Finite Group Databasebeta

← #14284383

Subgroups — #14284383

Order 1920.

392 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 78 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#11753620C211yesmaximal, characteristic
2#11751808C211yesmaximal, characteristic
3#11751808C211yesmaximal, characteristic
4#11746741C211yesmaximal, characteristic, complemented
5C3×#64870C211yesmaximal, characteristic, complemented
6#11746507C211yesmaximal, characteristic, complemented
7#11746506C211yesmaximal, characteristic, complemented
8#10604579—31nomaximal, Hall
9C4⋊C4×D15C411yescharacteristic
10C5×#890C411yescharacteristic
11C3×#4036C2211yescharacteristic
12#91437—21no—
13#91437C411yescharacteristic
14#91404—21no—
15C4×#1200C2211yescharacteristic
16#91388C2211yescharacteristic
17#91381C411yescharacteristic
18#91339—21no—
19#91336—21no—
20#91231C2211yescharacteristic
21#91231C2211yescharacteristic
22C3×#4002C2211yescharacteristic
23C3×#4002C2211yescharacteristic
24Dic3⋊#170—21no—
25Dic3⋊#170—21no—
26#91171—21no—
27#91171—21no—
28#68367—51nomaximal, Hall
29D5×#125—31no—
30#65683—31no—
31#65683—31no—
32#64870—31no—
33#64870—31no—
34#64870—31no—
35#64870D311yescharacteristic, complemented
36C2×C4×D15—21no—
37C2×C4×D15C2×C411yescharacteristic
38C2×#1200—21no—
39C2×#1200D411yescharacteristic
40C2×#1200D411yescharacteristic
41C2×C3⋊#170—21no—
42C2×C3⋊#170—21no—
43C2×C3×#170—21no—
44C2×C3×#170—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C4⋊Dic15C2×C411yescharacteristic
47#6712—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3C2×C411yescharacteristic
50C5×Dic3⋊C4—21no—
51C4×C5×Dic3C2×C411yescharacteristic
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×#683—21no—
55C3×C4×Dic5C2311yescharacteristic
56Dic3⋊Dic5—21no—
57#6669—21no—
58#6669—21no—
59#6669—21no—
60#6668—21no—
61Dic3×Dic5D411yescharacteristic
62Dic3×Dic5D411yescharacteristic
63D3×#125—51no—
64#4705—51no—
65#4705—51no—
66C3×#330—51no—
67#4543—51no—
68#4465—51no—
69#4465—51no—
70C5×#125—31no—
71D5×C4⋊C4—31no—
72D5×C4⋊C4—31no—
73D5×C4⋊C4—61no—
74D5×C4⋊C4—61no—
75#4036—31no—
76#4036C2×D311yescharacteristic
77#4035—61no—
78#4035—61no—
79C42×D5—31no—
80#4016—31no—
81#4003—61no—
82#4003—61no—
83#4002—31no—
84#4002—31no—
85#4002C2×D311yescharacteristic
86#4002C2×D311yescharacteristic
87C4⋊#170—61no—
88C4⋊#170—61no—
89#1534—151noSylow
90C22×D15C22⋊C411yescharacteristic
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×Dic15—21no—
94C2×Dic15C22⋊C411yescharacteristic
95C4×D15—22no—
96C4×D15—42no—
97C2×C5×Dic3—21no—
98C2×C5×Dic3C22⋊C411yescharacteristic
99C2×C5×Dic3C22⋊C411yescharacteristic
100C2×C3×Dic5—21no—
101C2×C3×Dic5C2×D411yescharacteristic
102C2×C3×Dic5C2×D411yescharacteristic
103#1200—41no—
104#1200—41no—
105#1200—42no—
106C3⋊#170—41no—
107C3⋊#170—41no—
108C3×#170—41no—
109C3×#170—41no—
110C3×#125—51no—
111D3×C4⋊C4—51no—
112D3×C4⋊C4—51no—
113D3×C4⋊C4—101no—
114D3×C4⋊C4—101no—
115#890—51no—
116#890AGL(1,𝔽5)11yescharacteristic
117#889—101no—
118#889—101no—
119C42×D3—51no—
120#870—51no—
121C3×#97—51no—
122C3×#97—51no—
123(C2×D3)⋊C8—101no—
124(C2×D3)⋊C8—101no—
125Dic3⋊C8—101no—
126Dic3⋊C8—101no—
127#803—51no—
128#803—51no—
129C2×C4×D5—31no—
130C2×C4×D5—31no—
131C2×C4×D5—31no—
132C2×C4×D5—61no—
133C2×C4×D5—61no—
134C2×#170—21no—
135C2×#170—21no—
136C2×#170—61no—
137C2×#170—61no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4C4×D311yescharacteristic
142C42×C5—31no—
143C4⋊Dic5—21no—
144C4⋊Dic5—31no—
145C4⋊Dic5—61no—
146C4⋊Dic5C4×D311yescharacteristic
147#683—21no—
148#683—61no—
149#683—61no—
150#683—61no—
151#683—61no—
152#683—61no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C4×Dic5C22×D311yescharacteristic
156C2×#125—151no—
157#432—151no—
158#432—151no—
159#330—51no—
160#330—151no—
161#330—151no—
162#330—151no—
163C22×C3×C5C2×C22⋊C411yescharacteristic
164C2×D15—21no—
165C2×D15—21no—
166C2×D15#10112yes—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169Dic15—21no—
170Dic15—41no—
171C3×Dic5—21no—
172C3×Dic5—21no—
173C3×Dic5—41no—
174C5×Dic3—21no—
175C5×Dic3—21no—
176C5×Dic3—41no—
177C2×C4×D3—51no—
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×C4×D3—101no—
181C2×C4×D3—101no—
182C2×C3×C8—101no—
