Finite Group Databasebeta

← C5×#70019 #14313452

Subgroups — C5×#70019 #14313452

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5805C211yesmaximal, characteristic
2C2×C3×C5×#99C211yesmaximal, characteristic, complemented
3C2×C5×#834C211yesmaximal, characteristic, complemented
4C5×#4474C212yesmaximal, complemented
5C5×#4473C212yesmaximal, complemented
6C5×#2127—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×C5×#235C411yescharacteristic, complemented
9C2×C3×C5×C22⋊C4—21no—
10C5×#953—21no—
11C5×#953—21no—
12C2×C5×#217—21no—
13C5×#940C411yescharacteristic, complemented
14C5×#940C2211yescharacteristic
15C5×#938—21no—
16C5×#938—21no—
17C5×#936C411yescharacteristic, complemented
18C5×#936C2211yescharacteristic
19C5×#926C411yescharacteristic, complemented
20C3×C5×#99—21no—
21C3×C5×#99C2212yes—
22C5×#834—21no—
23C5×#834C2212yes—
24#70019C511yesmaximal, characteristic, direct product factor, Hall
25C5×#535—31no—
26C2×C5×#99—31no—
27C2×C5×#99D311yescharacteristic, complemented
28C5×#354—32no—
29C5×#353—32no—
30C24×C3×C5D411yescharacteristic
31C24×C3×C5D411yescharacteristic
32C2×C3×C5×D4—41no—
33C2×C3×C5×D4—41no—
34C2×C3×C5×D4C2×C411yescharacteristic
35C2×C3×C5×D4D411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C2×C3×C5×D4C2311yescharacteristic
38C22×C3×C4×C5—41no—
39C22×C3×C4×C5C2×C411yescharacteristic
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C22×C5×Dic3—41no—
46C5×#235—41no—
47C5×#235—41no—
48C2×C5×D12C2×C411yescharacteristic, complemented
49C2×C4×C5×D3—21no—
50C2×C5×Dic6C2×C411yescharacteristic, complemented
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4—41no—
53C5×#217—21no—
54C5×#217—21no—
55C5×#217—21no—
56C5×#217—21no—
57C5×#217—21no—
58C5×#217—22no—
59C5×#217—41no—
60C5×C4⋊Dic3—21no—
61C4×C5×Dic3C2×C411yescharacteristic, complemented
62C4×C5×Dic3C2×C411yescharacteristic, complemented
63#5805C2×C511yescharacteristic
64C2×C3×#99C2×C511yescharacteristic, complemented
65C2×#834C2×C511yescharacteristic, complemented
66#4474C2×C512yescomplemented
67#4473C2×C512yescomplemented
68C2×C5×#41—31no—
69C22×C5×D4C2×D311yescharacteristic
70C5×#127—31no—
71C5×#127—31no—
72C5×#124—31no—
73C5×#124—31no—
74C5×#121—61no—
75C5×#121—61no—
76C5×#120—61no—
77C5×#120—61no—
78C5×#117—31no—
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—61no—
81C5×#99—21no—
82C5×#99—32no—
83C5×#99—61no—
84C5×#99C2×D312yes—
85#2127—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×C5C2×D411yescharacteristic
96C23×C3×C5C2×D411yescharacteristic
97C22×C5×D3—21no—
98C3×C5×D4—41no—
99C3×C5×D4—41no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—42no—
105C2×C3×C4×C5—82no—
106C2×C3×C4×C5C22⋊C411yescharacteristic
107C2×C3×C4×C5C22×C411yescharacteristic
108C5×#67—41no—
109C5×#67—41no—
110C5×#67—81no—
111C5×#67—81no—
112C5×#67—81no—
113C5×#67—81no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—42no—
118C2×C5×Dic3—82no—
119C5×D12—41no—
120C4×C5×D3—42no—
121C5×Dic6—41no—
122C22×C3×D4C22×C511yescharacteristic
123C2×#235C4×C511yescharacteristic, complemented
124C2×C3×C22⋊C4—21no—
125#953—21no—
126#953—21no—
127C2×#217—21no—
128#940C4×C511yescharacteristic, complemented
129#940C22×C511yescharacteristic
130#938—21no—
131#938—21no—
132#936C4×C511yescharacteristic, complemented
133#936C22×C511yescharacteristic
134#926C4×C511yescharacteristic, complemented
135C3×#99—21no—
136C3×#99C22×C512yes—
137#834—21no—
138#834C22×C512yes—
139C24×C5D1211yescharacteristic
140C24×C5#6711yescharacteristic
141C5×#41—121no—
142C5×#41—121no—
143C2×C5×Q8—31no—
144C2×C5×D4—31no—
145C2×C5×D4—41no—
146C2×C5×D4—41no—
147C2×C5×D4—61no—
148C2×C5×D4—61no—
149C2×C5×D4—61no—
150C2×C5×D4—61no—
151C2×C5×D4—61no—
152C2×C5×D4C4×D311yescharacteristic
153C2×C5×D4D1211yescharacteristic
154C2×C5×D4#6711yescharacteristic
155C2×C5×D4C22×D311yescharacteristic
156C22×C4×C5—41no—
157C22×C4×C5—61no—
158C22×C4×C5—121no—
159C22×C4×C5C4×D311yescharacteristic
160C5×C4⋊C4—61no—
161C5×C22⋊C4—22no—
162C5×C22⋊C4—41no—
163C5×C22⋊C4—61no—
164C5×C22⋊C4—61no—
165C5×C22⋊C4—61no—
166C5×C22⋊C4—61no—
167C5×C22⋊C4—61no—
168C5×C22⋊C4—62no—
169C5×C22⋊C4—121no—
170C42×C5—31no—
171C42×C5—31no—
172#535—31no—
173C2×#99—31no—
174C2×#99C5×D311yescharacteristic, complemented
175#354—32no—
176#353—32no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—42no—
187C22×C3×C5—42no—
188C22×C3×C5—81no—
189C22×C3×C5—81no—
190C22×C3×C5#9911yescharacteristic
191C22×C3×C5#9911yescharacteristic
192C22×C3×C5C2×C22⋊C411yescharacteristic
193C2×C5×D3—41no—
194C2×C5×D3—41no—
195C2×C5×D3—41no—
196C3×C4×C5—21no—
197C3×C4×C5—21no—
198C3×C4×C5—82no—
199C5×Dic3—41no—
200C5×Dic3—41no—
201C5×Dic3—41no—
202C5×Dic3—82no—
203C24×C3C5×D411yescharacteristic
204C24×C3C5×D411yescharacteristic
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×C4—41no—
212C22×C3×C4C2×C4×C511yescharacteristic
213C2×#67—21no—
214C2×#67—21no—
215C2×#67—21no—
216C2×#67—21no—
217C2×#67—21no—
218C22×Dic3—41no—
219#235—41no—
220#235—41no—
221C2×D12C2×C4×C511yescharacteristic, complemented
222C2×C4×D3—21no—
223C2×Dic6C2×C4×C511yescharacteristic, complemented
224C3×C22⋊C4—22no—
225C3×C22⋊C4—41no—
226#217—21no—
227#217—21no—
228#217—21no—
229#217—21no—
230#217—21no—
231#217—22no—
232#217—41no—
233C4⋊Dic3—21no—
234C4×Dic3C2×C4×C511yescharacteristic, complemented
