Finite Group Databasebeta

← #14299698

Subgroups — #14299698

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#11754125C211yesmaximal, characteristic
2C5×#5110C211yesmaximal, characteristic
3#11748478C211yesmaximal, characteristic, complemented
4#11748476C211yesmaximal, characteristic, complemented
5#11748355C211yesmaximal, characteristic
6#11746373C211yesmaximal, characteristic, complemented
7C3×#64772C211yesmaximal, characteristic, complemented
8#10600794—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91288—22no—
17D3×#681—22no—
18#91286—22no—
19C5×(C2×D3)⋊C8—22no—
20#90992—22no—
21#90991—22no—
22#90962C412yes—
23#90959C412yes—
24#68945—51nomaximal, Hall
25#66153—31no—
26C5×#408—31no—
27#65526—31no—
28#65413—31no—
29#65413—31no—
30#64772—31no—
31#64772D311yescharacteristic, complemented
32C22×C3×C4×C5C2311yescharacteristic
33C2×C5×#67Q812yes—
34C5×#235—21no—
35C5×#235—21no—
36C5×#235—21no—
37C5×#235—21no—
38C2×C5×D12C2×C411yescharacteristic
39C2×C4×C5×D3D412yes—
40C2×C5×Dic6C2×C411yescharacteristic
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8—21no—
44#6710—21no—
45#6710—21no—
46#6710C2×C412yes—
47#6710D412yes—
48C2×C3⋊#168—21no—
49C2×C3⋊#168—21no—
50C5×#208—21no—
51C5×#208—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#6650—24no—
60D3×#168—24no—
61#5745—51no—
62#5132—51no—
63#5125—51no—
64#5124—51no—
65#5110D511yescharacteristic
66C3×#341—51no—
67#4552—51no—
68C2×C5×#41—31no—
69C2×C5×M16—31no—
70C22×C5×C8C2×D311yescharacteristic
71#4094—62no—
72#4094—62no—
73C2×#681—31no—
74C2×#681—31no—
75C2×#681—62no—
76C2×#681C2×D311yescharacteristic
77C2×#681C2×D311yescharacteristic
78C5×C22⋊C8—62no—
79#3968—32no—
80#3965—32no—
81#3954—62no—
82#3954—62no—
83#1858—151noSylow
84C23×C3×C5C2×Q811yescharacteristic
85C22×C5×D3C4⋊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
92C5×#67—22no—
93C5×#67—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×C5×C8—41no—
102C3⋊#168—22no—
103C3⋊#168—22no—
104C3×#168—22no—
105C3×#168—22no—
106C5×C3⋊C8—41no—
107C2×#235C2×D511yescharacteristic
108C2×C3×M16—51no—
109C2×C3×M16—51no—
110C22×C3×C8C2×D511yescharacteristic
111C2×#208—51no—
112C2×#208—51no—
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—22no—
121#819—102no—
122C5×#41—61no—
123C5×#41—61no—
124C5×#41—61no—
125C5×#41—61no—
126C2×C5×Q8—31no—
127C2×C5×D4—32no—
128C2×C5×D4—31no—
129C22×C4×C5—32no—
130C22×C4×C5C22×D311yescharacteristic
131C5×M16—61no—
132C5×M16—61no—
133C2×C5×C8—21no—
134C2×C5×C8—21no—
135C2×C5×C8—21no—
136C2×C5×C8—61no—
137#681—21no—
138#681—21no—
139#681—32no—
140#681—32no—
141#681—64no—
142#681—61no—
143#681—61no—
144#681C4×D312yes—
145#681D1212yes—
146C2×#168—21no—
147C2×#168—21no—
148C2×#168—64no—
149C2×#168—61no—
150C2×#168—61no—
151#568—151no—
152#430—151no—
153#430—151no—
154#413—151no—
155#408—31no—
156#341—51no—
157#341—151no—
158C22×C3×C5—41no—
159C22×C3×C5C2×C4⋊C411yescharacteristic
160C22×C3×C5C22⋊Q811yescharacteristic
161C22×C3×C5C22⋊Q811yescharacteristic
162C2×C5×D3—22no—
163C2×C5×D3—42no—
164C3×C4×C5C4×D411yescharacteristic
165C3×C4×C5C4×D411yescharacteristic
166C3×C4×C5#12011yescharacteristic
167C3×C4×C5#12311yescharacteristic
168C5×Dic3—22no—
169C22×C3×C4C22×D511yescharacteristic
170C2×#67Dic1012yes—
171#235—21no—
172#235—21no—
173#235—21no—
174#235—21no—
175C2×D12C4×D511yescharacteristic
176C2×C4×D3C22⋊D512yes—
177C2×Dic6C4×D511yescharacteristic
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—52no—
190#208—52no—
191#208—101no—
192#208—101no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196ΓL(1,𝔽25)—104no—
197D3×C8—104no—
198C23×C5—32no—
199C23×C5D3×Q811yescharacteristic
200C5×Q8—61no—
201C5×Q8—61no—
202C5×D4—62no—
203C5×D4—62no—
204C5×D4—61no—
205C5×D4—61no—
206C2×C4×C5—32no—
207C2×C4×C5—62no—
