Finite Group Databasebeta

← C5×#72100 #14301239

Subgroups — C5×#72100 #14301239

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#137C211yesmaximal, characteristic
2C5×#5827C211yesmaximal, characteristic
3C2×C5×#837C211yesmaximal, characteristic
4C5×#5229C211yesmaximal, characteristic, complemented
5C5×#5225C211yesmaximal, characteristic, complemented
6C5×#4555C211yesmaximal, characteristic, complemented
7C5×#4554C211yesmaximal, characteristic, complemented
8C5×#1882—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C3×C5×Q8C2211yescharacteristic
11C3×C5×#137—22no—
12C3×C5×#137C414yescomplemented
13C2×C3×C5×Q16—21no—
14C2×C3×C5×SD16—21no—
15C2×C3×C5×M16C2211yescharacteristic
16C5×Q8×Dic3—21no—
17C5×D4×Dic3—21no—
18C5×D4×Dic3—22no—
19C5×#926—21no—
20C5×#926C2211yescharacteristic
21C2×C5×C4⋊Dic3—21no—
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C5×#208C2211yescharacteristic
25C5×#837—22no—
26C5×#835—21no—
27C5×#835—21no—
28C5×C3⋊#95—22no—
29#72100C511yesmaximal, characteristic, direct product factor, Hall
30C2×C5×#137D311yescharacteristic
31C5×#520—31no—
32C2×C5×#104—31no—
33C5×#419—31no—
34C5×#391—31no—
35C5×#343—31no—
36C5×#339—31no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41C2×C412yes—
40C3×C5×#41D412yes—
41C2×C3×C5×Q8—21no—
42C2×C3×C5×Q8—21no—
43C2×C3×C5×Q8—21no—
44C2×C3×C5×Q8—21no—
45C2×C3×C5×Q8—21no—
46C2×C3×C5×Q8C2×C412yescomplemented
47C2×C3×C5×Q8D411yescharacteristic
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4D411yescharacteristic
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C5×Dic3—21no—
54C22×C5×Dic3—22no—
55C22×C5×Dic3D412yes—
56C3×C5×Q16—24no—
57C3×C5×SD16—24no—
58C3×C5×M16—21no—
59C3×C5×M16C2×C412yescomplemented
60C2×C3×C5×C8—21no—
61C5×#217—22no—
62C5×#217—21no—
63C5×C4⋊Dic3—22no—
64C5×C4⋊Dic3—21no—
65C5×C4⋊Dic3—21no—
66C5×C4⋊Dic3D411yescharacteristic
67C5×C4⋊Dic3D411yescharacteristic
68C4×C5×Dic3—22no—
69C4×C5×Dic3—21no—
70C4×C5×Dic3—21no—
71C4×C5×Dic3—21no—
72C5×#208—21no—
73C5×#208—21no—
74C2×C5×C3⋊C8—21no—
75C2×C3×#137C2×C511yescharacteristic
76#5827C2×C511yescharacteristic
77C2×#837C2×C511yescharacteristic
78#5229C2×C511yescharacteristic, complemented
79#5225C2×C511yescharacteristic, complemented
80#4555C2×C511yescharacteristic, complemented
81#4554C2×C511yescharacteristic, complemented
82C2×C5×#41C2×D311yescharacteristic
83C22×C5×Q8C2×D311yescharacteristic
84C5×#137—22no—
85C5×#137Dic314yescomplemented
86C2×C5×Q16—21no—
87C2×C5×SD16—21no—
88C2×C5×M16—31no—
89C2×C5×M16C2×D311yescharacteristic
90C4×C5×Q8—61no—
91C4×C5×D4—62no—
92C4×C5×D4—61no—
93C5×#117—31no—
94C5×#117—61no—
95C2×C5×C4⋊C4—31no—
96C2×C5×C4⋊C4—61no—
97C2×C42×C5—31no—
98C5×#104—62no—
99C5×#103—61no—
100C5×#103—61no—
101C5×#95—62no—
102#1882—31noSylow
103C23×C3×C5—21no—
104C23×C3×C5C2×D411yescharacteristic
105C3×C5×Q8—21no—
106C3×C5×Q8—22no—
107C3×C5×Q8—22no—
108C3×C5×Q8—41no—
109C3×C5×Q8—41no—
110C3×C5×Q8C22⋊C412yes—
111C3×C5×D4—22no—
112C3×C5×D4—22no—
113C3×C5×D4—21no—
114C3×C5×D4C22⋊C412yes—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—41no—
