Finite Group Databasebeta

← C5×#79210 #14413503

Subgroups — C5×#79210 #14413503

Order 1920.

952 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
1C2×C5×#907C211yesmaximal, characteristic
2C5×#5523C211yesmaximal, characteristic
3C5×#5504C211yesmaximal, characteristic
4C3×C5×#428C211yesmaximal, characteristic, complemented
5C5×#5121C211yesmaximal, characteristic, complemented
6C5×#4998C211yesmaximal, characteristic, complemented
7C2×C5×#807C211yesmaximal, characteristic, complemented
8C5×#4881C212yesmaximal, complemented
9C5×D3×#107C212yesmaximal, complemented
10C5×#4861C212yesmaximal, complemented
11C5×#4860C212yesmaximal, complemented
12C5×#2913—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C4×C5×#67—22no—
18C5×#926C2211yescharacteristic
19C2×C5×C4⋊Dic3C2211yescharacteristic
20C22×C5×C3⋊C8C2211yescharacteristic
21C5×#907C418yescomplemented
22C2×C5×ΓL(1,𝔽25)C2212yes—
23C2×C5×D3×C8C2212yes—
24C5×#893—21no—
25C5×#892C2212yes—
26C5×#892C2212yes—
27C5×D3×C4⋊C4C2212yes—
28C5×D3×C4⋊C4C2212yes—
29C5×#887—21no—
30C5×#67⋊C4—22no—
31C4×C5×D12—21no—
32C4×C5×Dic6—21no—
33C3×C5×#107C2212yes—
34C3×C5×#106C2212yes—
35C5×#818C2212yes—
36C5×#817C2212yes—
37C5×#808C2211yescharacteristic
38C5×#808C2211yescharacteristic
39C5×#807C2212yes—
40C5×#807C2212yes—
41C5×#807C2211yescharacteristic
42C5×#807C2211yescharacteristic
43#79210C511yesmaximal, characteristic, direct product factor, Hall
44C2×C5×#131—31no—
45C5×#520—31no—
46C5×#520—31no—
47C5×#428—32no—
48C5×#428—32no—
49C5×#428—31no—
50C5×#428D311yescharacteristic, complemented
51C5×#427—32no—
52C5×#427—31no—
53C2×C5×#107—32no—
54C2×C5×#107—31no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×C5×#67D412yes—
58C22×C5×Dic3—21no—
59C5×#235C2×C414yes—
60C5×#235Q814yes—
61C2×C5×D12D411yescharacteristic
62C2×C4×C5×D3—22no—
63C2×C4×C5×D3—22no—
64C2×C4×C5×D3C2312yes—
65C2×C5×Dic6D411yescharacteristic
66C3×C5×M16C2×C414yescomplemented
67C2×C3×C5×C8C2312yes—
68C3×C5×C4⋊C4—21no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2312yes—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C22⋊C4—21no—
73C3×C42×C5—21no—
74C5×#217—21no—
75C5×(C2×D3)⋊C4—22no—
76C5×(C2×D3)⋊C4—22no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2311yescharacteristic
79C5×C4⋊Dic3C2312yes—
80C5×C4⋊Dic3C2311yescharacteristic
81C5×Dic3⋊C4—22no—
82C5×Dic3⋊C4—22no—
83C4×C5×Dic3—21no—
84C4×C5×Dic3—22no—
85C4×C5×Dic3—22no—
86C2×C5×C3⋊C8C2×C414yescomplemented
87C2×C5×C3⋊C8C2311yescharacteristic
88C2×C5×C3⋊C8C2311yescharacteristic
89C5×ΓL(1,𝔽25)C2×C418yescomplemented
90C5×D3×C8C2×C418yescomplemented
91C2×#907C2×C511yescharacteristic
