Finite Group Databasebeta

← #14284141

Subgroups — #14284141

Order 1920.

432 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 84 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#11752628C211yesmaximal, characteristic
2#11750808C211yesmaximal, characteristic, complemented
3#11746940C211yesmaximal, characteristic, complemented
4C5×#4464C211yesmaximal, characteristic, complemented
5C3×#64685C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic, complemented
8#10599137—31nomaximal, Hall
9C2×#6705—21no—
10C42×D15C2211yescharacteristic
11C5×#875C2211yescharacteristic
12C3×#4016C2211yescharacteristic
13#91466C411yescharacteristic
14#91435C411yescharacteristic
15#91406—21no—
16#91400—21no—
17#91383C411yescharacteristic
18#91367—21no—
19#91355—21no—
20#91344C411yescharacteristic
21C3×C5×#97C2211yescharacteristic
22C8×Dic15—21no—
23#91087C2211yescharacteristic
24C5×#803C2211yescharacteristic
25C3×#3935C2211yescharacteristic
26#90983—21no—
27#90957—21no—
28#68364—51nomaximal, Hall
29#66014—31no—
30#64996—31no—
31#64994—31no—
32C5×#329—31no—
33#64760—31no—
34#64685—31no—
35#64685D311yescharacteristic, complemented
36C2×C4×D15C2×C411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×C5×D12C2×C411yescharacteristic
40C2×C5×Dic6C2×C411yescharacteristic
41C2×#1203—21no—
42C2×D3×Dic5—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4×Dic15C2×C411yescharacteristic
46C4×Dic15D411yescharacteristic
47C4×Dic15D411yescharacteristic
48C2×C3⋊#168—21no—
49#6705—24no—
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C3×#683—21no—
57C2×C3×#168—21no—
58Dic3⋊Dic5—21no—
59#6668—21no—
60#6667—21no—
61(C2×D3)⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63Dic3×Dic5—21no—
64#5691—51no—
65#4707—51no—
66#4705—51no—
67C3×#330—51no—
68#4543—51no—
69#4464—51no—
70#4464D511yescharacteristic, complemented
71C5×#124—31no—
72#4092—31no—
73Q8×Dic5—31no—
74#4084—31no—
75D4×Dic5—31no—
76C2×#676—61no—
77#4029—61no—
78#4027—61no—
79#4025—61no—
80#4023—61no—
81C42×D5—31no—
82#4016C2×D311yescharacteristic
83C5×#97—31no—
84C5×#97C2×D311yescharacteristic
85#3952—61no—
86#3946—61no—
87C8×Dic5—61no—
88#3935—31no—
89#3935C2×D311yescharacteristic
90#1529—151noSylow
91C22×D15C22⋊C411yescharacteristic
92C22×C5×D3—21no—
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15C22⋊C411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C2×Dic15C22⋊C411yescharacteristic
99C4×D15—22no—
100C4×D15—41no—
101C4×D15—41no—
102C2×C5×Dic3—21no—
103C5×D12—41no—
104C5×Dic6—41no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—21no—
107#1203—42no—
108D3×Dic5—42no—
109C3×C5×C8—22no—
110C3⋊#168—22no—
111C3×#168—41no—
112C5×C3⋊C8—41no—
113C3×#125—51no—
114C2×ΓL(1,𝔽25)—101no—
115#898—101no—
116#897—51no—
117#895—51no—
118#894—101no—
119#893—51no—
120#893—101no—
121#892—101no—
122#887—51no—
123#875C2×D511yescharacteristic
124C42×D3—51no—
125C3×#97—51no—
126C3×#97C2×D511yescharacteristic
127(C2×D3)⋊C8—101no—
128Dic3⋊C8—101no—
129C8×Dic3—101no—
130#803—51no—
131#803C2×D511yescharacteristic
132C2×C5×Q8—31no—
133C2×C5×D4—31no—
134C2×C22⋊D5—61no—
135C22×Dic5—61no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—31no—
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—61no—
148C4⋊Dic5C4×D311yescharacteristic
149C4⋊Dic5C4×D311yescharacteristic
150#683—21no—
151#683—21no—
152#683—61no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C4×Dic5—31no—
156C4×Dic5—61no—
157C2×#168—21no—
158C2×#168—61no—
159#676—64no—
160#529—151no—
161#432—151no—
162C4×M16—151no—
163#330—51no—
164#330—151no—
165#329—31no—
166#329—151no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×D15—21no—
169C2×D15—21no—
170C2×D15—21no—
171C2×C5×D3—41no—
172C2×C5×D3—41no—
173C2×C5×D3—41no—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177Dic15—21no—
178Dic15—21no—
179Dic15#10412yes—
180C3×Dic5—41no—
181C3×Dic5—41no—
182C5×Dic3—41no—
183C2×D12—101no—
184C2×D12C4×D511yescharacteristic
185C2×C4×D3—51no—
186C2×C4×D3—51no—
187C2×C4×D3—51no—
188C2×C4×D3—101no—
189C2×Dic6C4×D511yescharacteristic
190C2×C3×C8—21no—
191C2×C3×C8—101no—
192C3×C4⋊C4—51no—
193C3×C4⋊C4—51no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4—101no—
