Finite Group Databasebeta

← C3×#10604878 #14280855

Subgroups — C3×#10604878 #14280855

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C3×D5⋊(C22⋊C8)C212yesmaximal, complemented
3C3×#64933C212yesmaximal, complemented
4C3×#64914C212yesmaximal, complemented
5#10604878C311yesmaximal, characteristic, direct product factor, Hall
6C23×C3×C4×C5C411yescharacteristic
7C22×C3×C22⋊D5C411yescharacteristic
8C22×C3×C4×D5C2211yescharacteristic
9C2×C3×D5⋊C8—22no—
10C2×C3×C22⋊Dic5C2211yescharacteristic
11C3×C4×C22⋊D5—22no—
12C3×C4×C22⋊D5—22no—
13C2×C3×#685C411yescharacteristic
14C2×C3×#683C2211yescharacteristic
15C2×C3×C4×Dic5C411yescharacteristic
16C3×C22⋊#170C2214yes—
17C3×#4003—22no—
18C3×#1459—51nomaximal, Hall
19C2×C4×C22⋊D5C2×C311yescharacteristic
20D5⋊(C22⋊C8)C2×C312yescomplemented
21#64933C2×C312yescomplemented
22#64914C2×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—42no—
37C2×C3×C4×D5D412yes—
38C2×C3×C4×D5D412yes—
39C2×C3×#170—24no—
40C3×D5⋊C8—44no—
41C3×C22⋊Dic5—22no—
42C3×#685—22no—
43C3×#683—22no—
44C3×C4×Dic5—21no—
45C3×C4×Dic5—21no—
46C2×C3×C4×D4—51no—
47C2×C3×C22⋊C8—52no—
48C3×#324—52no—
49C3×#323—52no—
50C23×C4×C5C3×C411yescharacteristic
51C22×C22⋊D5C3×C411yescharacteristic
52C22×C4×D5C22×C311yescharacteristic
53C2×D5⋊C8—22no—
54C2×C22⋊Dic5C22×C311yescharacteristic
55C4×C22⋊D5—22no—
56C4×C22⋊D5—22no—
57C2×#685C3×C411yescharacteristic
58C2×#683C22×C311yescharacteristic
59C2×C4×Dic5C3×C411yescharacteristic
60C22⋊#170C22×C314yes—
61#4003—22no—
62#1459—51noSylow
63C23×C3×C5—21no—
64C23×C3×C5—21no—
65C23×C3×C5—41no—
66C23×C3×C5—41no—
67C23×C3×C5C2×C812yescomplemented
68C23×C3×C5C22×C411yescharacteristic
69C22×C3×D5—41no—
70C22×C3×D5—41no—
71C22×C3×D5C22⋊C412yes—
72C22×C3×D5C2×C812yes—
73C22×C3×D5M1612yes—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—21no—
76C2×C3×C4×C5—42no—
77C2×C3×C4×C5—42no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5C22⋊C411yescharacteristic
81C3×C22⋊D5—28no—
82C2×C3×Dic5—21no—
83C2×C3×Dic5—21no—
84C2×C3×Dic5—21no—
85C2×C3×Dic5—41no—
86C2×C3×Dic5—41no—
87C2×C3×Dic5C2×C812yescomplemented
88C2×C3×Dic5C2×D412yes—
89C3×C4×D5—24no—
90C3×C4×D5—42no—
91C3×#170—44no—
92C22×C3×D4—51no—
93C23×C3×C4—51no—
94C23×C3×C4AGL(1,𝔽5)11yescharacteristic
95C22×C3×C8—102no—
96C3×C4×D4—102no—
97C3×C4×D4—102no—
98C2×C3×C4⋊C4—51no—
99C2×C3×C22⋊C4—51no—
100C2×C3×C22⋊C4—51no—
101C2×C3×C42—51no—
102C3×C22⋊C8—54no—
103C3×C22⋊C8—102no—
104C24×C5C2×C3×C411yescharacteristic
105C23×D5C2×C3×C411yescharacteristic
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—42no—
109C22×C4×C5C2×C3×C411yescharacteristic
110C22×C4×C5C2×C3×C411yescharacteristic
111C2×C22⋊D5—22no—
112C2×C22⋊D5—22no—
113C2×C22⋊D5C3×C814yescomplemented
114C22×Dic5C2×C3×C411yescharacteristic
115C22×Dic5C2×C3×C411yescharacteristic
116C22×Dic5C23×C311yescharacteristic
117C2×C4×D5—42no—
118C2×C4×D5C3×D412yes—
119C2×C4×D5C3×D412yes—
120C2×#170—24no—
121D5⋊C8—44no—
122C22⋊Dic5—22no—
123#685—22no—
124#683—22no—
125C4×Dic5—21no—
126C4×Dic5—21no—
127C2×C4×D4—51no—
128C2×C22⋊C8—52no—
129#324—52no—
130#323—52no—
131C22×C3×C5—21no—
132C22×C3×C5—21no—
133C22×C3×C5—22no—
134C22×C3×C5—42no—
