Finite Group Databasebeta

← C3×#10600953 #14305953

Subgroups — C3×#10600953 #14305953

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4086C211yesmaximal, characteristic
2C2×C3×C5×#102C211yesmaximal, characteristic, complemented
3C2×C3×#3964C211yesmaximal, characteristic, complemented
4C2×C3×#3953C211yesmaximal, characteristic, complemented
5C2×C3×#3947C211yesmaximal, characteristic, complemented
6C3×#65266C211yesmaximal, characteristic, complemented
7C2×C3×#3941C211yesmaximal, characteristic, complemented
8#10600953C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×C22⋊D5—22no—
11C22×C3×D20C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C3×#4086—22no—
15C3×#4086C414yescomplemented
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×C3×C4×Dic5C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19C3×C5×#102—22no—
20C3×#3964—22no—
21C3×#3963—22no—
22C3×#3953—22no—
23C3×#3947—22no—
24C3×#3941—22no—
25C3×#1961—51nomaximal, Hall
26C2×#4086C2×C311yescharacteristic
27C2×C5×#102C2×C311yescharacteristic, complemented
28C2×#3964C2×C311yescharacteristic, complemented
29C2×#3953C2×C311yescharacteristic, complemented
30C2×#3947C2×C311yescharacteristic, complemented
31#65266C2×C311yescharacteristic, complemented
32C2×#3941C2×C311yescharacteristic, complemented
33C24×C3×C5—21no—
34C23×C3×D5—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C412yes—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C2×C3×C22⋊D5—28no—
44C2×C3×C22⋊D5—44no—
45C2×C3×C22⋊D5—44no—
46C22×C3×Dic5—21no—
47C22×C3×Dic5D412yes—
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20—21no—
51C2×C3×D20—21no—
52C2×C3×D20—21no—
53C2×C3×D20C2×C412yes—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8D412yescomplemented
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—21no—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C3×C4×Dic5C2×C412yes—
62C3×C4×Dic5D412yes—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65C2×C3×#168D412yescomplemented
66C2×C3×#127—51no—
67C2×C3×#102—51no—
68C2×C3×#102—51no—
69C2×C3×#102—51no—
70C2×C3×#102D511yescharacteristic, complemented
71C2×C3×#97—51no—
72C3×#382—51no—
73C22×C5×D4C22×C311yescharacteristic
74C22×C22⋊D5—22no—
75C22×D20C22×C311yescharacteristic
76C22×C5×C8C22×C311yescharacteristic
77C2×C5×C4⋊C4C22×C311yescharacteristic
78#4086—22no—
79#4086C3×C414yescomplemented
80C2×C4⋊Dic5C22×C311yescharacteristic
81C2×C4×Dic5C22×C311yescharacteristic
82C22×#168C22×C311yescharacteristic
83C5×#102—22no—
84#3964—22no—
85#3963—22no—
86#3953—22no—
87#3947—22no—
88#3941—22no—
89#1961—51noSylow
90C23×C3×C5—22no—
91C23×C3×C5—41no—
92C23×C3×C5—41no—
93C23×C3×C5—42no—
94C23×C3×C5—42no—
95C23×C3×C5C2×D411yescharacteristic
96C22×C3×D5—22no—
97C22×C3×D5—41no—
98C22×C3×D5—41no—
99C22×C3×D5—42no—
100C22×C3×D5—42no—
101C3×C5×D4—22no—
102C3×C5×D4—22no—
103C3×C5×D4—41no—
104C3×C5×D4—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—42no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C3×C22⋊D5—416no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—42no—
