Finite Group Databasebeta

← C3×#10602710 #14290637

Subgroups — C3×#10602710 #14290637

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×D4×Q8C211yesmaximal, characteristic
2C3×#65368C211yesmaximal, characteristic, complemented
3C3×#65309C211yesmaximal, characteristic, complemented
4C3×#65308C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×Q8⋊#168C211yesmaximal, characteristic, complemented
7C3×D4⋊#168C211yesmaximal, characteristic
8#10602710C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8—21no—
10C3×C5×C4⋊Q8—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×C22⋊Q8—21no—
13C3×C5×C22⋊Q8—22no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4C2211yescharacteristic
17C2×C3×#687—21no—
18C3×#4015C2211yescharacteristic
19C3×#3967—21no—
20C3×#3942—21no—
21C3×#3940—21no—
22C3×#3940—22no—
23C3×C4⋊#168C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1651—51nomaximal, Hall
27C5×D4×Q8C2×C311yescharacteristic
28#65368C2×C311yescharacteristic, complemented
29#65309C2×C311yescharacteristic, complemented
30#65308C2×C311yescharacteristic
31#64767C2×C311yescharacteristic, complemented
32Q8⋊#168C2×C311yescharacteristic, complemented
33D4⋊#168C2×C311yescharacteristic
34C2×C3×C5×Q8—22no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—42no—
37C2×C3×C5×Q8—42no—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—21no—
42C2×C3×Dic10—21no—
43C3×C5×C4⋊C4—22no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C4⋊C4D412yes—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—22no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53C3×#687—42no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C3×D4×Q8D511yescharacteristic
60C3×#498—51no—
61C3×#475—51no—
62C3×#461—51no—
63C3×#332—51no—
64C3×Q8⋊C8—51no—
65C3×D4⋊C8—51no—
66C22×C5×Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8C22×C311yescharacteristic
69C5×C22⋊Q8—21no—
70C5×C22⋊Q8—22no—
71C4×C5×Q8C22×C311yescharacteristic
72C4×C5×D4—21no—
73C4×C5×D4C22×C311yescharacteristic
74C2×#687—21no—
75#4015C22×C311yescharacteristic
76#3967—21no—
77#3942—21no—
78#3940—21no—
79#3940—22no—
80C4⋊#168C22×C311yescharacteristic
81C4⋊#168C22×C311yescharacteristic
82C4×#168C22×C311yescharacteristic
83#1651—51noSylow
84C23×C3×C5—21no—
85C3×C5×Q8—21no—
86C3×C5×Q8—44no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C3×C5×Q8SD1612yescomplemented
90C3×C5×D4—21no—
91C3×C5×D4SD1612yes—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—44no—
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
102C2×C3×Dic5—41no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105C3×#168—22no—
106C3×#168—41no—
107C3×#168—41no—
108C22×C3×Q8—21no—
109C2×C3×SD16—101no—
110C3×C4⋊Q8—21no—
111C3×C4⋊Q8—51no—
112C3×C4⋊Q8C2×D511yescharacteristic
113C3×C22⋊Q8—21no—
114C3×C22⋊Q8—22no—
115C3×C4×Q8C2×D511yescharacteristic
116C3×C4×D4—21no—
117C3×C4×D4C2×D511yescharacteristic
118C3×#106—101no—
119C3×#106—102no—
120C3×C4⋊C8—51no—
121C3×C4⋊C8—51no—
122C3×#103—101no—
123C3×#103—101no—
124C3×C4×C8—51no—
125C2×C5×Q8—22no—
126C2×C5×Q8—21no—
