Subgroups — #15863152

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123398	C₂	1	2	yes	maximal
2	C₂×#11718369	C₂	1	1	yes	maximal, characteristic
3	#13114977	C₂	1	1	yes	maximal, characteristic, complemented
4	#13114975	C₂	1	2	yes	maximal, complemented
5	#13114973	C₂	1	2	yes	maximal, complemented
6	#13114972	C₂	1	2	yes	maximal, complemented
7	#13114561	C₂	1	2	yes	maximal
8	D₁₃×#341	C₂	1	2	yes	maximal
9	C₁₃×#1838	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₁₃	C₂²	1	4	yes	—
11	C₂²×#6094	C₂²	1	1	yes	characteristic
12	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88126	C₂²	1	1	yes	characteristic
14	C₁₃×#423	C₂²	1	2	yes	—
15	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
16	#11718779	C₂²	1	4	yes	—
17	C₂×#88055	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
19	#11718585	C₂²	1	2	yes	—
20	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
21	#11718500	—	2	8	no	—
22	#11718369	C₄	1	8	yes	—
23	C₁₃×#341	C₂²	1	2	yes	—
24	C₁₃×#341	C₂²	1	2	yes	—
25	#11718150	C₂²	1	4	yes	—
26	#11718150	C₂²	1	4	yes	—
27	#11718144	C₂²	1	2	yes	—
28	#11718144	C₂²	1	2	yes	—
29	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
30	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
31	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
32	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₂×#6103	Q₈	1	2	yes	—
35	C₂×#6101	Q₈	1	2	yes	—
36	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
37	C₂×#6099	C₂³	1	4	yes	—
38	C₂²×#1055	C₂³	1	1	yes	characteristic
39	C₂²×#1055	C₂³	1	1	yes	characteristic
40	M₁₆×D₁₃	—	2	8	no	—
41	M₁₆×D₁₃	—	2	8	no	—
42	C₂×#6094	—	2	4	no	—
43	C₂×#6094	—	2	4	no	—
44	C₂×#6094	C₂×C₄	1	4	yes	—
45	C₂×C₈×D₁₃	—	2	4	no	—
46	C₂×C₈×D₁₃	—	2	4	no	—
47	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
48	#88126	C₂×C₄	1	4	yes	—
49	#88126	D₄	1	4	yes	—
50	C₁₃×C₄⋊C₈	—	2	4	no	—
51	C₁₃×#97	C₂×C₄	1	4	yes	—
52	#88055	C₂×C₄	1	4	yes	—
53	#88054	—	2	8	no	—
54	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
55	C₄⋊#1055	—	2	4	no	—
56	C₄×#1055	C₂×C₄	1	4	yes	—
57	#20768	—	13	1	no	maximal, Sylow
58	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
60	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
61	C₂²×Dic₁₃	C₂×Q₈	1	2	yes	—
62	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
64	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
65	C₂×C₄×D₁₃	#41	1	4	yes	—
66	C₂×C₄×D₁₃	#41	1	4	yes	—
67	C₁₃×M₁₆	—	2	4	no	—
68	C₁₃×M₁₆	—	2	4	no	—
69	C₂×C₈×C₁₃	—	2	2	no	—
70	C₂×C₈×C₁₃	—	2	2	no	—
71	C₂×C₈×C₁₃	—	2	4	no	—
72	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
73	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
74	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
75	C₄²×C₁₃	C₂×D₄	1	2	yes	—
76	#6103	C₄⋊C₄	1	8	yes	—
77	#6101	C₄⋊C₄	1	8	yes	—
78	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
79	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
