Subgroups — #13131285

Order 1664.

656 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88237	C₂	1	2	yes	maximal
2	C₂×C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#11719136	C₂	1	4	yes	maximal
4	#11719060	C₂	1	2	yes	maximal, complemented
5	#11719059	C₂	1	2	yes	maximal, complemented
6	C₄×C₄⋊#261	C₂	1	4	yes	maximal, complemented
7	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
8	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊#261	C₂²	1	4	yes	—
10	#88237	—	2	8	no	—
11	C₂×C₄⋊#261	C₂²	1	8	yes	—
12	C₂×C₄⋊#261	C₂²	1	4	yes	—
13	C₂×C₄×#261	C₂²	1	4	yes	—
14	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic, complemented
16	C₂×C₄×Dic₁₃	C₄	1	2	yes	complemented
17	C₄²×D₁₃	C₄	1	1	yes	characteristic, complemented
18	C₄²×D₁₃	C₄	1	1	yes	characteristic, complemented
19	C₄²×D₁₃	C₄	1	2	yes	complemented
20	C₄²×D₁₃	C₂²	1	2	yes	—
21	C₄²×D₁₃	C₂²	1	1	yes	characteristic
22	C₄²×D₁₃	C₂²	1	1	yes	characteristic
23	(C₂×#261)⋊C₄	C₂²	1	8	yes	—
24	C₂³×D₁₃	C₂³	1	1	yes	characteristic
25	C₂²×#261	C₂³	1	8	yes	—
26	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
29	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×D₁₃	—	2	8	no	—
31	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
32	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×D₁₃	D₄	1	4	yes	—
36	C₂×C₄×D₁₃	Q₈	1	4	yes	—
37	C₂×C₄×D₁₃	C₂³	1	2	yes	—
38	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
39	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
40	C₂×C₄×D₁₃	C₂³	1	2	yes	—
41	C₂²⋊#261	—	2	8	no	—
42	C₄⋊#261	—	2	8	no	—
43	C₄⋊#261	—	2	16	no	—
44	C₄×#261	—	2	8	no	—
45	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₄²×C₁₃	C₂×C₄	1	2	yes	—
48	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
49	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
50	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
51	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
52	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
53	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
55	#2285	—	13	1	no	maximal, Sylow
56	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×D₁₃	—	2	4	no	—
58	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₂²×D₁₃	C₂×D₄	1	2	yes	—
60	C₂²×D₁₃	C₂×Q₈	1	2	yes	—
61	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
62	C₂×#261	—	2	8	no	—
63	C₂×#261	—	2	16	no	—
64	C₂×C₄×C₁₃	—	2	4	no	—
65	C₂×C₄×C₁₃	C₄⋊C₄	1	4	yes	complemented
66	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
67	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
