Finite Group Databasebeta

← C3×#10608029 #14324375

Subgroups — C3×#10608029 #14324375

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×#4086C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
3C2×C3×#4039C211yesmaximal, characteristic, complemented
4C3×C5×#390C211yesmaximal, characteristic, complemented
5C3×#65266C211yesmaximal, characteristic, complemented
6C3×#65247C214yesmaximal, complemented
7C3×#65245C214yesmaximal, complemented
8C3×#65228C211yesmaximal, characteristic, complemented
9C3×#65221C211yesmaximal, characteristic, complemented
10#10608029C311yesmaximal, 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×#685C2212yes—
23C2×C3×#685C2214yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C3×#4039—24no—
28C3×#3963C2212yes—
29C3×#3963C2212yes—
30C3×#3963C2214yes—
31C3×#2328—51nomaximal, Hall
32C2×#4086C2×C311yescharacteristic
33C2×D4×Dic5C2×C311yescharacteristic, complemented
34C2×#4039C2×C311yescharacteristic, complemented
35C5×#390C2×C311yescharacteristic, complemented
36#65266C2×C311yescharacteristic, complemented
37#65247C2×C314yescomplemented
38#65245C2×C314yescomplemented
39#65228C2×C311yescharacteristic, complemented
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×C5C2312yes—
47C22×C3×C4×C5C2312yes—
48C22×C3×C4×C5C2311yescharacteristic
49C2×C3×C22⋊D5—44no—
50C2×C3×C22⋊D5—44no—
51C2×C3×C22⋊D5C2×C4116yescomplemented
52C22×C3×Dic5—24no—
53C22×C3×Dic5—44no—
54C22×C3×Dic5C2312yes—
55C22×C3×Dic5C2312yes—
56C22×C3×Dic5C2311yescharacteristic
57C22×C3×Dic5C2311yescharacteristic
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—44no—
65C3×C42×C5—22no—
66C3×C22⋊Dic5—24no—
67C3×#685—24no—
68C3×#685—44no—
69C3×C4⋊Dic5—22no—
70C3×C4×Dic5C2×C414yescomplemented
71C3×C4×Dic5D414yescomplemented
72C2×C3×#127—51no—
73C2×C3×C4×D4—51no—
74C2×C3×C4×D4—51no—
75C3×#390—51no—
76C3×#390D511yescharacteristic, complemented
77C3×#386—54no—
78C3×#386—54no—
79C3×#382—51no—
80C3×#376—51no—
81C22×C5×D4C22×C311yescharacteristic
82C22×C22⋊D5C22×C314yes—
83C23×Dic5C22×C312yes—
84C22×D20C22×C311yescharacteristic
85C22×C4×D5C22×C312yes—
86C2×C5×C4⋊C4C22×C311yescharacteristic
87C2×C5×C22⋊C4C22×C314yes—
88C2×C42×C5C22×C311yescharacteristic
89C2×C22⋊Dic5C22×C312yes—
90#4086C3×C418yescomplemented
91D4×Dic5—24no—
92C2×#685C22×C312yes—
93C2×#685C22×C314yes—
94C2×C4⋊Dic5C22×C311yescharacteristic
95C2×C4×Dic5C22×C311yescharacteristic
96C2×C4×Dic5C22×C311yescharacteristic
97#4039—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—22no—
118C2×C3×C4×C5—24no—
119C2×C3×C4×C5C22×C412yes—
120C2×C3×C4×C5C2×D412yes—
121C2×C3×C4×C5#4112yes—
122C3×C22⋊D5—416no—
123C2×C3×Dic5—22no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—22no—
126C2×C3×Dic5—22no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—24no—
129C2×C3×Dic5—48no—
130C2×C3×Dic5C22×C414yes—
131C2×C3×Dic5C2×D412yes—
132C2×C3×Dic5C2×D412yes—
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×C4—52no—
140C3×#127—58no—
141C3×C4×D4—104no—
142C3×C4×D4—104no—
143C2×C3×C4⋊C4—51no—
144C2×C3×C4⋊C4C2×D511yescharacteristic
