Finite Group Databasebeta

← #14299697

Subgroups — #14299697

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754130C211yesmaximal, characteristic
2#11751211C211yesmaximal, characteristic
3#11748480C211yesmaximal, characteristic, complemented
4#11748476C211yesmaximal, characteristic, complemented
5#11748357C211yesmaximal, characteristic
6C5×#4552C211yesmaximal, characteristic, complemented
7C3×#64772C211yesmaximal, characteristic, complemented
8#10599738—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×C5×#208C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91292—22no—
17#91291—22no—
18#91290—22no—
19#91104—22no—
20#90993—22no—
21#90991—22no—
22#90963C412yes—
23#90960C412yes—
24#68945—51nomaximal, Hall
25#66079—31no—
26#65421—31no—
27#65414—31no—
28#65413—31no—
29#65399—31no—
30C5×#341—31no—
31#64772D311yescharacteristic, complemented
32C22×C3×C4×C5C2311yescharacteristic
33C2×#1220Q812yes—
34#6817—21no—
35#6817—21no—
36#6817—21no—
37#6817—21no—
38C2×D60C2×C411yescharacteristic
39C2×C4×D15D412yes—
40C2×Dic30C2×C411yescharacteristic
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8—21no—
44#6710—21no—
45#6710—21no—
46C2×C3⋊#168—21no—
47C5×#208—21no—
48C5×#208—21no—
49C5×#208C2×C412yes—
50C5×#208D412yes—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×#681—21no—
54C3×#681—21no—
55C3×#681C2×C412yes—
56C3×#681D412yes—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59#6651—24no—
60#6648—24no—
61#5745—51no—
62#5132—51no—
63#5125—51no—
64#5124—51no—
65#5110—51no—
66C3×#341—51no—
67#4552D511yescharacteristic, complemented
68C2×#709—31no—
69C2×C5×M16—31no—
70C2×C5×M16—31no—
71C22×C5×C8C2×D311yescharacteristic
72C2×#681—31no—
73C2×#681C2×D311yescharacteristic
74C2×#681C2×D311yescharacteristic
75#4053—62no—
76D5×M16—62no—
77#4047—62no—
78#3956—32no—
79#3955—32no—
80#3954—62no—
81#3952—62no—
82#3951—62no—
83#1858—151noSylow
84C23×C3×C5C2×Q811yescharacteristic
85C22×D15C4⋊C412yes—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5#4111yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92#1220—22no—
93#1220—22no—
94C2×Dic15C4⋊C412yes—
95D60—21no—
96D60—21no—
97C4×D15—22no—
98C4×D15—22no—
99Dic30—21no—
100Dic30—21no—
101C3×C5×C8—41no—
102C3⋊#168—41no—
103C3×#168—22no—
104C3×#168—22no—
105C5×C3⋊C8—22no—
106C5×C3⋊C8—22no—
107C2×#235—51no—
108C2×C3×M16—51no—
109C2×C3×M16—51no—
110C22×C3×C8C2×D511yescharacteristic
111C2×#208—51no—
112C2×#208C2×D511yescharacteristic
113C2×#208C2×D511yescharacteristic
114#907—102no—
115D3×M16—102no—
116#901—102no—
117#824—52no—
118#823—52no—
119#822—102no—
120(C2×D3)⋊C8—102no—
121#819—102no—
122C22×C4×C5C22×D311yescharacteristic
123C2×C22⋊D5—32no—
124#709—61no—
125#709—61no—
126#709—61no—
127#709—61no—
128C2×D20—31no—
129C2×C4×D5—32no—
130C2×Dic10—31no—
131C5×M16—32no—
132C5×M16—32no—
133C5×M16—61no—
134C5×M16—61no—
135C2×C5×C8—21no—
136C2×C5×C8—21no—
137C2×C5×C8—21no—
138C2×C5×C8—61no—
139C2×C5×C8—61no—
140#681—21no—
141#681—21no—
142#681—61no—
143#681—61no—
144#681C4×D312yes—
145#681D1212yes—
146C2×#168—21no—
147C2×#168—21no—
148C2×#168—61no—
149#676—64no—
150C8×D5—64no—
151#568—151no—
152#430—151no—
153#430—151no—
154#413—151no—
155#408—151no—
156#341—31no—
157#341—51no—
158C22×C3×C5—41no—
159C22×C3×C5C2×C4⋊C411yescharacteristic
160C22×C3×C5C22⋊Q811yescharacteristic
161C22×C3×C5C22⋊Q811yescharacteristic
162C2×D15—22no—
163C2×D15—42no—
164C3×C4×C5C4×D411yescharacteristic
165C3×C4×C5C4×D411yescharacteristic
166C3×C4×C5#12011yescharacteristic
167C3×C4×C5#12311yescharacteristic
168Dic15—22no—
169C22×C3×C4C22×D511yescharacteristic
170C2×#67—52no—
171#235—101no—
172#235—101no—
173#235—101no—
174#235—101no—
175C2×D12—51no—
176C2×C4×D3—52no—
177C2×Dic6—51no—
178C3×M16—52no—
179C3×M16—52no—
180C3×M16—101no—
181C3×M16—101no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—101no—
186C2×C3×C8—101no—
187#208—21no—
188#208—21no—
189#208—101no—
190#208—101no—
191#208C4×D512yes—
192#208D2012yes—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—101no—
