Finite Group Databasebeta

← C3×#10604879 #14280899

Subgroups — C3×#10604879 #14280899

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C3×#65754C212yesmaximal, complemented
3C3×#64933C212yesmaximal, complemented
4C3×#64915C212yesmaximal, complemented
5#10604879C311yesmaximal, characteristic, direct product factor, Hall
6C23×C3×C4×C5C411yescharacteristic
7C22×C3×C22⋊D5C411yescharacteristic
8C22×C3×C4×D5C411yescharacteristic
9C2×C3×C22⋊Dic5C2211yescharacteristic
10C3×C4×C22⋊D5—22no—
11C3×C4×C22⋊D5—22no—
12C2×C3×#685C2211yescharacteristic
13C2×C3×#683C411yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C3×C22⋊#170C2214yes—
16C3×#4004—22no—
17C3×C4×#170—22no—
18C3×#1460—51nomaximal, Hall
19C2×C4×C22⋊D5C2×C311yescharacteristic
20#65754C2×C312yescomplemented
21#64933C2×C312yescomplemented
22#64915C2×C312yescomplemented
23C24×C3×C5C2×C411yescharacteristic
24C23×C3×D5C2×C411yescharacteristic
25C22×C3×C4×C5—21no—
26C22×C3×C4×C5—21no—
27C22×C3×C4×C5—42no—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C2×C3×C22⋊D5—22no—
31C2×C3×C22⋊D5—22no—
32C2×C3×C22⋊D5C814yescomplemented
33C22×C3×Dic5C2×C411yescharacteristic
34C22×C3×Dic5C2×C411yescharacteristic
35C22×C3×Dic5C2311yescharacteristic
36C2×C3×C4×D5—21no—
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—42no—
39C2×C3×#170—24no—
40C3×C22⋊Dic5—22no—
41C3×#685—22no—
42C3×#683—22no—
43C3×C4×Dic5D412yes—
44C3×C4×Dic5D412yes—
45C2×C3×C4×D4—51no—
46C3×#431—52no—
47C3×#323—52no—
48C3×#323—52no—
49C23×C4×C5C3×C411yescharacteristic
50C22×C22⋊D5C3×C411yescharacteristic
51C22×C4×D5C3×C411yescharacteristic
52C2×C22⋊Dic5C22×C311yescharacteristic
53C4×C22⋊D5—22no—
54C4×C22⋊D5—22no—
55C2×#685C22×C311yescharacteristic
56C2×#683C3×C411yescharacteristic
57C2×C4×Dic5C22×C311yescharacteristic
58C22⋊#170C22×C314yes—
59#4004—22no—
60C4×#170—22no—
61#1460—51noSylow
62C23×C3×C5—21no—
63C23×C3×C5—21no—
64C23×C3×C5—41no—
65C23×C3×C5—41no—
66C23×C3×C5C2×C812yes—
67C23×C3×C5C22×C411yescharacteristic
68C22×C3×D5—21no—
69C22×C3×D5—21no—
70C22×C3×D5—41no—
71C22×C3×D5—41no—
72C22×C3×D5C2×C812yes—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—42no—
76C2×C3×C4×C5—42no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5C22⋊C411yescharacteristic
79C2×C3×C4×C5C22⋊C411yescharacteristic
80C3×C22⋊D5—28no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5—41no—
84C2×C3×Dic5C22⋊C412yes—
85C2×C3×Dic5C2×C812yes—
86C2×C3×Dic5M1612yes—
87C2×C3×Dic5C2×D412yes—
88C3×C4×D5—42no—
89C3×C4×D5—42no—
90C3×#170—44no—
91C22×C3×D4—51no—
92C23×C3×C4—51no—
93C23×C3×C4AGL(1,𝔽5)11yescharacteristic
94C3×C4×D4—102no—
95C3×C4×D4—102no—
96C2×C3×C4⋊C4—51no—
97C2×C3×C22⋊C4—51no—
98C2×C3×C22⋊C4—51no—
99C2×C3×C42—51no—
100C3×C4⋊C8—102no—
101C3×C22⋊C8—54no—
102C3×C4×C8—102no—
103C24×C5C2×C3×C411yescharacteristic
104C23×D5C2×C3×C411yescharacteristic
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—42no—
108C22×C4×C5C2×C3×C411yescharacteristic
109C22×C4×C5C2×C3×C411yescharacteristic
110C2×C22⋊D5—22no—
111C2×C22⋊D5—22no—
112C2×C22⋊D5C3×C814yescomplemented
113C22×Dic5C2×C3×C411yescharacteristic
114C22×Dic5C2×C3×C411yescharacteristic
115C22×Dic5C23×C311yescharacteristic
116C2×C4×D5—21no—
117C2×C4×D5—21no—
118C2×C4×D5—42no—
119C2×#170—24no—
