Finite Group Databasebeta

← C3×#10604589 #14307242

Subgroups — C3×#10604589 #14307242

Order 1920.

520 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
1C3×D5×#125C211yesmaximal, characteristic
2C3×C4×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
3C3×D5⋊(C4⋊C8)C211yesmaximal, characteristic
4C3×#64874C212yesmaximal
5C3×#64874C212yesmaximal
6#10604589C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
8C2×C3×C4×AGL(1,𝔽5)—21no—
9C2×C3×D5⋊C8C2212yes—
10C3×C5×#125C411yescharacteristic, complemented
11C3×D5×C4⋊C4—21no—
12C3×D5×C4⋊C4—21no—
13C3×D5×C4⋊C4C2211yescharacteristic
14C3×D5×C4⋊C4C2211yescharacteristic
15C3×#4036C411yescharacteristic, complemented
16C3×#4036C411yescharacteristic, complemented
17C3×#4035—21no—
18C3×#4035—21no—
19C3×C42×D5C2211yescharacteristic
20C3×#4016C411yescharacteristic, complemented
21C3×(C2×AGL(1,𝔽5))⋊C4—21no—
22C3×#4004—21no—
23C3×C4⋊#170—21no—
24C3×#1989—51nomaximal, Hall
25D5×#125C2×C311yescharacteristic
26C4×C4⋊AGL(1,𝔽5)C2×C311yescharacteristic
27D5⋊(C4⋊C8)C2×C311yescharacteristic
28#64874C2×C312yes—
29#64874C2×C312yes—
30C22×C3×AGL(1,𝔽5)—22no—
31C2×C3×C4×D5—21no—
32C2×C3×C4×D5—21no—
33C2×C3×C4×D5D411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×C3×C4×D5C2311yescharacteristic
36C2×C3×#170—22no—
37C3×C4⋊AGL(1,𝔽5)—22no—
38C3×C4⋊AGL(1,𝔽5)Q814yes—
39C3×C4×AGL(1,𝔽5)—42no—
40C3×D5⋊C8—24no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4C2×C411yescharacteristic
44C3×C5×C4⋊C4C2×C411yescharacteristic
45C3×C42×C5C2×C411yescharacteristic
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5C2×C411yescharacteristic
49C3×C4⋊Dic5C2×C411yescharacteristic
50C3×#683—21no—
51C3×#683—21no—
52C3×#683—21no—
53C3×#683—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×C4×Dic5C2×C411yescharacteristic
57C3×C4×Dic5D411yescharacteristic
58C3×C4×Dic5D411yescharacteristic
59C2×C3×#125—51no—
60C2×C3×C4⋊C8—51no—
61C3×C4×C4⋊C4—51no—
62C3×#340—52no—
63C3×#340—52no—
64C2×C4⋊AGL(1,𝔽5)C22×C312yes—
65C2×C4×AGL(1,𝔽5)—21no—
66C2×D5⋊C8C22×C312yes—
67C5×#125C3×C411yescharacteristic, complemented
68D5×C4⋊C4—21no—
69D5×C4⋊C4—21no—
70D5×C4⋊C4C22×C311yescharacteristic
71D5×C4⋊C4C22×C311yescharacteristic
72#4036C3×C411yescharacteristic, complemented
73#4036C3×C411yescharacteristic, complemented
74#4035—21no—
75#4035—21no—
76C42×D5C22×C311yescharacteristic
77#4016C3×C411yescharacteristic, complemented
78(C2×AGL(1,𝔽5))⋊C4—21no—
79#4004—21no—
80C4⋊#170—21no—
81#1989—51noSylow
82C22×C3×D5C2×D411yescharacteristic
83C2×C3×AGL(1,𝔽5)—24no—
84C2×C3×AGL(1,𝔽5)—42no—
85C2×C3×AGL(1,𝔽5)—42no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22⋊C411yescharacteristic
90C2×C3×C4×C5C22×C411yescharacteristic
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96C3×C4×D5—22no—
97C3×C4×D5—21no—
98C3×C4×D5—21no—
99C3×C4×D5—42no—
100C3×C4×D5—41no—
101C3×C4×D5—41no—
102C3×C4×D5C2×Q812yes—
103C3×C4×D5#4112yes—
104C3×#170—42no—
105C22×C3×C8—52no—
106C3×#125—51no—
107C3×#125—51no—
108C3×#125—51no—
109C3×#125—101no—
110C3×#125—101no—
111C3×#125AGL(1,𝔽5)11yescharacteristic, complemented
112C2×C3×C4⋊C4—52no—
113C2×C3×C4⋊C4—51no—
114C2×C3×C4⋊C4—51no—
115C2×C3×C4⋊C4—101no—
116C2×C3×C4⋊C4—101no—
117C2×C3×C42—51no—
118C2×C3×C42—101no—
119C3×C4⋊C8—101no—
120C3×C4⋊C8—101no—
121C3×#95—101no—
122C22×AGL(1,𝔽5)—22no—
123C2×C4×D5—21no—
124C2×C4×D5—21no—
125C2×C4×D5C3×D411yescharacteristic
126C2×C4×D5C3×D411yescharacteristic
