Finite Group Databasebeta

← C3×#10598992 #14289059

Subgroups — C3×#10598992 #14289059

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65897C211yesmaximal, characteristic, complemented
2C3×#65304C211yesmaximal, characteristic, complemented
3C3×#65132C211yesmaximal, characteristic, complemented
4C3×#64982C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6C3×#64701C211yesmaximal, characteristic, complemented
7C3×#64679C211yesmaximal, characteristic, complemented
8#10598992C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C3×#4084—21no—
11C2×C3×#686—21no—
12C3×#4076—21no—
13C3×#4072—21no—
14C2×C3×D40—21no—
15C2×C3×#677—22no—
16C3×#4038—21no—
17C3×#4031—22no—
18C3×#4020C2211yescharacteristic
19C3×C4×D20C2211yescharacteristic
20C3×#4015C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23C3×#3953—21no—
24C3×#3941—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1624—51nomaximal, Hall
27#65897C2×C311yescharacteristic, complemented
28#65304C2×C311yescharacteristic, complemented
29#65132C2×C311yescharacteristic, complemented
30#64982C2×C311yescharacteristic, complemented
31C5×D4⋊C8C2×C311yescharacteristic, complemented
32#64701C2×C311yescharacteristic, complemented
33#64679C2×C311yescharacteristic, complemented
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C3×C22⋊D5—22no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20D411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×C3×Dic10D412yes—
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2311yescharacteristic
48C3×C22⋊Dic5—22no—
49C3×#686—42no—
50C3×#685—22no—
51C3×#685—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×C4×Dic5—22no—
56C2×C3×#168—21no—
57C3×D40—42no—
58C3×#677—44no—
59C3×#555—51no—
60C3×#492—51no—
61C3×#459—51no—
62C3×#459—51no—
63C3×#333—51no—
64C3×D4⋊C8—51no—
65C3×D4⋊C8D511yescharacteristic, complemented
66C4×C5×D4C22×C311yescharacteristic
67#4084—21no—
68C2×#686—21no—
69#4076—21no—
70#4072—21no—
71C2×D40—21no—
72C2×#677—22no—
73#4038—21no—
74#4031—22no—
75#4020C22×C311yescharacteristic
76C4×D20C22×C311yescharacteristic
77#4015C22×C311yescharacteristic
78C5×C4⋊C8C22×C311yescharacteristic
79C4×C5×C8C22×C311yescharacteristic
80#3953—21no—
81#3941—21no—
82C4⋊#168C22×C311yescharacteristic
83#1624—51noSylow
84C23×C3×C5—21no—
85C22×C3×D5—21no—
86C22×C3×D5—41no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C2×C3×C4×C5—21no—
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—82no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—22no—
98C3×D20—21no—
99C3×D20—21no—
100C3×D20—42no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107C3×Dic10—42no—
108C3×C5×C8—22no—
109C3×C5×C8—41no—
110C3×#168—41no—
111C2×C3×SD16—102no—
112C2×C3×D8—101no—
113C2×C3×D8—101no—
114C3×C4⋊Q8—51no—
115C3×#127—51no—
116C3×#124—102no—
117C3×#121—101no—
118C3×#121—101no—
119C3×C4×D4—51no—
120C3×C4×D4C2×D511yescharacteristic
121C3×#117—101no—
122C3×#117—101no—
123C3×C4⋊C8—51no—
124C3×C4⋊C8C2×D511yescharacteristic
125C3×#102—101no—
126C3×#102—101no—
127C3×C4×C8C2×D511yescharacteristic
128C2×C5×D4C3×D411yescharacteristic
129C22×C4×C5—21no—
130C2×C22⋊D5—22no—
131C2×D20—21no—
132C2×D20—21no—
