Finite Group Databasebeta

← #14284140

Subgroups — #14284140

Order 1920.

432 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 94 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#11752683C211yesmaximal, characteristic
2C3×#64996C211yesmaximal, characteristic, complemented
3#11746870C211yesmaximal, characteristic, complemented
4#11746286C211yesmaximal, characteristic, complemented
5C5×#4464C211yesmaximal, characteristic, complemented
6#11745851C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic, complemented
8#10599137—31nomaximal, Hall
9#91759C2211yescharacteristic
10C5×#875C2211yescharacteristic
11C2×C3×#676—21no—
12C3×C42×D5C2211yescharacteristic
13#91449C411yescharacteristic
14#91447—21no—
15#91440—21no—
16Dic5×D12C411yescharacteristic
17#91398—21no—
18#91372—21no—
19#91359C411yescharacteristic
20Dic5×Dic6C411yescharacteristic
21C3×C5×#97C2211yescharacteristic
22#91087C2211yescharacteristic
23C5×#803C2211yescharacteristic
24C3×C8×Dic5—21no—
25C3×#3935C2211yescharacteristic
26#90982—21no—
27#90955—21no—
28#69861—51nomaximal, Hall
29#66014—31no—
30#64996D311yescharacteristic, complemented
31#64994—31no—
32C5×#329—31no—
33#64760—31no—
34#64685—31no—
35#64685—31no—
36C2×C5×D12C2×C411yescharacteristic
37C2×C5×Dic6C2×C411yescharacteristic
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×#1201—21no—
42C2×D3×Dic5—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15C2×C411yescharacteristic
46C4⋊Dic15C2×C411yescharacteristic
47#6712—21no—
48#6712—21no—
49C2×C3⋊#168—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4×Dic5C2×C411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C2×C3×#168—21no—
57C3×#676—24no—
58Dic3⋊Dic5—21no—
59#6669—21no—
60(C2×D3)⋊Dic5—21no—
61(C2×D3)⋊Dic5—21no—
62#6665—21no—
63Dic3×Dic5—21no—
64#5479—51no—
65C3×C4×M16—51no—
66#4926—51no—
67#4465—51no—
68#4465—51no—
69#4464—51no—
70#4464D511yescharacteristic, complemented
71C5×#124—31no—
72#4092—31no—
73Q8×Dic5—31no—
74#4084—31no—
75D4×Dic5—31no—
76C2×#676—21no—
77#4029—61no—
78#4027—61no—
79#4025—61no—
80#4023—61no—
81C42×D5C2×D311yescharacteristic
82#4016—31no—
83C5×#97—31no—
84C5×#97C2×D311yescharacteristic
85#3952—61no—
86#3946—61no—
87C8×Dic5—21no—
88#3935—31no—
89#3935C2×D311yescharacteristic
90#1529—151noSylow
91C22×C5×D3—21no—
92C22×C3×D5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×C5×Dic3—21no—
99C5×D12—41no—
100C5×Dic6—41no—
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C22⋊C411yescharacteristic
104C3×C4×D5—22no—
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107#1201—42no—
108D3×Dic5—42no—
109C3×C5×C8—22no—
110C3⋊#168—41no—
111C3×#168—22no—
112C5×C3⋊C8—41no—
113C2×C3×M16—101no—
114C2×C3×C42—51no—
115#930—51no—
116#929—101no—
117C4×#67—101no—
118#924—51no—
119#876—101no—
120#875C2×D511yescharacteristic
121C4×D12—51no—
122#872—101no—
123#870—51no—
124C4×Dic6—51no—
125C3×#97—51no—
126C3×#97C2×D511yescharacteristic
