Subgroups — #15756581

Order 3328.

382 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13114952	C₂	1	2	yes	maximal
2	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#13112671	C₂	1	1	yes	maximal, characteristic
4	#13112670	C₂	1	2	yes	maximal
5	C₁₃×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
9	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
10	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
12	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#1055	C₂²	1	2	yes	—
14	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
15	#11718142	—	2	2	no	—
16	#11718142	—	2	2	no	—
17	C₂²×C₈×C₁₃	—	2	2	no	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
24	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
25	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
26	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
27	C₂²×#1055	—	2	2	no	—
28	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
29	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
30	C₁₃×C₄⋊C₈	—	2	2	no	—
31	C₁₃×C₄⋊C₈	—	2	2	no	—
32	C₄×C₈×C₁₃	—	2	2	no	—
33	C₈×Dic₁₃	—	2	2	no	—
34	C₈×Dic₁₃	—	2	2	no	—
35	C₈×Dic₁₃	—	2	2	no	—
36	C₈×Dic₁₃	C₈	1	4	yes	complemented
37	C₄⋊#1055	—	2	2	no	—
38	C₄⋊#1055	—	2	2	no	—
39	C₄×#1055	—	2	2	no	—
40	#8785	—	13	1	no	maximal, Sylow
41	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
44	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
46	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
47	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	—	2	1	no	—
49	C₂×C₈×C₁₃	—	2	1	no	—
50	C₂×C₈×C₁₃	—	2	1	no	—
51	C₂×C₈×C₁₃	—	2	1	no	—
52	C₂×C₈×C₁₃	—	4	2	no	—
53	C₂×C₈×C₁₃	—	4	2	no	—
54	C₂×C₈×C₁₃	—	4	2	no	—
55	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
56	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
57	C₄²×C₁₃	#41	1	2	yes	—
58	C₄²×C₁₃	#41	1	2	yes	—
59	C₄×Dic₁₃	—	2	1	no	—
60	C₄×Dic₁₃	—	2	1	no	—
61	C₄×Dic₁₃	—	2	1	no	—
62	C₄×Dic₁₃	—	2	2	no	—
63	C₄×Dic₁₃	—	2	1	no	—
64	C₄×Dic₁₃	—	2	2	no	—
65	C₄×Dic₁₃	—	2	2	no	—
66	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
67	C₄×Dic₁₃	M₁₆	1	2	yes	—
68	C₂×#1055	—	2	1	no	—
69	C₂×#1055	—	2	1	no	—
70	C₂×#1055	—	2	1	no	—
71	C₂×#1055	—	2	1	no	—
72	C₂×#1055	—	4	2	no	—
73	C₂×#1055	—	4	2	no	—
74	C₂×#1055	—	4	2	no	—
75	C₂×#1055	C₂×C₈	1	2	yes	—
76	C₂×#1055	M₁₆	1	2	yes	—
77	#1831	—	13	2	no	—
78	C₄²×C₈	—	13	1	no	—
79	#1277	—	13	2	no	—
80	#1277	—	13	1	no	—
81	#1277	D₁₃	1	1	yes	characteristic
82	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	—	2	1	no	—
85	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
86	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
87	C₂×C₄×C₁₃	#124	1	2	yes	—
88	C₂×C₄×C₁₃	#125	1	2	yes	—
89	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#135	1	2	yes	—
