Finite Group Databasebeta

← #14297579

Subgroups — #14297579

Order 1920.

672 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 134 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×#91782C211yesmaximal, characteristic
2#11748437C212yesmaximal, complemented
3C2×#90960C212yesmaximal
4C5×#4530C211yesmaximal, characteristic, complemented
5C3×#64750C211yesmaximal, characteristic, complemented
6#10599787—31nomaximal, Hall
7C22×D60C2211yescharacteristic
8C22×C4×D15C412yes—
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×#6714C412yes—
11C2×C4×Dic15C2211yescharacteristic
12#91782—22no—
13#91782—22no—
14C2×C5×#208C2212yes—
15C2×C3×#681C2212yes—
16#90983—22no—
17#90983—22no—
18#90960—24no—
19#68994—51nomaximal, Hall
20C2×#4039—31no—
21C2×#3955—32no—
22#65407—32no—
23C5×#343—31no—
24#64750D311yescharacteristic, complemented
25C23×D15C2×C412yes—
26C22×C3×C4×C5C2×C412yes—
27C22×C3×C4×C5C2311yescharacteristic
28C22×Dic15C2×C411yescharacteristic
29C22×Dic15C2×C411yescharacteristic
30C2×D60—22no—
31C2×D60—22no—
32C2×D60D412yes—
33C2×D60Q812yes—
34C2×C4×D15—22no—
35C2×C4×D15—22no—
36C2×C4×D15—44no—
37C3×C5×C4⋊C4—22no—
38#6714—24no—
39C4×Dic15D412yes—
40C4×Dic15D412yes—
41C5×#208—22no—
42C5×#208—22no—
43C2×C5×C3⋊C8—22no—
44C3×#681—22no—
45C3×#681—22no—
46C2×C3×#168—22no—
47C2×#893—51no—
48C2×#823—52no—
49#5118—52no—
50C3×#343—51no—
51#4530D511yescharacteristic, complemented
52C22×D20—31no—
53C22×C4×D5—32no—
54C2×C5×M16—32no—
55C2×C5×C4⋊C4C2×D311yescharacteristic
56C2×#685—32no—
57C2×C4×Dic5—31no—
58C2×#681C2×D312yes—
59#4039—62no—
60#4039—62no—
61#3955—64no—
62#3946—62no—
63#3946—62no—
64#1800—151noSylow
65C23×C3×C5C22×C411yescharacteristic
66C22×D15—22no—
67C22×D15—22no—
68C22×D15—42no—
69C22×D15—42no—
70C22×D15C4⋊C414yes—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—42no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C2×C3×C4×C5C2×Q811yescharacteristic
76C2×C3×C4×C5#4112yes—
77C2×Dic15—22no—
78C2×Dic15—41no—
79C2×Dic15C22⋊C412yes—
80C2×Dic15C22⋊C411yescharacteristic
81C2×Dic15C22⋊C411yescharacteristic
82D60—24no—
83D60—24no—
84C4×D15—44no—
85C4×D15—44no—
86C3×#168—42no—
87C5×C3⋊C8—42no—
88C22×D12—51no—
89C22×C4×D3—52no—
90C2×C3×M16—52no—
91C2×C3×C4⋊C4C2×D511yescharacteristic
92C2×(C2×D3)⋊C4—52no—
93C2×C4×Dic3—51no—
94C2×#208C2×D512yes—
95#893—102no—
96#893—102no—
97#823—104no—
98Dic3⋊C8—102no—
99Dic3⋊C8—102no—
100C23×D5—32no—
101C22×C4×C5C4×D312yes—
102C22×C4×C5C22×D311yescharacteristic
103C22×Dic5—31no—
104C22×Dic5—31no—
105C2×D20—32no—
106C2×D20—32no—
107C2×D20—62no—
108C2×D20—62no—
109C2×C4×D5—62no—
110C2×C4×D5—62no—
111C2×C4×D5—124no—
112C5×M16—62no—
113C5×M16—62no—
114C2×C5×C8—62no—
115C5×C4⋊C4—22no—
116#685—64no—
117C4×Dic5—32no—
118C4×Dic5—32no—
119#681—22no—
120#681—22no—
121C2×#168—22no—
122C2×C4×D4—151no—
123#423—152no—
124C2×#100—152no—
125#343—31no—
126#343—51no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C22×C3×C5C2×C4⋊C411yescharacteristic
131C22×C3×C5#11711yescharacteristic
132C2×D15—24no—
133C2×D15—44no—
134C2×D15—42no—
135C2×D15—42no—
136C2×D15—44no—
137C3×C4×C5—42no—
138C3×C4×C5#12112yes—
139C3×C4×C5C22⋊Q812yes—
140Dic15—21no—
141Dic15—22no—
142Dic15#10012yescomplemented
143C23×D3—52no—
144C22×C3×C4C4×D512yes—
145C22×C3×C4C22×D511yescharacteristic
146C22×Dic3—51no—
147C22×Dic3—51no—
148C2×D12—52no—
149C2×D12—52no—
150C2×D12—102no—
151C2×D12—102no—
152C2×C4×D3—102no—
153C2×C4×D3—102no—
154C2×C4×D3—204no—
155C3×M16—102no—
156C3×M16—102no—
157C2×C3×C8—102no—
158C3×C4⋊C4—22no—
159(C2×D3)⋊C4—104no—
160C4×Dic3—52no—
161C4×Dic3—52no—
162#208—22no—
163#208—22no—
164C2×C3⋊C8—22no—
165C23×C5C2×C4×D311yescharacteristic
166C22×D5—34no—
167C22×D5—62no—
168C22×D5—62no—
169C22×D5—122no—
170C22×D5—122no—
171C2×C4×C5—22no—
172C2×C4×C5—42no—
173C2×C4×C5#23512yes—
174C2×C4×C5D3×D411yescharacteristic
175C2×C4×C5D3×D412yes—
176C2×C4×C5D3×Q811yescharacteristic