92#5523C2×C511yescharacteristic
93#5504C2×C511yescharacteristic
94C3×#428C2×C511yescharacteristic, complemented
95#5121C2×C511yescharacteristic, complemented
96#4998C2×C511yescharacteristic, complemented
97C2×#807C2×C511yescharacteristic, complemented
98#4881C2×C512yescomplemented
99D3×#107C2×C512yescomplemented
100#4861C2×C512yescomplemented
101#4860C2×C512yescomplemented
102C2×C5×#41—31no—
103C5×#131—38no—
104C2×C5×M16—32no—
105C2×C5×M16C2×D311yescharacteristic
106C22×C5×C8—31no—
107C22×C5×C8—32no—
108C4×C5×Q8—61no—
109C4×C5×Q8—61no—
110C4×C5×D4—61no—
111C4×C5×D4—62no—
112C4×C5×D4—61no—
113C4×C5×D4—62no—
114C5×#117—31no—
115C5×#117—32no—
116C5×#117—32no—
117C5×#117C2×D311yescharacteristic
118C2×C5×C4⋊C4—31no—
119C2×C5×C4⋊C4—32no—
120C2×C5×C4⋊C4—32no—
121C2×C5×C4⋊C4C2×D311yescharacteristic
122C5×#107—32no—
123C5×#107—31no—
124C5×#107—32no—
125C5×#107—32no—
126C5×#107—31no—
127C5×#107C2×D312yes—
128C5×#106—32no—
129C5×#106—31no—
130C5×#106—31no—
131C5×#106C2×D312yes—
132#2913—31noSylow
133C23×C3×C5C2×D411yescharacteristic
134C22×C5×D3C2×D412yes—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—81no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×Q812yes—
142C2×C3×C4×C5C2411yescharacteristic
143C5×#67C4⋊C418yes—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—81no—
148C2×C5×Dic3C2×D412yes—
149C5×D12C4⋊C414yes—
150C4×C5×D3—82no—
151C4×C5×D3—82no—
152C4×C5×D3C22×C414yes—
153C4×C5×D3C2×Q814yes—
154C5×Dic6C4⋊C414yes—
155C3×C5×C8C22×C414yes—
156C5×C3⋊C8C22×C412yes—
157C5×C3⋊C8C22×C412yes—
158C2×#235C22×C511yescharacteristic
159C2×C3×M16C22×C511yescharacteristic
160C3×#117C22×C511yescharacteristic
161C2×C3×C4⋊C4C22×C511yescharacteristic
162C4×#67—22no—
163#926C22×C511yescharacteristic
164C2×C4⋊Dic3C22×C511yescharacteristic
165C22×C3⋊C8C22×C511yescharacteristic
166#907C4×C518yescomplemented
167C2×ΓL(1,𝔽25)C22×C512yes—
168C2×D3×C8C22×C512yes—
169#893—21no—
170#892C22×C512yes—
171#892C22×C512yes—
172D3×C4⋊C4C22×C512yes—
173D3×C4⋊C4C22×C512yes—
174#887—21no—
175#67⋊C4—22no—
176C4×D12—21no—
177C4×Dic6—21no—
178C3×#107C22×C512yes—
179C3×#106C22×C512yes—
180#818C22×C512yes—
181#817C22×C512yes—
182#808C22×C511yescharacteristic
183#808C22×C511yescharacteristic
184#807C22×C511yescharacteristic
185#807C22×C512yes—
186#807C22×C512yes—
187#807C22×C511yescharacteristic
188C5×#41—34no—
189C5×#41—34no—
190C2×C5×Q8—31no—
191C2×C5×D4—32no—
192C2×C5×D4—31no—
193C22×C4×C5—21no—
194C22×C4×C5—32no—
195C22×C4×C5—62no—
196C22×C4×C5—62no—
197C22×C4×C5—61no—
198C22×C4×C5C22×D311yescharacteristic
199C5×M16—38no—
200C5×M16C4×D314yescomplemented
201C2×C5×C8—34no—
202C2×C5×C8—31no—
203C2×C5×C8—31no—
