Finite Group Databasebeta

← #14285176

Subgroups — #14285176

Order 1920.

396 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 103 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#11756487C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic
3#11750934C211yesmaximal, characteristic
4C3×C5×#333C211yesmaximal, characteristic, complemented
5#11746367C211yesmaximal, characteristic, complemented
6#11746307C211yesmaximal, characteristic, complemented
7#11746303C211yesmaximal, characteristic, complemented
8#10599279—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91835C412yes—
11Q8×Dic15C412yes—
12#91786—21no—
13#91781—21no—
14#91779—21no—
15#91776—21no—
16C42×D15C2211yescharacteristic
17#91758C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20#91104—21no—
21#91104—21no—
22#91099—21no—
23C8×Dic15—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68486—51nomaximal, Hall
27#66062—31no—
28#65124—31no—
29#65122—31no—
30C5×#333D311yescharacteristic, complemented
31#64766—31no—
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8C2×C412yes—
35C2×C4×D15C2×C411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×Dic30—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44#6714—22no—
45C4⋊Dic15—21no—
46C4⋊Dic15—22no—
47C4⋊Dic15C2×C412yes—
48#6712—22no—
49C4×Dic15—22no—
50C4×Dic15C2×C411yescharacteristic
51C4×Dic15D411yescharacteristic
52C4×Dic15D411yescharacteristic
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55#5728—51no—
56#4835—51no—
57#4833—51no—
58C3×#333D511yescharacteristic, complemented
59#4546—51no—
60#4486—51no—
61#4482—51no—
62C5×C4⋊Q8C2×D311yescharacteristic
63#4092—32no—
64Q8×Dic5—32no—
65#4043—61no—
66#4038—61no—
67#4036—61no—
68#4033—61no—
69C42×D5—31no—
70#4015—31no—
71C5×C4⋊C8C2×D311yescharacteristic
72C5×C4⋊C8C2×D311yescharacteristic
73#3952—61no—
74#3952—61no—
75#3947—61no—
76C8×Dic5—61no—
77C4⋊#168—31no—
78C4⋊#168—31no—
79#1554—151noSylow
80C22×D15C22⋊C411yescharacteristic
81C3×C5×Q8—42no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—22no—
87C2×Dic15C22⋊C411yescharacteristic
88C2×Dic15C22⋊C411yescharacteristic
89C2×Dic15C22⋊C411yescharacteristic
90C4×D15—21no—
91C4×D15—21no—
92C4×D15—21no—
93C4×D15—21no—
94C4×D15—41no—
95Dic30—41no—
96Dic30—41no—
97C3×C5×C8—41no—
98C3×C5×C8—41no—
99C3⋊#168—41no—
100C3⋊#168—41no—
101C3×C4⋊Q8C2×D511yescharacteristic
102#946—52no—
103Q8×Dic3—52no—
104#897—101no—
105#892—101no—
106#890—101no—
107#887—101no—
108C42×D3—51no—
109#869—51no—
110C3×C4⋊C8C2×D511yescharacteristic
111C3×C4⋊C8C2×D511yescharacteristic
112(C2×D3)⋊C8—101no—
113(C2×D3)⋊C8—101no—
114#815—101no—
115C8×Dic3—101no—
116C4⋊(C3⋊C8)—51no—
117C4⋊(C3⋊C8)—51no—
118C2×C5×Q8C4×D312yes—
119C2×C4×D5—31no—
120C2×C4×D5—31no—
121C2×C4×D5—31no—
122C2×Dic10—61no—
123C2×C5×C8—21no—
124C2×C5×C8—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C42×C5C22×D311yescharacteristic
128#685—62no—
129C4⋊Dic5—32no—
130C4⋊Dic5—62no—
131C4⋊Dic5—61no—
132#683—62no—
133C4×Dic5—31no—
134C4×Dic5—31no—
135C4×Dic5—31no—
136C4×Dic5—62no—
137C2×#168—61no—
138C2×#168—61no—
139#533—151no—
140#432—151no—
141#431—151no—
142#333—151no—
143#333D1511yescharacteristic, complemented
144#332—151no—
145#332—151no—
146C22×C3×C5C2×C22⋊C411yescharacteristic
147C2×D15—21no—
148C2×D15—21no—
149C2×D15—21no—
150C3×C4×C5—21no—
151C3×C4×C5—42no—
152C3×C4×C5#13511yescharacteristic
153C3×C4×C5#13511yescharacteristic
154C3×C4×C5#13711yescharacteristic
155C3×C4×C5#13711yescharacteristic
156Dic15—21no—
157Dic15—21no—
158Dic15—21no—
159Dic15—42no—
160C2×C3×Q8C4×D512yes—
161C2×C4×D3—51no—
162C2×C4×D3—51no—
163C2×C4×D3—51no—
164C2×Dic6—101no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C42C22×D511yescharacteristic
170(C2×D3)⋊C4—102no—
171C4⋊Dic3—52no—
172C4⋊Dic3—102no—
173C4⋊Dic3—101no—
174Dic3⋊C4—102no—
175C4×Dic3—51no—
176C4×Dic3—51no—
177C4×Dic3—51no—
178C4×Dic3—102no—
179C2×C3⋊C8—101no—
180C2×C3⋊C8—101no—
181C22×D5—31no—
182C5×Q8—42no—
183C2×C4×C5—22no—
