Finite Group Databasebeta

← #14289213

Subgroups — #14289213

Order 1920.

500 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 95 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#11756486C211yesmaximal, characteristic, complemented
2C3×C5×#486C211yesmaximal, characteristic, complemented
3#11751176C211yesmaximal, characteristic, complemented
4#11751173C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11746280C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10601998—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#127C2211yescharacteristic
12#91835—21no—
13C2×#6716—21no—
14C2×#6715—21no—
15#91785—22no—
16#91782—21no—
17#91777—21no—
18C4×D60C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C3×C5×#102—22no—
21C3×C4×C5×C8C2211yescharacteristic
22#91116—21no—
23#91116—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#71205—51nomaximal, Hall
27#66061—31no—
28C5×#486D311yescharacteristic, complemented
29#65364—31no—
30#65361—31no—
31#64767—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38Q8×D15—42no—
39Q8×D15—42no—
40C2×D60D411yescharacteristic
41C2×C4×D15—22no—
42C2×C4×D15—21no—
43C2×Dic30—22no—
44C2×Dic30D411yescharacteristic
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D412yes—
48C3×C42×C5C2311yescharacteristic
49#6716—42no—
50#6715—42no—
51#6714—22no—
52#6714—21no—
53C4⋊Dic15D411yescharacteristic
54C4⋊Dic15D411yescharacteristic
55#6712—22no—
56#6712—21no—
57C4×Dic15—21no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60#5727—51no—
61C3×#486D511yescharacteristic, complemented
62#5075—51no—
63#5072—51no—
64#4547—51no—
65#4459—51no—
66#4456—51no—
67C2×Q8×D5—61no—
68C5×C4⋊Q8C2×D311yescharacteristic
69C5×#127C2×D311yescharacteristic
70#4092—61no—
71C2×#687—61no—
72C2×#686—61no—
73#4042—62no—
74#4039—61no—
75#4034—61no—
76C4×D20—31no—
77C4×Dic10—31no—
78C5×#102—22no—
79C4×C5×C8C2×D311yescharacteristic
80#3964—61no—
81#3964—61no—
82C4⋊#168—31no—
83C4⋊#168—31no—
84#1627—151noSylow
85C23×C3×C5—41no—
86C22×D15—21no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C3×C5×D4—42no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×Dic15—21no—
99C2×Dic15—21no—
100C2×Dic15—21no—
101D60—21no—
102D60SD1612yescomplemented
103C4×D15—44no—
104C4×D15—41no—
105C4×D15—41no—
106Dic30—21no—
107Dic30—44no—
108Dic30D812yescomplemented
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C3⋊#168—41no—
112C2×D3×Q8—101no—
113C3×C4⋊Q8C2×D511yescharacteristic
114C3×#127C2×D511yescharacteristic
115#946—101no—
116C2×#214—101no—
117C2×#213—101no—
118#896—102no—
119#893—101no—
120#888—101no—
121C4×D12—51no—
122C4×Dic6—51no—
123C3×#102—22no—
124C3×C4×C8C2×D511yescharacteristic
125#832—101no—
126#832—101no—
127C4⋊(C3⋊C8)—51no—
128C4⋊(C3⋊C8)—51no—
129C2×C5×Q8—21no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133Q8×D5—122no—
134Q8×D5—122no—
135C2×D20—31no—
136C2×C4×D5—62no—
137C2×C4×D5—61no—
138C2×Dic10—31no—
139C2×Dic10—62no—
140C2×C5×C8—21no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4#6712yes—
143C42×C5C22×D311yescharacteristic
144#687—122no—
145#686—122no—
146#685—62no—
147#685—61no—
148C4⋊Dic5—31no—
149C4⋊Dic5—31no—
150#683—62no—
151#683—61no—
152C4×Dic5—61no—
153C2×#168—61no—
154C2×#168—61no—
155D4×Q8—151no—
156#486D1511yescharacteristic, complemented
157#460—151no—
158#459—151no—
159#332—151no—
160Q8⋊C8—151no—
161D4⋊C8—151no—
162C22×C3×C5—81no—
163C22×C3×C5—81no—
164C22×C3×C5—81no—
165C22×C3×C5#12011yescharacteristic
166C2×D15—22no—
167C2×D15—41no—
168C2×D15—41no—
169C3×C4×C5—21no—
170C3×C4×C5—42no—
171C3×C4×C5C2×D811yescharacteristic
172C3×C4×C5C2×SD1611yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C3×C4×C5#13711yescharacteristic
175Dic15—22no—
176Dic15—41no—
177Dic15—41no—
178C2×C3×Q8—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182D3×Q8—202no—
183D3×Q8—202no—
184C2×D12—51no—
185C2×C4×D3—102no—
186C2×C4×D3—101no—
187C2×Dic6—51no—
188C2×Dic6—102no—
189C2×C3×C8—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4C22⋊D512yes—
192C3×C42C22×D511yescharacteristic
193#214—202no—
194#213—202no—
195(C2×D3)⋊C4—102no—
196(C2×D3)⋊C4—101no—
197C4⋊Dic3—51no—
198C4⋊Dic3—51no—
199Dic3⋊C4—102no—
200Dic3⋊C4—101no—
201C4×Dic3—101no—
202C2×C3⋊C8—101no—
203C2×C3⋊C8—101no—
204C23×C5—41no—
205C22×D5—61no—
206C5×Q8—41no—
207C5×Q8—41no—
208C5×D4—42no—
209C5×D4—41no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4—41no—
