Finite Group Databasebeta

← C3×#10603990 #14300162

Subgroups — C3×#10603990 #14300162

Order 1920.

596 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×C3×#4009C211yesmaximal, characteristic
3C2×C3×#3993C211yesmaximal, characteristic
4C3×#65712C211yesmaximal, characteristic
5C3×D5×#103C211yesmaximal, characteristic
6C3×(C2×AGL(1,𝔽5))⋊C8C211yesmaximal, characteristic
7C3×#64874C211yesmaximal, characteristic
8#10603990C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5C2211yescharacteristic
10C3×Q8×AGL(1,𝔽5)—22no—
11C3×Q8×AGL(1,𝔽5)—22no—
12C2×C3×C4⋊AGL(1,𝔽5)—21no—
13C2×C3×C4⋊AGL(1,𝔽5)—21no—
14C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
15C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
16C2×C3×C4×AGL(1,𝔽5)—21no—
17C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
18C2×C3×D5⋊C8C2211yescharacteristic
19C2×C3×C8×D5C2211yescharacteristic
20C3×D5×C4⋊C4C2211yescharacteristic
21C3×#4009—22no—
22C3×(C2×AGL(1,𝔽5))⋊C4—21no—
23C3×#3993—22no—
24C3×C5×#103C411yescharacteristic, complemented
25C3×#3967C411yescharacteristic, complemented
26C3×#3948C411yescharacteristic, complemented
27C3×#3942C411yescharacteristic, complemented
28C3×#1865—51nomaximal, Hall
29C2×Q8×AGL(1,𝔽5)C2×C311yescharacteristic
30C2×#4009C2×C311yescharacteristic
31C2×#3993C2×C311yescharacteristic
32#65712C2×C311yescharacteristic
33D5×#103C2×C311yescharacteristic
34(C2×AGL(1,𝔽5))⋊C8C2×C311yescharacteristic
35#64874C2×C311yescharacteristic
36C22×C3×AGL(1,𝔽5)—21no—
37C22×C3×AGL(1,𝔽5)—21no—
38C22×C3×AGL(1,𝔽5)D411yescharacteristic
39C22×C3×AGL(1,𝔽5)D411yescharacteristic
40C2×C3×C5×Q8C2×C411yescharacteristic
41C3×Q8×D5—21no—
42C3×Q8×D5—21no—
43C3×Q8×D5D412yes—
44C3×Q8×D5Q812yes—
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5—21no—
47C2×C3×C4×D5C2311yescharacteristic
48C2×C3×Dic10—21no—
49C2×C3×Dic10C2×C411yescharacteristic
50C2×C3×#170—21no—
51C3×C4⋊AGL(1,𝔽5)—24no—
52C3×C4⋊AGL(1,𝔽5)—21no—
53C3×C4⋊AGL(1,𝔽5)—21no—
54C3×C4⋊AGL(1,𝔽5)—21no—
55C3×C4⋊AGL(1,𝔽5)—42no—
56C3×C4⋊AGL(1,𝔽5)D412yes—
57C3×C4×AGL(1,𝔽5)—24no—
58C3×C4×AGL(1,𝔽5)—21no—
59C3×C4×AGL(1,𝔽5)—21no—
60C3×D5⋊C8—21no—
61C3×D5⋊C8—21no—
62C2×C3×C5×C8C2×C411yescharacteristic
63C3×C5×C4⋊C4C2×C411yescharacteristic
64C3×C4⋊Dic5C2×C411yescharacteristic
65C3×#683—21no—
66C2×C3×#168C2×C411yescharacteristic
67C3×C8×D5—21no—
68C3×C8×D5—21no—
69C2×C3×C4×Q8—51no—
70C2×C3×#106—51no—
71C2×C3×#103—51no—
72C2×C3×#103—51no—
73C3×#389—51no—
74C3×#340—51no—
75C3×#336—51no—
76C2×Q8×D5C22×C311yescharacteristic
77Q8×AGL(1,𝔽5)—22no—
78Q8×AGL(1,𝔽5)—22no—
79C2×C4⋊AGL(1,𝔽5)—21no—
