Finite Group Databasebeta

← #14284268

Subgroups — #14284268

Order 1920.

436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 89 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#11756439C211yesmaximal, characteristic
2#11750806C211yesmaximal, characteristic, complemented
3D15×#97C211yesmaximal, characteristic, complemented
4C3×C5×#329C211yesmaximal, characteristic, complemented
5#11746361C211yesmaximal, characteristic, complemented
6#11746286C211yesmaximal, characteristic, complemented
7#11746286C211yesmaximal, characteristic, complemented
8#10599139—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10#91835C411yescharacteristic
11Q8×Dic15C411yescharacteristic
12#91827C411yescharacteristic
13D4×Dic15C411yescharacteristic
14C2×C8×D15—21no—
15#91772—21no—
16#91770—21no—
17#91768—21no—
18#91766—21no—
19C42×D15C2211yescharacteristic
20#91759C2211yescharacteristic
21C3×C5×#97C2211yescharacteristic
22C3×C5×#97C2211yescharacteristic
23#91104—21no—
24#91099—21no—
25#91098—21no—
26#91087C2211yescharacteristic
27#91087C2211yescharacteristic
28#68346—51nomaximal, Hall
29#66014—31no—
30#64994—31no—
31D5×#97—31no—
32C5×#329D311yescharacteristic, complemented
33#64760—31no—
34#64685—31no—
35#64685—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×C5×D4C2×C411yescharacteristic
38C2×#1220—21no—
39C22×Dic15—21no—
40C2×C4×D15C2×C411yescharacteristic
41C2×C4×D15D411yescharacteristic
42C2×C4×D15D411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C22⋊C4—21no—
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2311yescharacteristic
48#6719—21no—
49#6719—21no—
50#6714—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15C2×C411yescharacteristic
53C4⋊Dic15C2×C411yescharacteristic
54#6712—21no—
55#6712—21no—
56#6712—21no—
57C4×Dic15—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C8×D15—24no—
64#5680—51no—
65#4705—51no—
66D3×#97—51no—
67C3×#329D511yescharacteristic, complemented
68#4540—51no—
69#4465—51no—
70#4465—51no—
71C5×#124C2×D311yescharacteristic
72#4092—31no—
73Q8×Dic5—31no—
74#4084—31no—
75D4×Dic5—31no—
76C2×C8×D5—61no—
77#4029—61no—
78#4027—61no—
79#4025—61no—
80#4023—61no—
81C42×D5—31no—
82#4016—31no—
83C5×#97C2×D311yescharacteristic
84C5×#97C2×D311yescharacteristic
85#3952—61no—
86#3947—61no—
87#3946—61no—
88#3935—31no—
89#3935—31no—
90#1532—151noSylow
91C23×C3×C5—21no—
92C22×D15C22⋊C411yescharacteristic
93C3×C5×Q8—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99#1220—42no—
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—42no—
103C2×Dic15C22⋊C411yescharacteristic
104C2×Dic15C22⋊C411yescharacteristic
105C2×Dic15C22⋊C411yescharacteristic
106C4×D15—22no—
107C4×D15—41no—
108C4×D15—41no—
109C3×C5×C8—22no—
110C3×C5×C8—41no—
111C3⋊#168—22no—
112C3⋊#168—41no—
113C3×#124C2×D511yescharacteristic
114#946—51no—
115Q8×Dic3—51no—
116#938—51no—
117D4×Dic3—51no—
118C2×D3×C8—101no—
119#883—101no—
120#67⋊C4—101no—
121#879—101no—
122#877—101no—
123C42×D3—51no—
124#870—51no—
125C3×#97C2×D511yescharacteristic
126C3×#97C2×D511yescharacteristic
127(C2×D3)⋊C8—101no—
128#815—101no—
129Dic3⋊C8—101no—
130#803—51no—
131#803—51no—
132C2×C5×Q8C4×D311yescharacteristic
133C2×C5×D4C4×D311yescharacteristic
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—21no—
141C5×C22⋊C4—21no—
142C5×C22⋊C4—21no—
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—31no—
154C4×Dic5—31no—
155C4×Dic5—31no—
156C4×Dic5—61no—
157C2×#168—61no—
158C2×#168—61no—
159C8×D5—64no—
160#529—151no—
161#432—151no—
162C2×#97—151no—
163#330—151no—
164#330—151no—
165#329—151no—
166#329D1511yescharacteristic, complemented
167C22×C3×C5—41no—
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×D15—21no—
172C2×D15—21no—
173C2×D15#10412yes—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177C3×C4×C5—41no—
178Dic15—21no—
179Dic15—21no—
180Dic15—21no—
181Dic15—41no—
182Dic15—41no—
183C2×C3×Q8C4×D511yescharacteristic
184C2×C3×D4C4×D511yescharacteristic
185C2×#67—101no—
186C22×Dic3—101no—
187C2×C4×D3—51no—
188C2×C4×D3—51no—
189C2×C4×D3—51no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C3×C22⋊C4—21no—
193C3×C22⋊C4—21no—
194C3×C42C22×D511yescharacteristic
195#217—101no—
196#217—101no—
197(C2×D3)⋊C4—101no—
198C4⋊Dic3—51no—
199C4⋊Dic3—51no—
200C4⋊Dic3—101no—
201Dic3⋊C4—101no—
