Finite Group Databasebeta

← #14418626

Subgroups — #14418626

Order 1920.

696 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
1#11754617C211yesmaximal, characteristic
2C2×#91099C211yesmaximal, characteristic
3C5×#5102C211yesmaximal, characteristic
4C3×#65391C211yesmaximal, characteristic
5#11748437C211yesmaximal, characteristic
6#11748327C211yesmaximal, characteristic
7#11748320C211yesmaximal, characteristic
8#11747821C214yesmaximal, complemented
9#11747569C214yesmaximal, complemented
10#10610808—31nomaximal, Hall
11C22×C3×C5×C8C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C3×#4072C2211yescharacteristic
17C2×C3×#681C2211yescharacteristic
18#91576C414yes—
19#91470C412yes—
20C4×#1204C2214yes—
21#91384C412yes—
22#91099C2212yes—
23#91099C2212yes—
24C5×Dic3⋊C8C2214yes—
25C3×#3946C2214yes—
26#90983C2214yes—
27#90953C2212yes—
28#90952C2212yes—
29Dic3×#168C2212yes—
30Dic5×C3⋊C8C2212yes—
31#79077—51nomaximal, Hall
32#65851—31no—
33C5×#424—31no—
34#65411—31no—
35#65407—31no—
36#65391D311yescharacteristic
37C2×#3947—31no—
38#65286—31no—
39#65120—34no—
40#65117—34no—
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15C2×C412yes—
43C2×#1204C2×C414yes—
44C2×C3×C5×C8—22no—
45C2×C3×C5×C8C2312yes—
46C4×Dic15C2×C411yescharacteristic
47C4×Dic15C2×C411yescharacteristic
48C4×Dic15C2312yes—
49C2×C3⋊#168Q814yescomplemented
50C2×C3⋊#168C2311yescharacteristic
51C2×C3⋊#168C2311yescharacteristic
52C5×#217C2×C412yes—
53C5×C4⋊Dic3C2×C412yes—
54C4×C5×Dic3C2312yes—
55C5×#208—22no—
56C2×C5×C3⋊C8C2312yes—
57C3×C22⋊Dic5C2×C412yes—
58C3×C4⋊Dic5C2×C412yes—
59C3×C4×Dic5C2312yes—
60C3×#681—22no—
61C2×C3×#168C2312yes—
62Dic3⋊Dic5C2×C414yes—
63#6669C2×C414yes—
64#6668C2×C414yes—
65#5517—51no—
66C3×#424—51no—
67#5122—51no—
68#5118—51no—
69#5102D511yescharacteristic
70C2×#815—51no—
71#4997—51no—
72#4831—54no—
73#4828—54no—
74C2×C5×M16—31no—
75C22×C5×C8C2×D311yescharacteristic
76C5×#117—31no—
77#4072C2×D311yescharacteristic
78C2×C4×Dic5—31no—
79C2×#681C2×D311yescharacteristic
80C22×#168—31no—
81#4036—32no—
82#4034—32no—
83#4024—34no—
84C4×Dic10—34no—
85C5×C4⋊C8—34no—
86#3947—32no—
87#3947—32no—
88#3947—32no—
89#3946—34no—
90#3946C2×D314yes—
91C8×Dic5—32no—
92#3935—32no—
93C4×#168—32no—
94#2961—151noSylow
95C23×C3×C5C22×C411yescharacteristic
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×Q812yes—
98C2×C3×C4×C5#4112yes—
99C2×C3×C4×C5C2411yescharacteristic
100C2×Dic15—42no—
101C2×Dic15C22×C412yes—
102C2×Dic15C22×C412yes—
103C2×C5×Dic3C22×C414yes—
104C2×C3×Dic5C22×C414yes—
105#1204—44no—
106C3×C5×C8—22no—
107C3⋊#168C2×Q812yes—
