Finite Group Databasebeta

← #14284114

Subgroups — #14284114

Order 1920.

424 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 80 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#11751828C211yesmaximal, characteristic
3#11751756C211yesmaximal, characteristic
4#11746741C211yesmaximal, characteristic, complemented
5C3×#64870C211yesmaximal, characteristic, complemented
6#11746507C211yesmaximal, characteristic, complemented
7#11746506C211yesmaximal, characteristic, complemented
8#10604578—31nomaximal, Hall
9C2×#6740—21no—
10C4⋊C4×D15C411yescharacteristic
11C5×#890C411yescharacteristic
12C3×#4036C2211yescharacteristic
13#91437—21no—
14#91437C411yescharacteristic
15#91404—21no—
16C4×#1200C2211yescharacteristic
17#91388C2211yescharacteristic
18#91381C411yescharacteristic
19#91339—21no—
20#91336—21no—
21#91231C2211yescharacteristic
22#91231C2211yescharacteristic
23C3×#4002C2211yescharacteristic
24C3×#4002C2211yescharacteristic
25#91177—21no—
26#91171—21no—
27Dic3×#170—21no—
28#68363—51nomaximal, Hall
29D5×#125—31no—
30#65684—31no—
31C4×#700—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—
45#6740—24no—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C4⋊Dic15C2×C411yescharacteristic
48#6712—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3C2×C411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3C2×C411yescharacteristic
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5C2311yescharacteristic
57Dic3⋊Dic5—21no—
58#6669—21no—
59#6669—21no—
60#6669—21no—
61#6668—21no—
62Dic3×Dic5D411yescharacteristic
63Dic3×Dic5D411yescharacteristic
64D3×#125—51no—
65#4707—51no—
66#4705—51no—
67C3×#330—51no—
68#4543—51no—
69#4465—51no—
70#4465—51no—
71C2×#700—61no—
72C5×#125—31no—
73D5×C4⋊C4—31no—
74D5×C4⋊C4—31no—
75D5×C4⋊C4—61no—
76D5×C4⋊C4—61no—
77#4036—31no—
78#4036C2×D311yescharacteristic
79#4035—61no—
80#4035—61no—
81C42×D5—31no—
82#4016—31no—
83#4004—61no—
84#4003—61no—
85#4002—31no—
86#4002—31no—
87#4002C2×D311yescharacteristic
88#4002C2×D311yescharacteristic
89C4×#170—61no—
90#1528—151noSylow
91C22×D15C22⋊C411yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×Dic15—21no—
95C2×Dic15C22⋊C411yescharacteristic
96C4×D15—22no—
97C4×D15—42no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3C22⋊C411yescharacteristic
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C3×Dic5—21no—
102C2×C3×Dic5C2×D411yescharacteristic
103C2×C3×Dic5C2×D411yescharacteristic
104#1200—22no—
105#1200—41no—
106#1200—42no—
107C3⋊#170—22no—
108C3⋊#170—41no—
109C3×#170—22no—
110C3×#170—41no—
111C3×#125—51no—
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#890AGL(1,𝔽5)11yescharacteristic
119#889—101no—
120#889—101no—
121C42×D3—51no—
122#870—51no—
123C3×#97—51no—
124C3×#97—51no—
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×#170—21no—
136C2×#170—21no—
137C2×#170—61no—
138C2×#170—61no—
139#700—64no—
140C5×C4⋊C4—31no—
141C5×C4⋊C4—61no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4C4×D311yescharacteristic
144C42×C5—31no—
145C4⋊Dic5—21no—
146C4⋊Dic5—31no—
147C4⋊Dic5—61no—
148C4⋊Dic5C4×D311yescharacteristic
149#683—21no—
150#683—61no—
151#683—61no—
152#683—61no—
153#683—61no—
154#683—61no—
155C4×Dic5—31no—
156C4×Dic5—31no—
157C4×Dic5C22×D311yescharacteristic
158C2×#125—151no—
159#432—151no—
160C4×M16—151no—
161#330—51no—
162#330—151no—
163#330—151no—
164#330—151no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×D15—21no—
167C2×D15—21no—
168C2×D15#10412yes—
169C3×C4×C5—21no—
170C3×C4×C5—41no—
171Dic15—41no—
172Dic15#10112yes—
173C3×Dic5—21no—
174C3×Dic5—21no—
175C3×Dic5—41no—
176C5×Dic3—21no—
177C5×Dic3—21no—
178C5×Dic3—41no—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×C4×D3—51no—
182C2×C4×D3—101no—
183C2×C4×D3—101no—
184C2×C3×C8—101no—
185C2×C3×C8—101no—
186C3×C4⋊C4—51no—
187C3×C4⋊C4—101no—
188C3×C4⋊C4—101no—
189C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
190C3×C42—51no—
