Finite Group Databasebeta

← #14299886

Subgroups — #14299886

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
1C3×#66153C211yesmaximal, characteristic
2C2×#91121C211yesmaximal, characteristic
3C5×#5236C211yesmaximal, characteristic
4#11748478C211yesmaximal, characteristic, complemented
5#11748437C211yesmaximal, characteristic, complemented
6#11745988C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10601191—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C4×Dic15C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C5×#926C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4094—22no—
15C3×#4094—22no—
16C2×C3×#681—22no—
17C2×C3×#681C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91121C412yescomplemented
20#91121C412yescomplemented
21C5×#837—22no—
22#90992—22no—
23#90983—22no—
24#72028—51nomaximal, Hall
25#66153D311yescharacteristic
26C5×#421—31no—
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—
42C4×Dic15—21no—
43C4×Dic15C2×C411yescharacteristic
44C4×Dic15C2×C411yescharacteristic
45#6710—21no—
46#6710C2×C412yes—
47C2×C3⋊#168—21no—
48C5×#217—21no—
49C5×C4⋊Dic3—21no—
50C4×C5×Dic3—21no—
51C5×#208—21no—
52C5×#208—21no—
53C2×C5×C3⋊C8—21no—
54C3×#681—24no—
55C3×#681—21no—
56C3×#681—21no—
57C3×#681—21no—
58C3×#681D412yes—
59C2×C3×#168—24no—
60C2×C3×#168—21no—
61C2×C3×#168D412yes—
62C3×#568—51no—
63#5236D511yescharacteristic
64C2×#837—51no—
65#5124—51no—
66#5118—51no—
67#4556—51no—
68#4555—51no—
69C2×C5×#41C2×D311yescharacteristic
70C2×C5×M16—31no—
71C5×#117—31no—
72#4094—22no—
73#4094—22no—
74C2×C4×Dic5—31no—
75C2×#681—22no—
76C2×#681—31no—
77C2×#681C2×D311yescharacteristic
78C2×#681C2×D311yescharacteristic
79C5×#104—62no—
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×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×Q811yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—42no—
105C2×C5×Dic3—41no—
106C3⋊#168—22no—
107C3×#168—22no—
108C3×#168—22no—
109C5×C3⋊C8—41no—
110C2×C3×#41C2×D511yescharacteristic
111C3×#131—102no—
112C3×#131—102no—
113C2×C3×M16—51no—
114C2×C3×M16—51no—
115C2×C3×M16—102no—
116#926C2×D511yescharacteristic
117C2×C4×Dic3—51no—
118C2×#208—51no—
119C2×#208C2×D511yescharacteristic
120#837—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—61no—
136C5×M16—61no—
137C2×C5×C8—61no—
138C5×C4⋊C4—61no—
139C5×C22⋊C4—61no—
140C42×C5—61no—
141C4×Dic5—31no—
142C4×Dic5—31no—
143C4×Dic5—61no—
144#681—24no—
145#681—21no—
146#681—21no—
147#681—21no—
148#681—32no—
149#681—61no—
150#681#6712yes—
151C2×#168—24no—
152C2×#168—21no—
153C2×#168—61no—
154C2×#168#6712yes—
155#568—51no—
156#430—151no—
157#423—151no—
158#421—31no—
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×C5C2×C4⋊C411yescharacteristic
170C3×C4×C5C4×D411yescharacteristic
171C3×C4×C5#12011yescharacteristic
172C3×C4×C5C22⋊Q811yescharacteristic
173Dic15—22no—
174Dic15—41no—
175C5×Dic3—81no—
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—52no—
187C3×M16—104no—
188C3×M16—101no—
189C3×M16—101no—
190C3×M16—101no—
191C2×C3×C8—52no—
192C2×C3×C8—104no—
193C2×C3×C8—101no—
194#217—21no—
195C4⋊Dic3—21no—
196C4×Dic3—21no—
197C4×Dic3—51no—
198C4×Dic3—51no—
199C4×Dic3—101no—
200#208—21no—
201#208—21no—
202#208—52no—
203#208—101no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—101no—
206C23×C5—21no—
207C23×C5#23511yescharacteristic
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—121no—
218C2×C4×C5C2×Dic611yescharacteristic
219C2×C4×C5C2×C4×D311yescharacteristic
220C2×C4×C5#23511yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C2×C4×C5C2×#6711yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C2×Dic5—61no—
