Finite Group Databasebeta

← #14289252

Subgroups — #14289252

Order 1920.

500 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 92 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#11752551C211yesmaximal, characteristic, complemented
2C3×#64983C211yesmaximal, characteristic, complemented
3#11747068C211yesmaximal, characteristic, complemented
4#11747043C211yesmaximal, characteristic
5#11746280C211yesmaximal, characteristic, complemented
6C5×#4456C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599059—31nomaximal, Hall
9C2×D15⋊Q8—21no—
10C4×D60C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×#4020C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91469—21no—
15#91429—22no—
16#91428—21no—
17#91390—21no—
18C2×#6655—21no—
19C2×#6653—21no—
20C3×C4×C5×C8C2211yescharacteristic
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3953—22no—
24#90965—21no—
25#90964—21no—
26#71205—51nomaximal, Hall
27Q8×D20—31no—
28#65316—31no—
29#65132—31no—
30#64983D311yescharacteristic, complemented
31C5×Q8⋊C8—31no—
32#64706—31no—
33#64679—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×Dic10—21no—
41C2×#1204—22no—
42C2×#1200—22no—
43D15⋊Q8—42no—
44D15⋊Q8—42no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47#6714—21no—
48C4⋊Dic15D411yescharacteristic
49C2×C3⋊#168—21no—
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5D412yes—
56Dic3⋊Dic5—22no—
57#6667—22no—
58#6655—42no—
59#6653—42no—
60#5727—51no—
61C3×#486—51no—
62#5075—51no—
63#5072—51no—
64#4547—51no—
65#4459—51no—
66#4456D511yescharacteristic, complemented
67C2×Q8×D5—61no—
68C4×C5×Q8—31no—
69C2×#688—61no—
70C2×D40—61no—
71#4043—61no—
72#4043—62no—
73#4020C2×D311yescharacteristic
74C4×D20—31no—
75C4×D20—61no—
76#4015—61no—
77#4015C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C4×C5×C8C2×D311yescharacteristic
80#3953—22no—
81#3953—61no—
82#3941—61no—
83C4⋊#168—31no—
84#1627—151noSylow
85C22×D15—21no—
86C22×C3×D5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91D60—21no—
92D60SD1612yescomplemented
93C4×D15—41no—
94C4×D15—41no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—21no—
97C5×Dic6—21no—
98C5×Dic6D812yescomplemented
99C2×C3×Dic5—22no—
100C3×D20—42no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×Dic10—41no—
106C3×Dic10—41no—
107#1204—44no—
108#1200—44no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C5×C3⋊C8—41no—
112C2×D3×Q8—101no—
113C3×C4⋊Q8—51no—
114C3×#127—51no—
115#946—101no—
116C2×#214—101no—
117C2×#213—101no—
118#896—102no—
119#893—101no—
120#888—101no—
121C4×D12—51no—
122C4×Dic6C2×D511yescharacteristic
123C3×#102—102no—
124C3×C4×C8C2×D511yescharacteristic
125#832—101no—
126#832—101no—
127C4⋊(C3⋊C8)—51no—
128C4⋊(C3⋊C8)C2×D511yescharacteristic
129C2×C5×Q8—31no—
130Q8×D5—122no—
131Q8×D5—122no—
132C2×D20—21no—
133C2×D20—21no—
134C2×D20—21no—
135C2×D20—31no—
136C2×C4×D5—62no—
137C2×C4×D5—61no—
138C2×Dic10—21no—
139C2×Dic10—62no—
140C2×C5×C8—21no—
141C2×C5×C8—61no—
142C5×C4⋊C4—31no—
143C5×C4⋊C4—61no—
144C42×C5—61no—
145C42×C5C22×D311yescharacteristic
146#688—122no—
147#685—62no—
148#685—61no—
149C4⋊Dic5—21no—
150C4⋊Dic5—31no—
151C4⋊Dic5—62no—
152C4⋊Dic5#6712yes—
153C2×#168—61no—
154D40—122no—
155D4×Q8—151no—
156#486—51no—
157#460—151no—
158#459—151no—
159#332—151no—
160Q8⋊C8—31no—
161D4⋊C8—151no—
162C22×C3×C5#12011yescharacteristic
163C2×D15—22no—
164C2×D15—41no—
165C2×D15—41no—
166C2×C3×D5—81no—
167C2×C3×D5—81no—
168C2×C3×D5—81no—
169C3×C4×C5—21no—
170C3×C4×C5C2×D811yescharacteristic
171C3×C4×C5C2×SD1611yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174Dic15—41no—
175C3×Dic5—42no—
176C5×Dic3—22no—
177C5×Dic3—41no—
178C2×C3×Q8—101no—
179C2×C3×D4—101no—
180C2×C3×D4—101no—
181C2×C3×D4—101no—
182D3×Q8—202no—
183D3×Q8—202no—
184C2×D12—51no—
185C2×C4×D3—102no—
186C2×C4×D3—101no—
187C2×Dic6—102no—
188C2×Dic6D2011yescharacteristic
189C2×C3×C8—21no—
190C3×C4⋊C4—52no—
191C3×C4⋊C4—101no—
192C3×C42C22×D511yescharacteristic
193#214—202no—
194#213—202no—
195(C2×D3)⋊C4—102no—
196(C2×D3)⋊C4—101no—
197C4⋊Dic3—51no—
198C4⋊Dic3D2011yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—102no—
201C4×Dic3—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—101no—
204C22×D5—41no—
205C22×D5—61no—
206C5×Q8—32no—
207C5×Q8—61no—
208C2×C4×C5—61no—
209C2×C4×C5—61no—
