Subgroups — C₁₃×#32703 #15719042

Order 3328.

476 conjugacy classes of subgroups.

The subgroup lattice has 270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2103	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2102	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2080	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2050	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1938	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1881	C₂	1	2	yes	maximal
7	C₁₃×#1861	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1858	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1838	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#575	C₂²	1	1	yes	characteristic
11	C₁₃×#568	C₂²	1	2	yes	—
12	C₁₃×#430	C₂²	1	1	yes	characteristic
13	C₁₃×#430	C₂²	1	2	yes	—
14	C₁₃×#424	C₂²	1	2	yes	—
15	C₁₃×#423	C₂²	1	1	yes	characteristic
16	C₁₃×#423	C₂²	1	1	yes	characteristic
17	C₁₃×#421	C₂²	1	2	yes	—
18	C₂×C₁₃×#104	C₂²	1	2	yes	—
19	C₁₃×#416	C₂²	1	2	yes	—
20	C₁₃×#413	C₂²	1	2	yes	—
21	C₁₃×#408	C₂²	1	2	yes	—
22	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
23	C₁₃×#344	C₂²	1	2	yes	—
24	C₁₃×#344	C₂²	1	2	yes	—
25	C₁₃×#341	C₂²	1	2	yes	—
26	C₁₃×#341	C₂²	1	2	yes	—
27	C₁₃×#341	C₂²	1	2	yes	—
28	C₁₃×#339	C₂²	1	2	yes	—
29	C₁₃×#338	C₂²	1	1	yes	characteristic
30	C₁₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#41	C₂³	1	2	yes	—
32	C₁₃×#137	—	2	2	no	—
33	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
34	C₁₃×#135	—	4	1	no	—
35	C₁₃×#131	—	4	2	no	—
36	C₁₃×#131	—	4	2	no	—
37	C₂×C₁₃×M₁₆	—	4	2	no	—
38	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
39	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
40	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
41	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
42	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₁₃×#117	C₂³	1	2	yes	—
45	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
46	C₁₃×#108	—	4	2	no	—
47	C₁₃×#108	—	4	1	no	—
48	C₁₃×C₄⋊C₈	—	4	1	no	—
49	C₁₃×C₄⋊C₈	—	4	1	no	—
50	C₁₃×C₄⋊C₈	—	4	2	no	—
51	C₁₃×#104	—	2	4	no	—
52	C₁₃×#104	—	4	2	no	—
53	C₁₃×#103	—	2	2	no	—
54	C₁₃×#102	—	2	2	no	—
55	C₁₃×#101	—	2	2	no	—
56	C₁₃×#100	—	2	2	no	—
57	C₁₃×C₂²⋊C₈	—	4	2	no	—
58	C₁₃×#97	—	2	2	no	—
59	#32703	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₁₃×#41	—	2	2	no	—
61	C₁₃×#41	—	2	2	no	—
62	C₁₃×#41	—	2	2	no	—
63	C₁₃×#41	—	2	2	no	—
64	C₂×Q₈×C₁₃	#41	1	2	yes	—
65	C₂×D₄×C₁₃	—	2	2	no	—
66	C₂×D₄×C₁₃	#41	1	2	yes	—
67	C₂²×C₄×C₁₃	—	2	1	no	—
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
70	C₁₃×Q₁₆	—	4	1	no	—
71	C₁₃×SD₁₆	—	4	2	no	—
72	C₁₃×D₈	—	4	1	no	—
73	C₁₃×M₁₆	—	2	2	no	—
74	C₁₃×M₁₆	—	2	2	no	—
75	C₁₃×M₁₆	—	2	2	no	—
76	C₁₃×M₁₆	—	2	2	no	—
77	C₁₃×M₁₆	—	2	2	no	—
78	C₁₃×M₁₆	—	2	2	no	—
79	C₁₃×M₁₆	—	2	2	no	—
80	C₁₃×M₁₆	—	2	2	no	—
81	C₁₃×M₁₆	—	4	4	no	—
82	C₂×C₈×C₁₃	—	2	2	no	—
83	C₂×C₈×C₁₃	—	2	2	no	—
84	C₂×C₈×C₁₃	—	2	2	no	—
85	C₂×C₈×C₁₃	—	2	2	no	—
86	C₂×C₈×C₁₃	—	2	1	no	—
87	C₂×C₈×C₁₃	—	2	2	no	—
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	1	no	—
