Finite Group Databasebeta

← C3×#10603996 #14304640

Subgroups — C3×#10603996 #14304640

Order 1920.

496 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×(C2×AGL(1,𝔽5))⋊Q8C211yesmaximal, characteristic
2C2×C3×#4009C211yesmaximal, characteristic
3C2×C3×#3992C211yesmaximal, characteristic
4C3×#65712C211yesmaximal, characteristic
5C3×D5×#103C211yesmaximal, characteristic
6C3×#64893C211yesmaximal, characteristic
7C3×#64874C211yesmaximal, characteristic
8#10603996C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5C2211yescharacteristic
10C2×C3×C4⋊AGL(1,𝔽5)—21no—
11C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
12C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
13C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
14C2×C3×D5⋊C8C2211yescharacteristic
15C2×C3×C8×D5C2211yescharacteristic
16C3×D5×C4⋊C4C2211yescharacteristic
17C3×#4009—22no—
18C3×(C2×AGL(1,𝔽5))⋊C4—21no—
19C3×(C2×AGL(1,𝔽5))⋊C4—21no—
20C3×(C2×AGL(1,𝔽5))⋊C4—21no—
21C3×#3992—22no—
22C3×C5×#103C411yescharacteristic, complemented
23C3×#3967C411yescharacteristic, complemented
24C3×#3948C411yescharacteristic, complemented
25C3×#3942C411yescharacteristic, complemented
26C3×#1935—51nomaximal, Hall
27(C2×AGL(1,𝔽5))⋊Q8C2×C311yescharacteristic
28C2×#4009C2×C311yescharacteristic
29C2×#3992C2×C311yescharacteristic
30#65712C2×C311yescharacteristic
31D5×#103C2×C311yescharacteristic
32#64893C2×C311yescharacteristic
33#64874C2×C311yescharacteristic
34C22×C3×AGL(1,𝔽5)—21no—
35C22×C3×AGL(1,𝔽5)—21no—
36C22×C3×AGL(1,𝔽5)D411yescharacteristic
37C22×C3×AGL(1,𝔽5)D411yescharacteristic
38C2×C3×C5×Q8C2×C411yescharacteristic
39C3×Q8×D5—21no—
40C3×Q8×D5—21no—
41C3×Q8×D5—21no—
42C3×Q8×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5C2311yescharacteristic
46C2×C3×Dic10—21no—
47C2×C3×Dic10C2×C411yescharacteristic
48C2×C3×#170—21no—
49C3×C4⋊AGL(1,𝔽5)—21no—
50C3×C4⋊AGL(1,𝔽5)—21no—
51C3×C4⋊AGL(1,𝔽5)—21no—
52C3×C4⋊AGL(1,𝔽5)—21no—
53C3×C4⋊AGL(1,𝔽5)—42no—
54C3×C4×AGL(1,𝔽5)—21no—
55C3×C4×AGL(1,𝔽5)—21no—
56C3×D5⋊C8—21no—
57C3×D5⋊C8D412yes—
58C2×C3×C5×C8C2×C411yescharacteristic
59C3×C5×C4⋊C4C2×C411yescharacteristic
60C3×C4⋊Dic5C2×C411yescharacteristic
61C3×#683—21no—
62C2×C3×#168C2×C411yescharacteristic
63C3×C8×D5—21no—
64C3×C8×D5—21no—
65C2×C3×#103—51no—
66C2×C3×#103—51no—
67C2×C3×#97—51no—
68C3×#391—51no—
69C3×#389—51no—
70C3×#340—51no—
71C3×#340—51no—
72C2×Q8×D5C22×C311yescharacteristic
73C2×C4⋊AGL(1,𝔽5)—21no—
74C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
75C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
76C2×C4×AGL(1,𝔽5)C22×C311yescharacteristic
77C2×D5⋊C8C22×C311yescharacteristic
78C2×C8×D5C22×C311yescharacteristic
79D5×C4⋊C4C22×C311yescharacteristic
80#4009—22no—
81(C2×AGL(1,𝔽5))⋊C4—21no—
82(C2×AGL(1,𝔽5))⋊C4—21no—
83(C2×AGL(1,𝔽5))⋊C4—21no—
84#3992—22no—
85C5×#103C3×C411yescharacteristic, complemented
86#3967C3×C411yescharacteristic, complemented
87#3948C3×C411yescharacteristic, complemented
88#3942C3×C411yescharacteristic, complemented
89#1935—51noSylow
90C22×C3×D5C2×D411yescharacteristic
91C2×C3×AGL(1,𝔽5)—21no—
92C2×C3×AGL(1,𝔽5)—21no—
