Subgroups — #15763020

Order 3328.

432 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13114689	C₂	1	1	yes	maximal, characteristic
2	C₄×#88043	C₂	1	1	yes	maximal, characteristic
3	#13112717	C₂	1	2	yes	maximal
4	#13112717	C₂	1	2	yes	maximal
5	C₁₃×#2864	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#389	C₄	1	1	yes	characteristic
7	C₁₃×#389	C₄	1	1	yes	characteristic
8	C₁₃×#389	C₄	1	1	yes	characteristic
9	C₁₃×#389	C₄	1	1	yes	characteristic
10	C₁₃×#387	—	2	1	no	—
11	C₁₃×#387	—	2	1	no	—
12	C₁₃×#387	—	2	1	no	—
13	C₁₃×#387	—	2	1	no	—
14	C₁₃×#382	C₂²	1	1	yes	characteristic
15	C₁₃×#382	C₂²	1	1	yes	characteristic
16	C₄³×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#1055	—	2	1	no	—
18	C₂×#88043	—	2	1	no	—
19	C₂×#88043	C₂²	1	2	yes	—
20	C₂×#88043	C₂²	1	2	yes	—
21	C₂×C₄×#1055	—	2	1	no	—
22	#11718116	—	2	1	no	—
23	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
27	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×#1055	—	2	2	no	—
39	C₂²×#1055	—	2	2	no	—
40	C₁₃×#95	—	2	1	no	—
41	C₁₃×#95	—	2	1	no	—
42	C₁₃×#95	—	2	1	no	—
43	C₁₃×#95	—	2	1	no	—
44	C₁₃×#95	—	2	1	no	—
45	C₁₃×#95	—	2	1	no	—
46	C₁₃×#95	—	2	1	no	—
47	C₁₃×#95	—	2	1	no	—
48	C₄⋊#1055	—	2	4	no	—
49	#88043	—	2	4	no	—
50	#88043	—	2	2	no	—
51	#88043	—	2	4	no	—
52	#88043	Q₈	1	4	yes	—
53	C₄×#1055	—	2	4	no	—
54	#9892	—	13	1	no	maximal, Sylow
55	C₂²×C₄×C₁₃	—	2	1	no	—
56	C₂²×C₄×C₁₃	—	2	1	no	—
57	C₂²×C₄×C₁₃	—	2	1	no	—
58	C₂²×C₄×C₁₃	—	2	1	no	—
59	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₁₃×C₄⋊C₄	—	4	1	no	—
67	C₁₃×C₄⋊C₄	—	4	1	no	—
68	C₁₃×C₄⋊C₄	—	4	1	no	—
69	C₁₃×C₄⋊C₄	—	4	1	no	—
70	C₁₃×C₄⋊C₄	—	4	2	no	—
71	C₁₃×C₄⋊C₄	—	4	2	no	—
72	C₁₃×C₄⋊C₄	—	4	2	no	—
73	C₁₃×C₄⋊C₄	—	4	2	no	—
74	C₄²×C₁₃	—	2	2	no	—
75	C₄²×C₁₃	—	2	2	no	—
76	C₄²×C₁₃	—	2	2	no	—
77	C₄²×C₁₃	—	4	1	no	—
78	C₄²×C₁₃	—	4	1	no	—
79	C₄²×C₁₃	—	4	1	no	—
80	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
81	C₄²×C₁₃	#41	1	2	yes	—
82	C₂×#1055	—	2	4	no	—
83	C₂×#1055	—	2	4	no	—
84	C₂×#1055	—	2	4	no	—
85	C₂×#1055	—	2	4	no	—
86	C₂×#1055	—	4	2	no	—
87	C₂×#1055	—	4	2	no	—
88	#2864	D₁₃	1	1	yes	characteristic
89	#1767	—	13	1	no	—
90	C₄×#97	—	13	1	no	—
91	#1295	—	13	2	no	—
92	#1295	—	13	2	no	—
93	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₃	—	2	1	no	—
95	C₂×C₄×C₁₃	—	2	1	no	—
96	C₂×C₄×C₁₃	—	2	1	no	—
97	C₂×C₄×C₁₃	—	2	1	no	—
98	C₂×C₄×C₁₃	—	2	1	no	—
99	C₂×C₄×C₁₃	—	2	1	no	—
100	C₂×C₄×C₁₃	—	2	1	no	—
101	C₂×C₄×C₁₃	—	2	1	no	—
102	C₂×C₄×C₁₃	—	2	1	no	—
103	C₂×C₄×C₁₃	—	2	1	no	—
104	C₂×C₄×C₁₃	—	2	1	no	—
105	C₂×C₄×C₁₃	—	2	1	no	—
106	C₂×C₄×C₁₃	—	2	1	no	—
107	C₂×C₄×C₁₃	—	2	1	no	—
108	C₂×C₄×C₁₃	—	2	1	no	—
109	C₂×C₄×C₁₃	—	4	1	no	—
110	C₂×C₄×C₁₃	—	4	1	no	—
111	C₂×C₄×C₁₃	—	4	1	no	—
112	C₂×C₄×C₁₃	—	4	1	no	—
113	C₂×C₄×C₁₃	—	4	1	no	—
114	C₂×C₄×C₁₃	—	4	1	no	—
115	C₂×C₄×C₁₃	—	4	1	no	—
116	C₂×C₄×C₁₃	—	4	1	no	—
117	C₂×C₄×C₁₃	—	4	1	no	—
118	C₂×C₄×C₁₃	—	4	1	no	—
119	C₂×C₄×C₁₃	—	4	1	no	—
120	C₂×C₄×C₁₃	—	4	1	no	—
121	C₂×C₄×C₁₃	#104	1	2	yes	—