90	C₂×C₈×C₁₃	—	4	4	no	—
91	C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₄²×C₁₃	—	2	1	no	—
94	C₄²×C₁₃	—	2	2	no	—
95	C₄²×C₁₃	#41	1	2	yes	—
96	#2103	C₂×C₁₃	1	2	yes	complemented
97	#2102	C₂×C₁₃	1	1	yes	characteristic, complemented
98	#2080	C₂×C₁₃	1	2	yes	complemented
99	#2050	C₂×C₁₃	1	1	yes	characteristic
100	#1938	C₂×C₁₃	1	2	yes	complemented
101	#1881	C₂×C₁₃	1	2	yes	—
102	#1861	C₂×C₁₃	1	2	yes	complemented
103	#1858	C₂×C₁₃	1	2	yes	complemented
104	#1838	C₂×C₁₃	1	1	yes	characteristic, complemented
105	C₂³×C₁₃	—	2	2	no	—
106	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
107	Q₈×C₁₃	—	2	2	no	—
108	Q₈×C₁₃	—	2	2	no	—
109	D₄×C₁₃	—	2	2	no	—
110	D₄×C₁₃	—	2	2	no	—
111	D₄×C₁₃	—	4	2	no	—
112	D₄×C₁₃	—	4	2	no	—
113	C₂×C₄×C₁₃	—	2	2	no	—
114	C₂×C₄×C₁₃	—	2	2	no	—
115	C₂×C₄×C₁₃	—	4	2	no	—
116	C₂×C₄×C₁₃	—	4	2	no	—
117	C₂×C₄×C₁₃	—	4	2	no	—
118	C₂×C₄×C₁₃	—	8	1	no	—
119	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
120	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
121	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
122	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
123	C₈×C₁₃	—	4	1	no	—
124	C₈×C₁₃	—	4	1	no	—
125	C₈×C₁₃	—	4	2	no	—
126	C₈×C₁₃	—	4	2	no	—
127	C₈×C₁₃	—	4	2	no	—
128	C₈×C₁₃	—	4	2	no	—
129	#575	C₂²×C₁₃	1	1	yes	characteristic
130	#568	C₂²×C₁₃	1	2	yes	—
131	#430	C₂²×C₁₃	1	1	yes	characteristic
132	#430	C₂²×C₁₃	1	2	yes	—
133	#424	C₂²×C₁₃	1	2	yes	—
134	#423	C₂²×C₁₃	1	1	yes	characteristic
135	#423	C₂²×C₁₃	1	1	yes	characteristic
136	#421	C₂²×C₁₃	1	2	yes	—
137	C₂×#104	C₂²×C₁₃	1	2	yes	—
138	#416	C₂²×C₁₃	1	2	yes	—
139	#413	C₂²×C₁₃	1	2	yes	—
140	#408	C₂²×C₁₃	1	2	yes	—
141	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
142	#344	C₂²×C₁₃	1	2	yes	—
143	#344	C₂²×C₁₃	1	2	yes	—
144	#341	C₂²×C₁₃	1	2	yes	—
145	#341	C₂²×C₁₃	1	2	yes	—
146	#341	C₂²×C₁₃	1	2	yes	—
147	#339	C₂²×C₁₃	1	2	yes	—
148	#338	C₂²×C₁₃	1	1	yes	characteristic
149	H(3,ℤ/4)	C₂²×C₁₃	1	1	yes	characteristic
150	C₂²×C₁₃	—	4	1	no	—
151	C₂²×C₁₃	—	4	2	no	—
152	C₂²×C₁₃	—	8	2	no	—
153	C₂²×C₁₃	#539	1	1	yes	characteristic
154	C₂²×C₁₃	#539	1	2	yes	—
155	C₄×C₁₃	—	4	2	no	—
156	C₄×C₁₃	—	4	2	no	—
157	C₄×C₁₃	—	8	2	no	—
158	C₄×C₁₃	#551	1	1	yes	characteristic
159	C₄×C₁₃	#553	1	2	yes	—
160	C₄×C₁₃	H(3,𝔽₄)	1	1	yes	characteristic
161	C₂×#41	C₂³×C₁₃	1	2	yes	—
162	#137	—	2	2	no	—
163	AGL(1,ℤ/8)	—	2	2	no	—
164	#135	—	4	1	no	—
165	#131	—	4	2	no	—
166	#131	—	4	2	no	—
167	C₂×M₁₆	—	4	2	no	—
168	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
169	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
170	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
171	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
172	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
173	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
174	#117	C₂³×C₁₃	1	2	yes	—
175	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
176	#108	—	4	2	no	—
177	#108	—	4	1	no	—
178	C₄⋊C₈	—	4	1	no	—
179	C₄⋊C₈	—	4	1	no	—
