Finite Group Databasebeta

← C3×#10603955 #14304782

Subgroups — C3×#10603955 #14304782

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65776C211yesmaximal, characteristic
2C2×C3×#4008C211yesmaximal, characteristic
3C2×C3×C8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4C3×#65708C211yesmaximal, characteristic, complemented
5C3×#65061C211yesmaximal, characteristic
6C3×#64896C211yesmaximal, characteristic, complemented
7C3×#64875C211yesmaximal, characteristic, complemented
8#10603955C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711C2211yescharacteristic
10C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
11C2×C3×#700C2211yescharacteristic
12C2×C3×#700C2211yescharacteristic
13C2×C3×D5⋊C8C2211yescharacteristic
14C2×C3×C8×D5C2211yescharacteristic
15C3×#4038C2211yescharacteristic
16C3×C22⋊#170—21no—
17C3×C22⋊#170—21no—
18C3×#4008—22no—
19C3×#4004—21no—
20C3×C4⋊#170—21no—
21C3×C8×AGL(1,𝔽5)—22no—
22C3×C5×#102C411yescharacteristic, complemented
23C3×#3964C411yescharacteristic, complemented
24C3×#3948C411yescharacteristic, complemented
25C3×#3942C411yescharacteristic, complemented
26C3×#1937—51nomaximal, Hall
27#65776C2×C311yescharacteristic
28C2×#4008C2×C311yescharacteristic
29C2×C8×AGL(1,𝔽5)C2×C311yescharacteristic, complemented
30#65708C2×C311yescharacteristic, complemented
31#65061C2×C311yescharacteristic
32#64896C2×C311yescharacteristic, complemented
33#64875C2×C311yescharacteristic, complemented
34C22×C3×AGL(1,𝔽5)—21no—
35C2×C3×C5×D4C2×C411yescharacteristic
36C2×C3×C22⋊D5—21no—
37C22×C3×Dic5—21no—
38C3×#711—21no—
39C3×#711—21no—
40C3×#711—21no—
41C3×#711—21no—
42C2×C3×C4×D5C2311yescharacteristic
43C2×C3×Dic10C2×C411yescharacteristic
44C2×C3×#170—21no—
45C2×C3×#170—21no—
46C2×C3×#170D411yescharacteristic
47C2×C3×#170D411yescharacteristic
48C3×C4×AGL(1,𝔽5)—21no—
49C3×C4×AGL(1,𝔽5)D412yes—
50C3×#700—21no—
51C3×#700—21no—
52C3×#700—21no—
53C3×#700—21no—
54C3×D5⋊C8—21no—
55C3×D5⋊C8—21no—
56C2×C3×C5×C8C2×C411yescharacteristic
57C3×C5×C4⋊C4C2×C411yescharacteristic
58C3×#685—21no—
59C3×C4⋊Dic5C2×C411yescharacteristic
60C3×C4×Dic5—21no—
61C2×C3×#168C2×C411yescharacteristic
62C3×C8×D5—21no—
63C3×C8×D5—21no—
64C3×#424—51no—
65C2×C3×#104—51no—
66C3×#416—51no—
67C3×#408—51no—
68C2×C3×C4×C8—51no—
69C3×#341—51no—
70C3×#339—51no—
71C2×#711C22×C311yescharacteristic
72C2×C4×AGL(1,𝔽5)C22×C311yescharacteristic
73C2×#700C22×C311yescharacteristic
74C2×#700C22×C311yescharacteristic
75C2×D5⋊C8C22×C311yescharacteristic
76C2×C8×D5C22×C311yescharacteristic
77#4038C22×C311yescharacteristic
78C22⋊#170—21no—
79C22⋊#170—21no—
80#4008—22no—
81#4004—21no—
82C4⋊#170—21no—
83C8×AGL(1,𝔽5)—22no—
84C5×#102C3×C411yescharacteristic, complemented
85#3964C3×C411yescharacteristic, complemented
