Finite Group Databasebeta

← #14289822

Subgroups — #14289822

Order 1920.

388 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756491C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic, complemented
3#11750951C211yesmaximal, characteristic, complemented
4#11750943C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic
8#10599228—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91836—21no—
11Q8×Dic15—21no—
12#91787—22no—
13#91786—21no—
14#91781—21no—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17C4×Dic30C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20#91105—21no—
21#91102—21no—
22#91101—21no—
23#91100—21no—
24#91094—22no—
25C4×C3⋊#168C2211yescharacteristic
26#68435—51nomaximal, Hall
27#66066—31no—
28#65382—31no—
29#65139—31no—
30#65131—31no—
31C5×#332D311yescharacteristic, complemented
32#64704—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30—21no—
38C2×Dic30D411yescharacteristic
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D412yes—
43C3×C42×C5C2311yescharacteristic
44#6714—22no—
45#6714—22no—
46#6714—21no—
47C4⋊Dic15—22no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15D411yescharacteristic
51C4⋊Dic15D411yescharacteristic
52#6712—21no—
53C4×Dic15—22no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56#5732—51no—
57#5093—51no—
58#4850—51no—
59#4842—51no—
60C3×#332D511yescharacteristic, complemented
61#4484—51no—
62#4483—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64#4093—61no—
65Q8×Dic5—61no—
66#4044—62no—
67#4043—61no—
68#4038—61no—
69C4×D20—31no—
70#4015—31no—
71C4×Dic10—31no—
72C5×C4⋊C8C2×D311yescharacteristic
73C5×C4⋊C8C2×D311yescharacteristic
74#3953—61no—
75#3950—61no—
76#3949—61no—
77#3948—61no—
78#3942—62no—
79C4×#168—31no—
80#1638—151noSylow
81C22×D15—21no—
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—21no—
89C2×Dic15—21no—
90C2×Dic15—21no—
91C2×Dic15—41no—
92D60—21no—
93D60—21no—
94C4×D15—41no—
95C4×D15—41no—
96Dic30—21no—
97Dic30—21no—
98Dic30—42no—
99C3×C5×C8—41no—
100C3×C5×C8—41no—
101C3⋊#168—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103#947—101no—
104Q8×Dic3—101no—
105#898—102no—
106#897—101no—
107#892—101no—
108C4×D12—51no—
109#869—51no—
110C4×Dic6—51no—
111C3×C4⋊C8C2×D511yescharacteristic
112C3×C4⋊C8C2×D511yescharacteristic
113#821—101no—
114#818—101no—
115#817—101no—
116#816—101no—
117#810—102no—
118C4×C3⋊C8—51no—
119C2×C5×Q8—21no—
120C2×D20—31no—
121C2×C4×D5—61no—
122C2×Dic10—31no—
123C2×Dic10—61no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4D1212yes—
128C42×C5C22×D311yescharacteristic
129#685—62no—
130#685—62no—
131#685—61no—
132C4⋊Dic5—31no—
133C4⋊Dic5—31no—
134C4⋊Dic5—62no—
135C4⋊Dic5—61no—
136C4⋊Dic5—61no—
137#683—61no—
138C4×Dic5—62no—
139C4×Dic5—61no—
140C2×#168—61no—
141#556—151no—
142#487—151no—
143#477—151no—
144#476—151no—
145#332D1511yescharacteristic, complemented
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—42no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158Dic15—41no—
159Dic15—41no—
160Dic15—41no—
161Dic15—81no—
162C2×C3×Q8—21no—
163C2×D12—51no—
164C2×C4×D3—101no—
165C2×Dic6—51no—
166C2×Dic6—101no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4D2012yes—
171C3×C42C22×D511yescharacteristic
172(C2×D3)⋊C4—102no—
173(C2×D3)⋊C4—102no—
174(C2×D3)⋊C4—101no—
175C4⋊Dic3—51no—
176C4⋊Dic3—51no—
177C4⋊Dic3—102no—
178C4⋊Dic3—101no—
179C4⋊Dic3—101no—
180Dic3⋊C4—101no—
181C4×Dic3—102no—
182C4×Dic3—101no—
183C2×C3⋊C8—101no—
184C22×D5—61no—
185C5×Q8—41no—
186C5×Q8—41no—
187C2×C4×C5—22no—
188C2×C4×C5C2×D1211yescharacteristic
189C2×C4×C5D3×D411yescharacteristic
190C2×C4×C5D3×D411yescharacteristic
