Finite Group Databasebeta

← C3×#10602738 #14289944

Subgroups — C3×#10602738 #14289944

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#559C211yesmaximal, characteristic
2C3×#65359C211yesmaximal, characteristic
3C3×#65320C211yesmaximal, characteristic, complemented
4C3×#65309C211yesmaximal, characteristic, complemented
5C3×#64764C211yesmaximal, characteristic
6C3×Q8⋊#168C211yesmaximal, characteristic, complemented
7C3×Q8⋊#168C211yesmaximal, characteristic, complemented
8#10602738C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#127C2211yescharacteristic
10C3×C5×#124—21no—
11C3×C5×#124—21no—
12C3×C5×#123—22no—
13C3×C4×C5×Q8C2211yescharacteristic
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4—21no—
17C2×C3×#689—21no—
18C3×#4015C2211yescharacteristic
19C3×#3967—21no—
20C3×#3964—22no—
21C3×#3942—21no—
22C3×#3940—21no—
23C3×C4⋊#168C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1640—51nomaximal, Hall
27C5×#559C2×C311yescharacteristic
28#65359C2×C311yescharacteristic
29#65320C2×C311yescharacteristic, complemented
30#65309C2×C311yescharacteristic, complemented
31#64764C2×C311yescharacteristic
32Q8⋊#168C2×C311yescharacteristic, complemented
33Q8⋊#168C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4D412yes—
39C22×C3×C4×C5—22no—
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—22no—
47C3×C5×C22⋊C4—22no—
48C3×C42×C5—21no—
49C3×C42×C5—21no—
50C3×C42×C5C2311yescharacteristic
51C3×#689—42no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57C3×#559D511yescharacteristic
58C3×#486—51no—
59C3×#475—51no—
60C3×#462—51no—
61C3×#331—51no—
62C3×Q8⋊C8—51no—
63C3×Q8⋊C8—51no—
64C5×#127C22×C311yescharacteristic
65C5×#124—21no—
66C5×#124—21no—
67C5×#123—22no—
68C4×C5×Q8C22×C311yescharacteristic
69C4×C5×Q8C22×C311yescharacteristic
70C4×C5×D4—21no—
71C4×C5×D4—21no—
72C2×#689—21no—
73#4015C22×C311yescharacteristic
74#3967—21no—
75#3964—22no—
76#3942—21no—
77#3940—21no—
78C4⋊#168C22×C311yescharacteristic
79C4⋊#168C22×C311yescharacteristic
80C4×#168C22×C311yescharacteristic
81#1640—51noSylow
82C23×C3×C5—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—21no—
86C3×C5×Q8—21no—
87C3×C5×D4—42no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—82no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×Dic5—41no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3×#168—41no—
104C3×#168—41no—
105C3×#168—41no—
106C2×C3×Q16—101no—
107C3×C4⋊Q8—51no—
108C3×#127C2×D511yescharacteristic
109C3×#124—21no—
110C3×#124—21no—
111C3×#123—22no—
112C3×C4×Q8C2×D511yescharacteristic
113C3×C4×Q8C2×D511yescharacteristic
114C3×C4×D4—21no—
115C3×C4×D4—21no—
116C3×#106—101no—
117C3×C4⋊C8—51no—
118C3×C4⋊C8—51no—
119C3×#103—101no—
120C3×#103—101no—
121C3×#102—102no—
122C3×C4×C8—51no—
123C2×C5×Q8C3×D411yescharacteristic
124C2×C5×Q8C3×D411yescharacteristic
125C2×C5×D4—21no—
126C2×C5×D4—21no—
127C2×C5×D4C3×D412yes—
128C22×C4×C5—22no—
129C2×Dic10—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4C3×D411yescharacteristic
133C5×C4⋊C4C3×D411yescharacteristic
134C5×C22⋊C4—22no—
135C5×C22⋊C4—22no—
136C5×C22⋊C4—22no—
137C42×C5—21no—
138C42×C5—21no—
139C42×C5C23×C311yescharacteristic
140#689—42no—
141C4⋊Dic5—21no—
142C4⋊Dic5—21no—
143C2×#168—21no—
144C2×#168—21no—
145C2×#168—21no—
146#559C3×D511yescharacteristic
147#486—51no—
148#475—51no—
149#462—51no—
150#331—51no—
151Q8⋊C8—51no—
152Q8⋊C8—51no—
153C22×C3×C5—42no—
154C22×C3×C5—42no—
155C22×C3×C5—42no—
156C22×C3×C5#12011yescharacteristic
157C3×C4×C5—21no—
158C3×C4×C5—41no—
159C3×C4×C5—41no—
160C3×C4×C5—41no—
161C3×C4×C5—41no—
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13511yescharacteristic
164C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C3×C4×C5#13711yescharacteristic
166C3×Dic5—81no—
167C2×C3×Q8—101no—
168C2×C3×Q8C22⋊D511yescharacteristic
169C2×C3×Q8C22⋊D511yescharacteristic
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4C22⋊D512yes—
173C22×C3×C4—22no—
174C3×Q16—202no—
175C2×C3×C8—101no—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4C22⋊D511yescharacteristic
183C3×C4⋊C4C22⋊D511yescharacteristic
184C3×C22⋊C4—22no—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—22no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42C22×D511yescharacteristic
