Finite Group Databasebeta

← C3×#10600491 #14287718

Subgroups — C3×#10600491 #14287718

Order 1920.

632 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 106 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×#65817C211yesmaximal, characteristic, complemented
2C3×C5×#392C211yesmaximal, characteristic
3C3×#65507C212yesmaximal, complemented
4C3×#64745C211yesmaximal, characteristic, complemented
5C3×#64672C212yesmaximal, complemented
6#10600491C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4—21no—
8C22×C3×C5×D4C2211yescharacteristic
9C2×C3×C5×C22⋊C4—21no—
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×C3×C22⋊Dic5—21no—
12C2×C3×#687—22no—
13C3×#4070—21no—
14C3×#4070C2212yes—
15C3×#4024—22no—
16C3×#4024—22no—
17C3×C5×#95C2211yescharacteristic
18C3×#3964—22no—
19C3×C22⋊#168C2212yes—
20C3×#1596—51nomaximal, Hall
21#65817C2×C311yescharacteristic, complemented
22C5×#392C2×C311yescharacteristic
23#65507C2×C312yescomplemented
24#64745C2×C311yescharacteristic, complemented
25#64672C2×C312yescomplemented
26C24×C3×C5—21no—
27C24×C3×C5D411yescharacteristic
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4—42no—
30C2×C3×C5×D4—42no—
31C2×C3×C5×D4—42no—
32C2×C3×C5×D4—42no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5C2311yescharacteristic
36C22×C3×Dic5—21no—
37C22×C3×Dic5—21no—
38C2×C3×Dic10—21no—
39C2×C3×Dic10D412yescomplemented
40C3×C5×C22⋊C4—22no—
41C3×C5×C22⋊C4—42no—
42C3×C22⋊Dic5—22no—
43C3×C22⋊Dic5—22no—
44C3×#687—44no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5D412yescomplemented
47C3×#683—22no—
48C3×#683—22no—
49C2×C3×#168—22no—
50C3×#543—51no—
51C3×#450—52no—
52C3×#392D511yescharacteristic
53C3×#328—52no—
54C3×#323—51no—
55C22×C5×D4—21no—
56C22×C5×D4C22×C311yescharacteristic
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4C22×C311yescharacteristic
59C2×C22⋊Dic5—21no—
60C2×#687—22no—
61#4070—21no—
62#4070C22×C312yes—
63#4024—22no—
64#4024—22no—
65C5×#95C22×C311yescharacteristic
66#3964—22no—
67C22⋊#168C22×C312yes—
68#1596—51noSylow
69C23×C3×C5—21no—
70C23×C3×C5—21no—
71C23×C3×C5—22no—
72C23×C3×C5—41no—
73C23×C3×C5—41no—
74C23×C3×C5—41no—
75C23×C3×C5—41no—
76C23×C3×C5—41no—
77C23×C3×C5—41no—
78C23×C3×C5—41no—
79C23×C3×C5—41no—
80C23×C3×C5SD1612yescomplemented
81C23×C3×C5C2×D411yescharacteristic
82C3×C5×D4—24no—
83C3×C5×D4—42no—
84C3×C5×D4—48no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D412yes—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—81no—
95C2×C3×Dic5—81no—
96C3×Dic10—42no—
97C3×Dic10—81no—
98C3×#168—42no—
99C22×C3×D4—21no—
100C22×C3×D4C2×D511yescharacteristic
101C2×C3×SD16—102no—
102C3×C22⋊Q8—52no—
103C3×C22⋊Q8—102no—
104C3×C22⋊Q8—102no—
105C3×C22⋊Q8—101no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—101no—
108C2×C3×C22⋊C4C2×D511yescharacteristic
109C3×#102—102no—
110C3×C22⋊C8—52no—
111C3×#95C2×D511yescharacteristic
112C24×C5—21no—
113C24×C5C3×D411yescharacteristic
114C2×C5×D4—22no—
115C2×C5×D4—42no—
116C2×C5×D4—42no—
117C2×C5×D4—42no—
118C2×C5×D4—42no—
119C22×C4×C5—21no—
120C22×C4×C5C3×D411yescharacteristic
121C22×C4×C5C23×C311yescharacteristic
122C22×Dic5—21no—
123C22×Dic5—21no—
124C2×Dic10—21no—
