Subgroups — D₁₃⋊#568 #13131828

Order 1664.

1460 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₃	C₂	1	1	yes	maximal, characteristic
2	#11719629	C₂	1	8	yes	maximal, complemented
3	D₁₃⋊#131	C₂	1	8	yes	maximal, complemented
4	#11719625	C₂	1	2	yes	maximal, complemented
5	#11719621	C₂	1	6	yes	maximal, complemented
6	C₂×D₁₃⋊M₁₆	C₂	1	6	yes	maximal, complemented
7	C₂×C₁₃×#41	C₄	1	1	yes	characteristic
8	#41×D₁₃	C₄	1	4	yes	—
9	#41×D₁₃	C₄	1	4	yes	—
10	#41×D₁₃	C₂²	1	4	yes	—
11	#41×D₁₃	C₂²	1	4	yes	—
12	C₂×#6131	C₂²	1	1	yes	characteristic
13	C₂×Q₈×D₁₃	C₄	1	1	yes	characteristic
14	C₂×#6129	C₂²	1	3	yes	—
15	C₂×D₄×D₁₃	C₄	1	3	yes	—
16	C₂×#6127	C₄	1	3	yes	—
17	C₂²×C₄×D₁₃	C₂²	1	3	yes	—
18	C₂×#6122	C₂²	1	12	yes	complemented
19	#88240	C₂²	1	16	yes	complemented
20	#88238	C₂²	1	48	yes	complemented
21	D₁₃⋊M₁₆	C₂²	1	4	yes	—
22	D₁₃⋊M₁₆	C₂²	1	12	yes	complemented
23	D₁₃⋊M₁₆	C₂²	1	12	yes	complemented
24	D₁₃⋊M₁₆	C₂²	1	12	yes	complemented
25	C₂×#6118	C₂²	1	12	yes	complemented
26	C₂×D₁₃⋊C₈	C₂²	1	12	yes	complemented
27	C₂³×D₁₃	C₂×C₄	1	3	yes	—
28	C₁₃×#41	C₂×C₄	1	4	yes	—
29	C₁₃×#41	C₂×C₄	1	4	yes	—
30	C₂×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×D₄×C₁₃	C₂×C₄	1	3	yes	—
32	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
33	C₂×C₂²⋊D₁₃	C₂×C₄	1	6	yes	—
34	C₂²×Dic₁₃	C₂³	1	3	yes	—
35	#6131	C₂×C₄	1	4	yes	—
36	#6131	C₂³	1	4	yes	—
37	Q₈×D₁₃	C₂×C₄	1	4	yes	—
38	Q₈×D₁₃	C₂×C₄	1	4	yes	—
39	#6129	C₂×C₄	1	12	yes	—
40	#6129	C₂³	1	12	yes	—
41	D₄×D₁₃	C₂×C₄	1	12	yes	—
42	D₄×D₁₃	C₂×C₄	1	12	yes	—
43	#6127	C₂×C₄	1	12	yes	—
44	#6127	C₂×C₄	1	12	yes	—
45	C₂×D₅₂	C₂×C₄	1	3	yes	—
46	C₂×C₄×D₁₃	C₂×C₄	1	3	yes	—
47	C₂×C₄×D₁₃	C₂×C₄	1	3	yes	—
48	C₂×C₄×D₁₃	C₂×C₄	1	6	yes	—
49	C₂×C₄×D₁₃	C₂×C₄	1	6	yes	—
50	C₂×C₄×D₁₃	C₂³	1	6	yes	—
51	C₂×C₄×D₁₃	C₂³	1	6	yes	—
52	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄×D₁₃	C₂³	1	3	yes	—
54	C₂×Dic₂₆	C₂×C₄	1	3	yes	—
55	#6122	C₂³	1	8	yes	—
56	#6122	C₂³	1	24	yes	complemented
57	C₂×#1057	C₂³	1	24	yes	complemented
58	#6118	C₂³	1	8	yes	—
59	#6118	C₂³	1	24	yes	complemented
60	D₁₃⋊C₈	C₂³	1	8	yes	—
61	D₁₃⋊C₈	C₂³	1	24	yes	complemented
62	C₂×#568	—	13	1	no	maximal, Sylow
63	C₂³×C₁₃	C₂²×C₄	1	3	yes	—
64	C₂²×D₁₃	—	4	6	no	—
65	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₂²×D₁₃	C₂²×C₄	1	6	yes	—
67	C₂²×D₁₃	C₂²×C₄	1	3	yes	—
68	C₂²×D₁₃	C₂²×C₄	1	6	yes	—
69	Q₈×C₁₃	C₂²×C₄	1	4	yes	—
70	D₄×C₁₃	C₂²×C₄	1	12	yes	—
71	C₂×C₄×C₁₃	C₂²×C₄	1	3	yes	—
72	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂²×C₄	1	6	yes	—
74	C₂×C₄×C₁₃	C₂²×C₄	1	6	yes	—
