Finite Group Databasebeta

← #14313932

Subgroups — #14313932

Order 1920.

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

normal subgroups only

This group has 520 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
1C2×D8×D15C211yesmaximal, characteristic
2C2×#91082C211yesmaximal, characteristic, complemented
3#11750981C211yesmaximal, characteristic, complemented
4C3×C5×#357C211yesmaximal, characteristic, complemented
5#11746383C211yesmaximal, characteristic, complemented
6#11746330C211yesmaximal, characteristic, complemented
7#11746312C211yesmaximal, characteristic, complemented
8#10599983—31nomaximal, Hall
9C2×D4×D15—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C2×#6715—21no—
12D8×D15—22no—
13D8×D15C414yescomplemented
14C2×D120C2211yescharacteristic
15C2×C8×D15C2211yescharacteristic
16#91781—21no—
17C2×C3×C5×C16C2211yescharacteristic, complemented
18C3×C5×#107C2211yescharacteristic, complemented
19#91102C2211yescharacteristic, complemented
20C2×C3⋊#672C2211yescharacteristic, complemented
21#91092—21no—
22#91082—22no—
23#69190—51nomaximal, Hall
24C2×D5×D8—31no—
25C2×#3930—31no—
26#65169—31no—
27C5×#357D311yescharacteristic, complemented
28#64782—31no—
29#64729—31no—
30#64711—31no—
31C23×D15—41no—
32C2×C3×C5×D4—21no—
33C2×#1220—41no—
34D4×D15—24no—
35D4×D15—42no—
36C2×D60—21no—
37C2×C4×D15D411yescharacteristic
38C3×C5×D8—21no—
39C3×C5×D8C2×C412yes—
40C2×C3×C5×C8C2311yescharacteristic
41C3×C5×C4⋊C4—21no—
42#6715—24no—
43#6714—41no—
44C4⋊Dic15—21no—
45C4×Dic15—41no—
46C2×C3⋊#168D411yescharacteristic
47D120—21no—
48D120C2×C412yes—
49C8×D15C2×C412yes—
50C8×D15D412yes—
51C3×C5×C16—21no—
52C3⋊#672—21no—
53C2×D3×D8—51no—
54C2×#798—51no—
55#4880—51no—
56C3×#357D511yescharacteristic, complemented
57#4562—51no—
58#4509—51no—
59#4491—51no—
60C2×D4×D5—61no—
61C2×C5×D8C2×D311yescharacteristic
62C2×#686—61no—
63D5×D8—34no—
64D5×D8—62no—
65C2×D40—31no—
66C2×C8×D5—31no—
67#4038—61no—
68C2×C5×C16C2×D311yescharacteristic, complemented
69C5×#107C2×D311yescharacteristic, complemented
70#3950—31no—
71C2×#672—31no—
72#3940—61no—
73#3930—62no—
74#2140—151noSylow
75C23×C3×C5—41no—
76C22×D15—41no—
77C22×D15—44no—
78C22×D15—82no—
79C22×D15—82no—
80C22×D15D811yescharacteristic
81C3×C5×D4—22no—
82C3×C5×D4—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85#1220—44no—
86C2×Dic15—41no—
87C2×Dic15D811yescharacteristic
88D60—22no—
89D60—41no—
90C4×D15C22⋊C412yes—
91C4×D15SD1612yes—
92C3×C5×C8C22×C411yescharacteristic
93C3×C5×C8C2×D411yescharacteristic
94C3⋊#168C22⋊C412yes—
95C2×D3×D4—101no—
96C2×C3×D8C2×D511yescharacteristic
97C2×#213—101no—
98D3×D8—54no—
99D3×D8—102no—
100C2×D24—51no—
101C2×D3×C8—51no—
102#892—101no—
103C2×C3×C16C2×D511yescharacteristic, complemented
104C3×#107C2×D511yescharacteristic, complemented
105#818—51no—
106C2×C3⋊C16—51no—
107#808—101no—
108#798—102no—
