Finite Group Databasebeta

← #14290370

Subgroups — #14290370

Order 1920.

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

normal subgroups only

This group has 424 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
2C3×#65135C211yesmaximal, characteristic, complemented
3#11747085C211yesmaximal, characteristic, complemented
4#11746923C211yesmaximal, characteristic, complemented
5#11746304C211yesmaximal, characteristic, complemented
6C5×#4481C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10599288—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×C4×D20C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91465—21no—
14#91455—22no—
15#91450—21no—
16#91358—21no—
17#91347—21no—
18C2×#6658—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3953—21no—
23C3×#3950—21no—
24#90972—22no—
25#90971—21no—
26#71109—51nomaximal, Hall
27#66068—31no—
28#65370—31no—
29#65135D311yescharacteristic, complemented
30#65130—31no—
31C5×#333—31no—
32#64703—31no—
33#64703—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6D412yes—
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×Dic10—21no—
40C2×#1202—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43#6714—21no—
44C4⋊Dic15D411yescharacteristic
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C3×#685—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5D411yescharacteristic
53#6667—22no—
54#6665—22no—
55Dic3×Dic5—22no—
56#6658—42no—
57#5563—51no—
58C3×#474—51no—
59#5093—51no—
60#5083—51no—
61D4⋊(C3⋊C8)—51no—
62#4483—51no—
63#4481D511yescharacteristic, complemented
64C5×C4⋊Q8—31no—
65#4093—62no—
66C2×#677—61no—
67#4041—61no—
68#4041—61no—
69#4038—61no—
70#4038—61no—
71C4×D20—31no—
72C4×D20C2×D311yescharacteristic
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3967—62no—
77#3953—21no—
78#3950—21no—
79#3948—61no—
80C4×#168—31no—
81#1646—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—
88D60—21no—
89D60—21no—
90C4×D15—41no—
91C4×D15—41no—
92C2×C5×Dic3—22no—
93C5×Dic6—42no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—41no—
96C3×D20—21no—
97C3×D20—21no—
98C3×C4×D5—41no—
99C3×C4×D5—41no—
100C3×Dic10—41no—
101C3×Dic10—41no—
102#1202—82no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8—51no—
107C3×C4×D4—51no—
108C2×#215—101no—
109#938—101no—
110#930—101no—
111#926—101no—
112#892—101no—
113#885—102no—
114C4×D12—51no—
115#869C2×D511yescharacteristic
116C3×#107—101no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×#102—101no—
119#835—101no—
120#810—102no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8—51no—
123C2×C5×Q8—32no—
124C2×D20—31no—
125C2×D20—62no—
126C2×D20#6711yescharacteristic
127C2×C4×D5—21no—
128C2×C4×D5—61no—
129C2×Dic10—21no—
130C2×C5×C8—21no—
131C2×C5×C8—61no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C42×C5C22×D311yescharacteristic
135#685—21no—
136#685—62no—
137#685—62no—
138#685—61no—
139C4⋊Dic5—21no—
140C4⋊Dic5—21no—
141C4⋊Dic5—31no—
142C4⋊Dic5#6711yescharacteristic
143C4×Dic5—62no—
144C2×#168—61no—
145#677—122no—
146#555—151no—
147#487—151no—
148#474—51no—
149#461—151no—
150#333—31no—
151D4⋊C8—151no—
152D4⋊C8—151no—
153C22×C3×C5#12011yescharacteristic
154C2×D15—41no—
155C2×D15—41no—
156C2×D15—41no—
157C2×C3×D5—41no—
158C2×C3×D5—41no—
159C2×C3×D5—41no—
160C3×C4×C5—21no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—41no—
166C3×Dic5—41no—
167C3×Dic5—81no—
168C5×Dic3—42no—
169C2×C3×Q8—101no—
170C2×C3×D4—51no—
171C22×C3×C4—101no—
172C2×#67—102no—
173C2×D12—51no—
174C2×C4×D3—101no—
175C2×Dic6D2012yes—
176C2×C3×C8—21no—
177C3×C4⋊C4—51no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C22⋊C4—101no—
181C3×C42C22×D511yescharacteristic
182#217—102no—
183#215—202no—
184(C2×D3)⋊C4—102no—
185(C2×D3)⋊C4—101no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—51no—
189C4×Dic3—102no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C22×D5—21no—
193C22×D5—61no—
194C5×Q8—122no—
195C2×C4×C5—62no—
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—41no—
201C2×Dic5—61no—
