Finite Group Databasebeta

← #14289869

Subgroups — #14289869

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#11752483C211yesmaximal, characteristic
2C5×#4850C211yesmaximal, characteristic, complemented
3#11746923C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic
5#11746304C211yesmaximal, characteristic
6C3×#64706C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10601950—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91383—21no—
14#91374—21no—
15#91347—21no—
16#91345—22no—
17Dic3×Dic10—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C5×#818—21no—
21C5×#816—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90985—21no—
24#90972—22no—
25#90969—21no—
26#68435—51nomaximal, Hall
27#65918—31no—
28C5×#477—31no—
29#65373—31no—
30#65370—31no—
31Q8⋊#168—31no—
32#64706D311yescharacteristic, complemented
33#64703—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6—21no—
37C2×C5×Dic6D411yescharacteristic
38C2×C3×Dic10—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41#6714—21no—
42C4⋊Dic15D411yescharacteristic
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5D412yes—
51C2×C3×#168—21no—
52#6668—22no—
53#6667—22no—
54#6667—22no—
55Dic3×Dic5—22no—
56#5732—51no—
57#5093—51no—
58#4850D511yescharacteristic, complemented
59#4842—51no—
60C3×#332—51no—
61#4484—51no—
62#4483—51no—
63C5×C4⋊Q8—31no—
64C4×C5×Q8—31no—
65#4092—61no—
66#4044—62no—
67#4038—61no—
68#4021—61no—
69C4×D20—31no—
70#4015C2×D311yescharacteristic
71C4×Dic10—61no—
72C5×#107—61no—
73C5×C4⋊C8C2×D311yescharacteristic
74C5×#103—61no—
75#3967—62no—
76#3941—61no—
77#3940—61no—
78C4⋊#168C2×D311yescharacteristic
79C4×#168—31no—
80#1638—151noSylow
81C22×D15—21no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—21no—
86D60—21no—
87D60—21no—
88C4×D15—41no—
89C4×D15—41no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—41no—
93C5×Dic6—21no—
94C5×Dic6—21no—
95C5×Dic6—42no—
96C2×C3×Dic5—22no—
97C3×Dic10—41no—
98C3×Dic10—41no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3×#168—41no—
102C3×C4⋊Q8—51no—
103#947—101no—
104Q8×Dic3—101no—
105#898—102no—
106#897—101no—
107#892—101no—
108C4×D12—51no—
109#869C2×D511yescharacteristic
110C4×Dic6C2×D511yescharacteristic
111C3×C4⋊C8—51no—
112C3×C4⋊C8C2×D511yescharacteristic
113#821—101no—
114#818—21no—
115#817—101no—
116#816—21no—
117#810—102no—
118C4×C3⋊C8—51no—
119C2×C5×Q8—31no—
120C2×C5×Q8—61no—
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×Dic10—21no—
124C2×C5×C8—21no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C42×C5—61no—
130C42×C5C22×D311yescharacteristic
131#685—62no—
132#685—62no—
133#685—61no—
134C4⋊Dic5—21no—
135C4⋊Dic5—31no—
136C4⋊Dic5D1212yes—
137#683—62no—
138C4×Dic5—62no—
139C2×#168—21no—
140C2×#168—61no—
141#556—151no—
142#487—151no—
143#477—31no—
144#476—151no—
145#332—51no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C2×D15—41no—
150C2×D15—41no—
151C2×D15—41no—
152C3×C4×C5—21no—
153C3×C4×C5#13511yescharacteristic
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×C4×C5#13711yescharacteristic
157Dic15—41no—
158C3×Dic5—42no—
159C5×Dic3—41no—
160C5×Dic3—41no—
161C5×Dic3—81no—
162C2×C3×Q8—101no—
163C2×D12—51no—
164C2×C4×D3—101no—
165C2×Dic6—21no—
166C2×Dic6C22⋊D511yescharacteristic
167C2×C3×C8—21no—
168C2×C3×C8—101no—
169C3×C4⋊C4—52no—
170C3×C4⋊C4—101no—
171C3×C42C22×D511yescharacteristic
172(C2×D3)⋊C4—102no—
173(C2×D3)⋊C4—102no—
174(C2×D3)⋊C4—101no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—51no—
178C4⋊Dic3—102no—
179C4⋊Dic3C22⋊D511yescharacteristic
180Dic3⋊C4—21no—
181C4×Dic3—21no—
182C4×Dic3—102no—
183C2×C3⋊C8—101no—
184C22×D5—61no—
185C5×Q8—61no—