135C22×C3×C5—42no—
136C22×C3×C5—41no—
137C22×C3×C5—41no—
138C22×C3×C5C2×C22⋊C411yescharacteristic
139C22×C3×C5C22×C811yescharacteristic
140C22×C3×C5C2×M1611yescharacteristic
141C2×C3×D5—22no—
142C2×C3×D5—22no—
143C2×C3×D5—42no—
144C2×C3×D5—42no—
145C2×C3×D5C22⋊C814yes—
146C3×C4×C5—21no—
147C3×C4×C5—41no—
148C3×C4×C5#9912yes—
149C3×Dic5—22no—
150C3×Dic5—22no—
151C3×Dic5—41no—
152C24×C3—51no—
153C24×C3C2×AGL(1,𝔽5)11yescharacteristic
154C2×C3×D4—54no—
155C2×C3×D4—102no—
156C2×C3×D4—102no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—42no—
160C22×C3×C4—51no—
161C22×C3×C4—51no—
162C22×C3×C4—52no—
163C22×C3×C4—52no—
164C22×C3×C4—51no—
165C22×C3×C4—202no—
166C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
167C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
168C2×C3×C8—104no—
169C2×C3×C8—204no—
170C3×C4⋊C4—102no—
171C3×C22⋊C4—102no—
172C3×C22⋊C4—102no—
173C3×C42—101no—
174C3×C42—101no—
175C23×C5—21no—
176C23×C5—21no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5C2×C3×C812yescomplemented
180C23×C5C22×C3×C411yescharacteristic
181C22×D5—41no—
182C22×D5—41no—
183C22×D5C3×C22⋊C412yes—
184C22×D5C2×C3×C812yes—
185C22×D5C3×M1612yes—
186C2×C4×C5—22no—
187C2×C4×C5—21no—
188C2×C4×C5—42no—
189C2×C4×C5—42no—
190C2×C4×C5—41no—
191C2×C4×C5C3×C22⋊C411yescharacteristic
192C2×C4×C5C3×C22⋊C411yescharacteristic
193C22⋊D5—28no—
194C2×Dic5—21no—
195C2×Dic5—21no—
196C2×Dic5—21no—
197C2×Dic5—41no—
198C2×Dic5—41no—
199C2×Dic5C2×C3×C812yescomplemented
200C2×Dic5C2×C3×D412yes—
201C4×D5—24no—
202C4×D5—42no—
203#170—44no—
204C22×D4—51no—
205C23×C4—51no—
206C23×C4C3×AGL(1,𝔽5)11yescharacteristic
207C22×C8—102no—
208C4×D4—102no—
209C4×D4—102no—
210C2×C4⋊C4—51no—
211C2×C22⋊C4—51no—
212C2×C22⋊C4—51no—
213C2×C42—51no—
214C22⋊C8—54no—
215C22⋊C8—102no—
216C2×C3×C5—21no—
217C2×C3×C5—21no—
218C2×C3×C5—42no—
219C2×C3×C5C2×C22⋊C811yescharacteristic
220C2×C3×C5C2×#9911yescharacteristic
221C2×C3×C5#41311yescharacteristic
222C3×D5—24no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—41no—
226C23×C3—41no—
227C23×C3—52no—
228C23×C3—52no—
229C23×C3—52no—
230C23×C3—201no—
231C23×C3—201no—
232C23×C3D5⋊C812yescomplemented
233C23×C3C22×AGL(1,𝔽5)11yescharacteristic
234C3×D4—108no—
235C2×C3×C4—22no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—42no—
239C2×C3×C4—41no—
240C2×C3×C4—52no—
241C2×C3×C4—52no—
242C2×C3×C4—101no—
243C2×C3×C4—101no—
244C2×C3×C4—104no—
245C2×C3×C4—101no—
246C2×C3×C4—202no—
247C2×C3×C4—201no—
248C2×C3×C4—201no—
249C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
250C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
251C3×C8—204no—
252C22×C5—21no—
253C22×C5—21no—
254C22×C5—22no—
255C22×C5—42no—
256C22×C5—42no—
257C22×C5—41no—
258C22×C5—41no—
259C22×C5C2×C3×C22⋊C411yescharacteristic
260C22×C5C22×C3×C811yescharacteristic
261C22×C5C2×C3×M1611yescharacteristic
262C2×D5—22no—
263C2×D5—22no—
264C2×D5—42no—
265C2×D5—42no—
266C2×D5C3×C22⋊C814yes—
267C4×C5—21no—
268C4×C5—41no—
269C4×C5C3×#9912yes—
270Dic5—22no—
271Dic5—22no—
272Dic5—41no—
273C24—51no—
274C24C2×C3×AGL(1,𝔽5)11yescharacteristic
275C2×D4—54no—
276C2×D4—102no—
