Finite Group Databasebeta

← C3×#10602064 #14289416

Subgroups — C3×#10602064 #14289416

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66052C211yesmaximal, characteristic
2C3×C5×#492C211yesmaximal, characteristic, complemented
3C3×#65380C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5C3×#64764C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10602064C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711—21no—
10C2×C3×C5×SD16—22no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×#127C2211yescharacteristic
13C3×#4086—21no—
14C3×#4085—22no—
15C3×#4084—21no—
16C3×D4×Dic5—21no—
17C3×C4×D20C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C4×C5×C8C2211yescharacteristic
20C3×#3942—21no—
21C3×#3941—21no—
22C3×#3940—21no—
23C3×#3939—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1631—51nomaximal, Hall
27#66052C2×C311yescharacteristic
28C5×#492C2×C311yescharacteristic, complemented
29#65380C2×C311yescharacteristic, complemented
30#65373C2×C311yescharacteristic, complemented
31#64764C2×C311yescharacteristic, complemented
32#64679C2×C311yescharacteristic, complemented
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D412yes—
38C2×C3×C22⋊D5—22no—
39C2×C3×C22⋊D5—22no—
40C22×C3×Dic5—22no—
41C3×#711—42no—
42C3×#711—42no—
43C2×C3×D20D411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×C3×Dic10D411yescharacteristic
46C3×C5×SD16—44no—
47C2×C3×C5×C8—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C42×C5C2311yescharacteristic
51C3×C22⋊Dic5—22no—
52C3×#685—21no—
53C3×C4⋊Dic5D411yescharacteristic
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C3×#550—51no—
60C3×#492D511yescharacteristic, complemented
61C3×#477—51no—
62C3×#476—51no—
63C3×#331—51no—
64C3×Q8⋊C8—51no—
65C3×D4⋊C8—51no—
66C2×#711—21no—
67C2×C5×SD16—22no—
68C5×C4⋊Q8C22×C311yescharacteristic
69C5×#127C22×C311yescharacteristic
70#4086—21no—
71#4085—22no—
72#4084—21no—
73D4×Dic5—21no—
74C4×D20C22×C311yescharacteristic
75C4×Dic10C22×C311yescharacteristic
76C4×C5×C8C22×C311yescharacteristic
77#3942—21no—
78#3941—21no—
79#3940—21no—
80#3939—21no—
81C4⋊#168C22×C311yescharacteristic
82C4⋊#168C22×C311yescharacteristic
83#1631—51noSylow
84C23×C3×C5—22no—
85C22×C3×D5—21no—
86C3×C5×Q8—42no—
87C3×C5×D4—42no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C3×C22⋊D5—44no—
97C3×C22⋊D5—82no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—44no—
102C3×D20—21no—
103C3×D20—21no—
104C3×C4×D5—41no—
105C3×C4×D5—41no—
106C3×Dic10—21no—
107C3×Dic10SD1612yescomplemented
108C3×C5×C8—22no—
109C3×#168—41no—
110C3×#168—41no—
111C2×C3×#41—101no—
112C2×C3×SD16—22no—
113C3×C4⋊Q8C2×D511yescharacteristic
114C3×#127—101no—
115C3×#127C2×D511yescharacteristic
116C3×#121—101no—
117C3×#121—102no—
118C3×C4×Q8—51no—
119C3×C4×D4—51no—
120C3×C4×D4—101no—
121C3×#107—101no—
122C3×#106—101no—
123C3×C4⋊C8—51no—
124C3×C4⋊C8—51no—
125C3×#103—101no—
126C3×#102—101no—
127C3×C4×C8C2×D511yescharacteristic
128C2×C5×Q8—21no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4C3×D412yes—
132C2×C22⋊D5—22no—
133C2×C22⋊D5—22no—
134C22×Dic5—22no—
135#711—42no—