80C2×C4⋊AGL(1,𝔽5)—21no—
81C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
82C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
83C2×C4×AGL(1,𝔽5)—21no—
84C2×C4×AGL(1,𝔽5)C22×C311yescharacteristic
85C2×D5⋊C8C22×C311yescharacteristic
86C2×C8×D5C22×C311yescharacteristic
87D5×C4⋊C4C22×C311yescharacteristic
88#4009—22no—
89(C2×AGL(1,𝔽5))⋊C4—21no—
90#3993—22no—
91C5×#103C3×C411yescharacteristic, complemented
92#3967C3×C411yescharacteristic, complemented
93#3948C3×C411yescharacteristic, complemented
94#3942C3×C411yescharacteristic, complemented
95#1865—51noSylow
96C22×C3×D5C2×D411yescharacteristic
97C2×C3×AGL(1,𝔽5)—21no—
98C2×C3×AGL(1,𝔽5)—21no—
99C2×C3×AGL(1,𝔽5)—21no—
100C2×C3×AGL(1,𝔽5)—22no—
101C2×C3×AGL(1,𝔽5)—21no—
102C2×C3×AGL(1,𝔽5)—21no—
103C2×C3×AGL(1,𝔽5)—41no—
104C2×C3×AGL(1,𝔽5)—41no—
105C2×C3×AGL(1,𝔽5)—41no—
106C2×C3×AGL(1,𝔽5)—41no—
107C2×C3×AGL(1,𝔽5)—41no—
108C2×C3×AGL(1,𝔽5)SD1612yes—
109C3×C5×Q8—21no—
110C3×C5×Q8C4⋊C412yescomplemented
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5#4111yescharacteristic
117C3×C4×D5—22no—
118C3×C4×D5—22no—
119C3×C4×D5—41no—
120C3×C4×D5—41no—
121C3×C4×D5C2×D411yescharacteristic
122C3×C4×D5C2×D411yescharacteristic
123C3×C4×D5C2×Q811yescharacteristic
124C3×C4×D5#4111yescharacteristic
125C3×Dic10—21no—
126C3×Dic10—22no—
127C3×Dic10—22no—
128C3×Dic10C4⋊C412yescomplemented
129C3×#170—41no—
130C3×C5×C8—21no—
131C3×#168—21no—
132C22×C3×Q8—51no—
133C22×C3×C8—51no—
134C22×C3×C8—51no—
135C3×C4×Q8—102no—
136C3×C4×Q8—102no—
137C2×C3×C4⋊C4—51no—
138C2×C3×C4⋊C4—51no—
139C2×C3×C4⋊C4—51no—
140C2×C3×C4⋊C4—101no—
141C2×C3×C4⋊C4—101no—
142C2×C3×C42—51no—
143C2×C3×C42—101no—
144C3×#106—102no—
145C3×#103—51no—
146C3×#103—51no—
147C3×#103—51no—
148C3×#103—102no—
149C3×#103AGL(1,𝔽5)11yescharacteristic, complemented
150C3×#95—101no—
151C22×AGL(1,𝔽5)—21no—
152C22×AGL(1,𝔽5)—21no—
153C22×AGL(1,𝔽5)C3×D411yescharacteristic
154C22×AGL(1,𝔽5)C3×D411yescharacteristic
155C2×C5×Q8C2×C3×C411yescharacteristic
156Q8×D5—21no—
157Q8×D5—21no—
158Q8×D5C3×D412yes—
159Q8×D5C3×Q812yes—
160C2×C4×D5—21no—
161C2×C4×D5—21no—
162C2×C4×D5C23×C311yescharacteristic
163C2×Dic10—21no—
164C2×Dic10C2×C3×C411yescharacteristic
165C2×#170—21no—
166C4⋊AGL(1,𝔽5)—24no—
167C4⋊AGL(1,𝔽5)—21no—
168C4⋊AGL(1,𝔽5)—21no—
169C4⋊AGL(1,𝔽5)—21no—
170C4⋊AGL(1,𝔽5)—42no—
171C4⋊AGL(1,𝔽5)C3×D412yes—
172C4×AGL(1,𝔽5)—24no—
173C4×AGL(1,𝔽5)—21no—
174C4×AGL(1,𝔽5)—21no—
175D5⋊C8—21no—
176D5⋊C8—21no—
177C2×C5×C8C2×C3×C411yescharacteristic
178C5×C4⋊C4C2×C3×C411yescharacteristic
179C4⋊Dic5C2×C3×C411yescharacteristic
180#683—21no—
181C2×#168C2×C3×C411yescharacteristic
