Subgroups — C₁₃×#3240 #13112298

Order 1664.

328 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#529	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#485	C₂	1	2	yes	maximal, complemented
8	C₁₃×#482	C₂	1	2	yes	maximal
9	C₁₃×#479	C₂	1	2	yes	maximal, complemented
10	C₁₃×#478	C₂	1	2	yes	maximal, complemented
11	C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₃×#126	—	2	1	no	—
15	C₁₃×#125	C₂²	1	2	yes	—
16	C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₁₃×#124	C₂²	1	1	yes	characteristic
18	C₁₃×#123	—	2	1	no	—
19	C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₁₃×C₂²⋊Q₈	—	2	1	no	—
21	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₄×Q₈×C₁₃	—	2	1	no	—
24	C₄×Q₈×C₁₃	—	2	1	no	—
25	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₄×D₄×C₁₃	—	2	1	no	—
27	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#117	—	2	1	no	—
29	C₁₃×#117	C₂²	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#107	C₂²	1	2	yes	—
32	C₁₃×#107	C₂²	1	2	yes	—
33	C₁₃×#106	C₂²	1	2	yes	—
34	C₁₃×#106	C₂²	1	2	yes	—
35	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
36	C₁₃×#103	C₂²	1	2	yes	—
37	C₁₃×#103	C₂²	1	2	yes	—
38	C₁₃×#102	C₂²	1	2	yes	—
39	C₁₃×#102	C₂²	1	2	yes	—
40	C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₁₃×#97	C₂²	1	1	yes	characteristic
42	C₁₃×#97	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₁₃	—	2	1	no	—
44	C₂×Q₈×C₁₃	—	2	1	no	—
45	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×D₄×C₁₃	—	2	1	no	—
47	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	—	2	1	no	—
49	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂×C₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₄²×C₁₃	—	2	1	no	—
73	C₄²×C₁₃	—	2	2	no	—
74	C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	#3240	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂³×C₁₃	—	2	1	no	—
80	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
81	Q₈×C₁₃	—	2	2	no	—
82	Q₈×C₁₃	—	4	2	no	—
83	Q₈×C₁₃	—	4	2	no	—
84	D₄×C₁₃	—	2	2	no	—
85	D₄×C₁₃	—	4	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	2	1	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	2	2	no	—
91	C₂×C₄×C₁₃	—	2	1	no	—
92	C₂×C₄×C₁₃	—	4	1	no	—
93	C₂×C₄×C₁₃	—	4	1	no	—
94	C₂×C₄×C₁₃	—	4	2	no	—
95	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₈×C₁₃	—	2	2	no	—
102	C₈×C₁₃	—	2	2	no	—
103	#533	C₂×C₁₃	1	1	yes	characteristic, complemented
104	#529	C₂×C₁₃	1	1	yes	characteristic
105	#501	C₂×C₁₃	1	1	yes	characteristic, complemented
106	#501	C₂×C₁₃	1	1	yes	characteristic, complemented
107	#489	C₂×C₁₃	1	1	yes	characteristic, complemented
108	#489	C₂×C₁₃	1	1	yes	characteristic, complemented
109	#485	C₂×C₁₃	1	2	yes	complemented
110	#482	C₂×C₁₃	1	2	yes	—
111	#479	C₂×C₁₃	1	2	yes	complemented
112	#478	C₂×C₁₃	1	2	yes	complemented
113	#432	C₂×C₁₃	1	1	yes	characteristic, complemented
114	C₂²×C₁₃	—	2	1	no	—
115	C₂²×C₁₃	—	2	1	no	—
116	C₂²×C₁₃	—	2	1	no	—
117	C₂²×C₁₃	—	4	1	no	—
118	C₂²×C₁₃	—	4	1	no	—
119	C₂²×C₁₃	—	4	1	no	—
120	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
121	C₄×C₁₃	—	2	1	no	—
122	C₄×C₁₃	—	2	1	no	—
123	C₄×C₁₃	—	2	1	no	—
124	C₄×C₁₃	—	2	1	no	—
125	C₄×C₁₃	—	2	1	no	—
126	C₄×C₁₃	—	4	1	no	—
127	C₄×C₁₃	—	4	1	no	—
128	C₄×C₁₃	—	4	1	no	—
129	C₄×C₁₃	—	4	2	no	—
130	C₄×C₁₃	—	4	2	no	—
131	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
132	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
133	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
134	#126	—	2	1	no	—
135	#125	C₂²×C₁₃	1	1	yes	characteristic
136	#125	C₂²×C₁₃	1	2	yes	—
137	#124	C₂²×C₁₃	1	1	yes	characteristic
138	#123	—	2	1	no	—
139	C₂²⋊Q₈	—	2	1	no	—
140	C₂²⋊Q₈	—	2	1	no	—
141	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
142	#121	C₂²×C₁₃	1	1	yes	characteristic
143	C₄×Q₈	—	2	1	no	—
144	C₄×Q₈	—	2	1	no	—
