Finite Group Databasebeta

← C3×#10614060 #14324369

Subgroups — C3×#10614060 #14324369

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×C3×#4086C211yesmaximal, characteristic
3C2×C3×C4×D20C211yesmaximal, characteristic, complemented
4C3×#65510C211yesmaximal, characteristic, complemented
5C3×#65502C214yesmaximal, complemented
6C3×#65277C211yesmaximal, characteristic, complemented
7C3×#65266C211yesmaximal, characteristic, complemented
8C3×#65245C214yesmaximal, complemented
9C3×#65221C211yesmaximal, characteristic, complemented
10#10614060C311yesmaximal, characteristic, direct product factor, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C23×C3×C4×C5C2212yes—
13C22×C3×C22⋊D5C2214yes—
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5C2212yes—
16C3×C4×C5×D4—24no—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C22⋊C4C2212yes—
19C2×C3×C42×C5C2211yescharacteristic
20C2×C3×C22⋊Dic5C2214yes—
21C3×#4086C418yescomplemented
22C2×C3×#685C2212yes—
23C2×C3×#685C2214yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C3×C4×D20—24no—
28C3×#3963C2212yes—
29C3×#3963C2212yes—
30C3×#3963C2214yes—
31C3×#2328—51nomaximal, Hall
32C2×C4×C5×D4C2×C311yescharacteristic, complemented
33C2×#4086C2×C311yescharacteristic
34C2×C4×D20C2×C311yescharacteristic, complemented
35#65510C2×C311yescharacteristic, complemented
36#65502C2×C314yescomplemented
37#65277C2×C311yescharacteristic, complemented
38#65266C2×C311yescharacteristic, complemented
39#65245C2×C314yescomplemented
40#65221C2×C311yescharacteristic, complemented
41C24×C3×C5C2312yes—
42C23×C3×D5C2312yes—
43C2×C3×C5×D4—22no—
44C2×C3×C5×D4—22no—
45C2×C3×C5×D4C2×C414yescomplemented
46C22×C3×C4×C5—24no—
47C22×C3×C4×C5—44no—
48C22×C3×C4×C5C2312yes—
49C22×C3×C4×C5C2311yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C2×C3×C22⋊D5—44no—
53C2×C3×C22⋊D5—44no—
54C2×C3×C22⋊D5C2×C4116yescomplemented
55C22×C3×Dic5C2312yes—
56C22×C3×Dic5C2312yes—
57C22×C3×Dic5C2312yes—
58C2×C3×D20—22no—
59C2×C3×D20—22no—
60C2×C3×D20C2×C414yescomplemented
61C2×C3×C4×D5—24no—
62C2×C3×C4×D5—44no—
63C3×C5×C4⋊C4—22no—
64C3×C5×C22⋊C4—24no—
65C3×C42×C5D414yescomplemented
66C3×C22⋊Dic5—44no—
67C3×#685—24no—
68C3×#685—44no—
69C3×C4⋊Dic5—22no—
70C3×C4×Dic5—22no—
71C3×C4×Dic5C2×C414yescomplemented
72C2×C3×#127—51no—
73C2×C3×C4×D4—51no—
74C2×C3×C4×D4D511yescharacteristic, complemented
75C3×#390—51no—
76C3×#390—51no—
77C3×#386—54no—
78C3×#386—54no—
79C3×#382—51no—
80C3×#376—51no—
81C22×C5×D4C22×C311yescharacteristic
82C23×C4×C5C22×C312yes—
83C22×C22⋊D5C22×C314yes—
