Subgroups — #15751410

Order 3328.

410 conjugacy classes of subgroups.

The subgroup lattice has 310 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×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
3	#13112662	C₂	1	2	yes	maximal
4	#13112659	C₂	1	2	yes	maximal
5	C₁₃×#2863	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#391	C₄	1	1	yes	characteristic
7	C₁₃×#391	C₄	1	1	yes	characteristic
8	C₁₃×#391	C₂²	1	1	yes	characteristic
9	C₁₃×#389	C₄	1	1	yes	characteristic
10	C₁₃×#389	C₄	1	1	yes	characteristic
11	C₁₃×#389	C₂²	1	1	yes	characteristic
12	C₁₃×#387	—	2	1	no	—
13	C₁₃×#387	—	2	1	no	—
14	C₁₃×#387	—	2	1	no	—
15	C₁₃×#383	—	2	1	no	—
16	C₄³×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#1055	—	2	1	no	—
18	C₂×C₄⋊#1055	—	2	1	no	—
19	C₂×#88043	—	2	1	no	—
20	C₂×C₄×#1055	—	2	1	no	—
21	#11718116	C₂²	1	2	yes	—
22	#11718116	C₂²	1	2	yes	—
23	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
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×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	D₄	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	C₂³	1	1	yes	characteristic
37	C₂²×#1055	—	2	2	no	—
38	C₂²×#1055	—	2	2	no	—
39	C₁₃×#95	—	2	1	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	C₄⋊#1055	—	2	4	no	—
50	#88043	—	4	2	no	—
51	C₄×#1055	—	4	2	no	—
52	#7689	—	13	1	no	maximal, Sylow
53	C₂×Q₈×C₁₃	—	2	2	no	—
54	C₂×Q₈×C₁₃	—	4	1	no	—
55	C₂×Q₈×C₁₃	—	4	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	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
67	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
73	C₁₃×C₄⋊C₄	—	4	1	no	—
74	C₄²×C₁₃	—	2	2	no	—
75	C₄²×C₁₃	—	2	2	no	—
76	C₄²×C₁₃	—	2	2	no	—
77	C₄²×C₁₃	—	2	1	no	—
78	C₄²×C₁₃	—	2	1	no	—
79	C₄²×C₁₃	—	4	1	no	—
80	C₄²×C₁₃	—	4	1	no	—
81	C₄²×C₁₃	SD₁₆	1	2	yes	—
82	C₄²×C₁₃	Q₁₆	1	2	yes	—
83	C₂×#1055	—	2	4	no	—
84	C₂×#1055	—	2	4	no	—
85	C₂×#1055	—	4	2	no	—
86	C₂×#1055	—	4	2	no	—
87	C₂×#1055	—	4	2	no	—
88	C₂×#1055	—	4	2	no	—
89	#2863	D₁₃	1	1	yes	characteristic
90	#1767	—	13	1	no	—
91	C₄×C₄⋊C₈	—	13	1	no	—
92	#1272	—	13	2	no	—
93	#1271	—	13	2	no	—
94	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	Q₈×C₁₃	—	8	2	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	—	2	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	—	4	1	no	—
122	C₂×C₄×C₁₃	#103	1	2	yes	—
123	C₂×C₄×C₁₃	#103	1	2	yes	—
124	C₂×C₄×C₁₃	#104	1	2	yes	—
125	C₂×C₄×C₁₃	#104	1	2	yes	—
126	C₂×C₄×C₁₃	#131	1	2	yes	—
127	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
128	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
129	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
130	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
131	#1055	—	4	4	no	—
132	#1055	—	4	4	no	—
133	C₂×C₄⋊C₈	—	26	1	no	—
134	C₂×C₄⋊C₈	—	26	1	no	—
135	C₂×#97	—	26	1	no	—
136	C₂×C₄×C₈	—	26	1	no	—
137	#391	Dic₁₃	1	1	yes	characteristic
138	#391	Dic₁₃	1	1	yes	characteristic
139	#391	C₂×D₁₃	1	1	yes	characteristic
140	#389	Dic₁₃	1	1	yes	characteristic
141	#389	Dic₁₃	1	1	yes	characteristic
142	#389	C₂×D₁₃	1	1	yes	characteristic
143	#387	—	2	1	no	—
144	#387	—	2	1	no	—
145	#387	—	2	1	no	—
146	#383	—	2	1	no	—
147	C₄³	C₂×D₁₃	1	1	yes	characteristic
148	#336	—	13	2	no	—
149	#336	—	13	2	no	—
150	C₂²×C₁₃	#408	1	1	yes	characteristic
151	C₂²×C₁₃	#410	1	1	yes	characteristic
152	C₂²×C₁₃	#413	1	1	yes	characteristic
153	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
154	C₂²×C₁₃	#417	1	1	yes	characteristic
155	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
156	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
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	—	2	1	no	—
162	C₄×C₁₃	—	2	1	no	—
163	C₄×C₁₃	—	2	1	no	—
164	C₄×C₁₃	—	2	1	no	—
165	C₄×C₁₃	—	2	2	no	—
166	C₄×C₁₃	—	8	1	no	—
167	C₄×C₁₃	—	8	1	no	—
168	C₄×C₁₃	—	8	1	no	—
169	C₄×C₁₃	—	8	1	no	—
170	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
171	C₂²×C₈	—	26	2	no	—
172	C₂²×C₈	—	26	2	no	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
