Finite Group Databasebeta

← #14304763

Subgroups — #14304763

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
1C2×C3×C5×#104C211yesmaximal, characteristic
2#11751335C211yesmaximal, characteristic
3#11751334C211yesmaximal, characteristic
4#11751220C211yesmaximal, characteristic, complemented
5C2×C4×C3⋊#168C211yesmaximal, characteristic, complemented
6#11746379C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10601164—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C22×C3⋊#168C2211yescharacteristic
15C22×C3⋊#168C2211yescharacteristic
16C3×C5×#104—22no—
17#91119C412yescomplemented
18#91116C412yescomplemented
19#91114—22no—
20#91098—22no—
21C4×C3⋊#168—22no—
22#70371—51nomaximal, Hall
23C2×C5×#104D311yescharacteristic
24#65523—31no—
25#65522—31no—
26#65408—31no—
27C2×C4×#168—31no—
28#64778—31no—
29#64743—31no—
30C3×C5×#41—21no—
31C3×C5×#41—21no—
32C3×C5×#41—21no—
33C3×C5×#41—21no—
34C2×C3×C5×Q8C2×C411yescharacteristic
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C3×C5×M16—21no—
41C3×C5×M16—21no—
42C2×C3×C5×C8—21no—
43C3×C42×C5—21no—
44C3×C42×C5D412yes—
45#6719—21no—
46C4⋊Dic15C2×C412yes—
47C4×Dic15—21no—
48#6710—21no—
49#6710—21no—
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C2×C3⋊#168—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168C2×C412yes—
56C2×C3⋊#168D412yes—
57C2×C3×#104D511yescharacteristic
58#5234—51no—
59#5233—51no—
60#5119—51no—
61C2×C4×C3⋊C8—51no—
62#4558—51no—
63#4523—51no—
64C2×C5×#41C2×D311yescharacteristic
65C2×C5×M16C2×D311yescharacteristic
66C2×C42×C5C2×D311yescharacteristic
67#4072—31no—
68C2×#681—31no—
69C22×#168—31no—
70C22×#168—31no—
71C5×#104—22no—
72#3967—32no—
73#3964—32no—
74C22⋊#168—62no—
75#3946—62no—
76C4×#168—62no—
77#1937—151noSylow
78C23×C3×C5—21no—
79C23×C3×C5#4111yescharacteristic
80C3×C5×Q8—21no—
81C3×C5×Q8—21no—
82C3×C5×D4—21no—
83C3×C5×D4—21no—
84C3×C5×D4—41no—
85C3×C5×D4—41no—
86C2×C3×C4×C5—24no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C22×C411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×Dic15—22no—
98C3×C5×C8—41no—
99C3⋊#168—22no—
100C3⋊#168—22no—
101C3⋊#168—41no—
102C2×C3×#41C2×D511yescharacteristic
103C2×C3×M16C2×D511yescharacteristic
104C2×C3×C42C2×D511yescharacteristic
105#926—51no—
106C2×#208—51no—
107C22×C3⋊C8—51no—
108C22×C3⋊C8—51no—
109C3×#104—22no—
110#835—52no—
111#832—52no—
112#830—102no—
113Dic3⋊C8—102no—
114C4×C3⋊C8—102no—
115C5×#41—21no—
116C5×#41—21no—
117C5×#41—21no—
118C5×#41—21no—
119C2×C5×Q8C4×D311yescharacteristic
120C2×C5×D4—21no—
121C2×C5×D4C4×D311yescharacteristic
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5C22×D311yescharacteristic
125C5×M16—21no—
126C5×M16—21no—
127C2×C5×C8—21no—
128C42×C5—21no—
129C42×C5#6712yes—
130C22⋊Dic5—61no—
131C4⋊Dic5—32no—
132C4×Dic5—61no—
133#681—61no—
134#681—61no—
135C2×#168—32no—
136C2×#168—32no—
137C2×#168—61no—
138C2×#168—61no—
139C2×#168—61no—
140C2×#168—61no—
141C2×#168—61no—
142#424—151no—
143C2×#104D1511yescharacteristic
144#416—151no—
145#408—151no—
146C2×C4×C8—151no—
147#341—151no—
148#339—151no—
149C22×C3×C5—22no—
150C22×C3×C5—41no—
151C22×C3×C5—42no—
152C22×C3×C5C4×D411yescharacteristic
153C22×C3×C5#12311yescharacteristic
154C22×C3×C5#12611yescharacteristic
155C3×C4×C5—24no—
156C3×C4×C5—41no—
157C3×C4×C5#11711yescharacteristic
158C3×C4×C5C4×D411yescharacteristic
159C3×C4×C5#12111yescharacteristic
160C3×C4×C5#12411yescharacteristic
161Dic15—42no—
162C3×#41—21no—
163C3×#41—21no—
164C3×#41—21no—
165C3×#41—21no—
166C2×C3×Q8C4×D511yescharacteristic
167C2×C3×D4—21no—
168C2×C3×D4C4×D511yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4C22×D511yescharacteristic
172C3×M16—21no—
173C3×M16—21no—
174C2×C3×C8—21no—
175C3×C42—21no—
176C3×C42C22⋊D512yes—
177#217—101no—
178C4⋊Dic3—52no—
179C4×Dic3—101no—
180#208—101no—
181#208—101no—
182C2×C3⋊C8—52no—
183C2×C3⋊C8—52no—
184C2×C3⋊C8—101no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C23×C5—21no—
190C23×C5#23711yescharacteristic
191C5×Q8—21no—
192C5×Q8—21no—
193C5×D4—21no—
194C5×D4—21no—
195C5×D4—41no—
196C5×D4—41no—
197C2×C4×C5—24no—
198C2×C4×C5—22no—