182C8×D5—21no—
183C8×D5—21no—
184C2×C4×Q8—51no—
185C2×#106—51no—
186C2×#103—51no—
187C2×#103—51no—
188#389—51no—
189#340—51no—
190#336—51no—
191C22×C3×C5C4×D411yescharacteristic
192C2×C3×D5#12011yescharacteristic
193C2×C3×D5C22⋊Q811yescharacteristic
194C2×C3×D5C2×SD1611yescharacteristic
195C2×C3×D5#13511yescharacteristic
196C2×C3×D5#13711yescharacteristic
197C2×C3×D5#13711yescharacteristic
198C3×AGL(1,𝔽5)—22no—
199C3×AGL(1,𝔽5)—41no—
200C3×AGL(1,𝔽5)—42no—
201C3×AGL(1,𝔽5)—81no—
202C3×C4×C5—22no—
203C3×C4×C5—41no—
204C3×C4×C5C2×C4⋊C411yescharacteristic
205C3×C4×C5C4×D411yescharacteristic
206C3×Dic5—22no—
207C3×Dic5—41no—
208C3×Dic5C22⋊Q811yescharacteristic
209C3×Dic5#12311yescharacteristic
210C2×C3×Q8—52no—
211C2×C3×Q8—52no—
212C2×C3×Q8—51no—
213C2×C3×Q8—101no—
214C2×C3×Q8—101no—
215C2×C3×Q8—101no—
216C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
217C22×C3×C4—51no—
218C22×C3×C4—51no—
219C22×C3×C4—51no—
220C22×C3×C4—101no—
221C22×C3×C4—101no—
222C22×C3×C4—101no—
223C22×C3×C4—101no—
224C2×C3×C8—51no—
225C2×C3×C8—101no—
226C2×C3×C8—101no—
227C2×C3×C8—101no—
228C2×C3×C8—101no—
229C2×C3×C8—101no—
230C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
231C3×C4⋊C4—52no—
232C3×C4⋊C4—51no—
233C3×C4⋊C4—101no—
234C3×C4⋊C4—101no—
235C3×C4⋊C4—101no—
236C3×C4⋊C4—101no—
237C3×C4⋊C4—104no—
238C3×C4⋊C4—202no—
239C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
240C3×C42—101no—
241C3×C42—101no—
242C3×C42—104no—
243C22×D5C2×C3×D411yescharacteristic
244C2×AGL(1,𝔽5)—21no—
245C2×AGL(1,𝔽5)—21no—
246C2×AGL(1,𝔽5)—21no—
247C2×AGL(1,𝔽5)—22no—
248C2×AGL(1,𝔽5)—21no—
249C2×AGL(1,𝔽5)—21no—
250C2×AGL(1,𝔽5)—41no—
251C2×AGL(1,𝔽5)—41no—
252C2×AGL(1,𝔽5)—41no—
253C2×AGL(1,𝔽5)—41no—
254C2×AGL(1,𝔽5)—41no—
255C2×AGL(1,𝔽5)C3×SD1612yes—
256C5×Q8—21no—
257C5×Q8C3×C4⋊C412yescomplemented
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5C22×C3×C411yescharacteristic
261C2×Dic5—21no—
262C2×Dic5—21no—
263C2×Dic5C3×#4111yescharacteristic
264C4×D5—22no—
265C4×D5—22no—
266C4×D5—41no—
267C4×D5—41no—
268C4×D5C2×C3×D411yescharacteristic
269C4×D5C2×C3×D411yescharacteristic
270C4×D5C2×C3×Q811yescharacteristic
271C4×D5C3×#4111yescharacteristic
272Dic10—21no—
273Dic10—22no—
274Dic10—22no—
275Dic10C3×C4⋊C412yescomplemented
276#170—41no—
277C5×C8—21no—
278#168—21no—
279C22×Q8—51no—
280C22×C8—51no—
281C22×C8—51no—
282C4×Q8—102no—
283C4×Q8—102no—
284C2×C4⋊C4—51no—
285C2×C4⋊C4—51no—
286C2×C4⋊C4—51no—
287C2×C4⋊C4—101no—
288C2×C4⋊C4—101no—
289C2×C42—51no—
290C2×C42—101no—
291#106—102no—
292#103—51no—
293#103—51no—
294#103—51no—
