Finite Group Databasebeta

← C3×#10600504 #14288321

Subgroups — C3×#10600504 #14288321

Order 1920.

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

normal subgroups only

This group has 432 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×#65849C211yesmaximal, characteristic
2C3×C5×#398C211yesmaximal, characteristic, complemented
3C3×#65260C211yesmaximal, characteristic, complemented
4C3×#65256C211yesmaximal, characteristic
5C3×#64748C211yesmaximal, characteristic, complemented
6C3×#64672C211yesmaximal, characteristic, complemented
7C3×#64671C211yesmaximal, characteristic
8#10600504C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×C4⋊C4—21no—
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C3×#4076C2211yescharacteristic
13C3×#4075—21no—
14C3×C4×C22⋊D5—21no—
15C3×#4070C2211yescharacteristic
16C3×#4044—21no—
17C3×#4042—21no—
18C3×#4040—21no—
19C3×#4035—21no—
20C3×C5×#95—21no—
21C3×C5×#95C2211yescharacteristic
22C3×C22⋊#168C2211yescharacteristic
23C3×C22⋊#168C2211yescharacteristic
24C3×#3942—21no—
25C3×#3941—21no—
26C3×#3940—21no—
27C3×#3939—21no—
28C3×#1609—51nomaximal, Hall
29#65849C2×C311yescharacteristic
30C5×#398C2×C311yescharacteristic, complemented
31#65260C2×C311yescharacteristic, complemented
32#65256C2×C311yescharacteristic
33#64748C2×C311yescharacteristic, complemented
34#64672C2×C311yescharacteristic, complemented
35#64671C2×C311yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C2×C3×C22⋊D5—21no—
42C2×C3×D20D411yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×Dic10D411yescharacteristic
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—42no—
50C3×C22⋊Dic5—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×C4⋊Dic5D411yescharacteristic
57C3×#683—21no—
58C3×#683—21no—
59C3×#683—21no—
60C3×#683—21no—
61C3×C4×Dic5—21no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C3×#539—51no—
65C3×#483—51no—
66C3×#480—51no—
67C3×#398D511yescharacteristic, complemented
68C3×#328—51no—
69C3×#327—51no—
70C3×#324—51no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4C22×C311yescharacteristic
73C2×C5×C4⋊C4C22×C311yescharacteristic
74#4076C22×C311yescharacteristic
75#4075—21no—
76C4×C22⋊D5—21no—
77#4070C22×C311yescharacteristic
78#4044—21no—
79#4042—21no—
80#4040—21no—
81#4035—21no—
82C5×#95—21no—
83C5×#95C22×C311yescharacteristic
84C22⋊#168C22×C311yescharacteristic
85C22⋊#168C22×C311yescharacteristic
86#3942—21no—
87#3941—21no—
88#3940—21no—
89#3939—21no—
90#1609—51noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C3×D5—21no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C3×C22⋊D5—41no—
108C3×C22⋊D5—41no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C3×D20—41no—
113C3×C4×D5—81no—
114C3×Dic10—41no—
115C3×#168—41no—
116C3×#168—41no—
117C3×#126—101no—
118C3×#125—101no—
119C3×#123—101no—
120C3×#123—101no—
121C3×C22⋊Q8—51no—
122C3×C22⋊Q8—101no—
123C3×#121—51no—
124C3×C4×D4—101no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4C2×D511yescharacteristic
127C2×C3×C4⋊C4C2×D511yescharacteristic
128C3×#107—101no—
129C3×#106—101no—
130C3×#103—101no—
131C3×#102—101no—
132C3×C22⋊C8—51no—
133C3×C22⋊C8—51no—
134C3×#95—21no—
135C3×#95C2×D511yescharacteristic
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5C3×D411yescharacteristic
139C22×C4×C5C3×D411yescharacteristic
140C22×C4×C5C23×C311yescharacteristic
141C2×C22⋊D5—21no—
142C2×D20C3×D411yescharacteristic
143C2×C4×D5—21no—
144C2×Dic10C3×D411yescharacteristic
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—42no—
150C22⋊Dic5—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154#685—21no—
155C4⋊Dic5C3×D411yescharacteristic
156C4⋊Dic5C3×D411yescharacteristic
157#683—21no—
158#683—21no—
159#683—21no—
160#683—21no—
161C4×Dic5—21no—
162C2×#168—21no—
163C2×#168—21no—
164#539—51no—
165#483—51no—
166#480—51no—
167#398C3×D511yescharacteristic, complemented
168#328—51no—
169#327—51no—
170#324—51no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5#12011yescharacteristic
174C22×C3×C5#13511yescharacteristic
175C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
176C2×C3×D5—41no—
177C2×C3×D5—41no—
178C2×C3×D5—41no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—42no—
182C3×C4×C5—41no—
183C3×C4×C5—41no—
184C3×C4×C5—81no—
185C3×Dic5—41no—
186C3×Dic5—41no—
187C3×Dic5—41no—
188C2×C3×Q8—51no—
189C2×C3×D4—51no—
190C2×C3×D4—101no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—101no—
194C22×C3×C4C22⋊D511yescharacteristic
195C22×C3×C4C22⋊D511yescharacteristic
196C22×C3×C4C22×D511yescharacteristic
197C2×C3×C8—101no—
198C2×C3×C8—101no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—42no—
