Subgroups — C₁₃×#32467 #15718806

Order 3328.

714 conjugacy classes of subgroups.

The subgroup lattice has 272 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×#2086	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2077	C₂	1	4	yes	maximal, complemented
4	C₁₃×#1955	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1944	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×#106	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×C₁₃×#97	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	—	4	2	no	—
44	C₁₃×#107	—	4	2	no	—
45	C₁₃×#106	—	2	4	no	—
46	C₁₃×C₄⋊C₈	—	4	1	no	—
47	C₁₃×C₂²⋊C₈	—	2	8	no	—
48	C₁₃×#97	—	4	1	no	—
49	C₁₃×#95	—	2	4	no	—
50	C₁₃×#95	—	2	2	no	—
51	C₁₃×#95	—	2	4	no	—
52	#32467	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
54	C₂×D₄×C₁₃	—	2	4	no	—
55	C₂×D₄×C₁₃	—	4	1	no	—
56	C₂²×C₄×C₁₃	—	2	4	no	—
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	—	2	2	no	—
59	C₂²×C₄×C₁₃	—	2	4	no	—
60	C₂²×C₄×C₁₃	—	2	4	no	—
61	C₂²×C₄×C₁₃	—	2	4	no	—
62	C₂²×C₄×C₁₃	—	4	4	no	—
63	C₂²×C₄×C₁₃	—	8	4	no	—
64	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
68	C₂×C₈×C₁₃	—	2	2	no	—
69	C₂×C₈×C₁₃	—	2	2	no	—
70	C₂×C₈×C₁₃	—	2	4	no	—
71	C₂×C₈×C₁₃	—	2	2	no	—
72	C₂×C₈×C₁₃	#41	1	4	yes	—
73	C₁₃×C₄⋊C₄	—	2	4	no	—
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	—	4	1	no	—
78	C₁₃×C₄⋊C₄	—	4	4	no	—
79	C₁₃×C₄⋊C₄	—	8	4	no	—
80	C₁₃×C₂²⋊C₄	—	4	2	no	—
81	C₁₃×C₂²⋊C₄	—	4	4	no	—
82	C₁₃×C₂²⋊C₄	—	8	4	no	—
83	C₄²×C₁₃	—	2	1	no	—
84	C₄²×C₁₃	—	2	1	no	—
85	#2487	C₂×C₁₃	1	2	yes	—
86	#2086	C₂×C₁₃	1	2	yes	complemented
87	#2077	C₂×C₁₃	1	4	yes	complemented
88	#1955	C₂×C₁₃	1	1	yes	characteristic
89	#1944	C₂×C₁₃	1	2	yes	complemented
90	#1852	C₂×C₁₃	1	4	yes	complemented
91	C₂³×C₁₃	—	2	2	no	—
92	C₂³×C₁₃	—	2	4	no	—
93	C₂³×C₁₃	—	2	2	no	—
94	C₂³×C₁₃	—	2	4	no	—
95	C₂³×C₁₃	#137	1	4	yes	—
96	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
97	D₄×C₁₃	—	4	4	no	—
98	C₂×C₄×C₁₃	—	2	1	no	—
99	C₂×C₄×C₁₃	—	2	1	no	—
100	C₂×C₄×C₁₃	—	2	2	no	—
101	C₂×C₄×C₁₃	—	2	4	no	—
102	C₂×C₄×C₁₃	—	2	2	no	—
103	C₂×C₄×C₁₃	—	2	2	no	—
104	C₂×C₄×C₁₃	—	4	4	no	—
105	C₂×C₄×C₁₃	—	4	2	no	—
106	C₂×C₄×C₁₃	—	4	2	no	—
107	C₂×C₄×C₁₃	—	4	4	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	—	8	8	no	—
114	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
115	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
116	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
117	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
118	C₈×C₁₃	—	2	4	no	—
119	C₈×C₁₃	—	4	2	no	—
120	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
121	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
122	C₂×#107	C₂²×C₁₃	1	2	yes	—
123	C₂×#107	C₂²×C₁₃	1	2	yes	—
124	C₂×#106	C₂²×C₁₃	1	2	yes	—
125	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
126	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
127	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
128	#400	—	2	2	no	—
129	#399	—	2	2	no	—
130	#389	C₂²×C₁₃	1	4	yes	—
131	#386	—	2	2	no	—
132	#385	—	2	2	no	—
133	#380	C₂²×C₁₃	1	2	yes	—
134	#380	C₂²×C₁₃	1	4	yes	—
135	#340	C₂²×C₁₃	1	2	yes	—
136	#340	C₂²×C₁₃	1	4	yes	—
137	#340	C₂²×C₁₃	1	4	yes	—
138	C₂²×C₁₃	—	2	8	no	—
139	C₂²×C₁₃	—	2	4	no	—
140	C₂²×C₁₃	—	4	4	no	—
141	C₂²×C₁₃	—	4	2	no	—
142	C₂²×C₁₃	—	4	2	no	—
143	C₂²×C₁₃	#534	1	1	yes	characteristic
144	C₂²×C₁₃	#547	1	2	yes	—
145	C₂²×C₁₃	C₂×#137	1	2	yes	—
146	C₂²×C₁₃	#576	1	2	yes	—
147	C₄×C₁₃	—	4	1	no	—
148	C₄×C₁₃	—	4	1	no	—
149	C₄×C₁₃	—	4	2	no	—
150	C₄×C₁₃	—	8	4	no	—
151	C₄×C₁₃	—	8	4	no	—
152	C₄×C₁₃	#539	1	2	yes	—
153	C₄×C₁₃	#559	1	1	yes	characteristic
154	C₄×C₁₃	#563	1	1	yes	characteristic
155	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