136#711—42no—
137C2×D20C3×D411yescharacteristic
138C2×C4×D5—21no—
139C2×Dic10C3×D411yescharacteristic
140C5×SD16—44no—
141C2×C5×C8—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—21no—
144C42×C5C23×C311yescharacteristic
145C22⋊Dic5—22no—
146#685—21no—
147C4⋊Dic5C3×D411yescharacteristic
148C4⋊Dic5C3×D411yescharacteristic
149#683—21no—
150C4×Dic5—21no—
151C2×#168—21no—
152C2×#168—21no—
153#550—51no—
154#492C3×D511yescharacteristic, complemented
155#477—51no—
156#476—51no—
157#331—51no—
158Q8⋊C8—51no—
159D4⋊C8—51no—
160C22×C3×C5—42no—
161C22×C3×C5—42no—
162C22×C3×C5—42no—
163C22×C3×C5#12011yescharacteristic
164C2×C3×D5—41no—
165C2×C3×D5—41no—
166C2×C3×D5—41no—
167C3×C4×C5—21no—
168C3×C4×C5—81no—
169C3×C4×C5C2×SD1611yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173C3×Dic5—22no—
174C3×Dic5—41no—
175C3×Dic5—41no—
176C3×#41—202no—
177C3×#41—202no—
178C2×C3×Q8—21no—
179C2×C3×Q8—51no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—51no—
183C2×C3×D4—102no—
184C2×C3×D4—102no—
185C2×C3×D4C22⋊D512yes—
186C22×C3×C4—102no—
187C22×C3×C4—101no—
188C3×SD16—44no—
189C2×C3×C8—21no—
190C2×C3×C8—101no—
191C2×C3×C8—101no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—51no—
195C3×C4⋊C4—51no—
196C3×C4⋊C4—101no—
197C3×C22⋊C4—102no—
198C3×C22⋊C4—101no—
199C3×C42—101no—
200C3×C42C22×D511yescharacteristic
201C23×C5—22no—
202C22×D5—21no—
203C5×Q8—42no—
204C5×D4—42no—
205C5×D4—41no—
206C5×D4—41no—
207C5×D4—41no—
208C5×D4—41no—
209C2×C4×C5—41no—
210C2×C4×C5C2×C3×D411yescharacteristic
211C2×C4×C5C2×C3×D411yescharacteristic
212C2×C4×C5C2×C3×D411yescharacteristic
213C22⋊D5—44no—
214C22⋊D5—82no—
215C2×Dic5—21no—
216C2×Dic5—21no—
217C2×Dic5—21no—
218C2×Dic5—44no—
219D20—21no—
220D20—21no—
221C4×D5—41no—
222C4×D5—41no—
223Dic10—21no—
224Dic10C3×SD1612yescomplemented
225C5×C8—22no—
226#168—41no—
227#168—41no—
228C2×#41—101no—
229C2×SD16—22no—
230C4⋊Q8C2×C3×D511yescharacteristic
231#127—101no—
232#127C2×C3×D511yescharacteristic
233#121—101no—
234#121—102no—
235C4×Q8—51no—
236C4×D4—51no—
237C4×D4—101no—
238#107—101no—
239#106—101no—
240C4⋊C8—51no—
241C4⋊C8—51no—
242#103—101no—
243#102—101no—
244C4×C8C2×C3×D511yescharacteristic
245C2×C3×C5—82no—
246C2×C3×C5#45011yescharacteristic
247C2×C3×C5#45211yescharacteristic
248C2×C3×C5#45311yescharacteristic
249C3×D5—81no—
250C23×C3—22no—
251C23×C3—101no—
252C3×Q8—42no—
253C3×Q8—52no—
254C3×Q8—101no—
255C3×D4—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—101no—
261C3×D4—101no—
262C3×D4—204no—
263C3×D4—402no—
264C2×C3×C4—41no—
265C2×C3×C4—101no—
266C2×C3×C4—101no—
267C2×C3×C4—101no—
268C2×C3×C4—204no—
269C2×C3×C4—201no—
270C2×C3×C4—201no—
271C2×C3×C4D4×D511yescharacteristic
272C2×C3×C4D4×D511yescharacteristic
273C2×C3×C4C2×C22⋊D511yescharacteristic
274C3×C8—22no—
275C3×C8—201no—
276C3×C8—201no—
277C22×C5—42no—
278C22×C5—42no—
279C22×C5—42no—
280C22×C5C3×#12011yescharacteristic
281C2×D5—41no—
282C2×D5—41no—
283C2×D5—41no—
284C4×C5—21no—
285C4×C5—81no—
286C4×C5C2×C3×SD1611yescharacteristic
287C4×C5C3×#13511yescharacteristic
288C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