133C2×D20—21no—
134C2×D20C3×D411yescharacteristic
135C2×C4×D5—21no—
136C2×Dic10C3×D412yes—
137C2×C5×C8—21no—
138C2×C5×C8—21no—
139C5×C4⋊C4C3×D411yescharacteristic
140C5×C22⋊C4—21no—
141C42×C5C23×C311yescharacteristic
142C22⋊Dic5—22no—
143#686—42no—
144#685—22no—
145#685—21no—
146C4⋊Dic5—21no—
147C4⋊Dic5—21no—
148C4⋊Dic5C3×D411yescharacteristic
149C4×Dic5—22no—
150C2×#168—21no—
151D40—42no—
152#677—44no—
153#555—51no—
154#492—51no—
155#459—51no—
156#459—51no—
157#333—51no—
158D4⋊C8—51no—
159D4⋊C8C3×D511yescharacteristic, complemented
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5#12011yescharacteristic
164C2×C3×D5—41no—
165C2×C3×D5—41no—
166C2×C3×D5—41no—
167C2×C3×D5—81no—
168C2×C3×D5—81no—
169C2×C3×D5—81no—
170C3×C4×C5—21no—
171C3×C4×C5—41no—
172C3×C4×C5#13511yescharacteristic
173C3×C4×C5#13511yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
176C3×Dic5—41no—
177C3×Dic5—42no—
178C2×C3×Q8—52no—
179C2×C3×D4—51no—
180C2×C3×D4—102no—
181C2×C3×D4—101no—
182C2×C3×D4—101no—
183C2×C3×D4—101no—
184C2×C3×D4D2011yescharacteristic
185C22×C3×C4—21no—
186C22×C3×C4—101no—
187C3×SD16—204no—
188C3×D8—202no—
189C3×D8—202no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—101no—
193C3×C4⋊C4—51no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4—101no—
196C3×C4⋊C4D2011yescharacteristic
197C3×C22⋊C4—21no—
198C3×C22⋊C4—102no—
199C3×C22⋊C4—102no—
200C3×C22⋊C4—101no—
201C3×C42—102no—
202C3×C42C22×D511yescharacteristic
203C23×C5—21no—
204C22×D5—21no—
205C22×D5—41no—
206C5×D4—21no—
207C5×D4—21no—
208C2×C4×C5—21no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5C2×C3×D411yescharacteristic
212C2×C4×C5C2×C3×D411yescharacteristic
213C2×C4×C5C2×C3×D411yescharacteristic
214C22⋊D5—82no—
215C2×Dic5—21no—
216C2×Dic5—22no—
217D20—21no—
218D20—21no—
219D20—42no—
220D20—41no—
221D20—41no—
222D20—41no—
223D20—41no—
224C4×D5—41no—
225C4×D5—41no—
226Dic10—42no—
227C5×C8—22no—
228C5×C8—41no—
229#168—41no—
230C2×SD16—102no—
231C2×D8—101no—
232C2×D8—101no—
233C4⋊Q8—51no—
234#127—51no—
235#124—102no—
236#121—101no—
237#121—101no—
238C4×D4—51no—
239C4×D4C2×C3×D511yescharacteristic
240#117—101no—
241#117—101no—
242C4⋊C8—51no—
243C4⋊C8C2×C3×D511yescharacteristic
244#102—101no—
245#102—101no—
246C4×C8C2×C3×D511yescharacteristic
247C2×C3×C5—81no—
248C2×C3×C5#44911yescharacteristic
249C2×C3×C5#44911yescharacteristic
250C2×C3×C5#45311yescharacteristic
251C3×D5—81no—
252C3×D5—161no—
253C23×C3—21no—
254C23×C3—101no—
255C23×C3—201no—
256C3×Q8—202no—
257C3×D4—21no—
258C3×D4—21no—
259C3×D4—101no—
260C3×D4—101no—
261C3×D4—202no—
262C3×D4—201no—
263C3×D4—201no—
264C3×D4—201no—
265C3×D4—201no—
266C3×D4—402no—
267C2×C3×C4—21no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—101no—
271C2×C3×C4—102no—
272C2×C3×C4—201no—
273C2×C3×C4—201no—
274C2×C3×C4C2×D2011yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C3×C8—22no—
278C3×C8—41no—
279C3×C8—201no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5C3×#12011yescharacteristic
284C2×D5—41no—
285C2×D5—41no—
286C2×D5—41no—
287C2×D5—81no—
288C2×D5—81no—
289C2×D5—81no—
290C4×C5—21no—
291C4×C5—41no—
292C4×C5C3×#13511yescharacteristic
293C4×C5C3×#13511yescharacteristic
