Finite Group Databasebeta

← #14297846

Subgroups — #14297846

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
1#11754414C211yesmaximal, characteristic
2C2×#91089C211yesmaximal, characteristic
3C3×C4×#683C211yesmaximal, characteristic, complemented
4#11748431C211yesmaximal, characteristic, complemented
5C2×#90981C211yesmaximal, characteristic
6C5×#4523C211yesmaximal, characteristic, complemented
7#11745977C211yesmaximal, characteristic, complemented
8#10599563—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C5×#926C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×#683—21no—
15C2×C3×C4×Dic5C2211yescharacteristic
16C2×C3×C4×Dic5C2211yescharacteristic
17#91552—21no—
18#91552—21no—
19#91418C411yescharacteristic, complemented
20#91418C411yescharacteristic, complemented
21C4×#1200—21no—
22#91386—21no—
23#91333C411yescharacteristic, complemented
24#91333C411yescharacteristic, complemented
25#91089—22no—
26C3×#3963—21no—
27#90982—21no—
28#90982—21no—
29#90981—22no—
30#69494—51nomaximal, Hall
31#65856—31no—
32C2×#3957—31no—
33#65407—31no—
34C4×#683D311yescharacteristic, complemented
35C2×#3937—31no—
36C5×#339—31no—
37#64752—31no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41#6817—21no—
42#6817—21no—
43#6817D412yes—
44#6817Q812yes—
45C2×D60C2×C411yescharacteristic
46C2×C4×D15—21no—
47C2×Dic30C2×C411yescharacteristic
48C22×C3×Dic5—21no—
49C22×C3×Dic5D411yescharacteristic
50C22×C3×Dic5D411yescharacteristic
51C2×#1200—21no—
52C2×#1200—21no—
53C3×C42×C5—21no—
54C3×C42×C5—21no—
55#6710—21no—
56#6710—21no—
57C2×C3⋊#168—21no—
58C5×#217—21no—
59C5×C4⋊Dic3C2×C411yescharacteristic
60C5×C4⋊Dic3C2×C411yescharacteristic
61C4×C5×Dic3—21no—
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C3×#683—24no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5—21no—
68C3×C4×Dic5C2×C411yescharacteristic
69C3×C4×Dic5C2×C411yescharacteristic
70C3×C4×Dic5D411yescharacteristic
71C3×C4×Dic5D411yescharacteristic
72#6669—21no—
73#6669—21no—
74#6667—21no—
75#6667—21no—
76Dic3×Dic5—21no—
77Dic3×Dic5—21no—
78C4×#235—51no—
79C3×C4×C4⋊C4—51no—
80C2×#805—51no—
81C2×#805—51no—
82#4924—51no—
83#4523—51no—
84#4523D511yescharacteristic, complemented
85C2×#709—31no—
86C2×C5×M16—31no—
87C5×#117—31no—
88C2×C42×C5C2×D311yescharacteristic
89C2×#683—21no—
90C2×C4×Dic5C2×D311yescharacteristic
91C2×C4×Dic5C2×D311yescharacteristic
92C2×#681—31no—
93#4039—31no—
94#4039—31no—
95#4033—31no—
96#4033—31no—
97#4027—61no—
98#4027—61no—
99#4018—61no—
100C42×D5—61no—
101#3963—21no—
102#3957—62no—
103#3946—61no—
104#3946—61no—
105#3937—62no—
106#1806—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×D15—21no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×Q811yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118#1220—22no—
119#1220—22no—
120C2×Dic15—21no—
121D60—21no—
122D60C4⋊C412yescomplemented
123C4×D15—22no—
124C4×D15—22no—
125Dic30—21no—
126Dic30C4⋊C412yescomplemented
127C2×C5×Dic3—21no—
