Finite Group Databasebeta

← #14283155

Subgroups — #14283155

Order 1920.

588 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91813C211yesmaximal, characteristic
2C3×C4×C5×C22⋊C4C211yesmaximal, characteristic
3#11751308C211yesmaximal, characteristic
4#11746273C214yesmaximal, complemented
5#10600238—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×Dic30C411yescharacteristic, complemented
8C2×C3×C5×C22⋊C4—21no—
9C2×C3×C42×C5—21no—
10C2×#6719—21no—
11C2×C4⋊Dic15C411yescharacteristic, complemented
12#91813—21no—
13#91813—21no—
14#91813C412yescomplemented
15#91813C2212yes—
16C2×#6712—21no—
17C2×#6710—21no—
18C3×C5×#95C2212yes—
19#91114—21no—
20#91114C2212yes—
21#69445—51nomaximal, Hall
22C2×#4070—31no—
23C4×C5×C22⋊C4D311yescharacteristic
24#65496—31no—
25#64672—34no—
26C24×C3×C5D411yescharacteristic
27C22×C3×C4×C5—22no—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15—21no—
36C22×Dic15—21no—
37C2×Dic30—21no—
38C2×Dic30—42no—
39C2×Dic30C2×C412yes—
40C3×C5×C22⋊C4—24no—
41C3×C42×C5—42no—
42#6719—22no—
43#6719—22no—
44C4⋊Dic15—21no—
45C4⋊Dic15C2×C412yes—
46#6712—22no—
47#6712—22no—
48#6710—42no—
49C2×C3⋊#168—22no—
50C2×#924—51no—
51C3×C4×C22⋊C4D511yescharacteristic
52#5207—51no—
53#4452—54no—
54C23×C4×C5C2×D311yescharacteristic
55C22×Dic10—31no—
56C2×C5×C22⋊C4—21no—
57C2×C42×C5—21no—
58C2×C22⋊Dic5—61no—
59C2×C4⋊Dic5—31no—
60#4070—32no—
61#4070—32no—
62#4070—61no—
63#4070—61no—
64C2×#683—61no—
65C2×#681—61no—
66C5×#95C2×D312yes—
67C22⋊#168—32no—
68C22⋊#168—61no—
69#1508—151noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—41no—
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5—24no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—42no—
84C2×C3×C4×C5—42no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—22no—
90C2×Dic15—22no—
91C2×Dic15—42no—
92C2×Dic15—42no—
93Dic30—42no—
94Dic30—42no—
95C3⋊#168—42no—
96C23×C3×C4C2×D511yescharacteristic
97C22×Dic6—51no—
98C2×C3×C22⋊C4—21no—
99C2×C3×C42—21no—
100C2×#217—101no—
101C2×C4⋊Dic3—51no—
102#924—52no—
103#924—52no—
104#924—101no—
105#924—101no—
106C2×Dic3⋊C4—101no—
107C2×#208—101no—
108C3×#95C2×D512yes—
109#830—52no—
110#830—101no—
111C24×C5#6711yescharacteristic
112C22×C4×C5—22no—
113C22×C4×C5—42no—
114C22×C4×C5C4×D311yescharacteristic
115C22×C4×C5C4×D311yescharacteristic
116C22×C4×C5D1211yescharacteristic
117C22×C4×C5D1211yescharacteristic
118C22×C4×C5#6711yescharacteristic
119C22×C4×C5C22×D311yescharacteristic
120C22×Dic5—61no—
121C22×Dic5—61no—
122C2×Dic10—32no—
123C2×Dic10—61no—
124C2×Dic10—122no—
125C5×C22⋊C4—24no—
126C42×C5—42no—
127C22⋊Dic5—62no—
128C22⋊Dic5—62no—
129C4⋊Dic5—32no—
130C4⋊Dic5—61no—
131#683—62no—
132#683—62no—
133#681—122no—
134C2×#168—62no—
135C2×C22⋊Q8—151no—
136#407—151no—
137C4×C22⋊C4D1511yescharacteristic
138#328—154no—
139C22×C3×C5—21no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—44no—
147C22×C3×C5#10412yes—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C22×C3×C5#13712yes—
150C3×C4×C5—21no—
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—44no—
154C3×C4×C5#9912yes—
155Dic15—42no—
156Dic15—42no—
157C24×C3C22⋊D511yescharacteristic
158C22×C3×C4—22no—
159C22×C3×C4—42no—
160C22×C3×C4C4×D511yescharacteristic
161C22×C3×C4C4×D511yescharacteristic
162C22×C3×C4D2011yescharacteristic
163C22×C3×C4D2011yescharacteristic
164C22×C3×C4C22⋊D511yescharacteristic
165C22×C3×C4C22×D511yescharacteristic
166C22×Dic3—101no—
167C22×Dic3—101no—
168C2×Dic6—52no—
169C2×Dic6—101no—
170C2×Dic6—202no—
171C3×C22⋊C4—24no—
172C3×C42—42no—
173#217—102no—
174#217—102no—
175C4⋊Dic3—52no—
176C4⋊Dic3—101no—
177Dic3⋊C4—102no—
178Dic3⋊C4—102no—
179#208—202no—
180C2×C3⋊C8—102no—
181C23×C5—22no—
182C23×C5—22no—
183C23×C5—41no—
184C23×C5(C2×D3)⋊C411yescharacteristic
185C23×C5(C2×D3)⋊C411yescharacteristic
186C23×C5C2×#6711yescharacteristic
187C2×C4×C5—22no—
188C2×C4×C5—22no—
189C2×C4×C5—22no—
190C2×C4×C5—24no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—42no—
195C2×C4×C5—42no—
196C2×C4×C5(C2×D3)⋊C411yescharacteristic
197C2×C4×C5(C2×D3)⋊C411yescharacteristic