75	C₂²⋊D₁₃	C₂²×C₄	1	24	yes	—
76	C₂×Dic₁₃	C₂²×C₄	1	3	yes	—
77	C₂×Dic₁₃	C₂²×C₄	1	6	yes	—
78	C₂×Dic₁₃	C₂⁴	1	6	yes	—
79	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
80	D₅₂	C₂²×C₄	1	12	yes	—
81	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₄×D₁₃	C₂²×C₄	1	6	yes	—
84	C₄×D₁₃	C₂²×C₄	1	6	yes	—
85	C₄×D₁₃	C₂²×C₄	1	6	yes	—
86	C₄×D₁₃	C₂²×C₄	1	6	yes	—
87	C₄×D₁₃	C₂²×C₄	1	6	yes	—
88	C₄×D₁₃	C₂⁴	1	1	yes	characteristic
89	C₄×D₁₃	C₂⁴	1	6	yes	—
90	C₄×D₁₃	C₂⁴	1	1	yes	characteristic
91	Dic₂₆	C₂²×C₄	1	12	yes	—
92	#1057	C₂⁴	1	16	yes	—
93	C₂²×#41	—	13	1	no	—
94	#568	—	13	6	no	—
95	#568	—	13	2	no	—
96	#568	—	13	8	no	—
97	C₂×#131	—	13	8	no	—
98	C₂²×M₁₆	—	13	6	no	—
99	C₂²×C₁₃	—	4	3	no	—
100	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
101	C₂²×C₁₃	C₂³×C₄	1	6	yes	—
102	C₂×D₁₃	—	2	2	no	—
103	C₂×D₁₃	—	2	12	no	—
104	C₂×D₁₃	—	4	6	no	—
105	C₂×D₁₃	—	4	3	no	—
106	C₂×D₁₃	C₂³×C₄	1	1	yes	characteristic
107	C₂×D₁₃	C₂³×C₄	1	6	yes	—
108	C₂×D₁₃	C₂³×C₄	1	1	yes	characteristic
109	C₄×C₁₃	C₂³×C₄	1	6	yes	—
110	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
111	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
112	Dic₁₃	C₂³×C₄	1	6	yes	—
113	Dic₁₃	C₂³×C₄	1	1	yes	characteristic
114	Dic₁₃	C₂⁵	1	1	yes	characteristic
115	C₂×#41	—	13	4	no	—
116	C₂×#41	—	13	4	no	—
117	C₂×#41	—	13	4	no	—
118	C₂×#41	—	13	4	no	—
119	C₂×#41	—	13	1	no	—
120	C₂×#41	—	13	3	no	—
121	C₂×#41	—	13	3	no	—
122	C₂×#41	#261	1	1	yes	characteristic
123	C₂²×Q₈	—	13	1	no	—
124	C₂²×D₄	—	13	3	no	—
125	C₂³×C₄	—	13	3	no	—
126	#131	—	13	48	no	—
127	#131	—	13	16	no	—
128	C₂×M₁₆	—	13	4	no	—
129	C₂×M₁₆	—	13	12	no	—
130	C₂×M₁₆	—	13	12	no	—
131	C₂×M₁₆	—	13	12	no	—
132	C₂×M₁₆	—	13	12	no	—
133	C₂×M₁₆	—	13	12	no	—
134	C₂²×C₈	—	13	12	no	—
135	C₂×C₁₃	—	2	1	no	—
136	C₂×C₁₃	—	2	6	no	—
137	C₂×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
138	D₁₃	—	2	1	no	—
139	D₁₃	—	2	6	no	—
140	D₁₃	#568	1	2	yes	complemented
141	C₂⁴	—	13	3	no	—
142	#41	—	13	4	no	—
143	#41	—	13	4	no	—
144	#41	—	13	12	no	—
145	#41	—	13	12	no	—
146	#41	—	13	12	no	—
147	#41	—	13	12	no	—
148	#41	C₂×#261	1	4	yes	—
149	#41	C₂×#261	1	4	yes	—
150	C₂×Q₈	—	13	4	no	—
151	C₂×Q₈	—	13	4	no	—
152	C₂×Q₈	—	13	3	no	—
153	C₂×Q₈	C₂×#261	1	1	yes	characteristic
154	C₂×D₄	—	13	6	no	—
155	C₂×D₄	—	13	12	no	—
156	C₂×D₄	—	13	12	no	—
157	C₂×D₄	—	13	3	no	—
158	C₂×D₄	C₂×#261	1	3	yes	—
159	C₂²×C₄	—	13	3	no	—
160	C₂²×C₄	—	13	6	no	—
161	C₂²×C₄	—	13	1	no	—
162	C₂²×C₄	—	13	6	no	—
163	C₂²×C₄	—	13	3	no	—
164	C₂²×C₄	—	13	3	no	—
165	C₂²×C₄	—	13	3	no	—
166	C₂²×C₄	—	13	6	no	—