127C3×C4×C8—101no—
128#830—101no—
129C4⋊(C3⋊C8)—101no—
130#803—51no—
131#803C2×D511yescharacteristic
132C2×C5×Q8—31no—
133C2×C5×D4—31no—
134C2×C22⋊D5—61no—
135C22×Dic5—61no—
136C2×C4×D5C4×D311yescharacteristic
137C2×C4×D5D1211yescharacteristic
138C2×C4×D5#6711yescharacteristic
139C2×C5×C8—21no—
140C2×C5×C8—61no—
141C5×C22⋊C4—61no—
142C5×C22⋊C4—61no—
143C42×C5C22×D311yescharacteristic
144C22⋊Dic5—61no—
145C22⋊Dic5—61no—
146#685—61no—
147C4⋊Dic5—31no—
148C4⋊Dic5—31no—
149C4⋊Dic5—61no—
150#683—61no—
151#683—61no—
152#683—61no—
153C4×Dic5—61no—
154C4×Dic5C4×D311yescharacteristic
155C4×Dic5D1211yescharacteristic
156C4×Dic5#6711yescharacteristic
157C2×#168—21no—
158C2×#168—61no—
159#676—24no—
160#529—151no—
161#432—151no—
162C4×M16—51no—
163#330—151no—
164#330—151no—
165#329—31no—
166#329—151no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×C5×D3—41no—
169C2×C5×D3—41no—
170C2×C5×D3—41no—
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C2×C3×D5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177Dic15—41no—
178Dic15—41no—
179C3×Dic5—21no—
180C3×Dic5—21no—
181C3×Dic5#10412yes—
182C5×Dic3—41no—
183C22×C3×C4—51no—
184C22×C3×C4—51no—
185C22×C3×C4—51no—
186C2×#67—101no—
187C2×D12C4×D511yescharacteristic
188C2×C4×D3—101no—
189C2×Dic6C4×D511yescharacteristic
190C3×M16—104no—
191C2×C3×C8—21no—
192C2×C3×C8—101no—
193C3×C42—51no—
194C3×C42—51no—
195C3×C42—51no—
196C3×C42C22×D511yescharacteristic
197#217—101no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—101no—
201(C2×D3)⋊C4—101no—
202C4⋊Dic3—51no—
203C4⋊Dic3—51no—
204Dic3⋊C4—101no—
205Dic3⋊C4—101no—
206Dic3⋊C4—101no—
207Dic3⋊C4—101no—
208C4×Dic3—101no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—101no—
211C23×C5—61no—
212C22×D5(C2×D3)⋊C411yescharacteristic
213C5×Q8—121no—
214C5×D4—121no—
215C2×C4×C5—61no—
216C2×C4×C5C2×C4×D311yescharacteristic
217C2×C4×C5C2×D1211yescharacteristic
218C2×C4×C5C2×#6711yescharacteristic
219C22⋊D5—122no—
220C2×Dic5—61no—
221C2×Dic5—61no—
222C2×Dic5—122no—
223C2×Dic5(C2×D3)⋊C411yescharacteristic
224C2×Dic5(C2×D3)⋊C411yescharacteristic
225C2×Dic5(C2×D3)⋊C411yescharacteristic
226C4×D5—22no—
227C4×D5—41no—
228C4×D5—41no—
229C5×C8—22no—
230C5×C8—121no—
231#168—22no—
232#168—121no—
233C2×M16—101no—
234#126—301no—
235#125—151no—
236#124—31no—
237#123—301no—
238C22⋊Q8—151no—
239#121—151no—
240C4×Q8—151no—
241C4×D4—151no—
242C4×D4—301no—
243#117—301no—
244C2×C42—51no—
245C4⋊C8—301no—
246C22⋊C8—301no—
247#97—31no—
248#97—51no—
249#97—151no—
250#97D3×D511yescharacteristic
251C4×C8—101no—
252C2×C3×C5#41311yescharacteristic
253C2×C3×C5C2×#10411yescharacteristic
254C2×C3×C5#42111yescharacteristic
255C3×D5—41no—
256C5×D3—81no—
257C23×C3—51no—
258C22×D3—21no—
259C2×C3×C4—51no—
260C2×C3×C4—51no—
261C2×C3×C4—51no—
262C2×C3×C4—102no—
263C2×C3×C4—201no—
264C2×C3×C4—201no—
265C2×C3×C4C2×C4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4D4×D511yescharacteristic
