Finite Group Databasebeta

← #14301741

Subgroups — #14301741

Order 1920.

684 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5524C211yesmaximal, characteristic
2#11754125C211yesmaximal, characteristic, complemented
3#11748355C211yesmaximal, characteristic, complemented
4#11748346C211yesmaximal, characteristic, complemented
5#11748346C211yesmaximal, characteristic, complemented
6#11746354C211yesmaximal, characteristic, complemented
7C3×#64753C211yesmaximal, characteristic, complemented
8#10602507—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C4×C5×D3C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#897—21no—
15C5×#895—21no—
16C5×#886C412yes—
17C5×#882C412yes—
18C4×C5×D12—22no—
19C2×C3×#681C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91288—22no—
22D3×#681—22no—
23#91286—22no—
24#90962—21no—
25#90959—21no—
26(C2×D3)⋊#168—22no—
27(C2×D3)⋊#168—22no—
28#69036—51nomaximal, Hall
29C5×#525—31no—
30#66153—31no—
31#65526—31no—
32#65496—31no—
33#65496—31no—
34#64753—31no—
35#64753D311yescharacteristic, complemented
36C23×C5×D3C2×C411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C2×C5×#67C2×C412yes—
39C22×C5×Dic3C2×C411yescharacteristic
40C5×#235—21no—
41C5×#235—21no—
42C5×#235—21no—
43C5×#235—21no—
44C2×C5×D12—22no—
45C2×C5×D12D411yescharacteristic
46C2×C4×C5×D3—21no—
47C2×C4×C5×D3—21no—
48C2×C4×C5×D3—21no—
49C2×C4×C5×D3—21no—
50C2×C4×C5×D3—21no—
51C2×C4×C5×D3—21no—
52C2×C4×C5×D3D412yes—
53C2×C5×Dic6D411yescharacteristic
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4C2×C412yes—
56C3×C42×C5—21no—
57#6710—21no—
58#6710—21no—
59#6710—21no—
60#6710—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168D412yescomplemented
63C5×(C2×D3)⋊C4—22no—
64C5×(C2×D3)⋊C4—22no—
65C5×C4⋊Dic3—22no—
66C3×#681—21no—
67C3×#681—21no—
68C3×#681—21no—
69C3×#681—21no—
70C2×C3×#168—21no—
71C2×C3×#168D412yescomplemented
72#6650—24no—
73D3×#168—24no—
74#5745—51no—
75#5524D511yescharacteristic
76#5132—51no—
77#5126—51no—
78#5126—51no—
79C3×#344—51no—
80#4533—51no—
81C2×C5×#41—31no—
82C23×C4×C5—31no—
83C5×#123—32no—
84C5×C22⋊Q8—61no—
85C5×#121—61no—
86C5×#120—32no—
87C4×C5×D4—62no—
88C5×#117C2×D311yescharacteristic
89#4094—62no—
90#4094—62no—
91C2×#681—31no—
92C2×#681—31no—
93C2×#681—62no—
94C2×#681C2×D311yescharacteristic
95C2×#681C2×D311yescharacteristic
96#3968—61no—
97#3965—61no—
98C22⋊#168—62no—
99C22⋊#168—62no—
100#1891—151noSylow
101C23×C3×C5C22×C411yescharacteristic
102C22×C5×D3—21no—
103C22×C5×D3—21no—
104C22×C5×D3—21no—
105C22×C5×D3—42no—
106C22×C5×D3C22⋊C412yes—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C5×#67—22no—
115C5×#67—22no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—21no—
118C2×C5×Dic3—21no—
119C2×C5×Dic3C22⋊C412yes—
120C5×D12—21no—
121C5×D12—21no—
122C5×D12—44no—
123C4×C5×D3—22no—
124C4×C5×D3—22no—
125C4×C5×D3—41no—
126C4×C5×D3—41no—
127C4×C5×D3—41no—
128C4×C5×D3—41no—
129C5×Dic6—21no—
130C5×Dic6—21no—
131C3⋊#168—22no—
132C3⋊#168—41no—
133C3×#168—22no—
134C3×#168—41no—
135C2×#235C2×D511yescharacteristic
136C22×C4×D3C2×D511yescharacteristic
137C2×C3×M16—51no—
138C2×C3×M16—51no—
139C3×#117C2×D511yescharacteristic
140C2×#208—51no—
141C2×#208—51no—
142#907—102no—
143D3×M16—102no—
144#901—102no—
145#897—21no—
146#895—21no—
147#886Dic512yes—
148#882Dic512yes—
149C4×D12—22no—
150#824—101no—
151#823—101no—
152(C2×D3)⋊C8—102no—
153(C2×D3)⋊C8—102no—
154C24×C5—31no—
155C5×#41—61no—
156C5×#41—61no—
157C5×#41—61no—
158C5×#41—61no—
159C2×C5×Q8—31no—
160C2×C5×D4—32no—
161C2×C5×D4—31no—
162C2×C5×D4—62no—
163C22×C4×C5—32no—
164C22×C4×C5—31no—
165C22×C4×C5—61no—
