Finite Group Databasebeta

← #14300369

Subgroups — #14300369

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754120C211yesmaximal, characteristic
2#11751203C211yesmaximal, characteristic, complemented
3C5×#5102C211yesmaximal, characteristic, complemented
4C3×#65399C211yesmaximal, characteristic
5#11748624C211yesmaximal, characteristic
6#11745990C211yesmaximal, characteristic, complemented
7#11745989C211yesmaximal, characteristic, complemented
8#10601339—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91284—22no—
17#91283—22no—
18D5×#208—22no—
19#91098—22no—
20C5×Dic3⋊C8—22no—
21C3×#3952—22no—
22#90995C414yes—
23#70002—51nomaximal, Hall
24#66079—31no—
25C5×#424—31no—
26#65399D311yescharacteristic
27#65391—31no—
28#65295—31no—
29#64776—31no—
30#64753—31no—
31C22×C3×C4×C5C2311yescharacteristic
32C2×C3×C22⋊D5C2×C412yes—
33C3×#709—21no—
34C3×#709—21no—
35C3×#709—21no—
36C3×#709—21no—
37C2×C3×D20Q811yescharacteristic
38C2×C3×C4×D5D412yes—
39C2×C3×Dic10Q811yescharacteristic
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43#6719C2×C412yes—
44C4⋊Dic15—21no—
45C4×Dic15—21no—
46#6710—21no—
47#6710—21no—
48C2×C3⋊#168D412yes—
49C5×#217C2×C412yes—
50C5×C4⋊Dic3—21no—
51C4×C5×Dic3—21no—
52C5×#208—21no—
53C5×#208—21no—
54C2×C5×C3⋊C8D412yes—
55C3×#681—21no—
56C3×#681—21no—
57C2×C3×#168—21no—
58#6649—24no—
59D5×C3⋊C8—24no—
60#5819—51no—
61C3×#408—51no—
62#5240—51no—
63#5102—51no—
64#5102D511yescharacteristic, complemented
65#4559—51no—
66#4559—51no—
67C2×#709C2×D311yescharacteristic
68C2×C5×M16—31no—
69C22×C5×C8C2×D311yescharacteristic
70C5×#117—31no—
71#4072—31no—
72C2×#681—31no—
73C2×#681C2×D311yescharacteristic
74#4053—62no—
75D5×M16—62no—
76#4047—62no—
77C5×C4⋊C8—62no—
78#3952—22no—
79#3946—62no—
80#3938—34no—
81#1868—151noSylow
82C23×C3×C5C22×C411yescharacteristic
83C22×C3×D5C4⋊C412yes—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×Q811yescharacteristic
88C2×C3×C4×C5#4111yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90C2×Dic15—22no—
91C2×C5×Dic3—22no—
92C3×C22⋊D5—22no—
93C3×C22⋊D5—22no—
94C2×C3×Dic5C4⋊C412yes—
95C3×D20—21no—
96C3×D20—21no—
97C3×C4×D5—22no—
98C3×C4×D5—22no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101C3×C5×C8—41no—
102C3⋊#168—22no—
103C3×#168—41no—
104C5×C3⋊C8—22no—
105C2×C3×#41—51no—
106C2×C3×M16—51no—
107C22×C3×C8C2×D511yescharacteristic
108#948—102no—
109#948—102no—
110#926—51no—
111#926C2×D511yescharacteristic
112C2×#208—51no—
113C2×#208—102no—
114C2×#208C2×D511yescharacteristic
115C3×C22⋊C8—102no—
116#834—54no—
117Dic3⋊C8—22no—
118Dic3⋊C8—102no—
119C22×C4×C5C22×D311yescharacteristic
120C2×C22⋊D5C4×D312yes—
121#709—21no—
122#709—21no—
123#709—21no—
124#709—21no—
125C2×D20Dic611yescharacteristic
126C2×C4×D5#6712yes—
127C2×Dic10Dic611yescharacteristic
