Finite Group Databasebeta

← #14289863

Subgroups — #14289863

Order 1920.

388 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 88 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#11756343C211yesmaximal, characteristic
2C3×#65310C211yesmaximal, characteristic, complemented
3#11746942C211yesmaximal, characteristic
4#11746920C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745859C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic
8#10599040—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835—21no—
11#91787—22no—
12#91781—21no—
13#91764—21no—
14C4×D60C2211yescharacteristic
15#91758C2211yescharacteristic
16C4×Dic30—21no—
17C3×#4015C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C4×C5×C3⋊C8C2211yescharacteristic
20C3×#3967—21no—
21C3×#3939—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90987—21no—
24#90971—22no—
25#90968—21no—
26#71157—51nomaximal, Hall
27#65918—31no—
28#65310D311yescharacteristic, complemented
29#65131—31no—
30#64970—31no—
31C5×Q8⋊C8—31no—
32#64702—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30—21no—
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5—21no—
42C3×C42×C5C2311yescharacteristic
43#6714—22no—
44#6714—22no—
45#6714—21no—
46C4⋊Dic15—21no—
47C4⋊Dic15D412yes—
48C4⋊Dic15D411yescharacteristic
49#6712—22no—
50C4×Dic15—22no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#5584—51no—
57C3×#477—51no—
58#5084—51no—
59#5079—51no—
60#4535D511yescharacteristic, complemented
61#4486—51no—
62#4483—51no—
63C4×C5×Q8C2×D311yescharacteristic
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⋊C8—31no—
73C4×C5×C8—31no—
74#3967—21no—
75#3953—61no—
76#3949—61no—
77#3948—62no—
78#3939—21no—
79C4⋊#168C2×D311yescharacteristic
80#1638—151noSylow
81C22×D15—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—22no—
91D60—21no—
92D60—21no—
93C4×D15—41no—
94C4×D15—41no—
95Dic30—41no—
96Dic30—41no—
97C2×C3×Dic5—41no—
98C3×Dic10—42no—
99C3×#168—41no—
100C5×C3⋊C8—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8—51no—
103C3×C4×Q8C2×D511yescharacteristic
104#946—101no—
105#898—102no—
106#892—101no—
107#875—101no—
108C4×D12—51no—
109#869—51no—
110C4×Dic6—101no—
111C3×#107—101no—
112C3×C4⋊C8—51no—
113C3×#103—101no—
114#835—102no—
115#809—101no—
116#808—101no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4×C3⋊C8C2×D511yescharacteristic
119C2×C5×Q8#6711yescharacteristic
120C2×D20—31no—
121C2×C4×D5—61no—
122C2×Dic10—21no—
123C2×Dic10—61no—
124C2×C5×C8—61no—
125C2×C5×C8—61no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4#6711yescharacteristic
128C42×C5—21no—
129C42×C5C22×D311yescharacteristic
130#685—62no—
131#685—62no—
132#685—61no—
133C4⋊Dic5—21no—
134C4⋊Dic5—21no—
135C4⋊Dic5—32no—
136C4⋊Dic5—31no—
137C4⋊Dic5—61no—
138#683—62no—
139C4×Dic5—62no—
140C2×#168—21no—
141#556—151no—
142#487—151no—
143#477—51no—
144#476—151no—
145#332—151no—
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—41no—
154C3×C4×C5—41no—
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—42no—
160Dic15—41no—
161C3×Dic5—81no—
162C2×C3×Q8—101no—
163C2×C3×Q8D2011yescharacteristic
164C2×D12—51no—
165C2×C4×D3—101no—
166C2×Dic6—101no—
167C2×C3×C8—101no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C4⋊C4D2011yescharacteristic
172C3×C42—21no—
173C3×C42C22×D511yescharacteristic
174(C2×D3)⋊C4—102no—
175(C2×D3)⋊C4—102no—
176(C2×D3)⋊C4—101no—
177C4⋊Dic3—51no—
178C4⋊Dic3—52no—
179C4⋊Dic3—101no—
180Dic3⋊C4—102no—
181C4×Dic3—102no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C22×D5—61no—