294C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
295C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
296Dic5—41no—
297Dic5—42no—
298C2×Q8—52no—
299C2×D4—51no—
300C2×D4—102no—
301C2×D4—101no—
302C2×D4—101no—
303C2×D4—101no—
304C2×D4C3×D2011yescharacteristic
305C22×C4—21no—
306C22×C4—101no—
307SD16—204no—
308D8—202no—
309D8—202no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—101no—
313C4⋊C4—51no—
314C4⋊C4—101no—
315C4⋊C4—101no—
316C4⋊C4C3×D2011yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—102no—
319C22⋊C4—102no—
320C22⋊C4—101no—
321C42—102no—
322C42C22×C3×D511yescharacteristic
323C3×C5#162411yescharacteristic, complemented, Hall
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—201no—
328C22×C3—201no—
329C22×C3—201no—
330C22×C3—401no—
331C22×C3—401no—
332C22×C3—401no—
333C22×C3#402811yescharacteristic
334C3×C4—21no—
335C3×C4—41no—
336C3×C4—202no—
337C3×C4—201no—
338C3×C4#405011yescharacteristic
339C3×C4#405411yescharacteristic
340C3×C4#405711yescharacteristic
341C3×C4#406211yescharacteristic
342C2×C5—81no—
343C2×C5C3×#44911yescharacteristic
344C2×C5C3×#44911yescharacteristic
345C2×C5C3×#45311yescharacteristic
346D5—81no—
347D5—161no—
348C23—21no—
349C23—101no—
350C23—201no—
351Q8—202no—
352D4—21no—
353D4—21no—
354D4—101no—
355D4—101no—
356D4—202no—
357D4—201no—
358D4—201no—
359D4—201no—
360D4—201no—
361D4—402no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—101no—
366C2×C4—102no—
367C2×C4—201no—
368C2×C4—201no—
369C2×C4C2×C3×D2011yescharacteristic
370C2×C4C3×D4×D511yescharacteristic
371C2×C4C3×D4×D511yescharacteristic
372C8—22no—
373C8—41no—
374C8—201no—
375C2×C3—81no—
376C2×C3—401no—
377C2×C3—801no—
378C2×C3#6502311yescharacteristic
379C2×C3#6507011yescharacteristic
380C2×C3#6511111yescharacteristic
381C5C3×#162411yescharacteristic, complemented, Sylow
382C22—41no—
383C22—41no—
384C22—41no—
385C22—201no—
386C22—201no—
387C22—201no—
388C22—401no—
389C22—401no—
390C22—401no—
391C22C3×#402811yescharacteristic
392C4—21no—
393C4—41no—
394C4—202no—
395C4—201no—
396C4C3×#405011yescharacteristic
397C4C3×#405411yescharacteristic
398C4C3×#405711yescharacteristic
399C4C3×#406211yescharacteristic
400C3#1059899211yescharacteristic, direct product factor, Sylow
401C2—81no—
402C2—401no—
403C2—801no—
404C2C3×#6502311yescharacteristic
405C2C3×#6507011yescharacteristic
406C2C3×#6511111yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1624
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×#65897C2semidirect
2. C3×#65304C2semidirect
3. C3×#65132C2semidirect
4. C3×#64982C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C3×#64701C2semidirect
7. C3×#64679C2semidirect
8. #10598992C3direct (N × H)
27. #65897C2×C3semidirect
28. #65304C2×C3semidirect
29. #65132C2×C3semidirect
30. #64982C2×C3semidirect
31. C5×D4⋊C8C2×C3semidirect
32. #64701C2×C3semidirect
33. #64679C2×C3semidirect
65. C3×D4⋊C8D5semidirect
159. D4⋊C8C3×D5semidirect
323. C3×C5#1624semidirect
381. C5C3×#1624semidirect
400. C3#10598992direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658972
C3×#653042
C3×#651322
C3×#649822
C3×C5×D4⋊C82
C3×#647012
C3×#646792
#105989923
C3×#16245