Finite Group Databasebeta

← C3×#10599080 #14288189

Subgroups — C3×#10599080 #14288189

Order 1920.

520 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65951C211yesmaximal, characteristic
2C3×#65329C211yesmaximal, characteristic, complemented
3C3×#65028C211yesmaximal, characteristic, complemented
4C3×#64962C211yesmaximal, characteristic, complemented
5C3×C5×#327C211yesmaximal, characteristic, complemented
6C3×#64688C211yesmaximal, characteristic, complemented
7C3×#64672C211yesmaximal, characteristic, complemented
8#10599080C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×Dic10C2211yescharacteristic
10C3×C5×#121C2211yescharacteristic
11C3×#4085—21no—
12C3×#4083—21no—
13C3×D4×Dic5—21no—
14C2×C3×#687—21no—
15C2×C3×#685—21no—
16C2×C3×#685C2211yescharacteristic
17C3×#4070C2211yescharacteristic
18C2×C3×Dic20—21no—
19C3×#4044—21no—
20C3×#4032—21no—
21C3×#4031—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×#95C2211yescharacteristic
24C3×#3963—21no—
25C3×C22⋊#168C2211yescharacteristic
26C3×#3948—21no—
27C3×#3942—21no—
28C3×#1606—51nomaximal, Hall
29#65951C2×C311yescharacteristic
30#65329C2×C311yescharacteristic, complemented
31#65028C2×C311yescharacteristic, complemented
32#64962C2×C311yescharacteristic, complemented
33C5×#327C2×C311yescharacteristic, complemented
34#64688C2×C311yescharacteristic, complemented
35#64672C2×C311yescharacteristic, complemented
36C23×C3×D5D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5C2311yescharacteristic
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5—21no—
43C22×C3×Dic5—21no—
44C22×C3×Dic5—21no—
45C22×C3×Dic5D411yescharacteristic
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—42no—
49C2×C3×Dic10D411yescharacteristic
50C2×C3×C5×C8—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C5×C22⋊C4—21no—
53C3×C22⋊Dic5—21no—
54C3×C22⋊Dic5—21no—
55C3×#687—42no—
56C3×#685—21no—
57C3×#685—21no—
58C3×#685—21no—
59C3×#685—21no—
60C3×#685—42no—
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5D411yescharacteristic
63C3×#683—21no—
64C3×C4×Dic5—21no—
65C2×C3×#168—21no—
66C3×Dic20—42no—
67C3×#538—51no—
68C3×#451—51no—
69C3×#448—51no—
70C3×#393—51no—
71C3×#328—51no—
72C3×#327D511yescharacteristic, complemented
73C3×#323—51no—
74C22×Dic10C22×C311yescharacteristic
75C5×#121C22×C311yescharacteristic
76#4085—21no—
77#4083—21no—
78D4×Dic5—21no—
79C2×#687—21no—
80C2×#685—21no—
81C2×#685C22×C311yescharacteristic
82#4070C22×C311yescharacteristic
83C2×Dic20—21no—
84#4044—21no—
85#4032—21no—
86#4031—21no—
87C5×C22⋊C8C22×C311yescharacteristic
88C5×#95C22×C311yescharacteristic
89#3963—21no—
90C22⋊#168C22×C311yescharacteristic
91#3948—21no—
92#3942—21no—
93#1606—51noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C22×C3×D5—21no—
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5—41no—
100C22×C3×D5—41no—
101C3×C5×D4—41no—
102C3×C5×D4—41no—
103C3×C5×D4—41no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C3×C22⋊D5—81no—
112C3×C22⋊D5—81no—
113C2×C3×Dic5—22no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—81no—
121C3×Dic10—22no—
122C3×Dic10—22no—
123C3×Dic10—41no—
124C3×Dic10—41no—
125C3×Dic10—41no—
126C3×C5×C8—41no—
127C3×#168—41no—
128C22×C3×Q8—51no—
129C2×C3×Q16—101no—
130C2×C3×SD16—101no—
131C3×#126—101no—
132C3×#124—101no—
133C3×#123—101no—
134C3×C22⋊Q8—51no—
135C3×#121—101no—
136C3×#121C2×D511yescharacteristic
137C3×#120—101no—
138C3×C4×D4—101no—
139C2×C3×C22⋊C4—51no—
140C2×C3×C22⋊C4—101no—
141C3×#103—101no—
142C3×#103—101no—
143C3×C22⋊C8—51no—
144C3×C22⋊C8C2×D511yescharacteristic
145C3×#95—101no—
146C3×#95C2×D511yescharacteristic
147C23×D5C3×D411yescharacteristic
