Finite Group Databasebeta

← #14283915

Subgroups — #14283915

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756238C211yesmaximal, characteristic
2C2×C3×C5×#97C211yesmaximal, characteristic, complemented
3C4×#6710C211yesmaximal, characteristic, complemented
4#11746286C212yesmaximal, complemented
5#11746285C212yesmaximal, complemented
6#10600590—31nomaximal, Hall
7C22×C3×C5×C8—21no—
8C2×C3×C42×C5C2211yescharacteristic
9#91819C411yescharacteristic
10#91818—21no—
11C4×#1220—21no—
12#91813C411yescharacteristic
13C2×#6710—21no—
14#91765—21no—
15#91764C2211yescharacteristic
16C4×D60C411yescharacteristic
17#91761—21no—
18#91759C2211yescharacteristic
19C4×Dic30C411yescharacteristic
20C3×C5×#97—21no—
21C3×C5×#97C2212yes—
22#91087C2212yes—
23C4×C3⋊#168—21no—
24#69797—51nomaximal, Hall
25#65813—31no—
26C2×C5×#97D311yescharacteristic, complemented
27C4×#681—31no—
28#64685—32no—
29#64684—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C2×#1220—21no—
34C2×D60C2×C411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30C2×C411yescharacteristic
37C2×C3×C5×C8—24no—
38C2×C3×C5×C8—22no—
39C3×C42×C5C2×C411yescharacteristic
40C3×C42×C5D411yescharacteristic
41C3×C42×C5D411yescharacteristic
42C3×C42×C5C2311yescharacteristic
43#6719—21no—
44#6714—21no—
45#6714—21no—
46#6714—21no—
47#6714—21no—
48C4⋊Dic15C2×C411yescharacteristic
49C4⋊Dic15C2×C411yescharacteristic
50#6712—21no—
51#6712—21no—
52#6712—21no—
53#6712—21no—
54C4×Dic15—21no—
55#6710—24no—
56C2×C3⋊#168—22no—
57#5479—51no—
58C2×C3×#97D511yescharacteristic, complemented
59C4×#208—51no—
60#4465—52no—
61#4464—52no—
62C22×C5×C8—21no—
63C2×C42×C5C2×D311yescharacteristic
64#4076—31no—
65#4075—61no—
66C4×C22⋊D5—61no—
67#4070—31no—
68C2×#681—61no—
69#4022—61no—
70#4021—31no—
71C4×D20—31no—
72#4018—61no—
73#4016—31no—
74C4×Dic10—31no—
75C5×#97—21no—
76C5×#97C2×D312yes—
77#3935—32no—
78C4×#168—61no—
79#1524—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×D15—21no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91#1220—42no—
92C2×Dic15—21no—
93C2×Dic15—21no—
94C2×Dic15—21no—
95D60—41no—
96C4×D15—42no—
97Dic30—41no—
98C3×C5×C8—24no—
99C3⋊#168—24no—
100C22×C3×C8—21no—
101C2×C3×C42C2×D511yescharacteristic
102#930—51no—
103#929—101no—
104C4×#67—101no—
105#924—51no—
106C2×#208—101no—
107#876—101no—
108#875—51no—
109C4×D12—51no—
110#872—101no—
111#870—51no—
112C4×Dic6—51no—
113C3×#97—21no—
114C3×#97C2×D512yes—
115#803—52no—
116C4×C3⋊C8—101no—
117C22×C4×C5C4×D311yescharacteristic
118C22×C4×C5D1211yescharacteristic
119C22×C4×C5#6711yescharacteristic
120C2×C22⋊D5—61no—
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×Dic10—31no—
124C2×C5×C8—24no—
125C2×C5×C8—22no—
126C42×C5C4×D311yescharacteristic
127C42×C5D1211yescharacteristic
128C42×C5#6711yescharacteristic
129C42×C5C22×D311yescharacteristic
130C22⋊Dic5—61no—
131#685—61no—
132#685—61no—
133#685—61no—
134#685—61no—
135C4⋊Dic5—31no—
136C4⋊Dic5—31no—
137#683—61no—
138#683—61no—
139#683—61no—
140#683—61no—
141C4×Dic5—61no—
142#681—64no—
143C2×#168—62no—
144#529—151no—
145C4×M16—151no—
146C2×#97D1511yescharacteristic, complemented
147#330—152no—
148#329—152no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5#10412yes—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C2×D15—41no—
154C2×D15—41no—
155C2×D15—41no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5#10412yes—
162Dic15—41no—
163Dic15—41no—
164Dic15—41no—
165C22×C3×C4C4×D511yescharacteristic
166C22×C3×C4D2011yescharacteristic
167C22×C3×C4C22⋊D511yescharacteristic
168C2×#67—101no—
169C2×D12—51no—
170C2×C4×D3—101no—
171C2×Dic6—51no—
172C2×C3×C8—24no—
173C2×C3×C8—22no—
174C3×C42C4×D511yescharacteristic
175C3×C42D2011yescharacteristic
176C3×C42C22⋊D511yescharacteristic
177C3×C42C22×D511yescharacteristic
178#217—101no—
179(C2×D3)⋊C4—101no—
180(C2×D3)⋊C4—101no—
181(C2×D3)⋊C4—101no—
182(C2×D3)⋊C4—101no—
183C4⋊Dic3—51no—
184C4⋊Dic3—51no—
185Dic3⋊C4—101no—
186Dic3⋊C4—101no—
187Dic3⋊C4—101no—
188Dic3⋊C4—101no—
189C4×Dic3—101no—
190#208—104no—
191C2×C3⋊C8—102no—
192C23×C5(C2×D3)⋊C411yescharacteristic
193C22×D5—61no—
194C2×C4×C5—22no—
195C2×C4×C5—22no—
196C2×C4×C5—41no—
197C2×C4×C5(C2×D3)⋊C411yescharacteristic
