Finite Group Databasebeta

← C3×#10599250 #14289224

Subgroups — C3×#10599250 #14289224

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66061C211yesmaximal, characteristic, complemented
2C3×#65377C211yesmaximal, characteristic, complemented
3C3×#65137C211yesmaximal, characteristic, complemented
4C3×#65132C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7C3×#64703C211yesmaximal, characteristic, complemented
8#10599250C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4092—21no—
12C2×C3×D40—21no—
13C2×C3×#677—21no—
14C3×#4042—22no—
15C3×#4039—21no—
16C3×#4034—21no—
17C3×#4020C2211yescharacteristic
18C3×C4×D20C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×#3953—21no—
23C3×#3953—21no—
24C3×#3941—22no—
25C3×C4×#168C2211yescharacteristic
26C3×#1627—51nomaximal, Hall
27#66061C2×C311yescharacteristic, complemented
28#65377C2×C311yescharacteristic, complemented
29#65137C2×C311yescharacteristic, complemented
30#65132C2×C311yescharacteristic
31C5×#332C2×C311yescharacteristic, complemented
32#64704C2×C311yescharacteristic, complemented
33#64703C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C3×Q8×D5—42no—
36C3×Q8×D5—42no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20D411yescharacteristic
41C2×C3×C4×D5—22no—
42C2×C3×C4×D5—21no—
43C2×C3×Dic10—22no—
44C2×C3×Dic10D411yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D412yes—
49C3×C42×C5C2311yescharacteristic
50C3×#685—22no—
51C3×#685—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—22no—
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C2×C3×#168—21no—
58C3×D40—42no—
59C3×#677—42no—
60C3×D4×Q8—51no—
61C3×#486—51no—
62C3×#460—51no—
63C3×#459—51no—
64C3×#332D511yescharacteristic, complemented
65C3×Q8⋊C8—51no—
66C3×D4⋊C8—51no—
67C2×Q8×D5—21no—
68C5×C4⋊Q8C22×C311yescharacteristic
69#4092—21no—
70C2×D40—21no—
71C2×#677—21no—
72#4042—22no—
73#4039—21no—
74#4034—21no—
75#4020C22×C311yescharacteristic
76C4×D20C22×C311yescharacteristic
77C4×Dic10C22×C311yescharacteristic
78C5×C4⋊C8C22×C311yescharacteristic
79C5×C4⋊C8C22×C311yescharacteristic
80#3953—21no—
81#3953—21no—
82#3941—22no—
83C4×#168C22×C311yescharacteristic
84#1627—51noSylow
85C22×C3×D5—21no—
86C22×C3×D5—41no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C3×D20—21no—
97C3×D20—42no—
98C3×D20—41no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20SD1612yescomplemented
103C3×C4×D5—44no—
104C3×C4×D5—41no—
105C3×C4×D5—41no—
106C3×Dic10—21no—
107C3×Dic10—44no—
108C3×Dic10D812yescomplemented
109C3×C5×C8—41no—
110C3×C5×C8—41no—
111C3×#168—41no—
112C22×C3×Q8—101no—
113C2×C3×SD16—101no—
114C2×C3×D8—101no—
115C3×C4⋊Q8—101no—
116C3×C4⋊Q8C2×D511yescharacteristic
117C3×#127—51no—
118C3×C22⋊Q8—101no—
119C3×C22⋊Q8—102no—
120C3×C4×Q8—51no—
121C3×C4×D4—51no—
122C3×C4×D4—101no—
123C3×C4⋊C8C2×D511yescharacteristic
124C3×C4⋊C8C2×D511yescharacteristic
125C3×#102—101no—
126C3×#102—101no—
127C3×#102—102no—
128C3×C4×C8—51no—
129C2×C5×Q8—21no—
130Q8×D5—42no—
131Q8×D5—42no—
132C2×D20—21no—
133C2×D20—21no—
134C2×D20—21no—
135C2×D20C3×D411yescharacteristic
136C2×C4×D5—22no—
137C2×C4×D5—21no—
138C2×Dic10—22no—
