Finite Group Databasebeta

← C3×#10600962 #14300074

Subgroups — C3×#10600962 #14300074

Order 1920.

724 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×D4×Dic5C211yesmaximal, characteristic
2C2×C3×C5×#102C211yesmaximal, characteristic
3C2×C3×#3964C211yesmaximal, characteristic
4C3×#65262C211yesmaximal, characteristic, complemented
5C2×C3×#3940C211yesmaximal, characteristic, complemented
6C3×#64771C211yesmaximal, characteristic, complemented
7C3×#64770C211yesmaximal, characteristic, complemented
8#10600962C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C23×C3×Dic5—21no—
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C22⋊Dic5—21no—
14C3×D4×Dic5—22no—
15C3×D4×Dic5—22no—
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C2×C3×#683—21no—
19C2×C3×C4×Dic5C2211yescharacteristic
20C22×C3×#168C2211yescharacteristic
21C3×C5×#102—22no—
22C3×#3964C414yescomplemented
23C3×#3963—21no—
24C3×#3940—22no—
25C3×#1864—51nomaximal, Hall
26C2×D4×Dic5C2×C311yescharacteristic
27C2×C5×#102C2×C311yescharacteristic
28C2×#3964C2×C311yescharacteristic
29#65262C2×C311yescharacteristic, complemented
30C2×#3940C2×C311yescharacteristic, complemented
31#64771C2×C311yescharacteristic, complemented
32#64770C2×C311yescharacteristic, complemented
33C24×C3×C5—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C412yes—
38C2×C3×C5×D4D412yes—
39C2×C3×C5×D4Q812yes—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C22×C3×Dic5—24no—
43C22×C3×Dic5—21no—
44C22×C3×Dic5—21no—
45C22×C3×Dic5—42no—
46C22×C3×Dic5—42no—
47C22×C3×Dic5D411yescharacteristic
48C22×C3×Dic5D411yescharacteristic
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8—21no—
51C2×C3×C5×C8—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C22⋊Dic5—24no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5C2×C412yescomplemented
58C3×C4⋊Dic5D412yes—
59C3×#683—42no—
60C3×C4×Dic5—21no—
61C3×C4×Dic5—21no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C2×C3×#168C2×C412yescomplemented
65C2×C3×C4×D4—51no—
66C2×C3×#106—51no—
67C2×C3×#102—51no—
68C2×C3×#102D511yescharacteristic
69C3×#389—51no—
70C3×#340—51no—
71C3×#336—51no—
72C22×C5×D4C22×C311yescharacteristic
73C23×Dic5—21no—
74C22×C5×C8C22×C311yescharacteristic
75C2×C5×C4⋊C4C22×C311yescharacteristic
76C2×C22⋊Dic5—21no—
77D4×Dic5—22no—
78D4×Dic5—22no—
79C2×C4⋊Dic5C22×C311yescharacteristic
80C2×C4⋊Dic5C22×C311yescharacteristic
81C2×#683—21no—
82C2×C4×Dic5C22×C311yescharacteristic
83C22×#168C22×C311yescharacteristic
84C5×#102—22no—
85#3964C3×C414yescomplemented
86#3963—21no—
87#3940—22no—
88#1864—51noSylow
89C23×C3×C5—22no—
90C23×C3×C5—22no—
91C23×C3×C5—22no—
92C23×C3×C5—41no—
93C23×C3×C5—41no—
94C23×C3×C5—41no—
95C23×C3×C5—41no—
96C23×C3×C5C2×D411yescharacteristic
97C3×C5×D4—22no—
98C3×C5×D4—22no—
99C3×C5×D4—22no—
100C3×C5×D4C4⋊C414yescomplemented
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×Q811yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—48no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5SD1612yes—
123C3×C5×C8—41no—
124C3×#168—22no—
125C22×C3×D4C2×D511yescharacteristic
126C23×C3×C4—101no—
