Finite Group Databasebeta

← #14282040

Subgroups — #14282040

Order 1920.

436 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 100 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
1#11752513C211yesmaximal, characteristic
2#11750934C211yesmaximal, characteristic
3C4×#6651C211yesmaximal, characteristic
4C5×#4484C211yesmaximal, characteristic, complemented
5C3×#64704C211yesmaximal, characteristic, complemented
6#11745843C211yesmaximal, characteristic, complemented
7#11745841C211yesmaximal, characteristic, complemented
8#10599028—31nomaximal, Hall
9C42×D15C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C3×C4×Dic10C2211yescharacteristic
12#91470C411yescharacteristic
13C4×#1204—21no—
14#91390C411yescharacteristic
15#91386—21no—
16#91385C411yescharacteristic
17#91383C411yescharacteristic
18#91382—21no—
19#91377—21no—
20C2×#6651—21no—
21C3×C5×C4⋊C8C2211yescharacteristic
22#91104—21no—
23C8×Dic15—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26C3×C4×#168C2211yescharacteristic
27#90954—21no—
28#68235—51nomaximal, Hall
29#65912—31no—
30#65122—31no—
31C4×#676—31no—
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64704D311yescharacteristic, complemented
35#64676—31no—
36C2×C4×D15C2×C411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×C5×Dic6C2×C411yescharacteristic
40C2×C3×Dic10C2×C411yescharacteristic
41C2×#1204—21no—
42C2×C3×C5×C8—21no—
43C3×C42×C5C2311yescharacteristic
44C4×Dic15C2×C411yescharacteristic
45C4×Dic15D411yescharacteristic
46C4×Dic15D411yescharacteristic
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3C2×C411yescharacteristic
49C5×Dic3⋊C4—21no—
50C4×C5×Dic3—21no—
51C2×C5×C3⋊C8—21no—
52C3×C4⋊Dic5C2×C411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56Dic3⋊Dic5—21no—
57#6669—21no—
58#6669—21no—
59#6669—21no—
60#6668—21no—
61#6667—21no—
62#6667—21no—
63#6651—24no—
64#5578—51no—
65#4833—51no—
66C4×ΓL(1,𝔽25)—51no—
67C3×Q8⋊C8—51no—
68#4535—51no—
69#4484D511yescharacteristic, complemented
70#4456—51no—
71C4×C5×Q8—31no—
72#4092—31no—
73#4090—31no—
74C2×#676—61no—
75#4043—31no—
76#4042—61no—
77#4035—61no—
78#4034—31no—
79#4018—61no—
80C42×D5—31no—
81C4×Dic10—61no—
82C4×Dic10C2×D311yescharacteristic
83C5×C4⋊C8C2×D311yescharacteristic
84C4×C5×C8—31no—
85#3952—61no—
86#3947—61no—
87C8×Dic5—61no—
88C4⋊#168—31no—
89C4×#168C2×D311yescharacteristic
90#1485—151noSylow
91C22×D15C22⋊C411yescharacteristic
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15C22⋊C411yescharacteristic
96C2×Dic15C22⋊C411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C4×D15—21no—
99C4×D15—21no—
100C4×D15—21no—
101C4×D15—21no—
102C4×D15—22no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—21no—
105C5×Dic6—21no—
106C5×Dic6—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C3×Dic10—21no—
110C3×Dic10—21no—
111#1204—42no—
112C3×C5×C8—41no—
113C3⋊#168—41no—
114C3×#168—22no—
115C5×C3⋊C8—22no—
116C3×C4×Q8—51no—
117#946—51no—
118#944—51no—
119C2×ΓL(1,𝔽25)—101no—
120#897—51no—
121#896—101no—
