Finite Group Databasebeta

← #14289248

Subgroups — #14289248

Order 1920.

500 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 98 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
1Q8×D60C211yesmaximal, characteristic, complemented
2C3×#65316C211yesmaximal, characteristic, complemented
3#11747043C211yesmaximal, characteristic
4#11746890C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10599059—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C4×C5×Q8C2211yescharacteristic
11#91786—21no—
12#91786—22no—
13C4×D60—21no—
14C4×D60C2211yescharacteristic
15#91758—21no—
16#91758C2211yescharacteristic
17C2×C3×#688—21no—
18C3×#4020C2211yescharacteristic
19C2×#6653—21no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×#3941—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90965—22no—
25#90965—21no—
26#71035—51nomaximal, Hall
27Q8×D20—31no—
28#65316D311yescharacteristic, complemented
29#65132—31no—
30#64983—31no—
31C5×Q8⋊C8—31no—
32#64706—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35Q8×D15—42no—
36Q8×D15—42no—
37C2×D60D411yescharacteristic
38C2×C4×D15—22no—
39C2×C4×D15—21no—
40C2×Dic30—22no—
41C2×Dic30—21no—
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C42×C5—21no—
48C3×C42×C5C2311yescharacteristic
49#6714—22no—
50#6714—21no—
51C4⋊Dic15—22no—
52C4⋊Dic15—21no—
53C4⋊Dic15D411yescharacteristic
54C4⋊Dic15D412yes—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57C3×#688—42no—
58C2×C3×#168—21no—
59#6653—42no—
60Q8×D12—51no—
61C3×#460—51no—
62#5072—51no—
63#5070—51no—
64#4535D511yescharacteristic, complemented
65#4483—51no—
66#4482—51no—
67C2×Q8×D5—61no—
68C4×C5×Q8C2×D311yescharacteristic
69C2×#688—21no—
70C2×D40—61no—
71#4043—62no—
72#4043—61no—
73#4020C2×D311yescharacteristic
74C4×D20—31no—
75C4×D20—61no—
76#4015—31no—
77#4015—61no—
78C5×C4⋊C8—31no—
79C4×C5×C8—31no—
80#3953—61no—
81#3953—62no—
82#3941—21no—
83C4⋊#168C2×D311yescharacteristic
84#1627—151noSylow
85C22×D15—21no—
86C22×C3×D5—41no—
87C3×C5×Q8—21no—
88C3×C5×Q8D812yescomplemented
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×Dic15—21no—
95C2×Dic15—22no—
96D60—21no—
97D60SD1612yescomplemented
98C4×D15—44no—
99C4×D15—41no—
100C4×D15—41no—
101Dic30—44no—
102Dic30—41no—
103Dic30—41no—
104C3×D20—42no—
105C3×D20—41no—
106C3×D20—41no—
107C3×D20—41no—
108C3×D20—41no—
109C3×#168—41no—
110C5×C3⋊C8—41no—
111C5×C3⋊C8—41no—
112C2×D3×Q8—101no—
113C2×C3×SD16—101no—
114C3×#127—51no—
115C3×C4×Q8C2×D511yescharacteristic
116C2×#213—101no—
117#897—102no—
118#897—101no—
119C4×D12—51no—
120C4×D12—101no—
121#869—51no—
122#869—101no—
123C3×C4⋊C8—51no—
124C3×#102—101no—
125#832—102no—
126#832—101no—
127C4⋊(C3⋊C8)C2×D511yescharacteristic
128C4×C3⋊C8C2×D511yescharacteristic
129C2×C5×Q8#6711yescharacteristic
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—62no—
139C2×Dic10—61no—
140C2×C5×C8—61no—
141C2×C5×C8—61no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4#6711yescharacteristic
144C42×C5—21no—
145C42×C5C22×D311yescharacteristic
146#688—42no—
147#685—62no—
148#685—61no—
149C4⋊Dic5—32no—
150C4⋊Dic5—31no—
151C4⋊Dic5—62no—
152C4⋊Dic5—61no—
153C2×#168—21no—
154D40—122no—
155D4×Q8—151no—
156#486—151no—
157#460—51no—
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—22no—
170C3×C4×C5—21no—
171C3×C4×C5—41no—
172C3×C4×C5C2×D811yescharacteristic
173C3×C4×C5C2×SD1611yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C3×C4×C5#13711yescharacteristic
176Dic15—41no—
177Dic15—42no—
178C2×C3×Q8D2011yescharacteristic
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×Dic6—101no—
189C3×SD16—202no—
190C2×C3×C8—101no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4D2011yescharacteristic
193C3×C42—21no—
194C3×C42C22×D511yescharacteristic
195#213—202no—
196(C2×D3)⋊C4—102no—
197(C2×D3)⋊C4—101no—
198C4⋊Dic3—52no—
199C4⋊Dic3—51no—
200C4⋊Dic3—102no—
201C4⋊Dic3—101no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C22×D5—41no—
205C22×D5—61no—
206C5×Q8—21no—
