Finite Group Databasebeta

← #14300368

Subgroups — #14300368

Order 1920.

520 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 117 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#11756985C211yesmaximal, characteristic
2#11752434C211yesmaximal, characteristic
3#11752355C212yesmaximal, complemented
4C3×#65029C211yesmaximal, characteristic
5#11746738C212yesmaximal, complemented
6#10603921—31nomaximal, Hall
7C2×C3×#711C2211yescharacteristic
8C2×#6762—21no—
9C2×#6762C2211yescharacteristic
10C2×#6762C2212yes—
11C22×C3⋊#170C2211yescharacteristic
12#91990—22no—
13#91990—22no—
14D5⋊#208—21no—
15C3×#4023C2212yes—
16#91241—21no—
17#91233—22no—
18#91232—21no—
19C4⋊(C3⋊#170)—22no—
20C3×C5×#99C411yescharacteristic
21C3×#3966C411yescharacteristic
22C3×#3938C412yes—
23#70044—51nomaximal, Hall
24#66256—31no—
25#65775—31no—
26#65696—32no—
27#65029D311yescharacteristic
28#64867—32no—
29C2×C3×C5×D4C2×C411yescharacteristic
30C2×C3×C22⋊D5C2×C411yescharacteristic
31C2×C3×C22⋊D5Q811yescharacteristic
32C22×C3×Dic5D411yescharacteristic
33C22×C3×Dic5C2311yescharacteristic
34C3×#711—22no—
35C3×#711—22no—
36C2×C3×C4×D5D411yescharacteristic
37C2×C3×Dic10Q811yescharacteristic
38#6762—22no—
39#6762—22no—
40#6762—22no—
41#6762—22no—
42C2×C3⋊#170—21no—
43C2×C3⋊#170—21no—
44C2×C3⋊#170—22no—
45C2×C3⋊#170—21no—
46C2×C3⋊#170—21no—
47C2×C3⋊#170D412yes—
48C2×C3⋊#170D412yes—
49#6758—21no—
50#6758—21no—
51D5⋊(C3⋊C8)—22no—
52C3×C5×C22⋊C4C2×C412yes—
53C3×C22⋊Dic5C2×C412yes—
54C3×#683—22no—
55C3×C4×Dic5—22no—
56#5819—51no—
57C3×#410—51no—
58#5234—51no—
59#4999—52no—
60#4533—52no—
61C2×#711C2×D311yescharacteristic
62C2×#704—32no—
63C2×#704—31no—
64C2×#704—61no—
65C22×#170—31no—
66#4131—62no—
67#4131—62no—
68D5⋊M16—61no—
69#4023C2×D312yes—
70C22⋊#170—61no—
71#4004—62no—
72#4003—61no—
73C4⋊#170—62no—
74C5×#99Dic311yescharacteristic
75#3966Dic311yescharacteristic
76#3938Dic312yes—
77#1868—151noSylow
78C23×C3×C5C4⋊C411yescharacteristic
79C23×C3×C5C22×C411yescharacteristic
80C22×C3×D5C4⋊C411yescharacteristic
81C3×C5×D4—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5C4⋊C411yescharacteristic
84C3×C22⋊D5—22no—
85C3×C22⋊D5—22no—
86C2×C3×Dic5—21no—
87C2×C3×Dic5—21no—
88C2×C3×Dic5—22no—
89C2×C3×Dic5C4⋊C411yescharacteristic
90C2×C3×Dic5C2×D412yes—
91C2×C3×Dic5C2×D411yescharacteristic
92C2×C3×Dic5C2×Q811yescharacteristic
93C2×C3×Dic5#4112yes—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×Dic10—22no—
97C3⋊#170—22no—
98C3⋊#170—22no—
99C3⋊#170—41no—
100C3⋊#170—41no—
101C2×C3×#41—51no—
102C3×#117—52no—
103#948—102no—
104#948—102no—
105C2×#208—52no—
106C2×#208—51no—
107C2×#208—101no—
108C2×#208—101no—
109C22×C3⋊C8—51no—
110C3×#99—51no—
111C3×#99—52no—
112C3×#99AGL(1,𝔽5)11yescharacteristic
113#830—101no—
114#830—101no—
115C4⋊(C3⋊C8)—102no—
