Finite Group Databasebeta

← C2×C3×D5⋊#100 #14412049

Subgroups — C2×C3×D5⋊#100 #14412049

Order 1920.

1984 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic
2C2×C3×D5⋊M16C212yesmaximal, complemented
3C2×C3×#4013C214yesmaximal, complemented
4C3×D5⋊#100C218yesmaximal, direct product factor
5C2×D5⋊#100C311yesmaximal, characteristic, direct product factor, Hall
6C24×C3×D5C412yes—
7C22×C3×C5×D4C411yescharacteristic
8C22×C3×C22⋊D5C2212yes—
9C2×C3×D4×D5—22no—
10C2×C3×D4×D5—22no—
11C2×C3×D4×D5—24no—
12C2×C3×D4×D5C414yes—
13C2×C3×D4×D5C2214yes—
14C22×C3×D20C411yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C2×C3×#704C2214yescomplemented
17C3×D5⋊M16—24no—
18C3×D5⋊M16C2218yescomplemented
19C2×C3×#700—22no—
20C2×C3×D5⋊C8—22no—
21C3×#4013C22116yescomplemented
22C22×C3×#100—51nomaximal, Hall
23C22×D4×D5C2×C311yescharacteristic
24C2×D5⋊M16C2×C312yescomplemented
25C2×#4013C2×C314yescomplemented
26D5⋊#100C2×C318yesdirect product factor
27C24×C3×C5C2×C412yes—
28C23×C3×D5—24no—
29C23×C3×D5—22no—
30C23×C3×D5—22no—
31C23×C3×D5—48no—
32C23×C3×D5C2×C411yescharacteristic
33C23×C3×D5C2×C412yes—
34C23×C3×D5C2×C418yes—
35C2×C3×C5×D4—22no—
36C2×C3×C5×D4—22no—
37C2×C3×C5×D4C2×C414yes—
38C22×C3×C4×C5C2×C411yescharacteristic
39C2×C3×C22⋊D5—24no—
40C2×C3×C22⋊D5—24no—
41C2×C3×C22⋊D5C2×C414yes—
42C2×C3×C22⋊D5C2314yes—
43C22×C3×Dic5C2311yescharacteristic
44C3×D4×D5—28no—
45C3×D4×D5—28no—
46C3×D4×D5—28no—
47C3×D4×D5—28no—
48C2×C3×D20—22no—
49C2×C3×D20—22no—
50C2×C3×D20C2×C414yes—
51C2×C3×C4×D5C2×C412yes—
52C2×C3×C4×D5D412yes—
53C2×C3×C4×D5D412yes—
54C2×C3×C4×D5D414yes—
55C2×C3×C4×D5C2312yes—
56C3×#704—24no—
57C3×#704C2318yescomplemented
58C2×C3×#170—24no—
59C3×#700—28no—
60C3×D5⋊C8—28no—
61C23×C3×D4—51no—
62C22×C3×M16—52no—
63C2×C3×#100—58no—
64C2×C3×#100—54no—
65C24×D5C3×C412yes—
66C22×C5×D4C3×C411yescharacteristic
67C22×C22⋊D5C22×C312yes—
68C2×D4×D5—22no—
69C2×D4×D5—22no—
70C2×D4×D5—24no—
71C2×D4×D5C3×C414yes—
72C2×D4×D5C22×C314yes—
73C22×D20C3×C411yescharacteristic
74C22×C4×D5C22×C311yescharacteristic
75C2×#704C22×C314yescomplemented
76D5⋊M16—24no—
77D5⋊M16C22×C318yescomplemented
78C2×#700—22no—
79C2×D5⋊C8—22no—
80#4013C22×C3116yescomplemented
81C22×#100—51noSylow
82C23×C3×C5—22no—
83C23×C3×C5—22no—
84C23×C3×C5—44no—
85C23×C3×C5C22×C411yescharacteristic
86C23×C3×C5C22×C414yes—
87C22×C3×D5—24no—
88C22×C3×D5—22no—
89C22×C3×D5—22no—
90C22×C3×D5—28no—
91C22×C3×D5—28no—
92C22×C3×D5—48no—
93C22×C3×D5—416no—
94C22×C3×D5—416no—
95C22×C3×D5—48no—
96C22×C3×D5—44no—
97C22×C3×D5C22⋊C411yescharacteristic
98C22×C3×D5C22⋊C412yes—
99C22×C3×D5C22⋊C411yescharacteristic
100C22×C3×D5C22×C412yes—
101C22×C3×D5C22×C414yes—
102C3×C5×D4—28no—
103C2×C3×C4×C5C22⋊C412yes—
104C2×C3×C4×C5C22⋊C412yes—
105C2×C3×C4×C5C22×C412yes—
106C3×C22⋊D5—28no—
107C3×C22⋊D5—28no—
108C2×C3×Dic5C22×C411yescharacteristic
109C2×C3×Dic5C2×D412yes—
110C2×C3×Dic5C2×D412yes—
111C2×C3×Dic5C2411yescharacteristic
112C3×D20—28no—
113C3×C4×D5C22⋊C414yes—
