Finite Group Databasebeta

← C5×#70417 #14301366

Subgroups — C5×#70417 #14301366

Order 1920.

664 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×#5832C211yesmaximal, characteristic
2C5×#5745C211yesmaximal, characteristic, complemented
3C3×C5×#421C211yesmaximal, characteristic, complemented
4C5×#5236C211yesmaximal, characteristic, complemented
5C5×#5006C211yesmaximal, characteristic, complemented
6C5×#4555C211yesmaximal, characteristic, complemented
7C5×#4532C211yesmaximal, characteristic, complemented
8C5×#1884—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C5×#947C411yescharacteristic, complemented
14C5×#944C411yescharacteristic, complemented
15C5×#940C411yescharacteristic, complemented
16C5×#939—22no—
17C5×#936C411yescharacteristic, complemented
18C4×C5×#67—22no—
19C5×#926C2211yescharacteristic
20C2×C4×C5×Dic3C2211yescharacteristic
21C2×C5×#208C2211yescharacteristic
22C5×#907—22no—
23C5×D3×M16—22no—
24C5×#901—22no—
25C3×C5×#104—22no—
26C5×#837—22no—
27C5×#806—22no—
28#70417C511yesmaximal, characteristic, direct product factor, Hall
29C5×#568—31no—
30C5×#532—31no—
31C5×#421—31no—
32C5×#421D311yescharacteristic, complemented
33C5×#410—31no—
34C5×#339—31no—
35C5×#339—31no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C2×C5×#67—22no—
46C2×C5×#67D412yes—
47C22×C5×Dic3—21no—
48C5×#235—21no—
49C5×#235—21no—
50C5×#235—21no—
51C5×#235—21no—
52C2×C5×D12C2×C411yescharacteristic
53C2×C4×C5×D3D412yes—
54C2×C5×Dic6C2×C411yescharacteristic
55C3×C5×M16—21no—
56C3×C5×M16D412yescomplemented
57C2×C3×C5×C8—21no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C42×C5—21no—
61C5×#217—22no—
62C5×#217—21no—
63C5×(C2×D3)⋊C4—22no—
64C5×C4⋊Dic3—21no—
65C5×Dic3⋊C4—22no—
66C4×C5×Dic3—21no—
67C4×C5×Dic3—21no—
68C4×C5×Dic3C2×C411yescharacteristic
69C4×C5×Dic3C2×C411yescharacteristic
70C5×#208—21no—
71C5×#208D412yescomplemented
72C2×C5×C3⋊C8—21no—
73C5×ΓL(1,𝔽25)—24no—
74C5×D3×C8—24no—
75#5832C2×C511yescharacteristic
76#5745C2×C511yescharacteristic, complemented
77C3×#421C2×C511yescharacteristic, complemented
78#5236C2×C511yescharacteristic, complemented
79#5006C2×C511yescharacteristic, complemented
80#4555C2×C511yescharacteristic, complemented
81#4532C2×C511yescharacteristic, complemented
82C2×C5×#41—31no—
83C2×C5×#41C2×D311yescharacteristic
84C5×#131—62no—
85C5×#131—62no—
86C2×C5×M16—31no—
87C2×C5×M16—62no—
88C2×C5×M16C2×D311yescharacteristic
89C5×C4⋊Q8—31no—
90C5×#127—31no—
91C5×#124—31no—
92C5×#124—31no—
93C5×#121—62no—
94C4×C5×D4—62no—
95C5×#117—31no—
96C5×#117C2×D311yescharacteristic
97C2×C42×C5—31no—
98C5×#104—22no—
99C5×#104—62no—
100C5×#99—62no—
101#1884—31noSylow
102C23×C3×C5—21no—
103C23×C3×C5C2×D411yescharacteristic
104C22×C5×D3C22⋊C412yes—
105C3×C5×Q8—21no—
106C3×C5×Q8—21no—
107C3×C5×D4—21no—
108C3×C5×D4—21no—
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5C22×C411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×C3×C4×C5#4111yescharacteristic
121C5×#67—22no—
122C5×#67—22no—
123C5×#67—44no—
124C2×C5×Dic3—21no—
125C2×C5×Dic3—21no—
126C2×C5×Dic3—42no—
127C2×C5×Dic3—41no—
128C2×C5×Dic3C22⋊C412yes—
129C5×D12—21no—
130C5×D12—21no—
131C4×C5×D3—22no—
132C4×C5×D3—22no—
133C5×Dic6—21no—
134C5×Dic6—21no—
135C3×C5×C8—22no—
136C5×C3⋊C8—22no—
137C2×C3×#41C22×C511yescharacteristic
138C2×#235C22×C511yescharacteristic
139C2×C3×M16C22×C511yescharacteristic
140C3×#117C22×C511yescharacteristic
141#947C4×C511yescharacteristic, complemented
142#944C4×C511yescharacteristic, complemented
143#940C4×C511yescharacteristic, complemented
144#939—22no—
145#936C4×C511yescharacteristic, complemented
146C4×#67—22no—
147#926C22×C511yescharacteristic
148C2×C4×Dic3C22×C511yescharacteristic