177	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
178	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
179	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
180	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
181	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
182	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
183	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
184	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
185	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
186	C₄⋊C₈	—	26	4	no	—
187	C₄⋊C₈	—	26	4	no	—
188	#97	—	52	2	no	—
189	C₄×C₈	—	52	2	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	#95	—	2	1	no	—
198	#95	—	2	1	no	—
199	C₂×C₁₃	#1473	1	1	yes	characteristic
200	C₂×C₁₃	#1483	1	1	yes	characteristic
201	C₂×C₁₃	#1493	1	1	yes	characteristic
202	C₂×C₁₃	#1503	1	1	yes	characteristic
203	C₂×C₁₃	#1509	1	1	yes	characteristic
204	C₂×C₁₃	#1524	1	1	yes	characteristic
205	C₂×C₁₃	#1550	1	1	yes	characteristic
206	C₂×Q₈	—	2	2	no	—
207	C₂×Q₈	—	4	1	no	—
208	C₂×Q₈	—	4	1	no	—
209	C₂²×C₄	—	2	1	no	—
210	C₂²×C₄	—	2	1	no	—
211	C₂²×C₄	—	2	1	no	—
212	C₂²×C₄	—	2	1	no	—
213	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
214	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
215	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
216	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
217	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
218	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
219	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
220	C₂×C₈	—	26	4	no	—
221	C₂×C₈	—	26	4	no	—
222	C₂×C₈	—	52	2	no	—
223	C₂×C₈	—	52	2	no	—
224	C₂×C₈	—	52	2	no	—
225	C₂×C₈	—	52	2	no	—
226	C₄⋊C₄	—	2	2	no	—
227	C₄⋊C₄	—	4	1	no	—
228	C₄⋊C₄	—	4	1	no	—
229	C₄⋊C₄	—	4	2	no	—
230	C₄⋊C₄	—	4	2	no	—
231	C₄⋊C₄	—	4	1	no	—
232	C₄⋊C₄	—	4	1	no	—
233	C₄²	—	2	2	no	—
234	C₄²	—	2	2	no	—
235	C₄²	—	2	2	no	—
236	C₄²	—	2	1	no	—
237	C₄²	—	2	1	no	—
238	C₄²	—	4	1	no	—
239	C₄²	—	4	1	no	—
240	C₄²	#6106	1	2	yes	—
241	C₄²	#6107	1	2	yes	—
242	C₁₃	#7689	1	1	yes	characteristic, complemented, Sylow
243	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
244	Q₈	—	8	2	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	—	2	1	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	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	—	4	1	no	—
267	C₂×C₄	—	4	1	no	—
268	C₂×C₄	—	4	1	no	—
269	C₂×C₄	—	4	1	no	—
270	C₂×C₄	—	4	1	no	—
271	C₂×C₄	#88075	1	2	yes	—
272	C₂×C₄	#88075	1	2	yes	—
273	C₂×C₄	#88077	1	2	yes	—
274	C₂×C₄	#88077	1	2	yes	—
275	C₂×C₄	C₂×#6106	1	1	yes	characteristic
276	C₂×C₄	C₂×#6107	1	1	yes	characteristic
277	C₂×C₄	#88202	1	2	yes	—
278	C₂×C₄	#88203	1	1	yes	characteristic
279	C₂×C₄	#88205	1	1	yes	characteristic
280	C₈	—	52	4	no	—
281	C₈	—	52	4	no	—
282	C₂²	C₂×#88075	1	1	yes	characteristic
283	C₂²	#11718893	1	1	yes	characteristic
284	C₂²	#11718895	1	1	yes	characteristic
285	C₂²	C₂×#88077	1	1	yes	characteristic
286	C₂²	C₂×#88077	1	1	yes	characteristic
287	C₂²	#11718898	1	1	yes	characteristic
288	C₂²	#11718901	1	1	yes	characteristic
289	C₄	—	2	1	no	—
290	C₄	—	2	1	no	—
291	C₄	—	2	2	no	—
292	C₄	—	2	2	no	—
293	C₄	—	2	2	no	—
294	C₄	—	2	2	no	—
295	C₄	—	2	2	no	—
296	C₄	—	2	1	no	—
297	C₄	—	2	1	no	—
298	C₄	—	8	1	no	—
299	C₄	—	8	1	no	—
300	C₄	—	8	1	no	—
301	C₄	—	8	1	no	—
302	C₂	#13113205	1	1	yes	characteristic
303	C₂	#13113249	1	1	yes	characteristic
304	C₂	#13113291	1	1	yes	characteristic
305	C₂	#13113335	1	1	yes	characteristic
306	C₂	#13113361	1	1	yes	characteristic
307	C₂	#13113424	1	1	yes	characteristic
308	C₂	#13113526	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×#2863	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#2863	D₁₃
hypocenter	C₁₃	#7689
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2863

Complements

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

N	H ≅ G/N	type
242. C₁₃	#7689	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×C₄⋊#1055	2
#13112662	2
#13112659	2
C₁₃×#2863	2
#7689	13