Finite Group Databasebeta

← #14300388

Subgroups — #14300388

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#11754130C211yesmaximal, characteristic
2#11751107C211yesmaximal, characteristic
3C3×#65288C211yesmaximal, characteristic, complemented
4#11748435C211yesmaximal, characteristic, complemented
5#11748349C211yesmaximal, characteristic
6C5×#4533C211yesmaximal, characteristic, complemented
7#11745991C211yesmaximal, characteristic, complemented
8#10599827—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×C5×#208C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16#91292—22no—
17#91291—22no—
18#91290—22no—
19#91090C414yes—
20C3×C4⋊#168—22no—
21#90983—22no—
22#90957—22no—
23#70546—51nomaximal, Hall
24#66079—31no—
25#65418—31no—
26#65408—31no—
27#65295—31no—
28#65288D311yescharacteristic, complemented
29C5×#344—31no—
30#64779—31no—
31C22×C3×C4×C5C2311yescharacteristic
32C2×#1220C2×C412yes—
33#6817—21no—
34#6817—21no—
35#6817—21no—
36#6817—21no—
37C2×D60Q811yescharacteristic
38C2×C4×D15D412yes—
39C2×Dic30Q811yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C22⋊C4C2×C412yes—
42C3×C42×C5—21no—
43#6719C2×C412yes—
44C4⋊Dic15—21no—
45C4×Dic15—21no—
46C5×#208—21no—
47C5×#208—21no—
48C5×#208—21no—
49C5×#208—21no—
50C2×C5×C3⋊C8—21no—
51C2×C5×C3⋊C8D412yes—
52C3×#681—21no—
53C3×#681—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57C2×C3×#168D412yes—
58#6651—24no—
59#6648—24no—
60#5745—51no—
61C3×#424—51no—
62#5110—51no—
63#5102—51no—
64#5006—51no—
65#4556—51no—
66#4533D511yescharacteristic, complemented
67C2×#709—31no—
68C2×C5×M16—31no—
69C2×C5×M16—31no—
70C5×#117C2×D311yescharacteristic
71#4072—31no—
72C2×#681C2×D311yescharacteristic
73C22×#168C2×D311yescharacteristic
74#4053—62no—
75D5×M16—62no—
76#4047—62no—
77#3952—62no—
78#3946—62no—
79#3938—34no—
80C4⋊#168—22no—
81#1868—151noSylow
82C23×C3×C5C22×C411yescharacteristic
83C22×D15C4⋊C412yes—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×Q811yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90C2×C3×C4×C5#4111yescharacteristic
91#1220—22no—
92#1220—22no—
93C2×Dic15—22no—
94C2×Dic15C4⋊C412yes—
95D60—21no—
96D60—21no—
97C4×D15—22no—
98C4×D15—22no—
99Dic30—21no—
100Dic30—21no—
101C3×#168—22no—
102C3×#168—41no—
103C5×C3⋊C8—22no—
104C5×C3⋊C8—41no—
105C2×#235—51no—
106C2×C3×M16—51no—
107C22×C3×C8—51no—
108C3×#117C2×D511yescharacteristic
109#926—51no—
110C2×#208C2×D511yescharacteristic
111C2×#208C2×D511yescharacteristic
112#907—102no—
113D3×M16—102no—
114#901—102no—
115C3×C4⋊C8—102no—
116(C2×D3)⋊C8—102no—
117Dic3⋊C8—102no—
118#806—54no—
119C22×C4×C5C22×D311yescharacteristic
120C2×C22⋊D5—32no—
121#709—61no—
122#709—61no—
123#709—61no—
124#709—61no—
125C2×D20—31no—
126C2×C4×D5—32no—
127C2×Dic10—31no—
128C5×M16—61no—
129C5×M16—61no—
130C5×M16—61no—
131C5×M16—61no—
132C2×C5×C8—32no—
133C2×C5×C8—61no—
134C5×C4⋊C4—21no—
135C5×C22⋊C4C4×D312yes—
136C42×C5—21no—
137C22⋊Dic5—32no—
138C4⋊Dic5—61no—
139C4×Dic5—61no—
140#681—21no—
141#681—21no—
142C2×#168—21no—
143C2×#168—21no—
144C2×#168—21no—
145C2×#168#6712yes—
146#676—64no—
147C8×D5—64no—
148#568—151no—
149#424—51no—
150#424—151no—
151#410—151no—
152#408—151no—
153#344—31no—
154#344—151no—
155C22×C3×C5—41no—
156C22×C3×C5C2×C4⋊C411yescharacteristic
157C22×C3×C5C4×D411yescharacteristic
158C22×C3×C5C4×D411yescharacteristic
159C2×D15—22no—
160C2×D15—42no—
161C3×C4×C5—42no—
162C3×C4×C5#12011yescharacteristic
163C3×C4×C5C22⋊Q811yescharacteristic
164C3×C4×C5C22⋊Q811yescharacteristic
165C3×C4×C5#12311yescharacteristic
166Dic15—22no—
167Dic15—42no—
168C22×C3×C4C22×D511yescharacteristic
169C2×#67—52no—
170#235—101no—
171#235—101no—
172#235—101no—
173#235—101no—
174C2×D12—51no—
175C2×C4×D3—52no—
176C2×Dic6—51no—
177C3×M16—101no—
178C3×M16—101no—
179C2×C3×C8—52no—
180C2×C3×C8—101no—
181C2×C3×C8—101no—
182C2×C3×C8—101no—
183C3×C4⋊C4—21no—
184C3×C22⋊C4C4×D512yes—
185C3×C42—21no—
186#217—52no—
187C4⋊Dic3—101no—
188C4×Dic3—101no—
189#208—21no—
190#208—21no—
191#208—21no—
192#208—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8D2012yes—
195ΓL(1,𝔽25)—104no—
196D3×C8—104no—
197C23×C5C2×C4×D311yescharacteristic
198C22×D5—32no—
