Subgroups — C₁₃×#12606 #15698945

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2112	C₂	1	2	yes	maximal
3	C₂×C₁₃×#347	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1375	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₃×M₁₆	C₄	1	1	yes	characteristic
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
8	C₂×C₁₃×M₃₂	C₂²	1	4	yes	—
9	C₁₃×#405	—	2	4	no	—
10	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
14	C₁₃×C₂²⋊C₁₆	C₄	1	8	yes	complemented
15	C₁₃×#347	—	2	4	no	—
16	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₃×M₁₆	—	2	2	no	—
18	C₂×C₁₃×M₁₆	—	2	2	no	—
19	C₂×C₁₃×M₁₆	—	2	2	no	—
20	C₂²×C₈×C₁₃	—	2	2	no	—
21	C₂²×C₈×C₁₃	—	2	2	no	—
22	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₁₃×#117	—	2	2	no	—
28	C₁₃×#117	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
30	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₁₃×M₃₂	—	2	4	no	—
34	C₁₃×M₃₂	—	2	4	no	—
35	C₂×C₁₃×C₁₆	C₂×C₄	1	8	yes	—
36	C₁₃×#97	—	2	2	no	—
37	C₁₃×#97	D₄	1	4	yes	—
38	C₄×C₈×C₁₃	—	2	2	no	—
39	C₄×C₈×C₁₃	—	2	2	no	—
40	#12606	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂⁴×C₁₃	M₁₆	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	—	2	1	no	—
43	C₂²×C₄×C₁₃	—	2	1	no	—
44	C₂²×C₄×C₁₃	—	2	1	no	—
45	C₂²×C₄×C₁₃	—	2	1	no	—
46	C₂²×C₄×C₁₃	—	2	1	no	—
47	C₂²×C₄×C₁₃	—	2	1	no	—
48	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
49	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
51	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₁₃×M₁₆	—	2	8	no	—
53	C₂×C₈×C₁₃	—	2	1	no	—
54	C₂×C₈×C₁₃	—	2	1	no	—
55	C₂×C₈×C₁₃	—	2	1	no	—
56	C₂×C₈×C₁₃	—	2	1	no	—
57	C₂×C₈×C₁₃	—	2	1	no	—
58	C₂×C₈×C₁₃	—	2	1	no	—
59	C₂×C₈×C₁₃	—	2	8	no	—
60	C₂×C₈×C₁₃	C₄²	1	2	yes	—
61	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
63	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
64	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
65	C₂×C₈×C₁₃	#41	1	2	yes	—
66	C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₁₃×C₂²⋊C₄	—	2	4	no	—
68	C₄²×C₁₃	—	2	1	no	—
69	C₄²×C₁₃	—	2	1	no	—
70	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
71	C₄²×C₁₃	M₁₆	1	2	yes	—
72	C₁₃×C₁₆	—	2	8	no	—
73	C₂×#405	C₂×C₁₃	1	1	yes	characteristic
74	#2112	C₂×C₁₃	1	2	yes	—
75	C₂×#347	C₂×C₁₃	1	2	yes	complemented
76	#1375	C₂×C₁₃	1	2	yes	complemented
77	C₂³×C₁₃	—	2	1	no	—
78	C₂³×C₁₃	—	2	1	no	—
79	C₂³×C₁₃	—	4	2	no	—
80	C₂³×C₁₃	#97	1	2	yes	—
81	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₃	—	2	1	no	—
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	—	2	2	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	4	2	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	#97	1	2	yes	—
93	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
99	C₈×C₁₃	—	2	2	no	—
100	C₈×C₁₃	—	2	2	no	—
101	C₈×C₁₃	—	2	2	no	—
102	C₈×C₁₃	C₄×D₄	1	4	yes	—
103	C₂²×M₁₆	C₄×C₁₃	1	1	yes	characteristic
104	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
105	C₂×#117	C₄×C₁₃	1	1	yes	characteristic
106	C₂×M₃₂	C₂²×C₁₃	1	4	yes	—
107	#405	—	2	4	no	—
108	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
109	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
110	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic
111	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic
112	C₂²⋊C₁₆	C₄×C₁₃	1	8	yes	complemented
113	#347	—	2	4	no	—
114	C₂²×C₁₃	—	2	2	no	—
115	C₂²×C₁₃	—	2	4	no	—
116	C₂²×C₁₃	—	2	2	no	—
117	C₂²×C₁₃	—	4	2	no	—
118	C₂²×C₁₃	—	4	2	no	—
119	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
120	C₂²×C₁₃	#407	1	1	yes	characteristic
121	C₂²×C₁₃	#432	1	1	yes	characteristic
122	C₄×C₁₃	—	2	2	no	—
123	C₄×C₁₃	—	4	2	no	—
124	C₄×C₁₃	—	4	2	no	—
125	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
126	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
