Finite Group Databasebeta

← #14289853

Subgroups — #14289853

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
2C3×#65131C211yesmaximal, characteristic
3#11746924C211yesmaximal, characteristic, complemented
4#11746917C211yesmaximal, characteristic, complemented
5#11746305C211yesmaximal, characteristic, complemented
6C5×#4482C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic
8#10599228—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×C4×D20C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91368—21no—
14#91361—22no—
15#91360—21no—
16#91358—21no—
17#91344—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#3953—21no—
22C3×#3949—21no—
23#90990—21no—
24#90974—21no—
25#90970—22no—
26#71147—51nomaximal, Hall
27#66066—31no—
28#65382—31no—
29#65139—31no—
30#65131D311yescharacteristic
31C5×#332—31no—
32#64704—31no—
33#64703—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×Dic6—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×Dic10—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⋊Dic3D412yes—
47C2×C5×C3⋊C8—21no—
48C3×#685—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D411yescharacteristic
52Dic3⋊Dic5—22no—
53#6665—22no—
54#6665—22no—
55Dic3×Dic5—22no—
56#5542—51no—
57C3×#476—51no—
58#5091—51no—
59#5079—51no—
60D4⋊(C3⋊C8)—51no—
61#4484—51no—
62#4482D511yescharacteristic, complemented
63C5×C4⋊Q8—31no—
64#4093—61no—
65Q8×Dic5—61no—
66#4044—62no—
67#4043—61no—
68#4038—61no—
69C4×D20C2×D311yescharacteristic
70#4015C2×D311yescharacteristic
71C4×Dic10—31no—
72C5×C4⋊C8—31no—
73C5×C4⋊C8C2×D311yescharacteristic
74#3953—21no—
75#3950—61no—
76#3949—21no—
77#3948—61no—
78#3942—62no—
79C4×#168—31no—
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—
90C5×Dic6—41no—
91C5×Dic6—41no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—41no—
94C3×D20—21no—
95C3×D20—21no—
96C3×C4×D5—41no—
97C3×C4×D5—41no—
98C3×Dic10—42no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8—51no—
103C3×C4×D4—51no—
104#936—101no—
105#926—101no—
106#924—101no—
107#887—101no—
108#879—102no—
109#869C2×D511yescharacteristic
110C4×Dic6—51no—
111C3×#106—101no—
112C3×C4⋊C8C2×D511yescharacteristic
113C3×#102—101no—
114#835—102no—
115#810—101no—
116#807—101no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4×C3⋊C8—51no—
119C2×C5×Q8—61no—
120C2×D20#6711yescharacteristic
121C2×C4×D5—21no—
122C2×Dic10—21no—
123C2×Dic10—31no—
124C2×C5×C8—21no—
125C2×C5×C8—61no—
126C5×C4⋊C4—32no—
127C5×C4⋊C4—61no—
128C42×C5C22×D311yescharacteristic
129#685—21no—
130#685—62no—
131#685—62no—
132C4⋊Dic5—21no—
133C4⋊Dic5—21no—
134C4⋊Dic5—31no—
135C4⋊Dic5—62no—
136C4⋊Dic5#6711yescharacteristic
137#683—61no—
138C4×Dic5—62no—
139C4×Dic5—61no—
140C2×#168—61no—
141#556—151no—
142#487—151no—
143#477—151no—
144#476—51no—
145#332—31no—
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#13511yescharacteristic
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×C4×C5#13711yescharacteristic
157Dic15—41no—
158Dic15—41no—
159C3×Dic5—41no—
160C3×Dic5—81no—
161C5×Dic3—42no—
162C2×C3×Q8—101no—
163C2×C3×D4—51no—
164C22×C3×C4—101no—
165C2×Dic6—21no—
166C2×Dic6—51no—
167C2×C3×C8—21no—
168C3×C4⋊C4—51no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C22⋊C4—101no—
172C3×C42C22×D511yescharacteristic
173#217—102no—
174#217—102no—
175C4⋊Dic3—21no—
176C4⋊Dic3—51no—
177C4⋊Dic3D2012yes—
178Dic3⋊C4—102no—
179Dic3⋊C4—101no—
180C4×Dic3—102no—
