Finite Group Databasebeta

← #14313476

Subgroups — #14313476

Order 1920.

572 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 78 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
1#11756474C211yesmaximal, characteristic
2#11749171C212yesmaximal, complemented
3C5×#4545C211yesmaximal, characteristic, complemented
4C3×#64765C211yesmaximal, characteristic, complemented
5#11746011C212yesmaximal, complemented
6#10599943—31nomaximal, Hall
7C2×#6819C411yescharacteristic, complemented
8C2×D4×D15C2211yescharacteristic
9C3×C5×#127C2211yescharacteristic
10#91829C411yescharacteristic, complemented
11#91828—22no—
12#91826—22no—
13#91825C2211yescharacteristic
14#91764C411yescharacteristic, complemented
15#91761C411yescharacteristic, complemented
16#91561—22no—
17C5×#834C2212yes—
18C3×#3966C2212yes—
19#90997—22no—
20#69150—51nomaximal, Hall
21#66049—31no—
22D5×#99—32no—
23C5×#353—31no—
24#64765D311yescharacteristic, complemented
25#64693—32no—
26C23×D15D412yes—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C411yescharacteristic, complemented
29C2×C3×C5×D4C2311yescharacteristic
30C2×#1220—21no—
31C2×#1220—22no—
32C2×#1220D412yes—
33C22×Dic15—21no—
34#6819—42no—
35D4×D15—42no—
36C2×D60C2×C411yescharacteristic
37C2×C4×D15C2×C411yescharacteristic
38C2×Dic30C2×C411yescharacteristic, complemented
39C2×#1200—42no—
40C3×C42×C5C2×C411yescharacteristic, complemented
41#6719—22no—
42#6714—21no—
43#6714—22no—
44#6712—21no—
45C4×Dic15C2×C411yescharacteristic, complemented
46C5×#217—22no—
47C3×C22⋊Dic5—22no—
48#6667—42no—
49#5715—51no—
50D3×#99—52no—
51C3×#353—51no—
52#4545D511yescharacteristic, complemented
53#4473—52no—
54C2×#711—31no—
55C2×D4×D5—31no—
56C5×#127C2×D311yescharacteristic
57#4086—31no—
58#4085—62no—
59#4083—62no—
60#4082—31no—
61D5×C22⋊C4—62no—
62#4021—31no—
63#4018—31no—
64C5×#99—32no—
65#3966C2×D312yes—
66#3938—62no—
67#2127—151noSylow
68C23×C3×C5—21no—
69C23×C3×C5C2×D412yes—
70C22×D15—22no—
71C22×D15—22no—
72C22×D15—82no—
73C22×D15C22⋊C412yes—
74C22×D15C22⋊C411yescharacteristic
75C3×C5×D4—41no—
76C3×C5×D4—41no—
77C3×C5×D4—82no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5C22×C411yescharacteristic
80#1220—42no—
81#1220—42no—
82#1220—82no—
83C2×Dic15—21no—
84C2×Dic15—21no—
85C2×Dic15—42no—
86C2×Dic15C22⋊C411yescharacteristic
87D60—41no—
88C4×D15—22no—
89Dic30—41no—
90C2×C5×Dic3—42no—
91C2×C3×Dic5—42no—
92#1200—84no—
93C2×#237—51no—
94C2×D3×D4—51no—
95C3×#127C2×D511yescharacteristic
96#940—51no—
97#939—102no—
98#937—102no—
99#936—51no—
100D3×C22⋊C4—102no—
101#875—51no—
102#872—51no—
103C3×#99—52no—
104#834C2×D512yes—
105#806—102no—
106C23×D5—32no—
107C2×C5×D4—22no—
108C2×C5×D4C4×D311yescharacteristic, complemented
109C2×C5×D4C22×D311yescharacteristic
110C2×C22⋊D5—32no—
111C2×C22⋊D5—61no—
112C2×C22⋊D5—62no—
