Finite Group Databasebeta

← C3×#10598975 #14289890

Subgroups — C3×#10598975 #14289890

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×D20C211yesmaximal, characteristic
2C3×#65296C211yesmaximal, characteristic, complemented
3C3×#65130C211yesmaximal, characteristic, complemented
4C3×#64983C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64679C211yesmaximal, characteristic, complemented
8#10598975C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×D4×D5—21no—
10C22×C3×D20—21no—
11C3×C4×C5×D4C2211yescharacteristic
12C3×#4076—21no—
13C2×C3×#677—21no—
14C3×#4041—21no—
15C3×#4028—22no—
16C3×#4020C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18C3×#4015C2211yescharacteristic, complemented
19C3×C5×C4⋊C8C2211yescharacteristic, complemented
20C3×C4×C5×C8C2211yescharacteristic, complemented
21C3×#3964—21no—
22C3×#3953—22no—
23C3×#3948—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic, complemented
26C3×#1639—51nomaximal, Hall
27D4×D20C2×C311yescharacteristic
28#65296C2×C311yescharacteristic, complemented
29#65130C2×C311yescharacteristic, complemented
30#64983C2×C311yescharacteristic, complemented
31C5×D4⋊C8C2×C311yescharacteristic, complemented
32#64705C2×C311yescharacteristic, complemented
33#64679C2×C311yescharacteristic, complemented
34C23×C3×D5—22no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×C3×C22⋊D5—22no—
38C3×D4×D5—42no—
39C3×D4×D5—42no—
40C2×C3×D20—22no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20—42no—
44C2×C3×D20—42no—
45C2×C3×D20D411yescharacteristic
46C2×C3×D20D412yes—
47C2×C3×C4×D5—21no—
48C2×C3×Dic10—21no—
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C5×C22⋊C4—21no—
53C3×C42×C5C2311yescharacteristic
54C3×#685—22no—
55C3×#685—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C2×C3×#168—21no—
60C3×#677—42no—
61C3×D42—51no—
62C3×#486—51no—
63C3×#474—51no—
64C3×#461—51no—
65C3×#331—51no—
66C3×D4⋊C8—51no—
67C3×D4⋊C8D511yescharacteristic, complemented
68C2×D4×D5—21no—
69C22×D20—21no—
70C4×C5×D4C22×C311yescharacteristic
71#4076—21no—
72C2×#677—21no—
73#4041—21no—
74#4028—22no—
75#4020C22×C311yescharacteristic
76C4×D20C22×C311yescharacteristic
77#4015C22×C311yescharacteristic, complemented
78C5×C4⋊C8C22×C311yescharacteristic, complemented
79C4×C5×C8C22×C311yescharacteristic, complemented
80#3964—21no—
81#3953—22no—
82#3948—21no—
83#3939—21no—
84C4⋊#168C22×C311yescharacteristic, complemented
85#1639—51noSylow
86C23×C3×C5—21no—
87C22×C3×D5—21no—
88C22×C3×D5—22no—
89C22×C3×D5—44no—
90C22×C3×D5—44no—
91C22×C3×D5—82no—
92C3×C5×D4—21no—
93C3×C5×D4SD1612yescomplemented
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C3×C22⋊D5—44no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—41no—
103C3×D20—21no—
104C3×D20—42no—
105C3×D20—44no—
106C3×D20—41no—
107C3×D20—41no—
108C3×D20—41no—
109C3×D20—41no—
110C3×D20D812yes—
111C3×C4×D5—41no—
112C3×C4×D5—41no—
113C3×Dic10—41no—
114C3×Dic10—41no—
115C3×C5×C8—41no—
116C3×C5×C8—41no—
117C3×#168—41no—
118C22×C3×D4—101no—
119C22×C3×D4—101no—
120C2×C3×SD16—101no—
121C3×C4⋊Q8—51no—
122C3×#127—51no—
123C3×#121—101no—
124C3×#121—101no—
125C3×#120—102no—
126C3×C4×D4—51no—
127C3×C4×D4C2×D511yescharacteristic
128C3×#107—101no—
129C3×C4⋊C8—51no—
130C3×C4⋊C8C2×D511yescharacteristic, complemented
131C3×#103—101no—
132C3×#102—102no—
133C3×#102—101no—
134C3×C4×C8C2×D511yescharacteristic, complemented
135C23×D5—22no—
136C2×C5×D4C3×D411yescharacteristic
137C22×C4×C5—21no—
138C2×C22⋊D5—22no—
139D4×D5—42no—
140D4×D5—42no—
141C2×D20—22no—
142C2×D20—21no—
143C2×D20—21no—
144C2×D20—42no—
145C2×D20—42no—
146C2×D20C3×D411yescharacteristic
