Finite Group Databasebeta

← #14289614

Subgroups — #14289614

Order 1920.

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

normal subgroups only

This group has 436 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#11752715C211yesmaximal, characteristic
2#11750943C211yesmaximal, characteristic, complemented
3#11747096C211yesmaximal, characteristic, complemented
4#11746881C211yesmaximal, characteristic, complemented
5C5×#4481C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic, complemented
8#10599286—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13#91465—21no—
14#91455—22no—
15#91450—21no—
16#91358—21no—
17#91347—21no—
18C2×#6663—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91105—21no—
21#91101—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90987—21no—
25#90965—21no—
26#68203—51nomaximal, Hall
27#66068—31no—
28#65381—31no—
29#65131—31no—
30#65131—31no—
31C5×#333—31no—
32#64703—31no—
33#64703D311yescharacteristic, complemented
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30—21no—
37C2×C5×Dic6D412yes—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1202—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43#6714—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C4⋊Dic15D411yescharacteristic
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C2×C5×C3⋊C8—21no—
50C3×#685—21no—
51C3×C4⋊Dic5D411yescharacteristic
52C2×C3×#168—21no—
53#6667—22no—
54#6665—22no—
55Dic3×Dic5—22no—
56#6663—44no—
57#5563—51no—
58#5008—51no—
59#4842—51no—
60#4699—51no—
61C3×D4⋊C8—51no—
62#4481D511yescharacteristic, complemented
63#4459—51no—
64C5×C4⋊Q8—31no—
65#4093—62no—
66C2×#689—62no—
67#4041—61no—
68#4041—61no—
69#4038—61no—
70#4038—61no—
71C4×D20—31no—
72C4×D20C2×D311yescharacteristic
73#4015—31no—
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3953—61no—
77#3953—61no—
78#3949—61no—
79#3949—61no—
80C4×#168C2×D311yescharacteristic
81#1634—151noSylow
82C22×D15—21no—
83C22×C3×D5—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—41no—
89D60—21no—
90D60—21no—
91C4×D15—41no—
92C4×D15—41no—
93Dic30—42no—
94C2×C5×Dic3—22no—
95C5×Dic6—42no—
96C2×C3×Dic5—21no—
97C3×D20—21no—
98C3×D20—21no—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101#1202—82no—
102C3×C5×C8—41no—
103C3×#168—22no—
104C5×C3⋊C8—41no—
105C3×C4×D4—51no—
106#938—101no—
107#930—101no—
108#926—101no—
109C2×Dic12—102no—
110#892—101no—
111#885—102no—
112C4×D12—51no—
113#869—51no—
114#869C2×D511yescharacteristic
115C3×C4⋊C8C2×D511yescharacteristic
116C3×C4×C8—51no—
117#832—101no—
118#821—101no—
119#817—101no—
120#808—101no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C2×C5×Q8—32no—
123C2×D20—31no—
124C2×D20—62no—
125C2×D20D1211yescharacteristic
126C2×C4×D5—21no—
127C2×C4×D5—61no—
128C2×Dic10—61no—
129C2×C5×C8—21no—
130C2×C5×C8—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4—61no—
133C42×C5C22×D311yescharacteristic
134#689—124no—
135#685—21no—
136#685—62no—
137#685—62no—
138#685—61no—
139C4⋊Dic5—31no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4⋊Dic5D1211yescharacteristic
143C4×Dic5—62no—
144C2×#168—21no—
145#555—151no—
146#494—151no—
147#476—151no—
148#476—151no—
149#333—31no—
150D4⋊C8—51no—
151D4⋊C8—151no—
152C22×C3×C5#12011yescharacteristic
153C2×D15—41no—
154C2×D15—41no—
155C2×D15—41no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C2×C3×D5—41no—
159C3×C4×C5—21no—
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—41no—
165Dic15—81no—
166C3×Dic5—41no—
167C5×Dic3—42no—
168C2×C3×D4—51no—
169C22×C3×C4—101no—
170C2×#67—102no—
171C2×D12—51no—
172C2×C4×D3—101no—
173C2×Dic6—101no—
174C2×Dic6D2012yes—
175C2×C3×C8—21no—
176C2×C3×C8—101no—
177C3×C4⋊C4—51no—
178C3×C22⋊C4—101no—
179C3×C42C22×D511yescharacteristic
180#217—102no—
181(C2×D3)⋊C4—102no—
182(C2×D3)⋊C4—101no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—51no—
186C4⋊Dic3—101no—
187C4⋊Dic3—101no—
188C4×Dic3—102no—
189C2×C3⋊C8—21no—
190Dic12—204no—
191C22×D5—21no—
192C22×D5—61no—
193C5×Q8—122no—
194C2×C4×C5—62no—
