Finite Group Databasebeta

← C3×#10604907 #14297562

Subgroups — C3×#10604907 #14297562

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C2×C3×#4013C212yesmaximal
3C3×#65758C212yesmaximal, complemented
4C3×#64919C212yesmaximal, complemented
5#10604907C311yesmaximal, characteristic, direct product factor, Hall
6C23×C3×C4×C5C411yescharacteristic
7C22×C3×C22⋊D5C2211yescharacteristic
8C22×C3×C4×D5C411yescharacteristic
9C2×C3×#704C2214yes—
10C2×C3×C22⋊Dic5C411yescharacteristic
11C3×C4×C22⋊D5—22no—
12C3×C4×C22⋊D5—22no—
13C2×C3×#685C411yescharacteristic
14C2×C3×#683C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C3×#4013—24no—
17C3×#4004—22no—
18C3×C4⋊#170—22no—
19C3×#1800—51nomaximal, Hall
20C2×C4×C22⋊D5C2×C311yescharacteristic
21C2×#4013C2×C312yes—
22#65758C2×C312yescomplemented
23#64919C2×C312yescomplemented
24C24×C3×C5C2×C411yescharacteristic
25C23×C3×D5C2×C411yescharacteristic
26C22×C3×C4×C5—21no—
27C22×C3×C4×C5—21no—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×C3×C22⋊D5—22no—
32C2×C3×C22⋊D5—22no—
33C2×C3×C22⋊D5D412yes—
34C2×C3×C22⋊D5Q812yes—
35C22×C3×Dic5C2×C411yescharacteristic
36C22×C3×Dic5C2×C411yescharacteristic
37C22×C3×Dic5C2311yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5—42no—
41C3×#704—24no—
42C3×#704—24no—
43C2×C3×#170—24no—
44C3×C22⋊Dic5—22no—
45C3×#685—22no—
46C3×#683—22no—
47C3×C4×Dic5D412yes—
48C3×C4×Dic5D412yes—
49C2×C3×C4×D4—51no—
50C3×#423—52no—
51C2×C3×#100—52no—
52C3×#343—52no—
53C23×C4×C5C3×C411yescharacteristic
54C22×C22⋊D5C22×C311yescharacteristic
55C22×C4×D5C3×C411yescharacteristic
56C2×#704C22×C314yes—
57C2×C22⋊Dic5C3×C411yescharacteristic
58C4×C22⋊D5—22no—
59C4×C22⋊D5—22no—
60C2×#685C3×C411yescharacteristic
61C2×#683C22×C311yescharacteristic
62C2×C4×Dic5C22×C311yescharacteristic
63#4013—24no—
64#4004—22no—
65C4⋊#170—22no—
66#1800—51noSylow
67C23×C3×C5—21no—
68C23×C3×C5—21no—
69C23×C3×C5—41no—
70C23×C3×C5—41no—
71C23×C3×C5C4⋊C412yes—
72C23×C3×C5C22×C411yescharacteristic
73C22×C3×D5—21no—
74C22×C3×D5—21no—
75C22×C3×D5—41no—
76C22×C3×D5—41no—
77C22×C3×D5C4⋊C412yes—
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—42no—
81C2×C3×C4×C5—42no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C3×C22⋊D5—24no—
86C3×C22⋊D5—24no—
87C2×C3×Dic5—21no—
88C2×C3×Dic5—41no—
89C2×C3×Dic5—41no—
90C2×C3×Dic5C22⋊C412yes—
91C2×C3×Dic5C2×D411yescharacteristic
92C2×C3×Dic5C2×D412yes—
93C2×C3×Dic5C2×Q811yescharacteristic
94C2×C3×Dic5#4112yes—
95C3×C4×D5—42no—
96C3×C4×D5—42no—
97C3×#170—44no—
98C22×C3×D4—51no—
99C23×C3×C4—51no—
100C23×C3×C4AGL(1,𝔽5)11yescharacteristic
101C2×C3×M16—54no—
102C3×C4×D4—102no—
103C3×C4×D4—102no—
104C2×C3×C4⋊C4—51no—
105C2×C3×C22⋊C4—51no—
106C2×C3×C22⋊C4—51no—
107C2×C3×C42—51no—
108C3×C4⋊C8—102no—
109C3×C4⋊C8—102no—
110C3×#100—104no—
111C24×C5C2×C3×C411yescharacteristic
112C23×D5C2×C3×C411yescharacteristic
113C22×C4×C5—21no—
114C22×C4×C5—21no—
115C22×C4×C5—42no—
116C22×C4×C5C2×C3×C411yescharacteristic
117C22×C4×C5C2×C3×C411yescharacteristic
118C2×C22⋊D5—22no—
119C2×C22⋊D5—22no—
120C2×C22⋊D5C3×D412yes—
121C2×C22⋊D5C3×Q812yes—
122C22×Dic5C2×C3×C411yescharacteristic
123C22×Dic5C2×C3×C411yescharacteristic
124C22×Dic5C23×C311yescharacteristic
125C2×C4×D5—21no—
126C2×C4×D5—21no—
127C2×C4×D5—42no—
128#704—24no—
129#704—24no—
130C2×#170—24no—
131C22⋊Dic5—22no—
132#685—22no—
133#683—22no—
134C4×Dic5C3×D412yes—
135C4×Dic5C3×D412yes—
