Finite Group Databasebeta

← C5×#70094 #14313203

Subgroups — C5×#70094 #14313203

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5804C211yesmaximal, characteristic
2C2×C3×C5×#100C211yesmaximal, characteristic, complemented
3C2×C5×#834C211yesmaximal, characteristic, complemented
4C5×#4476C212yesmaximal, complemented
5C5×#4475C212yesmaximal, complemented
6C5×#2121—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×C5×#67C411yescharacteristic, complemented
9C2×C3×C5×M16—21no—
10C5×#953—21no—
11C2×C5×#217—21no—
12C2×C5×#217C411yescharacteristic, complemented
13C5×#939—21no—
14C5×#939—21no—
15C5×#937C411yescharacteristic, complemented
16C5×#937C2211yescharacteristic
17C5×#935C411yescharacteristic, complemented
18C5×#935C2211yescharacteristic
19C5×#929—21no—
20C3×C5×#100—21no—
21C3×C5×#100C2212yes—
22C5×#834—21no—
23C5×#834C2212yes—
24#70094C511yesmaximal, characteristic, direct product factor, Hall
25C5×#534—31no—
26C2×C5×#100D311yescharacteristic, complemented
27C2×C5×#99—31no—
28C5×#352—32no—
29C5×AΣL(1,𝔽16)—32no—
30C24×C3×C5C2×C411yescharacteristic
31C24×C3×C5D411yescharacteristic
32C23×C5×D3C2×C411yescharacteristic, complemented
33C2×C3×C5×D4—41no—
34C2×C3×C5×D4—41no—
35C2×C3×C5×D4C2×C411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C2×C3×C5×D4D411yescharacteristic
38C2×C3×C5×D4C2311yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—41no—
45C2×C5×#67—41no—
46C22×C5×Dic3—21no—
47C22×C5×Dic3—41no—
48C22×C5×Dic3C2×C411yescharacteristic, complemented
49C3×C5×M16—22no—
50C3×C5×M16—41no—
51C2×C3×C5×C8—41no—
52C5×#217—21no—
53C5×#217—21no—
54C5×#217—21no—
55C5×#217—22no—
56C5×#217—41no—
57C5×#217C2×C411yescharacteristic, complemented
58C5×#217C2×C411yescharacteristic, complemented
59C5×(C2×D3)⋊C4—21no—
60C5×(C2×D3)⋊C4—21no—
61C5×Dic3⋊C4—21no—
62C5×Dic3⋊C4—21no—
63#5804C2×C511yescharacteristic
64C2×C3×#100C2×C511yescharacteristic, complemented
65C2×#834C2×C511yescharacteristic, complemented
66#4476C2×C512yescomplemented
67#4475C2×C512yescomplemented
68C22×C5×D4—31no—
69C22×C5×D4C2×D311yescharacteristic
70C2×C5×M16—21no—
71C5×#123—31no—
72C5×#123—31no—
73C5×#123—61no—
74C5×#121—61no—
75C5×#121—61no—
76C5×#120—31no—
77C5×#120—31no—
78C5×#120—61no—
79C2×C5×C22⋊C4—31no—
80C2×C5×C22⋊C4—61no—
81C5×#100—21no—
82C5×#100C2×D312yes—
83C5×#99—32no—
84C5×#99—61no—
85#2121—31noSylow
86C23×C3×C5—21no—
87C23×C3×C5—21no—
88C23×C3×C5—21no—
89C23×C3×C5—21no—
90C23×C3×C5—81no—
91C23×C3×C5—81no—
92C23×C3×C5C22⋊C411yescharacteristic
93C23×C3×C5C22⋊C411yescharacteristic
94C23×C3×C5C22⋊C411yescharacteristic
95C23×C3×C5C22×C411yescharacteristic
96C23×C3×C5C2×D411yescharacteristic
97C22×C5×D3—21no—
98C22×C5×D3—41no—
99C22×C5×D3—81no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C3×C5×D4—41no—
103C3×C5×D4—41no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5C22⋊C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C5×#67—42no—
109C5×#67—41no—
110C5×#67—41no—
111C5×#67—81no—
112C5×#67—81no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3—42no—
118C2×C5×Dic3—81no—
119C2×C5×Dic3—82no—
120C3×C5×C8—42no—
121C22×C3×D4C22×C511yescharacteristic
122C22×#67C4×C511yescharacteristic, complemented
123C2×C3×M16—21no—
124#953—21no—
125C2×#217—21no—
126C2×#217C4×C511yescharacteristic, complemented
127#939—21no—
128#939—21no—
129#937C4×C511yescharacteristic, complemented
130#937C22×C511yescharacteristic
131#935C4×C511yescharacteristic, complemented
132#935C22×C511yescharacteristic
133#929—21no—
134C3×#100—21no—
135C3×#100C22×C512yes—
136#834—21no—
137#834C22×C512yes—
138C24×C5—31no—
139C24×C5C4×D311yescharacteristic
140C24×C5D1211yescharacteristic
141C2×C5×D4—41no—