204C3×C4⋊C4—51no—
205C3×C4⋊C4—51no—
206C3×C4⋊C4—101no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C22⋊C4—101no—
215C3×C42—101no—
216C23×C5C2×C3×D411yescharacteristic
217C22×D5—21no—
218C2×C4×C5—22no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5—21no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5C2×C3×D411yescharacteristic
231C2×C4×C5C2×C3×D411yescharacteristic
232C22⋊D5—41no—
233C22⋊D5—41no—
234C2×Dic5—21no—
235C2×Dic5—21no—
236C2×Dic5—21no—
237D20—41no—
238C4×D5—81no—
239Dic10—41no—
240#168—41no—
241#168—41no—
242#126—101no—
243#125—101no—
244#123—101no—
245#123—101no—
246C22⋊Q8—51no—
247C22⋊Q8—101no—
248#121—51no—
249C4×D4—101no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C2×C3×D511yescharacteristic
252C2×C4⋊C4C2×C3×D511yescharacteristic
253#107—101no—
254#106—101no—
255#103—101no—
256#102—101no—
257C22⋊C8—51no—
258C22⋊C8—51no—
259#95—21no—
260#95C2×C3×D511yescharacteristic
261C2×C3×C5—21no—
262C2×C3×C5—21no—
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45611yescharacteristic
265C2×C3×C5#45811yescharacteristic
266C3×D5—81no—
267C23×C3—101no—
268C23×C3C2×C22⋊D511yescharacteristic
269C3×Q8—201no—
270C3×D4—201no—
271C3×D4—201no—
272C3×D4—201no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—101no—
286C2×C3×C4—101no—
287C2×C3×C4—101no—
288C2×C3×C4—401no—
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C3×C8—201no—
292C3×C8—201no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5C3×#12011yescharacteristic
296C22×C5C3×#13511yescharacteristic
297C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
298C2×D5—41no—
299C2×D5—41no—
300C2×D5—41no—
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—42no—
304C4×C5—41no—
305C4×C5—41no—
306C4×C5—81no—
307Dic5—41no—
308Dic5—41no—
309Dic5—41no—
310C2×Q8—51no—
311C2×D4—51no—
312C2×D4—101no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—101no—
316C22×C4C3×C22⋊D511yescharacteristic
317C22×C4C3×C22⋊D511yescharacteristic
318C22×C4C22×C3×D511yescharacteristic
319C2×C8—101no—
320C2×C8—101no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—42no—
326C4⋊C4—51no—
327C4⋊C4—51no—
328C4⋊C4—101no—
329C4⋊C4—101no—
330C4⋊C4—101no—
331C4⋊C4—101no—
332C22⋊C4—101no—
333C22⋊C4—101no—
334C22⋊C4—101no—
335C22⋊C4—101no—
336C22⋊C4—101no—
337C42—101no—
338C3×C5#160911yescharacteristic, complemented, Hall
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—201no—
342C22×C3—201no—
343C22×C3—201no—
344C22×C3#407811yescharacteristic
345C22×C3#408311yescharacteristic
346C22×C3#409611yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—42no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—81no—
353C3×C4—201no—
354C3×C4—201no—
355C3×C4—201no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5C3×#44911yescharacteristic
359C2×C5C3×#45611yescharacteristic
360C2×C5C3×#45811yescharacteristic
361D5—81no—
362C23—101no—
363C23C2×C3×C22⋊D511yescharacteristic
364Q8—201no—
365D4—201no—
366D4—201no—
367D4—201no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—401no—
384C2×C4C3×D4×D511yescharacteristic
385C2×C4C3×D4×D511yescharacteristic
386C8—201no—
387C8—201no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—401no—
391C2×C3#6532611yescharacteristic
392C2×C3#6534211yescharacteristic
393C2×C3#6538411yescharacteristic
394C5C3×#160911yescharacteristic, complemented, Sylow
395C22—21no—
396C22—21no—
397C22—201no—
398C22—201no—
399C22—201no—
400C22C3×#407811yescharacteristic
401C22C3×#408311yescharacteristic
402C22C3×#409611yescharacteristic
403C4—21no—
404C4—21no—
405C4—42no—
406C4—41no—
407C4—41no—
408C4—81no—
409C4—201no—
410C4—201no—
411C4—201no—
412C3#1060050411yescharacteristic, direct product factor, Sylow
413C2—21no—
414C2—21no—
415C2—401no—
416C2C3×#6532611yescharacteristic
417C2C3×#6534211yescharacteristic
418C2C3×#6538411yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#398C2
socleC22×C3×C5#120
prime radicalC3×#4076C22
hypercenterC3×#398D5
hypocenterC5C3×#1609
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#398

Complements

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

NH ≅ G/Ntype
2. C3×C5×#398C2semidirect
3. C3×#65260C2semidirect
5. C3×#64748C2semidirect
6. C3×#64672C2semidirect
8. #10600504C3direct (N × H)
30. C5×#398C2×C3semidirect
31. #65260C2×C3semidirect
33. #64748C2×C3semidirect
34. #64672C2×C3semidirect
67. C3×#398D5semidirect
167. #398C3×D5semidirect
338. C3×C5#1609semidirect
394. C5C3×#1609semidirect
412. C3#10600504direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658492
C3×C5×#3982
C3×#652602
C3×#652562
C3×#647482
C3×#646722
C3×#646712
#106005043
C3×#16095