Subgroups — D₁₃⋊#3573 #16809654

Order 3328.

10858 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131832	C₂	1	12	yes	maximal, complemented
2	#13131831	C₂	1	20	yes	maximal, complemented
3	D₁₃⋊#568	C₂	1	15	yes	maximal, complemented
4	C₂×D₁₃⋊#131	C₂	1	15	yes	maximal, complemented
5	D₁₃×#585	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#585	C₄	1	1	yes	characteristic
7	#11719652	C₂²	1	6	yes	—
8	D₁₃×2₋¹⁺⁴	C₄	1	6	yes	—
9	#11719650	C₂²	1	10	yes	—
10	D₁₃×H(5,𝔽₂)	C₄	1	10	yes	—
11	#11719648	C₄	1	15	yes	—
12	C₂×#41×D₁₃	C₂²	1	15	yes	—
13	#11719629	C₂²	1	120	yes	complemented
14	D₁₃⋊#131	C₂²	1	20	yes	complemented
15	D₁₃⋊#131	C₂²	1	60	yes	complemented
16	D₁₃⋊#131	C₂²	1	120	yes	complemented
17	#11719625	C₂²	1	30	yes	complemented
18	C₂×#88240	C₂²	1	30	yes	complemented
19	#11719621	C₂²	1	90	yes	complemented
20	C₂×#88238	C₂²	1	90	yes	complemented
21	C₂×D₁₃⋊M₁₆	C₂²	1	45	yes	complemented
22	C₂²×D₁₃⋊C₈	C₂²	1	15	yes	complemented
23	C₁₃×2₋¹⁺⁴	C₂×C₄	1	6	yes	—
24	C₁₃×H(5,𝔽₂)	C₂×C₄	1	10	yes	—
25	C₂×C₁₃×#41	C₂×C₄	1	15	yes	—
26	#88257	C₂×C₄	1	60	yes	—
27	#88256	C₂×C₄	1	60	yes	—
28	#41×D₁₃	C₂×C₄	1	60	yes	—
29	#41×D₁₃	C₂×C₄	1	60	yes	—
30	#41×D₁₃	C₂³	1	20	yes	—
31	#41×D₁₃	C₂³	1	60	yes	—
32	#88254	C₂×C₄	1	30	yes	—
33	C₂×#6131	C₂³	1	15	yes	—
34	C₂×Q₈×D₁₃	C₂×C₄	1	15	yes	—
35	#88251	C₂×C₄	1	90	yes	—
36	C₂×#6129	C₂³	1	45	yes	—
37	C₂×D₄×D₁₃	C₂×C₄	1	45	yes	—
38	C₂×#6127	C₂×C₄	1	45	yes	—
39	C₂²×C₄×D₁₃	C₂³	1	15	yes	—
40	C₂×#6122	C₂³	1	90	yes	complemented
41	C₂²×#1057	C₂³	1	30	yes	complemented
42	#88240	C₂³	1	40	yes	complemented
43	#88240	C₂³	1	120	yes	complemented
44	#88238	C₂³	1	120	yes	complemented
45	#88238	C₂³	1	360	yes	complemented
46	D₁₃⋊M₁₆	C₂³	1	60	yes	—
47	D₁₃⋊M₁₆	C₂³	1	180	yes	complemented
48	C₂×#6118	C₂³	1	90	yes	complemented
49	C₂×D₁₃⋊C₈	C₂³	1	15	yes	—
50	C₂×D₁₃⋊C₈	C₂³	1	45	yes	—
51	C₂×D₁₃⋊C₈	C₂³	1	90	yes	complemented
52	C₂×#3573	—	13	1	no	maximal, Sylow
53	C₂³×D₁₃	C₂²×C₄	1	15	yes	—
54	C₁₃×#41	C₂²×C₄	1	20	yes	—
55	C₁₃×#41	C₂²×C₄	1	60	yes	—
56	C₂×Q₈×C₁₃	C₂²×C₄	1	15	yes	—
57	C₂×D₄×C₁₃	C₂²×C₄	1	45	yes	—
58	C₂²×C₄×C₁₃	C₂²×C₄	1	15	yes	—
59	C₂×C₂²⋊D₁₃	C₂²×C₄	1	90	yes	—
60	C₂²×Dic₁₃	C₂⁴	1	15	yes	—
61	#6131	C₂²×C₄	1	60	yes	—
62	#6131	C₂⁴	1	20	yes	—
63	Q₈×D₁₃	C₂²×C₄	1	20	yes	—
64	Q₈×D₁₃	C₂²×C₄	1	60	yes	—
65	#6129	C₂²×C₄	1	180	yes	—
66	#6129	C₂⁴	1	60	yes	—
67	D₄×D₁₃	C₂²×C₄	1	60	yes	—
68	D₄×D₁₃	C₂²×C₄	1	180	yes	—