95	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
96	C₂×Dic₁₃	—	2	1	no	—
97	C₂×Dic₁₃	—	2	1	no	—
98	C₂×Dic₁₃	—	2	1	no	—
99	C₂×Dic₁₃	—	2	1	no	—
100	C₂×Dic₁₃	—	2	1	no	—
101	C₂×Dic₁₃	—	2	1	no	—
102	C₂×Dic₁₃	—	2	1	no	—
103	C₂×Dic₁₃	—	2	1	no	—
104	C₂×Dic₁₃	C₄⋊C₈	1	2	yes	—
105	C₂×Dic₁₃	C₄⋊C₈	1	2	yes	—
106	C₂×Dic₁₃	#108	1	2	yes	—
107	C₂×Dic₁₃	#108	1	2	yes	—
108	C₈×C₁₃	—	2	2	no	—
109	C₈×C₁₃	—	2	2	no	—
110	C₈×C₁₃	—	8	2	no	—
111	#1055	—	2	2	no	—
112	#1055	—	2	2	no	—
113	#1055	—	8	2	no	—
114	C₂×C₄⋊C₈	—	13	2	no	—
115	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
116	C₂×C₄×C₈	—	13	1	no	—
117	C₂×C₄×C₈	—	13	1	no	—
118	C₂×C₄×C₈	—	13	1	no	—
119	C₂×C₄×C₈	—	13	1	no	—
120	C₂×C₄×C₈	—	13	1	no	—
121	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
122	C₄³	—	13	1	no	—
123	#336	—	26	2	no	—
124	#336	—	26	2	no	—
125	C₂²×C₁₃	#382	1	1	yes	characteristic
126	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
127	C₂²×C₁₃	#423	1	1	yes	characteristic
128	C₂²×C₁₃	#427	1	1	yes	characteristic
129	C₂²×C₁₃	#427	1	1	yes	characteristic
130	C₂²×C₁₃	C₂×#108	1	1	yes	characteristic
131	C₂²×C₁₃	C₂×#108	1	1	yes	characteristic
132	C₄×C₁₃	—	2	2	no	—
133	C₄×C₁₃	#431	1	1	yes	characteristic
134	C₄×C₁₃	#431	1	1	yes	characteristic
135	C₄×C₁₃	#432	1	1	yes	characteristic
136	C₄×C₁₃	#432	1	1	yes	characteristic
137	C₄×C₁₃	#488	1	2	yes	—
138	C₄×C₁₃	#488	1	2	yes	—
139	Dic₁₃	—	2	2	no	—
140	Dic₁₃	—	2	2	no	—
141	Dic₁₃	—	2	2	no	—
142	Dic₁₃	—	2	2	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	13	1	no	—
145	C₂²×C₈	—	13	1	no	—
146	C₂²×C₈	—	26	2	no	—
147	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
148	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
149	C₂×C₄²	—	13	1	no	—
150	C₂×C₄²	—	13	1	no	—
151	C₂×C₄²	—	13	1	no	—
152	C₂×C₄²	—	13	1	no	—
153	C₂×C₄²	—	13	1	no	—
154	C₂×C₄²	—	13	1	no	—
155	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	26	2	no	—
159	C₄⋊C₈	—	26	2	no	—
160	C₄×C₈	—	2	2	no	—
161	C₄×C₈	—	13	4	no	—
162	C₄×C₈	—	26	2	no	—
163	C₄×C₈	—	26	2	no	—
164	C₄×C₈	—	26	2	no	—
165	C₄×C₈	—	26	2	no	—
166	C₂×C₁₃	#1564	1	1	yes	characteristic
167	C₂×C₁₃	#1564	1	1	yes	characteristic
168	C₂×C₁₃	#1568	1	1	yes	characteristic
169	C₂×C₁₃	#1568	1	1	yes	characteristic
170	C₂×C₁₃	#1831	1	1	yes	characteristic
171	C₂×C₁₃	#1835	1	1	yes	characteristic
172	C₂×C₁₃	#1837	1	1	yes	characteristic
173	C₂²×C₄	—	13	1	no	—
174	C₂²×C₄	—	13	1	no	—
175	C₂²×C₄	—	13	1	no	—
176	C₂²×C₄	—	13	1	no	—
177	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
178	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
179	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	2	1	no	—
183	C₂×C₈	—	2	1	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	4	2	no	—
