Finite Group Databasebeta

← C3×#10601936 #14289341

Subgroups — C3×#10601936 #14289341

Order 1920.

628 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×D20C211yesmaximal, characteristic
2C3×C5×#476C211yesmaximal, characteristic, complemented
3C3×#65374C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64703C211yesmaximal, characteristic, complemented
8#10601936C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×D4×D5—21no—
10C22×C3×D20—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic, complemented
12C3×C4×C5×D4C2211yescharacteristic
13C2×C3×#688—22no—
14C3×#4076—21no—
15C3×#4041—21no—
16C3×#4028—22no—
17C3×#4020C2211yescharacteristic
18C3×C4×D20C2211yescharacteristic
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic, complemented
21C3×C5×#102—21no—
22C3×#3941—21no—
23C3×#3940—21no—
24C3×C4⋊#168C2211yescharacteristic, complemented
25C3×C4×#168C2211yescharacteristic, complemented
26C3×#1629—51nomaximal, Hall
27D4×D20C2×C311yescharacteristic
28C5×#476C2×C311yescharacteristic, complemented
29#65374C2×C311yescharacteristic, complemented
30#65373C2×C311yescharacteristic, complemented
31D4⋊#168C2×C311yescharacteristic, complemented
32#64705C2×C311yescharacteristic, complemented
33#64703C2×C311yescharacteristic, complemented
34C23×C3×D5—22no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×C3×C22⋊D5—22no—
39C3×D4×D5—42no—
40C3×D4×D5—42no—
41C2×C3×D20—22no—
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20—42no—
45C2×C3×D20—42no—
46C2×C3×D20D411yescharacteristic
47C2×C3×D20D412yes—
48C2×C3×C4×D5—21no—
49C2×C3×C5×C8—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C3×C42×C5C2311yescharacteristic
55C3×#688—44no—
56C3×#685—22no—
57C3×#685—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61C3×D42—51no—
62C3×#492—51no—
63C3×#476—51no—
64C3×#476D511yescharacteristic, complemented
65C3×#331—51no—
66C3×D4⋊C8—51no—
67C3×D4⋊C8—51no—
68C2×D4×D5—21no—
69C22×D20—21no—
70C5×C4⋊Q8C22×C311yescharacteristic, complemented
71C4×C5×D4C22×C311yescharacteristic
72C2×#688—22no—
73#4076—21no—
74#4041—21no—
75#4028—22no—
76#4020C22×C311yescharacteristic
77C4×D20C22×C311yescharacteristic
78C5×#106—21no—
79C5×C4⋊C8C22×C311yescharacteristic, complemented
80C5×#102—21no—
81#3941—21no—
82#3940—21no—
83C4⋊#168C22×C311yescharacteristic, complemented
84C4×#168C22×C311yescharacteristic, complemented
85#1629—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×Q8—42no—
93C3×C5×D4—21no—
94C3×C5×D4SD1612yescomplemented
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C3×C22⋊D5—44no—
103C2×C3×Dic5—21no—
104C3×D20—21no—
105C3×D20—42no—
106C3×D20—44no—
107C3×D20—41no—
108C3×D20—41no—
109C3×D20—41no—
110C3×D20—41no—
111C3×D20SD1612yescomplemented
112C3×C4×D5—41no—
113C3×C4×D5—41no—
114C3×C5×C8—41no—
115C3×#168—22no—
116C3×#168—41no—
117C22×C3×D4—101no—
118C22×C3×D4—101no—
119C2×C3×SD16—102no—
120C3×C4⋊Q8C2×D511yescharacteristic, complemented
121C3×#127—51no—
122C3×#121—101no—
123C3×#121—101no—
124C3×#120—102no—
125C3×C4×D4—51no—
126C3×C4×D4C2×D511yescharacteristic
127C3×#106—21no—
128C3×#106—101no—
129C3×C4⋊C8—51no—
130C3×C4⋊C8C2×D511yescharacteristic, complemented
131C3×#102—21no—
132C3×#102—101no—
133C3×C4×C8—51no—
134C23×D5—22no—
135C2×C5×Q8—21no—
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×C5×C8—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4C3×D411yescharacteristic
153C5×C22⋊C4—21no—
154C42×C5C23×C311yescharacteristic
155#688—44no—
156#685—22no—
