Subgroups — D₁₃×#444 #13123728

Order 1664.

464 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#135	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#131	C₂	1	2	yes	maximal, complemented
3	C₁₃×#444	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718858	C₂	1	1	yes	maximal, characteristic, complemented
5	#11718806	C₂	1	2	yes	maximal, complemented
6	#11718555	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	#11718484	C₂	1	2	yes	maximal, complemented
9	D₁₃×#104	C₂	1	2	yes	maximal, complemented
10	#11718378	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	#41×D₁₃	C₂²	1	2	yes	—
13	C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₁₃×#131	C₂²	1	2	yes	complemented
15	#88204	C₂²	1	2	yes	—
16	#88202	C₂²	1	2	yes	complemented
17	#88173	C₄	1	1	yes	characteristic, complemented
18	Q₁₆×D₁₃	C₄	1	1	yes	characteristic, complemented
19	#88170	C₄	1	2	yes	complemented
20	SD₁₆×D₁₃	C₄	1	2	yes	complemented
21	#88166	C₄	1	1	yes	characteristic, complemented
22	D₈×D₁₃	C₄	1	1	yes	characteristic, complemented
23	#88161	—	2	2	no	—
24	#88161	C₂²	1	2	yes	complemented
25	M₁₆×D₁₃	—	2	2	no	—
26	M₁₆×D₁₃	C₂²	1	2	yes	—
27	#88158	C₂²	1	1	yes	characteristic
28	#88155	—	2	2	no	—
29	#88155	C₂²	1	2	yes	complemented
30	C₂×C₈×D₁₃	—	2	2	no	—
31	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
33	C₄²×D₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#104	C₂²	1	2	yes	complemented
36	C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
37	#88077	C₂²	1	2	yes	complemented
38	#88065	C₂²	1	2	yes	complemented
39	#88062	C₂²	1	2	yes	complemented
40	#88059	C₂²	1	1	yes	characteristic, complemented
41	#88055	C₂²	1	1	yes	characteristic, complemented
42	#88055	C₂²	1	1	yes	characteristic, complemented
43	#88045	C₂²	1	2	yes	complemented
44	#88043	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#41	C₂³	1	2	yes	—
46	#6131	C₂×C₄	1	2	yes	—
47	Q₈×D₁₃	C₂×C₄	1	2	yes	—
48	#6129	—	2	2	no	—
49	#6129	C₂×C₄	1	2	yes	—
50	D₄×D₁₃	—	2	2	no	—
51	D₄×D₁₃	C₂×C₄	1	2	yes	—
52	#6127	—	2	2	no	—
53	#6127	C₂³	1	2	yes	—
54	C₂×C₄×D₁₃	—	2	2	no	—
55	C₂×C₄×D₁₃	—	2	1	no	—
56	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
58	C₁₃×SD₁₆	C₂×C₄	1	2	yes	complemented
59	C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
60	C₁₃×M₁₆	—	2	2	no	—
61	C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₂×C₈×C₁₃	—	2	2	no	—
63	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	#6107	C₂×C₄	1	2	yes	complemented
67	#6106	C₂×C₄	1	2	yes	complemented
68	#6105	C₂×C₄	1	2	yes	complemented
69	#6104	C₂×C₄	1	2	yes	complemented
70	C₄×Dic₁₃	—	2	1	no	—
71	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
72	#6099	—	2	2	no	—
73	#6099	C₂³	1	2	yes	—
74	C₂×#1055	—	2	2	no	—
