Finite Group Databasebeta

← #14304902

Subgroups — #14304902

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#11751103C211yesmaximal, characteristic
2C3×#65288C211yesmaximal, characteristic, complemented
3C2×#90980C211yesmaximal, characteristic
4#11748349C211yesmaximal, characteristic
5C2×#90953C211yesmaximal, characteristic, complemented
6C5×#4532C211yesmaximal, characteristic, complemented
7#11745982C211yesmaximal, characteristic, complemented
8#10599539—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C22×C3⋊#168C2211yescharacteristic
12C2×C4×C5×Dic3C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16#91094C412yescomplemented
17#91093C412yescomplemented
18C3×C4⋊#168—22no—
19#90980—22no—
20#90957—22no—
21#90953—22no—
22#70536—51nomaximal, Hall
23#65418—31no—
24#65291—31no—
25#65288D311yescharacteristic, complemented
26C2×#3937—31no—
27C2×#3935—31no—
28C5×#339—31no—
29#64778—31no—
30C22×C3×C4×C5C2311yescharacteristic
31C2×#1220—21no—
32#6817—21no—
33#6817—21no—
34#6817—21no—
35#6817—21no—
36C2×D60C2×C411yescharacteristic
37C2×C4×D15—21no—
38C2×Dic30C2×C411yescharacteristic
39C22×C5×Dic3—21no—
40C3×C5×C4⋊C4C2×C412yes—
41C3×C5×C22⋊C4—21no—
42C3×C42×C5—21no—
43C2×C3⋊#168—21no—
44C2×C3⋊#168—21no—
45C2×C3⋊#168C2×C412yes—
46C4×C5×Dic3—21no—
47C4×C5×Dic3D412yes—
48C5×#208—21no—
49C5×#208—21no—
50C2×C5×C3⋊C8—21no—
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#5002—51no—
62#4558—51no—
63#4532D511yescharacteristic, complemented
64C2×#709—31no—
65C2×C5×M16—31no—
66C5×#117C2×D311yescharacteristic
67C2×C42×C5—31no—
68C2×#681C2×D311yescharacteristic
69C22×#168—31no—
70C22×#168C2×D311yescharacteristic
71#3952—62no—
72#3942—32no—
73#3941—32no—
74#3937—62no—
75C4⋊#168—22no—
76#3935—62no—
77#1938—151noSylow
78C23×C3×C5#4111yescharacteristic
79C22×D15—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
87#1220—41no—
88#1220—41no—
89C2×Dic15—21no—
90D60—21no—
91D60—21no—
92C4×D15—41no—
93C4×D15—41no—
94Dic30—21no—
95Dic30—21no—
96C2×C5×Dic3—22no—
97C2×C5×Dic3—42no—
98C3⋊#168—22no—
99C3×#168—22no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C2×#235—51no—
103C2×C3×M16—51no—
104C22×C3×C8—51no—
105C3×#117C2×D511yescharacteristic
106C2×C4×Dic3C2×D511yescharacteristic
107C2×#208C2×D511yescharacteristic
108C22×C3⋊C8—51no—
109C3×C4⋊C8—102no—
110#825—102no—
111(C2×D3)⋊C8—102no—
112#815—102no—
113#810—52no—
114#809—52no—
115C22×C4×C5—61no—
116C22×C4×C5C22×D311yescharacteristic
117C2×C22⋊D5—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—61no—
126C5×M16—61no—
127C2×C5×C8—61no—
128C5×C4⋊C4C4×D312yes—
129C5×C22⋊C4—21no—
130C42×C5—21no—
131C42×C5—32no—
132C42×C5—61no—
133#681—21no—
134#681—21no—
135C2×#168—21no—
136C2×#168—21no—
137C2×#168—21no—
138C2×#168—32no—
139C2×#168—61no—
140C2×#168—61no—
141C2×#168#6712yes—
142#424—51no—
143C2×#104—151no—
144#416—151no—
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×D15—41no—
154C2×D15—42no—
155C3×C4×C5—42no—
156C3×C4×C5#11711yescharacteristic
157C3×C4×C5C4×D411yescharacteristic
158C3×C4×C5#12111yescharacteristic
159C3×C4×C5#12411yescharacteristic
160Dic15—41no—
161C5×Dic3—42no—
162C22×C3×C4C22×D511yescharacteristic
163C2×#67—101no—
164C22×Dic3—21no—
165#235—101no—
166#235—101no—
167#235—101no—
168#235—101no—
169C2×D12—51no—
170C2×C4×D3—101no—
171C2×Dic6—51no—
172C3×M16—101no—
173C3×M16—101no—
174C2×C3×C8—52no—
175C2×C3×C8—101no—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C3×C4⋊C4C4×D512yes—
179C3×C22⋊C4—21no—
180C3×C42—21no—
181C4×Dic3—21no—
182C4×Dic3D2012yes—
183#208—21no—
184#208—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—52no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C23×C5#23511yescharacteristic
190C22×D5—61no—
191C2×C4×C5—22no—
192C2×C4×C5—62no—
193C2×C4×C5—122no—
194C2×C4×C5C2×C4×D311yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5#23711yescharacteristic
197C2×C4×C5#23911yescharacteristic
