Subgroups — C₁₃×#2967 #13112025

Order 1664.

362 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#446	C₂	1	2	yes	maximal, complemented
3	C₁₃×#436	C₂	1	2	yes	maximal, complemented
4	C₁₃×#435	C₂	1	2	yes	maximal, complemented
5	C₁₃×#435	C₂	1	2	yes	maximal, complemented
6	C₁₃×#433	C₂	1	2	yes	maximal, complemented
7	C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#405	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
12	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
13	C₁₃×#126	C₄	1	2	yes	—
14	C₁₃×#125	C₄	1	1	yes	characteristic
15	C₁₃×#124	C₄	1	1	yes	characteristic
16	C₁₃×#123	C₄	1	2	yes	—
17	C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
18	C₁₃×#121	C₄	1	1	yes	characteristic
19	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₄×D₄×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#117	C₂²	1	2	yes	—
23	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
27	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
31	C₁₃×#97	C₂²	1	2	yes	—
32	C₁₃×#97	C₂²	1	2	yes	—
33	C₁₃×#97	C₂²	1	2	yes	—
34	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₄×C₈×C₁₃	C₂²	1	2	yes	—
37	C₂×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×D₄×C₁₃	C₂×C₄	1	2	yes	—
39	C₂×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
44	C₁₃×M₁₆	—	2	4	no	—
45	C₁₃×M₁₆	—	2	4	no	—
46	C₂×C₈×C₁₃	—	2	4	no	—
47	C₂×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
59	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₄²×C₁₃	C₂³	1	2	yes	—
66	C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	#2967	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂³×C₁₃	C₂²×C₄	1	2	yes	—
69	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	Q₈×C₁₃	—	4	1	no	—
71	D₄×C₁₃	—	4	1	no	—
72	D₄×C₁₃	—	4	2	no	—
73	C₂×C₄×C₁₃	—	2	2	no	—
74	C₂×C₄×C₁₃	—	2	2	no	—
75	C₂×C₄×C₁₃	—	2	2	no	—
76	C₂×C₄×C₁₃	—	4	1	no	—
77	C₂×C₄×C₁₃	—	4	1	no	—
78	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
84	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
87	C₈×C₁₃	—	2	2	no	—
88	C₈×C₁₃	—	2	2	no	—
89	C₈×C₁₃	—	2	2	no	—
90	C₈×C₁₃	#41	1	4	yes	—
91	#529	C₂×C₁₃	1	1	yes	characteristic
92	#446	C₂×C₁₃	1	2	yes	complemented
93	#436	C₂×C₁₃	1	2	yes	complemented
94	#435	C₂×C₁₃	1	2	yes	complemented
95	#435	C₂×C₁₃	1	2	yes	complemented
96	#433	C₂×C₁₃	1	2	yes	complemented
97	#432	C₂×C₁₃	1	1	yes	characteristic, complemented
98	#405	C₂×C₁₃	1	2	yes	complemented
99	C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
100	C₂²×C₁₃	—	2	2	no	—
101	C₂²×C₁₃	—	2	1	no	—
102	C₂²×C₁₃	—	2	1	no	—
103	C₂²×C₁₃	—	2	1	no	—
104	C₂²×C₁₃	—	2	2	no	—
105	C₂²×C₁₃	—	2	2	no	—
106	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
107	C₄×C₁₃	—	2	2	no	—
108	C₄×C₁₃	—	2	1	no	—
109	C₄×C₁₃	—	2	1	no	—
110	C₄×C₁₃	—	2	1	no	—
111	C₄×C₁₃	—	2	1	no	—
112	C₄×C₁₃	—	2	1	no	—
113	C₄×C₁₃	—	2	2	no	—
114	C₄×C₁₃	—	2	2	no	—
115	C₄×C₁₃	C₂×#41	1	2	yes	—
116	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
117	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
118	C₂²×C₈	C₂²×C₁₃	1	2	yes	—
119	#126	C₄×C₁₃	1	2	yes	—
120	#125	C₄×C₁₃	1	1	yes	characteristic
121	#124	C₄×C₁₃	1	1	yes	characteristic
122	#123	C₄×C₁₃	1	2	yes	—
123	C₂²⋊Q₈	C₄×C₁₃	1	1	yes	characteristic
124	#121	C₄×C₁₃	1	1	yes	characteristic
125	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
126	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
127	C₄×D₄	C₂²×C₁₃	1	2	yes	—
128	#117	C₂²×C₁₃	1	2	yes	—
129	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
130	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
131	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
132	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
133	C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
134	C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
135	C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
136	C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
137	#97	C₂²×C₁₃	1	2	yes	—