122	C₂×C₄×C₁₃	#104	1	2	yes	—
123	C₂×C₄×C₁₃	#104	1	2	yes	—
124	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
125	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
126	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
127	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
128	#1055	—	2	8	no	—
129	#1055	—	4	4	no	—
130	C₂×C₄⋊C₈	—	26	1	no	—
131	C₂×#97	—	13	2	no	—
132	C₂×#97	—	13	2	no	—
133	C₂×#97	—	26	1	no	—
134	C₂×C₄×C₈	—	26	1	no	—
135	#389	Dic₁₃	1	1	yes	characteristic
136	#389	Dic₁₃	1	1	yes	characteristic
137	#389	Dic₁₃	1	1	yes	characteristic
138	#389	Dic₁₃	1	1	yes	characteristic
139	#387	—	2	1	no	—
140	#387	—	2	1	no	—
141	#387	—	2	1	no	—
142	#387	—	2	1	no	—
143	#382	C₂×D₁₃	1	1	yes	characteristic
144	#382	C₂×D₁₃	1	1	yes	characteristic
145	C₄³	C₂×D₁₃	1	1	yes	characteristic
146	#336	—	26	1	no	—
147	C₂²×C₁₃	#391	1	1	yes	characteristic
148	C₂²×C₁₃	#413	1	1	yes	characteristic
149	C₂²×C₁₃	#413	1	1	yes	characteristic
150	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
151	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
152	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
153	C₂²×C₁₃	#421	1	1	yes	characteristic
154	C₄×C₁₃	—	2	1	no	—
155	C₄×C₁₃	—	2	1	no	—
156	C₄×C₁₃	—	2	2	no	—
157	C₄×C₁₃	—	2	2	no	—
158	C₄×C₁₃	—	2	2	no	—
159	C₄×C₁₃	—	2	2	no	—
160	C₄×C₁₃	—	2	2	no	—
161	C₄×C₁₃	—	4	1	no	—
162	C₄×C₁₃	—	8	1	no	—
163	C₄×C₁₃	—	8	1	no	—
164	C₄×C₁₃	—	8	1	no	—
165	C₄×C₁₃	—	8	1	no	—
166	C₂²×C₈	—	26	2	no	—
167	C₂²×C₈	—	26	2	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	—	2	1	no	—
170	C₂×C₄⋊C₄	—	2	1	no	—
171	C₂×C₄⋊C₄	—	2	1	no	—
172	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
173	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
174	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
175	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
176	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
177	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
178	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
179	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
180	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
181	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
182	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
183	C₄⋊C₈	—	26	4	no	—
184	#97	—	13	4	no	—
185	#97	—	26	4	no	—
186	#97	—	26	2	no	—
187	#97	—	26	4	no	—
188	C₄×C₈	—	26	4	no	—
189	#95	—	2	1	no	—
190	#95	—	2	1	no	—
191	#95	—	2	1	no	—
192	#95	—	2	1	no	—
193	#95	—	2	1	no	—
194	#95	—	2	1	no	—
195	#95	—	2	1	no	—
196	#95	—	2	1	no	—
197	C₂×C₁₃	#1524	1	1	yes	characteristic
198	C₂×C₁₃	#1524	1	1	yes	characteristic
199	C₂×C₁₃	#1529	1	1	yes	characteristic
200	C₂×C₁₃	#1532	1	1	yes	characteristic
201	C₂×C₁₃	#1986	1	1	yes	characteristic
202	C₂×C₁₃	#1994	1	1	yes	characteristic
203	C₂×C₁₃	#1998	1	1	yes	characteristic
204	C₂²×C₄	—	2	1	no	—
205	C₂²×C₄	—	2	1	no	—
206	C₂²×C₄	—	2	1	no	—
207	C₂²×C₄	—	2	1	no	—
208	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