142C2×C5×D4—41no—
143C2×C5×D4—61no—
144C2×C5×D4—61no—
145C2×C5×D4—61no—
146C2×C5×D4—61no—
147C2×C5×D4—121no—
148C2×C5×D4—121no—
149C2×C5×D4C4×D311yescharacteristic
150C2×C5×D4D1211yescharacteristic
151C2×C5×D4#6711yescharacteristic
152C2×C5×D4C22×D311yescharacteristic
153C22×C4×C5—31no—
154C22×C4×C5—61no—
155C22×C4×C5—121no—
156C22×C4×C5#6711yescharacteristic
157C5×M16—22no—
158C5×M16—41no—
159C2×C5×C8—41no—
160C5×C4⋊C4—61no—
161C5×C4⋊C4—61no—
162C5×C22⋊C4—31no—
163C5×C22⋊C4—31no—
164C5×C22⋊C4—61no—
165C5×C22⋊C4—61no—
166C5×C22⋊C4—61no—
167C5×C22⋊C4—61no—
168C5×C22⋊C4—61no—
169C5×C22⋊C4—62no—
170C5×C22⋊C4—121no—
171#534—31no—
172C2×#100C5×D311yescharacteristic, complemented
173C2×#99—31no—
174#352—32no—
175AΣL(1,𝔽16)—32no—
176C22×C3×C5—21no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—21no—
180C22×C3×C5—41no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—42no—
186C22×C3×C5—81no—
187C22×C3×C5—81no—
188C22×C3×C5—81no—
189C22×C3×C5#9911yescharacteristic
190C22×C3×C5#9911yescharacteristic
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C2×C5×D3—41no—
193C2×C5×D3—41no—
194C2×C5×D3—41no—
195C2×C5×D3—82no—
196C3×C4×C5—21no—
197C3×C4×C5—21no—
198C5×Dic3—41no—
199C5×Dic3—41no—
200C5×Dic3—41no—
201C5×Dic3—82no—
202C24×C3C2×C4×C511yescharacteristic
203C24×C3C5×D411yescharacteristic
204C23×D3C2×C4×C511yescharacteristic, complemented
205C2×C3×D4—41no—
206C2×C3×D4—41no—
207C2×C3×D4C2×C4×C511yescharacteristic
208C2×C3×D4C5×D411yescharacteristic
209C2×C3×D4C5×D411yescharacteristic
210C2×C3×D4C23×C511yescharacteristic
211C22×C3×C4C5×D411yescharacteristic
212C2×#67—21no—
213C2×#67—21no—
214C2×#67—21no—
215C2×#67—21no—
216C2×#67—41no—
217C2×#67—41no—
218C22×Dic3—21no—
219C22×Dic3—41no—
220C22×Dic3C2×C4×C511yescharacteristic, complemented
221C3×M16—22no—
222C3×M16—41no—
223C2×C3×C8—41no—
224#217—21no—
225#217—21no—
226#217—21no—
227#217—22no—
228#217—41no—
229#217C2×C4×C511yescharacteristic, complemented
230#217C2×C4×C511yescharacteristic, complemented
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—21no—
233Dic3⋊C4—21no—
234Dic3⋊C4—21no—
235C23×C5—21no—
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—61no—
240C23×C5—81no—
241C23×C5—81no—
242C23×C5—121no—
243C23×C5—241no—
244C23×C5(C2×D3)⋊C411yescharacteristic
245C23×C5(C2×D3)⋊C411yescharacteristic
246C23×C5(C2×D3)⋊C411yescharacteristic
247C23×C5C2×C4×D311yescharacteristic
248C23×C5C2×D1211yescharacteristic
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—41no—
252C5×D4—41no—
253C5×D4—122no—
254C5×D4—121no—
255C5×D4—121no—
256C5×D4—241no—
257C5×D4—241no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5—61no—
261C2×C4×C5—61no—
262C2×C4×C5—61no—
263C2×C4×C5—121no—
264C2×C4×C5—122no—
265C2×C4×C5—241no—
266C2×C4×C5—242no—
267C2×C4×C5(C2×D3)⋊C411yescharacteristic
268C2×C4×C5C2×#6711yescharacteristic
269C5×C8—42no—
270C22×D4—31no—
271C22×D4C2×C5×D311yescharacteristic
272C2×M16—21no—
273#123—31no—
274#123—31no—
275#123—61no—
276#121—61no—
277#121—61no—
278#120—31no—
279#120—31no—
280#120—61no—
281C2×C22⋊C4—31no—
282C2×C22⋊C4—61no—
283#100—21no—
284#100C2×C5×D312yes—
285#99—32no—
286#99—61no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5—41no—
291C2×C3×C5—41no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5C2×#9911yescharacteristic
295C5×D3—81no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—81no—
301C23×C3—81no—
302C23×C3C5×C22⋊C411yescharacteristic
303C23×C3C5×C22⋊C411yescharacteristic
304C23×C3C5×C22⋊C411yescharacteristic
305C23×C3C22×C4×C511yescharacteristic
306C23×C3C2×C5×D411yescharacteristic
307C22×D3—21no—
308C22×D3—41no—
