Finite Group Databasebeta

← C3×#10599052 #14288897

Subgroups — C3×#10599052 #14288897

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65911C211yesmaximal, characteristic, complemented
2C3×#65316C211yesmaximal, characteristic, complemented
3C3×#65132C211yesmaximal, characteristic, complemented
4C3×#64984C211yesmaximal, characteristic, complemented
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64679C211yesmaximal, characteristic, complemented
8#10599052C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#713—21no—
10C3×C4×C5×Q8C2211yescharacteristic
11C2×C3×#688—21no—
12C2×C3×D40—21no—
13C2×C3×D40—22no—
14C3×#4041—22no—
15C3×#4041—21no—
16C3×#4020—21no—
17C3×#4020C2211yescharacteristic
18C3×#4020C2211yescharacteristic
19C3×C4×D20—21no—
20C3×C4×D20C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23C3×#3953—21no—
24C3×#3941—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1621—51nomaximal, Hall
27#65911C2×C311yescharacteristic, complemented
28#65316C2×C311yescharacteristic, complemented
29#65132C2×C311yescharacteristic, complemented
30#64984C2×C311yescharacteristic, complemented
31C5×Q8⋊C8C2×C311yescharacteristic, complemented
32#64705C2×C311yescharacteristic, complemented
33#64679C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8D411yescharacteristic
35C3×#713—42no—
36C3×#713—42no—
37C2×C3×D20—22no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20—22no—
44C2×C3×D20D411yescharacteristic
45C2×C3×D20D412yes—
46C2×C3×C4×D5—22no—
47C2×C3×C4×D5—21no—
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C42×C5—21no—
53C3×C42×C5C2311yescharacteristic
54C3×#688—42no—
55C3×#685—22no—
56C3×#685—21no—
57C3×C4⋊Dic5D411yescharacteristic
58C2×C3×#168—21no—
59C3×D40—44no—
60C3×D40—42no—
61C3×#550—51no—
62C3×#493—51no—
63C3×#460—51no—
64C3×#459—51no—
65C3×#331—51no—
66C3×Q8⋊C8D511yescharacteristic, complemented
67C3×D4⋊C8—51no—
68C2×#713—21no—
69C4×C5×Q8C22×C311yescharacteristic
70C2×#688—21no—
71C2×D40—21no—
72C2×D40—22no—
73#4041—22no—
74#4041—21no—
75#4020—21no—
76#4020C22×C311yescharacteristic
77#4020C22×C311yescharacteristic
78C4×D20—21no—
79C4×D20C22×C311yescharacteristic
80C5×C4⋊C8C22×C311yescharacteristic
81C4×C5×C8C22×C311yescharacteristic
82#3953—21no—
83#3941—21no—
84C4⋊#168C22×C311yescharacteristic
85#1621—51noSylow
86C22×C3×D5—21no—
87C22×C3×D5—22no—
88C22×C3×D5—41no—
89C3×C5×Q8—21no—
90C3×C5×Q8D812yescomplemented
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×Dic5—21no—
97C3×D20—21no—
98C3×D20—21no—
99C3×D20—44no—
100C3×D20—42no—
101C3×D20—42no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×D20—41no—
106C3×D20—41no—
107C3×D20—41no—
108C3×D20—41no—
109C3×D20—41no—
110C3×D20—82no—
111C3×C4×D5—44no—
112C3×C4×D5—41no—
113C3×C4×D5—41no—
114C3×C5×C8—22no—
115C3×C5×C8—41no—
116C3×#168—41no—
117C2×C3×#41—101no—
118C2×C3×SD16—101no—
119C2×C3×D8—101no—
120C2×C3×D8—102no—
121C3×#127—51no—
122C3×#127—51no—
123C3×#127—101no—
124C3×#121—102no—
125C3×#121—101no—
126C3×C4×Q8C2×D511yescharacteristic
127C3×C4×D4—51no—
128C3×C4×D4—101no—
129C3×C4⋊C8—51no—
130C3×C4⋊C8C2×D511yescharacteristic
131C3×#102—101no—
132C3×#102—101no—
133C3×C4×C8C2×D511yescharacteristic
134C2×C5×Q8C3×D411yescharacteristic
135#713—42no—
136#713—42no—
137C2×D20—22no—
138C2×D20—21no—
139C2×D20—21no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20—22no—
