Finite Group Databasebeta

← #14289866

Subgroups — #14289866

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#11752486C211yesmaximal, characteristic
2C3×#65139C211yesmaximal, characteristic, complemented
3#11746942C211yesmaximal, characteristic
4#11746924C211yesmaximal, characteristic, complemented
5#11746304C211yesmaximal, characteristic
6C5×#4486C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10599228—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91390—21no—
14#91375—21no—
15#91347—21no—
16#91337—22no—
17Dic5×Dic6—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#3950—21no—
22C3×#3948—21no—
23#90987—21no—
24#90970—22no—
25#90968—21no—
26#71157—51nomaximal, Hall
27#66066—31no—
28#65382—31no—
29#65139D311yescharacteristic, complemented
30#65131—31no—
31C5×#332—31no—
32#64704—31no—
33#64703—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41#6714—21no—
42C4⋊Dic15D411yescharacteristic
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3D412yes—
46C2×C5×C3⋊C8—21no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5D411yescharacteristic
50C3×#683—21no—
51C3×C4×Dic5—21no—
52Dic3⋊Dic5—22no—
53#6667—22no—
54#6667—22no—
55Dic3×Dic5—22no—
56#5584—51no—
57C3×#477—51no—
58#5084—51no—
59#5079—51no—
60#4535—51no—
61#4486D511yescharacteristic, complemented
62#4483—51no—
63C5×C4⋊Q8—31no—
64#4093—61no—
65Q8×Dic5—61no—
66#4044—62no—
67#4043—61no—
68#4038—61no—
69C4×D20—31no—
70#4015C2×D311yescharacteristic
71C4×Dic10C2×D311yescharacteristic
72C5×C4⋊C8—31no—
73C5×C4⋊C8C2×D311yescharacteristic
74#3953—61no—
75#3950—21no—
76#3949—61no—
77#3948—21no—
78#3942—62no—
79C4×#168—31no—
80#1638—151noSylow
81C22×D15—21no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—21no—
86D60—21no—
87D60—21no—
88C4×D15—41no—
89C4×D15—41no—
90C2×C5×Dic3—22no—
91C5×Dic6—41no—
92C5×Dic6—41no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—41no—
96C3×Dic10—21no—
97C3×Dic10—21no—
98C3×Dic10—42no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8—51no—
103C3×C4×Q8—51no—
104#946—101no—
105#898—102no—
106#892—101no—
107#875—101no—
108C4×D12—51no—
109#869C2×D511yescharacteristic
110C4×Dic6—101no—
111C3×#107—101no—
112C3×C4⋊C8C2×D511yescharacteristic
113C3×#103—101no—
114#835—102no—
115#809—101no—
116#808—101no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4×C3⋊C8—51no—
119C2×C5×Q8—61no—
120C2×D20—31no—
121C2×C4×D5—61no—
122C2×Dic10—21no—
123C2×Dic10#6711yescharacteristic
124C2×C5×C8—21no—
125C2×C5×C8—61no—
126C5×C4⋊C4—32no—
127C5×C4⋊C4—61no—
128C42×C5C22×D311yescharacteristic
129#685—62no—
130#685—62no—
131#685—61no—
132C4⋊Dic5—21no—
133C4⋊Dic5—21no—
134C4⋊Dic5—31no—
135C4⋊Dic5—62no—
136C4⋊Dic5#6711yescharacteristic
137#683—21no—
138C4×Dic5—21no—
139C4×Dic5—62no—
140C2×#168—61no—
141#556—151no—
142#487—151no—
143#477—51no—
144#476—151no—
145#332—31no—
146Q8⋊C8—151no—
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—
158C3×Dic5—41no—
159C3×Dic5—41no—
160C3×Dic5—81no—
161C5×Dic3—42no—
162C2×C3×Q8—51no—
163C2×C3×Q8—101no—
164C2×D12—51no—
165C2×C4×D3—101no—
166C2×Dic6—21no—
167C2×C3×C8—21no—
168C3×C4⋊C4—51no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C4⋊C4—101no—
172C3×C42—101no—
173C3×C42C22×D511yescharacteristic
174(C2×D3)⋊C4—102no—
175(C2×D3)⋊C4—102no—
176(C2×D3)⋊C4—101no—
177C4⋊Dic3—21no—
178C4⋊Dic3—51no—
179C4⋊Dic3D2012yes—
180Dic3⋊C4—102no—
181C4×Dic3—102no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—101no—
184C22×D5—61no—
185C5×Q8—121no—
186C5×Q8—121no—
187C2×C4×C5—62no—
