Finite Group Databasebeta

← #14289834

Subgroups — #14289834

Order 1920.

388 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752507C211yesmaximal, characteristic
2#11751180C211yesmaximal, characteristic, complemented
3C5×#5091C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic
5#11745860C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic
8#10601950—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13#91364—21no—
14#91362—22no—
15#91359—21no—
16#91358—21no—
17#91340—21no—
18#91119—22no—
19C4×C3⋊#168C2211yescharacteristic
20C5×#810—21no—
21C5×#807—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3941—21no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71147—51nomaximal, Hall
27#65918—31no—
28C5×#477—31no—
29#65373D311yescharacteristic
30#65370—31no—
31Q8⋊#168—31no—
32#64706—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15D412yes—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3D411yescharacteristic
46C5×Dic3⋊C4—21no—
47C4×C5×Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C3×#685—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C2×C3×#168—21no—
52#6669—22no—
53#6665—22no—
54#6665—22no—
55Dic3×Dic5—22no—
56#5542—51no—
57C3×#476—51no—
58#5091D511yescharacteristic, complemented
59#5079—51no—
60D4⋊(C3⋊C8)—51no—
61#4484—51no—
62#4482—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C4×C5×Q8—31no—
65#4092—61no—
66#4044—62no—
67#4038—61no—
68#4021—61no—
69C4×D20C2×D311yescharacteristic
70#4015—31no—
71C4×Dic10—61no—
72C5×#107—61no—
73C5×C4⋊C8—31no—
74C5×#103—61no—
75#3967—62no—
76#3941—21no—
77#3940—21no—
78C4⋊#168C2×D311yescharacteristic
79C4×#168—31no—
80#1638—151noSylow
81C22×C3×D5—21no—
82C3×C5×Q8—42no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—22no—
88Dic30—41no—
89Dic30—41no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C5×Dic6—21no—
93C5×Dic6—21no—
94C2×C3×Dic5—21no—
95C3×D20—21no—
96C3×D20—21no—
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99C3⋊#168—41no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×C4×D4—51no—
104#936—101no—
105#926—101no—
106#924—101no—
107#887—101no—
108#879—102no—
109#869—51no—
110C4×Dic6C2×D511yescharacteristic
111C3×#106—101no—
112C3×C4⋊C8—51no—
113C3×#102—101no—
114#835—102no—
115#810—21no—
116#807—21no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4×C3⋊C8—51no—
119C2×C5×Q8—21no—
120C2×C5×Q8—31no—
121C2×D20#6711yescharacteristic
122C2×C4×D5—21no—
123C2×Dic10—61no—
124C2×C5×C8—61no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—61no—
129C42×C5—61no—
130C42×C5C22×D311yescharacteristic
131#685—21no—
132#685—62no—
133#685—62no—
134C4⋊Dic5—32no—
135C4⋊Dic5—61no—
136C4⋊Dic5#6711yescharacteristic
137#683—62no—
138C4×Dic5—62no—
139C2×#168—21no—
140C2×#168—61no—
141#556—151no—
142#487—151no—
143#477—31no—
144#476—51no—
145#332—151no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C2×C3×D5—41no—
150C2×C3×D5—41no—
151C2×C3×D5—41no—
152C3×C4×C5—21no—
153C3×C4×C5—81no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158Dic15—42no—
159C3×Dic5—41no—
160C5×Dic3—41no—
161C5×Dic3—41no—
162C2×C3×Q8—21no—
163C2×C3×D4—51no—
164C22×C3×C4—101no—
165C2×Dic6—101no—
166C2×Dic6C22⋊D511yescharacteristic
167C2×C3×C8—101no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—51no—
171C3×C22⋊C4—101no—
172C3×C42C22×D511yescharacteristic
173#217—102no—
174#217—102no—
175C4⋊Dic3—52no—
176C4⋊Dic3—101no—
177C4⋊Dic3C22⋊D511yescharacteristic
178Dic3⋊C4—21no—
179Dic3⋊C4—102no—
180C4×Dic3—21no—
181C4×Dic3—102no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—101no—
184C22×D5—21no—
185C5×Q8—42no—