198C2×C4×C5C2×C4×D311yescharacteristic
199C2×C4×C5C2×D1211yescharacteristic
200C2×Dic5—62no—
201C2×Dic5—62no—
202C2×Dic5—122no—
203C2×Dic5—122no—
204Dic10—122no—
205Dic10—122no—
206#168—122no—
207C22×Q8—151no—
208C23×C4C2×D1511yescharacteristic
209C2×M16—301no—
210C22⋊Q8—152no—
211C22⋊Q8—152no—
212C22⋊Q8—301no—
213C22⋊Q8—301no—
214C2×C4⋊C4—151no—
215C2×C4⋊C4—301no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—301no—
218C2×C42—21no—
219C22⋊C8—152no—
220C22⋊C8—301no—
221#95C2×D1512yes—
222C2×C3×C5—22no—
223C2×C3×C5—22no—
224C2×C3×C5—41no—
225C2×C3×C5C2×#9911yescharacteristic
226C2×C3×C5#41911yescharacteristic
227C2×C3×C5C2×#10411yescharacteristic
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—41no—
231C23×C3#68511yescharacteristic
232C23×C3#68511yescharacteristic
233C23×C3C2×C22⋊D511yescharacteristic
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—24no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4#68511yescharacteristic
244C2×C3×C4#68511yescharacteristic
245C2×C3×C4C2×C4×D511yescharacteristic
246C2×C3×C4C2×D2011yescharacteristic
247C2×Dic3—102no—
248C2×Dic3—102no—
249C2×Dic3—202no—
250C2×Dic3—202no—
251Dic6—202no—
252Dic6—202no—
253C3⋊C8—202no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—44no—
262C22×C5#80512yes—
263C22×C5C2×(C2×D3)⋊C411yescharacteristic
264C22×C5#95112yes—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—44no—
269C4×C5#80612yes—
270Dic5—122no—
271Dic5—122no—
272C24#122011yescharacteristic
273C2×Q8—152no—
274C2×Q8—301no—
275C2×Q8—602no—
276C22×C4—22no—
277C22×C4—42no—
278C22×C4—301no—
279C22×C4—301no—
280C22×C4C4×D1511yescharacteristic
281C22×C4C4×D1511yescharacteristic
282C22×C4D6011yescharacteristic
283C22×C4D6011yescharacteristic
284C22×C4#122011yescharacteristic
285C22×C4C22×D1511yescharacteristic
286M16—602no—
287C2×C8—302no—
288C4⋊C4—152no—
289C4⋊C4—301no—
290C4⋊C4—302no—
291C4⋊C4—302no—
292C22⋊C4—24no—
293C22⋊C4—302no—
294C22⋊C4—302no—
295C42—42no—
296C3×C5#150811yescharacteristic, complemented, Hall
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—44no—
305C22×C3#393712yes—
306C22×C3C2×#68511yescharacteristic
307C22×C3#409712yes—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—44no—
312C3×C4#393812yes—
313Dic3—202no—
314Dic3—202no—
315C2×C5—22no—
316C2×C5—22no—
317C2×C5—41no—
318C2×C5C2×#80511yescharacteristic
319C2×C5C2×#80611yescharacteristic
320C2×C5#500411yescharacteristic
321C23—22no—
322C23—22no—
323C23—41no—
324C23#671411yescharacteristic
325C23#671411yescharacteristic
326C23C2×#122011yescharacteristic
327Q8—602no—
328Q8—602no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—302no—
339C2×C4—302no—
340C2×C4—602no—
341C2×C4—602no—
342C2×C4#671411yescharacteristic
343C2×C4#671411yescharacteristic
344C2×C4C2×C4×D1511yescharacteristic
345C2×C4C2×D6011yescharacteristic
346C8—602no—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—41no—
350C2×C3C2×#393711yescharacteristic
351C2×C3C2×#393811yescharacteristic
352C2×C3#6529311yescharacteristic
353C5#6944511yescharacteristic, complemented, Sylow
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—44no—
362C22#9108912yes—
363C22C2×#671411yescharacteristic
364C22#9184012yes—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—44no—
369C4—602no—
370C4—602no—
371C4#9109012yes—
372C3#1060023811yescharacteristic, complemented, Sylow
373C2—22no—
374C2—22no—
375C2—41no—
376C2C2×#9108911yescharacteristic
377C2C2×#9109011yescharacteristic
378C2#1175110511yescharacteristic
subgroupG/H
centerC22C2×#6714
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C4×C5×C22⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4×C5C23
hypercenterC4×C22⋊C4D15
hypocenterC3×C5#1508
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746273C2semidirect
7. C22×Dic30C4semidirect
11. C2×C4⋊Dic15C4semidirect
14. #91813C4semidirect
296. C3×C5#1508semidirect
353. C5#69445semidirect
372. C3#10600238semidirect

Maximal subgroups

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

subgroupindex
C2×#918132
C3×C4×C5×C22⋊C42
#117513082
#117462732
#106002383
#694455