Finite Group Databasebeta

← #14298621

Subgroups — #14298621

Order 1920.

524 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 102 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#11754444C211yesmaximal, characteristic
2#11752404C211yesmaximal, characteristic
3C3×#65761C211yesmaximal, characteristic
4#11746525C212yesmaximal, complemented
5#11746520C212yesmaximal, complemented
6#10604377—31nomaximal, Hall
7C2×C3×#709C2211yescharacteristic
8#91989C2212yes—
9C3×D5⋊M16C2212yes—
10C2×C4×Dic15C411yescharacteristic, complemented
11C5×#926C411yescharacteristic, complemented
12#91559—21no—
13#91559—21no—
14#91434—21no—
15C4×D5×Dic3C411yescharacteristic, complemented
16C4×D5×Dic3C2211yescharacteristic
17#91357C411yescharacteristic, complemented
18#91357C2211yescharacteristic
19#91331—21no—
20#91240—21no—
21#91228—21no—
22C3×#4013—21no—
23C3×#4005—21no—
24#70131—51nomaximal, Hall
25#65856—31no—
26#65761D311yescharacteristic
27#65745—31no—
28#64863—32no—
29#64862—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×Dic15—21no—
32C2×C3×C22⋊D5D411yescharacteristic
33C2×C3×C22⋊D5D411yescharacteristic
34C3×#709—22no—
35C3×#709—22no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×C4×D5C2311yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40C2×D5×Dic3—21no—
41C2×D5×Dic3—21no—
42#6763—22no—
43C4⋊ΓL(1,𝔽16)—22no—
44C4×ΓL(1,𝔽16)—22no—
45C3×#704—22no—
46C3×#700—22no—
47C3×D5⋊C8—22no—
48C4×Dic15—21no—
49C4×Dic15C2×C411yescharacteristic
50C4×Dic15C2×C411yescharacteristic
51C5×#217—21no—
52C5×C4⋊Dic3—21no—
53C4×C5×Dic3C2×C411yescharacteristic
54C4×C5×Dic3C2×C411yescharacteristic
55#6668—21no—
56#6668—21no—
57#6665—21no—
58#6665—21no—
59Dic3×Dic5—21no—
60Dic3×Dic5—21no—
61Dic3×#41—51no—
62C3×#413—51no—
63#5240—51no—
64#4557—52no—
65#4555—52no—
66C2×#709C2×D311yescharacteristic
67#4130—32no—
68D5⋊M16C2×D312yes—
69C5×#117—31no—
70C2×C4×Dic5—31no—
71#4039—61no—
72#4033—61no—
73#4027—61no—
74#4027—61no—
75#4018—31no—
76#4018—31no—
77C42×D5—31no—
78C42×D5—31no—
79#4013—21no—
80#4011—61no—
81#4005—21no—
82#3999—61no—
83#1827—151noSylow
84C23×C3×C5C22⋊C411yescharacteristic
85C22×C3×D5C22⋊C411yescharacteristic
86C22×C3×D5C2×D411yescharacteristic
87C2×ΓL(1,𝔽16)—42no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22×C411yescharacteristic
92C2×Dic15—21no—
93C2×Dic15—21no—
94C2×Dic15—42no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—21no—
97C3×C22⋊D5—22no—
98C3×C22⋊D5—22no—
99C2×C3×Dic5C22⋊C411yescharacteristic
100C2×C3×Dic5C2×D411yescharacteristic
101C3×D20—22no—
102C3×C4×D5—21no—
103C3×C4×D5—21no—
104C3×C4×D5#4112yes—
105C3×C4×D5#4112yes—
106C3×Dic10—22no—
107D5×Dic3—42no—
108D5×Dic3—42no—
109C3×#170—42no—
110C2×C3×#41—51no—
111C2×C3×M16—52no—
112Q8×Dic3—101no—
113D4×Dic3—101no—
114D4×Dic3—101no—
115D4×Dic3—101no—
116#926—51no—
117#926—51no—
118#926—52no—
119#926AGL(1,𝔽5)11yescharacteristic, complemented
120C2×C4×Dic3—51no—
121C2×C4×Dic3—51no—
122C2×C4×Dic3—51no—
123C3×#101—101no—
124C3×#100—101no—
125#834—101no—
126#834—101no—
127C22×C4×C5C4×D311yescharacteristic
128C2×C22⋊D5D1211yescharacteristic
129C2×C22⋊D5#6711yescharacteristic
130C22×Dic5—61no—
131#709—22no—