109C23×D5—121no—
110C2×C5×D4—21no—
111C2×C22⋊D5—121no—
112D4×D5—64no—
113D4×D5—122no—
114C2×D20—61no—
115C2×C4×D5—31no—
116C5×D8—21no—
117C5×D8C4×D312yes—
118C2×C5×C8C22×D311yescharacteristic
119C5×C4⋊C4—21no—
120#686—64no—
121#685—121no—
122C4⋊Dic5—61no—
123C4×Dic5—121no—
124C2×#168—31no—
125D40—32no—
126D40—61no—
127C8×D5—32no—
128C8×D5—32no—
129C5×C16—21no—
130#672—61no—
131C22×D8—151no—
132C2×M32—151no—
133#427—151no—
134#357—151no—
135#357—151no—
136#357—151no—
137#357D1511yescharacteristic, complemented
138C22×C3×C5—42no—
139C22×C3×C5—81no—
140C22×C3×C5—81no—
141C22×C3×C5C2×D811yescharacteristic
142C2×D15—21no—
143C2×D15—21no—
144C2×D15—42no—
145C2×D15—88no—
146C2×D15—81no—
147C2×D15—81no—
148C2×D15#10212yes—
149C3×C4×C5—81no—
150C3×C4×C5C2×C22⋊C411yescharacteristic
151C3×C4×C5C2×SD1611yescharacteristic
152Dic15—81no—
153Dic15#10212yes—
154C23×D3—201no—
155C2×C3×D4—21no—
156C2×#67—201no—
157D3×D4—104no—
158D3×D4—202no—
159C2×D12—101no—
160C2×C4×D3—51no—
161C3×D8—21no—
162C3×D8C4×D512yes—
163C2×C3×C8C22×D511yescharacteristic
164C3×C4⋊C4—21no—
165#213—104no—
166(C2×D3)⋊C4—201no—
167C4⋊Dic3—101no—
168C4×Dic3—201no—
169C2×C3⋊C8—51no—
170D24—52no—
171D24—101no—
172D3×C8—52no—
173D3×C8—52no—
174C3×C16—21no—
175C3⋊C16—101no—
176C23×C5—41no—
177C22×D5—31no—
178C22×D5—124no—
179C22×D5—121no—
180C22×D5—242no—
181C22×D5—242no—
182C5×D4—22no—
183C5×D4—41no—
184C2×C4×C5—41no—
185C2×C4×C5D3×D411yescharacteristic
186C22⋊D5—124no—
187C2×Dic5—31no—
188C2×Dic5—121no—
189D20—62no—
190D20—121no—
191C4×D5—32no—
192C4×D5—32no—
193C5×C8C2×C4×D311yescharacteristic
194C5×C8D3×D411yescharacteristic
195#168—32no—
196C22×D4—301no—
197C2×D8—154no—
198C2×D8—151no—
199C2×D8—302no—
200C2×D8—301no—
201C2×D8C2×D1511yescharacteristic
202C22×C8—151no—
203#117—301no—
204M32—302no—
205C2×C16—151no—
206C2×C16C2×D1511yescharacteristic, complemented
207#107—151no—
208#107C2×D1511yescharacteristic, complemented
209#106—301no—
210C2×C3×C5—82no—
211C2×C3×C5C2×#10211yescharacteristic
212C2×C3×C5#50911yescharacteristic
213C2×C3×C5#50911yescharacteristic
214D15—22no—
215D15—82no—
216C23×C3—41no—
217C22×D3—51no—
218C22×D3—204no—
219C22×D3—201no—
220C22×D3—402no—
221C22×D3—402no—
222C3×D4—22no—
223C3×D4—41no—
224C2×C3×C4—41no—
225C2×C3×C4D4×D511yescharacteristic
226#67—204no—
227C2×Dic3—51no—
228C2×Dic3—201no—
229D12—102no—
230D12—201no—
231C4×D3—52no—
232C4×D3—52no—
233C3×C8C2×C4×D511yescharacteristic
234C3×C8D4×D511yescharacteristic
235C3⋊C8—52no—
236C22×C5—42no—
237C22×C5—81no—
238C22×C5—81no—
239C22×C5D3×D811yescharacteristic
240C2×D5—32no—
241C2×D5—61no—
242C2×D5—61no—
243C2×D5—122no—
244C2×D5—248no—
245C2×D5—241no—
246C2×D5—241no—
247C4×C5—81no—
248C4×C5D3×C22⋊C411yescharacteristic
249C4×C5D3×SD1611yescharacteristic
250Dic5—32no—
251Dic5—241no—
252C24—601no—
253C2×D4—21no—
254C2×D4—304no—
255C2×D4—301no—
