Finite Group Databasebeta

← C3×#10599650 #14304703

Subgroups — C3×#10599650 #14304703

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3953C211yesmaximal, characteristic
2C2×C3×#3947C211yesmaximal, characteristic, complemented
3C3×#65277C211yesmaximal, characteristic
4C3×#65274C211yesmaximal, characteristic, complemented
5C2×C3×#3941C211yesmaximal, characteristic
6C3×C5×#340C211yesmaximal, characteristic, complemented
7C3×#64749C211yesmaximal, characteristic, complemented
8#10599650C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×#685—21no—
14C2×C3×#685—21no—
15C2×C3×C4⋊Dic5—21no—
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×C3×C4×Dic5C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19C3×#3963—21no—
20C3×#3953—22no—
21C3×#3947—22no—
22C3×#3941C414yescomplemented
23C3×#1936—51nomaximal, Hall
24C2×#3953C2×C311yescharacteristic
25C2×#3947C2×C311yescharacteristic, complemented
26#65277C2×C311yescharacteristic
27#65274C2×C311yescharacteristic, complemented
28C2×#3941C2×C311yescharacteristic
29C5×#340C2×C311yescharacteristic, complemented
30#64749C2×C311yescharacteristic, complemented
31C23×C3×D5—21no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×C3×Dic5—21no—
36C22×C3×Dic5D411yescharacteristic
37C22×C3×Dic5D411yescharacteristic
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20C2×C412yes—
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8D412yes—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4C2×C412yes—
51C3×#685—42no—
52C3×#685—42no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—42no—
56C3×C4×Dic5—21no—
57C3×C4×Dic5—21no—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C2×C3×#168C2×C412yes—
61C2×C3×#102—51no—
62C2×C3×#102—51no—
63C2×C3×#97—51no—
64C3×#390—51no—
65C3×#389—51no—
66C3×#340—51no—
67C3×#340D511yescharacteristic, complemented
68C22×D20C22×C311yescharacteristic
69C22×C5×C8C22×C311yescharacteristic
70C2×C5×C4⋊C4C22×C311yescharacteristic
71C2×C5×C4⋊C4C22×C311yescharacteristic
72C2×#685—21no—
73C2×#685—21no—
74C2×C4⋊Dic5—21no—
75C2×C4⋊Dic5C22×C311yescharacteristic
76C2×C4×Dic5C22×C311yescharacteristic
77C22×#168C22×C311yescharacteristic
78#3963—21no—
79#3953—22no—
80#3947—22no—
81#3941C3×C414yescomplemented
82#1936—51noSylow
83C23×C3×C5C2×D411yescharacteristic
84C22×C3×D5—22no—
85C22×C3×D5—41no—
86C22×C3×D5—41no—
87C22×C3×D5—41no—
88C22×C3×D5—41no—
89C22×C3×D5—41no—
90C22×C3×D5—41no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×Dic5—21no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—41no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112C3×D20—22no—
113C3×D20—22no—
114C3×D20—41no—
115C3×D20—41no—
116C3×C5×C8—22no—
117C3×#168—22no—
118C22×C3×D4—51no—
119C22×C3×C8—51no—
120C22×C3×C8C2×D511yescharacteristic
121C2×C3×C4⋊C4—51no—
122C2×C3×C4⋊C4—101no—
123C2×C3×C4⋊C4C2×D511yescharacteristic
124C2×C3×C4⋊C4C2×D511yescharacteristic
125C2×C3×C22⋊C4—101no—
126C2×C3×C22⋊C4—101no—
127C2×C3×C42—51no—
128C3×#102—54no—
129C3×#102—102no—
130C3×#97—102no—
131C3×#95—101no—
132C23×D5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5C23×C311yescharacteristic
136C22×Dic5—21no—
137C22×Dic5C3×D411yescharacteristic
138C22×Dic5C3×D411yescharacteristic
139C2×D20—21no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20—21no—
144C2×D20C2×C3×C412yes—
145C2×C5×C8—21no—
146C2×C5×C8—21no—
147C2×C5×C8C3×D412yes—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4C2×C3×C412yes—
152#685—42no—
153#685—42no—
154C4⋊Dic5—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5—42no—
157C4×Dic5—21no—
158C4×Dic5—21no—
159C2×#168—21no—
160C2×#168—21no—
161C2×#168C2×C3×C412yes—
162C2×#102—51no—
163C2×#102—51no—
164C2×#97—51no—
165#390—51no—
166#389—51no—
167#340—51no—
168#340C3×D511yescharacteristic, complemented
169C22×C3×C5C4×D411yescharacteristic
170C22×C3×C5#12111yescharacteristic
171C22×C3×C5#12411yescharacteristic
