Finite Group Databasebeta

← #14280892

Subgroups — #14280892

Order 1920.

624 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91770C211yesmaximal, characteristic
2#11750819C212yesmaximal, complemented
3C3×C5×#323C211yesmaximal, characteristic, complemented
4#11746346C211yesmaximal, characteristic, complemented
5#11746289C212yesmaximal, complemented
6#10598894—31nomaximal, Hall
7C22×#1220C411yescharacteristic
8C23×Dic15C411yescharacteristic
9C22×C4×D15C411yescharacteristic
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×#6714C2211yescharacteristic
12C2×#6712C411yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14#91770—22no—
15#91770—22no—
16C3×C5×C22⋊C8C2212yes—
17#91114C2212yes—
18#91098—22no—
19C8×Dic15—22no—
20#68101—51nomaximal, Hall
21C2×#4027—31no—
22#65007—32no—
23C5×#323D311yescharacteristic, complemented
24#64745—31no—
25#64688—32no—
26C24×C3×C5C2×C411yescharacteristic
27C23×D15C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2311yescharacteristic
30C2×#1220—22no—
31C2×#1220—22no—
32C2×#1220C814yescomplemented
33C22×Dic15—21no—
34C22×Dic15—21no—
35C22×Dic15—42no—
36C22×Dic15C2×C411yescharacteristic
37C22×Dic15C2×C411yescharacteristic
38C22×Dic15C2×C411yescharacteristic
39C2×C4×D15—21no—
40C2×C4×D15—21no—
41C2×C4×D15—42no—
42C2×C3×C5×C8—22no—
43C3×C5×C22⋊C4—22no—
44#6714—22no—
45#6712—22no—
46C4×Dic15D412yes—
47C4×Dic15D412yes—
48C2×C3⋊#168—22no—
49C2×#67⋊C4—51no—
50#4718—52no—
51C3×#323D511yescharacteristic, complemented
52#4525—51no—
53#4468—52no—
54C22×C22⋊D5—31no—
55C23×Dic5—31no—
56C22×C4×D5—31no—
57C2×C5×C22⋊C4C2×D311yescharacteristic
58C2×#685—31no—
59C2×#683—31no—
60C2×C4×Dic5—31no—
61#4027—62no—
62#4027—62no—
63C5×C22⋊C8C2×D312yes—
64C22⋊#168—32no—
65#3946—62no—
66C8×Dic5—62no—
67#1460—151noSylow
68C23×C3×C5—21no—
69C23×C3×C5—21no—
70C23×C3×C5—41no—
71C23×C3×C5—41no—
72C23×C3×C5C2×C812yes—
73C23×C3×C5C22×C411yescharacteristic
74C22×D15—21no—
75C22×D15—21no—
76C22×D15—41no—
77C22×D15—41no—
78C22×D15C2×C812yes—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C2×D412yes—
83#1220—28no—
84C2×Dic15—22no—
85C2×Dic15—21no—
86C2×Dic15—42no—
87C2×Dic15—42no—
88C2×Dic15—41no—
89C2×Dic15C22⋊C411yescharacteristic
90C2×Dic15C22⋊C412yes—
91C2×Dic15C22⋊C411yescharacteristic
92C2×Dic15C2×C812yes—
93C2×Dic15M1612yes—
94C4×D15—42no—
95C4×D15—42no—
96C3×C5×C8—42no—
97C3⋊#168—42no—
98C22×#67—51no—
99C23×Dic3—51no—
100C22×C4×D3—51no—
101C2×C3×C22⋊C4C2×D511yescharacteristic
102C2×(C2×D3)⋊C4—51no—
103C2×Dic3⋊C4—51no—
104C2×C4×Dic3—51no—
105#67⋊C4—102no—
106#67⋊C4—102no—
107C3×C22⋊C8C2×D512yes—
108#830—52no—
109Dic3⋊C8—102no—
110C8×Dic3—102no—
111C24×C5C4×D311yescharacteristic
112C23×D5—31no—
113C22×C4×C5C4×D311yescharacteristic
114C22×C4×C5C22×D311yescharacteristic
115C2×C22⋊D5—34no—
116C2×C22⋊D5—62no—
117C2×C22⋊D5—62no—
118C22×Dic5—31no—
119C22×Dic5—31no—
120C22×Dic5—31no—
121C22×Dic5—61no—
122C22×Dic5—61no—
123C22×Dic5—122no—
124C2×C4×D5—61no—
125C2×C4×D5—61no—
126C2×C4×D5—122no—
127C2×C5×C8—22no—
