Finite Group Databasebeta

← #14289857

Subgroups — #14289857

Order 1920.

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

normal subgroups only

This group has 388 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
1#11752483C211yesmaximal, characteristic
2#11750943C211yesmaximal, characteristic
3#11746961C211yesmaximal, characteristic, complemented
4#11746921C211yesmaximal, characteristic, complemented
5C5×#4484C211yesmaximal, characteristic, complemented
6C3×#64702C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic
8#10599040—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10#91758C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91383—21no—
14#91374—21no—
15#91347—21no—
16#91345—22no—
17Dic3×Dic10—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19#91105—21no—
20#91101—21no—
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23#90988—21no—
24#90974—22no—
25#90973—21no—
26#68435—51nomaximal, Hall
27#65918—31no—
28#65310—31no—
29#65131—31no—
30#64970—31no—
31C5×Q8⋊C8—31no—
32#64702D311yescharacteristic, complemented
33#64679—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30—21no—
37C2×C5×Dic6D411yescharacteristic
38C2×C3×Dic10—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41#6714—21no—
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15D411yescharacteristic
45C5×C4⋊Dic3D411yescharacteristic
46C5×Dic3⋊C4—21no—
47C4×C5×Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5D412yes—
51C2×C3×#168—21no—
52#6668—22no—
53#6667—22no—
54#6667—22no—
55Dic3×Dic5—22no—
56#5732—51no—
57#5093—51no—
58#4850—51no—
59#4842—51no—
60C3×#332—51no—
61#4484D511yescharacteristic, complemented
62#4483—51no—
63C4×C5×Q8—31no—
64#4092—61no—
65#4044—62no—
66#4038—61no—
67#4021—61no—
68C4×D20—31no—
69#4015—31no—
70#4015C2×D311yescharacteristic
71C4×Dic10—61no—
72C5×C4⋊C8C2×D311yescharacteristic
73C4×C5×C8—31no—
74#3967—61no—
75#3953—61no—
76#3949—61no—
77#3948—62no—
78#3939—61no—
79C4⋊#168C2×D311yescharacteristic
80#1638—151noSylow
81C22×D15—21no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—21no—
86C2×Dic15—41no—
87D60—21no—
88D60—21no—
89C4×D15—41no—
90C4×D15—41no—
91Dic30—42no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—21no—
94C5×Dic6—21no—
95C5×Dic6—21no—
96C2×C3×Dic5—22no—
97C3×Dic10—41no—
98C3×Dic10—41no—
99C3×C5×C8—41no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8—51no—
103#947—101no—
104Q8×Dic3—101no—
105#898—102no—
106#897—101no—
107#892—101no—
108C4×D12—51no—
109#869—51no—
110C4×Dic6C2×D511yescharacteristic
111C3×C4⋊C8—51no—
112C3×C4⋊C8C2×D511yescharacteristic
113#821—101no—
114#818—101no—
115#817—101no—
116#816—101no—
117#810—102no—
118C4×C3⋊C8C2×D511yescharacteristic
119C2×C5×Q8—31no—
120C2×D20—31no—
121C2×C4×D5—61no—
122C2×Dic10—21no—
123C2×Dic10—61no—
124C2×C5×C8—21no—
125C2×C5×C8—61no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—61no—
128C42×C5—61no—
129C42×C5C22×D311yescharacteristic
130#685—62no—
131#685—62no—
132#685—61no—
133C4⋊Dic5—21no—
134C4⋊Dic5—31no—
135C4⋊Dic5—61no—
136C4⋊Dic5—61no—
137C4⋊Dic5D1212yes—
138#683—62no—
139C4×Dic5—62no—
140C2×#168—21no—
141#556—151no—
142#487—151no—
143#477—151no—
144#476—151no—
145#332—51no—
146Q8⋊C8—31no—
147D4⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C2×D15—41no—
150C2×D15—41no—
151C2×D15—41no—
152C3×C4×C5—21no—
153C3×C4×C5#13511yescharacteristic
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×C4×C5#13711yescharacteristic
157Dic15—41no—
158Dic15—81no—
159C3×Dic5—42no—
160C5×Dic3—41no—
161C5×Dic3—41no—
162C2×C3×Q8—101no—
163C2×D12—51no—
164C2×C4×D3—101no—
165C2×Dic6—101no—
166C2×Dic6D2011yescharacteristic
167C2×C3×C8—21no—
168C2×C3×C8—101no—
169C3×C4⋊C4—52no—
170C3×C4⋊C4—101no—
171C3×C42C22×D511yescharacteristic
172(C2×D3)⋊C4—102no—
173(C2×D3)⋊C4—102no—
174(C2×D3)⋊C4—101no—
175C4⋊Dic3—51no—
176C4⋊Dic3—102no—
177C4⋊Dic3—101no—