190C23×C5—22no—
191C5×Q8—21no—
192C5×Q8—21no—
193C5×Q8—21no—
194C5×Q8—21no—
195C5×D4—42no—
196C5×D4—41no—
197C5×D4—41no—
198C5×D4—41no—
199C5×D4—41no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—82no—
205C2×C4×C5C2×C3×D411yescharacteristic
206C2×C4×C5C2×C3×D411yescharacteristic
207C2×C4×C5C2×C3×D411yescharacteristic
208C2×Dic5—41no—
209Dic10—41no—
210Dic10—41no—
211#168—41no—
212#168—41no—
213#168—41no—
214C2×Q16—101no—
215C4⋊Q8—51no—
216#127C2×C3×D511yescharacteristic
217#124—21no—
218#124—21no—
219#123—22no—
220C4×Q8C2×C3×D511yescharacteristic
221C4×Q8C2×C3×D511yescharacteristic
222C4×D4—21no—
223C4×D4—21no—
224#106—101no—
225C4⋊C8—51no—
226C4⋊C8—51no—
227#103—101no—
228#103—101no—
229#102—102no—
230C4×C8—51no—
231C2×C3×C5—82no—
232C2×C3×C5#44911yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45511yescharacteristic
235C23×C3—22no—
236C3×Q8—21no—
237C3×Q8—21no—
238C3×Q8—21no—
239C3×Q8—21no—
240C3×Q8—201no—
241C3×Q8—201no—
242C3×D4—42no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—82no—
252C2×C3×C4—201no—
253C2×C3×C4C2×C22⋊D511yescharacteristic
254C2×C3×C4C2×C22⋊D511yescharacteristic
255C2×C3×C4C2×C22⋊D511yescharacteristic
256C3×C8—201no—
257C3×C8—201no—
258C3×C8—201no—
259C22×C5—42no—
260C22×C5—42no—
261C22×C5—42no—
262C22×C5C3×#12011yescharacteristic
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5—41no—
267C4×C5—41no—
268C4×C5C3×#13511yescharacteristic
269C4×C5C3×#13511yescharacteristic
270C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
271C4×C5C3×#13711yescharacteristic
272Dic5—81no—
273C2×Q8—101no—
274C2×Q8C3×C22⋊D511yescharacteristic
275C2×Q8C3×C22⋊D511yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4C3×C22⋊D512yes—
279C22×C4—22no—
280Q16—202no—
281C2×C8—101no—
282C2×C8—101no—
283C2×C8—101no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4C3×C22⋊D511yescharacteristic
289C4⋊C4C3×C22⋊D511yescharacteristic
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C42—21no—
294C42—21no—
295C42C22×C3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—42no—
300C22×C3#409911yescharacteristic
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—401no—
307C3×C4#409511yescharacteristic
308C3×C4#409611yescharacteristic
309C3×C4#409611yescharacteristic
310C3×C4#409711yescharacteristic
311C2×C5—82no—
312C2×C5C3×#44911yescharacteristic
313C2×C5C3×#45211yescharacteristic
314C2×C5C3×#45511yescharacteristic
315C23—22no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—201no—
321Q8—201no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—41no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—82no—
332C2×C4—201no—
333C2×C4C2×C3×C22⋊D511yescharacteristic
334C2×C4C2×C3×C22⋊D511yescharacteristic
335C2×C4C2×C3×C22⋊D511yescharacteristic
336C8—201no—
337C8—201no—
338C8—201no—
339C2×C3—82no—
340C2×C3#6552711yescharacteristic
341C2×C3#6552811yescharacteristic
342C2×C3#6553111yescharacteristic
343C5C3×#164011yescharacteristic, complemented, Sylow
344C22—42no—
345C22—42no—
346C22—42no—
347C22C3×#409911yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—401no—
354C4C3×#409511yescharacteristic
355C4C3×#409611yescharacteristic
356C4C3×#409611yescharacteristic
357C4C3×#409711yescharacteristic
358C3#1060273811yescharacteristic, direct product factor, Sylow
359C2—82no—
360C2C3×#6552711yescharacteristic
361C2C3×#6552811yescharacteristic
362C2C3×#6553111yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#559C2
socleC22×C3×C5#120
prime radicalC3×C5×#127C22
hypercenterC3×#559D5
hypocenterC5C3×#1640
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#559

Complements

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

NH ≅ G/Ntype
3. C3×#65320C2semidirect
4. C3×#65309C2semidirect
6. C3×Q8⋊#168C2semidirect
7. C3×Q8⋊#168C2semidirect
8. #10602738C3direct (N × H)
29. #65320C2×C3semidirect
30. #65309C2×C3semidirect
32. Q8⋊#168C2×C3semidirect
33. Q8⋊#168C2×C3semidirect
296. C3×C5#1640semidirect
343. C5C3×#1640semidirect
358. C3#10602738direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5592
C3×#653592
C3×#653202
C3×#653092
C3×#647642
C3×Q8⋊#1682
#106027383
C3×#16405