148C2×C5×D4—21no—
149C2×C5×D4C3×D411yescharacteristic
150C22×C4×C5—21no—
151C22×C4×C5C23×C311yescharacteristic
152C2×C22⋊D5—21no—
153C2×C22⋊D5—21no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5C3×D411yescharacteristic
157C2×Dic10—21no—
158C2×Dic10—21no—
159C2×Dic10—42no—
160C2×Dic10C3×D411yescharacteristic
161C2×C5×C8—21no—
162C5×C4⋊C4C3×D411yescharacteristic
163C5×C22⋊C4—21no—
164C22⋊Dic5—21no—
165C22⋊Dic5—21no—
166#687—42no—
167#685—21no—
168#685—21no—
169#685—21no—
170#685—21no—
171#685—42no—
172C4⋊Dic5—21no—
173C4⋊Dic5C3×D411yescharacteristic
174#683—21no—
175C4×Dic5—21no—
176C2×#168—21no—
177Dic20—42no—
178#538—51no—
179#451—51no—
180#448—51no—
181#393—51no—
182#328—51no—
183#327C3×D511yescharacteristic, complemented
184#323—51no—
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5—41no—
188C22×C3×C5—41no—
189C22×C3×C5—41no—
190C22×C3×C5#12011yescharacteristic
191C22×C3×C5#13511yescharacteristic
192C22×C3×C5#13711yescharacteristic
193C2×C3×D5—42no—
194C2×C3×D5—41no—
195C2×C3×D5—41no—
196C2×C3×D5—41no—
197C2×C3×D5—81no—
198C3×C4×C5—21no—
199C3×C4×C5—21no—
200C3×C4×C5—41no—
201C3×C4×C5—81no—
202C3×Dic5—41no—
203C3×Dic5—41no—
204C3×Dic5—42no—
205C3×Dic5—41no—
206C24×C3—51no—
207C2×C3×Q8—51no—
208C2×C3×Q8—101no—
209C2×C3×Q8—101no—
210C2×C3×Q8—202no—
211C2×C3×D4—21no—
212C2×C3×D4—101no—
213C2×C3×D4—101no—
214C2×C3×D4D2011yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—51no—
217C22×C3×C4—101no—
218C22×C3×C4—101no—
219C22×C3×C4C22×D511yescharacteristic
220C3×Q16—202no—
221C3×SD16—202no—
222C2×C3×C8—21no—
223C2×C3×C8—101no—
224C3×C4⋊C4—51no—
225C3×C4⋊C4—101no—
226C3×C4⋊C4—101no—
227C3×C4⋊C4D2011yescharacteristic
228C3×C22⋊C4—21no—
229C3×C22⋊C4—101no—
230C3×C22⋊C4—101no—
231C3×C22⋊C4—101no—
232C3×C22⋊C4—101no—
233C3×C22⋊C4—101no—
234C3×C22⋊C4—101no—
235C3×C22⋊C4—202no—
236C3×C42—101no—
237C23×C5—21no—
238C23×C5C2×C3×D411yescharacteristic
239C22×D5—21no—
240C22×D5—21no—
241C22×D5—21no—
242C22×D5—41no—
243C22×D5—41no—
244C5×D4—41no—
245C5×D4—41no—
246C5×D4—41no—
247C2×C4×C5—21no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5C2×C3×D411yescharacteristic
253C2×C4×C5C2×C3×D411yescharacteristic
254C22⋊D5—81no—
255C22⋊D5—81no—
256C2×Dic5—22no—
257C2×Dic5—21no—
258C2×Dic5—21no—
259C2×Dic5—21no—
260C2×Dic5—41no—
261C2×Dic5—41no—
262C2×Dic5—41no—
263C2×Dic5—81no—
264Dic10—22no—
265Dic10—22no—
266Dic10—41no—
267Dic10—41no—
268Dic10—41no—
269C5×C8—41no—
270#168—41no—
271C22×Q8—51no—
272C2×Q16—101no—
273C2×SD16—101no—
274#126—101no—
275#124—101no—
276#123—101no—
277C22⋊Q8—51no—
278#121—101no—
279#121C2×C3×D511yescharacteristic
280#120—101no—
281C4×D4—101no—
282C2×C22⋊C4—51no—
283C2×C22⋊C4—101no—
284#103—101no—
285#103—101no—
286C22⋊C8—51no—
287C22⋊C8C2×C3×D511yescharacteristic
288#95—101no—
289#95C2×C3×D511yescharacteristic
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—81no—
293C2×C3×C5#45211yescharacteristic
294C2×C3×C5#45511yescharacteristic
295C2×C3×C5B(4,𝔽2)11yescharacteristic
296C3×D5—81no—
297C23×C3—21no—
298C23×C3—101no—
299C23×C3—101no—
300C23×C3—101no—
301C23×C3—201no—
302C23×C3—201no—
303C23×C3D4×D511yescharacteristic
304C3×Q8—102no—
305C3×Q8—102no—
306C3×Q8—201no—
307C3×Q8—201no—
308C3×Q8—201no—
309C3×D4—41no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—401no—
313C3×D4—401no—
314C2×C3×C4—21no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—102no—
320C2×C3×C4—101no—
321C2×C3×C4—101no—
322C2×C3×C4—101no—
323C2×C3×C4—201no—
324C2×C3×C4—201no—
325C2×C3×C4—201no—
326C2×C3×C4—401no—
327C2×C3×C4C2×D2011yescharacteristic
328C2×C3×C4D4×D511yescharacteristic
329C3×C8—41no—