138	#97	C₂²×C₁₃	1	2	yes	—
139	#97	C₂²×C₁₃	1	2	yes	—
140	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
141	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
142	C₄×C₈	C₂²×C₁₃	1	2	yes	—
143	C₂×C₁₃	—	4	1	no	—
144	C₂×C₁₃	—	4	2	no	—
145	C₂×C₁₃	C₄×#41	1	1	yes	characteristic
146	C₂×C₁₃	#568	1	1	yes	characteristic
147	C₂×C₁₃	#568	1	1	yes	characteristic
148	C₂×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
149	C₂×D₄	C₂×C₄×C₁₃	1	2	yes	—
150	C₂×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
152	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
153	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
154	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
155	M₁₆	—	2	4	no	—
156	M₁₆	—	2	4	no	—
157	C₂×C₈	—	2	4	no	—
158	C₂×C₈	C₂³×C₁₃	1	2	yes	—
159	C₂×C₈	C₂³×C₁₃	1	2	yes	—
160	C₂×C₈	C₂³×C₁₃	1	2	yes	—
161	C₂×C₈	C₂³×C₁₃	1	2	yes	—
162	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
163	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
164	C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
165	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
166	C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
167	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
168	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
169	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
170	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
171	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
172	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
173	C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
174	C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
175	C₄²	C₂³×C₁₃	1	1	yes	characteristic
176	C₄²	C₂³×C₁₃	1	2	yes	—
177	C₄²	C₂³×C₁₃	1	1	yes	characteristic
178	C₁₃	#2967	1	1	yes	characteristic, direct product factor, Sylow
179	C₂³	C₂²×C₄×C₁₃	1	2	yes	—
180	C₂³	C₂²×C₄×C₁₃	1	1	yes	characteristic
181	Q₈	—	4	1	no	—
182	D₄	—	4	1	no	—
183	D₄	—	4	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	4	1	no	—
188	C₂×C₄	—	4	1	no	—
189	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
190	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
191	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
192	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
193	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
194	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
195	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
196	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
197	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
198	C₈	—	2	2	no	—
199	C₈	—	2	2	no	—
200	C₈	—	2	2	no	—
201	C₈	C₁₃×#41	1	4	yes	—
202	C₂²	—	2	2	no	—
203	C₂²	—	2	1	no	—
204	C₂²	—	2	1	no	—
205	C₂²	—	2	1	no	—
206	C₂²	—	2	2	no	—
207	C₂²	—	2	2	no	—
208	C₂²	C₂³×C₄×C₁₃	1	1	yes	characteristic
209	C₄	—	2	2	no	—
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	2	2	no	—
216	C₄	—	2	2	no	—
217	C₄	C₂×C₁₃×#41	1	2	yes	—
218	C₂	—	4	1	no	—
219	C₂	—	4	2	no	—
220	C₂	C₄×C₁₃×#41	1	1	yes	characteristic
221	C₂	C₁₃×#568	1	1	yes	characteristic
222	C₂	C₁₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₄
prime radical	C₁₃×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#446	C₂	semidirect
3. C₁₃×#436	C₂	semidirect
4. C₁₃×#435	C₂	semidirect
5. C₁₃×#435	C₂	semidirect
6. C₁₃×#433	C₂	semidirect
7. C₁₃×#432	C₂	semidirect
8. C₁₃×#405	C₂	semidirect
9. C₄×C₁₃×M₁₆	C₂	semidirect
67. #2967	C₁₃	direct (N × H)
92. #446	C₂×C₁₃	semidirect
93. #436	C₂×C₁₃	semidirect
94. #435	C₂×C₁₃	semidirect
95. #435	C₂×C₁₃	semidirect
96. #433	C₂×C₁₃	semidirect
97. #432	C₂×C₁₃	semidirect
98. #405	C₂×C₁₃	semidirect
99. C₄×M₁₆	C₂×C₁₃	semidirect
178. C₁₃	#2967	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×#529	2
C₁₃×#446	2
C₁₃×#436	2
C₁₃×#435	2
C₁₃×#433	2
C₁₃×#432	2
C₁₃×#405	2
C₄×C₁₃×M₁₆	2
#2967	13

Subgroups — C13×#2967 #13112025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2967 #13112025