132#709—22no—
133C2×D20D1211yescharacteristic
134C2×C4×D5—61no—
135C2×C4×D5—61no—
136C2×C4×D5C4×D311yescharacteristic
137C2×C4×D5C22×D311yescharacteristic
138C2×Dic10#6711yescharacteristic
139C22⋊AGL(1,𝔽5)—62no—
140#704—22no—
141C4⋊AGL(1,𝔽5)—62no—
142C4×AGL(1,𝔽5)—62no—
143#700—22no—
144D5⋊C8—22no—
145C5×C4⋊C4—61no—
146C5×C22⋊C4—61no—
147C42×C5—31no—
148C42×C5—31no—
149#685—61no—
150#685—61no—
151#683—61no—
152#683—61no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C4×Dic5—61no—
156C4×Dic5—61no—
157C4×Dic5—61no—
158C4×#41—151no—
159#413—51no—
160#410—151no—
161#339—152no—
162H(3,ℤ/4)—152no—
163C22×C3×C5—21no—
164C22×C3×C5—41no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×C3×D5—21no—
167C2×C3×D5—41no—
168C2×C3×D5—41no—
169C2×C3×D5#12312yes—
170ΓL(1,𝔽16)—82no—
171C3×C4×C5—21no—
172C3×C4×C5#11711yescharacteristic
173C3×C4×C5#11711yescharacteristic
174Dic15—22no—
175Dic15—41no—
176C3×Dic5—21no—
177C3×Dic5#12312yes—
178C5×Dic3—41no—
179C5×Dic3—41no—
180C3×#41—102no—
181C3×#41—102no—
182C2×C3×Q8—51no—
183C2×C3×D4—51no—
184C2×C3×D4—51no—
185C2×C3×D4—51no—
186C22×C3×C4—51no—
187C22×C3×C4—51no—
188C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
189C22×Dic3—101no—
190C22×Dic3—101no—
191C22×Dic3—101no—
192C3×M16—102no—
193C3×M16—102no—
194C2×C3×C8—102no—
195#217—21no—
196#217—101no—
197#217—101no—
198#217—102no—
199C4⋊Dic3—21no—
200C4⋊Dic3—101no—
201C4⋊Dic3—101no—
202C4⋊Dic3—102no—
203C4×Dic3—51no—
204C4×Dic3—51no—
205C4×Dic3—101no—
206C4×Dic3—101no—
207C4×Dic3—101no—
208C4×Dic3—102no—
209C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
210C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
211C23×C5(C2×D3)⋊C411yescharacteristic
212C22×D5(C2×D3)⋊C411yescharacteristic
213C22×D5C2×D1211yescharacteristic
214C2×AGL(1,𝔽5)—122no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—61no—
218C2×C4×C5—61no—
219C2×C4×C5(C2×D3)⋊C411yescharacteristic
220C2×C4×C5C2×C4×D311yescharacteristic
221C22⋊D5—22no—
222C22⋊D5—22no—
223C2×Dic5—61no—
224C2×Dic5—61no—
225C2×Dic5—122no—
226C2×Dic5(C2×D3)⋊C411yescharacteristic
227C2×Dic5C2×#6711yescharacteristic
228D20—22no—
229C4×D5—21no—
230C4×D5—21no—
231C4×D5—122no—
232C4×D5—122no—
233C4×D5#23712yes—
234C4×D5#23712yes—
235Dic10—22no—
236#170—42no—
237C2×#41—51no—
238C2×M16—52no—
239C4×Q8—301no—
240C4×D4—301no—
241C4×D4—301no—
242C4×D4—301no—
243#117—31no—
244#117—151no—
245#117—151no—
246#117—152no—
247C2×C42—151no—
248C2×C42—151no—
249C2×C42—151no—
250#101—101no—
251#100—101no—
252#99—301no—
253#99—301no—
254C2×C3×C5—21no—
255C2×C3×C5—41no—
256C2×C3×C5#38111yescharacteristic
257C3×D5—22no—
258C3×D5—41no—
259C23×C3—51no—
260C23×C3—51no—
261C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
262C3×Q8—102no—
263C3×D4—102no—
264C3×D4—102no—
265C3×D4—102no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—51no—
269C2×C3×C4—52no—
270C2×C3×C4—52no—
271C2×C3×C4—51no—
272C2×C3×C4—101no—
273C2×C3×C4—101no—
274C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
275C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—101no—
279C2×Dic3—101no—
280C2×Dic3—202no—
281C2×Dic3—202no—
282C2×Dic3—202no—
283C2×Dic3—202no—