120C22⋊Dic5—22no—
121#685—22no—
122#683—22no—
123C4×Dic5C3×D412yes—
124C4×Dic5C3×D412yes—
125C2×C4×D4—51no—
126#431—52no—
127#323—52no—
128#323—52no—
129C22×C3×C5—21no—
130C22×C3×C5—21no—
131C22×C3×C5—22no—
132C22×C3×C5—42no—
133C22×C3×C5—42no—
134C22×C3×C5—41no—
135C22×C3×C5—41no—
136C22×C3×C5C2×C22⋊C411yescharacteristic
137C22×C3×C5C22×C811yescharacteristic
138C22×C3×C5C2×M1611yescharacteristic
139C2×C3×D5—22no—
140C2×C3×D5—42no—
141C2×C3×D5—41no—
142C2×C3×D5—41no—
143C2×C3×D5—42no—
144C3×C4×C5—21no—
145C3×C4×C5—41no—
146C3×C4×C5#10012yes—
147C3×Dic5—22no—
148C3×Dic5—41no—
149C3×Dic5C22⋊C814yes—
150C24×C3—51no—
151C24×C3C2×AGL(1,𝔽5)11yescharacteristic
152C2×C3×D4—54no—
153C2×C3×D4—102no—
154C2×C3×D4—102no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—42no—
158C22×C3×C4—51no—
159C22×C3×C4—51no—
160C22×C3×C4—51no—
161C22×C3×C4—101no—
162C22×C3×C4—101no—
163C22×C3×C4—202no—
164C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
165C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
166C2×C3×C8—104no—
167C3×C4⋊C4—102no—
168C3×C22⋊C4—102no—
169C3×C22⋊C4—102no—
170C3×C42—52no—
171C3×C42—52no—
172C23×C5—21no—
173C23×C5—21no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5C2×C3×C812yes—
177C23×C5C22×C3×C411yescharacteristic
178C22×D5—21no—
179C22×D5—21no—
180C22×D5—41no—
181C22×D5—41no—
182C22×D5C2×C3×C812yes—
183C2×C4×C5—22no—
184C2×C4×C5—21no—
185C2×C4×C5—42no—
186C2×C4×C5—42no—
187C2×C4×C5—41no—
188C2×C4×C5C3×C22⋊C411yescharacteristic
189C2×C4×C5C3×C22⋊C411yescharacteristic
190C22⋊D5—28no—
191C2×Dic5—21no—
192C2×Dic5—41no—
193C2×Dic5—41no—
194C2×Dic5C3×C22⋊C412yes—
195C2×Dic5C2×C3×C812yes—
196C2×Dic5C3×M1612yes—
197C2×Dic5C2×C3×D412yes—
198C4×D5—42no—
199C4×D5—42no—
200#170—44no—
201C22×D4—51no—
202C23×C4—51no—
203C23×C4C3×AGL(1,𝔽5)11yescharacteristic
204C4×D4—102no—
205C4×D4—102no—
206C2×C4⋊C4—51no—
207C2×C22⋊C4—51no—
208C2×C22⋊C4—51no—
209C2×C42—51no—
210C4⋊C8—102no—
211C22⋊C8—54no—
212C4×C8—102no—
213C2×C3×C5—21no—
214C2×C3×C5—21no—
215C2×C3×C5—42no—
216C2×C3×C5C2×C22⋊C811yescharacteristic
217C2×C3×C5#41011yescharacteristic
218C2×C3×C5C2×#10011yescharacteristic
219C3×D5—42no—
220C23×C3—21no—
221C23×C3—21no—
222C23×C3—41no—
223C23×C3—41no—
224C23×C3—52no—
225C23×C3—101no—
226C23×C3—101no—
227C23×C3—201no—
228C23×C3—201no—
229C23×C3D5⋊C812yes—
230C23×C3C22×AGL(1,𝔽5)11yescharacteristic
231C3×D4—108no—
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4—42no—
235C2×C3×C4—42no—
236C2×C3×C4—41no—
237C2×C3×C4—52no—
238C2×C3×C4—52no—
239C2×C3×C4—52no—
240C2×C3×C4—52no—
241C2×C3×C4—101no—
242C2×C3×C4—202no—
243C2×C3×C4—201no—
244C2×C3×C4—202no—
245C2×C3×C4—201no—
246C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
247C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
248C3×C8—204no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—22no—
252C22×C5—42no—
253C22×C5—42no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5C2×C3×C22⋊C411yescharacteristic
257C22×C5C22×C3×C811yescharacteristic
258C22×C5C2×C3×M1611yescharacteristic
259C2×D5—22no—
260C2×D5—42no—
261C2×D5—41no—
262C2×D5—41no—
263C2×D5—42no—
264C4×C5—21no—
265C4×C5—41no—
266C4×C5C3×#10012yes—
267Dic5—22no—
268Dic5—41no—
269Dic5C3×C22⋊C814yes—
270C24—51no—
