Finite Group Databasebeta

← C3×#10601953 #14289419

Subgroups — C3×#10601953 #14289419

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65911C211yesmaximal, characteristic
2C3×C5×#477C211yesmaximal, characteristic, complemented
3C3×#65374C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64703C211yesmaximal, characteristic, complemented
8#10601953C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#713—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×Q8C2211yescharacteristic
12C2×C3×#688—22no—
13C3×#4041—22no—
14C3×#4041—21no—
15C3×#4020—21no—
16C3×#4020C2211yescharacteristic
17C3×C4×D20—21no—
18C3×C4×D20C2211yescharacteristic
19C3×C5×#107—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#103—21no—
22C3×#3941—21no—
23C3×#3940—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1631—51nomaximal, Hall
27#65911C2×C311yescharacteristic
28C5×#477C2×C311yescharacteristic, complemented
29#65374C2×C311yescharacteristic, complemented
30#65373C2×C311yescharacteristic, complemented
31Q8⋊#168C2×C311yescharacteristic, complemented
32#64705C2×C311yescharacteristic, complemented
33#64703C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C3×#713—42no—
37C3×#713—42no—
38C2×C3×D20—22no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—22no—
42C2×C3×D20D411yescharacteristic
43C2×C3×D20D412yes—
44C2×C3×C4×D5—22no—
45C2×C3×C4×D5—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4D411yescharacteristic
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53C3×#688—44no—
54C3×#685—22no—
55C3×#685—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C3×#550—51no—
60C3×#492—51no—
61C3×#477D511yescharacteristic, complemented
62C3×#476—51no—
63C3×#331—51no—
64C3×Q8⋊C8—51no—
65C3×D4⋊C8—51no—
66C2×#713—21no—
67C5×C4⋊Q8C22×C311yescharacteristic
68C4×C5×Q8C22×C311yescharacteristic
69C2×#688—22no—
70#4041—22no—
71#4041—21no—
72#4020—21no—
73#4020C22×C311yescharacteristic
74C4×D20—21no—
75C4×D20C22×C311yescharacteristic
76C5×#107—21no—
77C5×C4⋊C8C22×C311yescharacteristic
78C5×#103—21no—
79#3941—21no—
80#3940—21no—
81C4⋊#168C22×C311yescharacteristic
82C4×#168C22×C311yescharacteristic
83#1631—51noSylow
84C22×C3×D5—21no—
85C22×C3×D5—22no—
86C3×C5×Q8—21no—
87C3×C5×Q8—42no—
88C3×C5×Q8SD1612yescomplemented
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×Dic5—21no—
96C3×D20—21no—
97C3×D20—21no—
98C3×D20—44no—
99C3×D20—42no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—82no—
105C3×C4×D5—44no—
106C3×C4×D5—41no—
107C3×C4×D5—41no—
108C3×C5×C8—41no—
109C3×#168—22no—
110C3×#168—41no—
111C2×C3×#41—101no—
112C2×C3×SD16—102no—
113C3×C4⋊Q8C2×D511yescharacteristic
114C3×#127—51no—
115C3×#127—101no—
116C3×#121—102no—
117C3×#121—101no—
118C3×C4×Q8C2×D511yescharacteristic
119C3×C4×D4—51no—
120C3×C4×D4—101no—
121C3×#107—21no—
122C3×#106—101no—
123C3×C4⋊C8—51no—
124C3×C4⋊C8C2×D511yescharacteristic
125C3×#103—21no—
126C3×#102—101no—
127C3×C4×C8—51no—
128C2×C5×Q8—21no—
129C2×C5×Q8C3×D411yescharacteristic
130#713—42no—
131#713—42no—
132C2×D20—22no—
133C2×D20—21no—
134C2×D20—21no—
135C2×D20—22no—
136C2×D20C3×D411yescharacteristic
137C2×D20C3×D412yes—