196ΓL(1,𝔽25)—104no—
197D3×C8—104no—
198C23×C5D3×Q811yescharacteristic
199C22×D5—32no—
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5C2×D1211yescharacteristic
202C2×C4×C5#23511yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5#23711yescharacteristic
206C22⋊D5—62no—
207C22⋊D5—62no—
208C2×Dic5—32no—
209D20—61no—
210D20—61no—
211C4×D5—62no—
212C4×D5—62no—
213Dic10—61no—
214Dic10—61no—
215C5×C8—41no—
216C5×C8—62no—
217C5×C8—62no—
218#168—22no—
219#168—22no—
220#168—121no—
221C2×#41—151no—
222#131—302no—
223#131—302no—
224C2×M16—31no—
225C2×M16—31no—
226C2×M16—51no—
227C2×M16—51no—
228C2×M16—151no—
229C2×M16—302no—
230C22×C8D3×D511yescharacteristic
231#108—302no—
232#108—302no—
233#101—152no—
234#100—152no—
235C22⋊C8—302no—
236C2×C3×C5—21no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5#38511yescharacteristic
240D15—42no—
241C23×C3Q8×D511yescharacteristic
242C22×D3—52no—
243C2×C3×C4C2×C4×D511yescharacteristic
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4#70911yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4#71111yescharacteristic
249#67—102no—
250#67—102no—
251C2×Dic3—52no—
252D12—101no—
253D12—101no—
254C4×D3—102no—
255C4×D3—102no—
256Dic6—101no—
257Dic6—101no—
258C3×C8—41no—
259C3×C8—102no—
260C3×C8—102no—
261C3⋊C8—22no—
262C3⋊C8—22no—
263C3⋊C8—201no—
264C22×C5—41no—
265C22×C5D3×C4⋊C411yescharacteristic
266C22×C5#89611yescharacteristic
267C22×C5#89711yescharacteristic
268C2×D5—62no—
269C2×D5—122no—
270C4×C5C4×D1211yescharacteristic
271C4×C5#67⋊C411yescharacteristic
272C4×C5#88211yescharacteristic
273C4×C5#88311yescharacteristic
274Dic5—62no—
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—32no—
285M16—32no—
286M16—52no—
287M16—52no—
288M16—61no—
289M16—61no—
290M16—101no—
291M16—101no—
292M16—304no—
293M16—301no—
294M16—301no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—101no—
301C2×C8—101no—
302C2×C8—304no—
303C2×C8—301no—
304C3×C5#185811yescharacteristic, complemented, Hall
305C22×C3—41no—
306C22×C3D5×C4⋊C411yescharacteristic
307C22×C3#404211yescharacteristic
308C22×C3#404311yescharacteristic
309C2×D3—102no—
310C2×D3—202no—
311C3×C4C4×D2011yescharacteristic
312C3×C4#402711yescharacteristic
313C3×C4#402811yescharacteristic
314C3×C4#402911yescharacteristic
315Dic3—102no—
316C2×C5—21no—
317C2×C5—21no—
318C2×C5—21no—
319C2×C5#466811yescharacteristic
320D5—122no—
321C23—152no—
322C23D15⋊Q811yescharacteristic
323Q8—301no—
324Q8—301no—
325D4—302no—
326D4—302no—
327D4—301no—
328D4—301no—
329C2×C4—152no—
330C2×C4—302no—
331C2×C4—302no—
332C2×C4C4×D3×D511yescharacteristic
333C2×C4D5×D1211yescharacteristic
334C2×C4D3×D2011yescharacteristic
335C2×C4#677911yescharacteristic
336C2×C4#678211yescharacteristic
337C2×C4#679011yescharacteristic
338C8—41no—
339C8—62no—
340C8—62no—
341C8—102no—
342C8—102no—
343C8—601no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3#6495711yescharacteristic
348D3—202no—
349C5#6894511yescharacteristic, complemented, Sylow
350C22—41no—
351C22—302no—
352C22—602no—
353C22#9140411yescharacteristic
354C22#9141911yescharacteristic
355C22#9142911yescharacteristic
356C4—302no—
357C4#9139511yescharacteristic
358C4#9140511yescharacteristic
359C4#9147611yescharacteristic
360C4#9156211yescharacteristic
361C3#1059973811yescharacteristic, complemented, Sylow
362C2—21no—
363C2—21no—
364C2—21no—
365C2—602no—
366C2#1174889511yescharacteristic
subgroupG/H
centerC4#91476
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC2×C3×C5#385
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1858
LCSG ▷ C2×C3×C4×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
3. #11748480C2semidirect
4. #11748476C2semidirect
6. C5×#4552C2semidirect
7. C3×#64772C2semidirect
31. #64772D3semidirect
67. #4552D5semidirect
304. C3×C5#1858semidirect
349. C5#68945semidirect
361. C3#10599738semidirect

Maximal subgroups

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

subgroupindex
#117541302
#117512112
#117484802
#117484762
#117483572
C5×#45522
C3×#647722
#105997383
#689455