Subgroups — C₁₃×#2511 #13111569

Order 1664.

388 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#400	C₂	1	2	yes	maximal
2	C₁₃×#400	C₂	1	2	yes	maximal
3	C₁₃×#391	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#391	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#391	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#389	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#387	C₂	1	2	yes	maximal
8	C₁₃×#387	C₂	1	2	yes	maximal
9	C₁₃×#384	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
25	C₁₃×#95	C₂²	1	1	yes	characteristic
26	C₁₃×#95	C₂²	1	2	yes	—
27	C₁₃×#95	C₂²	1	1	yes	characteristic
28	C₁₃×#95	C₂²	1	2	yes	—
29	C₁₃×#95	C₂²	1	2	yes	—
30	C₁₃×#95	C₂²	1	2	yes	—
31	C₁₃×#95	C₂²	1	2	yes	—
32	C₁₃×#95	C₂²	1	2	yes	—
33	C₁₃×#95	C₂²	1	2	yes	—
34	C₁₃×#95	C₂²	1	2	yes	—
35	C₂×Q₈×C₁₃	—	2	2	no	—
36	C₂×Q₈×C₁₃	—	2	2	no	—
37	C₂×Q₈×C₁₃	—	2	2	no	—
38	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
42	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₁₃×C₄⋊C₄	—	4	2	no	—
55	C₁₃×C₄⋊C₄	—	4	2	no	—
56	C₁₃×C₄⋊C₄	Q₈	1	4	yes	complemented
57	C₄²×C₁₃	—	2	2	no	—
58	C₄²×C₁₃	—	2	2	no	—
59	C₄²×C₁₃	—	2	2	no	—
60	C₄²×C₁₃	—	4	2	no	—
61	#2511	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
63	Q₈×C₁₃	—	4	4	no	—
64	C₂×C₄×C₁₃	—	2	1	no	—
65	C₂×C₄×C₁₃	—	2	1	no	—
66	C₂×C₄×C₁₃	—	2	1	no	—
67	C₂×C₄×C₁₃	—	2	1	no	—
68	C₂×C₄×C₁₃	—	2	1	no	—
69	C₂×C₄×C₁₃	—	2	1	no	—
70	C₂×C₄×C₁₃	—	2	1	no	—
71	C₂×C₄×C₁₃	—	2	1	no	—
72	C₂×C₄×C₁₃	—	2	1	no	—
73	C₂×C₄×C₁₃	—	2	1	no	—
74	C₂×C₄×C₁₃	—	2	2	no	—
75	C₂×C₄×C₁₃	—	2	1	no	—
76	C₂×C₄×C₁₃	—	2	2	no	—
77	C₂×C₄×C₁₃	—	2	2	no	—
78	C₂×C₄×C₁₃	—	2	2	no	—
79	C₂×C₄×C₁₃	—	2	2	no	—
80	C₂×C₄×C₁₃	—	2	2	no	—
81	C₂×C₄×C₁₃	—	2	2	no	—
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	—	2	2	no	—
84	C₂×C₄×C₁₃	—	2	2	no	—
85	C₂×C₄×C₁₃	—	2	1	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	2	1	no	—
90	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
91	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
92	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
93	C₂×C₄×C₁₃	#41	1	2	yes	—
94	C₂×C₄×C₁₃	#41	1	2	yes	—
95	C₂×C₄×C₁₃	#41	1	2	yes	—
96	C₂×C₄×C₁₃	#41	1	2	yes	—
97	#400	C₂×C₁₃	1	2	yes	—
98	#400	C₂×C₁₃	1	2	yes	—
99	#391	C₂×C₁₃	1	1	yes	characteristic
100	#391	C₂×C₁₃	1	1	yes	characteristic
101	#391	C₂×C₁₃	1	1	yes	characteristic
102	#389	C₂×C₁₃	1	1	yes	characteristic
103	#387	C₂×C₁₃	1	2	yes	—
104	#387	C₂×C₁₃	1	2	yes	—
105	#384	C₂×C₁₃	1	1	yes	characteristic
106	C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
107	C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
108	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
109	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
110	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
111	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
112	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
113	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
114	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
115	C₄×C₁₃	—	2	2	no	—
116	C₄×C₁₃	—	2	2	no	—
117	C₄×C₁₃	—	2	2	no	—
118	C₄×C₁₃	—	2	2	no	—
119	C₄×C₁₃	—	4	2	no	—
120	C₄×C₁₃	—	4	1	no	—
121	C₄×C₁₃	—	4	2	no	—
122	C₄×C₁₃	—	4	1	no	—
123	C₄×C₁₃	—	4	2	no	—
124	C₄×C₁₃	—	4	2	no	—
125	C₄×C₁₃	#126	1	4	yes	—
126	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
127	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
128	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
129	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
130	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
