Finite Group Databasebeta

← #14304786

Subgroups — #14304786

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11751220C211yesmaximal, characteristic, complemented
2C2×C5×#825C211yesmaximal, characteristic
3#11748388C211yesmaximal, characteristic
4#11748347C211yesmaximal, characteristic
5C2×Dic3×#168C211yesmaximal, characteristic, complemented
6C3×#64778C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10601164—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16#91098—22no—
17C5×#825—22no—
18#90973C412yescomplemented
19#90967C412yescomplemented
20(C2×D3)⋊#168—22no—
21Dic3×#168—22no—
22#68918—51nomaximal, Hall
23C2×C5×#104—31no—
24#65523—31no—
25#65522—31no—
26#65408—31no—
27C2×C4×#168—31no—
28#64778D311yescharacteristic, complemented
29#64743—31no—
30C22×C3×C4×C5C2311yescharacteristic
31C2×C5×#67—21no—
32C22×C5×Dic3—21no—
33C5×#235—21no—
34C5×#235—21no—
35C5×#235—21no—
36C5×#235—21no—
37C2×C5×D12C2×C411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C5×Dic6C2×C411yescharacteristic
40C3×C5×M16—21no—
41C3×C5×M16—21no—
42C2×C3×C5×C8—21no—
43#6719—21no—
44C4⋊Dic15C2×C412yes—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C3⋊#168D412yes—
49C4×C5×Dic3—21no—
50C4×C5×Dic3D412yes—
51C3×#681—21no—
52C3×#681—21no—
53C2×C3×#168—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C2×C3×#168C2×C412yes—
57C2×#825D511yescharacteristic
58#5129—51no—
59#5119—51no—
60#5113—51no—
61C2×C8×Dic3—51no—
62C3×#341—51no—
63#4555—51no—
64C2×C5×#41—31no—
65C2×C5×M16C2×D311yescharacteristic
66C2×C42×C5—31no—
67#4072—31no—
68C2×#681C2×D311yescharacteristic
69C22×#168—31no—
70C22×#168C2×D311yescharacteristic
71C5×#104—62no—
72#3967—32no—
73#3964—32no—
74C22⋊#168—62no—
75#3946—62no—
76C4×#168—62no—
77#1937—151noSylow
78C23×C3×C5#4111yescharacteristic
79C22×C5×D3—21no—
80C2×C3×C4×C5C22×C411yescharacteristic
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5#4111yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×C3×C4×C5#4111yescharacteristic
86C2×Dic15—22no—
87C5×#67—41no—
88C5×#67—41no—
89C2×C5×Dic3—24no—
90C2×C5×Dic3—22no—
91C2×C5×Dic3—21no—
92C5×D12—21no—
93C5×D12—21no—
94C4×C5×D3—41no—
95C4×C5×D3—41no—
96C5×Dic6—21no—
97C5×Dic6—21no—
98C3×C5×C8—41no—
99C3⋊#168—22no—
100C3×#168—22no—
101C3×#168—41no—
102C2×#235C2×D511yescharacteristic
103C2×C3×M16—51no—
104C2×C3×M16C2×D511yescharacteristic
105C22×C3×C8—51no—
106#926—51no—
107C2×C4×Dic3C2×D511yescharacteristic
108C22×C3⋊C8—51no—
109#825—22no—
110#821—52no—
111(C2×D3)⋊C8—102no—
112#816—52no—
113Dic3⋊C8—102no—
114C8×Dic3—102no—
115C5×#41—61no—
116C5×#41—61no—
117C5×#41—61no—
118C5×#41—61no—
119C2×C5×Q8—31no—
120C2×C5×D4—31no—
121C2×C5×D4—61no—
122C22×C4×C5—61no—
123C22×C4×C5—61no—
124C22×C4×C5C22×D311yescharacteristic
125C5×M16—21no—
126C5×M16—21no—
127C2×C5×C8—21no—
128C42×C5—32no—
129C42×C5—61no—
130C22⋊Dic5—61no—
131C4⋊Dic5—32no—
132C4×Dic5—61no—
133#681—21no—
134#681—21no—
135C2×#168—21no—
136C2×#168—21no—
137C2×#168—21no—
138C2×#168—32no—
139C2×#168—61no—
140C2×#168—61no—
141C2×#168C4×D312yes—
142#424—151no—
143C2×#104—31no—
144#416—151no—
145#408—151no—
146C2×C4×C8—151no—
147#341—51no—
148#339—151no—
149C22×C3×C5—22no—
150C22×C3×C5C4×D411yescharacteristic
151C22×C3×C5#12311yescharacteristic
152C22×C3×C5#12611yescharacteristic
153C2×C5×D3—41no—
154C2×C5×D3—42no—
155C3×C4×C5#11711yescharacteristic
156C3×C4×C5C4×D411yescharacteristic
157C3×C4×C5#12111yescharacteristic
158C3×C4×C5#12411yescharacteristic
159Dic15—42no—
160C5×Dic3—24no—
161C5×Dic3—41no—
162C22×C3×C4C22×D511yescharacteristic
163C2×#67—21no—
164C22×Dic3—21no—
165#235—21no—
166#235—21no—
167#235—21no—
168#235—21no—
169C2×D12C4×D511yescharacteristic
170C2×C4×D3—21no—
171C2×Dic6C4×D511yescharacteristic
172C3×M16—21no—
173C3×M16—21no—
174C3×M16—101no—
175C3×M16—101no—
176C2×C3×C8—21no—
177C2×C3×C8—52no—
178C2×C3×C8—101no—
179C2×C3×C8—101no—
180C2×C3×C8—101no—
181#217—101no—
182C4⋊Dic3—52no—
183C4×Dic3—21no—
184C4×Dic3—101no—
185C4×Dic3C22⋊D512yes—
186C2×C3⋊C8—52no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C23×C5—61no—
190C23×C5#23911yescharacteristic
191C5×Q8—61no—
192C5×Q8—61no—
193C5×D4—61no—
