Finite Group Databasebeta

← C3×#10602685 #14287721

Subgroups — C3×#10602685 #14287721

Order 1920.

632 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 114 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×C5×#543C211yesmaximal, characteristic, complemented
2C3×#65335C212yesmaximal, complemented
3C3×#65249C211yesmaximal, characteristic
4C3×#64758C212yesmaximal, complemented
5C3×#64745C211yesmaximal, characteristic, complemented
6#10602685C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C22⋊D5—21no—
8C22×C3×D20C2211yescharacteristic
9C3×C5×C22⋊Q8—22no—
10C3×C5×C22⋊Q8—21no—
11C3×C5×C22⋊Q8—22no—
12C3×C5×C22⋊Q8C2212yes—
13C2×C3×C5×C22⋊C4—21no—
14C2×C3×C5×C22⋊C4C2211yescharacteristic
15C2×C3×#688—22no—
16C2×C3×#685—21no—
17C3×#3963C2211yescharacteristic
18C3×C22⋊#168C2212yes—
19C3×#3941—22no—
20C3×#1596—51nomaximal, Hall
21C5×#543C2×C311yescharacteristic, complemented
22#65335C2×C312yescomplemented
23#65249C2×C311yescharacteristic
24#64758C2×C312yescomplemented
25#64745C2×C311yescharacteristic, complemented
26C24×C3×C5D411yescharacteristic
27C23×C3×D5—21no—
28C2×C3×C5×Q8—21no—
29C2×C3×C5×Q8D412yescomplemented
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5C2311yescharacteristic
34C2×C3×C22⋊D5—42no—
35C2×C3×C22⋊D5—42no—
36C2×C3×C22⋊D5—42no—
37C22×C3×Dic5—21no—
38C2×C3×D20—22no—
39C2×C3×D20—42no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4D412yescomplemented
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—22no—
47C3×#688—44no—
48C3×#685—42no—
49C2×C3×#168—22no—
50C3×#543D511yescharacteristic, complemented
51C3×#450—52no—
52C3×#392—51no—
53C3×#328—52no—
54C3×#323—51no—
55C22×C22⋊D5—21no—
56C22×D20C22×C311yescharacteristic
57C5×C22⋊Q8—22no—
58C5×C22⋊Q8—21no—
59C5×C22⋊Q8—22no—
60C5×C22⋊Q8C22×C312yes—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4C22×C311yescharacteristic
63C2×#688—22no—
64C2×#685—21no—
65#3963C22×C311yescharacteristic
66C22⋊#168C22×C312yes—
67#3941—22no—
68#1596—51noSylow
69C23×C3×C5—21no—
70C23×C3×C5—21no—
71C23×C3×C5—41no—
72C23×C3×C5—41no—
73C23×C3×C5SD1612yescomplemented
74C23×C3×C5C2×D411yescharacteristic
75C22×C3×D5—22no—
76C22×C3×D5—41no—
77C22×C3×D5—41no—
78C22×C3×D5—41no—
79C22×C3×D5—41no—
80C22×C3×D5—41no—
81C22×C3×D5—41no—
82C3×C5×Q8—42no—
83C3×C5×Q8—81no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—81no—
90C2×C3×C4×C5—81no—
91C2×C3×C4×C5C2×D412yes—
92C3×C22⋊D5—48no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—41no—
95C2×C3×Dic5—41no—
96C3×D20—24no—
97C3×D20—42no—
98C3×#168—42no—
99C22×C3×D4—51no—
100C22×C3×D4—101no—
101C2×C3×SD16—102no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—21no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8C2×D512yes—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—101no—
108C2×C3×C22⋊C4C2×D511yescharacteristic
109C3×#102—102no—
110C3×C22⋊C8—52no—
111C3×#95—51no—
112C24×C5C3×D411yescharacteristic
113C23×D5—21no—
114C2×C5×Q8—21no—
115C2×C5×Q8C3×D412yescomplemented
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5C3×D411yescharacteristic
119C22×C4×C5C23×C311yescharacteristic
120C2×C22⋊D5—42no—
121C2×C22⋊D5—42no—
122C2×C22⋊D5—42no—
123C22×Dic5—21no—
124C2×D20—22no—
125C2×D20—42no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—22no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4C3×D412yescomplemented
130C5×C22⋊C4—22no—
131C5×C22⋊C4—22no—
132C5×C22⋊C4—22no—
133#688—44no—
134#685—42no—
135C2×#168—22no—
136#543C3×D511yescharacteristic, complemented
137#450—52no—
138#392—51no—
139#328—52no—
140#323—51no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—22no—
144C22×C3×C5—42no—
145C22×C3×C5—41no—
146C22×C3×C5—41no—
147C22×C3×C5—81no—
148C22×C3×C5#12011yescharacteristic
149C22×C3×C5C2×SD1611yescharacteristic
150C22×C3×C5#13711yescharacteristic
151C2×C3×D5—42no—
152C2×C3×D5—42no—
153C2×C3×D5—42no—
154C2×C3×D5—81no—
155C2×C3×D5—81no—
156C2×C3×D5—81no—
157C2×C3×D5—81no—
158C3×C4×C5—22no—
159C3×C4×C5—41no—
160C3×C4×C5—42no—
161C3×C4×C5—42no—
162C3×Dic5—42no—
163C24×C3—101no—
164C24×C3C22⋊D511yescharacteristic
165C2×C3×Q8—21no—
166C2×C3×Q8C22⋊D512yescomplemented
167C2×C3×D4—102no—
168C2×C3×D4—202no—
169C2×C3×D4—202no—
170C2×C3×D4—202no—
171C2×C3×D4—202no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—101no—
175C22×C3×C4C22⋊D511yescharacteristic
176C22×C3×C4C22×D511yescharacteristic
177C3×SD16—204no—
178C2×C3×C8—102no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—22no—
181C3×C4⋊C4—22no—
182C3×C4⋊C4C22⋊D512yescomplemented
183C3×C22⋊C4—22no—
184C3×C22⋊C4—22no—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—202no—