277C2×D4—102no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—51no—
282C22×C4—51no—
283C22×C4—52no—
284C22×C4—52no—
285C22×C4—51no—
286C22×C4—202no—
287C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
288C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
289C2×C8—104no—
290C2×C8—204no—
291C4⋊C4—102no—
292C22⋊C4—102no—
293C22⋊C4—102no—
294C42—101no—
295C42—101no—
296C3×C5#145911yescharacteristic, complemented, Hall
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—22no—
300C22×C3—42no—
301C22×C3—42no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—54no—
305C22×C3—102no—
306C22×C3—102no—
307C22×C3—202no—
308C22×C3—202no—
309C22×C3C2×D5⋊C811yescharacteristic
310C22×C3D5⋊M1611yescharacteristic
311C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
312C3×C4—21no—
313C3×C4—41no—
314C3×C4—102no—
315C3×C4—102no—
316C3×C4—201no—
317C3×C4#401112yes—
318C2×C5—21no—
319C2×C5—21no—
320C2×C5—42no—
321C2×C5C2×C3×C22⋊C811yescharacteristic
322C2×C5C2×C3×#9911yescharacteristic
323C2×C5C3×#41311yescharacteristic
324D5—24no—
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23—52no—
330C23—52no—
331C23—52no—
332C23—201no—
333C23—201no—
334C23C3×D5⋊C812yescomplemented
335C23C22×C3×AGL(1,𝔽5)11yescharacteristic
336D4—108no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—52no—
343C2×C4—52no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—104no—
347C2×C4—101no—
348C2×C4—202no—
349C2×C4—201no—
350C2×C4—201no—
351C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
352C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
353C8—204no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—42no—
357C2×C3—104no—
358C2×C3D5⋊(C22⋊C8)11yescharacteristic
359C2×C3#6576111yescharacteristic
360C2×C3C2×#401111yescharacteristic
361C5C3×#145911yescharacteristic, complemented, Sylow
362C22—21no—
363C22—21no—
364C22—22no—
365C22—42no—
366C22—42no—
367C22—41no—
368C22—41no—
369C22—54no—
370C22—102no—
371C22—102no—
372C22—202no—
373C22—202no—
374C22C2×C3×D5⋊C811yescharacteristic
375C22C3×D5⋊M1611yescharacteristic
376C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
377C4—21no—
378C4—41no—
379C4—102no—
380C4—102no—
381C4—201no—
382C4C3×#401112yes—
383C3#1060487811yescharacteristic, direct product factor, Sylow
384C2—21no—
385C2—21no—
386C2—42no—
387C2—104no—
388C2C3×D5⋊(C22⋊C8)11yescharacteristic
389C2C3×#6576111yescharacteristic
390C2C2×C3×#401111yescharacteristic
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×#1459
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×D5⋊(C22⋊C8)C2semidirect
3. C3×#64933C2semidirect
4. C3×#64914C2semidirect
5. #10604878C3direct (N × H)
20. D5⋊(C22⋊C8)C2×C3semidirect
21. #64933C2×C3semidirect
22. #64914C2×C3semidirect
32. C2×C3×C22⋊D5C8semidirect
67. C23×C3×C5C2×C8semidirect
87. C2×C3×Dic5C2×C8semidirect
113. C2×C22⋊D5C3×C8semidirect
179. C23×C5C2×C3×C8semidirect
199. C2×Dic5C2×C3×C8semidirect
232. C23×C3D5⋊C8semidirect
296. C3×C5#1459semidirect
334. C23C3×D5⋊C8semidirect
361. C5C3×#1459semidirect
383. C3#10604878direct (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×D5⋊(C22⋊C8)2
C3×#649332
C3×#649142
#106048783
C3×#14595