235C4×Dic3C2×C4×C511yescharacteristic, complemented
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—61no—
241C23×C5—81no—
242C23×C5—81no—
243C23×C5(C2×D3)⋊C411yescharacteristic
244C23×C5(C2×D3)⋊C411yescharacteristic
245C23×C5(C2×D3)⋊C411yescharacteristic
246C23×C5C2×D1211yescharacteristic
247C23×C5C2×#6711yescharacteristic
248C5×Q8—121no—
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—41no—
252C5×D4—41no—
253C5×D4—121no—
254C5×D4—121no—
255C5×D4—121no—
256C5×D4—241no—
257C5×D4—241no—
258C5×D4—241no—
259C5×D4—241no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—42no—
263C2×C4×C5—61no—
264C2×C4×C5—61no—
265C2×C4×C5—61no—
266C2×C4×C5—82no—
267C2×C4×C5—122no—
268C2×C4×C5—122no—
269C2×C4×C5—242no—
270C2×C4×C5(C2×D3)⋊C411yescharacteristic
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×#41—31no—
273C22×D4C2×C5×D311yescharacteristic
274#127—31no—
275#127—31no—
276#124—31no—
277#124—31no—
278#121—61no—
279#121—61no—
280#120—61no—
281#120—61no—
282#117—31no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—61no—
285#99—21no—
286#99—32no—
287#99—61no—
288#99C2×C5×D312yes—
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5—41no—
295C2×C3×C5—41no—
296C2×C3×C5C2×#9911yescharacteristic
297C5×D3—81no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—81no—
303C23×C3—81no—
304C23×C3C5×C22⋊C411yescharacteristic
305C23×C3C5×C22⋊C411yescharacteristic
306C23×C3C5×C22⋊C411yescharacteristic
307C23×C3C2×C5×D411yescharacteristic
308C23×C3C2×C5×D411yescharacteristic
309C22×D3—21no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—42no—
317C2×C3×C4—82no—
318C2×C3×C4C5×C22⋊C411yescharacteristic
319C2×C3×C4C22×C4×C511yescharacteristic
320#67—41no—
321#67—41no—
322#67—81no—
323#67—81no—
324#67—81no—
325#67—81no—
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—42no—
330C2×Dic3—82no—
331D12—41no—
332C4×D3—42no—
333Dic6—41no—
334C22×C5—21no—
335C22×C5—21no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—41no—
341C22×C5—41no—
342C22×C5—41no—
343C22×C5—42no—
344C22×C5—42no—
345C22×C5—81no—
346C22×C5—81no—
347C22×C5—121no—
348C22×C5—121no—
349C22×C5—121no—
350C22×C5#80611yescharacteristic
351C22×C5#80611yescharacteristic
352C22×C5C2×(C2×D3)⋊C411yescharacteristic
353C4×C5—21no—
354C4×C5—21no—
355C4×C5—82no—
356C4×C5—121no—
357C4×C5—121no—
358C4×C5—121no—
359C4×C5—242no—
360C24C5×D1211yescharacteristic
361C24C5×#6711yescharacteristic
362#41—121no—
363#41—121no—
364C2×Q8—31no—
365C2×D4—31no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—61no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4C4×C5×D311yescharacteristic
374C2×D4C5×D1211yescharacteristic
375C2×D4C5×#6711yescharacteristic
376C2×D4C22×C5×D311yescharacteristic
377C22×C4—41no—
378C22×C4—61no—
379C22×C4—121no—
380C22×C4C4×C5×D311yescharacteristic
381C4⋊C4—61no—
382C22⋊C4—22no—
383C22⋊C4—41no—
384C22⋊C4—61no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—61no—
389C22⋊C4—62no—
390C22⋊C4—121no—
391C42—31no—
392C42—31no—
393C3×C5#212711yescharacteristic, complemented, Hall
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—81no—
406C22×C3—81no—
407C22×C3C5×#9911yescharacteristic
408C22×C3C5×#9911yescharacteristic
409C22×C3C2×C5×C22⋊C411yescharacteristic
410C2×D3—41no—
411C2×D3—41no—
412C2×D3—41no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—82no—
416Dic3—41no—
417Dic3—41no—
418Dic3—41no—
419Dic3—82no—
420C2×C5—21no—
421C2×C5—21no—
422C2×C5—21no—
423C2×C5—41no—
424C2×C5—41no—
425C2×C5—41no—
426C2×C5—41no—
427C2×C5—241no—
428C2×C5C2×#80611yescharacteristic
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—61no—
434C23—81no—
435C23—81no—
436C23C5×(C2×D3)⋊C411yescharacteristic
437C23C5×(C2×D3)⋊C411yescharacteristic
438C23C5×(C2×D3)⋊C411yescharacteristic
439C23C2×C5×D1211yescharacteristic
440C23C2×C5×#6711yescharacteristic
441Q8—121no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—121no—
447D4—121no—
448D4—121no—
449D4—241no—
450D4—241no—
451D4—241no—
452D4—241no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—42no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4—82no—
460C2×C4—122no—
461C2×C4—122no—
462C2×C4—242no—
463C2×C4C5×(C2×D3)⋊C411yescharacteristic
464C2×C4C2×C4×C5×D311yescharacteristic
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—41no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—41no—
472C2×C3C2×C5×#9911yescharacteristic
473D3—81no—
474C5#7001911yescharacteristic, direct product factor, Sylow
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—42no—
485C22—42no—
486C22—81no—
487C22—81no—
488C22—121no—
489C22—121no—
490C22—121no—
491C22C5×#80611yescharacteristic
492C22C5×#80611yescharacteristic
493C22C2×C5×(C2×D3)⋊C411yescharacteristic
494C4—21no—
495C4—21no—
496C4—82no—
497C4—121no—
498C4—121no—
499C4—121no—
500C4—242no—
501C3C5×#212711yescharacteristic, complemented, Sylow
502C2—21no—
503C2—21no—
504C2—21no—
505C2—41no—
506C2—41no—
507C2—41no—
508C2—41no—
509C2—241no—
510C2C2×C5×#80611yescharacteristic
subgroupG/H
centerC2×C5C2×#806
commutatorC2×C3×C4C22×C4×C5
FrattiniC2×D4C22×C5×D3
FittingC2×C3×C5×#99C2
socleC2×C3×C5C2×#99
prime radicalC5×#5805C2
cosocleC2×C3×D4C23×C5
hypercenterC2×C5×#99D3
hypocenterC3C5×#2127
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ C2×C5×#99

