Finite Group Databasebeta

← #14296929

Subgroups — #14296929

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Q8×D5C211yesmaximal, characteristic
2C2×#91120C211yesmaximal, characteristic, complemented
3C2×C5×#836C211yesmaximal, characteristic, complemented
4C2×#90961C212yesmaximal, complemented
5#11748341C212yesmaximal
6#10600906—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C3×Q8×D5—22no—
9C2×C3×Q8×D5—22no—
10C2×C3×Q8×D5—24no—
11C2×C3×Q8×D5—24no—
12C22×C3×C4×D5C412yes—
13C22×C3×C4×D5C2211yescharacteristic
14C22×C3×Dic10C412yes—
15C22×C3×Dic10C2211yescharacteristic
16C2×#6710C2212yes—
17C2×C5×#208C2212yes—
18#91120—22no—
19C5×#836—22no—
20#90961—24no—
21#90955—24no—
22#72133—51nomaximal, Hall
23C22×Q8×D5D311yescharacteristic
24C2×C5×#101—31no—
25C2×#3968—31no—
26C2×#3956—32no—
27#65415—32no—
28C23×C3×D5C2×C411yescharacteristic
29C2×C3×C5×Q8—22no—
30C2×C3×C5×Q8—22no—
31C2×C3×C5×Q8D412yes—
32C2×C3×C5×Q8D412yes—
33C22×C3×C4×C5C2×C412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C22×C3×Dic5C2×C411yescharacteristic
36C22×C3×Dic5C2×C412yes—
37C3×Q8×D5—216no—
38C3×Q8×D5—216no—
39C2×C3×C4×D5—24no—
40C2×C3×C4×D5—24no—
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—22no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—24no—
45C2×C3×C4×D5D414yes—
46C2×C3×Dic10—24no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—22no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—24no—
51C2×C3×Dic10—24no—
52C2×C3×Dic10D414yes—
53#6710—22no—
54#6710—22no—
55C2×C3⋊#168—22no—
56C5×#208—22no—
57C5×#208—22no—
58C2×C5×C3⋊C8—22no—
59C23×C3×Q8—51no—
60C2×#836—51no—
61C2×#836—52no—
62C2×#836D511yescharacteristic, complemented
63#5207—52no—
64C22×C5×Q8C2×D311yescharacteristic
65C2×Q8×D5—22no—
66C2×Q8×D5—22no—
67C2×Q8×D5—24no—
68C2×Q8×D5—24no—
69C22×C4×D5Dic312yes—
70C22×C4×D5C2×D311yescharacteristic
71C22×Dic10Dic312yes—
72C22×Dic10C2×D311yescharacteristic
73C2×C5×M16—32no—
74C2×#681—32no—
75C5×#101—62no—
76#3968—62no—
77#3956—64no—
78#3952—64no—
79#1784—151noSylow
80C23×C3×C5C22×C411yescharacteristic
81C22×C3×D5—21no—
82C22×C3×D5—21no—
83C22×C3×D5—24no—
84C22×C3×D5C22⋊C412yes—
85C3×C5×Q8—24no—
86C3×C5×Q8—24no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5—22no—
89C2×C3×C4×C5C22⋊C414yes—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D412yes—
92C2×C3×C4×C5C2×D412yes—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×Dic5—21no—
95C2×C3×Dic5—22no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—22no—
98C2×C3×Dic5C22⋊C412yes—
99C2×C3×Dic5C22⋊C414yes—
100C3×C4×D5—216no—
101C3×C4×D5—24no—
102C3×C4×D5—24no—
103C3×Dic10—216no—
104C3×Dic10—24no—
105C3×Dic10—24no—
106C3⋊#168—42no—
107C5×C3⋊C8—42no—
108C22×C3×Q8—52no—
109C22×C3×Q8—51no—
110C22×C3×Q8—104no—
111C22×C3×Q8—104no—
112C22×C3×Q8—102no—
113C22×C3×Q8—102no—
114C22×C3×Q8C2×D511yescharacteristic
115C23×C3×C4—51no—
116C23×C3×C4—52no—
117C2×#208—52no—
118C2×#208C2×D512yes—
119#836—22no—
120#836—104no—
121#836—102no—
122#830—104no—