178C4⋊Dic3—101no—
179C4⋊Dic3D2011yescharacteristic
180Dic3⋊C4—21no—
181C4×Dic3—21no—
182C4×Dic3—102no—
183C2×C3⋊C8—21no—
184C22×D5—61no—
185C5×Q8—61no—
186C5×Q8—61no—
187C2×C4×C5—61no—
188C2×C4×C5—61no—
189C2×C4×C5C2×D1211yescharacteristic
190C2×C4×C5D3×D411yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×Dic5—22no—
193C2×Dic5—61no—
194C2×Dic5—121no—
195D20—61no—
196D20—61no—
197C4×D5—121no—
198C4×D5—121no—
199Dic10—41no—
200Dic10—41no—
201Dic10—122no—
202C5×C8—41no—
203C5×C8—121no—
204#168—41no—
205C4⋊Q8—51no—
206C4⋊Q8—151no—
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—31no—
211C4×Q8—301no—
212C4×D4—151no—
213#117—301no—
214#107—301no—
215#106—301no—
216C4⋊C8—51no—
217C4⋊C8D3×D511yescharacteristic
218#103—302no—
219#103—301no—
220#102—301no—
221C4×C8—31no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225D15—81no—
226C22×D3—101no—
227C3×Q8—201no—
228C3×Q8—201no—
229C2×C3×C4—102no—
230C2×C3×C4C2×D2011yescharacteristic
231C2×C3×C4D4×D511yescharacteristic
232C2×C3×C4D4×D511yescharacteristic
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—101no—
236C2×Dic3—201no—
237D12—101no—
238D12—101no—
239C4×D3—201no—
240C4×D3—201no—
241Dic6—21no—
242Dic6—21no—
243Dic6—202no—
244C3×C8—41no—
245C3×C8—201no—
246C3⋊C8—41no—
247C22×C5#88211yescharacteristic
248C2×D5—121no—
249C2×D5—121no—
250C2×D5—121no—
251C4×C5—21no—
252C4×C5—121no—
253C4×C5—121no—
254C4×C5#91211yescharacteristic
255C4×C5#91511yescharacteristic
256C4×C5#91611yescharacteristic
257C4×C5#91811yescharacteristic
258Dic5—42no—
259Dic5—121no—
260Dic5—241no—
261C2×Q8—31no—
262C2×Q8—101no—
263C2×Q8—301no—
264C2×D4—151no—
265C22×C4—301no—
266C2×C8—21no—
267C2×C8—61no—
268C2×C8—101no—
269C4⋊C4—31no—
270C4⋊C4—52no—
271C4⋊C4—61no—
272C4⋊C4—101no—
273C4⋊C4—151no—
274C4⋊C4—302no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—301no—
280C42—61no—
281C42—302no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3#402811yescharacteristic
285C2×D3—201no—
286C2×D3—201no—
287C2×D3—201no—
288C3×C4—21no—
289C3×C4—202no—
290C3×C4#405011yescharacteristic
291C3×C4#405511yescharacteristic
292C3×C4#406211yescharacteristic
293C3×C4#406411yescharacteristic
294Dic3—41no—
295Dic3—41no—
296Dic3—201no—
297Dic3—401no—
298C2×C5#475311yescharacteristic
299C2×C5#478311yescharacteristic
300C2×C5#480811yescharacteristic
301D5—241no—
302C23—301no—
303Q8—61no—
304Q8—61no—
305Q8—201no—
306Q8—201no—
307Q8—602no—
308D4—301no—
309D4—301no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—102no—
313C2×C4—301no—
314C2×C4—601no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4D5×D1211yescharacteristic
318C2×C4D3×D2011yescharacteristic
319C2×C4#679011yescharacteristic
320C8—41no—
321C8—121no—
322C8—201no—
323C2×C3#6502211yescharacteristic
324C2×C3#6509911yescharacteristic
325C2×C3#6511611yescharacteristic
326D3—401no—
327C5#6843511yescharacteristic, complemented, Sylow
328C22—601no—
329C22—601no—
330C22—601no—
331C22#9147611yescharacteristic
332C4—21no—
333C4—121no—
334C4—121no—
335C4—202no—
336C4—601no—
337C4—1201no—
338C4#9126311yescharacteristic
339C4#9127211yescharacteristic
340C4#9149711yescharacteristic
341C4#9152211yescharacteristic
342C3#1059904011yescharacteristic, complemented, Sylow
343C2—1201no—
344C2#1174751911yescharacteristic
345C2#1174816611yescharacteristic
346C2#1174826311yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1638
LCSG ▷ C3×C42×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
3. #11746961C2semidirect
4. #11746921C2semidirect
5. C5×#4484C2semidirect
6. C3×#64702C2semidirect
32. #64702D3semidirect
61. #4484D5semidirect
283. C3×C5#1638semidirect
327. C5#68435semidirect
342. C3#10599040semidirect

Maximal subgroups

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

subgroupindex
#117524832
#117509432
#117469612
#117469212
C5×#44842
C3×#647022
#117458382
#105990403
#684355