Finite Group Databasebeta

← C3×#10608024 #14322249

Subgroups — C3×#10608024 #14322249

Order 1920.

1848 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
1C2×C3×#4086C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
3C2×C3×#4039C211yesmaximal, characteristic, complemented
4C2×C3×#4027C214yesmaximal, complemented
5C3×C5×#390C211yesmaximal, characteristic, complemented
6C3×#65265C211yesmaximal, characteristic, complemented
7C3×#65246C214yesmaximal, complemented
8C3×#65228C211yesmaximal, characteristic, complemented
9C3×C42×Dic5C211yesmaximal, characteristic, complemented
10#10608024C311yesmaximal, characteristic, direct product factor, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C22×C3×C22⋊D5C2214yes—
13C23×C3×Dic5C2212yes—
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5C2212yes—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C5×C22⋊C4C2214yes—
18C2×C3×C42×C5C2211yescharacteristic
19C2×C3×C22⋊Dic5C2212yes—
20C3×#4086C418yescomplemented
21C3×D4×Dic5—24no—
22C2×C3×#685C2214yes—
23C2×C3×#685C2212yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×#683C2214yes—
26C2×C3×C4×Dic5C2212yes—
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2212yes—
30C3×#4039—24no—
31C3×#4027—216no—
32C3×C4×#127—51nomaximal, Hall
33C2×#4086C2×C311yescharacteristic
34C2×D4×Dic5C2×C311yescharacteristic, complemented
35C2×#4039C2×C311yescharacteristic, complemented
36C2×#4027C2×C314yescomplemented
37C5×#390C2×C311yescharacteristic, complemented
38#65265C2×C311yescharacteristic, complemented
39#65246C2×C314yescomplemented
40#65228C2×C311yescharacteristic, complemented
41C42×Dic5C2×C311yescharacteristic, complemented
42C24×C3×C5C2312yes—
43C23×C3×D5C2312yes—
44C2×C3×C5×D4—22no—
45C2×C3×C5×D4—22no—
46C2×C3×C5×D4C2×C414yescomplemented
47C22×C3×C4×C5C2312yes—
48C22×C3×C4×C5C2312yes—
49C22×C3×C4×C5C2311yescharacteristic
50C2×C3×C22⋊D5—28no—
51C2×C3×C22⋊D5—28no—
52C2×C3×C22⋊D5C2×C4116yescomplemented
53C22×C3×Dic5—24no—
54C22×C3×Dic5—28no—
55C22×C3×Dic5C2312yes—
56C22×C3×Dic5C2311yescharacteristic
57C22×C3×Dic5C2312yes—
58C22×C3×Dic5C2311yescharacteristic
59C2×C3×D20—22no—
60C2×C3×D20—22no—
61C2×C3×D20C2×C414yescomplemented
62C2×C3×C4×D5—28no—
63C2×C3×C4×D5—24no—
64C3×C5×C4⋊C4—22no—
65C3×C5×C22⋊C4—28no—
66C3×C42×C5—22no—
67C3×C22⋊Dic5—24no—
68C3×#685—28no—
69C3×#685—24no—
70C3×C4⋊Dic5—22no—
71C3×#683—28no—
72C3×C4×Dic5—24no—
73C3×C4×Dic5C2×C414yescomplemented
74C3×C4×Dic5D414yescomplemented
75C3×C4×Dic5D418yescomplemented
76C2×C3×#127—51no—
77C2×C3×C4×D4—51no—
78C2×C3×C4×D4—51no—
79C2×C3×C4×D4—54no—
80C3×#390—54no—
81C3×#390—51no—
82C3×#390D511yescharacteristic, complemented
83C3×#384—51no—
84C3×C43—51no—
85C22×C5×D4C22×C311yescharacteristic