125C2×Dic10C3×D412yescomplemented
126C5×C22⋊C4—22no—
127C5×C22⋊C4—42no—
128C22⋊Dic5—22no—
129C22⋊Dic5—22no—
130#687—44no—
131C4⋊Dic5—21no—
132C4⋊Dic5C3×D412yescomplemented
133#683—22no—
134#683—22no—
135C2×#168—22no—
136#543—51no—
137#450—52no—
138#392C3×D511yescharacteristic
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—42no—
146C22×C3×C5—42no—
147C22×C3×C5—41no—
148C22×C3×C5—41no—
149C22×C3×C5—42no—
150C22×C3×C5—81no—
151C22×C3×C5—81no—
152C22×C3×C5—81no—
153C22×C3×C5—81no—
154C22×C3×C5—81no—
155C22×C3×C5#12011yescharacteristic
156C22×C3×C5C2×SD1611yescharacteristic
157C22×C3×C5#13711yescharacteristic
158C3×C4×C5—22no—
159C3×C4×C5—42no—
160C3×C4×C5—41no—
161C3×Dic5—42no—
162C3×Dic5—42no—
163C24×C3—21no—
164C24×C3C22⋊D511yescharacteristic
165C2×C3×Q8—52no—
166C2×C3×Q8—101no—
167C2×C3×D4—22no—
168C2×C3×D4—42no—
169C2×C3×D4—42no—
170C2×C3×D4—42no—
171C2×C3×D4—42no—
172C22×C3×C4—21no—
173C22×C3×C4—101no—
174C22×C3×C4—101no—
175C22×C3×C4C22⋊D511yescharacteristic
176C22×C3×C4C22×D511yescharacteristic
177C3×SD16—204no—
178C2×C3×C8—102no—
179C3×C4⋊C4—52no—
180C3×C4⋊C4—102no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4—102no—
183C3×C22⋊C4—22no—
184C3×C22⋊C4—42no—
185C3×C22⋊C4—102no—
186C3×C22⋊C4—102no—
187C23×C5—21no—
188C23×C5—21no—
189C23×C5—22no—
190C23×C5—41no—
191C23×C5—41no—
192C23×C5—41no—
193C23×C5—41no—
194C23×C5—41no—
195C23×C5—41no—
196C23×C5—41no—
197C23×C5—41no—
198C23×C5C3×SD1612yescomplemented
199C23×C5C2×C3×D411yescharacteristic
200C5×D4—24no—
201C5×D4—42no—
202C5×D4—48no—
203C2×C4×C5—22no—
204C2×C4×C5—21no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5C2×C3×D412yes—
210C2×Dic5—22no—
211C2×Dic5—22no—
212C2×Dic5—81no—
213C2×Dic5—81no—
214Dic10—42no—
215Dic10—81no—
216#168—42no—
217C22×D4—21no—
218C22×D4C2×C3×D511yescharacteristic
219C2×SD16—102no—
220C22⋊Q8—52no—
221C22⋊Q8—102no—
222C22⋊Q8—102no—
223C22⋊Q8—101no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—101no—
226C2×C22⋊C4C2×C3×D511yescharacteristic
227#102—102no—
228C22⋊C8—52no—
229#95C2×C3×D511yescharacteristic
230C2×C3×C5—21no—
231C2×C3×C5—21no—
232C2×C3×C5—42no—
233C2×C3×C5—82no—
234C2×C3×C5#44811yescharacteristic
235C2×C3×C5#45311yescharacteristic
236C2×C3×C5B(4,𝔽2)11yescharacteristic
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—22no—
240C23×C3—41no—
241C23×C3—41no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—41no—
245C23×C3—41no—
246C23×C3—41no—
247C23×C3—41no—
248C23×C3#68712yescomplemented
249C23×C3C2×C22⋊D511yescharacteristic
250C3×Q8—202no—
251C3×Q8—401no—
252C3×D4—24no—
253C3×D4—42no—
254C3×D4—48no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—102no—
262C2×C3×C4—102no—
263C2×C3×C4—401no—
264C2×C3×C4—401no—
265C2×C3×C4D4×D512yes—
266C3×C8—202no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—22no—
270C22×C5—42no—
271C22×C5—42no—
272C22×C5—42no—
273C22×C5—41no—
274C22×C5—41no—
275C22×C5—42no—
276C22×C5—81no—
277C22×C5—81no—
278C22×C5—81no—
279C22×C5—81no—
280C22×C5—81no—
281C22×C5C3×#12011yescharacteristic
282C22×C5C2×C3×SD1611yescharacteristic
283C22×C5C3×#13711yescharacteristic
284C4×C5—22no—
285C4×C5—42no—
286C4×C5—41no—
287Dic5—42no—
