Subgroups — C₁₃×#32460 #15718799

Order 3328.

720 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2487	C₂	1	2	yes	maximal
2	C₁₃×#2087	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2076	C₂	1	4	yes	maximal, complemented
4	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1942	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1852	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₁₃×#107	C₂²	1	2	yes	—
10	C₂×C₁₃×#107	C₂²	1	2	yes	—
11	C₂×C₁₃×#107	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#400	—	2	2	no	—
16	C₁₃×#399	—	2	2	no	—
17	C₁₃×#389	C₂²	1	4	yes	—
18	C₁₃×#386	—	2	2	no	—
19	C₁₃×#385	—	2	2	no	—
20	C₁₃×#380	C₂²	1	2	yes	—
21	C₁₃×#380	C₂²	1	4	yes	—
22	C₁₃×#340	C₂²	1	2	yes	—
23	C₁₃×#340	C₂²	1	4	yes	—
24	C₁₃×#340	C₂²	1	4	yes	—
25	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	—	2	2	no	—
27	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
28	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
29	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
30	C₄×D₄×C₁₃	—	4	1	no	—
31	C₄×D₄×C₁₃	—	4	1	no	—
32	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
34	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
35	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
36	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
38	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
39	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
40	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
41	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
42	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
43	C₁₃×#107	—	2	4	no	—
44	C₁₃×#107	—	4	2	no	—
45	C₁₃×#107	—	4	2	no	—
46	C₁₃×C₄⋊C₈	—	4	1	no	—
47	C₁₃×C₂²⋊C₈	—	2	8	no	—
48	C₄×C₈×C₁₃	—	4	1	no	—
49	C₁₃×#95	—	2	4	no	—
50	C₁₃×#95	—	2	2	no	—
51	C₁₃×#95	—	2	4	no	—
52	#32460	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
54	C₂×D₄×C₁₃	—	4	1	no	—
55	C₂×D₄×C₁₃	—	4	1	no	—
56	C₂×D₄×C₁₃	Q₁₆	1	4	yes	—
57	C₂²×C₄×C₁₃	—	2	4	no	—
58	C₂²×C₄×C₁₃	—	2	2	no	—
59	C₂²×C₄×C₁₃	—	2	2	no	—
60	C₂²×C₄×C₁₃	—	2	4	no	—
61	C₂²×C₄×C₁₃	—	2	4	no	—
62	C₂²×C₄×C₁₃	—	2	4	no	—
63	C₂²×C₄×C₁₃	—	4	4	no	—
64	C₂²×C₄×C₁₃	—	8	4	no	—
65	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
69	C₂×C₈×C₁₃	—	2	2	no	—
70	C₂×C₈×C₁₃	—	2	2	no	—
71	C₂×C₈×C₁₃	—	2	4	no	—
72	C₂×C₈×C₁₃	—	2	2	no	—
73	C₂×C₈×C₁₃	#41	1	4	yes	—
74	C₁₃×C₄⋊C₄	—	2	4	no	—
75	C₁₃×C₄⋊C₄	—	2	4	no	—
76	C₁₃×C₄⋊C₄	—	2	4	no	—
77	C₁₃×C₄⋊C₄	—	2	4	no	—
78	C₁₃×C₄⋊C₄	—	4	1	no	—
79	C₁₃×C₄⋊C₄	—	4	4	no	—
80	C₁₃×C₄⋊C₄	—	8	4	no	—
81	C₁₃×C₂²⋊C₄	—	4	2	no	—
82	C₁₃×C₂²⋊C₄	—	4	4	no	—
83	C₁₃×C₂²⋊C₄	—	8	4	no	—
84	C₄²×C₁₃	—	2	1	no	—
85	C₄²×C₁₃	—	2	1	no	—
86	#2487	C₂×C₁₃	1	2	yes	—
87	#2087	C₂×C₁₃	1	2	yes	complemented
88	#2076	C₂×C₁₃	1	4	yes	complemented
89	#1954	C₂×C₁₃	1	1	yes	characteristic
90	#1942	C₂×C₁₃	1	2	yes	complemented
91	#1852	C₂×C₁₃	1	4	yes	complemented
92	C₂³×C₁₃	—	2	2	no	—
93	C₂³×C₁₃	—	2	4	no	—
94	C₂³×C₁₃	—	2	2	no	—
95	C₂³×C₁₃	—	2	4	no	—
96	C₂³×C₁₃	C₂×Q₁₆	1	4	yes	—
97	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
98	D₄×C₁₃	—	4	4	no	—