149C2×#208C22×C511yescharacteristic
150#907—22no—
151D3×M16—22no—
152#901—22no—
153C3×#104—22no—
154#837—22no—
155#806—22no—
156C5×#41—21no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C5×#41—61no—
161C5×#41—61no—
162C5×#41—61no—
163C5×#41—61no—
164C2×C5×Q8—31no—
165C2×C5×Q8C4×D311yescharacteristic
166C2×C5×D4—21no—
167C2×C5×D4—32no—
168C2×C5×D4—31no—
169C2×C5×D4—62no—
170C2×C5×D4C4×D311yescharacteristic
171C22×C4×C5—21no—
172C22×C4×C5—32no—
173C22×C4×C5—61no—
174C22×C4×C5C22×D311yescharacteristic
175C5×M16—21no—
176C5×M16—32no—
177C5×M16—64no—
178C5×M16—61no—
179C5×M16#6712yescomplemented
180C2×C5×C8—21no—
181C2×C5×C8—64no—
182C2×C5×C8—61no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—62no—
185C5×C4⋊C4—61no—
186C5×C22⋊C4—21no—
187C5×C22⋊C4—62no—
188C5×C22⋊C4—62no—
189C5×C22⋊C4—61no—
190C42×C5—21no—
191C42×C5—31no—
192C42×C5—31no—
193C42×C5—61no—
194C42×C5—61no—
195#568—31no—
196#532—31no—
197#421—31no—
198#421C5×D311yescharacteristic, complemented
199#410—31no—
200#339—31no—
201#339—31no—
202C22×C3×C5—41no—
203C22×C3×C5—42no—
204C22×C3×C5—41no—
205C22×C3×C5C2×C22⋊C411yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5#12111yescharacteristic
208C2×C5×D3—22no—
209C2×C5×D3—42no—
210C3×C4×C5—41no—
211C3×C4×C5—81no—
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12011yescharacteristic
215C3×C4×C5#12311yescharacteristic
216C5×Dic3—22no—
217C5×Dic3—22no—
218C5×Dic3—41no—
219C5×Dic3—81no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—21no—
224C2×C3×Q8C2×C4×C511yescharacteristic
225C2×C3×D4—21no—
226C2×C3×D4C2×C4×C511yescharacteristic
227C22×C3×C4—21no—
228C22×C3×C4C23×C511yescharacteristic
229C2×#67—22no—
230C2×#67C5×D412yes—
231C22×Dic3—21no—
232#235—21no—
233#235—21no—
234#235—21no—
235#235—21no—
236C2×D12C2×C4×C511yescharacteristic
237C2×C4×D3C5×D412yes—
238C2×Dic6C2×C4×C511yescharacteristic
239C3×M16—21no—
240C3×M16C5×D412yescomplemented
241C2×C3×C8—21no—
242C3×C4⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C42—21no—
245#217—22no—
246#217—21no—
247(C2×D3)⋊C4—22no—
248C4⋊Dic3—21no—
249Dic3⋊C4—22no—
250C4×Dic3—21no—
251C4×Dic3—21no—
252C4×Dic3C2×C4×C511yescharacteristic
253C4×Dic3C2×C4×C511yescharacteristic
254#208—21no—
255#208C5×D412yescomplemented
256C2×C3⋊C8—21no—
257ΓL(1,𝔽25)—24no—
258D3×C8—24no—
259C23×C5—21no—
260C23×C5—32no—
261C23×C5D3×D411yescharacteristic
262C5×Q8—21no—
263C5×Q8—21no—
264C5×Q8—61no—
265C5×Q8—61no—
266C5×D4—21no—
267C5×D4—21no—
268C5×D4—41no—
269C5×D4—41no—
270C5×D4—62no—
271C5×D4—62no—
272C5×D4—61no—
273C5×D4—61no—
274C5×D4—124no—
275C2×C4×C5—21no—
276C2×C4×C5—32no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—61no—
281C2×C4×C5—62no—
282C2×C4×C5—62no—
283C2×C4×C5—61no—
284C2×C4×C5—122no—
285C2×C4×C5—121no—
286C2×C4×C5C2×C4×D311yescharacteristic
287C2×C4×C5#23511yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5#23711yescharacteristic
291C2×C4×C5C2×#6711yescharacteristic
292C5×C8—22no—
293C5×C8—62no—
294C2×#41—31no—
295C2×#41C2×C5×D311yescharacteristic
296#131—62no—
297#131—62no—
298C2×M16—31no—
299C2×M16—62no—
300C2×M16C2×C5×D311yescharacteristic
301C4⋊Q8—31no—
302#127—31no—
303#124—31no—
304#124—31no—
305#121—62no—
306C4×D4—62no—
307#117—31no—
308#117C2×C5×D311yescharacteristic
309C2×C42—31no—
310#104—22no—
311#104—62no—
312#99—62no—
313C2×C3×C5—21no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5—81no—
317C2×C3×C5#38611yescharacteristic
318C5×D3—42no—
319C23×C3—21no—
320C23×C3C2×C5×D411yescharacteristic
321C22×D3C5×C22⋊C412yes—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×D4—21no—
325C3×D4—21no—
326C3×D4—41no—
327C3×D4—41no—
328C2×C3×C4—21no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4C22×C4×C511yescharacteristic
