Subgroups — #16016005

Order 3328.

590 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	C₂×#11718350	C₂	1	1	yes	maximal, characteristic
2	#13116642	C₂	1	8	yes	maximal, complemented
3	#13116592	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116446	C₂	1	2	yes	maximal
5	M₃₂×Dic₁₃	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6094	C₄	1	1	yes	characteristic
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88126	C₄	1	1	yes	characteristic
10	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×#88055	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88052	C₂²	1	2	yes	—
15	C₂×#88043	C₄	1	1	yes	characteristic
16	#11718350	C₄	1	4	yes	—
17	#11718350	C₂²	1	4	yes	—
18	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	complemented
19	#11718099	C₂²	1	8	yes	—
20	#11718094	C₂²	1	4	yes	complemented
21	C₁₆×Dic₁₃	C₂²	1	4	yes	complemented
22	C₄⋊#6090	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
26	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×#6103	C₈	1	2	yes	—
28	C₂×#6101	C₈	1	2	yes	—
29	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
31	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
32	C₂×#6094	—	2	4	no	—
33	C₂×#6094	C₂×C₄	1	4	yes	—
34	C₂×C₈×D₁₃	—	2	2	no	—
35	C₂×C₈×D₁₃	—	2	2	no	—
36	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₈×D₁₃	C₂³	1	2	yes	—
38	#88126	C₈	1	4	yes	—
39	#88126	C₂×C₄	1	4	yes	—
40	C₁₃×M₃₂	—	2	4	no	—
41	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
42	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
43	C₄×C₈×C₁₃	C₂³	1	2	yes	—
44	#88055	C₂×C₄	1	4	yes	—
45	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
46	C₈×Dic₁₃	C₂³	1	2	yes	—
47	#88052	—	2	4	no	—
48	C₂×#6090	C₂³	1	4	yes	—
49	#88043	C₂×C₄	1	4	yes	—
50	#33419	—	13	1	no	maximal, Sylow
51	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
53	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
55	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
56	C₂×C₄×D₁₃	—	2	2	no	—
57	C₂×C₄×D₁₃	—	2	2	no	—
58	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
59	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
62	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₃	#41	1	2	yes	—
64	C₂×C₈×C₁₃	#41	1	2	yes	—
65	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
66	C₄²×C₁₃	C₂×C₈	1	2	yes	—
67	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
68	#6103	C₂×C₈	1	8	yes	—
69	#6101	C₂×C₈	1	8	yes	—
70	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
71	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
72	C₂×#1055	—	2	2	no	—
73	C₂×#1055	M₁₆	1	4	yes	—
74	C₂×#1055	C₂²×C₄	1	2	yes	—
75	C₂×#1055	C₂²×C₄	1	2	yes	—
76	#6094	—	2	8	no	—
77	C₈×D₁₃	—	2	4	no	—
78	C₈×D₁₃	—	2	2	no	—
79	C₈×D₁₃	—	2	2	no	—
80	C₁₃×C₁₆	—	2	4	no	—
81	#6090	—	2	4	no	—
82	C₂×#405	—	13	1	no	—
83	#2164	—	13	8	no	—
84	#2150	—	13	1	no	—
85	#2150	D₁₃	1	1	yes	characteristic, complemented
86	#2112	—	13	2	no	—
87	C₄×M₃₂	—	13	2	no	—
88	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
89	C₂²×D₁₃	—	2	2	no	—
90	C₂²×D₁₃	—	4	2	no	—
91	C₂²×D₁₃	C₂²×C₈	1	2	yes	—
92	C₂×C₄×C₁₃	—	4	2	no	—
93	C₂×C₄×C₁₃	#117	1	2	yes	—
94	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
95	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
98	C₂×Dic₁₃	—	2	2	no	—
99	C₂×Dic₁₃	—	4	2	no	—
100	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
101	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
102	C₄×D₁₃	—	2	2	no	—
103	C₄×D₁₃	—	2	2	no	—
104	C₄×D₁₃	—	2	4	no	—
105	C₈×C₁₃	—	2	2	no	—
106	C₈×C₁₃	#117	1	2	yes	—
107	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
108	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
109	#1055	—	2	2	no	—
110	#1055	C₂×M₁₆	1	4	yes	—
111	C₂²×M₁₆	—	13	1	no	—
112	C₂³×C₈	—	13	1	no	—
113	C₂×#117	—	13	1	no	—
114	C₂×M₃₂	—	13	2	no	—
115	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
116	#405	—	13	4	no	—
117	#405	—	13	4	no	—
118	C₂×#97	—	13	1	no	—
119	C₂×#97	—	13	1	no	—
120	C₂×C₄×C₈	—	13	1	no	—
121	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
122	C₄⋊C₁₆	—	13	4	no	—
123	C₄⋊C₁₆	C₂×D₁₃	1	4	yes	complemented
124	C₂²⋊C₁₆	—	13	8	no	—
125	#346	—	13	4	no	—