186C5×Q8—61no—
187C5×Q8—61no—
188C2×C4×C5—41no—
189C2×C4×C5—61no—
190C2×C4×C5—61no—
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5C2×#6711yescharacteristic
194C2×Dic5—21no—
195C2×Dic5—62no—
196D20—21no—
197D20—21no—
198C4×D5—41no—
199C4×D5—41no—
200Dic10—121no—
201Dic10—121no—
202C5×C8—121no—
203#168—41no—
204#168—121no—
205C4⋊Q8—151no—
206C4⋊Q8D3×D511yescharacteristic
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—31no—
211C4×Q8—301no—
212C4×D4—51no—
213#117—301no—
214#107—61no—
215#106—101no—
216C4⋊C8—31no—
217C4⋊C8—51no—
218#103—61no—
219#103—302no—
220#102—101no—
221C4×C8—151no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225C3×D5—81no—
226C23×C3—101no—
227C3×Q8—42no—
228C3×D4—101no—
229C3×D4—101no—
230C2×C3×C4—41no—
231C2×C3×C4—101no—
232C2×C3×C4—201no—
233C2×C3×C4—201no—
234C2×C3×C4D4×D511yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4C2×C22⋊D511yescharacteristic
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—102no—
240Dic6—21no—
241Dic6—21no—
242Dic6—201no—
243Dic6—201no—
244C3×C8—201no—
245C3⋊C8—41no—
246C3⋊C8—201no—
247C22×C5#93711yescharacteristic
248C2×D5—41no—
249C2×D5—41no—
250C2×D5—41no—
251C4×C5—21no—
252C4×C5—81no—
253C4×C5—121no—
254C4×C5—121no—
255C4×C5#91511yescharacteristic
256C4×C5#91611yescharacteristic
257C4×C5#94211yescharacteristic
258C4×C5#95011yescharacteristic
259Dic5—41no—
260Dic5—122no—
261C2×Q8—21no—
262C2×Q8—31no—
263C2×Q8—301no—
264C2×D4—51no—
265C22×C4—101no—
266C2×C8—61no—
267C2×C8—101no—
268C2×C8—301no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—31no—
272C4⋊C4—51no—
273C4⋊C4—61no—
274C4⋊C4—152no—
275C4⋊C4—302no—
276C4⋊C4—301no—
277C22⋊C4—101no—
278C22⋊C4—302no—
279C22⋊C4—302no—
280C42—61no—
281C42—302no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—201no—
285C22×C3—201no—
286C22×C3—201no—
287C22×C3#408311yescharacteristic
288C3×C4—21no—
289C3×C4—81no—
290C3×C4—201no—
291C3×C4#406411yescharacteristic
292C3×C4#406511yescharacteristic
293C3×C4#408811yescharacteristic
294C3×C4#409611yescharacteristic
295Dic3—41no—
296Dic3—41no—
297Dic3—202no—
298C2×C5#504711yescharacteristic
299C2×C5#517311yescharacteristic
300C2×C5#520111yescharacteristic
301D5—81no—
302C23—101no—
303Q8—42no—
304Q8—61no—
305Q8—61no—
306Q8—601no—
307Q8—601no—
308D4—101no—
309D4—101no—
310C2×C4—41no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—101no—
314C2×C4—201no—
315C2×C4—201no—
316C2×C4—302no—
317C2×C4D5×#6711yescharacteristic
318C2×C4D3×C22⋊D511yescharacteristic
319C2×C4#679011yescharacteristic
320C8—121no—
321C8—201no—
322C8—601no—
323C2×C3—401no—
324C2×C3#6533611yescharacteristic
325C2×C3#6547611yescharacteristic
326C2×C3#6549011yescharacteristic
327C5#7114711yescharacteristic, complemented, Sylow
328C22—201no—
329C22—201no—
330C22—201no—
331C22#9157711yescharacteristic
332C4—21no—
333C4—81no—
334C4—121no—
335C4—121no—
336C4—201no—
337C4—602no—
338C4#9151511yescharacteristic
339C4#9151611yescharacteristic
340C4#9151711yescharacteristic
341C4#9151811yescharacteristic
342C3#1060195011yescharacteristic, complemented, Sylow
343C2—401no—
344C2#1174916611yescharacteristic
345C2#1174940311yescharacteristic
346C2#1174940611yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751180C2semidirect
3. C5×#5091C2semidirect
5. #11745860C2semidirect
6. #11745842C2semidirect
58. #5091D5semidirect
283. C3×C5#1638semidirect
327. C5#71147semidirect
342. C3#10601950semidirect

Maximal subgroups

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

subgroupindex
#117525072
#117511802
C5×#50912
C3×#653732
#117458602
#117458422
#117458342
#106019503
#711475