295#103—102no—
296#103C3×AGL(1,𝔽5)11yescharacteristic, complemented
297#95—101no—
298C2×C3×C5#38511yescharacteristic
299C2×C3×C5C4×SD1611yescharacteristic
300C2×C3×C5#44111yescharacteristic
301C3×D5#44811yescharacteristic
302C3×D5#45211yescharacteristic
303C3×D5#47511yescharacteristic
304C3×D5#47911yescharacteristic
305C23×C3—51no—
306C3×Q8—21no—
307C3×Q8—52no—
308C3×Q8—102no—
309C3×Q8—102no—
310C3×Q8—101no—
311C3×Q8C4⋊AGL(1,𝔽5)12yescomplemented
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—51no—
315C2×C3×C4—51no—
316C2×C3×C4—51no—
317C2×C3×C4—51no—
318C2×C3×C4—51no—
319C2×C3×C4—52no—
320C2×C3×C4—102no—
321C2×C3×C4—102no—
322C2×C3×C4—101no—
323C2×C3×C4—101no—
324C2×C3×C4—101no—
325C2×C3×C4—102no—
326C2×C3×C4—101no—
327C2×C3×C4—101no—
328C2×C3×C4—101no—
329C2×C3×C4—101no—
330C2×C3×C4—201no—
331C2×C3×C4—201no—
332C2×C3×C4—201no—
333C2×C3×C4—201no—
334C2×C3×C4—201no—
335C2×C3×C4—201no—
336C2×C3×C4—201no—
337C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
338C3×C8—21no—
339C3×C8—101no—
340C3×C8—201no—
341C22×C5C3×C4×D411yescharacteristic
342C2×D5C3×#12011yescharacteristic
343C2×D5C3×C22⋊Q811yescharacteristic
344C2×D5C2×C3×SD1611yescharacteristic
345C2×D5C3×#13511yescharacteristic
346C2×D5C3×#13711yescharacteristic
347C2×D5C3×#13711yescharacteristic
348AGL(1,𝔽5)—22no—
349AGL(1,𝔽5)—41no—
350AGL(1,𝔽5)—42no—
351AGL(1,𝔽5)—81no—
352C4×C5—22no—
353C4×C5—41no—
354C4×C5C2×C3×C4⋊C411yescharacteristic
355C4×C5C3×C4×D411yescharacteristic
356Dic5—22no—
357Dic5—41no—
358Dic5C3×C22⋊Q811yescharacteristic
359Dic5C3×#12311yescharacteristic
360C2×Q8—52no—
361C2×Q8—52no—
362C2×Q8—51no—
363C2×Q8—101no—
364C2×Q8—101no—
365C2×Q8—101no—
366C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
367C22×C4—51no—
368C22×C4—51no—
369C22×C4—51no—
370C22×C4—101no—
371C22×C4—101no—
372C22×C4—101no—
373C22×C4—101no—
374C2×C8—51no—
375C2×C8—101no—
376C2×C8—101no—
377C2×C8—101no—
378C2×C8—101no—
379C2×C8—101no—
380C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
381C4⋊C4—52no—
382C4⋊C4—51no—
383C4⋊C4—101no—
384C4⋊C4—101no—
385C4⋊C4—101no—
386C4⋊C4—101no—
387C4⋊C4—104no—
388C4⋊C4—202no—
389C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
390C42—101no—
391C42—101no—
392C42—104no—
393C3×C5#186511yescharacteristic, complemented, Hall
394C22×C3—51no—
395C22×C3—51no—
396C22×C3—51no—
397C22×C3—51no—
398C22×C3—51no—
399C22×C3—51no—
400C22×C3D4×AGL(1,𝔽5)11yescharacteristic
401C3×C4—22no—
402C3×C4—41no—
403C3×C4—51no—
404C3×C4—51no—
405C3×C4—102no—
406C3×C4—102no—
407C3×C4—201no—
408C3×C4—202no—
409C3×C4—201no—
410C3×C4—401no—