127C2×C5×Q8—42no—
128C2×C5×Q8—42no—
129C2×C5×Q8C3×D411yescharacteristic
130C2×C5×D4C3×D411yescharacteristic
131C22×C4×C5—22no—
132C22×C4×C5—21no—
133C2×Dic10—21no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4C3×D411yescharacteristic
138C5×C4⋊C4C3×D411yescharacteristic
139C5×C4⋊C4C3×D412yes—
140C5×C22⋊C4—22no—
141C5×C22⋊C4—21no—
142C42×C5—21no—
143C42×C5C23×C311yescharacteristic
144#687—42no—
145C4⋊Dic5—21no—
146C4⋊Dic5—21no—
147C2×#168—21no—
148C2×#168—21no—
149C2×#168—21no—
150D4×Q8C3×D511yescharacteristic
151#498—51no—
152#475—51no—
153#461—51no—
154#332—51no—
155Q8⋊C8—51no—
156D4⋊C8—51no—
157C22×C3×C5—22no—
158C22×C3×C5—41no—
159C22×C3×C5—41no—
160C22×C3×C5#12011yescharacteristic
161C3×C4×C5—22no—
162C3×C4×C5—21no—
163C3×C4×C5—42no—
164C3×C4×C5—41no—
165C3×C4×C5—41no—
166C3×C4×C5C2×SD1611yescharacteristic
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170C3×Dic5—81no—
171C2×C3×Q8—22no—
172C2×C3×Q8—21no—
173C2×C3×Q8—42no—
174C2×C3×Q8—42no—
175C2×C3×Q8—101no—
176C2×C3×Q8C22⋊D511yescharacteristic
177C2×C3×D4C22⋊D511yescharacteristic
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C3×SD16—202no—
181C2×C3×C8—101no—
182C2×C3×C8—101no—
183C2×C3×C8—101no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—101no—
188C3×C4⋊C4—101no—
189C3×C4⋊C4C22⋊D511yescharacteristic
190C3×C4⋊C4C22⋊D511yescharacteristic
191C3×C4⋊C4C22⋊D512yes—
192C3×C22⋊C4—22no—
193C3×C22⋊C4—21no—
194C3×C42—21no—
195C3×C42C22×D511yescharacteristic
196C23×C5—21no—
197C5×Q8—21no—
198C5×Q8—44no—
199C5×Q8—41no—
200C5×Q8—41no—
201C5×Q8C3×SD1612yescomplemented
202C5×D4—21no—
203C5×D4C3×SD1612yes—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—22no—
207C2×C4×C5—21no—
208C2×C4×C5—44no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5C2×C3×D411yescharacteristic
212C2×C4×C5C2×C3×D411yescharacteristic
213C2×C4×C5C2×C3×D411yescharacteristic
214C2×Dic5—41no—
215Dic10—41no—
216Dic10—41no—
217#168—22no—
218#168—41no—
219#168—41no—
220C22×Q8—21no—
221C2×SD16—101no—
222C4⋊Q8—21no—
223C4⋊Q8—51no—
224C4⋊Q8C2×C3×D511yescharacteristic
225C22⋊Q8—21no—
226C22⋊Q8—22no—
227C4×Q8C2×C3×D511yescharacteristic
228C4×D4—21no—
229C4×D4C2×C3×D511yescharacteristic
230#106—101no—
231#106—102no—
232C4⋊C8—51no—
233C4⋊C8—51no—
234#103—101no—
235#103—101no—
236C4×C8—51no—
237C2×C3×C5—42no—
238C2×C3×C5#44811yescharacteristic
239C2×C3×C5#45011yescharacteristic
240C2×C3×C5#45611yescharacteristic
241C23×C3—21no—
242C3×Q8—21no—
243C3×Q8—44no—
244C3×Q8—41no—
245C3×Q8—41no—
246C3×Q8—201no—
247C3×Q8—201no—
248C3×Q8#68712yescomplemented
249C3×D4—21no—
250C3×D4#68812yes—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—22no—
254C2×C3×C4—21no—
255C2×C3×C4—44no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—201no—
259C2×C3×C4C2×C22⋊D511yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262C3×C8—102no—
263C3×C8—201no—
264C3×C8—201no—
265C22×C5—22no—
266C22×C5—41no—
267C22×C5—41no—
268C22×C5C3×#12011yescharacteristic
269C4×C5—22no—
270C4×C5—21no—
271C4×C5—42no—
272C4×C5—41no—
273C4×C5—41no—