128C5×M16—61no—
129C5×M16—61no—
130C2×C5×C8—21no—
131C2×C5×C8—21no—
132C2×C5×C8—21no—
133C2×C5×C8—32no—
134C5×C4⋊C4—61no—
135C5×C22⋊C4—32no—
136C42×C5—61no—
137C22⋊Dic5—32no—
138C4⋊Dic5—61no—
139C4×Dic5—61no—
140#681—21no—
141#681—21no—
142#681—61no—
143#681—61no—
144C2×#168—21no—
145C2×#168—32no—
146#676—64no—
147C8×D5—64no—
148#568—151no—
149#424—31no—
150#424—151no—
151#410—151no—
152#408—51no—
153#344—151no—
154#344—151no—
155C22×C3×C5—41no—
156C22×C3×C5C2×C4⋊C411yescharacteristic
157C22×C3×C5C4×D411yescharacteristic
158C22×C3×C5C4×D411yescharacteristic
159C2×C3×D5—22no—
160C2×C3×D5—42no—
161C3×C4×C5#12011yescharacteristic
162C3×C4×C5C22⋊Q811yescharacteristic
163C3×C4×C5C22⋊Q811yescharacteristic
164C3×C4×C5#12311yescharacteristic
165Dic15—42no—
166C3×Dic5—22no—
167C5×Dic3—42no—
168C3×#41—101no—
169C3×#41—101no—
170C3×#41—101no—
171C3×#41—101no—
172C2×C3×Q8—51no—
173C2×C3×D4—52no—
174C2×C3×D4—51no—
175C22×C3×C4—52no—
176C22×C3×C4C22×D511yescharacteristic
177C3×M16—101no—
178C3×M16—101no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—101no—
183#217—52no—
184#217C4×D512yes—
185C4⋊Dic3—21no—
186C4⋊Dic3—101no—
187C4×Dic3—21no—
188C4×Dic3—101no—
189#208—21no—
190#208—21no—
191#208—104no—
192#208—101no—
193#208—101no—
194C2×C3⋊C8—52no—
195C2×C3⋊C8—104no—
196C2×C3⋊C8C22⋊D512yes—
197C23×C5C2×C4×D311yescharacteristic
198C22×D5Dic3⋊C412yes—
199C2×C4×C5—62no—
200C2×C4×C5C2×Dic611yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5#23711yescharacteristic
204C2×C4×C5#23711yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C22⋊D5—22no—
207C22⋊D5—22no—
208C2×Dic5—62no—
209C2×Dic5Dic3⋊C412yes—
210D20—21no—
211D20—21no—
212C4×D5—22no—
213C4×D5—22no—
214Dic10—21no—
215Dic10—21no—
216C5×C8—41no—
217C5×C8—62no—
218#168—41no—
219#168—62no—
220C2×#41—51no—
221#131—302no—
222#131—302no—
223C2×M16—31no—
224C2×M16—51no—
225C2×M16—151no—
226C2×M16—302no—
227C22×C8D3×D511yescharacteristic
228#117—31no—
229#117—151no—
230C4⋊C8—62no—
231C4⋊C8—302no—
232#99—154no—
233C22⋊C8—102no—
234C2×C3×C5—21no—
235C2×C3×C5—21no—
236C2×C3×C5—21no—
237C2×C3×C5#38511yescharacteristic
238C3×D5—42no—
239C23×C3—52no—
240C23×C3C2×C4×D511yescharacteristic
241C3×Q8—101no—
242C3×Q8—101no—
243C3×D4—102no—
244C3×D4—102no—
245C3×D4—101no—
246C3×D4—101no—
247C2×C3×C4—52no—
248C2×C3×C4—102no—
249C2×C3×C4—102no—
250C2×C3×C4#70911yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253C2×C3×C4Q8×D511yescharacteristic
254C2×C3×C4#71311yescharacteristic
255C2×C3×C4C2×C22⋊D511yescharacteristic
256C2×Dic3—22no—
257C2×Dic3—102no—
258C3×C8—41no—
259C3×C8—201no—
260C3⋊C8—22no—
261C3⋊C8—102no—
262C22×C5—41no—
263C22×C5#67⋊C411yescharacteristic
264C22×C5#67⋊C411yescharacteristic
265C22×C5C2×Dic3⋊C411yescharacteristic
266C2×D5—22no—