138C2×C4×D5—22no—
139C2×C4×D5—21no—
140C2×C5×C8—21no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4C3×D411yescharacteristic
145C42×C5—21no—
146C42×C5C23×C311yescharacteristic
147#688—44no—
148#685—22no—
149#685—21no—
150C4⋊Dic5C3×D411yescharacteristic
151C2×#168—21no—
152C2×#168—21no—
153#550—51no—
154#492—51no—
155#477C3×D511yescharacteristic, complemented
156#476—51no—
157#331—51no—
158Q8⋊C8—51no—
159D4⋊C8—51no—
160C22×C3×C5#12011yescharacteristic
161C2×C3×D5—42no—
162C2×C3×D5—41no—
163C2×C3×D5—41no—
164C2×C3×D5—42no—
165C2×C3×D5—42no—
166C2×C3×D5—41no—
167C3×C4×C5—22no—
168C3×C4×C5—21no—
169C3×C4×C5—41no—
170C3×C4×C5—81no—
171C3×C4×C5C2×SD1611yescharacteristic
172C3×C4×C5#13511yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C3×C4×C5#13711yescharacteristic
175C3×Dic5—41no—
176C3×#41—202no—
177C3×#41—202no—
178C2×C3×Q8—21no—
179C2×C3×Q8C22⋊D511yescharacteristic
180C2×C3×D4—51no—
181C2×C3×D4—52no—
182C2×C3×D4—102no—
183C2×C3×D4—102no—
184C2×C3×D4—101no—
185C2×C3×D4—101no—
186C22×C3×C4—102no—
187C22×C3×C4—101no—
188C3×SD16—204no—
189C2×C3×C8—21no—
190C2×C3×C8—101no—
191C2×C3×C8—101no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—51no—
196C3×C4⋊C4C22⋊D511yescharacteristic
197C3×C22⋊C4—102no—
198C3×C22⋊C4—101no—
199C3×C42—21no—
200C3×C42C22×D511yescharacteristic
201C22×D5—21no—
202C22×D5—22no—
203C5×Q8—21no—
204C5×Q8—42no—
205C5×Q8C3×SD1612yescomplemented
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—41no—
209C2×C4×C5C2×C3×D411yescharacteristic
210C2×C4×C5C2×C3×D411yescharacteristic
211C2×C4×C5C2×C3×D411yescharacteristic
212C2×Dic5—21no—
213D20—21no—
214D20—21no—
215D20—42no—
216D20—44no—
217D20—41no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—82no—
222C4×D5—44no—
223C4×D5—41no—
224C4×D5—41no—
225C5×C8—41no—
226#168—22no—
227#168—41no—
228C2×#41—101no—
229C2×SD16—102no—
230C4⋊Q8C2×C3×D511yescharacteristic
231#127—51no—
232#127—101no—
233#121—102no—
234#121—101no—
235C4×Q8C2×C3×D511yescharacteristic
236C4×D4—51no—
237C4×D4—101no—
238#107—21no—
239#106—101no—
240C4⋊C8—51no—
241C4⋊C8C2×C3×D511yescharacteristic
242#103—21no—
243#102—101no—
244C4×C8—51no—
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45211yescharacteristic
247C2×C3×C5#45311yescharacteristic
248C3×D5—81no—
249C3×D5—82no—
250C23×C3—101no—
251C23×C3—102no—
252C3×Q8—21no—
253C3×Q8—42no—
254C3×Q8#68812yescomplemented
255C3×D4—101no—
256C3×D4—101no—
257C3×D4—202no—
258C3×D4—204no—
259C3×D4—201no—
260C3×D4—201no—
261C3×D4—201no—
262C3×D4—201no—
263C3×D4—402no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—41no—
267C2×C3×C4—101no—
268C2×C3×C4—204no—
269C2×C3×C4—201no—
270C2×C3×C4—201no—
271C2×C3×C4D4×D511yescharacteristic
272C2×C3×C4D4×D511yescharacteristic
273C2×C3×C4C2×C22⋊D511yescharacteristic
274C3×C8—41no—
275C3×C8—102no—
276C3×C8—201no—
277C22×C5C3×#12011yescharacteristic
278C2×D5—42no—
279C2×D5—41no—
280C2×D5—41no—
281C2×D5—42no—
282C2×D5—42no—
283C2×D5—41no—
284C4×C5—22no—
285C4×C5—21no—
286C4×C5—41no—
287C4×C5—81no—
288C4×C5C2×C3×SD1611yescharacteristic
289C4×C5C3×#13511yescharacteristic