136C2×C4×D4—51no—
137#423—52no—
138C2×#100—52no—
139#343—52no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—22no—
143C22×C3×C5—42no—
144C22×C3×C5—42no—
145C22×C3×C5—41no—
146C22×C3×C5—41no—
147C22×C3×C5C2×C22⋊C411yescharacteristic
148C22×C3×C5C2×C4⋊C411yescharacteristic
149C22×C3×C5#11711yescharacteristic
150C2×C3×D5—22no—
151C2×C3×D5—42no—
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C2×C3×D5—42no—
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5#10012yescomplemented
158C3×Dic5—22no—
159C3×Dic5—41no—
160C3×Dic5#12112yes—
161C3×Dic5C22⋊Q812yes—
162C24×C3—51no—
163C24×C3C2×AGL(1,𝔽5)11yescharacteristic
164C2×C3×D4—52no—
165C2×C3×D4—52no—
166C2×C3×D4—102no—
167C2×C3×D4—102no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—42no—
171C22×C3×C4—51no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4—101no—
175C22×C3×C4—101no—
176C22×C3×C4—202no—
177C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
178C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
179C3×M16—104no—
180C3×M16—104no—
181C2×C3×C8—104no—
182C3×C4⋊C4—102no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—102no—
185C3×C42—52no—
186C3×C42—52no—
187C23×C5—21no—
188C23×C5—21no—
189C23×C5—41no—
190C23×C5—41no—
191C23×C5C3×C4⋊C412yes—
192C23×C5C22×C3×C411yescharacteristic
193C22×D5—21no—
194C22×D5—21no—
195C22×D5—41no—
196C22×D5—41no—
197C22×D5C3×C4⋊C412yes—
198C2×C4×C5—22no—
199C2×C4×C5—21no—
200C2×C4×C5—42no—
201C2×C4×C5—42no—
202C2×C4×C5—41no—
203C2×C4×C5C3×C22⋊C411yescharacteristic
204C2×C4×C5C3×C22⋊C411yescharacteristic
205C22⋊D5—24no—
206C22⋊D5—24no—
207C2×Dic5—21no—
208C2×Dic5—41no—
209C2×Dic5—41no—
210C2×Dic5C3×C22⋊C412yes—
211C2×Dic5C2×C3×D411yescharacteristic
212C2×Dic5C2×C3×D412yes—
213C2×Dic5C2×C3×Q811yescharacteristic
214C2×Dic5C3×#4112yes—
215C4×D5—42no—
216C4×D5—42no—
217#170—44no—
218C22×D4—51no—
219C23×C4—51no—
220C23×C4C3×AGL(1,𝔽5)11yescharacteristic
221C2×M16—54no—
222C4×D4—102no—
223C4×D4—102no—
224C2×C4⋊C4—51no—
225C2×C22⋊C4—51no—
226C2×C22⋊C4—51no—
227C2×C42—51no—
228C4⋊C8—102no—
229C4⋊C8—102no—
230#100—104no—
231C2×C3×C5—21no—
232C2×C3×C5—21no—
233C2×C3×C5—42no—
234C2×C3×C5#38011yescharacteristic
235C2×C3×C5C2×#10011yescharacteristic
236C2×C3×C5#41311yescharacteristic
237C3×D5—42no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—41no—
241C23×C3—41no—
242C23×C3—52no—
243C23×C3—101no—
244C23×C3—101no—
245C23×C3—201no—
246C23×C3—201no—
247C23×C3C4⋊AGL(1,𝔽5)12yes—
248C23×C3C22×AGL(1,𝔽5)11yescharacteristic
249C3×D4—104no—
250C3×D4—104no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—41no—
256C2×C3×C4—51no—
257C2×C3×C4—51no—
258C2×C3×C4—52no—
259C2×C3×C4—52no—
260C2×C3×C4—52no—
261C2×C3×C4—101no—
262C2×C3×C4—202no—
263C2×C3×C4—201no—
264C2×C3×C4—202no—
265C2×C3×C4—201no—
266C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
267C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
268C3×C8—204no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—22no—
272C22×C5—42no—
273C22×C5—42no—
274C22×C5—41no—
275C22×C5—41no—
276C22×C5C2×C3×C22⋊C411yescharacteristic
277C22×C5C2×C3×C4⋊C411yescharacteristic
278C22×C5C3×#11711yescharacteristic
279C2×D5—22no—
280C2×D5—42no—
281C2×D5—41no—
282C2×D5—41no—
283C2×D5—42no—
284C4×C5—21no—
285C4×C5—41no—
286C4×C5C3×#10012yescomplemented
287Dic5—22no—
288Dic5—41no—
289Dic5C3×#12112yes—
290Dic5C3×C22⋊Q812yes—
291C24—51no—