199C2×C4×C5—22no—
200C2×C4×C5#23511yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5D3×Q811yescharacteristic
204C2×C4×C5#23911yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C22⋊D5—62no—
207C22⋊D5—62no—
208C2×Dic5—32no—
209C2×Dic5—62no—
210D20—61no—
211D20—61no—
212C4×D5—62no—
213C4×D5—62no—
214Dic10—61no—
215Dic10—61no—
216C5×C8—62no—
217C5×C8—121no—
218#168—22no—
219#168—41no—
220C2×#41—151no—
221#131—302no—
222#131—302no—
223C2×M16—31no—
224C2×M16—31no—
225C2×M16—51no—
226C2×M16—302no—
227C22×C8—51no—
228#117—151no—
229#117D3×D511yescharacteristic
230C4⋊C8—102no—
231C4⋊C8—302no—
232#99—154no—
233C22⋊C8—302no—
234C2×C3×C5—21no—
235C2×C3×C5—21no—
236C2×C3×C5—21no—
237C2×C3×C5#38511yescharacteristic
238D15—42no—
239C23×C3C2×C4×D511yescharacteristic
240C22×D3—52no—
241C2×C3×C4—22no—
242C2×C3×C4C2×D2011yescharacteristic
243C2×C3×C4#70911yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4#71111yescharacteristic
247C2×C3×C4Q8×D511yescharacteristic
248#67—102no—
249#67—102no—
250C2×Dic3—52no—
251C2×Dic3—102no—
252D12—101no—
253D12—101no—
254C4×D3—102no—
255C4×D3—102no—
256Dic6—101no—
257Dic6—101no—
258C3×C8—102no—
259C3×C8—201no—
260C3⋊C8—22no—
261C3⋊C8—41no—
262C22×C5—41no—
263C22×C5D3×C4⋊C411yescharacteristic
264C22×C5#89311yescharacteristic
265C22×C5C4×#6711yescharacteristic
266C2×D5—62no—
267C2×D5—122no—
268C4×C5—42no—
269C4×C5#89411yescharacteristic
270C4×C5#89611yescharacteristic
271C4×C5#93711yescharacteristic
272C4×C5#94611yescharacteristic
273Dic5—62no—
274Dic5—122no—
275#41—301no—
276#41—301no—
277#41—301no—
278#41—301no—
279C2×Q8—151no—
280C2×D4—152no—
281C2×D4—151no—
282C22×C4—152no—
283C22×C4C2×D3×D511yescharacteristic
284M16—61no—
285M16—61no—
286M16—61no—
287M16—61no—
288M16—101no—
289M16—101no—
290M16—304no—
291C2×C8—32no—
292C2×C8—52no—
293C2×C8—61no—
294C2×C8—101no—
295C2×C8—101no—
296C2×C8—101no—
297C2×C8—304no—
298C4⋊C4—21no—
299C4⋊C4—301no—
300C22⋊C4—152no—
301C22⋊C4#120012yes—
302C42—21no—
303C42—301no—
304C3×C5#186811yescharacteristic, complemented, Hall
305C22×C3—41no—
306C22×C3C4×D2011yescharacteristic
307C22×C3#402711yescharacteristic
308C22×C3D5×C4⋊C411yescharacteristic
309C2×D3—102no—
310C2×D3—202no—
311C3×C4—42no—
312C3×C4#402811yescharacteristic
313C3×C4#402911yescharacteristic
314C3×C4#404211yescharacteristic
315C3×C4#404311yescharacteristic
316Dic3—102no—
317Dic3—202no—
318C2×C5—21no—
319C2×C5—21no—
320C2×C5—21no—
321C2×C5#498911yescharacteristic
322D5—122no—
323C23—152no—
324C23C2×#120011yescharacteristic
325Q8—301no—
326Q8—301no—
327D4—302no—
328D4—302no—
329D4—301no—
330D4—301no—
331C2×C4—22no—
332C2×C4—152no—
333C2×C4—302no—
334C2×C4—302no—
335C2×C4—302no—
336C2×C4#676911yescharacteristic
337C2×C4D15⋊Q811yescharacteristic
338C2×C4D3×D2011yescharacteristic
339C2×C4#677711yescharacteristic
340C2×C4#678211yescharacteristic
341C2×C4D5×#6711yescharacteristic
342C8—62no—
343C8—102no—
344C8—121no—
345C8—201no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3#6495711yescharacteristic
350D3—202no—
351C5#7054611yescharacteristic, complemented, Sylow
352C22—41no—
353C22—302no—
354C22—602no—
355C22#9142811yescharacteristic
356C22#9143711yescharacteristic
357C22#9155211yescharacteristic
358C4—42no—
359C4—302no—
360C4—602no—
361C4#9141111yescharacteristic
362C4#9142911yescharacteristic
363C4#9143811yescharacteristic
364C4#9147411yescharacteristic
365C3#1059982711yescharacteristic, complemented, Sylow
366C2—21no—
367C2—21no—
368C2—21no—
369C2—602no—
370C2#1174889811yescharacteristic
subgroupG/H
centerC4#91474
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#385
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1868
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. C3×#65288C2semidirect
4. #11748435C2semidirect
6. C5×#4533C2semidirect
7. #11745991C2semidirect
28. #65288D3semidirect
66. #4533D5semidirect
304. C3×C5#1868semidirect
351. C5#70546semidirect
365. C3#10599827semidirect

Maximal subgroups

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

subgroupindex
#117541302
#117511072
C3×#652882
#117484352
#117483492
C5×#45332
#117459912
#105998273
#705465