93C2×C3×AGL(1,𝔽5)—21no—
94C2×C3×AGL(1,𝔽5)—21no—
95C2×C3×AGL(1,𝔽5)—21no—
96C2×C3×AGL(1,𝔽5)—21no—
97C2×C3×AGL(1,𝔽5)—41no—
98C2×C3×AGL(1,𝔽5)—41no—
99C2×C3×AGL(1,𝔽5)—41no—
100C2×C3×AGL(1,𝔽5)—41no—
101C2×C3×AGL(1,𝔽5)—41no—
102C2×C3×AGL(1,𝔽5)—41no—
103C3×C5×Q8—21no—
104C3×C5×Q8—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5#4111yescharacteristic
111C3×C4×D5—41no—
112C3×C4×D5—41no—
113C3×C4×D5—41no—
114C3×C4×D5—41no—
115C3×C4×D5C2×D411yescharacteristic
116C3×C4×D5#4111yescharacteristic
117C3×C4×D5#4111yescharacteristic
118C3×C4×D5#4111yescharacteristic
119C3×Dic10—21no—
120C3×Dic10—21no—
121C3×Dic10—41no—
122C3×Dic10—41no—
123C3×#170—22no—
124C3×C5×C8—21no—
125C3×#168—21no—
126C22×C3×Q8—51no—
127C22×C3×C8—51no—
128C22×C3×C8—51no—
129C2×C3×C4⋊C4—51no—
130C2×C3×C4⋊C4—51no—
131C2×C3×C4⋊C4—51no—
132C2×C3×C4⋊C4—101no—
133C2×C3×C42—51no—
134C3×#103—51no—
135C3×#103—51no—
136C3×#103—51no—
137C3×#103—102no—
138C3×#103AGL(1,𝔽5)11yescharacteristic, complemented
139C3×#97—102no—
140C3×#95—101no—
141C3×#95—101no—
142C3×#95—101no—
143C22×AGL(1,𝔽5)—21no—
144C22×AGL(1,𝔽5)—21no—
145C22×AGL(1,𝔽5)C3×D411yescharacteristic
146C22×AGL(1,𝔽5)C3×D411yescharacteristic
147C2×C5×Q8C2×C3×C411yescharacteristic
148Q8×D5—21no—
149Q8×D5—21no—
150Q8×D5—21no—
151Q8×D5—21no—
152C2×C4×D5—21no—
153C2×C4×D5—21no—
154C2×C4×D5C23×C311yescharacteristic
155C2×Dic10—21no—
156C2×Dic10C2×C3×C411yescharacteristic
157C2×#170—21no—
158C4⋊AGL(1,𝔽5)—21no—
159C4⋊AGL(1,𝔽5)—21no—
160C4⋊AGL(1,𝔽5)—21no—
161C4⋊AGL(1,𝔽5)—21no—
162C4⋊AGL(1,𝔽5)—42no—
163C4×AGL(1,𝔽5)—21no—
164C4×AGL(1,𝔽5)—21no—
165D5⋊C8—21no—
166D5⋊C8C3×D412yes—
167C2×C5×C8C2×C3×C411yescharacteristic
168C5×C4⋊C4C2×C3×C411yescharacteristic
169C4⋊Dic5C2×C3×C411yescharacteristic
170#683—21no—
171C2×#168C2×C3×C411yescharacteristic
172C8×D5—21no—
173C8×D5—21no—
174C2×#103—51no—
175C2×#103—51no—
176C2×#97—51no—
177#391—51no—
178#389—51no—
179#340—51no—
180#340—51no—
181C22×C3×C5C4×D411yescharacteristic
182C2×C3×D5#12111yescharacteristic
183C2×C3×D5#12411yescharacteristic
184C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
185C2×C3×D5#13711yescharacteristic
186C2×C3×D5#13711yescharacteristic
187C2×C3×D5#13711yescharacteristic
188C3×AGL(1,𝔽5)—41no—
189C3×AGL(1,𝔽5)—41no—
190C3×AGL(1,𝔽5)—81no—
191C3×AGL(1,𝔽5)—81no—
192C3×C4×C5—41no—
193C3×C4×C5—41no—
194C3×C4×C5#11711yescharacteristic
195C3×C4×C5C4×D411yescharacteristic
196C3×Dic5—41no—
197C3×Dic5—41no—
198C3×Dic5#12311yescharacteristic
199C3×Dic5#12611yescharacteristic
200C2×C3×Q8—51no—
201C2×C3×Q8—101no—
202C2×C3×Q8—101no—
203C2×C3×Q8—101no—
204C2×C3×Q8—101no—
205C2×C3×Q8—101no—
206C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
207C22×C3×C4—51no—
208C22×C3×C4—51no—
209C22×C3×C4—51no—
210C22×C3×C4—101no—
211C22×C3×C4—101no—
212C22×C3×C4—101no—
213C22×C3×C4—101no—
214C2×C3×C8—52no—
215C2×C3×C8—51no—
216C2×C3×C8—101no—
217C2×C3×C8—101no—
218C2×C3×C8—101no—
219C2×C3×C8—101no—
220C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
221C3×C4⋊C4—51no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4—101no—
226C3×C4⋊C4—101no—
227C3×C4⋊C4—202no—