99	C₂×C₄×C₁₃	—	2	1	no	—
100	C₂×C₄×C₁₃	—	2	1	no	—
101	C₂×C₄×C₁₃	—	2	1	no	—
102	C₂×C₄×C₁₃	—	2	2	no	—
103	C₂×C₄×C₁₃	—	2	4	no	—
104	C₂×C₄×C₁₃	—	2	2	no	—
105	C₂×C₄×C₁₃	—	4	4	no	—
106	C₂×C₄×C₁₃	—	4	2	no	—
107	C₂×C₄×C₁₃	—	4	2	no	—
108	C₂×C₄×C₁₃	—	4	4	no	—
109	C₂×C₄×C₁₃	—	4	4	no	—
110	C₂×C₄×C₁₃	—	4	4	no	—
111	C₂×C₄×C₁₃	—	4	4	no	—
112	C₂×C₄×C₁₃	—	4	4	no	—
113	C₂×C₄×C₁₃	—	4	4	no	—
114	C₂×C₄×C₁₃	—	8	8	no	—
115	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
116	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
117	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
118	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
119	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
120	C₈×C₁₃	—	2	4	no	—
121	C₈×C₁₃	—	4	2	no	—
122	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
123	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
124	C₂×#107	C₂²×C₁₃	1	2	yes	—
125	C₂×#107	C₂²×C₁₃	1	2	yes	—
126	C₂×#107	C₂²×C₁₃	1	2	yes	—
127	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
128	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
129	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
130	#400	—	2	2	no	—
131	#399	—	2	2	no	—
132	#389	C₂²×C₁₃	1	4	yes	—
133	#386	—	2	2	no	—
134	#385	—	2	2	no	—
135	#380	C₂²×C₁₃	1	2	yes	—
136	#380	C₂²×C₁₃	1	4	yes	—
137	#340	C₂²×C₁₃	1	2	yes	—
138	#340	C₂²×C₁₃	1	4	yes	—
139	#340	C₂²×C₁₃	1	4	yes	—
140	C₂²×C₁₃	—	2	8	no	—
141	C₂²×C₁₃	—	2	4	no	—
142	C₂²×C₁₃	—	4	4	no	—
143	C₂²×C₁₃	—	4	2	no	—
144	C₂²×C₁₃	—	4	2	no	—
145	C₂²×C₁₃	#534	1	1	yes	characteristic
146	C₂²×C₁₃	#547	1	2	yes	—
147	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
148	C₂²×C₁₃	#575	1	1	yes	characteristic
149	C₂²×C₁₃	#576	1	2	yes	—
150	C₄×C₁₃	—	2	2	no	—
151	C₄×C₁₃	—	4	1	no	—
152	C₄×C₁₃	—	4	2	no	—
153	C₄×C₁₃	—	8	4	no	—
154	C₄×C₁₃	—	8	4	no	—
155	C₄×C₁₃	#539	1	2	yes	—
156	C₄×C₁₃	#559	1	1	yes	characteristic
157	C₄×C₁₃	#563	1	1	yes	characteristic
158	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
159	C₂³×C₄	—	2	2	no	—
160	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
161	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
162	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
163	C₄×D₄	—	4	1	no	—
164	C₄×D₄	—	4	1	no	—
165	C₂×C₄⋊C₄	—	2	2	no	—
166	C₂×C₄⋊C₄	—	2	4	no	—
167	C₂×C₄⋊C₄	—	4	2	no	—
168	C₂×C₄⋊C₄	—	4	2	no	—
169	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
170	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
171	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
172	C₂×C₂²⋊C₄	—	2	2	no	—
173	C₂×C₂²⋊C₄	—	2	4	no	—
174	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
175	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
176	#107	—	2	4	no	—
177	#107	—	4	2	no	—
178	#107	—	4	2	no	—
179	C₄⋊C₈	—	4	1	no	—
180	C₂²⋊C₈	—	2	8	no	—
181	C₄×C₈	—	4	1	no	—
182	#95	—	2	4	no	—
183	#95	—	2	2	no	—
184	#95	—	2	4	no	—
185	C₂×C₁₃	—	4	4	no	—
186	C₂×C₁₃	#2724	1	1	yes	characteristic
187	C₂×C₁₃	#3189	1	1	yes	characteristic
188	C₂×C₁₃	#3199	1	1	yes	characteristic
189	C₂×C₁₃	#3338	1	2	yes	—
190	C₂×C₁₃	#3355	1	2	yes	—