172C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
173C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
174C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C2×C3×D5—42no—
177C2×C3×D5—42no—
178C2×C3×D5—42no—
179C2×C3×D5—81no—
180C2×C3×D5—81no—
181C2×C3×D5—81no—
182C2×C3×D5—81no—
183C3×C4×C5—42no—
184C3×C4×C5—81no—
185C3×C4×C5#11711yescharacteristic
186C3×C4×C5C4×D411yescharacteristic
187C3×C4×C5#12311yescharacteristic
188C3×C4×C5#12611yescharacteristic
189C3×Dic5—41no—
190C3×Dic5—41no—
191C3×Dic5—81no—
192C24×C3—101no—
193C2×C3×D4—52no—
194C2×C3×D4—101no—
195C2×C3×D4—101no—
196C2×C3×D4—101no—
197C2×C3×D4—101no—
198C2×C3×D4—101no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—51no—
202C22×C3×C4—51no—
203C22×C3×C4—101no—
204C22×C3×C4C22×D511yescharacteristic
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—52no—
208C2×C3×C8—101no—
209C2×C3×C8—101no—
210C2×C3×C8D2012yes—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—101no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—202no—
217C3×C4⋊C4C4×D512yes—
218C3×C22⋊C4—202no—
219C3×C22⋊C4—202no—
220C3×C42—101no—
221C3×C42—101no—
222C23×C5C2×C3×D411yescharacteristic
223C22×D5—22no—
224C22×D5—41no—
225C22×D5—41no—
226C22×D5—41no—
227C22×D5—41no—
228C22×D5—41no—
229C22×D5—41no—
230C2×C4×C5—22no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5C22×C3×C411yescharacteristic
237C2×C4×C5C2×C3×D411yescharacteristic
238C2×C4×C5C3×#4111yescharacteristic
239C2×C4×C5C3×#4111yescharacteristic
240C2×C4×C5C3×#4111yescharacteristic
241C2×C4×C5C3×#4111yescharacteristic
242C2×Dic5—21no—
243C2×Dic5—21no—
244C2×Dic5—21no—
245C2×Dic5—21no—
246C2×Dic5—21no—
247C2×Dic5—21no—
248C2×Dic5—41no—
249C2×Dic5—41no—
250C2×Dic5—41no—
251D20—22no—
252D20—22no—
253D20—41no—
254D20—41no—
255C5×C8—22no—
256#168—22no—
257C22×D4—51no—
258C22×C8—51no—
259C22×C8C2×C3×D511yescharacteristic
260C2×C4⋊C4—51no—
261C2×C4⋊C4—101no—
262C2×C4⋊C4C2×C3×D511yescharacteristic
263C2×C4⋊C4C2×C3×D511yescharacteristic
264C2×C22⋊C4—101no—
265C2×C22⋊C4—101no—
266C2×C42—51no—
267#102—54no—
268#102—102no—
269#97—102no—
270#95—101no—
271C2×C3×C5#38811yescharacteristic
272C2×C3×C5#44011yescharacteristic
273C2×C3×C5#44211yescharacteristic
274C2×C3×C5#46811yescharacteristic
275C2×C3×C5#46911yescharacteristic
276C2×C3×C5#48911yescharacteristic
277C2×C3×C5#49011yescharacteristic
278C3×D5—82no—
279C23×C3—102no—
280C23×C3—201no—
281C23×C3—201no—
282C23×C3—201no—
283C23×C3—201no—
284C23×C3—201no—
285C23×C3—201no—
286C23×C3D4×D511yescharacteristic
287C3×D4—102no—
288C3×D4—102no—
289C3×D4—201no—
290C3×D4—201no—
291C2×C3×C4—22no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—101no—
298C2×C3×C4—101no—
299C2×C3×C4—101no—
300C2×C3×C4—101no—
301C2×C3×C4—101no—
302C2×C3×C4—101no—
303C2×C3×C4—201no—
304C2×C3×C4—201no—
305C2×C3×C4—201no—
306C2×C3×C4C2×C4×D511yescharacteristic
307C2×C3×C4C2×D2011yescharacteristic
308C2×C3×C4#70911yescharacteristic
309C2×C3×C4#71111yescharacteristic
310C2×C3×C4#71111yescharacteristic
311C2×C3×C4#71311yescharacteristic
312C3×C8—22no—
313C3×C8—102no—
314C22×C5C3×C4×D411yescharacteristic
315C22×C5C3×#12111yescharacteristic
316C22×C5C3×#12411yescharacteristic
317C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
318C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
319C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
320C22×C5C3×#13711yescharacteristic
321C2×D5—42no—
322C2×D5—42no—
323C2×D5—42no—
324C2×D5—81no—
325C2×D5—81no—
326C2×D5—81no—
327C2×D5—81no—
328C4×C5—42no—
329C4×C5—81no—
330C4×C5C3×#11711yescharacteristic
331C4×C5C3×C4×D411yescharacteristic
332C4×C5C3×#12311yescharacteristic
333C4×C5C3×#12611yescharacteristic
334Dic5—41no—
335Dic5—41no—
336Dic5—81no—
337C24—101no—
338C2×D4—52no—
339C2×D4—101no—
340C2×D4—101no—
341C2×D4—101no—
342C2×D4—101no—
343C2×D4—101no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—51no—