207C5×Q8#21312yescomplemented
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C2×Dic5—62no—
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—124no—
226Dic10—121no—
227Dic10—121no—
228C5×C8—121no—
229C5×C8—121no—
230#168—41no—
231C22×Q8—301no—
232C2×SD16—101no—
233C2×D8—301no—
234C4⋊Q8—151no—
235C4⋊Q8—301no—
236#127—51no—
237C22⋊Q8—302no—
238C22⋊Q8—301no—
239C4×Q8D3×D511yescharacteristic
240C4×D4—151no—
241C4×D4—301no—
242C4⋊C8—31no—
243C4⋊C8—51no—
244#102—101no—
245#102—301no—
246#102—302no—
247C4×C8—31no—
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—21no—
256C3×Q8D4012yescomplemented
257C3×D4—202no—
258C3×D4—201no—
259C3×D4—201no—
260C3×D4—201no—
261C3×D4—201no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4C2×D2011yescharacteristic
265C2×C3×C4D4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×Dic3—102no—
268C2×Dic3—101no—
269D12—52no—
270D12—101no—
271C4×D3—204no—
272C4×D3—201no—
273C4×D3—201no—
274Dic6—204no—
275Dic6—201no—
276Dic6—201no—
277C3×C8—201no—
278C3⋊C8—41no—
279C3⋊C8—41no—
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—22no—
289C4×C5—41no—
290C4×C5D3×SD1611yescharacteristic
291C4×C5#91511yescharacteristic
292C4×C5C2×#21311yescharacteristic
293C4×C5#94911yescharacteristic
294Dic5—121no—
295Dic5—122no—
296C2×Q8—302no—
297C2×Q8—301no—
298C2×Q8—602no—
299C2×Q8—602no—
300C2×Q8#120211yescharacteristic
301C2×D4—101no—
302C2×D4—101no—
303C2×D4—101no—
304C2×D4—151no—
305C22×C4—302no—
306C22×C4—301no—
307SD16—202no—
308D8—602no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—101no—
312C4⋊C4—21no—
313C4⋊C4—151no—
314C4⋊C4—152no—
315C4⋊C4—302no—
316C4⋊C4—301no—
317C4⋊C4#120211yescharacteristic
318C22⋊C4—302no—
319C22⋊C4—301no—
320C42—21no—
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—22no—
332C3×C4—41no—
333C3×C4C2×D4011yescharacteristic
334C3×C4#405411yescharacteristic
335C3×C4D5×SD1611yescharacteristic
336C3×C4#406411yescharacteristic
337Dic3—201no—
338Dic3—202no—
339C2×C5#503611yescharacteristic
340C2×C5#517011yescharacteristic
341C2×C5#520111yescharacteristic
342D5—122no—
343D5—161no—
344C23—201no—
345C23—301no—
346Q8—21no—
347Q8—604no—
348Q8—601no—
349Q8—601no—
350Q8#665312yescomplemented
351D4—152no—
352D4—202no—
353D4—201no—
354D4—201no—
355D4—201no—
356D4—201no—
357D4—301no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—302no—
361C2×C4—301no—
362C2×C4—604no—
363C2×C4—601no—
364C2×C4—601no—
365C2×C4C2×#120211yescharacteristic
366C2×C4#679011yescharacteristic
367C2×C4#679011yescharacteristic
368C8—121no—
369C8—121no—
370C8—201no—
371C2×C3—801no—
372C2×C3#6502111yescharacteristic
373C2×C3#6509511yescharacteristic
374C2×C3#6511611yescharacteristic
375D3—202no—
376C5#7103511yescharacteristic, complemented, Sylow
377C22—302no—
378C22—401no—
379C22—401no—
380C22—401no—
381C22—601no—
382C22—601no—
383C22#9157211yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—602no—
388C4—601no—
389C4C2×#665311yescharacteristic
390C4#9130111yescharacteristic
391C4#9150511yescharacteristic
392C4#9152211yescharacteristic
393C3#1059905911yescharacteristic, complemented, Sylow
394C2—602no—
395C2—801no—
396C2#1174852411yescharacteristic
397C2#1174928611yescharacteristic
398C2#1174946011yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#11747043C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1627
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
1. Q8×D60C2semidirect
2. C3×#65316C2semidirect
4. #11746890C2semidirect
5. C5×#4535C2semidirect
6. #11745860C2semidirect
7. #11745838C2semidirect
28. #65316D3semidirect
64. #4535D5semidirect
88. C3×C5×Q8D8semidirect
97. D60SD16semidirect
207. C5×Q8#213semidirect
256. C3×Q8D40semidirect
322. C3×C5#1627semidirect
350. Q8#6653semidirect
376. C5#71035semidirect
393. C3#10599059semidirect

Maximal subgroups

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

subgroupindex
Q8×D602
C3×#653162
#117470432
#117468902
C5×#45352
#117458602
#117458382
#105990593
#710355