127C22×C3×C8—51no—
128C22×C3×C8C2×D511yescharacteristic
129C3×C4×D4—102no—
130C3×C4×D4—102no—
131C2×C3×C4⋊C4—51no—
132C2×C3×C4⋊C4—51no—
133C2×C3×C4⋊C4—101no—
134C2×C3×C4⋊C4C2×D511yescharacteristic
135C2×C3×C22⋊C4—101no—
136C2×C3×C42—51no—
137C3×#106—102no—
138C3×#102—22no—
139C3×#102—54no—
140C3×#95—101no—
141C24×C5—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4C2×C3×C412yes—
146C2×C5×D4C3×D412yes—
147C2×C5×D4C3×Q812yes—
148C22×C4×C5—21no—
149C22×C4×C5C23×C311yescharacteristic
150C22×Dic5—24no—
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—42no—
154C22×Dic5—42no—
155C22×Dic5C3×D411yescharacteristic
156C22×Dic5C3×D411yescharacteristic
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C2×C5×C8—21no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C22⋊Dic5—24no—
163C4⋊Dic5—21no—
164C4⋊Dic5—21no—
165C4⋊Dic5C2×C3×C412yescomplemented
166C4⋊Dic5C3×D412yes—
167#683—42no—
168C4×Dic5—21no—
169C4×Dic5—21no—
170C2×#168—21no—
171C2×#168—21no—
172C2×#168C2×C3×C412yescomplemented
173C2×C4×D4—51no—
174C2×#106—51no—
175C2×#102—51no—
176C2×#102C3×D511yescharacteristic
177#389—51no—
178#340—51no—
179#336—51no—
180C22×C3×C5—24no—
181C22×C3×C5—42no—
182C22×C3×C5—42no—
183C22×C3×C5—42no—
184C22×C3×C5—42no—
185C22×C3×C5—42no—
186C22×C3×C5—42no—
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5#12011yescharacteristic
189C22×C3×C5C22⋊Q811yescharacteristic
190C22×C3×C5C2×SD1611yescharacteristic
191C22×C3×C5#13511yescharacteristic
192C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
193C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
194C3×C4×C5—81no—
195C3×C4×C5C2×C4⋊C411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5C22⋊Q811yescharacteristic
198C3×C4×C5#12311yescharacteristic
199C3×Dic5—22no—
200C3×Dic5—42no—
201C3×Dic5—41no—
202C3×Dic5—42no—
203C24×C3—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4Dic1012yes—
208C2×C3×D4C4×D512yes—
209C2×C3×D4C22⋊D512yes—
210C22×C3×C4—21no—
211C22×C3×C4—51no—
212C22×C3×C4—51no—
213C22×C3×C4—104no—
214C22×C3×C4—101no—
215C22×C3×C4—101no—
216C22×C3×C4—202no—
217C22×C3×C4—202no—
218C22×C3×C4C22×D511yescharacteristic
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—52no—
223C2×C3×C8—101no—
224C2×C3×C8—101no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—52no—
228C3×C4⋊C4—52no—
229C3×C4⋊C4—101no—
230C3×C4⋊C4—101no—
231C3×C4⋊C4—202no—
232C3×C22⋊C4—104no—
233C3×C42—101no—
234C3×C42—101no—
235C23×C5—22no—
236C23×C5—22no—
237C23×C5—22no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5—41no—
241C23×C5—41no—
242C23×C5C2×C3×D411yescharacteristic
243C5×D4—22no—
244C5×D4—22no—
245C5×D4—22no—
246C5×D4C3×C4⋊C414yescomplemented
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5C22×C3×C411yescharacteristic
251C2×C4×C5C2×C3×D411yescharacteristic
252C2×C4×C5C2×C3×D411yescharacteristic
253C2×C4×C5C2×C3×Q811yescharacteristic
254C2×C4×C5C3×#4111yescharacteristic
255C2×C4×C5C3×#4111yescharacteristic
256C2×Dic5—21no—
257C2×Dic5—21no—
258C2×Dic5—22no—
259C2×Dic5—21no—
260C2×Dic5—22no—
261C2×Dic5—21no—
262C2×Dic5—21no—
263C2×Dic5—48no—