128C2×C5×Dic3—21no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—41no—
132C2×C3×Dic5—41no—
133C2×C3×Dic5—41no—
134C2×C3×Dic5C22⋊C411yescharacteristic
135C2×C3×Dic5C22⋊C411yescharacteristic
136C2×C3×Dic5C22⋊C411yescharacteristic
137C2×C3×Dic5C22⋊C411yescharacteristic
138#1200—42no—
139#1200—42no—
140C3⋊#168—41no—
141C5×C3⋊C8—41no—
142C2×#235—51no—
143C2×C3×C4⋊C4—101no—
144C2×C3×C42—51no—
145C2×C3×C42—51no—
146C2×C3×C42C2×D511yescharacteristic
147C4×#67—101no—
148C4×#67—101no—
149#926C2×D511yescharacteristic
150C2×#208—51no—
151C2×#208C2×D511yescharacteristic
152C4×D12—51no—
153C4×D12—51no—
154#872—101no—
155C42×D3—101no—
156C4×Dic6—51no—
157C4×Dic6—51no—
158C3×#95—101no—
159#805—102no—
160#805—102no—
161C4⋊(C3⋊C8)—101no—
162C4⋊(C3⋊C8)—101no—
163C22×C4×C5—21no—
164C22×C4×C5C22×D311yescharacteristic
165C2×C22⋊D5—61no—
166C22×Dic5—21no—
167C22×Dic5#6711yescharacteristic
168C22×Dic5#6711yescharacteristic
169#709—32no—
170#709—32no—
171#709—61no—
172#709—61no—
173C2×D20—31no—
174C2×C4×D5—61no—
175C2×C4×D5—61no—
176C2×C4×D5—61no—
177C2×Dic10—31no—
178C5×M16—61no—
179C5×M16—61no—
180C2×C5×C8—61no—
181C5×C4⋊C4—31no—
182C5×C4⋊C4—31no—
183C5×C22⋊C4—61no—
184C42×C5—21no—
185C42×C5—21no—
186C42×C5—61no—
187#685—61no—
188#685—61no—
189#683—24no—
190#683—61no—
191#683—61no—
192C4×Dic5—21no—
193C4×Dic5—21no—
194C4×Dic5—61no—
195C4×Dic5—61no—
196C4×Dic5C4×D311yescharacteristic
197C4×Dic5C4×D311yescharacteristic
198C4×Dic5D1211yescharacteristic
199C4×Dic5D1211yescharacteristic
200#681—61no—
201#681—61no—
202C2×#168—61no—
203C4×#41—151no—
204#423—151no—
205C2×#104—151no—
206C2×#104—151no—
207C4×C4⋊C4—51no—
208#339—31no—
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×D15—22no—
216C2×D15—41no—
217C2×D15—41no—
218C3×C4×C5—42no—
219C3×C4×C5C2×C4⋊C411yescharacteristic
220C3×C4×C5#11711yescharacteristic
221C3×C4×C5#12111yescharacteristic
222C3×C4×C5C22⋊Q811yescharacteristic
223Dic15—22no—
224C3×Dic5—21no—
225C3×Dic5—21no—
226C3×Dic5—21no—
227C3×Dic5—42no—
228C3×Dic5#10412yescomplemented
229C5×Dic3—41no—
230C5×Dic3—41no—
231C22×C3×C4—21no—
232C22×C3×C4—51no—
233C22×C3×C4—51no—
234C22×C3×C4—101no—
235C22×C3×C4C22×D511yescharacteristic
236C2×#67—101no—
237#235—52no—
238#235—52no—
239#235—101no—
240#235—101no—
241C2×D12—51no—
242C2×C4×D3—101no—
243C2×C4×D3—101no—
244C2×C4×D3—101no—
245C2×Dic6—51no—
246C3×C4⋊C4—104no—
247C3×C42—21no—
248C3×C42—21no—
249C3×C42—51no—
250C3×C42—51no—
251C3×C42—51no—
252C3×C42—51no—
253C3×C42—101no—
254C3×C42—101no—
255#217—21no—
256(C2×D3)⋊C4—101no—
257(C2×D3)⋊C4—101no—
258C4⋊Dic3C4×D511yescharacteristic
259C4⋊Dic3C4×D511yescharacteristic
260Dic3⋊C4—101no—
261Dic3⋊C4—101no—
262C4×Dic3—21no—
263C4×Dic3—101no—
264C4×Dic3—101no—
265#208—21no—
266#208—21no—
267#208—101no—
268#208—101no—
269C2×C3⋊C8—21no—
270C2×C3⋊C8—101no—
271C23×C5C2×#6711yescharacteristic
272C22×D5—61no—
273C2×C4×C5—22no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—61no—
