Finite Group Databasebeta

← C2×C5×#4647 #14320708

Subgroups — C2×C5×#4647 #14320708

Order 1920.

1600 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
1C22×C5×C4⋊Dic3C211yesmaximal, characteristic
2C22×C5×Dic3⋊C4C211yesmaximal, characteristic
3C22×C5×Dic3⋊C4C211yesmaximal, characteristic
4C22×C5×Dic3⋊C4C211yesmaximal, characteristic
5C22×C4×C5×Dic3C211yesmaximal, characteristic
6C2×C3×C5×#95C211yesmaximal, characteristic
7C2×C5×C3⋊#95C211yesmaximal, characteristic
8C5×#4647C218yesmaximal, direct product factor
9C2×C5×#389—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C5×Dic3C2211yescharacteristic
17C2×C5×C4⋊Dic3—24no—
18C2×C5×C4⋊Dic3C2214yes—
19C2×C5×Dic3⋊C4—24no—
20C2×C5×Dic3⋊C4—24no—
21C2×C5×Dic3⋊C4C418yescomplemented
22C2×C5×Dic3⋊C4C2214yes—
23C2×C5×Dic3⋊C4C2214yes—
24C2×C5×Dic3⋊C4C2214yes—
25C2×C4×C5×Dic3—24no—
26C2×C4×C5×Dic3C2214yes—
27C3×C5×#95C2214yes—
28C5×C3⋊#95C2214yes—
29C2×#4647C511yesmaximal, characteristic, direct product factor, Hall
30C22×C5×C4⋊C4—31no—
31C22×C5×C4⋊C4—31no—
32C22×C5×C4⋊C4—31no—
33C22×C5×C4⋊C4—31no—
34C22×C42×C5—31no—
35C5×#389—38no—
36C2×C5×#95—31no—
37C2×C5×#95D311yescharacteristic
38C24×C3×C5C2311yescharacteristic
39C22×C3×C4×C5—22no—
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5—22no—
43C22×C3×C4×C5—22no—
44C22×C3×C4×C5—22no—
45C22×C3×C4×C5—22no—
46C22×C3×C4×C5C2×C414yes—
47C22×C3×C4×C5Q814yes—
48C22×C3×C4×C5C2312yes—
49C22×C3×C4×C5C2312yes—
50C22×C3×C4×C5C2312yes—
51C22×C5×Dic3—22no—
52C22×C5×Dic3—22no—
53C22×C5×Dic3—22no—
54C22×C5×Dic3—22no—
55C22×C5×Dic3—22no—
56C22×C5×Dic3—22no—
57C22×C5×Dic3—22no—
58C22×C5×Dic3C2×C414yes—
59C22×C5×Dic3C2×C414yes—
60C22×C5×Dic3D414yes—
61C22×C5×Dic3D414yes—
62C22×C5×Dic3Q814yes—
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2312yes—
65C22×C5×Dic3C2312yes—
66C22×C5×Dic3C2312yes—
67C5×C4⋊Dic3—28no—
68C5×Dic3⋊C4—28no—
69C5×Dic3⋊C4—28no—
70C5×Dic3⋊C4C2×C4116yescomplemented
71C4×C5×Dic3—28no—
72C22×C4⋊Dic3C2×C511yescharacteristic
73C22×Dic3⋊C4C2×C511yescharacteristic
74C22×Dic3⋊C4C2×C511yescharacteristic
75C22×Dic3⋊C4C2×C511yescharacteristic
76C22×C4×Dic3C2×C511yescharacteristic
77C2×C3×#95C2×C511yescharacteristic
78C2×C3⋊#95C2×C511yescharacteristic
79#4647C2×C518yesdirect product factor
80C23×C4×C5—31no—
81C23×C4×C5—31no—
82C23×C4×C5—31no—
83C23×C4×C5—31no—
84C23×C4×C5C2×D311yescharacteristic
85C23×C4×C5C2×D311yescharacteristic
86C23×C4×C5C2×D311yescharacteristic
87C2×C5×C4⋊C4—38no—
88C2×C5×C4⋊C4—34no—
89C2×C5×C4⋊C4—34no—
