Subgroups — #15873275

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718587	C₂	1	2	yes	maximal
2	#13115560	C₂	1	8	yes	maximal, complemented
3	#13114820	C₂	1	4	yes	maximal
4	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#117	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×#384	C₄	1	2	yes	—
8	C₁₃×#382	C₄	1	2	yes	—
9	C₁₃×#380	C₄	1	4	yes	—
10	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
11	C₂×C₂²⋊#1055	C₂²	1	4	yes	—
12	#11718587	—	2	8	no	—
13	C₂×C₄⋊#1055	C₂²	1	4	yes	—
14	C₂×C₄⋊#1055	C₂²	1	8	yes	—
15	C₂×#88043	C₂²	1	4	yes	—
16	#11718116	C₂²	1	8	yes	—
17	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
19	C₁₃×#117	—	4	4	no	—
20	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
21	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
22	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	D₄	1	4	yes	—
26	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
28	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
29	C₂²×#1055	C₂³	1	8	yes	—
30	C₁₃×#95	C₂×C₄	1	8	yes	—
31	C₂²⋊#1055	—	2	8	no	—
32	C₄⋊#1055	—	2	8	no	—
33	C₄⋊#1055	—	4	8	no	—
34	#88043	—	2	8	no	—
35	#21956	—	13	1	no	maximal, Sylow
36	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	—	2	2	no	—
38	C₂²×C₄×C₁₃	—	2	2	no	—
39	C₂²×C₄×C₁₃	—	4	4	no	—
40	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
41	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
42	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
43	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
48	C₁₃×C₄⋊C₄	—	4	8	no	—
49	C₁₃×C₄⋊C₄	—	4	4	no	—
50	C₁₃×C₂²⋊C₄	—	4	4	no	—
51	C₄²×C₁₃	—	2	8	no	—
52	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
53	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
54	C₄²×C₁₃	C₂×D₄	1	4	yes	—
55	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
56	C₂×#1055	—	2	8	no	—
57	C₂×#1055	—	2	8	no	—
58	C₂×#1055	—	2	8	no	—
59	C₂×#432	—	13	2	no	—
60	#2285	D₁₃	1	1	yes	characteristic
61	#1940	—	13	8	no	—
62	#1798	—	13	4	no	—
63	C₂³×C₁₃	—	2	1	no	—
64	C₂³×C₁₃	—	2	1	no	—
65	C₂³×C₁₃	—	2	4	no	—
66	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
67	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₃	—	2	1	no	—
69	C₂×C₄×C₁₃	—	2	1	no	—
70	C₂×C₄×C₁₃	—	2	4	no	—
71	C₂×C₄×C₁₃	—	2	4	no	—
72	C₂×C₄×C₁₃	—	2	4	no	—
73	C₂×C₄×C₁₃	—	2	4	no	—
74	C₂×C₄×C₁₃	—	2	8	no	—
75	C₂×C₄×C₁₃	—	2	16	no	—
76	C₂×C₄×C₁₃	—	4	8	no	—
77	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
78	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
79	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
80	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
82	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
83	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
84	#1055	—	4	8	no	—
85	C₂×#117	C₂×D₁₃	1	2	yes	—
86	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
87	#432	—	26	8	no	—
88	C₂×C₄⋊C₈	—	13	4	no	—
89	C₂×C₄⋊C₈	—	13	8	no	—
90	C₂×C₂²⋊C₈	—	13	4	no	—
91	C₂×#97	—	13	4	no	—
92	#384	Dic₁₃	1	2	yes	—
93	#382	Dic₁₃	1	2	yes	—
94	#380	Dic₁₃	1	4	yes	—
95	C₄×C₄⋊C₄	C₂×D₁₃	1	4	yes	—
96	#336	—	13	8	no	—
97	C₂²×C₁₃	—	2	2	no	—
98	C₂²×C₁₃	—	2	4	no	—
99	C₂²×C₁₃	—	4	2	no	—
100	C₂²×C₁₃	—	4	2	no	—
101	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
102	C₂²×C₁₃	#518	1	1	yes	characteristic
103	C₂²×C₁₃	#519	1	1	yes	characteristic
104	C₂²×C₁₃	#568	1	4	yes	—
105	C₄×C₁₃	—	2	2	no	—
106	C₄×C₁₃	—	2	4	no	—
107	C₄×C₁₃	—	2	4	no	—
