Finite Group Databasebeta

← C3×D5⋊#323 #14280747

Subgroups — C3×D5⋊#323 #14280747

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
2C3×D5⋊(C22⋊C8)C212yesmaximal, complemented
3C3×#64933C212yesmaximal, complemented
4C3×#64915C212yesmaximal, complemented
5D5⋊#323C311yesmaximal, characteristic, direct product factor, Hall
6C24×C3×D5C411yescharacteristic
7C22×C3×C4×D5C411yescharacteristic
8C22×C3×C4×D5C2211yescharacteristic
9C2×C3×D5⋊C8—22no—
10C2×C3×C5×C22⋊C4C411yescharacteristic
11C2×C3×C22⋊Dic5C2211yescharacteristic
12C2×C3×#685C411yescharacteristic
13C2×C3×#685C2211yescharacteristic
14C3×D5×C22⋊C4—22no—
15C3×D5×C22⋊C4—22no—
16C3×C22⋊#170C2214yescomplemented
17C3×#4003—22no—
18C2×C3×#323—51nomaximal, Hall
19C2×D5×C22⋊C4C2×C311yescharacteristic
20D5⋊(C22⋊C8)C2×C312yescomplemented
21#64933C2×C312yescomplemented
22#64915C2×C312yescomplemented
23C24×C3×C5C2×C411yescharacteristic
24C23×C3×D5—21no—
25C23×C3×D5—21no—
26C23×C3×D5—22no—
27C23×C3×D5—42no—
28C23×C3×D5—42no—
29C23×C3×D5C814yescomplemented
30C23×C3×D5C2×C411yescharacteristic
31C23×C3×D5C2×C411yescharacteristic
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×Dic5C2×C411yescharacteristic
35C22×C3×Dic5C2311yescharacteristic
36C2×C3×C4×D5—21no—
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—42no—
39C2×C3×C4×D5—42no—
40C2×C3×C4×D5D412yes—
41C2×C3×C4×D5D412yes—
42C2×C3×#170—24no—
43C3×D5⋊C8—44no—
44C3×C5×C22⋊C4—22no—
45C3×C22⋊Dic5—22no—
46C3×#685—22no—
47C3×#685—22no—
48C22×C3×C22⋊C4—51no—
49C2×C3×C22⋊C8—52no—
50C3×#323—52no—
51C3×#323—52no—
52C24×D5C3×C411yescharacteristic
53C22×C4×D5C3×C411yescharacteristic
54C22×C4×D5C22×C311yescharacteristic
55C2×D5⋊C8—22no—
56C2×C5×C22⋊C4C3×C411yescharacteristic
57C2×C22⋊Dic5C22×C311yescharacteristic
58C2×#685C3×C411yescharacteristic
59C2×#685C22×C311yescharacteristic
60D5×C22⋊C4—22no—
61D5×C22⋊C4—22no—
62C22⋊#170C22×C314yescomplemented
63#4003—22no—
64C2×#323—51noSylow
65C23×C3×C5—21no—
66C23×C3×C5—21no—
67C23×C3×C5—41no—
68C23×C3×C5—41no—
69C23×C3×C5C2×C812yescomplemented
70C23×C3×C5C22×C411yescharacteristic
71C22×C3×D5—22no—
72C22×C3×D5—22no—
73C22×C3×D5—21no—
74C22×C3×D5—21no—
75C22×C3×D5—24no—
76C22×C3×D5—24no—
77C22×C3×D5—42no—
78C22×C3×D5—42no—
79C22×C3×D5—48no—
80C22×C3×D5—48no—
81C22×C3×D5—42no—
82C22×C3×D5—42no—
83C22×C3×D5—41no—
84C22×C3×D5—41no—
85C22×C3×D5C22⋊C411yescharacteristic
86C22×C3×D5C22⋊C411yescharacteristic
87C22×C3×D5C2×C812yes—
88C22×C3×D5C2×C812yescomplemented
89C22×C3×D5M1612yes—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C22⋊C412yes—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—41no—
96C2×C3×Dic5—41no—
97C2×C3×Dic5C2×D412yes—
98C3×C4×D5—24no—
99C3×C4×D5—42no—
100C3×C4×D5—42no—
101C3×C4×D5—42no—
102C3×#170—44no—
103C25×C3—51no—
104C23×C3×C4—51no—
105C23×C3×C4—51no—
106C22×C3×C8—102no—
107C2×C3×C22⋊C4—51no—