188C2×C4×C5D3×D411yescharacteristic
189C2×C4×C5D3×D411yescharacteristic
190C2×C4×C5C2×#6711yescharacteristic
191C2×Dic5—21no—
192C2×Dic5—21no—
193C2×Dic5—41no—
194C2×Dic5—61no—
195D20—61no—
196D20—61no—
197C4×D5—121no—
198C4×D5—121no—
199Dic10—21no—
200Dic10—21no—
201Dic10—42no—
202C5×C8—41no—
203C5×C8—121no—
204#168—121no—
205C4⋊Q8—31no—
206C4⋊Q8—51no—
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—51no—
211C4×Q8—301no—
212C4×D4—151no—
213#117—301no—
214#107—101no—
215#106—301no—
216C4⋊C8—31no—
217C4⋊C8D3×D511yescharacteristic
218#103—101no—
219#103—302no—
220#102—301no—
221C4×C8—151no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225D15—81no—
226C22×D3—101no—
227C3×Q8—101no—
228C3×Q8—101no—
229C3×Q8—202no—
230C2×C3×C4—101no—
231C2×C3×C4—101no—
232C2×C3×C4—201no—
233C2×C3×C4C2×D2011yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×Dic3—22no—
237C2×Dic3—101no—
238D12—101no—
239D12—101no—
240C4×D3—201no—
241C4×D3—201no—
242Dic6—41no—
243Dic6—41no—
244C3×C8—41no—
245C3⋊C8—41no—
246C3⋊C8—201no—
247C22×C5#93711yescharacteristic
248C2×D5—121no—
249C2×D5—121no—
250C2×D5—121no—
251C4×C5—21no—
252C4×C5—122no—
253C4×C5#91811yescharacteristic
254C4×C5#91911yescharacteristic
255C4×C5#94211yescharacteristic
256C4×C5#95011yescharacteristic
257Dic5—41no—
258Dic5—41no—
259Dic5—81no—
260Dic5—121no—
261C2×Q8—51no—
262C2×Q8—61no—
263C2×Q8—101no—
264C2×D4—151no—
265C22×C4—301no—
266C2×C8—21no—
267C2×C8—61no—
268C2×C8—301no—
269C4⋊C4—32no—
270C4⋊C4—51no—
271C4⋊C4—61no—
272C4⋊C4—101no—
273C4⋊C4—101no—
274C4⋊C4—101no—
275C4⋊C4—151no—
276C4⋊C4—302no—
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—301no—
280C42—101no—
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—201no—
290C3×C4—201no—
291C3×C4—401no—
292C3×C4#405811yescharacteristic
293C3×C4#406111yescharacteristic
294C3×C4#406211yescharacteristic
295C3×C4#406411yescharacteristic
296Dic3—42no—
297Dic3—201no—
298C2×C5#504711yescharacteristic
299C2×C5#518711yescharacteristic
300C2×C5#520111yescharacteristic
301D5—241no—
302C23—301no—
303Q8—101no—
304Q8—101no—
305Q8—121no—
306Q8—121no—
307Q8—202no—
308D4—301no—
309D4—301no—
310C2×C4—62no—
311C2×C4—101no—
312C2×C4—101no—
313C2×C4—201no—
314C2×C4—301no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4D3×D2011yescharacteristic
318C2×C4#677711yescharacteristic
319C2×C4D5×#6711yescharacteristic
320C8—41no—
321C8—121no—
322C8—601no—
323C2×C3#6504211yescharacteristic
324C2×C3#6507211yescharacteristic
325C2×C3#6509911yescharacteristic
326D3—401no—
327C5#7115711yescharacteristic, complemented, Sylow
328C22—601no—
329C22—601no—
330C22—601no—
331C22#9147411yescharacteristic
332C4—21no—
333C4—122no—
334C4—201no—
335C4—201no—
336C4—401no—
337C4—601no—
338C4#9127911yescharacteristic
339C4#9128011yescharacteristic
340C4#9149211yescharacteristic
341C4#9151511yescharacteristic
342C3#1059922811yescharacteristic, complemented, Sylow
343C2—1201no—
344C2#1174751311yescharacteristic
345C2#1174815111yescharacteristic
346C2#1174825511yescharacteristic
subgroupG/H
centerC22#91474
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
2. C3×#65139C2semidirect
4. #11746924C2semidirect
6. C5×#4486C2semidirect
7. #11745840C2semidirect
29. #65139D3semidirect
61. #4486D5semidirect
283. C3×C5#1638semidirect
327. C5#71157semidirect
342. C3#10599228semidirect

Maximal subgroups

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

subgroupindex
#117524862
C3×#651392
#117469422
#117469242
#117463042
C5×#44862
#117458402
#105992283
#711575