264C2×Dic5—41no—
265C2×Dic5—41no—
266C2×Dic5—41no—
267C2×Dic5—41no—
268C2×Dic5C3×SD1612yes—
269C5×C8—41no—
270#168—22no—
271C22×D4C2×C3×D511yescharacteristic
272C23×C4—101no—
273C22×C8—51no—
274C22×C8C2×C3×D511yescharacteristic
275C4×D4—102no—
276C4×D4—102no—
277C2×C4⋊C4—51no—
278C2×C4⋊C4—51no—
279C2×C4⋊C4—101no—
280C2×C4⋊C4C2×C3×D511yescharacteristic
281C2×C22⋊C4—101no—
282C2×C42—51no—
283#106—102no—
284#102—22no—
285#102—54no—
286#95—101no—
287C2×C3×C5—44no—
288C2×C3×C5#38511yescharacteristic
289C2×C3×C5C4×SD1611yescharacteristic
290C2×C3×C5#44211yescharacteristic
291C2×C3×C5#44911yescharacteristic
292C2×C3×C5#45011yescharacteristic
293C2×C3×C5#47611yescharacteristic
294C2×C3×C5#47811yescharacteristic
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3D4×D511yescharacteristic
303C3×D4—22no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4#68314yescomplemented
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—52no—
311C2×C3×C4—101no—
312C2×C3×C4—101no—
313C2×C3×C4—102no—
314C2×C3×C4—101no—
315C2×C3×C4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—102no—
318C2×C3×C4—208no—
319C2×C3×C4—201no—
320C2×C3×C4—201no—
321C2×C3×C4—201no—
322C2×C3×C4—201no—
323C2×C3×C4C2×Dic1011yescharacteristic
324C2×C3×C4C2×C4×D511yescharacteristic
325C2×C3×C4D4×D511yescharacteristic
326C2×C3×C4#71111yescharacteristic
327C2×C3×C4#71111yescharacteristic
328C2×C3×C4C2×C22⋊D511yescharacteristic
329C3×C8—41no—
330C3×C8—102no—
331C22×C5—24no—
332C22×C5—42no—
333C22×C5—42no—
334C22×C5—42no—
335C22×C5—42no—
336C22×C5—42no—
337C22×C5—42no—
338C22×C5C3×C4×D411yescharacteristic
339C22×C5C3×#12011yescharacteristic
340C22×C5C3×C22⋊Q811yescharacteristic
341C22×C5C2×C3×SD1611yescharacteristic
342C22×C5C3×#13511yescharacteristic
343C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
344C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
345C4×C5—81no—
346C4×C5C2×C3×C4⋊C411yescharacteristic
347C4×C5C3×C4×D411yescharacteristic
348C4×C5C3×C22⋊Q811yescharacteristic
349C4×C5C3×#12311yescharacteristic
350Dic5—22no—
351Dic5—42no—
352Dic5—41no—
353Dic5—42no—
354C24—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4C3×Dic1012yes—
359C2×D4C3×C4×D512yes—
360C2×D4C3×C22⋊D512yes—
361C22×C4—21no—
362C22×C4—51no—
363C22×C4—51no—
364C22×C4—104no—
365C22×C4—101no—
366C22×C4—101no—
367C22×C4—202no—
368C22×C4—202no—
369C22×C4C22×C3×D511yescharacteristic
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—52no—
374C2×C8—101no—
375C2×C8—101no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—52no—
379C4⋊C4—52no—
380C4⋊C4—101no—
381C4⋊C4—101no—
382C4⋊C4—202no—
383C22⋊C4—104no—
384C42—101no—
385C42—101no—
386C3×C5#186411yescharacteristic, complemented, Hall
387C22×C3—24no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3#402411yescharacteristic
395C22×C3#402711yescharacteristic
396C22×C3#405711yescharacteristic
397C22×C3#405811yescharacteristic
398C22×C3D5×SD1611yescharacteristic
399C22×C3#406011yescharacteristic
400C22×C3#408311yescharacteristic
401C3×C4—81no—
402C3×C4—102no—
403C3×C4—202no—
404C3×C4—201no—
405C3×C4—202no—