108C3⋊#168C2×Q812yes—
109C3×#168—22no—
110C5×C3⋊C8—22no—
111C2×C3×M16—51no—
112C22×C3×C8C2×D511yescharacteristic
113C3×#117—51no—
114#926C2×D511yescharacteristic
115C2×C4×Dic3—51no—
116C2×#208C2×D511yescharacteristic
117C22×C3⋊C8—51no—
118#890—52no—
119#888—52no—
120#878—54no—
121C4×Dic6—54no—
122C3×C4⋊C8—54no—
123#815—52no—
124#815—52no—
125#815—52no—
126Dic3⋊C8—54no—
127Dic3⋊C8C2×D514yes—
128C8×Dic3—52no—
129#803—52no—
130C4×C3⋊C8—52no—
131C22×C4×C5C22×D311yescharacteristic
132C22×Dic5—32no—
133C2×Dic10—34no—
134C5×M16—62no—
135C2×C5×C8—22no—
136C2×C5×C8—32no—
137C2×C5×C8C22×D312yes—
138C5×C4⋊C4—32no—
139C5×C22⋊C4—32no—
140C42×C5—32no—
141C22⋊Dic5C4×D312yes—
142C4⋊Dic5—34no—
143C4⋊Dic5C4×D312yes—
144#683—34no—
145#683—34no—
146C4×Dic5—31no—
147C4×Dic5—31no—
148C4×Dic5—32no—
149C4×Dic5C22×D312yes—
150#681—22no—
151C2×#168—34no—
152C2×#168—31no—
153C2×#168—31no—
154C2×#168C22×D312yes—
155#533—151no—
156#446—154no—
157#446—154no—
158#424—31no—
159#424—51no—
160#423—151no—
161#405—151no—
162#405—151no—
163C2×#97—151no—
164C22×C3×C5—22no—
165C22×C3×C5C4×Q812yes—
166C22×C3×C5C23×C411yescharacteristic
167C3×C4×C5C4×Q812yes—
168C3×C4×C5C22×Q811yescharacteristic
169C3×C4×C5C2×#4111yescharacteristic
170Dic15—22no—
171Dic15—22no—
172C3×Dic5—24no—
173C5×Dic3—24no—
174C22×C3×C4C22×D511yescharacteristic
175C22×Dic3—52no—
176C2×Dic6—54no—
177C3×M16—102no—
178C2×C3×C8—22no—
179C2×C3×C8—52no—
180C2×C3×C8C22×D512yes—
181C3×C4⋊C4—52no—
182C3×C22⋊C4—52no—
183C3×C42—52no—
184#217C4×D512yes—
185C4⋊Dic3—54no—
186C4⋊Dic3C4×D512yes—
187Dic3⋊C4—54no—
188Dic3⋊C4—54no—
189C4×Dic3—51no—
190C4×Dic3—51no—
191C4×Dic3—52no—
192C4×Dic3C22×D512yes—
193#208—22no—
194C2×C3⋊C8—54no—
195C2×C3⋊C8—51no—
196C2×C3⋊C8—51no—
197C2×C3⋊C8C22×D512yes—
198C23×C5C2×C4×D311yescharacteristic
199C2×C4×C5—34no—
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5#23712yes—
202C2×C4×C5D3×Q812yes—
203C2×C4×C5C23×D311yescharacteristic
204C2×Dic5—32no—
205C2×Dic5—32no—
206C2×Dic5—122no—
207C2×Dic5C2×C4×D314yes—
208Dic10—124no—
209C5×C8—22no—
210C5×C8—62no—
211#168—22no—
212#168—32no—
213#168—32no—
214C2×M16—31no—
215C2×M16—51no—
216C22×C8—151no—
217C22×C8D3×D511yescharacteristic
218C4⋊Q8—152no—
219#125—152no—
220C22⋊Q8—154no—
221C4×Q8—154no—
222#117—31no—
223#117—51no—
224C2×C42—151no—
225C4⋊C8—34no—
226C4⋊C8—54no—
227C4⋊C8—154no—
228#97—152no—
229#97—152no—
230#97—152no—
231#97—152no—
232C4×C8—152no—
233C4×C8—152no—
234C2×C3×C5—22no—
235C2×C3×C5C2×C4×Q811yescharacteristic
236C2×C3×C5#56812yes—
237C23×C3C2×C4×D511yescharacteristic
238C2×C3×C4—54no—
