Finite Group Databasebeta

← C3×#10602057 #14288945

Subgroups — C3×#10602057 #14288945

Order 1920.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66064C211yesmaximal, characteristic, complemented
2C3×C5×#492C211yesmaximal, characteristic, complemented
3C3×#65364C211yesmaximal, characteristic, complemented
4C3×#65361C211yesmaximal, characteristic
5C3×#64766C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10602057C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×SD16—22no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#127C2211yescharacteristic
12C3×#4092—22no—
13C2×C3×#687—21no—
14C2×C3×#686—21no—
15C3×#4043—21no—
16C3×#4039—21no—
17C3×D5×C4⋊C4—21no—
18C3×#4036—21no—
19C3×C4×D20C2211yescharacteristic
20C3×C4×Dic10C2211yescharacteristic
21C3×C4×C5×C8C2211yescharacteristic
22C3×#3964—21no—
23C3×#3964—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1622—51nomaximal, Hall
27#66064C2×C311yescharacteristic, complemented
28C5×#492C2×C311yescharacteristic, complemented
29#65364C2×C311yescharacteristic, complemented
30#65361C2×C311yescharacteristic
31#64766C2×C311yescharacteristic, complemented
32#64679C2×C311yescharacteristic, complemented
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8D412yes—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5—22no—
41C2×C3×Dic10D411yescharacteristic
42C3×C5×SD16—44no—
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47C3×#687—42no—
48C3×#686—42no—
49C3×#685—22no—
50C3×#685—21no—
51C3×C4⋊Dic5—22no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—22no—
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C3×#554—51no—
60C3×#492D511yescharacteristic, complemented
61C3×#460—51no—
62C3×#459—51no—
63C3×#333—51no—
64C3×Q8⋊C8—51no—
65C3×D4⋊C8—51no—
66C2×C5×SD16—22no—
67C5×C4⋊Q8C22×C311yescharacteristic
68C5×#127C22×C311yescharacteristic
69#4092—22no—
70C2×#687—21no—
71C2×#686—21no—
72#4043—21no—
73#4039—21no—
74D5×C4⋊C4—21no—
75#4036—21no—
76C4×D20C22×C311yescharacteristic
77C4×Dic10C22×C311yescharacteristic
78C4×C5×C8C22×C311yescharacteristic
79#3964—21no—
80#3964—21no—
81C4⋊#168C22×C311yescharacteristic
82C4⋊#168C22×C311yescharacteristic
83#1622—51noSylow
84C23×C3×C5—41no—
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—22no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×D20—21no—
100C3×D20SD1612yescomplemented
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103C3×C4×D5—82no—
104C3×Dic10—21no—
105C3×Dic10—21no—
106C3×C5×C8—22no—
107C3×#168—41no—
108C3×#168—41no—
109C2×C3×SD16—22no—
110C2×C3×SD16—101no—
111C2×C3×D8—101no—
112C3×C4⋊Q8C2×D511yescharacteristic
113C3×#127C2×D511yescharacteristic
114C3×#125—101no—
115C3×C22⋊Q8—101no—
116C3×C22⋊Q8—102no—
117C3×C4×Q8—51no—
118C3×C4×D4—51no—
119C3×C4×D4—101no—
120C2×C3×C4⋊C4—101no—
121C3×C4⋊C8—51no—
122C3×C4⋊C8—51no—
123C3×#102—101no—
124C3×#102—101no—
125C3×C4×C8C2×D511yescharacteristic
126C2×C5×Q8C3×D412yes—
127C2×C5×D4—21no—
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×D20C3×D411yescharacteristic