120C2×C3×C4×C5—41no—
121C2×C3×C4×C5C22×C411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5#4111yescharacteristic
126C2×C3×C4×C5#4111yescharacteristic
127C2×C5×Dic3—22no—
128C2×C5×Dic3—21no—
129C2×C5×Dic3—22no—
130C2×C5×Dic3—21no—
131C2×C5×Dic3—41no—
132C2×C5×Dic3—41no—
133C2×C5×Dic3—42no—
134C2×C5×Dic3—82no—
135C3×C5×C8—22no—
136C5×C3⋊C8—41no—
137C2×C3×#41C22×C511yescharacteristic
138C22×C3×Q8C22×C511yescharacteristic
139C3×#137—22no—
140C3×#137C4×C514yescomplemented
141C2×C3×Q16—21no—
142C2×C3×SD16—21no—
143C2×C3×M16C22×C511yescharacteristic
144Q8×Dic3—21no—
145D4×Dic3—21no—
146D4×Dic3—22no—
147#926—21no—
148#926C22×C511yescharacteristic
149C2×C4⋊Dic3—21no—
150C2×C4⋊Dic3C22×C511yescharacteristic
151C2×C4×Dic3C22×C511yescharacteristic
152C2×#208C22×C511yescharacteristic
153#837—22no—
154#835—21no—
155#835—21no—
156C3⋊#95—22no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41C2×Dic312yes—
160C5×#41#6712yes—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8C2×Dic312yescomplemented
167C2×C5×Q8#6711yescharacteristic
168C2×C5×D4—21no—
169C2×C5×D4#6711yescharacteristic
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—32no—
173C22×C4×C5—61no—
174C22×C4×C5—62no—
175C22×C4×C5C22×D311yescharacteristic
176C5×Q16—24no—
177C5×SD16—24no—
178C5×M16—21no—
179C5×M16—61no—
180C5×M16—61no—
181C5×M16C2×Dic312yescomplemented
182C2×C5×C8—21no—
183C2×C5×C8—61no—
184C5×C4⋊C4—31no—
185C5×C4⋊C4—31no—
186C5×C4⋊C4—62no—
187C5×C4⋊C4—61no—
188C5×C4⋊C4—61no—
189C5×C22⋊C4—62no—
190C5×C22⋊C4—61no—
191C42×C5—62no—
192C42×C5—61no—
193C42×C5—61no—
194C42×C5—61no—
195C2×#137C5×D311yescharacteristic
196#520—31no—
197C2×#104—31no—
198#419—31no—
199#391—31no—
200#343—31no—
201#339—31no—
202C22×C3×C5—21no—
203C22×C3×C5—21no—
204C22×C3×C5—22no—
205C22×C3×C5—41no—
206C22×C3×C5—41no—
207C22×C3×C5C4×D411yescharacteristic
208C22×C3×C5#12011yescharacteristic
209C22×C3×C5#12111yescharacteristic
210C3×C4×C5—22no—
211C3×C4×C5—42no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216C5×Dic3—42no—
217C5×Dic3—42no—
218C5×Dic3—41no—
219C5×Dic3—41no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41C2×C4×C512yes—
223C3×#41C5×D412yes—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8C2×C4×C512yescomplemented
230C2×C3×Q8C5×D411yescharacteristic
231C2×C3×D4—21no—
232C2×C3×D4C5×D411yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C23×C511yescharacteristic
236C22×Dic3—21no—
237C22×Dic3—22no—
238C22×Dic3C5×D412yes—
239C3×Q16—24no—
240C3×SD16—24no—
241C3×M16—21no—
242C3×M16C2×C4×C512yescomplemented
243C2×C3×C8—21no—
244#217—22no—
245#217—21no—
246C4⋊Dic3—22no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249C4⋊Dic3C5×D411yescharacteristic
250C4⋊Dic3C5×D411yescharacteristic
251C4×Dic3—22no—
252C4×Dic3—21no—
253C4×Dic3—21no—
254C4×Dic3—21no—
255#208—21no—
256#208—21no—
257C2×C3⋊C8—21no—
258C23×C5—21no—
259C23×C5D3×D411yescharacteristic
260C5×Q8—21no—
261C5×Q8—22no—
262C5×Q8—22no—
263C5×Q8—41no—
264C5×Q8—41no—
265C5×Q8#21712yes—
