Finite Group Databasebeta

← #14284695

Subgroups — #14284695

Order 1920.

424 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 94 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#11753466C211yesmaximal, characteristic
2#11751884C211yesmaximal, characteristic
3#11751760C211yesmaximal, characteristic
4#11746744C211yesmaximal, characteristic, complemented
5C3×#64873C211yesmaximal, characteristic, complemented
6#11746511C211yesmaximal, characteristic, complemented
7#11746511C211yesmaximal, characteristic, complemented
8#10604443—31nomaximal, Hall
9C2×#6738—21no—
10#91786C411yescharacteristic
11C5×#887C411yescharacteristic
12C3×#4034C2211yescharacteristic
13#91411—21no—
14#91403—21no—
15C4×#1200C2211yescharacteristic
16#91383C411yescharacteristic
17#91376C2211yescharacteristic
18#91340C411yescharacteristic
19#91334—21no—
20Dic3×Dic10—21no—
21#91233C2211yescharacteristic
22#91233C2211yescharacteristic
23C3×#4004C2211yescharacteristic
24C3×#4004C2211yescharacteristic
25Dic3⋊#170—21no—
26#91171—21no—
27Dic3×#170—21no—
28#68418—51nomaximal, Hall
29#65912—31no—
30D5⋊(C4⋊C8)—31no—
31#65678—31no—
32#64931—31no—
33#64931—31no—
34#64873—31no—
35#64873D311yescharacteristic, complemented
36C2×C4×D15C2×C411yescharacteristic
37C2×Dic30C2×C411yescharacteristic
38C2×C5×Dic6C2×C411yescharacteristic
39C2×C3×Dic10—21no—
40C2×#1200D411yescharacteristic
41C2×#1200D411yescharacteristic
42C2×C3⋊#170—21no—
43C2×C3⋊#170—21no—
44C2×C3×#170—21no—
45C2×C3×#170—21no—
46#6738—42no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48#6714—21no—
49C4⋊Dic15—21no—
50C5×Dic3⋊C4—21no—
51C4×C5×Dic3—21no—
52C4×C5×Dic3C2×C411yescharacteristic
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×#683—21no—
55C3×C4×Dic5C2311yescharacteristic
56#6669—21no—
57#6668—21no—
58#6668—21no—
59#6668—21no—
60#6667—21no—
61Dic3×Dic5—21no—
62Dic3×Dic5D411yescharacteristic
63Dic3×Dic5D411yescharacteristic
64#5728—51no—
65#4833—51no—
66D3×C4⋊C8—51no—
67C3×#332—51no—
68#4547—51no—
69#4481—51no—
70#4481—51no—
71C2×D5⋊C8—61no—
72C4×C5×Q8—31no—
73#4092—31no—
74#4090—31no—
75#4043—31no—
76#4042—61no—
77#4035—61no—
78#4034C2×D311yescharacteristic
79#4018—61no—
80C42×D5—31no—
81C4×Dic10—31no—
82C4×Dic10—61no—
83#4004—31no—
84#4004—31no—
85#4004C2×D311yescharacteristic
86#4004C2×D311yescharacteristic
87#4003—61no—
88C4⋊#170—61no—
89C4×#170—61no—
90#1542—151noSylow
91C22×D15C22⋊C411yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×Dic15—21no—
95C2×Dic15C22⋊C411yescharacteristic
96C4×D15—41no—
97Dic30—41no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3C22⋊C411yescharacteristic
100C2×C5×Dic3C22⋊C411yescharacteristic
101C5×Dic6—41no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5C2×D411yescharacteristic
104C2×C3×Dic5C2×D411yescharacteristic
105C3×Dic10—41no—
106C3×Dic10—41no—
107#1200—21no—
108#1200—21no—
109#1200SD1612yes—
110#1200Q1612yes—
111C3⋊#170—41no—
112C3⋊#170—41no—
113C3×#170—41no—
114C3×#170—41no—
115C3×C4⋊Q8—51no—
116#946—101no—
117Q8×Dic3—101no—
118C2×D3×C8—101no—
