Finite Group Databasebeta

← C3×#10601989 #14289086

Subgroups — C3×#10601989 #14289086

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66060C211yesmaximal, characteristic, complemented
2C3×C5×#486C211yesmaximal, characteristic, complemented
3C3×#65361C211yesmaximal, characteristic, complemented
4C3×#65361C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic, complemented
7C3×#64679C211yesmaximal, characteristic, complemented
8#10601989C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#713—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#127C2211yescharacteristic
12C3×#4092—21no—
13C2×C3×#686—21no—
14C2×C3×#686—21no—
15C3×#4041—21no—
16C3×#4040—22no—
17C3×D5×C4⋊C4—21no—
18C3×C4×D20C2211yescharacteristic
19C3×C4×D20C2211yescharacteristic
20C3×C5×#102—22no—
21C3×C4×C5×C8C2211yescharacteristic
22C3×#3964—21no—
23C3×#3964—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1625—51nomaximal, Hall
27#66060C2×C311yescharacteristic, complemented
28C5×#486C2×C311yescharacteristic, complemented
29#65361C2×C311yescharacteristic, complemented
30#65361C2×C311yescharacteristic, complemented
31#64767C2×C311yescharacteristic, complemented
32#64679C2×C311yescharacteristic, complemented
33#64679C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C3×#713—42no—
39C3×#713—42no—
40C2×C3×D20—22no—
41C2×C3×D20D411yescharacteristic
42C2×C3×D20D411yescharacteristic
43C2×C3×C4×D5—22no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D412yes—
49C3×C42×C5C2311yescharacteristic
50C3×#686—42no—
51C3×#686—42no—
52C3×#685—22no—
53C3×#685—21no—
54C3×#685—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×C4⋊Dic5D411yescharacteristic
57C3×#683—22no—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C3×#547—51no—
61C3×#486D511yescharacteristic, complemented
62C3×#459—51no—
63C3×#459—51no—
64C3×#332—51no—
65C3×D4⋊C8—51no—
66C3×D4⋊C8—51no—
67C2×#713—21no—
68C5×C4⋊Q8C22×C311yescharacteristic
69C5×#127C22×C311yescharacteristic
70#4092—21no—
71C2×#686—21no—
72C2×#686—21no—
73#4041—21no—
74#4040—22no—
75D5×C4⋊C4—21no—
76C4×D20C22×C311yescharacteristic
77C4×D20C22×C311yescharacteristic
78C5×#102—22no—
79C4×C5×C8C22×C311yescharacteristic
80#3964—21no—
81#3964—21no—
82C4⋊#168C22×C311yescharacteristic
83C4⋊#168C22×C311yescharacteristic
84#1625—51noSylow
85C23×C3×C5—41no—
86C22×C3×D5—21no—
87C22×C3×D5—21no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C3×C5×D4—42no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3×D20—21no—
102C3×D20—21no—
103C3×D20—21no—
104C3×D20—44no—
105C3×D20D812yescomplemented
106C3×C4×D5—44no—
107C3×C4×D5—41no—
108C3×C4×D5—41no—
109C3×C4×D5—41no—
110C3×C4×D5—41no—
111C3×C5×C8—41no—
112C3×#168—41no—
113C3×#168—41no—
114C2×C3×#41—101no—
115C2×C3×D8—101no—
116C2×C3×D8—101no—
117C3×C4⋊Q8C2×D511yescharacteristic
118C3×#127C2×D511yescharacteristic
119C3×#123—102no—
120C3×C22⋊Q8—101no—
121C3×#121—101no—
122C3×C4×D4—51no—
123C3×C4×D4—51no—
124C2×C3×C4⋊C4—101no—
125C3×C4⋊C8—51no—
126C3×C4⋊C8—51no—
127C3×#102—22no—
128C3×#102—101no—
129C3×#102—101no—
130C3×C4×C8C2×D511yescharacteristic
131C2×C5×Q8—21no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135#713—42no—
136#713—42no—
137C2×D20—22no—
138C2×D20C3×D411yescharacteristic
139C2×D20C3×D411yescharacteristic
140C2×C4×D5—22no—
141C2×C4×D5—21no—
