Finite Group Databasebeta

← C3×#10601939 #14289623

Subgroups — C3×#10601939 #14289623

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65889C211yesmaximal, characteristic
2C3×C5×#476C211yesmaximal, characteristic, complemented
3C3×#65373C211yesmaximal, characteristic, complemented
4C3×#65370C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7C3×#64702C211yesmaximal, characteristic, complemented
8#10601939C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C3×#4076—21no—
13C2×C3×C4⋊Dic5—21no—
14C3×#4043—21no—
15C3×#4032—22no—
16C3×C4×D20C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×C5×#106—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#102—21no—
21C3×#3967—22no—
22C3×#3941—21no—
23C3×#3940—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1635—51nomaximal, Hall
27#65889C2×C311yescharacteristic
28C5×#476C2×C311yescharacteristic, complemented
29#65373C2×C311yescharacteristic, complemented
30#65370C2×C311yescharacteristic, complemented
31D4⋊#168C2×C311yescharacteristic, complemented
32#64703C2×C311yescharacteristic, complemented
33#64702C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×C3×C22⋊D5—22no—
38C22×C3×Dic5—22no—
39C3×#711—42no—
40C3×#711—42no—
41C2×C3×D20D411yescharacteristic
42C2×C3×C4×D5—21no—
43C2×C3×Dic10—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C22⋊C4—21no—
49C3×C42×C5C2311yescharacteristic
50C3×#685—22no—
51C3×#685—21no—
52C3×C4⋊Dic5—22no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×C4⋊Dic5D412yes—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58C3×#547—51no—
59C3×#487—51no—
60C3×#476—51no—
61C3×#476D511yescharacteristic, complemented
62C3×#332—51no—
63C3×D4⋊C8—51no—
64C3×D4⋊C8—51no—
65C2×#711—21no—
66C5×C4⋊Q8C22×C311yescharacteristic
67C4×C5×D4C22×C311yescharacteristic
68#4076—21no—
69C2×C4⋊Dic5—21no—
70#4043—21no—
71#4032—22no—
72C4×D20C22×C311yescharacteristic
73#4015C22×C311yescharacteristic
74C5×#106—21no—
75C5×C4⋊C8C22×C311yescharacteristic
76C5×#102—21no—
77#3967—22no—
78#3941—21no—
79#3940—21no—
80C4⋊#168C22×C311yescharacteristic
81C4×#168C22×C311yescharacteristic
82#1635—51noSylow
83C23×C3×C5—21no—
84C22×C3×D5—21no—
85C3×C5×Q8—42no—
86C3×C5×D4—21no—
87C3×C5×D4SD1612yes—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C3×C22⋊D5—44no—
96C2×C3×Dic5—22no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—44no—
99C3×D20—21no—
100C3×D20—21no—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105C3×C5×C8—41no—
106C3×#168—41no—
107C3×#168—41no—
108C2×C3×#41—101no—
109C3×C4⋊Q8—51no—
110C3×C4⋊Q8C2×D511yescharacteristic
111C3×#123—102no—
112C3×C22⋊Q8—101no—
113C3×#121—101no—
114C3×C4×D4—51no—
115C3×C4×D4C2×D511yescharacteristic
116C2×C3×C4⋊C4—101no—
117C3×#106—21no—
118C3×#106—101no—
119C3×C4⋊C8—51no—
120C3×C4⋊C8C2×D511yescharacteristic
121C3×#103—102no—
122C3×#102—21no—
123C3×#102—101no—
124C3×C4×C8—51no—
125C2×C5×Q8—21no—
126C2×C5×D4C3×D411yescharacteristic
127C22×C4×C5—21no—
128C2×C22⋊D5—22no—
129C22×Dic5—22no—
130#711—42no—
131#711—42no—
132C2×D20C3×D411yescharacteristic