69	#6127	C₂²×C₄	1	60	yes	—
70	#6127	C₂²×C₄	1	180	yes	—
71	C₂×D₅₂	C₂²×C₄	1	45	yes	—
72	C₂×C₄×D₁₃	C₂²×C₄	1	45	yes	—
73	C₂×C₄×D₁₃	C₂²×C₄	1	45	yes	—
74	C₂×C₄×D₁₃	C₂⁴	1	15	yes	—
75	C₂×C₄×D₁₃	C₂⁴	1	45	yes	—
76	C₂×Dic₂₆	C₂²×C₄	1	45	yes	—
77	#6122	C₂⁴	1	120	yes	—
78	C₂×#1057	C₂⁴	1	30	yes	—
79	C₂×#1057	C₂⁴	1	90	yes	—
80	#6118	C₂⁴	1	120	yes	—
81	D₁₃⋊C₈	C₂⁴	1	1	yes	characteristic
82	D₁₃⋊C₈	C₂⁴	1	15	yes	—
83	D₁₃⋊C₈	C₂⁴	1	30	yes	—
84	D₁₃⋊C₈	C₂⁴	1	90	yes	—
85	C₂×#585	—	13	1	no	—
86	#3573	—	13	20	no	—
87	#3573	—	13	12	no	—
88	C₂×#568	—	13	15	no	—
89	C₂²×#131	—	13	15	no	—
90	C₂³×C₁₃	C₂³×C₄	1	15	yes	—
91	C₂²×D₁₃	—	4	30	no	—
92	C₂²×D₁₃	C₂³×C₄	1	15	yes	—
93	C₂²×D₁₃	C₂³×C₄	1	45	yes	—
94	Q₈×C₁₃	C₂³×C₄	1	20	yes	—
95	D₄×C₁₃	C₂³×C₄	1	60	yes	—
96	C₂×C₄×C₁₃	C₂³×C₄	1	45	yes	—
97	C₂×C₄×C₁₃	C₂³×C₄	1	15	yes	—
98	C₂²⋊D₁₃	C₂³×C₄	1	120	yes	—
99	C₂×Dic₁₃	C₂³×C₄	1	45	yes	—
100	C₂×Dic₁₃	C₂⁵	1	15	yes	—
101	D₅₂	C₂³×C₄	1	60	yes	—
102	C₄×D₁₃	C₂³×C₄	1	15	yes	—
103	C₄×D₁₃	C₂³×C₄	1	15	yes	—
104	C₄×D₁₃	C₂³×C₄	1	90	yes	—
105	C₄×D₁₃	C₂⁵	1	1	yes	characteristic
106	C₄×D₁₃	C₂⁵	1	15	yes	—
107	Dic₂₆	C₂³×C₄	1	60	yes	—
108	#1057	C₂⁵	1	2	yes	—
109	#1057	C₂⁵	1	30	yes	—
110	#585	—	13	6	no	—
111	#585	—	13	10	no	—
112	#585	—	13	15	no	—
113	#585	#261	1	1	yes	characteristic
114	C₂×2₋¹⁺⁴	—	13	6	no	—
115	C₂×H(5,𝔽₂)	—	13	10	no	—
116	C₂²×#41	—	13	15	no	—
117	#568	—	13	90	no	—
118	#568	—	13	30	no	—
119	#568	—	13	120	no	—
120	C₂×#131	—	13	90	no	—
121	C₂×#131	—	13	30	no	—
122	C₂×#131	—	13	20	no	—
123	C₂×#131	—	13	60	no	—
124	C₂×#131	—	13	120	no	—
125	C₂²×M₁₆	—	13	45	no	—
126	C₂³×C₈	—	13	15	no	—
127	C₂²×C₁₃	—	4	15	no	—
128	C₂²×C₁₃	C₂⁴×C₄	1	15	yes	—
129	C₂×D₁₃	—	2	30	no	—
130	C₂×D₁₃	—	4	45	no	—
131	C₂×D₁₃	C₂⁴×C₄	1	15	yes	—
132	C₂×D₁₃	C₂⁴×C₄	1	1	yes	characteristic
133	C₄×C₁₃	C₂⁴×C₄	1	15	yes	—
134	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
135	Dic₁₃	C₂⁴×C₄	1	15	yes	—
136	Dic₁₃	C₂⁶	1	1	yes	characteristic
137	2₋¹⁺⁴	—	13	60	no	—
138	2₋¹⁺⁴	—	13	30	no	—
139	2₋¹⁺⁴	C₂×#261	1	6	yes	—
140	H(5,𝔽₂)	—	13	60	no	—
141	H(5,𝔽₂)	—	13	90	no	—
142	H(5,𝔽₂)	C₂×#261	1	10	yes	—
143	C₂×#41	—	13	20	no	—
144	C₂×#41	—	13	60	no	—
145	C₂×#41	—	13	60	no	—
146	C₂×#41	—	13	60	no	—
147	C₂×#41	—	13	15	no	—
148	C₂×#41	—	13	45	no	—
149	C₂×#41	—	13	45	no	—
150	C₂×#41	C₂×#261	1	15	yes	—
151	C₂²×Q₈	—	13	15	no	—
152	C₂²×D₄	—	13	45	no	—
153	C₂³×C₄	—	13	15	no	—
