Finite Group Databasebeta

← #14304898

Subgroups — #14304898

Order 1920.

444 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#11751203C211yesmaximal, characteristic, complemented
2C2×C5×#815C211yesmaximal, characteristic, complemented
3C3×#65399C211yesmaximal, characteristic
4C2×#90977C211yesmaximal, characteristic
5#11748365C211yesmaximal, characteristic
6#11745983C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10600636—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91098—22no—
17C5×#815—22no—
18C3×#3952—22no—
19#90977—22no—
20#90971C412yescomplemented
21#90965C412yescomplemented
22#69998—51nomaximal, Hall
23C2×C5×#97—31no—
24#65402—31no—
25#65399D311yescharacteristic
26#65391—31no—
27C2×#3937—31no—
28#64772—31no—
29#64743—31no—
30C22×C3×C4×C5C2311yescharacteristic
31C22×C5×Dic3—21no—
32C2×C3×C22⋊D5—21no—
33C3×#709—21no—
34C3×#709—21no—
35C3×#709—21no—
36C3×#709—21no—
37C2×C3×D20C2×C411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×Dic10C2×C411yescharacteristic
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8D412yes—
43#6719—21no—
44C4⋊Dic15C2×C412yes—
45C4×Dic15—21no—
46#6710—21no—
47#6710—21no—
48C2×C3⋊#168—21no—
49C4×C5×Dic3—21no—
50C4×C5×Dic3D412yes—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C2×C5×C3⋊C8C2×C412yes—
54C3×#681—21no—
55C3×#681—21no—
56C2×C3×#168—21no—
57C3×#408—51no—
58C2×#837—51no—
59#5233—51no—
60#5102—51no—
61C2×#815D511yescharacteristic, complemented
62#4558—51no—
63#4555—51no—
64C2×#709C2×D311yescharacteristic
65C22×C5×C8—31no—
66C22×C5×C8C2×D311yescharacteristic
67C2×C42×C5—31no—
68#4072—31no—
69C2×#681—31no—
70C2×#681C2×D311yescharacteristic
71C5×#97—62no—
72#3953—32no—
73#3952—22no—
74#3948—32no—
75#3946—62no—
76#3937—62no—
77#1938—151noSylow
78C23×C3×C5#4111yescharacteristic
79C22×C3×D5—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—
87C2×C5×Dic3—22no—
88C2×C5×Dic3—42no—
89C3×C22⋊D5—41no—
90C3×C22⋊D5—41no—
91C2×C3×Dic5—21no—
92C3×D20—21no—
93C3×D20—21no—
94C3×C4×D5—41no—
95C3×C4×D5—41no—
96C3×Dic10—21no—
97C3×Dic10—21no—
98C3×C5×C8—22no—
99C3⋊#168—41no—
100C3×#168—41no—
101C5×C3⋊C8—22no—
102C2×C3×#41—51no—
103C2×C3×M16—51no—
104C22×C3×C8C2×D511yescharacteristic
105#926—51no—
106C2×C4×Dic3C2×D511yescharacteristic
107C2×#208—51no—
108C22×C3⋊C8C2×D511yescharacteristic
109C3×C22⋊C8—102no—
110#837—102no—
111#835—52no—
112#832—52no—
113#815—22no—
114Dic3⋊C8—102no—
115C22×C4×C5—61no—
116C22×C4×C5C22×D311yescharacteristic
117C2×C22⋊D5—21no—
118#709—21no—
119#709—21no—
120#709—21no—
121#709—21no—
122C2×D20C4×D311yescharacteristic
123C2×C4×D5—21no—
124C2×Dic10C4×D311yescharacteristic
125C2×C5×C8—21no—
126C2×C5×C8—21no—
127C2×C5×C8—32no—
128C2×C5×C8—61no—
129C2×C5×C8—61no—
130C2×C5×C8#6712yes—
131C42×C5—32no—
132C42×C5—61no—
133C22⋊Dic5—61no—
134C4⋊Dic5—32no—
135C4×Dic5—61no—
136#681—21no—
137#681—21no—
138#681—61no—
139#681—61no—
140C2×#168—21no—
141C2×#168—61no—
142#424—151no—
143C2×#104—151no—
144#416—151no—
145#408—51no—
146C2×#97—31no—
147#341—151no—
148#339—151no—
149C22×C3×C5—22no—
150C22×C3×C5C4×D411yescharacteristic
151C22×C3×C5#12311yescharacteristic
152C22×C3×C5#12611yescharacteristic
153C2×C3×D5—41no—
154C2×C3×D5—42no—
155C3×C4×C5#11711yescharacteristic
156C3×C4×C5C4×D411yescharacteristic
157C3×C4×C5#12111yescharacteristic
158C3×C4×C5#12411yescharacteristic
159Dic15—42no—
160C3×Dic5—41no—
161C5×Dic3—42no—
162C3×#41—101no—
163C3×#41—101no—
164C3×#41—101no—
165C3×#41—101no—
166C2×C3×Q8—51no—
167C2×C3×D4—51no—
168C2×C3×D4—101no—
169C22×C3×C4—101no—
170C22×C3×C4C22×D511yescharacteristic
171C22×Dic3—21no—
172C3×M16—101no—
173C3×M16—101no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—101no—
177C2×C3×C8D2012yes—
178#217—101no—
179C4⋊Dic3—52no—
180C4×Dic3—21no—
181C4×Dic3—101no—
182C4×Dic3C22⋊D512yes—
183#208—101no—
184#208—101no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8C4×D512yes—
189C23×C5#23511yescharacteristic
190C22×D5—21no—
191C2×C4×C5—62no—
192C2×C4×C5—122no—
193C2×C4×C5C2×C4×D311yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×C4×C5#23711yescharacteristic
196C2×C4×C5#23711yescharacteristic
