Finite Group Databasebeta

← #14289847

Subgroups — #14289847

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#11752508C211yesmaximal, characteristic
2C5×#4681C211yesmaximal, characteristic, complemented
3#11746963C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic
5#11746277C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic
7#11745857C211yesmaximal, characteristic, complemented
8#10602022—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13#91368—21no—
14#91361—22no—
15#91360—21no—
16#91358—21no—
17#91344—21no—
18C3×C4×C5×C8C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×#816—22no—
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90986—21no—
24#90975—21no—
25#90964—21no—
26#68205—51nomaximal, Hall
27#66066—31no—
28C5×#487—31no—
29#65380—31no—
30#65373—31no—
31#64767—31no—
32#64679D311yescharacteristic
33#64676—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×Dic6—21no—
36C2×C5×Dic6—21no—
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15D411yescharacteristic
42#6712—21no—
43C4×Dic15—21no—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3D412yes—
49C3×#685—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C2×C3×#168—21no—
52Dic3⋊Dic5—22no—
53#6665—22no—
54#6665—22no—
55Dic3×Dic5—22no—
56#5542—51no—
57#5008—51no—
58#4850—51no—
59#4681D511yescharacteristic, complemented
60C3×D4⋊C8—51no—
61#4486—51no—
62#4456—51no—
63C5×C4⋊Q8—31no—
64C5×C4⋊Q8—31no—
65#4093—61no—
66Q8×Dic5—61no—
67#4044—62no—
68#4043—61no—
69#4038—61no—
70C4×D20C2×D311yescharacteristic
71C4×Dic10—31no—
72C5×#103—62no—
73C4×C5×C8C2×D311yescharacteristic
74#3942—61no—
75#3941—61no—
76#3940—61no—
77#3939—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80#1638—151noSylow
81C22×C3×D5—21no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—21no—
86C2×Dic15—21no—
87Dic30—21no—
88Dic30—21no—
89C2×C5×Dic3—22no—
90C2×C5×Dic3—41no—
91C5×Dic6—41no—
92C5×Dic6—41no—
93C5×Dic6—42no—
94C2×C3×Dic5—21no—
95C3×D20—21no—
96C3×D20—21no—
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3×#168—41no—
102C3×C4×D4—51no—
103#936—101no—
104#926—101no—
105#924—101no—
106#887—101no—
107#879—102no—
108#869C2×D511yescharacteristic
109#869C2×D511yescharacteristic
110C4×Dic6—51no—
111C3×C4⋊C8—51no—
112C3×C4×C8C2×D511yescharacteristic
113#832—101no—
114#818—101no—
115#816—22no—
116#816—101no—
117#808—101no—
118C4⋊(C3⋊C8)—51no—
119C2×C5×Q8—61no—
120C2×C5×Q8—61no—
121C2×D20D1211yescharacteristic
122C2×C4×D5—21no—
123C2×Dic10—31no—
124C2×C5×C8—21no—
125C5×C4⋊C4—32no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C42×C5C22×D311yescharacteristic
130#685—21no—
131#685—62no—
132#685—62no—
133C4⋊Dic5—31no—
134C4⋊Dic5—62no—
135C4⋊Dic5D1211yescharacteristic
136#683—61no—
137C4×Dic5—62no—
138C4×Dic5—61no—
139C2×#168—21no—
140C2×#168—61no—
141#556—151no—
142#487—31no—
143#477—151no—
144#476—151no—
145#332—151no—
146Q8⋊C8—151no—
147D4⋊C8—51no—
148C22×C3×C5#12011yescharacteristic
149C2×C3×D5—41no—
150C2×C3×D5—41no—
151C2×C3×D5—41no—
152C3×C4×C5—21no—
153C3×C4×C5#13511yescharacteristic
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×C4×C5#13711yescharacteristic
157Dic15—41no—
158Dic15—41no—
159C3×Dic5—41no—
160C5×Dic3—42no—
161C5×Dic3—81no—
162C2×C3×D4—51no—
163C22×C3×C4—101no—
164C2×Dic6—21no—
165C2×Dic6—21no—
166C2×Dic6—51no—
167C2×C3×C8—21no—
168C2×C3×C8—101no—
169C3×C4⋊C4—51no—
170C3×C22⋊C4—101no—
171C3×C42C22×D511yescharacteristic
172#217—102no—
173#217—102no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—51no—
178C4⋊Dic3C22⋊D512yes—
179Dic3⋊C4—102no—
180Dic3⋊C4—101no—
