Finite Group Databasebeta

← C5×#82639 #14330849

Subgroups — C5×#82639 #14330849

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C5×#5221C212yesmaximal, complemented
3C5×#5220C212yesmaximal, complemented
4C5×#5220C212yesmaximal, complemented
5C5×#5212C211yesmaximal, characteristic, complemented
6C5×#5211C211yesmaximal, characteristic, complemented
7C5×#4980C212yesmaximal, complemented
8C5×#4951C212yesmaximal, complemented
9C5×#4950C212yesmaximal, complemented
10C5×#2377—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C22×C3×C5×D4C2212yes—
13C23×C3×C4×C5C2211yescharacteristic
14C23×C5×Dic3C2212yes—
15C3×C5×#121C418yescomplemented
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C5×C22⋊C4C2212yes—
18C2×C5×#217C2212yes—
19C2×C5×#217C2212yes—
20C2×C5×#217C2212yes—
21C2×C5×#217C2212yes—
22C2×C5×#217C2211yescharacteristic
23C2×C5×#217C2211yescharacteristic
24C2×C5×C4⋊Dic3C2212yes—
25C2×C5×C4⋊Dic3C2212yes—
26C2×C4×C5×Dic3C2212yes—
27C5×C3⋊#95C2211yescharacteristic
28C5×C3⋊#95C2212yes—
29C5×C3⋊#95C2211yescharacteristic
30C5×C3⋊#95C2212yes—
31C5×C3⋊#95C2212yes—
32C5×C3⋊#95C2212yes—
33#82639C511yesmaximal, characteristic, direct product factor, Hall
34C2×C5×#121D311yescharacteristic
35C5×#390—32no—
36C5×#388—32no—
37C5×#387—32no—
38C5×#386—32no—
39C5×#386—32no—
40C5×#385—32no—
41C5×#381—31no—
42C5×#380—31no—
43C24×C3×C5C2311yescharacteristic
44C24×C3×C5C2312yes—
45C2×C3×C5×D4—42no—
46C2×C3×C5×D4—42no—
47C2×C3×C5×D4—42no—
48C2×C3×C5×D4C2×C414yes—
49C2×C3×C5×D4C2×C418yescomplemented
50C22×C3×C4×C5—42no—
51C22×C3×C4×C5C2×C414yescomplemented
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C5×Dic3—42no—
56C22×C5×Dic3—42no—
57C22×C5×Dic3—42no—
58C22×C5×Dic3C2312yes—
59C22×C5×Dic3C2312yes—
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2312yes—
62C3×C5×C4⋊C4C2×C414yescomplemented
63C3×C5×C22⋊C4C2×C418yescomplemented
64C5×#217—42no—
65C5×#217—42no—
66C5×#217—41no—
67C5×#217—42no—
68C5×#217—42no—
69C5×#217—41no—
70C5×C4⋊Dic3—42no—
71C5×C4⋊Dic3—42no—
72C4×C5×Dic3—42no—
73C2×C3×#121C2×C511yescharacteristic
74#5221C2×C512yescomplemented
75#5220C2×C512yescomplemented
76#5220C2×C512yescomplemented
77#5212C2×C511yescharacteristic, complemented
78#5211C2×C511yescharacteristic, complemented
79#4980C2×C512yescomplemented
80#4951C2×C512yescomplemented
81#4950C2×C512yescomplemented
82C22×C5×D4C2×D311yescharacteristic
83C22×C5×D4C2×D312yes—
84C23×C4×C5—32no—
85C23×C4×C5C2×D311yescharacteristic
86C5×#121Dic318yescomplemented
87C2×C5×C4⋊C4—32no—
88C2×C5×C4⋊C4—32no—
89C2×C5×C4⋊C4C2×D311yescharacteristic
90C2×C5×C22⋊C4—31no—
91C2×C5×C22⋊C4—31no—
92C2×C5×C22⋊C4—32no—
93C2×C5×C22⋊C4—32no—
94C2×C5×C22⋊C4—32no—
95C2×C5×C22⋊C4—32no—
96C2×C5×C22⋊C4C2×D312yes—
97C2×C42×C5—32no—
98C5×#95—32no—
99C5×#95—31no—
100C5×#95—32no—
101C5×#95—31no—
102C5×#95—32no—
103C5×#95—32no—
104#2377—31noSylow
105C23×C3×C5—21no—
106C23×C3×C5—22no—
107C23×C3×C5—22no—
108C23×C3×C5—22no—
109C23×C3×C5—22no—
110C23×C3×C5—22no—
111C23×C3×C5—22no—
112C23×C3×C5—22no—
113C23×C3×C5—21no—
114C23×C3×C5—22no—
115C23×C3×C5C22×C414yes—
116C23×C3×C5C22×C412yes—
117C23×C3×C5C2411yescharacteristic
