Finite Group Databasebeta

← C3×#10604535 #14301714

Subgroups — C3×#10604535 #14301714

Order 1920.

684 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66256C211yesmaximal, characteristic, complemented
2C3×#65990C211yesmaximal, characteristic
3C3×#65777C211yesmaximal, characteristic, complemented
4C3×#65755C212yesmaximal, complemented
5C3×#64867C212yesmaximal, complemented
6#10604535C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#711C2211yescharacteristic
8C22×C3×C4×D5C2211yescharacteristic
9C2×C3×#704—21no—
10C2×C3×#704C2212yes—
11C2×C3×#704C2212yes—
12C3×#4131—24no—
13C3×D5⋊M16—21no—
14C3×C5×#123C411yescharacteristic
15C3×#4083C411yescharacteristic
16C3×#4075C411yescharacteristic
17C3×#4042—21no—
18C3×#4039—21no—
19C3×#4030—21no—
20C3×#4028C411yescharacteristic
21C3×#4027—21no—
22C3×#4023C2211yescharacteristic
23C3×#4013—21no—
24C3×#4005—21no—
25C3×#4003—24no—
26C3×#1891—51nomaximal, Hall
27#66256C2×C311yescharacteristic, complemented
28#65990C2×C311yescharacteristic
29#65777C2×C311yescharacteristic, complemented
30#65755C2×C312yescomplemented
31#64867C2×C312yescomplemented
32C23×C3×D5C2×C411yescharacteristic
33C2×C3×C5×D4C2×C411yescharacteristic
34C22×C3×C4×C5C2×C411yescharacteristic
35C2×C3×C22⋊D5—21no—
36C2×C3×C22⋊D5C2×C411yescharacteristic
37C2×C3×C22⋊D5D411yescharacteristic
38C22×C3×Dic5D411yescharacteristic
39C22×C3×Dic5C2311yescharacteristic
40C3×#711—22no—
41C3×#711—22no—
42C2×C3×D20—21no—
43C2×C3×C4×D5—22no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5—22no—
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×Dic10D411yescharacteristic
49C3×#704—22no—
50C3×#704—22no—
51C3×#704—22no—
52C3×#704—22no—
53C3×#704—22no—
54C2×C3×#170—22no—
55C2×C3×#170—22no—
56C2×C3×#170D414yescomplemented
57C3×#700—22no—
58C3×D5⋊C8—22no—
59C3×C5×C4⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4C2×C411yescharacteristic
62C3×C22⋊Dic5C2×C411yescharacteristic
63C3×#685—21no—
64C3×#685—21no—
65C3×#685—21no—
66C3×#683—21no—
67C3×#683—21no—
68C3×C4×Dic5—21no—
69C3×#568—51no—
70C3×#525—51no—
71C3×#413—51no—
72C3×#407—52no—
73C3×#344—52no—
74C2×#711C22×C311yescharacteristic
75C22×C4×D5C22×C311yescharacteristic
76C2×#704—21no—
77C2×#704C22×C312yes—
78C2×#704C22×C312yes—
79#4131—24no—
80D5⋊M16—21no—
81C5×#123C3×C411yescharacteristic
82#4083C3×C411yescharacteristic
83#4075C3×C411yescharacteristic
84#4042—21no—
85#4039—21no—
86#4030—21no—
87#4028C3×C411yescharacteristic
88#4027—21no—
89#4023C22×C311yescharacteristic
90#4013—21no—
91#4005—21no—
92#4003—24no—
93#1891—51noSylow
94C23×C3×C5C22⋊C411yescharacteristic
95C23×C3×C5C22×C411yescharacteristic
96C22×C3×D5—21no—
97C22×C3×D5—22no—
98C22×C3×D5—42no—
99C22×C3×D5C22⋊C411yescharacteristic
100C3×C5×D4—22no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5C22⋊C411yescharacteristic