213C2×C4×C5—22no—
214C2×C4×C5D3×D411yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216C2×C4×C5C2×#6711yescharacteristic
217C2×Dic5—61no—
218C2×Dic5—61no—
219C2×Dic5—61no—
220D20—32no—
221D20—61no—
222C4×D5—124no—
223C4×D5—121no—
224C4×D5—121no—
225Dic10—32no—
226Dic10—61no—
227Dic10—124no—
228C5×C8—41no—
229#168—121no—
230#168—121no—
231C22×Q8—301no—
232C2×SD16—301no—
233C2×D8—301no—
234C4⋊Q8—301no—
235C4⋊Q8C2×D1511yescharacteristic
236#127C2×D1511yescharacteristic
237C22⋊Q8—301no—
238C22⋊Q8—302no—
239C4×Q8—151no—
240C4×D4—151no—
241C4×D4—301no—
242C4⋊C8—151no—
243C4⋊C8—151no—
244#102—22no—
245#102—301no—
246#102—301no—
247C4×C8C2×D1511yescharacteristic
248C2×C3×C5—161no—
249C2×C3×C5#44711yescharacteristic
250C2×C3×C5#44811yescharacteristic
251C2×C3×C5#45411yescharacteristic
252D15—42no—
253C23×C3—41no—
254C22×D3—101no—
255C3×Q8—41no—
256C3×Q8—41no—
257C3×D4—42no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C2×C3×C4—22no—
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265C2×C3×C4C2×C22⋊D511yescharacteristic
266C2×Dic3—101no—
267C2×Dic3—101no—
268C2×Dic3—101no—
269D12—52no—
270D12—101no—
271C4×D3—204no—
272C4×D3—201no—
273C4×D3—201no—
274Dic6—52no—
275Dic6—101no—
276Dic6—204no—
277C3×C8—41no—
278C3⋊C8—201no—
279C3⋊C8—201no—
280C22×C5—81no—
281C22×C5—81no—
282C22×C5—81no—
283C22×C5#93711yescharacteristic
284C2×D5—62no—
285C2×D5—121no—
286C2×D5—121no—
287C4×C5—21no—
288C4×C5—42no—
289C4×C5D3×D811yescharacteristic
290C4×C5#91111yescharacteristic
291C4×C5D3×SD1611yescharacteristic
292C4×C5#91511yescharacteristic
293Dic5—62no—
294Dic5—121no—
295Dic5—121no—
296C2×Q8—21no—
297C2×Q8—151no—
298C2×Q8—302no—
299C2×Q8—602no—
300C2×Q8—602no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—151no—
305C22×C4—302no—
306C22×C4—301no—
307SD16—602no—
308D8—602no—
309C2×C8—21no—
310C2×C8—301no—
311C2×C8—301no—
312C4⋊C4—21no—
313C4⋊C4—151no—
314C4⋊C4—151no—
315C4⋊C4—302no—
316C4⋊C4—301no—
317C4⋊C4#122012yes—
318C22⋊C4—302no—
319C22⋊C4—301no—
320C42—301no—
321C42C22×D1511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3—81no—
324C22×C3—81no—
325C22×C3—81no—
326C22×C3#408311yescharacteristic
327C2×D3—102no—
328C2×D3—201no—
329C2×D3—201no—
330C3×C4—21no—
331C3×C4—42no—
332C3×C4D5×D811yescharacteristic
333C3×C4#405711yescharacteristic
334C3×C4D5×SD1611yescharacteristic
335C3×C4#406111yescharacteristic
336Dic3—102no—
337Dic3—201no—
338Dic3—201no—
339C2×C5—161no—
340C2×C5#506211yescharacteristic
341C2×C5#515611yescharacteristic
342C2×C5#517011yescharacteristic
343D5—122no—
344C23—41no—
345C23—301no—
346Q8—41no—
347Q8—41no—
348Q8—152no—
349Q8—301no—
350Q8—604no—
351D4—42no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—152no—
357D4—301no—
358C2×C4—22no—
359C2×C4—301no—
360C2×C4—301no—
361C2×C4—301no—
362C2×C4—604no—
363C2×C4—601no—
364C2×C4—601no—
365C2×C4D4×D1511yescharacteristic
366C2×C4D4×D1511yescharacteristic
367C2×C4C2×#122011yescharacteristic
368C8—41no—
369C8—601no—
370C8—601no—
371C2×C3—161no—
372C2×C3#6535111yescharacteristic
373C2×C3#6544511yescharacteristic
374C2×C3#6545911yescharacteristic
375D3—202no—
376C5#7120511yescharacteristic, complemented, Sylow
377C22—81no—
378C22—81no—
379C22—81no—
380C22—302no—
381C22—601no—
382C22—601no—
383C22#9182611yescharacteristic
384C4—21no—
385C4—42no—
386C4—302no—
387C4—601no—
388C4—601no—
389C4D8×D1511yescharacteristic
390C4#9180011yescharacteristic
391C4SD16×D1511yescharacteristic
392C4#9180411yescharacteristic
393C3#1060199811yescharacteristic, complemented, Sylow
394C2—161no—
395C2—602no—
396C2#1175116311yescharacteristic
397C2#1175125711yescharacteristic
398C2#1175127111yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#486C2
socleC22×C3×C5#120
prime radical#11751173C2
hypercenter#486D15
hypocenterC3×C5#1627
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11756486C2semidirect
2. C3×C5×#486C2semidirect
3. #11751176C2semidirect
5. #11746368C2semidirect
6. #11746280C2semidirect
7. #11746277C2semidirect
28. C5×#486D3semidirect
61. C3×#486D5semidirect
102. D60SD16semidirect
108. Dic30D8semidirect
156. #486D15semidirect
322. C3×C5#1627semidirect
376. C5#71205semidirect
393. C3#10601998semidirect

Maximal subgroups

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

subgroupindex
#117564862
C3×C5×#4862
#117511762
#117511732
#117463682
#117462802
#117462772
#106019983
#712055