Finite Group Databasebeta

← #14285104

Subgroups — #14285104

Order 1920.

416 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 100 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#11752484C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic
3#11747000C211yesmaximal, characteristic
4C5×#4486C211yesmaximal, characteristic, complemented
5C3×#64702C211yesmaximal, characteristic, complemented
6#11745858C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599218—31nomaximal, Hall
9C42×D15C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12#91390—21no—
13#91384C412yes—
14#91383—21no—
15#91347C412yes—
16#91344—21no—
17#91331—21no—
18C2×#6648—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91104—21no—
21#91099—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25#90983—21no—
26#68424—51nomaximal, Hall
27#66062—31no—
28#65124—31no—
29D5×C4⋊C8—31no—
30C5×#332—31no—
31#64767—31no—
32#64706—31no—
33#64702D311yescharacteristic, complemented
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C5×Dic6—21no—
38C2×C3×Dic10—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4×Dic15C2×C411yescharacteristic
42C4×Dic15D411yescharacteristic
43C4×Dic15D411yescharacteristic
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3C2×C412yes—
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5C2×C412yes—
50C2×C3×#168—21no—
51Dic3⋊Dic5—22no—
52#6668—22no—
53#6667—22no—
54Dic3×Dic5—22no—
55#6648—42no—
56#5728—51no—
57#4835—51no—
58D3×C4⋊C8—51no—
59C3×#332—51no—
60#4547—51no—
61#4486D511yescharacteristic, complemented
62#4482—51no—
63C5×C4⋊Q8—31no—
64#4092—61no—
65Q8×Dic5—61no—
66C2×C8×D5—61no—
67#4043—61no—
68#4038—32no—
69#4036—32no—
70#4033—61no—
71C42×D5—31no—
72#4015C2×D311yescharacteristic
73C5×C4⋊C8—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75#3952—61no—
76#3947—61no—
77#3946—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80#1552—151noSylow
81C22×D15C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15C22⋊C411yescharacteristic
86C2×Dic15C22⋊C411yescharacteristic
87C2×Dic15C22⋊C411yescharacteristic
88C4×D15—22no—
89C4×D15—21no—
90C4×D15—21no—
91C4×D15—21no—
92C4×D15—21no—
93C2×C5×Dic3—22no—
94C5×Dic6—41no—
95C5×Dic6—41no—
96C2×C3×Dic5—22no—
97C3×Dic10—41no—
98C3×Dic10—41no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3×#168—41no—
102C5×C3⋊C8—41no—
103C3×C4⋊Q8—51no—
104#946—101no—
105Q8×Dic3—101no—
106C2×D3×C8—101no—
107#897—101no—
108#892—52no—
109#890—52no—
110#887—101no—
111C42×D3—51no—
112#869C2×D511yescharacteristic
113C3×C4⋊C8—51no—
114C3×C4⋊C8C2×D511yescharacteristic
115(C2×D3)⋊C8—101no—
116#815—101no—
117Dic3⋊C8—101no—
118C4⋊(C3⋊C8)—51no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—61no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×C4×D5—31no—
124C2×Dic10—21no—
125C2×C5×C8—21no—
126C2×C5×C8—61no—
127C5×C4⋊C4—32no—
128C5×C4⋊C4—61no—
129C42×C5C22×D311yescharacteristic
130#685—62no—
131C4⋊Dic5—21no—
132C4⋊Dic5—62no—
133C4⋊Dic5C4×D312yes—
134#683—62no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—31no—
138C4×Dic5—62no—
139C2×#168—21no—
140C2×#168—61no—
141C8×D5—122no—
142#533—151no—
143#432—151no—
144C2×C4⋊C8—151no—
145#332—31no—
146#332—51no—
147#332—151no—
148#332—151no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×D15—21no—
151C2×D15—21no—
152C2×D15#10112yes—
153C3×C4×C5—21no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
157C3×C4×C5#13711yescharacteristic
158Dic15—21no—
159Dic15—21no—
160Dic15—21no—
161C3×Dic5—42no—
162C5×Dic3—42no—
163C2×C3×Q8—101no—
164C2×C4×D3—51no—
165C2×C4×D3—51no—
166C2×C4×D3—51no—
167C2×Dic6—21no—
168C2×C3×C8—21no—
169C2×C3×C8—101no—
170C3×C4⋊C4—52no—
171C3×C4⋊C4—101no—
172C3×C42C22×D511yescharacteristic
173(C2×D3)⋊C4—102no—
174C4⋊Dic3—21no—
175C4⋊Dic3—102no—
176C4⋊Dic3C4×D512yes—
177Dic3⋊C4—102no—
178C4×Dic3—51no—
179C4×Dic3—51no—
180C4×Dic3—51no—