75	C₂×#1055	C₂³	1	1	yes	characteristic
76	C₂×#1055	C₂³	1	1	yes	characteristic
77	Dic₅₂	C₂×C₄	1	1	yes	characteristic, complemented
78	D₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
79	#6095	C₂×C₄	1	2	yes	complemented
80	#6094	—	2	2	no	—
81	#6094	—	2	2	no	—
82	#6094	—	2	2	no	—
83	C₈×D₁₃	—	2	2	no	—
84	C₈×D₁₃	—	2	2	no	—
85	C₈×D₁₃	—	2	2	no	—
86	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
87	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
88	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
89	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
90	C₈×D₁₃	D₄	1	2	yes	—
91	C₈×D₁₃	D₄	1	2	yes	—
92	C₂×#444	—	13	1	no	maximal, Sylow
93	C₂²×D₁₃	—	2	2	no	—
94	C₂²×D₁₃	#41	1	1	yes	characteristic
95	Q₈×C₁₃	C₂²×C₄	1	2	yes	—
96	D₄×C₁₃	—	2	2	no	—
97	D₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂×C₄×C₁₃	—	2	2	no	—
99	C₂×C₄×C₁₃	—	2	1	no	—
100	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂²⋊D₁₃	—	2	2	no	—
102	C₂²⋊D₁₃	—	2	2	no	—
103	C₂²⋊D₁₃	—	2	2	no	—
104	C₂×Dic₁₃	—	2	2	no	—
105	C₂×Dic₁₃	—	2	1	no	—
106	C₂×Dic₁₃	#41	1	1	yes	characteristic
107	D₅₂	—	2	2	no	—
108	D₅₂	C₂²×C₄	1	2	yes	—
109	C₄×D₁₃	—	2	2	no	—
110	C₄×D₁₃	—	2	2	no	—
111	C₄×D₁₃	—	2	2	no	—
112	C₄×D₁₃	—	4	2	no	—
113	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
116	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
117	Dic₂₆	—	2	2	no	—
118	Dic₂₆	C₂²×C₄	1	2	yes	—
119	C₈×C₁₃	—	2	2	no	—
120	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₈×C₁₃	C₂×D₄	1	2	yes	—
123	#1055	—	2	2	no	—
124	#1055	C₂²×C₄	1	1	yes	characteristic
125	#1055	C₂²×C₄	1	1	yes	characteristic
126	#1055	C₂×D₄	1	2	yes	—
127	C₂×#135	—	13	1	no	—
128	C₂×#131	—	13	2	no	—
129	#444	—	13	1	no	—
130	#444	—	13	2	no	—
131	#444	—	13	1	no	—
132	#444	—	13	2	no	—
133	#444	—	13	1	no	—
134	#444	D₁₃	1	1	yes	characteristic, direct product factor
135	C₂×#108	—	13	1	no	—
136	C₂×#104	—	13	2	no	—
137	C₂×#97	—	13	1	no	—
138	C₂²×C₁₃	—	2	2	no	—
139	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
140	C₂×D₁₃	—	2	2	no	—
141	C₂×D₁₃	—	2	2	no	—
142	C₂×D₁₃	—	4	4	no	—
143	C₂×D₁₃	C₄×D₄	1	1	yes	characteristic
144	C₂×D₁₃	C₄×D₄	1	1	yes	characteristic
145	C₄×C₁₃	—	2	2	no	—
146	C₄×C₁₃	—	4	1	no	—
147	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
148	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
149	Dic₁₃	—	2	2	no	—
150	Dic₁₃	—	4	1	no	—
151	Dic₁₃	C₄×D₄	1	1	yes	characteristic
152	Dic₁₃	C₄×D₄	1	1	yes	characteristic
153	C₂×#41	—	13	2	no	—
154	#135	—	13	2	no	—
155	#135	—	13	1	no	—
156	#135	—	13	2	no	—
157	#135	—	13	1	no	—
158	#135	—	13	1	no	—
159	#135	C₂×D₁₃	1	1	yes	characteristic
160	C₂×Q₁₆	—	13	1	no	—
161	C₂×SD₁₆	—	13	2	no	—
162	C₂×D₈	—	13	1	no	—
163	#131	—	13	2	no	—
164	#131	—	13	2	no	—