157#685—21no—
158C4⋊Dic5C3×D411yescharacteristic
159C2×#168—21no—
160C2×#168—21no—
161D42—51no—
162#492—51no—
163#476—51no—
164#476C3×D511yescharacteristic, complemented
165#331—51no—
166D4⋊C8—51no—
167D4⋊C8—51no—
168C22×C3×C5—22no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5#12011yescharacteristic
172C2×C3×D5—22no—
173C2×C3×D5—41no—
174C2×C3×D5—41no—
175C2×C3×D5—42no—
176C2×C3×D5—42no—
177C2×C3×D5—42no—
178C2×C3×D5—88no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—81no—
182C3×C4×C5C2×SD1611yescharacteristic
183C3×C4×C5C2×SD1611yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
186C3×Dic5—41no—
187C24×C3—102no—
188C2×C3×Q8—21no—
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—202no—
196C2×C3×D4—202no—
197C2×C3×D4—202no—
198C2×C3×D4—202no—
199C2×C3×D4C22⋊D511yescharacteristic
200C22×C3×C4—21no—
201C22×C3×C4—101no—
202C3×SD16—204no—
203C2×C3×C8—21no—
204C2×C3×C8—101no—
205C2×C3×C8—101no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—51no—
209C3×C4⋊C4C22⋊D511yescharacteristic
210C3×C22⋊C4—21no—
211C3×C22⋊C4—102no—
212C3×C22⋊C4—101no—
213C3×C42C22×D511yescharacteristic
214C23×C5—21no—
215C22×D5—21no—
216C22×D5—22no—
217C22×D5—44no—
218C22×D5—44no—
219C22×D5—82no—
220C5×Q8—42no—
221C5×D4—21no—
222C5×D4C3×SD1612yescomplemented
223C2×C4×C5—21no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5C2×C3×D411yescharacteristic
228C2×C4×C5C2×C3×D411yescharacteristic
229C2×C4×C5C2×C3×D411yescharacteristic
230C22⋊D5—44no—
231C2×Dic5—21no—
232D20—21no—
233D20—42no—
234D20—44no—
235D20—41no—
236D20—41no—
237D20—41no—
238D20—41no—
239D20C3×SD1612yescomplemented
240C4×D5—41no—
241C4×D5—41no—
242C5×C8—41no—
243#168—22no—
244#168—41no—
245C22×D4—101no—
246C22×D4—101no—
247C2×SD16—102no—
248C4⋊Q8C2×C3×D511yescharacteristic, complemented
249#127—51no—
250#121—101no—
251#121—101no—
252#120—102no—
253C4×D4—51no—
254C4×D4C2×C3×D511yescharacteristic
255#106—21no—
256#106—101no—
257C4⋊C8—51no—
258C4⋊C8C2×C3×D511yescharacteristic, complemented
259#102—21no—
260#102—101no—
261C4×C8—51no—
262C2×C3×C5—42no—
263C2×C3×C5#45011yescharacteristic
264C2×C3×C5#45011yescharacteristic
265C2×C3×C5#45311yescharacteristic
266C3×D5—42no—
267C3×D5—82no—
268C23×C3—21no—
269C23×C3—101no—
270C23×C3—102no—
271C23×C3—204no—
272C23×C3—204no—
273C23×C3—402no—
274C3×Q8—42no—
275C3×D4—21no—
276C3×D4—52no—
277C3×D4—101no—
278C3×D4—202no—
279C3×D4—204no—
280C3×D4—204no—
281C3×D4—201no—
282C3×D4—201no—
283C3×D4—201no—
284C3×D4—201no—
285C3×D4#68812yescomplemented
286C2×C3×C4—21no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—101no—
291C2×C3×C4—201no—
292C2×C3×C4—201no—
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C2×C3×C4C2×C22⋊D511yescharacteristic
296C3×C8—41no—
297C3×C8—102no—
298C3×C8—201no—
299C22×C5—22no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5C3×#12011yescharacteristic
303C2×D5—22no—
304C2×D5—41no—
305C2×D5—41no—
306C2×D5—42no—
307C2×D5—42no—
308C2×D5—42no—
309C2×D5—88no—
310C4×C5—21no—
311C4×C5—41no—
312C4×C5—81no—
313C4×C5C2×C3×SD1611yescharacteristic
314C4×C5C2×C3×SD1611yescharacteristic
315C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
316C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
317Dic5—41no—
318C24—102no—
319C2×Q8—21no—
320C2×D4—51no—
321C2×D4—52no—
322C2×D4—102no—
323C2×D4—102no—
324C2×D4—101no—
325C2×D4—101no—
326C2×D4—202no—
327C2×D4—202no—
328C2×D4—202no—
329C2×D4—202no—
330C2×D4C3×C22⋊D511yescharacteristic
331C22×C4—21no—