266C5×D4—22no—
267C5×D4—22no—
268C5×D4—21no—
269C5×D4#21712yes—
270C2×C4×C5—21no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—62no—
277C2×C4×C5—61no—
278C2×C4×C5—61no—
279C2×C4×C5—62no—
280C2×C4×C5—121no—
281C2×C4×C5—121no—
282C2×C4×C5—122no—
283C2×C4×C5—242no—
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5#23711yescharacteristic
286C2×C4×C5#23711yescharacteristic
287C2×C4×C5C22×Dic311yescharacteristic
288C2×C4×C5C2×#6711yescharacteristic
289C2×C4×C5C2×#6711yescharacteristic
290C5×C8—22no—
291C5×C8—121no—
292C2×#41C2×C5×D311yescharacteristic
293C22×Q8C2×C5×D311yescharacteristic
294#137—22no—
295#137C5×Dic314yescomplemented
296C2×Q16—21no—
297C2×SD16—21no—
298C2×M16—31no—
299C2×M16C2×C5×D311yescharacteristic
300C4×Q8—61no—
301C4×D4—62no—
302C4×D4—61no—
303#117—31no—
304#117—61no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—61no—
307C2×C42—31no—
308#104—62no—
309#103—61no—
310#103—61no—
311#95—62no—
312C2×C3×C5—21no—
313C2×C3×C5—21no—
314C2×C3×C5—42no—
315C2×C3×C5#38611yescharacteristic
316C2×C3×C5#45511yescharacteristic
317C2×C3×C5#45611yescharacteristic
318C23×C3—21no—
319C23×C3C2×C5×D411yescharacteristic
320C3×Q8—21no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—41no—
324C3×Q8—41no—
325C3×Q8C5×C22⋊C412yes—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—21no—
329C3×D4C5×C22⋊C412yes—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4C22×C4×C511yescharacteristic
337C2×C3×C4C2×C5×D411yescharacteristic
338C2×C3×C4C2×C5×D411yescharacteristic
339C2×C3×C4C2×C5×D411yescharacteristic
340C2×C3×C4C5×#4111yescharacteristic
341C2×C3×C4C5×#4111yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—21no—
344C2×Dic3—22no—
345C2×Dic3—21no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—42no—
349C2×Dic3—82no—
350C3×C8—22no—
351C3⋊C8—41no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—22no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5D4×Dic311yescharacteristic
358C22×C5#93711yescharacteristic
359C22×C5#93911yescharacteristic
360C4×C5—22no—
361C4×C5—42no—
362C4×C5—122no—
363C4×C5—122no—
364C4×C5—121no—
365C4×C5—121no—
366C4×C5D4×Dic311yescharacteristic
367C4×C5#93511yescharacteristic
368C4×C5#93911yescharacteristic
369C4×C5C2×#21711yescharacteristic
370#41—21no—
371#41—21no—
372#41C2×C5×Dic312yes—
373#41C5×#6712yes—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8C2×C5×Dic312yescomplemented
380C2×Q8C5×#6711yescharacteristic
381C2×D4—21no—
382C2×D4C5×#6711yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—32no—
386C22×C4—61no—
387C22×C4—62no—
388C22×C4C22×C5×D311yescharacteristic
389Q16—24no—
390SD16—24no—
391M16—21no—
392M16—61no—
393M16—61no—
394M16C2×C5×Dic312yescomplemented
395C2×C8—21no—
396C2×C8—61no—
397C4⋊C4—31no—
398C4⋊C4—31no—
399C4⋊C4—62no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C22⋊C4—62no—
403C22⋊C4—61no—
404C42—62no—
405C42—61no—
406C42—61no—
407C42—61no—
408C3×C5#188211yescharacteristic, complemented, Hall
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3C4×C5×D411yescharacteristic
