Finite Group Databasebeta

← #14297829

Subgroups — #14297829

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic5×#235C211yesmaximal, characteristic
2C2×C5×#825C211yesmaximal, characteristic
3C3×#65407C211yesmaximal, characteristic, complemented
4C4×#6668C211yesmaximal, characteristic, complemented
5C2×#90978C211yesmaximal, characteristic
6#11746376C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10601148—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16Dic5×#67—21no—
17Dic5×#67—21no—
18C2×#6668—21no—
19Dic5×D12C411yescharacteristic, complemented
20Dic5×D12C411yescharacteristic, complemented
21C4×D3×Dic5—21no—
22#91371—21no—
23Dic5×Dic6C411yescharacteristic, complemented
24Dic5×Dic6C411yescharacteristic, complemented
25C5×#825—22no—
26C3×#3946—21no—
27C3×#3946—21no—
28#90994—21no—
29#90978—22no—
30#70529—51nomaximal, Hall
31#41×Dic5—31no—
32C2×C5×#104—31no—
33C2×#3969—31no—
34#65407D311yescharacteristic, complemented
35C4×#683—31no—
36#64775—31no—
37#64743—31no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C2×C5×#67—21no—
41C22×C5×Dic3—21no—
42C5×#235—21no—
43C5×#235—21no—
44C5×#235D412yes—
45C5×#235Q812yes—
46C2×C5×D12C2×C411yescharacteristic
47C2×C4×C5×D3—21no—
48C2×C5×Dic6C2×C411yescharacteristic
49C22×C3×Dic5D411yescharacteristic
50C22×C3×Dic5D411yescharacteristic
51C2×D3×Dic5—21no—
52C2×D3×Dic5—21no—
53C3×C5×M16—21no—
54C3×C5×M16—21no—
55C2×C3×C5×C8—21no—
56#6719—21no—
57C4⋊Dic15C2×C411yescharacteristic
58C4⋊Dic15C2×C411yescharacteristic
59C4×Dic15—21no—
60C4×Dic15—21no—
61C4×Dic15—21no—
62C4×C5×Dic3—21no—
63C4×C5×Dic3—21no—
64C3×C4×Dic5C2×C411yescharacteristic
65C3×C4×Dic5C2×C411yescharacteristic
66C3×C4×Dic5D411yescharacteristic
67C3×C4×Dic5D411yescharacteristic
68C3×#681—21no—
69C3×#681—21no—
70C2×C3×#168—21no—
71Dic3⋊Dic5—21no—
72Dic3⋊Dic5—21no—
73#6668—24no—
74(C2×D3)⋊Dic5—21no—
75(C2×D3)⋊Dic5—21no—
76Dic3×Dic5—21no—
77Dic3×Dic5—21no—
78C4×#235—51no—
79C3×#423—51no—
80C2×#825—51no—
81C2×#825D511yescharacteristic
82C4×C4⋊Dic3—51no—
83#4555—51no—
84#4555—51no—
85C2×C5×#41—31no—
86C2×C5×M16C2×D311yescharacteristic
87C2×C42×C5—31no—
88Q8×Dic5—31no—
89Q8×Dic5—31no—
90D4×Dic5—31no—
91D4×Dic5—31no—
92D4×Dic5—61no—
93D4×Dic5—61no—
94#4072—31no—
95#4072—61no—
96C2×#683—61no—
97C2×C4×Dic5—31no—
98C2×C4×Dic5—61no—
99C2×C4×Dic5C2×D311yescharacteristic
100C2×#681C2×D311yescharacteristic
101C5×#104—62no—
102#3969—62no—
103#3963—61no—
104#3946—21no—
105#3946—21no—
106#1806—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×C5×D3—21no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×Q811yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—22no—
116C2×Dic15—21no—
117C2×Dic15—21no—
118C2×Dic15—41no—
119C2×Dic15—41no—
120C5×#67—22no—
121C5×#67—22no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3—41no—
126C5×D12—21no—
127C5×D12C4⋊C412yescomplemented
128C4×C5×D3—22no—
129C4×C5×D3—22no—
130C5×Dic6—21no—
131C5×Dic6C4⋊C412yescomplemented
132C2×C3×Dic5—22no—
133C2×C3×Dic5—41no—