84C22×D20C22×C311yescharacteristic
85C22×C4×D5C22×C312yes—
86C4×C5×D4—24no—
87C2×C5×C4⋊C4C22×C311yescharacteristic
88C2×C5×C22⋊C4C22×C312yes—
89C2×C42×C5C22×C311yescharacteristic
90C2×C22⋊Dic5C22×C314yes—
91#4086C3×C418yescomplemented
92C2×#685C22×C312yes—
93C2×#685C22×C314yes—
94C2×C4⋊Dic5C22×C311yescharacteristic
95C2×C4×Dic5C22×C311yescharacteristic
96C2×C4×Dic5C22×C311yescharacteristic
97C4×D20—24no—
98#3963C22×C312yes—
99#3963C22×C312yes—
100#3963C22×C314yes—
101#2328—51noSylow
102C23×C3×C5—22no—
103C23×C3×C5—22no—
104C23×C3×C5—24no—
105C23×C3×C5—24no—
106C23×C3×C5C22×C414yes—
107C23×C3×C5C2411yescharacteristic
108C22×C3×D5—22no—
109C22×C3×D5—22no—
110C22×C3×D5—24no—
111C22×C3×D5—24no—
112C22×C3×D5C22×C414yes—
113C3×C5×D4—28no—
114C2×C3×C4×C5—22no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—24no—
118C2×C3×C4×C5—48no—
119C2×C3×C4×C5C22×C412yes—
120C2×C3×C4×C5C2×D412yes—
121C2×C3×C4×C5C2×D412yes—
122C2×C3×C4×C5C2×D412yes—
123C2×C3×C4×C5#4112yes—
124C3×C22⋊D5—416no—
125C2×C3×Dic5—22no—
126C2×C3×Dic5—22no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—22no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—24no—
132C2×C3×Dic5C22×C414yes—
133C3×D20—28no—
134C3×C4×D5—48no—
135C22×C3×D4—54no—
136C22×C3×D4—51no—
137C22×C3×D4C2×D511yescharacteristic
138C23×C3×C4—52no—
139C23×C3×C4C2×D512yes—
140C3×#127—58no—
141C3×C4×D4—24no—
142C3×C4×D4—104no—
143C2×C3×C4⋊C4—51no—
144C2×C3×C4⋊C4C2×D511yescharacteristic
145C2×C3×C22⋊C4—52no—
146C2×C3×C22⋊C4—54no—
147C2×C3×C22⋊C4—54no—
148C2×C3×C22⋊C4C2×D512yes—
149C2×C3×C42—51no—
150C2×C3×C42—51no—
151C2×C3×C42C2×D511yescharacteristic
152C3×#95—52no—
153C3×#95—52no—
154C3×#95—54no—
155C24×C5C23×C312yes—
156C23×D5C23×C312yes—
157C2×C5×D4—22no—
158C2×C5×D4—22no—
159C2×C5×D4C2×C3×C414yescomplemented
160C22×C4×C5—24no—
161C22×C4×C5—44no—
162C22×C4×C5C23×C312yes—
163C22×C4×C5C23×C311yescharacteristic
164C22×C4×C5C23×C311yescharacteristic
165C22×C4×C5C23×C311yescharacteristic
166C2×C22⋊D5—44no—
167C2×C22⋊D5—44no—
168C2×C22⋊D5C2×C3×C4116yescomplemented
169C22×Dic5C23×C312yes—
170C22×Dic5C23×C312yes—
171C22×Dic5C23×C312yes—
172C2×D20—22no—
173C2×D20—22no—
174C2×D20C2×C3×C414yescomplemented
175C2×C4×D5—24no—
176C2×C4×D5—44no—
177C5×C4⋊C4—22no—
178C5×C22⋊C4—24no—
179C42×C5C3×D414yescomplemented
180C22⋊Dic5—44no—
181#685—24no—
182#685—44no—
183C4⋊Dic5—22no—
184C4×Dic5—22no—
185C4×Dic5C2×C3×C414yescomplemented
186C2×#127—51no—
187C2×C4×D4—51no—
188C2×C4×D4C3×D511yescharacteristic, complemented
189#390—51no—
190#390—51no—
191#386—54no—
192#386—54no—