116C4⋊(C3⋊C8)—102no—
117C2×C5×D4C2×Dic311yescharacteristic
118C2×C22⋊D5Dic611yescharacteristic
119C2×C22⋊D5C2×Dic311yescharacteristic
120C22×Dic5D1211yescharacteristic
121C22×Dic5C22×D311yescharacteristic
122#711—22no—
123#711—22no—
124C2×C4×D5D1211yescharacteristic
125C2×Dic10Dic611yescharacteristic
126#704—62no—
127#704—62no—
128#704—62no—
129#704—62no—
130C2×#170—32no—
131C2×#170—32no—
132C2×#170—61no—
133C2×#170—61no—
134C2×#170—61no—
135C2×#170—61no—
136C2×#170—62no—
137#700—61no—
138#700—61no—
139D5⋊C8—62no—
140C5×C22⋊C4C2×Dic312yes—
141C22⋊Dic5C2×Dic312yes—
142#683—22no—
143C4×Dic5—22no—
144#568—151no—
145#424—152no—
146#410—51no—
147#408—151no—
148#344—152no—
149C22×C3×C5—21no—
150C22×C3×C5—41no—
151C22×C3×C5—41no—
152C22×C3×C5C2×C4⋊C411yescharacteristic
153C22×C3×C5C4×D412yes—
154C2×C3×D5—21no—
155C2×C3×D5—41no—
156C3×C4×C5—21no—
157C3×C4×C5—42no—
158C3×Dic5—21no—
159C3×Dic5—42no—
160C3×Dic5#12011yescharacteristic
161C3×Dic5C22⋊Q812yes—
162C3×Dic5#12311yescharacteristic
163C3×#41—102no—
164C3×#41—102no—
165C2×C3×Q8—51no—
166C2×C3×D4—51no—
167C2×C3×D4—51no—
168C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4—51no—
172C3×C4⋊C4—102no—
173C3×C22⋊C4—52no—
174C3×C22⋊C4C2×AGL(1,𝔽5)12yes—
175C3×C42—102no—
176#208—102no—
177#208—102no—
178#208—101no—
179#208—101no—
180#208—102no—
181#208—102no—
182C2×C3⋊C8—52no—
183C2×C3⋊C8—52no—
184C2×C3⋊C8—102no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—102no—
188C2×C3⋊C8—101no—
189C2×C3⋊C8—101no—
190C23×C5C4⋊Dic311yescharacteristic
191C23×C5C22×Dic311yescharacteristic
192C22×D5C4⋊Dic311yescharacteristic
193C5×D4—22no—
194C2×C4×C5—22no—
195C2×C4×C5C4⋊Dic311yescharacteristic
196C22⋊D5—22no—
197C22⋊D5—22no—
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—22no—
201C2×Dic5C4⋊Dic311yescharacteristic
202C2×Dic5C2×Dic611yescharacteristic
203C2×Dic5C2×D1211yescharacteristic
204C2×Dic5D3×D412yes—
205C2×Dic5#23712yes—
206C4×D5—21no—
207C4×D5—21no—
208Dic10—22no—
209#170—62no—
210#170—62no—
211#170—121no—
212#170—121no—
213C2×#41—51no—
214#131—302no—
215#131—302no—
216C2×M16—152no—
217C2×M16—151no—
218C2×M16—301no—
219C2×M16—301no—
220C22×C8—151no—
221#117—52no—
222C4⋊C8—302no—
223C4⋊C8—302no—
224#99—51no—
225#99—52no—
226#99ΓL(1,𝔽16)11yescharacteristic
227C22⋊C8—301no—
228C22⋊C8—301no—
229C2×C3×C5—22no—
230C2×C3×C5—21no—
231C2×C3×C5—41no—
232C2×C3×C5#38511yescharacteristic
233C3×D5—41no—
234C23×C3—51no—
235C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
236C23×C3C22×AGL(1,𝔽5)11yescharacteristic
237C3×Q8—102no—
238C3×D4—22no—
239C3×D4—102no—
240C3×D4—102no—
241C2×C3×C4—22no—
242C2×C3×C4—51no—
243C2×C3×C4—51no—
244C2×C3×C4—52no—
245C2×C3×C4—52no—
246C2×C3×C4—51no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—102no—