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C2×Dic5—22no—
214C2×Dic5—61no—
215D20—32no—
216D20—42no—
217D20—41no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—61no—
222C4×D5—124no—
223C4×D5—121no—
224C4×D5—121no—
225Dic10—41no—
226Dic10—41no—
227Dic10—124no—
228C5×C8—41no—
229C5×C8—121no—
230#168—121no—
231C22×Q8—301no—
232C2×SD16—301no—
233C2×D8—301no—
234C4⋊Q8—51no—
235C4⋊Q8—301no—
236#127—51no—
237C22⋊Q8—301no—
238C22⋊Q8—302no—
239C4×Q8—31no—
240C4×D4—151no—
241C4×D4—301no—
242C4⋊C8—31no—
243C4⋊C8—151no—
244#102—102no—
245#102—301no—
246#102—301no—
247C4×C8D3×D511yescharacteristic
248C2×C3×C5#44711yescharacteristic
249C2×C3×C5#44811yescharacteristic
250C2×C3×C5#45411yescharacteristic
251D15—42no—
252C3×D5—161no—
253C23×C3—201no—
254C22×D3—101no—
255C3×Q8—201no—
256C3×Q8—201no—
257C3×D4—202no—
258C3×D4—201no—
259C3×D4—201no—
260C3×D4—201no—
261C3×D4—201no—
262C2×C3×C4—102no—
263C2×C3×C4C2×D2011yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265C2×C3×C4D4×D511yescharacteristic
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—101no—
269D12—52no—
270D12—101no—
271C4×D3—204no—
272C4×D3—201no—
273C4×D3—201no—
274Dic6—21no—
275Dic6—204no—
276Dic6D4012yescomplemented
277C3×C8—41no—
278C3⋊C8—41no—
279C3⋊C8—201no—
280C22×C5#93711yescharacteristic
281C2×D5—62no—
282C2×D5—81no—
283C2×D5—81no—
284C2×D5—81no—
285C2×D5—121no—
286C2×D5—121no—
287C4×C5—21no—
288C4×C5—62no—
289C4×C5—121no—
290C4×C5D3×D811yescharacteristic
291C4×C5#91111yescharacteristic
292C4×C5D3×SD1611yescharacteristic
293C4×C5#91511yescharacteristic
294Dic5—42no—
295Dic5—121no—
296C2×Q8—31no—
297C2×Q8—101no—
298C2×Q8—302no—
299C2×Q8—602no—
300C2×Q8—602no—
301C2×D4—101no—
302C2×D4—101no—
303C2×D4—101no—
304C2×D4—151no—
305C22×C4—302no—
306C22×C4—301no—
307SD16—602no—
308D8—602no—
309C2×C8—21no—
310C2×C8—61no—
311C2×C8—301no—
312C4⋊C4—31no—
313C4⋊C4—52no—
314C4⋊C4—61no—
315C4⋊C4—101no—
316C4⋊C4—151no—
317C4⋊C4—302no—
318C22⋊C4—302no—
319C22⋊C4—301no—
320C42—61no—
321C42C2×D3×D511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3—401no—
324C22×C3—401no—
325C22×C3—401no—
326C22×C3#402811yescharacteristic
327C2×D3—102no—
328C2×D3—201no—
329C2×D3—201no—
330C3×C4—21no—
331C3×C4—202no—
332C3×C4C2×D4011yescharacteristic
333C3×C4#405411yescharacteristic
334C3×C4D5×SD1611yescharacteristic
335C3×C4#406411yescharacteristic
336Dic3—22no—
337Dic3—41no—
338Dic3—201no—
339C2×C5#506211yescharacteristic
340C2×C5#515611yescharacteristic
341C2×C5#517011yescharacteristic
342D5—122no—
343D5—161no—
344C23—201no—
345C23—301no—
346Q8—32no—
347Q8—61no—
348Q8—201no—
349Q8—201no—
350Q8—604no—
351D4—152no—
352D4—202no—
353D4—201no—
354D4—201no—
355D4—201no—
356D4—201no—
357D4—301no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—102no—
361C2×C4—301no—
362C2×C4—604no—
363C2×C4—601no—
364C2×C4—601no—
365C2×C4D3×D2011yescharacteristic
366C2×C4#677711yescharacteristic
367C2×C4D5×#6711yescharacteristic
368C8—41no—
369C8—121no—
370C8—601no—
371C2×C3—801no—
372C2×C3#6502111yescharacteristic
373C2×C3#6509511yescharacteristic
374C2×C3#6511611yescharacteristic
375D3—202no—
376C5#7120511yescharacteristic, complemented, Sylow
377C22—302no—
378C22—401no—
379C22—401no—
380C22—401no—
381C22—601no—
382C22—601no—
383C22#9147411yescharacteristic
384C4—21no—
385C4—62no—
386C4—121no—
387C4—202no—
388C4—601no—
389C4D3×D4011yescharacteristic
390C4#9125411yescharacteristic
391C4#9125511yescharacteristic
392C4#9127811yescharacteristic
393C3#1059905911yescharacteristic, complemented, Sylow
394C2—602no—
395C2—801no—
396C2#1174712111yescharacteristic
397C2#1174789111yescharacteristic
398C2#1174811211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11747043C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1627
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
1. #11752551C2semidirect
2. C3×#64983C2semidirect
3. #11747068C2semidirect
5. #11746280C2semidirect
6. C5×#4456C2semidirect
7. #11745855C2semidirect
30. #64983D3semidirect
66. #4456D5semidirect
92. D60SD16semidirect
98. C5×Dic6D8semidirect
276. Dic6D40semidirect
322. C3×C5#1627semidirect
376. C5#71205semidirect
393. C3#10599059semidirect

Maximal subgroups

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

subgroupindex
#117525512
C3×#649832
#117470682
#117470432
#117462802
C5×#44562
#117458552
#105990593
#712055