Subgroups — #15753451

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13113150	C₂	1	2	yes	maximal
2	#13113128	C₂	1	2	yes	maximal, complemented
3	#13112681	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×M₁₆	C₄	1	1	yes	characteristic
6	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
8	C₁₃×#405	—	2	4	no	—
9	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
10	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	#11718586	C₂²	1	4	yes	—
14	#11718120	C₄	1	4	yes	—
15	#11718117	C₄	1	4	yes	—
16	#11718046	—	2	4	no	—
17	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₃×M₁₆	—	2	2	no	—
19	C₂×C₁₃×M₁₆	—	2	2	no	—
20	C₂×C₁₃×M₁₆	—	2	2	no	—
21	C₂²×C₈×C₁₃	—	2	2	no	—
22	C₂²×C₈×C₁₃	—	2	2	no	—
23	C₂²×C₈×C₁₃	—	2	2	no	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₁₃×#117	—	2	2	no	—
29	C₁₃×#117	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₁₃×#97	—	2	2	no	—
35	C₁₃×#97	—	2	2	no	—
36	C₄×C₈×C₁₃	—	2	2	no	—
37	C₄×C₈×C₁₃	D₄	1	4	yes	—
38	C₂²⋊#1055	C₂×C₄	1	8	yes	—
39	C₄⋊#1055	—	2	4	no	—
40	C₄×#1055	—	2	4	no	—
41	#8157	—	13	1	no	maximal, Sylow
42	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	—	2	1	no	—
44	C₂²×C₄×C₁₃	—	2	1	no	—
45	C₂²×C₄×C₁₃	—	2	1	no	—
46	C₂²×C₄×C₁₃	—	2	1	no	—
47	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
49	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
50	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
51	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
52	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
53	C₁₃×M₁₆	—	2	8	no	—
54	C₂×C₈×C₁₃	—	2	8	no	—
55	C₂×C₈×C₁₃	—	2	1	no	—
56	C₂×C₈×C₁₃	—	2	1	no	—
57	C₂×C₈×C₁₃	—	2	1	no	—
58	C₂×C₈×C₁₃	—	2	1	no	—
59	C₂×C₈×C₁₃	—	2	1	no	—
60	C₂×C₈×C₁₃	—	2	1	no	—
61	C₂×C₈×C₁₃	—	2	1	no	—
62	C₂×C₈×C₁₃	—	2	1	no	—
63	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
64	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
65	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
66	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
67	C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₁₃×C₂²⋊C₄	—	2	4	no	—
69	C₄²×C₁₃	—	2	1	no	—
70	C₄²×C₁₃	—	2	1	no	—
71	C₄²×C₁₃	C₂×D₄	1	2	yes	—
72	C₄²×C₁₃	#41	1	2	yes	—
73	C₂×#1055	—	2	8	no	—
74	C₂×#405	D₁₃	1	1	yes	characteristic
75	#1458	—	13	2	no	—
76	#1452	—	13	2	no	—
77	#1281	—	13	2	no	—
78	C₂³×C₁₃	—	2	1	no	—
79	C₂³×C₁₃	—	2	1	no	—
80	C₂³×C₁₃	—	4	2	no	—
81	C₂³×C₁₃	#97	1	2	yes	—
82	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	—	2	1	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	4	2	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	#97	1	2	yes	—
93	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
95	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
96	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
100	C₈×C₁₃	—	2	2	no	—
101	C₈×C₁₃	—	2	2	no	—
102	C₈×C₁₃	—	2	2	no	—
103	C₈×C₁₃	—	2	2	no	—
104	#1055	—	4	8	no	—
105	C₂²×M₁₆	Dic₁₃	1	1	yes	characteristic
106	C₂³×C₈	Dic₁₃	1	1	yes	characteristic
107	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
108	#431	—	13	4	no	—
109	#405	—	2	4	no	—
110	C₂×#97	Dic₁₃	1	1	yes	characteristic
111	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
112	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
113	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
114	#324	—	13	4	no	—
115	#323	—	13	4	no	—
116	#322	—	26	4	no	—
117	C₂²×C₁₃	—	2	2	no	—
118	C₂²×C₁₃	—	2	2	no	—
119	C₂²×C₁₃	—	4	2	no	—
120	C₂²×C₁₃	—	4	2	no	—
121	C₂²×C₁₃	—	4	2	no	—
122	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
124	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
125	C₄×C₁₃	—	2	2	no	—
126	C₄×C₁₃	—	2	4	no	—
127	C₄×C₁₃	—	4	2	no	—
128	C₄×C₁₃	#407	1	1	yes	characteristic