147C2×D20C3×D412yes—
148C2×C4×D5—21no—
149C2×Dic10—21no—
150C2×C5×C8—21no—
151C2×C5×C8—21no—
152C5×C4⋊C4C3×D411yescharacteristic
153C5×C22⋊C4—21no—
154C42×C5C23×C311yescharacteristic
155#685—22no—
156#685—21no—
157C4⋊Dic5—21no—
158C4⋊Dic5—21no—
159C4⋊Dic5C3×D411yescharacteristic
160C2×#168—21no—
161#677—42no—
162D42—51no—
163#486—51no—
164#474—51no—
165#461—51no—
166#331—51no—
167D4⋊C8—51no—
168D4⋊C8C3×D511yescharacteristic, complemented
169C22×C3×C5—22no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5#12011yescharacteristic
173C2×C3×D5—22no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—42no—
177C2×C3×D5—42no—
178C2×C3×D5—42no—
179C2×C3×D5—88no—
180C3×C4×C5—21no—
181C3×C4×C5—41no—
182C3×C4×C5C2×D811yescharacteristic
183C3×C4×C5C2×SD1611yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
186C3×Dic5—41no—
187C3×Dic5—81no—
188C24×C3—102no—
189C2×C3×Q8—101no—
190C2×C3×D4—51no—
191C2×C3×D4—52no—
192C2×C3×D4—102no—
193C2×C3×D4—102no—
194C2×C3×D4—101no—
195C2×C3×D4—101no—
196C2×C3×D4—202no—
197C2×C3×D4—202no—
198C2×C3×D4—202no—
199C2×C3×D4—202no—
200C2×C3×D4D2011yescharacteristic
201C22×C3×C4—21no—
202C22×C3×C4—101no—
203C3×SD16—202no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—101no—
207C3×C4⋊C4—51no—
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210C3×C4⋊C4D2011yescharacteristic
211C3×C22⋊C4—21no—
212C3×C22⋊C4—102no—
213C3×C22⋊C4—101no—
214C3×C42C22×D511yescharacteristic
215C23×C5—21no—
216C22×D5—21no—
217C22×D5—22no—
218C22×D5—44no—
219C22×D5—44no—
220C22×D5—82no—
221C5×D4—21no—
222C5×D4C3×SD1612yescomplemented
223C2×C4×C5—21no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5C2×C3×D411yescharacteristic
227C2×C4×C5C2×C3×D411yescharacteristic
228C2×C4×C5C2×C3×D411yescharacteristic
229C22⋊D5—44no—
230C2×Dic5—21no—
231C2×Dic5—41no—
232D20—21no—
233D20—42no—
234D20—44no—
235D20—41no—
236D20—41no—
237D20—41no—
238D20—41no—
239D20C3×D812yes—
240C4×D5—41no—
241C4×D5—41no—
242Dic10—41no—
243Dic10—41no—
244C5×C8—41no—
245C5×C8—41no—
246#168—41no—
247C22×D4—101no—
248C22×D4—101no—
249C2×SD16—101no—
250C4⋊Q8—51no—
251#127—51no—
252#121—101no—
253#121—101no—
254#120—102no—
255C4×D4—51no—
256C4×D4C2×C3×D511yescharacteristic
257#107—101no—
258C4⋊C8—51no—
259C4⋊C8C2×C3×D511yescharacteristic, complemented
260#103—101no—
261#102—102no—
262#102—101no—
263C4×C8C2×C3×D511yescharacteristic, complemented
264C2×C3×C5—42no—
265C2×C3×C5#44711yescharacteristic
266C2×C3×C5#45011yescharacteristic
267C2×C3×C5#45511yescharacteristic
268C3×D5—42no—
269C3×D5—82no—
270C23×C3—21no—
271C23×C3—101no—
272C23×C3—102no—
273C23×C3—204no—
274C23×C3—204no—
275C23×C3—402no—
276C3×Q8—201no—
277C3×Q8—201no—
278C3×D4—21no—
279C3×D4—52no—
280C3×D4—101no—
281C3×D4—202no—
282C3×D4—204no—
283C3×D4—204no—
284C3×D4—201no—
285C3×D4—201no—
286C3×D4—201no—
287C3×D4—201no—
288C3×D4#67712yescomplemented
289C2×C3×C4—21no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—101no—
293C2×C3×C4—201no—
294C2×C3×C4—201no—
295C2×C3×C4—201no—
296C2×C3×C4C2×D2011yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C3×C8—41no—
300C3×C8—41no—
301C3×C8—201no—
302C22×C5—22no—
303C22×C5—41no—
304C22×C5—41no—
305C22×C5C3×#12011yescharacteristic
306C2×D5—22no—
307C2×D5—41no—
308C2×D5—41no—
309C2×D5—42no—
310C2×D5—42no—
311C2×D5—42no—
312C2×D5—88no—
313C4×C5—21no—
314C4×C5—41no—
315C4×C5C2×C3×D811yescharacteristic
316C4×C5C2×C3×SD1611yescharacteristic
317C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
318C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
319Dic5—41no—
320Dic5—81no—
321C24—102no—
322C2×Q8—101no—
323C2×D4—51no—