180	C₄⋊C₈	—	4	2	no	—
181	#104	—	2	4	no	—
182	#104	—	4	2	no	—
183	#103	—	2	2	no	—
184	#102	—	2	2	no	—
185	#101	—	2	2	no	—
186	#100	—	2	2	no	—
187	C₂²⋊C₈	—	4	2	no	—
188	#97	—	2	2	no	—
189	C₂×C₁₃	—	2	1	no	—
190	C₂×C₁₃	—	2	2	no	—
191	C₂×C₁₃	—	8	2	no	—
192	C₂×C₁₃	#2782	1	1	yes	characteristic
193	#41	—	2	2	no	—
194	#41	—	2	2	no	—
195	#41	—	2	2	no	—
196	#41	—	2	2	no	—
197	C₂×Q₈	C₁₃×#41	1	2	yes	—
198	C₂×D₄	—	2	2	no	—
199	C₂×D₄	C₁₃×#41	1	2	yes	—
200	C₂²×C₄	—	2	1	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
203	Q₁₆	—	4	1	no	—
204	SD₁₆	—	4	2	no	—
205	D₈	—	4	1	no	—
206	M₁₆	—	2	2	no	—
207	M₁₆	—	2	2	no	—
208	M₁₆	—	2	2	no	—
209	M₁₆	—	2	2	no	—
210	M₁₆	—	2	2	no	—
211	M₁₆	—	2	2	no	—
212	M₁₆	—	2	2	no	—
213	M₁₆	—	2	2	no	—
214	M₁₆	—	4	4	no	—
215	C₂×C₈	—	2	2	no	—
216	C₂×C₈	—	2	2	no	—
217	C₂×C₈	—	2	2	no	—
218	C₂×C₈	—	2	2	no	—
219	C₂×C₈	—	2	1	no	—
220	C₂×C₈	—	2	2	no	—
221	C₂×C₈	—	2	2	no	—
222	C₂×C₈	—	2	1	no	—
223	C₂×C₈	—	4	4	no	—
224	C₄⋊C₄	—	2	2	no	—
225	C₂²⋊C₄	—	2	2	no	—
226	C₄²	—	2	1	no	—
227	C₄²	—	2	2	no	—
228	C₄²	C₁₃×#41	1	2	yes	—
229	C₁₃	#32703	1	1	yes	characteristic, direct product factor, Sylow
230	C₂³	—	2	2	no	—
231	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
232	Q₈	—	2	2	no	—
233	Q₈	—	2	2	no	—
234	D₄	—	2	2	no	—
235	D₄	—	2	2	no	—
236	D₄	—	4	2	no	—
237	D₄	—	4	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	4	2	no	—
241	C₂×C₄	—	4	2	no	—
242	C₂×C₄	—	4	2	no	—
243	C₂×C₄	—	8	1	no	—
244	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
245	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
246	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
248	C₈	—	4	1	no	—
249	C₈	—	4	1	no	—
250	C₈	—	4	2	no	—
251	C₈	—	4	2	no	—
252	C₈	—	4	2	no	—
253	C₈	—	4	2	no	—
254	C₂²	—	4	1	no	—
255	C₂²	—	4	2	no	—
256	C₂²	—	8	2	no	—
257	C₂²	C₁₃×#539	1	1	yes	characteristic
258	C₂²	C₁₃×#539	1	2	yes	—
259	C₄	—	4	2	no	—
260	C₄	—	4	2	no	—
261	C₄	—	8	2	no	—
262	C₄	C₁₃×#551	1	1	yes	characteristic
263	C₄	C₁₃×#553	1	2	yes	—
264	C₄	C₁₃×H(3,𝔽₄)	1	1	yes	characteristic
265	C₂	—	2	1	no	—
266	C₂	—	2	2	no	—
267	C₂	—	8	2	no	—
268	C₂	C₁₃×#2782	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	H(3,𝔽₄)
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂×C₁₃	#2782
prime radical	C₁₃×#575	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2103	C₂	semidirect
2. C₁₃×#2102	C₂	semidirect
3. C₁₃×#2080	C₂	semidirect
5. C₁₃×#1938	C₂	semidirect
7. C₁₃×#1861	C₂	semidirect
8. C₁₃×#1858	C₂	semidirect
9. C₁₃×#1838	C₂	semidirect
59. #32703	C₁₃	direct (N × H)
96. #2103	C₂×C₁₃	semidirect
97. #2102	C₂×C₁₃	semidirect
98. #2080	C₂×C₁₃	semidirect
100. #1938	C₂×C₁₃	semidirect
102. #1861	C₂×C₁₃	semidirect
103. #1858	C₂×C₁₃	semidirect
104. #1838	C₂×C₁₃	semidirect
229. C₁₃	#32703	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×#2103	2
C₁₃×#2102	2
C₁₃×#2080	2
C₁₃×#2050	2
C₁₃×#1938	2
C₁₃×#1881	2
C₁₃×#1861	2
C₁₃×#1858	2
C₁₃×#1838	2
#32703	13

Subgroups — C13×#32703 #15719042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32703 #15719042