Finite Group Databasebeta

← C5×#69004 #14301230

Subgroups — C5×#69004 #14301230

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×C5×#909C211yesmaximal, characteristic
2C5×#5504C211yesmaximal, characteristic
3C2×C5×#825C211yesmaximal, characteristic
4C5×#5120C211yesmaximal, characteristic, complemented
5C5×#4973C211yesmaximal, characteristic, complemented
6C3×C5×#343C211yesmaximal, characteristic, complemented
7C5×#4555C211yesmaximal, characteristic, complemented
8C5×#1882—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C4×C5×#67—22no—
15C5×#926C2211yescharacteristic
16C2×C4×C5×Dic3C2211yescharacteristic
17C5×#909—22no—
18C5×#909C414yescomplemented
19C2×C5×Dic12—21no—
20C2×C5×#204—21no—
21C5×#893—21no—
22C5×#892—21no—
23C5×D3×C4⋊C4—21no—
24C5×#887—21no—
25C5×C3⋊#95—22no—
26C5×#825—22no—
27C5×#816—21no—
28C5×#816—21no—
29#69004C511yesmaximal, characteristic, direct product factor, Hall
30C2×C5×#137—31no—
31C5×#520—31no—
32C2×C5×#104—31no—
33C5×#419—31no—
34C5×#391—31no—
35C5×#343D311yescharacteristic, complemented
36C5×#339—31no—
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C2×C5×#67—21no—
40C22×C5×Dic3—21no—
41C22×C5×Dic3—21no—
42C5×#235—21no—
43C5×#235—21no—
44C5×#235C2×C412yes—
45C5×#235D412yes—
46C2×C5×D12D411yescharacteristic
47C2×C4×C5×D3—21no—
48C2×C4×C5×D3—22no—
49C2×C5×Dic6—21no—
50C2×C5×Dic6—21no—
51C2×C5×Dic6—21no—
52C2×C5×Dic6—21no—
53C2×C5×Dic6—21no—
54C2×C5×Dic6C2×C412yescomplemented
55C2×C5×Dic6D411yescharacteristic
56C3×C5×M16—21no—
57C3×C5×M16—21no—
58C3×C5×M16—21no—
59C3×C5×M16C2×C412yescomplemented
60C2×C3×C5×C8—21no—
61C2×C3×C5×C8—21no—
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4—21no—
64C5×#217—21no—
65C5×(C2×D3)⋊C4—22no—
66C5×C4⋊Dic3D411yescharacteristic
67C5×C4⋊Dic3D411yescharacteristic
68C5×Dic3⋊C4—22no—
69C4×C5×Dic3—22no—
70C4×C5×Dic3—21no—
71C4×C5×Dic3—21no—
72C4×C5×Dic3—21no—
73C5×Dic12—24no—
74C5×#204—24no—
75C2×#909C2×C511yescharacteristic
76#5504C2×C511yescharacteristic
77C2×#825C2×C511yescharacteristic
78#5120C2×C511yescharacteristic, complemented
79#4973C2×C511yescharacteristic, complemented
80C3×#343C2×C511yescharacteristic, complemented
81#4555C2×C511yescharacteristic, complemented
82C2×C5×#41—31no—
83C22×C5×Q8—31no—
84C5×#137—34no—
85C5×#137—62no—
86C2×C5×Q16—61no—
87C2×C5×SD16—61no—
88C2×C5×M16C2×D311yescharacteristic
89C2×C5×M16C2×D311yescharacteristic
90C4×C5×Q8—61no—
91C4×C5×D4—61no—
92C4×C5×D4—62no—
93C5×#117—31no—
94C5×#117—61no—
95C2×C5×C4⋊C4—61no—
96C2×C5×C4⋊C4C2×D311yescharacteristic
97C2×C42×C5—31no—
98C5×#104—62no—
99C5×#103—61no—
100C5×#103—61no—
101C5×#95—62no—
102#1882—31noSylow
103C23×C3×C5C2×D411yescharacteristic
104C22×C5×D3—21no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—42no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C5×#67—22no—
