Finite Group Databasebeta

← #14304904

Subgroups — #14304904

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
1C5×#5002C211yesmaximal, characteristic
2C3×#65288C211yesmaximal, characteristic, complemented
3C2×#90978C211yesmaximal, characteristic
4#11748345C211yesmaximal, characteristic
5C2×#90954C211yesmaximal, characteristic, complemented
6#11746353C211yesmaximal, characteristic, complemented
7#11745983C211yesmaximal, characteristic, complemented
8#10601081—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C22×C5×C3⋊C8C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C5×#810C412yescomplemented
17C5×#809C412yescomplemented
18C3×C4⋊#168—22no—
19#90978—22no—
20(C2×D3)⋊#168—22no—
21#90954—22no—
22#70536—51nomaximal, Hall
23C5×#416—31no—
24C2×#3969—31no—
25#65523—31no—
26C2×#3947—31no—
27#65288D311yescharacteristic, complemented
28#64772—31no—
29#64752—31no—
30C22×C3×C4×C5C2311yescharacteristic
31C22×Dic15—21no—
32C2×C5×#67—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×C4⋊C4C2×C412yes—
41C3×C5×C22⋊C4—21no—
42C3×C42×C5—21no—
43C4×Dic15—21no—
44C4×Dic15D412yes—
45#6710—21no—
46#6710—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8C2×C412yes—
51C3×#681—21no—
52C3×#681—21no—
53C2×C3×#168—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C2×C3×#168D412yes—
57C3×#424—51no—
58C2×#825—51no—
59#5110—51no—
60C2×#815—51no—
61#5002D511yescharacteristic
62#4558—51no—
63#4532—51no—
64C2×C5×#41—31no—
65C22×C5×C8—31no—
66C5×#117C2×D311yescharacteristic
67C2×C4×Dic5—31no—
68C2×#681—31no—
69C2×#681C2×D311yescharacteristic
70C22×#168C2×D311yescharacteristic
71C5×#103—32no—
72C5×#102—32no—
73#3969—62no—
74C22⋊#168—62no—
75#3947—62no—
76C4⋊#168—22no—
77#1938—151noSylow
78C23×C3×C5#4111yescharacteristic
79C22×C5×D3—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×Dic15—22no—
88C2×Dic15—42no—
89C5×#67—41no—
90C5×#67—41no—
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⋊#168—41no—
99C3×#168—22no—
100C3×#168—41no—
101C5×C3⋊C8—22no—
102C2×#235C2×D511yescharacteristic
103C2×C3×M16—51no—
104C22×C3×C8—51no—
105C3×#117C2×D511yescharacteristic
106C2×C4×Dic3—51no—
107C2×#208—51no—
108C22×C3⋊C8C2×D511yescharacteristic
109C3×C4⋊C8—102no—
110#825—102no—
111(C2×D3)⋊C8—102no—
112#815—102no—
113#810Dic512yescomplemented
114#809Dic512yescomplemented
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×C5C22×D311yescharacteristic
124C22×Dic5—61no—
125C2×C5×C8—32no—
126C2×C5×C8—61no—
127C2×C5×C8—61no—
128C5×C4⋊C4C4×D312yes—
129C5×C22⋊C4—21no—
130C42×C5—21no—
131C4×Dic5—32no—
132C4×Dic5—61no—
133#681—21no—
134#681—21no—
135#681—61no—
136#681—61no—
137C2×#168—21no—
138C2×#168—21no—
139C2×#168—21no—
140C2×#168—61no—
141C2×#168#6712yes—
142#424—51no—
143C2×#104—151no—
144#416—31no—
145#408—151no—
146C2×#97—151no—
147#341—151no—
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—42no—
156C3×C4×C5#11711yescharacteristic
157C3×C4×C5C4×D411yescharacteristic
158C3×C4×C5#12111yescharacteristic
159C3×C4×C5#12411yescharacteristic
160Dic15—42no—
161C5×Dic3—41no—
162C22×C3×C4C22×D511yescharacteristic
163C2×#67—21no—
164C22×Dic3—101no—
165#235—21no—
166#235—21no—
167#235—21no—
168#235—21no—
169C2×D12C2×Dic511yescharacteristic
170C2×C4×D3—21no—
171C2×Dic6C2×Dic511yescharacteristic
172C3×M16—101no—
173C3×M16—101no—
174C2×C3×C8—52no—
175C2×C3×C8—101no—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C3×C4⋊C4C2×Dic512yes—
179C3×C22⋊C4—21no—
180C3×C42—21no—
181C4×Dic3—52no—
182C4×Dic3—101no—
183#208—101no—
184#208—101no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8C2×Dic512yes—
189C23×C5—61no—
190C23×C5#23511yescharacteristic
191C5×Q8—61no—
192C5×Q8—61no—
193C5×D4—61no—
194C5×D4—61no—
195C5×D4—121no—
196C5×D4—121no—
197C2×C4×C5—22no—
198C2×C4×C5—61no—
199C2×C4×C5—121no—
200C2×C4×C5—121no—
201C2×C4×C5C2×C4×D311yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5#23711yescharacteristic