80	#6099	—	2	4	no	—
81	#6099	—	2	4	no	—
82	C₂×#1055	—	2	2	no	—
83	C₂×#1055	—	2	2	no	—
84	C₂×#1055	—	2	4	no	—
85	C₂×#1055	C₂²×C₄	1	2	yes	—
86	C₂×#1055	C₂²×C₄	1	2	yes	—
87	#6094	—	2	8	no	—
88	#6094	—	4	8	no	—
89	C₈×D₁₃	—	2	8	no	—
90	C₈×D₁₃	—	4	8	no	—
91	#2905	—	13	2	no	—
92	C₂×#405	—	13	1	no	—
93	#1838	—	13	1	no	—
94	#1838	—	13	2	no	—
95	#1838	D₁₃	1	1	yes	characteristic, complemented
96	#1837	—	13	2	no	—
97	#1837	—	13	2	no	—
98	#1738	—	13	2	no	—
99	C₂×#341	—	13	2	no	—
100	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
101	C₂²×D₁₃	—	4	2	no	—
102	C₂²×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
103	C₂²×D₁₃	#125	1	4	yes	—
104	C₂×C₄×C₁₃	—	4	2	no	—
105	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
106	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
108	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
109	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
110	C₂×Dic₁₃	—	4	2	no	—
111	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
112	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
113	C₂×Dic₁₃	#125	1	4	yes	—
114	C₄×D₁₃	#117	1	4	yes	—
115	C₄×D₁₃	#117	1	4	yes	—
116	C₄×D₁₃	#124	1	8	yes	—
117	C₈×C₁₃	—	2	2	no	—
118	C₈×C₁₃	—	2	2	no	—
119	C₈×C₁₃	—	4	4	no	—
120	#1055	—	2	2	no	—
121	#1055	—	2	2	no	—
122	#1055	—	4	4	no	—
123	C₂²×M₁₆	—	13	1	no	—
124	C₂²×M₁₆	—	13	4	no	—
125	C₂³×C₈	—	13	1	no	—
126	C₂×#117	—	13	1	no	—
127	#424	—	26	8	no	—
128	#423	—	13	4	no	—
129	#423	—	13	2	no	—
130	#423	C₂×D₁₃	1	2	yes	—
131	#405	—	13	8	no	—
132	C₂×#97	—	13	1	no	—
133	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
134	C₂×C₄×C₈	—	13	1	no	—
135	C₂×C₄×C₈	—	13	1	no	—
136	#341	—	13	4	no	—
137	#341	—	13	4	no	—
138	#341	—	13	2	no	—
139	#341	—	13	2	no	—
140	#341	C₂×D₁₃	1	2	yes	—
141	#341	C₂×D₁₃	1	2	yes	—
142	C₂²×C₁₃	—	2	2	no	—
143	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
144	C₂²×C₁₃	C₂×#125	1	2	yes	—
145	C₂×D₁₃	—	2	4	no	—
146	C₂×D₁₃	—	4	4	no	—
147	C₂×D₁₃	#382	1	4	yes	—
148	C₄×C₁₃	—	2	4	no	—
149	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
150	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
151	C₄×C₁₃	C₂×#124	1	2	yes	—
152	Dic₁₃	—	2	4	no	—
153	Dic₁₃	#382	1	4	yes	—
154	C₂³×C₄	—	13	1	no	—
155	C₂×M₁₆	—	13	4	no	—
156	C₂×M₁₆	—	13	4	no	—
157	C₂×M₁₆	—	26	4	no	—
158	C₂×M₁₆	—	26	4	no	—
159	C₂×M₁₆	—	26	8	no	—
160	C₂×M₁₆	—	26	8	no	—
161	C₂×M₁₆	C₂²×D₁₃	1	4	yes	—
162	C₂²×C₈	—	13	1	no	—
163	C₂²×C₈	—	13	1	no	—
164	C₂²×C₈	—	13	4	no	—
165	C₂²×C₈	—	26	4	no	—
166	C₂²×C₈	—	26	4	no	—
167	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
168	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
169	#117	—	13	4	no	—
170	#117	—	13	4	no	—
171	C₂×C₄⋊C₄	—	13	2	no	—
172	C₂×C₂²⋊C₄	—	13	2	no	—
173	C₂×C₄²	—	13	1	no	—
174	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
175	C₄⋊C₈	—	2	4	no	—
176	C₄⋊C₈	—	26	8	no	—
177	C₄⋊C₈	—	26	4	no	—