90C2×C5×C4⋊C4—34no—
91C2×C5×C4⋊C4—34no—
92C2×C5×C4⋊C4—64no—
93C2×C5×C4⋊C4—64no—
94C2×C5×C4⋊C4—64no—
95C2×C42×C5—34no—
96C2×C42×C5—64no—
97C5×#95—34no—
98C5×#95C2×D314yes—
99C2×#389—31noSylow
100C23×C3×C5C22×C412yes—
101C23×C3×C5C2×D412yes—
102C23×C3×C5C2×D412yes—
103C23×C3×C5C2×Q812yes—
104C23×C3×C5C2×Q812yes—
105C23×C3×C5#4112yes—
106C23×C3×C5#4112yes—
107C23×C3×C5C2411yescharacteristic
108C2×C3×C4×C5—28no—
109C2×C3×C4×C5—28no—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—22no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—44no—
118C2×C3×C4×C5C22×C414yes—
119C2×C3×C4×C5C2×Q814yes—
120C2×C5×Dic3—28no—
121C2×C5×Dic3—28no—
122C2×C5×Dic3—22no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3—22no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—22no—
128C2×C5×Dic3—22no—
129C2×C5×Dic3—44no—
130C2×C5×Dic3C4⋊C4116yescomplemented
131C2×C5×Dic3C22×C414yes—
132C2×C5×Dic3C22×C414yes—
133C2×C5×Dic3C2×D414yes—
134C2×C5×Dic3C2×D414yes—
135C2×C5×Dic3C2×Q814yes—
136C23×C3×C4C22×C511yescharacteristic
137C23×C3×C4C22×C511yescharacteristic
138C23×C3×C4C22×C511yescharacteristic
139C23×Dic3C22×C511yescharacteristic
140C23×Dic3C22×C511yescharacteristic
141C23×Dic3C22×C511yescharacteristic
142C23×Dic3C22×C511yescharacteristic
143C2×C4⋊Dic3—24no—
144C2×C4⋊Dic3C22×C514yes—
145C2×Dic3⋊C4—24no—
146C2×Dic3⋊C4—24no—
147C2×Dic3⋊C4C4×C518yescomplemented
148C2×Dic3⋊C4C22×C514yes—
149C2×Dic3⋊C4C22×C514yes—
150C2×Dic3⋊C4C22×C514yes—
151C2×C4×Dic3—24no—
152C2×C4×Dic3C22×C514yes—
153C3×#95C22×C514yes—
154C3⋊#95C22×C514yes—
155C24×C5C22×D311yescharacteristic
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—34no—
164C22×C4×C5—34no—
165C22×C4×C5—34no—
166C22×C4×C5—32no—
167C22×C4×C5—34no—
168C22×C4×C5—34no—
169C22×C4×C5—32no—
170C22×C4×C5—32no—
171C22×C4×C5—32no—
172C22×C4×C5—62no—
173C22×C4×C5—62no—
174C22×C4×C5—62no—
175C22×C4×C5—62no—
176C22×C4×C5—62no—
177C22×C4×C5—62no—
178C22×C4×C5—62no—
179C22×C4×C5Dic614yes—
180C22×C4×C5C4×D314yes—
181C22×C4×C5C22×D312yes—
182C22×C4×C5C22×D312yes—
183C22×C4×C5C22×D312yes—
184C5×C4⋊C4—316no—
185C5×C4⋊C4—68no—
186C5×C4⋊C4—68no—
187C5×C4⋊C4—68no—
188C42×C5—68no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C42—31no—
194#389—38no—
195C2×#95—31no—
196C2×#95C5×D311yescharacteristic
197C22×C3×C5C2×C4⋊C414yes—
198C22×C3×C5C4×D414yes—
199C22×C3×C5C4×Q814yes—
200C22×C3×C5#12114yes—
201C22×C3×C5C22⋊Q814yes—
202C22×C3×C5#12514yes—
203C22×C3×C5C4⋊Q814yes—
204C22×C3×C5C23×C411yescharacteristic