142C2×C4×D5—21no—
143C2×C5×C8—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4C3×D412yes—
146C42×C5C23×C311yescharacteristic
147#686—42no—
148#686—42no—
149#685—22no—
150#685—21no—
151#685—21no—
152C4⋊Dic5C3×D411yescharacteristic
153C4⋊Dic5C3×D411yescharacteristic
154#683—22no—
155C2×#168—21no—
156C2×#168—21no—
157#547—51no—
158#486C3×D511yescharacteristic, complemented
159#459—51no—
160#459—51no—
161#332—51no—
162D4⋊C8—51no—
163D4⋊C8—51no—
164C22×C3×C5—81no—
165C22×C3×C5—81no—
166C22×C3×C5—81no—
167C22×C3×C5#12011yescharacteristic
168C2×C3×D5—22no—
169C2×C3×D5—41no—
170C2×C3×D5—41no—
171C2×C3×D5—41no—
172C2×C3×D5—41no—
173C2×C3×D5—41no—
174C3×C4×C5—21no—
175C3×C4×C5—42no—
176C3×C4×C5C2×D811yescharacteristic
177C3×C4×C5#13511yescharacteristic
178C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
179C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
180C3×Dic5—41no—
181C3×Dic5—41no—
182C3×#41—202no—
183C3×#41—202no—
184C2×C3×Q8—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—51no—
189C2×C3×D4—51no—
190C2×C3×D4—102no—
191C22×C3×C4—102no—
192C22×C3×C4—101no—
193C22×C3×C4—101no—
194C3×D8—202no—
195C3×D8—202no—
196C2×C3×C8—21no—
197C2×C3×C8—101no—
198C2×C3×C8—101no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—51no—
201C3×C4⋊C4—51no—
202C3×C4⋊C4—102no—
203C3×C4⋊C4C22⋊D512yes—
204C3×C22⋊C4—102no—
205C3×C22⋊C4—101no—
206C3×C22⋊C4—101no—
207C3×C42C22×D511yescharacteristic
208C23×C5—41no—
209C22×D5—21no—
210C22×D5—21no—
211C5×Q8—41no—
212C5×Q8—41no—
213C5×D4—42no—
214C5×D4—41no—
215C5×D4—41no—
216C5×D4—41no—
217C5×D4—41no—
218C2×C4×C5—22no—
219C2×C4×C5C2×C3×D411yescharacteristic
220C2×C4×C5C2×C3×D411yescharacteristic
221C2×C4×C5C2×C3×D411yescharacteristic
222C2×Dic5—21no—
223C2×Dic5—21no—
224D20—21no—
225D20—21no—
226D20—21no—
227D20—44no—
228D20C3×D812yescomplemented
229C4×D5—44no—
230C4×D5—41no—
231C4×D5—41no—
232C4×D5—41no—
233C4×D5—41no—
234C5×C8—41no—
235#168—41no—
236#168—41no—
237C2×#41—101no—
238C2×D8—101no—
239C2×D8—101no—
240C4⋊Q8C2×C3×D511yescharacteristic
241#127C2×C3×D511yescharacteristic
242#123—102no—
243C22⋊Q8—101no—
244#121—101no—
245C4×D4—51no—
246C4×D4—51no—
247C2×C4⋊C4—101no—
248C4⋊C8—51no—
249C4⋊C8—51no—
250#102—22no—
251#102—101no—
252#102—101no—
253C4×C8C2×C3×D511yescharacteristic
254C2×C3×C5—161no—
255C2×C3×C5#44711yescharacteristic
256C2×C3×C5#44911yescharacteristic
257C2×C3×C5#45411yescharacteristic
258C3×D5—42no—
259C3×D5—81no—
260C23×C3—41no—
261C23×C3—101no—
262C23×C3—101no—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×D4—42no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—41no—
269C3×D4—41no—
270C3×D4—52no—
271C3×D4—101no—
272C3×D4—101no—
273C3×D4—101no—
274C3×D4—204no—
275C2×C3×C4—22no—
276C2×C3×C4—101no—
277C2×C3×C4—101no—
278C2×C3×C4—204no—
279C2×C3×C4—201no—
280C2×C3×C4—201no—
281C2×C3×C4—201no—
282C2×C3×C4—201no—
283C2×C3×C4D4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285C2×C3×C4C2×C22⋊D511yescharacteristic
286C3×C8—41no—
287C3×C8—201no—
288C3×C8—201no—
289C22×C5—81no—
290C22×C5—81no—
291C22×C5—81no—
292C22×C5C3×#12011yescharacteristic
293C2×D5—22no—
294C2×D5—41no—
295C2×D5—41no—
296C2×D5—41no—
297C2×D5—41no—
298C2×D5—41no—
299C4×C5—21no—
300C4×C5—42no—
301C4×C5C2×C3×D811yescharacteristic
302C4×C5C3×#13511yescharacteristic
