Finite Group Databasebeta

← C3×#10600301 #14283409

Subgroups — C3×#10600301 #14283409

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66125C211yesmaximal, characteristic
2C3×C5×#380C211yesmaximal, characteristic, complemented
3C3×#65496C211yesmaximal, characteristic, complemented
4C3×#64672C212yesmaximal, complemented
5C3×#64671C212yesmaximal, complemented
6#10600301C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×#709C411yescharacteristic, complemented
9C2×C3×C5×C4⋊C4—21no—
10C2×C3×C5×C22⋊C4—21no—
11C3×#4099—21no—
12C3×#4076C411yescharacteristic, complemented
13C3×#4076C2211yescharacteristic
14C3×#4075—21no—
15C3×C4×C22⋊D5—21no—
16C3×C4×C22⋊D5—21no—
17C3×#4072C411yescharacteristic, complemented
18C3×#4070C411yescharacteristic, complemented
19C3×#4070C2211yescharacteristic
20C2×C3×#681—21no—
21C3×C5×#95C2212yes—
22C3×C22⋊#168—21no—
23C3×C22⋊#168C2212yes—
24C3×#1513—51nomaximal, Hall
25#66125C2×C311yescharacteristic
26C5×#380C2×C311yescharacteristic, complemented
27#65496C2×C311yescharacteristic, complemented
28#64672C2×C312yescomplemented
29#64671C2×C312yescomplemented
30C24×C3×C5D411yescharacteristic
31C22×C3×C4×C5—22no—
32C22×C3×C4×C5—42no—
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5C2×C411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C3×#709—42no—
43C2×C3×D20C2×C411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×C3×Dic10C2×C411yescharacteristic
46C3×C5×C4⋊C4—42no—
47C3×C5×C22⋊C4—42no—
48C3×C22⋊Dic5—21no—
49C3×C22⋊Dic5—21no—
50C3×C22⋊Dic5—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C3×#683—21no—
57C3×C4×Dic5—21no—
58C3×#681—42no—
59C2×C3×#168—22no—
60C3×#525—51no—
61C3×#407—51no—
62C3×#380D511yescharacteristic, complemented
63C3×#328—52no—
64C3×#327—52no—
65C23×C4×C5C22×C311yescharacteristic
66C2×#709C3×C411yescharacteristic, complemented
67C2×C5×C4⋊C4—21no—
68C2×C5×C22⋊C4—21no—
69#4099—21no—
70#4076C3×C411yescharacteristic, complemented
71#4076C22×C311yescharacteristic
72#4075—21no—
73C4×C22⋊D5—21no—
74C4×C22⋊D5—21no—
75#4072C3×C411yescharacteristic, complemented
76#4070C3×C411yescharacteristic, complemented
77#4070C22×C311yescharacteristic
78C2×#681—21no—
79C5×#95C22×C312yes—
80C22⋊#168—21no—
81C22⋊#168C22×C312yes—
82#1513—51noSylow
83C23×C3×C5—21no—
84C23×C3×C5—21no—
85C23×C3×C5—41no—
86C23×C3×C5—41no—
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C22⋊C411yescharacteristic
89C23×C3×C5C2×D411yescharacteristic
90C22×C3×D5—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—42no—
98C2×C3×C4×C5—42no—
99C2×C3×C4×C5—42no—
100C2×C3×C4×C5C22⋊C411yescharacteristic
101C2×C3×C4×C5C22⋊C411yescharacteristic
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C3×C22⋊D5—42no—
105C3×C22⋊D5—42no—
106C3×C22⋊D5—41no—
107C3×C22⋊D5—41no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C3×D20—41no—
112C3×C4×D5—42no—
113C3×Dic10—41no—
114C3×#168—42no—
115C2×C3×#41—51no—
116C23×C3×C4C2×D511yescharacteristic
117C2×C3×M16—101no—
118C3×#123—101no—
119C3×C22⋊Q8—51no—
120C3×C22⋊Q8—51no—
121C3×#121—51no—
122C3×#121—51no—
123C3×#120—101no—
124C3×C4×D4—101no—
125C3×C4×D4—101no—
126C3×#117—51no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C3×C22⋊C8—52no—
130C3×C22⋊C8—101no—
131C3×#95C2×D512yes—
132C24×C5C3×D411yescharacteristic
133C22×C4×C5—22no—
134C22×C4×C5—42no—
135C22×C4×C5C2×C3×C411yescharacteristic
136C22×C4×C5C2×C3×C411yescharacteristic
137C22×C4×C5C3×D411yescharacteristic
138C22×C4×C5C3×D411yescharacteristic
139C22×C4×C5C3×D411yescharacteristic
140C22×C4×C5C23×C311yescharacteristic
141C2×C22⋊D5—21no—
142C2×C22⋊D5—21no—
143C2×C22⋊D5—21no—