114C5×#67—22no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—22no—
117C2×C5×Dic3—22no—
118C2×C5×Dic3—21no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3—41no—
124C5×D12—21no—
125C5×D12C22⋊C412yes—
126C4×C5×D3—22no—
127C4×C5×D3—22no—
128C4×C5×D3—82no—
129C5×Dic6—21no—
130C5×Dic6—22no—
131C5×Dic6—22no—
132C5×Dic6—41no—
133C5×Dic6—41no—
134C5×Dic6C22⋊C412yes—
135C3×C5×C8—22no—
136C3×C5×C8—41no—
137C2×#235C22×C511yescharacteristic
138C22×Dic6C22×C511yescharacteristic
139C2×C3×M16C22×C511yescharacteristic
140C2×C3×M16C22×C511yescharacteristic
141C2×C3×C4⋊C4C22×C511yescharacteristic
142C4×#67—22no—
143#926C22×C511yescharacteristic
144C2×C4×Dic3C22×C511yescharacteristic
145#909—22no—
146#909C4×C514yescomplemented
147C2×Dic12—21no—
148C2×#204—21no—
149#893—21no—
150#892—21no—
151D3×C4⋊C4—21no—
152#887—21no—
153C3⋊#95—22no—
154#825—22no—
155#816—21no—
156#816—21no—
157C5×#41—32no—
158C5×#41—32no—
159C5×#41—61no—
160C5×#41—61no—
161C2×C5×Q8—32no—
162C2×C5×Q8—31no—
163C2×C5×Q8—61no—
164C2×C5×Q8—61no—
165C2×C5×Q8—61no—
166C2×C5×Q8—61no—
167C2×C5×Q8—61no—
168C2×C5×D4—31no—
169C2×C5×D4—61no—
170C22×C4×C5—62no—
171C22×C4×C5—61no—
172C22×C4×C5—61no—
173C22×C4×C5—61no—
174C22×C4×C5D1212yes—
175C22×C4×C5C22×D311yescharacteristic
176C5×Q16—64no—
177C5×SD16—64no—
178C5×M16—21no—
179C5×M16—21no—
180C5×M16—21no—
181C5×M16C4×D312yescomplemented
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—31no—
187C5×C4⋊C4—31no—
188C5×C4⋊C4—62no—
189C5×C22⋊C4—62no—
190C5×C22⋊C4—61no—
191C42×C5—62no—
192C42×C5—61no—
193C42×C5—61no—
194C42×C5—61no—
195C2×#137—31no—
196#520—31no—
197C2×#104—31no—
198#419—31no—
199#391—31no—
200#343C5×D311yescharacteristic, complemented
201#339—31no—
202C22×C3×C5—21no—
203C22×C3×C5—21no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C2×C5×D3—22no—
208C2×C5×D3—41no—
209C2×C5×D3—41no—
210C3×C4×C5—42no—
211C3×C4×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215C5×Dic3—22no—
216C5×Dic3—42no—
217C5×Dic3—42no—
218C5×Dic3—41no—
219C5×Dic3—41no—
220C22×C3×C4C5×D412yes—
221C22×C3×C4C23×C511yescharacteristic
222C2×#67—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225#235—21no—
226#235—21no—
227#235C2×C4×C512yes—
228#235C5×D412yes—
229C2×D12C5×D411yescharacteristic
230C2×C4×D3—21no—
231C2×C4×D3—22no—
232C2×Dic6—21no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6—21no—
237C2×Dic6C2×C4×C512yescomplemented
238C2×Dic6C5×D411yescharacteristic
239C3×M16—21no—
240C3×M16—21no—
241C3×M16—21no—
242C3×M16C2×C4×C512yescomplemented
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247#217—21no—
248(C2×D3)⋊C4—22no—
249C4⋊Dic3C5×D411yescharacteristic
250C4⋊Dic3C5×D411yescharacteristic
251Dic3⋊C4—22no—
252C4×Dic3—22no—
253C4×Dic3—21no—
254C4×Dic3—21no—
255C4×Dic3—21no—
256Dic12—24no—
257#204—24no—
258C23×C5—61no—