191C4⋊Dic3—21no—
192C4⋊Dic3—51no—
193C4⋊Dic3—101no—
194C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
195Dic3⋊C4—21no—
196Dic3⋊C4—101no—
197Dic3⋊C4—101no—
198Dic3⋊C4—101no—
199Dic3⋊C4—101no—
200Dic3⋊C4—101no—
201C4×Dic3—51no—
202C4×Dic3—51no—
203C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
204C2×C3⋊C8—101no—
205C2×C3⋊C8—101no—
206ΓL(1,𝔽25)—104no—
207C22×D5—31no—
208C2×C4×C5—21no—
209C2×C4×C5—31no—
210C2×C4×C5—31no—
211C2×C4×C5—61no—
212C2×C4×C5C2×C4×D311yescharacteristic
213C2×Dic5—21no—
214C2×Dic5—31no—
215C2×Dic5—61no—
216C2×Dic5D3×D411yescharacteristic
217C2×Dic5D3×D411yescharacteristic
218C4×D5—62no—
219C4×D5—62no—
220C4×D5—121no—
221C4×D5—122no—
222C4×D5—122no—
223#170—22no—
224#170—41no—
225#170—62no—
226#170—121no—
227C2×M16—301no—
228#125—31no—
229#125—51no—
230#125—151no—
231#125—151no—
232#125—301no—
233#125—301no—
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—51no—
242#97—51no—
243#97—151no—
244#97—151no—
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—51no—
253C2×C3×C4—51no—
254C2×C3×C4—101no—
255C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
256C2×Dic3—21no—
257C2×Dic3—51no—
258C2×Dic3—101no—
259C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
260C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
261C4×D3—102no—
262C4×D3—102no—
263C4×D3—201no—
264C4×D3—202no—
265C4×D3—202no—
266C3×C8—102no—
267C3×C8—201no—
268C3⋊C8—102no—
269C3⋊C8—201no—
270C22×C5D3×C22⋊C411yescharacteristic
271C2×D5—32no—
272C2×D5—61no—
273C2×D5—61no—
274C4×C5—21no—
275C4×C5—41no—
276C4×C5—61no—
277C4×C5—61no—
278C4×C5—121no—
279Dic5—21no—
280Dic5—21no—
281Dic5—32no—
282Dic5—41no—
283Dic5—121no—
284C22×C4—151no—
285C22×C4—151no—
286C22×C4—151no—
287C22×C4—301no—
288C22×C4—301no—
289M16—304no—
290C2×C8—101no—
291C2×C8—101no—
292C2×C8—301no—
293C2×C8—301no—
294C4⋊C4—31no—
295C4⋊C4—51no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—101no—
299C4⋊C4—101no—
300C4⋊C4—151no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C4⋊C4—301no—
304C4⋊C4—301no—
305C4⋊C4—301no—
306C4⋊C4—301no—
307C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
308C42—31no—
309C42—51no—
310C42—151no—
311C42—151no—
312C3×C5#152811yescharacteristic, complemented, Hall
313C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
314C2×D3—52no—
315C2×D3—101no—
316C2×D3—101no—
317C3×C4—21no—
318C3×C4—41no—
319C3×C4—101no—
320C3×C4—101no—
321C3×C4—201no—
322Dic3—21no—
323Dic3—21no—
324Dic3—41no—
325Dic3—52no—
326Dic3—201no—
327C2×C5D3×#10111yescharacteristic
328C2×C5D3×#10411yescharacteristic
329C2×C5#482111yescharacteristic
330D5—62no—
331C23—151no—
332C2×C4—21no—
333C2×C4—31no—
334C2×C4—31no—
335C2×C4—51no—
336C2×C4—51no—
337C2×C4—61no—
338C2×C4—101no—
339C2×C4—151no—
340C2×C4—302no—
341C2×C4—302no—
342C2×C4—301no—
343C2×C4—602no—
344C2×C4—601no—
345C2×C4—602no—
346C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
347C8—102no—
348C8—201no—
349C8—302no—
350C8—601no—
351C2×C3D5⋊#10111yescharacteristic
352C2×C3D5⋊#10411yescharacteristic
353C2×C3#6579511yescharacteristic
354D3—102no—
355C5#6836311yescharacteristic, complemented, Sylow
356C22—152no—
357C22—301no—
358C22—301no—
359C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
360C4—21no—
361C4—41no—
362C4—61no—
363C4—61no—
364C4—101no—
365C4—101no—
366C4—121no—
367C4—152no—
368C4—201no—
369C4—601no—
370C3#1060457811yescharacteristic, complemented, Sylow
371C2—302no—
372C2#1175191811yescharacteristic
373C2#1175194911yescharacteristic
374C2#1175195911yescharacteristic
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#1528
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
312. C3×C5#1528semidirect
355. C5#68363semidirect
370. C3#10604578semidirect

Maximal subgroups

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

subgroupindex
#117536202
#117518282
#117517562
#117467412
C3×#648702
#117465072
#117465062
#106045783
#683635