Finite Group Databasebeta

← #14299854

Subgroups — #14299854

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756578C211yesmaximal, characteristic
2C3×C5×#421C211yesmaximal, characteristic
3C2×#91121C211yesmaximal, characteristic
4#11751225C211yesmaximal, characteristic, complemented
5#11751219C211yesmaximal, characteristic, complemented
6#11746354C211yesmaximal, characteristic, complemented
7#11746353C211yesmaximal, characteristic, complemented
8#10601191—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91837—22no—
13#91837—22no—
14C2×C4×Dic15C2211yescharacteristic
15C2×#6710—22no—
16C2×#6710C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C3×C5×#104—22no—
20#91121C412yescomplemented
21#91121C412yescomplemented
22#91106—22no—
23#91098—22no—
24#70398—51nomaximal, Hall
25#66153—31no—
26C5×#421D311yescharacteristic
27C2×#3969—31no—
28#65413—31no—
29#65407—31no—
30#64753—31no—
31#64752—31no—
32C3×C5×#41—21no—
33C3×C5×#41—21no—
34C3×C5×#41C2×C412yes—
35C3×C5×#41D412yes—
36C2×C3×C5×Q8Q811yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4Q811yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5C2311yescharacteristic
41C22×Dic15—21no—
42C3×C5×M16—21no—
43C3×C5×M16—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C22⋊C4—21no—
47C3×C42×C5—21no—
48C4×Dic15—21no—
49C4×Dic15C2×C411yescharacteristic
50C4×Dic15C2×C411yescharacteristic
51#6710—24no—
52#6710—21no—
53#6710—21no—
54#6710—21no—
55#6710—21no—
56#6710C2×C412yes—
57#6710D412yes—
58C2×C3⋊#168—24no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61C2×C3⋊#168D412yes—
62#5819—51no—
63C3×#421D511yescharacteristic
64C2×#837—51no—
65#5124—51no—
66#5118—51no—
67#4533—51no—
68#4532—51no—
69C2×C5×#41C2×D311yescharacteristic
70C2×C5×M16C2×D311yescharacteristic
71C5×#117C2×D311yescharacteristic
72#4094—62no—
73#4094—62no—
74C2×C4×Dic5—31no—
75C2×#681—31no—
76C2×#681—31no—
77C2×#681—31no—
78C2×#681—62no—
79C5×#104—22no—
80#3969—32no—
81#3969—32no—
82#3954—62no—
83#3946—62no—
84#1861—151noSylow
85C23×C3×C5—21no—
86C23×C3×C5#4111yescharacteristic
87C3×C5×Q8—21no—
88C3×C5×Q8C4⋊C412yes—
89C3×C5×D4—22no—
90C3×C5×D4—22no—
91C3×C5×D4—21no—
92C3×C5×D4C4⋊C412yes—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×Q811yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—42no—
106C3×C5×C8—41no—
107C3⋊#168—22no—
108C3⋊#168—22no—
109C3⋊#168—22no—
110C2×C3×#41C2×D511yescharacteristic
111C2×C3×M16C2×D511yescharacteristic
112C3×#117C2×D511yescharacteristic
113#948—102no—
114#948—102no—
115C2×C4×Dic3—51no—
116C2×#208—51no—
117C2×#208—51no—
118C2×#208—51no—
119C2×#208—102no—
120C3×#104—22no—
121#837—52no—
122#837—52no—
123#822—102no—
124Dic3⋊C8—102no—
125C5×#41—21no—
126C5×#41—21no—
127C5×#41C4×D312yes—
128C5×#41#6712yes—
129C2×C5×Q8Dic611yescharacteristic
130C2×C5×D4—21no—
131C2×C5×D4Dic611yescharacteristic
132C22×C4×C5—21no—
133C22×C4×C5C22×D311yescharacteristic
134C22×Dic5—61no—
135C5×M16—21no—
136C5×M16—21no—
137C2×C5×C8—21no—
138C5×C4⋊C4—21no—