198C2×C4×C5#23911yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C22⋊D5—121no—
201C22⋊D5—121no—
202C2×Dic5—61no—
203D20—61no—
204D20—61no—
205C4×D5—121no—
206C4×D5—121no—
207Dic10—61no—
208Dic10—61no—
209C5×C8—121no—
210#168—22no—
211#168—41no—
212#168—62no—
213C2×#41—151no—
214C2×M16—31no—
215C2×M16—51no—
216C22×C8—51no—
217C22×C8—151no—
218#117D3×D511yescharacteristic
219C2×C42—31no—
220C4⋊C8—102no—
221#104—302no—
222#103—152no—
223#102—152no—
224C22⋊C8—302no—
225#97—302no—
226C2×C3×C5—21no—
227C2×C3×C5—21no—
228C2×C3×C5#38811yescharacteristic
229C2×C3×C5#44412yes—
230D15—81no—
231C23×C3#71111yescharacteristic
232C22×D3—101no—
233C2×C3×C4—22no—
234C2×C3×C4C2×C4×D511yescharacteristic
235C2×C3×C4C2×D2011yescharacteristic
236C2×C3×C4#70911yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×C3×C4#71111yescharacteristic
239C2×C3×C4#71311yescharacteristic
240#67—201no—
241#67—201no—
242C2×Dic3—22no—
243C2×Dic3—42no—
244C2×Dic3—101no—
245D12—101no—
246D12—101no—
247C4×D3—201no—
248C4×D3—201no—
249Dic6—101no—
250Dic6—101no—
251C3×C8—102no—
252C3×C8—201no—
253C3⋊C8—41no—
254C3⋊C8—102no—
255C22×C5—22no—
256C22×C5#89411yescharacteristic
257C22×C5#89811yescharacteristic
258C22×C5C4×#6711yescharacteristic
259C2×D5—122no—
260C2×D5—121no—
261C4×C5—42no—
262C4×C5—122no—
263C4×C5#89211yescharacteristic
264C4×C5#89311yescharacteristic
265C4×C5#93911yescharacteristic
266C4×C5#94711yescharacteristic
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—61no—
276C22×C4—301no—
277C22×C4C2×D3×D511yescharacteristic
278M16—61no—
279M16—61no—
280M16—101no—
281M16—101no—
282C2×C8—52no—
283C2×C8—61no—
284C2×C8—101no—
285C2×C8—101no—
286C2×C8—101no—
287C2×C8—152no—
288C2×C8—301no—
289C2×C8—301no—
290C4⋊C4#120012yes—
291C22⋊C4—21no—
292C42—21no—
293C42—32no—
294C42—61no—
295C3×C5#193811yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3#402711yescharacteristic
298C22×C3#403211yescharacteristic
299C22×C3#404411yescharacteristic
300C2×D3—202no—
301C2×D3—201no—
302C3×C4—42no—
303C3×C4C4×D2011yescharacteristic
304C3×C4#403111yescharacteristic
305C3×C4#403811yescharacteristic
306C3×C4#404111yescharacteristic
307Dic3—42no—
308Dic3—201no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5#499011yescharacteristic
312C2×C5#514512yes—
313D5—241no—
314C23—301no—
315C23#678211yescharacteristic
316Q8—301no—
317Q8—301no—
318D4—301no—
319D4—301no—
320D4—601no—
321D4—601no—
322C2×C4—22no—
323C2×C4—62no—
324C2×C4—122no—
325C2×C4—301no—
326C2×C4—601no—
327C2×C4—601no—
328C2×C4#676611yescharacteristic
329C2×C4#676811yescharacteristic
330C2×C4#676911yescharacteristic
331C2×C4D3×D2011yescharacteristic
332C2×C4C2×#120011yescharacteristic
333C2×C4D5×#6711yescharacteristic
334C8—102no—
335C8—121no—
336C8—201no—
337C8—302no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3#6495911yescharacteristic
341C2×C3#6511212yes—
342D3—401no—
343C5#7053611yescharacteristic, complemented, Sylow
344C22—22no—
345C22—602no—
346C22—601no—
347C22#9134511yescharacteristic
348C22#9142711yescharacteristic
349C22#9155211yescharacteristic
350C4—42no—
351C4—122no—
352C4—601no—
353C4#9132611yescharacteristic
354C4#9134711yescharacteristic
355C4#9140911yescharacteristic
356C4#9142811yescharacteristic
357C3#1059953911yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—1201no—
361C2#1174867811yescharacteristic
362C2#1174943512yes—
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C4×D4
prime radicalC2×#6817C22
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×#90953C2semidirect
6. C5×#4532C2semidirect
7. #11745982C2semidirect
16. #91094C4semidirect
17. #91093C4semidirect
25. #65288D3semidirect
63. #4532D5semidirect
295. C3×C5#1938semidirect
343. C5#70536semidirect
357. C3#10599539semidirect

Maximal subgroups

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

subgroupindex
#117511032
C3×#652882
C2×#909802
#117483492
C2×#909532
C5×#45322
#117459822
#105995393
#705365