Finite Group Databasebeta

← C3×#10600497 #14287859

Subgroups — C3×#10600497 #14287859

Order 1920.

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

normal subgroups only

This group has 532 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×#65834C211yesmaximal, characteristic, complemented
2C3×C5×#394C211yesmaximal, characteristic
3C3×#65507C212yesmaximal
4C3×#64748C211yesmaximal, characteristic, complemented
5C3×#64672C212yesmaximal, complemented
6#10600497C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×C3×C5×C22⋊C4—21no—
10C2×C3×C5×C22⋊C4—21no—
11C2×C3×#687—22no—
12C3×#4072—21no—
13C3×#4070—21no—
14C3×#4070C2212yes—
15C3×#4036—22no—
16C3×#4034—22no—
17C3×C5×#95C2211yescharacteristic
18C3×#3964—22no—
19C3×C22⋊#168C2212yes—
20C3×#1599—51nomaximal, Hall
21#65834C2×C311yescharacteristic, complemented
22C5×#394C2×C311yescharacteristic
23#65507C2×C312yes—
24#64748C2×C311yescharacteristic, complemented
25#64672C2×C312yescomplemented
26C24×C3×C5—21no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4—42no—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C2×C3×Dic10—21no—
34C2×C3×Dic10D412yes—
35C3×C5×C4⋊C4—22no—
36C3×C5×C22⋊C4—42no—
37C3×C5×C22⋊C4—42no—
38C3×C22⋊Dic5—22no—
39C3×#687—44no—
40C3×C4⋊Dic5—21no—
41C3×C4⋊Dic5—21no—
42C3×C4⋊Dic5—21no—
43C3×C4⋊Dic5D412yes—
44C3×#683—22no—
45C3×#683—22no—
46C3×C4×Dic5—22no—
47C2×C3×#168—22no—
48C3×#544—51no—
49C3×#450—52no—
50C3×#394D511yescharacteristic
51C3×#328—52no—
52C3×#324—51no—
53C22×C5×D4C22×C311yescharacteristic
54C2×C5×C4⋊C4C22×C311yescharacteristic
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×#687—22no—
58#4072—21no—
59#4070—21no—
60#4070C22×C312yes—
61#4036—22no—
62#4034—22no—
63C5×#95C22×C311yescharacteristic
64#3964—22no—
65C22⋊#168C22×C312yes—
66#1599—51noSylow
67C23×C3×C5—22no—
68C23×C3×C5—41no—
69C23×C3×C5—41no—
70C23×C3×C5—41no—
71C23×C3×C5—41no—
72C23×C3×C5—41no—
73C23×C3×C5—41no—
74C23×C3×C5C2×D411yescharacteristic
75C3×C5×D4—24no—
76C3×C5×D4—42no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5SD1612yescomplemented
86C2×C3×C4×C5C2×D412yes—
87C2×C3×Dic5—22no—
88C2×C3×Dic5—22no—
89C3×Dic10—42no—
90C3×Dic10—81no—
91C3×#168—42no—
92C22×C3×D4C2×D511yescharacteristic
93C2×C3×SD16—102no—
94C3×C4⋊Q8—102no—
95C3×#125—102no—
96C3×C22⋊Q8—52no—
97C3×C22⋊Q8—101no—
98C3×#117—101no—
99C2×C3×C4⋊C4C2×D511yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C3×#102—102no—
103C3×C22⋊C8—52no—
104C3×#95C2×D511yescharacteristic
105C24×C5—21no—
106C2×C5×D4—22no—
107C2×C5×D4—42no—
108C22×C4×C5—21no—
109C22×C4×C5C3×D411yescharacteristic
110C22×C4×C5C3×D411yescharacteristic
111C22×C4×C5C23×C311yescharacteristic
112C2×Dic10—21no—
113C2×Dic10C3×D412yes—
114C5×C4⋊C4—22no—
115C5×C22⋊C4—42no—
116C5×C22⋊C4—42no—
117C22⋊Dic5—22no—
118#687—44no—
119C4⋊Dic5—21no—
120C4⋊Dic5—21no—
121C4⋊Dic5—21no—
122C4⋊Dic5C3×D412yes—
123#683—22no—
124#683—22no—
125C4×Dic5—22no—
126C2×#168—22no—
127#544—51no—
128#450—52no—
129#394C3×D511yescharacteristic
130#328—52no—
131#324—51no—
132C22×C3×C5—21no—
133C22×C3×C5—21no—
134C22×C3×C5—42no—
135C22×C3×C5—42no—
136C22×C3×C5—42no—
137C22×C3×C5—81no—
138C22×C3×C5—81no—
139C22×C3×C5—81no—
140C22×C3×C5—81no—
141C22×C3×C5#12011yescharacteristic
142C22×C3×C5C2×SD1611yescharacteristic
143C22×C3×C5#13711yescharacteristic
144C3×C4×C5—22no—
145C3×C4×C5—22no—
146C3×C4×C5—41no—
147C3×C4×C5—81no—
148C3×Dic5—42no—
149C3×Dic5—42no—
150C24×C3—21no—
151C2×C3×Q8—52no—
152C2×C3×Q8—101no—
153C2×C3×D4—22no—
154C2×C3×D4—42no—
155C22×C3×C4—21no—
156C22×C3×C4C22⋊D511yescharacteristic
157C22×C3×C4C22⋊D511yescharacteristic
158C22×C3×C4C22×D511yescharacteristic
159C3×SD16—204no—
160C2×C3×C8—102no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—52no—
163C3×C4⋊C4—102no—
164C3×C4⋊C4—101no—
165C3×C4⋊C4—101no—
166C3×C4⋊C4—101no—
167C3×C4⋊C4—102no—
168C3×C22⋊C4—42no—
169C3×C22⋊C4—42no—
170C3×C22⋊C4—102no—
171C3×C42—102no—
172C23×C5—22no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5C2×C3×D411yescharacteristic
180C5×D4—24no—
181C5×D4—42no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5C3×SD1612yescomplemented
