Finite Group Databasebeta

← C3×#10603965 #14300233

Subgroups — C3×#10603965 #14300233

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4131C211yesmaximal, characteristic
2C2×C3×#4008C211yesmaximal, characteristic
3C2×C3×#3995C211yesmaximal, characteristic, complemented
4C3×#65708C211yesmaximal, characteristic, complemented
5C3×#65061C211yesmaximal, characteristic
6C3×(C2×AGL(1,𝔽5))⋊C8C211yesmaximal, characteristic, complemented
7C3×#64875C211yesmaximal, characteristic, complemented
8#10603965C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711C2211yescharacteristic
10C2×C3×#704—21no—
11C22×C3×#170—21no—
12C3×#4131—22no—
13C3×#4131—22no—
14C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
15C2×C3×#700C2211yescharacteristic
16C2×C3×#700C2211yescharacteristic
17C2×C3×D5⋊C8C2211yescharacteristic
18C2×C3×C8×D5C2211yescharacteristic
19C3×#4038C2211yescharacteristic
20C3×#4008—22no—
21C3×#4004—21no—
22C3×C4⋊#170—21no—
23C3×#3995—22no—
24C3×C5×#102C411yescharacteristic, complemented
25C3×#3964C411yescharacteristic, complemented
26C3×#3948C411yescharacteristic, complemented
27C3×#3942C411yescharacteristic, complemented
28C3×#1866—51nomaximal, Hall
29C2×#4131C2×C311yescharacteristic
30C2×#4008C2×C311yescharacteristic
31C2×#3995C2×C311yescharacteristic, complemented
32#65708C2×C311yescharacteristic, complemented
33#65061C2×C311yescharacteristic
34(C2×AGL(1,𝔽5))⋊C8C2×C311yescharacteristic, complemented
35#64875C2×C311yescharacteristic, complemented
36C22×C3×AGL(1,𝔽5)—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C2×C3×C22⋊D5—21no—
39C22×C3×Dic5—21no—
40C3×#711—21no—
41C3×#711—21no—
42C3×#711D412yes—
43C3×#711Q812yes—
44C2×C3×C4×D5C2311yescharacteristic
45C2×C3×Dic10C2×C411yescharacteristic
46C3×#704—24no—
47C2×C3×#170—24no—
48C2×C3×#170—21no—
49C2×C3×#170—21no—
50C2×C3×#170D411yescharacteristic
51C2×C3×#170D411yescharacteristic
52C3×C4×AGL(1,𝔽5)—21no—
53C3×C4×AGL(1,𝔽5)—21no—
54C3×#700—21no—
55C3×#700—21no—
56C3×#700—21no—
57C3×#700D412yes—
58C3×D5⋊C8—21no—
59C3×D5⋊C8—21no—
60C2×C3×C5×C8C2×C411yescharacteristic
61C3×C5×C4⋊C4C2×C411yescharacteristic
62C3×#685—21no—
63C3×C4⋊Dic5C2×C411yescharacteristic
64C3×C4×Dic5—21no—
65C2×C3×#168C2×C411yescharacteristic
66C3×C8×D5—21no—
67C3×C8×D5—21no—
68C2×C3×#131—51no—
69C2×C3×#108—51no—
70C3×#424—51no—
71C2×C3×#104—51no—
72C3×#416—51no—
73C3×#339—51no—
74C3×#336—51no—
75C2×#711C22×C311yescharacteristic
76C2×#704—21no—
77C22×#170—21no—
78#4131—22no—
79#4131—22no—
80C2×C4×AGL(1,𝔽5)C22×C311yescharacteristic
81C2×#700C22×C311yescharacteristic
82C2×#700C22×C311yescharacteristic
83C2×D5⋊C8C22×C311yescharacteristic
84C2×C8×D5C22×C311yescharacteristic
85#4038C22×C311yescharacteristic
86#4008—22no—
87#4004—21no—
88C4⋊#170—21no—
89#3995—22no—
90C5×#102C3×C411yescharacteristic, complemented