191C2×Dic5—61no—
192C2×Dic5—61no—
193C2×Dic5—61no—
194C2×Dic5—121no—
195D20—61no—
196D20—61no—
197C4×D5—121no—
198C4×D5—121no—
199Dic10—61no—
200Dic10—61no—
201Dic10—122no—
202C5×C8—41no—
203C5×C8—41no—
204#168—121no—
205C4⋊Q8—151no—
206C4⋊Q8C2×D1511yescharacteristic
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—151no—
211C4×Q8—301no—
212C4×D4—151no—
213#117—301no—
214#107—301no—
215#106—301no—
216C4⋊C8C2×D1511yescharacteristic
217C4⋊C8C2×D1511yescharacteristic
218#103—301no—
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—41no—
228C3×Q8—41no—
229C2×C3×C4—22no—
230C2×C3×C4C2×D2011yescharacteristic
231C2×C3×C4D4×D511yescharacteristic
232C2×C3×C4D4×D511yescharacteristic
233C2×Dic3—101no—
234C2×Dic3—101no—
235C2×Dic3—101no—
236C2×Dic3—201no—
237D12—101no—
238D12—101no—
239C4×D3—201no—
240C4×D3—201no—
241Dic6—101no—
242Dic6—101no—
243Dic6—202no—
244C3×C8—41no—
245C3×C8—41no—
246C3⋊C8—201no—
247C22×C5#88211yescharacteristic
248C2×D5—121no—
249C2×D5—121no—
250C2×D5—121no—
251C4×C5—21no—
252C4×C5—42no—
253C4×C5#91211yescharacteristic
254C4×C5#91511yescharacteristic
255C4×C5#91611yescharacteristic
256C4×C5#91811yescharacteristic
257Dic5—121no—
258Dic5—121no—
259Dic5—121no—
260Dic5—241no—
261C2×Q8—21no—
262C2×Q8—151no—
263C2×Q8—301no—
264C2×D4—151no—
265C22×C4—301no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—301no—
269C4⋊C4—21no—
270C4⋊C4—151no—
271C4⋊C4—151no—
272C4⋊C4—302no—
273C4⋊C4—301no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4D6012yes—
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—301no—
280C42—302no—
281C42—301no—
282C42C22×D1511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3#402811yescharacteristic
285C2×D3—201no—
286C2×D3—201no—
287C2×D3—201no—
288C3×C4—21no—
289C3×C4—42no—
290C3×C4#405811yescharacteristic
291C3×C4#406111yescharacteristic
292C3×C4#406211yescharacteristic
293C3×C4#406411yescharacteristic
294Dic3—201no—
295Dic3—201no—
296Dic3—201no—
297Dic3—401no—
298C2×C5#475311yescharacteristic
299C2×C5#478311yescharacteristic
300C2×C5#480811yescharacteristic
301D5—241no—
302C23—301no—
303Q8—41no—
304Q8—41no—
305Q8—301no—
306Q8—301no—
307Q8—602no—
308D4—301no—
309D4—301no—
310C2×C4—22no—
311C2×C4—301no—
312C2×C4—301no—
313C2×C4—301no—
314C2×C4—601no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4C2×D6011yescharacteristic
318C2×C4D4×D1511yescharacteristic
319C2×C4D4×D1511yescharacteristic
320C8—41no—
321C8—41no—
322C8—601no—
323C2×C3#6504211yescharacteristic
324C2×C3#6507211yescharacteristic
325C2×C3#6509911yescharacteristic
326D3—401no—
327C5#6843511yescharacteristic, complemented, Sylow
328C22—601no—
329C22—601no—
330C22—601no—
331C22#9177111yescharacteristic
332C4—21no—
333C4—42no—
334C4—601no—
335C4—601no—
336C4—601no—
337C4—1201no—
338C4#9180111yescharacteristic
339C4#9180411yescharacteristic
340C4#9180511yescharacteristic
341C4#9180711yescharacteristic
342C3#1059922811yescharacteristic, complemented, Sylow
343C2—1201no—
344C2#1175085411yescharacteristic
345C2#1175088411yescharacteristic
346C2#1175090911yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#332C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#332D15
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #11751194C2semidirect
3. #11750951C2semidirect
5. C3×C5×#332C2semidirect
6. #11746305C2semidirect
31. C5×#332D3semidirect
60. C3×#332D5semidirect
145. #332D15semidirect
283. C3×C5#1638semidirect
327. C5#68435semidirect
342. C3#10599228semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117511942
#117509512
#117509432
C3×C5×#3322
#117463052
#117463042
#105992283
#684355