154	#131	—	13	120	no	—
155	#131	—	13	40	no	—
156	#131	—	13	360	no	—
157	#131	—	13	120	no	—
158	C₂×M₁₆	—	13	60	no	—
159	C₂×M₁₆	—	13	90	no	—
160	C₂×M₁₆	—	13	180	no	—
161	C₂×M₁₆	—	13	90	no	—
162	C₂²×C₈	—	13	15	no	—
163	C₂²×C₈	—	13	45	no	—
164	C₂²×C₈	—	13	90	no	—
165	C₂²×C₈	—	13	30	no	—
166	C₂×C₁₃	—	2	15	no	—
167	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
168	D₁₃	—	2	15	no	—
169	D₁₃	#3573	1	2	yes	complemented
170	C₂⁴	—	13	15	no	—
171	#41	—	13	20	no	—
172	#41	—	13	60	no	—
173	#41	—	13	60	no	—
174	#41	—	13	180	no	—
175	#41	—	13	60	no	—
176	#41	—	13	180	no	—
177	#41	C₂²×#261	1	20	yes	—
178	#41	C₂²×#261	1	60	yes	—
179	C₂×Q₈	—	13	20	no	—
180	C₂×Q₈	—	13	60	no	—
181	C₂×Q₈	—	13	45	no	—
182	C₂×Q₈	C₂²×#261	1	15	yes	—
183	C₂×D₄	—	13	90	no	—
184	C₂×D₄	—	13	60	no	—
185	C₂×D₄	—	13	180	no	—
186	C₂×D₄	—	13	45	no	—
187	C₂×D₄	C₂²×#261	1	45	yes	—
188	C₂²×C₄	—	13	15	no	—
189	C₂²×C₄	—	13	15	no	—
190	C₂²×C₄	—	13	45	no	—
191	C₂²×C₄	—	13	45	no	—
192	C₂²×C₄	—	13	45	no	—
193	C₂²×C₄	C₂²×#261	1	15	yes	—
194	M₁₆	—	13	120	no	—
195	M₁₆	—	13	120	no	—
196	C₂×C₈	—	13	1	no	—
197	C₂×C₈	—	13	15	no	—
198	C₂×C₈	—	13	30	no	—
199	C₂×C₈	—	13	30	no	—
200	C₂×C₈	—	13	90	no	—
201	C₂×C₈	—	13	90	no	—
202	C₁₃	C₂×#3573	1	1	yes	characteristic, complemented, Sylow
203	C₂³	—	13	15	no	—
204	C₂³	—	13	45	no	—
205	C₂³	—	52	30	no	—
206	C₂³	C₂³×#261	1	15	yes	—
207	Q₈	—	13	60	no	—
208	Q₈	C₂³×#261	1	20	yes	—
209	D₄	—	13	120	no	—
210	D₄	—	13	60	no	—
211	D₄	C₂³×#261	1	60	yes	—
212	C₂×C₄	—	13	15	no	—
213	C₂×C₄	—	13	45	no	—
214	C₂×C₄	—	13	15	no	—
215	C₂×C₄	—	13	15	no	—
216	C₂×C₄	—	13	90	no	—
217	C₂×C₄	—	13	1	no	—
218	C₂×C₄	—	13	15	no	—
219	C₂×C₄	C₂³×#261	1	45	yes	—
220	C₂×C₄	C₂³×#261	1	15	yes	—
221	C₈	—	13	2	no	—
222	C₈	—	13	30	no	—
223	C₂²	—	4	15	no	—
224	C₂²	—	13	1	no	—
225	C₂²	—	13	15	no	—
226	C₂²	—	26	30	no	—
227	C₂²	—	52	45	no	—
228	C₂²	C₂⁴×#261	1	15	yes	—
229	C₄	—	13	15	no	—
230	C₄	—	13	1	no	—
231	C₄	C₂⁴×#261	1	15	yes	—
232	C₄	C₂⁴×#261	1	1	yes	characteristic
233	C₂	—	2	15	no	—
234	C₂	—	13	2	no	—
235	C₂	—	26	15	no	—
236	C₂	C₂⁵×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂⁴×#261
commutator, socle	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂	C₂⁵×#261
Fitting	C₁₃×#585	C₄
prime radical	D₁₃×#585	C₂
cosocle	Dic₁₃	C₂⁶
hypercenter	#585	#261
hypocenter	C₁₃	C₂×#3573
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #585