347C22×C4—51no—
348C22×C4—101no—
349C22×C4C22×C3×D511yescharacteristic
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—52no—
353C2×C8—101no—
354C2×C8—101no—
355C2×C8C3×D2012yes—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—101no—
360C4⋊C4—101no—
361C4⋊C4—202no—
362C4⋊C4C3×C4×D512yes—
363C22⋊C4—202no—
364C22⋊C4—202no—
365C42—101no—
366C42—101no—
367C3×C5#193611yescharacteristic, complemented, Hall
368C22×C3—202no—
369C22×C3—202no—
370C22×C3—202no—
371C22×C3—401no—
372C22×C3—401no—
373C22×C3—401no—
374C22×C3—401no—
375C22×C3#402711yescharacteristic
376C22×C3#403111yescharacteristic
377C22×C3#404111yescharacteristic
378C22×C3#405711yescharacteristic
379C22×C3#406011yescharacteristic
380C22×C3#406011yescharacteristic
381C22×C3#406411yescharacteristic
382C3×C4—42no—
383C3×C4—81no—
384C3×C4—201no—
385C3×C4—201no—
386C3×C4—401no—
387C3×C4C4×D2011yescharacteristic
388C3×C4#403211yescharacteristic
389C3×C4#403811yescharacteristic
390C3×C4#404411yescharacteristic
391C2×C5C3×#38811yescharacteristic
392C2×C5C3×#44011yescharacteristic
393C2×C5C3×#44211yescharacteristic
394C2×C5C3×#46811yescharacteristic
395C2×C5C3×#46911yescharacteristic
396C2×C5C3×#48911yescharacteristic
397C2×C5C3×#49011yescharacteristic
398D5—82no—
399C23—102no—
400C23—201no—
401C23—201no—
402C23—201no—
403C23—201no—
404C23—201no—
405C23—201no—
406C23C3×D4×D511yescharacteristic
407D4—102no—
408D4—102no—
409D4—201no—
410D4—201no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—101no—
418C2×C4—101no—
419C2×C4—101no—
420C2×C4—101no—
421C2×C4—101no—
422C2×C4—101no—
423C2×C4—201no—
424C2×C4—201no—
425C2×C4—201no—
426C2×C4C2×C3×C4×D511yescharacteristic
427C2×C4C2×C3×D2011yescharacteristic
428C2×C4C3×#70911yescharacteristic
429C2×C4C3×#71111yescharacteristic
430C2×C4C3×#71111yescharacteristic
431C2×C4C3×#71311yescharacteristic
432C8—22no—
433C8—102no—
434C2×C3—402no—
435C2×C3#6495911yescharacteristic
436C2×C3#6505311yescharacteristic
437C2×C3#6507411yescharacteristic
438C2×C3#6508411yescharacteristic
439C2×C3#6510611yescharacteristic
440C2×C3#6515411yescharacteristic
441C2×C3#6517511yescharacteristic
442C5C3×#193611yescharacteristic, complemented, Sylow
443C22—202no—
444C22—202no—
445C22—202no—
446C22—401no—
447C22—401no—
448C22—401no—
449C22—401no—
450C22C3×#402711yescharacteristic
451C22C3×#403111yescharacteristic
452C22C3×#404111yescharacteristic
453C22C3×#405711yescharacteristic
454C22C3×#406011yescharacteristic
455C22C3×#406011yescharacteristic
456C22C3×#406411yescharacteristic
457C4—42no—
458C4—81no—
459C4—201no—
460C4—201no—
461C4—401no—
462C4C3×C4×D2011yescharacteristic
463C4C3×#403211yescharacteristic
464C4C3×#403811yescharacteristic
465C4C3×#404411yescharacteristic
466C3#1059965011yescharacteristic, direct product factor, Sylow
467C2—402no—
468C2C3×#6495911yescharacteristic
469C2C3×#6505311yescharacteristic
470C2C3×#6507411yescharacteristic
471C2C3×#6508411yescharacteristic
472C2C3×#6510611yescharacteristic
473C2C3×#6515411yescharacteristic
474C2C3×#6517511yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#340C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#340D5
hypocenterC5C3×#1936
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C3×#340

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3947C2semidirect
4. C3×#65274C2semidirect
6. C3×C5×#340C2semidirect
7. C3×#64749C2semidirect
8. #10599650C3direct (N × H)
22. C3×#3941C4semidirect
25. C2×#3947C2×C3semidirect
27. #65274C2×C3semidirect
29. C5×#340C2×C3semidirect
30. #64749C2×C3semidirect
67. C3×#340D5semidirect
81. #3941C3×C4semidirect
168. #340C3×D5semidirect
367. C3×C5#1936semidirect
442. C5C3×#1936semidirect
466. C3#10599650direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#39532
C2×C3×#39472
C3×#652772
C3×#652742
C2×C3×#39412
C3×C5×#3402
C3×#647492
#105996503
C3×#19365