198C2×C4×C5(C2×D3)⋊C411yescharacteristic
199C2×C4×C5(C2×D3)⋊C411yescharacteristic
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5C2×D1211yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C22⋊D5—122no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C2×Dic5—61no—
207D20—121no—
208C4×D5—122no—
209Dic10—121no—
210C5×C8—24no—
211#168—64no—
212C2×M16—301no—
213C22×C8—21no—
214#126—301no—
215#125—151no—
216#124—151no—
217#123—301no—
218C22⋊Q8—151no—
219#121—151no—
220C4×Q8—151no—
221C4×D4—151no—
222C4×D4—301no—
223#117—301no—
224C2×C42C2×D1511yescharacteristic
225#97—21no—
226#97—152no—
227#97C2×D1512yes—
228C4×C8—301no—
229C2×C3×C5—22no—
230C2×C3×C5#41311yescharacteristic
231C2×C3×C5C2×#10411yescharacteristic
232C2×C3×C5C2×#10411yescharacteristic
233D15—81no—
234C23×C3#68511yescharacteristic
235C22×D3—101no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—41no—
239C2×C3×C4#68511yescharacteristic
240C2×C3×C4#68511yescharacteristic
241C2×C3×C4#68511yescharacteristic
242C2×C3×C4C2×C4×D511yescharacteristic
243C2×C3×C4C2×D2011yescharacteristic
244C2×C3×C4C2×C22⋊D511yescharacteristic
245#67—202no—
246C2×Dic3—101no—
247C2×Dic3—101no—
248C2×Dic3—101no—
249D12—201no—
250C4×D3—202no—
251Dic6—201no—
252C3×C8—24no—
253C3⋊C8—104no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5#82512yes—
257C22×C5C2×(C2×D3)⋊C411yescharacteristic
258C2×D5—121no—
259C2×D5—121no—
260C2×D5—121no—
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5#80512yes—
267Dic5—121no—
268Dic5—121no—
269Dic5—121no—
270C2×Q8—151no—
271C2×D4—151no—
272C2×D4—301no—
273C22×C4—301no—
274C22×C4C4×D1511yescharacteristic
275C22×C4D6011yescharacteristic
276C22×C4#122011yescharacteristic
277M16—304no—
278C2×C8—24no—
279C2×C8—22no—
280C2×C8—302no—
281C4⋊C4—151no—
282C4⋊C4—151no—
283C4⋊C4—301no—
284C4⋊C4—301no—
285C4⋊C4—301no—
286C4⋊C4—301no—
287C22⋊C4—301no—
288C22⋊C4—301no—
289C22⋊C4—301no—
290C22⋊C4—301no—
291C22⋊C4—301no—
292C42—301no—
293C42C4×D1511yescharacteristic
294C42D6011yescharacteristic
295C42#122011yescharacteristic
296C42C22×D1511yescharacteristic
297C3×C5#152411yescharacteristic, complemented, Hall
298C22×C3—21no—
299C22×C3—21no—
300C22×C3#395712yes—
301C22×C3C2×#68511yescharacteristic
302C2×D3—201no—
303C2×D3—201no—
304C2×D3—201no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4#393712yes—
311Dic3—201no—
312Dic3—201no—
313Dic3—201no—
314C2×C5—22no—
315C2×C5C2×#80511yescharacteristic
316C2×C5#513211yescharacteristic
317C2×C5C2×#82511yescharacteristic
318D5—241no—
319C23—301no—
320C23#671411yescharacteristic
321Q8—601no—
322D4—601no—
323D4—602no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—301no—
328C2×C4—301no—
329C2×C4—301no—
330C2×C4—602no—
331C2×C4#671411yescharacteristic
332C2×C4#671411yescharacteristic
333C2×C4#671411yescharacteristic
334C2×C4C2×C4×D1511yescharacteristic
335C2×C4C2×D6011yescharacteristic
336C2×C4C2×#122011yescharacteristic
337C8—24no—
338C8—304no—
339C2×C3—22no—
340C2×C3C2×#393711yescharacteristic
341C2×C3#6542111yescharacteristic
342C2×C3C2×#395711yescharacteristic
343D3—401no—
344C5#6979711yescharacteristic, complemented, Sylow
345C22—21no—
346C22—21no—
347C22—601no—
348C22—601no—
349C22—601no—
350C22#9110912yes—
351C22C2×#671411yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—601no—
358C4—601no—
359C4—601no—
360C4#9108912yes—
361C3#1060059011yescharacteristic, complemented, Sylow
362C2—22no—
363C2—1201no—
364C2C2×#9108911yescharacteristic
365C2#1175123311yescharacteristic
366C2C2×#9110911yescharacteristic
subgroupG/H
centerC2×C4#6714
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC2×C3×C5×#97C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C4
cosocleC3×C42×C5C23
hypercenterC2×#97D15
hypocenterC3×C5#1524
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#97C2semidirect
3. C4×#6710C2semidirect
4. #11746286C2semidirect
5. #11746285C2semidirect
26. C2×C5×#97D3semidirect
58. C2×C3×#97D5semidirect
146. C2×#97D15semidirect
297. C3×C5#1524semidirect
344. C5#69797semidirect
361. C3#10600590semidirect

Maximal subgroups

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

subgroupindex
#117562382
C2×C3×C5×#972
C4×#67102
#117462862
#117462852
#106005903
#697975