Subgroups — C₁₃×#33657 #15719996

Order 3328.

566 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2916	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2238	C₂	1	8	yes	maximal, complemented
4	C₁₃×#2155	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#361	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2115	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
8	C₁₃×#568	—	2	1	no	—
9	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
10	C₁₃×#535	—	2	1	no	—
11	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
12	C₁₃×#469	C₂²	1	4	yes	—
13	C₁₃×#466	—	2	2	no	—
14	C₁₃×#430	—	2	1	no	—
15	C₁₃×#430	C₂²	1	4	yes	complemented
16	C₂×C₁₃×#108	—	2	2	no	—
17	C₂×C₁₃×#108	C₂²	1	2	yes	—
18	C₁₃×#427	C₂²	1	1	yes	characteristic
19	C₁₃×#418	—	2	1	no	—
20	C₁₃×#365	C₂²	1	8	yes	complemented
21	C₁₃×#361	C₂²	1	8	yes	—
22	C₁₃×#349	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
24	C₂²×D₄×C₁₃	—	2	1	no	—
25	C₂×C₁₃×D₈	—	2	1	no	—
26	C₂×C₁₃×D₈	—	2	2	no	—
27	C₂×C₁₃×D₈	—	2	2	no	—
28	C₂×C₁₃×D₈	C₂³	1	2	yes	—
29	C₁₃×#131	—	2	2	no	—
30	C₁₃×#131	—	2	2	no	—
31	C₁₃×#131	—	4	4	no	—
32	C₂×C₁₃×M₁₆	—	2	4	no	—
33	C₂×C₁₃×M₁₆	—	2	2	no	—
34	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
35	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
36	C₂²×C₈×C₁₃	D₄	1	2	yes	—
37	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
38	C₁₃×#127	—	4	1	no	—
39	C₁₃×#124	—	4	1	no	—
40	C₁₃×#121	—	2	4	no	—
41	C₁₃×#120	—	4	2	no	—
42	C₁₃×#117	—	2	1	no	—
43	C₁₃×M₃₂	—	2	2	no	—
44	C₁₃×M₃₂	C₂³	1	4	yes	—
45	C₂×C₁₃×C₁₆	—	2	2	no	—
46	C₁₃×#108	—	2	2	no	—
47	C₁₃×#108	—	2	4	no	—
48	C₁₃×#108	C₂³	1	4	yes	—
49	C₁₃×#107	—	2	1	no	—
50	C₁₃×#106	C₂³	1	2	yes	—
51	C₁₃×#102	—	2	4	no	—
52	#33657	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂⁴×C₁₃	—	4	1	no	—
54	C₁₃×#41	—	2	2	no	—
55	C₁₃×#41	—	2	2	no	—
56	C₂×Q₈×C₁₃	SD₁₆	1	1	yes	characteristic
57	C₂×D₄×C₁₃	—	2	2	no	—
58	C₂×D₄×C₁₃	—	4	4	no	—
59	C₂×D₄×C₁₃	—	4	2	no	—
60	C₂×D₄×C₁₃	—	4	1	no	—
61	C₂×D₄×C₁₃	—	4	2	no	—
62	C₂×D₄×C₁₃	SD₁₆	1	2	yes	—
63	C₂×D₄×C₁₃	SD₁₆	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
65	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₁₃×D₈	—	2	4	no	—
67	C₁₃×D₈	—	4	1	no	—
68	C₁₃×D₈	—	4	1	no	—
69	C₁₃×M₁₆	—	2	2	no	—
70	C₁₃×M₁₆	—	2	4	no	—
71	C₁₃×M₁₆	—	2	4	no	—
72	C₁₃×M₁₆	—	4	4	no	—
73	C₁₃×M₁₆	—	4	2	no	—
74	C₂×C₈×C₁₃	—	2	2	no	—
75	C₂×C₈×C₁₃	—	2	2	no	—
76	C₂×C₈×C₁₃	—	4	4	no	—
77	C₂×C₈×C₁₃	—	4	2	no	—
78	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
79	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₁₃	#41	1	2	yes	—
81	C₂×C₈×C₁₃	#41	1	2	yes	—
82	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
83	C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₁₃×C₂²⋊C₄	—	4	1	no	—
85	C₁₃×C₂²⋊C₄	—	4	4	no	—
86	C₄²×C₁₃	—	4	1	no	—
87	C₁₃×C₁₆	—	2	4	no	—
88	#3058	C₂×C₁₃	1	1	yes	characteristic
89	#2916	C₂×C₁₃	1	1	yes	characteristic, complemented
90	#2238	C₂×C₁₃	1	8	yes	complemented
91	#2155	C₂×C₁₃	1	2	yes	complemented