271C24C2×C3×AGL(1,𝔽5)11yescharacteristic
272C2×D4—54no—
273C2×D4—102no—
274C2×D4—102no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—51no—
281C22×C4—101no—
282C22×C4—101no—
283C22×C4—202no—
284C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
285C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
286C2×C8—104no—
287C4⋊C4—102no—
288C22⋊C4—102no—
289C22⋊C4—102no—
290C42—52no—
291C42—52no—
292C3×C5#146011yescharacteristic, complemented, Hall
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—22no—
296C22×C3—42no—
297C22×C3—42no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—102no—
301C22×C3—202no—
302C22×C3—202no—
303C22×C3—201no—
304C22×C3—201no—
305C22×C3C2×D5⋊C811yescharacteristic
306C22×C3D5⋊M1611yescharacteristic
307C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
308C3×C4—21no—
309C3×C4—41no—
310C3×C4—54no—
311C3×C4—102no—
312C3×C4—201no—
313C3×C4#401312yes—
314C2×C5—21no—
315C2×C5—21no—
316C2×C5—42no—
317C2×C5C2×C3×C22⋊C811yescharacteristic
318C2×C5C3×#41011yescharacteristic
319C2×C5C2×C3×#10011yescharacteristic
320D5—42no—
321C23—21no—
322C23—21no—
323C23—41no—
324C23—41no—
325C23—52no—
326C23—101no—
327C23—101no—
328C23—201no—
329C23—201no—
330C23C3×D5⋊C812yes—
331C23C22×C3×AGL(1,𝔽5)11yescharacteristic
332D4—108no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—52no—
339C2×C4—52no—
340C2×C4—52no—
341C2×C4—52no—
342C2×C4—101no—
343C2×C4—202no—
344C2×C4—201no—
345C2×C4—202no—
346C2×C4—201no—
347C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
348C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
349C8—204no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—42no—
353C2×C3—202no—
354C2×C3#6574511yescharacteristic
355C2×C3D5⋊(C22⋊C8)11yescharacteristic
356C2×C3C2×#401311yescharacteristic
357C5C3×#146011yescharacteristic, complemented, Sylow
358C22—21no—
359C22—21no—
360C22—22no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—102no—
366C22—202no—
367C22—202no—
368C22—201no—
369C22—201no—
370C22C2×C3×D5⋊C811yescharacteristic
371C22C3×D5⋊M1611yescharacteristic
372C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
373C4—21no—
374C4—41no—
375C4—54no—
376C4—102no—
377C4—201no—
378C4C3×#401312yes—
379C3#1060487911yescharacteristic, direct product factor, Sylow
380C2—21no—
381C2—21no—
382C2—42no—
383C2—202no—
384C2C3×#6574511yescharacteristic
385C2C3×D5⋊(C22⋊C8)11yescharacteristic
386C2C2×C3×#401311yescharacteristic
subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC22×C5C22×C3×C8
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC23×C3×C4×C5C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C22⋊D5C4
cosocleC22×Dic5C23×C3
hypercenterC23×C3×C4AGL(1,𝔽5)
hypocenterC5C3×#1460
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C23×C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×#65754C2semidirect
3. C3×#64933C2semidirect
4. C3×#64915C2semidirect
5. #10604879C3direct (N × H)
20. #65754C2×C3semidirect
21. #64933C2×C3semidirect
22. #64915C2×C3semidirect
32. C2×C3×C22⋊D5C8semidirect
112. C2×C22⋊D5C3×C8semidirect
292. C3×C5#1460semidirect
357. C5C3×#1460semidirect
379. C3#10604879direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C3×#657542
C3×#649332
C3×#649152
#106048793
C3×#14605