Subgroups — #13129250

Order 1664.

1002 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	#11719530	C₂	1	4	yes	maximal, complemented
3	#11719427	C₂	1	2	yes	maximal, complemented
4	#11719418	C₂	1	2	yes	maximal, complemented
5	#11719377	C₂	1	4	yes	maximal, complemented
6	#11719308	C₂	1	8	yes	maximal, complemented
7	#11719247	C₂	1	4	yes	maximal, complemented
8	D₄×Dic₂₆	C₂	1	4	yes	maximal, complemented
9	#11719175	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#41	C₂²	1	2	yes	—
11	C₂²×Dic₂₆	C₂²	1	4	yes	—
12	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₁₃×#124	C₂²	1	2	yes	—
15	C₁₃×#121	C₂²	1	4	yes	—
16	C₄×D₄×C₁₃	C₂²	1	4	yes	—
17	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	#88198	C₂²	1	8	yes	—
19	#88190	C₂²	1	8	yes	—
20	#88190	C₂²	1	8	yes	—
21	#88189	C₂²	1	8	yes	—
22	#88189	C₂²	1	8	yes	—
23	D₄×Dic₁₃	C₂²	1	8	yes	—
24	#88180	C₂²	1	4	yes	—
25	#88180	C₂²	1	4	yes	—
26	#88178	C₂²	1	4	yes	—
27	#88178	C₂²	1	4	yes	—
28	#88178	C₂²	1	8	yes	—
29	#88142	C₂²	1	8	yes	—
30	#88141	C₂²	1	8	yes	—
31	#88133	C₂²	1	16	yes	—
32	#88132	C₂²	1	16	yes	—
33	#88124	C₂²	1	4	yes	—
34	#88123	C₂²	1	2	yes	—
35	#88123	C₂²	1	2	yes	—
36	C₄×Dic₂₆	C₂²	1	4	yes	—
37	C₄×Dic₂₆	C₂²	1	4	yes	—
38	C₁₃×#41	—	4	4	no	—
39	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
40	C₂×D₄×C₁₃	C₂³	1	4	yes	—
41	C₂×D₄×C₁₃	C₂³	1	2	yes	—
42	C₂×D₄×C₁₃	C₂³	1	4	yes	—
43	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
46	C₂²×Dic₁₃	C₂³	1	8	yes	—
47	C₂×Dic₂₆	—	4	8	no	—
48	C₂×Dic₂₆	C₂³	1	4	yes	—
49	C₂×Dic₂₆	C₂³	1	4	yes	—
50	C₂×Dic₂₆	C₂³	1	8	yes	—
51	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
52	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
53	C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₄²×C₁₃	C₂³	1	2	yes	—
55	C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²⋊Dic₁₃	C₂³	1	16	yes	—
57	C₂²⋊Dic₁₃	C₂³	1	8	yes	—
58	C₂²⋊Dic₁₃	C₂³	1	8	yes	—
59	C₄⋊Dic₁₃	C₂³	1	4	yes	—
60	C₄⋊Dic₁₃	C₂³	1	4	yes	—
61	C₄⋊Dic₁₃	C₂³	1	4	yes	—
62	C₄⋊Dic₁₃	C₂³	1	4	yes	—
63	#6101	C₂³	1	8	yes	—
64	#6101	C₂³	1	8	yes	—
65	#6101	C₂³	1	16	yes	—
66	C₄×Dic₁₃	C₂³	1	8	yes	—
67	C₄×Dic₁₃	C₂³	1	8	yes	—
68	#3550	—	13	1	no	maximal, Sylow
69	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
70	C₂³×C₁₃	C₂⁴	1	4	yes	—
71	Q₈×C₁₃	—	4	2	no	—
72	D₄×C₁₃	—	2	8	no	—
73	D₄×C₁₃	—	4	4	no	—
74	D₄×C₁₃	—	4	2	no	—
75	C₂×C₄×C₁₃	—	2	8	no	—
76	C₂×C₄×C₁₃	—	2	2	no	—
77	C₂×C₄×C₁₃	—	2	4	no	—
78	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
79	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
81	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
83	C₂×Dic₁₃	—	4	8	no	—
84	C₂×Dic₁₃	C₂⁴	1	8	yes	—
85	C₂×Dic₁₃	C₂⁴	1	8	yes	—
86	Dic₂₆	—	2	8	no	—
87	Dic₂₆	—	2	8	no	—
88	Dic₂₆	—	4	8	no	—
89	#563	—	13	4	no	—
90	#559	—	13	2	no	—
91	Q₈²	—	13	2	no	—
92	#556	—	13	4	no	—
93	D₄×Q₈	—	13	4	no	—
94	#542	—	13	8	no	—
95	#536	—	13	4	no	—
96	#533	—	13	2	no	—
97	#532	D₁₃	1	1	yes	characteristic
98	C₂²×C₁₃	—	2	4	no	—
99	C₂²×C₁₃	—	2	1	no	—
100	C₂²×C₁₃	—	2	2	no	—
101	C₂²×C₁₃	—	2	8	no	—
102	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
103	C₄×C₁₃	—	2	4	no	—
104	C₄×C₁₃	—	2	1	no	—
105	C₄×C₁₃	—	2	2	no	—
106	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
107	C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
108	Dic₁₃	—	2	8	no	—
109	Dic₁₃	—	2	8	no	—
110	C₂×#41	C₂×D₁₃	1	2	yes	—
111	C₂²×Q₈	—	13	4	no	—
