Finite Group Databasebeta

← #14300387

Subgroups — #14300387

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#11754125C211yesmaximal, characteristic
2#11751100C211yesmaximal, characteristic, complemented
3C5×#5006C211yesmaximal, characteristic
4#11748441C211yesmaximal, characteristic, complemented
5#11748347C211yesmaximal, characteristic
6C3×#64753C211yesmaximal, characteristic, complemented
7#11745989C211yesmaximal, characteristic, complemented
8#10600837—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91288—22no—
17D3×#681—22no—
18#91286—22no—
19C4⋊(C3⋊#168)—22no—
20C5×#806C414yes—
21Dic3⋊#168—22no—
22(C2×D3)⋊#168—22no—
23#69034—51nomaximal, Hall
24#66153—31no—
25C5×#410—31no—
26#65523—31no—
27#65288—31no—
28#65288—31no—
29#64753—31no—
30#64753D311yescharacteristic, complemented
31C22×C3×C4×C5C2311yescharacteristic
32C2×C5×#67C2×C412yes—
33C5×#235—21no—
34C5×#235—21no—
35C5×#235—21no—
36C5×#235—21no—
37C2×C5×D12Q811yescharacteristic
38C2×C4×C5×D3D412yes—
39C2×C5×Dic6Q811yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C22⋊C4C2×C412yes—
42C3×C42×C5—21no—
43#6710—21no—
44#6710—21no—
45C2×C3⋊#168—21no—
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C3⋊#168D412yes—
49C5×#217C2×C412yes—
50C5×C4⋊Dic3—21no—
51C4×C5×Dic3—21no—
52C3×#681—21no—
53C3×#681—21no—
54C3×#681—21no—
55C3×#681—21no—
56C2×C3×#168—21no—
57C2×C3×#168D412yes—
58#6650—24no—
59D3×#168—24no—
60#5745—51no—
61#5129—51no—
62#5119—51no—
63#5006D511yescharacteristic
64#4999—51no—
65C3×#344—51no—
66#4559—51no—
67C2×C5×#41—31no—
68C5×#117—31no—
69C5×#117C2×D311yescharacteristic
70#4094—62no—
71#4094—62no—
72C2×#681—31no—
73C2×#681—62no—
74C2×#681C2×D311yescharacteristic
75C2×#681C2×D311yescharacteristic
76C22×#168—31no—
77C5×#99—34no—
78C22⋊#168—62no—
79C4⋊#168—62no—
80C4⋊#168—62no—
81#1868—151noSylow
82C23×C3×C5C22×C411yescharacteristic
83C22×C5×D3C4⋊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
91C5×#67—22no—
92C5×#67—22no—
93C2×C5×Dic3—22no—
94C2×C5×Dic3C4⋊C412yes—
95C5×D12—21no—
96C5×D12—21no—
97C4×C5×D3—22no—
98C4×C5×D3—22no—
99C5×Dic6—21no—
100C5×Dic6—21no—
101C3⋊#168—22no—
102C3⋊#168—41no—
103C3×#168—22no—
104C3×#168—41no—
105C2×#235C2×D511yescharacteristic
106C2×C3×M16—51no—
107C2×C3×M16—51no—
108C3×#117C2×D511yescharacteristic
109#926C2×D511yescharacteristic
110C2×#208—51no—
111C22×C3⋊C8—51no—
112#907—102no—
113D3×M16—102no—
114#901—102no—
115(C2×D3)⋊C8—102no—
116Dic3⋊C8—102no—
117#806Dic514yes—
118C4⋊(C3⋊C8)—102no—
119C5×#41—61no—
120C5×#41—61no—
121C5×#41—61no—
122C5×#41—61no—
123C2×C5×Q8—31no—
124C2×C5×D4—32no—
125C2×C5×D4—31no—
126C22×C4×C5—32no—
127C22×C4×C5C22×D311yescharacteristic
128C5×C4⋊C4—21no—
129C5×C4⋊C4—61no—
130C5×C22⋊C4—32no—
131C5×C22⋊C4C4×D312yes—