332C22×C4—101no—
333SD16—204no—
334C2×C8—21no—
335C2×C8—101no—
336C2×C8—101no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—51no—
340C4⋊C4C3×C22⋊D511yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—102no—
343C22⋊C4—101no—
344C42C22×C3×D511yescharacteristic
345C3×C5#162911yescharacteristic, complemented, Hall
346C22×C3—22no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—102no—
350C22×C3—201no—
351C22×C3—201no—
352C22×C3—202no—
353C22×C3—202no—
354C22×C3—202no—
355C22×C3—408no—
356C22×C3#408311yescharacteristic
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—81no—
360C3×C4—201no—
361C3×C4D5×SD1611yescharacteristic
362C3×C4#406011yescharacteristic
363C3×C4C2×#68811yescharacteristic
364C3×C4#409511yescharacteristic
365C2×C5—42no—
366C2×C5C3×#45011yescharacteristic
367C2×C5C3×#45011yescharacteristic
368C2×C5C3×#45311yescharacteristic
369D5—42no—
370D5—82no—
371C23—21no—
372C23—101no—
373C23—102no—
374C23—204no—
375C23—204no—
376C23—402no—
377Q8—42no—
378D4—21no—
379D4—52no—
380D4—101no—
381D4—202no—
382D4—204no—
383D4—204no—
384D4—201no—
385D4—201no—
386D4—201no—
387D4—201no—
388D4C3×#68812yescomplemented
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—101no—
394C2×C4—201no—
395C2×C4—201no—
396C2×C4C3×D4×D511yescharacteristic
397C2×C4C3×D4×D511yescharacteristic
398C2×C4C2×C3×C22⋊D511yescharacteristic
399C8—41no—
400C8—102no—
401C8—201no—
402C2×C3—42no—
403C2×C3—202no—
404C2×C3—402no—
405C2×C3#6533511yescharacteristic
406C2×C3#6545811yescharacteristic
407C2×C3#6548711yescharacteristic
408C5C3×#162911yescharacteristic, complemented, Sylow
409C22—22no—
410C22—41no—
411C22—41no—
412C22—102no—
413C22—201no—
414C22—201no—
415C22—202no—
416C22—202no—
417C22—202no—
418C22—408no—
419C22C3×#408311yescharacteristic
420C4—21no—
421C4—41no—
422C4—81no—
423C4—201no—
424C4C3×D5×SD1611yescharacteristic
425C4C3×#406011yescharacteristic
426C4C2×C3×#68811yescharacteristic
427C4C3×#409511yescharacteristic
428C3#1060193611yescharacteristic, direct product factor, Sylow
429C2—42no—
430C2—202no—
431C2—402no—
432C2C3×#6533511yescharacteristic
433C2C3×#6545811yescharacteristic
434C2C3×#6548711yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#476C2
socleC22×C3×C5#120
prime radicalC3×D4×D20C2
hypercenterC3×#476D5
hypocenterC5C3×#1629
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
2. C3×C5×#476C2semidirect
3. C3×#65374C2semidirect
4. C3×#65373C2semidirect
5. C3×D4⋊#168C2semidirect
6. C3×#64705C2semidirect
7. C3×#64703C2semidirect
8. #10601936C3direct (N × H)
11. C3×C5×C4⋊Q8C22semidirect
20. C3×C5×C4⋊C8C22semidirect
24. C3×C4⋊#168C22semidirect
25. C3×C4×#168C22semidirect
28. C5×#476C2×C3semidirect
29. #65374C2×C3semidirect
30. #65373C2×C3semidirect
31. D4⋊#168C2×C3semidirect
32. #64705C2×C3semidirect
33. #64703C2×C3semidirect
64. C3×#476D5semidirect
70. C5×C4⋊Q8C22×C3semidirect
79. C5×C4⋊C8C22×C3semidirect
83. C4⋊#168C22×C3semidirect
84. C4×#168C22×C3semidirect
94. C3×C5×D4SD16semidirect
111. C3×D20SD16semidirect
120. C3×C4⋊Q8C2×D5semidirect
130. C3×C4⋊C8C2×D5semidirect
164. #476C3×D5semidirect
222. C5×D4C3×SD16semidirect
239. D20C3×SD16semidirect
248. C4⋊Q8C2×C3×D5semidirect
258. C4⋊C8C2×C3×D5semidirect
285. C3×D4#688semidirect
345. C3×C5#1629semidirect
388. D4C3×#688semidirect
408. C5C3×#1629semidirect
428. C3#10601936direct (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×C5×#4762
C3×#653742
C3×#653732
C3×D4⋊#1682
C3×#647052
C3×#647032
#106019363
C3×#16295