259C23×C5C2×D1211yescharacteristic
260C5×Q8—32no—
261C5×Q8—61no—
262C5×Q8—62no—
263C5×Q8—62no—
264C5×Q8—121no—
265C5×Q8—121no—
266C5×D4—32no—
267C5×D4—62no—
268C5×D4—62no—
269C5×D4—61no—
270C2×C4×C5—22no—
271C2×C4×C5—42no—
272C2×C4×C5—61no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5—62no—
276C2×C4×C5—62no—
277C2×C4×C5—61no—
278C2×C4×C5—61no—
279C2×C4×C5—121no—
280C2×C4×C5—121no—
281C2×C4×C5—121no—
282C2×C4×C5—121no—
283C2×C4×C5—242no—
284C2×C4×C5C2×C4×D311yescharacteristic
285C2×C4×C5#23511yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5#23911yescharacteristic
290C5×C8—22no—
291C5×C8—41no—
292C2×#41—31no—
293C22×Q8—31no—
294#137—34no—
295#137—62no—
296C2×Q16—61no—
297C2×SD16—61no—
298C2×M16C2×C5×D311yescharacteristic
299C2×M16C2×C5×D311yescharacteristic
300C4×Q8—61no—
301C4×D4—61no—
302C4×D4—62no—
303#117—31no—
304#117—61no—
305C2×C4⋊C4—61no—
306C2×C4⋊C4C2×C5×D311yescharacteristic
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#38611yescharacteristic
315C2×C3×C5#45511yescharacteristic
316C2×C3×C5#45611yescharacteristic
317C5×D3—42no—
318C23×C3C2×C5×D411yescharacteristic
319C22×D3—21no—
320C2×C3×C4—22no—
321C2×C3×C4—42no—
322C2×C3×C4C22×C4×C511yescharacteristic
323C2×C3×C4C2×C5×D411yescharacteristic
324C2×C3×C4C2×C5×D411yescharacteristic
325C2×C3×C4C2×C5×D411yescharacteristic
326C2×C3×C4C5×#4111yescharacteristic
327C2×C3×C4C5×#4111yescharacteristic
328#67—22no—
329#67—22no—
330C2×Dic3—21no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339D12—21no—
340D12C5×C22⋊C412yes—
341C4×D3—22no—
342C4×D3—22no—
343C4×D3—82no—
344Dic6—21no—
345Dic6—22no—
346Dic6—22no—
347Dic6—41no—
348Dic6—41no—
349Dic6C5×C22⋊C412yes—
350C3×C8—22no—
351C3×C8—41no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—62no—
355C22×C5—121no—
356C22×C5—121no—
357C22×C5C4×D1211yescharacteristic
358C22×C5#88211yescharacteristic
359C22×C5#89511yescharacteristic
360C4×C5—42no—
361C4×C5—62no—
362C4×C5—122no—
363C4×C5—122no—
364C4×C5—121no—
365C4×C5—121no—
366C4×C5D3×C22⋊C411yescharacteristic
367C4×C5#88411yescharacteristic
368C4×C5#89311yescharacteristic
369C4×C5#89411yescharacteristic
370#41—32no—
371#41—32no—
372#41—61no—
373#41—61no—
374C2×Q8—32no—
375C2×Q8—31no—
376C2×Q8—61no—
377C2×Q8—61no—
378C2×Q8—61no—
379C2×Q8—61no—
380C2×Q8—61no—
381C2×D4—31no—
382C2×D4—61no—
383C22×C4—62no—
384C22×C4—61no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4C5×D1212yes—
388C22×C4C22×C5×D311yescharacteristic
389Q16—64no—
390SD16—64no—
391M16—21no—
392M16—21no—
393M16—21no—
394M16C4×C5×D312yescomplemented
395C2×C8—21no—
396C2×C8—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—31no—
400C4⋊C4—31no—
401C4⋊C4—62no—
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×C3C4×C5×D411yescharacteristic
412C22×C3C5×#12011yescharacteristic
413C22×C3C5×#12111yescharacteristic