139C2×Dic10C3×D411yescharacteristic
140C2×C5×C8—21no—
141C2×C5×C8—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4C3×D412yes—
144C42×C5C23×C311yescharacteristic
145#685—22no—
146#685—21no—
147C4⋊Dic5C3×D411yescharacteristic
148C4⋊Dic5C3×D411yescharacteristic
149#683—22no—
150#683—21no—
151C4×Dic5—21no—
152C2×#168—21no—
153D40—42no—
154#677—42no—
155D4×Q8—51no—
156#486—51no—
157#460—51no—
158#459—51no—
159#332C3×D511yescharacteristic, complemented
160Q8⋊C8—51no—
161D4⋊C8—51no—
162C22×C3×C5#12011yescharacteristic
163C2×C3×D5—22no—
164C2×C3×D5—41no—
165C2×C3×D5—41no—
166C2×C3×D5—81no—
167C2×C3×D5—81no—
168C2×C3×D5—81no—
169C3×C4×C5—21no—
170C3×C4×C5—42no—
171C3×C4×C5C2×D811yescharacteristic
172C3×C4×C5C2×SD1611yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C3×C4×C5#13711yescharacteristic
175C3×Dic5—22no—
176C3×Dic5—41no—
177C3×Dic5—41no—
178C2×C3×Q8—21no—
179C2×C3×Q8—51no—
180C2×C3×Q8—102no—
181C2×C3×Q8—202no—
182C2×C3×Q8—202no—
183C2×C3×D4—51no—
184C2×C3×D4—101no—
185C2×C3×D4—101no—
186C2×C3×D4—101no—
187C22×C3×C4—102no—
188C22×C3×C4—101no—
189C3×SD16—202no—
190C3×D8—202no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—101no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—51no—
196C3×C4⋊C4—51no—
197C3×C4⋊C4—102no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4D2012yes—
200C3×C22⋊C4—102no—
201C3×C22⋊C4—101no—
202C3×C42—101no—
203C3×C42C22×D511yescharacteristic
204C22×D5—21no—
205C22×D5—41no—
206C5×Q8—41no—
207C5×Q8—41no—
208C2×C4×C5—22no—
209C2×C4×C5C2×C3×D411yescharacteristic
210C2×C4×C5C2×C3×D411yescharacteristic
211C2×C4×C5C2×C3×D411yescharacteristic
212C2×Dic5—21no—
213C2×Dic5—21no—
214C2×Dic5—21no—
215D20—21no—
216D20—42no—
217D20—41no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20C3×SD1612yescomplemented
222C4×D5—44no—
223C4×D5—41no—
224C4×D5—41no—
225Dic10—21no—
226Dic10—44no—
227Dic10C3×D812yescomplemented
228C5×C8—41no—
229C5×C8—41no—
230#168—41no—
231C22×Q8—101no—
232C2×SD16—101no—
233C2×D8—101no—
234C4⋊Q8—101no—
235C4⋊Q8C2×C3×D511yescharacteristic
236#127—51no—
237C22⋊Q8—101no—
238C22⋊Q8—102no—
239C4×Q8—51no—
240C4×D4—51no—
241C4×D4—101no—
242C4⋊C8C2×C3×D511yescharacteristic
243C4⋊C8C2×C3×D511yescharacteristic
244#102—101no—
245#102—101no—
246#102—102no—
247C4×C8—51no—
248C2×C3×C5#44711yescharacteristic
249C2×C3×C5#44811yescharacteristic
250C2×C3×C5#45411yescharacteristic
251C3×D5—42no—
252C3×D5—161no—
253C23×C3—101no—
254C23×C3—201no—
255C3×Q8—41no—
256C3×Q8—41no—
257C3×Q8—52no—
258C3×Q8—101no—
259C3×Q8—204no—
260C3×D4—52no—
261C3×D4—101no—
262C3×D4—202no—
263C3×D4—201no—
264C3×D4—201no—
265C3×D4—201no—
266C3×D4—201no—
267C2×C3×C4—22no—
268C2×C3×C4—101no—
269C2×C3×C4—101no—
270C2×C3×C4—101no—
271C2×C3×C4—204no—
272C2×C3×C4—201no—
273C2×C3×C4—201no—
274C2×C3×C4C2×D2011yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C3×C8—41no—
278C3×C8—41no—
279C3×C8—201no—
280C22×C5C3×#12011yescharacteristic
281C2×D5—22no—
282C2×D5—41no—
283C2×D5—41no—
284C2×D5—81no—
285C2×D5—81no—
286C2×D5—81no—
287C4×C5—21no—
288C4×C5—42no—
289C4×C5C2×C3×D811yescharacteristic
290C4×C5C2×C3×SD1611yescharacteristic
