461C23—51no—
462Q8—21no—
463Q8—52no—
464Q8—102no—
465Q8—102no—
466Q8—101no—
467Q8Dic3⋊AGL(1,𝔽5)12yes—
468C2×C4—21no—
469C2×C4—31no—
470C2×C4—31no—
471C2×C4—51no—
472C2×C4—51no—
473C2×C4—51no—
474C2×C4—51no—
475C2×C4—51no—
476C2×C4—61no—
477C2×C4—102no—
478C2×C4—102no—
479C2×C4—101no—
480C2×C4—151no—
481C2×C4—151no—
482C2×C4—201no—
483C2×C4—201no—
484C2×C4—201no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4—301no—
488C2×C4—301no—
489C2×C4—301no—
490C2×C4—601no—
491C2×C4—601no—
492C2×C4—601no—
493C2×C4—601no—
494C2×C4—601no—
495C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
496C8—201no—
497C8—601no—
498C2×C3—51no—
499C2×C3—51no—
500C2×C3—51no—
501C2×C3—51no—
502C2×C3#6576511yescharacteristic
503C2×C3#6578211yescharacteristic
504C2×C3#6579411yescharacteristic
505C5#7022211yescharacteristic, complemented, Sylow
506C22—51no—
507C22—51no—
508C22—51no—
509C22—51no—
510C22—51no—
511C22—51no—
512C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
513C4—22no—
514C4—51no—
515C4—51no—
516C4—61no—
517C4—61no—
518C4—102no—
519C4—121no—
520C4—301no—
521C4—301no—
522C4—401no—
523C4—601no—
524C4—1201no—
525C4#9192311yescharacteristic
526C4C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
527C3#1060445211yescharacteristic, complemented, Sylow
528C2—51no—
529C2—51no—
530C2—51no—
531C2—51no—
532C2#1175196211yescharacteristic
533C2#1175197111yescharacteristic
534C2#1175202811yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#1805
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
14. Q8×Dic15C4semidirect
15. C5×Q8×Dic3C4semidirect
21. #91331C4semidirect
23. Dic3×Dic10C4semidirect
151. Q8×Dic3AGL(1,𝔽5)semidirect
432. C3×C5#1805semidirect
505. C5#70222semidirect
527. C3#10604452semidirect

Maximal subgroups

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

subgroupindex
Q8×D5×Dic32
C2×#912382
C2×C3×#40092
D5⋊(Dic3⋊C8)2
#117517512
#117465302
#117465282
#106044523
#702225