Finite Group Databasebeta

← #14302007

Subgroups — #14302007

Order 1920.

716 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
1C2×#91761C211yesmaximal, characteristic, complemented
2#11754592C211yesmaximal, characteristic
3C2×C5×#805C211yesmaximal, characteristic, complemented
4C2×#90978C211yesmaximal, characteristic, complemented
5#11748351C211yesmaximal, characteristic, complemented
6C3×#64743C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10601176—31nomaximal, Hall
9C22×C4×D15C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C2×#6714—21no—
13C2×#6712—21no—
14C2×C4×Dic15C2211yescharacteristic
15#91761—22no—
16#91761—22no—
17C2×C5×#208C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91573—21no—
21#91543—21no—
22#91466C412yescomplemented
23C4×#1203—22no—
24#91383C412yescomplemented
25C5×#805—22no—
26#90978—22no—
27#90957—22no—
28#68757—51nomaximal, Hall
29#66162—31no—
30C2×#4018—31no—
31C2×C5×#104—31no—
32C2×#3969—31no—
33#65415—31no—
34#64775—31no—
35#64743D311yescharacteristic, complemented
36C23×D15D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15D411yescharacteristic
41C2×C4×D15—21no—
42C2×C4×D15—21no—
43C2×C4×D15—21no—
44C2×C4×D15—21no—
45C2×C4×D15C2×C412yes—
46C2×C4×D15D412yes—
47C2×C5×#67—21no—
48C5×#235—21no—
49C5×#235—21no—
50C5×#235—21no—
51C5×#235—21no—
52C2×C5×D12C2×C411yescharacteristic
53C2×C4×C5×D3—21no—
54C2×C5×Dic6C2×C411yescharacteristic
55C2×#1203—22no—
56C3×C42×C5—21no—
57C3×C42×C5D412yescomplemented
58#6714—24no—
59#6712—24no—
60C4×Dic15—21no—
61C4×Dic15D412yescomplemented
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C3×C22⋊Dic5—21no—
66C3×C4⋊Dic5C2×C412yes—
67C3×C4×Dic5—21no—
68C3×#681—21no—
69C3×#681—21no—
70C2×C3×#168—21no—
71#6668—22no—
72#6667—22no—
73(C2×D3)⋊Dic5—22no—
74#5524—51no—
75C2×#872—51no—
76C2×#825—51no—
77#5126—51no—
78C2×#805D511yescharacteristic, complemented
79C3×#339—51no—
80#4532—51no—
81C2×C5×#41—31no—
82C22×C4×D5—31no—
83C2×C5×M16—31no—
84C2×C42×C5C2×D311yescharacteristic
85#4092—32no—
86#4084—32no—
87#4083—61no—
88#4081—61no—
89C4×C22⋊D5—62no—
90C2×#685—61no—
91#4072C2×D311yescharacteristic
92C2×#683—61no—
93C2×C4×Dic5—31no—
94C2×#681C2×D311yescharacteristic
95#4018—62no—
96#4018—62no—
97C5×#104—62no—
98#3969—62no—
99#3952—62no—
100#1897—151noSylow
101C23×C3×C5C2×D411yescharacteristic
102C22×D15—21no—
103C22×D15—21no—
104C22×D15—42no—
105C22×D15C22⋊C412yes—
106C22×C5×D3—21no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—42no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—21no—
116C2×Dic15—21no—
117C2×Dic15—22no—
118C2×Dic15—42no—
119C2×Dic15C22⋊C412yes—
120C4×D15—22no—
121C4×D15—22no—
122C4×D15—22no—
123C4×D15—22no—
124C5×#67—41no—
125C5×#67—41no—
126C2×C5×Dic3—21no—
127C5×D12—21no—
128C5×D12—21no—