118C3×C5×D4—44no—
119C3×C5×D4—48no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—44no—
125C2×C3×C4×C5C22×C412yes—
126C2×C3×C4×C5C22×C414yes—
127C2×C3×C4×C5C22×C412yes—
128C2×C5×Dic3—22no—
129C2×C5×Dic3—22no—
130C2×C5×Dic3—22no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3—22no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—48no—
141C22×C3×D4C22×C511yescharacteristic
142C22×C3×D4C22×C512yes—
143C23×C3×C4C22×C511yescharacteristic
144C23×Dic3C22×C512yes—
145C3×#121C4×C518yescomplemented
146C2×C3×C4⋊C4C22×C511yescharacteristic
147C2×C3×C22⋊C4C22×C512yes—
148C2×#217C22×C512yes—
149C2×#217C22×C512yes—
150C2×#217C22×C512yes—
151C2×#217C22×C512yes—
152C2×#217C22×C511yescharacteristic
153C2×#217C22×C511yescharacteristic
154C2×C4⋊Dic3C22×C512yes—
155C2×C4⋊Dic3C22×C512yes—
156C2×C4×Dic3C22×C512yes—
157C3⋊#95C22×C511yescharacteristic
158C3⋊#95C22×C512yes—
159C3⋊#95C22×C511yescharacteristic
160C3⋊#95C22×C512yes—
161C3⋊#95C22×C512yes—
162C3⋊#95C22×C512yes—
163C24×C5C22×D311yescharacteristic
164C24×C5C22×D312yes—
165C2×C5×D4—42no—
166C2×C5×D4—42no—
167C2×C5×D4—42no—
168C2×C5×D4C2×Dic314yes—
169C2×C5×D4C2×Dic318yescomplemented
170C22×C4×C5—32no—
171C22×C4×C5—32no—
172C22×C4×C5—32no—
173C22×C4×C5—32no—
174C22×C4×C5—42no—
175C22×C4×C5—122no—
176C22×C4×C5—122no—
177C22×C4×C5—122no—
178C22×C4×C5C2×Dic314yescomplemented
179C22×C4×C5C22×D312yes—
180C22×C4×C5C22×D311yescharacteristic
181C22×C4×C5C22×D311yescharacteristic
182C5×C4⋊C4—122no—
183C5×C4⋊C4—122no—
184C5×C4⋊C4C2×Dic314yescomplemented
185C5×C22⋊C4—122no—
186C5×C22⋊C4—122no—
187C5×C22⋊C4—122no—
188C5×C22⋊C4—121no—
189C5×C22⋊C4—122no—
190C5×C22⋊C4—121no—
191C5×C22⋊C4C2×Dic318yescomplemented
192C42×C5—122no—
193C2×#121C5×D311yescharacteristic
194#390—32no—
195#388—32no—
196#387—32no—
197#386—32no—
198#386—32no—
199#385—32no—
200#381—31no—
201#380—31no—
202C22×C3×C5—22no—
203C22×C3×C5—22no—
204C22×C3×C5—24no—
205C22×C3×C5—24no—
206C22×C3×C5—22no—
207C22×C3×C5—24no—
208C22×C3×C5—42no—
209C22×C3×C5—42no—
210C22×C3×C5—42no—
211C22×C3×C5—42no—
212C22×C3×C5—42no—
213C22×C3×C5—42no—
214C22×C3×C5C23×C411yescharacteristic
215C22×C3×C5H(5,𝔽2)12yes—
216C22×C3×C5H(5,𝔽2)12yes—
217C22×C3×C5H(5,𝔽2)11yescharacteristic
218C22×C3×C52−1+411yescharacteristic
219C3×C4×C5—22no—
220C3×C4×C5—22no—
221C3×C4×C5—24no—
222C5×Dic3—42no—
223C5×Dic3—42no—
224C5×Dic3—42no—
225C5×Dic3—42no—
226C24×C3C23×C511yescharacteristic
227C24×C3C23×C512yes—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4C2×C4×C514yes—
232C2×C3×D4C2×C4×C518yescomplemented
233C22×C3×C4—42no—
234C22×C3×C4C2×C4×C514yescomplemented
235C22×C3×C4C23×C511yescharacteristic
236C22×C3×C4C23×C512yes—
237C22×C3×C4C23×C511yescharacteristic
238C22×Dic3—42no—
239C22×Dic3—42no—
240C22×Dic3—42no—
241C22×Dic3C23×C512yes—
242C22×Dic3C23×C512yes—
243C22×Dic3C23×C512yes—
244C22×Dic3C23×C512yes—
245C3×C4⋊C4C2×C4×C514yescomplemented
246C3×C22⋊C4C2×C4×C518yescomplemented
247#217—42no—
248#217—42no—
249#217—41no—
250#217—42no—
251#217—42no—
252#217—41no—
253C4⋊Dic3—42no—
254C4⋊Dic3—42no—
255C4×Dic3—42no—
256C23×C5—22no—
257C23×C5—22no—
258C23×C5—22no—
