Subgroups — C₁₃×#2572 #13111630

Order 1664.

476 conjugacy classes of subgroups.

The subgroup lattice has 234 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	1	yes	maximal, characteristic, complemented
2	C₁₃×#394	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#393	C₂	1	2	yes	maximal, complemented
4	C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#388	C₂	1	2	yes	maximal, complemented
6	C₁₃×#386	C₂	1	2	yes	maximal
7	C₁₃×#383	C₂	1	2	yes	maximal, complemented
8	C₁₃×#381	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#95	C₂²	1	2	yes	—
23	C₁₃×#95	C₂²	1	2	yes	—
24	C₁₃×#95	C₂²	1	1	yes	characteristic
25	C₁₃×#95	C₂²	1	2	yes	—
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	C₂⁴×C₁₃	C₂³	1	2	yes	—
32	C₂×Q₈×C₁₃	—	2	2	no	—
33	C₂×Q₈×C₁₃	—	4	1	no	—
34	C₂×Q₈×C₁₃	—	4	1	no	—
35	C₂×D₄×C₁₃	—	2	4	no	—
36	C₂×D₄×C₁₃	—	4	1	no	—
37	C₂²×C₄×C₁₃	—	2	4	no	—
38	C₂²×C₄×C₁₃	—	2	4	no	—
39	C₂²×C₄×C₁₃	—	4	2	no	—
40	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
41	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×C₄⋊C₄	—	4	1	no	—
49	C₁₃×C₄⋊C₄	—	4	1	no	—
50	C₁₃×C₂²⋊C₄	—	2	4	no	—
51	C₁₃×C₂²⋊C₄	—	2	4	no	—
52	C₁₃×C₂²⋊C₄	—	2	4	no	—
53	C₁₃×C₂²⋊C₄	—	4	2	no	—
54	C₁₃×C₂²⋊C₄	—	4	2	no	—
55	C₄²×C₁₃	—	2	4	no	—
56	C₄²×C₁₃	—	4	1	no	—
57	#2572	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂³×C₁₃	—	2	2	no	—
59	C₂³×C₁₃	—	2	2	no	—
60	C₂³×C₁₃	—	2	2	no	—
61	C₂³×C₁₃	—	2	2	no	—
62	C₂³×C₁₃	—	2	2	no	—
63	C₂³×C₁₃	—	2	2	no	—
64	C₂³×C₁₃	#41	1	4	yes	—
65	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
66	Q₈×C₁₃	—	4	4	no	—
67	D₄×C₁₃	—	4	4	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	1	no	—
71	C₂×C₄×C₁₃	—	2	1	no	—
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	—	2	2	no	—
74	C₂×C₄×C₁₃	—	2	2	no	—
75	C₂×C₄×C₁₃	—	2	2	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	2	no	—
86	C₂×C₄×C₁₃	—	2	1	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	4	8	no	—
89	C₂×C₄×C₁₃	#41	1	4	yes	—
90	C₂×C₄×C₁₃	#41	1	2	yes	—
91	#400	C₂×C₁₃	1	1	yes	characteristic, complemented
92	#394	C₂×C₁₃	1	1	yes	characteristic
93	#393	C₂×C₁₃	1	2	yes	complemented
94	#391	C₂×C₁₃	1	1	yes	characteristic, complemented
95	#388	C₂×C₁₃	1	2	yes	complemented
96	#386	C₂×C₁₃	1	2	yes	—
97	#383	C₂×C₁₃	1	2	yes	complemented
98	#381	C₂×C₁₃	1	2	yes	complemented
99	C₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
100	C₂²×C₁₃	—	2	4	no	—
101	C₂²×C₁₃	—	2	4	no	—
102	C₂²×C₁₃	—	2	4	no	—
103	C₂²×C₁₃	—	4	2	no	—
104	C₂²×C₁₃	—	4	2	no	—
105	C₂²×C₁₃	—	4	2	no	—
106	C₂²×C₁₃	—	4	2	no	—
107	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
108	C₂²×C₁₃	C₂×#41	1	2	yes	—
109	C₂²×C₁₃	C₂×#41	1	2	yes	—
110	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
111	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
112	C₄×C₁₃	—	2	2	no	—
113	C₄×C₁₃	—	2	4	no	—
114	C₄×C₁₃	—	4	2	no	—
115	C₄×C₁₃	—	4	2	no	—
116	C₄×C₁₃	—	4	1	no	—
117	C₄×C₁₃	—	4	2	no	—
118	C₄×C₁₃	—	4	1	no	—
119	C₄×C₁₃	—	4	2	no	—
120	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
121	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
122	C₂³×C₄	C₂²×C₁₃	1	2	yes	—
123	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
124	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
125	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
126	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
127	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
128	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
129	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