129C4×C5×D3—41no—
130C4×C5×D3—41no—
131C5×Dic6—21no—
132C5×Dic6—21no—
133C2×C3×Dic5—22no—
134#1203—44no—
135C3×#168—41no—
136C5×C3⋊C8—41no—
137C2×#235C2×D511yescharacteristic
138C22×C4×D3—51no—
139C2×C3×M16—51no—
140C3×#117—51no—
141C2×C3×C42C2×D511yescharacteristic
142C2×(C2×D3)⋊C4—101no—
143C2×Dic3⋊C4—101no—
144C2×C4×Dic3—51no—
145C2×#208C2×D511yescharacteristic
146#897—52no—
147#895—52no—
148#886—101no—
149#882—101no—
150C4×D12—102no—
151#872—102no—
152#872—102no—
153#825—102no—
154(C2×D3)⋊C8—102no—
155#805—22no—
156C23×D5—31no—
157C5×#41—61no—
158C5×#41—61no—
159C5×#41—61no—
160C5×#41—61no—
161C2×C5×Q8—31no—
162C2×C5×D4—31no—
163C2×C5×D4—61no—
164C22×C4×C5—21no—
165C22×C4×C5—61no—
166C22×C4×C5C22×D311yescharacteristic
167C2×C22⋊D5—62no—
168C22×Dic5—31no—
169C22×Dic5—61no—
170C2×C4×D5—32no—
171C2×C4×D5—32no—
172C2×C4×D5—61no—
173C2×C4×D5—61no—
174C2×C4×D5—61no—
175C2×C4×D5—61no—
176C5×M16—61no—
177C5×M16—61no—
178C2×C5×C8—61no—
179C42×C5—21no—
180C42×C5D1212yescomplemented
181C22⋊Dic5—21no—
182C22⋊Dic5—62no—
183#685—62no—
184#685—64no—
185C4⋊Dic5C4×D312yes—
186#683—62no—
187#683—64no—
188C4×Dic5—21no—
189C4×Dic5—32no—
190C4×Dic5—61no—
191#681—21no—
192#681—21no—
193C2×#168—21no—
194#525—151no—
195C2×#117—151no—
196C2×#104—31no—
197C2×#104—151no—
198#407—151no—
199#339—51no—
200#339—151no—
201C22×C3×C5—22no—
202C22×C3×C5C2×C22⋊C411yescharacteristic
203C22×C3×C5#12011yescharacteristic
204C22×C3×C5#12311yescharacteristic
205C2×D15—22no—
206C2×D15—22no—
207C2×D15—22no—
208C2×D15—42no—
209C2×D15—42no—
210C2×C5×D3—41no—
211C2×C5×D3—42no—
212C3×C4×C5—42no—
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5C4×D411yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12111yescharacteristic
217Dic15—22no—
218Dic15—42no—
219C3×Dic5—42no—
220C5×Dic3—41no—
221C23×D3—51no—
222C22×C3×C4—21no—
223C22×C3×C4C22×D511yescharacteristic
224C2×#67—21no—
225C22×Dic3—51no—
226C22×Dic3—101no—
227#235—21no—
228#235—21no—
229#235—21no—
230#235—21no—
231C2×D12—102no—
232C2×D12C4×D511yescharacteristic
233C2×C4×D3—21no—
234C2×C4×D3—52no—
235C2×C4×D3—52no—
236C2×C4×D3—101no—
237C2×C4×D3—101no—
238C2×C4×D3—101no—
239C2×C4×D3—101no—
240C2×Dic6C4×D511yescharacteristic
241C3×M16—101no—
242C3×M16—101no—
243C2×C3×C8—101no—
244C3×C4⋊C4—52no—
245C3×C22⋊C4—101no—
246C3×C42—21no—
247C3×C42—101no—
248C3×C42C22⋊D512yescomplemented
249(C2×D3)⋊C4—102no—
250(C2×D3)⋊C4—102no—
251(C2×D3)⋊C4—104no—
252C4⋊Dic3—102no—
253Dic3⋊C4—104no—
254C4×Dic3—52no—
255C4×Dic3—101no—
256#208—21no—
257#208—21no—
258C2×C3⋊C8—21no—
259C23×C5—61no—
260C23×C5D3×D411yescharacteristic
261C22×D5—32no—
262C22×D5—61no—
263C22×D5—61no—
264C22×D5—122no—
265C5×Q8—61no—
266C5×Q8—61no—
267C5×D4—61no—
268C5×D4—61no—
269C5×D4—121no—
270C5×D4—121no—
271C2×C4×C5—22no—
272C2×C4×C5—42no—