204C2×C5×C8—38no—
205C2×C5×C8C22×D312yes—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—32no—
208C5×C4⋊C4—31no—
209C5×C4⋊C4—31no—
210C5×C4⋊C4—62no—
211C5×C4⋊C4—62no—
212C5×C4⋊C4—61no—
213C5×C4⋊C4C22×D311yescharacteristic
214C5×C4⋊C4C22×D312yes—
215C5×C4⋊C4C22×D311yescharacteristic
216C5×C22⋊C4—21no—
217C5×C22⋊C4—62no—
218C5×C22⋊C4—62no—
219C5×C22⋊C4—61no—
220C42×C5—21no—
221C42×C5—62no—
222C42×C5—62no—
223C42×C5—61no—
224C2×#131—31no—
225#520—31no—
226#520—31no—
227#428—31no—
228#428—32no—
229#428—32no—
230#428C5×D311yescharacteristic, complemented
231#427—31no—
232#427—32no—
233C2×#107—31no—
234C2×#107—32no—
235C22×C3×C5—21no—
236C22×C3×C5—21no—
237C22×C3×C5C2×C4⋊C412yes—
238C22×C3×C5C22×D411yescharacteristic
239C2×C5×D3—22no—
240C2×C5×D3—22no—
241C2×C5×D3C2×C4⋊C414yes—
242C3×C4×C5—41no—
243C3×C4×C5—42no—
244C3×C4×C5—41no—
245C3×C4×C5C2×C4⋊C412yes—
246C3×C4×C5C23×C411yescharacteristic
247C3×C4×C5C22×Q811yescharacteristic
248C5×Dic3—41no—
249C5×Dic3—42no—
250C5×Dic3—41no—
251C5×Dic3C2×C4⋊C414yes—
252C22×C3×C4—21no—
253C22×C3×C4C23×C511yescharacteristic
254C2×#67C5×D412yes—
255C22×Dic3—21no—
256#235C2×C4×C514yes—
257#235C5×Q814yes—
258C2×D12C5×D411yescharacteristic
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3C23×C512yes—
262C2×Dic6C5×D411yescharacteristic
263C3×M16C2×C4×C514yescomplemented
264C2×C3×C8C23×C512yes—
265C3×C4⋊C4—21no—
266C3×C4⋊C4C23×C512yes—
267C3×C4⋊C4C23×C511yescharacteristic
268C3×C4⋊C4C23×C511yescharacteristic
269C3×C22⋊C4—21no—
270C3×C42—21no—
271#217—21no—
272(C2×D3)⋊C4—22no—
273(C2×D3)⋊C4—22no—
274C4⋊Dic3—21no—
275C4⋊Dic3C23×C512yes—
276C4⋊Dic3C23×C511yescharacteristic
277C4⋊Dic3C23×C511yescharacteristic
278Dic3⋊C4—22no—
279Dic3⋊C4—22no—
280C4×Dic3—21no—
281C4×Dic3—22no—
282C4×Dic3—22no—
283C2×C3⋊C8C2×C4×C514yescomplemented
284C2×C3⋊C8C23×C511yescharacteristic
285C2×C3⋊C8C23×C511yescharacteristic
286ΓL(1,𝔽25)C2×C4×C518yescomplemented
287D3×C8C2×C4×C518yescomplemented
288C23×C5—32no—
289C23×C5D3×D411yescharacteristic
290C5×Q8—34no—
291C5×D4—38no—
292C5×D4—34no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—22no—
296C2×C4×C5—32no—
297C2×C4×C5—34no—
298C2×C4×C5—34no—
299C2×C4×C5—61no—
300C2×C4×C5—62no—
301C2×C4×C5—61no—
302C2×C4×C5—81no—
303C2×C4×C5—242no—
304C2×C4×C5—242no—
305C2×C4×C5—241no—
306C2×C4×C5C2×C4×D312yes—
307C2×C4×C5D3×D411yescharacteristic
308C2×C4×C5D3×Q812yes—
309C2×C4×C5C23×D311yescharacteristic
310C5×C8—32no—
311C5×C8—32no—
312C5×C8C2×C4×D314yes—
313C2×#41—31no—
314#131—38no—
315C2×M16—32no—
316C2×M16C2×C5×D311yescharacteristic
317C22×C8—31no—
318C22×C8—32no—
319C4×Q8—61no—
320C4×Q8—61no—
321C4×D4—61no—
