Finite Group Databasebeta

← C3×#10599249 #14289161

Subgroups — C3×#10599249 #14289161

Order 1920.

420 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66055C211yesmaximal, characteristic, complemented
2C3×#65377C211yesmaximal, characteristic
3C3×#65137C211yesmaximal, characteristic
4C3×#65137C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7C3×#64704C211yesmaximal, characteristic, complemented
8#10599249C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×Q8×Dic5—21no—
11C3×#4090—21no—
12C2×C3×#677—21no—
13C2×C3×#677—21no—
14C3×#4036—21no—
15C3×#4035—22no—
16C3×#4033—21no—
17C3×#4020C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×#3953—21no—
23C3×#3953—21no—
24C3×#3941—22no—
25C3×C4×#168C2211yescharacteristic
26C3×#1626—51nomaximal, Hall
27#66055C2×C311yescharacteristic, complemented
28#65377C2×C311yescharacteristic
29#65137C2×C311yescharacteristic
30#65137C2×C311yescharacteristic
31C5×#332C2×C311yescharacteristic, complemented
32#64704C2×C311yescharacteristic, complemented
33#64704C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D412yes—
44C3×C42×C5C2311yescharacteristic
45C3×C4⋊Dic5—22no—
46C3×C4⋊Dic5D411yescharacteristic
47C3×C4⋊Dic5D411yescharacteristic
48C3×#683—22no—
49C3×#683—22no—
50C3×#683—21no—
51C3×#683—21no—
52C3×C4×Dic5—22no—
53C3×C4×Dic5—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56C3×#677—42no—
57C3×#677—42no—
58C3×#557—51no—
59C3×#486—51no—
60C3×#460—51no—
61C3×#460—51no—
62C3×#332D511yescharacteristic, complemented
63C3×Q8⋊C8—51no—
64C3×Q8⋊C8—51no—
65C5×C4⋊Q8C22×C311yescharacteristic
66Q8×Dic5—21no—
67#4090—21no—
68C2×#677—21no—
69C2×#677—21no—
70#4036—21no—
71#4035—22no—
72#4033—21no—
73#4020C22×C311yescharacteristic
74C4×Dic10C22×C311yescharacteristic
75C4×Dic10C22×C311yescharacteristic
76C5×C4⋊C8C22×C311yescharacteristic
77C5×C4⋊C8C22×C311yescharacteristic
78#3953—21no—
79#3953—21no—
80#3941—22no—
81C4×#168C22×C311yescharacteristic
82#1626—51noSylow
83C22×C3×D5—41no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C3×D20—42no—
95C3×D20—41no—
96C3×D20—41no—
97C3×D20—41no—
98C3×D20—41no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101C3×Dic10—21no—
102C3×Dic10SD1612yescomplemented
103C3×C5×C8—41no—
104C3×C5×C8—41no—
105C3×#168—41no—
106C2×C3×SD16—101no—
107C2×C3×SD16—101no—
108C3×C4⋊Q8—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×#127—51no—
111C3×#125—101no—
112C3×#125—102no—
113C3×C4×Q8—51no—
114C3×C4×Q8—51no—
115C3×C4×Q8—101no—
116C3×C4×Q8—101no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×C4⋊C8C2×D511yescharacteristic
119C3×#102—101no—
120C3×#102—101no—
121C3×#102—102no—
122C3×C4×C8—51no—
123C2×C5×Q8—21no—
124C2×D20—21no—
125C2×D20—21no—
126C2×D20—21no—
127C2×Dic10C3×D411yescharacteristic
128C2×Dic10C3×D411yescharacteristic
129C2×C5×C8—21no—
130C2×C5×C8—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4C3×D412yes—
133C42×C5C23×C311yescharacteristic
134C4⋊Dic5—22no—
135C4⋊Dic5C3×D411yescharacteristic
136C4⋊Dic5C3×D411yescharacteristic
137#683—22no—
138#683—22no—
139#683—21no—
140#683—21no—
141C4×Dic5—22no—
142C4×Dic5—21no—
143C4×Dic5—21no—
144C2×#168—21no—
145#677—42no—
146#677—42no—
147#557—51no—
148#486—51no—
149#460—51no—
150#460—51no—
151#332C3×D511yescharacteristic, complemented
152Q8⋊C8—51no—
153Q8⋊C8—51no—
154C22×C3×C5#12011yescharacteristic
155C2×C3×D5—81no—
156C2×C3×D5—81no—
157C2×C3×D5—81no—
158C3×C4×C5—21no—
159C3×C4×C5—42no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×Dic5—22no—
165C3×Dic5—41no—
166C3×Dic5—41no—
167C3×Dic5—41no—
168C2×C3×Q8—21no—
169C2×C3×Q8—51no—
170C2×C3×Q8—51no—
171C2×C3×D4—101no—
172C2×C3×D4—101no—
173C2×C3×D4—101no—
174C3×SD16—202no—
175C3×SD16—202no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—101no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—51no—
181C3×C4⋊C4—51no—
182C3×C4⋊C4—102no—
183C3×C4⋊C4—102no—
184C3×C4⋊C4—102no—
185C3×C4⋊C4—101no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4D2012yes—
188C3×C42—102no—
189C3×C42—101no—
190C3×C42—101no—
191C3×C42C22×D511yescharacteristic
192C22×D5—41no—
193C5×Q8—41no—
194C5×Q8—41no—
195C2×C4×C5—22no—
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×C4×C5C2×C3×D411yescharacteristic