130	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
131	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
132	#95	C₂²×C₁₃	1	2	yes	—
133	#95	C₂²×C₁₃	1	2	yes	—
134	#95	C₂²×C₁₃	1	1	yes	characteristic
135	#95	C₂²×C₁₃	1	2	yes	—
136	#95	C₂²×C₁₃	1	2	yes	—
137	#95	C₂²×C₁₃	1	1	yes	characteristic
138	#95	C₂²×C₁₃	1	2	yes	—
139	#95	C₂²×C₁₃	1	2	yes	—
140	#95	C₂²×C₁₃	1	2	yes	—
141	C₂×C₁₃	—	4	4	no	—
142	C₂×C₁₃	#529	1	2	yes	—
143	C₂×C₁₃	#538	1	1	yes	characteristic
144	C₂×C₁₃	#551	1	2	yes	—
145	C₂×C₁₃	#551	1	1	yes	characteristic
146	C₂×C₁₃	#555	1	1	yes	characteristic
147	C₂⁴	C₂³×C₁₃	1	2	yes	—
148	C₂×Q₈	—	2	2	no	—
149	C₂×Q₈	—	4	1	no	—
150	C₂×Q₈	—	4	1	no	—
151	C₂×D₄	—	2	4	no	—
152	C₂×D₄	—	4	1	no	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	—	2	4	no	—
155	C₂²×C₄	—	4	2	no	—
156	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
157	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
158	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
159	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
160	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
161	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
162	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
163	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
164	C₄⋊C₄	—	4	1	no	—
165	C₄⋊C₄	—	4	1	no	—
166	C₂²⋊C₄	—	2	4	no	—
167	C₂²⋊C₄	—	2	4	no	—
168	C₂²⋊C₄	—	2	4	no	—
169	C₂²⋊C₄	—	4	2	no	—
170	C₂²⋊C₄	—	4	2	no	—
171	C₄²	—	2	4	no	—
172	C₄²	—	4	1	no	—
173	C₁₃	#2572	1	1	yes	characteristic, direct product factor, Sylow
174	C₂³	—	2	2	no	—
175	C₂³	—	2	2	no	—
176	C₂³	—	2	2	no	—
177	C₂³	—	2	2	no	—
178	C₂³	—	2	2	no	—
179	C₂³	—	2	2	no	—
180	C₂³	C₁₃×#41	1	4	yes	—
181	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
182	Q₈	—	4	4	no	—
183	D₄	—	4	4	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	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	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	4	8	no	—
205	C₂×C₄	C₁₃×#41	1	4	yes	—
206	C₂×C₄	C₁₃×#41	1	2	yes	—
207	C₂²	—	2	4	no	—
208	C₂²	—	2	4	no	—
209	C₂²	—	2	4	no	—
210	C₂²	—	4	2	no	—
211	C₂²	—	4	2	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
215	C₂²	C₂×C₁₃×#41	1	2	yes	—
216	C₂²	C₂×C₁₃×#41	1	2	yes	—
217	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
218	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
219	C₄	—	2	2	no	—
220	C₄	—	2	4	no	—
221	C₄	—	4	2	no	—
222	C₄	—	4	2	no	—
223	C₄	—	4	1	no	—
224	C₄	—	4	2	no	—
225	C₄	—	4	1	no	—
226	C₄	—	4	2	no	—
227	C₂	—	4	4	no	—
228	C₂	C₁₃×#529	1	2	yes	—
229	C₂	C₁₃×#538	1	1	yes	characteristic
230	C₂	C₁₃×#551	1	2	yes	—
231	C₂	C₁₃×#551	1	1	yes	characteristic
232	C₂	C₁₃×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
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
1. C₁₃×#400	C₂	semidirect
3. C₁₃×#393	C₂	semidirect
4. C₁₃×#391	C₂	semidirect
5. C₁₃×#388	C₂	semidirect
7. C₁₃×#383	C₂	semidirect
8. C₁₃×#381	C₂	semidirect
9. C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
57. #2572	C₁₃	direct (N × H)
91. #400	C₂×C₁₃	semidirect
93. #393	C₂×C₁₃	semidirect
94. #391	C₂×C₁₃	semidirect
95. #388	C₂×C₁₃	semidirect
97. #383	C₂×C₁₃	semidirect
98. #381	C₂×C₁₃	semidirect
99. C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
173. C₁₃	#2572	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×#394	2
C₁₃×#393	2
C₁₃×#391	2
C₁₃×#388	2
C₁₃×#386	2
C₁₃×#383	2
C₁₃×#381	2
C₄×C₁₃×C₂²⋊C₄	2
#2572	13

Subgroups — C13×#2572 #13111630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2572 #13111630