303C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
304C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
305Dic5—41no—
306Dic5—41no—
307#41—202no—
308#41—202no—
309C2×Q8—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—51no—
314C2×D4—51no—
315C2×D4—102no—
316C22×C4—102no—
317C22×C4—101no—
318C22×C4—101no—
319D8—202no—
320D8—202no—
321C2×C8—21no—
322C2×C8—101no—
323C2×C8—101no—
324C4⋊C4—21no—
325C4⋊C4—51no—
326C4⋊C4—51no—
327C4⋊C4—102no—
328C4⋊C4C3×C22⋊D512yes—
329C22⋊C4—102no—
330C22⋊C4—101no—
331C22⋊C4—101no—
332C42C22×C3×D511yescharacteristic
333C3×C5#162511yescharacteristic, complemented, Hall
334C22×C3—81no—
335C22×C3—81no—
336C22×C3—81no—
337C22×C3—102no—
338C22×C3—201no—
339C22×C3—201no—
340C22×C3—201no—
341C22×C3—201no—
342C22×C3—201no—
343C22×C3#408311yescharacteristic
344C3×C4—21no—
345C3×C4—42no—
346C3×C4—201no—
347C3×C4—201no—
348C3×C4D5×D811yescharacteristic
349C3×C4#405711yescharacteristic
350C3×C4#406011yescharacteristic
351C3×C4#406211yescharacteristic
352C2×C5—161no—
353C2×C5C3×#44711yescharacteristic
354C2×C5C3×#44911yescharacteristic
355C2×C5C3×#45411yescharacteristic
356D5—42no—
357D5—81no—
358C23—41no—
359C23—101no—
360C23—101no—
361Q8—41no—
362Q8—41no—
363D4—42no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—52no—
369D4—101no—
370D4—101no—
371D4—101no—
372D4—204no—
373C2×C4—22no—
374C2×C4—101no—
375C2×C4—101no—
376C2×C4—204no—
377C2×C4—201no—
378C2×C4—201no—
379C2×C4—201no—
380C2×C4—201no—
381C2×C4C3×D4×D511yescharacteristic
382C2×C4C3×D4×D511yescharacteristic
383C2×C4C2×C3×C22⋊D511yescharacteristic
384C8—41no—
385C8—201no—
386C8—201no—
387C2×C3—161no—
388C2×C3—202no—
389C2×C3—401no—
390C2×C3#6535111yescharacteristic
391C2×C3#6544511yescharacteristic
392C2×C3#6546111yescharacteristic
393C5C3×#162511yescharacteristic, complemented, Sylow
394C22—81no—
395C22—81no—
396C22—81no—
397C22—102no—
398C22—201no—
399C22—201no—
400C22—201no—
401C22—201no—
402C22—201no—
403C22C3×#408311yescharacteristic
404C4—21no—
405C4—42no—
406C4—201no—
407C4—201no—
408C4C3×D5×D811yescharacteristic
409C4C3×#405711yescharacteristic
410C4C3×#406011yescharacteristic
411C4C3×#406211yescharacteristic
412C3#1060198911yescharacteristic, direct product factor, Sylow
413C2—161no—
414C2—202no—
415C2—401no—
416C2C3×#6535111yescharacteristic
417C2C3×#6544511yescharacteristic
418C2C3×#6546111yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#486C2
socleC22×C3×C5#120
hypercenterC3×#486D5
hypocenterC5C3×#1625
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#486

Complements

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

NH ≅ G/Ntype
1. C3×#66060C2semidirect
2. C3×C5×#486C2semidirect
3. C3×#65361C2semidirect
4. C3×#65361C2semidirect
5. C3×#64767C2semidirect
6. C3×#64679C2semidirect
7. C3×#64679C2semidirect
8. #10601989C3direct (N × H)
27. #66060C2×C3semidirect
28. C5×#486C2×C3semidirect
29. #65361C2×C3semidirect
30. #65361C2×C3semidirect
31. #64767C2×C3semidirect
32. #64679C2×C3semidirect
33. #64679C2×C3semidirect
61. C3×#486D5semidirect
105. C3×D20D8semidirect
158. #486C3×D5semidirect
228. D20C3×D8semidirect
333. C3×C5#1625semidirect
393. C5C3×#1625semidirect
412. C3#10601989direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660602
C3×C5×#4862
C3×#653612
C3×#647672
C3×#646792
#106019893
C3×#16255