165	#131	—	13	2	no	—
166	#131	—	26	2	no	—
167	#131	—	26	2	no	—
168	#131	C₂×D₁₃	1	2	yes	complemented
169	C₂×M₁₆	—	13	2	no	—
170	C₂×M₁₆	—	26	2	no	—
171	C₂²×C₈	—	13	1	no	—
172	C₂²×C₈	—	13	1	no	—
173	C₂²×C₈	—	26	2	no	—
174	C₂×C₄²	—	13	1	no	—
175	#108	—	13	2	no	—
176	#108	—	13	1	no	—
177	#108	C₂×D₁₃	1	1	yes	characteristic, complemented
178	#104	—	13	2	no	—
179	#104	—	13	2	no	—
180	#104	—	13	2	no	—
181	#104	C₂×D₁₃	1	2	yes	complemented
182	#97	—	13	1	no	—
183	#97	—	13	1	no	—
184	#97	—	13	1	no	—
185	#97	C₂×D₁₃	1	1	yes	characteristic, complemented
186	C₂×C₁₃	—	2	1	no	—
187	C₂×C₁₃	—	4	2	no	—
188	C₂×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
189	D₁₃	—	2	1	no	—
190	D₁₃	—	4	2	no	—
191	D₁₃	#444	1	2	yes	direct product factor
192	#41	—	13	2	no	—
193	#41	—	13	2	no	—
194	#41	—	13	2	no	—
195	#41	—	26	2	no	—
196	#41	—	26	2	no	—
197	#41	C₂²×D₁₃	1	2	yes	—
198	C₂×Q₈	—	13	2	no	—
199	C₂×D₄	—	13	2	no	—
200	C₂×D₄	—	26	2	no	—
201	C₂²×C₄	—	13	1	no	—
202	C₂²×C₄	—	26	2	no	—
203	C₂²×C₄	—	26	1	no	—
204	Q₁₆	—	13	2	no	—
205	Q₁₆	—	13	1	no	—
206	Q₁₆	C₄×D₁₃	1	1	yes	characteristic, complemented
207	SD₁₆	—	13	2	no	—
208	SD₁₆	—	13	2	no	—
209	SD₁₆	—	13	2	no	—
210	SD₁₆	C₄×D₁₃	1	2	yes	complemented
211	D₈	—	13	2	no	—
212	D₈	—	13	1	no	—
213	D₈	C₄×D₁₃	1	1	yes	characteristic, complemented
214	M₁₆	—	2	2	no	—
215	M₁₆	—	13	2	no	—
216	M₁₆	—	26	2	no	—
217	M₁₆	—	26	2	no	—
218	M₁₆	—	26	2	no	—
219	M₁₆	—	26	2	no	—
220	M₁₆	C₂²×D₁₃	1	2	yes	—
221	C₂×C₈	—	2	2	no	—
222	C₂×C₈	—	13	1	no	—
223	C₂×C₈	—	13	1	no	—
224	C₂×C₈	—	13	1	no	—
225	C₂×C₈	—	13	1	no	—
226	C₂×C₈	—	13	1	no	—
227	C₂×C₈	—	13	1	no	—
228	C₂×C₈	—	13	2	no	—
229	C₂×C₈	—	13	2	no	—
230	C₂×C₈	—	26	2	no	—
231	C₂×C₈	—	26	2	no	—
232	C₂×C₈	—	26	2	no	—
233	C₂×C₈	—	26	2	no	—
234	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
235	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
236	C₄²	—	13	1	no	—
237	C₄²	—	26	1	no	—
238	C₄²	C₂²×D₁₃	1	1	yes	characteristic
239	C₁₃	C₂×#444	1	1	yes	characteristic, complemented, Sylow
240	C₂³	—	13	1	no	—
241	C₂³	—	26	2	no	—
242	Q₈	—	13	2	no	—
243	Q₈	—	26	2	no	—
244	Q₈	C₂×C₄×D₁₃	1	2	yes	—
245	D₄	—	2	2	no	—
246	D₄	—	13	2	no	—
247	D₄	—	26	2	no	—
248	D₄	—	26	2	no	—
249	D₄	—	26	2	no	—
250	D₄	—	26	2	no	—
251	D₄	C₂×C₄×D₁₃	1	2	yes	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	13	1	no	—
255	C₂×C₄	—	13	1	no	—
256	C₂×C₄	—	13	1	no	—
257	C₂×C₄	—	13	1	no	—
258	C₂×C₄	—	13	1	no	—
259	C₂×C₄	—	26	2	no	—
260	C₂×C₄	—	26	2	no	—
261	C₂×C₄	—	26	2	no	—
262	C₂×C₄	—	26	2	no	—
263	C₂×C₄	—	26	1	no	—
264	C₂×C₄	—	52	2	no	—
265	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
266	C₈	—	2	2	no	—
267	C₈	—	13	1	no	—
268	C₈	—	13	1	no	—
269	C₈	—	13	2	no	—
270	C₈	—	26	2	no	—