187	C₂×C₈	—	13	2	no	—
188	C₂×C₈	—	13	2	no	—
189	C₂×C₈	—	26	1	no	—
190	C₂×C₈	—	26	1	no	—
191	C₂×C₈	—	26	1	no	—
192	C₂×C₈	—	26	1	no	—
193	C₂×C₈	—	52	2	no	—
194	C₂×C₈	—	52	2	no	—
195	C₂×C₈	—	52	2	no	—
196	C₂×C₈	C₈×D₁₃	1	2	yes	—
197	C₂×C₈	#6094	1	2	yes	—
198	C₄²	—	13	2	no	—
199	C₄²	—	13	2	no	—
200	C₄²	—	26	2	no	—
201	C₄²	—	26	2	no	—
202	C₄²	—	26	1	no	—
203	C₄²	—	26	1	no	—
204	C₄²	—	26	1	no	—
205	C₄²	—	26	2	no	—
206	C₄²	—	26	1	no	—
207	C₄²	#6127	1	2	yes	—
208	C₄²	#6129	1	2	yes	—
209	C₁₃	#8785	1	1	yes	characteristic, complemented, Sylow
210	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	13	2	no	—
214	C₂×C₄	—	13	2	no	—
215	C₂×C₄	—	13	2	no	—
216	C₂×C₄	—	13	2	no	—
217	C₂×C₄	—	26	1	no	—
218	C₂×C₄	—	26	1	no	—
219	C₂×C₄	—	26	1	no	—
220	C₂×C₄	—	26	1	no	—
221	C₂×C₄	—	26	1	no	—
222	C₂×C₄	—	26	1	no	—
223	C₂×C₄	—	26	1	no	—
224	C₂×C₄	—	26	1	no	—
225	C₂×C₄	#88126	1	1	yes	characteristic
226	C₂×C₄	#88131	1	1	yes	characteristic
227	C₂×C₄	#88139	1	2	yes	—
228	C₂×C₄	#88143	1	2	yes	—
229	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
230	C₂×C₄	C₂×#6094	1	1	yes	characteristic
231	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
232	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
233	C₂×C₄	#88166	1	1	yes	characteristic
234	C₂×C₄	#88170	1	2	yes	—
235	C₂×C₄	#88173	1	1	yes	characteristic
236	C₈	—	2	2	no	—
237	C₈	—	2	2	no	—
238	C₈	—	8	2	no	—
239	C₈	—	26	2	no	—
240	C₈	—	26	2	no	—
241	C₈	—	104	2	no	—
242	C₂²	#11718311	1	1	yes	characteristic
243	C₂²	D₁₃×C₄⋊C₈	1	1	yes	characteristic
244	C₂²	#11718498	1	1	yes	characteristic
245	C₂²	#11718521	1	1	yes	characteristic
246	C₂²	#11718541	1	1	yes	characteristic
247	C₂²	D₁₃×#108	1	1	yes	characteristic
248	C₂²	D₁₃×#108	1	1	yes	characteristic
249	C₄	—	2	2	no	—
250	C₄	—	26	2	no	—
251	C₄	—	26	2	no	—
252	C₄	—	26	2	no	—
253	C₄	—	26	2	no	—
254	C₄	#11718346	1	1	yes	characteristic
255	C₄	#11718366	1	1	yes	characteristic
256	C₄	#11718379	1	1	yes	characteristic
257	C₄	#11718380	1	1	yes	characteristic
258	C₄	#11718429	1	2	yes	—
259	C₄	#11718461	1	2	yes	—
260	C₂	#13113581	1	1	yes	characteristic
261	C₂	#13113583	1	1	yes	characteristic
262	C₂	#13113596	1	1	yes	characteristic
263	C₂	#13113598	1	1	yes	characteristic
264	C₂	#13114951	1	1	yes	characteristic
265	C₂	#13114965	1	1	yes	characteristic
266	C₂	#13114972	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1277	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1277	D₁₃
hypocenter	C₁₃	#8785
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
36. C₈×Dic₁₃	C₈	semidirect
209. C₁₃	#8785	semidirect

Maximal subgroups

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

subgroup	index
#13114952	2
C₄×C₈×Dic₁₃	2
#13112671	2
#13112670	2
C₁₃×#1277	2
#8785	13