122#889—101no—
123#888—51no—
124#872—101no—
125C42×D3—51no—
126C4×Dic6—101no—
127C4×Dic6C2×D511yescharacteristic
128C3×C4⋊C8C2×D511yescharacteristic
129C3×C4×C8—51no—
130(C2×D3)⋊C8—101no—
131#815—101no—
132C8×Dic3—101no—
133C4⋊(C3⋊C8)—51no—
134C4×C3⋊C8C2×D511yescharacteristic
135C2×C5×Q8—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×Dic10—61no—
140C2×Dic10C4×D311yescharacteristic
141C2×C5×C8—21no—
142C2×C5×C8—61no—
143C5×C4⋊C4—31no—
144C5×C4⋊C4—61no—
145C42×C5—61no—
146C42×C5C22×D311yescharacteristic
147#685—61no—
148#685—61no—
149C4⋊Dic5—61no—
150C4⋊Dic5C4×D311yescharacteristic
151#683—21no—
152#683—61no—
153#683—61no—
154#683—61no—
155#683—61no—
156C4×Dic5—21no—
157C4×Dic5—31no—
158C4×Dic5—31no—
159C4×Dic5—31no—
160C2×#168—21no—
161C2×#168—61no—
162#676—64no—
163#533—151no—
164#431—151no—
165C4×M16—151no—
166Q8⋊C8—31no—
167Q8⋊C8—51no—
168Q8⋊C8—151no—
169Q8⋊C8—151no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×D15—21no—
172C2×D15—21no—
173C2×D15—21no—
174C3×C4×C5—21no—
175C3×C4×C5#13111yescharacteristic
176C3×C4×C5#13111yescharacteristic
177C3×C4×C5#13711yescharacteristic
178C3×C4×C5#13711yescharacteristic
179Dic15—21no—
180Dic15—21no—
181Dic15#10412yes—
182C3×Dic5—41no—
183C3×Dic5—41no—
184C5×Dic3—41no—
185C5×Dic3—41no—
186C2×C3×Q8—51no—
187C2×C4×D3—51no—
188C2×C4×D3—51no—
189C2×C4×D3—51no—
190C2×Dic6—101no—
191C2×Dic6C4×D511yescharacteristic
192C2×C3×C8—21no—
193C2×C3×C8—101no—
194C3×C4⋊C4—51no—
195C3×C4⋊C4—101no—
196C3×C42—101no—
197C3×C42C22×D511yescharacteristic
198(C2×D3)⋊C4—101no—
199(C2×D3)⋊C4—101no—
200C4⋊Dic3—101no—
201C4⋊Dic3C4×D511yescharacteristic
202Dic3⋊C4—21no—
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205Dic3⋊C4—101no—
206Dic3⋊C4—101no—
207C4×Dic3—21no—
208C4×Dic3—51no—
209C4×Dic3—51no—
210C4×Dic3—51no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—101no—
213ΓL(1,𝔽25)—104no—
214C22×D5—31no—
215C5×Q8—61no—
216C5×Q8—61no—
217C2×C4×C5—61no—
218C2×C4×C5—61no—
219C2×C4×C5C2×C4×D311yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C2×Dic5—21no—
223C2×Dic5—21no—
224C2×Dic5—31no—
225C2×Dic5—31no—
226C2×Dic5—31no—
227C4×D5—62no—
228C4×D5—61no—
229C4×D5—61no—
230C4×D5—61no—
231C4×D5—61no—
232Dic10—21no—
233Dic10—21no—
234Dic10—122no—
235C5×C8—41no—
236C5×C8—62no—
237#168—22no—
238#168—121no—
239C2×M16—301no—
240C4⋊Q8—151no—
241C4⋊Q8—151no—
242#125—301no—
243C22⋊Q8—151no—
244C22⋊Q8—151no—
245C22⋊Q8—301no—
246C4×Q8—31no—
247C4×Q8—51no—
248C4×Q8—301no—
249#117—301no—
250C2×C42—151no—
251C4⋊C8—151no—
252C4⋊C8D3×D511yescharacteristic
253C22⋊C8—301no—
254#97—301no—
255C4×C8—31no—
256C4×C8—51no—
257C4×C8—301no—
258C2×C3×C5#40811yescharacteristic
259C2×C3×C5#41911yescharacteristic
260C2×C3×C5C2×#10411yescharacteristic
261D15—41no—
262C22×D3—51no—
263C3×Q8—101no—
264C3×Q8—101no—
265C2×C3×C4—101no—
266C2×C3×C4—101no—
267C2×C3×C4C2×C4×D511yescharacteristic
268C2×C3×C4D4×D511yescharacteristic
269C2×C3×C4D4×D511yescharacteristic
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—51no—
