Finite Group Databasebeta

← #14316193

Subgroups — #14316193

Order 1920.

512 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 86 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×D5×D24C211yesmaximal, characteristic
2C3×#65176C211yesmaximal, characteristic, complemented
3C2×#90943C211yesmaximal, characteristic, complemented
4C2×#90941C211yesmaximal, characteristic, complemented
5#11746312C211yesmaximal, characteristic, complemented
6C5×#4491C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic, complemented
8#10599986—31nomaximal, Hall
9C2×D5×D12—21no—
10C2×D120C2211yescharacteristic
11C2×C5×D24C2211yescharacteristic
12C2×C3×Dic20C2211yescharacteristic, complemented
13C2×C3×C8×D5C2211yescharacteristic
14C3×#4043—21no—
15C2×#6654—21no—
16D5×D24—22no—
17D5×D24—22no—
18C3×C5×#107C2211yescharacteristic, complemented
19C2×C3⋊#672C2211yescharacteristic, complemented
20C2×C5×C3⋊C16C2211yescharacteristic, complemented
21C3×#3942—21no—
22#90943—22no—
23#90941—22no—
24#71085—51nomaximal, Hall
25C2×D5×D8—31no—
26C2×#3959—31no—
27C2×#3932—31no—
28#65176D311yescharacteristic, complemented
29C5×#357—31no—
30#64727—31no—
31#64711—31no—
32C22×D3×D5—41no—
33C2×D60—21no—
34C2×C5×D12—21no—
35C2×C3×C4×D5D411yescharacteristic
36C2×C3×Dic10—21no—
37C2×#1203—41no—
38D5×D12—24no—
39D5×D12—42no—
40C2×C3×C5×C8C2311yescharacteristic
41C3×C5×C4⋊C4—21no—
42D120—21no—
43D120D412yes—
44C5×D24—21no—
45C5×D24D412yes—
46C3×#685—41no—
47C3×C4⋊Dic5—41no—
48C2×C3×#168D411yescharacteristic
49C3×Dic20—21no—
50C3×Dic20—21no—
51C3×C8×D5—21no—
52C3×C8×D5—21no—
53#6654—24no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C22×D24—51no—
57C3×#467—51no—
58C2×#828—51no—
59C2×#828—51no—
60#4549—51no—
61#4491—51no—
62#4491D511yescharacteristic, complemented
63C2×D4×D5—61no—
64C2×C5×D8—31no—
65C2×#686—61no—
66D5×D8—62no—
67D5×D8—62no—
68C2×Dic20C2×D311yescharacteristic, complemented
69C2×D40—31no—
70C2×C8×D5C2×D311yescharacteristic
71#4043—21no—
72C2×C5×C16—31no—
73C5×#107C2×D311yescharacteristic, complemented
74#3959—62no—
75C2×#672—31no—
76#3942—21no—
77#3932—62no—
78#2187—151noSylow
79C22×D15—41no—
80C22×C5×D3—41no—
81C22×C3×D5D811yescharacteristic
82C2×D3×D5—44no—
83C2×D3×D5—82no—
84C2×D3×D5—82no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87D60—22no—
88D60—41no—
89C5×D12—22no—
90C5×D12—41no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5D811yescharacteristic
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×Dic10—41no—
96C3×Dic10—41no—
97#1203—44no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C3×#168—21no—
101C22×D12—101no—
102C2×C3×Q16—51no—
103C22×C3×C8—51no—
104C3×C22⋊Q8—101no—
105C2×D24—51no—
106C2×D24—102no—
107C2×D24—101no—
108C2×D24—102no—
109C2×D24C2×D511yescharacteristic
110C3×#107C2×D511yescharacteristic, complemented
111C3×#103—101no—
112#828—102no—
113#828—102no—
114C2×C3⋊C16—51no—
115C2×C3⋊C16C2×D511yescharacteristic, complemented