166C22×C4×C5—61no—
167C22×C4×C5—61no—
168C22×C4×C5—61no—
169C22×C4×C5—61no—
170C22×C4×C5—61no—
171C22×C4×C5C22×D311yescharacteristic
172C5×C4⋊C4—21no—
173C5×C4⋊C4—62no—
174C5×C22⋊C4—62no—
175C5×C22⋊C4—62no—
176C5×C22⋊C4C4×D312yes—
177C42×C5—21no—
178#681—21no—
179#681—21no—
180#681—21no—
181#681—21no—
182#681—64no—
183#681—61no—
184#681—61no—
185#681—61no—
186#681—61no—
187C2×#168—21no—
188C2×#168—32no—
189C2×#168—64no—
190C2×#168—61no—
191C2×#168D1212yescomplemented
192#568—151no—
193#525—31no—
194#413—151no—
195#407—151no—
196#407—151no—
197#344—51no—
198#344—151no—
199C22×C3×C5—41no—
200C22×C3×C5C2×C22⋊C411yescharacteristic
201C22×C3×C5C4×D411yescharacteristic
202C22×C3×C5C4×D411yescharacteristic
203C2×C5×D3—22no—
204C2×C5×D3—22no—
205C2×C5×D3—22no—
206C2×C5×D3—22no—
207C2×C5×D3—41no—
208C2×C5×D3—41no—
209C2×C5×D3—41no—
210C2×C5×D3—41no—
211C2×C5×D3—42no—
212C3×C4×C5—42no—
213C3×C4×C5#12011yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12311yescharacteristic
217C5×Dic3—22no—
218C5×Dic3—41no—
219C23×D3C2×Dic511yescharacteristic
220C22×C3×C4C22×D511yescharacteristic
221C2×#67C2×Dic512yes—
222C22×Dic3C2×Dic511yescharacteristic
223#235—21no—
224#235—21no—
225#235—21no—
226#235—21no—
227C2×D12—22no—
228C2×D12C22⋊D511yescharacteristic
229C2×C4×D3—21no—
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3C22⋊D512yes—
236C2×Dic6C22⋊D511yescharacteristic
237C3×M16—101no—
238C3×M16—101no—
239C3×M16—101no—
240C3×M16—101no—
241C2×C3×C8—52no—
242C2×C3×C8—101no—
243C3×C4⋊C4—21no—
244C3×C22⋊C4C2×Dic512yes—
245C3×C42—21no—
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4—22no—
248C4⋊Dic3—22no—
249#208—101no—
250#208—101no—
251#208—101no—
252#208—101no—
253C2×C3⋊C8—52no—
254C2×C3⋊C8—101no—
255ΓL(1,𝔽25)—104no—
256D3×C8—104no—
257C23×C5—32no—
258C23×C5—61no—
259C23×C5—61no—
260C23×C5—61no—
261C23×C5—122no—
262C23×C5C2×C4×D311yescharacteristic
263C5×Q8—61no—
264C5×Q8—61no—
265C5×D4—62no—
266C5×D4—62no—
267C5×D4—61no—
268C5×D4—61no—
269C5×D4—124no—
270C2×C4×C5—22no—
271C2×C4×C5—32no—
272C2×C4×C5—62no—
273C2×C4×C5—62no—
274C2×C4×C5—61no—
275C2×C4×C5—61no—
276C2×C4×C5—61no—
277C2×C4×C5—121no—
278C2×C4×C5—121no—
279C2×C4×C5—121no—
280C2×C4×C5—121no—
281C2×C4×C5C2×D1211yescharacteristic
282C2×C4×C5#23511yescharacteristic
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5#23911yescharacteristic
287#168—22no—
288#168—41no—
289#168—62no—
290#168—121no—
291C2×#41—31no—
292C23×C4—31no—
293#131—302no—
294#131—302no—
295C2×M16—51no—
296C2×M16—51no—
297C2×M16—151no—
298C2×M16—151no—
299C2×M16—302no—
300#123—32no—
301C22⋊Q8—61no—
302#121—61no—
303#120—32no—
304C4×D4—62no—
305#117D3×D511yescharacteristic
306#101—301no—
307#100—301no—
308C22⋊C8—302no—
309C22⋊C8—302no—
310C2×C3×C5—21no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5#38611yescharacteristic
314C5×D3—42no—
315C5×D3—42no—
316C23×C3C22×Dic511yescharacteristic
317C22×D3—21no—
318C22×D3—21no—
319C22×D3—21no—
320C22×D3—42no—
321C22×D3C22⋊Dic512yes—
322C2×C3×C4—22no—
323C2×C3×C4D4×D511yescharacteristic
324C2×C3×C4D4×D511yescharacteristic
325C2×C3×C4#71111yescharacteristic
326C2×C3×C4#71111yescharacteristic
327C2×C3×C4C2×C22⋊D511yescharacteristic
328C2×C3×C4C2×C22⋊D511yescharacteristic
329#67—22no—
330#67—22no—
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3C22⋊Dic512yes—
335D12—21no—
336D12—21no—
337D12—44no—
338C4×D3—22no—
339C4×D3—22no—
340C4×D3—41no—
341C4×D3—41no—
342C4×D3—41no—
343C4×D3—41no—
344Dic6—21no—
345Dic6—21no—
346C3×C8—102no—
347C3×C8—201no—
348C3⋊C8—102no—
349C3⋊C8—201no—
350C22×C5—41no—
351C22×C5—62no—