145	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
146	C₄×D₄	—	2	1	no	—
147	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
148	#117	—	2	1	no	—
149	#117	C₂²×C₁₃	1	2	yes	—
150	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
151	#107	C₂²×C₁₃	1	2	yes	—
152	#107	C₂²×C₁₃	1	2	yes	—
153	#106	C₂²×C₁₃	1	2	yes	—
154	#106	C₂²×C₁₃	1	2	yes	—
155	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
156	#103	C₂²×C₁₃	1	2	yes	—
157	#103	C₂²×C₁₃	1	2	yes	—
158	#102	C₂²×C₁₃	1	2	yes	—
159	#102	C₂²×C₁₃	1	2	yes	—
160	C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
161	#97	C₂²×C₁₃	1	1	yes	characteristic
162	#97	C₂²×C₁₃	1	1	yes	characteristic
163	C₂×C₁₃	—	4	1	no	—
164	C₂×C₁₃	—	8	1	no	—
165	C₂×C₁₃	#536	1	1	yes	characteristic
166	C₂×C₁₃	#575	1	1	yes	characteristic
167	C₂×C₁₃	#575	1	1	yes	characteristic
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
171	C₂×D₄	—	2	1	no	—
172	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	D₄×C₁₃	1	1	yes	characteristic
175	C₂²×C₄	D₄×C₁₃	1	1	yes	characteristic
176	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
177	C₂×C₈	C₂³×C₁₃	1	2	yes	—
178	C₂×C₈	C₂³×C₁₃	1	2	yes	—
179	C₄⋊C₄	—	2	1	no	—
180	C₄⋊C₄	—	2	1	no	—
181	C₄⋊C₄	—	2	1	no	—
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
188	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
189	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
190	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
191	C₂²⋊C₄	—	2	2	no	—
192	C₂²⋊C₄	—	2	1	no	—
193	C₂²⋊C₄	—	2	1	no	—
194	C₂²⋊C₄	—	2	1	no	—
195	C₂²⋊C₄	—	2	1	no	—
196	C₂²⋊C₄	—	2	1	no	—
197	C₄²	—	2	1	no	—
198	C₄²	—	2	2	no	—
199	C₄²	D₄×C₁₃	1	1	yes	characteristic
200	C₄²	D₄×C₁₃	1	1	yes	characteristic
201	C₄²	C₂³×C₁₃	1	1	yes	characteristic
202	C₄²	C₂³×C₁₃	1	1	yes	characteristic
203	C₁₃	#3240	1	1	yes	characteristic, direct product factor, Sylow
204	C₂³	—	2	1	no	—
205	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
206	Q₈	—	2	2	no	—
207	Q₈	—	4	2	no	—
208	Q₈	—	4	2	no	—
209	D₄	—	2	2	no	—
210	D₄	—	4	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	4	1	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
221	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
222	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
223	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
224	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
225	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
226	C₈	—	2	2	no	—
227	C₈	—	2	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	4	1	no	—
232	C₂²	—	4	1	no	—
233	C₂²	—	4	1	no	—
234	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	—	2	1	no	—
240	C₄	—	4	1	no	—
241	C₄	—	4	1	no	—
242	C₄	—	4	1	no	—
243	C₄	—	4	2	no	—
244	C₄	—	4	2	no	—
245	C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
246	C₂	—	4	1	no	—
247	C₂	—	8	1	no	—
248	C₂	C₁₃×#536	1	1	yes	characteristic
249	C₂	C₁₃×#575	1	1	yes	characteristic
250	C₂	C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#533	C₂	semidirect
3. C₁₃×#501	C₂	semidirect
4. C₁₃×#501	C₂	semidirect
5. C₁₃×#489	C₂	semidirect
6. C₁₃×#489	C₂	semidirect
7. C₁₃×#485	C₂	semidirect
9. C₁₃×#479	C₂	semidirect
10. C₁₃×#478	C₂	semidirect
11. C₁₃×#432	C₂	semidirect
78. #3240	C₁₃	direct (N × H)
103. #533	C₂×C₁₃	semidirect
105. #501	C₂×C₁₃	semidirect
106. #501	C₂×C₁₃	semidirect
107. #489	C₂×C₁₃	semidirect
108. #489	C₂×C₁₃	semidirect
109. #485	C₂×C₁₃	semidirect
111. #479	C₂×C₁₃	semidirect
112. #478	C₂×C₁₃	semidirect
113. #432	C₂×C₁₃	semidirect
203. C₁₃	#3240	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×#533	2
C₁₃×#529	2
C₁₃×#501	2
C₁₃×#489	2
C₁₃×#485	2
C₁₃×#482	2
C₁₃×#479	2
C₁₃×#478	2
C₁₃×#432	2
#3240	13

Subgroups — C13×#3240 #13112298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3240 #13112298