204C2×C4×C5#23911yescharacteristic
205C2×C4×C5#23911yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C2×Dic5—62no—
208C2×Dic5—122no—
209C5×C8—62no—
210#168—22no—
211#168—41no—
212#168—121no—
213C2×#41—31no—
214C2×M16—51no—
215C2×M16—151no—
216C22×C8—31no—
217C22×C8—51no—
218#117D3×D511yescharacteristic
219C2×C42—151no—
220C4⋊C8—102no—
221#104—302no—
222#103—32no—
223#102—32no—
224C22⋊C8—302no—
225#97—302no—
226C2×C3×C5—21no—
227C2×C3×C5—21no—
228C2×C3×C5#38811yescharacteristic
229C2×C3×C5#44412yes—
230C5×D3—81no—
231C23×C3#71111yescharacteristic
232C22×D3—21no—
233C2×C3×C4—22no—
234C2×C3×C4#70911yescharacteristic
235C2×C3×C4#70911yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×C3×C4#71111yescharacteristic
239C2×C3×C4C22×Dic511yescharacteristic
240#67—41no—
241#67—41no—
242C2×Dic3—21no—
243C2×Dic3—102no—
244C2×Dic3—202no—
245D12—21no—
246D12—21no—
247C4×D3—41no—
248C4×D3—41no—
249Dic6—21no—
250Dic6—21no—
251C3×C8—102no—
252C3×C8—201no—
253C3⋊C8—22no—
254C3⋊C8—201no—
255C22×C5—22no—
256C22×C5—122no—
257C22×C5—121no—
258C22×C5#89411yescharacteristic
259C22×C5#89811yescharacteristic
260C22×C5C4×#6711yescharacteristic
261C4×C5—42no—
262C4×C5—121no—
263C4×C5#89211yescharacteristic
264C4×C5#89311yescharacteristic
265C4×C5#93911yescharacteristic
266C4×C5#94711yescharacteristic
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—301no—
277C22×C4C2×D3×D511yescharacteristic
278M16—101no—
279M16—101no—
280M16—301no—
281M16—301no—
282C2×C8—32no—
283C2×C8—52no—
284C2×C8—61no—
285C2×C8—61no—
286C2×C8—101no—
287C2×C8—101no—
288C2×C8—101no—
289C2×C8—301no—
290C4⋊C4D3×Dic512yes—
291C22⋊C4—21no—
292C42—21no—
293C42—152no—
294C42—301no—
295C3×C5#193811yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3#402511yescharacteristic
298C22×C3#402911yescharacteristic
299C22×C3D4×Dic511yescharacteristic
300C2×D3—42no—
301C2×D3—41no—
302C3×C4—42no—
303C3×C4#403011yescharacteristic
304C3×C4#403111yescharacteristic
305C3×C4#407211yescharacteristic
306C3×C4D4×Dic511yescharacteristic
307Dic3—41no—
308Dic3—202no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5—241no—
312C2×C5#499011yescharacteristic
313C2×C5#514512yes—
314C23—61no—
315C23#678211yescharacteristic
316Q8—61no—
317Q8—61no—
318D4—61no—
319D4—61no—
320D4—121no—
321D4—121no—
322C2×C4—22no—
323C2×C4—61no—
324C2×C4—121no—
325C2×C4—121no—
326C2×C4—302no—
327C2×C4—602no—
328C2×C4#676511yescharacteristic
329C2×C4#676811yescharacteristic
330C2×C4#676911yescharacteristic
331C2×C4#677711yescharacteristic
332C2×C4C2×D3×Dic511yescharacteristic
333C2×C4D5×#6711yescharacteristic
334C8—62no—
335C8—102no—
336C8—201no—
337C8—601no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3#6524011yescharacteristic
341C2×C3#6548612yes—
342D3—81no—
343C5#7053611yescharacteristic, complemented, Sylow
344C22—22no—
345C22—122no—
346C22—121no—
347C22#9134111yescharacteristic
348C22#9143811yescharacteristic
349C22Dic5×#6711yescharacteristic
350C4—42no—
351C4—121no—
352C4—602no—
353C4#9132611yescharacteristic
354C4#9133811yescharacteristic
355C4#9140811yescharacteristic
356C4#9143511yescharacteristic
357C3#1060108111yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—241no—
361C2#1174867511yescharacteristic
362C2#1174943312yes—
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C4×D4
prime radicalC2×C5×#235C22
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
2. C3×#65288C2semidirect
5. C2×#90954C2semidirect
6. #11746353C2semidirect
7. #11745983C2semidirect
16. C5×#810C4semidirect
17. C5×#809C4semidirect
27. #65288D3semidirect
113. #810Dic5semidirect
114. #809Dic5semidirect
295. C3×C5#1938semidirect
343. C5#70536semidirect
357. C3#10601081semidirect

Maximal subgroups

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

subgroupindex
C5×#50022
C3×#652882
C2×#909782
#117483452
C2×#909542
#117463532
#117459832
#106010813
#705365