86C22×C22⋊D5C22×C314yes—
87C23×Dic5C22×C312yes—
88C22×D20C22×C311yescharacteristic
89C22×C4×D5C22×C312yes—
90C2×C5×C4⋊C4C22×C311yescharacteristic
91C2×C5×C22⋊C4C22×C314yes—
92C2×C42×C5C22×C311yescharacteristic
93C2×C22⋊Dic5C22×C312yes—
94#4086C3×C418yescomplemented
95D4×Dic5—24no—
96C2×#685C22×C314yes—
97C2×#685C22×C312yes—
98C2×C4⋊Dic5C22×C311yescharacteristic
99C2×#683C22×C314yes—
100C2×C4×Dic5C22×C312yes—
101C2×C4×Dic5C22×C311yescharacteristic
102C2×C4×Dic5C22×C312yes—
103C2×C4×Dic5C22×C311yescharacteristic
104#4039—24no—
105#4027—216no—
106C4×#127—51noSylow
107C23×C3×C5—22no—
108C23×C3×C5—24no—
109C23×C3×C5—24no—
110C23×C3×C5—22no—
111C23×C3×C5C22×C414yes—
112C23×C3×C5C2411yescharacteristic
113C22×C3×D5—22no—
114C22×C3×D5—24no—
115C22×C3×D5—22no—
116C22×C3×D5—24no—
117C22×C3×D5C22×C414yes—
118C3×C5×D4—28no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—24no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5C22×C412yes—
124C2×C3×C4×C5C2×D414yes—
125C2×C3×C4×C5C2×D412yes—
126C2×C3×C4×C5#4112yes—
127C3×C22⋊D5—232no—
128C2×C3×Dic5—22no—
129C2×C3×Dic5—24no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—48no—
132C2×C3×Dic5C22×C414yes—
133C2×C3×Dic5C2×D412yes—
134C2×C3×Dic5C2×D414yes—
135C2×C3×Dic5C2×D412yes—
136C2×C3×Dic5C2×D414yes—
137C2×C3×Dic5#4114yes—
138C3×D20—28no—
139C3×C4×D5—48no—
140C22×C3×D4—54no—
141C22×C3×D4—51no—
142C22×C3×D4C2×D511yescharacteristic
143C23×C3×C4—52no—
144C23×C3×C4—52no—
145C3×#127—58no—
146C3×C4×D4—1016no—
147C3×C4×D4—104no—
148C3×C4×D4—104no—
149C2×C3×C4⋊C4—54no—
150C2×C3×C4⋊C4—51no—
151C2×C3×C4⋊C4C2×D511yescharacteristic
152C2×C3×C22⋊C4—52no—
153C2×C3×C22⋊C4—52no—
154C2×C3×C22⋊C4—54no—
155C2×C3×C22⋊C4C2×D514yes—
156C2×C3×C42—51no—
157C2×C3×C42—52no—
158C2×C3×C42—51no—
159C2×C3×C42—52no—
160C2×C3×C42C2×D511yescharacteristic
161C24×C5C23×C312yes—
162C23×D5C23×C312yes—
163C2×C5×D4—22no—
164C2×C5×D4—22no—
165C2×C5×D4C2×C3×C414yescomplemented
166C22×C4×C5C23×C312yes—
167C22×C4×C5C23×C312yes—
168C22×C4×C5C23×C311yescharacteristic
169C2×C22⋊D5—28no—
170C2×C22⋊D5—28no—
171C2×C22⋊D5C2×C3×C4116yescomplemented
172C22×Dic5—28no—
173C22×Dic5—24no—
174C22×Dic5C23×C312yes—
175C22×Dic5C23×C311yescharacteristic
176C22×Dic5C23×C312yes—
177C22×Dic5C23×C311yescharacteristic
178C2×D20—22no—
179C2×D20—22no—
180C2×D20C2×C3×C414yescomplemented
181C2×C4×D5—28no—
182C2×C4×D5—24no—
183C5×C4⋊C4—22no—
184C5×C22⋊C4—28no—
185C42×C5—22no—
186C22⋊Dic5—24no—
187#685—28no—
188#685—24no—
189C4⋊Dic5—22no—
190#683—28no—
191C4×Dic5—24no—
192C4×Dic5C2×C3×C414yescomplemented
193C4×Dic5C3×D418yescomplemented
194C4×Dic5C3×D414yescomplemented
195C2×#127—51no—
196C2×C4×D4—51no—
197C2×C4×D4—51no—
198C2×C4×D4—54no—
