Finite Group Databasebeta

← #14289509

Subgroups — #14289509

Order 1920.

428 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 90 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#11756489C211yesmaximal, characteristic
2C3×#65381C211yesmaximal, characteristic, complemented
3#11746942C211yesmaximal, characteristic
4#11746917C211yesmaximal, characteristic, complemented
5C5×#4546C211yesmaximal, characteristic, complemented
6#11745845C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic
8#10599285—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91835—22no—
11#91786—21no—
12#91782—21no—
13C4⋊C4×D15—21no—
14#91779—21no—
15C4×D60C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C2×C3×#689—22no—
18C3×#4015C2211yescharacteristic
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×#168C2211yescharacteristic
22#90990—21no—
23#90987—21no—
24#90974—21no—
25#90968—21no—
26#71303—51nomaximal, Hall
27#66064—31no—
28#65381D311yescharacteristic, complemented
29#65139—31no—
30#65131—31no—
31C5×#333—31no—
32#64704—31no—
33#64703—31no—
34C2×C3×C5×Q8D412yes—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C4×D15—22no—
38C2×Dic30D411yescharacteristic
39C2×C3×Dic10—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43#6714—22no—
44#6714—21no—
45C4⋊Dic15—22no—
46C4⋊Dic15D411yescharacteristic
47C4⋊Dic15D411yescharacteristic
48#6712—22no—
49#6712—21no—
50C4×Dic15—21no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×#689—44no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C2×C3×#168—21no—
57#5730—51no—
58C3×#494—51no—
59#5091—51no—
60#5084—51no—
61#4546D511yescharacteristic, complemented
62#4459—51no—
63#4456—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65#4092—62no—
66C2×#689—22no—
67#4043—61no—
68#4039—61no—
69D5×C4⋊C4—61no—
70#4036—61no—
71C4×D20—31no—
72#4015C2×D311yescharacteristic
73C4×Dic10—31no—
74C5×C4⋊C8—31no—
75C5×C4⋊C8—31no—
76#3953—61no—
77#3950—61no—
78#3949—61no—
79#3948—61no—
80C4×#168C2×D311yescharacteristic
81#1632—151noSylow
82C22×D15—21no—
83C3×C5×Q8—42no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—21no—
89C2×Dic15—21no—
90C2×Dic15—21no—
91D60—21no—
92D60Q1612yescomplemented
93C4×D15—41no—
94C4×D15—41no—
95C4×D15—82no—
96Dic30—21no—
97Dic30—21no—
98C2×C3×Dic5—41no—
99C3×Dic10—42no—
100C3×#168—22no—
101C5×C3⋊C8—41no—
102C5×C3⋊C8—41no—
103C2×C3×Q16—102no—
104C3×C4⋊Q8—51no—
105C3×C4⋊Q8C2×D511yescharacteristic
106#946—102no—
107#897—101no—
108#893—101no—
109D3×C4⋊C4—101no—
110#890—101no—
111C4×D12—51no—
112C4×Dic6—51no—
113C3×C4×C8—51no—
114#810—101no—
115#809—101no—
116#808—101no—
117#807—101no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8#6712yes—
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×C4×D5—62no—
124C2×Dic10—21no—
125C2×Dic10—31no—
126C2×C5×C8—61no—
127C2×C5×C8—61no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C42×C5C22×D311yescharacteristic
131#689—44no—
132#685—62no—
133#685—61no—
134C4⋊Dic5—21no—
135C4⋊Dic5—21no—
136C4⋊Dic5—31no—
137C4⋊Dic5—31no—
138C4⋊Dic5—62no—
139#683—62no—
140#683—61no—
141C4×Dic5—61no—
142C2×#168—21no—
143#554—151no—
144#494—51no—
145#477—151no—
146#476—151no—
147#333—31no—
148Q8⋊C8—151no—
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×D15—22no—
152C2×D15—41no—
153C2×D15—41no—
154C3×C4×C5—21no—
155C3×C4×C5—42no—
156C3×C4×C5C2×Q1611yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—41no—
161Dic15—41no—
162Dic15—41no—
163C3×Dic5—81no—
164C2×C3×Q8—101no—
165C2×C3×Q8D2012yes—
166C2×D12—51no—
167C2×C4×D3—101no—
168C2×C4×D3—102no—
169C2×Dic6—51no—
170C3×Q16—204no—
171C2×C3×C8—101no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C42C22×D511yescharacteristic
177(C2×D3)⋊C4—102no—
178(C2×D3)⋊C4—101no—
179C4⋊Dic3—51no—
180C4⋊Dic3—51no—
181C4⋊Dic3—102no—