132C42×C5—21no—
133C42×C5—61no—
134#681—21no—
135#681—21no—
136#681—21no—
137#681—21no—
138#681—64no—
139#681—61no—
140#681—61no—
141C2×#168—21no—
142C2×#168—32no—
143C2×#168—64no—
144C2×#168—61no—
145C2×#168—61no—
146C2×#168—61no—
147C2×#168D1212yes—
148#568—151no—
149#424—151no—
150#424—151no—
151#410—31no—
152#408—151no—
153#344—51no—
154#344—151no—
155C22×C3×C5—41no—
156C22×C3×C5C2×C4⋊C411yescharacteristic
157C22×C3×C5C4×D411yescharacteristic
158C22×C3×C5C4×D411yescharacteristic
159C2×C5×D3—22no—
160C2×C5×D3—42no—
161C3×C4×C5—42no—
162C3×C4×C5#12011yescharacteristic
163C3×C4×C5C22⋊Q811yescharacteristic
164C3×C4×C5C22⋊Q811yescharacteristic
165C3×C4×C5#12311yescharacteristic
166C5×Dic3—22no—
167C5×Dic3—42no—
168C22×C3×C4C22×D511yescharacteristic
169C2×#67C2×Dic512yes—
170#235—21no—
171#235—21no—
172#235—21no—
173#235—21no—
174C2×D12Dic1011yescharacteristic
175C2×C4×D3D2012yes—
176C2×Dic6Dic1011yescharacteristic
177C3×M16—101no—
178C3×M16—101no—
179C3×M16—101no—
180C3×M16—101no—
181C2×C3×C8—52no—
182C2×C3×C8—101no—
183C3×C4⋊C4—21no—
184C3×C22⋊C4C2×Dic512yes—
185C3×C42—21no—
186#217C2×Dic512yes—
187C4⋊Dic3—21no—
188C4×Dic3—21no—
189#208—101no—
190#208—101no—
191C2×C3⋊C8—52no—
192C2×C3⋊C8—101no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195ΓL(1,𝔽25)—104no—
196D3×C8—104no—
197C23×C5—32no—
198C23×C5C2×C4×D311yescharacteristic
199C5×Q8—61no—
200C5×Q8—61no—
201C5×D4—62no—
202C5×D4—62no—
203C5×D4—61no—
204C5×D4—61no—
205C2×C4×C5—22no—
206C2×C4×C5—32no—
207C2×C4×C5—62no—
208C2×C4×C5—62no—
209C2×C4×C5—62no—
210C2×C4×C5C2×D1211yescharacteristic
211C2×C4×C5#23511yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5#23711yescharacteristic
215C2×C4×C5D3×Q811yescharacteristic
216#168—22no—
217#168—41no—
218#168—62no—
219#168—121no—
220C2×#41—31no—
221#131—302no—
222#131—302no—
223C2×M16—51no—
224C2×M16—51no—
225C2×M16—151no—
226C2×M16—302no—
227C22×C8—151no—
228#117—31no—
229#117D3×D511yescharacteristic
230C4⋊C8—302no—
231C4⋊C8—302no—
232#99—34no—
233C22⋊C8—302no—
234C2×C3×C5—21no—
235C2×C3×C5—21no—
236C2×C3×C5—21no—
237C2×C3×C5#38511yescharacteristic
238C5×D3—42no—
239C23×C3C22×Dic511yescharacteristic
240C22×D3C4⋊Dic512yes—
241C2×C3×C4—22no—
242C2×C3×C4C2×Dic1011yescharacteristic
243C2×C3×C4C2×D2011yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4#71111yescharacteristic
247C2×C3×C4#71111yescharacteristic
248#67—22no—
249#67—22no—
250C2×Dic3—22no—
251C2×Dic3C4⋊Dic512yes—
252D12—21no—
253D12—21no—
254C4×D3—22no—
255C4×D3—22no—
256Dic6—21no—
257Dic6—21no—
258C3×C8—102no—
259C3×C8—201no—
260C3⋊C8—102no—
261C3⋊C8—201no—
262C22×C5—41no—
263C22×C5—62no—
264C22×C5—122no—
265C22×C5C4×D1211yescharacteristic
266C22×C5#67⋊C411yescharacteristic
267C22×C5D3×C4⋊C411yescharacteristic