193#382—51no—
194#376—51no—
195C22×C3×C5—24no—
196C22×C3×C5—28no—
197C22×C3×C5—42no—
198C22×C3×C5—42no—
199C22×C3×C5—44no—
200C22×C3×C5C23×C411yescharacteristic
201C22×C3×C5C22×D411yescharacteristic
202C22×C3×C5C2×#4111yescharacteristic
203C22×C3×C5H(5,𝔽2)12yes—
204C22×C3×C5H(5,𝔽2)12yes—
205C2×C3×D5—24no—
206C2×C3×D5—28no—
207C2×C3×D5—42no—
208C2×C3×D5—42no—
209C2×C3×D5—44no—
210C3×C4×C5—22no—
211C3×C4×C5—22no—
212C3×C4×C5—42no—
213C3×C4×C5C4×D414yes—
214C3×Dic5—24no—
215C3×Dic5—42no—
216C3×Dic5—42no—
217C24×C3—52no—
218C24×C3C22×D512yes—
219C2×C3×D4—22no—
220C2×C3×D4—22no—
221C2×C3×D4—516no—
222C2×C3×D4—54no—
223C2×C3×D4—102no—
224C2×C3×D4—102no—
225C2×C3×D4—204no—
226C2×C3×D4—204no—
227C2×C3×D4C4×D514yescomplemented
228C22×C3×C4—24no—
229C22×C3×C4—44no—
230C22×C3×C4—52no—
231C22×C3×C4—52no—
232C22×C3×C4—52no—
233C22×C3×C4—104no—
234C22×C3×C4—204no—
235C22×C3×C4C22×D512yes—
236C22×C3×C4C22×D511yescharacteristic
237C22×C3×C4C22×D511yescharacteristic
238C22×C3×C4C22×D511yescharacteristic
239C3×C4⋊C4—22no—
240C3×C4⋊C4—102no—
241C3×C22⋊C4—24no—
242C3×C22⋊C4—104no—
243C3×C22⋊C4—204no—
244C3×C22⋊C4—204no—
245C3×C42—54no—
246C3×C42—102no—
247C3×C42C22⋊D514yescomplemented
248C23×C5—22no—
249C23×C5—22no—
250C23×C5—24no—
251C23×C5—24no—
252C23×C5C22×C3×C414yes—
253C23×C5C24×C311yescharacteristic
254C22×D5—22no—
255C22×D5—22no—
256C22×D5—24no—
257C22×D5—24no—
258C22×D5C22×C3×C414yes—
259C5×D4—28no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—24no—
264C2×C4×C5—48no—
265C2×C4×C5C22×C3×C412yes—
266C2×C4×C5C2×C3×D412yes—
267C2×C4×C5C2×C3×D412yes—
268C2×C4×C5C2×C3×D412yes—
269C2×C4×C5C3×#4112yes—
270C22⋊D5—416no—
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—22no—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—22no—
277C2×Dic5—24no—
278C2×Dic5C22×C3×C414yes—
279D20—28no—
280C4×D5—48no—
281C22×D4—54no—
282C22×D4—51no—
283C22×D4C2×C3×D511yescharacteristic
284C23×C4—52no—
285C23×C4C2×C3×D512yes—
286#127—58no—
287C4×D4—24no—
288C4×D4—104no—
289C2×C4⋊C4—51no—
290C2×C4⋊C4C2×C3×D511yescharacteristic
291C2×C22⋊C4—52no—
292C2×C22⋊C4—54no—
293C2×C22⋊C4—54no—
294C2×C22⋊C4C2×C3×D512yes—
295C2×C42—51no—
296C2×C42—51no—
297C2×C42C2×C3×D511yescharacteristic
298#95—52no—
299#95—52no—
300#95—54no—
301C2×C3×C5—44no—
302C2×C3×C5C2×C4×D411yescharacteristic
303C2×C3×C5#51812yes—
304C2×C3×C5#53511yescharacteristic
305C2×C3×C5#53511yescharacteristic
306C2×C3×C5#54012yes—
307C3×D5—44no—
308C23×C3—22no—
309C23×C3—24no—
310C23×C3—24no—
311C23×C3—22no—
312C23×C3—54no—
313C23×C3—102no—
314C23×C3—104no—