177C2×Dic5—31no—
178C2×Dic5—32no—
179C2×Dic5—31no—
180C2×Dic5—62no—
181C2×Dic5—121no—
182D20—64no—
183D20—64no—
184C4×D5—124no—
185C4×D5—124no—
186C5×C8—122no—
187#168—42no—
188C22×D4—151no—
189C23×C4—152no—
190C2×M16—32no—
191C2×M16—52no—
192C4×D4—302no—
193C4×D4—302no—
194C2×C4⋊C4D3×D511yescharacteristic
195C2×C22⋊C4—152no—
196C2×C42—151no—
197C4⋊C8—302no—
198C4⋊C8—302no—
199#100—304no—
200C2×C3×C5—21no—
201C2×C3×C5—21no—
202C2×C3×C5#38011yescharacteristic
203C2×C3×C5C2×#10011yescharacteristic
204C2×C3×C5#41311yescharacteristic
205D15—44no—
206C23×C3C2×C4×D511yescharacteristic
207C22×D3—54no—
208C22×D3—102no—
209C22×D3—102no—
210C22×D3—202no—
211C22×D3—202no—
212C2×C3×C4—22no—
213C2×C3×C4—42no—
214C2×C3×C4#70912yes—
215C2×C3×C4D4×D511yescharacteristic
216C2×C3×C4D4×D512yes—
217C2×C3×C4Q8×D511yescharacteristic
218C2×Dic3—51no—
219C2×Dic3—52no—
220C2×Dic3—51no—
221C2×Dic3—102no—
222C2×Dic3—201no—
223D12—104no—
224D12—104no—
225C4×D3—204no—
226C4×D3—204no—
227C3×C8—202no—
228C3⋊C8—42no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5#87211yescharacteristic
232C22×C5D3×C22⋊C411yescharacteristic
233C22×C5D3×C4⋊C411yescharacteristic
234C2×D5—64no—
235C2×D5—124no—
236C2×D5—122no—
237C2×D5—122no—
238C2×D5—124no—
239C4×C5—42no—
240C4×C5#88412yes—
241C4×C5#89612yes—
242Dic5—32no—
243Dic5—61no—
244Dic5—62no—
245C24—152no—
246C2×D4—152no—
247C2×D4—152no—
248C2×D4—302no—
249C2×D4—302no—
250C22×C4—151no—
251C22×C4—151no—
252C22×C4—302no—
253C22×C4—302no—
254C22×C4—604no—
255C22×C4#120012yes—
256C22×C4C2×D3×D511yescharacteristic
257M16—62no—
258M16—62no—
259M16—102no—
260M16—102no—
261C2×C8—62no—
262C2×C8—102no—
263C4⋊C4—22no—
264C22⋊C4—304no—
265C42—152no—
266C42—152no—
267C3×C5#180011yescharacteristic, complemented, Hall
268C22×C3—21no—
269C22×C3—21no—
270C22×C3#401811yescharacteristic
271C22×C3D5×C22⋊C411yescharacteristic
272C22×C3D5×C4⋊C411yescharacteristic
273C2×D3—104no—
274C2×D3—204no—
275C2×D3—202no—
276C2×D3—202no—
277C2×D3—204no—
278C3×C4—42no—
279C3×C4#403012yes—
280C3×C4#404212yes—
281Dic3—52no—
282Dic3—101no—
283Dic3—102no—
284C2×C5—21no—
285C2×C5—21no—
286C2×C5#466711yescharacteristic
287C2×C5D3×#10011yescharacteristic
288C2×C5#475111yescharacteristic
289D5—124no—
290C23—154no—
291C23—302no—
292C23—302no—
293C23—602no—
294C23—602no—
295C23C2×#120011yescharacteristic
296D4—304no—
297D4—304no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—151no—
301C2×C4—152no—
302C2×C4—151no—
303C2×C4—302no—
304C2×C4—604no—
305C2×C4—604no—
306C2×C4—601no—
307C2×C4D15⋊Q811yescharacteristic
308C2×C4#677112yes—
309C2×C4#677711yescharacteristic
310C2×C4#679012yes—
311C8—122no—
312C8—202no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3#6495611yescharacteristic
316C2×C3D5×#10011yescharacteristic
317C2×C3#6504011yescharacteristic
318D3—204no—
319C5#6899411yescharacteristic, complemented, Sylow
320C22—21no—
321C22—21no—
322C22—304no—
323C22—604no—
324C22—604no—
325C22—602no—
326C22—602no—
327C22#9138611yescharacteristic
328C22#9143711yescharacteristic
329C22#9156111yescharacteristic
330C4—42no—
331C4—152no—
332C4—301no—
333C4—302no—
334C4#9137712yes—
335C4#9146112yes—
336C3#1059978711yescharacteristic, complemented, Sylow
337C2—21no—
338C2—21no—
339C2—604no—
340C2#1174886311yescharacteristic
341C2#1174912711yescharacteristic
342C2#1174937411yescharacteristic
subgroupG/H
centerC22#91561
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1800
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11748437C2semidirect
4. C5×#4530C2semidirect
5. C3×#64750C2semidirect
24. #64750D3semidirect
51. #4530D5semidirect
142. Dic15#100semidirect
267. C3×C5#1800semidirect
319. C5#68994semidirect
336. C3#10599787semidirect

Maximal subgroups

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

subgroupindex
C2×#917822
#117484372
C2×#909602
C5×#45302
C3×#647502
#105997873
#689945