108	C₄×C₁₃	—	4	8	no	—
109	C₄×C₁₃	#537	1	2	yes	—
110	C₄×C₁₃	#544	1	2	yes	—
111	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
112	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
113	C₂²×C₈	—	13	8	no	—
114	#117	—	4	4	no	—
115	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
116	C₂×C₄⋊C₄	C₂×Dic₁₃	1	8	yes	—
117	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	4	yes	—
118	C₂×C₄²	Dic₂₆	1	4	yes	—
119	C₂×C₄²	D₅₂	1	4	yes	—
120	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
121	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
122	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
123	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
124	C₄⋊C₈	—	26	8	no	—
125	C₄⋊C₈	—	52	8	no	—
126	C₂²⋊C₈	—	26	8	no	—
127	#97	—	26	8	no	—
128	#95	C₂×Dic₁₃	1	8	yes	—
129	C₂×C₁₃	—	4	2	no	—
130	C₂×C₁₃	#2316	1	1	yes	characteristic
131	C₂×C₁₃	#2905	1	2	yes	—
132	C₂×C₁₃	#2980	1	2	yes	—
133	C₂×C₁₃	#2987	1	2	yes	—
134	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
135	C₂²×C₄	—	2	2	no	—
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	—	4	4	no	—
138	C₂²×C₄	C₄⋊Dic₁₃	1	8	yes	—
139	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
140	C₂²×C₄	C₂×D₅₂	1	2	yes	—
141	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
142	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
143	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
144	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
145	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
146	C₂×C₈	—	26	8	no	—
147	C₂×C₈	—	26	8	no	—
148	C₂×C₈	—	26	8	no	—
149	C₄⋊C₄	—	4	4	no	—
150	C₄⋊C₄	—	4	8	no	—
151	C₂²⋊C₄	—	4	4	no	—
152	C₄²	—	2	8	no	—
153	C₄²	C₄⋊Dic₁₃	1	4	yes	—
154	C₄²	C₄⋊Dic₁₃	1	4	yes	—
155	C₄²	C₂×Dic₂₆	1	4	yes	—
156	C₄²	C₂×D₅₂	1	4	yes	—
157	C₁₃	#21956	1	1	yes	characteristic, complemented, Sylow
158	C₂³	—	2	1	no	—
159	C₂³	—	2	1	no	—
160	C₂³	—	2	4	no	—
161	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
162	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	2	4	no	—
169	C₂×C₄	—	2	8	no	—
170	C₂×C₄	—	2	16	no	—
171	C₂×C₄	—	4	8	no	—
172	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
173	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
174	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
175	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
176	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
177	C₂×C₄	#88251	1	2	yes	—
178	C₂×C₄	#88254	1	2	yes	—
179	C₈	—	52	8	no	—
180	C₂²	—	2	2	no	—
181	C₂²	—	2	4	no	—
182	C₂²	—	4	2	no	—
183	C₂²	—	4	2	no	—
184	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
185	C₂²	#11719503	1	1	yes	characteristic
186	C₂²	#11719517	1	1	yes	characteristic
187	C₂²	#11719524	1	4	yes	—
188	C₄	—	2	2	no	—
189	C₄	—	2	4	no	—
190	C₄	—	2	4	no	—
191	C₄	—	4	8	no	—
192	C₄	#11719205	1	2	yes	—
193	C₄	#11719215	1	2	yes	—
194	C₂	—	4	2	no	—
195	C₂	#13117454	1	1	yes	characteristic
196	C₂	#13123400	1	2	yes	—
197	C₂	#13123907	1	2	yes	—
198	C₂	#13123942	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2285	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2285	D₁₃
hypocenter	C₁₃	#21956
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2285

Complements

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

N	H ≅ G/N	type
2. #13115560	C₂	semidirect
157. C₁₃	#21956	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718587	2
#13115560	2
#13114820	2
C₁₃×#2285	2
#21956	13