194C5×D4—61no—
195C5×D4—121no—
196C5×D4—121no—
197C2×C4×C5—64no—
198C2×C4×C5—62no—
199C2×C4×C5—61no—
200C2×C4×C5—121no—
201C2×C4×C5—121no—
202C2×C4×C5C2×C4×D311yescharacteristic
203C2×C4×C5#23511yescharacteristic
204C2×C4×C5#23511yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5#23711yescharacteristic
208C2×Dic5—62no—
209C5×C8—41no—
210#168—22no—
211#168—41no—
212#168—62no—
213C2×#41—31no—
214C2×M16—51no—
215C2×M16D3×D511yescharacteristic
216C22×C8—51no—
217C22×C8—151no—
218#117—151no—
219C2×C42—31no—
220C4⋊C8—302no—
221#104—62no—
222#103—152no—
223#102—152no—
224C22⋊C8—302no—
225C4×C8—302no—
226C2×C3×C5—21no—
227C2×C3×C5—21no—
228C2×C3×C5#38811yescharacteristic
229C2×C3×C5#44312yes—
230C5×D3—81no—
231C23×C3#71111yescharacteristic
232C22×D3—21no—
233C2×C3×C4C2×C4×D511yescharacteristic
234C2×C3×C4#70911yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4#71111yescharacteristic
237C2×C3×C4#71111yescharacteristic
238C2×C3×C4C2×C22⋊D511yescharacteristic
239#67—41no—
240#67—41no—
241C2×Dic3—24no—
242C2×Dic3—22no—
243C2×Dic3—21no—
244C2×Dic3—102no—
245D12—21no—
246D12—21no—
247C4×D3—41no—
248C4×D3—41no—
249Dic6—21no—
250Dic6—21no—
251C3×C8—41no—
252C3×C8—102no—
253C3×C8—201no—
254C3⋊C8—102no—
255C22×C5—22no—
256C22×C5—122no—
257C22×C5—121no—
258C22×C5#89311yescharacteristic
259C22×C5#89411yescharacteristic
260C22×C5#89811yescharacteristic
261C4×C5—64no—
262C4×C5—121no—
263C4×C5#87211yescharacteristic
264C4×C5#67⋊C411yescharacteristic
265C4×C5#88411yescharacteristic
266C4×C5#88511yescharacteristic
267Dic5—122no—
268#41—61no—
269#41—61no—
270#41—61no—
271#41—61no—
272C2×Q8—31no—
273C2×D4—31no—
274C2×D4—61no—
275C22×C4—61no—
276C22×C4—61no—
277C22×C4C2×D3×D511yescharacteristic
278M16—21no—
279M16—21no—
280M16—101no—
281M16—101no—
282C2×C8—21no—
283C2×C8—52no—
284C2×C8—101no—
285C2×C8—101no—
286C2×C8—101no—
287C2×C8—152no—
288C2×C8—301no—
289C2×C8—301no—
290C4⋊C4—152no—
291C22⋊C4—301no—
292C42—32no—
293C42—61no—
294C42—301no—
295C3×C5#193711yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3#402511yescharacteristic
298C22×C3#402711yescharacteristic
299C22×C3#408111yescharacteristic
300C2×D3—42no—
301C2×D3—41no—
302C3×C4#402311yescharacteristic
303C3×C4#403111yescharacteristic
304C3×C4C4×C22⋊D511yescharacteristic
305C3×C4#408411yescharacteristic
306Dic3—24no—
307Dic3—41no—
308Dic3—202no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5—241no—
312C2×C5#466911yescharacteristic
313C2×C5#489512yes—
314C23—61no—
315C23#676811yescharacteristic
316Q8—61no—
317Q8—61no—
318D4—61no—
319D4—61no—
320D4—121no—
321D4—121no—
322C2×C4—64no—
323C2×C4—62no—
324C2×C4—61no—
325C2×C4—121no—
326C2×C4—121no—
327C2×C4—302no—
328C2×C4#676511yescharacteristic
329C2×C4#677211yescharacteristic
330C2×C4C4×D3×D511yescharacteristic
331C2×C4#678211yescharacteristic
332C2×C4D3×C22⋊D511yescharacteristic
333C2×C4#679011yescharacteristic
334C8—41no—
335C8—102no—
336C8—201no—
337C8—302no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3#6511312yes—
341C2×C3#6523311yescharacteristic
342D3—81no—
343C5#6891811yescharacteristic, complemented, Sylow
344C22—22no—
345C22—122no—
346C22—121no—
347C22#9134111yescharacteristic
348C22#9140611yescharacteristic
349C22#9142311yescharacteristic
350C4—64no—
351C4—121no—
352C4—602no—
353C4#9139811yescharacteristic
354C4#9144111yescharacteristic
355C4#9146211yescharacteristic
356C4#9155711yescharacteristic
357C3#1060116411yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—241no—
361C2#1174817612yes—
362C2#1174872011yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C4×D4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1937
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #11751220C2semidirect
5. C2×Dic3×#168C2semidirect
6. C3×#64778C2semidirect
7. #11745976C2semidirect
18. #90973C4semidirect
19. #90967C4semidirect
28. #64778D3semidirect
295. C3×C5#1937semidirect
343. C5#68918semidirect
357. C3#10601164semidirect

Maximal subgroups

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

subgroupindex
#117512202
C2×C5×#8252
#117483882
#117483472
C2×Dic3×#1682
C3×#647782
#117459762
#106011643
#689185