112	C₄⋊Q₈	—	13	8	no	—
113	C₄⋊Q₈	—	13	8	no	—
114	C₄⋊Q₈	—	13	2	no	—
115	C₄⋊Q₈	—	13	2	no	—
116	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
117	#127	C₂×D₁₃	1	1	yes	characteristic
118	#126	—	13	16	no	—
119	#125	—	13	4	no	—
120	#124	—	13	8	no	—
121	#124	—	13	8	no	—
122	#124	C₂×D₁₃	1	2	yes	—
123	#123	—	13	8	no	—
124	#123	—	13	8	no	—
125	C₂²⋊Q₈	—	13	4	no	—
126	C₂²⋊Q₈	—	13	4	no	—
127	C₂²⋊Q₈	—	13	8	no	—
128	C₂²⋊Q₈	—	13	16	no	—
129	#121	C₂×D₁₃	1	4	yes	—
130	C₄×Q₈	—	13	8	no	—
131	C₄×Q₈	—	13	4	no	—
132	C₄×Q₈	—	13	4	no	—
133	C₄×D₄	—	13	8	no	—
134	C₄×D₄	C₂×D₁₃	1	4	yes	—
135	#117	—	13	4	no	—
136	#117	—	13	4	no	—
137	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
138	C₂×C₁₃	—	4	4	no	—
139	C₂×C₁₃	—	4	1	no	—
140	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
141	C₂×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
142	#41	—	4	4	no	—
143	C₂×Q₈	—	13	4	no	—
144	C₂×Q₈	—	13	4	no	—
145	C₂×Q₈	—	13	8	no	—
146	C₂×Q₈	—	52	8	no	—
147	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
148	C₂×D₄	C₂²×D₁₃	1	4	yes	—
149	C₂×D₄	C₂²×D₁₃	1	4	yes	—
150	C₂×D₄	C₂²×D₁₃	1	2	yes	—
151	C₂²×C₄	—	13	8	no	—
152	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
153	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
154	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
155	C₄⋊C₄	—	13	4	no	—
156	C₄⋊C₄	—	13	4	no	—
157	C₄⋊C₄	—	13	4	no	—
158	C₄⋊C₄	—	13	4	no	—
159	C₄⋊C₄	—	13	8	no	—
160	C₄⋊C₄	—	13	16	no	—
161	C₄⋊C₄	—	13	8	no	—
162	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
163	C₂²⋊C₄	—	13	8	no	—
164	C₂²⋊C₄	—	13	8	no	—
165	C₂²⋊C₄	—	13	16	no	—
166	C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
167	C₄²	—	13	8	no	—
168	C₄²	—	13	8	no	—
169	C₄²	C₂²×D₁₃	1	2	yes	—
170	C₄²	C₂²×D₁₃	1	1	yes	characteristic
171	C₄²	C₂²×D₁₃	1	1	yes	characteristic
172	C₁₃	#3550	1	1	yes	characteristic, complemented, Sylow
173	C₂³	C₂³×D₁₃	1	1	yes	characteristic
174	C₂³	C₂³×D₁₃	1	4	yes	—
175	Q₈	—	4	2	no	—
176	Q₈	—	26	8	no	—
177	Q₈	—	26	8	no	—
178	Q₈	—	52	8	no	—
179	D₄	—	2	8	no	—
180	D₄	—	4	2	no	—
181	D₄	—	4	4	no	—
182	C₂×C₄	—	2	8	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	13	8	no	—
186	C₂×C₄	—	13	8	no	—
187	C₂×C₄	—	52	8	no	—
188	C₂×C₄	C₂³×D₁₃	1	4	yes	—
189	C₂×C₄	C₂³×D₁₃	1	2	yes	—
190	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
191	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
192	C₂×C₄	C₂³×D₁₃	1	2	yes	—
193	C₂²	—	2	4	no	—
194	C₂²	—	2	1	no	—
195	C₂²	—	2	2	no	—
196	C₂²	—	2	8	no	—
197	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
198	C₄	—	2	1	no	—
199	C₄	—	2	4	no	—
200	C₄	—	2	2	no	—
201	C₄	—	26	8	no	—
202	C₄	—	26	8	no	—
203	C₄	#88251	1	2	yes	—
204	C₄	#88257	1	4	yes	—
205	C₂	—	4	4	no	—
206	C₂	—	4	1	no	—
207	C₂	C₂×#88251	1	1	yes	characteristic
208	C₂	C₂×#88257	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting, prime radical	C₁₃×#532	C₂
hypercenter	#532	D₁₃
hypocenter	C₁₃	#3550
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
2. #11719530	C₂	semidirect
3. #11719427	C₂	semidirect
4. #11719418	C₂	semidirect
5. #11719377	C₂	semidirect
6. #11719308	C₂	semidirect
7. #11719247	C₂	semidirect
8. D₄×Dic₂₆	C₂	semidirect
9. #11719175	C₂	semidirect
172. C₁₃	#3550	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#532	2
#11719530	2
#11719427	2
#11719418	2
#11719377	2
#11719308	2
#11719247	2
D₄×Dic₂₆	2
#11719175	2
#3550	13