123C23×D5C2×Dic311yescharacteristic
124C2×C5×Q8—22no—
125C2×C5×Q8—22no—
126C2×C5×Q8#6712yes—
127C2×C5×Q8#6712yes—
128C22×C4×C5C2×Dic312yes—
129C22×C4×C5C22×D311yescharacteristic
130C22×Dic5C2×Dic311yescharacteristic
131C22×Dic5C2×Dic312yes—
132Q8×D5—216no—
133Q8×D5—216no—
134C2×C4×D5—24no—
135C2×C4×D5—24no—
136C2×C4×D5—21no—
137C2×C4×D5—21no—
138C2×C4×D5—22no—
139C2×C4×D5—24no—
140C2×C4×D5#6714yes—
141C2×Dic10—24no—
142C2×Dic10—21no—
143C2×Dic10—21no—
144C2×Dic10—22no—
145C2×Dic10—24no—
146C2×Dic10—24no—
147C2×Dic10#6714yes—
148C5×M16—62no—
149C5×M16—62no—
150C2×C5×C8—62no—
151#681—62no—
152#681—62no—
153C2×#168—62no—
154C23×Q8—51no—
155C2×#101—31no—
156C2×#101—152no—
157C2×#101—151no—
158#407—152no—
159C22×C3×C5—22no—
160C22×C3×C5C2×C22⋊C411yescharacteristic
161C22×C3×C5C2×C22⋊C411yescharacteristic
162C22×C3×C5C2×C22⋊C411yescharacteristic
163C2×C3×D5—24no—
164C2×C3×D5—24no—
165C2×C3×D5—22no—
166C2×C3×D5—22no—
167C2×C3×D5#10114yescomplemented
168C3×C4×C5—24no—
169C3×C4×C5#12012yes—
170C3×C4×C5#12012yes—
171C3×Dic5—22no—
172C3×Dic5—24no—
173C24×C3—51no—
174C2×C3×Q8—22no—
175C2×C3×Q8—22no—
176C2×C3×Q8—54no—
177C2×C3×Q8—104no—
178C2×C3×Q8—104no—
179C2×C3×Q8—1016no—
180C2×C3×Q8—1016no—
181C2×C3×Q8—104no—
182C2×C3×Q8—101no—
183C2×C3×Q8—102no—
184C2×C3×Q8—101no—
185C2×C3×Q8D2012yes—
186C2×C3×Q8C22⋊D512yes—
187C22×C3×C4—51no—
188C22×C3×C4—52no—
189C22×C3×C4—54no—
190C22×C3×C4—104no—
191C22×C3×C4—104no—
192C22×C3×C4—104no—
193C22×C3×C4—101no—
194C22×C3×C4—102no—
195C22×C3×C4—101no—
196C22×C3×C4C4×D512yes—
197C22×C3×C4C22×D511yescharacteristic
198#208—22no—
199#208—22no—
200#208—102no—
201#208—102no—
202C2×C3⋊C8—22no—
203C2×C3⋊C8—102no—
204C23×C5C22×Dic311yescharacteristic
205C22×D5—21no—
206C22×D5—21no—
207C22×D5—24no—
208C22×D5#21712yes—
209C5×Q8—24no—
210C5×Q8—24no—
211C2×C4×C5—22no—
212C2×C4×C5—22no—
213C2×C4×C5#21714yes—
214C2×C4×C5C2×#6711yescharacteristic
215C2×C4×C5C2×#6711yescharacteristic
216C2×C4×C5C2×#6712yes—
217C2×C4×C5C2×#6712yes—
218C2×Dic5—21no—
219C2×Dic5—22no—
220C2×Dic5—21no—
221C2×Dic5—22no—
222C2×Dic5#21712yes—
223C2×Dic5#21714yes—
224C4×D5—216no—
225C4×D5—24no—
226C4×D5—24no—
227Dic10—216no—
228Dic10—24no—
229Dic10—24no—
230C5×C8—122no—
231#168—122no—
232C22×Q8—52no—
233C22×Q8—51no—
234C22×Q8—104no—
235C22×Q8—104no—
236C22×Q8—102no—
237C22×Q8—102no—
238C22×Q8D3×D511yescharacteristic
239C23×C4—51no—
240C23×C4—52no—
241C2×M16—32no—
242C2×M16—152no—
243#101—62no—
244#101—304no—
245#101—302no—
246C22⋊C8—304no—
247C2×C3×C5—21no—
248C2×C3×C5—21no—
249C2×C3×C5#37911yescharacteristic
250C2×C3×C5C2×#10112yes—
251C3×D5—24no—
252C23×C3—52no—
253C23×C3—104no—
254C23×C3—101no—
255C23×C3—101no—
256C23×C3C2×C4×D511yescharacteristic
257C3×Q8—24no—
258C3×Q8—24no—
259C3×Q8—1016no—
260C3×Q8—104no—
261C3×Q8—104no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—52no—
265C2×C3×C4—54no—
266C2×C3×C4—1016no—
267C2×C3×C4—101no—
268C2×C3×C4—102no—
269C2×C3×C4—102no—
270C2×C3×C4—101no—
271C2×C3×C4—104no—
272C2×C3×C4—104no—