289C4×C5C3×#13711yescharacteristic
290Dic5—22no—
291Dic5—41no—
292Dic5—41no—
293#41—202no—
294#41—202no—
295C2×Q8—21no—
296C2×Q8—51no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—51no—
300C2×D4—102no—
301C2×D4—102no—
302C2×D4C3×C22⋊D512yes—
303C22×C4—102no—
304C22×C4—101no—
305SD16—44no—
306C2×C8—21no—
307C2×C8—101no—
308C2×C8—101no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—51no—
312C4⋊C4—51no—
313C4⋊C4—101no—
314C22⋊C4—102no—
315C22⋊C4—101no—
316C42—101no—
317C42C22×C3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—201no—
323C22×C3—201no—
324C22×C3—201no—
325C22×C3#408311yescharacteristic
326C3×C4—21no—
327C3×C4—81no—
328C3×C4—102no—
329C3×C4—201no—
330C3×C4—201no—
331C3×C4D5×SD1611yescharacteristic
332C3×C4#406011yescharacteristic
333C3×C4#406111yescharacteristic
334C3×C4#406211yescharacteristic
335C2×C5—82no—
336C2×C5C3×#45011yescharacteristic
337C2×C5C3×#45211yescharacteristic
338C2×C5C3×#45311yescharacteristic
339D5—81no—
340C23—22no—
341C23—101no—
342Q8—42no—
343Q8—52no—
344Q8—101no—
345D4—42no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—101no—
351D4—101no—
352D4—204no—
353D4—402no—
354C2×C4—41no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4—101no—
358C2×C4—204no—
359C2×C4—201no—
360C2×C4—201no—
361C2×C4C3×D4×D511yescharacteristic
362C2×C4C3×D4×D511yescharacteristic
363C2×C4C2×C3×C22⋊D511yescharacteristic
364C8—22no—
365C8—201no—
366C8—201no—
367C2×C3—82no—
368C2×C3—401no—
369C2×C3#6536611yescharacteristic
370C2×C3#6545811yescharacteristic
371C2×C3#6546211yescharacteristic
372C5C3×#163111yescharacteristic, complemented, Sylow
373C22—42no—
374C22—42no—
375C22—42no—
376C22—201no—
377C22—201no—
378C22—201no—
379C22C3×#408311yescharacteristic
380C4—21no—
381C4—81no—
382C4—102no—
383C4—201no—
384C4—201no—
385C4C3×D5×SD1611yescharacteristic
386C4C3×#406011yescharacteristic
387C4C3×#406111yescharacteristic
388C4C3×#406211yescharacteristic
389C3#1060206411yescharacteristic, direct product factor, Sylow
390C2—82no—
391C2—401no—
392C2C3×#6536611yescharacteristic
393C2C3×#6545811yescharacteristic
394C2C3×#6546211yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#492C2
socleC22×C3×C5#120
prime radicalC3×#66052C2
hypercenterC3×#492D5
hypocenterC5C3×#1631
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#492

Complements

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

NH ≅ G/Ntype
2. C3×C5×#492C2semidirect
3. C3×#65380C2semidirect
4. C3×#65373C2semidirect
5. C3×#64764C2semidirect
6. C3×#64679C2semidirect
7. C3×#64676C2semidirect
8. #10602064C3direct (N × H)
28. C5×#492C2×C3semidirect
29. #65380C2×C3semidirect
30. #65373C2×C3semidirect
31. #64764C2×C3semidirect
32. #64679C2×C3semidirect
33. #64676C2×C3semidirect
60. C3×#492D5semidirect
107. C3×Dic10SD16semidirect
154. #492C3×D5semidirect
224. Dic10C3×SD16semidirect
318. C3×C5#1631semidirect
372. C5C3×#1631semidirect
389. C3#10602064direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660522
C3×C5×#4922
C3×#653802
C3×#653732
C3×#647642
C3×#646792
C3×#646762
#106020643
C3×#16315