Finite Group Databasebeta

← #14284033

Subgroups — #14284033

Order 1920.

528 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×#124C211yesmaximal, characteristic
2#11750808C211yesmaximal, characteristic, complemented
3#11750806C211yesmaximal, characteristic, complemented
4C3×C5×#329C211yesmaximal, characteristic, complemented
5#11746361C211yesmaximal, characteristic, complemented
6#11746285C211yesmaximal, characteristic, complemented
7#11746285C211yesmaximal, characteristic, complemented
8#10599136—31nomaximal, Hall
9C2×Q8×D15C411yescharacteristic
10C2×D4×D15C411yescharacteristic
11C3×C5×#124C2211yescharacteristic
12#91836C411yescharacteristic
13#91825C411yescharacteristic
14C2×#6705—21no—
15#91774—21no—
16#91774—21no—
17C22⋊C4×D15—21no—
18C22⋊C4×D15—21no—
19#91764C2211yescharacteristic
20C42×D15C2211yescharacteristic
21C3×C5×#97C2211yescharacteristic, complemented
22C3×C5×#97C2211yescharacteristic, complemented
23#91104—21no—
24#91098—21no—
25C8×Dic15—21no—
26#91087C2211yescharacteristic, complemented
27#91087C2211yescharacteristic, complemented
28#68343—51nomaximal, Hall
29D5×#124—31no—
30#64996—31no—
31#64994—31no—
32C5×#329D311yescharacteristic, complemented
33#64760—31no—
34#64684—31no—
35#64684—31no—
36C23×D15—21no—
37C2×C3×C5×Q8C2×C411yescharacteristic
38C2×C3×C5×D4C2×C411yescharacteristic
39C2×#1220—21no—
40Q8×D15—42no—
41D4×D15—42no—
42C2×D60C2×C411yescharacteristic
43C2×C4×D15—21no—
44C2×C4×D15C2×C411yescharacteristic
45C2×C4×D15D411yescharacteristic
46C2×C4×D15D411yescharacteristic
47C2×Dic30—21no—
48C2×Dic30C2×C411yescharacteristic
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8—21no—
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53C3×C42×C5C2311yescharacteristic
54#6719—21no—
55#6719—21no—
56#6714—21no—
57#6714—21no—
58#6714—21no—
59#6714—21no—
60C4×Dic15C2×C411yescharacteristic
61C4×Dic15D411yescharacteristic
62C4×Dic15D411yescharacteristic
63C2×C3⋊#168—21no—
64C2×C3⋊#168—21no—
65#6705—24no—
66D3×#124—51no—
67#4707—51no—
68#4705—51no—
69C3×#329D511yescharacteristic, complemented
70#4540—51no—
71#4464—51no—
72#4464—51no—
73C2×Q8×D5—31no—
74C2×D4×D5—31no—
75C5×#124C2×D311yescharacteristic
76#4093—31no—
77#4082—31no—
78C2×#676—61no—
79#4031—61no—
80#4031—61no—
81D5×C22⋊C4—61no—
82D5×C22⋊C4—61no—
83#4021—31no—
84C42×D5—31no—
85C5×#97C2×D311yescharacteristic, complemented
86C5×#97C2×D311yescharacteristic, complemented
87#3952—61no—
88#3946—61no—
89C8×Dic5—61no—
90#3935—31no—
91#3935—31no—
92#1527—151noSylow
93C23×C3×C5—21no—
94C22×D15—21no—
95C22×D15—42no—
96C22×D15—42no—
97C22×D15—42no—
98C22×D15C22⋊C411yescharacteristic
99C3×C5×Q8—41no—
100C3×C5×D4—41no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105#1220—42no—
106C2×Dic15—21no—
107C2×Dic15C22⋊C411yescharacteristic
108C2×Dic15C22⋊C411yescharacteristic
109C2×Dic15C22⋊C411yescharacteristic
110D60—41no—
111C4×D15—22no—
112C4×D15—22no—
113C4×D15—41no—
114C4×D15—42no—
115Dic30—42no—
116Dic30—41no—
117C3×C5×C8—22no—
118C3×C5×C8—41no—
119C3⋊#168—22no—
120C3⋊#168—41no—
121C2×D3×Q8—51no—
122C2×D3×D4—51no—
123C3×#124C2×D511yescharacteristic
124#947—51no—
125#936—51no—
126C2×ΓL(1,𝔽25)—101no—
127#885—101no—
128#885—101no—
129D3×C22⋊C4—101no—
130D3×C22⋊C4—101no—
131#875—51no—
132C42×D3—51no—
133C3×#97C2×D511yescharacteristic, complemented
134C3×#97C2×D511yescharacteristic, complemented