202Dic3⋊C4—101no—
203Dic3⋊C4—101no—
204C4×Dic3—51no—
205C4×Dic3—51no—
206C4×Dic3—51no—
207C4×Dic3—101no—
208C2×C3⋊C8—101no—
209C2×C3⋊C8—101no—
210D3×C8—104no—
211C23×C5—21no—
212C22×D5—31no—
213C5×Q8—41no—
214C5×D4—41no—
215C2×C4×C5—21no—
216C2×C4×C5C2×C4×D311yescharacteristic
217C2×C4×C5D3×D411yescharacteristic
218C2×C4×C5D3×D411yescharacteristic
219C22⋊D5—122no—
220C2×Dic5—31no—
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5—61no—
224C2×Dic5—61no—
225C2×Dic5—122no—
226C4×D5—62no—
227C4×D5—121no—
228C4×D5—121no—
229C5×C8—22no—
230C5×C8—41no—
231#168—62no—
232#168—121no—
233C22×C8—301no—
234#126—301no—
235#125—151no—
236#124C2×D1511yescharacteristic
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—151no—
248#97—151no—
249#97—301no—
250#97C2×D1511yescharacteristic
251#97C2×D1511yescharacteristic
252C2×C3×C5—81no—
253C2×C3×C5#41311yescharacteristic
254C2×C3×C5C2×#10411yescharacteristic
255C2×C3×C5#42111yescharacteristic
256D15—22no—
257C23×C3—21no—
258C22×D3—51no—
259C3×Q8—41no—
260C3×D4—41no—
261C2×C3×C4—21no—
262C2×C3×C4C2×C4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265#67—202no—
266C2×Dic3—51no—
267C2×Dic3—51no—
268C2×Dic3—51no—
269C2×Dic3—101no—
270C2×Dic3—101no—
271C2×Dic3—202no—
272C4×D3—102no—
273C4×D3—201no—
274C4×D3—201no—
275C3×C8—22no—
276C3×C8—41no—
277C3⋊C8—102no—
278C3⋊C8—201no—
279C22×C5—41no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5D3×C22⋊C411yescharacteristic
283C2×D5—32no—
284C2×D5—61no—
285C2×D5—61no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—41no—
290Dic5—61no—
291Dic5—61no—
292Dic5—61no—
293Dic5—121no—
294Dic5—121no—
295C2×Q8C4×D1511yescharacteristic
296C2×D4—301no—
297C2×D4C4×D1511yescharacteristic
298C22×C4—151no—
299C22×C4—151no—
300C22×C4—151no—
301C22×C4—301no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—304no—
305C2×C8—301no—
306C2×C8—301no—
307C4⋊C4—151no—
308C4⋊C4—151no—
309C4⋊C4—301no—
310C4⋊C4—301no—
311C4⋊C4—301no—
312C4⋊C4—301no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—301no—
316C22⋊C4—301no—
317C22⋊C4—301no—
318C42—151no—
319C42—151no—
320C42—151no—
321C42—301no—
322C42C22×D1511yescharacteristic
323C3×C5#153211yescharacteristic, complemented, Hall
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3D5×C22⋊C411yescharacteristic
328C2×D3—52no—
329C2×D3—101no—
330C2×D3—101no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—41no—
335Dic3—101no—
336Dic3—101no—
337Dic3—101no—
338Dic3—201no—
339Dic3—201no—
340C2×C5—81no—
341C2×C5#474511yescharacteristic
342C2×C5D3×#10411yescharacteristic
343C2×C5#482111yescharacteristic
344D5—62no—
345C23—21no—
346C23—151no—
347Q8—41no—
348D4—41no—
349D4—602no—
350C2×C4—21no—
351C2×C4—151no—
352C2×C4—151no—
353C2×C4—151no—
354C2×C4—302no—
355C2×C4—301no—
356C2×C4—301no—
357C2×C4—601no—
358C2×C4—601no—
359C2×C4—602no—
360C2×C4C2×C4×D1511yescharacteristic
361C2×C4D4×D1511yescharacteristic
362C2×C4D4×D1511yescharacteristic
363C8—22no—
364C8—41no—
365C8—302no—
366C8—601no—
367C2×C3—81no—
368C2×C3#6503411yescharacteristic
369C2×C3D5×#10411yescharacteristic
370C2×C3#6511011yescharacteristic
371D3—102no—
372C5#6834611yescharacteristic, complemented, Sylow
373C22—41no—
374C22—41no—
375C22—41no—
376C22—152no—
377C22—301no—
378C22—301no—
379C22C22⋊C4×D1511yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—41no—
384C4—301no—
385C4—301no—
386C4—301no—
387C4—601no—
388C4—601no—
389C3#1059913911yescharacteristic, complemented, Sylow
390C2—81no—
391C2—302no—
392C2#1175084611yescharacteristic
393C2D15×#10411yescharacteristic
394C2#1175092211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#329C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91827C4
cosocleC3×C42×C5C23
hypercenter#329D15
hypocenterC3×C5#1532
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. #11750806C2semidirect
3. D15×#97C2semidirect
4. C3×C5×#329C2semidirect
5. #11746361C2semidirect
6. #11746286C2semidirect
7. #11746286C2semidirect
32. C5×#329D3semidirect
67. C3×#329D5semidirect
166. #329D15semidirect
323. C3×C5#1532semidirect
372. C5#68346semidirect
389. C3#10599139semidirect

Maximal subgroups

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

subgroupindex
#117564392
#117508062
D15×#972
C3×C5×#3292
#117463612
#117462862
#105991393
#683465