131	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
132	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
133	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
134	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
135	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
136	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
137	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
138	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
139	#95	C₂²×C₁₃	1	1	yes	characteristic
140	#95	C₂²×C₁₃	1	2	yes	—
141	#95	C₂²×C₁₃	1	1	yes	characteristic
142	#95	C₂²×C₁₃	1	2	yes	—
143	#95	C₂²×C₁₃	1	2	yes	—
144	#95	C₂²×C₁₃	1	2	yes	—
145	#95	C₂²×C₁₃	1	2	yes	—
146	#95	C₂²×C₁₃	1	2	yes	—
147	#95	C₂²×C₁₃	1	2	yes	—
148	#95	C₂²×C₁₃	1	2	yes	—
149	C₂×C₁₃	C₂×#126	1	1	yes	characteristic
150	C₂×C₁₃	#533	1	1	yes	characteristic
151	C₂×C₁₃	#542	1	1	yes	characteristic
152	C₂×C₁₃	#552	1	1	yes	characteristic
153	C₂×C₁₃	#554	1	1	yes	characteristic
154	C₂×C₁₃	#557	1	1	yes	characteristic
155	C₂×C₁₃	#559	1	1	yes	characteristic
156	C₂×Q₈	—	2	2	no	—
157	C₂×Q₈	—	2	2	no	—
158	C₂×Q₈	—	2	2	no	—
159	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
160	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
161	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
162	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
163	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
164	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
165	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
166	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
167	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
168	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
169	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	2	4	no	—
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	Q₈×C₁₃	1	4	yes	complemented
178	C₄²	—	2	2	no	—
179	C₄²	—	2	2	no	—
180	C₄²	—	2	2	no	—
181	C₄²	—	4	2	no	—
182	C₁₃	#2511	1	1	yes	characteristic, direct product factor, Sylow
183	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
184	Q₈	—	4	4	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
212	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
213	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
214	C₂×C₄	C₁₃×#41	1	2	yes	—
215	C₂×C₄	C₁₃×#41	1	2	yes	—
216	C₂×C₄	C₁₃×#41	1	2	yes	—
217	C₂×C₄	C₁₃×#41	1	2	yes	—
218	C₂²	C₂²×Q₈×C₁₃	1	1	yes	characteristic
219	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
220	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
221	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
222	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
223	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
224	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
225	C₄	—	2	2	no	—
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	1	no	—
231	C₄	—	4	2	no	—
232	C₄	—	4	1	no	—
233	C₄	—	4	2	no	—
234	C₄	—	4	2	no	—
235	C₄	C₁₃×#126	1	4	yes	—
236	C₂	C₂×C₁₃×#126	1	1	yes	characteristic
237	C₂	C₁₃×#533	1	1	yes	characteristic
238	C₂	C₁₃×#542	1	1	yes	characteristic
239	C₂	C₁₃×#552	1	1	yes	characteristic
240	C₂	C₁₃×#554	1	1	yes	characteristic
241	C₂	C₁₃×#557	1	1	yes	characteristic
242	C₂	C₁₃×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
56. C₁₃×C₄⋊C₄	Q₈	semidirect
61. #2511	C₁₃	direct (N × H)
177. C₄⋊C₄	Q₈×C₁₃	semidirect
182. C₁₃	#2511	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#400	2
C₁₃×#391	2
C₁₃×#389	2
C₁₃×#387	2
C₁₃×#384	2
C₄×C₁₃×C₄⋊C₄	2
#2511	13

Subgroups — C13×#2511 #13111569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2511 #13111569