Finite Group Databasebeta

← #14304789

Subgroups — #14304789

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×#91109C211yesmaximal, characteristic
2C3×#65408C211yesmaximal, characteristic, complemented
3#11748411C211yesmaximal, characteristic
4#11748349C211yesmaximal, characteristic
5C2×#90951C211yesmaximal, characteristic, complemented
6C5×#4558C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10599711—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C2×C5×#208C2211yescharacteristic
13C22×C5×C3⋊C8C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16#91109—22no—
17C3×#3946—22no—
18#90974C412yescomplemented
19#90968C412yescomplemented
20#90957—22no—
21#90951—22no—
22#70535—51nomaximal, Hall
23C2×#3957—31no—
24#65418—31no—
25#65408D311yescharacteristic, complemented
26#65402—31no—
27C2×C8×Dic5—31no—
28C5×#341—31no—
29#64775—31no—
30C22×C3×C4×C5C2311yescharacteristic
31C2×#1220—21no—
32C22×Dic15—21no—
33#6817—21no—
34#6817—21no—
35#6817—21no—
36#6817—21no—
37C2×D60C2×C411yescharacteristic
38C2×C4×D15—21no—
39C2×Dic30C2×C411yescharacteristic
40C3×C5×M16—21no—
41C3×C5×M16—21no—
42C2×C3×C5×C8—21no—
43C4×Dic15—21no—
44C4×Dic15D412yes—
45C5×#208—21no—
46C5×#208—21no—
47C2×C5×C3⋊C8—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8C2×C412yes—
51C3×C22⋊Dic5—21no—
52C3×C4⋊Dic5C2×C412yes—
53C3×C4×Dic5—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C2×C3×#168D412yes—
57C3×#424—51no—
58C2×#825—51no—
59#5110—51no—
60C2×C8×Dic3—51no—
61#5002—51no—
62#4558D511yescharacteristic, complemented
63#4532—51no—
64C2×#709—31no—
65C2×C5×M16—31no—
66C2×C5×M16C2×D311yescharacteristic
67C22×C5×C8—31no—
68#4072C2×D311yescharacteristic
69C2×C4×Dic5—31no—
70C22×#168C2×D311yescharacteristic
71#3957—62no—
72#3953—32no—
73#3952—62no—
74#3948—32no—
75#3946—22no—
76C8×Dic5—62no—
77#1937—151noSylow
78C23×C3×C5#4111yescharacteristic
79C22×D15—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
86#1220—41no—
87#1220—41no—
88C2×Dic15—24no—
89C2×Dic15—22no—
90C2×Dic15—21no—
91D60—21no—
92D60—21no—
93C4×D15—41no—
94C4×D15—41no—
95Dic30—21no—
96Dic30—21no—
97C2×C3×Dic5—22no—
98C3×C5×C8—41no—
99C3×#168—22no—
100C5×C3⋊C8—22no—
101C5×C3⋊C8—41no—
102C2×#235—51no—
103C2×C3×M16C2×D511yescharacteristic
104C22×C3×C8—51no—
105C3×#117—51no—
106C2×C4×Dic3—51no—
107C2×#208C2×D511yescharacteristic
108C22×C3⋊C8C2×D511yescharacteristic
109C3×C4⋊C8—102no—
110#825—102no—
111(C2×D3)⋊C8—102no—
112C8×Dic3—102no—
113#810—52no—
114#809—52no—
115C22×C4×C5C22×D311yescharacteristic
116C2×C22⋊D5—61no—
117C22×Dic5—61no—
118#709—61no—
119#709—61no—
120#709—61no—
121#709—61no—
122C2×D20—31no—
123C2×C4×D5—61no—
124C2×Dic10—31no—
125C5×M16—21no—
126C5×M16—21no—
127C5×M16—61no—
128C5×M16—61no—
129C2×C5×C8—21no—
130C2×C5×C8—32no—
131C2×C5×C8—61no—
132C2×C5×C8—61no—
133C2×C5×C8—61no—
134C22⋊Dic5—21no—
135C4⋊Dic5C4×D312yes—
136C4×Dic5—21no—
137C4×Dic5—32no—
138C4×Dic5—61no—
139C2×#168—21no—
140C2×#168—21no—
141C2×#168#6712yes—
142#424—51no—
143C2×#104—151no—
144#416—151no—
145#408—151no—
146C2×C4×C8—151no—
147#341—31no—
148#339—151no—
149C22×C3×C5—22no—
150C22×C3×C5C4×D411yescharacteristic
151C22×C3×C5#12311yescharacteristic
152C22×C3×C5#12611yescharacteristic
153C2×D15—41no—
154C2×D15—42no—
155C3×C4×C5#11711yescharacteristic
156C3×C4×C5C4×D411yescharacteristic
157C3×C4×C5#12111yescharacteristic
158C3×C4×C5#12411yescharacteristic
159Dic15—24no—
160Dic15—41no—
161C3×Dic5—42no—
162C22×C3×C4C22×D511yescharacteristic
163C2×#67—101no—
164C22×Dic3—101no—
165#235—101no—
166#235—101no—
167#235—101no—
168#235—101no—
169C2×D12—51no—
170C2×C4×D3—101no—
171C2×Dic6—51no—
172C3×M16—21no—
173C3×M16—21no—
174C2×C3×C8—21no—
175C2×C3×C8—52no—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C3×C4⋊C4—52no—
179C3×C22⋊C4—101no—
180C3×C42—101no—
181C4×Dic3—52no—
182C4×Dic3—101no—
183#208—21no—
184#208—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8C4×D512yes—
189C23×C5#23511yescharacteristic
190C22×D5—61no—