144C2×D20C3×D411yescharacteristic
145C2×D20C3×D412yes—
146C2×C4×D5—22no—
147C2×C4×D5—21no—
148C2×C5×C8—21no—
149C2×C5×C8—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4C3×D411yescharacteristic
152C42×C5—21no—
153C42×C5C23×C311yescharacteristic
154#688—42no—
155#685—22no—
156#685—21no—
157C4⋊Dic5C3×D411yescharacteristic
158C2×#168—21no—
159D40—44no—
160D40—42no—
161#550—51no—
162#493—51no—
163#460—51no—
164#459—51no—
165#331—51no—
166Q8⋊C8C3×D511yescharacteristic, complemented
167D4⋊C8—51no—
168C22×C3×C5#12011yescharacteristic
169C2×C3×D5—42no—
170C2×C3×D5—41no—
171C2×C3×D5—41no—
172C2×C3×D5—42no—
173C2×C3×D5—42no—
174C2×C3×D5—41no—
175C2×C3×D5—81no—
176C2×C3×D5—81no—
177C2×C3×D5—81no—
178C3×C4×C5—22no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5C2×D811yescharacteristic
182C3×C4×C5#13511yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×Dic5—41no—
186C3×#41—202no—
187C3×#41—202no—
188C2×C3×Q8D2011yescharacteristic
189C2×C3×D4—51no—
190C2×C3×D4—52no—
191C2×C3×D4—102no—
192C2×C3×D4—102no—
193C2×C3×D4—101no—
194C2×C3×D4—101no—
195C2×C3×D4—101no—
196C2×C3×D4—101no—
197C2×C3×D4—101no—
198C22×C3×C4—102no—
199C22×C3×C4—101no—
200C3×SD16—202no—
201C3×D8—204no—
202C3×D8—202no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—101no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—51no—
208C3×C4⋊C4D2011yescharacteristic
209C3×C22⋊C4—102no—
210C3×C22⋊C4—101no—
211C3×C42—21no—
212C3×C42C22×D511yescharacteristic
213C22×D5—21no—
214C22×D5—22no—
215C22×D5—41no—
216C5×Q8—21no—
217C5×Q8C3×D812yescomplemented
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5C2×C3×D411yescharacteristic
221C2×C4×C5C2×C3×D411yescharacteristic
222C2×C4×C5C2×C3×D411yescharacteristic
223C2×Dic5—21no—
224D20—21no—
225D20—21no—
226D20—42no—
227D20—44no—
228D20—42no—
229D20—41no—
230D20—41no—
231D20—41no—
232D20—41no—
233D20—41no—
234D20—41no—
235D20—41no—
236D20—41no—
237D20—82no—
238C4×D5—44no—
239C4×D5—41no—
240C4×D5—41no—
241C5×C8—22no—
242C5×C8—41no—
243#168—41no—
244C2×#41—101no—
245C2×SD16—101no—
246C2×D8—101no—
247C2×D8—102no—
248#127—51no—
249#127—51no—
250#127—101no—
251#121—102no—
252#121—101no—
253C4×Q8C2×C3×D511yescharacteristic
254C4×D4—51no—
255C4×D4—101no—
256C4⋊C8—51no—
257C4⋊C8C2×C3×D511yescharacteristic
258#102—101no—
259#102—101no—
260C4×C8C2×C3×D511yescharacteristic
261C2×C3×C5#44711yescharacteristic
262C2×C3×C5#44911yescharacteristic
263C2×C3×C5#45311yescharacteristic
264C3×D5—81no—
265C3×D5—82no—
266C3×D5—161no—
267C23×C3—101no—
268C23×C3—102no—
269C23×C3—201no—
270C3×Q8—21no—
271C3×Q8D4012yescomplemented
272C3×D4—101no—
273C3×D4—101no—
274C3×D4—202no—
275C3×D4—204no—
276C3×D4—202no—
277C3×D4—201no—
278C3×D4—201no—
279C3×D4—201no—
280C3×D4—201no—
281C3×D4—201no—
282C3×D4—201no—
283C3×D4—201no—
284C3×D4—201no—
285C3×D4—402no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—101no—
289C2×C3×C4—204no—
290C2×C3×C4—201no—
291C2×C3×C4—201no—
292C2×C3×C4C2×D2011yescharacteristic
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C3×C8—22no—
296C3×C8—41no—
297C3×C8—201no—
298C22×C5C3×#12011yescharacteristic
299C2×D5—42no—
300C2×D5—41no—
301C2×D5—41no—
302C2×D5—42no—
303C2×D5—42no—
304C2×D5—41no—
305C2×D5—81no—
306C2×D5—81no—
307C2×D5—81no—
308C4×C5—22no—
309C4×C5—21no—
310C4×C5—41no—
311C4×C5C2×C3×D811yescharacteristic
312C4×C5C3×#13511yescharacteristic