268#67—202no—
269C2×Dic3—21no—
270C2×Dic3—101no—
271C2×Dic3—101no—
272D12—41no—
273C4×D3—202no—
274Dic6—41no—
275C3×C8—22no—
276C3×C8—102no—
277C3⋊C8—41no—
278C3⋊C8—201no—
279C22×C5—121no—
280C22×C5—121no—
281C22×C5—121no—
282C22×C5C2×(C2×D3)⋊C411yescharacteristic
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—121no—
290Dic5—21no—
291Dic5—21no—
292Dic5—121no—
293Dic5—121no—
294Dic5#80512yes—
295C2×Q8—31no—
296C2×D4—31no—
297C2×D4—301no—
298C22×C4—51no—
299C22×C4—51no—
300C22×C4—51no—
301C22×C4—301no—
302M16—104no—
303C2×C8—21no—
304C2×C8—61no—
305C2×C8—101no—
306C2×C8—301no—
307C4⋊C4—151no—
308C4⋊C4—151no—
309C4⋊C4—301no—
310C4⋊C4—301no—
311C4⋊C4—301no—
312C4⋊C4—301no—
313C22⋊C4—61no—
314C22⋊C4—61no—
315C22⋊C4—301no—
316C22⋊C4—301no—
317C22⋊C4—301no—
318C42—51no—
319C42—51no—
320C42—51no—
321C42—301no—
322C42C2×D3×D511yescharacteristic
323C3×C5#152911yescharacteristic, complemented, Hall
324C22×C3—101no—
325C22×C3—101no—
326C22×C3—101no—
327C22×C3D5×C22⋊C411yescharacteristic
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—52no—
335C3×C4—101no—
336C3×C4—101no—
337Dic3—41no—
338Dic3—201no—
339Dic3—201no—
340C2×C5—241no—
341C2×C5C2×#80511yescharacteristic
342C2×C5#513211yescharacteristic
343C2×C5#513911yescharacteristic
344D5—41no—
345C23—51no—
346C23—61no—
347Q8—121no—
348D4—121no—
349D4—602no—
350C2×C4—51no—
351C2×C4—51no—
352C2×C4—51no—
353C2×C4—61no—
354C2×C4—102no—
355C2×C4—201no—
356C2×C4—201no—
357C2×C4—301no—
358C2×C4—301no—
359C2×C4—602no—
360C2×C4C4×D3×D511yescharacteristic
361C2×C4D5×D1211yescharacteristic
362C2×C4D5×#6711yescharacteristic
363C8—22no—
364C8—102no—
365C8—121no—
366C8—601no—
367C2×C3—201no—
368C2×C3#6503411yescharacteristic
369C2×C3D5×#10411yescharacteristic
370C2×C3#6511011yescharacteristic
371D3—81no—
372C5#6986111yescharacteristic, complemented, Sylow
373C22—101no—
374C22—101no—
375C22—101no—
376C22—121no—
377C22—121no—
378C22—121no—
379C22D5×(C2×D3)⋊C411yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—52no—
384C4—101no—
385C4—101no—
386C4—121no—
387C4—601no—
388C4—601no—
389C3#1059913711yescharacteristic, complemented, Sylow
390C2—201no—
391C2—241no—
392C2D5×#80511yescharacteristic
393C2#1174822911yescharacteristic
394C2#1174823011yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91449C4
cosocleC3×C42×C5C23
hypercenter#97D3×D5
hypocenterC3×C5#1529
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C3×#64996C2semidirect
3. #11746870C2semidirect
4. #11746286C2semidirect
5. C5×#4464C2semidirect
6. #11745851C2semidirect
7. #11745847C2semidirect
30. #64996D3semidirect
70. #4464D5semidirect
323. C3×C5#1529semidirect
372. C5#69861semidirect
389. C3#10599137semidirect

Maximal subgroups

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

subgroupindex
#117526832
C3×#649962
#117468702
#117462862
C5×#44642
#117458512
#117458472
#105991373
#698615