187C23×C5—21no—
188C23×C5—21no—
189C23×C5—41no—
190C23×C5—41no—
191C23×C5C3×SD1612yescomplemented
192C23×C5C2×C3×D411yescharacteristic
193C22×D5—22no—
194C22×D5—41no—
195C22×D5—41no—
196C22×D5—41no—
197C22×D5—41no—
198C22×D5—41no—
199C22×D5—41no—
200C5×Q8—42no—
201C5×Q8—81no—
202C2×C4×C5—22no—
203C2×C4×C5—21no—
204C2×C4×C5—22no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—81no—
208C2×C4×C5—81no—
209C2×C4×C5C2×C3×D412yes—
210C22⋊D5—48no—
211C2×Dic5—22no—
212C2×Dic5—41no—
213C2×Dic5—41no—
214D20—24no—
215D20—42no—
216#168—42no—
217C22×D4—51no—
218C22×D4—101no—
219C2×SD16—102no—
220C22⋊Q8—22no—
221C22⋊Q8—21no—
222C22⋊Q8—22no—
223C22⋊Q8C2×C3×D512yes—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—101no—
226C2×C22⋊C4C2×C3×D511yescharacteristic
227#102—102no—
228C22⋊C8—52no—
229#95—51no—
230C2×C3×C5—21no—
231C2×C3×C5—21no—
232C2×C3×C5—42no—
233C2×C3×C5#44811yescharacteristic
234C2×C3×C5#45311yescharacteristic
235C2×C3×C5B(4,𝔽2)11yescharacteristic
236C3×D5—82no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—41no—
240C23×C3—41no—
241C23×C3—102no—
242C23×C3—201no—
243C23×C3—201no—
244C23×C3—201no—
245C23×C3—201no—
246C23×C3—201no—
247C23×C3—201no—
248C23×C3#68812yescomplemented
249C23×C3C2×C22⋊D511yescharacteristic
250C3×Q8—42no—
251C3×Q8—81no—
252C3×D4—104no—
253C3×D4—202no—
254C3×D4—208no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—22no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—81no—
261C2×C3×C4—81no—
262C2×C3×C4—102no—
263C2×C3×C4—201no—
264C2×C3×C4—201no—
265C2×C3×C4C2×C22⋊D512yes—
266C3×C8—202no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—22no—
270C22×C5—42no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—81no—
274C22×C5C3×#12011yescharacteristic
275C22×C5C2×C3×SD1611yescharacteristic
276C22×C5C3×#13711yescharacteristic
277C2×D5—42no—
278C2×D5—42no—
279C2×D5—42no—
280C2×D5—81no—
281C2×D5—81no—
282C2×D5—81no—
283C2×D5—81no—
284C4×C5—22no—
285C4×C5—41no—
286C4×C5—42no—
287C4×C5—42no—
288Dic5—42no—
289C24—101no—
290C24C3×C22⋊D511yescharacteristic
291C2×Q8—21no—
292C2×Q8C3×C22⋊D512yescomplemented
293C2×D4—102no—
294C2×D4—202no—
295C2×D4—202no—
296C2×D4—202no—
297C2×D4—202no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—101no—
301C22×C4C3×C22⋊D511yescharacteristic
302C22×C4C22×C3×D511yescharacteristic
303SD16—204no—
304C2×C8—102no—
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4C3×C22⋊D512yescomplemented
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—202no—
313C3×C5#159611yescharacteristic, complemented, Hall
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—22no—
317C22×C3—42no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—81no—
321C22×C3—202no—
322C22×C3—202no—
323C22×C3—202no—
324C22×C3—401no—
325C22×C3—401no—
326C22×C3—401no—
327C22×C3—401no—
328C22×C3C2×#68811yescharacteristic
329C22×C3#408811yescharacteristic
330C22×C3#409911yescharacteristic
331C3×C4—22no—
332C3×C4—41no—
333C3×C4—42no—
334C3×C4—42no—
335C3×C4—202no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5—42no—
339C2×C5C3×#44811yescharacteristic
340C2×C5C3×#45311yescharacteristic
341C2×C5C3×B(4,𝔽2)11yescharacteristic
342D5—82no—
343C23—21no—
344C23—21no—
345C23—41no—
346C23—41no—
347C23—102no—
348C23—201no—
349C23—201no—
350C23—201no—
351C23—201no—
352C23—201no—
353C23—201no—
354C23C3×#68812yescomplemented
355C23C2×C3×C22⋊D511yescharacteristic
356Q8—42no—
357Q8—81no—
358D4—104no—
359D4—202no—
360D4—208no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—102no—
369C2×C4—201no—
370C2×C4—201no—
371C2×C4C2×C3×C22⋊D512yes—
372C8—202no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—42no—
376C2×C3—402no—
377C2×C3#6551611yescharacteristic
378C2×C3#6553011yescharacteristic
379C2×C3#6553311yescharacteristic
380C5C3×#159611yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—22no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—81no—
388C22—202no—
389C22—202no—
390C22—202no—
391C22—401no—
392C22—401no—
393C22—401no—
394C22—401no—
395C22C2×C3×#68811yescharacteristic
396C22C3×#408811yescharacteristic
397C22C3×#409911yescharacteristic
398C4—22no—
399C4—41no—
400C4—42no—
401C4—42no—
402C4—202no—
403C3#1060268511yescharacteristic, direct product factor, Sylow
404C2—21no—
405C2—21no—
406C2—42no—
407C2—402no—
408C2C3×#6551611yescharacteristic
409C2C3×#6553011yescharacteristic
410C2C3×#6553311yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#543C2
socleC22×C3×C5#120
prime radicalC3×#65249C2
hypercenterC3×#543D5
hypocenterC5C3×#1596
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#543

