Finite Group Databasebeta

← C3×#10599913 #14316311

Subgroups — C3×#10599913 #14316311

Order 1920.

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

normal subgroups only

This group has 452 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×#66082C211yesmaximal, characteristic, complemented
2C3×#65424C211yesmaximal, characteristic, complemented
3C3×#65197C212yesmaximal, complemented
4C3×C5×#349C211yesmaximal, characteristic, complemented
5C3×#64738C212yesmaximal, complemented
6#10599913C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#709—21no—
8C2×C3×C5×M16C2211yescharacteristic
9C3×#4076—21no—
10C3×#4055—22no—
11C3×#4054—22no—
12C3×#4050—21no—
13C3×#4050C2212yes—
14C2×C3×D40C2211yescharacteristic, complemented
15C3×C5×M32C2212yescomplemented
16C3×#3953—21no—
17C3×#3949C2211yescharacteristic, complemented
18C3×#3932—22no—
19C3×D80—22no—
20C3×#2190—51nomaximal, Hall
21#66082C2×C311yescharacteristic, complemented
22#65424C2×C311yescharacteristic, complemented
23#65197C2×C312yescomplemented
24C5×#349C2×C311yescharacteristic, complemented
25#64738C2×C312yescomplemented
26C22×C3×C4×C5D411yescharacteristic
27C2×C3×C22⋊D5—41no—
28C2×C3×C22⋊D5—41no—
29C3×#709—22no—
30C3×#709—22no—
31C3×#709—41no—
32C3×#709—41no—
33C2×C3×D20—21no—
34C2×C3×D20—21no—
35C2×C3×C4×D5—41no—
36C2×C3×Dic10—21no—
37C3×C5×M16—22no—
38C2×C3×C5×C8D411yescharacteristic
39C2×C3×C5×C8C2311yescharacteristic
40C3×#685—41no—
41C3×C4⋊Dic5—21no—
42C3×Dic20—21no—
43C3×Dic20D412yescomplemented
44C3×D40—21no—
45C3×D40—22no—
46C3×D40D412yescomplemented
47C3×#677—22no—
48C3×#677—22no—
49C3×C5×C16—22no—
50C3×#575—51no—
51C3×#509—52no—
52C3×#469—51no—
53C3×#360—52no—
54C3×#349D511yescharacteristic, complemented
55C2×#709—21no—
56C2×C5×M16C22×C311yescharacteristic
57#4076—21no—
58#4055—22no—
59#4054—22no—
60#4050—21no—
61#4050C22×C312yes—
62C2×D40C22×C311yescharacteristic, complemented
63C5×M32C22×C312yescomplemented
64#3953—21no—
65#3949C22×C311yescharacteristic, complemented
66#3932—22no—
67D80—22no—
68#2190—51noSylow
69C23×C3×C5D811yescharacteristic
70C22×C3×D5—41no—
71C22×C3×D5—41no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5D811yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C3×C22⋊D5—42no—
77C3×C22⋊D5—42no—
78C3×C22⋊D5—82no—
79C2×C3×Dic5—41no—
80C2×C3×Dic5—41no—
81C3×D20—22no—
82C3×D20—41no—
83C3×D20—41no—
84C3×D20—41no—
85C3×C4×D5—42no—
86C3×C4×D5—42no—
87C3×Dic10—22no—
88C3×Dic10—41no—
89C3×C5×C8—21no—
90C3×C5×C8C2×D412yes—
91C2×C3×#41—101no—
92C3×#137—102no—
93C3×AGL(1,ℤ/8)—102no—
94C3×#135—52no—
95C3×#135—101no—
96C2×C3×D8—51no—
97C2×C3×M16C2×D511yescharacteristic
98C3×#121—101no—
99C3×SD32—102no—
100C3×D16—102no—
101C3×M32C2×D512yescomplemented
102C3×#106—51no—
103C3×#102—101no—
104C22×C4×C5C3×D411yescharacteristic
105C2×C22⋊D5—41no—
106C2×C22⋊D5—41no—
107#709—22no—