252C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
253C3⋊C8—102no—
254C3⋊C8—102no—
255C3⋊C8—201no—
256C3⋊C8—201no—
257C22×C5—21no—
258C22×C5—41no—
259C22×C5—41no—
260C22×C5C2×C4⋊Dic311yescharacteristic
261C22×C5D4×Dic312yes—
262C2×D5—21no—
263C2×D5—41no—
264C4×C5—21no—
265C4×C5—42no—
266Dic5—21no—
267Dic5—42no—
268Dic5#87812yes—
269Dic5#88211yescharacteristic
270Dic5#88611yescharacteristic
271#41—102no—
272#41—102no—
273C2×Q8—51no—
274C2×D4—51no—
275C2×D4—51no—
276C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
277C22×C4—51no—
278C22×C4—51no—
279C22×C4—51no—
280M16—302no—
281M16—302no—
282M16—301no—
283M16—301no—
284M16—302no—
285M16—302no—
286C2×C8—152no—
287C2×C8—152no—
288C2×C8—302no—
289C2×C8—301no—
290C2×C8—301no—
291C2×C8—301no—
292C2×C8—301no—
293C2×C8—302no—
294C4⋊C4—102no—
295C22⋊C4—52no—
296C22⋊C4C2×ΓL(1,𝔽16)12yes—
297C42—102no—
298C3×C5#186811yescharacteristic, complemented, Hall
299C22×C3—21no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—101no—
303C22×C3—201no—
304C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
305C22×C3D4×AGL(1,𝔽5)12yes—
306C3×C4—21no—
307C3×C4—42no—
308C3×C4—51no—
309C3×C4—52no—
310C3×C4—51no—
311C3×C4—101no—
312C3×C4—202no—
313C2×C5—22no—
314C2×C5—21no—
315C2×C5—41no—
316C2×C5#495011yescharacteristic
317D5—41no—
318C23—51no—
319C23C4⋊ΓL(1,𝔽16)11yescharacteristic
320C23C22×ΓL(1,𝔽16)11yescharacteristic
321Q8—102no—
322D4—22no—
323D4—102no—
324D4—102no—
325C2×C4—22no—
326C2×C4—51no—
327C2×C4—51no—
328C2×C4—52no—
329C2×C4—52no—
330C2×C4—51no—
331C2×C4—101no—
332C2×C4—101no—
333C2×C4—101no—
334C2×C4—101no—
335C2×C4—102no—
336C2×C4C4⋊ΓL(1,𝔽16)11yescharacteristic
337C8—302no—
338C8—302no—
339C8—601no—
340C8—601no—
341C2×C3—22no—
342C2×C3—21no—
343C2×C3—41no—
344C2×C3—201no—
345C2×C3#6569911yescharacteristic
346C5#7004411yescharacteristic, complemented, Sylow
347C22—21no—
348C22—41no—
349C22—41no—
350C22—101no—
351C22—201no—
352C22C2×C4⋊ΓL(1,𝔽16)11yescharacteristic
353C22D4×ΓL(1,𝔽16)12yes—
354C4—21no—
355C4—42no—
356C4—51no—
357C4—51no—
358C4—52no—
359C4—101no—
360C4—202no—
361C3#1060392111yescharacteristic, complemented, Sylow
362C2—22no—
363C2—21no—
364C2—41no—
365C2—201no—
366C2#1175235811yescharacteristic
subgroupG/H
centerC2#11752358
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC3×C5×#99C4
socleC2×C3×C5#385
prime radicalC2×C3×#711C22
cosocleC22×C3×Dic5C23
hypercenter#99ΓL(1,𝔽16)
hypocenterC3×C5#1868
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
3. #11752355C2semidirect
5. #11746738C2semidirect
298. C3×C5#1868semidirect
346. C5#70044semidirect
361. C3#10603921semidirect

Maximal subgroups

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

subgroupindex
#117569852
#117524342
#117523552
C3×#650292
#117467382
#106039213
#700445