191C2×C4×C5C2×C4×D311yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5#23711yescharacteristic
194C2×C4×C5#23911yescharacteristic
195C2×C4×C5#23911yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C22⋊D5—121no—
198C22⋊D5—121no—
199C2×Dic5—22no—
200C2×Dic5—64no—
201C2×Dic5—62no—
202C2×Dic5—61no—
203D20—61no—
204D20—61no—
205C4×D5—121no—
206C4×D5—121no—
207Dic10—61no—
208Dic10—61no—
209C5×C8—41no—
210C5×C8—62no—
211C5×C8—121no—
212#168—22no—
213C2×#41—151no—
214C2×M16—31no—
215C2×M16D3×D511yescharacteristic
216C22×C8—31no—
217C22×C8—51no—
218#117—51no—
219C2×C42—151no—
220C4⋊C8—102no—
221#104—302no—
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—
230D15—81no—
231C23×C3#71311yescharacteristic
232C22×D3—101no—
233C2×C3×C4—102no—
234C2×C3×C4C2×C4×D511yescharacteristic
235C2×C3×C4#70911yescharacteristic
236C2×C3×C4#70911yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4#71111yescharacteristic
240#67—201no—
241#67—201no—
242C2×Dic3—104no—
243C2×Dic3—102no—
244C2×Dic3—101no—
245D12—101no—
246D12—101no—
247C4×D3—201no—
248C4×D3—201no—
249Dic6—101no—
250Dic6—101no—
251C3×C8—41no—
252C3×C8—102no—
253C3⋊C8—22no—
254C3⋊C8—41no—
255C22×C5—22no—
256C22×C5#89411yescharacteristic
257C22×C5#89811yescharacteristic
258C22×C5C4×#6711yescharacteristic
259C2×D5—122no—
260C2×D5—121no—
261C4×C5#89211yescharacteristic
262C4×C5#89311yescharacteristic
263C4×C5#93911yescharacteristic
264C4×C5#94711yescharacteristic
265Dic5—42no—
266Dic5—64no—
267Dic5—121no—
268#41—301no—
269#41—301no—
270#41—301no—
271#41—301no—
272C2×Q8—151no—
273C2×D4—151no—
274C2×D4—301no—
275C22×C4—301no—
276C22×C4—301no—
277C22×C4C2×D3×D511yescharacteristic
278M16—21no—
279M16—21no—
280M16—61no—
281M16—61no—
282C2×C8—21no—
283C2×C8—32no—
284C2×C8—52no—
285C2×C8—61no—
286C2×C8—61no—
287C2×C8—61no—
288C2×C8—101no—
289C2×C8—101no—
290C4⋊C4—52no—
291C22⋊C4—101no—
292C42—101no—
293C42—152no—
294C42—301no—
295C3×C5#193711yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3#403911yescharacteristic
298C22×C3#404011yescharacteristic
299C22×C3#404411yescharacteristic
300C2×D3—202no—
301C2×D3—201no—
302C3×C4—202no—
303C3×C4#401811yescharacteristic
304C3×C4#402711yescharacteristic
305C3×C4#403011yescharacteristic
306C3×C4#403111yescharacteristic
307Dic3—104no—
308Dic3—201no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5#499011yescharacteristic
312C2×C5#514412yes—
313D5—241no—
314C23—301no—
315C23#677311yescharacteristic
316Q8—301no—
317Q8—301no—
318D4—301no—
319D4—301no—
320D4—601no—
321D4—601no—
322C2×C4—102no—
323C2×C4—304no—
324C2×C4—302no—
325C2×C4—301no—
326C2×C4—601no—
327C2×C4—601no—
328C2×C4#676811yescharacteristic
329C2×C4#676911yescharacteristic
330C2×C4C4×D3×D511yescharacteristic
331C2×C4#677911yescharacteristic
332C2×C4D5×#6711yescharacteristic
333C2×C4#679011yescharacteristic
334C8—41no—
335C8—62no—
336C8—102no—
337C8—121no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3#6495811yescharacteristic
341C2×C3#6518412yes—
342D3—401no—
343C5#7053511yescharacteristic, complemented, Sylow
344C22—22no—
345C22—601no—
346C22—602no—
347C22#9133711yescharacteristic
348C22#9143311yescharacteristic
349C22#9144411yescharacteristic
350C4—202no—
351C4—304no—
352C4—601no—
353C4#9132611yescharacteristic
354C4#9140311yescharacteristic
355C4#9140611yescharacteristic
356C4#9155011yescharacteristic
357C3#1059971111yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—1201no—
361C2#1174820712yes—
362C2#1174866611yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C4×D4
prime radicalC2×#6817C22
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
2. C3×#65408C2semidirect
5. C2×#90951C2semidirect
6. C5×#4558C2semidirect
7. #11745973C2semidirect
18. #90974C4semidirect
19. #90968C4semidirect
25. #65408D3semidirect
62. #4558D5semidirect
295. C3×C5#1937semidirect
343. C5#70535semidirect
357. C3#10599711semidirect

Maximal subgroups

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

subgroupindex
C2×#911092
C3×#654082
#117484112
#117483492
C2×#909512
C5×#45582
#117459732
#105997113
#705355