119#897—51no—
120#897—51no—
121#892—101no—
122#890—101no—
123#887—51no—
124#887AGL(1,𝔽5)11yescharacteristic
125C42×D3—51no—
126#869—51no—
127C3×C4⋊C8—51no—
128C3×C4⋊C8—51no—
129(C2×D3)⋊C8—101no—
130Dic3⋊C8—101no—
131C8×Dic3—101no—
132C4⋊(C3⋊C8)—51no—
133C4⋊(C3⋊C8)—51no—
134C2×C5×Q8—31no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×Dic10—21no—
139C2×Dic10—31no—
140C2×#170—21no—
141C2×#170—21no—
142C2×#170—61no—
143C2×#170—61no—
144D5⋊C8—122no—
145C5×C4⋊C4—61no—
146C5×C4⋊C4C4×D311yescharacteristic
147C42×C5—31no—
148C42×C5—61no—
149#685—61no—
150#685—61no—
151C4⋊Dic5—61no—
152C4⋊Dic5C4×D311yescharacteristic
153#683—21no—
154#683—61no—
155#683—61no—
156#683—61no—
157#683—61no—
158C4×Dic5—31no—
159C4×Dic5—31no—
160C4×Dic5—61no—
161C4×Dic5C22×D311yescharacteristic
162#533—151no—
163#431—151no—
164C2×C4⋊C8—151no—
165#333—151no—
166#333—151no—
167#332—51no—
168#332—151no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C2×D15—21no—
171C2×D15—21no—
172C2×D15#10312yes—
173C3×C4×C5—21no—
174C3×C4×C5—41no—
175Dic15—21no—
176Dic15—41no—
177C3×Dic5—41no—
178C3×Dic5C2×SD1611yescharacteristic
179C3×Dic5C2×Q1611yescharacteristic
180C3×Dic5#13511yescharacteristic
181C3×Dic5#13511yescharacteristic
182C5×Dic3—21no—
183C5×Dic3—41no—
184C5×Dic3#10312yes—
185C2×C3×Q8—101no—
186C2×C4×D3—51no—
187C2×C4×D3—51no—
188C2×C4×D3—51no—
189C2×Dic6—51no—
190C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
191C2×C3×C8—101no—
192C2×C3×C8—101no—
193C3×C4⋊C4—51no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
196C3×C42—51no—
197(C2×D3)⋊C4—101no—
198(C2×D3)⋊C4—101no—
199C4⋊Dic3—101no—
200C4⋊Dic3—101no—
201C4⋊Dic3—101no—
202C4⋊Dic3—101no—
203Dic3⋊C4—21no—
204Dic3⋊C4—101no—
205C4×Dic3—21no—
206C4×Dic3—51no—
207C4×Dic3—51no—
208C4×Dic3—101no—
209C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
210C2×C3⋊C8—101no—
211C2×C3⋊C8—101no—
212D3×C8—202no—
213C22×D5—31no—
214C5×Q8—121no—
215C2×C4×C5—21no—
216C2×C4×C5—31no—
217C2×C4×C5—31no—
218C2×C4×C5—61no—
219C2×C4×C5C2×C4×D311yescharacteristic
220C2×Dic5—21no—
221C2×Dic5—31no—
222C2×Dic5—61no—
223C2×Dic5D3×D411yescharacteristic
224C2×Dic5D3×D411yescharacteristic
225C4×D5—32no—
226C4×D5—32no—
227C4×D5—61no—
228C4×D5—61no—
229C4×D5—121no—
230Dic10—41no—
231Dic10—41no—
232Dic10—121no—
233#170—41no—
234#170—41no—
235#170—121no—
236#170—121no—
237C22×C8—301no—
238C4⋊Q8—51no—
239C4⋊Q8—151no—
240#125—301no—
241C22⋊Q8—151no—
242C22⋊Q8—151no—
243C22⋊Q8—301no—
244C4×Q8—31no—
245C4×Q8—151no—
246C4×Q8—301no—
247#117—301no—
248C2×C42—151no—
249C4⋊C8—51no—
250C4⋊C8—51no—
251C4⋊C8—151no—
252C4⋊C8—151no—
253C4⋊C8—301no—
254C22⋊C8—301no—
255C4×C8—301no—
256C2×C3×C5#41311yescharacteristic
257C2×C3×C5C2×#10311yescharacteristic
258C2×C3×C5#41611yescharacteristic
259D15—22no—
260C22×D3—51no—
261C3×Q8—201no—
262C3×Q8—201no—
263C2×C3×C4—21no—
264C2×C3×C4—51no—
265C2×C3×C4—51no—
266C2×C3×C4—101no—
267C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
268C2×Dic3—21no—
269C2×Dic3—51no—
270C2×Dic3—101no—
