Finite Group Databasebeta

← #14285211

Subgroups — #14285211

Order 1920.

396 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 84 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#11751790C211yesmaximal, characteristic
3#11751760C211yesmaximal, characteristic
4#11746744C211yesmaximal, characteristic, complemented
5C3×#64873C211yesmaximal, characteristic, complemented
6#11746511C211yesmaximal, characteristic, complemented
7#11746511C211yesmaximal, characteristic, complemented
8#10604445—31nomaximal, Hall
9#91786C411yescharacteristic
10C5×#887C411yescharacteristic
11C3×#4034C2211yescharacteristic
12#91411—21no—
13#91403—21no—
14C4×#1200C2211yescharacteristic
15#91383C411yescharacteristic
16#91376C2211yescharacteristic
17#91340C411yescharacteristic
18#91334—21no—
19Dic3×Dic10—21no—
20#91233C2211yescharacteristic
21#91233C2211yescharacteristic
22C3×#4004C2211yescharacteristic
23C3×#4004C2211yescharacteristic
24#91171—21no—
25#91171—21no—
26#91169—21no—
27Dic3×#170—21no—
28#68427—51nomaximal, Hall
29#65912—31no—
30#65684—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—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47#6714—21no—
48C4⋊Dic15—21no—
49C5×Dic3⋊C4—21no—
50C4×C5×Dic3—21no—
51C4×C5×Dic3C2×C411yescharacteristic
52C3×C4⋊Dic5C2×C411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5C2311yescharacteristic
55#6669—21no—
56#6668—21no—
57#6668—21no—
58#6668—21no—
59#6667—21no—
60Dic3×Dic5—21no—
61Dic3×Dic5D411yescharacteristic
62Dic3×Dic5D411yescharacteristic
63#5728—51no—
64#4835—51no—
65#4833—51no—
66C3×#332—51no—
67#4547—51no—
68#4481—51no—
69#4481—51no—
70C4×C5×Q8—31no—
71#4092—31no—
72#4090—31no—
73#4043—31no—
74#4042—61no—
75#4035—61no—
76#4034C2×D311yescharacteristic
77#4018—61no—
78C42×D5—31no—
79C4×Dic10—31no—
80C4×Dic10—61no—
81#4004—31no—
82#4004—31no—
83#4004C2×D311yescharacteristic
84#4004C2×D311yescharacteristic
85#4003—61no—
86#4003—61no—
87#4002—61no—
88C4×#170—61no—
89#1554—151noSylow
90C22×D15C22⋊C411yescharacteristic
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×Dic15—21no—
94C2×Dic15C22⋊C411yescharacteristic
95C4×D15—41no—
96Dic30—41no—
97C2×C5×Dic3—21no—
98C2×C5×Dic3C22⋊C411yescharacteristic
99C2×C5×Dic3C22⋊C411yescharacteristic
100C5×Dic6—41no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5C2×D411yescharacteristic
103C2×C3×Dic5C2×D411yescharacteristic
104C3×Dic10—41no—
105C3×Dic10—41no—
106#1200—21no—
107#1200—21no—
108#1200—21no—
109#1200—21no—
110C3⋊#170—41no—
111C3⋊#170—41no—
112C3×#170—41no—
113C3×#170—41no—
114C3×C4⋊Q8—51no—
115#946—101no—
116Q8×Dic3—101no—
117#897—51no—
118#897—51no—
119#892—101no—
120#890—101no—
121#887—51no—
122#887AGL(1,𝔽5)11yescharacteristic
123C42×D3—51no—
124#869—51no—
125C3×C4⋊C8—51no—
126C3×C4⋊C8—51no—
127(C2×D3)⋊C8—101no—
128(C2×D3)⋊C8—101no—
129#815—101no—