144#709—42no—
145C2×D20C2×C3×C411yescharacteristic
146C2×C4×D5—21no—
147C2×Dic10C2×C3×C411yescharacteristic
148C5×C4⋊C4—42no—
149C5×C22⋊C4—42no—
150C22⋊Dic5—21no—
151C22⋊Dic5—21no—
152C22⋊Dic5—21no—
153#685—21no—
154#685—21no—
155C4⋊Dic5C2×C3×C411yescharacteristic
156C4⋊Dic5C2×C3×C411yescharacteristic
157#683—21no—
158#683—21no—
159C4×Dic5—21no—
160#681—42no—
161C2×#168—22no—
162#525—51no—
163#407—51no—
164#380C3×D511yescharacteristic, complemented
165#328—52no—
166#327—52no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—21no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—42no—
176C22×C3×C5—42no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×C3×D5—41no—
181C2×C3×D5—41no—
182C2×C3×D5—41no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—21no—
186C3×C4×C5—82no—
187C3×C4×C5#9912yes—
188C3×Dic5—41no—
189C3×Dic5—41no—
190C3×Dic5—41no—
191C24×C3C22⋊D511yescharacteristic
192C3×#41—202no—
193C2×C3×Q8—51no—
194C2×C3×D4—51no—
195C2×C3×D4—101no—
196C2×C3×D4—101no—
197C2×C3×D4—101no—
198C22×C3×C4—22no—
199C22×C3×C4—42no—
200C22×C3×C4—101no—
201C22×C3×C4C4×D511yescharacteristic
202C22×C3×C4C4×D511yescharacteristic
203C22×C3×C4D2011yescharacteristic
204C22×C3×C4D2011yescharacteristic
205C22×C3×C4C22⋊D511yescharacteristic
206C22×C3×C4C22×D511yescharacteristic
207C3×M16—202no—
208C2×C3×C8—102no—
209C3×C4⋊C4—42no—
210C3×C4⋊C4—51no—
211C3×C4⋊C4—51no—
212C3×C4⋊C4—101no—
213C3×C4⋊C4—101no—
214C3×C22⋊C4—42no—
215C3×C22⋊C4—101no—
216C3×C22⋊C4—101no—
217C3×C22⋊C4—101no—
218C3×C22⋊C4—101no—
219C3×C22⋊C4—101no—
220C3×C42—101no—
221C23×C5—21no—
222C23×C5—21no—
223C23×C5—41no—
224C23×C5—41no—
225C23×C5C3×C22⋊C411yescharacteristic
226C23×C5C3×C22⋊C411yescharacteristic
227C23×C5C2×C3×D411yescharacteristic
228C22×D5—21no—
229C2×C4×C5—22no—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—42no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5C3×C22⋊C411yescharacteristic
239C2×C4×C5C3×C22⋊C411yescharacteristic
240C2×C4×C5C22×C3×C411yescharacteristic
241C2×C4×C5C2×C3×D411yescharacteristic
242C22⋊D5—42no—
243C22⋊D5—42no—
244C22⋊D5—41no—
245C22⋊D5—41no—
246C2×Dic5—21no—
247C2×Dic5—21no—
248C2×Dic5—21no—
249D20—41no—
250C4×D5—42no—
251Dic10—41no—
252#168—42no—
253C2×#41—51no—
254C23×C4C2×C3×D511yescharacteristic
255C2×M16—101no—
256#123—101no—
257C22⋊Q8—51no—
258C22⋊Q8—51no—
259#121—51no—
260#121—51no—
261#120—101no—
262C4×D4—101no—
263C4×D4—101no—
264#117—51no—
265C2×C4⋊C4—21no—
266C2×C22⋊C4—21no—
267C22⋊C8—52no—
268C22⋊C8—101no—
269#95C2×C3×D512yes—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5—41no—
273C2×C3×C5—41no—
274C2×C3×C5C2×#9911yescharacteristic
275C2×C3×C5#41711yescharacteristic
276C2×C3×C5#42111yescharacteristic
277C3×D5—81no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—101no—
283C23×C3#68511yescharacteristic
284C23×C3#68511yescharacteristic
285C23×C3C2×C22⋊D511yescharacteristic
286C3×Q8—201no—
287C3×D4—201no—
288C3×D4—202no—
289C3×D4—202no—
290C3×D4—201no—
291C3×D4—201no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—101no—
302C2×C3×C4—101no—
303C2×C3×C4—101no—
304C2×C3×C4—202no—
305C2×C3×C4#68511yescharacteristic
306C2×C3×C4#68511yescharacteristic
307C2×C3×C4C2×C4×D511yescharacteristic
308C2×C3×C4C2×D2011yescharacteristic
309C3×C8—202no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—21no—
317C22×C5—21no—
318C22×C5—42no—
319C22×C5—42no—
320C22×C5C2×C3×C22⋊C411yescharacteristic
321C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
322C22×C5C3×#13711yescharacteristic
323C2×D5—41no—
324C2×D5—41no—
325C2×D5—41no—
326C4×C5—21no—
327C4×C5—21no—