178	#97	—	13	4	no	—
179	#97	C₄×D₁₃	1	4	yes	—
180	C₄×C₈	—	13	4	no	—
181	C₄×C₈	—	13	4	no	—
182	C₂×C₁₃	—	2	2	no	—
183	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
184	C₂×C₁₃	#2916	1	2	yes	—
185	D₁₃	—	2	4	no	—
186	C₂⁴	—	13	1	no	—
187	C₂²×C₄	—	13	1	no	—
188	C₂²×C₄	—	13	2	no	—
189	C₂²×C₄	—	13	2	no	—
190	C₂²×C₄	—	13	4	no	—
191	C₂²×C₄	—	13	4	no	—
192	C₂²×C₄	—	13	2	no	—
193	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
194	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
195	M₁₆	—	2	4	no	—
196	M₁₆	—	2	4	no	—
197	M₁₆	—	26	8	no	—
198	M₁₆	—	26	4	no	—
199	M₁₆	—	26	4	no	—
200	M₁₆	—	52	8	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	13	2	no	—
205	C₂×C₈	—	13	2	no	—
206	C₂×C₈	—	26	8	no	—
207	C₂×C₈	—	26	2	no	—
208	C₂×C₈	—	26	2	no	—
209	C₂×C₈	—	26	4	no	—
210	C₂×C₈	—	52	8	no	—
211	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
212	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
213	C₄⋊C₄	—	13	8	no	—
214	C₂²⋊C₄	—	13	8	no	—
215	C₄²	—	13	2	no	—
216	C₄²	—	13	2	no	—
217	C₄²	C₂×C₄×D₁₃	1	2	yes	—
218	C₄²	D₄×D₁₃	1	2	yes	—
219	C₁₃	#20768	1	1	yes	characteristic, complemented, Sylow
220	C₂³	—	13	2	no	—
221	C₂³	—	13	4	no	—
222	C₂³	—	52	2	no	—
223	C₂³	C₂×Q₈×D₁₃	1	1	yes	characteristic
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	13	2	no	—
226	C₂×C₄	—	13	4	no	—
227	C₂×C₄	—	13	4	no	—
228	C₂×C₄	—	13	4	no	—
229	C₂×C₄	—	13	8	no	—
230	C₂×C₄	—	13	4	no	—
231	C₂×C₄	—	52	2	no	—
232	C₂×C₄	C₄⋊C₄×D₁₃	1	4	yes	—
233	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
234	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
235	C₂×C₄	#41×D₁₃	1	2	yes	—
236	C₂×C₄	#41×D₁₃	1	2	yes	—
237	C₈	—	2	2	no	—
238	C₈	—	2	2	no	—
239	C₈	—	4	4	no	—
240	C₈	—	26	2	no	—
241	C₈	—	26	2	no	—
242	C₈	—	52	4	no	—
243	C₂²	—	2	2	no	—
244	C₂²	—	13	4	no	—
245	C₂²	—	26	4	no	—
246	C₂²	—	52	4	no	—
247	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
248	C₂²	D₁₃×#125	1	2	yes	—
249	C₄	—	2	4	no	—
250	C₄	—	13	4	no	—
251	C₄	—	26	4	no	—
252	C₄	D₁₃×#117	1	1	yes	characteristic
253	C₄	D₁₃×#117	1	1	yes	characteristic
254	C₄	D₁₃×#124	1	2	yes	—
255	C₂	—	2	2	no	—
256	C₂	—	26	4	no	—
257	C₂	D₁₃×#382	1	1	yes	characteristic
258	C₂	#13123446	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1838	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1838	D₁₃
hypocenter	C₁₃	#20768
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1838

Complements

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

N	H ≅ G/N	type
3. #13114977	C₂	semidirect
4. #13114975	C₂	semidirect
5. #13114973	C₂	semidirect
6. #13114972	C₂	semidirect
9. C₁₃×#1838	C₂	semidirect
95. #1838	D₁₃	semidirect
219. C₁₃	#20768	semidirect

Maximal subgroups

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

subgroup	index
#13123398	2
C₂×#11718369	2
#13114977	2
#13114975	2
#13114973	2
#13114972	2
#13114561	2
D₁₃×#341	2
C₁₃×#1838	2
#20768	13