139C5×C22⋊C4—21no—
140C42×C5—21no—
141C4×Dic5—31no—
142C4×Dic5—31no—
143C4×Dic5—61no—
144#681—32no—
145#681—32no—
146#681—64no—
147#681—61no—
148#681—61no—
149#681—61no—
150#681—61no—
151C2×#168—32no—
152C2×#168—64no—
153C2×#168—61no—
154C2×#168—61no—
155#568—151no—
156#430—151no—
157#423—151no—
158#421D1511yescharacteristic
159C2×#104—151no—
160#344—151no—
161#339—151no—
162C22×C3×C5—22no—
163C22×C3×C5—41no—
164C22×C3×C5—81no—
165C22×C3×C5C4×D411yescharacteristic
166C22×C3×C5C22⋊Q811yescharacteristic
167C22×C3×C5#12311yescharacteristic
168C3×C4×C5—22no—
169C3×C4×C5—81no—
170C3×C4×C5C2×C4⋊C411yescharacteristic
171C3×C4×C5C4×D411yescharacteristic
172C3×C4×C5#12011yescharacteristic
173C3×C4×C5C22⋊Q811yescharacteristic
174Dic15—22no—
175Dic15—41no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41C4×D512yes—
179C3×#41C22⋊D512yes—
180C2×C3×Q8Dic1011yescharacteristic
181C2×C3×D4—21no—
182C2×C3×D4Dic1011yescharacteristic
183C22×C3×C4—21no—
184C22×C3×C4C22×D511yescharacteristic
185C22×Dic3—101no—
186C3×M16—21no—
187C3×M16—21no—
188C2×C3×C8—21no—
189C3×C4⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C42—21no—
192C4×Dic3—51no—
193C4×Dic3—51no—
194C4×Dic3—101no—
195#208—52no—
196#208—52no—
197#208—104no—
198#208—101no—
199#208—101no—
200#208—101no—
201#208—101no—
202C2×C3⋊C8—52no—
203C2×C3⋊C8—104no—
204C2×C3⋊C8—101no—
205C2×C3⋊C8—101no—
206C23×C5—21no—
207C23×C5#23711yescharacteristic
208C5×Q8—21no—
209C5×Q8Dic3⋊C412yes—
210C5×D4—22no—
211C5×D4—22no—
212C5×D4—21no—
213C5×D4Dic3⋊C412yes—
214C2×C4×C5—21no—
215C2×C4×C5—22no—
216C2×C4×C5—22no—
217C2×C4×C5—41no—
218C2×C4×C5C2×Dic611yescharacteristic
219C2×C4×C5C2×C4×D311yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C2×C4×C5#23711yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C2×Dic5—61no—
225C2×Dic5—61no—
226C2×Dic5—122no—
227C5×C8—41no—
228#168—62no—
229#168—62no—
230#168—62no—
231C2×#41C2×D1511yescharacteristic
232#131—302no—
233#131—302no—
234C2×M16—151no—
235C2×M16—151no—
236C2×M16—151no—
237C2×M16—302no—
238C2×M16C2×D1511yescharacteristic
239#117C2×D1511yescharacteristic
240C2×C42—151no—
241#108—302no—
242C4⋊C8—302no—
243#104—22no—
244#104—152no—
245#104—152no—
246C2×C3×C5—21no—
247C2×C3×C5—21no—
248C2×C3×C5—21no—
249C2×C3×C5—42no—
250C2×C3×C5#38511yescharacteristic
251C23×C3—21no—
252C23×C3#71111yescharacteristic
253C3×Q8—21no—
254C3×Q8#68312yes—
255C3×D4—22no—
256C3×D4—22no—
257C3×D4—21no—
258C3×D4#68312yes—
259C2×C3×C4—21no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—41no—
263C2×C3×C4C2×Dic1011yescharacteristic
264C2×C3×C4C2×C4×D511yescharacteristic
265C2×C3×C4D4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4#71111yescharacteristic
268C2×C3×C4C2×C22⋊D511yescharacteristic
269C2×Dic3—101no—
270C2×Dic3—101no—
271C2×Dic3—202no—
272C3×C8—41no—
273C3⋊C8—102no—
274C3⋊C8—102no—
275C3⋊C8—102no—
276C22×C5—22no—
277C22×C5—41no—
278C22×C5—81no—
279C22×C5#87811yescharacteristic
280C22×C5#67⋊C411yescharacteristic
281C22×C5#93511yescharacteristic