273C2×C3×C4#68514yes—
274C2×C3×C4C2×D2011yescharacteristic
275C2×C3×C4D4×D512yes—
276C2×C3×C4D4×D512yes—
277C2×C3×C4C2×C22⋊D511yescharacteristic
278C3⋊C8—42no—
279C3⋊C8—202no—
280C22×C5—22no—
281C22×C5C2×#21711yescharacteristic
282C22×C5C2×#21711yescharacteristic
283C22×C5C2×#21711yescharacteristic
284C2×D5—24no—
285C2×D5—24no—
286C2×D5—22no—
287C2×D5—22no—
288C2×D5#83614yescomplemented
289C4×C5—24no—
290C4×C5#95312yes—
291C4×C5#95312yes—
292Dic5—22no—
293Dic5—24no—
294C24—51no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—54no—
298C2×Q8—104no—
299C2×Q8—104no—
300C2×Q8—1016no—
301C2×Q8—1016no—
302C2×Q8—104no—
303C2×Q8—101no—
304C2×Q8—101no—
305C2×Q8—102no—
306C2×Q8#120112yes—
307C2×Q8#120212yes—
308C22×C4—52no—
309C22×C4—51no—
310C22×C4—54no—
311C22×C4—104no—
312C22×C4—104no—
313C22×C4—104no—
314C22×C4—101no—
315C22×C4—101no—
316C22×C4—102no—
317C22×C4D5×Dic312yes—
318C22×C4C2×D3×D511yescharacteristic
319M16—62no—
320M16—62no—
321M16—302no—
322M16—302no—
323C2×C8—62no—
324C2×C8—302no—
325C3×C5#178411yescharacteristic, complemented, Hall
326C22×C3—22no—
327C22×C3—54no—
328C22×C3—104no—
329C22×C3—104no—
330C22×C3—102no—
331C22×C3—102no—
332C22×C3D5×C22⋊C411yescharacteristic
333C22×C3D5×C22⋊C411yescharacteristic
334C22×C3C2×#68511yescharacteristic
335C3×C4—24no—
336C3×C4—102no—
337C3×C4—104no—
338C3×C4#402812yes—
339C3×C4#408312yes—
340C2×C5—21no—
341C2×C5—21no—
342C2×C5C2×#83612yes—
343C2×C5#524711yescharacteristic
344D5—24no—
345C23—52no—
346C23—104no—
347C23—101no—
348C23—101no—
349C23C2×D5×Dic311yescharacteristic
350Q8—24no—
351Q8—24no—
352Q8—1016no—
353Q8—104no—
354Q8—104no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—54no—
358C2×C4—52no—
359C2×C4—1016no—
360C2×C4—102no—
361C2×C4—101no—
362C2×C4—101no—
363C2×C4—102no—
364C2×C4—104no—
365C2×C4—104no—
366C2×C4#666514yes—
367C2×C4C2×#120111yescharacteristic
368C2×C4C2×#120211yescharacteristic
369C2×C4D5×#6712yes—
370C2×C4D5×#6712yes—
371C8—122no—
372C8—602no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—104no—
376C2×C3D5×#10112yes—
377C2×C3#6524411yescharacteristic
378C5#7213311yescharacteristic, complemented, Sylow
379C22—22no—
380C22—54no—
381C22—104no—
382C22—104no—
383C22—102no—
384C22—102no—
385C22C2×#666511yescharacteristic
386C22D5×#21711yescharacteristic
387C22D5×#21711yescharacteristic
388C4—24no—
389C4—104no—
390C4—102no—
391C4#9156312yes—
392C4#9156412yes—
393C3#1060090611yescharacteristic, complemented, Sylow
394C2—21no—
395C2—21no—
396C2—104no—
397C2D5×#83612yes—
398C2#1174948811yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1784
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#91120C2semidirect
3. C2×C5×#836C2semidirect
4. C2×#90961C2semidirect
62. C2×#836D5semidirect
167. C2×C3×D5#101semidirect
288. C2×D5#836semidirect
325. C3×C5#1784semidirect
378. C5#72133semidirect
393. C3#10600906semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Q8×D52
C2×#911202
C2×C5×#8362
C2×#909612
#117483412
#106009063
#721335