205C22×C3×C5C22×D411yescharacteristic
206C22×C3×C5C22×D411yescharacteristic
207C22×C3×C5C22×Q811yescharacteristic
208C22×C3×C5C22×Q811yescharacteristic
209C22×C3×C5C2×#4111yescharacteristic
210C22×C3×C5C2×#4111yescharacteristic
211C3×C4×C5—24no—
212C3×C4×C5—24no—
213C3×C4×C5—42no—
214C5×Dic3—24no—
215C5×Dic3—24no—
216C5×Dic3—42no—
217C5×Dic3C2×C4⋊C418yescomplemented
218C24×C3C23×C511yescharacteristic
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4C2×C4×C514yes—
227C22×C3×C4C5×Q814yes—
228C22×C3×C4C23×C512yes—
229C22×C3×C4C23×C512yes—
230C22×C3×C4C23×C512yes—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3C2×C4×C514yes—
239C22×Dic3C2×C4×C514yes—
240C22×Dic3C5×D414yes—
241C22×Dic3C5×D414yes—
242C22×Dic3C5×Q814yes—
243C22×Dic3C23×C512yes—
244C22×Dic3C23×C512yes—
245C22×Dic3C23×C512yes—
246C22×Dic3C23×C512yes—
247C4⋊Dic3—28no—
248Dic3⋊C4—28no—
249Dic3⋊C4—28no—
250Dic3⋊C4C2×C4×C5116yescomplemented
251C4×Dic3—28no—
252C23×C5C2×Dic612yes—
253C23×C5C2×C4×D312yes—
254C23×C5#23512yes—
255C23×C5D3×D412yes—
256C23×C5D3×D412yes—
257C23×C5#23712yes—
258C23×C5D3×Q812yes—
259C23×C5C23×D311yescharacteristic
260C2×C4×C5—28no—
261C2×C4×C5—28no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—316no—
270C2×C4×C5—34no—
271C2×C4×C5—34no—
272C2×C4×C5—34no—
273C2×C4×C5—34no—
274C2×C4×C5—34no—
275C2×C4×C5—44no—
276C2×C4×C5—68no—
277C2×C4×C5—68no—
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—124no—
286C2×C4×C5C2×Dic614yes—
287C2×C4×C5C2×C4×D314yes—
288C23×C4—31no—
289C23×C4—31no—
290C23×C4—31no—
291C23×C4—31no—
292C23×C4C2×C5×D311yescharacteristic
293C23×C4C2×C5×D311yescharacteristic
294C23×C4C2×C5×D311yescharacteristic
295C2×C4⋊C4—38no—
296C2×C4⋊C4—34no—
297C2×C4⋊C4—34no—
298C2×C4⋊C4—34no—
299C2×C4⋊C4—34no—
300C2×C4⋊C4—64no—
301C2×C4⋊C4—64no—
302C2×C4⋊C4—64no—
303C2×C42—34no—
304C2×C42—64no—
305#95—34no—
306#95C2×C5×D314yes—
307C2×C3×C5#38918yescomplemented
308C2×C3×C5C22×C4⋊C411yescharacteristic
309C2×C3×C5C2×C4×D411yescharacteristic
310C2×C3×C5C2×C4×Q811yescharacteristic
311C2×C3×C5C2×#12111yescharacteristic
312C2×C3×C5C2×C22⋊Q811yescharacteristic
313C2×C3×C5C2×#12511yescharacteristic
314C2×C3×C5C2×C4⋊Q811yescharacteristic
315C23×C3C22×C4×C512yes—
316C23×C3C2×C5×D412yes—
317C23×C3C2×C5×D412yes—
318C23×C3C2×C5×Q812yes—
319C23×C3C2×C5×Q812yes—
320C23×C3C5×#4112yes—
321C23×C3C5×#4112yes—
322C23×C3C24×C511yescharacteristic
323C2×C3×C4—28no—
324C2×C3×C4—28no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—44no—
333C2×C3×C4C22×C4×C514yes—