199C2×C4×C5—21no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5C2×C4×D311yescharacteristic
203C2×C4×C5#23511yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5#23711yescharacteristic
206C2×C4×C5#23711yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C2×Dic5—62no—
209C5×C8—41no—
210#168—62no—
211#168—62no—
212#168—121no—
213C2×#41C2×D1511yescharacteristic
214C2×M16—151no—
215C2×M16C2×D1511yescharacteristic
216C22×C8—151no—
217C22×C8—151no—
218#117—151no—
219C2×C42C2×D1511yescharacteristic
220C4⋊C8—302no—
221#104—22no—
222#103—152no—
223#102—152no—
224C22⋊C8—302no—
225C4×C8—302no—
226C2×C3×C5—21no—
227C2×C3×C5—21no—
228C2×C3×C5—81no—
229C2×C3×C5#38811yescharacteristic
230C2×C3×C5#44312yes—
231C23×C3—21no—
232C23×C3#71111yescharacteristic
233C3×Q8—21no—
234C3×Q8—21no—
235C3×D4—21no—
236C3×D4—21no—
237C3×D4—41no—
238C3×D4—41no—
239C2×C3×C4—24no—
240C2×C3×C4—22no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4C2×C4×D511yescharacteristic
245C2×C3×C4#70911yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4#71111yescharacteristic
248C2×C3×C4#71111yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C2×Dic3—102no—
251C3×C8—41no—
252C3⋊C8—102no—
253C3⋊C8—102no—
254C3⋊C8—201no—
255C22×C5—22no—
256C22×C5—41no—
257C22×C5—42no—
258C22×C5#87911yescharacteristic
259C22×C5#67⋊C411yescharacteristic
260C22×C5#93511yescharacteristic
261C4×C5—24no—
262C4×C5—41no—
263C4×C5#87711yescharacteristic
264C4×C5#88511yescharacteristic
265C4×C5C4×#6711yescharacteristic
266C4×C5#93811yescharacteristic
267Dic5—122no—
268#41—21no—
269#41—21no—
270#41—21no—
271#41—21no—
272C2×Q8C4×D1511yescharacteristic
273C2×D4—21no—
274C2×D4C4×D1511yescharacteristic
275C22×C4—21no—
276C22×C4—21no—
277C22×C4C22×D1511yescharacteristic
278M16—21no—
279M16—21no—
280M16—301no—
281M16—301no—
282C2×C8—21no—
283C2×C8—152no—
284C2×C8—152no—
285C2×C8—301no—
286C2×C8—301no—
287C2×C8—301no—
288C2×C8—301no—
289C2×C8—301no—
290C4⋊C4—152no—
291C22⋊C4—301no—
292C42—21no—
293C42—301no—
294C42#122012yes—
295C3×C5#193711yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3—42no—
298C22×C3—41no—
299C22×C3#402511yescharacteristic
300C22×C3#402711yescharacteristic
301C22×C3#408111yescharacteristic
302C3×C4—24no—
303C3×C4—41no—
304C3×C4#402311yescharacteristic
305C3×C4#403111yescharacteristic
306C3×C4C4×C22⋊D511yescharacteristic
307C3×C4#408411yescharacteristic
308Dic3—202no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5—81no—
312C2×C5#482412yes—
313C2×C5#494411yescharacteristic
314C23—21no—
315C23#681911yescharacteristic
316Q8—21no—
317Q8—21no—
318D4—21no—
319D4—21no—
320D4—41no—
321D4—41no—
322C2×C4—24no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—302no—
328C2×C4C2×C4×D1511yescharacteristic
329C2×C4#681711yescharacteristic
330C2×C4D4×D1511yescharacteristic
331C2×C4#681911yescharacteristic
332C2×C4#681911yescharacteristic
333C2×C4C2×#122011yescharacteristic
334C8—41no—
335C8—302no—
336C8—302no—
337C8—601no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—81no—
341C2×C3#6511312yes—
342C2×C3#6523311yescharacteristic
343C5#7037111yescharacteristic, complemented, Sylow
344C22—22no—
345C22—42no—
346C22—41no—
347C22#9176811yescharacteristic
348C22#9177011yescharacteristic
349C22#9182411yescharacteristic
350C4—24no—
351C4—41no—
352C4—602no—
353C4#9176611yescharacteristic
354C4#9177411yescharacteristic
355C4C4×#122011yescharacteristic
356C4#9182711yescharacteristic
357C3#1060116411yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—81no—
361C2#1175092512yes—
362C2#1175104511yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#104C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4×C5C23
hypercenterC2×#104D15
hypocenterC3×C5#1937
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
4. #11751220C2semidirect
5. C2×C4×C3⋊#168C2semidirect
6. #11746379C2semidirect
7. #11746344C2semidirect
17. #91119C4semidirect
18. #91116C4semidirect
295. C3×C5#1937semidirect
343. C5#70371semidirect
357. C3#10601164semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1042
#117513352
#117513342
#117512202
C2×C4×C3⋊#1682
#117463792
#117463442
#106011643
#703715