70	C₂×Dic₁₃	—	2	4	no	—
71	C₂×Dic₁₃	C₄⋊C₄	1	4	yes	complemented
72	C₂×Dic₁₃	C₂²×C₄	1	2	yes	—
73	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₂×Dic₁₃	C₂²×C₄	1	2	yes	—
76	C₄×D₁₃	—	2	4	no	—
77	C₄×D₁₃	—	2	4	no	—
78	C₄×D₁₃	—	2	4	no	—
79	C₄×D₁₃	C₄⋊C₄	1	4	yes	complemented
80	C₄×D₁₃	C₄⋊C₄	1	4	yes	complemented
81	C₄×D₁₃	C₂×D₄	1	2	yes	—
82	C₄×D₁₃	C₂×D₄	1	2	yes	—
83	C₄×D₁₃	C₂×Q₈	1	2	yes	—
84	C₄×D₁₃	C₂×Q₈	1	2	yes	—
85	C₄×D₁₃	#41	1	8	yes	—
86	C₂×#117	—	13	2	no	—
87	C₂²×C₄²	—	13	1	no	—
88	#384	—	13	2	no	—
89	#382	—	13	2	no	—
90	#380	—	13	4	no	—
91	C₄×C₄⋊C₄	—	13	4	no	—
92	C₂²×C₁₃	—	2	2	no	—
93	C₂²×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
94	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
95	C₂×D₁₃	—	2	2	no	—
96	C₂×D₁₃	—	2	4	no	—
97	C₂×D₁₃	—	2	4	no	—
98	C₂×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
99	C₂×D₁₃	C₂²×D₄	1	1	yes	characteristic
100	C₂×D₁₃	C₂²×Q₈	1	1	yes	characteristic
101	C₂×D₁₃	C₂×#41	1	4	yes	—
102	#261	—	4	8	no	—
103	C₄×C₁₃	—	2	2	no	—
104	C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
105	C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
106	C₄×C₁₃	#117	1	4	yes	complemented
107	Dic₁₃	—	2	2	no	—
108	Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
109	Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
110	Dic₁₃	#117	1	4	yes	complemented
111	C₂³×C₄	—	13	1	no	—
112	C₂³×C₄	—	13	2	no	—
113	#117	—	26	8	no	—
114	C₂×C₄⋊C₄	—	13	4	no	—
115	C₂×C₄⋊C₄	—	13	8	no	—
116	C₂×C₂²⋊C₄	—	13	4	no	—
117	C₂×C₄²	—	13	2	no	—
118	C₂×C₄²	—	13	1	no	—
119	C₂×C₄²	—	13	1	no	—
120	C₂×C₄²	—	13	1	no	—
121	C₂×C₄²	—	13	2	no	—
122	C₂×C₄²	—	13	2	no	—
123	C₂×C₄²	—	13	1	no	—
124	C₂×C₄²	—	13	1	no	—
125	C₂×C₄²	—	13	4	no	—
126	C₂×C₄²	#261	1	1	yes	characteristic, complemented
127	#95	—	13	8	no	—
128	C₂×C₁₃	—	2	2	no	—
129	C₂×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₁₃	C₂×#117	1	2	yes	—
131	D₁₃	—	2	2	no	—
132	D₁₃	#532	1	2	yes	—
133	D₁₃	#533	1	2	yes	—
134	C₂⁴	—	13	1	no	—
135	C₂²×C₄	—	13	1	no	—
136	C₂²×C₄	—	13	4	no	—
137	C₂²×C₄	—	13	4	no	—
138	C₂²×C₄	—	13	1	no	—
139	C₂²×C₄	—	13	2	no	—
140	C₂²×C₄	—	13	1	no	—
141	C₂²×C₄	—	13	1	no	—
142	C₂²×C₄	—	13	1	no	—
143	C₂²×C₄	—	13	2	no	—
144	C₂²×C₄	—	13	2	no	—
145	C₂²×C₄	—	13	2	no	—
146	C₂²×C₄	—	13	2	no	—
147	C₂²×C₄	—	13	8	no	—
148	C₂²×C₄	—	26	8	no	—
149	C₂²×C₄	C₂×#261	1	2	yes	—
150	C₂²×C₄	C₂×#261	1	1	yes	characteristic
151	C₄⋊C₄	—	26	8	no	—
152	C₄⋊C₄	—	26	16	no	—
153	C₂²⋊C₄	—	26	8	no	—
154	C₄²	—	13	2	no	—
155	C₄²	—	13	1	no	—
156	C₄²	—	13	2	no	—
157	C₄²	—	13	2	no	—