108#709—22no—
109#709—41no—
110#709—41no—
111C2×D20—21no—
112C2×D20—21no—
113C2×C4×D5—41no—
114C2×Dic10—21no—
115C5×M16—22no—
116C2×C5×C8C3×D411yescharacteristic
117C2×C5×C8C23×C311yescharacteristic
118#685—41no—
119C4⋊Dic5—21no—
120Dic20—21no—
121Dic20C3×D412yescomplemented
122D40—21no—
123D40—22no—
124D40C3×D412yescomplemented
125#677—22no—
126#677—22no—
127C5×C16—22no—
128#575—51no—
129#509—52no—
130#469—51no—
131#360—52no—
132#349C3×D511yescharacteristic, complemented
133C22×C3×C5—21no—
134C22×C3×C5—41no—
135C22×C3×C5C2×D811yescharacteristic
136C2×C3×D5—42no—
137C2×C3×D5—82no—
138C2×C3×D5—81no—
139C2×C3×D5—81no—
140C2×C3×D5—81no—
141C3×C4×C5—21no—
142C3×C4×C5#12011yescharacteristic
143C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
144C3×Dic5—42no—
145C3×Dic5—81no—
146C3×#41—102no—
147C3×#41—102no—
148C3×#41—201no—
149C3×#41—201no—
150C2×C3×Q8—101no—
151C2×C3×D4—101no—
152C2×C3×D4—101no—
153C2×C3×D4—201no—
154C2×C3×D4—201no—
155C22×C3×C4—201no—
156C22×C3×C4D2011yescharacteristic
157C3×Q16—52no—
158C3×Q16—101no—
159C3×SD16—102no—
160C3×SD16—102no—
161C3×D8—52no—
162C3×D8—101no—
163C3×D8—102no—
164C3×M16—22no—
165C2×C3×C8D2011yescharacteristic
166C2×C3×C8C22×D511yescharacteristic
167C3×C4⋊C4—101no—
168C3×C22⋊C4—201no—
169C3×C16—22no—
170C23×C5C3×D811yescharacteristic
171C22×D5—41no—
172C22×D5—41no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5C3×D811yescharacteristic
176C2×C4×C5C2×C3×D411yescharacteristic
177C22⋊D5—42no—
178C22⋊D5—42no—
179C22⋊D5—82no—
180C2×Dic5—41no—
181C2×Dic5—41no—
182D20—22no—
183D20—41no—
184D20—41no—
185D20—41no—
186C4×D5—42no—
187C4×D5—42no—
188Dic10—22no—
189Dic10—41no—
190C5×C8—21no—
191C5×C8C2×C3×D412yes—
192C2×#41—101no—
193#137—102no—
194AGL(1,ℤ/8)—102no—
195#135—52no—
196#135—101no—
197C2×D8—51no—
198C2×M16C2×C3×D511yescharacteristic
199#121—101no—
200SD32—102no—
201D16—102no—
202M32C2×C3×D512yescomplemented
203#106—51no—
204#102—101no—
205C2×C3×C5—21no—
206C2×C3×C5—41no—
207C2×C3×C5#44711yescharacteristic
208C3×D5—82no—
209C3×D5—161no—
210C23×C3—201no—
211C23×C3—201no—
212C23×C3D4011yescharacteristic
213C3×Q8—102no—
214C3×Q8—201no—
215C3×D4—102no—
216C3×D4—201no—
217C3×D4—202no—
218C3×D4—202no—
219C3×D4—201no—
220C3×D4—201no—
221C3×D4—402no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—202no—
225C2×C3×C4—201no—
226C2×C3×C4—202no—
227C2×C3×C4—201no—
228C2×C3×C4D4011yescharacteristic
229C2×C3×C4C2×D2011yescharacteristic
230C3×C8—21no—
231C3×C8D4×D512yes—
232C22×C5—21no—
233C22×C5—41no—
234C22×C5C2×C3×D811yescharacteristic
235C2×D5—42no—
236C2×D5—82no—
237C2×D5—81no—
238C2×D5—81no—
239C2×D5—81no—
240C4×C5—21no—
241C4×C5C3×#12011yescharacteristic
242C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
243Dic5—42no—
244Dic5—81no—
245#41—102no—
246#41—102no—
247#41—201no—
248#41—201no—
249C2×Q8—101no—
