Finite Group Databasebeta

← C3×#10600498 #14288039

Subgroups — C3×#10600498 #14288039

Order 1920.

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

normal subgroups only

This group has 488 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×#395C211yesmaximal, characteristic, complemented
3C3×#65517C211yesmaximal, characteristic, complemented
4C3×#65516C211yesmaximal, characteristic
5C3×#64748C211yesmaximal, characteristic, complemented
6C3×#64672C211yesmaximal, characteristic, complemented
7C3×#64671C211yesmaximal, characteristic
8#10600498C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×C4⋊C4—21no—
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×#689—21no—
13C2×C3×#688—21no—
14C3×#4076C2211yescharacteristic
15C3×#4075—21no—
16C3×C4×C22⋊D5—21no—
17C3×#4070C2211yescharacteristic
18C3×#4044—21no—
19C3×#4042—21no—
20C3×#4040—21no—
21C3×#4035—21no—
22C3×C5×#95—21no—
23C3×C5×#95C2211yescharacteristic
24C3×#3967—21no—
25C3×#3967—21no—
26C3×C22⋊#168C2211yescharacteristic
27C3×C22⋊#168C2211yescharacteristic
28C3×#1603—51nomaximal, Hall
29#65849C2×C311yescharacteristic
30C5×#395C2×C311yescharacteristic, complemented
31#65517C2×C311yescharacteristic, complemented
32#65516C2×C311yescharacteristic
33#64748C2×C311yescharacteristic, complemented
34#64672C2×C311yescharacteristic, complemented
35#64671C2×C311yescharacteristic
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—42no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5C2311yescharacteristic
44C2×C3×C22⋊D5—21no—
45C2×C3×D20D411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×Dic10D411yescharacteristic
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—42no—
51C3×C22⋊Dic5—21no—
52C3×#689—42no—
53C3×#688—42no—
54C3×#685—21no—
55C3×#685—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C3×C4⋊Dic5D411yescharacteristic
60C3×#683—21no—
61C3×#683—21no—
62C3×#683—21no—
63C3×#683—21no—
64C3×C4×Dic5—21no—
65C2×C3×#168—21no—
66C2×C3×#168—21no—
67C3×#539—51no—
68C3×#451—51no—
69C3×#448—51no—
70C3×#395D511yescharacteristic, complemented
71C3×#328—51no—
72C3×#327—51no—
73C3×#324—51no—
74C22×C5×Q8C22×C311yescharacteristic
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4C22×C311yescharacteristic
77C2×#689—21no—
78C2×#688—21no—
79#4076C22×C311yescharacteristic
80#4075—21no—
81C4×C22⋊D5—21no—
82#4070C22×C311yescharacteristic
83#4044—21no—
84#4042—21no—
85#4040—21no—
86#4035—21no—
87C5×#95—21no—
88C5×#95C22×C311yescharacteristic
89#3967—21no—
90#3967—21no—
91C22⋊#168C22×C311yescharacteristic
92C22⋊#168C22×C311yescharacteristic
93#1603—51noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—21no—
96C3×C5×Q8—22no—
97C3×C5×Q8—22no—
98C3×C5×Q8—41no—
99C3×C5×Q8—41no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—22no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C3×C22⋊D5—41no—
115C3×C22⋊D5—41no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—21no—
119C3×D20—41no—
120C3×C4×D5—81no—
121C3×Dic10—41no—
122C3×#168—41no—
123C3×#168—41no—
124C22×C3×Q8C2×D511yescharacteristic
125C2×C3×Q16—101no—
126C2×C3×SD16—101no—
127C3×#126—101no—
128C3×#125—101no—
129C3×#123—101no—
130C3×#123—101no—
131C3×C22⋊Q8—51no—
132C3×C22⋊Q8—101no—
133C3×#121—51no—
134C3×C4×D4—101no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4C2×D511yescharacteristic