274C4×C5C2×C3×SD1611yescharacteristic
275C4×C5C2×C3×SD1611yescharacteristic
276C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
277C4×C5C3×#13711yescharacteristic
278Dic5—81no—
279C2×Q8—22no—
280C2×Q8—21no—
281C2×Q8—42no—
282C2×Q8—42no—
283C2×Q8—101no—
284C2×Q8C3×C22⋊D511yescharacteristic
285C2×D4C3×C22⋊D511yescharacteristic
286C22×C4—22no—
287C22×C4—21no—
288SD16—202no—
289C2×C8—101no—
290C2×C8—101no—
291C2×C8—101no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—101no—
296C4⋊C4—101no—
297C4⋊C4C3×C22⋊D511yescharacteristic
298C4⋊C4C3×C22⋊D511yescharacteristic
299C4⋊C4C3×C22⋊D512yes—
300C22⋊C4—22no—
301C22⋊C4—21no—
302C42—21no—
303C42C22×C3×D511yescharacteristic
304C3×C5#165111yescharacteristic, complemented, Hall
305C22×C3—22no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3#409911yescharacteristic
309C3×C4—22no—
310C3×C4—21no—
311C3×C4—42no—
312C3×C4—41no—
313C3×C4—41no—
314C3×C4—401no—
315C3×C4#407811yescharacteristic
316C3×C4C2×#68711yescharacteristic
317C3×C4C2×#68811yescharacteristic
318C3×C4#408811yescharacteristic
319C2×C5—42no—
320C2×C5C3×#44811yescharacteristic
321C2×C5C3×#45011yescharacteristic
322C2×C5C3×#45611yescharacteristic
323C23—21no—
324Q8—21no—
325Q8—44no—
326Q8—41no—
327Q8—41no—
328Q8—201no—
329Q8—201no—
330Q8C3×#68712yescomplemented
331D4—21no—
332D4C3×#68812yes—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—44no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—201no—
341C2×C4C2×C3×C22⋊D511yescharacteristic
342C2×C4C2×C3×C22⋊D511yescharacteristic
343C2×C4C2×C3×C22⋊D511yescharacteristic
344C8—102no—
345C8—201no—
346C8—201no—
347C2×C3—42no—
348C2×C3#6550711yescharacteristic
349C2×C3#6551611yescharacteristic
350C2×C3#6553511yescharacteristic
351C5C3×#165111yescharacteristic, complemented, Sylow
352C22—22no—
353C22—41no—
354C22—41no—
355C22C3×#409911yescharacteristic
356C4—22no—
357C4—21no—
358C4—42no—
359C4—41no—
360C4—41no—
361C4—401no—
362C4C3×#407811yescharacteristic
363C4C2×C3×#68711yescharacteristic
364C4C2×C3×#68811yescharacteristic
365C4C3×#408811yescharacteristic
366C3#1060271011yescharacteristic, direct product factor, Sylow
367C2—42no—
368C2C3×#6550711yescharacteristic
369C2C3×#6551611yescharacteristic
370C2C3×#6553511yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×D4×Q8C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC3×D4×Q8D5
hypocenterC5C3×#1651
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×D4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#65368C2semidirect
3. C3×#65309C2semidirect
5. C3×#64767C2semidirect
6. C3×Q8⋊#168C2semidirect
8. #10602710C3direct (N × H)
28. #65368C2×C3semidirect
29. #65309C2×C3semidirect
31. #64767C2×C3semidirect
32. Q8⋊#168C2×C3semidirect
89. C3×C5×Q8SD16semidirect
201. C5×Q8C3×SD16semidirect
248. C3×Q8#687semidirect
304. C3×C5#1651semidirect
330. Q8C3×#687semidirect
351. C5C3×#1651semidirect
366. C3#10602710direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D4×Q82
C3×#653682
C3×#653092
C3×#653082
C3×#647672
C3×Q8⋊#1682
C3×D4⋊#1682
#106027103
C3×#16515