145C2×C3×C22⋊C4—52no—
146C2×C3×C22⋊C4—52no—
147C2×C3×C22⋊C4—54no—
148C2×C3×C22⋊C4C2×D514yes—
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×C5C23×C312yes—
161C22×C4×C5C23×C312yes—
162C22×C4×C5C23×C311yescharacteristic
163C2×C22⋊D5—44no—
164C2×C22⋊D5—44no—
165C2×C22⋊D5C2×C3×C4116yescomplemented
166C22×Dic5—24no—
167C22×Dic5—44no—
168C22×Dic5C23×C312yes—
169C22×Dic5C23×C312yes—
170C22×Dic5C23×C311yescharacteristic
171C22×Dic5C23×C311yescharacteristic
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—44no—
179C42×C5—22no—
180C22⋊Dic5—24no—
181#685—24no—
182#685—44no—
183C4⋊Dic5—22no—
184C4×Dic5C2×C3×C414yescomplemented
185C4×Dic5C3×D414yescomplemented
186C2×#127—51no—
187C2×C4×D4—51no—
188C2×C4×D4—51no—
189#390—51no—
190#390C3×D511yescharacteristic, complemented
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—42no—
211C3×C4×C5—42no—
212C3×C4×C5C4×D414yes—
213C3×Dic5—24no—
214C3×Dic5—22no—
215C3×Dic5—22no—
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—52no—
229C22×C3×C4—51no—
230C22×C3×C4—51no—
231C22×C3×C4—52no—
232C22×C3×C4—104no—
233C22×C3×C4—104no—
234C22×C3×C4—204no—
235C22×C3×C4—204no—
236C22×C3×C4C22×D512yes—
237C22×C3×C4C22×D512yes—
238C22×C3×C4C22×D511yescharacteristic
239C3×C4⋊C4—22no—
240C3×C4⋊C4—102no—
241C3×C22⋊C4—44no—
242C3×C22⋊C4—104no—
243C3×C22⋊C4—104no—
244C3×C22⋊C4—204no—
245C3×C42—22no—
246C3×C42—54no—
247C3×C42—54no—
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—22no—
264C2×C4×C5—24no—
265C2×C4×C5C22×C3×C412yes—
266C2×C4×C5C2×C3×D412yes—
267C2×C4×C5C3×#4112yes—
268C22⋊D5—416no—
269C2×Dic5—22no—
270C2×Dic5—22no—
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—22no—
274C2×Dic5—24no—
275C2×Dic5—48no—
276C2×Dic5C22×C3×C414yes—
277C2×Dic5C2×C3×D412yes—
278C2×Dic5C2×C3×D412yes—
279D20—28no—
280C4×D5—48no—
281C22×D4—54no—
282C22×D4—51no—
283C22×D4C2×C3×D511yescharacteristic
284C23×C4—52no—
285C23×C4—52no—
286#127—58no—
287C4×D4—104no—
288C4×D4—104no—
289C2×C4⋊C4—51no—
290C2×C4⋊C4C2×C3×D511yescharacteristic
291C2×C22⋊C4—52no—
292C2×C22⋊C4—52no—
293C2×C22⋊C4—54no—
294C2×C22⋊C4C2×C3×D514yes—
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—22no—
310C23×C3—24no—
311C23×C3—24no—
312C23×C3—54no—
313C23×C3—102no—
314C23×C3—102no—
315C23×C3—104no—
316C23×C3—104no—
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—22no—
325C2×C3×C4—24no—
326C2×C3×C4—22no—
327C2×C3×C4—54no—
328C2×C3×C4—52no—
329C2×C3×C4—52no—
330C2×C3×C4—102no—
331C2×C3×C4—102no—
332C2×C3×C4—102no—
333C2×C3×C4—102no—
334C2×C3×C4—102no—
335C2×C3×C4—104no—
336C2×C3×C4—208no—
337C2×C3×C4—208no—
338C2×C3×C4C2×C4×D512yes—
339C2×C3×C4D4×D512yes—
340C2×C3×C4#71112yes—
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—42no—
357C4×C5—42no—
358C4×C5C3×C4×D414yes—
359Dic5—24no—
360Dic5—22no—
361Dic5—22no—
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—52no—
375C22×C4—51no—
376C22×C4—51no—
377C22×C4—52no—
378C22×C4—104no—
379C22×C4—104no—
380C22×C4—204no—
381C22×C4—204no—
382C22×C4C22×C3×D512yes—
383C22×C4C22×C3×D512yes—
