Finite Group Databasebeta

← C3×#10601805 #14289092

Subgroups — C3×#10601805 #14289092

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×#65885C211yesmaximal, characteristic, complemented
2C3×C5×#459C211yesmaximal, characteristic, complemented
3C3×#65361C211yesmaximal, characteristic, complemented
4C3×#65359C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64703C211yesmaximal, characteristic, complemented
8#10601805C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709—21no—
10C2×C3×C5×D8—21no—
11C3×C5×#127C2211yescharacteristic
12C3×C4×C5×D4C2211yescharacteristic
13C3×#4084—21no—
14C2×C3×#686—21no—
15C3×#4070—21no—
16C3×D5×C4⋊C4—21no—
17C3×#4029—22no—
18C3×C4×D20C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#102—21no—
22C3×#3964—22no—
23C3×#3964—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1625—51nomaximal, Hall
27#65885C2×C311yescharacteristic, complemented
28C5×#459C2×C311yescharacteristic, complemented
29#65361C2×C311yescharacteristic, complemented
30#65359C2×C311yescharacteristic, complemented
31D4⋊#168C2×C311yescharacteristic, complemented
32#64706C2×C311yescharacteristic, complemented
33#64703C2×C311yescharacteristic, complemented
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C2×C3×C22⋊D5—22no—
40C3×#709—42no—
41C3×#709—42no—
42C2×C3×D20D411yescharacteristic
43C2×C3×C4×D5—22no—
44C2×C3×C4×D5—21no—
45C2×C3×Dic10—21no—
46C3×C5×D8—42no—
47C2×C3×C5×C8—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—21no—
50C3×C42×C5C2311yescharacteristic
51C3×C22⋊Dic5—22no—
52C3×#686—42no—
53C3×#685—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5D412yes—
56C3×C4⋊Dic5D411yescharacteristic
57C3×#683—22no—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C3×#547—51no—
61C3×#486—51no—
62C3×#459—51no—
63C3×#459D511yescharacteristic, complemented
64C3×#332—51no—
65C3×D4⋊C8—51no—
66C3×D4⋊C8—51no—
67C2×#709—21no—
68C2×C5×D8—21no—
69C5×#127C22×C311yescharacteristic
70C4×C5×D4C22×C311yescharacteristic
71#4084—21no—
72C2×#686—21no—
73#4070—21no—
74D5×C4⋊C4—21no—
75#4029—22no—
76C4×D20C22×C311yescharacteristic
77#4015C22×C311yescharacteristic
78C5×C4⋊C8C22×C311yescharacteristic
79C5×#102—21no—
80#3964—22no—
81#3964—21no—
82C4⋊#168C22×C311yescharacteristic
83C4×#168C22×C311yescharacteristic
84#1625—51noSylow
85C23×C3×C5—21no—
86C23×C3×C5—41no—
87C22×C3×D5—21no—
88C3×C5×D4—21no—
89C3×C5×D4—21no—
90C3×C5×D4—42no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C3×C22⋊D5—44no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—22no—
104C3×D20—21no—
105C3×D20D812yescomplemented
106C3×C4×D5—44no—
107C3×C4×D5—41no—
108C3×C4×D5—41no—
109C3×Dic10—41no—
110C3×Dic10—41no—
111C3×C5×C8—41no—
112C3×#168—41no—
113C3×#168—41no—
114C2×C3×#41—101no—
115C2×C3×D8—21no—
116C2×C3×D8—101no—
117C3×C4⋊Q8—51no—
118C3×#127C2×D511yescharacteristic
119C3×#123—102no—
120C3×C22⋊Q8—101no—
121C3×#121—101no—
122C3×C4×D4—51no—
123C3×C4×D4C2×D511yescharacteristic
124C2×C3×C4⋊C4—101no—
125C3×C4⋊C8—51no—
126C3×C4⋊C8C2×D511yescharacteristic
127C3×#102—21no—
128C3×#102—101no—
129C3×#102—102no—
130C3×C4×C8—51no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4C3×D411yescharacteristic
135C22×C4×C5—21no—
136C2×C22⋊D5—22no—