128C5×C22⋊C4—22no—
129#685—62no—
130#683—62no—
131C4×Dic5—32no—
132C4×Dic5—32no—
133C2×#168—62no—
134C2×C4×D4—151no—
135#431—152no—
136#323—151no—
137#323—152no—
138#323D1511yescharacteristic, complemented
139C22×C3×C5—21no—
140C22×C3×C5—21no—
141C22×C3×C5—22no—
142C22×C3×C5—42no—
143C22×C3×C5—42no—
144C22×C3×C5—41no—
145C22×C3×C5—41no—
146C22×C3×C5C2×C22⋊C411yescharacteristic
147C22×C3×C5C22×C811yescharacteristic
148C22×C3×C5C2×M1611yescharacteristic
149C2×D15—22no—
150C2×D15—42no—
151C2×D15—41no—
152C2×D15—41no—
153C2×D15—42no—
154C3×C4×C5—22no—
155C3×C4×C5—41no—
156Dic15—21no—
157Dic15—41no—
158Dic15C22⋊C814yes—
159Dic15#10012yes—
160C24×C3C4×D511yescharacteristic
161C23×D3—51no—
162C22×C3×C4C4×D511yescharacteristic
163C22×C3×C4C22×D511yescharacteristic
164C2×#67—54no—
165C2×#67—102no—
166C2×#67—102no—
167C22×Dic3—51no—
168C22×Dic3—51no—
169C22×Dic3—51no—
170C22×Dic3—101no—
171C22×Dic3—101no—
172C22×Dic3—202no—
173C2×C4×D3—101no—
174C2×C4×D3—101no—
175C2×C4×D3—202no—
176C2×C3×C8—22no—
177C3×C22⋊C4—22no—
178(C2×D3)⋊C4—102no—
179Dic3⋊C4—102no—
180C4×Dic3—52no—
181C4×Dic3—52no—
182C2×C3⋊C8—102no—
183C23×C5—21no—
184C23×C5—21no—
185C23×C5—41no—
186C23×C5—41no—
187C23×C5D3×C812yes—
188C23×C5C2×C4×D311yescharacteristic
189C22×D5—32no—
190C22×D5—61no—
191C22×D5—61no—
192C22×D5—121no—
193C22×D5—121no—
194C2×C4×C5—21no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5D3×D412yes—
198C22⋊D5—68no—
199C2×Dic5—32no—
200C2×Dic5—31no—
201C2×Dic5—32no—
202C2×Dic5—32no—
203C2×Dic5—31no—
204C2×Dic5—62no—
205C2×Dic5—61no—
206C2×Dic5—122no—
207C2×Dic5—122no—
208C2×Dic5—121no—
209C4×D5—122no—
210C4×D5—122no—
211C5×C8—42no—
212#168—122no—
213C22×D4—151no—
214C23×C4—151no—
215C23×C4—151no—
216C4×D4—302no—
217C4×D4—302no—
218C2×C4⋊C4—151no—
219C2×C22⋊C4—151no—
220C2×C22⋊C4C2×D1511yescharacteristic
221C2×C42—151no—
222C4⋊C8—302no—
223C22⋊C8—152no—
224C22⋊C8C2×D1512yes—
225C4×C8—302no—
226C2×C3×C5—21no—
227C2×C3×C5—21no—
228C2×C3×C5—42no—
229C2×C3×C5C2×C22⋊C811yescharacteristic
230C2×C3×C5#41011yescharacteristic
231C2×C3×C5C2×#10011yescharacteristic
232D15—42no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—41no—
236C23×C3—41no—
237C23×C3C8×D512yes—
238C23×C3C2×C4×D511yescharacteristic
239C22×D3—52no—
240C22×D3—101no—
241C22×D3—101no—
242C22×D3—201no—
243C22×D3—201no—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4D4×D512yes—
248#67—108no—
249C2×Dic3—52no—
250C2×Dic3—51no—
251C2×Dic3—52no—
252C2×Dic3—52no—
253C2×Dic3—51no—
254C2×Dic3—102no—
255C2×Dic3—101no—
256C2×Dic3—202no—
257C2×Dic3—202no—
258C2×Dic3—201no—
259C4×D3—202no—
260C4×D3—202no—
261C3×C8—42no—
262C3⋊C8—202no—
263C22×C5—21no—
264C22×C5—21no—
265C22×C5—22no—
266C22×C5—42no—
267C22×C5—42no—
268C22×C5—41no—
269C22×C5—41no—
270C22×C5D3×C22⋊C411yescharacteristic
271C22×C5C2×D3×C811yescharacteristic
272C22×C5D3×M1611yescharacteristic
273C2×D5—62no—
274C2×D5—122no—
275C2×D5—121no—
276C2×D5—121no—
277C2×D5—122no—
278C4×C5—22no—
279C4×C5—41no—
280Dic5—34no—
281Dic5—32no—
282Dic5—61no—