105C3×C22⋊D5—22no—
106C3×C22⋊D5—22no—
107C3×C22⋊D5—42no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5C22⋊C411yescharacteristic
112C2×C3×Dic5C2×D412yes—
113C2×C3×Dic5C2×D411yescharacteristic
114C2×C3×Dic5C2×D411yescharacteristic
115C2×C3×Dic5#4112yes—
116C3×D20—42no—
117C3×C4×D5—21no—
118C3×C4×D5—21no—
119C3×C4×D5—41no—
120C3×C4×D5—42no—
121C3×C4×D5—41no—
122C3×Dic10—22no—
123C3×#170—24no—
124C3×#170—42no—
125C2×C3×#41—51no—
126C23×C3×C4—51no—
127C3×#131—104no—
128C2×C3×M16—52no—
129C2×C3×M16—52no—
130C2×C3×M16—101no—
131C2×C3×M16—101no—
132C3×#123—51no—
133C3×#123AGL(1,𝔽5)11yescharacteristic
134C3×C22⋊Q8—101no—
135C3×#121—101no—
136C3×#120—51no—
137C3×#120—51no—
138C3×C4×D4—101no—
139C3×C4×D4—101no—
140C3×#117—51no—
141C3×#101—101no—
142C3×#100—101no—
143C3×C22⋊C8—104no—
144C23×D5C2×C3×C411yescharacteristic
145C2×C5×D4C2×C3×C411yescharacteristic
146C22×C4×C5C2×C3×C411yescharacteristic
147C2×C22⋊D5—21no—
148C2×C22⋊D5C2×C3×C411yescharacteristic
149C2×C22⋊D5C3×D411yescharacteristic
150C22×Dic5C3×D411yescharacteristic
151C22×Dic5C23×C311yescharacteristic
152#711—22no—
153#711—22no—
154C2×D20—21no—
155C2×C4×D5—22no—
156C2×C4×D5—21no—
157C2×C4×D5—21no—
158C2×C4×D5—22no—
159C2×C4×D5C3×D411yescharacteristic
160C2×Dic10C3×D411yescharacteristic
161#704—22no—
162#704—22no—
163#704—22no—
164#704—22no—
165#704—22no—
166C2×#170—22no—
167C2×#170—22no—
168C2×#170C3×D414yescomplemented
169#700—22no—
170D5⋊C8—22no—
171C5×C4⋊C4—21no—
172C5×C22⋊C4—21no—
173C5×C22⋊C4C2×C3×C411yescharacteristic
174C22⋊Dic5C2×C3×C411yescharacteristic
175#685—21no—
176#685—21no—
177#685—21no—
178#683—21no—
179#683—21no—
180C4×Dic5—21no—
181#568—51no—
182#525—51no—
183#413—51no—
184#407—52no—
185#344—52no—
186C22×C3×C5—21no—
187C22×C3×C5—41no—
188C22×C3×C5—41no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5C4×D412yes—
191C2×C3×D5—22no—
192C2×C3×D5—24no—
193C2×C3×D5—21no—
194C2×C3×D5—41no—
195C2×C3×D5—42no—
196C2×C3×D5—41no—
197C2×C3×D5—41no—
198C3×C4×C5—21no—
199C3×C4×C5—41no—
200C3×C4×C5—41no—
201C3×Dic5—21no—
202C3×Dic5—41no—
203C3×Dic5#12011yescharacteristic
204C3×Dic5#12112yes—
205C3×Dic5#12311yescharacteristic
206C24×C3—51no—
207C3×#41—102no—
208C3×#41—102no—
209C2×C3×Q8—51no—
210C2×C3×D4—51no—
211C2×C3×D4—51no—
212C2×C3×D4—101no—
213C2×C3×D4—101no—
214C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
215C22×C3×C4—51no—
216C22×C3×C4—51no—
217C22×C3×C4—51no—
218C22×C3×C4—102no—
219C22×C3×C4—101no—
220C22×C3×C4—101no—
221C22×C3×C4—102no—
222C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
223C3×M16—102no—
224C3×M16—102no—
225C3×M16—102no—
226C3×M16—102no—
227C3×M16—102no—
228C3×M16—102no—
229C2×C3×C8—54no—
230C2×C3×C8—102no—
231C2×C3×C8—102no—
232C2×C3×C8—102no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—101no—
235C3×C4⋊C4—101no—