116C23×D5—121no—
117C2×C5×D4—61no—
118C2×C22⋊D5—121no—
119D4×D5—64no—
120D4×D5—122no—
121C2×D20—61no—
122C2×C4×D5#6711yescharacteristic
123C2×Dic10—21no—
124C5×D8—32no—
125C5×D8—61no—
126C2×C5×C8C22×D311yescharacteristic
127C5×C4⋊C4—21no—
128#686—64no—
129#685—41no—
130C4⋊Dic5—41no—
131C2×#168#6711yescharacteristic
132Dic20—21no—
133Dic20—21no—
134D40—32no—
135D40—61no—
136C8×D5—21no—
137C8×D5—21no—
138C5×C16—61no—
139#672—61no—
140C22×D8—151no—
141C2×SD32—151no—
142C2×SD32—151no—
143#467—51no—
144#357—31no—
145#357—151no—
146C22⋊C16—151no—
147C22×C3×C5C2×D811yescharacteristic
148C2×D15—42no—
149C2×D15—81no—
150C2×D15—81no—
151C2×C5×D3—42no—
152C2×C5×D3—81no—
153C2×C5×D3—81no—
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5SD3212yescomplemented
157D3×D5—88no—
158C3×C4×C5—81no—
159C3×C4×C5#12011yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×Dic5—21no—
162C3×Dic5—81no—
163C23×D3—201no—
164C2×C3×Q8—101no—
165C22×C3×C4—51no—
166C2×D12—21no—
167C2×D12—104no—
168C2×D12—101no—
169C2×D12—202no—
170C2×D12—201no—
171C3×Q16—101no—
172C3×Q16—101no—
173C2×C3×C8—51no—
174C2×C3×C8—101no—
175C2×C3×C8—101no—
176C2×C3×C8C22×D511yescharacteristic
177C3×C4⋊C4—21no—
178C3×C4⋊C4—201no—
179C3×C22⋊C4—201no—
180D24—21no—
181D24—52no—
182D24—104no—
183D24—101no—
184D24D2012yes—
185C3⋊C16—21no—
186C3⋊C16—101no—
187C23×C5—121no—
188C22×D5—124no—
189C22×D5—121no—
190C22×D5—242no—
191C22×D5—242no—
192C22×D5#21311yescharacteristic
193C5×D4—62no—
194C5×D4—121no—
195C2×C4×C5—41no—
196C2×C4×C5C2×#6711yescharacteristic
197C22⋊D5—124no—
198C2×Dic5—41no—
199C2×Dic5#21311yescharacteristic
200D20—62no—
201D20—121no—
202C4×D5—21no—
203C4×D5—21no—
204Dic10—41no—
205Dic10—41no—
206C5×C8D3×D411yescharacteristic
207C5×C8D3×D411yescharacteristic
208#168—21no—
209C22×D4—301no—
210C2×Q16—51no—
211C2×D8—31no—
212C2×D8—151no—
213C2×D8—301no—
214C2×D8—302no—
215C2×D8—302no—
216C22×C8—51no—
217C22⋊Q8—101no—
218SD32—302no—
219SD32—302no—
220C2×C16—31no—
221C2×C16—151no—
222#107D3×D511yescharacteristic, complemented
223#103—101no—
224C2×C3×C5#44711yescharacteristic
225C2×C3×C5C2×SD3211yescharacteristic
226C2×C3×C5#50911yescharacteristic
227D15—82no—
228C3×D5—22no—
229C5×D3—82no—
230C23×C3—51no—
231C22×D3—41no—
232C22×D3—204no—
233C22×D3—201no—
234C22×D3—402no—
235C22×D3—402no—
236C3×Q8—201no—
237C3×Q8—201no—
238C2×C3×C4—41no—
239C2×C3×C4—51no—
240C2×C3×C4—101no—
241C2×C3×C4—101no—
242C2×C3×C4—201no—
243C2×C3×C4D4×D511yescharacteristic
244D12—22no—
245D12—41no—
246D12—102no—
247D12—204no—
248D12—201no—
249C3×C8—101no—
250C3×C8C2×D2011yescharacteristic
251C3×C8D4×D511yescharacteristic
252C22×C5—122no—
253C22×C5—241no—
254C22×C5—241no—
255C22×C5C2×#21311yescharacteristic
256C2×D5—21no—
257C2×D5—21no—
258C2×D5—122no—
259C2×D5—248no—
260C2×D5—241no—
261C2×D5—241no—
262C2×D5#82812yescomplemented
263C4×C5—81no—
264C4×C5#93711yescharacteristic