202D20—21no—
203D20—21no—
204D20—61no—
205D20—61no—
206D20—242no—
207C4×D5—41no—
208C4×D5—41no—
209C4×D5—121no—
210C4×D5—121no—
211Dic10—41no—
212Dic10—41no—
213C5×C8—41no—
214C5×C8—121no—
215#168—121no—
216C2×SD16—301no—
217C4⋊Q8—31no—
218C4⋊Q8—51no—
219#124—302no—
220#121—301no—
221#121—301no—
222C4×D4—51no—
223C4×D4—151no—
224#117—301no—
225#117—301no—
226#107—101no—
227C4⋊C8—31no—
228C4⋊C8D3×D511yescharacteristic
229#103—302no—
230#103—301no—
231#102—101no—
232C4×C8—151no—
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45211yescharacteristic
235C2×C3×C5#45511yescharacteristic
236D15—81no—
237C3×D5—81no—
238C23×C3—101no—
239C22×D3—101no—
240C3×Q8—201no—
241C3×Q8—201no—
242C3×D4—101no—
243C3×D4—101no—
244C2×C3×C4—101no—
245C2×C3×C4—201no—
246C2×C3×C4—201no—
247C2×C3×C4—201no—
248C2×C3×C4C2×D2011yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251#67—402no—
252C2×Dic3—22no—
253C2×Dic3—101no—
254D12—101no—
255D12—101no—
256C4×D3—201no—
257C4×D3—201no—
258Dic6—42no—
259C3×C8—41no—
260C3⋊C8—41no—
261C3⋊C8—201no—
262C22×C5#93711yescharacteristic
263C2×D5—41no—
264C2×D5—41no—
265C2×D5—41no—
266C2×D5—121no—
267C2×D5—121no—
268C2×D5—121no—
269C4×C5—21no—
270C4×C5—122no—
271C4×C5#91111yescharacteristic
272C4×C5#91211yescharacteristic
273C4×C5#94211yescharacteristic
274C4×C5#95011yescharacteristic
275Dic5—41no—
276Dic5—81no—
277Dic5—121no—
278C2×Q8—32no—
279C2×Q8—101no—
280C2×D4—51no—
281C2×D4—151no—
282C2×D4—302no—
283C22×C4—101no—
284C22×C4—301no—
285SD16—602no—
286C2×C8—21no—
287C2×C8—61no—
288C2×C8—301no—
289C4⋊C4—51no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—101no—
293C4⋊C4—101no—
294C4⋊C4—151no—
295C22⋊C4—101no—
296C22⋊C4—302no—
297C22⋊C4—302no—
298C22⋊C4—301no—
299C42—302no—
300C42C2×D3×D511yescharacteristic
301C3×C5#164611yescharacteristic, complemented, Hall
302C22×C3—201no—
303C22×C3—201no—
304C22×C3—201no—
305C22×C3#402811yescharacteristic
306C2×D3—201no—
307C2×D3—201no—
308C2×D3—201no—
309C3×C4—21no—
310C3×C4—201no—
311C3×C4—401no—
312C3×C4#406011yescharacteristic
313C3×C4#406211yescharacteristic
314C3×C4#406411yescharacteristic
315C3×C4#406511yescharacteristic
316Dic3—42no—
317Dic3—201no—
318C2×C5#504711yescharacteristic
319C2×C5#515811yescharacteristic
320C2×C5#520211yescharacteristic
321D5—81no—
322D5—241no—
323C23—101no—
324C23—301no—
325Q8—122no—
326Q8—201no—
327Q8—201no—
328D4—101no—
329D4—101no—
330D4—301no—
331D4—301no—
332D4—1202no—
333C2×C4—62no—
334C2×C4—101no—
335C2×C4—201no—
336C2×C4—201no—
337C2×C4—201no—
338C2×C4—301no—
339C2×C4—601no—
340C2×C4—601no—
341C2×C4D3×D2011yescharacteristic
342C2×C4#677711yescharacteristic
343C2×C4D5×#6711yescharacteristic
344C8—41no—
345C8—121no—
346C8—601no—
347C2×C3—401no—
348C2×C3#6503511yescharacteristic
349C2×C3#6509911yescharacteristic
350C2×C3#6510011yescharacteristic
351D3—401no—
352C5#7110911yescharacteristic, complemented, Sylow
353C22—201no—
354C22—201no—
355C22—201no—
356C22—601no—
357C22—601no—
358C22—601no—
359C22#9147411yescharacteristic
360C4—21no—
361C4—122no—
362C4—201no—
363C4—401no—
364C4—601no—
365C4#9125811yescharacteristic
366C4#9127711yescharacteristic
367C4#9149211yescharacteristic
368C4#9151511yescharacteristic
369C3#1059928811yescharacteristic, complemented, Sylow
370C2—401no—
371C2—1201no—
372C2#1174751311yescharacteristic
373C2#1174815011yescharacteristic
374C2#1174824111yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752715C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1646
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×#65135C2semidirect
3. #11747085C2semidirect
4. #11746923C2semidirect
5. #11746304C2semidirect
6. C5×#4481C2semidirect
7. #11745834C2semidirect
29. #65135D3semidirect
63. #4481D5semidirect
301. C3×C5#1646semidirect
352. C5#71109semidirect
369. C3#10599288semidirect

Maximal subgroups

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

subgroupindex
#117527152
C3×#651352
#117470852
#117469232
#117463042
C5×#44812
#117458342
#105992883
#711095