Finite Group Databasebeta

← #14297578

Subgroups — #14297578

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4039C211yesmaximal, characteristic
2#11748431C212yesmaximal, complemented
3C2×#90958C212yesmaximal
4#11746351C211yesmaximal, characteristic, complemented
5C5×#4530C211yesmaximal, characteristic, complemented
6#10599787—31nomaximal, Hall
7C22×C3×D20C2211yescharacteristic
8C22×C3×C4×D5C412yes—
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×#6710C2212yes—
11C2×C5×#208C2212yes—
12C2×C3×#685C412yes—
13C2×C3×C4×Dic5C2211yescharacteristic
14C3×#4039—22no—
15C3×#4039—22no—
16#90982—22no—
17#90982—22no—
18#90958—24no—
19#71617—51nomaximal, Hall
20C2×#4039D311yescharacteristic
21C2×#3955—32no—
22#65407—32no—
23C5×#343—31no—
24#64750—31no—
25C23×C3×D5C2×C412yes—
26C22×C3×C4×C5C2×C412yes—
27C22×C3×C4×C5C2311yescharacteristic
28C22×C3×Dic5C2×C411yescharacteristic
29C22×C3×Dic5C2×C411yescharacteristic
30C2×C3×D20—22no—
31C2×C3×D20—22no—
32C2×C3×D20D412yes—
33C2×C3×D20Q812yes—
34C2×C3×C4×D5—22no—
35C2×C3×C4×D5—22no—
36C2×C3×C4×D5—44no—
37C3×C5×C4⋊C4—22no—
38#6710—22no—
39#6710—22no—
40C2×C3⋊#168—22no—
41C5×#208—22no—
42C5×#208—22no—
43C2×C5×C3⋊C8—22no—
44C3×#685—24no—
45C3×C4×Dic5D412yes—
46C3×C4×Dic5D412yes—
47C2×C3×C4×D4—51no—
48C2×#833—52no—
49#4924—52no—
50#4530—51no—
51#4530D511yescharacteristic, complemented
52C22×D20C2×D311yescharacteristic
53C22×C4×D5Dic312yes—
54C2×C5×M16—32no—
55C2×C5×C4⋊C4C2×D311yescharacteristic
56C2×#685Dic312yes—
57C2×C4×Dic5C2×D311yescharacteristic
58C2×#681—32no—
59#4039—22no—
60#4039—22no—
61#3955—64no—
62#3946—62no—
63#3946—62no—
64#1800—151noSylow
65C23×C3×C5C22×C411yescharacteristic
66C22×C3×D5—22no—
67C22×C3×D5—22no—
68C22×C3×D5—42no—
69C22×C3×D5—42no—
70C22×C3×D5C4⋊C414yes—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—42no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C2×C3×C4×C5C2×Q811yescharacteristic
76C2×C3×C4×C5#4112yes—
77C2×C3×Dic5—22no—
78C2×C3×Dic5—41no—
79C2×C3×Dic5C22⋊C412yes—
80C2×C3×Dic5C22⋊C411yescharacteristic
81C2×C3×Dic5C22⋊C411yescharacteristic
82C3×D20—24no—
83C3×D20—24no—
84C3×C4×D5—44no—
85C3×C4×D5—44no—
86C3⋊#168—42no—
87C5×C3⋊C8—42no—
88C22×C3×D4—51no—
89C23×C3×C4—52no—
90C3×C4×D4—102no—
91C3×C4×D4—102no—
92C2×C3×C4⋊C4C2×D511yescharacteristic
93C2×C3×C22⋊C4—52no—
94C2×C3×C42—51no—
95C2×#208—52no—
96C2×#208C2×D512yes—
97#833—104no—
98C4⋊(C3⋊C8)—102no—
99C4⋊(C3⋊C8)—102no—
100C23×D5C2×Dic312yes—
101C22×C4×C5C2×Dic312yes—
102C22×C4×C5C22×D311yescharacteristic
103C22×Dic5C2×Dic311yescharacteristic
104C22×Dic5C2×Dic311yescharacteristic
105C2×D20—22no—
106C2×D20—22no—