315C23×C3—104no—
316C23×C3—102no—
317C23×C3C2×C4×D514yes—
318C23×C3C23×D511yescharacteristic
319C3×D4—28no—
320C3×D4—108no—
321C3×D4—2016no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—24no—
325C2×C3×C4—22no—
326C2×C3×C4—48no—
327C2×C3×C4—54no—
328C2×C3×C4—102no—
329C2×C3×C4—102no—
330C2×C3×C4—102no—
331C2×C3×C4—102no—
332C2×C3×C4—102no—
333C2×C3×C4—104no—
334C2×C3×C4—102no—
335C2×C3×C4—208no—
336C2×C3×C4C2×C4×D512yes—
337C2×C3×C4#70912yes—
338C2×C3×C4C2×C22⋊D512yes—
339C2×C3×C4C2×C22⋊D512yes—
340C2×C3×C4C2×C22⋊D512yes—
341C22×C5—24no—
342C22×C5—28no—
343C22×C5—42no—
344C22×C5—42no—
345C22×C5—44no—
346C22×C5C23×C3×C411yescharacteristic
347C22×C5C22×C3×D411yescharacteristic
348C22×C5C2×C3×#4111yescharacteristic
349C22×C5C3×H(5,𝔽2)12yes—
350C22×C5C3×H(5,𝔽2)12yes—
351C2×D5—24no—
352C2×D5—28no—
353C2×D5—42no—
354C2×D5—42no—
355C2×D5—44no—
356C4×C5—22no—
357C4×C5—22no—
358C4×C5—42no—
359C4×C5C3×C4×D414yes—
360Dic5—24no—
361Dic5—42no—
362Dic5—42no—
363C24—52no—
364C24C22×C3×D512yes—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—516no—
368C2×D4—54no—
369C2×D4—102no—
370C2×D4—102no—
371C2×D4—204no—
372C2×D4—204no—
373C2×D4C3×C4×D514yescomplemented
374C22×C4—24no—
375C22×C4—44no—
376C22×C4—52no—
377C22×C4—52no—
378C22×C4—52no—
379C22×C4—104no—
380C22×C4—204no—
381C22×C4C22×C3×D512yes—
382C22×C4C22×C3×D511yescharacteristic
383C22×C4C22×C3×D511yescharacteristic
384C22×C4C22×C3×D511yescharacteristic
385C4⋊C4—22no—
386C4⋊C4—102no—
387C22⋊C4—24no—
388C22⋊C4—104no—
389C22⋊C4—204no—
390C22⋊C4—204no—
391C42—54no—
392C42—102no—
393C42C3×C22⋊D514yescomplemented
394C3×C5#232811yescharacteristic, complemented, Hall
395C22×C3—24no—
396C22×C3—28no—
397C22×C3—42no—
398C22×C3—44no—
399C22×C3—42no—
400C22×C3—104no—
401C22×C3—108no—
402C22×C3—202no—
403C22×C3—204no—
404C22×C3—202no—
405C22×C3C22×C4×D511yescharacteristic
406C22×C3C2×#70911yescharacteristic
407C22×C3#414412yes—
408C22×C3#414912yes—
409C22×C3C22×C22⋊D511yescharacteristic
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—42no—
413C3×C4—104no—
414C3×C4—202no—
415C3×C4—202no—
416C3×C4C4×C22⋊D514yes—
417C2×C5—44no—
418C2×C5C2×C3×C4×D411yescharacteristic
419C2×C5C3×#51812yes—
420C2×C5C3×#53511yescharacteristic
421C2×C5C3×#53511yescharacteristic
422C2×C5C3×#54012yes—
423D5—44no—
424C23—22no—
425C23—24no—
426C23—24no—
427C23—22no—
428C23—54no—
429C23—102no—
430C23—104no—
431C23—104no—
432C23—102no—
433C23C2×C3×C4×D514yes—
434C23C23×C3×D511yescharacteristic
435D4—28no—
436D4—108no—
437D4—2016no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—48no—