181C4×Dic3—101no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—101no—
184C22×D5—21no—
185C5×Q8—121no—
186C5×Q8—121no—
187C2×C4×C5—62no—
188C2×C4×C5D3×D411yescharacteristic
189C2×C4×C5D3×D411yescharacteristic
190C2×C4×C5C2×#6711yescharacteristic
191C2×Dic5—21no—
192C2×Dic5—41no—
193C2×Dic5—61no—
194C2×Dic5—61no—
195D20—21no—
196D20—21no—
197C4×D5—41no—
198C4×D5—41no—
199Dic10—42no—
200Dic10—61no—
201Dic10—61no—
202C5×C8—41no—
203C5×C8—121no—
204#168—121no—
205C4⋊Q8—31no—
206C4⋊Q8—51no—
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—101no—
216C4⋊C8—31no—
217C4⋊C8D3×D511yescharacteristic
218#103—302no—
219#103—301no—
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—202no—
228C3×D4—101no—
229C3×D4—101no—
230C2×C3×C4—101no—
231C2×C3×C4—201no—
232C2×C3×C4—201no—
233C2×C3×C4—201no—
234C2×C3×C4C2×D2011yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×Dic3—22no—
238C2×Dic3—101no—
239C2×Dic3—101no—
240Dic6—41no—
241Dic6—41no—
242Dic6—101no—
243Dic6—101no—
244C3×C8—41no—
245C3⋊C8—41no—
246C3⋊C8—201no—
247C22×C5#93711yescharacteristic
248C2×D5—41no—
249C2×D5—41no—
250C2×D5—41no—
251C4×C5—21no—
252C4×C5—122no—
253C4×C5#91511yescharacteristic
254C4×C5#91611yescharacteristic
255C4×C5#94211yescharacteristic
256C4×C5#95011yescharacteristic
257Dic5—41no—
258Dic5—81no—
259Dic5—121no—
260Dic5—121no—
261C2×Q8—61no—
262C2×Q8—101no—
263C2×Q8—151no—
264C2×D4—51no—
265C22×C4—101no—
266C2×C8—21no—
267C2×C8—61no—
268C2×C8—301no—
269C4⋊C4—32no—
270C4⋊C4—51no—
271C4⋊C4—61no—
272C4⋊C4—101no—
273C4⋊C4—101no—
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#402811yescharacteristic
288C3×C4—21no—
289C3×C4—201no—
290C3×C4—401no—
291C3×C4#405811yescharacteristic
292C3×C4#406111yescharacteristic
293C3×C4#406211yescharacteristic
294C3×C4#406411yescharacteristic
295Dic3—42no—
296Dic3—201no—
297Dic3—201no—
298C2×C5#504711yescharacteristic
299C2×C5#517311yescharacteristic
300C2×C5#520111yescharacteristic
301D5—81no—
302C23—101no—
303Q8—121no—
304Q8—121no—
305Q8—202no—
306Q8—301no—
307Q8—301no—
308D4—101no—
309D4—101no—
310C2×C4—62no—
311C2×C4—101no—
312C2×C4—201no—
313C2×C4—201no—
314C2×C4—201no—
315C2×C4—301no—
316C2×C4—301no—
317C2×C4D3×D2011yescharacteristic
318C2×C4#677711yescharacteristic
319C2×C4D5×#6711yescharacteristic
320C8—41no—
321C8—121no—
322C8—601no—
323C2×C3—401no—
324C2×C3#6504211yescharacteristic
325C2×C3#6507211yescharacteristic
326C2×C3#6509911yescharacteristic
327C5#7114711yescharacteristic, complemented, Sylow
328C22—201no—
329C22—201no—
330C22—201no—
331C22#9147411yescharacteristic
332C4—21no—
333C4—122no—
334C4—201no—
335C4—401no—
336C4—601no—
337C4—601no—
338C4#9127611yescharacteristic
339C4#9127811yescharacteristic
340C4#9149011yescharacteristic
341C4#9151311yescharacteristic
342C3#1059922811yescharacteristic, complemented, Sylow
343C2—401no—
344C2#1174751111yescharacteristic
345C2#1174814811yescharacteristic
346C2#1174825511yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊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
3. #11746924C2semidirect
4. #11746917C2semidirect
5. #11746305C2semidirect
6. C5×#4482C2semidirect
62. #4482D5semidirect
283. C3×C5#1638semidirect
327. C5#71147semidirect
342. C3#10599228semidirect

Maximal subgroups

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

subgroupindex
#117525082
C3×#651312
#117469242
#117469172
#117463052
C5×#44822
#117458342
#105992283
#711475