283Dic5—121no—
284C24—151no—
285C24C4×D1511yescharacteristic
286C2×D4—154no—
287C2×D4—302no—
288C2×D4—302no—
289C22×C4—151no—
290C22×C4—151no—
291C22×C4—151no—
292C22×C4—301no—
293C22×C4—301no—
294C22×C4—301no—
295C22×C4—301no—
296C22×C4—602no—
297C22×C4—602no—
298C22×C4C4×D1511yescharacteristic
299C22×C4C22×D1511yescharacteristic
300C2×C8—22no—
301C2×C8—302no—
302C4⋊C4—302no—
303C22⋊C4—22no—
304C22⋊C4—302no—
305C42—152no—
306C42—152no—
307C3×C5#146011yescharacteristic, complemented, Hall
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—22no—
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3D5×C22⋊C411yescharacteristic
316C22×C3C2×C8×D511yescharacteristic
317C22×C3D5×M1611yescharacteristic
318C2×D3—102no—
319C2×D3—202no—
320C2×D3—201no—
321C2×D3—201no—
322C2×D3—202no—
323C3×C4—22no—
324C3×C4—41no—
325Dic3—52no—
326Dic3—54no—
327Dic3—101no—
328Dic3—201no—
329C2×C5—21no—
330C2×C5—21no—
331C2×C5—42no—
332C2×C5D3×C22⋊C811yescharacteristic
333C2×C5#474011yescharacteristic
334C2×C5D3×#10011yescharacteristic
335D5—122no—
336C23—21no—
337C23—21no—
338C23—41no—
339C23—41no—
340C23—152no—
341C23—301no—
342C23—301no—
343C23—601no—
344C23—601no—
345C23C8×D1512yes—
346C23C2×C4×D1511yescharacteristic
347D4—308no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—152no—
352C2×C4—151no—
353C2×C4—152no—
354C2×C4—152no—
355C2×C4—151no—
356C2×C4—302no—
357C2×C4—301no—
358C2×C4—602no—
359C2×C4—602no—
360C2×C4—602no—
361C2×C4—602no—
362C2×C4—601no—
363C2×C4D4×D1512yes—
364C8—42no—
365C8—602no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—42no—
369C2×C3D5×C22⋊C811yescharacteristic
370C2×C3#6502911yescharacteristic
371C2×C3D5×#10011yescharacteristic
372D3—202no—
373C5#6810111yescharacteristic, complemented, Sylow
374C22—21no—
375C22—21no—
376C22—22no—
377C22—42no—
378C22—42no—
379C22—41no—
380C22—41no—
381C22—302no—
382C22—602no—
383C22—602no—
384C22—601no—
385C22—601no—
386C22C22⋊C4×D1511yescharacteristic
387C22C2×C8×D1511yescharacteristic
388C22M16×D1511yescharacteristic
389C4—22no—
390C4—41no—
391C4—154no—
392C4—152no—
393C4—301no—
394C4—601no—
395C3#1059889411yescharacteristic, complemented, Sylow
396C2—21no—
397C2—21no—
398C2—42no—
399C2—602no—
400C2D15×C22⋊C811yescharacteristic
401C2#1175084111yescharacteristic
402C2D15×#10011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC22×C3×C5C22×C8
FrattiniC22×C4C22×D15
FittingC3×C5×#323C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1220C4
cosocleC22×C3×C4×C5C23
hypercenter#323D15
hypocenterC3×C5#1460
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #11750819C2semidirect
3. C3×C5×#323C2semidirect
4. #11746346C2semidirect
5. #11746289C2semidirect
23. C5×#323D3semidirect
32. C2×#1220C8semidirect
51. C3×#323D5semidirect
138. #323D15semidirect
307. C3×C5#1460semidirect
373. C5#68101semidirect
395. C3#10598894semidirect

Maximal subgroups

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

subgroupindex
C2×#917702
#117508192
C3×C5×#3232
#117463462
#117462892
#105988943
#681015