127	C₄×C₁₃	#407	1	1	yes	characteristic
128	C₄×C₁₃	#432	1	1	yes	characteristic
129	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
130	C₂×M₁₆	—	2	2	no	—
131	C₂×M₁₆	—	2	2	no	—
132	C₂×M₁₆	—	2	2	no	—
133	C₂²×C₈	—	2	2	no	—
134	C₂²×C₈	—	2	2	no	—
135	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
136	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
137	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
138	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
139	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
140	#117	—	2	2	no	—
141	#117	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	1	no	—
143	C₂×C₂²⋊C₄	—	2	1	no	—
144	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
145	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
146	M₃₂	—	2	4	no	—
147	M₃₂	—	2	4	no	—
148	C₂×C₁₆	C₂×C₄×C₁₃	1	8	yes	—
149	#97	—	2	2	no	—
150	#97	D₄×C₁₃	1	4	yes	—
151	C₄×C₈	—	2	2	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂×C₁₃	—	2	1	no	—
154	C₂×C₁₃	—	2	1	no	—
155	C₂×C₁₃	—	4	2	no	—
156	C₂×C₁₃	#1749	1	1	yes	characteristic
157	C₂×C₁₃	#2110	1	2	yes	—
158	C₂⁴	C₁₃×M₁₆	1	1	yes	characteristic
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	2	1	no	—
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	C₄²×C₁₃	1	2	yes	—
166	C₂²×C₄	C₁₃×M₁₆	1	1	yes	characteristic
167	C₂²×C₄	C₁₃×M₁₆	1	2	yes	—
168	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
169	M₁₆	—	2	8	no	—
170	C₂×C₈	—	2	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	2	1	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	2	8	no	—
177	C₂×C₈	C₄²×C₁₃	1	2	yes	—
178	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
179	C₂×C₈	C₁₃×M₁₆	1	2	yes	—
180	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
181	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
182	C₂×C₈	C₁₃×#41	1	2	yes	—
183	C₄⋊C₄	—	2	4	no	—
184	C₂²⋊C₄	—	2	4	no	—
185	C₄²	—	2	1	no	—
186	C₄²	—	2	1	no	—
187	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
188	C₄²	C₁₃×M₁₆	1	2	yes	—
189	C₁₆	—	2	8	no	—
190	C₁₃	#12606	1	1	yes	characteristic, direct product factor, Sylow
191	C₂³	—	2	1	no	—
192	C₂³	—	2	1	no	—
193	C₂³	—	4	2	no	—
194	C₂³	C₁₃×#97	1	2	yes	—
195	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	C₁₃×#97	1	2	yes	—
207	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
208	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
210	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
211	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
212	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	—	2	2	no	—
215	C₈	—	2	2	no	—
216	C₈	C₄×D₄×C₁₃	1	4	yes	—
217	C₂²	—	2	2	no	—
218	C₂²	—	2	2	no	—
219	C₂²	—	2	4	no	—
220	C₂²	—	4	2	no	—
221	C₂²	—	4	2	no	—
222	C₂²	C₂×C₁₃×#97	1	1	yes	characteristic
223	C₂²	C₁₃×#407	1	1	yes	characteristic
224	C₂²	C₁₃×#432	1	1	yes	characteristic
225	C₄	—	2	2	no	—
226	C₄	—	4	2	no	—
227	C₄	—	4	2	no	—
228	C₄	C₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
229	C₄	C₄×C₁₃×M₁₆	1	1	yes	characteristic
230	C₄	C₁₃×#407	1	1	yes	characteristic
231	C₄	C₁₃×#432	1	1	yes	characteristic
232	C₂	—	2	1	no	—
233	C₂	—	2	1	no	—
234	C₂	—	4	2	no	—
235	C₂	C₁₃×#1749	1	1	yes	characteristic
236	C₂	C₁₃×#2110	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂⁴×C₁₃	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#347	C₂	semidirect
4. C₁₃×#1375	C₂	semidirect
14. C₁₃×C₂²⋊C₁₆	C₄	semidirect
40. #12606	C₁₃	direct (N × H)
75. C₂×#347	C₂×C₁₃	semidirect
76. #1375	C₂×C₁₃	semidirect
112. C₂²⋊C₁₆	C₄×C₁₃	semidirect
190. C₁₃	#12606	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#405	2
C₁₃×#2112	2
C₂×C₁₃×#347	2
C₁₃×#1375	2
#12606	13

Subgroups — C13×#12606 #15698945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12606 #15698945