Finite Group Databasebeta

← #14298387

Subgroups — #14298387

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic5C211yesmaximal, characteristic
2#11751308C211yesmaximal, characteristic
3C5×#5207C211yesmaximal, characteristic
4#11745985C214yesmaximal, complemented
5#10600766—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C23×C3×Dic5C412yes—
8C2×#6710C2212yes—
9C2×C5×#208C2212yes—
10C2×C3×C4⋊Dic5—21no—
11C2×C3×C4⋊Dic5—21no—
12C2×C3×C4⋊Dic5—21no—
13C2×C3×C4⋊Dic5—21no—
14C2×C3×C4⋊Dic5C412yes—
15C2×C3×C4⋊Dic5C2212yes—
16#91114—21no—
17#91114—21no—
18C5×#830—21no—
19C5×#830—21no—
20#71562—51nomaximal, Hall
21C22×C4⋊Dic5D311yescharacteristic
22C5×#407—31no—
23#65496—31no—
24#64774—34no—
25C24×C3×C5C2×C411yescharacteristic
26C22×C3×C4×C5—24no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5D411yescharacteristic
29C22×C3×C4×C5D411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C22×C3×Dic5—22no—
34C22×C3×Dic5—22no—
35C22×C3×Dic5—44no—
36C22×C3×Dic5C2×C414yes—
37#6710—24no—
38C2×C3⋊#168—22no—
39C5×#208—24no—
40C2×C5×C3⋊C8—22no—
41C3×C4⋊Dic5—22no—
42C3×C4⋊Dic5—22no—
43C3×C4⋊Dic5—22no—
44C3×C4⋊Dic5—22no—
45C22×C3×C4⋊C4—51no—
46#5207—51no—
47#5207D511yescharacteristic
48#4530—54no—
49C23×C4×C5C2×D311yescharacteristic
50C23×Dic5Dic312yes—
51C2×C5×M16—32no—
52C2×C4⋊Dic5—21no—
53C2×C4⋊Dic5—21no—
54C2×C4⋊Dic5—21no—
55C2×C4⋊Dic5—21no—
56C2×C4⋊Dic5Dic312yes—
57C2×C4⋊Dic5C2×D312yes—
58C2×#681—32no—
59C5×C22⋊C8—61no—
60C5×C22⋊C8—61no—
61C22⋊#168—61no—
62C22⋊#168—61no—
63#1821—151noSylow
64C23×C3×C5—22no—
65C23×C3×C5—22no—
66C23×C3×C5—22no—
67C23×C3×C5C22⋊C411yescharacteristic
68C23×C3×C5C22⋊C411yescharacteristic
69C23×C3×C5C22×C411yescharacteristic
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5C22⋊C411yescharacteristic
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4114yes—
80C2×C3×Dic5—24no—
81C2×C3×Dic5—44no—
82C2×C3×Dic5—44no—
83C2×C3×Dic5—44no—
84C3⋊#168—42no—
85C5×C3⋊C8—42no—
86C23×C3×C4—52no—
87C23×C3×C4C2×D511yescharacteristic
88C2×C3×C4⋊C4—52no—
89C2×C3×C4⋊C4—52no—
90C2×C3×C4⋊C4—101no—
91C2×C3×C4⋊C4—101no—
92C2×C3×C4⋊C4—101no—
93C2×C3×C4⋊C4—101no—
94C2×#208—52no—
95C2×#208C2×D512yes—
96#830—21no—
97#830—21no—
98#830—101no—
99#830—101no—
100C24×C5C2×Dic311yescharacteristic
101C22×C4×C5—24no—
102C22×C4×C5C2×Dic311yescharacteristic
103C22×C4×C5#6711yescharacteristic
104C22×C4×C5#6711yescharacteristic
105C22×C4×C5#6711yescharacteristic
106C22×C4×C5#6711yescharacteristic
107C22×C4×C5C22×D311yescharacteristic
108C22×Dic5—22no—
109C22×Dic5—22no—
110C22×Dic5—44no—
111C22×Dic5C2×Dic314yes—
112C5×M16—64no—
113C2×C5×C8—62no—
114C4⋊Dic5—22no—
115C4⋊Dic5—22no—
116C4⋊Dic5—22no—
117C4⋊Dic5—22no—
118#681—64no—
119C2×#168—62no—
120C22×C4⋊C4—51no—
121#407—31no—
122#407—151no—
123#343—154no—
124C22×C3×C5—28no—
125C22×C3×C5—21no—
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5—21no—
130C22×C3×C5—21no—
131C22×C3×C5#10012yes—
132C22×C3×C5#10112yes—
133C22×C3×C5C2×C22⋊C411yescharacteristic
134C22×C3×C5#11712yes—
135C3×C4×C5—21no—
136C3×C4×C5—21no—
137C3×C4×C5#12312yes—
138C3×C4×C5#12312yes—
139C3×Dic5—44no—
140C24×C3C4×D511yescharacteristic
141C22×C3×C4—24no—
142C22×C3×C4—54no—
143C22×C3×C4—102no—
144C22×C3×C4—102no—
145C22×C3×C4—204no—
146C22×C3×C4C4×D511yescharacteristic
147C22×C3×C4D2011yescharacteristic
148C22×C3×C4D2011yescharacteristic
149C22×C3×C4C22⋊D511yescharacteristic
150C22×C3×C4C22⋊D511yescharacteristic
151C22×C3×C4C22×D511yescharacteristic
152C3×C4⋊C4—102no—
153C3×C4⋊C4—102no—
154C3×C4⋊C4—102no—
155C3×C4⋊C4—102no—
156#208—24no—
157#208—104no—
158C2×C3⋊C8—22no—
159C2×C3⋊C8—102no—
160C23×C5—22no—
161C23×C5—22no—
162C23×C5—22no—
163C23×C5#21711yescharacteristic
164C23×C5#21711yescharacteristic
165C23×C5C22×Dic311yescharacteristic
166C2×C4×C5—22no—
167C2×C4×C5—22no—