415C22×C3C5×#12011yescharacteristic
416C22×C3C5×#12111yescharacteristic
417C3×C4—22no—
418C3×C4—42no—
419C3×C4C2×C5×C22⋊C411yescharacteristic
420C3×C4C4×C5×D411yescharacteristic
421C3×C4C5×#12111yescharacteristic
422C3×C4C5×#12311yescharacteristic
423Dic3—42no—
424Dic3—42no—
425Dic3—41no—
426Dic3—41no—
427C2×C5—21no—
428C2×C5—21no—
429C2×C5—42no—
430C2×C5#520211yescharacteristic
431C2×C5#520511yescharacteristic
432C2×C5#522011yescharacteristic
433C23—21no—
434C23C5×D3×D411yescharacteristic
435Q8—21no—
436Q8—22no—
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8C5×#21712yes—
441D4—22no—
442D4—22no—
443D4—21no—
444D4C5×#21712yes—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—62no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—62no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—122no—
458C2×C4—242no—
459C2×C4C5×D3×D411yescharacteristic
460C2×C4C5×#23711yescharacteristic
461C2×C4C5×#23711yescharacteristic
462C2×C4C22×C5×Dic311yescharacteristic
463C2×C4C2×C5×#6711yescharacteristic
464C2×C4C2×C5×#6711yescharacteristic
465C8—22no—
466C8—121no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—42no—
470C2×C3C5×#38611yescharacteristic
471C2×C3C5×#45511yescharacteristic
472C2×C3C5×#45611yescharacteristic
473C5#7210011yescharacteristic, direct product factor, Sylow
474C22—21no—
475C22—21no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22C5×D4×Dic311yescharacteristic
480C22C5×#93711yescharacteristic
481C22C5×#93911yescharacteristic
482C4—22no—
483C4—42no—
484C4—122no—
485C4—122no—
486C4—121no—
487C4—121no—
488C4C5×D4×Dic311yescharacteristic
489C4C5×#93511yescharacteristic
490C4C5×#93911yescharacteristic
491C4C2×C5×#21711yescharacteristic
492C3C5×#188211yescharacteristic, complemented, Sylow
493C2—21no—
494C2—21no—
495C2—42no—
496C2C5×#520211yescharacteristic
497C2C5×#520511yescharacteristic
498C2C5×#522011yescharacteristic
subgroupG/H
centerC22×C5#937
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#137C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#137D3
hypocenterC3C5×#1882
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#137

Complements

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

NH ≅ G/Ntype
4. C5×#5229C2semidirect
5. C5×#5225C2semidirect
6. C5×#4555C2semidirect
7. C5×#4554C2semidirect
12. C3×C5×#137C4semidirect
29. #72100C5direct (N × H)
46. C2×C3×C5×Q8C2×C4semidirect
59. C3×C5×M16C2×C4semidirect
78. #5229C2×C5semidirect
79. #5225C2×C5semidirect
80. #4555C2×C5semidirect
81. #4554C2×C5semidirect
85. C5×#137Dic3semidirect
140. C3×#137C4×C5semidirect
166. C2×C5×Q8C2×Dic3semidirect
181. C5×M16C2×Dic3semidirect
229. C2×C3×Q8C2×C4×C5semidirect
242. C3×M16C2×C4×C5semidirect
295. #137C5×Dic3semidirect
379. C2×Q8C2×C5×Dic3semidirect
394. M16C2×C5×Dic3semidirect
408. C3×C5#1882semidirect
473. C5#72100direct (N × H)
492. C3C5×#1882semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1372
C5×#58272
C2×C5×#8372
C5×#52292
C5×#52252
C5×#45552
C5×#45542
C5×#18823
#721005