Finite Group Databasebeta

← #14289813

Subgroups — #14289813

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#11756301C211yesmaximal, characteristic
2C3×C5×#476C211yesmaximal, characteristic
3#11751192C211yesmaximal, characteristic, complemented
4#11751180C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic
6#11746305C211yesmaximal, characteristic, complemented
7#11746303C211yesmaximal, characteristic, complemented
8#10601940—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×D4C2211yescharacteristic
11#91825—21no—
12#91815—21no—
13#91813—21no—
14#91776—21no—
15#91768—22no—
16#91758C2211yescharacteristic
17C4×Dic30C2211yescharacteristic
18C3×C5×#106—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#102—21no—
21#91119—22no—
22#91094—21no—
23#91091—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71147—51nomaximal, Hall
27#65876—31no—
28C5×#476D311yescharacteristic
29#65380—31no—
30#65370—31no—
31D4⋊#168—31no—
32#64704—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×Dic30—21no—
38C2×Dic30D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45#6719—22no—
46#6719—22no—
47C4⋊Dic15—21no—
48C4⋊Dic15D411yescharacteristic
49C4⋊Dic15D412yes—
50#6712—22no—
51#6712—21no—
52C4×Dic15—22no—
53C4×Dic15—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56#5542—51no—
57C3×#476D511yescharacteristic
58#5091—51no—
59#5079—51no—
60D4⋊(C3⋊C8)—51no—
61#4484—51no—
62#4482—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C4×C5×D4C2×D311yescharacteristic
65#4082—61no—
66#4072—61no—
67#4070—61no—
68#4033—61no—
69#4025—62no—
70#4015—31no—
71C4×Dic10—31no—
72C5×#106—21no—
73C5×C4⋊C8C2×D311yescharacteristic
74C5×#102—21no—
75#3967—62no—
76#3942—61no—
77#3939—61no—
78C4⋊#168—31no—
79C4×#168—31no—
80#1638—151noSylow
81C23×C3×C5—21no—
82C3×C5×Q8—42no—
83C3×C5×D4—21no—
84C3×C5×D4—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×Dic15—21no—
93C2×Dic15—21no—
94C2×Dic15—22no—
95Dic30—21no—
96Dic30—21no—
97Dic30—41no—
98Dic30—41no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3⋊#168—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×C4×D4C2×D511yescharacteristic
104#936—101no—
105#926—101no—
106#924—101no—
107#887—101no—
108#879—102no—
109#869—51no—
110C4×Dic6—51no—
111C3×#106—21no—
112C3×C4⋊C8C2×D511yescharacteristic
113C3×#102—21no—
114#835—102no—
115#810—101no—
116#807—101no—
117C4⋊(C3⋊C8)—51no—
118C4×C3⋊C8—51no—
119C2×C5×Q8—21no—
120C2×C5×D4#6711yescharacteristic
121C22×C4×C5—21no—
122C2×Dic10—31no—
123C2×Dic10—61no—
124C2×C5×C8—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4#6711yescharacteristic
128C5×C22⋊C4—21no—
129C42×C5C22×D311yescharacteristic
130C22⋊Dic5—62no—
131C22⋊Dic5—62no—
132C4⋊Dic5—31no—
133C4⋊Dic5—32no—
134C4⋊Dic5—61no—
135#683—62no—
136#683—61no—
137C4×Dic5—62no—
138C4×Dic5—61no—
139C2×#168—61no—
140C2×#168—61no—
141#556—151no—
142#487—151no—
143#477—151no—
144#476D1511yescharacteristic
145#332—151no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5#12011yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5—81no—
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—41no—
160Dic15—42no—
161Dic15—41no—
162C2×C3×Q8—21no—
163C2×C3×D4C22⋊D511yescharacteristic
164C22×C3×C4—21no—
165C2×Dic6—51no—
166C2×Dic6—101no—
167C2×C3×C8—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4C22⋊D511yescharacteristic
171C3×C22⋊C4—21no—
172C3×C42C22×D511yescharacteristic
173#217—102no—
174#217—102no—
175C4⋊Dic3—51no—
176C4⋊Dic3—52no—
177C4⋊Dic3—101no—
178Dic3⋊C4—102no—
179Dic3⋊C4—101no—
180C4×Dic3—102no—
181C4×Dic3—101no—
182C2×C3⋊C8—101no—
183C2×C3⋊C8—101no—
184C23×C5—21no—
185C5×Q8—42no—
186C5×D4—21no—