181C4×Dic3—102no—
182C4×Dic3—101no—
183C2×C3⋊C8—101no—
184C22×D5—21no—
185C5×Q8—122no—
186C5×Q8—121no—
187C5×Q8—121no—
188C2×C4×C5—62no—
189C2×C4×C5—121no—
190C2×C4×C5C2×D1211yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×Dic5—21no—
194C2×Dic5—61no—
195C2×Dic5—61no—
196D20—21no—
197D20—21no—
198C4×D5—41no—
199C4×D5—41no—
200Dic10—61no—
201Dic10—61no—
202C5×C8—41no—
203#168—41no—
204#168—121no—
205C4⋊Q8—31no—
206C4⋊Q8—31no—
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—151no—
211C4×Q8—301no—
212C4×D4—51no—
213#117—301no—
214#107—301no—
215#106—301no—
216C4⋊C8—51no—
217C4⋊C8—151no—
218#103—62no—
219#103—301no—
220#102—301no—
221C4×C8D3×D511yescharacteristic
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225C3×D5—81no—
226C23×C3—101no—
227C3×D4—101no—
228C3×D4—101no—
229C2×C3×C4—101no—
230C2×C3×C4—201no—
231C2×C3×C4—201no—
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C2×Dic3—22no—
236C2×Dic3—41no—
237C2×Dic3—101no—
238C2×Dic3—101no—
239Dic6—41no—
240Dic6—41no—
241Dic6—42no—
242Dic6—101no—
243Dic6—101no—
244C3×C8—41no—
245C3×C8—201no—
246C3⋊C8—201no—
247C22×C5#88211yescharacteristic
248C2×D5—41no—
249C2×D5—41no—
250C2×D5—41no—
251C4×C5—21no—
252C4×C5—122no—
253C4×C5—241no—
254C4×C5#90411yescharacteristic
255C4×C5#90911yescharacteristic
256C4×C5#91211yescharacteristic
257C4×C5#91511yescharacteristic
258Dic5—41no—
259Dic5—121no—
260Dic5—121no—
261C2×Q8—61no—
262C2×Q8—61no—
263C2×Q8—151no—
264C2×D4—51no—
265C22×C4—101no—
266C2×C8—21no—
267C2×C8—101no—
268C2×C8—301no—
269C4⋊C4—32no—
270C4⋊C4—51no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—151no—
275C4⋊C4—302no—
276C4⋊C4—301no—
277C22⋊C4—101no—
278C22⋊C4—302no—
279C22⋊C4—302no—
280C42—302no—
281C42—301no—
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—201no—
290C3×C4#406111yescharacteristic
291C3×C4#406211yescharacteristic
292C3×C4#406411yescharacteristic
293C3×C4#406511yescharacteristic
294Dic3—42no—
295Dic3—81no—
296Dic3—201no—
297Dic3—201no—
298C2×C5#473311yescharacteristic
299C2×C5#478311yescharacteristic
300C2×C5#482711yescharacteristic
301D5—81no—
302C23—101no—
303Q8—122no—
304Q8—121no—
305Q8—121no—
306Q8—301no—
307Q8—301no—
308D4—101no—
309D4—101no—
310C2×C4—62no—
311C2×C4—101no—
312C2×C4—121no—
313C2×C4—201no—
314C2×C4—201no—
315C2×C4—301no—
316C2×C4—301no—
317C2×C4D5×D1211yescharacteristic
318C2×C4#677711yescharacteristic
319C2×C4D3×C22⋊D511yescharacteristic
320C8—41no—
321C8—201no—
322C8—601no—
323C2×C3—401no—
324C2×C3#6535111yescharacteristic
325C2×C3#6546211yescharacteristic
326C2×C3#6547611yescharacteristic
327C5#6820511yescharacteristic, complemented, Sylow
328C22—201no—
329C22—201no—
330C22—201no—
331C22#9147511yescharacteristic
332C4—21no—
333C4—122no—
334C4—201no—
335C4—241no—
336C4—601no—
337C4—601no—
338C4#9126011yescharacteristic
339C4#9126911yescharacteristic
340C4#9127711yescharacteristic
341C4#9127811yescharacteristic
342C3#1060202211yescharacteristic, complemented, Sylow
343C2—401no—
344C2#1174712311yescharacteristic
345C2#1174815411yescharacteristic
346C2#1174815511yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
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×#4681C2semidirect
3. #11746963C2semidirect
5. #11746277C2semidirect
7. #11745857C2semidirect
59. #4681D5semidirect
283. C3×C5#1638semidirect
327. C5#68205semidirect
342. C3#10602022semidirect

Maximal subgroups

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

subgroupindex
#117525082
C5×#46812
#117469632
#117468802
#117462772
C3×#646792
#117458572
#106020223
#682055