313C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
314C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
315Dic5—41no—
316#41—202no—
317#41—202no—
318C2×Q8C3×D2011yescharacteristic
319C2×D4—51no—
320C2×D4—52no—
321C2×D4—102no—
322C2×D4—102no—
323C2×D4—101no—
324C2×D4—101no—
325C2×D4—101no—
326C2×D4—101no—
327C2×D4—101no—
328C22×C4—102no—
329C22×C4—101no—
330SD16—202no—
331D8—204no—
332D8—202no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—101no—
336C4⋊C4—21no—
337C4⋊C4—51no—
338C4⋊C4C3×D2011yescharacteristic
339C22⋊C4—102no—
340C22⋊C4—101no—
341C42—21no—
342C42C22×C3×D511yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—201no—
345C22×C3—202no—
346C22×C3—202no—
347C22×C3—201no—
348C22×C3—202no—
349C22×C3—201no—
350C22×C3—401no—
351C22×C3—401no—
352C22×C3—401no—
353C22×C3#402811yescharacteristic
354C3×C4—21no—
355C3×C4—22no—
356C3×C4—41no—
357C3×C4—201no—
358C3×C4C2×D4011yescharacteristic
359C3×C4#405411yescharacteristic
360C3×C4#406011yescharacteristic
361C3×C4#406511yescharacteristic
362C2×C5C3×#44711yescharacteristic
363C2×C5C3×#44911yescharacteristic
364C2×C5C3×#45311yescharacteristic
365D5—81no—
366D5—82no—
367D5—161no—
368C23—101no—
369C23—102no—
370C23—201no—
371Q8—21no—
372Q8C3×D4012yescomplemented
373D4—101no—
374D4—101no—
375D4—202no—
376D4—204no—
377D4—202no—
378D4—201no—
379D4—201no—
380D4—201no—
381D4—201no—
382D4—201no—
383D4—201no—
384D4—201no—
385D4—201no—
386D4—402no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—101no—
390C2×C4—204no—
391C2×C4—201no—
392C2×C4—201no—
393C2×C4C2×C3×D2011yescharacteristic
394C2×C4C3×D4×D511yescharacteristic
395C2×C4C3×D4×D511yescharacteristic
396C8—22no—
397C8—41no—
398C8—201no—
399C2×C3—401no—
400C2×C3—402no—
401C2×C3—801no—
402C2×C3#6502111yescharacteristic
403C2×C3#6510011yescharacteristic
404C2×C3#6511111yescharacteristic
405C5C3×#162111yescharacteristic, complemented, Sylow
406C22—201no—
407C22—202no—
408C22—202no—
409C22—201no—
410C22—202no—
411C22—201no—
412C22—401no—
413C22—401no—
414C22—401no—
415C22C3×#402811yescharacteristic
416C4—21no—
417C4—22no—
418C4—41no—
419C4—201no—
420C4C2×C3×D4011yescharacteristic
421C4C3×#405411yescharacteristic
422C4C3×#406011yescharacteristic
423C4C3×#406511yescharacteristic
424C3#1059905211yescharacteristic, direct product factor, Sylow
425C2—401no—
426C2—402no—
427C2—801no—
428C2C3×#6502111yescharacteristic
429C2C3×#6510011yescharacteristic
430C2C3×#6511111yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
hypercenterC3×Q8⋊C8D5
hypocenterC5C3×#1621
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×#65911C2semidirect
2. C3×#65316C2semidirect
3. C3×#65132C2semidirect
4. C3×#64984C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. C3×#64705C2semidirect
7. C3×#64679C2semidirect
8. #10599052C3direct (N × H)
27. #65911C2×C3semidirect
28. #65316C2×C3semidirect
29. #65132C2×C3semidirect
30. #64984C2×C3semidirect
31. C5×Q8⋊C8C2×C3semidirect
32. #64705C2×C3semidirect
33. #64679C2×C3semidirect
66. C3×Q8⋊C8D5semidirect
90. C3×C5×Q8D8semidirect
166. Q8⋊C8C3×D5semidirect
217. C5×Q8C3×D8semidirect
271. C3×Q8D40semidirect
343. C3×C5#1621semidirect
372. Q8C3×D40semidirect
405. C5C3×#1621semidirect
424. C3#10599052direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659112
C3×#653162
C3×#651322
C3×#649842
C3×C5×Q8⋊C82
C3×#647052
C3×#646792
#105990523
C3×#16215