225C2×Dic5—61no—
226C2×Dic5—122no—
227C5×C8—121no—
228#168—22no—
229#168—22no—
230#168—62no—
231C2×#41D3×D511yescharacteristic
232#131—102no—
233#131—102no—
234C2×M16—31no—
235C2×M16—51no—
236C2×M16—51no—
237C2×M16—102no—
238C2×M16—151no—
239#117—31no—
240C2×C42—151no—
241#108—302no—
242C4⋊C8—302no—
243#104—62no—
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×C4C2×Dic1011yescharacteristic
263C2×C3×C4C2×C4×D511yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265C2×C3×C4D4×D511yescharacteristic
266C2×C3×C4#71111yescharacteristic
267C2×C3×C4C2×C22⋊D511yescharacteristic
268C2×Dic3—41no—
269C2×Dic3—101no—
270C2×Dic3—101no—
271C2×Dic3—202no—
272C3×C8—102no—
273C3×C8—102no—
274C3⋊C8—41no—
275C3⋊C8—102no—
276C22×C5—22no—
277C22×C5—41no—
278C22×C5—81no—
279C22×C5#92411yescharacteristic
280C22×C5C4×#6711yescharacteristic
281C22×C5#92911yescharacteristic
282C4×C5—22no—
283C4×C5—241no—
284C4×C5C2×Dic3⋊C411yescharacteristic
285C4×C5#92411yescharacteristic
286C4×C5C4×#6711yescharacteristic
287C4×C5#95311yescharacteristic
288Dic5—62no—
289Dic5—121no—
290#41—21no—
291#41—21no—
292#41#120012yes—
293#41#120112yes—
294C2×Q8#120411yescharacteristic
295C2×D4—21no—
296C2×D4#120411yescharacteristic
297C22×C4—21no—
298C22×C4—301no—
299C22×C4C2×D3×D511yescharacteristic
300M16—52no—
301M16—61no—
302M16—61no—
303M16—104no—
304M16—101no—
305M16—101no—
306M16—101no—
307M16—152no—
308M16—301no—
309C2×C8—52no—
310C2×C8—61no—
311C2×C8—104no—
312C2×C8—101no—
313C2×C8—301no—
314C4⋊C4—61no—
315C22⋊C4—61no—
316C42—61no—
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#402411yescharacteristic
329C3×C4#402711yescharacteristic
330C3×C4C2×#68311yescharacteristic
331C3×C4#408311yescharacteristic
332Dic3—81no—
333Dic3—102no—
334Dic3—201no—
335C2×C5—21no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5—42no—
339C2×C5#521011yescharacteristic
340C23—21no—
341C23#678211yescharacteristic
342Q8—21no—
343Q8#666912yes—
344D4—22no—
345D4—22no—
346D4—21no—
347D4#666912yes—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—121no—
352C2×C4—301no—
353C2×C4—301no—
354C2×C4—602no—
355C2×C4#678211yescharacteristic
356C2×C4C2×#120011yescharacteristic
357C2×C4C2×#120111yescharacteristic
358C2×C4C2×#120411yescharacteristic
359C2×C4D5×#6711yescharacteristic
360C2×C4D5×#6711yescharacteristic
361C8—102no—
362C8—102no—
363C8—121no—
364C8—302no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—42no—
369C2×C3#6523511yescharacteristic
370C5#7202811yescharacteristic, complemented, Sylow
371C22—22no—
372C22—41no—
373C22—81no—
374C22#9153911yescharacteristic
375C22#9155211yescharacteristic
376C22#9157411yescharacteristic
377C4—22no—
378C4—241no—
379C4—302no—
380C4—601no—
381C4C2×#666911yescharacteristic
382C4#9155211yescharacteristic
383C4#9156311yescharacteristic
384C4#9157411yescharacteristic
385C3#1060119111yescharacteristic, complemented, Sylow
386C2—21no—
387C2—21no—
388C2—21no—
389C2—42no—
390C2#1174950811yescharacteristic
subgroupG/H
centerC4#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC2×C3×C5#385
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1861
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #11748478C2semidirect
5. #11748437C2semidirect
6. #11745988C2semidirect
7. #11745975C2semidirect
19. #91121C4semidirect
20. #91121C4semidirect
320. C3×C5#1861semidirect
370. C5#72028semidirect
385. C3#10601191semidirect

Maximal subgroups

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

subgroupindex
C3×#661532
C2×#911212
C5×#52362
#117484782
#117484372
#117459882
#117459752
#106011913
#720285