334C2×C3×C4C2×C5×Q814yes—
335C2×Dic3—28no—
336C2×Dic3—28no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—44no—
345C2×Dic3C5×C4⋊C4116yescomplemented
346C2×Dic3C22×C4×C514yes—
347C2×Dic3C22×C4×C514yes—
348C2×Dic3C2×C5×D414yes—
349C2×Dic3C2×C5×D414yes—
350C2×Dic3C2×C5×Q814yes—
351C22×C5C4×Dic614yes—
352C22×C5#87814yes—
353C22×C5#67⋊C414yes—
354C22×C5#88414yes—
355C22×C5#88814yes—
356C22×C5#88914yes—
357C22×C5D3×C4⋊C414yes—
358C22×C5C22×Dic611yescharacteristic
359C22×C5C22×C4×D311yescharacteristic
360C22×C5C2×#23511yescharacteristic
361C22×C5C2×D3×D411yescharacteristic
362C22×C5C2×D3×D411yescharacteristic
363C22×C5C2×#23711yescharacteristic
364C22×C5C2×D3×Q811yescharacteristic
365C4×C5—24no—
366C4×C5—24no—
367C4×C5—38no—
368C4×C5—42no—
369C4×C5—64no—
370C4×C5—64no—
371C4×C5—122no—
372C24C22×C5×D311yescharacteristic
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—34no—
381C22×C4—34no—
382C22×C4—34no—
383C22×C4—32no—
384C22×C4—34no—
385C22×C4—34no—
386C22×C4—32no—
387C22×C4—32no—
388C22×C4—32no—
389C22×C4—62no—
390C22×C4—62no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4C5×Dic614yes—
397C22×C4C4×C5×D314yes—
398C22×C4C22×C5×D312yes—
399C22×C4C22×C5×D312yes—
400C22×C4C22×C5×D312yes—
401C4⋊C4—316no—
402C4⋊C4—68no—
403C4⋊C4—68no—
404C4⋊C4—68no—
405C42—68no—
406C3×C5C2×#38911yescharacteristic, complemented, Hall
407C22×C3C2×C5×C4⋊C414yes—
408C22×C3C4×C5×D414yes—
409C22×C3C4×C5×Q814yes—
410C22×C3C5×#12114yes—
411C22×C3C5×C22⋊Q814yes—
412C22×C3C5×#12514yes—
413C22×C3C5×C4⋊Q814yes—
414C22×C3C23×C4×C511yescharacteristic
415C22×C3C22×C5×D411yescharacteristic
416C22×C3C22×C5×D411yescharacteristic
417C22×C3C22×C5×Q811yescharacteristic
418C22×C3C22×C5×Q811yescharacteristic
419C22×C3C2×C5×#4111yescharacteristic
420C22×C3C2×C5×#4111yescharacteristic
421C3×C4—24no—
422C3×C4—24no—
423C3×C4—42no—
424Dic3—24no—
425Dic3—24no—
426Dic3—42no—
427Dic3C2×C5×C4⋊C418yescomplemented
428C2×C5#464718yesdirect product factor
429C2×C5C2×C4×Dic611yescharacteristic
430C2×C5C2×#87811yescharacteristic
431C2×C5C2×#67⋊C411yescharacteristic
432C2×C5C2×#88411yescharacteristic
433C2×C5C2×#88811yescharacteristic
434C2×C5C2×#88911yescharacteristic
435C2×C5C2×D3×C4⋊C411yescharacteristic
436C23C2×C5×Dic612yes—
437C23C2×C4×C5×D312yes—
438C23C5×#23512yes—
439C23C5×D3×D412yes—
440C23C5×D3×D412yes—
441C23C5×#23712yes—
442C23C5×D3×Q812yes—
443C23C23×C5×D311yescharacteristic
444C2×C4—28no—
445C2×C4—28no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—316no—