411C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
412C3×C4D4×AGL(1,𝔽5)11yescharacteristic
413C2×C5C3×#38511yescharacteristic
414C2×C5C3×C4×SD1611yescharacteristic
415C2×C5C3×#44111yescharacteristic
416D5C3×#44811yescharacteristic
417D5C3×#45211yescharacteristic
418D5C3×#47511yescharacteristic
419D5C3×#47911yescharacteristic
420C23—51no—
421Q8—21no—
422Q8—52no—
423Q8—102no—
424Q8—102no—
425Q8—101no—
426Q8C3×C4⋊AGL(1,𝔽5)12yescomplemented
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—51no—
430C2×C4—51no—
431C2×C4—51no—
432C2×C4—51no—
433C2×C4—51no—
434C2×C4—52no—
435C2×C4—102no—
436C2×C4—102no—
437C2×C4—101no—
438C2×C4—101no—
439C2×C4—101no—
440C2×C4—102no—
441C2×C4—101no—
442C2×C4—101no—
443C2×C4—101no—
444C2×C4—101no—
445C2×C4—201no—
446C2×C4—201no—
447C2×C4—201no—
448C2×C4—201no—
449C2×C4—201no—
450C2×C4—201no—
451C2×C4—201no—
452C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
453C8—21no—
454C8—101no—
455C8—201no—
456C2×C3—51no—
457C2×C3—51no—
458C2×C3—51no—
459C2×C3—51no—
460C2×C3#6569911yescharacteristic
461C2×C3SD16×AGL(1,𝔽5)11yescharacteristic
462C2×C3#6573911yescharacteristic
463C5C3×#186511yescharacteristic, complemented, Sylow
464C22—51no—
465C22—51no—
466C22—51no—
467C22—51no—
468C22—51no—
469C22—51no—
470C22C3×D4×AGL(1,𝔽5)11yescharacteristic
471C4—22no—
472C4—41no—
473C4—51no—
474C4—51no—
475C4—102no—
476C4—102no—
477C4—201no—
478C4—202no—
479C4—201no—
480C4—401no—
481C4C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
482C4C3×D4×AGL(1,𝔽5)11yescharacteristic
483C3#1060399011yescharacteristic, direct product factor, Sylow
484C2—51no—
485C2—51no—
486C2—51no—
487C2—51no—
488C2C3×#6569911yescharacteristic
489C2C3×SD16×AGL(1,𝔽5)11yescharacteristic
490C2C3×#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×#1865
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. #10603990C3direct (N × H)
24. C3×C5×#103C4semidirect
25. C3×#3967C4semidirect
26. C3×#3948C4semidirect
27. C3×#3942C4semidirect
91. C5×#103C3×C4semidirect
92. #3967C3×C4semidirect
93. #3948C3×C4semidirect
94. #3942C3×C4semidirect
110. C3×C5×Q8C4⋊C4semidirect
128. C3×Dic10C4⋊C4semidirect
149. C3×#103AGL(1,𝔽5)semidirect
257. C5×Q8C3×C4⋊C4semidirect
275. Dic10C3×C4⋊C4semidirect
296. #103C3×AGL(1,𝔽5)semidirect
311. C3×Q8C4⋊AGL(1,𝔽5)semidirect
393. C3×C5#1865semidirect
426. Q8C3×C4⋊AGL(1,𝔽5)semidirect
463. C5C3×#1865semidirect
483. C3#10603990direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×Q8×AGL(1,𝔽5)2
C2×C3×#40092
C2×C3×#39932
C3×#657122
C3×D5×#1032
C3×(C2×AGL(1,𝔽5))⋊C82
C3×#648742
#106039903
C3×#18655