282C4×C5—22no—
283C4×C5—81no—
284C4×C5#87811yescharacteristic
285C4×C5#67⋊C411yescharacteristic
286C4×C5C2×Dic3⋊C411yescharacteristic
287C4×C5#93711yescharacteristic
288Dic5—62no—
289Dic5—121no—
290#41—21no—
291#41—21no—
292#41C4×D1512yes—
293#41#122012yes—
294C2×Q8Dic3011yescharacteristic
295C2×D4—21no—
296C2×D4Dic3011yescharacteristic
297C22×C4—21no—
298C22×C4—301no—
299C22×C4C22×D1511yescharacteristic
300M16—21no—
301M16—21no—
302M16—152no—
303M16—152no—
304M16—304no—
305M16—301no—
306M16—301no—
307M16—301no—
308M16—301no—
309C2×C8—21no—
310C2×C8—152no—
311C2×C8—304no—
312C2×C8—301no—
313C2×C8—301no—
314C4⋊C4—21no—
315C22⋊C4—21no—
316C42—21no—
317C42—151no—
318C42—151no—
319C42—301no—
320C3×C5#186111yescharacteristic, complemented, Hall
321C22×C3—22no—
322C22×C3—41no—
323C22×C3—81no—
324C22×C3#402411yescharacteristic
325C22×C3#402711yescharacteristic
326C22×C3#408111yescharacteristic
327C3×C4—22no—
328C3×C4—81no—
329C3×C4#402411yescharacteristic
330C3×C4#402711yescharacteristic
331C3×C4C2×#68311yescharacteristic
332C3×C4#408311yescharacteristic
333Dic3—102no—
334Dic3—201no—
335C2×C5—21no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5—42no—
339C2×C5#494611yescharacteristic
340C23—21no—
341C23#681911yescharacteristic
342Q8—21no—
343Q8#671212yes—
344D4—22no—
345D4—22no—
346D4—21no—
347D4#671212yes—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—301no—
353C2×C4—301no—
354C2×C4—602no—
355C2×C4C2×Dic3011yescharacteristic
356C2×C4C2×C4×D1511yescharacteristic
357C2×C4D4×D1511yescharacteristic
358C2×C4D4×D1511yescharacteristic
359C2×C4#681911yescharacteristic
360C2×C4C2×#122011yescharacteristic
361C8—41no—
362C8—302no—
363C8—302no—
364C8—302no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—42no—
369C2×C3#6523511yescharacteristic
370C5#7039811yescharacteristic, complemented, Sylow
371C22—22no—
372C22—41no—
373C22—81no—
374C22#9176711yescharacteristic
375C22#9177011yescharacteristic
376C22#9182411yescharacteristic
377C4—22no—
378C4—81no—
379C4—302no—
380C4—601no—
381C4#9176711yescharacteristic
382C4#9177011yescharacteristic
383C4C2×#671211yescharacteristic
384C4#9182611yescharacteristic
385C3#1060119111yescharacteristic, complemented, Sylow
386C2—21no—
387C2—21no—
388C2—21no—
389C2—42no—
390C2#1175104711yescharacteristic
subgroupG/H
centerC4#91826
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#421C2
socleC2×C3×C5#385
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4×C5C23
hypercenter#421D15
hypocenterC3×C5#1861
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
4. #11751225C2semidirect
5. #11751219C2semidirect
6. #11746354C2semidirect
7. #11746353C2semidirect
20. #91121C4semidirect
21. #91121C4semidirect
320. C3×C5#1861semidirect
370. C5#70398semidirect
385. C3#10601191semidirect

Maximal subgroups

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

subgroupindex
#117565782
C3×C5×#4212
C2×#911212
#117512252
#117512192
#117463542
#117463532
#106011913
#703985