127C2×C4×D5C23×C311yescharacteristic
128C2×#170—22no—
129C4⋊AGL(1,𝔽5)—22no—
130C4⋊AGL(1,𝔽5)C3×Q814yes—
131C4×AGL(1,𝔽5)—42no—
132D5⋊C8—24no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4C2×C3×C411yescharacteristic
136C5×C4⋊C4C2×C3×C411yescharacteristic
137C42×C5C2×C3×C411yescharacteristic
138C4⋊Dic5—21no—
139C4⋊Dic5—21no—
140C4⋊Dic5C2×C3×C411yescharacteristic
141C4⋊Dic5C2×C3×C411yescharacteristic
142#683—21no—
143#683—21no—
144#683—21no—
145#683—21no—
146#683—21no—
147#683—21no—
148C4×Dic5C2×C3×C411yescharacteristic
149C4×Dic5C3×D411yescharacteristic
150C4×Dic5C3×D411yescharacteristic
151C2×#125—51no—
152C2×C4⋊C8—51no—
153C4×C4⋊C4—51no—
154#340—52no—
155#340—52no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C2×C3×D5C22⋊Q812yes—
158C2×C3×D5#13512yes—
159C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
160C2×C3×D5#13711yescharacteristic
161C3×AGL(1,𝔽5)—44no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5—41no—
166C3×C4×C5C4×Q812yes—
167C3×Dic5—21no—
168C3×Dic5—21no—
169C3×Dic5—41no—
170C3×Dic5—41no—
171C3×Dic5#12411yescharacteristic
172C3×Dic5C4⋊Q811yescharacteristic
173C22×C3×C4—51no—
174C22×C3×C4—51no—
175C22×C3×C4—51no—
176C22×C3×C4—101no—
177C22×C3×C4—101no—
178C22×C3×C4—102no—
179C2×C3×C8—102no—
180C2×C3×C8—104no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—54no—
184C3×C4⋊C4—51no—
185C3×C4⋊C4—51no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4—101no—
188C3×C4⋊C4—101no—
189C3×C4⋊C4—101no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4—101no—
192C3×C4⋊C4—102no—
193C3×C4⋊C4—101no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
196C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
197C3×C42—51no—
198C3×C42—51no—
199C3×C42—51no—
200C3×C42—202no—
201C3×C42C2×AGL(1,𝔽5)11yescharacteristic
202C22×D5C2×C3×D411yescharacteristic
203C2×AGL(1,𝔽5)—24no—
204C2×AGL(1,𝔽5)—42no—
205C2×AGL(1,𝔽5)—42no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5C3×C22⋊C411yescharacteristic
209C2×C4×C5C3×C22⋊C411yescharacteristic
210C2×C4×C5C22×C3×C411yescharacteristic
211C2×Dic5—21no—
212C2×Dic5—21no—
213C2×Dic5C3×C22⋊C411yescharacteristic
214C2×Dic5C3×C22⋊C411yescharacteristic
215C2×Dic5C2×C3×D411yescharacteristic
216C4×D5—22no—
217C4×D5—21no—
218C4×D5—21no—
219C4×D5—42no—
220C4×D5—41no—
221C4×D5—41no—
222C4×D5C2×C3×Q812yes—
223C4×D5C3×#4112yes—
224#170—42no—
225C22×C8—52no—
226#125—51no—
227#125—51no—
228#125—51no—
229#125—101no—
230#125—101no—
231#125C3×AGL(1,𝔽5)11yescharacteristic, complemented
232C2×C4⋊C4—52no—
233C2×C4⋊C4—51no—
234C2×C4⋊C4—51no—
235C2×C4⋊C4—101no—
236C2×C4⋊C4—101no—
237C2×C42—51no—
238C2×C42—101no—
239C4⋊C8—101no—
240C4⋊C8—101no—
241#95—101no—
242C2×C3×C5#39111yescharacteristic
243C2×C3×C5#41611yescharacteristic
244C2×C3×C5#41711yescharacteristic
245C3×D5#47812yes—
246C3×D5#47912yes—
247C23×C3—51no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—51no—
251C2×C3×C4—52no—
252C2×C3×C4—52no—
253C2×C3×C4—51no—
254C2×C3×C4—51no—
255C2×C3×C4—101no—
256C2×C3×C4—101no—
257C2×C3×C4—102no—
258C2×C3×C4—104no—
259C2×C3×C4—101no—
260C2×C3×C4—101no—
261C2×C3×C4—201no—
262C2×C3×C4—201no—
263C2×C3×C4—202no—
264C2×C3×C4—202no—
265C2×C3×C4—202no—
266C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
267C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
268C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
269C3×C8—202no—
270C22×C5C2×C3×C22⋊C411yescharacteristic