259C23×C5—22no—
260C23×C5—22no—
261C23×C5—22no—
262C23×C5—21no—
263C23×C5—22no—
264C23×C5—21no—
265C23×C5—22no—
266C23×C5C22×Dic314yes—
267C23×C5C22×Dic312yes—
268C23×C5C23×D311yescharacteristic
269C5×D4—44no—
270C5×D4—48no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—44no—
276C2×C4×C5—62no—
277C2×C4×C5—62no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5—62no—
281C2×C4×C5—62no—
282C2×C4×C5—62no—
283C2×C4×C5—62no—
284C2×C4×C5—62no—
285C2×C4×C5—62no—
286C2×C4×C5—62no—
287C2×C4×C5—62no—
288C2×C4×C5—128no—
289C2×C4×C5C22×Dic312yes—
290C2×C4×C5C22×Dic314yes—
291C2×C4×C5C22×Dic312yes—
292C22×D4C2×C5×D311yescharacteristic
293C22×D4C2×C5×D312yes—
294C23×C4—32no—
295C23×C4C2×C5×D311yescharacteristic
296#121C5×Dic318yescomplemented
297C2×C4⋊C4—32no—
298C2×C4⋊C4—32no—
299C2×C4⋊C4C2×C5×D311yescharacteristic
300C2×C22⋊C4—31no—
301C2×C22⋊C4—31no—
302C2×C22⋊C4—32no—
303C2×C22⋊C4—32no—
304C2×C22⋊C4—32no—
305C2×C22⋊C4—32no—
306C2×C22⋊C4C2×C5×D312yes—
307C2×C42—32no—
308#95—32no—
309#95—31no—
310#95—32no—
311#95—31no—
312#95—32no—
313#95—32no—
314C2×C3×C5—42no—
315C2×C3×C5—44no—
316C2×C3×C5#51811yescharacteristic
317C2×C3×C5#51811yescharacteristic
318C2×C3×C5#52011yescharacteristic
319C2×C3×C5#56012yes—
320C2×C3×C5#56212yes—
321C23×C3—21no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—21no—
330C23×C3—22no—
331C23×C3C22×C4×C514yes—
332C23×C3C22×C4×C512yes—
333C23×C3C24×C511yescharacteristic
334C3×D4—44no—
335C3×D4—48no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—44no—
341C2×C3×C4C22×C4×C512yes—
342C2×C3×C4C22×C4×C514yes—
343C2×C3×C4C22×C4×C512yes—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—48no—
357C22×C5—22no—
358C22×C5—22no—
359C22×C5—24no—
360C22×C5—24no—
361C22×C5—22no—
362C22×C5—24no—
363C22×C5—42no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5—42no—
367C22×C5—42no—
368C22×C5—42no—
369C22×C5#100412yes—
370C22×C5#100412yes—
371C22×C5#100911yescharacteristic
372C22×C5#101011yescharacteristic
373C22×C5C23×Dic311yescharacteristic
374C4×C5—22no—
375C4×C5—22no—
376C4×C5—24no—
377C4×C5—122no—
378C4×C5—122no—
379C4×C5—122no—
380C4×C5—122no—
381C24C22×C5×D311yescharacteristic
382C24C22×C5×D312yes—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4C2×C5×Dic314yes—
387C2×D4C2×C5×Dic318yescomplemented
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—32no—
391C22×C4—32no—
392C22×C4—42no—
393C22×C4—122no—
394C22×C4—122no—
395C22×C4—122no—
396C22×C4C2×C5×Dic314yescomplemented
397C22×C4C22×C5×D311yescharacteristic
398C22×C4C22×C5×D312yes—
399C22×C4C22×C5×D311yescharacteristic
400C4⋊C4—122no—
401C4⋊C4—122no—
402C4⋊C4C2×C5×Dic314yescomplemented
403C22⋊C4—122no—
404C22⋊C4—122no—
405C22⋊C4—122no—
406C22⋊C4—121no—
407C22⋊C4—122no—
408C22⋊C4—121no—
409C22⋊C4C2×C5×Dic318yescomplemented
410C42—122no—
411C3×C5#237711yescharacteristic, complemented, Hall
412C22×C3—22no—
413C22×C3—22no—
414C22×C3—24no—
415C22×C3—24no—
416C22×C3—22no—
417C22×C3—24no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3C23×C4×C511yescharacteristic
425C22×C3C5×H(5,𝔽2)12yes—
426C22×C3C5×H(5,𝔽2)12yes—
427C22×C3C5×H(5,𝔽2)11yescharacteristic