118C2×C3×Dic5C22⋊C414yes—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20—41no—
122C3×D20—41no—
123C3×C5×C8—22no—
124C3×#168—22no—
125C22×C3×D4—51no—
126C22×C3×D4—102no—
127C22×C3×D4C2×D511yescharacteristic
128C22×C3×C8—51no—
129C22×C3×C8C2×D511yescharacteristic
130C3×#127—54no—
131C3×#127—102no—
132C2×C3×C4⋊C4—51no—
133C2×C3×C4⋊C4C2×D511yescharacteristic
134C2×C3×C42—51no—
135C3×#102—22no—
136C3×#102—102no—
137C3×#102—102no—
138C3×#102—102no—
139C3×#97—102no—
140C3×#95—102no—
141C24×C5—21no—
142C23×D5—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4C2×C3×C412yes—
149C22×C4×C5—21no—
150C22×C4×C5C23×C311yescharacteristic
151C2×C22⋊D5—28no—
152C2×C22⋊D5—44no—
153C2×C22⋊D5—44no—
154C22×Dic5—21no—
155C22×Dic5C3×D412yes—
156C2×D20—21no—
157C2×D20—21no—
158C2×D20—21no—
159C2×D20—21no—
160C2×D20—21no—
161C2×D20C2×C3×C412yes—
162C2×C5×C8—21no—
163C2×C5×C8—21no—
164C2×C5×C8C3×D412yescomplemented
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C4⋊Dic5—21no—
168C4⋊Dic5—21no—
169C4×Dic5C2×C3×C412yes—
170C4×Dic5C3×D412yes—
171C2×#168—21no—
172C2×#168—21no—
173C2×#168C3×D412yescomplemented
174C2×#127—51no—
175C2×#102—51no—
176C2×#102—51no—
177C2×#102—51no—
178C2×#102C3×D511yescharacteristic, complemented
179C2×#97—51no—
180#382—51no—
181C22×C3×C5—42no—
182C22×C3×C5—44no—
183C22×C3×C5—82no—
184C22×C3×C5—81no—
185C22×C3×C5—81no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5#12411yescharacteristic
188C22×C3×C5#12711yescharacteristic
189C22×C3×C5AGL(1,ℤ/8)12yes—
190C22×C3×C5AGL(1,ℤ/8)12yes—
191C2×C3×D5—42no—
192C2×C3×D5—44no—
193C2×C3×D5—82no—
194C2×C3×D5—81no—
195C2×C3×D5—81no—
196C3×C4×C5—81no—
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5C4×D411yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12111yescharacteristic
201C3×Dic5—24no—
202C3×Dic5—81no—
203C24×C3—21no—
204C24×C3—101no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—52no—
211C2×C3×D4—108no—
212C2×C3×D4—101no—
213C2×C3×D4—101no—
214C2×C3×D4—101no—
215C2×C3×D4—101no—
216C2×C3×D4—101no—
217C2×C3×D4—204no—
218C2×C3×D4—204no—
219C2×C3×D4C4×D512yes—
220C22×C3×C4—21no—
221C22×C3×C4—52no—
222C22×C3×C4—101no—
223C22×C3×C4C22×D511yescharacteristic
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—52no—
227C2×C3×C8—101no—
228C2×C3×C8—101no—
229C2×C3×C8C22⋊D512yescomplemented
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—101no—
233C3×C4⋊C4—101no—
234C3×C42—52no—
235C3×C42—52no—
236C23×C5—22no—
237C23×C5—41no—
238C23×C5—41no—
239C23×C5—42no—
240C23×C5—42no—
241C23×C5C2×C3×D411yescharacteristic
242C22×D5—22no—
243C22×D5—41no—
244C22×D5—41no—
245C22×D5—42no—
246C22×D5—42no—
247C5×D4—22no—
248C5×D4—22no—
249C5×D4—41no—
250C5×D4—41no—
251C2×C4×C5—41no—
252C2×C4×C5—42no—
253C2×C4×C5C22×C3×C411yescharacteristic
254C2×C4×C5C2×C3×D411yescharacteristic
255C2×C4×C5C2×C3×D411yescharacteristic
256C2×C4×C5C2×C3×D411yescharacteristic