187C5×D4—21no—
188C2×C4×C5—21no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5C2×#6711yescharacteristic
195C2×Dic5—61no—
196C2×Dic5—61no—
197C2×Dic5—62no—
198Dic10—61no—
199Dic10—61no—
200Dic10—121no—
201Dic10—121no—
202C5×C8—41no—
203#168—121no—
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×D4C2×D1511yescharacteristic
213#117—301no—
214#107—301no—
215#106—21no—
216C4⋊C8—151no—
217C4⋊C8C2×D1511yescharacteristic
218#103—301no—
219#103—302no—
220#102—21no—
221C4×C8—151no—
222C2×C3×C5—81no—
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45211yescharacteristic
225C2×C3×C5#45411yescharacteristic
226C23×C3—21no—
227C3×Q8—42no—
228C3×D4—21no—
229C3×D4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4D4×D511yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4C2×C22⋊D511yescharacteristic
237C2×Dic3—101no—
238C2×Dic3—101no—
239C2×Dic3—102no—
240Dic6—101no—
241Dic6—101no—
242Dic6—201no—
243Dic6—201no—
244C3×C8—41no—
245C3⋊C8—201no—
246C3⋊C8—201no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—41no—
250C22×C5#93711yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—81no—
254C4×C5#91511yescharacteristic
255C4×C5#91611yescharacteristic
256C4×C5#94211yescharacteristic
257C4×C5#95011yescharacteristic
258Dic5—121no—
259Dic5—121no—
260Dic5—122no—
261C2×Q8—21no—
262C2×Q8—151no—
263C2×Q8—301no—
264C2×D4#122011yescharacteristic
265C22×C4—21no—
266C2×C8—21no—
267C2×C8—301no—
268C2×C8—301no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—152no—
272C4⋊C4—151no—
273C4⋊C4—302no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4#122011yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—302no—
279C22⋊C4—302no—
280C42—302no—
281C42—301no—
282C42C22×D1511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3#408311yescharacteristic
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—81no—
291C3×C4#406111yescharacteristic
292C3×C4#406211yescharacteristic
293C3×C4#408811yescharacteristic
294C3×C4#409611yescharacteristic
295Dic3—202no—
296Dic3—201no—
297Dic3—201no—
298C2×C5—81no—
299C2×C5#504711yescharacteristic
300C2×C5#517311yescharacteristic
301C2×C5#520111yescharacteristic
302C23—21no—
303Q8—42no—
304Q8—301no—
305Q8—301no—
306Q8—601no—
307Q8—601no—
308D4—21no—
309D4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—301no—
315C2×C4—302no—
316C2×C4—301no—
317C2×C4D4×D1511yescharacteristic
318C2×C4D4×D1511yescharacteristic
319C2×C4C2×#122011yescharacteristic
320C8—41no—
321C8—601no—
322C8—601no—
323C2×C3—81no—
324C2×C3#6533611yescharacteristic
325C2×C3#6546211yescharacteristic
326C2×C3#6549011yescharacteristic
327C5#7114711yescharacteristic, complemented, Sylow
328C22—41no—
329C22—41no—
330C22—41no—
331C22#9182611yescharacteristic
332C4—21no—
333C4—41no—
334C4—81no—
335C4—601no—
336C4—601no—
337C4—602no—
338C4#9180411yescharacteristic
339C4#9180511yescharacteristic
340C4#9183111yescharacteristic
341C4#9183911yescharacteristic
342C3#1060194011yescharacteristic, complemented, Sylow
343C2—81no—
344C2#1175114811yescharacteristic
345C2#1175127411yescharacteristic
346C2#1175130211yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#476C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenter#476D15
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
3. #11751192C2semidirect
4. #11751180C2semidirect
6. #11746305C2semidirect
7. #11746303C2semidirect
283. C3×C5#1638semidirect
327. C5#71147semidirect
342. C3#10601940semidirect

Maximal subgroups

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

subgroupindex
#117563012
C3×C5×#4762
#117511922
#117511802
D4⋊(C3⋊#168)2
#117463052
#117463032
#106019403
#711475