273C2×C4×C5—61no—
274C2×C4×C5—121no—
275C2×C4×C5—121no—
276C2×C4×C5C2×C4×D311yescharacteristic
277C2×C4×C5C2×D1211yescharacteristic
278C2×C4×C5#23511yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5#23911yescharacteristic
282C22⋊D5—124no—
283C2×Dic5—22no—
284C2×Dic5—32no—
285C2×Dic5—61no—
286C2×Dic5—61no—
287C2×Dic5—62no—
288C2×Dic5—122no—
289C4×D5—62no—
290C4×D5—62no—
291C4×D5—62no—
292C4×D5—62no—
293C5×C8—121no—
294#168—41no—
295C2×#41—31no—
296C23×C4—151no—
297C2×M16—31no—
298C2×M16—51no—
299#123—301no—
300C22⋊Q8—152no—
301#121—152no—
302#120—301no—
303C4×D4—302no—
304#117—51no—
305#117—302no—
306#117—302no—
307C2×C4⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—151no—
310C2×C42D3×D511yescharacteristic
311#104—62no—
312#104—302no—
313C22⋊C8—302no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#38611yescharacteristic
317C2×C3×C5#42112yes—
318D15—42no—
319C5×D3—81no—
320C23×C3D4×D511yescharacteristic
321C22×D3—21no—
322C22×D3—52no—
323C22×D3—101no—
324C22×D3—101no—
325C22×D3—202no—
326C2×C3×C4—22no—
327C2×C3×C4—42no—
328C2×C3×C4—102no—
329C2×C3×C4C2×C4×D511yescharacteristic
330C2×C3×C4#70911yescharacteristic
331C2×C3×C4D4×D511yescharacteristic
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4#71111yescharacteristic
334C2×C3×C4C2×C22⋊D511yescharacteristic
335#67—41no—
336#67—41no—
337C2×Dic3—21no—
338C2×Dic3—52no—
339C2×Dic3—101no—
340C2×Dic3—101no—
341C2×Dic3—102no—
342C2×Dic3—202no—
343D12—21no—
344D12—21no—
345D12—204no—
346C4×D3—41no—
347C4×D3—41no—
348C4×D3—102no—
349C4×D3—102no—
350C4×D3—102no—
351C4×D3—102no—
352Dic6—21no—
353Dic6—21no—
354C3×C8—201no—
355C3⋊C8—41no—
356C22×C5—22no—
357C22×C5—121no—
358C22×C5—122no—
359C22×C5D3×C22⋊C411yescharacteristic
360C22×C5#88211yescharacteristic
361C22×C5#89411yescharacteristic
362C2×D5—62no—
363C2×D5—62no—
364C2×D5—62no—
365C2×D5—122no—
366C2×D5—122no—
367C4×C5—42no—
368C4×C5—121no—
369C4×C5C4×D1211yescharacteristic
370C4×C5#88411yescharacteristic
371C4×C5#89311yescharacteristic
372C4×C5#89511yescharacteristic
373Dic5—42no—
374Dic5—62no—
375Dic5—122no—
376C24—151no—
377#41—61no—
378#41—61no—
379#41—61no—
380#41—61no—
381C2×Q8—31no—
382C2×D4—31no—
383C2×D4—61no—
384C2×D4—302no—
385C22×C4—21no—
386C22×C4—61no—
387C22×C4—151no—
388C22×C4—152no—
389C22×C4—152no—
390C22×C4—301no—
391C22×C4—301no—
392C22×C4—301no—
393C22×C4—301no—
394C22×C4—301no—
395C22×C4C2×D3×D511yescharacteristic
396M16—61no—
397M16—61no—
398M16—101no—
399M16—101no—
400C2×C8—61no—
401C2×C8—101no—
402C4⋊C4—52no—
403C4⋊C4—304no—
404C4⋊C4—302no—
405C22⋊C4—101no—
406C22⋊C4—304no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—21no—
410C42—101no—
411C42—152no—
412C42—301no—
413C42#120312yescomplemented
414C3×C5#189711yescharacteristic, complemented, Hall