454C2×C4—34no—
455C2×C4—34no—
456C2×C4—34no—
457C2×C4—34no—
458C2×C4—34no—
459C2×C4—44no—
460C2×C4—68no—
461C2×C4—68no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—124no—
470C2×C4C2×C5×Dic614yes—
471C2×C4C2×C4×C5×D314yes—
472C2×C3C5×#38918yescomplemented
473C2×C3C22×C5×C4⋊C411yescharacteristic
474C2×C3C2×C4×C5×D411yescharacteristic
475C2×C3C2×C4×C5×Q811yescharacteristic
476C2×C3C2×C5×#12111yescharacteristic
477C2×C3C2×C5×C22⋊Q811yescharacteristic
478C2×C3C2×C5×#12511yescharacteristic
479C2×C3C2×C5×C4⋊Q811yescharacteristic
480C5C2×#464711yescharacteristic, direct product factor, Sylow
481C22C4×C5×Dic614yes—
482C22C5×#87814yes—
483C22C5×#67⋊C414yes—
484C22C5×#88414yes—
485C22C5×#88814yes—
486C22C5×#88914yes—
487C22C5×D3×C4⋊C414yes—
488C22C22×C5×Dic611yescharacteristic
489C22C22×C4×C5×D311yescharacteristic
490C22C2×C5×#23511yescharacteristic
491C22C2×C5×D3×D411yescharacteristic
492C22C2×C5×D3×D411yescharacteristic
493C22C2×C5×#23711yescharacteristic
494C22C2×C5×D3×Q811yescharacteristic
495C4—24no—
496C4—24no—
497C4—38no—
498C4—42no—
499C4—64no—
500C4—64no—
501C4—122no—
502C3C2×C5×#38911yescharacteristic, complemented, Sylow
503C2C5×#464718yesdirect product factor
504C2C2×C4×C5×Dic611yescharacteristic
505C2C2×C5×#87811yescharacteristic
506C2C2×C5×#67⋊C411yescharacteristic
507C2C2×C5×#88411yescharacteristic
508C2C2×C5×#88811yescharacteristic
509C2C2×C5×#88911yescharacteristic
510C2C2×C5×D3×C4⋊C411yescharacteristic
subgroupG/H
centerC24×C5C22×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC2×C3×C5×#95C2
socle, prime radicalC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC2×C5×#95D3
hypocenterC3C2×C5×#389
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C2×C5×#95

Complements

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

NH ≅ G/Ntype
8. C5×#4647C2direct (N × H)
21. C2×C5×Dic3⋊C4C4semidirect
29. C2×#4647C5direct (N × H)
70. C5×Dic3⋊C4C2×C4semidirect
79. #4647C2×C5direct (N × H)
130. C2×C5×Dic3C4⋊C4semidirect
147. C2×Dic3⋊C4C4×C5semidirect
217. C5×Dic3C2×C4⋊C4semidirect
250. Dic3⋊C4C2×C4×C5semidirect
307. C2×C3×C5#389semidirect
345. C2×Dic3C5×C4⋊C4semidirect
406. C3×C5C2×#389semidirect
427. Dic3C2×C5×C4⋊C4semidirect
428. C2×C5#4647direct (N × H)
472. C2×C3C5×#389semidirect
480. C5C2×#4647direct (N × H)
502. C3C2×C5×#389semidirect
503. C2C5×#4647direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C4⋊Dic32
C22×C5×Dic3⋊C42
C22×C4×C5×Dic32
C2×C3×C5×#952
C2×C5×C3⋊#952
C5×#46472
C2×C5×#3893
C2×#46475