271	C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
272	C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
273	C₈	D₄×D₁₃	1	2	yes	—
274	C₂²	—	2	2	no	—
275	C₂²	—	13	1	no	—
276	C₂²	—	13	1	no	—
277	C₂²	—	26	2	no	—
278	C₂²	—	26	2	no	—
279	C₂²	—	52	4	no	—
280	C₂²	#41×D₁₃	1	1	yes	characteristic
281	C₄	—	2	2	no	—
282	C₄	—	4	1	no	—
283	C₄	—	13	1	no	—
284	C₄	—	13	1	no	—
285	C₄	—	26	2	no	—
286	C₄	—	52	1	no	—
287	C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
288	C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
289	C₂	—	2	1	no	—
290	C₂	—	4	2	no	—
291	C₂	—	13	2	no	—
292	C₂	—	26	1	no	—
293	C₂	—	52	2	no	—
294	C₂	C₄×D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₁₃
commutator	C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₃
Fitting	C₁₃×#444	C₂
socle	C₂×C₁₃	C₂×C₄×D₄
prime radical	D₁₃×#135	C₂
cosocle	C₂×C₄×C₁₃	C₂⁴
hypercenter	#444	D₁₃
hypocenter	C₁₃	C₂×#444
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #444

Complements

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

N	H ≅ G/N	type
2. D₁₃×#131	C₂	semidirect
3. C₁₃×#444	C₂	semidirect
4. #11718858	C₂	semidirect
5. #11718806	C₂	semidirect
6. #11718555	C₂	semidirect
7. D₁₃×#108	C₂	semidirect
8. #11718484	C₂	semidirect
9. D₁₃×#104	C₂	semidirect
10. #11718378	C₂	semidirect
11. D₁₃×#97	C₂	semidirect
14. C₁₃×#131	C₂²	semidirect
16. #88202	C₂²	semidirect
17. #88173	C₄	semidirect
18. Q₁₆×D₁₃	C₄	semidirect
19. #88170	C₄	semidirect
20. SD₁₆×D₁₃	C₄	semidirect
21. #88166	C₄	semidirect
22. D₈×D₁₃	C₄	semidirect
24. #88161	C₂²	semidirect
29. #88155	C₂²	semidirect
34. C₁₃×#108	C₂²	semidirect
35. C₁₃×#104	C₂²	semidirect
36. C₁₃×#97	C₂²	semidirect
37. #88077	C₂²	semidirect
38. #88065	C₂²	semidirect
39. #88062	C₂²	semidirect
40. #88059	C₂²	semidirect
41. #88055	C₂²	semidirect
42. #88055	C₂²	semidirect
43. #88045	C₂²	semidirect
44. #88043	C₂²	semidirect
57. C₁₃×Q₁₆	C₂×C₄	semidirect
58. C₁₃×SD₁₆	C₂×C₄	semidirect
59. C₁₃×D₈	C₂×C₄	semidirect
66. #6107	C₂×C₄	semidirect
67. #6106	C₂×C₄	semidirect
68. #6105	C₂×C₄	semidirect
69. #6104	C₂×C₄	semidirect
77. Dic₅₂	C₂×C₄	semidirect
78. D₁₀₄	C₂×C₄	semidirect
79. #6095	C₂×C₄	semidirect
134. #444	D₁₃	direct (N × H)
168. #131	C₂×D₁₃	semidirect
177. #108	C₂×D₁₃	semidirect
181. #104	C₂×D₁₃	semidirect
185. #97	C₂×D₁₃	semidirect
191. D₁₃	#444	direct (N × H)
206. Q₁₆	C₄×D₁₃	semidirect
210. SD₁₆	C₄×D₁₃	semidirect
213. D₈	C₄×D₁₃	semidirect
239. C₁₃	C₂×#444	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#135	2
D₁₃×#131	2
C₁₃×#444	2
#11718858	2
#11718806	2
#11718555	2
D₁₃×#108	2
#11718484	2
D₁₃×#104	2
#11718378	2
D₁₃×#97	2
C₂×#444	13

Subgroups — D13×#444 #13123728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#444 #13123728