196C3×C42C22×D511yescharacteristic
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—101no—
200(C2×D3)⋊C4—101no—
201(C2×D3)⋊C4—101no—
202C4⋊Dic3—101no—
203Dic3⋊C4—101no—
204C4×Dic3—51no—
205C4×Dic3—51no—
206C4×Dic3—51no—
207C4×Dic3—101no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—101no—
210ΓL(1,𝔽25)—104no—
211C23×C5—61no—
212C22×D5—31no—
213C5×Q8—121no—
214C5×D4—121no—
215C2×C4×C5—61no—
216C2×C4×C5C2×C4×D311yescharacteristic
217C2×C4×C5D3×D411yescharacteristic
218C2×C4×C5D3×D411yescharacteristic
219C22⋊D5—122no—
220C2×Dic5—21no—
221C2×Dic5—21no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—122no—
226C4×D5—62no—
227C4×D5—121no—
228C4×D5—121no—
229C5×C8—22no—
230C5×C8—121no—
231#168—41no—
232#168—62no—
233C2×M16—301no—
234#126—301no—
235#125—51no—
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—151no—
245C4⋊C8—301no—
246C22⋊C8—301no—
247#97—31no—
248#97—51no—
249#97—151no—
250#97D3×D511yescharacteristic
251C4×C8—301no—
252C2×C3×C5#41311yescharacteristic
253C2×C3×C5C2×#10411yescharacteristic
254C2×C3×C5#42111yescharacteristic
255D15—41no—
256C5×D3—81no—
257C22×D3—21no—
258C22×D3—51no—
259C2×C3×C4—101no—
260C2×C3×C4—101no—
261C2×C3×C4C2×C4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×Dic3—21no—
265C2×Dic3—51no—
266C2×Dic3—51no—
267C2×Dic3—51no—
268D12—41no—
269D12—202no—
270C4×D3—102no—
271C4×D3—202no—
272C4×D3—201no—
273C4×D3—201no—
274Dic6—41no—
275C3×C8—22no—
276C3×C8—201no—
277C3⋊C8—41no—
278C3⋊C8—102no—
279C22×C5—121no—
280C22×C5—121no—
281C22×C5—121no—
282C22×C5D3×C22⋊C411yescharacteristic
283C2×D5—61no—
284C2×D5—61no—
285C2×D5—61no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—121no—
290Dic5—32no—
291Dic5—41no—
292Dic5—41no—
293Dic5—61no—
294Dic5—61no—
295C2×Q8—31no—
296C2×D4—31no—
297C2×D4—301no—
298C22×C4—151no—
299C22×C4—151no—
300C22×C4—151no—
301C22×C4—301no—
302M16—304no—
303C2×C8—21no—
304C2×C8—61no—
305C2×C8—101no—
306C2×C8—301no—
307C4⋊C4—51no—
308C4⋊C4—51no—
309C4⋊C4—101no—
310C4⋊C4—101no—
311C4⋊C4—301no—
312C4⋊C4—301no—
313C22⋊C4—61no—
314C22⋊C4—61no—
315C22⋊C4—301no—
316C22⋊C4—301no—
317C22⋊C4—301no—
318C42—151no—
319C42—151no—
320C42—151no—
321C42—301no—
322C42C2×D3×D511yescharacteristic
323C3×C5#152911yescharacteristic, complemented, Hall
324C22×C3D5×C22⋊C411yescharacteristic
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—101no—
329C2×D3—101no—
330C2×D3—101no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—201no—
335C3×C4—201no—
336Dic3—41no—
337Dic3—52no—
338Dic3—101no—
339Dic3—101no—
340C2×C5—241no—
341C2×C5#475111yescharacteristic
342C2×C5D3×#10411yescharacteristic
343C2×C5#482111yescharacteristic
344D5—121no—
345C23—61no—
346C23—151no—
347Q8—121no—
348D4—121no—
349D4—602no—
350C2×C4—61no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—151no—
354C2×C4—151no—
355C2×C4—151no—
356C2×C4—302no—
357C2×C4—601no—
358C2×C4—601no—
359C2×C4—602no—
360C2×C4C4×D3×D511yescharacteristic
361C2×C4#677711yescharacteristic
362C2×C4#679011yescharacteristic
363C8—22no—
364C8—121no—
365C8—201no—
366C8—302no—
367C2×C3#6503411yescharacteristic
368C2×C3D5×#10411yescharacteristic
369C2×C3#6511011yescharacteristic
370D3—81no—
371D3—201no—
372C5#6836411yescharacteristic, complemented, Sylow
373C22—121no—
374C22—121no—
375C22—121no—
376C22—301no—
377C22—301no—
378C22—301no—
379C22#9147311yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—121no—
384C4—152no—
385C4—201no—
386C4—201no—
387C4—301no—
388C4—301no—
389C3#1059913711yescharacteristic, complemented, Sylow
390C2—241no—
391C2—601no—
392C2#1174711211yescharacteristic
393C2#1174823711yescharacteristic
394C2#1174823911yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91466C4
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. #11750808C2semidirect
3. #11746940C2semidirect
4. C5×#4464C2semidirect
5. C3×#64685C2semidirect
6. #11745849C2semidirect
7. #11745847C2semidirect
35. #64685D3semidirect
70. #4464D5semidirect
323. C3×C5#1529semidirect
372. C5#68364semidirect
389. C3#10599137semidirect

Maximal subgroups

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

subgroupindex
#117526282
#117508082
#117469402
C5×#44642
C3×#646852
#117458492
#117458472
#105991373
#683645