86#3948C3×C411yescharacteristic, complemented
87#3942C3×C411yescharacteristic, complemented
88#1937—51noSylow
89C23×C3×C5—21no—
90C22×C3×D5#4111yescharacteristic
91C2×C3×AGL(1,𝔽5)—22no—
92C2×C3×AGL(1,𝔽5)—22no—
93C2×C3×AGL(1,𝔽5)—22no—
94C3×C5×D4—21no—
95C3×C5×D4—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C3×C22⋊D5—41no—
99C3×C22⋊D5—41no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—41no—
103C2×C3×Dic5—41no—
104C2×C3×Dic5C2×D411yescharacteristic
105C3×C4×D5C2×D411yescharacteristic
106C3×C4×D5#4111yescharacteristic
107C3×C4×D5#4111yescharacteristic
108C3×C4×D5#4111yescharacteristic
109C3×Dic10—21no—
110C3×Dic10—21no—
111C3×#170—21no—
112C3×#170—21no—
113C3×#170—41no—
114C3×#170—41no—
115C3×C5×C8—21no—
116C3×#168—21no—
117C2×C3×#41—51no—
118C2×C3×M16—51no—
119C2×C3×M16—51no—
120C22×C3×C8—51no—
121C22×C3×C8—51no—
122C3×#117—51no—
123C2×C3×C42—51no—
124C3×C4⋊C8—101no—
125C3×C4⋊C8—101no—
126C3×#104—102no—
127C3×#103—51no—
128C3×#103—51no—
129C3×#102—51no—
130C3×#102AGL(1,𝔽5)11yescharacteristic, complemented
131C3×C22⋊C8—101no—
132C3×C22⋊C8—101no—
133C3×C4×C8—102no—
134C22×AGL(1,𝔽5)—21no—
135C2×C5×D4C2×C3×C411yescharacteristic
136C2×C22⋊D5—21no—
137C22×Dic5—21no—
138#711—21no—
139#711—21no—
140#711—21no—
141#711—21no—
142C2×C4×D5C23×C311yescharacteristic
143C2×Dic10C2×C3×C411yescharacteristic
144C2×#170—21no—
145C2×#170—21no—
146C2×#170C3×D411yescharacteristic
147C2×#170C3×D411yescharacteristic
148C4×AGL(1,𝔽5)—21no—
149C4×AGL(1,𝔽5)C3×D412yes—
150#700—21no—
151#700—21no—
152#700—21no—
153#700—21no—
154D5⋊C8—21no—
155D5⋊C8—21no—
156C2×C5×C8C2×C3×C411yescharacteristic
157C5×C4⋊C4C2×C3×C411yescharacteristic
158#685—21no—
159C4⋊Dic5C2×C3×C411yescharacteristic
160C4×Dic5—21no—
161C2×#168C2×C3×C411yescharacteristic
162C8×D5—21no—
163C8×D5—21no—
164#424—51no—
165C2×#104—51no—
166#416—51no—
167#408—51no—
168C2×C4×C8—51no—
169#341—51no—
170#339—51no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5—41no—
174C22×C3×C5C4×D411yescharacteristic
175C2×C3×D5—21no—
176C2×C3×D5—21no—
177C2×C3×D5#12311yescharacteristic
178C2×C3×D5#12611yescharacteristic
179C3×AGL(1,𝔽5)—24no—
180C3×C4×C5—41no—
181C3×C4×C5#11711yescharacteristic
182C3×C4×C5C4×D411yescharacteristic
183C3×Dic5—41no—
184C3×Dic5—41no—
185C3×Dic5#12111yescharacteristic
186C3×Dic5#12411yescharacteristic
187C3×#41—101no—
188C3×#41—101no—
189C3×#41—101no—
190C3×#41—101no—
191C2×C3×Q8—51no—
192C2×C3×D4—101no—
193C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
194C22×C3×C4—51no—
195C22×C3×C4—101no—
196C22×C3×C4—101no—
197C3×M16—101no—
198C3×M16—101no—
199C3×M16—101no—
200C3×M16—101no—
201C2×C3×C8—51no—
202C2×C3×C8—51no—
203C2×C3×C8—51no—
204C2×C3×C8—101no—
205C2×C3×C8—101no—
206C2×C3×C8—101no—