273C2×Dic3—51no—
274C2×Dic3—51no—
275C4×D3—102no—
276C4×D3—101no—
277C4×D3—101no—
278C4×D3—101no—
279C4×D3—101no—
280Dic6—21no—
281Dic6—21no—
282Dic6—202no—
283C3×C8—41no—
284C3×C8—102no—
285C3⋊C8—22no—
286C3⋊C8—201no—
287C22×C5D3×C22⋊C411yescharacteristic
288C2×D5—61no—
289C2×D5—61no—
290C2×D5—61no—
291C4×C5—21no—
292C4×C5—121no—
293C4×C5—121no—
294C4×C5#90111yescharacteristic
295C4×C5#90711yescharacteristic
296C4×C5#91511yescharacteristic
297C4×C5#91811yescharacteristic
298Dic5—32no—
299Dic5—41no—
300Dic5—41no—
301Dic5—61no—
302Dic5—61no—
303C2×Q8—31no—
304C2×Q8—51no—
305C2×Q8—301no—
306C22×C4—151no—
307C22×C4—151no—
308C22×C4—151no—
309M16—304no—
310C2×C8—21no—
311C2×C8—61no—
312C2×C8—101no—
313C2×C8—301no—
314C4⋊C4—31no—
315C4⋊C4—51no—
316C4⋊C4—61no—
317C4⋊C4—101no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C4⋊C4—301no—
323C22⋊C4—301no—
324C22⋊C4—301no—
325C42—61no—
326C42—101no—
327C42—151no—
328C42—151no—
329C42—151no—
330C42C2×D3×D511yescharacteristic
331C3×C5#148511yescharacteristic, complemented, Hall
332C22×C3D5×C22⋊C411yescharacteristic
333C2×D3—101no—
334C2×D3—101no—
335C2×D3—101no—
336C3×C4—21no—
337C3×C4—201no—
338C3×C4—201no—
339C3×C4#404711yescharacteristic
340C3×C4#405311yescharacteristic
341C3×C4#406111yescharacteristic
342C3×C4#406411yescharacteristic
343Dic3—41no—
344Dic3—41no—
345Dic3—52no—
346Dic3—101no—
347Dic3—101no—
348C2×C5#472711yescharacteristic
349C2×C5#480211yescharacteristic
350C2×C5D3×#10411yescharacteristic
351D5—121no—
352C23—151no—
353Q8—61no—
354Q8—61no—
355Q8—101no—
356Q8—101no—
357Q8—602no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—151no—
363C2×C4—151no—
364C2×C4—151no—
365C2×C4—302no—
366C2×C4—301no—
367C2×C4—301no—
368C2×C4—301no—
369C2×C4—301no—
370C2×C4C4×D3×D511yescharacteristic
371C2×C4#677711yescharacteristic
372C2×C4#679011yescharacteristic
373C8—41no—
374C8—62no—
375C8—102no—
376C8—601no—
377C2×C3#6501611yescharacteristic
378C2×C3#6509111yescharacteristic
379C2×C3D5×#10411yescharacteristic
380D3—201no—
381C5#6823511yescharacteristic, complemented, Sylow
382C22—301no—
383C22—301no—
384C22—301no—
385C22#9147311yescharacteristic
386C4—21no—
387C4—121no—
388C4—121no—
389C4—152no—
390C4—201no—
391C4—201no—
392C4—301no—
393C4—301no—
394C4#9126511yescharacteristic
395C4#9126811yescharacteristic
396C4#9148811yescharacteristic
397C4#9151211yescharacteristic
398C3#1059902811yescharacteristic, complemented, Sylow
399C2—601no—
400C2#1174749111yescharacteristic
401C2#1174814311yescharacteristic
402C2#1174823611yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C5×#4484C2semidirect
5. C3×#64704C2semidirect
6. #11745843C2semidirect
7. #11745841C2semidirect
34. #64704D3semidirect
69. #4484D5semidirect
331. C3×C5#1485semidirect
381. C5#68235semidirect
398. C3#10599028semidirect

Maximal subgroups

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

subgroupindex
#117525132
#117509342
C4×#66512
C5×#44842
C3×#647042
#117458432
#117458412
#105990283
#682355