129	C₄×C₁₃	#407	1	1	yes	characteristic
130	C₄×C₁₃	#432	1	1	yes	characteristic
131	C₄×C₁₃	#432	1	1	yes	characteristic
132	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
133	C₂×M₁₆	—	2	2	no	—
134	C₂×M₁₆	—	2	2	no	—
135	C₂×M₁₆	—	2	2	no	—
136	C₂²×C₈	—	2	2	no	—
137	C₂²×C₈	—	2	2	no	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
140	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
141	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
142	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
143	#117	—	2	2	no	—
144	#117	—	2	2	no	—
145	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
146	C₂×C₂²⋊C₄	C₄×D₁₃	1	2	yes	—
147	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
148	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
149	C₄⋊C₈	—	26	4	no	—
150	C₂²⋊C₈	—	13	8	no	—
151	#97	—	2	2	no	—
152	#97	—	2	2	no	—
153	C₄×C₈	—	2	2	no	—
154	C₄×C₈	—	26	4	no	—
155	C₄×C₈	C₂²⋊D₁₃	1	4	yes	—
156	C₂×C₁₃	—	2	1	no	—
157	C₂×C₁₃	—	2	1	no	—
158	C₂×C₁₃	—	4	2	no	—
159	C₂×C₁₃	#1749	1	1	yes	characteristic
160	C₂×C₁₃	#1757	1	2	yes	—
161	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
162	C₂²×C₄	—	2	1	no	—
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	#6099	1	2	yes	—
167	C₂²×C₄	#6099	1	2	yes	—
168	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
169	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
170	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
171	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
172	M₁₆	—	2	8	no	—
173	C₂×C₈	—	2	8	no	—
174	C₂×C₈	—	2	1	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	1	no	—
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	26	8	no	—
183	C₂×C₈	#6099	1	2	yes	—
184	C₂×C₈	#6099	1	2	yes	—
185	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
186	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
187	C₄⋊C₄	—	2	4	no	—
188	C₂²⋊C₄	—	2	4	no	—
189	C₄²	—	2	1	no	—
190	C₄²	—	2	1	no	—
191	C₄²	#6127	1	2	yes	—
192	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
193	C₁₃	#8157	1	1	yes	characteristic, complemented, Sylow
194	C₂³	—	2	1	no	—
195	C₂³	—	2	1	no	—
196	C₂³	—	4	2	no	—
197	C₂³	#88043	1	2	yes	—
198	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	#88043	1	2	yes	—
209	C₂×C₄	C₂×#6099	1	1	yes	characteristic
210	C₂×C₄	C₂×#6099	1	1	yes	characteristic
211	C₂×C₄	C₂×#6099	1	1	yes	characteristic
212	C₂×C₄	C₂×#6099	1	1	yes	characteristic
213	C₂×C₄	#88180	1	1	yes	characteristic
214	C₂×C₄	C₄×C₂²⋊D₁₃	1	4	yes	—
215	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
216	C₈	—	2	2	no	—
217	C₈	—	2	2	no	—
218	C₈	—	2	2	no	—
219	C₈	—	2	2	no	—
220	C₈	—	52	8	no	—
221	C₂²	—	2	2	no	—
222	C₂²	—	2	2	no	—
223	C₂²	—	4	2	no	—
224	C₂²	—	4	2	no	—
225	C₂²	—	4	2	no	—
226	C₂²	C₂×#88043	1	1	yes	characteristic
227	C₂²	C₄×#6099	1	1	yes	characteristic
228	C₂²	C₄×C₂²⋊Dic₁₃	1	1	yes	characteristic
229	C₄	—	2	4	no	—
230	C₄	—	2	2	no	—
231	C₄	—	4	2	no	—
232	C₄	#11718587	1	1	yes	characteristic
233	C₄	#11718587	1	1	yes	characteristic
234	C₄	#11718868	1	1	yes	characteristic
235	C₄	#11718868	1	1	yes	characteristic
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	—	4	2	no	—
239	C₂	#13114598	1	1	yes	characteristic
240	C₂	#13114636	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₁₃
commutator	C₂³×C₁₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	C₄×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	#8157
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. #13113128	C₂	semidirect
3. #13112681	C₂	semidirect
193. C₁₃	#8157	semidirect

Maximal subgroups

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

subgroup	index
#13113150	2
#13113128	2
#13112681	2
C₂×C₁₃×#405	2
#8157	13