291C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
292C4×C5C3×#13711yescharacteristic
293Dic5—22no—
294Dic5—41no—
295Dic5—41no—
296C2×Q8—21no—
297C2×Q8—51no—
298C2×Q8—102no—
299C2×Q8—202no—
300C2×Q8—202no—
301C2×D4—51no—
302C2×D4—101no—
303C2×D4—101no—
304C2×D4—101no—
305C22×C4—102no—
306C22×C4—101no—
307SD16—202no—
308D8—202no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—101no—
312C4⋊C4—21no—
313C4⋊C4—51no—
314C4⋊C4—51no—
315C4⋊C4—102no—
316C4⋊C4—101no—
317C4⋊C4C3×D2012yes—
318C22⋊C4—102no—
319C22⋊C4—101no—
320C42—101no—
321C42C22×C3×D511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3—102no—
324C22×C3—201no—
325C22×C3—201no—
326C22×C3—401no—
327C22×C3—401no—
328C22×C3—401no—
329C22×C3#402811yescharacteristic
330C3×C4—21no—
331C3×C4—42no—
332C3×C4—102no—
333C3×C4—201no—
334C3×C4—201no—
335C3×C4D5×D811yescharacteristic
336C3×C4D5×SD1611yescharacteristic
337C3×C4#406011yescharacteristic
338C3×C4#406411yescharacteristic
339C2×C5C3×#44711yescharacteristic
340C2×C5C3×#44811yescharacteristic
341C2×C5C3×#45411yescharacteristic
342D5—42no—
343D5—161no—
344C23—101no—
345C23—201no—
346Q8—41no—
347Q8—41no—
348Q8—52no—
349Q8—101no—
350Q8—204no—
351D4—52no—
352D4—101no—
353D4—202no—
354D4—201no—
355D4—201no—
356D4—201no—
357D4—201no—
358C2×C4—22no—
359C2×C4—101no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—204no—
363C2×C4—201no—
364C2×C4—201no—
365C2×C4C2×C3×D2011yescharacteristic
366C2×C4C3×D4×D511yescharacteristic
367C2×C4C3×D4×D511yescharacteristic
368C8—41no—
369C8—41no—
370C8—201no—
371C2×C3—202no—
372C2×C3—801no—
373C2×C3#6504211yescharacteristic
374C2×C3#6506211yescharacteristic
375C2×C3#6509511yescharacteristic
376C5C3×#162711yescharacteristic, complemented, Sylow
377C22—102no—
378C22—201no—
379C22—201no—
380C22—401no—
381C22—401no—
382C22—401no—
383C22C3×#402811yescharacteristic
384C4—21no—
385C4—42no—
386C4—102no—
387C4—201no—
388C4—201no—
389C4C3×D5×D811yescharacteristic
390C4C3×D5×SD1611yescharacteristic
391C4C3×#406011yescharacteristic
392C4C3×#406411yescharacteristic
393C3#1059925011yescharacteristic, direct product factor, Sylow
394C2—202no—
395C2—801no—
396C2C3×#6504211yescharacteristic
397C2C3×#6506211yescharacteristic
398C2C3×#6509511yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#332C2
socleC22×C3×C5#120
prime radicalC3×#65132C2
hypercenterC3×#332D5
hypocenterC5C3×#1627
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×#66061C2semidirect
2. C3×#65377C2semidirect
3. C3×#65137C2semidirect
5. C3×C5×#332C2semidirect
6. C3×#64704C2semidirect
7. C3×#64703C2semidirect
8. #10599250C3direct (N × H)
27. #66061C2×C3semidirect
28. #65377C2×C3semidirect
29. #65137C2×C3semidirect
31. C5×#332C2×C3semidirect
32. #64704C2×C3semidirect
33. #64703C2×C3semidirect
64. C3×#332D5semidirect
102. C3×D20SD16semidirect
108. C3×Dic10D8semidirect
159. #332C3×D5semidirect
221. D20C3×SD16semidirect
227. Dic10C3×D8semidirect
322. C3×C5#1627semidirect
376. C5C3×#1627semidirect
393. C3#10599250direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660612
C3×#653772
C3×#651372
C3×#651322
C3×C5×#3322
C3×#647042
C3×#647032
#105992503
C3×#16275