428C22×C3C5×2−1+411yescharacteristic
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—24no—
432Dic3—42no—
433Dic3—42no—
434Dic3—42no—
435Dic3—42no—
436C2×C5—42no—
437C2×C5—44no—
438C2×C5#562012yes—
439C2×C5#562112yes—
440C2×C5#579811yescharacteristic
441C2×C5#579811yescharacteristic
442C2×C5#582711yescharacteristic
443C23—22no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—21no—
450C23—22no—
451C23—21no—
452C23—22no—
453C23C22×C5×Dic314yes—
454C23C22×C5×Dic312yes—
455C23C23×C5×D311yescharacteristic
456D4—44no—
457D4—48no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—44no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—128no—
476C2×C4C22×C5×Dic312yes—
477C2×C4C22×C5×Dic314yes—
478C2×C4C22×C5×Dic312yes—
479C2×C3—42no—
480C2×C3—44no—
481C2×C3C5×#51811yescharacteristic
482C2×C3C5×#51811yescharacteristic
483C2×C3C5×#52011yescharacteristic
484C2×C3C5×#56012yes—
485C2×C3C5×#56212yes—
486C5#8263911yescharacteristic, direct product factor, Sylow
487C22—22no—
488C22—22no—
489C22—24no—
490C22—24no—
491C22—22no—
492C22—24no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22C5×#100412yes—
500C22C5×#100412yes—
501C22C5×#100911yescharacteristic
502C22C5×#101011yescharacteristic
503C22C23×C5×Dic311yescharacteristic
504C4—22no—
505C4—22no—
506C4—24no—
507C4—122no—
508C4—122no—
509C4—122no—
510C4—122no—
511C3C5×#237711yescharacteristic, complemented, Sylow
512C2—42no—
513C2—44no—
514C2C5×#562012yes—
515C2C5×#562112yes—
516C2C5×#579811yescharacteristic
517C2C5×#579811yescharacteristic
518C2C5×#582711yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
Fitting, prime radicalC2×C3×C5×#121C2
socleC23×C3×C5C24
cosocleC23×C3C24×C5
hypercenterC2×C5×#121D3
hypocenterC3C5×#2377
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×#121

Complements

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

NH ≅ G/Ntype
2. C5×#5221C2semidirect
3. C5×#5220C2semidirect
4. C5×#5220C2semidirect
5. C5×#5212C2semidirect
6. C5×#5211C2semidirect
7. C5×#4980C2semidirect
8. C5×#4951C2semidirect
9. C5×#4950C2semidirect
15. C3×C5×#121C4semidirect
33. #82639C5direct (N × H)
49. C2×C3×C5×D4C2×C4semidirect
51. C22×C3×C4×C5C2×C4semidirect
62. C3×C5×C4⋊C4C2×C4semidirect
63. C3×C5×C22⋊C4C2×C4semidirect
74. #5221C2×C5semidirect
75. #5220C2×C5semidirect
76. #5220C2×C5semidirect
77. #5212C2×C5semidirect
78. #5211C2×C5semidirect
79. #4980C2×C5semidirect
80. #4951C2×C5semidirect
81. #4950C2×C5semidirect
86. C5×#121Dic3semidirect
145. C3×#121C4×C5semidirect
169. C2×C5×D4C2×Dic3semidirect
178. C22×C4×C5C2×Dic3semidirect
184. C5×C4⋊C4C2×Dic3semidirect
191. C5×C22⋊C4C2×Dic3semidirect
232. C2×C3×D4C2×C4×C5semidirect
234. C22×C3×C4C2×C4×C5semidirect
245. C3×C4⋊C4C2×C4×C5semidirect
246. C3×C22⋊C4C2×C4×C5semidirect
296. #121C5×Dic3semidirect
387. C2×D4C2×C5×Dic3semidirect
396. C22×C4C2×C5×Dic3semidirect
402. C4⋊C4C2×C5×Dic3semidirect
409. C22⋊C4C2×C5×Dic3semidirect
411. C3×C5#2377semidirect
486. C5#82639direct (N × H)
511. C3C5×#2377semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1212
C5×#52212
C5×#52202
C5×#52122
C5×#52112
C5×#49802
C5×#49512
C5×#49502
C5×#23773
#826395