167	C₂²×C₄	—	13	6	no	—
168	C₂²×C₄	C₂×#261	1	3	yes	—
169	M₁₆	—	13	8	no	—
170	M₁₆	—	13	8	no	—
171	M₁₆	—	13	24	no	—
172	M₁₆	—	13	24	no	—
173	C₂×C₈	—	13	8	no	—
174	C₂×C₈	—	13	24	no	—
175	C₂×C₈	—	13	24	no	—
176	C₁₃	C₂×#568	1	1	yes	characteristic, complemented, Sylow
177	C₂³	—	13	1	no	—
178	C₂³	—	13	6	no	—
179	C₂³	—	13	6	no	—
180	C₂³	—	13	3	no	—
181	C₂³	—	52	6	no	—
182	C₂³	C₂²×#261	1	3	yes	—
183	Q₈	—	13	12	no	—
184	Q₈	C₂²×#261	1	4	yes	—
185	D₄	—	13	24	no	—
186	D₄	—	13	12	no	—
187	D₄	C₂²×#261	1	12	yes	—
188	C₂×C₄	—	13	6	no	—
189	C₂×C₄	—	13	1	no	—
190	C₂×C₄	—	13	3	no	—
191	C₂×C₄	—	13	6	no	—
192	C₂×C₄	—	13	6	no	—
193	C₂×C₄	—	13	1	no	—
194	C₂×C₄	—	13	1	no	—
195	C₂×C₄	—	13	6	no	—
196	C₂×C₄	—	13	6	no	—
197	C₂×C₄	—	13	6	no	—
198	C₂×C₄	—	13	6	no	—
199	C₂×C₄	—	13	1	no	—
200	C₂×C₄	—	13	1	no	—
201	C₂×C₄	—	13	6	no	—
202	C₂×C₄	C₂²×#261	1	3	yes	—
203	C₂×C₄	C₂²×#261	1	6	yes	—
204	C₂×C₄	C₂²×#261	1	1	yes	characteristic
205	C₂×C₄	C₂²×#261	1	6	yes	—
206	C₈	—	13	16	no	—
207	C₂²	—	4	3	no	—
208	C₂²	—	13	1	no	—
209	C₂²	—	13	1	no	—
210	C₂²	—	13	6	no	—
211	C₂²	—	26	12	no	—
212	C₂²	—	26	2	no	—
213	C₂²	—	52	3	no	—
214	C₂²	—	52	6	no	—
215	C₂²	C₂³×#261	1	1	yes	characteristic
216	C₂²	C₂³×#261	1	6	yes	—
217	C₄	—	13	1	no	—
218	C₄	—	13	6	no	—
219	C₄	—	13	1	no	—
220	C₄	C₂³×#261	1	1	yes	characteristic
221	C₄	C₂³×#261	1	6	yes	—
222	C₄	C₂³×#261	1	1	yes	characteristic
223	C₂	—	2	1	no	—
224	C₂	—	2	6	no	—
225	C₂	—	13	2	no	—
226	C₂	—	26	1	no	—
227	C₂	—	26	6	no	—
228	C₂	C₂⁴×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂³×#261
commutator, socle	C₂×C₁₃	C₂⁴×C₄
Frattini	C₂	C₂⁴×#261
Fitting	C₂×C₁₃×#41	C₄
prime radical	C₂×#41×D₁₃	C₂
cosocle	Dic₁₃	C₂⁵
hypercenter	C₂×#41	#261
hypocenter	C₁₃	C₂×#568
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. #11719629	C₂	semidirect
3. D₁₃⋊#131	C₂	semidirect
4. #11719625	C₂	semidirect
5. #11719621	C₂	semidirect
6. C₂×D₁₃⋊M₁₆	C₂	semidirect
18. C₂×#6122	C₂²	semidirect
19. #88240	C₂²	semidirect
20. #88238	C₂²	semidirect
22. D₁₃⋊M₁₆	C₂²	semidirect
23. D₁₃⋊M₁₆	C₂²	semidirect
24. D₁₃⋊M₁₆	C₂²	semidirect
25. C₂×#6118	C₂²	semidirect
26. C₂×D₁₃⋊C₈	C₂²	semidirect
56. #6122	C₂³	semidirect
57. C₂×#1057	C₂³	semidirect
59. #6118	C₂³	semidirect
61. D₁₃⋊C₈	C₂³	semidirect
140. D₁₃	#568	semidirect
176. C₁₃	C₂×#568	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₃	2
#11719629	2
D₁₃⋊#131	2
#11719625	2
#11719621	2
C₂×D₁₃⋊M₁₆	2
C₂×#568	13

Subgroups — D13⋊#568 #13131828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#568 #13131828