209	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
210	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
211	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
212	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
213	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
214	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
215	C₂×C₈	—	26	4	no	—
216	C₂×C₈	—	26	4	no	—
217	C₂×C₈	—	26	4	no	—
218	C₂×C₈	—	26	4	no	—
219	C₂×C₈	—	52	2	no	—
220	C₂×C₈	—	52	2	no	—
221	C₄⋊C₄	—	4	1	no	—
222	C₄⋊C₄	—	4	1	no	—
223	C₄⋊C₄	—	4	1	no	—
224	C₄⋊C₄	—	4	1	no	—
225	C₄⋊C₄	—	4	2	no	—
226	C₄⋊C₄	—	4	2	no	—
227	C₄⋊C₄	—	4	2	no	—
228	C₄⋊C₄	—	4	2	no	—
229	C₄²	—	2	2	no	—
230	C₄²	—	2	2	no	—
231	C₄²	—	2	2	no	—
232	C₄²	—	4	1	no	—
233	C₄²	—	4	1	no	—
234	C₄²	—	4	1	no	—
235	C₄²	Q₈×D₁₃	1	2	yes	—
236	C₄²	#6131	1	2	yes	—
237	C₁₃	#9892	1	1	yes	characteristic, complemented, Sylow
238	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	2	1	no	—
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	1	no	—
252	C₂×C₄	—	2	1	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	4	1	no	—
255	C₂×C₄	—	4	1	no	—
256	C₂×C₄	—	4	1	no	—
257	C₂×C₄	—	4	1	no	—
258	C₂×C₄	—	4	1	no	—
259	C₂×C₄	—	4	1	no	—
260	C₂×C₄	—	4	1	no	—
261	C₂×C₄	—	4	1	no	—
262	C₂×C₄	—	4	1	no	—
263	C₂×C₄	—	4	1	no	—
264	C₂×C₄	—	4	1	no	—
265	C₂×C₄	—	4	1	no	—
266	C₂×C₄	#88077	1	2	yes	—
267	C₂×C₄	#88077	1	2	yes	—
268	C₂×C₄	#88077	1	2	yes	—
269	C₂×C₄	#88198	1	1	yes	characteristic
270	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
271	C₂×C₄	#88200	1	2	yes	—
272	C₂×C₄	#88201	1	1	yes	characteristic
273	C₈	—	26	8	no	—
274	C₈	—	52	4	no	—
275	C₂²	#11718891	1	1	yes	characteristic
276	C₂²	C₂×#88077	1	1	yes	characteristic
277	C₂²	C₂×#88077	1	1	yes	characteristic
278	C₂²	C₂×#88077	1	1	yes	characteristic
279	C₂²	#11718897	1	1	yes	characteristic
280	C₂²	#11718898	1	1	yes	characteristic
281	C₂²	#11718898	1	1	yes	characteristic
282	C₄	—	2	2	no	—
283	C₄	—	2	2	no	—
284	C₄	—	2	2	no	—
285	C₄	—	2	1	no	—
286	C₄	—	2	1	no	—
287	C₄	—	2	2	no	—
288	C₄	—	2	2	no	—
289	C₄	—	4	1	no	—
290	C₄	—	8	1	no	—
291	C₄	—	8	1	no	—
292	C₄	—	8	1	no	—
293	C₄	—	8	1	no	—
294	C₂	#13113424	1	1	yes	characteristic
295	C₂	#13113424	1	1	yes	characteristic
296	C₂	#13113443	1	1	yes	characteristic
297	C₂	#13113456	1	1	yes	characteristic
298	C₂	#13115781	1	1	yes	characteristic
299	C₂	#13115814	1	1	yes	characteristic
300	C₂	#13115830	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₃
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#2864	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#2864	D₁₃
hypocenter	C₁₃	#9892
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2864

Complements

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

N	H ≅ G/N	type
237. C₁₃	#9892	semidirect

Maximal subgroups

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

subgroup	index
#13114689	2
C₄×#88043	2
#13112717	2
C₁₃×#2864	2
#9892	13