133C2×C4×D5—21no—
134C2×Dic10—21no—
135C2×C5×C8—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4C3×D411yescharacteristic
139C5×C22⋊C4—21no—
140C42×C5C23×C311yescharacteristic
141#685—22no—
142#685—21no—
143C4⋊Dic5—22no—
144C4⋊Dic5—21no—
145C4⋊Dic5C3×D411yescharacteristic
146C4⋊Dic5C3×D412yes—
147C2×#168—21no—
148C2×#168—21no—
149#547—51no—
150#487—51no—
151#476—51no—
152#476C3×D511yescharacteristic, complemented
153#332—51no—
154D4⋊C8—51no—
155D4⋊C8—51no—
156C22×C3×C5—22no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5#12011yescharacteristic
160C2×C3×D5—41no—
161C2×C3×D5—41no—
162C2×C3×D5—41no—
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5—81no—
166C3×C4×C5C2×SD1611yescharacteristic
167C3×C4×C5#13511yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170C3×Dic5—42no—
171C3×Dic5—41no—
172C3×#41—202no—
173C3×#41—202no—
174C2×C3×Q8—21no—
175C2×C3×Q8—101no—
176C2×C3×D4—51no—
177C2×C3×D4—102no—
178C2×C3×D4C22⋊D511yescharacteristic
179C22×C3×C4—21no—
180C22×C3×C4—102no—
181C22×C3×C4—101no—
182C2×C3×C8—21no—
183C2×C3×C8—101no—
184C2×C3×C8—101no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—52no—
188C3×C4⋊C4—51no—
189C3×C4⋊C4—102no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4C22⋊D511yescharacteristic
192C3×C22⋊C4—21no—
193C3×C22⋊C4—102no—
194C3×C22⋊C4—101no—
195C3×C42C22×D511yescharacteristic
196C23×C5—21no—
197C22×D5—21no—
198C5×Q8—42no—
199C5×D4—21no—
200C5×D4C3×SD1612yes—
201C2×C4×C5—21no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5C2×C3×D411yescharacteristic
206C2×C4×C5C2×C3×D411yescharacteristic
207C2×C4×C5C2×C3×D411yescharacteristic
208C22⋊D5—44no—
209C2×Dic5—22no—
210C2×Dic5—21no—
211C2×Dic5—44no—
212D20—21no—
213D20—21no—
214C4×D5—41no—
215C4×D5—41no—
216Dic10—41no—
217Dic10—41no—
218C5×C8—41no—
219#168—41no—
220#168—41no—
221C2×#41—101no—
222C4⋊Q8—51no—
223C4⋊Q8C2×C3×D511yescharacteristic
224#123—102no—
225C22⋊Q8—101no—
226#121—101no—
227C4×D4—51no—
228C4×D4C2×C3×D511yescharacteristic
229C2×C4⋊C4—101no—
230#106—21no—
231#106—101no—
232C4⋊C8—51no—
233C4⋊C8C2×C3×D511yescharacteristic
234#103—102no—
235#102—21no—
236#102—101no—
237C4×C8—51no—
238C2×C3×C5—42no—
239C2×C3×C5#45011yescharacteristic
240C2×C3×C5#45211yescharacteristic
241C2×C3×C5#45411yescharacteristic
242C3×D5—81no—
243C23×C3—21no—
244C23×C3—101no—
245C3×Q8—42no—
246C3×Q8—201no—
247C3×Q8—201no—
248C3×D4—21no—
249C3×D4—101no—
250C3×D4—101no—
251C3×D4—204no—
252C3×D4#68812yes—
253C2×C3×C4—21no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—101no—
258C2×C3×C4—102no—
259C2×C3×C4—204no—
260C2×C3×C4—201no—
261C2×C3×C4—201no—
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4C2×C22⋊D511yescharacteristic
265C3×C8—41no—
266C3×C8—201no—
267C3×C8—201no—
268C22×C5—22no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5C3×#12011yescharacteristic
272C2×D5—41no—
273C2×D5—41no—
274C2×D5—41no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—81no—
278C4×C5C2×C3×SD1611yescharacteristic
279C4×C5C3×#13511yescharacteristic