228C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
229C3×C42—101no—
230C3×C42—101no—
231C22×D5C2×C3×D411yescharacteristic
232C2×AGL(1,𝔽5)—21no—
233C2×AGL(1,𝔽5)—21no—
234C2×AGL(1,𝔽5)—21no—
235C2×AGL(1,𝔽5)—21no—
236C2×AGL(1,𝔽5)—21no—
237C2×AGL(1,𝔽5)—21no—
238C2×AGL(1,𝔽5)—41no—
239C2×AGL(1,𝔽5)—41no—
240C2×AGL(1,𝔽5)—41no—
241C2×AGL(1,𝔽5)—41no—
242C2×AGL(1,𝔽5)—41no—
243C2×AGL(1,𝔽5)—41no—
244C5×Q8—21no—
245C5×Q8—21no—
246C2×C4×C5—21no—
247C2×C4×C5—21no—
248C2×C4×C5C22×C3×C411yescharacteristic
249C2×Dic5—21no—
250C2×Dic5—21no—
251C2×Dic5C3×#4111yescharacteristic
252C4×D5—41no—
253C4×D5—41no—
254C4×D5—41no—
255C4×D5—41no—
256C4×D5C2×C3×D411yescharacteristic
257C4×D5C3×#4111yescharacteristic
258C4×D5C3×#4111yescharacteristic
259C4×D5C3×#4111yescharacteristic
260Dic10—21no—
261Dic10—21no—
262Dic10—41no—
263Dic10—41no—
264#170—22no—
265C5×C8—21no—
266#168—21no—
267C22×Q8—51no—
268C22×C8—51no—
269C22×C8—51no—
270C2×C4⋊C4—51no—
271C2×C4⋊C4—51no—
272C2×C4⋊C4—51no—
273C2×C4⋊C4—101no—
274C2×C42—51no—
275#103—51no—
276#103—51no—
277#103—51no—
278#103—102no—
279#103C3×AGL(1,𝔽5)11yescharacteristic, complemented
280#97—102no—
281#95—101no—
282#95—101no—
283#95—101no—
284C2×C3×C5#38811yescharacteristic
285C2×C3×C5#44011yescharacteristic
286C2×C3×C5#44111yescharacteristic
287C3×D5#46811yescharacteristic
288C3×D5#47011yescharacteristic
289C3×D5#48911yescharacteristic
290C3×D5#49111yescharacteristic
291C23×C3—51no—
292C3×Q8—21no—
293C3×Q8—21no—
294C3×Q8—101no—
295C3×Q8—101no—
296C3×Q8—201no—
297C3×Q8—201no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—51no—
301C2×C3×C4—51no—
302C2×C3×C4—51no—
303C2×C3×C4—51no—
304C2×C3×C4—51no—
305C2×C3×C4—101no—
306C2×C3×C4—101no—
307C2×C3×C4—101no—
308C2×C3×C4—101no—
309C2×C3×C4—101no—
310C2×C3×C4—101no—
311C2×C3×C4—101no—
312C2×C3×C4—101no—
313C2×C3×C4—201no—
314C2×C3×C4—201no—
315C2×C3×C4—201no—
316C2×C3×C4—201no—
317C2×C3×C4—201no—
318C2×C3×C4—201no—
319C2×C3×C4—201no—
320C2×C3×C4—201no—
321C2×C3×C4—201no—
322C2×C3×C4—201no—
323C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
324C3×C8—21no—
325C3×C8—102no—
326C3×C8—101no—
327C22×C5C3×C4×D411yescharacteristic
328C2×D5C3×#12111yescharacteristic
329C2×D5C3×#12411yescharacteristic
330C2×D5C3×AGL(1,ℤ/8)11yescharacteristic
331C2×D5C3×#13711yescharacteristic
332C2×D5C3×#13711yescharacteristic
333C2×D5C3×#13711yescharacteristic
334AGL(1,𝔽5)—41no—
335AGL(1,𝔽5)—41no—
336AGL(1,𝔽5)—81no—
337AGL(1,𝔽5)—81no—
338C4×C5—41no—
339C4×C5—41no—
340C4×C5C3×#11711yescharacteristic
341C4×C5C3×C4×D411yescharacteristic
342Dic5—41no—
343Dic5—41no—
344Dic5C3×#12311yescharacteristic
345Dic5C3×#12611yescharacteristic
346C2×Q8—51no—
347C2×Q8—101no—
348C2×Q8—101no—
349C2×Q8—101no—
350C2×Q8—101no—
351C2×Q8—101no—
352C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
353C22×C4—51no—
354C22×C4—51no—
355C22×C4—51no—
356C22×C4—101no—
357C22×C4—101no—
358C22×C4—101no—
359C22×C4—101no—
360C2×C8—52no—
361C2×C8—51no—
362C2×C8—101no—
363C2×C8—101no—
364C2×C8—101no—
365C2×C8—101no—
366C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
367C4⋊C4—51no—
368C4⋊C4—101no—