197C2×C4×C5#23711yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C22⋊D5—41no—
200C22⋊D5—41no—
201C2×Dic5—21no—
202C2×Dic5—62no—
203D20—21no—
204D20—21no—
205C4×D5—41no—
206C4×D5—41no—
207Dic10—21no—
208Dic10—21no—
209C5×C8—22no—
210C5×C8—62no—
211#168—41no—
212#168—121no—
213C2×#41—51no—
214C2×M16—51no—
215C2×M16—151no—
216C22×C8—31no—
217C22×C8D3×D511yescharacteristic
218#117—151no—
219C2×C42—31no—
220C4⋊C8—302no—
221#104—302no—
222#103—152no—
223#102—152no—
224C22⋊C8—102no—
225#97—62no—
226C2×C3×C5—21no—
227C2×C3×C5—21no—
228C2×C3×C5#38811yescharacteristic
229C2×C3×C5#44412yes—
230C3×D5—81no—
231C23×C3—101no—
232C23×C3#70911yescharacteristic
233C3×Q8—101no—
234C3×Q8—101no—
235C3×D4—101no—
236C3×D4—101no—
237C3×D4—201no—
238C3×D4—201no—
239C2×C3×C4—101no—
240C2×C3×C4—201no—
241C2×C3×C4—201no—
242C2×C3×C4C2×C4×D511yescharacteristic
243C2×C3×C4C2×D2011yescharacteristic
244C2×C3×C4#70911yescharacteristic
245C2×C3×C4#70911yescharacteristic
246C2×C3×C4#70911yescharacteristic
247C2×C3×C4C2×C22⋊D511yescharacteristic
248C2×Dic3—22no—
249C2×Dic3—42no—
250C2×Dic3—102no—
251C3×C8—22no—
252C3×C8—201no—
253C3⋊C8—22no—
254C3⋊C8—201no—
255C22×C5—22no—
256C22×C5#87911yescharacteristic
257C22×C5#88311yescharacteristic
258C22×C5C4×#6711yescharacteristic
259C2×D5—42no—
260C2×D5—41no—
261C4×C5—122no—
262C4×C5#87711yescharacteristic
263C4×C5#67⋊C411yescharacteristic
264C4×C5#93611yescharacteristic
265C4×C5#93911yescharacteristic
266Dic5—41no—
267Dic5—122no—
268#41—101no—
269#41—101no—
270#41—101no—
271#41—101no—
272C2×Q8—51no—
273C2×D4—51no—
274C2×D4—101no—
275C22×C4—61no—
276C22×C4—101no—
277C22×C4C2×D3×D511yescharacteristic
278M16—101no—
279M16—101no—
280M16—301no—
281M16—301no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—32no—
285C2×C8—61no—
286C2×C8—61no—
287C2×C8—101no—
288C2×C8—301no—
289C2×C8#120212yes—
290C4⋊C4—152no—
291C22⋊C4—301no—
292C42—32no—
293C42—61no—
294C42—301no—
295C3×C5#193811yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3—201no—
298C22×C3—202no—
299C22×C3C4×D2011yescharacteristic
300C22×C3#402211yescharacteristic
301C22×C3#407511yescharacteristic
302C3×C4—201no—
303C3×C4#401811yescharacteristic
304C3×C4#402111yescharacteristic
305C3×C4C4×C22⋊D511yescharacteristic
306C3×C4#407611yescharacteristic
307Dic3—42no—
308Dic3—202no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5#494511yescharacteristic
312C2×C5#514512yes—
313D5—81no—
314C23—101no—
315C23#677111yescharacteristic
316Q8—101no—
317Q8—101no—
318D4—101no—
319D4—101no—
320D4—201no—
321D4—201no—
322C2×C4—62no—
323C2×C4—101no—
324C2×C4—122no—
325C2×C4—201no—
326C2×C4—201no—
327C2×C4—302no—
328C2×C4#676511yescharacteristic
329C2×C4#676511yescharacteristic
330C2×C4C4×D3×D511yescharacteristic
331C2×C4#677911yescharacteristic
332C2×C4C2×#120211yescharacteristic
333C2×C4D3×C22⋊D511yescharacteristic
334C8—22no—
335C8—62no—
336C8—201no—
337C8—601no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—401no—
341C2×C3#6500612yes—
342C2×C3#6522911yescharacteristic
343C5#6999811yescharacteristic, complemented, Sylow
344C22—22no—
345C22—201no—
346C22—202no—
347C22#9136311yescharacteristic
348C22C4×#120211yescharacteristic
349C22#9145211yescharacteristic
350C4—122no—
351C4—201no—
352C4—602no—
353C4#9136411yescharacteristic
354C4#9139311yescharacteristic
355C4#9144111yescharacteristic
356C4#9156911yescharacteristic
357C3#1060063611yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—401no—
361C2#1174807712yes—
362C2#1174870611yescharacteristic
subgroupG/H
centerC2×C4C2×#1202
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C4×D4
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1938
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #11751203C2semidirect
2. C2×C5×#815C2semidirect
6. #11745983C2semidirect
7. #11745976C2semidirect
20. #90971C4semidirect
21. #90965C4semidirect
61. C2×#815D5semidirect
295. C3×C5#1938semidirect
343. C5#69998semidirect
357. C3#10600636semidirect

Maximal subgroups

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

subgroupindex
#117512032
C2×C5×#8152
C3×#653992
C2×#909772
#117483652
#117459832
#117459762
#106006363
#699985