92	C₂×#361	C₂×C₁₃	1	2	yes	complemented
93	#2115	C₂×C₁₃	1	1	yes	characteristic, complemented
94	C₂³×C₁₃	—	4	2	no	—
95	C₂³×C₁₃	—	8	2	no	—
96	C₂³×C₁₃	—	16	2	no	—
97	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
98	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
99	Q₈×C₁₃	—	2	2	no	—
100	D₄×C₁₃	—	2	4	no	—
101	D₄×C₁₃	—	2	2	no	—
102	D₄×C₁₃	—	4	2	no	—
103	D₄×C₁₃	—	4	2	no	—
104	D₄×C₁₃	—	8	2	no	—
105	D₄×C₁₃	—	16	4	no	—
106	C₂×C₄×C₁₃	—	2	2	no	—
107	C₂×C₄×C₁₃	—	2	2	no	—
108	C₂×C₄×C₁₃	—	4	2	no	—
109	C₂×C₄×C₁₃	#123	1	2	yes	—
110	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
111	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
112	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
113	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
114	C₈×C₁₃	—	2	2	no	—
115	C₈×C₁₃	—	4	4	no	—
116	C₈×C₁₃	#123	1	1	yes	characteristic
117	C₈×C₁₃	#123	1	1	yes	characteristic
118	C₈×C₁₃	C₂×#41	1	2	yes	—
119	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
120	#568	—	2	1	no	—
121	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
122	#535	—	2	1	no	—
123	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
124	#469	C₂²×C₁₃	1	4	yes	—
125	#466	—	2	2	no	—
126	#430	—	2	1	no	—
127	#430	C₂²×C₁₃	1	4	yes	complemented
128	C₂×#108	—	2	2	no	—
129	C₂×#108	C₂²×C₁₃	1	2	yes	—
130	#427	C₂²×C₁₃	1	1	yes	characteristic
131	#418	—	2	1	no	—
132	#365	C₂²×C₁₃	1	8	yes	complemented
133	#361	C₂²×C₁₃	1	8	yes	—
134	#349	C₂²×C₁₃	1	4	yes	complemented
135	C₂²×C₁₃	—	2	2	no	—
136	C₂²×C₁₃	—	4	1	no	—
137	C₂²×C₁₃	—	4	2	no	—
138	C₂²×C₁₃	—	8	4	no	—
139	C₂²×C₁₃	—	8	2	no	—
140	C₂²×C₁₃	—	16	4	no	—
141	C₂²×C₁₃	#481	1	2	yes	—
142	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
143	C₄×C₁₃	—	2	2	no	—
144	C₄×C₁₃	—	8	2	no	—
145	C₄×C₁₃	#481	1	2	yes	—
146	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
147	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
149	C₂²×D₄	—	2	1	no	—
150	C₂×D₈	—	2	1	no	—
151	C₂×D₈	—	2	2	no	—
152	C₂×D₈	—	2	2	no	—
153	C₂×D₈	C₂³×C₁₃	1	2	yes	—
154	#131	—	2	2	no	—
155	#131	—	2	2	no	—
156	#131	—	4	4	no	—
157	C₂×M₁₆	—	2	4	no	—
158	C₂×M₁₆	—	2	2	no	—
159	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
160	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
161	C₂²×C₈	D₄×C₁₃	1	2	yes	—
162	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
163	#127	—	4	1	no	—
164	#124	—	4	1	no	—
165	#121	—	2	4	no	—
166	#120	—	4	2	no	—
167	#117	—	2	1	no	—
168	M₃₂	—	2	2	no	—
169	M₃₂	C₂³×C₁₃	1	4	yes	—
170	C₂×C₁₆	—	2	2	no	—
171	#108	—	2	2	no	—
172	#108	—	2	4	no	—
173	#108	C₂³×C₁₃	1	4	yes	—
174	#107	—	2	1	no	—
175	#106	C₂³×C₁₃	1	2	yes	—
176	#102	—	2	4	no	—
177	C₂×C₁₃	—	2	1	no	—
178	C₂×C₁₃	—	2	2	no	—
179	C₂×C₁₃	—	4	2	no	—
180	C₂×C₁₃	—	16	2	no	—
181	C₂×C₁₃	C₂×#481	1	1	yes	characteristic
182	C₂⁴	—	4	1	no	—
183	#41	—	2	2	no	—
184	#41	—	2	2	no	—
185	C₂×Q₈	C₁₃×SD₁₆	1	1	yes	characteristic
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	—	4	4	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂×D₄	—	4	1	no	—