250C2×D4—101no—
251C2×D4—101no—
252C2×D4—201no—
253C2×D4—201no—
254C22×C4—201no—
255C22×C4C3×D2011yescharacteristic
256Q16—52no—
257Q16—101no—
258SD16—102no—
259SD16—102no—
260D8—52no—
261D8—101no—
262D8—102no—
263M16—22no—
264C2×C8C3×D2011yescharacteristic
265C2×C8C22×C3×D511yescharacteristic
266C4⋊C4—101no—
267C22⋊C4—201no—
268C16—22no—
269C3×C5#219011yescharacteristic, complemented, Hall
270C22×C3—21no—
271C22×C3—41no—
272C22×C3—202no—
273C22×C3—401no—
274C22×C3—401no—
275C22×C3—402no—
276C22×C3—401no—
277C22×C3C2×D4011yescharacteristic
278C3×C4—21no—
279C3×C4—202no—
280C3×C4—401no—
281C3×C4#402811yescharacteristic
282C3×C4#405411yescharacteristic
283C2×C5—21no—
284C2×C5—41no—
285C2×C5C3×#44711yescharacteristic
286D5—82no—
287D5—161no—
288C23—201no—
289C23—201no—
290C23C3×D4011yescharacteristic
291Q8—102no—
292Q8—201no—
293D4—102no—
294D4—201no—
295D4—202no—
296D4—202no—
297D4—201no—
298D4—201no—
299D4—402no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—202no—
303C2×C4—201no—
304C2×C4—202no—
305C2×C4—201no—
306C2×C4C3×D4011yescharacteristic
307C2×C4C2×C3×D2011yescharacteristic
308C8—21no—
309C8C3×D4×D512yes—
310C2×C3—21no—
311C2×C3—41no—
312C2×C3—402no—
313C2×C3—801no—
314C2×C3#6502111yescharacteristic
315C5C3×#219011yescharacteristic, complemented, Sylow
316C22—21no—
317C22—41no—
318C22—202no—
319C22—401no—
320C22—401no—
321C22—402no—
322C22—401no—
323C22C2×C3×D4011yescharacteristic
324C4—21no—
325C4—202no—
326C4—401no—
327C4C3×#402811yescharacteristic
328C4C3×#405411yescharacteristic
329C3#1059991311yescharacteristic, direct product factor, Sylow
330C2—21no—
331C2—41no—
332C2—402no—
333C2—801no—
334C2C3×#6502111yescharacteristic
subgroupG/H
centerC2×C3#65021
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#349C2
socleC2×C3×C5#447
hypercenterC3×#349D5
hypocenterC5C3×#2190
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×M16 ◁ C3×#349

Complements

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

NH ≅ G/Ntype
1. C3×#66082C2semidirect
2. C3×#65424C2semidirect
3. C3×#65197C2semidirect
4. C3×C5×#349C2semidirect
5. C3×#64738C2semidirect
6. #10599913C3direct (N × H)
14. C2×C3×D40C22semidirect
15. C3×C5×M32C22semidirect
17. C3×#3949C22semidirect
21. #66082C2×C3semidirect
22. #65424C2×C3semidirect
23. #65197C2×C3semidirect
24. C5×#349C2×C3semidirect
25. #64738C2×C3semidirect
43. C3×Dic20D4semidirect
46. C3×D40D4semidirect
54. C3×#349D5semidirect
62. C2×D40C22×C3semidirect
63. C5×M32C22×C3semidirect
65. #3949C22×C3semidirect
101. C3×M32C2×D5semidirect
121. Dic20C3×D4semidirect
124. D40C3×D4semidirect
132. #349C3×D5semidirect
202. M32C2×C3×D5semidirect
269. C3×C5#2190semidirect
315. C5C3×#2190semidirect
329. C3#10599913direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660822
C3×#654242
C3×#651972
C3×C5×#3492
C3×#647382
#105999133
C3×#21905