91#3964C3×C411yescharacteristic, complemented
92#3948C3×C411yescharacteristic, complemented
93#3942C3×C411yescharacteristic, complemented
94#1866—51noSylow
95C23×C3×C5—21no—
96C22×C3×D5#4111yescharacteristic
97C2×C3×AGL(1,𝔽5)—22no—
98C2×C3×AGL(1,𝔽5)—41no—
99C2×C3×AGL(1,𝔽5)—41no—
100C3×C5×D4—21no—
101C3×C5×D4C4⋊C412yes—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C3×C22⋊D5—22no—
105C3×C22⋊D5—22no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5C2×D411yescharacteristic
111C3×C4×D5C2×D411yescharacteristic
112C3×C4×D5C2×D411yescharacteristic
113C3×C4×D5C2×Q811yescharacteristic
114C3×C4×D5#4111yescharacteristic
115C3×Dic10—21no—
116C3×Dic10C4⋊C412yes—
117C3×#170—21no—
118C3×#170—21no—
119C3×#170—22no—
120C3×#170—41no—
121C3×C5×C8—21no—
122C3×#168—21no—
123C2×C3×#41—51no—
124C3×#131—102no—
125C3×#131—102no—
126C2×C3×M16—51no—
127C2×C3×M16—51no—
128C2×C3×M16—101no—
129C22×C3×C8—51no—
130C22×C3×C8—51no—
131C22×C3×C8—101no—
132C3×#117—51no—
133C2×C3×C42—51no—
134C3×#108—102no—
135C3×C4⋊C8—101no—
136C3×C4⋊C8—101no—
137C3×#104—102no—
138C3×#103—51no—
139C3×#103—51no—
140C3×#102—51no—
141C3×#102AGL(1,𝔽5)11yescharacteristic, complemented
142C22×AGL(1,𝔽5)—21no—
143C2×C5×D4C2×C3×C411yescharacteristic
144C2×C22⋊D5—21no—
145C22×Dic5—21no—
146#711—21no—
147#711—21no—
148#711C3×D412yes—
149#711C3×Q812yes—
150C2×C4×D5C23×C311yescharacteristic
151C2×Dic10C2×C3×C411yescharacteristic
152#704—24no—
153C2×#170—24no—
154C2×#170—21no—
155C2×#170—21no—
156C2×#170C3×D411yescharacteristic
157C2×#170C3×D411yescharacteristic
158C4×AGL(1,𝔽5)—21no—
159C4×AGL(1,𝔽5)—21no—
160#700—21no—
161#700—21no—
162#700—21no—
163#700C3×D412yes—
164D5⋊C8—21no—
165D5⋊C8—21no—
166C2×C5×C8C2×C3×C411yescharacteristic
167C5×C4⋊C4C2×C3×C411yescharacteristic
168#685—21no—
169C4⋊Dic5C2×C3×C411yescharacteristic
170C4×Dic5—21no—
171C2×#168C2×C3×C411yescharacteristic
172C8×D5—21no—
173C8×D5—21no—
174C2×#131—51no—
175C2×#108—51no—
176#424—51no—
177C2×#104—51no—
178#416—51no—
179#339—51no—
180#336—51no—
181C22×C3×C5—22no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5C4×D411yescharacteristic
185C2×C3×D5—21no—
186C2×C3×D5—21no—
187C2×C3×D5C22⋊Q811yescharacteristic
188C2×C3×D5#12311yescharacteristic
189C3×AGL(1,𝔽5)—42no—
190C3×C4×C5—41no—
191C3×C4×C5C2×C4⋊C411yescharacteristic
192C3×C4×C5C4×D411yescharacteristic
193C3×Dic5—22no—
194C3×Dic5—41no—
195C3×Dic5#12011yescharacteristic
196C3×Dic5C22⋊Q811yescharacteristic
197C3×#41—52no—
198C3×#41—52no—
199C3×#41—101no—
200C3×#41—101no—
201C2×C3×Q8—51no—
202C2×C3×D4—101no—
203C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
204C22×C3×C4—51no—
205C22×C3×C4—101no—
206C22×C3×C4—101no—
207C3×M16—52no—
208C3×M16—101no—
209C3×M16—104no—
210C3×M16—101no—
211C3×M16—101no—
212C2×C3×C8—51no—
213C2×C3×C8—51no—