126	C₄×C₁₆	—	13	4	no	—
127	C₂²×C₁₃	—	2	2	no	—
128	C₂²×C₁₃	#431	1	2	yes	—
129	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
130	C₂×D₁₃	—	2	4	no	—
131	C₂×D₁₃	—	2	2	no	—
132	C₂×D₁₃	—	4	4	no	—
133	C₄×C₁₃	—	2	4	no	—
134	C₄×C₁₃	#431	1	2	yes	—
135	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
136	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
137	Dic₁₃	—	2	4	no	—
138	Dic₁₃	—	2	2	no	—
139	C₂³×C₄	—	13	1	no	—
140	C₂×M₁₆	—	13	4	no	—
141	C₂×M₁₆	—	26	4	no	—
142	C₂²×C₈	—	13	1	no	—
143	C₂²×C₈	—	13	1	no	—
144	C₂²×C₈	—	13	2	no	—
145	C₂²×C₈	—	13	2	no	—
146	C₂²×C₈	—	26	2	no	—
147	C₂²×C₈	—	26	2	no	—
148	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
149	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
150	#117	—	13	4	no	—
151	#117	—	13	4	no	—
152	C₂×C₄⋊C₄	—	13	2	no	—
153	C₂×C₂²⋊C₄	—	13	2	no	—
154	C₂×C₄²	—	13	1	no	—
155	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
156	M₃₂	—	2	4	no	—
157	M₃₂	—	26	4	no	—
158	C₂×C₁₆	—	13	4	no	—
159	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
160	#97	—	13	4	no	—
161	#97	—	13	4	no	—
162	C₄×C₈	—	13	2	no	—
163	C₄×C₈	—	13	2	no	—
164	C₄×C₈	C₄×D₁₃	1	2	yes	—
165	C₄×C₈	C₂²×D₁₃	1	2	yes	—
166	C₂×C₁₃	—	2	2	no	—
167	C₂×C₁₃	C₂×#431	1	1	yes	characteristic
168	C₂×C₁₃	#3407	1	2	yes	—
169	D₁₃	—	4	2	no	—
170	C₂⁴	—	13	1	no	—
171	C₂²×C₄	—	13	1	no	—
172	C₂²×C₄	—	13	2	no	—
173	C₂²×C₄	—	13	2	no	—
174	C₂²×C₄	—	13	2	no	—
175	C₂²×C₄	—	26	2	no	—
176	C₂²×C₄	—	26	2	no	—
177	C₂²×C₄	C₈×D₁₃	1	2	yes	—
178	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
179	M₁₆	—	26	8	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	13	4	no	—
182	C₂×C₈	—	13	2	no	—
183	C₂×C₈	—	13	2	no	—
184	C₂×C₈	—	26	2	no	—
185	C₂×C₈	—	26	4	no	—
186	C₂×C₈	—	26	2	no	—
187	C₂×C₈	—	26	2	no	—
188	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
189	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
190	C₂×C₈	#6129	1	2	yes	—
191	C₂×C₈	#6131	1	2	yes	—
192	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
193	C₄⋊C₄	—	13	8	no	—
194	C₂²⋊C₄	—	13	8	no	—
195	C₄²	—	13	2	no	—
196	C₄²	—	13	2	no	—
197	C₄²	C₈×D₁₃	1	2	yes	—
198	C₄²	C₂×C₄×D₁₃	1	2	yes	—
199	C₁₆	—	2	4	no	—
200	C₁₆	—	26	4	no	—
201	C₁₃	#33419	1	1	yes	characteristic, complemented, Sylow
202	C₂³	—	13	2	no	—
203	C₂³	—	26	2	no	—
204	C₂³	—	52	2	no	—
205	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	13	4	no	—
208	C₂×C₄	—	13	2	no	—
209	C₂×C₄	—	26	2	no	—
210	C₂×C₄	—	26	2	no	—
211	C₂×C₄	—	26	2	no	—
212	C₂×C₄	—	26	4	no	—
213	C₂×C₄	—	52	2	no	—
214	C₂×C₄	#88146	1	2	yes	—
215	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
216	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
217	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
218	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
219	C₈	—	2	2	no	—
220	C₈	—	13	4	no	—
221	C₈	—	26	2	no	—
222	C₈	#88146	1	2	yes	—
223	C₈	C₂×#6129	1	1	yes	characteristic
224	C₈	C₂×#6131	1	1	yes	characteristic
225	C₂²	—	2	2	no	—
226	C₂²	—	26	4	no	—
227	C₂²	—	26	2	no	—
228	C₂²	—	52	4	no	—
229	C₂²	#11718494	1	2	yes	—
230	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
231	C₄	—	2	4	no	—
232	C₄	—	26	4	no	—
233	C₄	—	26	2	no	—
234	C₄	#11718494	1	2	yes	—
235	C₄	C₂×#88146	1	1	yes	characteristic
236	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
237	C₂	—	2	2	no	—
238	C₂	—	52	2	no	—
239	C₂	C₂×#11718494	1	1	yes	characteristic
240	C₂	#13127938	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#2150	C₂
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2150	D₁₃
hypocenter	C₁₃	#33419
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #2150

Complements

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

N	H ≅ G/N	type
2. #13116642	C₂	semidirect
3. #13116592	C₂	semidirect
5. M₃₂×Dic₁₃	C₂	semidirect
6. C₁₃×#2150	C₂	semidirect
18. C₁₃×C₄⋊C₁₆	C₂²	semidirect
20. #11718094	C₂²	semidirect
21. C₁₆×Dic₁₃	C₂²	semidirect
22. C₄⋊#6090	C₂²	semidirect
85. #2150	D₁₃	semidirect
123. C₄⋊C₁₆	C₂×D₁₃	semidirect
201. C₁₃	#33419	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718350	2
#13116642	2
#13116592	2
#13116446	2
M₃₂×Dic₁₃	2
C₁₃×#2150	2
#33419	13