184C2×C4×C5C2×C4×D311yescharacteristic
185C2×C4×C5D3×D411yescharacteristic
186C2×C4×C5D3×D411yescharacteristic
187C2×Dic5—31no—
188C2×Dic5—31no—
189C2×Dic5—31no—
190C2×Dic5—62no—
191C4×D5—61no—
192C4×D5—61no—
193C4×D5—61no—
194C4×D5—61no—
195C4×D5—121no—
196Dic10—121no—
197Dic10—121no—
198C5×C8—41no—
199C5×C8—41no—
200#168—121no—
201#168—121no—
202C4⋊Q8—151no—
203C4⋊Q8C2×D1511yescharacteristic
204#125—301no—
205C22⋊Q8—152no—
206C22⋊Q8—301no—
207C4×Q8—152no—
208C4×Q8—301no—
209#117—301no—
210C2×C42—151no—
211C4⋊C8—151no—
212C4⋊C8—151no—
213C4⋊C8C2×D1511yescharacteristic
214C4⋊C8C2×D1511yescharacteristic
215C22⋊C8—301no—
216C22⋊C8—301no—
217#97—301no—
218C4×C8—301no—
219C2×C3×C5#41311yescharacteristic
220C2×C3×C5#41611yescharacteristic
221C2×C3×C5#41911yescharacteristic
222D15—41no—
223C22×D3—51no—
224C3×Q8—42no—
225C2×C3×C4—22no—
226C2×C3×C4C2×C4×D511yescharacteristic
227C2×C3×C4D4×D511yescharacteristic
228C2×C3×C4D4×D511yescharacteristic
229C2×Dic3—51no—
230C2×Dic3—51no—
231C2×Dic3—51no—
232C2×Dic3—102no—
233C4×D3—101no—
234C4×D3—101no—
235C4×D3—101no—
236C4×D3—101no—
237C4×D3—201no—
238Dic6—201no—
239Dic6—201no—
240C3×C8—41no—
241C3×C8—41no—
242C3⋊C8—201no—
243C3⋊C8—201no—
244C22×C5D3×C22⋊C411yescharacteristic
245C2×D5—61no—
246C2×D5—61no—
247C2×D5—61no—
248C4×C5—21no—
249C4×C5—42no—
250C4×C5#91511yescharacteristic
251C4×C5#91611yescharacteristic
252C4×C5#91811yescharacteristic
253C4×C5#91911yescharacteristic
254Dic5—61no—
255Dic5—61no—
256Dic5—61no—
257Dic5—122no—
258C2×Q8—301no—
259C2×Q8C4×D1512yes—
260C22×C4—151no—
261C22×C4—151no—
262C22×C4—151no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—301no—
266C2×C8—301no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—152no—
270C4⋊C4—302no—
271C4⋊C4—302no—
272C4⋊C4—301no—
273C22⋊C4—302no—
274C42—151no—
275C42—151no—
276C42—151no—
277C42—302no—
278C42C22×D1511yescharacteristic
279C3×C5#155411yescharacteristic, complemented, Hall
280C22×C3D5×C22⋊C411yescharacteristic
281C2×D3—101no—
282C2×D3—101no—
283C2×D3—101no—
284C3×C4—21no—
285C3×C4—42no—
286C3×C4#406111yescharacteristic
287C3×C4#406211yescharacteristic
288C3×C4#406411yescharacteristic
289C3×C4#406511yescharacteristic
290Dic3—101no—
291Dic3—101no—
292Dic3—101no—
293Dic3—202no—
294C2×C5#474511yescharacteristic
295C2×C5#480211yescharacteristic
296C2×C5#480411yescharacteristic
297D5—121no—
298C23—151no—
299Q8—42no—
300Q8—601no—
301Q8—601no—
302C2×C4—22no—
303C2×C4—151no—
304C2×C4—151no—
305C2×C4—151no—
306C2×C4—301no—
307C2×C4—301no—
308C2×C4—301no—
309C2×C4—301no—
310C2×C4—302no—
311C2×C4—601no—
312C2×C4C2×C4×D1511yescharacteristic
313C2×C4D4×D1511yescharacteristic
314C2×C4D4×D1511yescharacteristic
315C8—41no—
316C8—41no—
317C8—601no—
318C8—601no—
319C2×C3#6503411yescharacteristic
320C2×C3#6509111yescharacteristic
321C2×C3#6509311yescharacteristic
322D3—201no—
323C5#6848611yescharacteristic, complemented, Sylow
324C22—301no—
325C22—301no—
326C22—301no—
327C22C22⋊C4×D1511yescharacteristic
328C4—21no—
329C4—42no—
330C4—301no—
331C4—301no—
332C4—301no—
333C4—602no—
334C4#9180411yescharacteristic
335C4#9180511yescharacteristic
336C4#9180711yescharacteristic
337C4#9180811yescharacteristic
338C3#1059927911yescharacteristic, complemented, Sylow
339C2—601no—
340C2#1175084611yescharacteristic
341C2#1175090311yescharacteristic
342C2#1175090511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#333C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenter#333D15
hypocenterC3×C5#1554
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. C3×C5×#333C2semidirect
5. #11746367C2semidirect
6. #11746307C2semidirect
7. #11746303C2semidirect
30. C5×#333D3semidirect
58. C3×#333D5semidirect
143. #333D15semidirect
279. C3×C5#1554semidirect
323. C5#68486semidirect
338. C3#10599279semidirect

Maximal subgroups

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

subgroupindex
#117564872
#117509362
#117509342
C3×C5×#3332
#117463672
#117463072
#117463032
#105992793
#684865