324C2×D4—52no—
325C2×D4—102no—
326C2×D4—102no—
327C2×D4—101no—
328C2×D4—101no—
329C2×D4—202no—
330C2×D4—202no—
331C2×D4—202no—
332C2×D4—202no—
333C2×D4C3×D2011yescharacteristic
334C22×C4—21no—
335C22×C4—101no—
336SD16—202no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—101no—
340C4⋊C4—51no—
341C4⋊C4—101no—
342C4⋊C4—101no—
343C4⋊C4C3×D2011yescharacteristic
344C22⋊C4—21no—
345C22⋊C4—102no—
346C22⋊C4—101no—
347C42C22×C3×D511yescharacteristic
348C3×C5#163911yescharacteristic, complemented, Hall
349C22×C3—22no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—102no—
353C22×C3—201no—
354C22×C3—201no—
355C22×C3—202no—
356C22×C3—202no—
357C22×C3—202no—
358C22×C3—408no—
359C22×C3#402811yescharacteristic
360C3×C4—21no—
361C3×C4—41no—
362C3×C4—201no—
363C3×C4—401no—
364C3×C4C2×#67711yescharacteristic
365C3×C4#405411yescharacteristic
366C3×C4D5×D811yescharacteristic
367C3×C4#406011yescharacteristic
368C2×C5—42no—
369C2×C5C3×#44711yescharacteristic
370C2×C5C3×#45011yescharacteristic
371C2×C5C3×#45511yescharacteristic
372D5—42no—
373D5—82no—
374C23—21no—
375C23—101no—
376C23—102no—
377C23—204no—
378C23—204no—
379C23—402no—
380Q8—201no—
381Q8—201no—
382D4—21no—
383D4—52no—
384D4—101no—
385D4—202no—
386D4—204no—
387D4—204no—
388D4—201no—
389D4—201no—
390D4—201no—
391D4—201no—
392D4C3×#67712yescomplemented
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—101no—
397C2×C4—201no—
398C2×C4—201no—
399C2×C4—201no—
400C2×C4C2×C3×D2011yescharacteristic
401C2×C4C3×D4×D511yescharacteristic
402C2×C4C3×D4×D511yescharacteristic
403C8—41no—
404C8—41no—
405C8—201no—
406C2×C3—42no—
407C2×C3—202no—
408C2×C3—402no—
409C2×C3#6502011yescharacteristic
410C2×C3#6506211yescharacteristic
411C2×C3#6511411yescharacteristic
412C5C3×#163911yescharacteristic, complemented, Sylow
413C22—22no—
414C22—41no—
415C22—41no—
416C22—102no—
417C22—201no—
418C22—201no—
419C22—202no—
420C22—202no—
421C22—202no—
422C22—408no—
423C22C3×#402811yescharacteristic
424C4—21no—
425C4—41no—
426C4—201no—
427C4—401no—
428C4C2×C3×#67711yescharacteristic
429C4C3×#405411yescharacteristic
430C4C3×D5×D811yescharacteristic
431C4C3×#406011yescharacteristic
432C3#1059897511yescharacteristic, direct product factor, Sylow
433C2—42no—
434C2—202no—
435C2—402no—
436C2C3×#6502011yescharacteristic
437C2C3×#6506211yescharacteristic
438C2C3×#6511411yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC3×D4×D20C2
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1639
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
2. C3×#65296C2semidirect
3. C3×#65130C2semidirect
4. C3×#64983C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C3×#64705C2semidirect
7. C3×#64679C2semidirect
8. #10598975C3direct (N × H)
18. C3×#4015C22semidirect
19. C3×C5×C4⋊C8C22semidirect
20. C3×C4×C5×C8C22semidirect
25. C3×C4⋊#168C22semidirect
28. #65296C2×C3semidirect
29. #65130C2×C3semidirect
30. #64983C2×C3semidirect
31. C5×D4⋊C8C2×C3semidirect
32. #64705C2×C3semidirect
33. #64679C2×C3semidirect
67. C3×D4⋊C8D5semidirect
77. #4015C22×C3semidirect
78. C5×C4⋊C8C22×C3semidirect
79. C4×C5×C8C22×C3semidirect
84. C4⋊#168C22×C3semidirect
93. C3×C5×D4SD16semidirect
130. C3×C4⋊C8C2×D5semidirect
134. C3×C4×C8C2×D5semidirect
168. D4⋊C8C3×D5semidirect
222. C5×D4C3×SD16semidirect
259. C4⋊C8C2×C3×D5semidirect
263. C4×C8C2×C3×D5semidirect
288. C3×D4#677semidirect
348. C3×C5#1639semidirect
392. D4C3×#677semidirect
412. C5C3×#1639semidirect
432. C3#10598975direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D4×D202
C3×#652962
C3×#651302
C3×#649832
C3×C5×D4⋊C82
C3×#647052
C3×#646792
#105989753
C3×#16395