271C2×D5C3×C22⋊Q812yes—
272C2×D5C3×#13512yes—
273C2×D5C3×AGL(1,ℤ/8)11yescharacteristic
274C2×D5C3×#13711yescharacteristic
275AGL(1,𝔽5)—44no—
276C4×C5—21no—
277C4×C5—21no—
278C4×C5—41no—
279C4×C5—41no—
280C4×C5C3×C4×Q812yes—
281Dic5—21no—
282Dic5—21no—
283Dic5—41no—
284Dic5—41no—
285Dic5C3×#12411yescharacteristic
286Dic5C3×C4⋊Q811yescharacteristic
287C22×C4—51no—
288C22×C4—51no—
289C22×C4—51no—
290C22×C4—101no—
291C22×C4—101no—
292C22×C4—102no—
293C2×C8—102no—
294C2×C8—104no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—54no—
298C4⋊C4—51no—
299C4⋊C4—51no—
300C4⋊C4—101no—
301C4⋊C4—101no—
302C4⋊C4—101no—
303C4⋊C4—101no—
304C4⋊C4—101no—
305C4⋊C4—101no—
306C4⋊C4—102no—
307C4⋊C4—101no—
308C4⋊C4—101no—
309C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
310C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
311C42—51no—
312C42—51no—
313C42—51no—
314C42—202no—
315C42C2×C3×AGL(1,𝔽5)11yescharacteristic
316C3×C5#198911yescharacteristic, complemented, Hall
317C22×C3—51no—
318C22×C3—51no—
319C22×C3—52no—
320C22×C3—52no—
321C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4—51no—
327C3×C4—51no—
328C3×C4—101no—
329C3×C4—101no—
330C3×C4—204no—
331C3×C4—201no—
332C3×C4—201no—
333C3×C4Q8×AGL(1,𝔽5)12yes—
334C2×C5C3×#39111yescharacteristic
335C2×C5C3×#41611yescharacteristic
336C2×C5C3×#41711yescharacteristic
337D5C3×#47812yes—
338D5C3×#47912yes—
339C23—51no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—51no—
343C2×C4—52no—
344C2×C4—52no—
345C2×C4—51no—
346C2×C4—51no—
347C2×C4—101no—
348C2×C4—101no—
349C2×C4—102no—
350C2×C4—104no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—201no—
354C2×C4—201no—
355C2×C4—202no—
356C2×C4—202no—
357C2×C4—202no—
358C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
359C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
360C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
361C8—202no—
362C2×C3—52no—
363C2×C3—52no—
364C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
365C2×C3#6579311yescharacteristic
366C2×C3#6579411yescharacteristic
367C5C3×#198911yescharacteristic, complemented, Sylow
368C22—52no—
369C22—51no—
370C22—51no—
371C22—52no—
372C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
373C4—21no—
374C4—21no—
375C4—41no—
376C4—41no—
377C4—51no—
378C4—51no—
379C4—101no—
380C4—101no—
381C4—204no—
382C4—201no—
383C4—201no—
384C4C3×Q8×AGL(1,𝔽5)12yes—
385C3#1060458911yescharacteristic, direct product factor, Sylow
386C2—52no—
387C2—52no—
388C2C3×(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
389C2C3×#6579311yescharacteristic
390C2C3×#6579411yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#125C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C4×D5C23×C3
hypercenterC3×#125AGL(1,𝔽5)
hypocenterC5C3×#1989
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#125

Complements

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

NH ≅ G/Ntype
6. #10604589C3direct (N × H)
10. C3×C5×#125C4semidirect
15. C3×#4036C4semidirect
16. C3×#4036C4semidirect
20. C3×#4016C4semidirect
67. C5×#125C3×C4semidirect
72. #4036C3×C4semidirect
73. #4036C3×C4semidirect
77. #4016C3×C4semidirect
111. C3×#125AGL(1,𝔽5)semidirect
231. #125C3×AGL(1,𝔽5)semidirect
316. C3×C5#1989semidirect
367. C5C3×#1989semidirect
385. C3#10604589direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#1252
C3×C4×C4⋊AGL(1,𝔽5)2
C3×D5⋊(C4⋊C8)2
C3×#648742
#106045893
C3×#19895