Finite Group Databasebeta

← #14282152

Subgroups — #14282152

Order 1920.

492 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6819C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic, complemented
3#11750786C211yesmaximal, characteristic, complemented
4C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10598966—31nomaximal, Hall
9C2×#6819C411yescharacteristic
10C3×C4×C5×D4C2211yescharacteristic
11D4×Dic15C411yescharacteristic
12C4×#1220—21no—
13C2×C4×Dic15—21no—
14#91781C411yescharacteristic
15#91776C411yescharacteristic
16#91770—21no—
17#91766—21no—
18C42×D15C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C4×C5×C8C2211yescharacteristic
22#91104—21no—
23#91104—21no—
24#91099—21no—
25#91098—21no—
26C4⋊(C3⋊#168)C2211yescharacteristic
27C4×C3⋊#168C2211yescharacteristic
28#68173—51nomaximal, Hall
29C4×#711—31no—
30#65124—31no—
31#64974—31no—
32C5×D4⋊C8D311yescharacteristic, complemented
33D4⋊#168—31no—
34#64704—31no—
35#64676—31no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×#1220—21no—
39C22×Dic15—21no—
40C22×Dic15—21no—
41#6819—22no—
42#6819—22no—
43C2×C4×D15C2×C411yescharacteristic
44C2×C4×D15D411yescharacteristic
45C2×C4×D15D411yescharacteristic
46C2×Dic30C2×C411yescharacteristic
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C3×C5×C4⋊C4C2×C411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C42×C5C2311yescharacteristic
52#6719—21no—
53#6714—21no—
54C4⋊Dic15C2×C411yescharacteristic
55#6712—21no—
56#6712—21no—
57C4×Dic15—21no—
58C4×Dic15—21no—
59C4×Dic15—21no—
60C4×Dic15C2×C411yescharacteristic
61C4×Dic15D411yescharacteristic
62C4×Dic15D411yescharacteristic
63C2×C3⋊#168—21no—
64C2×C3⋊#168—21no—
65C4×#237—51no—
66#4835—51no—
67#4685—51no—
68C3×D4⋊C8D511yescharacteristic, complemented
69D4⋊(C3⋊C8)—51no—
70#4484—51no—
71#4456—51no—
72C2×#711—31no—
73C4×C5×D4C2×D311yescharacteristic
74D4×Dic5—31no—
75C4×C22⋊D5—61no—
76C2×C4×Dic5—61no—
77#4038—31no—
78#4033—31no—
79#4027—61no—
80#4023—61no—
81C42×D5—31no—
82C4×Dic10—31no—
83C5×C4⋊C8C2×D311yescharacteristic
84C4×C5×C8C2×D311yescharacteristic
85#3952—61no—
86#3952—61no—
87#3947—61no—
88#3946—61no—
89C4⋊#168—31no—
90C4×#168—31no—
91#1488—151noSylow
92C23×C3×C5—21no—
93C22×D15C22⋊C411yescharacteristic
94C3×C5×D4—21no—
95C3×C5×D4M1612yes—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102#1220—24no—
103C2×Dic15—24no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—42no—
107C2×Dic15C22⋊C411yescharacteristic
108C2×Dic15C22⋊C411yescharacteristic
109C2×Dic15C22⋊C411yescharacteristic
110C4×D15—21no—
111C4×D15—21no—
112C4×D15—21no—
113C4×D15—21no—
114C4×D15—41no—
115Dic30—21no—
116Dic30M1612yes—
117C3×C5×C8—41no—
118C3×C5×C8—41no—
119C3⋊#168—41no—
120C3⋊#168—41no—
121C2×#237—51no—
122C3×C4×D4C2×D511yescharacteristic
123D4×Dic3—51no—
124C4×#67—101no—
125C2×C4×Dic3—101no—
126#892—51no—
127#887—51no—
128#67⋊C4—101no—
129#877—101no—
130C42×D3—51no—
131C4×Dic6—51no—
132C3×C4⋊C8C2×D511yescharacteristic
133C3×C4×C8C2×D511yescharacteristic
134(C2×D3)⋊C8—101no—
135(C2×D3)⋊C8—101no—
136#815—101no—
137Dic3⋊C8—101no—
138C4⋊(C3⋊C8)—51no—
139C4×C3⋊C8—51no—
140C2×C5×D4C4×D311yescharacteristic
141C22×C4×C5—21no—
142C2×C22⋊D5—61no—
143C22×Dic5—61no—
144C22×Dic5—61no—
145#711—62no—