181C4×Dic3—102no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—101no—
184D3×C8—202no—
185C22×D5—31no—
186C5×Q8—121no—
187C5×Q8—121no—
188C2×C4×C5—62no—
189C2×C4×C5C2×C4×D311yescharacteristic
190C2×C4×C5D3×D411yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×Dic5—22no—
193C2×Dic5—31no—
194C2×Dic5—31no—
195C2×Dic5—31no—
196C4×D5—62no—
197C4×D5—61no—
198C4×D5—61no—
199C4×D5—61no—
200C4×D5—61no—
201Dic10—41no—
202Dic10—41no—
203C5×C8—41no—
204C5×C8—121no—
205#168—41no—
206#168—121no—
207C22×C8—301no—
208C4⋊Q8—31no—
209C4⋊Q8—51no—
210#125—152no—
211C22⋊Q8—301no—
212C22⋊Q8—301no—
213C4×Q8—301no—
214C4×Q8—301no—
215#117—152no—
216C2×C42—151no—
217C4⋊C8—31no—
218C4⋊C8—51no—
219C4⋊C8—151no—
220C4⋊C8—301no—
221C4⋊C8D3×D511yescharacteristic
222C22⋊C8—301no—
223#97—301no—
224C2×C3×C5C2×#10111yescharacteristic
225C2×C3×C5#41611yescharacteristic
226C2×C3×C5#41711yescharacteristic
227D15—22no—
228C22×D3—51no—
229C3×Q8—201no—
230C3×Q8—201no—
231C2×C3×C4—102no—
232C2×C3×C4C2×C4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×Dic3—22no—
236C2×Dic3—51no—
237C2×Dic3—51no—
238C2×Dic3—51no—
239C4×D3—102no—
240C4×D3—101no—
241C4×D3—101no—
242C4×D3—101no—
243C4×D3—101no—
244Dic6—41no—
245Dic6—41no—
246C3×C8—41no—
247C3×C8—201no—
248C3⋊C8—41no—
249C3⋊C8—201no—
250C22×C5D3×C22⋊C411yescharacteristic
251C2×D5—32no—
252C2×D5—61no—
253C2×D5—61no—
254C4×C5—21no—
255C4×C5—122no—
256C4×C5#91211yescharacteristic
257C4×C5#91411yescharacteristic
258C4×C5#91611yescharacteristic
259C4×C5#91811yescharacteristic
260Dic5—42no—
261Dic5—61no—
262Dic5—61no—
263Dic5—61no—
264C2×Q8—61no—
265C2×Q8—101no—
266C22×C4—151no—
267C22×C4—151no—
268C22×C4—151no—
269C2×C8—21no—
270C2×C8—61no—
271C2×C8—101no—
272C2×C8—301no—
273C2×C8—602no—
274C4⋊C4—32no—
275C4⋊C4—52no—
276C4⋊C4—61no—
277C4⋊C4—101no—
278C4⋊C4—302no—
279C4⋊C4—302no—
280C22⋊C4—302no—
281C42—151no—
282C42—151no—
283C42—151no—
284C42—302no—
285C42C2×D3×D511yescharacteristic
286C3×C5#155211yescharacteristic, complemented, Hall
287C22×C3D5×C22⋊C411yescharacteristic
288C2×D3—52no—
289C2×D3—101no—
290C2×D3—101no—
291C3×C4—21no—
292C3×C4—202no—
293C3×C4#405711yescharacteristic
294C3×C4#406111yescharacteristic
295C3×C4#406211yescharacteristic
296C3×C4#406511yescharacteristic
297Dic3—42no—
298Dic3—101no—
299Dic3—101no—
300Dic3—101no—
301C2×C5D3×#10111yescharacteristic
302C2×C5#477211yescharacteristic
303C2×C5#480311yescharacteristic
304D5—62no—
305C23—151no—
306Q8—121no—
307Q8—121no—
308Q8—201no—
309Q8—201no—
310C2×C4—62no—
311C2×C4—102no—
312C2×C4—151no—
313C2×C4—151no—
314C2×C4—151no—
315C2×C4—302no—
316C2×C4—301no—
317C2×C4—301no—
318C2×C4—301no—
319C2×C4—301no—
320C2×C4C4×D3×D511yescharacteristic
321C2×C4#677711yescharacteristic
322C2×C4#679011yescharacteristic
323C8—41no—
324C8—121no—
325C8—201no—
326C8—601no—
327C2×C3D5×#10111yescharacteristic
328C2×C3#6506011yescharacteristic
329C2×C3#6509311yescharacteristic
330D3—102no—
331C5#6842411yescharacteristic, complemented, Sylow
332C22—152no—
333C22—301no—
334C22—301no—
335C22#9147311yescharacteristic
336C4—21no—
337C4—122no—
338C4—202no—
339C4—301no—
340C4—301no—
341C4—301no—
342C4#9125711yescharacteristic
343C4#9128011yescharacteristic
344C4#9149711yescharacteristic
345C4#9152111yescharacteristic
346C3#1059921811yescharacteristic, complemented, Sylow
347C2—302no—
348C2#1174750611yescharacteristic
349C2#1174814611yescharacteristic
350C2#1174822711yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1552
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C5×#4486C2semidirect
5. C3×#64702C2semidirect
6. #11745858C2semidirect
7. #11745855C2semidirect
33. #64702D3semidirect
61. #4486D5semidirect
286. C3×C5#1552semidirect
331. C5#68424semidirect
346. C3#10599218semidirect

Maximal subgroups

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

subgroupindex
#117524842
#117509362
#117470002
C5×#44862
C3×#647022
#117458582
#117458552
#105992183
#684245