277C2×C4×C5—61no—
278C2×C4×C5C2×C4×D311yescharacteristic
279C2×C4×C5C2×D1211yescharacteristic
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5#23711yescharacteristic
282C2×C4×C5D3×Q811yescharacteristic
283C2×C4×C5#23911yescharacteristic
284C22⋊D5—62no—
285C22⋊D5—62no—
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—41no—
289C2×Dic5—41no—
290C2×Dic5—41no—
291C2×Dic5—61no—
292C2×Dic5(C2×D3)⋊C411yescharacteristic
293C2×Dic5(C2×D3)⋊C411yescharacteristic
294C2×Dic5(C2×D3)⋊C411yescharacteristic
295C2×Dic5(C2×D3)⋊C411yescharacteristic
296D20—32no—
297D20—61no—
298C4×D5—62no—
299C4×D5—62no—
300C4×D5—122no—
301C4×D5—122no—
302Dic10—32no—
303Dic10—61no—
304C5×C8—121no—
305#168—121no—
306C2×#41—151no—
307C2×M16—31no—
308C2×M16—151no—
309C4×Q8—151no—
310C4×Q8—151no—
311C4×D4—151no—
312C4×D4—151no—
313C4×D4—301no—
314C4×D4—301no—
315#117—31no—
316#117—301no—
317C2×C4⋊C4—101no—
318C2×C42—51no—
319C2×C42—51no—
320C2×C42—301no—
321C2×C42D3×D511yescharacteristic
322C4⋊C8—301no—
323C4⋊C8—301no—
324#104—302no—
325#104—302no—
326#95—101no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5#38011yescharacteristic
330C2×C3×C5C2×#10411yescharacteristic
331C2×C3×C5#42111yescharacteristic
332D15—42no—
333C23×C3D4×D511yescharacteristic
334C22×D3—101no—
335C2×C3×C4—22no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—51no—
339C2×C3×C4—51no—
340C2×C3×C4—51no—
341C2×C3×C4—51no—
342C2×C3×C4—102no—
343C2×C3×C4—102no—
344C2×C3×C4—201no—
345C2×C3×C4—201no—
346C2×C3×C4—201no—
347C2×C3×C4C2×C4×D511yescharacteristic
348C2×C3×C4#70911yescharacteristic
349C2×C3×C4#70911yescharacteristic
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4Q8×D511yescharacteristic
353#67—102no—
354#67—102no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—101no—
358D12—52no—
359D12—101no—
360C4×D3—102no—
361C4×D3—102no—
362C4×D3—202no—
363C4×D3—202no—
364Dic6—52no—
365Dic6—101no—
366C3⋊C8—41no—
367C3⋊C8—201no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5C2×(C2×D3)⋊C411yescharacteristic
371C22×C5#93811yescharacteristic
372C22×C5#94611yescharacteristic
373C2×D5—62no—
374C2×D5—121no—
375C2×D5—121no—
376C4×C5—42no—
377C4×C5—121no—
378C4×C5—121no—
379C4×C5D3×C4⋊C411yescharacteristic
380C4×C5#89211yescharacteristic
381C4×C5#89511yescharacteristic
382C4×C5#89711yescharacteristic
383Dic5—21no—
384Dic5—21no—
385Dic5—21no—
386Dic5—42no—
387Dic5—62no—
388Dic5#80512yescomplemented
389#41—152no—
390#41—152no—
391#41—301no—
392#41—301no—
393C2×Q8—151no—
394C2×D4—151no—
395C2×D4—301no—
396C22×C4—21no—
397C22×C4—51no—
398C22×C4—51no—
399C22×C4—101no—
400C22×C4—301no—
401C22×C4—301no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404M16—61no—
405M16—61no—
406M16—301no—
407M16—301no—
408C2×C8—61no—
409C2×C8—301no—
410C4⋊C4—31no—
411C4⋊C4—31no—
412C4⋊C4—104no—
413C4⋊C4—301no—
414C4⋊C4—301no—
415C22⋊C4—61no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C42—21no—
419C42—21no—
420C42—51no—