134C2×C3×Dic5C22⋊C411yescharacteristic
135C2×C3×Dic5C22⋊C411yescharacteristic
136C2×C3×Dic5C22⋊C411yescharacteristic
137C2×C3×Dic5C22⋊C411yescharacteristic
138D3×Dic5—42no—
139D3×Dic5—42no—
140C3×C5×C8—41no—
141C3×#168—41no—
142C2×#235C2×D511yescharacteristic
143C2×C3×M16—51no—
144C2×C3×M16C2×D511yescharacteristic
145C2×C3×C42—51no—
146C4×#67—101no—
147C4×#67—101no—
148#926—51no—
149C2×C4⋊Dic3—101no—
150C2×C4×Dic3—51no—
151C2×C4×Dic3C2×D511yescharacteristic
152C4×D12—51no—
153C4×D12—51no—
154#872—101no—
155C42×D3—101no—
156C4×Dic6—51no—
157C4×Dic6—51no—
158C3×C4⋊C8—101no—
159C3×C4⋊C8—101no—
160C3⋊#95—101no—
161#825—22no—
162#825—102no—
163C5×#41—32no—
164C5×#41—32no—
165C5×#41—61no—
166C5×#41—61no—
167C2×C5×Q8—31no—
168C2×C5×D4—31no—
169C2×C5×D4—61no—
170C22×C4×C5—61no—
171C22×C4×C5—61no—
172C22×C4×C5C22×D311yescharacteristic
173C22×Dic5—61no—
174C22×Dic5—61no—
175C22×Dic5—61no—
176C22×Dic5D1211yescharacteristic
177C22×Dic5D1211yescharacteristic
178C5×M16—21no—
179C5×M16—21no—
180C2×C5×C8—21no—
181C42×C5—61no—
182C42×C5—61no—
183C22⋊Dic5—61no—
184C22⋊Dic5—61no—
185C22⋊Dic5—61no—
186C4⋊Dic5—31no—
187C4⋊Dic5—31no—
188C4⋊Dic5—61no—
189C4⋊Dic5—61no—
190#683—64no—
191C4×Dic5—61no—
192C4×Dic5—61no—
193C4×Dic5—61no—
194C4×Dic5—61no—
195C4×Dic5—61no—
196C4×Dic5C4×D311yescharacteristic
197C4×Dic5C4×D311yescharacteristic
198C4×Dic5#6711yescharacteristic
199C4×Dic5#6711yescharacteristic
200#681—21no—
201#681—21no—
202C2×#168—21no—
203C4×#41—151no—
204#423—51no—
205C2×#104—31no—
206C2×#104—151no—
207C4×C4⋊C4—151no—
208#339—151no—
209#339—151no—
210C22×C3×C5—21no—
211C22×C3×C5—21no—
212C22×C3×C5C2×C22⋊C411yescharacteristic
213C22×C3×C5#12111yescharacteristic
214C22×C3×C5C22⋊Q811yescharacteristic
215C2×C5×D3—22no—
216C2×C5×D3—41no—
217C2×C5×D3—41no—
218C3×C4×C5C2×C4⋊C411yescharacteristic
219C3×C4×C5#11711yescharacteristic
220C3×C4×C5#12111yescharacteristic
221C3×C4×C5C22⋊Q811yescharacteristic
222Dic15—42no—
223Dic15—41no—
224Dic15—41no—
225C3×Dic5—21no—
226C3×Dic5—21no—
227C3×Dic5—21no—
228C3×Dic5#10412yescomplemented
229C5×Dic3—22no—
230C5×Dic3—42no—
231C22×C3×C4—51no—
232C22×C3×C4—51no—
233C22×C3×C4C22×D511yescharacteristic
234C2×#67—21no—
235C22×Dic3—21no—
236C22×Dic3—101no—
237#235—21no—
238#235—21no—
239#235Dic1012yes—
240#235C22⋊D512yes—
241C2×D12C4×D511yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—101no—
244C2×C4×D3—101no—
245C2×Dic6C4×D511yescharacteristic
246C3×M16—21no—
247C3×M16—21no—
248C3×M16—101no—
249C3×M16—101no—
250C2×C3×C8—21no—
251C2×C3×C8—101no—
252C3×C42—51no—
253C3×C42—51no—
254C3×C42—51no—
255C3×C42—51no—
256#217—101no—
257(C2×D3)⋊C4—101no—
258(C2×D3)⋊C4—101no—
259C4⋊Dic3—51no—
260C4⋊Dic3—51no—
261C4⋊Dic3—104no—
262Dic3⋊C4—101no—
263Dic3⋊C4—101no—
264C4×Dic3—21no—
265C4×Dic3—21no—
266C4×Dic3—101no—
267C4×Dic3—101no—
268C4×Dic3—101no—
269C4×Dic3—101no—
270C4×Dic3—101no—
271C23×C5—61no—
272C23×C5C2×D1211yescharacteristic
273C5×Q8—32no—
274C5×Q8—61no—
275C5×D4—32no—
276C5×D4—62no—