199#390—54no—
200#390—51no—
201#390C3×D511yescharacteristic, complemented
202#384—51no—
203C43—51no—
204C22×C3×C5—28no—
205C22×C3×C5—24no—
206C22×C3×C5—42no—
207C22×C3×C5—44no—
208C22×C3×C5—42no—
209C22×C3×C5C23×C411yescharacteristic
210C22×C3×C5C22×D411yescharacteristic
211C22×C3×C5C22×D412yes—
212C22×C3×C5C2×#4111yescharacteristic
213C22×C3×C5C2×#4112yes—
214C2×C3×D5—24no—
215C2×C3×D5—28no—
216C2×C3×D5—42no—
217C2×C3×D5—44no—
218C2×C3×D5—42no—
219C3×C4×C5—24no—
220C3×C4×C5—42no—
221C3×C4×C5C4×D414yescomplemented
222C3×Dic5—22no—
223C3×Dic5—42no—
224C3×Dic5C4×D418yescomplemented
225C3×Dic5#12714yescomplemented
226C24×C3—52no—
227C24×C3C22×D512yes—
228C2×C3×D4—22no—
229C2×C3×D4—22no—
230C2×C3×D4—516no—
231C2×C3×D4—54no—
232C2×C3×D4—108no—
233C2×C3×D4—108no—
234C2×C3×D4—102no—
235C2×C3×D4—102no—
236C2×C3×D4C4×D514yescomplemented
237C22×C3×C4—52no—
238C22×C3×C4—51no—
239C22×C3×C4—51no—
240C22×C3×C4—52no—
241C22×C3×C4—108no—
242C22×C3×C4—104no—
243C22×C3×C4—108no—
244C22×C3×C4—104no—
245C22×C3×C4C22×D512yes—
246C22×C3×C4C22×D512yes—
247C22×C3×C4C22×D511yescharacteristic
248C3×C4⋊C4—22no—
249C3×C4⋊C4—108no—
250C3×C4⋊C4—102no—
251C3×C22⋊C4—28no—
252C3×C22⋊C4—104no—
253C3×C22⋊C4—104no—
254C3×C22⋊C4—108no—
255C3×C42—22no—
256C3×C42—54no—
257C3×C42—58no—
258C3×C42—54no—
259C3×C42—104no—
260C23×C5—22no—
261C23×C5—24no—
262C23×C5—24no—
263C23×C5—22no—
264C23×C5C22×C3×C414yes—
265C23×C5C24×C311yescharacteristic
266C22×D5—22no—
267C22×D5—24no—
268C22×D5—22no—
269C22×D5—24no—
270C22×D5C22×C3×C414yes—
271C5×D4—28no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—24no—
275C2×C4×C5—22no—
276C2×C4×C5C22×C3×C412yes—
277C2×C4×C5C2×C3×D414yes—
278C2×C4×C5C2×C3×D412yes—
279C2×C4×C5C3×#4112yes—
280C22⋊D5—232no—
281C2×Dic5—22no—
282C2×Dic5—24no—
283C2×Dic5—22no—
284C2×Dic5—48no—
285C2×Dic5C22×C3×C414yes—
286C2×Dic5C2×C3×D412yes—
287C2×Dic5C2×C3×D414yes—
288C2×Dic5C2×C3×D414yes—
289C2×Dic5C2×C3×D412yes—
290C2×Dic5C3×#4114yes—
291D20—28no—
292C4×D5—48no—
293C22×D4—54no—
294C22×D4—51no—
295C22×D4C2×C3×D511yescharacteristic
296C23×C4—52no—
297C23×C4—52no—
298#127—58no—
299C4×D4—1016no—
300C4×D4—104no—
301C4×D4—104no—
302C2×C4⋊C4—54no—
303C2×C4⋊C4—51no—
304C2×C4⋊C4C2×C3×D511yescharacteristic
305C2×C22⋊C4—52no—
306C2×C22⋊C4—52no—
307C2×C22⋊C4—54no—
308C2×C22⋊C4C2×C3×D514yes—
309C2×C42—52no—
310C2×C42—51no—
311C2×C42—51no—
312C2×C42—52no—
313C2×C42C2×C3×D511yescharacteristic
314C2×C3×C5—44no—
315C2×C3×C5C2×C4×D411yescharacteristic
316C2×C3×C5C2×C4×D412yes—
317C2×C3×C5C2×#12711yescharacteristic
318C2×C3×C5#53212yes—
319C2×C3×C5#53211yescharacteristic
320C3×D5—44no—
321C23×C3—24no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—24no—
325C23×C3—54no—