Complements

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

N	H ≅ G/N	type
1. #13131832	C₂	semidirect
2. #13131831	C₂	semidirect
3. D₁₃⋊#568	C₂	semidirect
4. C₂×D₁₃⋊#131	C₂	semidirect
13. #11719629	C₂²	semidirect
14. D₁₃⋊#131	C₂²	semidirect
15. D₁₃⋊#131	C₂²	semidirect
16. D₁₃⋊#131	C₂²	semidirect
17. #11719625	C₂²	semidirect
18. C₂×#88240	C₂²	semidirect
19. #11719621	C₂²	semidirect
20. C₂×#88238	C₂²	semidirect
21. C₂×D₁₃⋊M₁₆	C₂²	semidirect
22. C₂²×D₁₃⋊C₈	C₂²	semidirect
40. C₂×#6122	C₂³	semidirect
41. C₂²×#1057	C₂³	semidirect
42. #88240	C₂³	semidirect
43. #88240	C₂³	semidirect
44. #88238	C₂³	semidirect
45. #88238	C₂³	semidirect
47. D₁₃⋊M₁₆	C₂³	semidirect
48. C₂×#6118	C₂³	semidirect
51. C₂×D₁₃⋊C₈	C₂³	semidirect
169. D₁₃	#3573	semidirect
202. C₁₃	C₂×#3573	semidirect

Maximal subgroups

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

subgroup	index
#13131832	2
#13131831	2
D₁₃⋊#568	2
C₂×D₁₃⋊#131	2
D₁₃×#585	2
C₂×#3573	13

Subgroups — D13⋊#3573 #16809654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#3573 #16809654