156	C₂³×C₄	—	2	2	no	—
157	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
158	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
159	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
160	C₄×D₄	—	4	1	no	—
161	C₄×D₄	—	4	1	no	—
162	C₂×C₄⋊C₄	—	2	2	no	—
163	C₂×C₄⋊C₄	—	2	4	no	—
164	C₂×C₄⋊C₄	—	4	2	no	—
165	C₂×C₄⋊C₄	—	4	2	no	—
166	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
167	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
168	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
169	C₂×C₂²⋊C₄	—	2	2	no	—
170	C₂×C₂²⋊C₄	—	2	4	no	—
171	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
172	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
173	#107	—	4	2	no	—
174	#107	—	4	2	no	—
175	#106	—	2	4	no	—
176	C₄⋊C₈	—	4	1	no	—
177	C₂²⋊C₈	—	2	8	no	—
178	#97	—	4	1	no	—
179	#95	—	2	4	no	—
180	#95	—	2	2	no	—
181	#95	—	2	4	no	—
182	C₂×C₁₃	—	4	4	no	—
183	C₂×C₁₃	#2724	1	1	yes	characteristic
184	C₂×C₁₃	#3195	1	1	yes	characteristic
185	C₂×C₁₃	#3199	1	1	yes	characteristic
186	C₂×C₁₃	#3346	1	4	yes	—
187	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
188	C₂×D₄	—	2	4	no	—
189	C₂×D₄	—	4	1	no	—
190	C₂²×C₄	—	2	4	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	4	no	—
194	C₂²×C₄	—	2	4	no	—
195	C₂²×C₄	—	2	4	no	—
196	C₂²×C₄	—	4	4	no	—
197	C₂²×C₄	—	8	4	no	—
198	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
199	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
200	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
201	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	C₁₃×#41	1	4	yes	—
207	C₄⋊C₄	—	2	4	no	—
208	C₄⋊C₄	—	2	4	no	—
209	C₄⋊C₄	—	2	4	no	—
210	C₄⋊C₄	—	2	4	no	—
211	C₄⋊C₄	—	4	1	no	—
212	C₄⋊C₄	—	4	4	no	—
213	C₄⋊C₄	—	8	4	no	—
214	C₂²⋊C₄	—	4	2	no	—
215	C₂²⋊C₄	—	4	4	no	—
216	C₂²⋊C₄	—	8	4	no	—
217	C₄²	—	2	1	no	—
218	C₄²	—	2	1	no	—
219	C₁₃	#32467	1	1	yes	characteristic, direct product factor, Sylow
220	C₂³	—	2	2	no	—
221	C₂³	—	2	4	no	—
222	C₂³	—	2	2	no	—
223	C₂³	—	2	4	no	—
224	C₂³	C₁₃×#137	1	4	yes	—
225	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
226	D₄	—	4	4	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	4	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	4	no	—
237	C₂×C₄	—	4	4	no	—
238	C₂×C₄	—	4	4	no	—
239	C₂×C₄	—	4	4	no	—
240	C₂×C₄	—	4	4	no	—
241	C₂×C₄	—	4	4	no	—
242	C₂×C₄	—	8	8	no	—
243	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
244	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
247	C₈	—	2	4	no	—
248	C₈	—	4	2	no	—
249	C₂²	—	2	8	no	—
250	C₂²	—	2	4	no	—
251	C₂²	—	4	4	no	—
252	C₂²	—	4	2	no	—
253	C₂²	—	4	2	no	—
254	C₂²	C₁₃×#534	1	1	yes	characteristic
255	C₂²	C₁₃×#547	1	2	yes	—
256	C₂²	C₂×C₁₃×#137	1	2	yes	—
257	C₂²	C₁₃×#576	1	2	yes	—
258	C₄	—	4	1	no	—
259	C₄	—	4	1	no	—
260	C₄	—	4	2	no	—
261	C₄	—	8	4	no	—
262	C₄	—	8	4	no	—
263	C₄	C₁₃×#539	1	2	yes	—
264	C₄	C₁₃×#559	1	1	yes	characteristic
265	C₄	C₁₃×#563	1	1	yes	characteristic
266	C₂	—	4	4	no	—
267	C₂	C₁₃×#2724	1	1	yes	characteristic
268	C₂	C₁₃×#3195	1	1	yes	characteristic
269	C₂	C₁₃×#3199	1	1	yes	characteristic
270	C₂	C₁₃×#3346	1	4	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×#2086	C₂	semidirect
3. C₁₃×#2077	C₂	semidirect
5. C₁₃×#1944	C₂	semidirect
6. C₁₃×#1852	C₂	semidirect
52. #32467	C₁₃	direct (N × H)
86. #2086	C₂×C₁₃	semidirect
87. #2077	C₂×C₁₃	semidirect
89. #1944	C₂×C₁₃	semidirect
90. #1852	C₂×C₁₃	semidirect
219. C₁₃	#32467	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×#2086	2
C₁₃×#2077	2
C₁₃×#1955	2
C₁₃×#1944	2
C₁₃×#1852	2
#32467	13

Subgroups — C13×#32467 #15718806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32467 #15718806