207C2×C3×C8—101no—
208C2×C3×C8—101no—
209C2×C3×C8—101no—
210C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
211C3×C4⋊C4—51no—
212C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
213C3×C22⋊C4—101no—
214C3×C42—52no—
215C3×C42—101no—
216C3×C42—101no—
217C23×C5—21no—
218C22×D5C3×#4111yescharacteristic
219C2×AGL(1,𝔽5)—22no—
220C2×AGL(1,𝔽5)—22no—
221C2×AGL(1,𝔽5)—22no—
222C5×D4—21no—
223C5×D4—21no—
224C2×C4×C5—21no—
225C2×C4×C5C22×C3×C411yescharacteristic
226C22⋊D5—41no—
227C22⋊D5—41no—
228C2×Dic5—21no—
229C2×Dic5—21no—
230C2×Dic5—41no—
231C2×Dic5—41no—
232C2×Dic5C2×C3×D411yescharacteristic
233C4×D5C2×C3×D411yescharacteristic
234C4×D5C3×#4111yescharacteristic
235C4×D5C3×#4111yescharacteristic
236C4×D5C3×#4111yescharacteristic
237Dic10—21no—
238Dic10—21no—
239#170—21no—
240#170—21no—
241#170—41no—
242#170—41no—
243C5×C8—21no—
244#168—21no—
245C2×#41—51no—
246C2×M16—51no—
247C2×M16—51no—
248C22×C8—51no—
249C22×C8—51no—
250#117—51no—
251C2×C42—51no—
252C4⋊C8—101no—
253C4⋊C8—101no—
254#104—102no—
255#103—51no—
256#103—51no—
257#102—51no—
258#102C3×AGL(1,𝔽5)11yescharacteristic, complemented
259C22⋊C8—101no—
260C22⋊C8—101no—
261C4×C8—102no—
262C2×C3×C5—81no—
263C2×C3×C5#38811yescharacteristic
264C2×C3×C5#44311yescharacteristic
265C2×C3×C5#44311yescharacteristic
266C3×D5—21no—
267C3×D5—21no—
268C23×C3—21no—
269C23×C3—51no—
270C3×Q8—101no—
271C3×Q8—101no—
272C3×D4—21no—
273C3×D4—21no—
274C3×D4—201no—
275C3×D4—201no—
276C2×C3×C4—21no—
277C2×C3×C4—51no—
278C2×C3×C4—51no—
279C2×C3×C4—51no—
280C2×C3×C4—51no—
281C2×C3×C4—51no—
282C2×C3×C4—102no—
283C2×C3×C4—102no—
284C2×C3×C4—102no—
285C2×C3×C4—101no—
286C2×C3×C4—101no—
287C2×C3×C4—201no—
288C2×C3×C4—201no—
289C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
290C3×C8—21no—
291C3×C8—101no—
292C3×C8—101no—
293C3×C8—101no—
294C3×C8—201no—
295C3×C8—201no—
296C22×C5—41no—
297C22×C5—41no—
298C22×C5—41no—
299C22×C5C3×C4×D411yescharacteristic
300C2×D5—21no—
301C2×D5—21no—
302C2×D5C3×#12311yescharacteristic
303C2×D5C3×#12611yescharacteristic
304AGL(1,𝔽5)—24no—
305C4×C5—41no—
306C4×C5C3×#11711yescharacteristic
307C4×C5C3×C4×D411yescharacteristic
308Dic5—41no—
309Dic5—41no—
310Dic5C3×#12111yescharacteristic
311Dic5C3×#12411yescharacteristic
312#41—101no—
313#41—101no—
314#41—101no—
315#41—101no—
316C2×Q8—51no—
317C2×D4—101no—
318C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
319C22×C4—51no—
320C22×C4—101no—
321C22×C4—101no—
322M16—101no—
323M16—101no—
324M16—101no—
325M16—101no—
326C2×C8—51no—
327C2×C8—51no—
328C2×C8—51no—
329C2×C8—101no—
330C2×C8—101no—
331C2×C8—101no—
332C2×C8—101no—
333C2×C8—101no—
334C2×C8—101no—
335C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
336C4⋊C4—51no—
337C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