114C3×C4×D5C22⋊C414yes—
115C3×C4×D5C2×D414yes—
116C3×C4×D5C2×D414yes—
117C3×#170—28no—
118C25×C3—52no—
119C22×C3×D4—52no—
120C22×C3×D4—54no—
121C22×C3×D4—54no—
122C22×C3×D4—51no—
123C22×C3×D4—102no—
124C22×C3×D4—104no—
125C22×C3×D4—102no—
126C22×C3×D4AGL(1,𝔽5)11yescharacteristic
127C23×C3×C4—51no—
128C2×C3×M16—58no—
129C2×C3×M16—54no—
130C2×C3×M16—102no—
131C2×C3×M16—104no—
132C22×C3×C8—102no—
133C3×#100—516no—
134C24×C5C2×C3×C412yes—
135C23×D5—24no—
136C23×D5—22no—
137C23×D5—22no—
138C23×D5—48no—
139C23×D5C2×C3×C411yescharacteristic
140C23×D5C2×C3×C412yes—
141C23×D5C2×C3×C418yes—
142C2×C5×D4—22no—
143C2×C5×D4—22no—
144C2×C5×D4C2×C3×C414yes—
145C22×C4×C5C2×C3×C411yescharacteristic
146C2×C22⋊D5—24no—
147C2×C22⋊D5—24no—
148C2×C22⋊D5C2×C3×C414yes—
149C2×C22⋊D5C23×C314yes—
150C22×Dic5C23×C311yescharacteristic
151D4×D5—28no—
152D4×D5—28no—
153D4×D5—28no—
154D4×D5—28no—
155C2×D20—22no—
156C2×D20—22no—
157C2×D20C2×C3×C414yes—
158C2×C4×D5C2×C3×C412yes—
159C2×C4×D5C3×D412yes—
160C2×C4×D5C3×D412yes—
161C2×C4×D5C3×D414yes—
162C2×C4×D5C23×C312yes—
163#704—24no—
164#704C23×C318yescomplemented
165C2×#170—24no—
166#700—28no—
167D5⋊C8—28no—
168C23×D4—51no—
169C22×M16—52no—
170C2×#100—54no—
171C2×#100—58no—
172C22×C3×C5—22no—
173C22×C3×C5—24no—
174C22×C3×C5—44no—
175C22×C3×C5—44no—
176C22×C3×C5—44no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C22×C3×C5C23×C411yescharacteristic
180C2×C3×D5—22no—
181C2×C3×D5—24no—
182C2×C3×D5—24no—
183C2×C3×D5—24no—
184C2×C3×D5—416no—
185C2×C3×D5—44no—
186C2×C3×D5—44no—
187C2×C3×D5—416no—
188C2×C3×D5—44no—
189C2×C3×D5#10014yescomplemented
190C2×C3×D5C2×C22⋊C412yes—
191C2×C3×D5C2×C22⋊C412yes—
192C3×C4×C5C2×C22⋊C414yes—
193C3×Dic5C2×C22⋊C412yes—
194C3×Dic5C22×D412yes—
195C24×C3—51no—
196C24×C3—58no—
197C24×C3—52no—
198C24×C3—104no—
199C24×C3—102no—
200C24×C3—102no—
201C24×C3—208no—
202C24×C3C2×AGL(1,𝔽5)12yes—
203C2×C3×D4—22no—
204C2×C3×D4—22no—
205C2×C3×D4—54no—
206C2×C3×D4—54no—
207C2×C3×D4—54no—
208C2×C3×D4—108no—
209C2×C3×D4—108no—
210C2×C3×D4—108no—
211C2×C3×D4—108no—
212C2×C3×D4—104no—
213C2×C3×D4—104no—
214C2×C3×D4—102no—
215C2×C3×D4—102no—
216C2×C3×D4C2×AGL(1,𝔽5)14yes—
217C22×C3×C4—51no—
218C22×C3×C4—52no—
219C22×C3×C4—54no—
220C22×C3×C4—52no—
221C22×C3×C4—52no—
222C22×C3×C4—52no—
223C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
224C3×M16—58no—
225C3×M16—108no—
226C3×M16—104no—
227C2×C3×C8—108no—
228C2×C3×C8—104no—
229C23×C5—22no—
230C23×C5—22no—
231C23×C5—44no—
232C23×C5C22×C3×C411yescharacteristic
233C23×C5C22×C3×C414yes—
234C22×D5—24no—
235C22×D5—22no—
236C22×D5—22no—
237C22×D5—28no—
238C22×D5—28no—
239C22×D5—48no—
240C22×D5—416no—
241C22×D5—416no—
242C22×D5—48no—
243C22×D5—44no—
244C22×D5C3×C22⋊C411yescharacteristic
245C22×D5C3×C22⋊C412yes—
246C22×D5C3×C22⋊C411yescharacteristic
247C22×D5C22×C3×C412yes—
248C22×D5C22×C3×C414yes—
249C5×D4—28no—
250C2×C4×C5C3×C22⋊C412yes—
251C2×C4×C5C3×C22⋊C412yes—
252C2×C4×C5C22×C3×C412yes—
253C22⋊D5—28no—
254C22⋊D5—28no—