191C2×C4×C5C2×C3×D412yes—
192C2×Dic5—22no—
193C2×Dic5—22no—
194Dic10—42no—
195Dic10—81no—
196#168—42no—
197C22×D4C2×C3×D511yescharacteristic
198C2×SD16—102no—
199C4⋊Q8—102no—
200#125—102no—
201C22⋊Q8—52no—
202C22⋊Q8—101no—
203#117—101no—
204C2×C4⋊C4C2×C3×D511yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207#102—102no—
208C22⋊C8—52no—
209#95C2×C3×D511yescharacteristic
210C2×C3×C5—21no—
211C2×C3×C5—21no—
212C2×C3×C5—82no—
213C2×C3×C5#44811yescharacteristic
214C2×C3×C5#45411yescharacteristic
215C2×C3×C5B(4,𝔽2)11yescharacteristic
216C23×C3—22no—
217C23×C3—41no—
218C23×C3—41no—
219C23×C3—41no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3—41no—
223C23×C3C2×C22⋊D511yescharacteristic
224C3×Q8—202no—
225C3×Q8—401no—
226C3×D4—24no—
227C3×D4—42no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—102no—
237C2×C3×C4—102no—
238C2×C3×C4#68712yescomplemented
239C2×C3×C4D4×D512yes—
240C3×C8—202no—
241C22×C5—21no—
242C22×C5—21no—
243C22×C5—42no—
244C22×C5—42no—
245C22×C5—42no—
246C22×C5—81no—
247C22×C5—81no—
248C22×C5—81no—
249C22×C5—81no—
250C22×C5C3×#12011yescharacteristic
251C22×C5C2×C3×SD1611yescharacteristic
252C22×C5C3×#13711yescharacteristic
253C4×C5—22no—
254C4×C5—22no—
255C4×C5—41no—
256C4×C5—81no—
257Dic5—42no—
258Dic5—42no—
259C24—21no—
260C2×Q8—52no—
261C2×Q8—101no—
262C2×D4—22no—
263C2×D4—42no—
264C22×C4—21no—
265C22×C4C3×C22⋊D511yescharacteristic
266C22×C4C3×C22⋊D511yescharacteristic
267C22×C4C22×C3×D511yescharacteristic
268SD16—204no—
269C2×C8—102no—
270C4⋊C4—22no—
271C4⋊C4—52no—
272C4⋊C4—101no—
273C4⋊C4—101no—
274C4⋊C4—101no—
275C4⋊C4—102no—
276C4⋊C4—102no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—102no—
280C42—102no—
281C3×C5#159911yescharacteristic, complemented, Hall
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—42no—
285C22×C3—42no—
286C22×C3—42no—
287C22×C3—81no—
288C22×C3—81no—
289C22×C3—81no—
290C22×C3—81no—
291C22×C3C2×#68711yescharacteristic
292C22×C3#408311yescharacteristic
293C22×C3#409711yescharacteristic
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—41no—
297C3×C4—81no—
298C3×C4—202no—
299C3×C4—202no—
300C2×C5—21no—
301C2×C5—21no—
302C2×C5—82no—
303C2×C5C3×#44811yescharacteristic
304C2×C5C3×#45411yescharacteristic
305C2×C5C3×B(4,𝔽2)11yescharacteristic
306C23—22no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23C2×C3×C22⋊D511yescharacteristic
314Q8—202no—
315Q8—401no—
316D4—24no—
317D4—42no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—102no—
327C2×C4—102no—
328C2×C4C3×#68712yescomplemented
329C2×C4C3×D4×D512yes—
330C8—202no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—82no—
334C2×C3#6532111yescharacteristic
335C2×C3#6532911yescharacteristic
336C2×C3#6535111yescharacteristic
337C5C3×#159911yescharacteristic, complemented, Sylow
338C22—21no—
339C22—21no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22C2×C3×#68711yescharacteristic
348C22C3×#408311yescharacteristic
349C22C3×#409711yescharacteristic
350C4—22no—
351C4—22no—
352C4—41no—
353C4—81no—
354C4—202no—
355C4—202no—
356C3#1060049711yescharacteristic, direct product factor, Sylow
357C2—21no—
358C2—21no—
359C2—82no—
360C2C3×#6532111yescharacteristic
361C2C3×#6532911yescharacteristic
362C2C3×#6535111yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#394C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
hypercenterC3×#394D5
hypocenterC5C3×#1599
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#394

Complements

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

NH ≅ G/Ntype
1. C3×#65834C2semidirect
4. C3×#64748C2semidirect
5. C3×#64672C2semidirect
6. #10600497C3direct (N × H)
21. #65834C2×C3semidirect
24. #64748C2×C3semidirect
25. #64672C2×C3semidirect
85. C2×C3×C4×C5SD16semidirect
190. C2×C4×C5C3×SD16semidirect
238. C2×C3×C4#687semidirect
281. C3×C5#1599semidirect
328. C2×C4C3×#687semidirect
337. C5C3×#1599semidirect
356. C3#10600497direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658342
C3×C5×#3942
C3×#655072
C3×#647482
C3×#646722
#106004973
C3×#15995