168C2×C4×C5—22no—
169C2×C4×C5—22no—
170C2×C4×C5—22no—
171C2×C4×C5#21711yescharacteristic
172C2×C4×C5#21711yescharacteristic
173C2×C4×C5#23514yes—
174C2×C4×C5C2×#6711yescharacteristic
175C2×C4×C5C2×#6711yescharacteristic
176C2×Dic5—24no—
177C2×Dic5—44no—
178C2×Dic5—44no—
179C2×Dic5—44no—
180C5×C8—122no—
181#168—122no—
182C23×C4—52no—
183C23×C4D3×D511yescharacteristic
184C2×M16—32no—
185C2×M16—152no—
186C2×C4⋊C4—52no—
187C2×C4⋊C4—52no—
188C2×C4⋊C4—101no—
189C2×C4⋊C4—101no—
190C2×C4⋊C4—101no—
191C2×C4⋊C4—101no—
192C22⋊C8—61no—
193C22⋊C8—61no—
194C22⋊C8—301no—
195C22⋊C8—301no—
196C2×C3×C5—22no—
197C2×C3×C5—22no—
198C2×C3×C5—22no—
199C2×C3×C5#38111yescharacteristic
200C2×C3×C5C2×#10011yescharacteristic
201C2×C3×C5C2×#10111yescharacteristic
202C23×C3—22no—
203C23×C3—22no—
204C23×C3—22no—
205C23×C3#68511yescharacteristic
206C23×C3#68511yescharacteristic
207C23×C3C2×C4×D511yescharacteristic
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—104no—
214C2×C3×C4—204no—
215C2×C3×C4—204no—
216C2×C3×C4—204no—
217C2×C3×C4#68511yescharacteristic
218C2×C3×C4#68511yescharacteristic
219C2×C3×C4C2×D2011yescharacteristic
220C2×C3×C4#71114yes—
221C2×C3×C4C2×C22⋊D511yescharacteristic
222C3⋊C8—42no—
223C3⋊C8—202no—
224C22×C5—28no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5#83312yes—
232C22×C5#83612yes—
233C22×C5#92612yes—
234C22×C5C2×#21711yescharacteristic
235C4×C5—21no—
236C4×C5—21no—
237C4×C5#92912yes—
238C4×C5#92912yes—
239Dic5—44no—
240C24D5×Dic311yescharacteristic
241C22×C4—24no—
242C22×C4—54no—
243C22×C4—102no—
244C22×C4—102no—
245C22×C4—204no—
246C22×C4D5×Dic311yescharacteristic
247C22×C4#120111yescharacteristic
248C22×C4#120111yescharacteristic
249C22×C4#120211yescharacteristic
250C22×C4#120211yescharacteristic
251C22×C4C2×D3×D511yescharacteristic
252M16—64no—
253M16—304no—
254C2×C8—62no—
255C2×C8—302no—
256C4⋊C4—102no—
257C4⋊C4—102no—
258C4⋊C4—102no—
259C4⋊C4—102no—
260C3×C5#182111yescharacteristic, complemented, Hall
261C22×C3—28no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3#395512yes—
269C22×C3#395612yes—
270C22×C3#402312yes—
271C22×C3C2×#68511yescharacteristic
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—204no—
275C3×C4#403212yes—
276C3×C4#408112yes—
277C2×C5—22no—
278C2×C5—22no—
279C2×C5—22no—
280C2×C5#521111yescharacteristic
281C2×C5C2×#83311yescharacteristic
282C2×C5C2×#83611yescharacteristic
283C23—22no—
284C23—22no—
285C23—22no—
286C23#666511yescharacteristic
287C23#666511yescharacteristic
288C23C2×D5×Dic311yescharacteristic
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—104no—
295C2×C4—204no—
296C2×C4—204no—
297C2×C4—204no—
298C2×C4#666511yescharacteristic
299C2×C4#666511yescharacteristic
300C2×C4#678214yes—
301C2×C4C2×#120111yescharacteristic
302C2×C4C2×#120211yescharacteristic
303C8—122no—
304C8—602no—
305C2×C3—22no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3#6523211yescharacteristic
309C2×C3C2×#395511yescharacteristic
310C2×C3C2×#395611yescharacteristic
311C5#7156211yescharacteristic, complemented, Sylow
312C22—28no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22#9095812yes—
320C22#9096112yes—
321C22#9152812yes—
322C22C2×#666511yescharacteristic
323C4—21no—
324C4—21no—
325C4—204no—
326C4#9153912yes—
327C4#9154612yes—
328C3#1060076611yescharacteristic, complemented, Sylow
329C2—22no—
330C2—22no—
331C2—22no—
332C2C2×#9095811yescharacteristic
333C2C2×#9096111yescharacteristic
334C2#1174947111yescharacteristic
subgroupG/H
centerC22C2×#6665
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1821
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #11745985C2semidirect
260. C3×C5#1821semidirect
311. C5#71562semidirect
328. C3#10600766semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic52
#117513082
C5×#52072
#117459852
#106007663
#715625