113C22×Dic5—61no—
114#711—122no—
115D4×D5—122no—
116C2×D20—31no—
117C2×C4×D5—31no—
118C2×C4×D5—122no—
119C2×Dic10—31no—
120C5×C22⋊C4—62no—
121C42×C5C4×D311yescharacteristic, complemented
122C22⋊Dic5—22no—
123C22⋊Dic5—62no—
124#685—61no—
125#685—62no—
126#685—122no—
127#683—61no—
128C4×Dic5—31no—
129#535—151no—
130C2×#99—152no—
131#354—152no—
132#353—31no—
133#353—51no—
134C22×C3×C5—22no—
135C22×C3×C5—42no—
136C22×C3×C5—42no—
137C22×C3×C5—41no—
138C22×C3×C5C2×C22⋊C411yescharacteristic
139C2×D15—22no—
140C2×D15—41no—
141C2×D15—44no—
142C2×D15—42no—
143C2×D15—82no—
144C2×D15#9912yes—
145C3×C4×C5—21no—
146C3×C4×C5—41no—
147Dic15—21no—
148Dic15—41no—
149Dic15—41no—
150C3×Dic5—82no—
151C5×Dic3—82no—
152C23×D3—52no—
153C2×C3×D4—22no—
154C2×C3×D4C4×D511yescharacteristic, complemented
155C2×C3×D4C22×D511yescharacteristic
156C2×#67—52no—
157C2×#67—101no—
158C2×#67—102no—
159C22×Dic3—101no—
160#237—202no—
161D3×D4—202no—
162C2×D12—51no—
163C2×C4×D3—51no—
164C2×C4×D3—202no—
165C2×Dic6—51no—
166C3×C22⋊C4—102no—
167C3×C42C4×D511yescharacteristic, complemented
168#217—22no—
169#217—102no—
170(C2×D3)⋊C4—101no—
171(C2×D3)⋊C4—102no—
172(C2×D3)⋊C4—202no—
173Dic3⋊C4—101no—
174C4×Dic3—51no—
175C23×C5—21no—
176C23×C5D3×D412yes—
177C22×D5—31no—
178C22×D5—32no—
179C22×D5—62no—
180C22×D5—62no—
181C22×D5—242no—
182C5×D4—41no—
183C5×D4—41no—
184C5×D4—82no—
185C2×C4×C5—21no—
186C2×C4×C5—122no—
187C2×C4×C5C2×C4×D311yescharacteristic
188C22⋊D5—122no—
189C22⋊D5—122no—
190C22⋊D5—242no—
191C2×Dic5—31no—
192C2×Dic5—42no—
193C2×Dic5—61no—
194C2×Dic5—61no—
195C2×Dic5—122no—
196D20—121no—
197C4×D5—62no—
198C4×D5—244no—
199Dic10—121no—
200C2×#41—151no—
201C22×D4—151no—
202#127—151no—
203#127D3×D511yescharacteristic
204#124—151no—
205#124—151no—
206#121—302no—
207#120—302no—
208#117—151no—
209C2×C22⋊C4—302no—
210#99—32no—
211#99—52no—
212#99—302no—
213C2×C3×C5—21no—
214C2×C3×C5—42no—
215C2×C3×C5—81no—
216C2×C3×C5C2×#9911yescharacteristic
217D15—22no—
218D15—42no—
219C23×C3—21no—
220C23×C3D4×D512yes—
221C22×D3—51no—
222C22×D3—52no—
223C22×D3—102no—
224C22×D3—102no—
225C22×D3—402no—
226C3×D4—41no—
227C3×D4—41no—
228C3×D4—82no—
229C2×C3×C4—21no—
230C2×C3×C4—202no—
231C2×C3×C4C2×C4×D511yescharacteristic
232#67—202no—
233#67—202no—
234#67—402no—
235C2×Dic3—42no—
236C2×Dic3—51no—
237C2×Dic3—101no—
238C2×Dic3—101no—
239C2×Dic3—202no—
240D12—201no—
241C4×D3—102no—
242C4×D3—404no—
243Dic6—201no—
244C22×C5—22no—
245C22×C5—42no—
246C22×C5—42no—
247C22×C5—41no—
248C22×C5D3×C22⋊C411yescharacteristic
249C2×D5—32no—
250C2×D5—62no—
251C2×D5—121no—
252C2×D5—124no—
253C2×D5—122no—
254C2×D5—242no—
255C4×C5—21no—
256C4×C5—41no—
257C4×C5—242no—
258Dic5—61no—
259Dic5—82no—
260Dic5—121no—
261Dic5—121no—
262C24—152no—
263#41—602no—
264C2×Q8—151no—
265C2×D4—22no—
266C2×D4—152no—
267C2×D4—151no—