292C24C2×C3×AGL(1,𝔽5)11yescharacteristic
293C2×D4—52no—
294C2×D4—52no—
295C2×D4—102no—
296C2×D4—102no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—42no—
300C22×C4—51no—
301C22×C4—51no—
302C22×C4—51no—
303C22×C4—101no—
304C22×C4—101no—
305C22×C4—202no—
306C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
307C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
308M16—104no—
309M16—104no—
310C2×C8—104no—
311C4⋊C4—102no—
312C22⋊C4—102no—
313C22⋊C4—102no—
314C42—52no—
315C42—52no—
316C3×C5#180011yescharacteristic, complemented, Hall
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—22no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—102no—
325C22×C3—202no—
326C22×C3—202no—
327C22×C3—201no—
328C22×C3—201no—
329C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
330C22×C3#413011yescharacteristic
331C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
332C3×C4—21no—
333C3×C4—41no—
334C3×C4—52no—
335C3×C4—52no—
336C3×C4—102no—
337C3×C4—201no—
338C3×C4#401312yescomplemented
339C2×C5—21no—
340C2×C5—21no—
341C2×C5—42no—
342C2×C5C3×#38011yescharacteristic
343C2×C5C2×C3×#10011yescharacteristic
344C2×C5C3×#41311yescharacteristic
345D5—42no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—52no—
351C23—101no—
352C23—101no—
353C23—201no—
354C23—201no—
355C23C3×C4⋊AGL(1,𝔽5)12yes—
356C23C22×C3×AGL(1,𝔽5)11yescharacteristic
357D4—104no—
358D4—104no—
359C2×C4—22no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—51no—
365C2×C4—51no—
366C2×C4—52no—
367C2×C4—52no—
368C2×C4—52no—
369C2×C4—101no—
370C2×C4—202no—
371C2×C4—201no—
372C2×C4—202no—
373C2×C4—201no—
374C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
375C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
376C8—204no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—42no—
380C2×C3—202no—
381C2×C3#6576111yescharacteristic
382C2×C3#6576511yescharacteristic
383C2×C3C2×#401311yescharacteristic
384C5C3×#180011yescharacteristic, complemented, Sylow
385C22—21no—
386C22—21no—
387C22—22no—
388C22—42no—
389C22—42no—
390C22—41no—
391C22—41no—
392C22—102no—
393C22—202no—
394C22—202no—
395C22—201no—
396C22—201no—
397C22C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
398C22C3×#413011yescharacteristic
399C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
400C4—21no—
401C4—41no—
402C4—52no—
403C4—52no—
404C4—102no—
405C4—201no—
406C4C3×#401312yescomplemented
407C3#1060490711yescharacteristic, direct product factor, Sylow
408C2—21no—
409C2—21no—
410C2—42no—
411C2—202no—
412C2C3×#6576111yescharacteristic
413C2C3×#6576511yescharacteristic
414C2C2×C3×#401311yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC23×C3×C4×C5C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C22⋊D5C22
cosocleC22×Dic5C23×C3
hypercenterC23×C3×C4AGL(1,𝔽5)
hypocenterC5C3×#1800
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C23×C3×C4

Complements

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

NH ≅ G/Ntype
3. C3×#65758C2semidirect
4. C3×#64919C2semidirect
5. #10604907C3direct (N × H)
22. #65758C2×C3semidirect
23. #64919C2×C3semidirect
157. C3×C4×C5#100semidirect
286. C4×C5C3×#100semidirect
316. C3×C5#1800semidirect
338. C3×C4#4013semidirect
384. C5C3×#1800semidirect
406. C4C3×#4013semidirect
407. C3#10604907direct (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
C2×C3×#40132
C3×#657582
C3×#649192
#106049073
C3×#18005