146#711—62no—
147C2×C4×D5—31no—
148C2×C4×D5—31no—
149C2×C4×D5—31no—
150C2×Dic10—31no—
151C2×C5×C8—21no—
152C2×C5×C8—21no—
153C5×C4⋊C4C4×D311yescharacteristic
154C5×C22⋊C4—21no—
155C42×C5C22×D311yescharacteristic
156C22⋊Dic5—61no—
157#685—61no—
158C4⋊Dic5—31no—
159#683—61no—
160#683—61no—
161C4×Dic5—31no—
162C4×Dic5—31no—
163C4×Dic5—31no—
164C4×Dic5—61no—
165C4×Dic5—61no—
166C4×Dic5—61no—
167C2×#168—61no—
168C2×#168—61no—
169C4×#41—151no—
170#432—151no—
171#431—151no—
172Q8⋊C8—151no—
173Q8⋊C8—151no—
174D4⋊C8—151no—
175D4⋊C8D1511yescharacteristic, complemented
176C22×C3×C5—22no—
177C22×C3×C5—41no—
178C22×C3×C5—41no—
179C22×C3×C5C2×C22⋊C411yescharacteristic
180C2×D15—21no—
181C2×D15—21no—
182C2×D15—21no—
183C3×C4×C5—21no—
184C3×C4×C5—41no—
185C3×C4×C5C2×M1611yescharacteristic
186C3×C4×C5C2×M1611yescharacteristic
187C3×C4×C5#13511yescharacteristic
188C3×C4×C5#13511yescharacteristic
189Dic15—22no—
190Dic15—21no—
191Dic15—21no—
192Dic15—21no—
193Dic15—41no—
194C2×C3×D4C4×D511yescharacteristic
195C22×C3×C4—21no—
196C2×#67—101no—
197C22×Dic3—101no—
198C22×Dic3—101no—
199#237—102no—
200#237—102no—
201C2×C4×D3—51no—
202C2×C4×D3—51no—
203C2×C4×D3—51no—
204C2×Dic6—51no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C3×C4⋊C4C4×D511yescharacteristic
208C3×C22⋊C4—21no—
209C3×C42C22×D511yescharacteristic
210#217—101no—
211(C2×D3)⋊C4—101no—
212C4⋊Dic3—51no—
213Dic3⋊C4—101no—
214Dic3⋊C4—101no—
215C4×Dic3—51no—
216C4×Dic3—51no—
217C4×Dic3—51no—
218C4×Dic3—101no—
219C4×Dic3—101no—
220C4×Dic3—101no—
221C2×C3⋊C8—101no—
222C2×C3⋊C8—101no—
223C23×C5—21no—
224C22×D5—31no—
225C5×D4—21no—
226C5×D4ΓL(1,𝔽25)12yes—
227C2×C4×C5—21no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5C2×C4×D311yescharacteristic
231C2×C4×C5D3×D411yescharacteristic
232C2×C4×C5D3×D411yescharacteristic
233C22⋊D5—64no—
234C2×Dic5—31no—
235C2×Dic5—31no—
236C2×Dic5—31no—
237C2×Dic5—64no—
238C2×Dic5—61no—
239C2×Dic5—61no—
240C2×Dic5—122no—
241C4×D5—61no—
242C4×D5—61no—
243C4×D5—61no—
244C4×D5—61no—
245C4×D5—121no—
246Dic10—32no—
247Dic10—61no—
248C5×C8—41no—
249C5×C8—41no—
250#168—121no—
251#168—121no—
252C2×#41—151no—
253C4×Q8—151no—
254C4×Q8—151no—
255C4×D4—151no—
256C4×D4—301no—
257C4×D4—301no—
258C4×D4C2×D1511yescharacteristic
259#117—151no—
260#117—301no—
261C2×C42—151no—
262C2×C42—301no—
263C4⋊C8—151no—
264C4⋊C8—301no—
265C4⋊C8C2×D1511yescharacteristic
266C22⋊C8—301no—
267C22⋊C8—301no—
268#97—301no—
269C4×C8—151no—
270C4×C8C2×D1511yescharacteristic
271C2×C3×C5—42no—
272C2×C3×C5#40711yescharacteristic
273C2×C3×C5#41611yescharacteristic
274C2×C3×C5#42111yescharacteristic
275D15—41no—
276C23×C3—21no—
277C22×D3—51no—
278C3×D4—21no—
279C3×D4#67612yes—
280C2×C3×C4—21no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4C2×C4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285C2×C3×C4D4×D511yescharacteristic
286#67—104no—
287C2×Dic3—51no—
288C2×Dic3—51no—
289C2×Dic3—51no—
290C2×Dic3—104no—
291C2×Dic3—101no—
292C2×Dic3—101no—
293C2×Dic3—202no—
294C4×D3—101no—
295C4×D3—101no—
296C4×D3—101no—
297C4×D3—101no—
298C4×D3—201no—
299Dic6—52no—
300Dic6—101no—
301C3×C8—41no—
302C3×C8—41no—
303C3⋊C8—201no—
304C3⋊C8—201no—
305C22×C5—22no—
306C22×C5—41no—
307C22×C5—41no—
308C22×C5D3×C22⋊C411yescharacteristic