108C2×C3×C22⋊C4—51no—
109C2×C3×C22⋊C4—51no—
110C2×C3×C22⋊C4—102no—
111C2×C3×C22⋊C4—102no—
112C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic
113C3×C22⋊C8—54no—
114C3×C22⋊C8—102no—
115C24×C5C2×C3×C411yescharacteristic
116C23×D5—21no—
117C23×D5—21no—
118C23×D5—22no—
119C23×D5—42no—
120C23×D5—42no—
121C23×D5C3×C814yescomplemented
122C23×D5C2×C3×C411yescharacteristic
123C23×D5C2×C3×C411yescharacteristic
124C22×C4×C5C2×C3×C411yescharacteristic
125C22×C4×C5C2×C3×C411yescharacteristic
126C22×Dic5C2×C3×C411yescharacteristic
127C22×Dic5C23×C311yescharacteristic
128C2×C4×D5—21no—
129C2×C4×D5—21no—
130C2×C4×D5—42no—
131C2×C4×D5—42no—
132C2×C4×D5C3×D412yes—
133C2×C4×D5C3×D412yes—
134C2×#170—24no—
135D5⋊C8—44no—
136C5×C22⋊C4—22no—
137C22⋊Dic5—22no—
138#685—22no—
139#685—22no—
140C22×C22⋊C4—51no—
141C2×C22⋊C8—52no—
142#323—52no—
143#323—52no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—22no—
147C22×C3×C5—42no—
148C22×C3×C5—42no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C22×C3×C5C22×C811yescharacteristic
153C22×C3×C5C2×M1611yescharacteristic
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5—24no—
157C2×C3×D5—24no—
158C2×C3×D5—22no—
159C2×C3×D5—48no—
160C2×C3×D5—42no—
161C2×C3×D5—41no—
162C2×C3×D5—41no—
163C2×C3×D5—48no—
164C2×C3×D5—42no—
165C2×C3×D5C22⋊C812yes—
166C2×C3×D5C22⋊C812yes—
167C2×C3×D5#9912yes—
168C2×C3×D5#10012yes—
169C3×C4×C5—22no—
170C3×C4×C5—41no—
171C3×Dic5—22no—
172C3×Dic5—41no—
173C24×C3—51no—
174C24×C3—54no—
175C24×C3—51no—
176C24×C3—101no—
177C24×C3—101no—
178C24×C3—102no—
179C24×C3—202no—
180C24×C3—202no—
181C24×C3C2×AGL(1,𝔽5)11yescharacteristic
182C22×C3×C4—51no—
183C22×C3×C4—52no—
184C22×C3×C4—52no—
185C22×C3×C4—51no—
186C22×C3×C4—101no—
187C22×C3×C4—101no—
188C22×C3×C4—202no—
189C22×C3×C4—202no—
190C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
191C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
192C2×C3×C8—104no—
193C2×C3×C8—204no—
194C3×C22⋊C4—22no—
195C3×C22⋊C4—102no—
196C3×C22⋊C4—102no—
197C3×C22⋊C4—102no—
198C23×C5—21no—
199C23×C5—21no—
200C23×C5—41no—
201C23×C5—41no—
202C23×C5C2×C3×C812yescomplemented
203C23×C5C22×C3×C411yescharacteristic
204C22×D5—22no—
205C22×D5—22no—
206C22×D5—21no—
207C22×D5—21no—
208C22×D5—24no—
209C22×D5—24no—
210C22×D5—42no—
211C22×D5—42no—
212C22×D5—48no—
213C22×D5—48no—
214C22×D5—42no—
215C22×D5—42no—
216C22×D5—41no—
217C22×D5—41no—
218C22×D5C3×C22⋊C411yescharacteristic
219C22×D5C3×C22⋊C411yescharacteristic
220C22×D5C2×C3×C812yes—
221C22×D5C2×C3×C812yescomplemented
222C22×D5C3×M1612yes—
223C2×C4×C5—21no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5C3×C22⋊C412yes—
227C2×Dic5—21no—
228C2×Dic5—41no—
229C2×Dic5—41no—
230C2×Dic5C2×C3×D412yes—
231C4×D5—24no—
232C4×D5—42no—
233C4×D5—42no—
234C4×D5—42no—
235#170—44no—
236C25—51no—
237C23×C4—51no—
238C23×C4—51no—