236C3×C22⋊C4—21no—
237C3×C22⋊C4—51no—
238C3×C22⋊C4—101no—
239C3×C22⋊C4—101no—
240C3×C22⋊C4—101no—
241C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
242C3×C42—101no—
243C23×C5C3×C22⋊C411yescharacteristic
244C23×C5C22×C3×C411yescharacteristic
245C22×D5—21no—
246C22×D5—22no—
247C22×D5—42no—
248C22×D5C3×C22⋊C411yescharacteristic
249C5×D4—22no—
250C2×C4×C5—21no—
251C2×C4×C5—21no—
252C2×C4×C5—22no—
253C2×C4×C5C3×C22⋊C411yescharacteristic
254C22⋊D5—22no—
255C22⋊D5—22no—
256C22⋊D5—42no—
257C2×Dic5—21no—
258C2×Dic5—21no—
259C2×Dic5—21no—
260C2×Dic5C3×C22⋊C411yescharacteristic
261C2×Dic5C2×C3×D412yes—
262C2×Dic5C2×C3×D411yescharacteristic
263C2×Dic5C2×C3×D411yescharacteristic
264C2×Dic5C3×#4112yes—
265D20—42no—
266C4×D5—21no—
267C4×D5—21no—
268C4×D5—41no—
269C4×D5—42no—
270C4×D5—41no—
271Dic10—22no—
272#170—24no—
273#170—42no—
274C2×#41—51no—
275C23×C4—51no—
276#131—104no—
277C2×M16—52no—
278C2×M16—52no—
279C2×M16—101no—
280C2×M16—101no—
281#123—51no—
282#123C3×AGL(1,𝔽5)11yescharacteristic
283C22⋊Q8—101no—
284#121—101no—
285#120—51no—
286#120—51no—
287C4×D4—101no—
288C4×D4—101no—
289#117—51no—
290#101—101no—
291#100—101no—
292C22⋊C8—104no—
293C2×C3×C5—21no—
294C2×C3×C5—22no—
295C2×C3×C5—41no—
296C2×C3×C5#38611yescharacteristic
297C3×D5—42no—
298C3×D5—41no—
299C23×C3—51no—
300C23×C3—102no—
301C23×C3—101no—
302C23×C3—202no—
303C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
304C23×C3C22×AGL(1,𝔽5)11yescharacteristic
305C3×Q8—102no—
306C3×D4—22no—
307C3×D4—102no—
308C3×D4—102no—
309C3×D4—202no—
310C3×D4—202no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—52no—
315C2×C3×C4—52no—
316C2×C3×C4—51no—
317C2×C3×C4—51no—
318C2×C3×C4—51no—
319C2×C3×C4—101no—
320C2×C3×C4—101no—
321C2×C3×C4—101no—
322C2×C3×C4—101no—
323C2×C3×C4—101no—
324C2×C3×C4—201no—
325C2×C3×C4—202no—
326C2×C3×C4—201no—
327C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
328C3×C8—104no—
329C3×C8—202no—
330C22×C5—21no—
331C22×C5—41no—
332C22×C5—41no—
333C22×C5C2×C3×C22⋊C411yescharacteristic
334C22×C5C3×C4×D412yes—
335C2×D5—22no—
336C2×D5—24no—
337C2×D5—21no—
338C2×D5—41no—
339C2×D5—42no—
340C2×D5—41no—
341C2×D5—41no—
342C4×C5—21no—
343C4×C5—41no—
344C4×C5—41no—
345Dic5—21no—
346Dic5—41no—
347Dic5C3×#12011yescharacteristic
348Dic5C3×#12112yes—
349Dic5C3×#12311yescharacteristic
350C24—51no—
351#41—102no—
352#41—102no—
353C2×Q8—51no—
354C2×D4—51no—
355C2×D4—51no—
356C2×D4—101no—
357C2×D4—101no—
358C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
359C22×C4—51no—
360C22×C4—51no—
361C22×C4—51no—
362C22×C4—102no—
363C22×C4—101no—
364C22×C4—101no—
365C22×C4—102no—
366C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
367M16—102no—
368M16—102no—
369M16—102no—
370M16—102no—
371M16—102no—
372M16—102no—
373C2×C8—54no—
374C2×C8—102no—
375C2×C8—102no—
376C2×C8—102no—
377C4⋊C4—21no—