271C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
272C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
273C4×D3—52no—
274C4×D3—52no—
275C4×D3—101no—
276C4×D3—101no—
277C4×D3—201no—
278Dic6—41no—
279Dic6—201no—
280C3×C8—201no—
281C3×C8—201no—
282C3⋊C8—201no—
283C3⋊C8—201no—
284C22×C5D3×C22⋊C411yescharacteristic
285C2×D5—32no—
286C2×D5—61no—
287C2×D5—61no—
288C4×C5—21no—
289C4×C5—32no—
290C4×C5—41no—
291C4×C5—61no—
292C4×C5—121no—
293Dic5—41no—
294Dic5—61no—
295Dic5—121no—
296Dic5#91211yescharacteristic
297Dic5D3×SD1611yescharacteristic
298Dic5#91611yescharacteristic
299Dic5D3×Q1611yescharacteristic
300C2×Q8—31no—
301C2×Q8—101no—
302C2×Q8—151no—
303C22×C4—151no—
304C22×C4—151no—
305C22×C4—151no—
306C2×C8—101no—
307C2×C8—101no—
308C2×C8—301no—
309C2×C8—301no—
310C2×C8—602no—
311C4⋊C4—51no—
312C4⋊C4—61no—
313C4⋊C4—101no—
314C4⋊C4—301no—
315C4⋊C4—301no—
316C4⋊C4—301no—
317C4⋊C4—301no—
318C4⋊C4—301no—
319C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
320C22⋊C4—301no—
321C22⋊C4—301no—
322C42—31no—
323C42—51no—
324C42—61no—
325C42—151no—
326C42—151no—
327C42—301no—
328C3×C5#154211yescharacteristic, complemented, Hall
329C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
330C2×D3—52no—
331C2×D3—101no—
332C2×D3—101no—
333C3×C4—21no—
334C3×C4—41no—
335C3×C4—51no—
336C3×C4—51no—
337C3×C4—51no—
338C3×C4—51no—
339C3×C4—201no—
340Dic3—21no—
341Dic3—41no—
342Dic3—101no—
343Dic3—201no—
344Dic3#400912yes—
345C2×C5#475111yescharacteristic
346C2×C5#477211yescharacteristic
347C2×C5D3×#10311yescharacteristic
348D5—62no—
349C23—151no—
350Q8—121no—
351Q8—201no—
352Q8—201no—
353Q8—601no—
354C2×C4—21no—
355C2×C4—31no—
356C2×C4—31no—
357C2×C4—51no—
358C2×C4—51no—
359C2×C4—61no—
360C2×C4—101no—
361C2×C4—152no—
362C2×C4—152no—
363C2×C4—151no—
364C2×C4—301no—
365C2×C4—301no—
366C2×C4—301no—
367C2×C4—601no—
368C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
369C8—201no—
370C8—201no—
371C8—601no—
372C8—601no—
373C2×C3#6576111yescharacteristic
374C2×C3C2×#400911yescharacteristic
375C2×C3#6579411yescharacteristic
376D3—102no—
377C5#6841811yescharacteristic, complemented, Sylow
378C22—152no—
379C22—301no—
380C22—301no—
381C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
382C4—21no—
383C4—32no—
384C4—41no—
385C4—51no—
386C4—51no—
387C4—51no—
388C4—51no—
389C4—61no—
390C4—121no—
391C4—201no—
392C4—301no—
393C4—601no—
394C3#1060444311yescharacteristic, complemented, Sylow
395C2—302no—
396C2#1175191711yescharacteristic
397C2#1175194711yescharacteristic
398C2D3×#400911yescharacteristic
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#1542
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. #11746744C2semidirect
5. C3×#64873C2semidirect
6. #11746511C2semidirect
7. #11746511C2semidirect
35. #64873D3semidirect
328. C3×C5#1542semidirect
377. C5#68418semidirect
394. C3#10604443semidirect

Maximal subgroups

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

subgroupindex
#117534662
#117518842
#117517602
#117467442
C3×#648732
#117465112
#106044433
#684185