Finite Group Databasebeta

← #14289851

Subgroups — #14289851

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
2C3×#64970C211yesmaximal, characteristic, complemented
3#11746959C211yesmaximal, characteristic, complemented
4#11746942C211yesmaximal, characteristic
5#11746280C211yesmaximal, characteristic
6C5×#4456C211yesmaximal, characteristic, complemented
7#11745856C211yesmaximal, characteristic, complemented
8#10599040—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91383—21no—
14#91374—21no—
15#91347—21no—
16#91345—22no—
17Dic3×Dic10—21no—
18C3×C4×C5×C8C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#3948—22no—
22#90989—21no—
23#90987—21no—
24#90972—21no—
25#90968—21no—
26#71229—51nomaximal, Hall
27#65918—31no—
28#65310—31no—
29#65131—31no—
30#64970D311yescharacteristic, complemented
31C5×Q8⋊C8—31no—
32#64702—31no—
33#64679—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×Dic10—21no—
38C2×C3×Dic10—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41#6714—21no—
42C4⋊Dic15D411yescharacteristic
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3D411yescharacteristic
45C5×Dic3⋊C4—21no—
46C4×C5×Dic3—21no—
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D412yes—
52#6668—22no—
53#6667—22no—
54#6667—22no—
55Dic3×Dic5—22no—
56#5732—51no—
57C3×#487—51no—
58#5091—51no—
59#5084—51no—
60#4547—51no—
61#4459—51no—
62#4456D511yescharacteristic, complemented
63C4×C5×Q8—31no—
64#4092—61no—
65#4044—62no—
66#4038—61no—
67#4021—61no—
68C4×D20—31no—
69#4015C2×D311yescharacteristic
70#4015C2×D311yescharacteristic
71C4×Dic10—61no—
72C5×C4⋊C8—31no—
73C4×C5×C8C2×D311yescharacteristic
74#3967—61no—
75#3953—61no—
76#3949—61no—
77#3948—22no—
78#3939—61no—
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—21no—
91C2×C5×Dic3—21no—
92C5×Dic6—21no—
93C5×Dic6—21no—
94C2×C3×Dic5—22no—
95C2×C3×Dic5—41no—
96C3×Dic10—41no—
97C3×Dic10—41no—
98C3×Dic10—42no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8—51no—
103C3×C4⋊Q8—51no—
104#947—101no—
105Q8×Dic3—101no—
106#898—102no—
107#897—101no—
108#892—101no—
109C4×D12—51no—
110C4×Dic6C2×D511yescharacteristic
111C3×#103—102no—
112C3×C4×C8C2×D511yescharacteristic
113#810—101no—
114#809—101no—
115#808—101no—
116#807—101no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C2×C5×Q8—31no—
120C2×D20—31no—
121C2×C4×D5—61no—
122C2×Dic10—21no—
123C2×Dic10—21no—
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—21no—
135C4⋊Dic5—21no—
136C4⋊Dic5—31no—
137C4⋊Dic5#6712yes—
138#683—62no—
139C4×Dic5—62no—
140C2×#168—61no—
141#556—151no—
142#487—51no—
143#477—151no—
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#13511yescharacteristic
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×C4×C5#13711yescharacteristic
157Dic15—41no—
158C3×Dic5—42no—
159C3×Dic5—81no—
160C5×Dic3—41no—
161C5×Dic3—41no—
162C2×C3×Q8—101no—
163C2×C3×Q8—101no—
164C2×D12—51no—
165C2×C4×D3—101no—
166C2×Dic6D2011yescharacteristic
167C2×C3×C8—21no—
168C3×C4⋊C4—52no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C4⋊C4—101no—
172C3×C42C22×D511yescharacteristic
173(C2×D3)⋊C4—102no—
174(C2×D3)⋊C4—102no—
175(C2×D3)⋊C4—101no—
176C4⋊Dic3—51no—
177C4⋊Dic3—102no—
178C4⋊Dic3D2011yescharacteristic