130C8×Dic3—101no—
131C4⋊(C3⋊C8)—51no—
132C4⋊(C3⋊C8)—51no—
133C2×C5×Q8—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×Dic10—21no—
138C2×Dic10—31no—
139C2×#170—21no—
140C2×#170—21no—
141C2×#170—61no—
142C2×#170—61no—
143C5×C4⋊C4—61no—
144C5×C4⋊C4C4×D311yescharacteristic
145C42×C5—31no—
146C42×C5—61no—
147#685—61no—
148#685—61no—
149C4⋊Dic5—61no—
150C4⋊Dic5C4×D311yescharacteristic
151#683—21no—
152#683—61no—
153#683—61no—
154#683—61no—
155#683—61no—
156C4×Dic5—31no—
157C4×Dic5—31no—
158C4×Dic5—61no—
159C4×Dic5C22×D311yescharacteristic
160#533—151no—
161#432—151no—
162#431—151no—
163#333—151no—
164#333—151no—
165#332—51no—
166#332—151no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×D15—21no—
169C2×D15—21no—
170C2×D15—21no—
171C3×C4×C5—21no—
172C3×C4×C5—41no—
173Dic15—21no—
174Dic15—41no—
175C3×Dic5—41no—
176C3×Dic5#13511yescharacteristic
177C3×Dic5#13511yescharacteristic
178C3×Dic5#13711yescharacteristic
179C3×Dic5#13711yescharacteristic
180C5×Dic3—21no—
181C5×Dic3—21no—
182C5×Dic3—41no—
183C2×C3×Q8—101no—
184C2×C4×D3—51no—
185C2×C4×D3—51no—
186C2×C4×D3—51no—
187C2×Dic6—51no—
188C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
189C2×C3×C8—101no—
190C2×C3×C8—101no—
191C3×C4⋊C4—51no—
192C3×C4⋊C4—101no—
193C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
194C3×C42—51no—
195(C2×D3)⋊C4—101no—
196(C2×D3)⋊C4—101no—
197C4⋊Dic3—101no—
198C4⋊Dic3—101no—
199C4⋊Dic3—101no—
200C4⋊Dic3—101no—
201Dic3⋊C4—21no—
202Dic3⋊C4—101no—
203C4×Dic3—21no—
204C4×Dic3—51no—
205C4×Dic3—51no—
206C4×Dic3—101no—
207C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
208C2×C3⋊C8—101no—
209C2×C3⋊C8—101no—
210C22×D5—31no—
211C5×Q8—121no—
212C2×C4×C5—21no—
213C2×C4×C5—31no—
214C2×C4×C5—31no—
215C2×C4×C5—61no—
216C2×C4×C5C2×C4×D311yescharacteristic
217C2×Dic5—21no—
218C2×Dic5—31no—
219C2×Dic5—61no—
220C2×Dic5D3×D411yescharacteristic
221C2×Dic5D3×D411yescharacteristic
222C4×D5—61no—
223C4×D5—61no—
224C4×D5—61no—
225C4×D5—61no—
226C4×D5—121no—
227Dic10—41no—
228Dic10—41no—
229Dic10—121no—
230#170—41no—
231#170—41no—
232#170—121no—
233#170—121no—
234C4⋊Q8—51no—
235C4⋊Q8—151no—
236#125—301no—
237C22⋊Q8—151no—
238C22⋊Q8—151no—
239C22⋊Q8—301no—
240C4×Q8—31no—
241C4×Q8—151no—
242C4×Q8—301no—
243#117—301no—
244C2×C42—151no—
245C4⋊C8—51no—
246C4⋊C8—51no—
247C4⋊C8—151no—
248C4⋊C8—151no—
249C22⋊C8—301no—
250C22⋊C8—301no—
251#97—301no—
252C4×C8—301no—
253C2×C3×C5#41311yescharacteristic
254C2×C3×C5#41611yescharacteristic
255C2×C3×C5#41911yescharacteristic
256D15—41no—
257C22×D3—51no—
258C3×Q8—201no—
259C3×Q8—201no—
260C2×C3×C4—21no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—101no—
264C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
265C2×Dic3—21no—
266C2×Dic3—51no—
267C2×Dic3—101no—
268C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