239C22×C8—102no—
240C2×C22⋊C4—51no—
241C2×C22⋊C4—51no—
242C2×C22⋊C4—51no—
243C2×C22⋊C4—102no—
244C2×C22⋊C4—102no—
245C2×C22⋊C4C3×AGL(1,𝔽5)11yescharacteristic
246C22⋊C8—54no—
247C22⋊C8—102no—
248C2×C3×C5—21no—
249C2×C3×C5—21no—
250C2×C3×C5—42no—
251C2×C3×C5C2×C22⋊C811yescharacteristic
252C2×C3×C5C2×#9911yescharacteristic
253C2×C3×C5C2×#10011yescharacteristic
254C3×D5—22no—
255C3×D5—42no—
256C3×D5#32314yescomplemented
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—41no—
260C23×C3—41no—
261C23×C3—51no—
262C23×C3—52no—
263C23×C3—52no—
264C23×C3—51no—
265C23×C3—52no—
266C23×C3—102no—
267C23×C3—102no—
268C23×C3—104no—
269C23×C3—104no—
270C23×C3—101no—
271C23×C3—101no—
272C23×C3—201no—
273C23×C3—201no—
274C23×C3—202no—
275C23×C3—202no—
276C23×C3—208no—
277C23×C3—208no—
278C23×C3—202no—
279C23×C3—202no—
280C23×C3D5⋊C812yescomplemented
281C23×C3C22×AGL(1,𝔽5)11yescharacteristic
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—52no—
286C2×C3×C4—104no—
287C2×C3×C4—101no—
288C2×C3×C4—202no—
289C2×C3×C4—202no—
290C2×C3×C4—202no—
291C2×C3×C4—201no—
292C2×C3×C4—201no—
293C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
294C3×C8—204no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5—22no—
298C22×C5—42no—
299C22×C5—42no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5C2×C3×C22⋊C411yescharacteristic
303C22×C5C22×C3×C811yescharacteristic
304C22×C5C2×C3×M1611yescharacteristic
305C2×D5—21no—
306C2×D5—21no—
307C2×D5—24no—
308C2×D5—24no—
309C2×D5—22no—
310C2×D5—48no—
311C2×D5—42no—
312C2×D5—41no—
313C2×D5—41no—
314C2×D5—48no—
315C2×D5—42no—
316C2×D5C3×C22⋊C812yes—
317C2×D5C3×C22⋊C812yes—
318C2×D5C3×#9912yes—
319C2×D5C3×#10012yes—
320C4×C5—22no—
321C4×C5—41no—
322Dic5—22no—
323Dic5—41no—
324C24—51no—
325C24—54no—
326C24—51no—
327C24—101no—
328C24—101no—
329C24—102no—
330C24—202no—
331C24—202no—
332C24C2×C3×AGL(1,𝔽5)11yescharacteristic
333C22×C4—51no—
334C22×C4—52no—
335C22×C4—52no—
336C22×C4—51no—
337C22×C4—101no—
338C22×C4—101no—
339C22×C4—202no—
340C22×C4—202no—
341C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
342C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
343C2×C8—104no—
344C2×C8—204no—
345C22⋊C4—22no—
346C22⋊C4—102no—
347C22⋊C4—102no—
348C22⋊C4—102no—
349C3×C5C2×#32311yescharacteristic, complemented, Hall
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—22no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—52no—
358C22×C3—52no—
359C22×C3—52no—
360C22×C3—52no—
361C22×C3—104no—
362C22×C3—104no—
363C22×C3—101no—
364C22×C3—101no—
365C22×C3—102no—
366C22×C3—202no—
367C22×C3—202no—
368C22×C3—208no—
369C22×C3—208no—
370C22×C3—201no—
371C22×C3—201no—
372C22×C3C2×D5⋊C811yescharacteristic
373C22×C3D5⋊M1611yescharacteristic
374C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
375C3×C4—22no—
376C3×C4—41no—
377C3×C4—102no—