135(C2×D3)⋊C8—101no—
136Dic3⋊C8—101no—
137C8×Dic3—101no—
138#803—51no—
139#803—51no—
140C23×D5—61no—
141C2×C5×Q8C4×D311yescharacteristic
142C2×C5×D4C4×D311yescharacteristic
143C2×C22⋊D5—61no—
144Q8×D5—122no—
145D4×D5—122no—
146C2×D20—31no—
147C2×C4×D5—31no—
148C2×C4×D5—31no—
149C2×C4×D5—31no—
150C2×C4×D5—61no—
151C2×Dic10—31no—
152C2×Dic10—61no—
153C2×C5×C8—21no—
154C2×C5×C8—21no—
155C5×C22⋊C4—21no—
156C5×C22⋊C4—21no—
157C42×C5C22×D311yescharacteristic
158C22⋊Dic5—61no—
159C22⋊Dic5—61no—
160#685—61no—
161#685—61no—
162#685—61no—
163#685—61no—
164C4×Dic5—31no—
165C4×Dic5—31no—
166C4×Dic5—31no—
167C2×#168—61no—
168C2×#168—61no—
169#676—64no—
170C2×#124—151no—
171#432—151no—
172C4×M16—151no—
173#329—151no—
174#329—151no—
175#329—151no—
176#329D1511yescharacteristic, complemented
177C22×C3×C5—41no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C2×D15—21no—
182C2×D15—21no—
183C2×D15—41no—
184C2×D15—41no—
185C2×D15—41no—
186C2×D15—84no—
187C2×D15#10412yes—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—41no—
192Dic15—21no—
193Dic15—21no—
194Dic15—41no—
195Dic15#10012yes—
196C23×D3—101no—
197C2×C3×Q8C4×D511yescharacteristic
198C2×C3×D4C4×D511yescharacteristic
199C2×#67—101no—
200D3×Q8—202no—
201D3×D4—202no—
202C2×D12—51no—
203C2×C4×D3—51no—
204C2×C4×D3—51no—
205C2×C4×D3—51no—
206C2×C4×D3—101no—
207C2×Dic6—51no—
208C2×Dic6—101no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C3×C22⋊C4—21no—
212C3×C22⋊C4—21no—
213C3×C42C22×D511yescharacteristic
214#217—101no—
215#217—101no—
216(C2×D3)⋊C4—101no—
217(C2×D3)⋊C4—101no—
218(C2×D3)⋊C4—101no—
219(C2×D3)⋊C4—101no—
220C4×Dic3—51no—
221C4×Dic3—51no—
222C4×Dic3—51no—
223C2×C3⋊C8—101no—
224C2×C3⋊C8—101no—
225ΓL(1,𝔽25)—104no—
226C23×C5—21no—
227C22×D5—31no—
228C22×D5—61no—
229C22×D5—122no—
230C22×D5—122no—
231C22×D5—122no—
232C5×Q8—41no—
233C5×D4—41no—
234C2×C4×C5—21no—
235C2×C4×C5C2×C4×D311yescharacteristic
236C2×C4×C5D3×D411yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C22⋊D5—122no—
239C2×Dic5—31no—
240C2×Dic5—31no—
241C2×Dic5—31no—
242C2×Dic5—61no—
243D20—121no—
244C4×D5—62no—
245C4×D5—62no—
246C4×D5—121no—
247C4×D5—122no—
248Dic10—122no—
249Dic10—121no—
250C5×C8—22no—
251C5×C8—41no—
252#168—62no—
253#168—121no—
254C22×Q8—151no—
255C22×D4—151no—
256C2×M16—301no—
257#124—151no—
258#124—151no—
259#124—151no—
260#124—301no—
261#124—301no—
262#124C2×D1511yescharacteristic
263C2×C22⋊C4—301no—
264C2×C22⋊C4—301no—
265C2×C42—151no—
266C4⋊C8—301no—
267C22⋊C8—301no—
268#97—151no—
269#97—151no—
270#97C2×D1511yescharacteristic, complemented
271#97C2×D1511yescharacteristic, complemented
272C4×C8—301no—
273C2×C3×C5—81no—
274C2×C3×C5C2×#10011yescharacteristic
275C2×C3×C5C2×#10411yescharacteristic
276C2×C3×C5#42111yescharacteristic
277D15—22no—
278D15—81no—
279C23×C3—21no—
280C22×D3—51no—
281C22×D3—101no—
282C22×D3—202no—
283C22×D3—202no—
284C22×D3—202no—
285C3×Q8—41no—
286C3×D4—41no—
287C2×C3×C4—21no—
288C2×C3×C4C2×C4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291#67—202no—
292C2×Dic3—51no—
293C2×Dic3—51no—
294C2×Dic3—51no—
295C2×Dic3—101no—
296D12—201no—
297C4×D3—102no—
298C4×D3—102no—
299C4×D3—201no—
300C4×D3—202no—
301Dic6—202no—
302Dic6—201no—
303C3×C8—22no—
304C3×C8—41no—
305C3⋊C8—102no—
306C3⋊C8—201no—
307C22×C5—41no—
308C22×C5—41no—
309C22×C5—41no—
310C22×C5D3×C22⋊C411yescharacteristic
311C2×D5—32no—
312C2×D5—61no—