208C2×C4×C5—62no—
209C2×C4×C5C2×C4×D311yescharacteristic
210C2×C4×C5C2×D1211yescharacteristic
211C2×C4×C5#23511yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5#23711yescharacteristic
215C5×C8—41no—
216C5×C8—121no—
217#168—22no—
218#168—22no—
219#168—62no—
220#168—62no—
221C2×#41—31no—
222#131—302no—
223#131—302no—
224C2×M16—31no—
225C2×M16—51no—
226C2×M16—51no—
227C2×M16—151no—
228C2×M16—151no—
229C2×M16—302no—
230C22×C8D3×D511yescharacteristic
231#108—302no—
232#108—302no—
233#101—152no—
234#100—152no—
235C22⋊C8—62no—
236C2×C3×C5—21no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5#38511yescharacteristic
240C5×D3—42no—
241C23×C3C2×Dic1011yescharacteristic
242C22×D3#68312yes—
243C2×C3×C4C2×C4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4#71111yescharacteristic
247C2×C3×C4#71111yescharacteristic
248C2×C3×C4C2×C22⋊D511yescharacteristic
249#67—22no—
250#67—22no—
251C2×Dic3#68312yes—
252D12—21no—
253D12—21no—
254C4×D3—22no—
255C4×D3—22no—
256Dic6—21no—
257Dic6—21no—
258C3×C8—41no—
259C3×C8—102no—
260C3×C8—102no—
261C3⋊C8—41no—
262C3⋊C8—102no—
263C3⋊C8—102no—
264C22×C5—41no—
265C22×C5—62no—
266C22×C5—122no—
267C22×C5D3×C4⋊C411yescharacteristic
268C22×C5#89611yescharacteristic
269C22×C5#89711yescharacteristic
270C4×C5—62no—
271C4×C5C4×D1211yescharacteristic
272C4×C5#67⋊C411yescharacteristic
273C4×C5#88211yescharacteristic
274C4×C5#88311yescharacteristic
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—52no—
285M16—52no—
286M16—61no—
287M16—61no—
288M16—101no—
289M16—101no—
290M16—152no—
291M16—152no—
292M16—304no—
293M16—301no—
294M16—301no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—61no—
299C2×C8—101no—
300C2×C8—101no—
301C2×C8—304no—
302C2×C8—301no—
303C2×C8—301no—
304C3×C5#185811yescharacteristic, complemented, Hall
305C22×C3—41no—
306C22×C3#402411yescharacteristic
307C22×C3#402411yescharacteristic
308C22×C3C2×#68311yescharacteristic
309C2×D3—22no—
310C2×D3—42no—
311C3×C4#402711yescharacteristic
312C3×C4#402711yescharacteristic
313C3×C4#408111yescharacteristic
314C3×C4#408311yescharacteristic
315Dic3—22no—
316C2×C5—21no—
317C2×C5—21no—
318C2×C5—21no—
319C2×C5—122no—
320C2×C5#466811yescharacteristic
321C23—32no—
322C23D3×Dic1011yescharacteristic
323Q8—61no—
324Q8—61no—
325D4—62no—
326D4—62no—
327D4—61no—
328D4—61no—
329C2×C4—32no—
330C2×C4—62no—
331C2×C4—62no—
332C2×C4C4×D3×D511yescharacteristic
333C2×C4D5×D1211yescharacteristic
334C2×C4#677711yescharacteristic
335C2×C4#678011yescharacteristic
336C2×C4#678211yescharacteristic
337C2×C4D3×C22⋊D511yescharacteristic
338C8—41no—
339C8—102no—
340C8—102no—
341C8—121no—
342C8—302no—
343C8—302no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3#6523511yescharacteristic
348D3—42no—
349C5#6894511yescharacteristic, complemented, Sylow
350C22—41no—
351C22—62no—
352C22—122no—
353C22D3×#68311yescharacteristic
354C22#9141711yescharacteristic
355C22#9143611yescharacteristic
356C4—62no—
357C4#9140511yescharacteristic
358C4#9144211yescharacteristic
359C4#9147511yescharacteristic
360C4#9155511yescharacteristic
361C3#1060079411yescharacteristic, complemented, Sylow
362C2—21no—
363C2—21no—
364C2—21no—
365C2—122no—
366C2#1174889311yescharacteristic
subgroupG/H
centerC4#91475
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC2×C3×C5#385
prime radicalC2×C5×#235C22
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. #11748478C2semidirect
4. #11748476C2semidirect
6. #11746373C2semidirect
7. C3×#64772C2semidirect
31. #64772D3semidirect
304. C3×C5#1858semidirect
349. C5#68945semidirect
361. C3#10600794semidirect

Maximal subgroups

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

subgroupindex
#117541252
C5×#51102
#117484782
#117484762
#117483552
#117463732
C3×#647722
#106007943
#689455