269C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
270C4×D3—101no—
271C4×D3—101no—
272C4×D3—101no—
273C4×D3—101no—
274C4×D3—201no—
275Dic6—41no—
276Dic6—201no—
277C3×C8—201no—
278C3×C8—201no—
279C3⋊C8—201no—
280C3⋊C8—201no—
281C22×C5D3×C22⋊C411yescharacteristic
282C2×D5—61no—
283C2×D5—61no—
284C2×D5—61no—
285C4×C5—21no—
286C4×C5—41no—
287C4×C5—61no—
288C4×C5—61no—
289C4×C5—121no—
290Dic5—41no—
291Dic5—61no—
292Dic5—121no—
293Dic5#91211yescharacteristic
294Dic5#91511yescharacteristic
295Dic5#91611yescharacteristic
296Dic5#91811yescharacteristic
297C2×Q8—31no—
298C2×Q8—101no—
299C2×Q8—151no—
300C22×C4—151no—
301C22×C4—151no—
302C22×C4—151no—
303C2×C8—101no—
304C2×C8—101no—
305C2×C8—301no—
306C2×C8—301no—
307C4⋊C4—51no—
308C4⋊C4—61no—
309C4⋊C4—101no—
310C4⋊C4—301no—
311C4⋊C4—301no—
312C4⋊C4—301no—
313C4⋊C4—301no—
314C4⋊C4—301no—
315C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
316C22⋊C4—301no—
317C22⋊C4—301no—
318C42—31no—
319C42—51no—
320C42—61no—
321C42—151no—
322C42—151no—
323C42—301no—
324C3×C5#155411yescharacteristic, complemented, Hall
325C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
326C2×D3—101no—
327C2×D3—101no—
328C2×D3—101no—
329C3×C4—21no—
330C3×C4—41no—
331C3×C4—51no—
332C3×C4—51no—
333C3×C4—51no—
334C3×C4—51no—
335C3×C4—201no—
336Dic3—21no—
337Dic3—21no—
338Dic3—41no—
339Dic3—101no—
340Dic3—201no—
341C2×C5#475111yescharacteristic
342C2×C5#477211yescharacteristic
343C2×C5#480211yescharacteristic
344D5—121no—
345C23—151no—
346Q8—121no—
347Q8—201no—
348Q8—201no—
349Q8—601no—
350C2×C4—21no—
351C2×C4—31no—
352C2×C4—31no—
353C2×C4—51no—
354C2×C4—51no—
355C2×C4—61no—
356C2×C4—101no—
357C2×C4—151no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—301no—
361C2×C4—301no—
362C2×C4—301no—
363C2×C4—601no—
364C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
365C8—201no—
366C8—201no—
367C8—601no—
368C8—601no—
369C2×C3#6576111yescharacteristic
370C2×C3#6578211yescharacteristic
371C2×C3#6579411yescharacteristic
372D3—201no—
373C5#6842711yescharacteristic, complemented, Sylow
374C22—301no—
375C22—301no—
376C22—301no—
377C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
378C4—21no—
379C4—41no—
380C4—51no—
381C4—51no—
382C4—51no—
383C4—51no—
384C4—61no—
385C4—61no—
386C4—121no—
387C4—201no—
388C4—301no—
389C4—601no—
390C3#1060444511yescharacteristic, complemented, Sylow
391C2—601no—
392C2#1175191711yescharacteristic
393C2#1175194711yescharacteristic
394C2#1175196211yescharacteristic
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#1554
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
324. C3×C5#1554semidirect
373. C5#68427semidirect
390. C3#10604445semidirect

Maximal subgroups

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

subgroupindex
#117534662
#117517902
#117517602
#117467442
C3×#648732
#117465112
#106044453
#684275