186C5×Q8—61no—
187C5×Q8—122no—
188C2×C4×C5—61no—
189C2×C4×C5—61no—
190C2×C4×C5—121no—
191C2×C4×C5C2×D1211yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×Dic5—22no—
195C2×Dic5—61no—
196D20—61no—
197D20—61no—
198C4×D5—121no—
199C4×D5—121no—
200Dic10—41no—
201Dic10—41no—
202C5×C8—41no—
203#168—41no—
204#168—121no—
205C4⋊Q8—31no—
206C4⋊Q8—51no—
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—31no—
211C4×Q8—301no—
212C4×D4—151no—
213#117—301no—
214#107—61no—
215#106—301no—
216C4⋊C8—51no—
217C4⋊C8D3×D511yescharacteristic
218#103—61no—
219#103—302no—
220#102—301no—
221C4×C8—151no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225D15—81no—
226C22×D3—101no—
227C3×Q8—201no—
228C3×Q8—201no—
229C2×C3×C4—102no—
230C2×C3×C4D4×D511yescharacteristic
231C2×C3×C4D4×D511yescharacteristic
232C2×C3×C4C2×C22⋊D511yescharacteristic
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—41no—
236C2×Dic3—101no—
237D12—101no—
238D12—101no—
239C4×D3—201no—
240C4×D3—201no—
241Dic6—21no—
242Dic6—21no—
243Dic6—42no—
244C3×C8—41no—
245C3×C8—201no—
246C3⋊C8—201no—
247C22×C5#88211yescharacteristic
248C2×D5—121no—
249C2×D5—121no—
250C2×D5—121no—
251C4×C5—21no—
252C4×C5—121no—
253C4×C5—121no—
254C4×C5—241no—
255C4×C5#91211yescharacteristic
256C4×C5#91511yescharacteristic
257C4×C5#91611yescharacteristic
258C4×C5#91811yescharacteristic
259Dic5—42no—
260Dic5—121no—
261C2×Q8—31no—
262C2×Q8—61no—
263C2×Q8—101no—
264C2×D4—151no—
265C22×C4—301no—
266C2×C8—21no—
267C2×C8—101no—
268C2×C8—301no—
269C4⋊C4—31no—
270C4⋊C4—52no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—101no—
275C4⋊C4—151no—
276C4⋊C4—302no—
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—301no—
280C42—61no—
281C42—302no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3#408311yescharacteristic
285C2×D3—201no—
286C2×D3—201no—
287C2×D3—201no—
288C3×C4—21no—
289C3×C4—202no—
290C3×C4#406411yescharacteristic
291C3×C4#406511yescharacteristic
292C3×C4#408811yescharacteristic
293C3×C4#409611yescharacteristic
294Dic3—41no—
295Dic3—41no—
296Dic3—81no—
297Dic3—201no—
298C2×C5#475311yescharacteristic
299C2×C5#478311yescharacteristic
300C2×C5#480811yescharacteristic
301D5—241no—
302C23—301no—
303Q8—61no—
304Q8—61no—
305Q8—122no—
306Q8—201no—
307Q8—201no—
308D4—301no—
309D4—301no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—102no—
313C2×C4—121no—
314C2×C4—301no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4D5×D1211yescharacteristic
318C2×C4#677711yescharacteristic
319C2×C4D3×C22⋊D511yescharacteristic
320C8—41no—
321C8—201no—
322C8—601no—
323C2×C3#6533611yescharacteristic
324C2×C3#6547611yescharacteristic
325C2×C3#6549011yescharacteristic
326D3—401no—
327C5#6843511yescharacteristic, complemented, Sylow
328C22—601no—
329C22—601no—
330C22—601no—
331C22#9147511yescharacteristic
332C4—21no—
333C4—121no—
334C4—121no—
335C4—202no—
336C4—241no—
337C4—601no—
338C4#9127711yescharacteristic
339C4#9127811yescharacteristic
340C4#9149511yescharacteristic
341C4#9152011yescharacteristic
342C3#1060195011yescharacteristic, complemented, Sylow
343C2—1201no—
344C2#1174751611yescharacteristic
345C2#1174815411yescharacteristic
346C2#1174825911yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×#4850C2semidirect
3. #11746923C2semidirect
6. C3×#64706C2semidirect
7. #11745842C2semidirect
32. #64706D3semidirect
58. #4850D5semidirect
283. C3×C5#1638semidirect
327. C5#68435semidirect
342. C3#10601950semidirect

Maximal subgroups

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

subgroupindex
#117524832
C5×#48502
#117469232
#117468852
#117463042
C3×#647062
#117458422
#106019503
#684355