333C2×C3×C4C2×C5×D411yescharacteristic
334C2×C3×C4C2×C5×D411yescharacteristic
335C2×C3×C4C2×C5×D411yescharacteristic
336C2×C3×C4C5×#4111yescharacteristic
337C2×C3×C4C5×#4111yescharacteristic
338#67—22no—
339#67—22no—
340#67—44no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—42no—
344C2×Dic3—41no—
345C2×Dic3C5×C22⋊C412yes—
346D12—21no—
347D12—21no—
348C4×D3—22no—
349C4×D3—22no—
350Dic6—21no—
351Dic6—21no—
352C3×C8—22no—
353C3⋊C8—22no—
354C22×C5—41no—
355C22×C5—42no—
356C22×C5—41no—
357C22×C5—62no—
358C22×C5—122no—
359C22×C5D3×C22⋊C411yescharacteristic
360C22×C5#88411yescharacteristic
361C22×C5#93811yescharacteristic
362C4×C5—41no—
363C4×C5—62no—
364C4×C5—62no—
365C4×C5—81no—
366C4×C5—121no—
367C4×C5—241no—
368C4×C5#67⋊C411yescharacteristic
369C4×C5#88311yescharacteristic
370C4×C5C4×#6711yescharacteristic
371C4×C5#93711yescharacteristic
372#41—21no—
373#41—21no—
374#41—21no—
375#41—21no—
376#41—61no—
377#41—61no—
378#41—61no—
379#41—61no—
380C2×Q8—31no—
381C2×Q8C4×C5×D311yescharacteristic
382C2×D4—21no—
383C2×D4—32no—
384C2×D4—31no—
385C2×D4—62no—
386C2×D4C4×C5×D311yescharacteristic
387C22×C4—21no—
388C22×C4—32no—
389C22×C4—61no—
390C22×C4C22×C5×D311yescharacteristic
391M16—21no—
392M16—32no—
393M16—64no—
394M16—61no—
395M16C5×#6712yescomplemented
396C2×C8—21no—
397C2×C8—64no—
398C2×C8—61no—
399C4⋊C4—21no—
400C4⋊C4—62no—
401C4⋊C4—61no—
402C22⋊C4—21no—
403C22⋊C4—62no—
404C22⋊C4—62no—
405C22⋊C4—61no—
406C42—21no—
407C42—31no—
408C42—31no—
409C42—61no—
410C42—61no—
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3—42no—
414C22×C3—41no—
415C22×C3C2×C5×C22⋊C411yescharacteristic
416C22×C3C5×#12111yescharacteristic
417C22×C3C5×#12111yescharacteristic
418C2×D3—22no—
419C2×D3—42no—
420C3×C4—41no—
421C3×C4—81no—
422C3×C4C4×C5×D411yescharacteristic
423C3×C4C4×C5×D411yescharacteristic
424C3×C4C5×#12011yescharacteristic
425C3×C4C5×#12311yescharacteristic
426Dic3—22no—
427Dic3—22no—
428Dic3—41no—
429Dic3—81no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5—81no—
434C2×C5—122no—
435C2×C5#495611yescharacteristic
436C23—21no—
437C23—32no—
438C23C5×D3×D411yescharacteristic
439Q8—21no—
440Q8—21no—
441Q8—61no—
442Q8—61no—
443D4—21no—
444D4—21no—
445D4—41no—
446D4—41no—
447D4—62no—
448D4—62no—
449D4—61no—
450D4—61no—
451D4—124no—
452C2×C4—21no—
453C2×C4—32no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—61no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—61no—
461C2×C4—122no—
462C2×C4—121no—
463C2×C4C2×C4×C5×D311yescharacteristic
464C2×C4C5×#23511yescharacteristic
465C2×C4C5×D3×D411yescharacteristic
466C2×C4C5×D3×D411yescharacteristic
467C2×C4C5×#23711yescharacteristic
468C2×C4C2×C5×#6711yescharacteristic
469C8—22no—
470C8—62no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—81no—
475C2×C3C5×#38611yescharacteristic
476D3—42no—
477C5#7041711yescharacteristic, direct product factor, Sylow
478C22—41no—
479C22—42no—
480C22—41no—
481C22—62no—
482C22—122no—
483C22C5×D3×C22⋊C411yescharacteristic
484C22C5×#88411yescharacteristic
485C22C5×#93811yescharacteristic
486C4—41no—
487C4—62no—
488C4—62no—
489C4—81no—
490C4—121no—
491C4—241no—
492C4C5×#67⋊C411yescharacteristic
493C4C5×#88311yescharacteristic
494C4C4×C5×#6711yescharacteristic
495C4C5×#93711yescharacteristic
496C3C5×#188411yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—81no—
501C2—122no—
502C2C5×#495611yescharacteristic
subgroupG/H
centerC4×C5#937
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#421C2
socleC2×C3×C5#386
prime radicalC5×#5832C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#421D3
hypocenterC3C5×#1884
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C5×#421