198C2×C4×C5C2×C3×D411yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—21no—
201C2×Dic5—21no—
202C2×Dic5—21no—
203D20—42no—
204D20—41no—
205D20—41no—
206D20—41no—
207D20—41no—
208Dic10—21no—
209Dic10—21no—
210Dic10—21no—
211Dic10C3×SD1612yescomplemented
212C5×C8—41no—
213C5×C8—41no—
214#168—41no—
215C2×SD16—101no—
216C2×SD16—101no—
217C4⋊Q8—101no—
218C4⋊Q8C2×C3×D511yescharacteristic
219#127—51no—
220#125—101no—
221#125—102no—
222C4×Q8—51no—
223C4×Q8—51no—
224C4×Q8—101no—
225C4×Q8—101no—
226C4⋊C8C2×C3×D511yescharacteristic
227C4⋊C8C2×C3×D511yescharacteristic
228#102—101no—
229#102—101no—
230#102—102no—
231C4×C8—51no—
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—161no—
236C23×C3—201no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—52no—
240C3×Q8—101no—
241C3×Q8—101no—
242C3×Q8—101no—
243C3×D4—202no—
244C3×D4—201no—
245C3×D4—201no—
246C3×D4—201no—
247C3×D4—201no—
248C2×C3×C4—22no—
249C2×C3×C4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—101no—
252C2×C3×C4—101no—
253C2×C3×C4C2×D2011yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C3×C8—41no—
257C3×C8—41no—
258C3×C8—201no—
259C22×C5C3×#12011yescharacteristic
260C2×D5—81no—
261C2×D5—81no—
262C2×D5—81no—
263C4×C5—21no—
264C4×C5—42no—
265C4×C5C2×C3×SD1611yescharacteristic
266C4×C5C3×#13511yescharacteristic
267C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
268C4×C5C3×#13711yescharacteristic
269Dic5—22no—
270Dic5—41no—
271Dic5—41no—
272Dic5—41no—
273C2×Q8—21no—
274C2×Q8—51no—
275C2×Q8—51no—
276C2×D4—101no—
277C2×D4—101no—
278C2×D4—101no—
279SD16—202no—
280SD16—202no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—101no—
284C4⋊C4—21no—
285C4⋊C4—51no—
286C4⋊C4—51no—
287C4⋊C4—102no—
288C4⋊C4—102no—
289C4⋊C4—102no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4C3×D2012yes—
293C42—102no—
294C42—101no—
295C42—101no—
296C42C22×C3×D511yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3—401no—
299C22×C3—401no—
300C22×C3—401no—
301C22×C3#402811yescharacteristic
302C3×C4—21no—
303C3×C4—42no—
304C3×C4—102no—
305C3×C4—201no—
306C3×C4—201no—
307C3×C4—201no—
308C3×C4#405711yescharacteristic
309C3×C4D5×SD1611yescharacteristic
310C3×C4#406211yescharacteristic
311C3×C4#406411yescharacteristic
312C2×C5C3×#44811yescharacteristic
313C2×C5C3×#44911yescharacteristic
314C2×C5C3×#45411yescharacteristic
315D5—161no—
316C23—201no—
317Q8—41no—
318Q8—41no—
319Q8—52no—
320Q8—101no—
321Q8—101no—
322Q8—101no—
323D4—202no—
324D4—201no—
325D4—201no—
326D4—201no—
327D4—201no—
328C2×C4—22no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—101no—
332C2×C4—101no—
333C2×C4C2×C3×D2011yescharacteristic
334C2×C4C3×D4×D511yescharacteristic
335C2×C4C3×D4×D511yescharacteristic
336C8—41no—
337C8—41no—
338C8—201no—
339C2×C3—801no—
340C2×C3#6504211yescharacteristic
341C2×C3#6507011yescharacteristic
342C2×C3#6509511yescharacteristic
343C5C3×#162611yescharacteristic, complemented, Sylow
344C22—401no—
345C22—401no—
346C22—401no—
347C22C3×#402811yescharacteristic
348C4—21no—
349C4—42no—
350C4—102no—
351C4—201no—
352C4—201no—
353C4—201no—
354C4C3×#405711yescharacteristic
355C4C3×D5×SD1611yescharacteristic
356C4C3×#406211yescharacteristic
357C4C3×#406411yescharacteristic
358C3#1059924911yescharacteristic, direct product factor, Sylow
359C2—801no—
360C2C3×#6504211yescharacteristic
361C2C3×#6507011yescharacteristic
362C2C3×#6509511yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#332C2
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC3×#332D5
hypocenterC5C3×#1626
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
1. C3×#66055C2semidirect
5. C3×C5×#332C2semidirect
6. C3×#64704C2semidirect
7. C3×#64704C2semidirect
8. #10599249C3direct (N × H)
27. #66055C2×C3semidirect
31. C5×#332C2×C3semidirect
32. #64704C2×C3semidirect
33. #64704C2×C3semidirect
62. C3×#332D5semidirect
102. C3×Dic10SD16semidirect
151. #332C3×D5semidirect
211. Dic10C3×SD16semidirect
297. C3×C5#1626semidirect
343. C5C3×#1626semidirect
358. C3#10599249direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660552
C3×#653772
C3×#651372
C3×C5×#3322
C3×#647042
#105992493
C3×#16265