107C2×D20Dic612yes—
108C2×D20D1212yes—
109C2×C4×D5—22no—
110C2×C4×D5—22no—
111C2×C4×D5—44no—
112C5×M16—62no—
113C5×M16—62no—
114C2×C5×C8—62no—
115C5×C4⋊C4—22no—
116#685—24no—
117C4×Dic5#6712yes—
118C4×Dic5#6712yes—
119#681—62no—
120#681—62no—
121C2×#168—62no—
122C2×C4×D4—51no—
123#423—152no—
124C2×#100—152no—
125#343—31no—
126#343—151no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C22×C3×C5C2×C4⋊C411yescharacteristic
131C22×C3×C5#11711yescharacteristic
132C2×C3×D5—24no—
133C2×C3×D5—44no—
134C2×C3×D5—42no—
135C2×C3×D5—42no—
136C2×C3×D5—44no—
137C3×C4×C5—42no—
138C3×C4×C5#12112yes—
139C3×C4×C5C22⋊Q812yes—
140C3×Dic5—21no—
141C3×Dic5—22no—
142C3×Dic5#10012yescomplemented
143C24×C3—52no—
144C2×C3×D4—52no—
145C2×C3×D4—52no—
146C2×C3×D4—102no—
147C2×C3×D4—102no—
148C22×C3×C4—51no—
149C22×C3×C4—51no—
150C22×C3×C4—102no—
151C22×C3×C4—102no—
152C22×C3×C4—204no—
153C22×C3×C4C4×D512yes—
154C22×C3×C4C22×D511yescharacteristic
155C3×C4⋊C4—22no—
156C3×C22⋊C4—104no—
157C3×C42—52no—
158C3×C42—52no—
159#208—22no—
160#208—22no—
161#208—102no—
162#208—102no—
163C2×C3⋊C8—22no—
164C2×C3⋊C8—102no—
165C23×C5C22×Dic311yescharacteristic
166C22×D5—22no—
167C22×D5—22no—
168C22×D5—42no—
169C22×D5—42no—
170C22×D5C4⋊Dic314yes—
171C2×C4×C5—22no—
172C2×C4×C5—42no—
173C2×C4×C5C2×Dic611yescharacteristic
174C2×C4×C5C2×D1211yescharacteristic
175C2×C4×C5#23512yes—
176C2×C4×C5C2×#6712yes—
177C2×Dic5—22no—
178C2×Dic5—41no—
179C2×Dic5#21712yes—
180C2×Dic5#21711yescharacteristic
181C2×Dic5#21711yescharacteristic
182D20—24no—
183D20—24no—
184C4×D5—44no—
185C4×D5—44no—
186C5×C8—122no—
187#168—122no—
188C22×D4—51no—
189C23×C4—52no—
190C2×M16—32no—
191C2×M16—152no—
192C4×D4—102no—
193C4×D4—102no—
194C2×C4⋊C4D3×D511yescharacteristic
195C2×C22⋊C4—52no—
196C2×C42—51no—
197C4⋊C8—302no—
198C4⋊C8—302no—
199#100—304no—
200C2×C3×C5—21no—
201C2×C3×C5—21no—
202C2×C3×C5#38011yescharacteristic
203C2×C3×C5C2×#10011yescharacteristic
204C2×C3×C5#41311yescharacteristic
205C3×D5—44no—
206C23×C3—54no—
207C23×C3—102no—
208C23×C3—102no—
209C23×C3—202no—
210C23×C3—202no—
211C23×C3C2×C4×D511yescharacteristic
212C3×D4—104no—
213C3×D4—104no—
214C2×C3×C4—22no—
215C2×C3×C4—42no—
216C2×C3×C4—51no—
217C2×C3×C4—52no—
218C2×C3×C4—51no—
219C2×C3×C4—102no—
220C2×C3×C4—204no—
221C2×C3×C4—204no—
222C2×C3×C4—201no—
223C2×C3×C4#70912yes—
224C2×C3×C4D4×D511yescharacteristic
225C2×C3×C4D4×D512yes—
226C2×C3×C4Q8×D511yescharacteristic
227C3⋊C8—42no—
228C3⋊C8—202no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5C2×C4⋊Dic311yescharacteristic
232C22×C5#92611yescharacteristic
233C22×C5C2×#21711yescharacteristic
234C2×D5—24no—