378C3×C4—201no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5—42no—
382C2×C5C2×C3×C22⋊C811yescharacteristic
383C2×C5C2×C3×#9911yescharacteristic
384C2×C5C2×C3×#10011yescharacteristic
385D5—22no—
386D5—42no—
387D5C3×#32314yescomplemented
388C23—21no—
389C23—21no—
390C23—41no—
391C23—41no—
392C23—51no—
393C23—52no—
394C23—52no—
395C23—51no—
396C23—52no—
397C23—102no—
398C23—102no—
399C23—104no—
400C23—104no—
401C23—101no—
402C23—101no—
403C23—201no—
404C23—201no—
405C23—202no—
406C23—202no—
407C23—208no—
408C23—208no—
409C23—202no—
410C23—202no—
411C23C3×D5⋊C812yescomplemented
412C23C22×C3×AGL(1,𝔽5)11yescharacteristic
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—52no—
417C2×C4—104no—
418C2×C4—101no—
419C2×C4—202no—
420C2×C4—202no—
421C2×C4—202no—
422C2×C4—201no—
423C2×C4—201no—
424C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
425C8—204no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—42no—
429C2×C3—54no—
430C2×C3—102no—
431C2×C3—202no—
432C2×C3D5⋊(C22⋊C8)11yescharacteristic
433C2×C3D5⋊#9911yescharacteristic
434C2×C3D5⋊#10011yescharacteristic
435C5C2×C3×#32311yescharacteristic, complemented, Sylow
436C22—21no—
437C22—21no—
438C22—22no—
439C22—42no—
440C22—42no—
441C22—41no—
442C22—41no—
443C22—52no—
444C22—52no—
445C22—52no—
446C22—52no—
447C22—104no—
448C22—104no—
449C22—101no—
450C22—101no—
451C22—102no—
452C22—202no—
453C22—202no—
454C22—208no—
455C22—208no—
456C22—201no—
457C22—201no—
458C22C2×C3×D5⋊C811yescharacteristic
459C22C3×D5⋊M1611yescharacteristic
460C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
461C4—22no—
462C4—41no—
463C4—102no—
464C4—201no—
465C3D5⋊#32311yescharacteristic, direct product factor, Sylow
466C2—21no—
467C2—21no—
468C2—42no—
469C2—54no—
470C2—102no—
471C2—202no—
472C2C3×D5⋊(C22⋊C8)11yescharacteristic
473C2C3×D5⋊#9911yescharacteristic
474C2C3×D5⋊#10011yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C22×C3×C8
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×D5C4
cosocleC22×Dic5C23×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C2×C3×#323
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×D5⋊(C22⋊C8)C2semidirect
3. C3×#64933C2semidirect
4. C3×#64915C2semidirect
5. D5⋊#323C3direct (N × H)
16. C3×C22⋊#170C22semidirect
20. D5⋊(C22⋊C8)C2×C3semidirect
21. #64933C2×C3semidirect
22. #64915C2×C3semidirect
29. C23×C3×D5C8semidirect
62. C22⋊#170C22×C3semidirect
69. C23×C3×C5C2×C8semidirect
88. C22×C3×D5C2×C8semidirect
121. C23×D5C3×C8semidirect
202. C23×C5C2×C3×C8semidirect
221. C22×D5C2×C3×C8semidirect
256. C3×D5#323semidirect
280. C23×C3D5⋊C8semidirect
349. C3×C5C2×#323semidirect
387. D5C3×#323semidirect
411. C23C3×D5⋊C8semidirect
435. C5C2×C3×#323semidirect
465. C3D5⋊#323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×C22⋊C42
C3×D5⋊(C22⋊C8)2
C3×#649332
C3×#649152
D5⋊#3233
C2×C3×#3235