290C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
291C4×C5C3×#13711yescharacteristic
292Dic5—41no—
293#41—202no—
294#41—202no—
295C2×Q8—21no—
296C2×Q8C3×C22⋊D511yescharacteristic
297C2×D4—51no—
298C2×D4—52no—
299C2×D4—102no—
300C2×D4—102no—
301C2×D4—101no—
302C2×D4—101no—
303C22×C4—102no—
304C22×C4—101no—
305SD16—204no—
306C2×C8—21no—
307C2×C8—101no—
308C2×C8—101no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—51no—
313C4⋊C4C3×C22⋊D511yescharacteristic
314C22⋊C4—102no—
315C22⋊C4—101no—
316C42—21no—
317C42C22×C3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—202no—
320C22×C3—201no—
321C22×C3—201no—
322C22×C3—202no—
323C22×C3—202no—
324C22×C3—201no—
325C22×C3#408311yescharacteristic
326C3×C4—22no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—81no—
330C3×C4—201no—
331C3×C4#406411yescharacteristic
332C3×C4#406511yescharacteristic
333C3×C4C2×#68811yescharacteristic
334C3×C4#409511yescharacteristic
335C2×C5C3×#45011yescharacteristic
336C2×C5C3×#45211yescharacteristic
337C2×C5C3×#45311yescharacteristic
338D5—81no—
339D5—82no—
340C23—101no—
341C23—102no—
342Q8—21no—
343Q8—42no—
344Q8C3×#68812yescomplemented
345D4—101no—
346D4—101no—
347D4—202no—
348D4—204no—
349D4—201no—
350D4—201no—
351D4—201no—
352D4—201no—
353D4—402no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—101no—
358C2×C4—204no—
359C2×C4—201no—
360C2×C4—201no—
361C2×C4C3×D4×D511yescharacteristic
362C2×C4C3×D4×D511yescharacteristic
363C2×C4C2×C3×C22⋊D511yescharacteristic
364C8—41no—
365C8—102no—
366C8—201no—
367C2×C3—401no—
368C2×C3—402no—
369C2×C3#6533511yescharacteristic
370C2×C3#6547611yescharacteristic
371C2×C3#6548711yescharacteristic
372C5C3×#163111yescharacteristic, complemented, Sylow
373C22—202no—
374C22—201no—
375C22—201no—
376C22—202no—
377C22—202no—
378C22—201no—
379C22C3×#408311yescharacteristic
380C4—22no—
381C4—21no—
382C4—41no—
383C4—81no—
384C4—201no—
385C4C3×#406411yescharacteristic
386C4C3×#406511yescharacteristic
387C4C2×C3×#68811yescharacteristic
388C4C3×#409511yescharacteristic
389C3#1060195311yescharacteristic, direct product factor, Sylow
390C2—401no—
391C2—402no—
392C2C3×#6533511yescharacteristic
393C2C3×#6547611yescharacteristic
394C2C3×#6548711yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#477C2
socleC22×C3×C5#120
prime radicalC3×#65911C2
hypercenterC3×#477D5
hypocenterC5C3×#1631
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
2. C3×C5×#477C2semidirect
3. C3×#65374C2semidirect
4. C3×#65373C2semidirect
5. C3×Q8⋊#168C2semidirect
6. C3×#64705C2semidirect
7. C3×#64703C2semidirect
8. #10601953C3direct (N × H)
28. C5×#477C2×C3semidirect
29. #65374C2×C3semidirect
30. #65373C2×C3semidirect
31. Q8⋊#168C2×C3semidirect
32. #64705C2×C3semidirect
33. #64703C2×C3semidirect
61. C3×#477D5semidirect
88. C3×C5×Q8SD16semidirect
155. #477C3×D5semidirect
205. C5×Q8C3×SD16semidirect
254. C3×Q8#688semidirect
318. C3×C5#1631semidirect
344. Q8C3×#688semidirect
372. C5C3×#1631semidirect
389. C3#10601953direct (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×C5×#4772
C3×#653742
C3×#653732
C3×Q8⋊#1682
C3×#647052
C3×#647032
#106019533
C3×#16315