182Dic3⋊C4—102no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C22×D5—61no—
188C5×Q8—42no—
189C2×C4×C5—22no—
190C2×C4×C5D3×D411yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5C2×#6711yescharacteristic
193C2×Dic5—41no—
194C2×Dic5—61no—
195C2×Dic5—61no—
196C2×Dic5—61no—
197D20—32no—
198D20—61no—
199C4×D5—121no—
200C4×D5—121no—
201C4×D5—242no—
202Dic10—42no—
203Dic10—61no—
204Dic10—61no—
205C5×C8—121no—
206C5×C8—121no—
207#168—22no—
208C2×Q16—102no—
209C4⋊Q8—51no—
210C4⋊Q8D3×D511yescharacteristic
211#125—301no—
212C22⋊Q8—301no—
213C22⋊Q8—302no—
214C4×Q8—151no—
215C4×D4—151no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—301no—
219#106—301no—
220C4⋊C8—31no—
221C4⋊C8—31no—
222#103—301no—
223#102—301no—
224C4×C8—51no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228D15—42no—
229C22×D3—101no—
230C3×Q8—42no—
231C3×Q8—202no—
232C2×C3×C4—22no—
233C2×C3×C4—201no—
234C2×C3×C4C2×D2011yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×Dic3—101no—
238C2×Dic3—101no—
239C2×Dic3—101no—
240D12—52no—
241D12—101no—
242C4×D3—201no—
243C4×D3—201no—
244C4×D3—402no—
245Dic6—101no—
246Dic6—101no—
247C3×C8—102no—
248C3⋊C8—41no—
249C3⋊C8—41no—
250C22×C5#93711yescharacteristic
251C2×D5—62no—
252C2×D5—121no—
253C2×D5—121no—
254C4×C5—21no—
255C4×C5—42no—
256C4×C5D3×Q1611yescharacteristic
257C4×C5#91811yescharacteristic
258C4×C5#91811yescharacteristic
259C4×C5#91911yescharacteristic
260Dic5—81no—
261Dic5—121no—
262Dic5—121no—
263Dic5—121no—
264C2×Q8—101no—
265C2×Q8—151no—
266C2×Q8#120212yes—
267C2×D4—151no—
268C22×C4—302no—
269C22×C4—301no—
270Q16—204no—
271C2×C8—61no—
272C2×C8—61no—
273C2×C8—101no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—101no—
277C4⋊C4—101no—
278C4⋊C4—151no—
279C4⋊C4—151no—
280C4⋊C4—302no—
281C4⋊C4—302no—
282C4⋊C4—301no—
283C22⋊C4—302no—
284C22⋊C4—301no—
285C42—301no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#402811yescharacteristic
289C2×D3—102no—
290C2×D3—201no—
291C2×D3—201no—
292C3×C4—21no—
293C3×C4—42no—
294C3×C4—401no—
295C3×C4#406111yescharacteristic
296C3×C4#406211yescharacteristic
297C3×C4D5×Q1611yescharacteristic
298C3×C4#406411yescharacteristic
299Dic3—201no—
300Dic3—201no—
301Dic3—201no—
302C2×C5#507711yescharacteristic
303C2×C5#518611yescharacteristic
304C2×C5#518711yescharacteristic
305D5—122no—
306C23—301no—
307Q8—42no—
308Q8—202no—
309Q8—301no—
310Q8—301no—
311D4—152no—
312D4—301no—
313C2×C4—22no—
314C2×C4—201no—
315C2×C4—301no—
316C2×C4—301no—
317C2×C4—301no—
318C2×C4—601no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4C2×#120211yescharacteristic
322C2×C4#679011yescharacteristic
323C2×C4#679011yescharacteristic
324C8—102no—
325C8—121no—
326C8—121no—
327C2×C3#6503611yescharacteristic
328C2×C3#6509711yescharacteristic
329C2×C3#6509911yescharacteristic
330D3—202no—
331C5#7130311yescharacteristic, complemented, Sylow
332C22—302no—
333C22—601no—
334C22—601no—
335C22#9157211yescharacteristic
336C4—21no—
337C4—42no—
338C4—401no—
339C4—601no—
340C4—601no—
341C4—601no—
342C4#9151111yescharacteristic
343C4#9151211yescharacteristic
344C4#9152311yescharacteristic
345C4#9152411yescharacteristic
346C3#1059928511yescharacteristic, complemented, Sylow
347C2—602no—
348C2#1174914211yescharacteristic
349C2#1174930911yescharacteristic
350C2#1174931011yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1632
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×#65381C2semidirect
4. #11746917C2semidirect
5. C5×#4546C2semidirect
6. #11745845C2semidirect
28. #65381D3semidirect
61. #4546D5semidirect
92. D60Q16semidirect
287. C3×C5#1632semidirect
331. C5#71303semidirect
346. C3#10599285semidirect

Maximal subgroups

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

subgroupindex
#117564892
C3×#653812
#117469422
#117469172
C5×#45462
#117458452
#117458392
#105992853
#713035