284C3×C8—202no—
285C22×C5—21no—
286C22×C5—41no—
287C22×C5C2×(C2×D3)⋊C411yescharacteristic
288C2×D5—21no—
289C2×D5—41no—
290C2×D5—41no—
291C2×D5#88612yes—
292AGL(1,𝔽5)—242no—
293C4×C5—21no—
294C4×C5—121no—
295C4×C5—121no—
296C4×C5#87711yescharacteristic
297C4×C5#87711yescharacteristic
298Dic5—21no—
299Dic5—62no—
300Dic5—121no—
301Dic5#93512yes—
302#41—102no—
303#41—102no—
304C2×Q8—51no—
305C2×D4—51no—
306C2×D4—51no—
307C2×D4—51no—
308C22×C4—51no—
309C22×C4—51no—
310C22×C4—301no—
311C22×C4—301no—
312C22×C4—301no—
313C22×C4D3×AGL(1,𝔽5)11yescharacteristic
314M16—102no—
315M16—102no—
316C2×C8—102no—
317C4⋊C4—61no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C4⋊C4—302no—
321C22⋊C4—61no—
322C22⋊C4—301no—
323C22⋊C4—301no—
324C22⋊C4—302no—
325C42—31no—
326C42—31no—
327C42—151no—
328C42—151no—
329C42—301no—
330C42—301no—
331C42—302no—
332C42—301no—
333C3×C5#182711yescharacteristic, complemented, Hall
334C22×C3—21no—
335C22×C3—41no—
336C22×C3—52no—
337C22×C3—101no—
338C22×C3—201no—
339C22×C3—201no—
340C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
341C3×C4—21no—
342C3×C4—52no—
343C3×C4—101no—
344C3×C4#413011yescharacteristic
345C3×C4#413011yescharacteristic
346Dic3—41no—
347Dic3—41no—
348Dic3—102no—
349Dic3—201no—
350Dic3—402no—
351C2×C5—21no—
352C2×C5—41no—
353C2×C5#494311yescharacteristic
354D5—22no—
355D5—41no—
356C23—51no—
357C23—51no—
358C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
359Q8—102no—
360D4—102no—
361D4—102no—
362D4—102no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—51no—
366C2×C4—52no—
367C2×C4—52no—
368C2×C4—51no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—101no—
372C2×C4—101no—
373C2×C4—301no—
374C2×C4—301no—
375C2×C4—602no—
376C2×C4—602no—
377C2×C4—602no—
378C2×C4—602no—
379C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
380C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
381C8—202no—
382C2×C3—21no—
383C2×C3—41no—
384C2×C3—102no—
385C2×C3—201no—
386C2×C3#6576411yescharacteristic
387C5#7013111yescharacteristic, complemented, Sylow
388C22—21no—
389C22—41no—
390C22—52no—
391C22—101no—
392C22—201no—
393C22—201no—
394C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
395C4—21no—
396C4—52no—
397C4—101no—
398C4—121no—
399C4—121no—
400C4—302no—
401C4—601no—
402C4—1202no—
403C4#9192311yescharacteristic
404C4#9192311yescharacteristic
405C3#1060437711yescharacteristic, complemented, Sylow
406C2—21no—
407C2—41no—
408C2—102no—
409C2—201no—
410C2#1175198411yescharacteristic
subgroupG/H
centerC4#91923
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5#381
prime radicalC2×C3×#709C22
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1827
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746525C2semidirect
5. #11746520C2semidirect
10. C2×C4×Dic15C4semidirect
11. C5×#926C4semidirect
15. C4×D5×Dic3C4semidirect
17. #91357C4semidirect
119. #926AGL(1,𝔽5)semidirect
333. C3×C5#1827semidirect
387. C5#70131semidirect
405. C3#10604377semidirect

Maximal subgroups

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

subgroupindex
#117544442
#117524042
C3×#657612
#117465252
#117465202
#106043773
#701315