239C2×C3×C4C2×C4×D511yescharacteristic
240C2×C3×C4#71112yes—
241C2×C3×C4Q8×D512yes—
242C2×C3×C4C23×D511yescharacteristic
243C2×Dic3—52no—
244C2×Dic3—52no—
245C2×Dic3—202no—
246C2×Dic3C2×C4×D514yes—
247Dic6—204no—
248C3×C8—22no—
249C3×C8—102no—
250C3⋊C8—22no—
251C3⋊C8—52no—
252C3⋊C8—52no—
253C22×C5—22no—
254C22×C5#88712yes—
255C22×C5C22×C4×D311yescharacteristic
256C4×C5—64no—
257C4×C5#88712yes—
258C4×C5C2×#23711yescharacteristic
259C4×C5C2×D3×Q811yescharacteristic
260Dic5—24no—
261Dic5—62no—
262Dic5—62no—
263C2×Q8—154no—
264C22×C4—152no—
265C22×C4C2×D3×D511yescharacteristic
266M16—62no—
267M16—102no—
268C2×C8—22no—
269C2×C8—32no—
270C2×C8—52no—
271C2×C8—154no—
272C2×C8—151no—
273C2×C8—151no—
274C2×C8C2×D3×D512yes—
275C4⋊C4—32no—
276C4⋊C4—52no—
277C4⋊C4—154no—
278C4⋊C4—154no—
279C4⋊C4—154no—
280C22⋊C4—32no—
281C22⋊C4—52no—
282C42—32no—
283C42—52no—
284C42—151no—
285C42—151no—
286C42—152no—
287C3×C5#296111yescharacteristic, complemented, Hall
288C22×C3—22no—
289C22×C3#403312yes—
290C22×C3C22×C4×D511yescharacteristic
291C3×C4—104no—
292C3×C4#403312yes—
293C3×C4C2×#71111yescharacteristic
294C3×C4C2×Q8×D511yescharacteristic
295Dic3—24no—
296Dic3—102no—
297Dic3—102no—
298C2×C5—22no—
299C2×C5C2×#88711yescharacteristic
300C2×C5#575012yes—
301C23C4×D3×D511yescharacteristic
302Q8—604no—
303C2×C4—34no—
304C2×C4—54no—
305C2×C4—152no—
306C2×C4—152no—
307C2×C4—602no—
308C2×C4D15⋊Q812yes—
309C2×C4C4×D3×D511yescharacteristic
310C2×C4#678012yes—
311C2×C4C22×D3×D511yescharacteristic
312C8—22no—
313C8—62no—
314C8—102no—
315C8—152no—
316C8—152no—
317C2×C3—22no—
318C2×C3C2×#403311yescharacteristic
319C2×C3#6608412yes—
320C5#7907711yescharacteristic, complemented, Sylow
321C22—22no—
322C22#9132512yes—
323C22C2×C4×D3×D511yescharacteristic
324C4—64no—
325C4—104no—
326C4—302no—
327C4—302no—
328C4#9132512yes—
329C4C2×D15⋊Q811yescharacteristic
330C4C2×#678011yescharacteristic
331C3#1061080811yescharacteristic, complemented, Sylow
332C2—22no—
333C2#1175395312yes—
334C2C2×#9132511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C5×C8C22
prime radicalC23×C3×C5C22×C4
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#2961
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
8. #11747821C2semidirect
9. #11747569C2semidirect
49. C2×C3⋊#168Q8semidirect
287. C3×C5#2961semidirect
320. C5#79077semidirect
331. C3#10610808semidirect

Maximal subgroups

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

subgroupindex
#117546172
C2×#910992
C5×#51022
C3×#653912
#117484372
#117483272
#117483202
#117478212
#117475692
#106108083
#790775