Finite Group Databasebeta

← #14304901

Subgroups — #14304901

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#11751100C211yesmaximal, characteristic, complemented
2C3×#65291C211yesmaximal, characteristic
3C2×#90977C211yesmaximal, characteristic
4#11748343C211yesmaximal, characteristic
5C2×#90953C211yesmaximal, characteristic, complemented
6C5×#4532C211yesmaximal, characteristic, complemented
7#11745984C211yesmaximal, characteristic, complemented
8#10599539—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C4⋊(C3⋊#168)—22no—
17C3×#3942C412yescomplemented
18C3×#3941C412yescomplemented
19#90977—22no—
20#90955—22no—
21#90953—22no—
22#70288—51nomaximal, Hall
23#65418—31no—
24#65291D311yescharacteristic
25#65288—31no—
26C2×#3937—31no—
27C2×#3935—31no—
28C5×#339—31no—
29#64778—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
40C3×C5×C4⋊C4C2×C412yes—
41C3×C5×C22⋊C4—21no—
42C3×C42×C5—21no—
43#6710—21no—
44#6710—21no—
45C2×C3⋊#168—21no—
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C3⋊#168D412yes—
49C4×C5×Dic3—21no—
50C4×C5×Dic3D412yes—
51C5×#208—21no—
52C5×#208—21no—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C2×C3×#168C2×C412yes—
57C3×#416—51no—
58C2×#837—51no—
59#5234—51no—
60C2×#815—51no—
61#4999—51no—
62#4552—51no—
63#4532D511yescharacteristic, complemented
64C2×#709C2×D311yescharacteristic
65C2×C5×M16—31no—
66C5×#117C2×D311yescharacteristic
67C2×C42×C5—31no—
68C2×#681—31no—
69C22×#168—31no—
70C22×#168C2×D311yescharacteristic
71#3952—62no—
72#3942Dic312yescomplemented
73#3941Dic312yescomplemented
74#3937—62no—
75C4⋊#168—62no—
76#3935—62no—
77#1938—151noSylow
78C23×C3×C5#4111yescharacteristic
79C22×C3×D5—21no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5C22×C411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×C3×C4×C5#4111yescharacteristic
86C2×C3×C4×C5#4111yescharacteristic
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⋊#168—22no—
99C3⋊#168—41no—
100C3×#168—22no—
101C5×C3⋊C8—41no—
102C2×C3×#41—51no—
103C22×C3×C8—51no—
104C3×#117C2×D511yescharacteristic
105C2×C4×Dic3C2×D511yescharacteristic
106C2×#208—51no—
107C2×#208C2×D511yescharacteristic
108C22×C3⋊C8—51no—
109C3×#103—52no—
110C3×#102—52no—
111#837—102no—
112#830—102no—
113#815—102no—
114C4⋊(C3⋊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×D20C2×Dic311yescharacteristic
123C2×C4×D5—21no—
124C2×Dic10C2×Dic311yescharacteristic
125C5×M16—61no—
126C5×M16—61no—
127C2×C5×C8—61no—
128C5×C4⋊C4C2×Dic312yes—
129C5×C22⋊C4—21no—
130C42×C5—21no—
131C42×C5—32no—
132C42×C5—61no—
133#681—61no—
134#681—61no—
135C2×#168—21no—
136C2×#168—21no—
137C2×#168—32no—
138C2×#168—61no—
139C2×#168—61no—
140C2×#168—61no—
141C2×#168C2×Dic312yes—
142#424—151no—
143C2×#104—151no—
144#416—51no—
145#408—151no—
146C2×#97—151no—
147#341—151no—
148#339—31no—
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—42no—
156C3×C4×C5#11711yescharacteristic
157C3×C4×C5C4×D411yescharacteristic
158C3×C4×C5#12111yescharacteristic
159C3×C4×C5#12411yescharacteristic
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—
172C2×C3×C8—52no—
173C2×C3×C8—101no—
174C2×C3×C8—101no—
175C3×C4⋊C4C4×D512yes—
176C3×C22⋊C4—21no—
177C3×C42—21no—
178C4×Dic3—21no—
179C4×Dic3D2012yes—
180#208—21no—
181#208—21no—
182#208—101no—
183#208—101no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—52no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C23×C5#23711yescharacteristic
190C22×D5—21no—
191C2×C4×C5—22no—
192C2×C4×C5—62no—
193C2×C4×C5—122no—
194C2×C4×C5#23511yescharacteristic
195C2×C4×C5#23511yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5#23711yescharacteristic
199C2×C4×C5C22×Dic311yescharacteristic
200C22⋊D5—41no—
201C22⋊D5—41no—
202C2×Dic5—21no—
203D20—21no—
204D20—21no—
205C4×D5—41no—
206C4×D5—41no—
207Dic10—21no—
208Dic10—21no—
