Finite Group Databasebeta

← #14284076

Subgroups — #14284076

Order 1920.

424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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
1D15×#125C211yesmaximal, characteristic
2#11750808C211yesmaximal, characteristic
3#11750806C211yesmaximal, characteristic
4C3×C5×#330C211yesmaximal, characteristic, complemented
5#11746364C211yesmaximal, characteristic, complemented
6#11746286C211yesmaximal, characteristic, complemented
7#11746286C211yesmaximal, characteristic, complemented
8#10599156—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C2×#6705—21no—
11C4⋊C4×D15—21no—
12C4⋊C4×D15—21no—
13C4⋊C4×D15C411yescharacteristic
14C4⋊C4×D15C411yescharacteristic
15#91779C411yescharacteristic
16#91779C411yescharacteristic
17#91778—21no—
18#91778—21no—
19C42×D15C2211yescharacteristic
20#91759C2211yescharacteristic
21C3×C5×#97C2211yescharacteristic
22C3×C5×#97C2211yescharacteristic
23#91104—21no—
24#91098—21no—
25C8×Dic15—21no—
26#91087C2211yescharacteristic
27#91087C2211yescharacteristic
28#68363—51nomaximal, Hall
29D5×#125—31no—
30#64996—31no—
31#64994—31no—
32C5×#330D311yescharacteristic, complemented
33#64763—31no—
34#64685—31no—
35#64685—31no—
36C2×C4×D15—21no—
37C2×C4×D15—21no—
38C2×C4×D15C2×C411yescharacteristic
39C2×C4×D15D411yescharacteristic
40C2×C4×D15D411yescharacteristic
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C42×C5C2311yescharacteristic
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15C2×C411yescharacteristic
51C4⋊Dic15C2×C411yescharacteristic
52#6712—21no—
53#6712—21no—
54#6712—21no—
55#6712—21no—
56#6712—21no—
57#6712—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63#6705—24no—
64D3×#125—51no—
65#4707—51no—
66#4705—51no—
67C3×#330D511yescharacteristic, complemented
68#4543—51no—
69#4465—51no—
70#4465—51no—
71C5×#125C2×D311yescharacteristic
72C2×#676—61no—
73D5×C4⋊C4—31no—
74D5×C4⋊C4—31no—
75D5×C4⋊C4—61no—
76D5×C4⋊C4—61no—
77#4036—31no—
78#4036—31no—
79#4035—61no—
80#4035—61no—
81C42×D5—31no—
82#4016—31no—
83C5×#97C2×D311yescharacteristic
84C5×#97C2×D311yescharacteristic
85#3952—61no—
86#3946—61no—
87C8×Dic5—61no—
88#3935—31no—
89#3935—31no—
90#1528—151noSylow
91C22×D15C22⋊C411yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×Dic15C22⋊C411yescharacteristic
100C2×Dic15C22⋊C411yescharacteristic
101C2×Dic15C22⋊C411yescharacteristic
102C4×D15—22no—
103C4×D15—22no—
104C4×D15—41no—
105C4×D15—42no—
106C4×D15—42no—
107C3×C5×C8—22no—
108C3×C5×C8—41no—
109C3⋊#168—22no—
110C3⋊#168—41no—
111C3×#125C2×D511yescharacteristic
112C2×ΓL(1,𝔽25)—101no—
113D3×C4⋊C4—51no—
114D3×C4⋊C4—51no—
115D3×C4⋊C4—101no—
116D3×C4⋊C4—101no—
117#890—51no—
118#890—51no—
119#889—101no—
120#889—101no—
121C42×D3—51no—
122#870—51no—
123C3×#97C2×D511yescharacteristic
124C3×#97C2×D511yescharacteristic
125(C2×D3)⋊C8—101no—
126Dic3⋊C8—101no—
127C8×Dic3—101no—
128#803—51no—
129#803—51no—
130C2×C4×D5—31no—
131C2×C4×D5—31no—
132C2×C4×D5—31no—
133C2×C4×D5—61no—
134C2×C4×D5—61no—
135C2×C5×C8—21no—
136C2×C5×C8—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4C4×D311yescharacteristic
140C5×C4⋊C4C4×D311yescharacteristic
141C42×C5C22×D311yescharacteristic
142C4⋊Dic5—31no—
143C4⋊Dic5—31no—
144C4⋊Dic5—61no—
145C4⋊Dic5—61no—
146#683—61no—
147#683—61no—
148#683—61no—
149#683—61no—
150#683—61no—
151#683—61no—
152C4×Dic5—31no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C2×#168—61no—
156C2×#168—61no—
157#676—64no—
158C2×#125—151no—
159#432—151no—
160C4×M16—151no—
161#330—151no—
162#330—151no—
163#330—151no—
164#330D1511yescharacteristic, complemented
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×D15—21no—
167C2×D15—21no—
168C2×D15#10412yes—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—41no—
173C3×C4×C5—41no—
174Dic15—21no—
175Dic15—21no—
176Dic15—41no—
177Dic15—41no—
178Dic15#10112yes—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×C4×D3—51no—
182C2×C4×D3—101no—
183C2×C4×D3—101no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4C4×D511yescharacteristic
189C3×C4⋊C4C4×D511yescharacteristic
190C3×C42C22×D511yescharacteristic