328C4×C5—21no—
329C4×C5—82no—
330C4×C5C3×#9912yes—
331Dic5—41no—
332Dic5—41no—
333Dic5—41no—
334C24C3×C22⋊D511yescharacteristic
335#41—202no—
336C2×Q8—51no—
337C2×D4—51no—
338C2×D4—101no—
339C2×D4—101no—
340C2×D4—101no—
341C22×C4—22no—
342C22×C4—42no—
343C22×C4—101no—
344C22×C4C3×C4×D511yescharacteristic
345C22×C4C3×C4×D511yescharacteristic
346C22×C4C3×D2011yescharacteristic
347C22×C4C3×D2011yescharacteristic
348C22×C4C3×C22⋊D511yescharacteristic
349C22×C4C22×C3×D511yescharacteristic
350M16—202no—
351C2×C8—102no—
352C4⋊C4—42no—
353C4⋊C4—51no—
354C4⋊C4—51no—
355C4⋊C4—101no—
356C4⋊C4—101no—
357C22⋊C4—42no—
358C22⋊C4—101no—
359C22⋊C4—101no—
360C22⋊C4—101no—
361C22⋊C4—101no—
362C22⋊C4—101no—
363C42—101no—
364C3×C5#151311yescharacteristic, complemented, Hall
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—201no—
376C22×C3—201no—
377C22×C3—201no—
378C22×C3C2×#68511yescharacteristic
379C22×C3#407811yescharacteristic
380C22×C3#408811yescharacteristic
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—82no—
385C3×C4—201no—
386C3×C4—201no—
387C3×C4—201no—
388C3×C4#393812yes—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—41no—
392C2×C5—41no—
393C2×C5C2×C3×#9911yescharacteristic
394C2×C5C3×#41711yescharacteristic
395C2×C5C3×#42111yescharacteristic
396D5—81no—
397C23—21no—
398C23—21no—
399C23—41no—
400C23—41no—
401C23—101no—
402C23C3×#68511yescharacteristic
403C23C3×#68511yescharacteristic
404C23C2×C3×C22⋊D511yescharacteristic
405Q8—201no—
406D4—201no—
407D4—202no—
408D4—202no—
409D4—201no—
410D4—201no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—101no—
421C2×C4—101no—
422C2×C4—101no—
423C2×C4—202no—
424C2×C4C3×#68511yescharacteristic
425C2×C4C3×#68511yescharacteristic
426C2×C4C2×C3×C4×D511yescharacteristic
427C2×C4C2×C3×D2011yescharacteristic
428C8—202no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—41no—
432C2×C3—41no—
433C2×C3—401no—
434C2×C3C2×#393811yescharacteristic
435C2×C3#6525511yescharacteristic
436C2×C3#6529411yescharacteristic
437C5C3×#151311yescharacteristic, complemented, Sylow
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—201no—
449C22—201no—
450C22—201no—
451C22C2×C3×#68511yescharacteristic
452C22C3×#407811yescharacteristic
453C22C3×#408811yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—82no—
458C4—201no—
459C4—201no—
460C4—201no—
461C4C3×#393812yes—
462C3#1060030111yescharacteristic, direct product factor, Sylow
463C2—21no—
464C2—21no—
465C2—41no—
466C2—41no—
467C2—401no—
468C2C2×C3×#393811yescharacteristic
469C2C3×#6525511yescharacteristic
470C2C3×#6529411yescharacteristic
subgroupG/H
centerC22×C3C2×#685
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#380C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66125C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#380D5
hypocenterC5C3×#1513
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
2. C3×C5×#380C2semidirect
3. C3×#65496C2semidirect
4. C3×#64672C2semidirect
5. C3×#64671C2semidirect
6. #10600301C3direct (N × H)
8. C2×C3×#709C4semidirect
12. C3×#4076C4semidirect
17. C3×#4072C4semidirect
18. C3×#4070C4semidirect
26. C5×#380C2×C3semidirect
27. #65496C2×C3semidirect
28. #64672C2×C3semidirect
29. #64671C2×C3semidirect
62. C3×#380D5semidirect
66. C2×#709C3×C4semidirect
70. #4076C3×C4semidirect
75. #4072C3×C4semidirect
76. #4070C3×C4semidirect
164. #380C3×D5semidirect
364. C3×C5#1513semidirect
437. C5C3×#1513semidirect
462. C3#10600301direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661252
C3×C5×#3802
C3×#654962
C3×#646722
C3×#646712
#106003013
C3×#15135