352C22×C5—62no—
353C22×C5—62no—
354C22×C5—62no—
355C22×C5—122no—
356C22×C5—121no—
357C22×C5—121no—
358C22×C5—121no—
359C22×C5—121no—
360C22×C5C4×D1211yescharacteristic
361C22×C5D3×C22⋊C411yescharacteristic
362C22×C5#89311yescharacteristic
363C4×C5—42no—
364C4×C5—62no—
365C4×C5—121no—
366C4×C5#88211yescharacteristic
367C4×C5#88411yescharacteristic
368C4×C5#89411yescharacteristic
369C4×C5#89511yescharacteristic
370C24—31no—
371#41—61no—
372#41—61no—
373#41—61no—
374#41—61no—
375C2×Q8—31no—
376C2×D4—32no—
377C2×D4—31no—
378C2×D4—62no—
379C22×C4—32no—
380C22×C4—31no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4—61no—
384C22×C4—61no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4C2×D3×D511yescharacteristic
388M16—101no—
389M16—101no—
390M16—101no—
391M16—101no—
392M16—304no—
393M16—301no—
394M16—301no—
395M16—301no—
396M16—301no—
397C2×C8—52no—
398C2×C8—101no—
399C2×C8—152no—
400C2×C8—304no—
401C2×C8—301no—
402C4⋊C4—21no—
403C4⋊C4—62no—
404C22⋊C4—62no—
405C22⋊C4—62no—
406C22⋊C4D3×Dic512yes—
407C42—21no—
408C3×C5#189111yescharacteristic, complemented, Hall
409C22×C3—41no—
410C22×C3D4×Dic511yescharacteristic
411C22×C3D4×Dic511yescharacteristic
412C22×C3C2×C22⋊Dic511yescharacteristic
413C2×D3—22no—
414C2×D3—22no—
415C2×D3—22no—
416C2×D3—22no—
417C2×D3—41no—
418C2×D3—41no—
419C2×D3—41no—
420C2×D3—41no—
421C2×D3—42no—
422C3×C4—42no—
423C3×C4#408111yescharacteristic
424C3×C4#408311yescharacteristic
425C3×C4#408511yescharacteristic
426C3×C4#408511yescharacteristic
427Dic3—22no—
428Dic3—41no—
429C2×C5—21no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—122no—
433C2×C5—122no—
434C2×C5#466511yescharacteristic
435C23—32no—
436C23—61no—
437C23—61no—
438C23—61no—
439C23—122no—
440C23C2×D3×Dic511yescharacteristic
441Q8—61no—
442Q8—61no—
443D4—62no—
444D4—62no—
445D4—61no—
446D4—61no—
447D4—124no—
448C2×C4—22no—
449C2×C4—32no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—121no—
459C2×C4#676811yescharacteristic
460C2×C4#677211yescharacteristic
461C2×C4D5×D1211yescharacteristic
462C2×C4#677711yescharacteristic
463C2×C4D3×C22⋊D511yescharacteristic
464C2×C4D3×C22⋊D511yescharacteristic
465C8—102no—
466C8—201no—
467C8—302no—
468C8—601no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3#6550911yescharacteristic
473D3—42no—
474D3—42no—
475C5#6903611yescharacteristic, complemented, Sylow
476C22—41no—
477C22—62no—
478C22—62no—
479C22—62no—
480C22—62no—
481C22—122no—
482C22—121no—
483C22—121no—
484C22—121no—
485C22—121no—
486C22Dic5×D1211yescharacteristic
487C22#9143511yescharacteristic
488C22D3×C22⋊Dic511yescharacteristic
489C4—42no—
490C4—62no—
491C4—121no—
492C4#9141611yescharacteristic
493C4#9142311yescharacteristic
494C4#9145311yescharacteristic
495C4#9147511yescharacteristic
496C3#1060250711yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—122no—
501C2—122no—
502C2#1174890111yescharacteristic
subgroupG/H
centerC4#91475
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC5×#5524C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1891
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11754125C2semidirect
3. #11748355C2semidirect
4. #11748346C2semidirect
5. #11748346C2semidirect
6. #11746354C2semidirect
7. C3×#64753C2semidirect
35. #64753D3semidirect
62. C2×C3⋊#168D4semidirect
71. C2×C3×#168D4semidirect
191. C2×#168D12semidirect
408. C3×C5#1891semidirect
475. C5#69036semidirect
496. C3#10602507semidirect

Maximal subgroups

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

subgroupindex
C5×#55242
#117541252
#117483552
#117483462
#117463542
C3×#647532
#106025073
#690365