235C2×D5—44no—
236C2×D5—42no—
237C2×D5—42no—
238C2×D5—44no—
239C4×C5—42no—
240C4×C5#92412yes—
241C4×C5#93012yes—
242Dic5—21no—
243Dic5—22no—
244Dic5#83312yescomplemented
245C24—52no—
246C2×D4—52no—
247C2×D4—52no—
248C2×D4—102no—
249C2×D4—102no—
250C22×C4—51no—
251C22×C4—51no—
252C22×C4—102no—
253C22×C4—102no—
254C22×C4—204no—
255C22×C4D5×Dic312yes—
256C22×C4C2×D3×D511yescharacteristic
257M16—62no—
258M16—62no—
259M16—302no—
260M16—302no—
261C2×C8—62no—
262C2×C8—302no—
263C4⋊C4—22no—
264C22⋊C4—104no—
265C42—52no—
266C42—52no—
267C3×C5#180011yescharacteristic, complemented, Hall
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—104no—
271C22×C3—204no—
272C22×C3—204no—
273C22×C3—202no—
274C22×C3—202no—
275C22×C3#401811yescharacteristic
276C22×C3D5×C22⋊C411yescharacteristic
277C22×C3D5×C4⋊C411yescharacteristic
278C3×C4—42no—
279C3×C4—52no—
280C3×C4—101no—
281C3×C4—102no—
282C3×C4#403012yes—
283C3×C4#404212yes—
284C2×C5—21no—
285C2×C5—21no—
286C2×C5#521211yescharacteristic
287C2×C5C2×#83311yescharacteristic
288C2×C5#523711yescharacteristic
289D5—44no—
290C23—54no—
291C23—102no—
292C23—102no—
293C23—202no—
294C23—202no—
295C23C2×D5×Dic311yescharacteristic
296D4—104no—
297D4—104no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—51no—
301C2×C4—52no—
302C2×C4—51no—
303C2×C4—102no—
304C2×C4—204no—
305C2×C4—204no—
306C2×C4—201no—
307C2×C4D5×Dic611yescharacteristic
308C2×C4#677112yes—
309C2×C4D5×D1211yescharacteristic
310C2×C4D5×#6712yes—
311C8—122no—
312C8—602no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—204no—
316C2×C3#6495611yescharacteristic
317C2×C3D5×#10011yescharacteristic
318C2×C3#6504011yescharacteristic
319C5#7161711yescharacteristic, complemented, Sylow
320C22—21no—
321C22—21no—
322C22—104no—
323C22—204no—
324C22—204no—
325C22—202no—
326C22—202no—
327C22#9135711yescharacteristic
328C22D5×C4⋊Dic311yescharacteristic
329C22D5×#21711yescharacteristic
330C4—42no—
331C4—52no—
332C4—101no—
333C4—102no—
334C4#9134912yes—
335C4#9144812yes—
336C3#1059978711yescharacteristic, complemented, Sylow
337C2—21no—
338C2—21no—
339C2—204no—
340C2#1174873811yescharacteristic
341C2D5×#83311yescharacteristic
342C2#1174936911yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1800
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11748431C2semidirect
4. #11746351C2semidirect
5. C5×#4530C2semidirect
51. #4530D5semidirect
142. C3×Dic5#100semidirect
244. Dic5#833semidirect
267. C3×C5#1800semidirect
319. C5#71617semidirect
336. C3#10599787semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40392
#117484312
C2×#909582
#117463512
C5×#45302
#105997873
#716175