309C22×D3—81no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4C5×C22⋊C411yescharacteristic
317C2×C3×C4C2×C5×D411yescharacteristic
318#67—42no—
319#67—41no—
320#67—41no—
321#67—81no—
322#67—81no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—41no—
327C2×Dic3—42no—
328C2×Dic3—81no—
329C2×Dic3—82no—
330C3×C8—42no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5—41no—
336C22×C5—41no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—42no—
341C22×C5—81no—
342C22×C5—81no—
343C22×C5—81no—
344C22×C5—121no—
345C22×C5—121no—
346C22×C5—121no—
347C22×C5—242no—
348C22×C5#80611yescharacteristic
349C22×C5#80611yescharacteristic
350C22×C5C2×(C2×D3)⋊C411yescharacteristic
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—121no—
354C4×C5—121no—
355C4×C5—121no—
356C4×C5—242no—
357C24—31no—
358C24C4×C5×D311yescharacteristic
359C24C5×D1211yescharacteristic
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—61no—
366C2×D4—121no—
367C2×D4—121no—
368C2×D4C4×C5×D311yescharacteristic
369C2×D4C5×D1211yescharacteristic
370C2×D4C5×#6711yescharacteristic
371C2×D4C22×C5×D311yescharacteristic
372C22×C4—31no—
373C22×C4—61no—
374C22×C4—121no—
375C22×C4C5×#6711yescharacteristic
376M16—22no—
377M16—41no—
378C2×C8—41no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C22⋊C4—31no—
382C22⋊C4—31no—
383C22⋊C4—61no—
384C22⋊C4—61no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—62no—
389C22⋊C4—121no—
390C3×C5#212111yescharacteristic, complemented, Hall
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—42no—
401C22×C3—81no—
402C22×C3—81no—
403C22×C3—81no—
404C22×C3C5×#9911yescharacteristic
405C22×C3C5×#9911yescharacteristic
406C22×C3C2×C5×C22⋊C411yescharacteristic
407C2×D3—41no—
408C2×D3—41no—
409C2×D3—41no—
410C2×D3—82no—
411C3×C4—21no—
412C3×C4—21no—
413Dic3—41no—
414Dic3—41no—
415Dic3—41no—
416Dic3—82no—
417C2×C5—21no—
418C2×C5—21no—
419C2×C5—21no—
420C2×C5—41no—
421C2×C5—41no—
422C2×C5—41no—
423C2×C5—41no—
424C2×C5—241no—
425C2×C5C2×#80611yescharacteristic
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—61no—
431C23—81no—
432C23—81no—
433C23—121no—
434C23—241no—
435C23C5×(C2×D3)⋊C411yescharacteristic
436C23C5×(C2×D3)⋊C411yescharacteristic
437C23C5×(C2×D3)⋊C411yescharacteristic
438C23C2×C4×C5×D311yescharacteristic
439C23C2×C5×D1211yescharacteristic
440D4—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—122no—
445D4—121no—
446D4—121no—
447D4—241no—
448D4—241no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—121no—
455C2×C4—122no—
456C2×C4—241no—
457C2×C4—242no—
458C2×C4C5×(C2×D3)⋊C411yescharacteristic
459C2×C4C2×C5×#6711yescharacteristic
460C8—42no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—41no—
465C2×C3—41no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3C2×C5×#9911yescharacteristic
469D3—81no—
470C5#7009411yescharacteristic, direct product factor, Sylow
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—42no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—121no—
485C22—121no—
486C22—121no—
487C22—242no—
488C22C5×#80611yescharacteristic
489C22C5×#80611yescharacteristic
490C22C2×C5×(C2×D3)⋊C411yescharacteristic
491C4—21no—
492C4—21no—
493C4—121no—
494C4—121no—
495C4—121no—
496C4—242no—
497C3C5×#212111yescharacteristic, complemented, Sylow
498C2—21no—
499C2—21no—
500C2—21no—
501C2—41no—
502C2—41no—
503C2—41no—
504C2—41no—
505C2—241no—
506C2C2×C5×#80611yescharacteristic
subgroupG/H
centerC2×C5C2×#806
commutatorC23×C3C22×C4×C5
FrattiniC2×D4C22×C5×D3
FittingC2×C3×C5×#100C2
socleC2×C3×C5C2×#99
prime radicalC5×#5804C2
cosocleC2×C3×D4C23×C5
hypercenterC2×C5×#100D3
hypocenterC3C5×#2121
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ C2×C5×#100