190	C₂×D₄	—	4	2	no	—
191	C₂×D₄	C₁₃×SD₁₆	1	2	yes	—
192	C₂×D₄	C₁₃×SD₁₆	1	1	yes	characteristic
193	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
194	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
195	D₈	—	2	4	no	—
196	D₈	—	4	1	no	—
197	D₈	—	4	1	no	—
198	M₁₆	—	2	2	no	—
199	M₁₆	—	2	4	no	—
200	M₁₆	—	2	4	no	—
201	M₁₆	—	4	4	no	—
202	M₁₆	—	4	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	4	4	no	—
206	C₂×C₈	—	4	2	no	—
207	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
208	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
209	C₂×C₈	C₁₃×#41	1	2	yes	—
210	C₂×C₈	C₁₃×#41	1	2	yes	—
211	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
212	C₄⋊C₄	—	2	2	no	—
213	C₂²⋊C₄	—	4	1	no	—
214	C₂²⋊C₄	—	4	4	no	—
215	C₄²	—	4	1	no	—
216	C₁₆	—	2	4	no	—
217	C₁₃	#33657	1	1	yes	characteristic, direct product factor, Sylow
218	C₂³	—	4	2	no	—
219	C₂³	—	8	2	no	—
220	C₂³	—	16	2	no	—
221	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
222	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
223	Q₈	—	2	2	no	—
224	D₄	—	2	4	no	—
225	D₄	—	2	2	no	—
226	D₄	—	4	2	no	—
227	D₄	—	4	2	no	—
228	D₄	—	8	2	no	—
229	D₄	—	16	4	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	C₁₃×#123	1	2	yes	—
234	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
235	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
236	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
237	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
238	C₈	—	2	2	no	—
239	C₈	—	4	4	no	—
240	C₈	C₁₃×#123	1	1	yes	characteristic
241	C₈	C₁₃×#123	1	1	yes	characteristic
242	C₈	C₂×C₁₃×#41	1	2	yes	—
243	C₂²	—	2	2	no	—
244	C₂²	—	4	1	no	—
245	C₂²	—	4	2	no	—
246	C₂²	—	8	4	no	—
247	C₂²	—	8	2	no	—
248	C₂²	—	16	4	no	—
249	C₂²	C₁₃×#481	1	2	yes	—
250	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
251	C₄	—	2	2	no	—
252	C₄	—	8	2	no	—
253	C₄	C₁₃×#481	1	2	yes	—
254	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
255	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂	—	2	1	no	—
257	C₂	—	2	2	no	—
258	C₂	—	4	2	no	—
259	C₂	—	16	2	no	—
260	C₂	C₂×C₁₃×#481	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×#481
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2916	C₂	semidirect
3. C₁₃×#2238	C₂	semidirect
4. C₁₃×#2155	C₂	semidirect
5. C₂×C₁₃×#361	C₂	semidirect
6. C₁₃×#2115	C₂	semidirect
15. C₁₃×#430	C₂²	semidirect
20. C₁₃×#365	C₂²	semidirect
22. C₁₃×#349	C₂²	semidirect
52. #33657	C₁₃	direct (N × H)
89. #2916	C₂×C₁₃	semidirect
90. #2238	C₂×C₁₃	semidirect
91. #2155	C₂×C₁₃	semidirect
92. C₂×#361	C₂×C₁₃	semidirect
93. #2115	C₂×C₁₃	semidirect
127. #430	C₂²×C₁₃	semidirect
132. #365	C₂²×C₁₃	semidirect
134. #349	C₂²×C₁₃	semidirect
217. C₁₃	#33657	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×#3058	2
C₁₃×#2916	2
C₁₃×#2238	2
C₁₃×#2155	2
C₂×C₁₃×#361	2
C₁₃×#2115	2
#33657	13

Subgroups — C13×#33657 #15719996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33657 #15719996