195C2×C4×C5C2×D1211yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×Dic5—21no—
199C2×Dic5—61no—
200C2×Dic5—121no—
201D20—21no—
202D20—21no—
203D20—61no—
204D20—61no—
205D20—242no—
206C4×D5—41no—
207C4×D5—41no—
208C4×D5—121no—
209C4×D5—121no—
210Dic10—122no—
211C5×C8—41no—
212C5×C8—121no—
213#168—22no—
214C2×Q16—302no—
215C4⋊Q8—31no—
216C4⋊Q8—151no—
217#124—302no—
218#121—301no—
219#121—301no—
220C4×D4—51no—
221C4×D4—151no—
222#117—301no—
223#117—301no—
224#106—301no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8D3×D511yescharacteristic
228#102—301no—
229#102—301no—
230C4×C8—51no—
231C2×C3×C5#45211yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45311yescharacteristic
234D15—81no—
235C3×D5—81no—
236C23×C3—101no—
237C22×D3—101no—
238C3×D4—101no—
239C3×D4—101no—
240C2×C3×C4—101no—
241C2×C3×C4—201no—
242C2×C3×C4—201no—
243C2×C3×C4C2×D2011yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246#67—402no—
247C2×Dic3—22no—
248C2×Dic3—101no—
249C2×Dic3—201no—
250D12—101no—
251D12—101no—
252C4×D3—201no—
253C4×D3—201no—
254Dic6—42no—
255Dic6—202no—
256C3×C8—41no—
257C3×C8—102no—
258C3⋊C8—41no—
259C22×C5#88211yescharacteristic
260C2×D5—41no—
261C2×D5—41no—
262C2×D5—41no—
263C2×D5—121no—
264C2×D5—121no—
265C2×D5—121no—
266C4×C5—21no—
267C4×C5—122no—
268C4×C5#90411yescharacteristic
269C4×C5#90911yescharacteristic
270C4×C5#91211yescharacteristic
271C4×C5#91511yescharacteristic
272Dic5—41no—
273Dic5—121no—
274Dic5—241no—
275C2×Q8—32no—
276C2×Q8—301no—
277C2×D4—51no—
278C2×D4—151no—
279C2×D4—302no—
280C22×C4—101no—
281C22×C4—301no—
282Q16—604no—
283C2×C8—21no—
284C2×C8—61no—
285C2×C8—101no—
286C4⋊C4—51no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—151no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C22⋊C4—101no—
293C22⋊C4—302no—
294C22⋊C4—302no—
295C22⋊C4—301no—
296C42—302no—
297C42C2×D3×D511yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—201no—
300C22×C3—201no—
301C22×C3—201no—
302C22×C3#402811yescharacteristic
303C2×D3—201no—
304C2×D3—201no—
305C2×D3—201no—
306C3×C4—21no—
307C3×C4—201no—
308C3×C4#406211yescharacteristic
309C3×C4#406211yescharacteristic
310C3×C4#406411yescharacteristic
311C3×C4#406411yescharacteristic
312Dic3—42no—
313Dic3—201no—
314Dic3—401no—
315C2×C5#473311yescharacteristic
316C2×C5#478311yescharacteristic
317C2×C5#482211yescharacteristic
318D5—81no—
319D5—241no—
320C23—101no—
321C23—301no—
322Q8—122no—
323Q8—602no—
324D4—101no—
325D4—101no—
326D4—301no—
327D4—301no—
328D4—1202no—
329C2×C4—62no—
330C2×C4—101no—
331C2×C4—201no—
332C2×C4—201no—
333C2×C4—301no—
334C2×C4—601no—
335C2×C4—601no—
336C2×C4—601no—
337C2×C4D5×D1211yescharacteristic
338C2×C4D3×D2011yescharacteristic
339C2×C4#679011yescharacteristic
340C8—41no—
341C8—102no—
342C8—121no—
343C2×C3—401no—
344C2×C3#6503611yescharacteristic
345C2×C3#6509911yescharacteristic
346C2×C3#6509911yescharacteristic
347D3—401no—
348C5#6820311yescharacteristic, complemented, Sylow
349C22—201no—
350C22—201no—
351C22—201no—
352C22—601no—
353C22—601no—
354C22—601no—
355C22#9147611yescharacteristic
356C4—21no—
357C4—122no—
358C4—201no—
359C4—601no—
360C4—1201no—
361C4#9126111yescharacteristic
362C4#9126911yescharacteristic
363C4#9149711yescharacteristic
364C4#9152211yescharacteristic
365C3#1059928611yescharacteristic, complemented, Sylow
366C2—401no—
367C2—1201no—
368C2#1174751911yescharacteristic
369C2#1174816511yescharacteristic
370C2#1174824911yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752715C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1634
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. #11750943C2semidirect
3. #11747096C2semidirect
4. #11746881C2semidirect
5. C5×#4481C2semidirect
6. C3×#64703C2semidirect
7. #11745839C2semidirect
33. #64703D3semidirect
62. #4481D5semidirect
298. C3×C5#1634semidirect
348. C5#68203semidirect
365. C3#10599286semidirect

Maximal subgroups

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

subgroupindex
#117527152
#117509432
#117470962
#117468812
C5×#44812
C3×#647032
#117458392
#105992863
#682035