268C2×D4—301no—
269C2×D4—302no—
270C2×D4—602no—
271C2×D4#120011yescharacteristic, complemented
272C2×D4C2×D3×D511yescharacteristic
273C22×C4—151no—
274C22×C4—301no—
275C22×C4—602no—
276C4⋊C4—301no—
277C22⋊C4—62no—
278C22⋊C4—102no—
279C22⋊C4—301no—
280C22⋊C4—302no—
281C22⋊C4—302no—
282C22⋊C4—602no—
283C42—151no—
284C42#120011yescharacteristic, complemented
285C3×C5#212711yescharacteristic, complemented, Hall
286C22×C3—22no—
287C22×C3—42no—
288C22×C3—42no—
289C22×C3—41no—
290C22×C3D5×C22⋊C411yescharacteristic
291C2×D3—52no—
292C2×D3—102no—
293C2×D3—201no—
294C2×D3—204no—
295C2×D3—202no—
296C2×D3—402no—
297C3×C4—21no—
298C3×C4—41no—
299C3×C4—402no—
300Dic3—82no—
301Dic3—101no—
302Dic3—201no—
303Dic3—201no—
304C2×C5—21no—
305C2×C5—42no—
306C2×C5—81no—
307C2×C5D3×#9911yescharacteristic
308D5—62no—
309D5—122no—
310C23—21no—
311C23—151no—
312C23—152no—
313C23—302no—
314C23—302no—
315C23—1202no—
316C23#679012yes—
317Q8—601no—
318D4—41no—
319D4—41no—
320D4—82no—
321D4—601no—
322D4—602no—
323D4—602no—
324D4—1202no—
325C2×C4—21no—
326C2×C4—122no—
327C2×C4—151no—
328C2×C4—202no—
329C2×C4—302no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—602no—
333C2×C4—1204no—
334C2×C4C2×#120011yescharacteristic
335C2×C3—21no—
336C2×C3—42no—
337C2×C3—81no—
338C2×C3D5×#9911yescharacteristic
339D3—102no—
340D3—202no—
341C5#6915011yescharacteristic, complemented, Sylow
342C22—22no—
343C22—42no—
344C22—42no—
345C22—41no—
346C22—152no—
347C22—302no—
348C22—601no—
349C22—602no—
350C22—604no—
351C22—1202no—
352C22#9156111yescharacteristic
353C4—21no—
354C4—41no—
355C4—242no—
356C4—301no—
357C4—402no—
358C4—601no—
359C4—601no—
360C3#1059994311yescharacteristic, complemented, Sylow
361C2—21no—
362C2—42no—
363C2—81no—
364C2—302no—
365C2—602no—
366C2#1174917111yescharacteristic
subgroupG/H
centerC2#11749171
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#127C22
socleC2×C3×C5C2×#99
prime radical#11756474C2
cosocleC2×C3×C5×D4C23
hypercenter#127D3×D5
hypocenterC3×C5#2127
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11749171C2semidirect
3. C5×#4545C2semidirect
4. C3×#64765C2semidirect
5. #11746011C2semidirect
7. C2×#6819C4semidirect
10. #91829C4semidirect
14. #91764C4semidirect
15. #91761C4semidirect
24. #64765D3semidirect
28. C2×C3×C5×D4C2×C4semidirect
38. C2×Dic30C2×C4semidirect
40. C3×C42×C5C2×C4semidirect
45. C4×Dic15C2×C4semidirect
52. #4545D5semidirect
108. C2×C5×D4C4×D3semidirect
121. C42×C5C4×D3semidirect
154. C2×C3×D4C4×D5semidirect
167. C3×C42C4×D5semidirect
271. C2×D4#1200semidirect
284. C42#1200semidirect
285. C3×C5#2127semidirect
341. C5#69150semidirect
360. C3#10599943semidirect

Maximal subgroups

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

subgroupindex
#117564742
#117491712
C5×#45452
C3×#647652
#117460112
#105999433
#691505