414C2×D3—22no—
415C2×D3—41no—
416C2×D3—41no—
417C3×C4—42no—
418C3×C4C2×C5×C22⋊C411yescharacteristic
419C3×C4C4×C5×D411yescharacteristic
420C3×C4C5×#12111yescharacteristic
421C3×C4C5×#12311yescharacteristic
422Dic3—22no—
423Dic3—42no—
424Dic3—42no—
425Dic3—41no—
426Dic3—41no—
427C2×C5—21no—
428C2×C5—21no—
429C2×C5—122no—
430C2×C5#466511yescharacteristic
431C2×C5#474611yescharacteristic
432C2×C5#475211yescharacteristic
433C23—61no—
434C23C2×C5×D1211yescharacteristic
435Q8—32no—
436Q8—61no—
437Q8—62no—
438Q8—62no—
439Q8—121no—
440Q8—121no—
441D4—32no—
442D4—62no—
443D4—62no—
444D4—61no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—61no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—242no—
459C2×C4C2×C4×C5×D311yescharacteristic
460C2×C4C5×#23511yescharacteristic
461C2×C4C5×D3×D411yescharacteristic
462C2×C4C5×D3×D411yescharacteristic
463C2×C4C5×D3×D411yescharacteristic
464C2×C4C5×#23911yescharacteristic
465C8—22no—
466C8—41no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3C5×#38611yescharacteristic
470C2×C3C5×#45511yescharacteristic
471C2×C3C5×#45611yescharacteristic
472D3—42no—
473C5#6900411yescharacteristic, direct product factor, Sylow
474C22—21no—
475C22—21no—
476C22—62no—
477C22—121no—
478C22—121no—
479C22C4×C5×D1211yescharacteristic
480C22C5×#88211yescharacteristic
481C22C5×#89511yescharacteristic
482C4—42no—
483C4—62no—
484C4—122no—
485C4—122no—
486C4—121no—
487C4—121no—
488C4C5×D3×C22⋊C411yescharacteristic
489C4C5×#88411yescharacteristic
490C4C5×#89311yescharacteristic
491C4C5×#89411yescharacteristic
492C3C5×#188211yescharacteristic, complemented, Sylow
493C2—21no—
494C2—21no—
495C2—122no—
496C2C5×#466511yescharacteristic
497C2C5×#474611yescharacteristic
498C2C5×#475211yescharacteristic
subgroupG/H
centerC22×C5#882
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#343C2
socleC22×C3×C5#120
prime radicalC2×C5×#235C22
cosocleC22×C3×C4C23×C5
hypercenterC5×#343D3
hypocenterC3C5×#1882
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#343

Complements

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

NH ≅ G/Ntype
4. C5×#5120C2semidirect
5. C5×#4973C2semidirect
6. C3×C5×#343C2semidirect
7. C5×#4555C2semidirect
18. C5×#909C4semidirect
29. #69004C5direct (N × H)
35. C5×#343D3semidirect
54. C2×C5×Dic6C2×C4semidirect
59. C3×C5×M16C2×C4semidirect
78. #5120C2×C5semidirect
79. #4973C2×C5semidirect
80. C3×#343C2×C5semidirect
81. #4555C2×C5semidirect
146. #909C4×C5semidirect
181. C5×M16C4×D3semidirect
200. #343C5×D3semidirect
237. C2×Dic6C2×C4×C5semidirect
242. C3×M16C2×C4×C5semidirect
394. M16C4×C5×D3semidirect
408. C3×C5#1882semidirect
473. C5#69004direct (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×C5×#9092
C5×#55042
C2×C5×#8252
C5×#51202
C5×#49732
C3×C5×#3432
C5×#45552
C5×#18823
#690045