330C3×C8—201no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—41no—
334C22×C5—41no—
335C22×C5—41no—
336C22×C5C3×#12011yescharacteristic
337C22×C5C3×#13511yescharacteristic
338C22×C5C3×#13711yescharacteristic
339C2×D5—42no—
340C2×D5—41no—
341C2×D5—41no—
342C2×D5—41no—
343C2×D5—81no—
344C4×C5—21no—
345C4×C5—21no—
346C4×C5—41no—
347C4×C5—81no—
348Dic5—41no—
349Dic5—41no—
350Dic5—42no—
351Dic5—41no—
352C24—51no—
353C2×Q8—51no—
354C2×Q8—101no—
355C2×Q8—101no—
356C2×Q8—202no—
357C2×D4—21no—
358C2×D4—101no—
359C2×D4—101no—
360C2×D4C3×D2011yescharacteristic
361C22×C4—21no—
362C22×C4—51no—
363C22×C4—101no—
364C22×C4—101no—
365C22×C4C22×C3×D511yescharacteristic
366Q16—202no—
367SD16—202no—
368C2×C8—21no—
369C2×C8—101no—
370C4⋊C4—51no—
371C4⋊C4—101no—
372C4⋊C4—101no—
373C4⋊C4C3×D2011yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—101no—
376C22⋊C4—101no—
377C22⋊C4—101no—
378C22⋊C4—101no—
379C22⋊C4—101no—
380C22⋊C4—101no—
381C22⋊C4—202no—
382C42—101no—
383C3×C5#160611yescharacteristic, complemented, Hall
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—202no—
390C22×C3—201no—
391C22×C3—201no—
392C22×C3—201no—
393C22×C3—401no—
394C22×C3#402811yescharacteristic
395C22×C3#405811yescharacteristic
396C22×C3#406111yescharacteristic
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—41no—
400C3×C4—81no—
401C3×C4—202no—
402C3×C4—201no—
403C3×C4—201no—
404C3×C4—201no—
405C2×C5—21no—
406C2×C5—21no—
407C2×C5—81no—
408C2×C5C3×#45211yescharacteristic
409C2×C5C3×#45511yescharacteristic
410C2×C5C3×B(4,𝔽2)11yescharacteristic
411D5—81no—
412C23—21no—
413C23—101no—
414C23—101no—
415C23—101no—
416C23—201no—
417C23—201no—
418C23C3×D4×D511yescharacteristic
419Q8—102no—
420Q8—102no—
421Q8—201no—
422Q8—201no—
423Q8—201no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—401no—
428D4—401no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—102no—
435C2×C4—101no—
436C2×C4—101no—
437C2×C4—101no—
438C2×C4—201no—
439C2×C4—201no—
440C2×C4—201no—
441C2×C4—401no—
442C2×C4C2×C3×D2011yescharacteristic
443C2×C4C3×D4×D511yescharacteristic
444C8—41no—
445C8—201no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—81no—
449C2×C3—401no—
450C2×C3#6503011yescharacteristic
451C2×C3#6507211yescharacteristic
452C2×C3#6511411yescharacteristic
453C5C3×#160611yescharacteristic, complemented, Sylow
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—202no—
460C22—201no—
461C22—201no—
462C22—201no—
463C22—401no—
464C22C3×#402811yescharacteristic
465C22C3×#405811yescharacteristic
466C22C3×#406111yescharacteristic
467C4—21no—
468C4—21no—
469C4—41no—
470C4—81no—
471C4—202no—
472C4—201no—
473C4—201no—
474C4—201no—
475C3#1059908011yescharacteristic, direct product factor, Sylow
476C2—21no—
477C2—21no—
478C2—81no—
479C2—401no—
480C2C3×#6503011yescharacteristic
481C2C3×#6507211yescharacteristic
482C2C3×#6511411yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#327C2
socleC22×C3×C5#120
prime radicalC3×#65951C2
hypercenterC3×#327D5
hypocenterC5C3×#1606
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
2. C3×#65329C2semidirect
3. C3×#65028C2semidirect
4. C3×#64962C2semidirect
5. C3×C5×#327C2semidirect
6. C3×#64688C2semidirect
7. C3×#64672C2semidirect
8. #10599080C3direct (N × H)
30. #65329C2×C3semidirect
31. #65028C2×C3semidirect
32. #64962C2×C3semidirect
33. C5×#327C2×C3semidirect
34. #64688C2×C3semidirect
35. #64672C2×C3semidirect
72. C3×#327D5semidirect
183. #327C3×D5semidirect
383. C3×C5#1606semidirect
453. C5C3×#1606semidirect
475. C3#10599080direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659512
C3×#653292
C3×#650282
C3×#649622
C3×C5×#3272
C3×#646882
C3×#646722
#105990803
C3×#16065