421C42—51no—
422C42—51no—
423C42—51no—
424C42—61no—
425C42—101no—
426C42—101no—
427C42—301no—
428C42—301no—
429C3×C5#180611yescharacteristic, complemented, Hall
430C22×C3—21no—
431C22×C3—21no—
432C22×C3D5×C22⋊C411yescharacteristic
433C22×C3#403011yescharacteristic
434C22×C3#404211yescharacteristic
435C2×D3—102no—
436C2×D3—201no—
437C2×D3—201no—
438C3×C4—42no—
439C3×C4—52no—
440C3×C4—101no—
441C3×C4—101no—
442C3×C4—101no—
443C3×C4—202no—
444C3×C4#401811yescharacteristic
445C3×C4#403011yescharacteristic
446C3×C4D5×C4⋊C411yescharacteristic
447C3×C4#404211yescharacteristic
448Dic3—41no—
449Dic3—41no—
450Dic3—102no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5C2×#80511yescharacteristic
454C2×C5#498711yescharacteristic
455C2×C5#500511yescharacteristic
456D5—122no—
457C23—301no—
458C23D5×#6711yescharacteristic
459Q8—152no—
460Q8—301no—
461D4—152no—
462D4—302no—
463D4—302no—
464D4—301no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—51no—
469C2×C4—51no—
470C2×C4—51no—
471C2×C4—51no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—102no—
475C2×C4—102no—
476C2×C4—201no—
477C2×C4—201no—
478C2×C4—201no—
479C2×C4—301no—
480C2×C4—302no—
481C2×C4—302no—
482C2×C4—602no—
483C2×C4—602no—
484C2×C4#676911yescharacteristic
485C2×C4D15⋊Q811yescharacteristic
486C2×C4C4×D3×D511yescharacteristic
487C2×C4D5×D1211yescharacteristic
488C2×C4#677911yescharacteristic
489C2×C4#679011yescharacteristic
490C8—121no—
491C8—601no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3#6495611yescharacteristic
495C2×C3D5×#10411yescharacteristic
496C2×C3#6511011yescharacteristic
497D3—202no—
498C5#6949411yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—302no—
502C22—601no—
503C22—601no—
504C22#9141111yescharacteristic
505C22D5×(C2×D3)⋊C411yescharacteristic
506C22#9153311yescharacteristic
507C4—42no—
508C4—52no—
509C4—101no—
510C4—101no—
511C4—101no—
512C4—121no—
513C4—121no—
514C4—202no—
515C4—302no—
516C4#9140311yescharacteristic
517C4#9140411yescharacteristic
518C4#9141911yescharacteristic
519C4#9142011yescharacteristic
520C3#1059956311yescharacteristic, complemented, Sylow
521C2—21no—
522C2—21no—
523C2—602no—
524C2D5×#80511yescharacteristic
525C2#1174710911yescharacteristic
526C2#1174887611yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1806
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C4×#683C2semidirect
4. #11748431C2semidirect
6. C5×#4523C2semidirect
7. #11745977C2semidirect
19. #91418C4semidirect
20. #91418C4semidirect
23. #91333C4semidirect
24. #91333C4semidirect
34. C4×#683D3semidirect
84. #4523D5semidirect
122. D60C4⋊C4semidirect
126. Dic30C4⋊C4semidirect
228. C3×Dic5#104semidirect
388. Dic5#805semidirect
429. C3×C5#1806semidirect
498. C5#69494semidirect
520. C3#10599563semidirect

Maximal subgroups

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

subgroupindex
#117544142
C2×#910892
C3×C4×#6832
#117484312
C2×#909812
C5×#45232
#117459772
#105995633
#694945