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#100C2semidirect
3. C2×C5×#834C2semidirect
4. C5×#4476C2semidirect
5. C5×#4475C2semidirect
8. C22×C5×#67C4semidirect
12. C2×C5×#217C4semidirect
15. C5×#937C4semidirect
17. C5×#935C4semidirect
24. #70094C5direct (N × H)
26. C2×C5×#100D3semidirect
32. C23×C5×D3C2×C4semidirect
48. C22×C5×Dic3C2×C4semidirect
57. C5×#217C2×C4semidirect
58. C5×#217C2×C4semidirect
64. C2×C3×#100C2×C5semidirect
65. C2×#834C2×C5semidirect
66. #4476C2×C5semidirect
67. #4475C2×C5semidirect
122. C22×#67C4×C5semidirect
126. C2×#217C4×C5semidirect
129. #937C4×C5semidirect
131. #935C4×C5semidirect
172. C2×#100C5×D3semidirect
204. C23×D3C2×C4×C5semidirect
220. C22×Dic3C2×C4×C5semidirect
229. #217C2×C4×C5semidirect
230. #217C2×C4×C5semidirect
390. C3×C5#2121semidirect
470. C5#70094direct (N × H)
497. C3C5×#2121semidirect

Maximal subgroups

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

subgroupindex
C5×#58042
C2×C3×C5×#1002
C2×C5×#8342
C5×#44762
C5×#44752
C5×#21213
#700945