378C4⋊C4—101no—
379C4⋊C4—101no—
380C22⋊C4—21no—
381C22⋊C4—51no—
382C22⋊C4—101no—
383C22⋊C4—101no—
384C22⋊C4—101no—
385C22⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
386C42—101no—
387C3×C5#189111yescharacteristic, complemented, Hall
388C22×C3—21no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—102no—
392C22×C3—104no—
393C22×C3—101no—
394C22×C3—201no—
395C22×C3—201no—
396C22×C3—202no—
397C22×C3—201no—
398C22×C3D4×AGL(1,𝔽5)12yes—
399C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
400C3×C4—21no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—51no—
404C3×C4—52no—
405C3×C4—51no—
406C3×C4—101no—
407C3×C4—201no—
408C2×C5—21no—
409C2×C5—22no—
410C2×C5—41no—
411C2×C5C3×#38611yescharacteristic
412D5—42no—
413D5—41no—
414C23—51no—
415C23—102no—
416C23—101no—
417C23—202no—
418C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
419C23C22×C3×AGL(1,𝔽5)11yescharacteristic
420Q8—102no—
421D4—22no—
422D4—102no—
423D4—102no—
424D4—202no—
425D4—202no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—52no—
430C2×C4—52no—
431C2×C4—51no—
432C2×C4—51no—
433C2×C4—51no—
434C2×C4—101no—
435C2×C4—101no—
436C2×C4—101no—
437C2×C4—101no—
438C2×C4—101no—
439C2×C4—201no—
440C2×C4—202no—
441C2×C4—201no—
442C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
443C8—104no—
444C8—202no—
445C2×C3—21no—
446C2×C3—22no—
447C2×C3—41no—
448C2×C3—202no—
449C2×C3—201no—
450C2×C3#6577911yescharacteristic
451C5C3×#189111yescharacteristic, complemented, Sylow
452C22—21no—
453C22—41no—
454C22—41no—
455C22—102no—
456C22—104no—
457C22—101no—
458C22—201no—
459C22—201no—
460C22—202no—
461C22—201no—
462C22C3×D4×AGL(1,𝔽5)12yes—
463C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
464C4—21no—
465C4—41no—
466C4—41no—
467C4—51no—
468C4—52no—
469C4—51no—
470C4—101no—
471C4—201no—
472C3#1060453511yescharacteristic, direct product factor, Sylow
473C2—21no—
474C2—22no—
475C2—41no—
476C2—202no—
477C2—201no—
478C2C3×#6577911yescharacteristic
subgroupG/H
centerC2×C3#65779
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#123C4
socleC2×C3×C5#386
prime radicalC3×#65990C2
cosocleC22×Dic5C23×C3
hypercenterC3×#123AGL(1,𝔽5)
hypocenterC5C3×#1891
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#123

Complements

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

NH ≅ G/Ntype
1. C3×#66256C2semidirect
3. C3×#65777C2semidirect
4. C3×#65755C2semidirect
5. C3×#64867C2semidirect
6. #10604535C3direct (N × H)
27. #66256C2×C3semidirect
29. #65777C2×C3semidirect
30. #65755C2×C3semidirect
31. #64867C2×C3semidirect
56. C2×C3×#170D4semidirect
168. C2×#170C3×D4semidirect
387. C3×C5#1891semidirect
451. C5C3×#1891semidirect
472. C3#10604535direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#662562
C3×#659902
C3×#657772
C3×#657552
C3×#648672
#106045353
C3×#18915