268C4×C5—42no—
269C4×C5—62no—
270C4×C5—122no—
271C4×C5#88211yescharacteristic
272C4×C5#88311yescharacteristic
273C4×C5#89611yescharacteristic
274C4×C5#89711yescharacteristic
275#41—61no—
276#41—61no—
277#41—61no—
278#41—61no—
279C2×Q8—31no—
280C2×D4—32no—
281C2×D4—31no—
282C22×C4—32no—
283C22×C4C2×D3×D511yescharacteristic
284M16—101no—
285M16—101no—
286M16—101no—
287M16—101no—
288M16—304no—
289M16—301no—
290M16—301no—
291C2×C8—52no—
292C2×C8—101no—
293C2×C8—152no—
294C2×C8—304no—
295C2×C8—301no—
296C2×C8—301no—
297C2×C8—301no—
298C4⋊C4—21no—
299C4⋊C4—61no—
300C22⋊C4—32no—
301C22⋊C4D3×Dic512yes—
302C42—21no—
303C42—61no—
304C3×C5#186811yescharacteristic, complemented, Hall
305C22×C3—41no—
306C22×C3C2×C4⋊Dic511yescharacteristic
307C22×C3D4×Dic511yescharacteristic
308C22×C3D4×Dic511yescharacteristic
309C2×D3—22no—
310C2×D3—42no—
311C3×C4—42no—
312C3×C4#402411yescharacteristic
313C3×C4#402411yescharacteristic
314C3×C4#402811yescharacteristic
315C3×C4#403211yescharacteristic
316Dic3—22no—
317Dic3—42no—
318C2×C5—21no—
319C2×C5—21no—
320C2×C5—21no—
321C2×C5—122no—
322C2×C5#466811yescharacteristic
323C23—32no—
324C23C2×D3×Dic511yescharacteristic
325Q8—61no—
326Q8—61no—
327D4—62no—
328D4—62no—
329D4—61no—
330D4—61no—
331C2×C4—22no—
332C2×C4—32no—
333C2×C4—62no—
334C2×C4—62no—
335C2×C4—62no—
336C2×C4D3×Dic1011yescharacteristic
337C2×C4#677211yescharacteristic
338C2×C4D5×D1211yescharacteristic
339C2×C4D3×D2011yescharacteristic
340C2×C4#678011yescharacteristic
341C2×C4#679011yescharacteristic
342C8—102no—
343C8—201no—
344C8—302no—
345C8—601no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3#6523911yescharacteristic
350D3—42no—
351C5#6903411yescharacteristic, complemented, Sylow
352C22—41no—
353C22—62no—
354C22—122no—
355C22Dic5×D1211yescharacteristic
356C22D3×C4⋊Dic511yescharacteristic
357C22#67⋊Dic511yescharacteristic
358C4—42no—
359C4—62no—
360C4—122no—
361C4#9141711yescharacteristic
362C4#9143211yescharacteristic
363C4#9145711yescharacteristic
364C4#9147611yescharacteristic
365C3#1060083711yescharacteristic, complemented, Sylow
366C2—21no—
367C2—21no—
368C2—21no—
369C2—122no—
370C2#1174890311yescharacteristic
subgroupG/H
centerC4#91476
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#385
prime radicalC2×C5×#235C22
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
2. #11751100C2semidirect
4. #11748441C2semidirect
6. C3×#64753C2semidirect
7. #11745989C2semidirect
30. #64753D3semidirect
304. C3×C5#1868semidirect
351. C5#69034semidirect
365. C3#10600837semidirect

Maximal subgroups

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

subgroupindex
#117541252
#117511002
C5×#50062
#117484412
#117483472
C3×#647532
#117459892
#106008373
#690345