137C3×#103—101no—
138C3×#103—101no—
139C3×C22⋊C8—51no—
140C3×C22⋊C8—51no—
141C3×#95—21no—
142C3×#95C2×D511yescharacteristic
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—42no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5C3×D411yescharacteristic
149C22×C4×C5C3×D411yescharacteristic
150C22×C4×C5C23×C311yescharacteristic
151C2×C22⋊D5—21no—
152C2×D20C3×D411yescharacteristic
153C2×C4×D5—21no—
154C2×Dic10C3×D411yescharacteristic
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—42no—
158C22⋊Dic5—21no—
159#689—42no—
160#688—42no—
161#685—21no—
162#685—21no—
163#685—21no—
164#685—21no—
165C4⋊Dic5C3×D411yescharacteristic
166C4⋊Dic5C3×D411yescharacteristic
167#683—21no—
168#683—21no—
169#683—21no—
170#683—21no—
171C4×Dic5—21no—
172C2×#168—21no—
173C2×#168—21no—
174#539—51no—
175#451—51no—
176#448—51no—
177#395C3×D511yescharacteristic, complemented
178#328—51no—
179#327—51no—
180#324—51no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5#12011yescharacteristic
184C22×C3×C5#13511yescharacteristic
185C22×C3×C5#13711yescharacteristic
186C2×C3×D5—41no—
187C2×C3×D5—41no—
188C2×C3×D5—41no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—42no—
192C3×C4×C5—41no—
193C3×C4×C5—41no—
194C3×C4×C5—42no—
195C3×Dic5—41no—
196C3×Dic5—41no—
197C3×Dic5—41no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—42no—
201C2×C3×Q8—51no—
202C2×C3×D4—51no—
203C2×C3×D4—101no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—101no—
207C22×C3×C4C22⋊D511yescharacteristic
208C22×C3×C4C22⋊D511yescharacteristic
209C22×C3×C4C22×D511yescharacteristic
210C3×Q16—202no—
211C3×SD16—202no—
212C2×C3×C8—101no—
213C2×C3×C8—101no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—42no—
217C3×C4⋊C4—51no—
218C3×C4⋊C4—51no—
219C3×C4⋊C4—101no—
220C3×C4⋊C4—101no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—101no—
223C3×C22⋊C4—101no—
224C3×C22⋊C4—101no—
225C3×C22⋊C4—101no—
226C3×C22⋊C4—101no—
227C3×C22⋊C4—101no—
228C3×C42—101no—
229C23×C5C2×C3×D411yescharacteristic
230C22×D5—21no—
231C5×Q8—22no—
232C5×Q8—22no—
233C5×Q8—41no—
234C5×Q8—41no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—21no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5C2×C3×D411yescharacteristic
248C2×C4×C5C2×C3×D411yescharacteristic
249C22⋊D5—41no—
250C22⋊D5—41no—
251C2×Dic5—21no—
252C2×Dic5—21no—
253C2×Dic5—21no—
254D20—41no—
255C4×D5—81no—
256Dic10—41no—
257#168—41no—
258#168—41no—
259C22×Q8C2×C3×D511yescharacteristic
260C2×Q16—101no—
261C2×SD16—101no—
262#126—101no—
263#125—101no—
264#123—101no—
265#123—101no—
266C22⋊Q8—51no—
267C22⋊Q8—101no—
268#121—51no—
269C4×D4—101no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C2×C3×D511yescharacteristic
272#103—101no—
273#103—101no—
274C22⋊C8—51no—
275C22⋊C8—51no—
276#95—21no—
277#95C2×C3×D511yescharacteristic
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5#45211yescharacteristic
281C2×C3×C5#45611yescharacteristic
282C2×C3×C5B(4,𝔽2)11yescharacteristic
283C3×D5—81no—
284C23×C3—101no—
285C23×C3C2×C22⋊D511yescharacteristic
286C3×Q8—22no—
287C3×Q8—22no—
288C3×Q8—41no—
289C3×Q8—41no—
290C3×Q8—201no—
291C3×D4—201no—
292C3×D4—201no—
293C3×D4—201no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—101no—
307C2×C3×C4—101no—
308C2×C3×C4—101no—
309C2×C3×C4—401no—