Complements

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

NH ≅ G/Ntype
2. C5×#5745C2semidirect
3. C3×C5×#421C2semidirect
4. C5×#5236C2semidirect
5. C5×#5006C2semidirect
6. C5×#4555C2semidirect
7. C5×#4532C2semidirect
13. C5×#947C4semidirect
14. C5×#944C4semidirect
15. C5×#940C4semidirect
17. C5×#936C4semidirect
28. #70417C5direct (N × H)
32. C5×#421D3semidirect
56. C3×C5×M16D4semidirect
71. C5×#208D4semidirect
76. #5745C2×C5semidirect
77. C3×#421C2×C5semidirect
78. #5236C2×C5semidirect
79. #5006C2×C5semidirect
80. #4555C2×C5semidirect
81. #4532C2×C5semidirect
141. #947C4×C5semidirect
142. #944C4×C5semidirect
143. #940C4×C5semidirect
145. #936C4×C5semidirect
179. C5×M16#67semidirect
198. #421C5×D3semidirect
240. C3×M16C5×D4semidirect
255. #208C5×D4semidirect
395. M16C5×#67semidirect
411. C3×C5#1884semidirect
477. C5#70417direct (N × H)
496. C3C5×#1884semidirect

Maximal subgroups

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

subgroupindex
C5×#58322
C5×#57452
C3×C5×#4212
C5×#52362
C5×#50062
C5×#45552
C5×#45322
C5×#18843
#704175