214C2×C3×C8—51no—
215C2×C3×C8—101no—
216C2×C3×C8—101no—
217C2×C3×C8—101no—
218C2×C3×C8—101no—
219C2×C3×C8—101no—
220C2×C3×C8—104no—
221C2×C3×C8—101no—
222C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
223C3×C4⋊C4—51no—
224C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
225C3×C22⋊C4—101no—
226C3×C42—101no—
227C3×C42—101no—
228C3×C42—101no—
229C23×C5—21no—
230C22×D5C3×#4111yescharacteristic
231C2×AGL(1,𝔽5)—22no—
232C2×AGL(1,𝔽5)—41no—
233C2×AGL(1,𝔽5)—41no—
234C5×D4—21no—
235C5×D4C3×C4⋊C412yes—
236C2×C4×C5—21no—
237C2×C4×C5C22×C3×C411yescharacteristic
238C22⋊D5—22no—
239C22⋊D5—22no—
240C2×Dic5—21no—
241C2×Dic5—22no—
242C2×Dic5—22no—
243C2×Dic5—21no—
244C2×Dic5C2×C3×D411yescharacteristic
245C4×D5C2×C3×D411yescharacteristic
246C4×D5C2×C3×D411yescharacteristic
247C4×D5C2×C3×Q811yescharacteristic
248C4×D5C3×#4111yescharacteristic
249Dic10—21no—
250Dic10C3×C4⋊C412yes—
251#170—21no—
252#170—21no—
253#170—22no—
254#170—41no—
255C5×C8—21no—
256#168—21no—
257C2×#41—51no—
258#131—102no—
259#131—102no—
260C2×M16—51no—
261C2×M16—51no—
262C2×M16—101no—
263C22×C8—51no—
264C22×C8—51no—
265C22×C8—101no—
266#117—51no—
267C2×C42—51no—
268#108—102no—
269C4⋊C8—101no—
270C4⋊C8—101no—
271#104—102no—
272#103—51no—
273#103—51no—
274#102—51no—
275#102C3×AGL(1,𝔽5)11yescharacteristic, complemented
276C2×C3×C5—42no—
277C2×C3×C5#38511yescharacteristic
278C2×C3×C5#44311yescharacteristic
279C2×C3×C5#44411yescharacteristic
280C3×D5—21no—
281C3×D5—21no—
282C23×C3—21no—
283C23×C3—51no—
284C3×Q8—52no—
285C3×Q8—101no—
286C3×D4—21no—
287C3×D4—102no—
288C3×D4—102no—
289C3×D4C4⋊AGL(1,𝔽5)12yes—
290C2×C3×C4—21no—
291C2×C3×C4—51no—
292C2×C3×C4—51no—
293C2×C3×C4—51no—
294C2×C3×C4—51no—
295C2×C3×C4—51no—
296C2×C3×C4—102no—
297C2×C3×C4—102no—
298C2×C3×C4—101no—
299C2×C3×C4—102no—
300C2×C3×C4—101no—
301C2×C3×C4—201no—
302C2×C3×C4—201no—
303C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
304C3×C8—21no—
305C3×C8—101no—
306C3×C8—101no—
307C3×C8—102no—
308C3×C8—101no—
309C3×C8—201no—
310C22×C5—22no—
311C22×C5—41no—
312C22×C5—41no—
313C22×C5C3×C4×D411yescharacteristic
314C2×D5—21no—
315C2×D5—21no—
316C2×D5C3×C22⋊Q811yescharacteristic
317C2×D5C3×#12311yescharacteristic
318AGL(1,𝔽5)—42no—
319C4×C5—41no—
320C4×C5C2×C3×C4⋊C411yescharacteristic
321C4×C5C3×C4×D411yescharacteristic
322Dic5—22no—
323Dic5—41no—
324Dic5C3×#12011yescharacteristic
325Dic5C3×C22⋊Q811yescharacteristic
326#41—52no—
327#41—52no—
328#41—101no—
329#41—101no—
330C2×Q8—51no—
331C2×D4—101no—
332C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
333C22×C4—51no—
334C22×C4—101no—
335C22×C4—101no—
336M16—52no—
337M16—101no—
338M16—104no—
339M16—101no—
340M16—101no—
341C2×C8—51no—
342C2×C8—51no—
343C2×C8—51no—
344C2×C8—101no—
345C2×C8—101no—
346C2×C8—101no—
347C2×C8—101no—
348C2×C8—101no—
349C2×C8—104no—