322C4×D4—62no—
323C4×D4—61no—
324C4×D4—62no—
325#117—31no—
326#117—32no—
327#117—32no—
328#117C2×C5×D311yescharacteristic
329C2×C4⋊C4—31no—
330C2×C4⋊C4—32no—
331C2×C4⋊C4—32no—
332C2×C4⋊C4C2×C5×D311yescharacteristic
333#107—32no—
334#107—31no—
335#107—32no—
336#107—32no—
337#107—31no—
338#107C2×C5×D312yes—
339#106—32no—
340#106—31no—
341#106—31no—
342#106C2×C5×D312yes—
343C2×C3×C5—22no—
344C2×C3×C5C22×C4⋊C411yescharacteristic
345C2×C3×C5#57611yescharacteristic
346C2×C3×C5#57811yescharacteristic
347C5×D3—24no—
348C23×C3C2×C5×D411yescharacteristic
349C22×D3C2×C5×D412yes—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—81no—
354C2×C3×C4C22×C4×C512yes—
355C2×C3×C4C2×C5×D411yescharacteristic
356C2×C3×C4C2×C5×Q812yes—
357C2×C3×C4C24×C511yescharacteristic
358#67C5×C4⋊C418yes—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—81no—
363C2×Dic3C2×C5×D412yes—
364D12C5×C4⋊C414yes—
365C4×D3—82no—
366C4×D3—82no—
367C4×D3C22×C4×C514yes—
368C4×D3C2×C5×Q814yes—
369Dic6C5×C4⋊C414yes—
370C3×C8C22×C4×C514yes—
371C3⋊C8C22×C4×C512yes—
372C3⋊C8C22×C4×C512yes—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—34no—
376C22×C5—62no—
377C22×C5—62no—
378C22×C5D3×C4⋊C412yes—
379C22×C5C2×D3×D411yescharacteristic
380C4×C5—34no—
381C4×C5—42no—
382C4×C5—41no—
383C4×C5—41no—
384C4×C5—121no—
385C4×C5—122no—
386C4×C5—121no—
387C4×C5D3×C4⋊C412yes—
388C4×C5C22×C4×D311yescharacteristic
389C4×C5C2×D3×Q811yescharacteristic
390#41—34no—
391#41—34no—
392C2×Q8—31no—
393C2×D4—32no—
394C2×D4—31no—
395C22×C4—21no—
396C22×C4—32no—
397C22×C4—62no—
398C22×C4—62no—
399C22×C4—61no—
400C22×C4C22×C5×D311yescharacteristic
401M16—38no—
402M16C4×C5×D314yescomplemented
403C2×C8—34no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—38no—
407C2×C8C22×C5×D312yes—
408C4⋊C4—21no—
409C4⋊C4—31no—
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—62no—
413C4⋊C4—62no—
414C4⋊C4—61no—
415C4⋊C4C22×C5×D311yescharacteristic
416C4⋊C4C22×C5×D311yescharacteristic
417C4⋊C4C22×C5×D312yes—
418C22⋊C4—21no—
419C22⋊C4—62no—
420C22⋊C4—62no—
421C22⋊C4—61no—
422C42—21no—
423C42—62no—
424C42—62no—
425C42—61no—
426C3×C5#291311yescharacteristic, complemented, Hall
427C22×C3—21no—
428C22×C3—21no—
429C22×C3C2×C5×C4⋊C412yes—
430C22×C3C22×C5×D411yescharacteristic
431C2×D3—22no—
432C2×D3—22no—
433C2×D3C2×C5×C4⋊C414yes—
434C3×C4—41no—
435C3×C4—42no—
436C3×C4—41no—
437C3×C4C2×C5×C4⋊C412yes—
438C3×C4C23×C4×C511yescharacteristic
439C3×C4C22×C5×Q811yescharacteristic
440Dic3—41no—
441Dic3—42no—
442Dic3—41no—
443Dic3C2×C5×C4⋊C414yes—
444C2×C5—22no—
445C2×C5—64no—
446C2×C5C2×D3×C4⋊C411yescharacteristic
447C2×C5#577411yescharacteristic