338C22⋊C4—101no—
339C42—52no—
340C42—101no—
341C42—101no—
342C3×C5#193711yescharacteristic, complemented, Hall
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—51no—
347C22×C3—51no—
348C22×C3—101no—
349C22×C3—101no—
350C22×C3D4×AGL(1,𝔽5)11yescharacteristic
351C3×C4—41no—
352C3×C4—51no—
353C3×C4—51no—
354C3×C4—104no—
355C3×C4—201no—
356C3×C4—201no—
357C3×C4#413011yescharacteristic
358C3×C4D4×AGL(1,𝔽5)11yescharacteristic
359C2×C5—81no—
360C2×C5C3×#38811yescharacteristic
361C2×C5C3×#44311yescharacteristic
362C2×C5C3×#44311yescharacteristic
363D5—21no—
364D5—21no—
365C23—21no—
366C23—51no—
367Q8—101no—
368Q8—101no—
369D4—21no—
370D4—21no—
371D4—201no—
372D4—201no—
373C2×C4—21no—
374C2×C4—51no—
375C2×C4—51no—
376C2×C4—51no—
377C2×C4—51no—
378C2×C4—51no—
379C2×C4—102no—
380C2×C4—102no—
381C2×C4—102no—
382C2×C4—101no—
383C2×C4—101no—
384C2×C4—201no—
385C2×C4—201no—
386C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
387C8—21no—
388C8—101no—
389C8—101no—
390C8—101no—
391C8—201no—
392C8—201no—
393C2×C3—81no—
394C2×C3—101no—
395C2×C3—101no—
396C2×C3#6570011yescharacteristic
397C2×C3#6573211yescharacteristic
398C2×C3#6573611yescharacteristic
399C5C3×#193711yescharacteristic, complemented, Sylow
400C22—41no—
401C22—41no—
402C22—41no—
403C22—51no—
404C22—51no—
405C22—101no—
406C22—101no—
407C22C3×D4×AGL(1,𝔽5)11yescharacteristic
408C4—41no—
409C4—51no—
410C4—51no—
411C4—104no—
412C4—201no—
413C4—201no—
414C4C3×#413011yescharacteristic
415C4C3×D4×AGL(1,𝔽5)11yescharacteristic
416C3#1060395511yescharacteristic, direct product factor, Sylow
417C2—81no—
418C2—101no—
419C2—101no—
420C2C3×#6570011yescharacteristic
421C2C3×#6573211yescharacteristic
422C2C3×#6573611yescharacteristic
subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#102C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×#711C22
cosocleC2×C4×D5C23×C3
hypercenterC3×#102AGL(1,𝔽5)
hypocenterC5C3×#1937
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
3. C2×C3×C8×AGL(1,𝔽5)C2semidirect
4. C3×#65708C2semidirect
6. C3×#64896C2semidirect
7. C3×#64875C2semidirect
8. #10603955C3direct (N × H)
22. C3×C5×#102C4semidirect
23. C3×#3964C4semidirect
24. C3×#3948C4semidirect
25. C3×#3942C4semidirect
29. C2×C8×AGL(1,𝔽5)C2×C3semidirect
30. #65708C2×C3semidirect
32. #64896C2×C3semidirect
33. #64875C2×C3semidirect
84. C5×#102C3×C4semidirect
85. #3964C3×C4semidirect
86. #3948C3×C4semidirect
87. #3942C3×C4semidirect
130. C3×#102AGL(1,𝔽5)semidirect
258. #102C3×AGL(1,𝔽5)semidirect
342. C3×C5#1937semidirect
399. C5C3×#1937semidirect
416. C3#10603955direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#657762
C2×C3×#40082
C2×C3×C8×AGL(1,𝔽5)2
C3×#657082
C3×#650612
C3×#648962
C3×#648752
#106039553
C3×#19375