255C2×Dic5C22×C3×C411yescharacteristic
256C2×Dic5C2×C3×D412yes—
257C2×Dic5C2×C3×D412yes—
258C2×Dic5C24×C311yescharacteristic
259D20—28no—
260C4×D5C3×C22⋊C414yes—
261C4×D5C3×C22⋊C414yes—
262C4×D5C2×C3×D414yes—
263C4×D5C2×C3×D414yes—
264#170—28no—
265C25—52no—
266C22×D4—52no—
267C22×D4—54no—
268C22×D4—54no—
269C22×D4—51no—
270C22×D4—102no—
271C22×D4—102no—
272C22×D4—104no—
273C22×D4C3×AGL(1,𝔽5)11yescharacteristic
274C23×C4—51no—
275C2×M16—58no—
276C2×M16—54no—
277C2×M16—102no—
278C2×M16—104no—
279C22×C8—102no—
280#100—516no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5—44no—
284C2×C3×C5C2×#10012yescomplemented
285C2×C3×C5C22×C22⋊C411yescharacteristic
286C3×D5—22no—
287C3×D5—44no—
288C3×D5C2×#10014yescomplemented
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—44no—
292C23×C3—51no—
293C23×C3—52no—
294C23×C3—51no—
295C23×C3—52no—
296C23×C3—54no—
297C23×C3—104no—
298C23×C3—108no—
299C23×C3—108no—
300C23×C3—102no—
301C23×C3—102no—
302C23×C3—204no—
303C23×C3—208no—
304C23×C3—2016no—
305C23×C3—2016no—
306C23×C3—208no—
307C23×C3C22×AGL(1,𝔽5)11yescharacteristic
308C23×C3C22×AGL(1,𝔽5)14yes—
309C3×D4—28no—
310C3×D4—108no—
311C3×D4—108no—
312C3×D4—108no—
313C2×C3×C4—52no—
314C2×C3×C4—52no—
315C2×C3×C4—51no—
316C2×C3×C4—51no—
317C2×C3×C4—54no—
318C2×C3×C4—54no—
319C2×C3×C4—54no—
320C2×C3×C4—54no—
321C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
322C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
323C2×C3×C4C22×AGL(1,𝔽5)12yes—
324C3×C8—108no—
325C22×C5—22no—
326C22×C5—24no—
327C22×C5—44no—
328C22×C5—44no—
329C22×C5—44no—
330C22×C5C2×C3×C22⋊C411yescharacteristic
331C22×C5C2×C3×C22⋊C411yescharacteristic
332C22×C5C23×C3×C411yescharacteristic
333C2×D5—22no—
334C2×D5—24no—
335C2×D5—24no—
336C2×D5—24no—
337C2×D5—416no—
338C2×D5—44no—
339C2×D5—44no—
340C2×D5—416no—
341C2×D5—44no—
342C2×D5C3×#10014yescomplemented
343C2×D5C2×C3×C22⋊C412yes—
344C2×D5C2×C3×C22⋊C412yes—
345C4×C5C2×C3×C22⋊C414yes—
346Dic5C2×C3×C22⋊C412yes—
347Dic5C22×C3×D412yes—
348C24—51no—
349C24—58no—
350C24—52no—
351C24—102no—
352C24—104no—
353C24—102no—
354C24—208no—
355C24C2×C3×AGL(1,𝔽5)12yes—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—54no—
359C2×D4—54no—
360C2×D4—54no—
361C2×D4—108no—
362C2×D4—108no—
363C2×D4—108no—
364C2×D4—108no—
365C2×D4—104no—
366C2×D4—104no—
367C2×D4—102no—
368C2×D4—102no—
369C2×D4C2×C3×AGL(1,𝔽5)14yes—
370C22×C4—51no—
371C22×C4—52no—
372C22×C4—52no—
373C22×C4—54no—
374C22×C4—52no—
375C22×C4—52no—
376C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
377M16—58no—
378M16—108no—
379M16—104no—
380C2×C8—108no—
381C2×C8—104no—
382C3×C5C22×#10011yescharacteristic, complemented, Hall
383C22×C3—22no—
384C22×C3—24no—
385C22×C3—44no—
386C22×C3—44no—
387C22×C3—44no—
388C22×C3—52no—
389C22×C3—54no—
390C22×C3—52no—
391C22×C3—104no—
392C22×C3—104no—
393C22×C3—102no—
394C22×C3—104no—
395C22×C3—204no—
396C22×C3—204no—
397C22×C3—2016no—
398C22×C3—2016no—
399C22×C3—204no—
400C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