267C2×D5—42no—
268C4×C5—122no—
269C4×C5#87811yescharacteristic
270C4×C5#87811yescharacteristic
271C4×C5#93511yescharacteristic
272C4×C5#93711yescharacteristic
273Dic5—22no—
274Dic5—122no—
275#41—101no—
276#41—101no—
277#41—101no—
278#41—101no—
279C2×Q8—51no—
280C2×D4—52no—
281C2×D4—51no—
282C22×C4—52no—
283C22×C4C2×D3×D511yescharacteristic
284M16—61no—
285M16—61no—
286M16—101no—
287M16—101no—
288M16—304no—
289M16—301no—
290M16—301no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—32no—
295C2×C8—101no—
296C2×C8—152no—
297C2×C8—304no—
298C4⋊C4—61no—
299C4⋊C4—301no—
300C22⋊C4—32no—
301C22⋊C4—152no—
302C42—61no—
303C42—301no—
304C3×C5#186811yescharacteristic, complemented, Hall
305C22×C3—41no—
306C22×C3—102no—
307C22×C3—202no—
308C22×C3D5×C4⋊C411yescharacteristic
309C22×C3#403911yescharacteristic
310C22×C3C4×C22⋊D511yescharacteristic
311C3×C4—102no—
312C3×C4#404011yescharacteristic
313C3×C4#404211yescharacteristic
314C3×C4#408311yescharacteristic
315C3×C4#409211yescharacteristic
316Dic3—42no—
317Dic3—202no—
318C2×C5—21no—
319C2×C5—21no—
320C2×C5—21no—
321C2×C5#494611yescharacteristic
322D5—42no—
323C23—52no—
324C23C4×D3×D511yescharacteristic
325Q8—101no—
326Q8—101no—
327D4—102no—
328D4—102no—
329D4—101no—
330D4—101no—
331C2×C4—52no—
332C2×C4—62no—
333C2×C4—102no—
334C2×C4—102no—
335C2×C4—302no—
336C2×C4D5×Dic611yescharacteristic
337C2×C4#676511yescharacteristic
338C2×C4#676611yescharacteristic
339C2×C4D5×#6711yescharacteristic
340C2×C4D3×C22⋊D511yescharacteristic
341C2×C4#679011yescharacteristic
342C8—41no—
343C8—62no—
344C8—201no—
345C8—302no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—202no—
350C2×C3#6527811yescharacteristic
351C5#7000211yescharacteristic, complemented, Sylow
352C22—41no—
353C22—102no—
354C22—202no—
355C22D5×Dic3⋊C411yescharacteristic
356C22#9139611yescharacteristic
357C22#9144111yescharacteristic
358C4—102no—
359C4—122no—
360C4—602no—
361C4#9140711yescharacteristic
362C4#9142111yescharacteristic
363C4#9143111yescharacteristic
364C4#9157711yescharacteristic
365C3#1060133911yescharacteristic, complemented, Sylow
366C2—21no—
367C2—21no—
368C2—21no—
369C2—202no—
370C2#1174889111yescharacteristic
subgroupG/H
centerC4#91577
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC2×C3×C5#385
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1868
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #11751203C2semidirect
3. C5×#5102C2semidirect
6. #11745990C2semidirect
7. #11745989C2semidirect
64. #5102D5semidirect
304. C3×C5#1868semidirect
351. C5#70002semidirect
365. C3#10601339semidirect

Maximal subgroups

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

subgroupindex
#117541202
#117512032
C5×#51022
C3×#653992
#117486242
#117459902
#117459892
#106013393
#700025