288Dic5—42no—
289C24—21no—
290C24C3×C22⋊D511yescharacteristic
291C2×Q8—52no—
292C2×Q8—101no—
293C2×D4—22no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—42no—
298C22×C4—21no—
299C22×C4—101no—
300C22×C4—101no—
301C22×C4C3×C22⋊D511yescharacteristic
302C22×C4C22×C3×D511yescharacteristic
303SD16—204no—
304C2×C8—102no—
305C4⋊C4—52no—
306C4⋊C4—102no—
307C4⋊C4—101no—
308C4⋊C4—102no—
309C22⋊C4—22no—
310C22⋊C4—42no—
311C22⋊C4—102no—
312C22⋊C4—102no—
313C3×C5#159611yescharacteristic, complemented, Hall
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—22no—
317C22×C3—42no—
318C22×C3—42no—
319C22×C3—42no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—42no—
323C22×C3—81no—
324C22×C3—81no—
325C22×C3—81no—
326C22×C3—81no—
327C22×C3—81no—
328C22×C3C2×#68711yescharacteristic
329C22×C3#408311yescharacteristic
330C22×C3#409711yescharacteristic
331C3×C4—22no—
332C3×C4—42no—
333C3×C4—41no—
334C3×C4—202no—
335C3×C4—202no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5—42no—
339C2×C5—82no—
340C2×C5C3×#44811yescharacteristic
341C2×C5C3×#45311yescharacteristic
342C2×C5C3×B(4,𝔽2)11yescharacteristic
343C23—21no—
344C23—21no—
345C23—22no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23C3×#68712yescomplemented
355C23C2×C3×C22⋊D511yescharacteristic
356Q8—202no—
357Q8—401no—
358D4—24no—
359D4—42no—
360D4—48no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—102no—
368C2×C4—102no—
369C2×C4—401no—
370C2×C4—401no—
371C2×C4C3×D4×D512yes—
372C8—202no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—42no—
376C2×C3—82no—
377C2×C3#6532111yescharacteristic
378C2×C3#6532911yescharacteristic
379C2×C3#6536611yescharacteristic
380C5C3×#159611yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—22no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—42no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22C2×C3×#68711yescharacteristic
396C22C3×#408311yescharacteristic
397C22C3×#409711yescharacteristic
398C4—22no—
399C4—42no—
400C4—41no—
401C4—202no—
402C4—202no—
403C3#1060049111yescharacteristic, direct product factor, Sylow
404C2—21no—
405C2—21no—
406C2—42no—
407C2—82no—
408C2C3×#6532111yescharacteristic
409C2C3×#6532911yescharacteristic
410C2C3×#6536611yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
Fitting, prime radicalC3×C5×#392C2
socleC22×C3×C5#120
hypercenterC3×#392D5
hypocenterC5C3×#1596
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#392

Complements

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

NH ≅ G/Ntype
1. C3×#65817C2semidirect
3. C3×#65507C2semidirect
4. C3×#64745C2semidirect
5. C3×#64672C2semidirect
6. #10600491C3direct (N × H)
21. #65817C2×C3semidirect
23. #65507C2×C3semidirect
24. #64745C2×C3semidirect
25. #64672C2×C3semidirect
39. C2×C3×Dic10D4semidirect
46. C3×C4⋊Dic5D4semidirect
80. C23×C3×C5SD16semidirect
125. C2×Dic10C3×D4semidirect
132. C4⋊Dic5C3×D4semidirect
198. C23×C5C3×SD16semidirect
248. C23×C3#687semidirect
313. C3×C5#1596semidirect
354. C23C3×#687semidirect
380. C5C3×#1596semidirect
403. C3#10600491direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658172
C3×C5×#3922
C3×#655072
C3×#647452
C3×#646722
#106004913
C3×#15965