Finite Group Databasebeta

← C3×#10599206 #14292517

Subgroups — C3×#10599206 #14292517

Order 1920.

368 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65364C211yesmaximal, characteristic, complemented
2C3×#65362C211yesmaximal, characteristic
3C3×#65137C211yesmaximal, characteristic, complemented
4C3×#65120C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64700C211yesmaximal, characteristic, complemented
8#10599206C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#127C2211yescharacteristic
10C2×C3×#687—21no—
11C2×C3×#686—21no—
12C2×C3×#686—21no—
13C2×C3×#677—21no—
14C3×#4020C2211yescharacteristic
15C3×C4×Dic10C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×C4⋊C8C2211yescharacteristic
18C3×#3964—21no—
19C3×#3953—21no—
20C3×#3947—21no—
21C3×#3946—21no—
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24C3×#1688—51nomaximal, Hall
25#65364C2×C311yescharacteristic, complemented
26#65362C2×C311yescharacteristic
27#65137C2×C311yescharacteristic, complemented
28#65120C2×C311yescharacteristic, complemented
29C5×#331C2×C311yescharacteristic, complemented
30#64705C2×C311yescharacteristic, complemented
31#64700C2×C311yescharacteristic, complemented
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C3×#687—42no—
43C3×#686—42no—
44C3×#686—42no—
45C3×C4⋊Dic5D411yescharacteristic
46C3×#683—21no—
47C3×C4×Dic5—21no—
48C2×C3×#168—21no—
49C2×C3×#168D411yescharacteristic
50C2×C3×#168D411yescharacteristic
51C3×#677—42no—
52C3×#493—51no—
53C3×#460—51no—
54C3×#460—51no—
55C3×#446—51no—
56C3×#334—51no—
57C3×#331—51no—
58C3×#331D511yescharacteristic, complemented
59C5×#127C22×C311yescharacteristic
60C2×#687—21no—
61C2×#686—21no—
62C2×#686—21no—
63C2×#677—21no—
64#4020C22×C311yescharacteristic
65C4×Dic10C22×C311yescharacteristic
66C5×C4⋊C8C22×C311yescharacteristic
67C5×C4⋊C8C22×C311yescharacteristic
68#3964—21no—
69#3953—21no—
70#3947—21no—
71#3946—21no—
72C4⋊#168C22×C311yescharacteristic
73C4×#168C22×C311yescharacteristic
74#1688—51noSylow
75C23×C3×C5—41no—
76C22×C3×D5—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—81no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×C3×Dic5—21no—
86C2×C3×Dic5—21no—
87C3×D20—41no—
88C3×D20—41no—
89C3×D20—41no—
90C3×D20—41no—
91C3×D20—81no—
92C3×Dic10—21no—
93C3×Dic10—21no—
94C3×C5×C8—41no—
95C3×C5×C8—41no—
96C3×#168—21no—
97C3×#168—41no—
98C3×#168SD1612yescomplemented
99C2×C3×SD16—101no—
100C2×C3×SD16—101no—
101C2×C3×D8—101no—
102C2×C3×D8—101no—
103C3×#127—51no—
104C3×#127C2×D511yescharacteristic
105C3×C4×Q8—51no—
106C3×C4⋊C8—51no—
107C3×C4⋊C8—101no—
108C3×C4⋊C8C2×D511yescharacteristic
109C3×C4⋊C8C2×D511yescharacteristic
110C3×#102—101no—
111C3×#102—101no—
112C3×#97—101no—
113C3×C4×C8—51no—
114C2×C5×D4—21no—
115C2×C5×D4—21no—
116C2×C5×D4—21no—
117C2×D20—21no—
118C2×D20—21no—
119C2×D20—21no—
120C2×Dic10C3×D411yescharacteristic
121C2×C5×C8—21no—
122C2×C5×C8—21no—
123C42×C5C23×C311yescharacteristic
124#687—42no—
125#686—42no—
126#686—42no—
127C4⋊Dic5C3×D411yescharacteristic
128#683—21no—
129C4×Dic5—21no—
130C2×#168—21no—
131C2×#168C3×D411yescharacteristic
132C2×#168C3×D411yescharacteristic
133#677—42no—
134#493—51no—
135#460—51no—
136#460—51no—
137#446—51no—
138#334—51no—
139#331—51no—
140#331C3×D511yescharacteristic, complemented
141C22×C3×C5—81no—
142C22×C3×C5—81no—
143C22×C3×C5—81no—
144C22×C3×C5#12111yescharacteristic
145C2×C3×D5—81no—
146C2×C3×D5—81no—
147C2×C3×D5—81no—
148C3×C4×C5—21no—
149C3×C4×C5C2×SD1611yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
152C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
153C3×Dic5—41no—
154C3×Dic5—41no—
155C2×C3×Q8—51no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—101no—
160C2×C3×D4—101no—
161C2×C3×D4—101no—
162C3×SD16—202no—
163C3×SD16—202no—
164C3×D8—202no—
165C3×D8—202no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—51no—
169C2×C3×C8—51no—
170C2×C3×C8—101no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—101no—
173C3×C42—101no—
174C3×C42C22×D511yescharacteristic
175C23×C5—41no—
176C22×D5—41no—
177C5×D4—41no—
178C5×D4—41no—
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—81no—
182C2×C4×C5C2×C3×D411yescharacteristic
183C2×C4×C5C2×C3×D411yescharacteristic
184C2×C4×C5C3×#4111yescharacteristic
185C2×Dic5—21no—