131C2×C4×D5—21no—
132C2×C4×D5—22no—
133C2×Dic10C3×D411yescharacteristic
134C5×SD16—44no—
135C2×C5×C8—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C42×C5C23×C311yescharacteristic
139#687—42no—
140#686—42no—
141#685—22no—
142#685—21no—
143C4⋊Dic5—22no—
144C4⋊Dic5C3×D411yescharacteristic
145C4⋊Dic5C3×D411yescharacteristic
146#683—22no—
147#683—21no—
148C4×Dic5—21no—
149C2×#168—21no—
150C2×#168—21no—
151#554—51no—
152#492C3×D511yescharacteristic, complemented
153#460—51no—
154#459—51no—
155#333—51no—
156Q8⋊C8—51no—
157D4⋊C8—51no—
158C22×C3×C5—81no—
159C22×C3×C5—81no—
160C22×C3×C5—81no—
161C22×C3×C5#12011yescharacteristic
162C2×C3×D5—22no—
163C2×C3×D5—41no—
164C2×C3×D5—41no—
165C3×C4×C5—21no—
166C3×C4×C5—42no—
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C3×C4×C5#13711yescharacteristic
171C3×Dic5—41no—
172C3×Dic5—41no—
173C3×Dic5—41no—
174C2×C3×Q8—51no—
175C2×C3×Q8C22⋊D512yes—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—51no—
180C22×C3×C4—102no—
181C22×C3×C4—101no—
182C3×SD16—44no—
183C3×SD16—202no—
184C3×D8—202no—
185C2×C3×C8—21no—
186C2×C3×C8—101no—
187C2×C3×C8—101no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—51no—
191C3×C4⋊C4—51no—
192C3×C4⋊C4—102no—
193C3×C4⋊C4—102no—
194C3×C4⋊C4—101no—
195C3×C22⋊C4—102no—
196C3×C22⋊C4—101no—
197C3×C42—101no—
198C3×C42C22×D511yescharacteristic
199C23×C5—41no—
200C22×D5—21no—
201C5×Q8—42no—
202C5×D4—42no—
203C5×D4—41no—
204C5×D4—41no—
205C5×D4—41no—
206C5×D4—41no—
207C2×C4×C5—22no—
208C2×C4×C5C2×C3×D411yescharacteristic
209C2×C4×C5C2×C3×D411yescharacteristic
210C2×C4×C5C2×C3×D411yescharacteristic
211C2×Dic5—21no—
212C2×Dic5—21no—
213C2×Dic5—21no—
214D20—21no—
215D20C3×SD1612yescomplemented
216C4×D5—41no—
217C4×D5—41no—
218C4×D5—82no—
219Dic10—21no—
220Dic10—21no—
221C5×C8—22no—
222#168—41no—
223#168—41no—
224C2×SD16—22no—
225C2×SD16—101no—
226C2×D8—101no—
227C4⋊Q8C2×C3×D511yescharacteristic
228#127C2×C3×D511yescharacteristic
229#125—101no—
230C22⋊Q8—101no—
231C22⋊Q8—102no—
232C4×Q8—51no—
233C4×D4—51no—
234C4×D4—101no—
235C2×C4⋊C4—101no—
236C4⋊C8—51no—
237C4⋊C8—51no—
238#102—101no—
239#102—101no—
240C4×C8C2×C3×D511yescharacteristic
241C2×C3×C5—161no—
242C2×C3×C5#44811yescharacteristic
243C2×C3×C5#44911yescharacteristic
244C2×C3×C5#45311yescharacteristic
245C3×D5—42no—
246C23×C3—41no—
247C23×C3—101no—
248C3×Q8—42no—
249C3×Q8—101no—
250C3×Q8—101no—
251C3×D4—42no—
252C3×D4—41no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4—52no—
257C3×D4—101no—
258C2×C3×C4—22no—
259C2×C3×C4—101no—
260C2×C3×C4—101no—
261C2×C3×C4—101no—
262C2×C3×C4—201no—
263C2×C3×C4—201no—
264C2×C3×C4—402no—
265C2×C3×C4D4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4C2×C22⋊D511yescharacteristic
268C3×C8—22no—
269C3×C8—201no—
270C3×C8—201no—
271C22×C5—81no—
272C22×C5—81no—
273C22×C5—81no—
274C22×C5C3×#12011yescharacteristic
275C2×D5—22no—
276C2×D5—41no—
277C2×D5—41no—
278C4×C5—21no—
279C4×C5—42no—
280C4×C5C2×C3×SD1611yescharacteristic
281C4×C5C3×#13511yescharacteristic