277C5×D4—62no—
278C5×D4—61no—
279C2×C4×C5—61no—
280C2×C4×C5—62no—
281C2×C4×C5—62no—
282C2×C4×C5—62no—
283C2×C4×C5—121no—
284C2×C4×C5—121no—
285C2×C4×C5C2×C4×D311yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5#23711yescharacteristic
288C2×C4×C5D3×Q811yescharacteristic
289C2×C4×C5#23911yescharacteristic
290C2×C4×C5C2×#6711yescharacteristic
291C2×Dic5—22no—
292C2×Dic5—41no—
293C2×Dic5—62no—
294C2×Dic5—61no—
295C2×Dic5—61no—
296C2×Dic5—122no—
297C2×Dic5—121no—
298C2×Dic5—121no—
299C2×Dic5—122no—
300C2×Dic5(C2×D3)⋊C411yescharacteristic
301C2×Dic5(C2×D3)⋊C411yescharacteristic
302C2×Dic5(C2×D3)⋊C411yescharacteristic
303C2×Dic5(C2×D3)⋊C411yescharacteristic
304C5×C8—41no—
305#168—41no—
306C2×#41—31no—
307C2×M16—51no—
308C2×M16D3×D511yescharacteristic
309C4×Q8—151no—
310C4×Q8—151no—
311C4×D4—151no—
312C4×D4—151no—
313C4×D4—301no—
314C4×D4—301no—
315#117—151no—
316#117—301no—
317C2×C4⋊C4—301no—
318C2×C42—31no—
319C2×C42—51no—
320C2×C42—151no—
321C2×C42—301no—
322C4⋊C8—101no—
323C4⋊C8—101no—
324#104—62no—
325#104—302no—
326#95—301no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5#38011yescharacteristic
330C2×C3×C5C2×#10411yescharacteristic
331C2×C3×C5#42111yescharacteristic
332C5×D3—42no—
333C23×C3D4×D511yescharacteristic
334C22×D3—21no—
335C2×C3×C4—51no—
336C2×C3×C4—51no—
337C2×C3×C4—51no—
338C2×C3×C4—51no—
339C2×C3×C4—102no—
340C2×C3×C4—201no—
341C2×C3×C4C2×Dic1011yescharacteristic
342C2×C3×C4C2×C4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4#71111yescharacteristic
345C2×C3×C4#71111yescharacteristic
346C2×C3×C4C2×C22⋊D511yescharacteristic
347#67—22no—
348#67—22no—
349C2×Dic3—21no—
350C2×Dic3—22no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—102no—
354C2×Dic3—101no—
355C2×Dic3—101no—
356C2×Dic3—201no—
357C2×Dic3—201no—
358D12—21no—
359D12#68312yescomplemented
360C4×D3—22no—
361C4×D3—22no—
362C4×D3—202no—
363C4×D3—202no—
364Dic6—21no—
365Dic6#68312yescomplemented
366C3×C8—41no—
367C3×C8—201no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5—62no—
371C22×C5—121no—
372C22×C5—121no—
373C22×C5#89511yescharacteristic
374C22×C5#89711yescharacteristic
375C22×C5C2×(C2×D3)⋊C411yescharacteristic
376C4×C5—62no—
377C4×C5—122no—
378C4×C5D3×C4⋊C411yescharacteristic
379C4×C5#89211yescharacteristic
380C4×C5#93811yescharacteristic
381C4×C5#94611yescharacteristic
382Dic5—21no—
383Dic5—21no—
384Dic5—21no—
385Dic5—122no—
386Dic5—121no—
387Dic5—121no—
388Dic5#82512yescomplemented
389#41—32no—
390#41—32no—
391#41—61no—
392#41—61no—
393C2×Q8—31no—
394C2×D4—31no—
395C2×D4—61no—
396C22×C4—51no—
397C22×C4—51no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—301no—
401C22×C4—301no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404M16—21no—
405M16—21no—
406M16—101no—
407M16—101no—
408C2×C8—21no—
409C2×C8—101no—
410C4⋊C4—151no—
411C4⋊C4—151no—
412C4⋊C4—301no—
413C4⋊C4—301no—
414C4⋊C4—304no—
415C22⋊C4—301no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C42—51no—
419C42—51no—
420C42—51no—