186C2×Dic5—21no—
187D20—41no—
188D20—41no—
189D20—41no—
190D20—41no—
191D20—81no—
192Dic10—21no—
193Dic10—21no—
194C5×C8—41no—
195C5×C8—41no—
196#168—21no—
197#168—41no—
198#168C3×SD1612yescomplemented
199C2×SD16—101no—
200C2×SD16—101no—
201C2×D8—101no—
202C2×D8—101no—
203#127—51no—
204#127C2×C3×D511yescharacteristic
205C4×Q8—51no—
206C4⋊C8—51no—
207C4⋊C8—101no—
208C4⋊C8C2×C3×D511yescharacteristic
209C4⋊C8C2×C3×D511yescharacteristic
210#102—101no—
211#102—101no—
212#97—101no—
213C4×C8—51no—
214C2×C3×C5—161no—
215C2×C3×C5#46011yescharacteristic
216C2×C3×C5#46911yescharacteristic
217C2×C3×C5#47211yescharacteristic
218C3×D5—161no—
219C23×C3—41no—
220C23×C3—201no—
221C3×Q8—101no—
222C3×Q8—101no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—41no—
226C3×D4—41no—
227C3×D4—81no—
228C3×D4—201no—
229C3×D4—201no—
230C3×D4—201no—
231C3×D4—201no—
232C3×D4—401no—
233C2×C3×C4—101no—
234C2×C3×C4—101no—
235C2×C3×C4#70911yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C3×C8—41no—
239C3×C8—41no—
240C3×C8—52no—
241C3×C8—101no—
242C3×C8—201no—
243C22×C5—81no—
244C22×C5—81no—
245C22×C5—81no—
246C22×C5C3×#12111yescharacteristic
247C2×D5—81no—
248C2×D5—81no—
249C2×D5—81no—
250C4×C5—21no—
251C4×C5C2×C3×SD1611yescharacteristic
252C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
253C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
254C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
255Dic5—41no—
256Dic5—41no—
257C2×Q8—51no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—101no—
262C2×D4—101no—
263C2×D4—101no—
264SD16—202no—
265SD16—202no—
266D8—202no—
267D8—202no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—51no—
271C2×C8—51no—
272C2×C8—101no—
273C4⋊C4—51no—
274C4⋊C4—101no—
275C42—101no—
276C42C22×C3×D511yescharacteristic
277C3×C5#168811yescharacteristic, complemented, Hall
278C22×C3—81no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3—401no—
282C22×C3—401no—
283C22×C3—401no—
284C22×C3#403011yescharacteristic
285C3×C4—21no—
286C3×C4—201no—
287C3×C4—201no—
288C3×C4#405711yescharacteristic
289C3×C4#405711yescharacteristic
290C3×C4D5×SD1611yescharacteristic
291C3×C4#406011yescharacteristic
292C2×C5—161no—
293C2×C5C3×#46011yescharacteristic
294C2×C5C3×#46911yescharacteristic
295C2×C5C3×#47211yescharacteristic
296D5—161no—
297C23—41no—
298C23—201no—
299Q8—101no—
300Q8—101no—
301D4—41no—
302D4—41no—
303D4—41no—
304D4—41no—
305D4—81no—
306D4—201no—
307D4—201no—
308D4—201no—
309D4—201no—
310D4—401no—
311C2×C4—101no—
312C2×C4—101no—
313C2×C4C3×#70911yescharacteristic
314C2×C4C3×D4×D511yescharacteristic
315C2×C4C3×D4×D511yescharacteristic
316C8—41no—
317C8—41no—
318C8—52no—
319C8—101no—
320C8—201no—
321C2×C3—161no—
322C2×C3—801no—
323C2×C3#6503811yescharacteristic
324C2×C3#6505111yescharacteristic
325C2×C3#6507111yescharacteristic
326C5C3×#168811yescharacteristic, complemented, Sylow
327C22—81no—
328C22—81no—
329C22—81no—
330C22—401no—
331C22—401no—
332C22—401no—
333C22C3×#403011yescharacteristic
334C4—21no—
335C4—201no—
336C4—201no—
337C4C3×#405711yescharacteristic
338C4C3×#405711yescharacteristic
339C4C3×D5×SD1611yescharacteristic
340C4C3×#406011yescharacteristic
341C3#1059920611yescharacteristic, direct product factor, Sylow
342C2—161no—
343C2—801no—
344C2C3×#6503811yescharacteristic
345C2C3×#6505111yescharacteristic
346C2C3×#6507111yescharacteristic
subgroupG/H
centerC22×C3#4030
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#331C2
socleC22×C3×C5#121
prime radicalC3×#65362C2
hypercenterC3×#331D5
hypocenterC5C3×#1688
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
1. C3×#65364C2semidirect
3. C3×#65137C2semidirect
4. C3×#65120C2semidirect
5. C3×C5×#331C2semidirect
6. C3×#64705C2semidirect
7. C3×#64700C2semidirect
8. #10599206C3direct (N × H)
25. #65364C2×C3semidirect
27. #65137C2×C3semidirect
28. #65120C2×C3semidirect
29. C5×#331C2×C3semidirect
30. #64705C2×C3semidirect
31. #64700C2×C3semidirect
58. C3×#331D5semidirect
98. C3×#168SD16semidirect
140. #331C3×D5semidirect
198. #168C3×SD16semidirect
277. C3×C5#1688semidirect
326. C5C3×#1688semidirect
341. C3#10599206direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653642
C3×#653622
C3×#651372
C3×#651202
C3×C5×#3312
C3×#647052
C3×#647002
#105992063
C3×#16885