448C2×C5#577911yescharacteristic
449C23—32no—
450C23C5×D3×D411yescharacteristic
451Q8—34no—
452D4—38no—
453D4—34no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—32no—
458C2×C4—34no—
459C2×C4—34no—
460C2×C4—61no—
461C2×C4—62no—
462C2×C4—61no—
463C2×C4—81no—
464C2×C4—242no—
465C2×C4—242no—
466C2×C4—241no—
467C2×C4C2×C4×C5×D312yes—
468C2×C4C5×D3×D411yescharacteristic
469C2×C4C5×D3×Q812yes—
470C2×C4C23×C5×D311yescharacteristic
471C8—32no—
472C8—32no—
473C8C2×C4×C5×D314yes—
474C2×C3—22no—
475C2×C3C22×C5×C4⋊C411yescharacteristic
476C2×C3C5×#57611yescharacteristic
477C2×C3C5×#57811yescharacteristic
478D3—24no—
479C5#7921011yescharacteristic, direct product factor, Sylow
480C22—21no—
481C22—21no—
482C22—34no—
483C22—62no—
484C22—62no—
485C22C5×D3×C4⋊C412yes—
486C22C2×C5×D3×D411yescharacteristic
487C4—34no—
488C4—42no—
489C4—41no—
490C4—41no—
491C4—121no—
492C4—122no—
493C4—121no—
494C4C5×D3×C4⋊C412yes—
495C4C22×C4×C5×D311yescharacteristic
496C4C2×C5×D3×Q811yescharacteristic
497C3C5×#291311yescharacteristic, complemented, Sylow
498C2—22no—
499C2—64no—
500C2C2×C5×D3×C4⋊C411yescharacteristic
501C2C5×#577411yescharacteristic
502C2C5×#577911yescharacteristic
subgroupG/H
centerC22×C5C2×D3×D4
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#428C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
cosocleC2×C3×C4C24×C5
hypercenterC5×#428D3
hypocenterC3C5×#2913
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#428

Complements

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

NH ≅ G/Ntype
4. C3×C5×#428C2semidirect
5. C5×#5121C2semidirect
6. C5×#4998C2semidirect
7. C2×C5×#807C2semidirect
8. C5×#4881C2semidirect
9. C5×D3×#107C2semidirect
10. C5×#4861C2semidirect
11. C5×#4860C2semidirect
21. C5×#907C4semidirect
43. #79210C5direct (N × H)
50. C5×#428D3semidirect
66. C3×C5×M16C2×C4semidirect
86. C2×C5×C3⋊C8C2×C4semidirect
89. C5×ΓL(1,𝔽25)C2×C4semidirect
90. C5×D3×C8C2×C4semidirect
94. C3×#428C2×C5semidirect
95. #5121C2×C5semidirect
96. #4998C2×C5semidirect
97. C2×#807C2×C5semidirect
98. #4881C2×C5semidirect
99. D3×#107C2×C5semidirect
100. #4861C2×C5semidirect
101. #4860C2×C5semidirect
166. #907C4×C5semidirect
200. C5×M16C4×D3semidirect
230. #428C5×D3semidirect
263. C3×M16C2×C4×C5semidirect
283. C2×C3⋊C8C2×C4×C5semidirect
286. ΓL(1,𝔽25)C2×C4×C5semidirect
287. D3×C8C2×C4×C5semidirect
402. M16C4×C5×D3semidirect
426. C3×C5#2913semidirect
479. C5#79210direct (N × H)
497. C3C5×#2913semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9072
C5×#55232
C5×#55042
C3×C5×#4282
C5×#51212
C5×#49982
C2×C5×#8072
C5×#48812
C5×D3×#1072
C5×#48612
C5×#48602
C5×#29133
#792105