326C23×C3—102no—
327C23×C3—104no—
328C23×C3—102no—
329C23×C3—104no—
330C23×C3C2×C4×D514yes—
331C23×C3C23×D511yescharacteristic
332C3×D4—28no—
333C3×D4—1032no—
334C3×D4—108no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—24no—
338C2×C3×C4—22no—
339C2×C3×C4—54no—
340C2×C3×C4—54no—
341C2×C3×C4—52no—
342C2×C3×C4—54no—
343C2×C3×C4—54no—
344C2×C3×C4—52no—
345C2×C3×C4—102no—
346C2×C3×C4—102no—
347C2×C3×C4—104no—
348C2×C3×C4—208no—
349C2×C3×C4—208no—
350C2×C3×C4C2×C4×D512yes—
351C2×C3×C4D4×D514yes—
352C2×C3×C4D4×D512yes—
353C2×C3×C4#71112yes—
354C22×C5—28no—
355C22×C5—24no—
356C22×C5—42no—
357C22×C5—44no—
358C22×C5—42no—
359C22×C5C23×C3×C411yescharacteristic
360C22×C5C22×C3×D412yes—
361C22×C5C22×C3×D411yescharacteristic
362C22×C5C2×C3×#4111yescharacteristic
363C22×C5C2×C3×#4112yes—
364C2×D5—24no—
365C2×D5—28no—
366C2×D5—42no—
367C2×D5—44no—
368C2×D5—42no—
369C4×C5—24no—
370C4×C5—42no—
371C4×C5C3×C4×D414yescomplemented
372Dic5—22no—
373Dic5—42no—
374Dic5C3×C4×D418yescomplemented
375Dic5C3×#12714yescomplemented
376C24—52no—
377C24C22×C3×D512yes—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—516no—
381C2×D4—54no—
382C2×D4—108no—
383C2×D4—108no—
384C2×D4—102no—
385C2×D4—102no—
386C2×D4C3×C4×D514yescomplemented
387C22×C4—52no—
388C22×C4—51no—
389C22×C4—51no—
390C22×C4—52no—
391C22×C4—108no—
392C22×C4—104no—
393C22×C4—108no—
394C22×C4—104no—
395C22×C4C22×C3×D512yes—
396C22×C4C22×C3×D512yes—
397C22×C4C22×C3×D511yescharacteristic
398C4⋊C4—22no—
399C4⋊C4—108no—
400C4⋊C4—102no—
401C22⋊C4—28no—
402C22⋊C4—104no—
403C22⋊C4—104no—
404C22⋊C4—108no—
405C42—22no—
406C42—54no—
407C42—58no—
408C42—54no—
409C42—104no—
410C3×C5C4×#12711yescharacteristic, complemented, Hall
411C22×C3—24no—
412C22×C3—28no—
413C22×C3—42no—
414C22×C3—44no—
415C22×C3—42no—
416C22×C3—104no—
417C22×C3—108no—
418C22×C3—202no—
419C22×C3—204no—
420C22×C3—202no—
421C22×C3C22×C4×D511yescharacteristic
422C22×C3C2×D4×D511yescharacteristic
423C22×C3C2×D4×D512yes—
424C22×C3C2×#71111yescharacteristic
425C22×C3D5×#4112yes—
426C3×C4—24no—
427C3×C4—42no—
428C3×C4—54no—
429C3×C4—58no—
430C3×C4—102no—
431C3×C4—202no—
432C3×C4#402714yescomplemented
433C2×C5—44no—
434C2×C5C2×C3×C4×D412yes—
435C2×C5C2×C3×C4×D411yescharacteristic
436C2×C5C2×C3×#12711yescharacteristic
437C2×C5C3×#53212yes—
438C2×C5C3×#53211yescharacteristic
439D5—44no—
440C23—24no—
441C23—22no—
442C23—22no—
443C23—24no—
444C23—54no—
445C23—104no—
446C23—102no—
447C23—102no—
448C23—104no—
449C23C2×C3×C4×D514yes—
450C23C23×C3×D511yescharacteristic
451D4—28no—
452D4—1032no—
453D4—108no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—54no—
459C2×C4—54no—
460C2×C4—54no—
461C2×C4—52no—
462C2×C4—54no—
463C2×C4—52no—
464C2×C4—102no—