183C2×C3×C8—101no—
184C3×C4⋊C4—51no—
185C3×C4⋊C4—101no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
188C3×C42—51no—
189C4⋊Dic3—21no—
190C4⋊Dic3—51no—
191C4⋊Dic3—101no—
192C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—101no—
195Dic3⋊C4—101no—
196Dic3⋊C4—101no—
197Dic3⋊C4—101no—
198Dic3⋊C4—101no—
199C4×Dic3—51no—
200C4×Dic3—51no—
201C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
202C2×C3⋊C8—101no—
203C2×C3⋊C8—101no—
204C22×D5—31no—
205C2×C4×C5—21no—
206C2×C4×C5—31no—
207C2×C4×C5—31no—
208C2×C4×C5—61no—
209C2×C4×C5C2×C4×D311yescharacteristic
210C2×Dic5—21no—
211C2×Dic5—31no—
212C2×Dic5—61no—
213C2×Dic5D3×D411yescharacteristic
214C2×Dic5D3×D411yescharacteristic
215C4×D5—62no—
216C4×D5—121no—
217C4×D5—121no—
218C4×D5—122no—
219C4×D5—122no—
220#170—41no—
221#170—41no—
222#170—121no—
223#170—121no—
224#125—31no—
225#125—51no—
226#125—151no—
227#125—151no—
228#125—301no—
229#125—301no—
230C2×C4⋊C4—151no—
231C2×C4⋊C4—151no—
232C2×C4⋊C4—301no—
233C2×C4⋊C4—301no—
234C2×C42—151no—
235C4⋊C8—301no—
236C4⋊C8—301no—
237C22⋊C8—301no—
238C22⋊C8—301no—
239#97—51no—
240#97—51no—
241#97—151no—
242#97—151no—
243C2×C3×C5C2×#10111yescharacteristic
244C2×C3×C5#42111yescharacteristic
245C2×C3×C5#42111yescharacteristic
246D15—22no—
247C22×D3—51no—
248C2×C3×C4—21no—
249C2×C3×C4—51no—
250C2×C3×C4—51no—
251C2×C3×C4—101no—
252C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
253C2×Dic3—21no—
254C2×Dic3—51no—
255C2×Dic3—101no—
256C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
257C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
258C4×D3—102no—
259C4×D3—201no—
260C4×D3—201no—
261C4×D3—202no—
262C4×D3—202no—
263C3×C8—201no—
264C3×C8—201no—
265C3⋊C8—201no—
266C3⋊C8—201no—
267C22×C5D3×C22⋊C411yescharacteristic
268C2×D5—32no—
269C2×D5—61no—
270C2×D5—61no—
271C4×C5—21no—
272C4×C5—41no—
273C4×C5—61no—
274C4×C5—61no—
275C4×C5—121no—
276Dic5—21no—
277Dic5—21no—
278Dic5—41no—
279Dic5—61no—
280Dic5—121no—
281C22×C4—151no—
282C22×C4—151no—
283C22×C4—151no—
284C22×C4—301no—
285C22×C4—301no—
286C2×C8—101no—
287C2×C8—101no—
288C2×C8—301no—
289C2×C8—301no—
290C4⋊C4—31no—
291C4⋊C4—51no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C4⋊C4—101no—
295C4⋊C4—101no—
296C4⋊C4—151no—
297C4⋊C4—301no—
298C4⋊C4—301no—
299C4⋊C4—301no—
300C4⋊C4—301no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
304C42—31no—
305C42—51no—
306C42—151no—
307C42—151no—
308C3×C5#153411yescharacteristic, complemented, Hall
309C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
310C2×D3—52no—
311C2×D3—101no—
312C2×D3—101no—
313C3×C4—21no—
314C3×C4—41no—
315C3×C4—101no—
316C3×C4—101no—
317C3×C4—201no—
318Dic3—21no—
319Dic3—21no—
320Dic3—41no—
321Dic3—101no—
322Dic3—201no—
323C2×C5D3×#10111yescharacteristic
324C2×C5#482111yescharacteristic
325C2×C5#482111yescharacteristic
326D5—62no—
327C23—151no—
328C2×C4—21no—
329C2×C4—31no—
330C2×C4—31no—
331C2×C4—51no—
332C2×C4—51no—
333C2×C4—61no—
334C2×C4—101no—
335C2×C4—151no—
336C2×C4—302no—
337C2×C4—301no—
338C2×C4—602no—
339C2×C4—601no—
340C2×C4—601no—
341C2×C4—602no—
342C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
343C8—201no—
344C8—201no—
345C8—601no—
346C8—601no—
347C2×C3D5⋊#10111yescharacteristic
348C2×C3#6579511yescharacteristic
349C2×C3#6579511yescharacteristic
350D3—102no—
351C5#6836711yescharacteristic, complemented, Sylow
352C22—152no—
353C22—301no—
354C22—301no—
355C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
356C4—21no—
357C4—41no—
358C4—61no—
359C4—61no—
360C4—101no—
361C4—101no—
362C4—121no—
363C4—201no—
364C4—301no—
365C4—601no—
366C3#1060457911yescharacteristic, complemented, Sylow
367C2—302no—
368C2#1175191811yescharacteristic
369C2#1175194911yescharacteristic
370C2#1175197311yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1534
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746741C2semidirect
5. C3×#64870C2semidirect
6. #11746507C2semidirect
7. #11746506C2semidirect
35. #64870D3semidirect
308. C3×C5#1534semidirect
351. C5#68367semidirect
366. C3#10604579semidirect

Maximal subgroups

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

subgroupindex
#117536202
#117518082
#117467412
C3×#648702
#117465072
#117465062
#106045793
#683675