158	C₄²	—	13	2	no	—
159	C₄²	—	13	1	no	—
160	C₄²	—	13	2	no	—
161	C₄²	—	26	8	no	—
162	C₄²	C₂×#261	1	1	yes	characteristic
163	C₄²	C₂×#261	1	1	yes	characteristic
164	C₄²	C₂×#261	1	2	yes	—
165	C₁₃	#2285	1	1	yes	characteristic, complemented, Sylow
166	C₂³	—	13	1	no	—
167	C₂³	—	13	2	no	—
168	C₂³	—	13	2	no	—
169	C₂³	—	13	1	no	—
170	C₂³	—	26	4	no	—
171	C₂³	C₂²×#261	1	1	yes	characteristic
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	13	4	no	—
174	C₂×C₄	—	13	1	no	—
175	C₂×C₄	—	13	1	no	—
176	C₂×C₄	—	13	2	no	—
177	C₂×C₄	—	13	2	no	—
178	C₂×C₄	—	13	2	no	—
179	C₂×C₄	—	13	4	no	—
180	C₂×C₄	—	13	4	no	—
181	C₂×C₄	—	13	2	no	—
182	C₂×C₄	—	13	2	no	—
183	C₂×C₄	—	13	8	no	—
184	C₂×C₄	—	13	2	no	—
185	C₂×C₄	—	26	4	no	—
186	C₂×C₄	—	26	4	no	—
187	C₂×C₄	—	26	4	no	—
188	C₂×C₄	—	26	4	no	—
189	C₂×C₄	—	26	8	no	—
190	C₂×C₄	—	26	16	no	—
191	C₂×C₄	C₄⋊#261	1	4	yes	complemented
192	C₂×C₄	C₂²×#261	1	2	yes	—
193	C₂×C₄	C₂²×#261	1	1	yes	characteristic
194	C₂×C₄	C₂²×#261	1	2	yes	—
195	C₂×C₄	C₂²×#261	1	1	yes	characteristic
196	C₂²	—	2	2	no	—
197	C₂²	—	13	1	no	—
198	C₂²	—	13	1	no	—
199	C₂²	—	13	4	no	—
200	C₂²	—	13	2	no	—
201	C₂²	—	26	4	no	—
202	C₂²	—	26	4	no	—
203	C₂²	—	26	2	no	—
204	C₂²	C₂×C₄⋊#261	1	2	yes	—
205	C₂²	C₂³×#261	1	1	yes	characteristic
206	C₄	—	2	2	no	—
207	C₄	—	13	2	no	—
208	C₄	—	13	2	no	—
209	C₄	—	13	4	no	—
210	C₄	—	26	2	no	—
211	C₄	—	52	8	no	—
212	C₄	C₂×C₄⋊#261	1	2	yes	—
213	C₄	C₂×C₄⋊#261	1	2	yes	—
214	C₄	#88237	1	4	yes	complemented
215	C₂	—	2	2	no	—
216	C₂	—	13	2	no	—
217	C₂	—	13	2	no	—
218	C₂	—	26	2	no	—
219	C₂	C₂²×C₄⋊#261	1	1	yes	characteristic
220	C₂	C₂×#88237	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂³×C₄
Frattini	C₂²	C₂³×#261
Fitting	C₂×C₄²×C₁₃	C₄
prime radical	C₂³×D₁₃	C₂³
cosocle	C₂²×D₁₃	C₂⁴
hypercenter	C₂×C₄²	#261
hypocenter	C₁₃	#2285
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #11719060	C₂	semidirect
5. #11719059	C₂	semidirect
6. C₄×C₄⋊#261	C₂	semidirect
14. C₂×C₄²×C₁₃	C₄	semidirect
15. C₂×C₄×Dic₁₃	C₄	semidirect
16. C₂×C₄×Dic₁₃	C₄	semidirect
17. C₄²×D₁₃	C₄	semidirect
18. C₄²×D₁₃	C₄	semidirect
19. C₄²×D₁₃	C₄	semidirect
65. C₂×C₄×C₁₃	C₄⋊C₄	semidirect
71. C₂×Dic₁₃	C₄⋊C₄	semidirect
79. C₄×D₁₃	C₄⋊C₄	semidirect
80. C₄×D₁₃	C₄⋊C₄	semidirect
106. C₄×C₁₃	#117	semidirect
110. Dic₁₃	#117	semidirect
126. C₂×C₄²	#261	semidirect
165. C₁₃	#2285	semidirect
191. C₂×C₄	C₄⋊#261	semidirect
214. C₄	#88237	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88237	2
C₂×C₄²×D₁₃	2
#11719136	2
#11719060	2
#11719059	2
C₄×C₄⋊#261	2
#2285	13