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#99C2semidirect
3. C2×C5×#834C2semidirect
4. C5×#4474C2semidirect
5. C5×#4473C2semidirect
8. C2×C5×#235C4semidirect
13. C5×#940C4semidirect
17. C5×#936C4semidirect
19. C5×#926C4semidirect
24. #70019C5direct (N × H)
27. C2×C5×#99D3semidirect
48. C2×C5×D12C2×C4semidirect
50. C2×C5×Dic6C2×C4semidirect
61. C4×C5×Dic3C2×C4semidirect
62. C4×C5×Dic3C2×C4semidirect
64. C2×C3×#99C2×C5semidirect
65. C2×#834C2×C5semidirect
66. #4474C2×C5semidirect
67. #4473C2×C5semidirect
123. C2×#235C4×C5semidirect
128. #940C4×C5semidirect
132. #936C4×C5semidirect
134. #926C4×C5semidirect
174. C2×#99C5×D3semidirect
221. C2×D12C2×C4×C5semidirect
223. C2×Dic6C2×C4×C5semidirect
234. C4×Dic3C2×C4×C5semidirect
235. C4×Dic3C2×C4×C5semidirect
393. C3×C5#2127semidirect
474. C5#70019direct (N × H)
501. C3C5×#2127semidirect

Maximal subgroups

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

subgroupindex
C5×#58052
C2×C3×C5×#992
C2×C5×#8342
C5×#44742
C5×#44732
C5×#21273
#700195