191	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
192	C₂×D₄	—	4	1	no	—
193	C₂×D₄	—	4	1	no	—
194	C₂×D₄	C₁₃×Q₁₆	1	4	yes	—
195	C₂²×C₄	—	2	4	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	—	2	4	no	—
199	C₂²×C₄	—	2	4	no	—
200	C₂²×C₄	—	2	4	no	—
201	C₂²×C₄	—	4	4	no	—
202	C₂²×C₄	—	8	4	no	—
203	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
204	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
205	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
206	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
207	C₂×C₈	—	2	2	no	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	—	2	4	no	—
210	C₂×C₈	—	2	2	no	—
211	C₂×C₈	C₁₃×#41	1	4	yes	—
212	C₄⋊C₄	—	2	4	no	—
213	C₄⋊C₄	—	2	4	no	—
214	C₄⋊C₄	—	2	4	no	—
215	C₄⋊C₄	—	2	4	no	—
216	C₄⋊C₄	—	4	1	no	—
217	C₄⋊C₄	—	4	4	no	—
218	C₄⋊C₄	—	8	4	no	—
219	C₂²⋊C₄	—	4	2	no	—
220	C₂²⋊C₄	—	4	4	no	—
221	C₂²⋊C₄	—	8	4	no	—
222	C₄²	—	2	1	no	—
223	C₄²	—	2	1	no	—
224	C₁₃	#32460	1	1	yes	characteristic, direct product factor, Sylow
225	C₂³	—	2	2	no	—
226	C₂³	—	2	4	no	—
227	C₂³	—	2	2	no	—
228	C₂³	—	2	4	no	—
229	C₂³	C₂×C₁₃×Q₁₆	1	4	yes	—
230	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
231	D₄	—	4	4	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	4	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	4	4	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	2	no	—
241	C₂×C₄	—	4	4	no	—
242	C₂×C₄	—	4	4	no	—
243	C₂×C₄	—	4	4	no	—
244	C₂×C₄	—	4	4	no	—
245	C₂×C₄	—	4	4	no	—
246	C₂×C₄	—	4	4	no	—
247	C₂×C₄	—	8	8	no	—
248	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
249	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
250	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
251	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
252	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
253	C₈	—	2	4	no	—
254	C₈	—	4	2	no	—
255	C₂²	—	2	8	no	—
256	C₂²	—	2	4	no	—
257	C₂²	—	4	4	no	—
258	C₂²	—	4	2	no	—
259	C₂²	—	4	2	no	—
260	C₂²	C₁₃×#534	1	1	yes	characteristic
261	C₂²	C₁₃×#547	1	2	yes	—
262	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
263	C₂²	C₁₃×#575	1	1	yes	characteristic
264	C₂²	C₁₃×#576	1	2	yes	—
265	C₄	—	2	2	no	—
266	C₄	—	4	1	no	—
267	C₄	—	4	2	no	—
268	C₄	—	8	4	no	—
269	C₄	—	8	4	no	—
270	C₄	C₁₃×#539	1	2	yes	—
271	C₄	C₁₃×#559	1	1	yes	characteristic
272	C₄	C₁₃×#563	1	1	yes	characteristic
273	C₂	—	4	4	no	—
274	C₂	C₁₃×#2724	1	1	yes	characteristic
275	C₂	C₁₃×#3189	1	1	yes	characteristic
276	C₂	C₁₃×#3199	1	1	yes	characteristic
277	C₂	C₁₃×#3338	1	2	yes	—
278	C₂	C₁₃×#3355	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2087	C₂	semidirect
3. C₁₃×#2076	C₂	semidirect
5. C₁₃×#1942	C₂	semidirect
6. C₁₃×#1852	C₂	semidirect
52. #32460	C₁₃	direct (N × H)
87. #2087	C₂×C₁₃	semidirect
88. #2076	C₂×C₁₃	semidirect
90. #1942	C₂×C₁₃	semidirect
91. #1852	C₂×C₁₃	semidirect
224. C₁₃	#32460	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×#2487	2
C₁₃×#2087	2
C₁₃×#2076	2
C₁₃×#1954	2
C₁₃×#1942	2
C₁₃×#1852	2
#32460	13

Subgroups — C13×#32460 #15718799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32460 #15718799