209C5×C8—121no—
210#168—22no—
211#168—62no—
212#168—121no—
213C2×#41—51no—
214C2×M16—31no—
215C2×M16—151no—
216C22×C8—51no—
217C22×C8—151no—
218#117D3×D511yescharacteristic
219C2×C42—31no—
220C4⋊C8—302no—
221#104—302no—
222#103—52no—
223#102—52no—
224C22⋊C8—302no—
225#97—302no—
226C2×C3×C5—21no—
227C2×C3×C5—21no—
228C2×C3×C5#38811yescharacteristic
229C2×C3×C5#44412yes—
230C3×D5—81no—
231C23×C3—101no—
232C23×C3#71111yescharacteristic
233C3×Q8—101no—
234C3×Q8—101no—
235C3×D4—101no—
236C3×D4—101no—
237C3×D4—201no—
238C3×D4—201no—
239C2×C3×C4—22no—
240C2×C3×C4—101no—
241C2×C3×C4—201no—
242C2×C3×C4—201no—
243C2×C3×C4C2×C4×D511yescharacteristic
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4#70911yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4#71111yescharacteristic
248C2×C3×C4#71311yescharacteristic
249C2×Dic3—22no—
250C2×Dic3—42no—
251C3×C8—102no—
252C3⋊C8—41no—
253C3⋊C8—102no—
254C3⋊C8—201no—
255C22×C5—22no—
256C22×C5#87911yescharacteristic
257C22×C5#88311yescharacteristic
258C22×C5D4×Dic311yescharacteristic
259C2×D5—42no—
260C2×D5—41no—
261C4×C5—42no—
262C4×C5—122no—
263C4×C5#88411yescharacteristic
264C4×C5#88511yescharacteristic
265C4×C5#92611yescharacteristic
266C4×C5D4×Dic311yescharacteristic
267Dic5—41no—
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—61no—
279M16—61no—
280M16—301no—
281M16—301no—
282C2×C8—52no—
283C2×C8—61no—
284C2×C8—101no—
285C2×C8—101no—
286C2×C8—152no—
287C2×C8—301no—
288C2×C8—301no—
289C2×C8—301no—
290C4⋊C4D5×Dic312yes—
291C22⋊C4—21no—
292C42—21no—
293C42—32no—
294C42—61no—
295C3×C5#193811yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3—202no—
298C22×C3—201no—
299C22×C3#402711yescharacteristic
300C22×C3#403211yescharacteristic
301C22×C3#404411yescharacteristic
302C3×C4—42no—
303C3×C4—201no—
304C3×C4C4×D2011yescharacteristic
305C3×C4#403111yescharacteristic
306C3×C4#403811yescharacteristic
307C3×C4#404111yescharacteristic
308Dic3—42no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5#495111yescharacteristic
312C2×C5#519712yes—
313D5—81no—
314C23—101no—
315C23#678011yescharacteristic
316Q8—101no—
317Q8—101no—
318D4—101no—
319D4—101no—
320D4—201no—
321D4—201no—
322C2×C4—22no—
323C2×C4—62no—
324C2×C4—101no—
325C2×C4—122no—
326C2×C4—201no—
327C2×C4—201no—
328C2×C4#676511yescharacteristic
329C2×C4#677211yescharacteristic
330C2×C4#677311yescharacteristic
331C2×C4D3×D2011yescharacteristic
332C2×C4C2×D5×Dic311yescharacteristic
333C2×C4#679011yescharacteristic
334C8—102no—
335C8—121no—
336C8—302no—
337C8—601no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—401no—
341C2×C3#6495911yescharacteristic
342C2×C3#6511212yes—
343C5#7028811yescharacteristic, complemented, Sylow
344C22—22no—
345C22—202no—
346C22—201no—
347C22#9136211yescharacteristic
348C22#9145711yescharacteristic
349C22#9155911yescharacteristic
350C4—42no—
351C4—122no—
352C4—201no—
353C4#9135811yescharacteristic
354C4Dic3×D2011yescharacteristic
355C4#9145911yescharacteristic
356C4#9146211yescharacteristic
357C3#1059953911yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—401no—
361C2#1174877211yescharacteristic
362C2#1174944112yes—
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C4×D4
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1938
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11751100C2semidirect
5. C2×#90953C2semidirect
6. C5×#4532C2semidirect
7. #11745984C2semidirect
17. C3×#3942C4semidirect
18. C3×#3941C4semidirect
63. #4532D5semidirect
72. #3942Dic3semidirect
73. #3941Dic3semidirect
295. C3×C5#1938semidirect
343. C5#70288semidirect
357. C3#10599539semidirect

Maximal subgroups

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

subgroupindex
#117511002
C3×#652912
C2×#909772
#117483432
C2×#909532
C5×#45322
#117459842
#105995393
#702885