Complements

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

NH ≅ G/Ntype
1. C3×C5×#543C2semidirect
2. C3×#65335C2semidirect
4. C3×#64758C2semidirect
5. C3×#64745C2semidirect
6. #10602685C3direct (N × H)
21. C5×#543C2×C3semidirect
22. #65335C2×C3semidirect
24. #64758C2×C3semidirect
25. #64745C2×C3semidirect
29. C2×C3×C5×Q8D4semidirect
43. C3×C5×C4⋊C4D4semidirect
50. C3×#543D5semidirect
73. C23×C3×C5SD16semidirect
115. C2×C5×Q8C3×D4semidirect
129. C5×C4⋊C4C3×D4semidirect
136. #543C3×D5semidirect
166. C2×C3×Q8C22⋊D5semidirect
182. C3×C4⋊C4C22⋊D5semidirect
191. C23×C5C3×SD16semidirect
248. C23×C3#688semidirect
292. C2×Q8C3×C22⋊D5semidirect
308. C4⋊C4C3×C22⋊D5semidirect
313. C3×C5#1596semidirect
354. C23C3×#688semidirect
380. C5C3×#1596semidirect
403. C3#10602685direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5432
C3×#653352
C3×#652492
C3×#647582
C3×#647452
#106026853
C3×#15965