465C2×C4—104no—
466C2×C4—102no—
467C2×C4—208no—
468C2×C4—208no—
469C2×C4C2×C3×C4×D512yes—
470C2×C4C3×D4×D514yes—
471C2×C4C3×D4×D512yes—
472C2×C4C3×#71112yes—
473C2×C3—44no—
474C2×C3—204no—
475C2×C3C2×#402711yescharacteristic
476C2×C3C4×D4×D512yes—
477C2×C3#6593012yes—
478C2×C3#6600211yescharacteristic
479C2×C3D5×#12711yescharacteristic
480C5C3×C4×#12711yescharacteristic, complemented, Sylow
481C22—28no—
482C22—24no—
483C22—44no—
484C22—42no—
485C22—42no—
486C22—108no—
487C22—104no—
488C22—204no—
489C22—202no—
490C22—202no—
491C22C22×C3×C4×D511yescharacteristic
492C22C2×C3×D4×D512yes—
493C22C2×C3×D4×D511yescharacteristic
494C22C2×C3×#71111yescharacteristic
495C22C3×D5×#4112yes—
496C4—24no—
497C4—42no—
498C4—58no—
499C4—54no—
500C4—102no—
501C4—202no—
502C4C3×#402714yescomplemented
503C3#1060802411yescharacteristic, direct product factor, Sylow
504C2—44no—
505C2—204no—
506C2C2×C3×#402711yescharacteristic
507C2C3×C4×D4×D512yes—
508C2C3×#6593012yes—
509C2C3×#6600211yescharacteristic
510C2C3×D5×#12711yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#390C2
socleC23×C3×C5C24
prime radicalC2×C3×#4086C2
cosocleC23×C5C24×C3
hypercenterC3×#390D5
hypocenterC5C3×C4×#127
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic5C2semidirect
3. C2×C3×#4039C2semidirect
4. C2×C3×#4027C2semidirect
5. C3×C5×#390C2semidirect
6. C3×#65265C2semidirect
7. C3×#65246C2semidirect
8. C3×#65228C2semidirect
9. C3×C42×Dic5C2semidirect
10. #10608024C3direct (N × H)
20. C3×#4086C4semidirect
34. C2×D4×Dic5C2×C3semidirect
35. C2×#4039C2×C3semidirect
36. C2×#4027C2×C3semidirect
37. C5×#390C2×C3semidirect
38. #65265C2×C3semidirect
39. #65246C2×C3semidirect
40. #65228C2×C3semidirect
41. C42×Dic5C2×C3semidirect
46. C2×C3×C5×D4C2×C4semidirect
52. C2×C3×C22⋊D5C2×C4semidirect
61. C2×C3×D20C2×C4semidirect
73. C3×C4×Dic5C2×C4semidirect
74. C3×C4×Dic5D4semidirect
75. C3×C4×Dic5D4semidirect
82. C3×#390D5semidirect
94. #4086C3×C4semidirect
165. C2×C5×D4C2×C3×C4semidirect
171. C2×C22⋊D5C2×C3×C4semidirect
180. C2×D20C2×C3×C4semidirect
192. C4×Dic5C2×C3×C4semidirect
193. C4×Dic5C3×D4semidirect
194. C4×Dic5C3×D4semidirect
201. #390C3×D5semidirect
221. C3×C4×C5C4×D4semidirect
224. C3×Dic5C4×D4semidirect
225. C3×Dic5#127semidirect
236. C2×C3×D4C4×D5semidirect
371. C4×C5C3×C4×D4semidirect
374. Dic5C3×C4×D4semidirect
375. Dic5C3×#127semidirect
386. C2×D4C3×C4×D5semidirect
410. C3×C5C4×#127semidirect
432. C3×C4#4027semidirect
480. C5C3×C4×#127semidirect
502. C4C3×#4027semidirect
503. C3#10608024direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40862
C2×C3×D4×Dic52
C2×C3×#40392
C2×C3×#40272
C3×C5×#3902
C3×#652652
C3×#652462
C3×#652282
C3×C42×Dic52
#106080243
C3×C4×#1275