309C2×D5—61no—
310C2×D5—61no—
311C2×D5—61no—
312C4×C5—21no—
313C4×C5—41no—
314C4×C5C2×ΓL(1,𝔽25)11yescharacteristic
315C4×C5D3×M1611yescharacteristic
316C4×C5#91211yescharacteristic
317C4×C5#91611yescharacteristic
318Dic5—62no—
319Dic5—61no—
320Dic5—61no—
321Dic5—61no—
322Dic5—121no—
323#41—302no—
324#41—302no—
325C2×Q8—151no—
326C2×D4—301no—
327C2×D4C4×D1511yescharacteristic
328C22×C4—21no—
329C22×C4—151no—
330C22×C4—151no—
331C22×C4—151no—
332C22×C4—301no—
333C22×C4—301no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—301no—
337C2×C8—301no—
338C4⋊C4—151no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C4⋊C4C4×D1511yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C42—151no—
346C42—151no—
347C42—151no—
348C42—301no—
349C42—301no—
350C42—301no—
351C42C22×D1511yescharacteristic
352C3×C5#148811yescharacteristic, complemented, Hall
353C22×C3—22no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3D5×C22⋊C411yescharacteristic
357C2×D3—101no—
358C2×D3—101no—
359C2×D3—101no—
360C3×C4—21no—
361C3×C4—41no—
362C3×C4C2×#67611yescharacteristic
363C3×C4D5×M1611yescharacteristic
364C3×C4#405811yescharacteristic
365C3×C4#406211yescharacteristic
366Dic3—101no—
367Dic3—101no—
368Dic3—102no—
369Dic3—101no—
370Dic3—201no—
371C2×C5—42no—
372C2×C5#472611yescharacteristic
373C2×C5#477211yescharacteristic
374C2×C5#482111yescharacteristic
375D5—121no—
376C23—21no—
377C23—151no—
378Q8—152no—
379Q8—301no—
380D4—21no—
381D4—304no—
382D4#670512yes—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—151no—
387C2×C4—151no—
388C2×C4—151no—
389C2×C4—304no—
390C2×C4—301no—
391C2×C4—301no—
392C2×C4—301no—
393C2×C4—301no—
394C2×C4—301no—
395C2×C4—301no—
396C2×C4—601no—
397C2×C4—602no—
398C2×C4C2×C4×D1511yescharacteristic
399C2×C4D4×D1511yescharacteristic
400C2×C4D4×D1511yescharacteristic
401C8—41no—
402C8—41no—
403C8—601no—
404C8—601no—
405C2×C3—42no—
406C2×C3#6501511yescharacteristic
407C2×C3#6506111yescharacteristic
408C2×C3#6511011yescharacteristic
409D3—201no—
410C5#6817311yescharacteristic, complemented, Sylow
411C22—22no—
412C22—41no—
413C22—41no—
414C22—301no—
415C22—301no—
416C22—301no—
417C22C22⋊C4×D1511yescharacteristic
418C4—21no—
419C4—41no—
420C4—301no—
421C4—301no—
422C4—302no—
423C4—301no—
424C4—601no—
425C4C2×#670511yescharacteristic
426C4M16×D1511yescharacteristic
427C4#9180111yescharacteristic
428C4#9180511yescharacteristic
429C3#1059896611yescharacteristic, complemented, Sylow
430C2—42no—
431C2—601no—
432C2#1175082711yescharacteristic
433C2#1175087311yescharacteristic
434C2#1175092211yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6819C4
cosocleC3×C42×C5C23
hypercenterD4⋊C8D15
hypocenterC3×C5#1488
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750936C2semidirect
3. #11750786C2semidirect
4. C3×C5×D4⋊C8C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11746305C2semidirect
7. #11746277C2semidirect
32. C5×D4⋊C8D3semidirect
68. C3×D4⋊C8D5semidirect
175. D4⋊C8D15semidirect
352. C3×C5#1488semidirect
410. C5#68173semidirect
429. C3#10598966semidirect

Maximal subgroups

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

subgroupindex
C4×#68192
#117509362
#117507862
C3×C5×D4⋊C82
D4⋊(C3⋊#168)2
#117463052
#117462772
#105989663
#681735