384C22×C4C22×C3×D511yescharacteristic
385C4⋊C4—22no—
386C4⋊C4—102no—
387C22⋊C4—44no—
388C22⋊C4—104no—
389C22⋊C4—104no—
390C22⋊C4—204no—
391C42—22no—
392C42—54no—
393C42—54no—
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×D4×D511yescharacteristic
407C22×C3C2×#71111yescharacteristic
408C22×C3#414412yes—
409C22×C3#414912yes—
410C3×C4—42no—
411C3×C4—42no—
412C3×C4—102no—
413C3×C4—104no—
414C3×C4—102no—
415C3×C4—202no—
416C3×C4#402714yes—
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—22no—
426C23—24no—
427C23—24no—
428C23—54no—
429C23—102no—
430C23—102no—
431C23—104no—
432C23—104no—
433C23C2×C3×C4×D514yes—
434C23C23×C3×D511yescharacteristic
435D4—28no—
436D4—108no—
437D4—2016no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—54no—
444C2×C4—52no—
445C2×C4—52no—
446C2×C4—102no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—102no—
450C2×C4—102no—
451C2×C4—104no—
452C2×C4—208no—
453C2×C4—208no—
454C2×C4C2×C3×C4×D512yes—
455C2×C4C3×D4×D512yes—
456C2×C4C3×#71112yes—
457C2×C3—44no—
458C2×C3—204no—
459C2×C3C2×#402711yescharacteristic
460C2×C3#6587912yes—
461C2×C3#6595312yes—
462C2×C3#6600811yescharacteristic
463C2×C3#6604911yescharacteristic
464C5C3×#232811yescharacteristic, complemented, Sylow
465C22—28no—
466C22—24no—
467C22—44no—
468C22—42no—
469C22—42no—
470C22—108no—
471C22—104no—
472C22—204no—
473C22—202no—
474C22—202no—
475C22C22×C3×C4×D511yescharacteristic
476C22C2×C3×D4×D511yescharacteristic
477C22C2×C3×#71111yescharacteristic
478C22C3×#414412yes—
479C22C3×#414912yes—
480C4—42no—
481C4—42no—
482C4—104no—
483C4—102no—
484C4—102no—
485C4—202no—
486C4C3×#402714yes—
487C3#1060802911yescharacteristic, direct product factor, Sylow
488C2—44no—
489C2—204no—
490C2C2×C3×#402711yescharacteristic
491C2C3×#6587912yes—
492C2C3×#6595312yes—
493C2C3×#6600811yescharacteristic
494C2C3×#6604911yescharacteristic
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×#2328
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. C3×C5×#390C2semidirect
5. C3×#65266C2semidirect
6. C3×#65247C2semidirect
7. C3×#65245C2semidirect
8. C3×#65228C2semidirect
9. C3×#65221C2semidirect
10. #10608029C3direct (N × H)
20. C3×#4086C4semidirect
33. C2×D4×Dic5C2×C3semidirect
34. C2×#4039C2×C3semidirect
35. C5×#390C2×C3semidirect
36. #65266C2×C3semidirect
37. #65247C2×C3semidirect
38. #65245C2×C3semidirect
39. #65228C2×C3semidirect
40. #65221C2×C3semidirect
45. C2×C3×C5×D4C2×C4semidirect
51. C2×C3×C22⋊D5C2×C4semidirect
60. C2×C3×D20C2×C4semidirect
70. C3×C4×Dic5C2×C4semidirect
71. C3×C4×Dic5D4semidirect
76. C3×#390D5semidirect
90. #4086C3×C4semidirect
159. C2×C5×D4C2×C3×C4semidirect
165. C2×C22⋊D5C2×C3×C4semidirect
174. C2×D20C2×C3×C4semidirect
184. C4×Dic5C2×C3×C4semidirect
185. C4×Dic5C3×D4semidirect
190. #390C3×D5semidirect
227. C2×C3×D4C4×D5semidirect
373. C2×D4C3×C4×D5semidirect
394. C3×C5#2328semidirect
464. C5C3×#2328semidirect
487. C3#10608029direct (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
C3×C5×#3902
C3×#652662
C3×#652472
C3×#652452
C3×#652282
C3×#652212
#106080293
C3×#23285