350C2×C8—101no—
351C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
352C4⋊C4—51no—
353C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
354C22⋊C4—101no—
355C42—101no—
356C42—101no—
357C42—101no—
358C3×C5#186611yescharacteristic, complemented, Hall
359C22×C3—22no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—51no—
363C22×C3—51no—
364C22×C3—101no—
365C22×C3—101no—
366C22×C3D4×AGL(1,𝔽5)11yescharacteristic
367C3×C4—41no—
368C3×C4—51no—
369C3×C4—51no—
370C3×C4—102no—
371C3×C4—202no—
372C3×C4—201no—
373C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
374C3×C4D4×AGL(1,𝔽5)11yescharacteristic
375C2×C5—42no—
376C2×C5C3×#38511yescharacteristic
377C2×C5C3×#44311yescharacteristic
378C2×C5C3×#44411yescharacteristic
379D5—21no—
380D5—21no—
381C23—21no—
382C23—51no—
383Q8—52no—
384Q8—101no—
385D4—21no—
386D4—102no—
387D4—102no—
388D4C3×C4⋊AGL(1,𝔽5)12yes—
389C2×C4—21no—
390C2×C4—51no—
391C2×C4—51no—
392C2×C4—51no—
393C2×C4—51no—
394C2×C4—51no—
395C2×C4—102no—
396C2×C4—102no—
397C2×C4—101no—
398C2×C4—102no—
399C2×C4—101no—
400C2×C4—201no—
401C2×C4—201no—
402C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
403C8—21no—
404C8—101no—
405C8—101no—
406C8—102no—
407C8—101no—
408C8—201no—
409C2×C3—42no—
410C2×C3—101no—
411C2×C3—101no—
412C2×C3#6569911yescharacteristic
413C2×C3#6573311yescharacteristic
414C2×C3#6573611yescharacteristic
415C5C3×#186611yescharacteristic, complemented, Sylow
416C22—22no—
417C22—41no—
418C22—41no—
419C22—51no—
420C22—51no—
421C22—101no—
422C22—101no—
423C22C3×D4×AGL(1,𝔽5)11yescharacteristic
424C4—41no—
425C4—51no—
426C4—51no—
427C4—102no—
428C4—202no—
429C4—201no—
430C4C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
431C4C3×D4×AGL(1,𝔽5)11yescharacteristic
432C3#1060396511yescharacteristic, direct product factor, Sylow
433C2—42no—
434C2—101no—
435C2—101no—
436C2C3×#6569911yescharacteristic
437C2C3×#6573311yescharacteristic
438C2C3×#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×#1866
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×#3995C2semidirect
4. C3×#65708C2semidirect
6. C3×(C2×AGL(1,𝔽5))⋊C8C2semidirect
7. C3×#64875C2semidirect
8. #10603965C3direct (N × H)
24. C3×C5×#102C4semidirect
25. C3×#3964C4semidirect
26. C3×#3948C4semidirect
27. C3×#3942C4semidirect
31. C2×#3995C2×C3semidirect
32. #65708C2×C3semidirect
34. (C2×AGL(1,𝔽5))⋊C8C2×C3semidirect
35. #64875C2×C3semidirect
90. C5×#102C3×C4semidirect
91. #3964C3×C4semidirect
92. #3948C3×C4semidirect
93. #3942C3×C4semidirect
141. C3×#102AGL(1,𝔽5)semidirect
275. #102C3×AGL(1,𝔽5)semidirect
358. C3×C5#1866semidirect
415. C5C3×#1866semidirect
432. C3#10603965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41312
C2×C3×#40082
C2×C3×#39952
C3×#657082
C3×#650612
C3×(C2×AGL(1,𝔽5))⋊C82
C3×#648752
#106039653
C3×#18665