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C3×C8—201no—
313C3×C8—201no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5C3×#12011yescharacteristic
317C22×C5C3×#13511yescharacteristic
318C22×C5C3×#13711yescharacteristic
319C2×D5—41no—
320C2×D5—41no—
321C2×D5—41no—
322C4×C5—21no—
323C4×C5—21no—
324C4×C5—42no—
325C4×C5—41no—
326C4×C5—41no—
327C4×C5—42no—
328Dic5—41no—
329Dic5—41no—
330Dic5—41no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—42no—
334C2×Q8—51no—
335C2×D4—51no—
336C2×D4—101no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—101no—
340C22×C4C3×C22⋊D511yescharacteristic
341C22×C4C3×C22⋊D511yescharacteristic
342C22×C4C22×C3×D511yescharacteristic
343Q16—202no—
344SD16—202no—
345C2×C8—101no—
346C2×C8—101no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—42no—
350C4⋊C4—51no—
351C4⋊C4—51no—
352C4⋊C4—101no—
353C4⋊C4—101no—
354C4⋊C4—101no—
355C4⋊C4—101no—
356C22⋊C4—101no—
357C22⋊C4—101no—
358C22⋊C4—101no—
359C22⋊C4—101no—
360C22⋊C4—101no—
361C42—101no—
362C3×C5#160311yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—201no—
366C22×C3—201no—
367C22×C3—201no—
368C22×C3#408311yescharacteristic
369C22×C3#408811yescharacteristic
370C22×C3#409611yescharacteristic
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—201no—
378C3×C4—201no—
379C3×C4—201no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5C3×#45211yescharacteristic
383C2×C5C3×#45611yescharacteristic
384C2×C5C3×B(4,𝔽2)11yescharacteristic
385D5—81no—
386C23—101no—
387C23C2×C3×C22⋊D511yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—41no—
391Q8—41no—
392Q8—201no—
393D4—201no—
394D4—201no—
395D4—201no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—101no—
409C2×C4—101no—
410C2×C4—101no—
411C2×C4—401no—
412C2×C4C3×D4×D511yescharacteristic
413C2×C4C3×D4×D511yescharacteristic
414C8—201no—
415C8—201no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—401no—
419C2×C3#6532111yescharacteristic
420C2×C3#6533611yescharacteristic
421C2×C3#6538411yescharacteristic
422C5C3×#160311yescharacteristic, complemented, Sylow
423C22—21no—
424C22—21no—
425C22—201no—
426C22—201no—
427C22—201no—
428C22C3×#408311yescharacteristic
429C22C3×#408811yescharacteristic
430C22C3×#409611yescharacteristic
431C4—21no—
432C4—21no—
433C4—42no—
434C4—42no—
435C4—41no—
436C4—41no—
437C4—201no—
438C4—201no—
439C4—201no—
440C3#1060049811yescharacteristic, direct product factor, Sylow
441C2—21no—
442C2—21no—
443C2—401no—
444C2C3×#6532111yescharacteristic
445C2C3×#6533611yescharacteristic
446C2C3×#6538411yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#395C2
socleC22×C3×C5#120
prime radicalC3×#4076C22
hypercenterC3×#395D5
hypocenterC5C3×#1603
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#395

Complements

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

NH ≅ G/Ntype
2. C3×C5×#395C2semidirect
3. C3×#65517C2semidirect
5. C3×#64748C2semidirect
6. C3×#64672C2semidirect
8. #10600498C3direct (N × H)
30. C5×#395C2×C3semidirect
31. #65517C2×C3semidirect
33. #64748C2×C3semidirect
34. #64672C2×C3semidirect
70. C3×#395D5semidirect
177. #395C3×D5semidirect
362. C3×C5#1603semidirect
422. C5C3×#1603semidirect
440. C3#10600498direct (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×#3952
C3×#655172
C3×#655162
C3×#647482
C3×#646722
C3×#646712
#106004983
C3×#16035