369C4⋊C4—101no—
370C4⋊C4—101no—
371C4⋊C4—101no—
372C4⋊C4—101no—
373C4⋊C4—202no—
374C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
375C42—101no—
376C42—101no—
377C3×C5#193511yescharacteristic, complemented, Hall
378C22×C3—51no—
379C22×C3—51no—
380C22×C3—51no—
381C22×C3—51no—
382C22×C3—51no—
383C22×C3—51no—
384C22×C3D4×AGL(1,𝔽5)11yescharacteristic
385C3×C4—41no—
386C3×C4—41no—
387C3×C4—51no—
388C3×C4—51no—
389C3×C4—201no—
390C3×C4—201no—
391C3×C4—201no—
392C3×C4—201no—
393C3×C4—401no—
394C3×C4—401no—
395C3×C4#413011yescharacteristic
396C3×C4D4×AGL(1,𝔽5)11yescharacteristic
397C2×C5C3×#38811yescharacteristic
398C2×C5C3×#44011yescharacteristic
399C2×C5C3×#44111yescharacteristic
400D5C3×#46811yescharacteristic
401D5C3×#47011yescharacteristic
402D5C3×#48911yescharacteristic
403D5C3×#49111yescharacteristic
404C23—51no—
405Q8—21no—
406Q8—21no—
407Q8—101no—
408Q8—101no—
409Q8—201no—
410Q8—201no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—51no—
414C2×C4—51no—
415C2×C4—51no—
416C2×C4—51no—
417C2×C4—51no—
418C2×C4—101no—
419C2×C4—101no—
420C2×C4—101no—
421C2×C4—101no—
422C2×C4—101no—
423C2×C4—101no—
424C2×C4—101no—
425C2×C4—101no—
426C2×C4—201no—
427C2×C4—201no—
428C2×C4—201no—
429C2×C4—201no—
430C2×C4—201no—
431C2×C4—201no—
432C2×C4—201no—
433C2×C4—201no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
437C8—21no—
438C8—102no—
439C8—101no—
440C2×C3—51no—
441C2×C3—51no—
442C2×C3—51no—
443C2×C3—51no—
444C2×C3#6570011yescharacteristic
445C2×C3#6573511yescharacteristic
446C2×C3#6573911yescharacteristic
447C5C3×#193511yescharacteristic, complemented, Sylow
448C22—51no—
449C22—51no—
450C22—51no—
451C22—51no—
452C22—51no—
453C22—51no—
454C22C3×D4×AGL(1,𝔽5)11yescharacteristic
455C4—41no—
456C4—41no—
457C4—51no—
458C4—51no—
459C4—201no—
460C4—201no—
461C4—201no—
462C4—201no—
463C4—401no—
464C4—401no—
465C4C3×#413011yescharacteristic
466C4C3×D4×AGL(1,𝔽5)11yescharacteristic
467C3#1060399611yescharacteristic, direct product factor, Sylow
468C2—51no—
469C2—51no—
470C2—51no—
471C2—51no—
472C2C3×#6570011yescharacteristic
473C2C3×#6573511yescharacteristic
474C2C3×#6573911yescharacteristic
subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#103C4
socleC22×C3×C5C4×D4
prime radicalC22×C3×D5C2×D4
cosocleC2×C4×D5C23×C3
hypercenterC3×#103AGL(1,𝔽5)
hypocenterC5C3×#1935
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#103

Complements

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

NH ≅ G/Ntype
8. #10603996C3direct (N × H)
22. C3×C5×#103C4semidirect
23. C3×#3967C4semidirect
24. C3×#3948C4semidirect
25. C3×#3942C4semidirect
85. C5×#103C3×C4semidirect
86. #3967C3×C4semidirect
87. #3948C3×C4semidirect
88. #3942C3×C4semidirect
138. C3×#103AGL(1,𝔽5)semidirect
279. #103C3×AGL(1,𝔽5)semidirect
377. C3×C5#1935semidirect
447. C5C3×#1935semidirect
467. C3#10603996direct (N × H)

Maximal subgroups

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

subgroupindex
C3×(C2×AGL(1,𝔽5))⋊Q82
C2×C3×#40092
C2×C3×#39922
C3×#657122
C3×D5×#1032
C3×#648932
C3×#648742
#106039963
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