256C2×D4—602no—
257C2×D4—601no—
258C22×C4—151no—
259D8—21no—
260D8—152no—
261D8—304no—
262D8—301no—
263D8C4×D1512yes—
264C2×C8—151no—
265C2×C8—152no—
266C2×C8—152no—
267C2×C8C22×D1511yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—301no—
270C22⋊C4—601no—
271C42—601no—
272C16—21no—
273C16—301no—
274C3×C5#214011yescharacteristic, complemented, Hall
275C22×C3—42no—
276C22×C3—81no—
277C22×C3—81no—
278C22×C3D5×D811yescharacteristic
279C2×D3—52no—
280C2×D3—101no—
281C2×D3—101no—
282C2×D3—202no—
283C2×D3—408no—
284C2×D3—401no—
285C2×D3—401no—
286C3×C4—81no—
287C3×C4D5×C22⋊C411yescharacteristic
288C3×C4D5×SD1611yescharacteristic
289Dic3—52no—
290Dic3—401no—
291C2×C5—82no—
292C2×C5D3×#10211yescharacteristic
293C2×C5#491111yescharacteristic
294C2×C5#491411yescharacteristic
295D5—62no—
296D5—242no—
297C23—41no—
298C23—151no—
299C23—604no—
300C23—601no—
301C23—1202no—
302C23—1202no—
303D4—22no—
304D4—41no—
305D4—302no—
306D4—604no—
307D4—601no—
308C2×C4—41no—
309C2×C4—151no—
310C2×C4—152no—
311C2×C4—152no—
312C2×C4—601no—
313C2×C4D4×D1511yescharacteristic
314C8—152no—
315C8C2×C4×D1511yescharacteristic
316C8D4×D1511yescharacteristic
317C2×C3—82no—
318C2×C3D5×#10211yescharacteristic
319C2×C3#6520011yescharacteristic
320C2×C3#6520311yescharacteristic
321D3—102no—
322D3—402no—
323C5#6919011yescharacteristic, complemented, Sylow
324C22—42no—
325C22—81no—
326C22—81no—
327C22—152no—
328C22—301no—
329C22—301no—
330C22—602no—
331C22—1208no—
332C22—1201no—
333C22—1201no—
334C22D8×D1511yescharacteristic
335C4—81no—
336C4—152no—
337C4—1201no—
338C4C22⋊C4×D1511yescharacteristic
339C4SD16×D1511yescharacteristic
340C3#1059998311yescharacteristic, complemented, Sylow
341C2—82no—
342C2—302no—
343C2—1202no—
344C2D15×#10211yescharacteristic
345C2#1175101211yescharacteristic
346C2#1175101511yescharacteristic
subgroupG/H
centerC22D8×D15
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C22×D15
FittingC3×C5×#357C2
socleC22×C3×C5C2×D8
prime radicalC2×D8×D15C2
cosocleC2×C3×C5×C8C23
hypercenter#357D15
hypocenterC3×C5#2140
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C2×#91082C2semidirect
3. #11750981C2semidirect
4. C3×C5×#357C2semidirect
5. #11746383C2semidirect
6. #11746330C2semidirect
7. #11746312C2semidirect
13. D8×D15C4semidirect
17. C2×C3×C5×C16C22semidirect
18. C3×C5×#107C22semidirect
19. #91102C22semidirect
20. C2×C3⋊#672C22semidirect
27. C5×#357D3semidirect
56. C3×#357D5semidirect
68. C2×C5×C16C2×D3semidirect
69. C5×#107C2×D3semidirect
103. C2×C3×C16C2×D5semidirect
104. C3×#107C2×D5semidirect
137. #357D15semidirect
206. C2×C16C2×D15semidirect
208. #107C2×D15semidirect
274. C3×C5#2140semidirect
323. C5#69190semidirect
340. C3#10599983semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D152
C2×#910822
#117509812
C3×C5×#3572
#117463832
#117463302
#117463122
#105999833
#691905