265C4×C5#94911yescharacteristic
266Dic5—21no—
267Dic5—81no—
268C24—601no—
269C2×Q8—101no—
270C2×D4—61no—
271C2×D4—304no—
272C2×D4—301no—
273C2×D4—601no—
274C2×D4—602no—
275C22×C4—51no—
276Q16—101no—
277Q16—101no—
278D8—32no—
279D8—61no—
280D8—152no—
281D8—304no—
282D8—301no—
283C2×C8—51no—
284C2×C8—101no—
285C2×C8—101no—
286C2×C8C2×D3×D511yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—201no—
289C22⋊C4—201no—
290C16—61no—
291C16—301no—
292C3×C5#218711yescharacteristic, complemented, Hall
293C22×C3—52no—
294C22×C3—101no—
295C22×C3—101no—
296C22×C3D5×D811yescharacteristic
297C2×D3—42no—
298C2×D3—81no—
299C2×D3—81no—
300C2×D3—202no—
301C2×D3—408no—
302C2×D3—401no—
303C2×D3—401no—
304C3×C4—81no—
305C3×C4—101no—
306C3×C4—401no—
307C3×C4#402811yescharacteristic
308C3×C4#406011yescharacteristic
309C2×C5—242no—
310C2×C5#503611yescharacteristic
311C2×C5C2×#82811yescharacteristic
312C2×C5#519311yescharacteristic
313D5—22no—
314D5—242no—
315C23—51no—
316C23—121no—
317C23—604no—
318C23—601no—
319C23—1202no—
320C23—1202no—
321Q8—201no—
322Q8—201no—
323D4—62no—
324D4—121no—
325D4—302no—
326D4—604no—
327D4—601no—
328C2×C4—41no—
329C2×C4—51no—
330C2×C4—101no—
331C2×C4—101no—
332C2×C4—201no—
333C2×C4D5×#6711yescharacteristic
334C8—101no—
335C8D3×D2011yescharacteristic
336C8#677711yescharacteristic
337C2×C3—102no—
338C2×C3#6506211yescharacteristic
339C2×C3#6520011yescharacteristic
340C2×C3D5×SD3211yescharacteristic
341D3—82no—
342D3—402no—
343C5#7108511yescharacteristic, complemented, Sylow
344C22—52no—
345C22—101no—
346C22—101no—
347C22—122no—
348C22—241no—
349C22—241no—
350C22—602no—
351C22—1208no—
352C22—1201no—
353C22—1201no—
354C22D5×#21311yescharacteristic
355C4—81no—
356C4—101no—
357C4—401no—
358C4#9147411yescharacteristic
359C4#9150211yescharacteristic
360C3#1059998611yescharacteristic, complemented, Sylow
361C2—102no—
362C2—242no—
363C2—1202no—
364C2#1174748011yescharacteristic
365C2#1174826511yescharacteristic
366C2D5×#82811yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC2×D5×D24C2
hypercenter#107D3×D5
hypocenterC3×C5#2187
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
2. C3×#65176C2semidirect
3. C2×#90943C2semidirect
4. C2×#90941C2semidirect
5. #11746312C2semidirect
6. C5×#4491C2semidirect
7. #11745879C2semidirect
12. C2×C3×Dic20C22semidirect
18. C3×C5×#107C22semidirect
19. C2×C3⋊#672C22semidirect
20. C2×C5×C3⋊C16C22semidirect
28. #65176D3semidirect
62. #4491D5semidirect
68. C2×Dic20C2×D3semidirect
73. C5×#107C2×D3semidirect
110. C3×#107C2×D5semidirect
115. C2×C3⋊C16C2×D5semidirect
156. C2×C3×D5SD32semidirect
222. #107D3×D5semidirect
262. C2×D5#828semidirect
292. C3×C5#2187semidirect
343. C5#71085semidirect
360. C3#10599986semidirect

Maximal subgroups

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

subgroupindex
C2×D5×D242
C3×#651762
C2×#909432
C2×#909412
#117463122
C5×#44912
#117458792
#105999863
#710855