137#709—42no—
138#709—42no—
139C2×D20C3×D411yescharacteristic
140C2×C4×D5—22no—
141C2×C4×D5—21no—
142C2×Dic10—21no—
143C5×D8—42no—
144C2×C5×C8—21no—
145C5×C4⋊C4C3×D411yescharacteristic
146C5×C22⋊C4—21no—
147C42×C5C23×C311yescharacteristic
148C22⋊Dic5—22no—
149#686—42no—
150#685—21no—
151C4⋊Dic5—21no—
152C4⋊Dic5C3×D412yes—
153C4⋊Dic5C3×D411yescharacteristic
154#683—22no—
155C2×#168—21no—
156C2×#168—21no—
157#547—51no—
158#486—51no—
159#459—51no—
160#459C3×D511yescharacteristic, complemented
161#332—51no—
162D4⋊C8—51no—
163D4⋊C8—51no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5—81no—
168C22×C3×C5—81no—
169C22×C3×C5—81no—
170C22×C3×C5#12011yescharacteristic
171C2×C3×D5—22no—
172C2×C3×D5—41no—
173C2×C3×D5—41no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C3×C4×C5C2×D811yescharacteristic
177C3×C4×C5#13511yescharacteristic
178C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
179C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
180C3×Dic5—42no—
181C3×Dic5—41no—
182C3×#41—202no—
183C3×#41—202no—
184C2×C3×Q8—101no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—51no—
189C2×C3×D4—102no—
190C2×C3×D4C22⋊D511yescharacteristic
191C22×C3×C4—21no—
192C22×C3×C4—102no—
193C22×C3×C4—101no—
194C3×D8—42no—
195C3×D8—202no—
196C2×C3×C8—21no—
197C2×C3×C8—101no—
198C2×C3×C8—101no—
199C3×C4⋊C4—51no—
200C3×C4⋊C4—52no—
201C3×C4⋊C4—102no—
202C3×C4⋊C4—101no—
203C3×C4⋊C4C22⋊D511yescharacteristic
204C3×C22⋊C4—21no—
205C3×C22⋊C4—102no—
206C3×C22⋊C4—101no—
207C3×C42C22×D511yescharacteristic
208C23×C5—21no—
209C23×C5—41no—
210C22×D5—21no—
211C5×D4—21no—
212C5×D4—21no—
213C5×D4—42no—
214C5×D4—41no—
215C5×D4—41no—
216C5×D4—41no—
217C5×D4—41no—
218C2×C4×C5—21no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5C2×C3×D411yescharacteristic
222C2×C4×C5C2×C3×D411yescharacteristic
223C2×C4×C5C2×C3×D411yescharacteristic
224C22⋊D5—44no—
225C2×Dic5—21no—
226C2×Dic5—22no—
227D20—21no—
228D20C3×D812yescomplemented
229C4×D5—44no—
230C4×D5—41no—
231C4×D5—41no—
232Dic10—41no—
233Dic10—41no—
234C5×C8—41no—
235#168—41no—
236#168—41no—
237C2×#41—101no—
238C2×D8—21no—
239C2×D8—101no—
240C4⋊Q8—51no—
241#127C2×C3×D511yescharacteristic
242#123—102no—
243C22⋊Q8—101no—
244#121—101no—
245C4×D4—51no—
246C4×D4C2×C3×D511yescharacteristic
247C2×C4⋊C4—101no—
248C4⋊C8—51no—
249C4⋊C8C2×C3×D511yescharacteristic
250#102—21no—
251#102—101no—
252#102—102no—
253C4×C8—51no—
254C2×C3×C5—81no—
255C2×C3×C5—161no—
256C2×C3×C5#44711yescharacteristic
257C2×C3×C5#44911yescharacteristic
258C2×C3×C5#45411yescharacteristic
259C3×D5—42no—
260C23×C3—21no—
261C23×C3—41no—
262C23×C3—101no—
263C3×Q8—201no—
264C3×Q8—201no—
265C3×D4—21no—
266C3×D4—21no—
267C3×D4—42no—
268C3×D4—41no—
269C3×D4—41no—
270C3×D4—41no—
271C3×D4—41no—
272C3×D4—52no—
273C3×D4—101no—
274C3×D4—204no—
275C2×C3×C4—21no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—101no—
279C2×C3×C4—102no—
280C2×C3×C4—204no—
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—41no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5—81no—
293C22×C5—81no—
294C22×C5—81no—
295C22×C5C3×#12011yescharacteristic
296C2×D5—22no—
297C2×D5—41no—
298C2×D5—41no—
299C4×C5—21no—
300C4×C5—41no—
301C4×C5C2×C3×D811yescharacteristic