401C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
402C22×C3C23×AGL(1,𝔽5)11yescharacteristic
403C3×C4—52no—
404C3×C4—52no—
405C3×C4C2×C22⋊AGL(1,𝔽5)14yes—
406C2×C5—21no—
407C2×C5—21no—
408C2×C5—44no—
409C2×C5C2×C3×#10012yescomplemented
410C2×C5C22×C3×C22⋊C411yescharacteristic
411D5—22no—
412D5—44no—
413D5C2×C3×#10014yescomplemented
414C23—22no—
415C23—22no—
416C23—44no—
417C23—51no—
418C23—52no—
419C23—51no—
420C23—52no—
421C23—54no—
422C23—104no—
423C23—108no—
424C23—108no—
425C23—102no—
426C23—102no—
427C23—204no—
428C23—208no—
429C23—2016no—
430C23—2016no—
431C23—208no—
432C23C22×C3×AGL(1,𝔽5)11yescharacteristic
433C23C22×C3×AGL(1,𝔽5)14yes—
434D4—28no—
435D4—108no—
436D4—108no—
437D4—108no—
438C2×C4—52no—
439C2×C4—52no—
440C2×C4—51no—
441C2×C4—51no—
442C2×C4—54no—
443C2×C4—54no—
444C2×C4—54no—
445C2×C4—54no—
446C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
447C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
448C2×C4C22×C3×AGL(1,𝔽5)12yes—
449C8—108no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—44no—
453C2×C3—54no—
454C2×C3—102no—
455C2×C3—204no—
456C2×C3D5⋊#10012yesdirect product factor
457C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
458C5C22×C3×#10011yescharacteristic, complemented, Sylow
459C22—22no—
460C22—24no—
461C22—44no—
462C22—44no—
463C22—44no—
464C22—54no—
465C22—52no—
466C22—52no—
467C22—104no—
468C22—104no—
469C22—102no—
470C22—104no—
471C22—204no—
472C22—204no—
473C22—2016no—
474C22—2016no—
475C22—204no—
476C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
477C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
478C22C23×C3×AGL(1,𝔽5)11yescharacteristic
479C4—52no—
480C4—52no—
481C4C2×C3×C22⋊AGL(1,𝔽5)14yes—
482C3C2×D5⋊#10011yescharacteristic, direct product factor, Sylow
483C2—21no—
484C2—21no—
485C2—44no—
486C2—54no—
487C2—102no—
488C2—204no—
489C2C3×D5⋊#10012yesdirect product factor
490C2C22×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D4×D5C2
cosocleC2×Dic5C24×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C22×C3×#100
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5⋊M16C2semidirect
3. C2×C3×#4013C2semidirect
4. C3×D5⋊#100C2direct (N × H)
5. C2×D5⋊#100C3direct (N × H)
16. C2×C3×#704C22semidirect
18. C3×D5⋊M16C22semidirect
21. C3×#4013C22semidirect
24. C2×D5⋊M16C2×C3semidirect
25. C2×#4013C2×C3semidirect
26. D5⋊#100C2×C3direct (N × H)
57. C3×#704C23semidirect
75. C2×#704C22×C3semidirect
77. D5⋊M16C22×C3semidirect
80. #4013C22×C3semidirect
164. #704C23×C3semidirect
189. C2×C3×D5#100semidirect
284. C2×C3×C5C2×#100semidirect
288. C3×D5C2×#100semidirect
342. C2×D5C3×#100semidirect
382. C3×C5C22×#100semidirect
409. C2×C5C2×C3×#100semidirect
413. D5C2×C3×#100semidirect
456. C2×C3D5⋊#100direct (N × H)
458. C5C22×C3×#100semidirect
482. C3C2×D5⋊#100direct (N × H)
489. C2C3×D5⋊#100direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C2×C3×D5⋊M162
C2×C3×#40132
C3×D5⋊#1002
C2×D5⋊#1003
C22×C3×#1005