415C22×C3—22no—
416C22×C3D5×C22⋊C411yescharacteristic
417C22×C3#402911yescharacteristic
418C22×C3#408311yescharacteristic
419C2×D3—42no—
420C2×D3—41no—
421C2×D3—102no—
422C2×D3—102no—
423C2×D3—102no—
424C2×D3—202no—
425C2×D3—202no—
426C3×C4—42no—
427C3×C4—202no—
428C3×C4#402711yescharacteristic
429C3×C4#403011yescharacteristic
430C3×C4C4×C22⋊D511yescharacteristic
431C3×C4#408411yescharacteristic
432Dic3—41no—
433Dic3—102no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—241no—
438C2×C5#466511yescharacteristic
439C2×C5#482112yes—
440D5—122no—
441C23—61no—
442C23—152no—
443C23—301no—
444C23—301no—
445C23—602no—
446C23#679011yescharacteristic
447Q8—61no—
448Q8—61no—
449D4—61no—
450D4—61no—
451D4—121no—
452D4—121no—
453D4—604no—
454C2×C4—22no—
455C2×C4—42no—
456C2×C4—61no—
457C2×C4—102no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—152no—
461C2×C4—301no—
462C2×C4—301no—
463C2×C4—302no—
464C2×C4—302no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—302no—
468C2×C4—602no—
469C2×C4#676811yescharacteristic
470C2×C4#677111yescharacteristic
471C2×C4C4×D3×D511yescharacteristic
472C2×C4#677711yescharacteristic
473C2×C4C2×#120311yescharacteristic
474C2×C4#679011yescharacteristic
475C8—121no—
476C8—201no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3#6511012yes—
480C2×C3#6524511yescharacteristic
481D3—81no—
482D3—202no—
483C5#6875711yescharacteristic, complemented, Sylow
484C22—22no—
485C22—122no—
486C22—121no—
487C22—302no—
488C22—302no—
489C22—302no—
490C22—602no—
491C22—602no—
492C22#9135511yescharacteristic
493C22#9147311yescharacteristic
494C22#9157311yescharacteristic
495C4—42no—
496C4—121no—
497C4—202no—
498C4—302no—
499C4—602no—
500C4#9140611yescharacteristic
501C4C4×#120311yescharacteristic
502C4#9146111yescharacteristic
503C4#9146611yescharacteristic
504C3#1060117611yescharacteristic, complemented, Sylow
505C2—21no—
506C2—21no—
507C2—241no—
508C2—602no—
509C2#1174711312yes—
510C2#1174891811yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754592C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1897
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
1. C2×#91761C2semidirect
3. C2×C5×#805C2semidirect
4. C2×#90978C2semidirect
5. #11748351C2semidirect
6. C3×#64743C2semidirect
7. #11745973C2semidirect
22. #91466C4semidirect
24. #91383C4semidirect
35. #64743D3semidirect
57. C3×C42×C5D4semidirect
61. C4×Dic15D4semidirect
78. C2×#805D5semidirect
180. C42×C5D12semidirect
248. C3×C42C22⋊D5semidirect
413. C42#1203semidirect
414. C3×C5#1897semidirect
483. C5#68757semidirect
504. C3#10601176semidirect

Maximal subgroups

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

subgroupindex
C2×#917612
#117545922
C2×C5×#8052
C2×#909782
#117483512
C3×#647432
#117459732
#106011763
#687575