443C2×C4—54no—
444C2×C4—102no—
445C2×C4—102no—
446C2×C4—102no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—104no—
450C2×C4—102no—
451C2×C4—208no—
452C2×C4C2×C3×C4×D512yes—
453C2×C4C3×#70912yes—
454C2×C4C2×C3×C22⋊D512yes—
455C2×C4C2×C3×C22⋊D512yes—
456C2×C4C2×C3×C22⋊D512yes—
457C2×C3—44no—
458C2×C3—204no—
459C2×C3#6587912yes—
460C2×C3#6589612yes—
461C2×C3C2×C4×C22⋊D511yescharacteristic
462C2×C3#6613911yescharacteristic
463C2×C3#6616411yescharacteristic
464C5C3×#232811yescharacteristic, complemented, Sylow
465C22—24no—
466C22—28no—
467C22—42no—
468C22—44no—
469C22—42no—
470C22—104no—
471C22—108no—
472C22—202no—
473C22—204no—
474C22—202no—
475C22C22×C3×C4×D511yescharacteristic
476C22C2×C3×#70911yescharacteristic
477C22C3×#414412yes—
478C22C3×#414912yes—
479C22C22×C3×C22⋊D511yescharacteristic
480C4—22no—
481C4—22no—
482C4—42no—
483C4—104no—
484C4—202no—
485C4—202no—
486C4C3×C4×C22⋊D514yes—
487C3#1061406011yescharacteristic, direct product factor, Sylow
488C2—44no—
489C2—204no—
490C2C3×#6587912yes—
491C2C3×#6589612yes—
492C2C2×C3×C4×C22⋊D511yescharacteristic
493C2C3×#6613911yescharacteristic
494C2C3×#6616411yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4086C2
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#2328
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×D4C2semidirect
3. C2×C3×C4×D20C2semidirect
4. C3×#65510C2semidirect
5. C3×#65502C2semidirect
6. C3×#65277C2semidirect
7. C3×#65266C2semidirect
8. C3×#65245C2semidirect
9. C3×#65221C2semidirect
10. #10614060C3direct (N × H)
21. C3×#4086C4semidirect
32. C2×C4×C5×D4C2×C3semidirect
34. C2×C4×D20C2×C3semidirect
35. #65510C2×C3semidirect
36. #65502C2×C3semidirect
37. #65277C2×C3semidirect
38. #65266C2×C3semidirect
39. #65245C2×C3semidirect
40. #65221C2×C3semidirect
45. C2×C3×C5×D4C2×C4semidirect
54. C2×C3×C22⋊D5C2×C4semidirect
60. C2×C3×D20C2×C4semidirect
65. C3×C42×C5D4semidirect
71. C3×C4×Dic5C2×C4semidirect
74. C2×C3×C4×D4D5semidirect
91. #4086C3×C4semidirect
159. C2×C5×D4C2×C3×C4semidirect
168. C2×C22⋊D5C2×C3×C4semidirect
174. C2×D20C2×C3×C4semidirect
179. C42×C5C3×D4semidirect
185. C4×Dic5C2×C3×C4semidirect
188. C2×C4×D4C3×D5semidirect
227. C2×C3×D4C4×D5semidirect
247. C3×C42C22⋊D5semidirect
373. C2×D4C3×C4×D5semidirect
393. C42C3×C22⋊D5semidirect
394. C3×C5#2328semidirect
464. C5C3×#2328semidirect
487. C3#10614060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×C3×#40862
C2×C3×C4×D202
C3×#655102
C3×#655022
C3×#652772
C3×#652662
C3×#652452
C3×#652212
#106140603
C3×#23285