421C42—51no—
422C42—61no—
423C42—61no—
424C42—301no—
425C42—301no—
426C42—301no—
427C42—301no—
428C42—301no—
429C3×C5#180611yescharacteristic, complemented, Hall
430C22×C3—21no—
431C22×C3—21no—
432C22×C3#402411yescharacteristic
433C22×C3D5×C22⋊C411yescharacteristic
434C22×C3#408511yescharacteristic
435C2×D3—22no—
436C2×D3—41no—
437C2×D3—41no—
438C3×C4—52no—
439C3×C4—101no—
440C3×C4—101no—
441C3×C4—101no—
442C3×C4#402311yescharacteristic
443C3×C4#402411yescharacteristic
444C3×C4C2×#68311yescharacteristic
445C3×C4#408511yescharacteristic
446Dic3—22no—
447Dic3—42no—
448Dic3—202no—
449Dic3—201no—
450Dic3—201no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5—122no—
454C2×C5#498711yescharacteristic
455C2×C5C2×#82511yescharacteristic
456C2×C5#513911yescharacteristic
457C23—61no—
458C23D5×D1211yescharacteristic
459Q8—32no—
460Q8—61no—
461D4—32no—
462D4—62no—
463D4—62no—
464D4—61no—
465C2×C4—51no—
466C2×C4—51no—
467C2×C4—51no—
468C2×C4—51no—
469C2×C4—61no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—102no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—201no—
477C2×C4—302no—
478C2×C4—301no—
479C2×C4—301no—
480C2×C4—602no—
481C2×C4—602no—
482C2×C4—601no—
483C2×C4—601no—
484C2×C4D3×Dic1011yescharacteristic
485C2×C4#676811yescharacteristic
486C2×C4C4×D3×D511yescharacteristic
487C2×C4#678011yescharacteristic
488C2×C4D5×#6711yescharacteristic
489C2×C4D3×C22⋊D511yescharacteristic
490C8—41no—
491C8—201no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3D5×#10411yescharacteristic
495C2×C3#6511011yescharacteristic
496C2×C3#6523111yescharacteristic
497D3—42no—
498C5#7052911yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—62no—
502C22—121no—
503C22—121no—
504C22#9141611yescharacteristic
505C22#9141711yescharacteristic
506C22D5×(C2×D3)⋊C411yescharacteristic
507C4—52no—
508C4—62no—
509C4—101no—
510C4—101no—
511C4—101no—
512C4—122no—
513C4—602no—
514C4—601no—
515C4—601no—
516C4D3×#68311yescharacteristic
517C4#9140011yescharacteristic
518C4#9141011yescharacteristic
519C4#9156511yescharacteristic
520C3#1060114811yescharacteristic, complemented, Sylow
521C2—21no—
522C2—21no—
523C2—122no—
524C2D5×#82511yescharacteristic
525C2#1174822911yescharacteristic
526C2#1174887411yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1806
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#65407C2semidirect
4. C4×#6668C2semidirect
6. #11746376C2semidirect
7. #11745976C2semidirect
19. Dic5×D12C4semidirect
20. Dic5×D12C4semidirect
23. Dic5×Dic6C4semidirect
24. Dic5×Dic6C4semidirect
34. #65407D3semidirect
127. C5×D12C4⋊C4semidirect
131. C5×Dic6C4⋊C4semidirect
228. C3×Dic5#104semidirect
359. D12#683semidirect
365. Dic6#683semidirect
388. Dic5#825semidirect
429. C3×C5#1806semidirect
498. C5#70529semidirect
520. C3#10601148semidirect

Maximal subgroups

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

subgroupindex
Dic5×#2352
C2×C5×#8252
C3×#654072
C4×#66682
C2×#909782
#117463762
#117459762
#106011483
#705295