280C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
281C4×C5C3×#13711yescharacteristic
282Dic5—42no—
283Dic5—41no—
284#41—202no—
285#41—202no—
286C2×Q8—21no—
287C2×Q8—101no—
288C2×D4—51no—
289C2×D4—102no—
290C2×D4C3×C22⋊D511yescharacteristic
291C22×C4—21no—
292C22×C4—102no—
293C22×C4—101no—
294C2×C8—21no—
295C2×C8—101no—
296C2×C8—101no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—52no—
300C4⋊C4—51no—
301C4⋊C4—102no—
302C4⋊C4—101no—
303C4⋊C4C3×C22⋊D511yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—102no—
306C22⋊C4—101no—
307C42C22×C3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—22no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—201no—
313C22×C3—201no—
314C22×C3—201no—
315C22×C3#408311yescharacteristic
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—81no—
319C3×C4—201no—
320C3×C4—202no—
321C3×C4#406111yescharacteristic
322C3×C4#406211yescharacteristic
323C3×C4C2×#68811yescharacteristic
324C3×C4#409511yescharacteristic
325C2×C5—42no—
326C2×C5C3×#45011yescharacteristic
327C2×C5C3×#45211yescharacteristic
328C2×C5C3×#45411yescharacteristic
329D5—81no—
330C23—21no—
331C23—101no—
332Q8—42no—
333Q8—201no—
334Q8—201no—
335D4—21no—
336D4—101no—
337D4—101no—
338D4—204no—
339D4C3×#68812yes—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—101no—
345C2×C4—102no—
346C2×C4—204no—
347C2×C4—201no—
348C2×C4—201no—
349C2×C4C3×D4×D511yescharacteristic
350C2×C4C3×D4×D511yescharacteristic
351C2×C4C2×C3×C22⋊D511yescharacteristic
352C8—41no—
353C8—201no—
354C8—201no—
355C2×C3—42no—
356C2×C3—401no—
357C2×C3#6533511yescharacteristic
358C2×C3#6546211yescharacteristic
359C2×C3#6549011yescharacteristic
360C5C3×#163511yescharacteristic, complemented, Sylow
361C22—22no—
362C22—41no—
363C22—41no—
364C22—201no—
365C22—201no—
366C22—201no—
367C22C3×#408311yescharacteristic
368C4—21no—
369C4—41no—
370C4—81no—
371C4—201no—
372C4—202no—
373C4C3×#406111yescharacteristic
374C4C3×#406211yescharacteristic
375C4C2×C3×#68811yescharacteristic
376C4C3×#409511yescharacteristic
377C3#1060193911yescharacteristic, direct product factor, Sylow
378C2—42no—
379C2—401no—
380C2C3×#6533511yescharacteristic
381C2C3×#6546211yescharacteristic
382C2C3×#6549011yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#476C2
socleC22×C3×C5#120
prime radicalC3×#65889C2
hypercenterC3×#476D5
hypocenterC5C3×#1635
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
2. C3×C5×#476C2semidirect
3. C3×#65373C2semidirect
4. C3×#65370C2semidirect
5. C3×D4⋊#168C2semidirect
6. C3×#64703C2semidirect
7. C3×#64702C2semidirect
8. #10601939C3direct (N × H)
28. C5×#476C2×C3semidirect
29. #65373C2×C3semidirect
30. #65370C2×C3semidirect
31. D4⋊#168C2×C3semidirect
32. #64703C2×C3semidirect
33. #64702C2×C3semidirect
61. C3×#476D5semidirect
152. #476C3×D5semidirect
308. C3×C5#1635semidirect
360. C5C3×#1635semidirect
377. C3#10601939direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658892
C3×C5×#4762
C3×#653732
C3×#653702
C3×D4⋊#1682
C3×#647032
C3×#647022
#106019393
C3×#16355