257C2×C4×C5C3×#4111yescharacteristic
258C2×C4×C5C3×#4111yescharacteristic
259C22⋊D5—416no—
260C2×Dic5—22no—
261C2×Dic5—22no—
262C2×Dic5—41no—
263C2×Dic5—42no—
264C2×Dic5C3×C22⋊C414yes—
265D20—22no—
266D20—22no—
267D20—41no—
268D20—41no—
269C5×C8—22no—
270#168—22no—
271C22×D4—51no—
272C22×D4—102no—
273C22×D4C2×C3×D511yescharacteristic
274C22×C8—51no—
275C22×C8C2×C3×D511yescharacteristic
276#127—54no—
277#127—102no—
278C2×C4⋊C4—51no—
279C2×C4⋊C4C2×C3×D511yescharacteristic
280C2×C42—51no—
281#102—22no—
282#102—102no—
283#102—102no—
284#102—102no—
285#97—102no—
286#95—102no—
287C2×C3×C5—82no—
288C2×C3×C5#39011yescharacteristic
289C2×C3×C5#41812yes—
290C2×C3×C5#49012yes—
291C2×C3×C5#49611yescharacteristic
292C2×C3×C5#49611yescharacteristic
293C3×D5—82no—
294C23×C3—22no—
295C23×C3—41no—
296C23×C3—42no—
297C23×C3—42no—
298C23×C3—41no—
299C23×C3—102no—
300C23×C3—201no—
301C23×C3—202no—
302C23×C3—202no—
303C23×C3—201no—
304C23×C3D4×D511yescharacteristic
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—41no—
308C3×D4—41no—
309C3×D4—102no—
310C3×D4—102no—
311C3×D4—2016no—
312C3×D4—201no—
313C3×D4—201no—
314C2×C3×C4—42no—
315C2×C3×C4—41no—
316C2×C3×C4—54no—
317C2×C3×C4—102no—
318C2×C3×C4—102no—
319C2×C3×C4—202no—
320C2×C3×C4—201no—
321C2×C3×C4C2×C4×D511yescharacteristic
322C2×C3×C4#70911yescharacteristic
323C2×C3×C4D4×D511yescharacteristic
324C2×C3×C4D4×D511yescharacteristic
325C2×C3×C4#71111yescharacteristic
326C2×C3×C4C2×C22⋊D511yescharacteristic
327C3×C8—22no—
328C3×C8—102no—
329C22×C5—42no—
330C22×C5—44no—
331C22×C5—82no—
332C22×C5—81no—
333C22×C5—81no—
334C22×C5C2×C3×C22⋊C411yescharacteristic
335C22×C5C3×#12411yescharacteristic
336C22×C5C3×#12711yescharacteristic
337C22×C5C3×AGL(1,ℤ/8)12yes—
338C22×C5C3×AGL(1,ℤ/8)12yes—
339C2×D5—42no—
340C2×D5—44no—
341C2×D5—82no—
342C2×D5—81no—
343C2×D5—81no—
344C4×C5—81no—
345C4×C5C3×C4×D411yescharacteristic
346C4×C5C3×C4×D411yescharacteristic
347C4×C5C3×#12111yescharacteristic
348C4×C5C3×#12111yescharacteristic
349Dic5—24no—
350Dic5—81no—
351C24—21no—
352C24—101no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—52no—
359C2×D4—108no—
360C2×D4—101no—
361C2×D4—101no—
362C2×D4—101no—
363C2×D4—101no—
364C2×D4—101no—
365C2×D4—204no—
366C2×D4—204no—
367C2×D4C3×C4×D512yes—
368C22×C4—21no—
369C22×C4—52no—
370C22×C4—101no—
371C22×C4C22×C3×D511yescharacteristic
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—52no—
375C2×C8—101no—
376C2×C8—101no—
377C2×C8C3×C22⋊D512yescomplemented
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—101no—
381C4⋊C4—101no—
382C42—52no—
383C42—52no—
384C3×C5#196111yescharacteristic, complemented, Hall
385C22×C3—44no—
386C22×C3—42no—
387C22×C3—82no—
388C22×C3—81no—
389C22×C3—81no—
390C22×C3—204no—
391C22×C3—202no—
392C22×C3—402no—
393C22×C3—401no—
394C22×C3—401no—
395C22×C3D5×C22⋊C411yescharacteristic
396C22×C3#403111yescharacteristic
397C22×C3#405712yes—
398C22×C3#406012yes—
399C22×C3#408611yescharacteristic
400C3×C4—81no—