179Dic3⋊C4—21no—
180C4×Dic3—21no—
181C4×Dic3—102no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—101no—
184C22×D5—61no—
185C5×Q8—61no—
186C5×Q8—61no—
187C2×C4×C5—61no—
188C2×C4×C5—61no—
189C2×C4×C5D3×D411yescharacteristic
190C2×C4×C5D3×D411yescharacteristic
191C2×C4×C5C2×#6711yescharacteristic
192C2×Dic5—22no—
193C2×Dic5—41no—
194C2×Dic5—61no—
195D20—61no—
196D20—61no—
197C4×D5—121no—
198C4×D5—121no—
199Dic10—41no—
200Dic10—41no—
201Dic10—42no—
202C5×C8—41no—
203C5×C8—121no—
204#168—121no—
205C4⋊Q8—51no—
206C4⋊Q8—51no—
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—31no—
217C4⋊C8—151no—
218#103—102no—
219#103—301no—
220#102—301no—
221C4×C8D3×D511yescharacteristic
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225D15—81no—
226C22×D3—101no—
227C3×Q8—202no—
228C3×Q8—201no—
229C3×Q8—201no—
230C2×C3×C4—102no—
231C2×C3×C4—201no—
232C2×C3×C4C2×D2011yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—101no—
238D12—101no—
239D12—101no—
240C4×D3—201no—
241C4×D3—201no—
242Dic6—21no—
243Dic6—21no—
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—121no—
253C4×C5—121no—
254C4×C5#91511yescharacteristic
255C4×C5#91611yescharacteristic
256C4×C5#91811yescharacteristic
257C4×C5#91911yescharacteristic
258Dic5—42no—
259Dic5—81no—
260Dic5—121no—
261C2×Q8—31no—
262C2×Q8—101no—
263C2×Q8—101no—
264C2×D4—151no—
265C22×C4—301no—
266C2×C8—21no—
267C2×C8—61no—
268C2×C8—301no—
269C4⋊C4—31no—
270C4⋊C4—52no—
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—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—401no—
291C3×C4#405011yescharacteristic
292C3×C4#405511yescharacteristic
293C3×C4#406211yescharacteristic
294C3×C4#406411yescharacteristic
295Dic3—41no—
296Dic3—41no—
297Dic3—201no—
298C2×C5#506211yescharacteristic
299C2×C5#517311yescharacteristic
300C2×C5#518711yescharacteristic
301D5—241no—
302C23—301no—
303Q8—61no—
304Q8—61no—
305Q8—202no—
306Q8—201no—
307Q8—201no—
308D4—301no—
309D4—301no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—102no—
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#6502211yescharacteristic
324C2×C3#6509911yescharacteristic
325C2×C3#6511611yescharacteristic
326D3—401no—
327C5#7122911yescharacteristic, complemented, Sylow
328C22—601no—
329C22—601no—
330C22—601no—
331C22#9147411yescharacteristic
332C4—21no—
333C4—121no—
334C4—121no—
335C4—202no—
336C4—401no—
337C4—601no—
338C4#9126311yescharacteristic
339C4#9127511yescharacteristic
340C4#9127611yescharacteristic
341C4#9127811yescharacteristic
342C3#1059904011yescharacteristic, complemented, Sylow
343C2—1201no—
344C2#1174712111yescharacteristic
345C2#1174814811yescharacteristic
346C2#1174815211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×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×#64970C2semidirect
3. #11746959C2semidirect
6. C5×#4456C2semidirect
7. #11745856C2semidirect
30. #64970D3semidirect
62. #4456D5semidirect
283. C3×C5#1638semidirect
327. C5#71229semidirect
342. C3#10599040semidirect

Maximal subgroups

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

subgroupindex
#117524832
C3×#649702
#117469592
#117469422
#117462802
C5×#44562
#117458562
#105990403
#712295