313C2×D5—61no—
314C2×D5—121no—
315C2×D5—121no—
316C2×D5—121no—
317C2×D5—244no—
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—41no—
322Dic5—32no—
323Dic5—61no—
324Dic5—61no—
325Dic5—121no—
326C24—301no—
327C2×Q8—151no—
328C2×Q8—301no—
329C2×Q8—602no—
330C2×Q8C4×D1511yescharacteristic
331C2×D4—151no—
332C2×D4—301no—
333C2×D4—602no—
334C2×D4C4×D1511yescharacteristic
335C22×C4—151no—
336C22×C4—151no—
337C22×C4—151no—
338C22×C4—301no—
339M16—304no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—301no—
343C2×C8—301no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—301no—
347C22⋊C4—301no—
348C22⋊C4—301no—
349C22⋊C4—301no—
350C22⋊C4—301no—
351C22⋊C4—301no—
352C42—151no—
353C42—151no—
354C42—151no—
355C42C22×D1511yescharacteristic
356C3×C5#152711yescharacteristic, complemented, Hall
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3D5×C22⋊C411yescharacteristic
361C2×D3—52no—
362C2×D3—101no—
363C2×D3—101no—
364C2×D3—201no—
365C2×D3—201no—
366C2×D3—201no—
367C2×D3—404no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—41no—
372Dic3—52no—
373Dic3—101no—
374Dic3—101no—
375Dic3—201no—
376C2×C5—81no—
377C2×C5D3×#10011yescharacteristic
378C2×C5D3×#10411yescharacteristic
379C2×C5#482111yescharacteristic
380D5—62no—
381D5—241no—
382C23—21no—
383C23—151no—
384C23—301no—
385C23—602no—
386C23—602no—
387C23—602no—
388Q8—41no—
389Q8—601no—
390Q8—602no—
391D4—41no—
392D4—601no—
393D4—602no—
394C2×C4—21no—
395C2×C4—151no—
396C2×C4—151no—
397C2×C4—151no—
398C2×C4—302no—
399C2×C4—302no—
400C2×C4—301no—
401C2×C4—601no—
402C2×C4—602no—
403C2×C4C2×C4×D1511yescharacteristic
404C2×C4D4×D1511yescharacteristic
405C2×C4D4×D1511yescharacteristic
406C8—22no—
407C8—41no—
408C8—302no—
409C8—601no—
410C2×C3—81no—
411C2×C3D5×#10011yescharacteristic
412C2×C3D5×#10411yescharacteristic
413C2×C3#6511011yescharacteristic
414D3—102no—
415D3—401no—
416C5#6834311yescharacteristic, complemented, Sylow
417C22—41no—
418C22—41no—
419C22—41no—
420C22—152no—
421C22—301no—
422C22—301no—
423C22—601no—
424C22—601no—
425C22—601no—
426C22—1204no—
427C22C22⋊C4×D1511yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—41no—
432C4—152no—
433C4—301no—
434C4—301no—
435C4—601no—
436C3#1059913611yescharacteristic, complemented, Sylow
437C2—81no—
438C2—302no—
439C2—1201no—
440C2D15×#10011yescharacteristic
441C2D15×#10411yescharacteristic
442C2#1175092211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#329C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×D4×D15C4
cosocleC3×C42×C5C23
hypercenter#329D15
hypocenterC3×C5#1527
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #11750808C2semidirect
3. #11750806C2semidirect
4. C3×C5×#329C2semidirect
5. #11746361C2semidirect
6. #11746285C2semidirect
7. #11746285C2semidirect
21. C3×C5×#97C22semidirect
22. C3×C5×#97C22semidirect
26. #91087C22semidirect
27. #91087C22semidirect
32. C5×#329D3semidirect
69. C3×#329D5semidirect
85. C5×#97C2×D3semidirect
86. C5×#97C2×D3semidirect
133. C3×#97C2×D5semidirect
134. C3×#97C2×D5semidirect
176. #329D15semidirect
270. #97C2×D15semidirect
271. #97C2×D15semidirect
356. C3×C5#1527semidirect
416. C5#68343semidirect
436. C3#10599136semidirect

Maximal subgroups

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

subgroupindex
D15×#1242
#117508082
#117508062
C3×C5×#3292
#117463612
#117462852
#105991363
#683435