191C4⋊Dic3—51no—
192C4⋊Dic3—51no—
193C4⋊Dic3—101no—
194C4⋊Dic3—101no—
195Dic3⋊C4—101no—
196Dic3⋊C4—101no—
197Dic3⋊C4—101no—
198Dic3⋊C4—101no—
199Dic3⋊C4—101no—
200Dic3⋊C4—101no—
201C4×Dic3—51no—
202C4×Dic3—51no—
203C4×Dic3—51no—
204C2×C3⋊C8—101no—
205C2×C3⋊C8—101no—
206ΓL(1,𝔽25)—104no—
207C22×D5—31no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5C2×C4×D311yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×Dic5—31no—
214C2×Dic5—31no—
215C2×Dic5—31no—
216C2×Dic5—61no—
217C2×Dic5—61no—
218C4×D5—62no—
219C4×D5—62no—
220C4×D5—121no—
221C4×D5—122no—
222C4×D5—122no—
223C5×C8—22no—
224C5×C8—41no—
225#168—62no—
226#168—121no—
227C2×M16—301no—
228#125—151no—
229#125—151no—
230#125—151no—
231#125—301no—
232#125—301no—
233#125C2×D1511yescharacteristic
234C2×C4⋊C4—151no—
235C2×C4⋊C4—151no—
236C2×C4⋊C4—301no—
237C2×C4⋊C4—301no—
238C2×C42—151no—
239C4⋊C8—301no—
240C22⋊C8—301no—
241#97—151no—
242#97—151no—
243#97C2×D1511yescharacteristic
244#97C2×D1511yescharacteristic
245C4×C8—301no—
246C2×C3×C5C2×#10111yescharacteristic
247C2×C3×C5C2×#10411yescharacteristic
248C2×C3×C5#42111yescharacteristic
249D15—22no—
250C22×D3—51no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4C2×C4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×Dic3—51no—
257C2×Dic3—51no—
258C2×Dic3—51no—
259C2×Dic3—101no—
260C2×Dic3—101no—
261C4×D3—102no—
262C4×D3—102no—
263C4×D3—201no—
264C4×D3—202no—
265C4×D3—202no—
266C3×C8—22no—
267C3×C8—41no—
268C3⋊C8—102no—
269C3⋊C8—201no—
270C22×C5D3×C22⋊C411yescharacteristic
271C2×D5—32no—
272C2×D5—61no—
273C2×D5—61no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—41no—
278C4×C5—41no—
279Dic5—32no—
280Dic5—61no—
281Dic5—61no—
282Dic5—121no—
283Dic5—121no—
284C22×C4—151no—
285C22×C4—151no—
286C22×C4—151no—
287C22×C4—301no—
288C22×C4—301no—
289M16—304no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—301no—
293C2×C8—301no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—151no—
297C4⋊C4—151no—
298C4⋊C4—301no—
299C4⋊C4—301no—
300C4⋊C4—301no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C4⋊C4—301no—
304C4⋊C4—301no—
305C4⋊C4—301no—
306C4⋊C4C4×D1511yescharacteristic
307C4⋊C4C4×D1511yescharacteristic
308C42—151no—
309C42—151no—
310C42—151no—
311C42C22×D1511yescharacteristic
312C3×C5#152811yescharacteristic, complemented, Hall
313C22×C3D5×C22⋊C411yescharacteristic
314C2×D3—52no—
315C2×D3—101no—
316C2×D3—101no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—41no—
321C3×C4—41no—
322Dic3—52no—
323Dic3—101no—
324Dic3—101no—
325Dic3—201no—
326Dic3—201no—
327C2×C5D3×#10111yescharacteristic
328C2×C5D3×#10411yescharacteristic
329C2×C5#482111yescharacteristic
330D5—62no—
331C23—151no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—151no—
335C2×C4—151no—
336C2×C4—151no—
337C2×C4—302no—
338C2×C4—302no—
339C2×C4—301no—
340C2×C4—301no—
341C2×C4—601no—
342C2×C4—602no—
343C2×C4—602no—
344C2×C4C2×C4×D1511yescharacteristic
345C2×C4D4×D1511yescharacteristic
346C2×C4D4×D1511yescharacteristic
347C8—22no—
348C8—41no—
349C8—302no—
350C8—601no—
351C2×C3D5×#10111yescharacteristic
352C2×C3D5×#10411yescharacteristic
353C2×C3#6511011yescharacteristic
354D3—102no—
355C5#6836311yescharacteristic, complemented, Sylow
356C22—152no—
357C22—301no—
358C22—301no—
359C22C22⋊C4×D1511yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—152no—
366C4—301no—
367C4—301no—
368C4—601no—
369C4—601no—
370C3#1059915611yescharacteristic, complemented, Sylow
371C2—302no—
372C2D15×#10111yescharacteristic
373C2D15×#10411yescharacteristic
374C2#1175092211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenter#330D15
hypocenterC3×C5#1528
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. C3×C5×#330C2semidirect
5. #11746364C2semidirect
6. #11746286C2semidirect
7. #11746286C2semidirect
32. C5×#330D3semidirect
67. C3×#330D5semidirect
164. #330D15semidirect
312. C3×C5#1528semidirect
355. C5#68363semidirect
370. C3#10599156semidirect

Maximal subgroups

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

subgroupindex
D15×#1252
#117508082
#117508062
C3×C5×#3302
#117463642
#117462862
#105991563
#683635