302C4×C5C3×#13511yescharacteristic
303C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
304C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
305Dic5—42no—
306Dic5—41no—
307#41—202no—
308#41—202no—
309C2×Q8—101no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—51no—
314C2×D4—102no—
315C2×D4C3×C22⋊D511yescharacteristic
316C22×C4—21no—
317C22×C4—102no—
318C22×C4—101no—
319D8—42no—
320D8—202no—
321C2×C8—21no—
322C2×C8—101no—
323C2×C8—101no—
324C4⋊C4—51no—
325C4⋊C4—52no—
326C4⋊C4—102no—
327C4⋊C4—101no—
328C4⋊C4C3×C22⋊D511yescharacteristic
329C22⋊C4—21no—
330C22⋊C4—102no—
331C22⋊C4—101no—
332C42C22×C3×D511yescharacteristic
333C3×C5#162511yescharacteristic, complemented, Hall
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—81no—
338C22×C3—81no—
339C22×C3—81no—
340C22×C3—102no—
341C22×C3—201no—
342C22×C3—201no—
343C22×C3#408311yescharacteristic
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—201no—
347C3×C4—202no—
348C3×C4D5×D811yescharacteristic
349C3×C4#405711yescharacteristic
350C3×C4#407811yescharacteristic
351C3×C4#409611yescharacteristic
352C2×C5—81no—
353C2×C5—161no—
354C2×C5C3×#44711yescharacteristic
355C2×C5C3×#44911yescharacteristic
356C2×C5C3×#45411yescharacteristic
357D5—42no—
358C23—21no—
359C23—41no—
360C23—101no—
361Q8—201no—
362Q8—201no—
363D4—21no—
364D4—21no—
365D4—42no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—52no—
371D4—101no—
372D4—204no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—101no—
377C2×C4—102no—
378C2×C4—204no—
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—81no—
388C2×C3—161no—
389C2×C3—202no—
390C2×C3#6532611yescharacteristic
391C2×C3#6544511yescharacteristic
392C2×C3#6549011yescharacteristic
393C5C3×#162511yescharacteristic, complemented, Sylow
394C22—41no—
395C22—41no—
396C22—41no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—102no—
401C22—201no—
402C22—201no—
403C22C3×#408311yescharacteristic
404C4—21no—
405C4—41no—
406C4—201no—
407C4—202no—
408C4C3×D5×D811yescharacteristic
409C4C3×#405711yescharacteristic
410C4C3×#407811yescharacteristic
411C4C3×#409611yescharacteristic
412C3#1060180511yescharacteristic, direct product factor, Sylow
413C2—81no—
414C2—161no—
415C2—202no—
416C2C3×#6532611yescharacteristic
417C2C3×#6544511yescharacteristic
418C2C3×#6549011yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#459C2
socleC22×C3×C5#120
hypercenterC3×#459D5
hypocenterC5C3×#1625
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C3×#65885C2semidirect
2. C3×C5×#459C2semidirect
3. C3×#65361C2semidirect
4. C3×#65359C2semidirect
5. C3×D4⋊#168C2semidirect
6. C3×#64706C2semidirect
7. C3×#64703C2semidirect
8. #10601805C3direct (N × H)
27. #65885C2×C3semidirect
28. C5×#459C2×C3semidirect
29. #65361C2×C3semidirect
30. #65359C2×C3semidirect
31. D4⋊#168C2×C3semidirect
32. #64706C2×C3semidirect
33. #64703C2×C3semidirect
63. C3×#459D5semidirect
105. C3×D20D8semidirect
160. #459C3×D5semidirect
228. D20C3×D8semidirect
333. C3×C5#1625semidirect
393. C5C3×#1625semidirect
412. C3#10601805direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658852
C3×C5×#4592
C3×#653612
C3×#653592
C3×D4⋊#1682
C3×#647062
C3×#647032
#106018053
C3×#16255