406C3×C4#402411yescharacteristic
407C3×C4#402711yescharacteristic
408C3×C4C2×#68311yescharacteristic
409C3×C4#408111yescharacteristic
410C2×C5—44no—
411C2×C5C3×#38511yescharacteristic
412C2×C5C3×C4×SD1611yescharacteristic
413C2×C5C3×#44211yescharacteristic
414C2×C5C3×#44911yescharacteristic
415C2×C5C3×#45011yescharacteristic
416C2×C5C3×#47611yescharacteristic
417C2×C5C3×#47811yescharacteristic
418C23—22no—
419C23—22no—
420C23—22no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23C3×D4×D511yescharacteristic
426D4—22no—
427D4—22no—
428D4—22no—
429D4C3×#68314yescomplemented
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—52no—
434C2×C4—101no—
435C2×C4—101no—
436C2×C4—101no—
437C2×C4—102no—
438C2×C4—102no—
439C2×C4—101no—
440C2×C4—101no—
441C2×C4—208no—
442C2×C4—201no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4—201no—
446C2×C4C2×C3×Dic1011yescharacteristic
447C2×C4C2×C3×C4×D511yescharacteristic
448C2×C4C3×D4×D511yescharacteristic
449C2×C4C3×#71111yescharacteristic
450C2×C4C3×#71111yescharacteristic
451C2×C4C2×C3×C22⋊D511yescharacteristic
452C8—41no—
453C8—102no—
454C2×C3—44no—
455C2×C3#6504711yescharacteristic
456C2×C3#6505011yescharacteristic
457C2×C3#6505511yescharacteristic
458C2×C3#6507411yescharacteristic
459C2×C3#6523511yescharacteristic
460C2×C3#6544711yescharacteristic
461C2×C3#6545811yescharacteristic
462C5C3×#186411yescharacteristic, complemented, Sylow
463C22—24no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22C3×#402411yescharacteristic
471C22C3×#402711yescharacteristic
472C22C3×#405711yescharacteristic
473C22C3×#405811yescharacteristic
474C22C3×D5×SD1611yescharacteristic
475C22C3×#406011yescharacteristic
476C22C3×#408311yescharacteristic
477C4—81no—
478C4—102no—
479C4—202no—
480C4—201no—
481C4—202no—
482C4C3×#402411yescharacteristic
483C4C3×#402711yescharacteristic
484C4C2×C3×#68311yescharacteristic
485C4C3×#408111yescharacteristic
486C3#1060096211yescharacteristic, direct product factor, Sylow
487C2—44no—
488C2C3×#6504711yescharacteristic
489C2C3×#6505011yescharacteristic
490C2C3×#6505511yescharacteristic
491C2C3×#6507411yescharacteristic
492C2C3×#6523511yescharacteristic
493C2C3×#6544711yescharacteristic
494C2C3×#6545811yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#102D5
hypocenterC5C3×#1864
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
4. C3×#65262C2semidirect
5. C2×C3×#3940C2semidirect
6. C3×#64771C2semidirect
7. C3×#64770C2semidirect
8. #10600962C3direct (N × H)
22. C3×#3964C4semidirect
29. #65262C2×C3semidirect
30. C2×#3940C2×C3semidirect
31. #64771C2×C3semidirect
32. #64770C2×C3semidirect
57. C3×C4⋊Dic5C2×C4semidirect
64. C2×C3×#168C2×C4semidirect
85. #3964C3×C4semidirect
100. C3×C5×D4C4⋊C4semidirect
165. C4⋊Dic5C2×C3×C4semidirect
172. C2×#168C2×C3×C4semidirect
246. C5×D4C3×C4⋊C4semidirect
306. C3×D4#683semidirect
386. C3×C5#1864semidirect
429. D4C3×#683semidirect
462. C5C3×#1864semidirect
486. C3#10600962direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic52
C2×C3×C5×#1022
C2×C3×#39642
C3×#652622
C2×C3×#39402
C3×#647712
C3×#647702
#106009623
C3×#18645