282C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
283C4×C5C3×#13711yescharacteristic
284Dic5—41no—
285Dic5—41no—
286Dic5—41no—
287C2×Q8—51no—
288C2×Q8C3×C22⋊D512yes—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—51no—
293C22×C4—102no—
294C22×C4—101no—
295SD16—44no—
296SD16—202no—
297D8—202no—
298C2×C8—21no—
299C2×C8—101no—
300C2×C8—101no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—51no—
304C4⋊C4—51no—
305C4⋊C4—102no—
306C4⋊C4—102no—
307C4⋊C4—101no—
308C22⋊C4—102no—
309C22⋊C4—101no—
310C42—101no—
311C42C22×C3×D511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3—81no—
314C22×C3—81no—
315C22×C3—81no—
316C22×C3—102no—
317C22×C3—201no—
318C22×C3—201no—
319C22×C3#408311yescharacteristic
320C3×C4—21no—
321C3×C4—42no—
322C3×C4—201no—
323C3×C4—201no—
324C3×C4—201no—
325C3×C4D5×SD1611yescharacteristic
326C3×C4#406011yescharacteristic
327C3×C4#406111yescharacteristic
328C3×C4#406211yescharacteristic
329C2×C5—161no—
330C2×C5C3×#44811yescharacteristic
331C2×C5C3×#44911yescharacteristic
332C2×C5C3×#45311yescharacteristic
333D5—42no—
334C23—41no—
335C23—101no—
336Q8—42no—
337Q8—101no—
338Q8—101no—
339D4—42no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—41no—
344D4—52no—
345D4—101no—
346C2×C4—22no—
347C2×C4—101no—
348C2×C4—101no—
349C2×C4—101no—
350C2×C4—201no—
351C2×C4—201no—
352C2×C4—402no—
353C2×C4C3×D4×D511yescharacteristic
354C2×C4C3×D4×D511yescharacteristic
355C2×C4C2×C3×C22⋊D511yescharacteristic
356C8—22no—
357C8—201no—
358C8—201no—
359C2×C3—161no—
360C2×C3—202no—
361C2×C3#6536611yescharacteristic
362C2×C3#6545911yescharacteristic
363C2×C3#6546111yescharacteristic
364C5C3×#162211yescharacteristic, complemented, Sylow
365C22—81no—
366C22—81no—
367C22—81no—
368C22—102no—
369C22—201no—
370C22—201no—
371C22C3×#408311yescharacteristic
372C4—21no—
373C4—42no—
374C4—201no—
375C4—201no—
376C4—201no—
377C4C3×D5×SD1611yescharacteristic
378C4C3×#406011yescharacteristic
379C4C3×#406111yescharacteristic
380C4C3×#406211yescharacteristic
381C3#1060205711yescharacteristic, direct product factor, Sylow
382C2—161no—
383C2—202no—
384C2C3×#6536611yescharacteristic
385C2C3×#6545911yescharacteristic
386C2C3×#6546111yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#492C2
socleC22×C3×C5#120
prime radicalC3×#65361C2
hypercenterC3×#492D5
hypocenterC5C3×#1622
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
1. C3×#66064C2semidirect
2. C3×C5×#492C2semidirect
3. C3×#65364C2semidirect
5. C3×#64766C2semidirect
6. C3×#64679C2semidirect
7. C3×#64676C2semidirect
8. #10602057C3direct (N × H)
27. #66064C2×C3semidirect
28. C5×#492C2×C3semidirect
29. #65364C2×C3semidirect
31. #64766C2×C3semidirect
32. #64679C2×C3semidirect
33. #64676C2×C3semidirect
60. C3×#492D5semidirect
100. C3×D20SD16semidirect
152. #492C3×D5semidirect
215. D20C3×SD16semidirect
312. C3×C5#1622semidirect
364. C5C3×#1622semidirect
381. C3#10602057direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660642
C3×C5×#4922
C3×#653642
C3×#653612
C3×#647662
C3×#646792
C3×#646762
#106020573
C3×#16225