185C5×Q8—21no—
186C5×Q8—21no—
187C2×C4×C5—21no—
188C2×C4×C5—21no—
189C2×C4×C5D3×D411yescharacteristic
190C2×C4×C5D3×D411yescharacteristic
191C2×C4×C5C2×#6711yescharacteristic
192C2×Dic5—41no—
193C2×Dic5—61no—
194C2×Dic5—62no—
195D20—61no—
196D20—61no—
197C4×D5—121no—
198C4×D5—121no—
199Dic10—42no—
200Dic10—121no—
201Dic10—121no—
202C5×C8—121no—
203C5×C8—121no—
204#168—41no—
205C4⋊Q8—51no—
206C4⋊Q8—151no—
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—301no—
211C4×Q8D3×D511yescharacteristic
212C4×D4—151no—
213#117—301no—
214#107—101no—
215#106—301no—
216C4⋊C8—31no—
217C4⋊C8—51no—
218#103—101no—
219#103—302no—
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—21no—
228C3×Q8—21no—
229C3×Q8—202no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—201no—
233C2×C3×C4C2×D2011yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×Dic3—101no—
237C2×Dic3—102no—
238D12—101no—
239D12—101no—
240C4×D3—201no—
241C4×D3—201no—
242Dic6—201no—
243Dic6—201no—
244C3×C8—201no—
245C3⋊C8—41no—
246C3⋊C8—41no—
247C22×C5#93711yescharacteristic
248C2×D5—121no—
249C2×D5—121no—
250C2×D5—121no—
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—41no—
254C4×C5#91811yescharacteristic
255C4×C5#91911yescharacteristic
256C4×C5#94211yescharacteristic
257C4×C5#95011yescharacteristic
258Dic5—81no—
259Dic5—122no—
260Dic5—121no—
261C2×Q8—101no—
262C2×Q8—301no—
263C2×Q8#120211yescharacteristic
264C2×D4—151no—
265C22×C4—301no—
266C2×C8—61no—
267C2×C8—61no—
268C2×C8—101no—
269C4⋊C4—21no—
270C4⋊C4—101no—
271C4⋊C4—101no—
272C4⋊C4—152no—
273C4⋊C4—151no—
274C4⋊C4—302no—
275C4⋊C4—301no—
276C4⋊C4#120211yescharacteristic
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—301no—
280C42—21no—
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—41no—
290C3×C4—41no—
291C3×C4—401no—
292C3×C4#405011yescharacteristic
293C3×C4#405511yescharacteristic
294C3×C4#406211yescharacteristic
295C3×C4#406411yescharacteristic
296Dic3—202no—
297Dic3—201no—
298C2×C5#504711yescharacteristic
299C2×C5#518711yescharacteristic
300C2×C5#520111yescharacteristic
301D5—241no—
302C23—301no—
303Q8—21no—
304Q8—21no—
305Q8—202no—
306Q8—601no—
307Q8—601no—
308D4—301no—
309D4—301no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—201no—
313C2×C4—301no—
314C2×C4—302no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4C2×#120211yescharacteristic
318C2×C4#679011yescharacteristic
319C2×C4#679011yescharacteristic
320C8—121no—
321C8—121no—
322C8—201no—
323C2×C3#6502211yescharacteristic
324C2×C3#6509911yescharacteristic
325C2×C3#6511611yescharacteristic
326D3—401no—
327C5#7115711yescharacteristic, complemented, Sylow
328C22—601no—
329C22—601no—
330C22—601no—
331C22#9157211yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—401no—
336C4—602no—
337C4—601no—
338C4#9131111yescharacteristic
339C4#9131511yescharacteristic
340C4#9151211yescharacteristic
341C4#9152311yescharacteristic
342C3#1059904011yescharacteristic, complemented, Sylow
343C2—1201no—
344C2#1174855211yescharacteristic
345C2#1174930911yescharacteristic
346C2#1174946011yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#65310C2semidirect
4. #11746920C2semidirect
5. C5×#4535C2semidirect
6. #11745859C2semidirect
28. #65310D3semidirect
60. #4535D5semidirect
283. C3×C5#1638semidirect
327. C5#71157semidirect
342. C3#10599040semidirect

Maximal subgroups

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

subgroupindex
#117563432
C3×#653102
#117469422
#117469202
C5×#45352
#117458592
#117458382
#105990403
#711575