401C3×C4—104no—
402C3×C4—401no—
403C3×C4#402711yescharacteristic
404C3×C4#403011yescharacteristic
405C3×C4C4×C22⋊D511yescharacteristic
406C3×C4#408511yescharacteristic
407C2×C5—82no—
408C2×C5C3×#39011yescharacteristic
409C2×C5C3×#41812yes—
410C2×C5C3×#49012yes—
411C2×C5C3×#49611yescharacteristic
412C2×C5C3×#49611yescharacteristic
413D5—82no—
414C23—22no—
415C23—41no—
416C23—41no—
417C23—42no—
418C23—42no—
419C23—102no—
420C23—201no—
421C23—201no—
422C23—202no—
423C23—202no—
424C23C3×D4×D511yescharacteristic
425D4—22no—
426D4—22no—
427D4—41no—
428D4—41no—
429D4—102no—
430D4—102no—
431D4—2016no—
432D4—201no—
433D4—201no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—54no—
437C2×C4—102no—
438C2×C4—102no—
439C2×C4—201no—
440C2×C4—202no—
441C2×C4C2×C3×C4×D511yescharacteristic
442C2×C4C3×#70911yescharacteristic
443C2×C4C3×D4×D511yescharacteristic
444C2×C4C3×D4×D511yescharacteristic
445C2×C4C3×#71111yescharacteristic
446C2×C4C2×C3×C22⋊D511yescharacteristic
447C8—22no—
448C8—102no—
449C2×C3—82no—
450C2×C3—402no—
451C2×C3#6505312yes—
452C2×C3#6505912yes—
453C2×C3#6524611yescharacteristic
454C2×C3#6544311yescharacteristic
455C2×C3#6546511yescharacteristic
456C5C3×#196111yescharacteristic, complemented, Sylow
457C22—44no—
458C22—42no—
459C22—82no—
460C22—81no—
461C22—81no—
462C22—204no—
463C22—202no—
464C22—402no—
465C22—401no—
466C22—401no—
467C22C3×D5×C22⋊C411yescharacteristic
468C22C3×#403111yescharacteristic
469C22C3×#405712yes—
470C22C3×#406012yes—
471C22C3×#408611yescharacteristic
472C4—81no—
473C4—104no—
474C4—401no—
475C4C3×#402711yescharacteristic
476C4C3×#403011yescharacteristic
477C4C3×C4×C22⋊D511yescharacteristic
478C4C3×#408511yescharacteristic
479C3#1060095311yescharacteristic, direct product factor, Sylow
480C2—82no—
481C2—402no—
482C2C3×#6505312yes—
483C2C3×#6505912yes—
484C2C3×#6524611yescharacteristic
485C2C3×#6544311yescharacteristic
486C2C3×#6546511yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC2×C3×#4086C2
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#102D5
hypocenterC5C3×#1961
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#102C2semidirect
3. C2×C3×#3964C2semidirect
4. C2×C3×#3953C2semidirect
5. C2×C3×#3947C2semidirect
6. C3×#65266C2semidirect
7. C2×C3×#3941C2semidirect
8. #10600953C3direct (N × H)
15. C3×#4086C4semidirect
27. C2×C5×#102C2×C3semidirect
28. C2×#3964C2×C3semidirect
29. C2×#3953C2×C3semidirect
30. C2×#3947C2×C3semidirect
31. #65266C2×C3semidirect
32. C2×#3941C2×C3semidirect
56. C2×C3×C5×C8D4semidirect
65. C2×C3×#168D4semidirect
70. C2×C3×#102D5semidirect
79. #4086C3×C4semidirect
164. C2×C5×C8C3×D4semidirect
173. C2×#168C3×D4semidirect
178. C2×#102C3×D5semidirect
229. C2×C3×C8C22⋊D5semidirect
377. C2×C8C3×C22⋊D5semidirect
384. C3×C5#1961semidirect
456. C5C3×#1961semidirect
479. C3#10600953direct (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×C5×#1022
C2×C3×#39642
C2×C3×#39532
C2×C3×#39472
C3×#652662
C2×C3×#39412
#106009533
C3×#19615