Subgroups — C₁₃×#12595 #15698934

Order 3328.

326 conjugacy classes of subgroups.

The subgroup lattice has 176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#347	C₂	1	2	yes	maximal
2	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1377	C₂	1	2	yes	maximal
4	C₁₃×#1376	C₂	1	2	yes	maximal
5	C₂×C₁₃×M₃₂	C₂²	1	4	yes	—
6	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
7	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
8	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₄³×C₁₃	C₄	1	1	yes	characteristic
13	C₁₃×#347	C₄	1	8	yes	complemented
14	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	—	2	2	no	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₁₃×M₃₂	—	2	4	no	—
23	C₁₃×M₃₂	C₂×C₄	1	8	yes	—
24	C₂×C₁₃×C₁₆	—	2	4	no	—
25	C₁₃×#97	—	2	2	no	—
26	C₁₃×#97	—	2	2	no	—
27	C₁₃×#97	—	2	2	no	—
28	C₁₃×#97	C₂×C₄	1	4	yes	—
29	C₄×C₈×C₁₃	—	2	2	no	—
30	C₄×C₈×C₁₃	—	2	2	no	—
31	#12595	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₄×C₁₃	—	2	1	no	—
33	C₂²×C₄×C₁₃	—	2	1	no	—
34	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
35	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₃	—	2	1	no	—
37	C₂×C₈×C₁₃	—	2	1	no	—
38	C₂×C₈×C₁₃	—	2	1	no	—
39	C₂×C₈×C₁₃	—	2	1	no	—
40	C₂×C₈×C₁₃	—	2	1	no	—
41	C₂×C₈×C₁₃	—	2	1	no	—
42	C₂×C₈×C₁₃	C₄²	1	2	yes	—
43	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
44	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
45	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
46	C₂×C₈×C₁₃	#41	1	2	yes	—
47	C₂×C₈×C₁₃	#41	1	2	yes	—
48	C₄²×C₁₃	—	2	1	no	—
49	C₄²×C₁₃	—	2	1	no	—
50	C₄²×C₁₃	—	2	1	no	—
51	C₄²×C₁₃	—	2	1	no	—
52	C₄²×C₁₃	—	4	4	no	—
53	C₄²×C₁₃	C₄²	1	2	yes	—
54	C₄²×C₁₃	M₁₆	1	2	yes	—
55	C₁₃×C₁₆	—	2	8	no	—
56	C₂×#347	C₂×C₁₃	1	2	yes	—
57	C₄×#97	C₂×C₁₃	1	1	yes	characteristic
58	#1377	C₂×C₁₃	1	2	yes	—
59	#1376	C₂×C₁₃	1	2	yes	—
60	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
61	C₂×C₄×C₁₃	—	2	4	no	—
62	C₂×C₄×C₁₃	—	2	2	no	—
63	C₂×C₄×C₁₃	—	2	2	no	—
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	4	2	no	—
66	C₂×C₄×C₁₃	—	4	2	no	—
67	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
69	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
73	C₈×C₁₃	—	2	2	no	—
74	C₈×C₁₃	—	2	2	no	—
75	C₈×C₁₃	—	2	2	no	—
76	C₈×C₁₃	#117	1	4	yes	—
77	C₂×M₃₂	C₂²×C₁₃	1	4	yes	—
78	C₂×#97	C₄×C₁₃	1	1	yes	characteristic
79	C₂×#97	C₄×C₁₃	1	1	yes	characteristic
80	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
81	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
82	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic
83	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
84	C₄³	C₄×C₁₃	1	1	yes	characteristic
85	#347	C₄×C₁₃	1	8	yes	complemented
86	C₂²×C₁₃	—	2	2	no	—
87	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
88	C₂²×C₁₃	#432	1	1	yes	characteristic
89	C₂²×C₁₃	#432	1	1	yes	characteristic
90	C₄×C₁₃	—	2	4	no	—
91	C₄×C₁₃	—	4	2	no	—
92	C₄×C₁₃	—	4	2	no	—
93	C₄×C₁₃	#376	1	1	yes	characteristic
94	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
95	C₄×C₁₃	#432	1	1	yes	characteristic
96	C₄×C₁₃	#432	1	1	yes	characteristic
97	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
98	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
99	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
100	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
101	C₂×C₄²	—	2	2	no	—
102	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
103	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
104	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
105	M₃₂	—	2	4	no	—
106	M₃₂	C₂×C₄×C₁₃	1	8	yes	—
107	C₂×C₁₆	—	2	4	no	—
108	#97	—	2	2	no	—
109	#97	—	2	2	no	—
110	#97	—	2	2	no	—
111	#97	C₂×C₄×C₁₃	1	4	yes	—
112	C₄×C₈	—	2	2	no	—
113	C₄×C₈	—	2	2	no	—
114	C₂×C₁₃	—	2	1	no	—
115	C₂×C₁₃	—	2	1	no	—
116	C₂×C₁₃	#1745	1	1	yes	characteristic
117	C₂×C₁₃	#2165	1	2	yes	—
118	C₂²×C₄	—	2	1	no	—
119	C₂²×C₄	—	2	1	no	—
120	C₂²×C₄	C₁₃×M₁₆	1	2	yes	—
121	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
122	C₂×C₈	—	2	1	no	—
123	C₂×C₈	—	2	1	no	—
124	C₂×C₈	—	2	1	no	—
125	C₂×C₈	—	2	1	no	—
126	C₂×C₈	—	2	1	no	—
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	C₄²×C₁₃	1	2	yes	—
129	C₂×C₈	C₁₃×M₁₆	1	2	yes	—
130	C₂×C₈	C₁₃×M₁₆	1	2	yes	—
131	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
132	C₂×C₈	C₁₃×#41	1	2	yes	—
133	C₂×C₈	C₁₃×#41	1	2	yes	—
134	C₄²	—	2	1	no	—
135	C₄²	—	2	1	no	—
136	C₄²	—	2	1	no	—
137	C₄²	—	2	1	no	—
138	C₄²	—	4	4	no	—
139	C₄²	C₄²×C₁₃	1	2	yes	—
140	C₄²	C₁₃×M₁₆	1	2	yes	—
141	C₁₆	—	2	8	no	—
142	C₁₃	#12595	1	1	yes	characteristic, direct product factor, Sylow
143	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	4	2	no	—
149	C₂×C₄	—	4	2	no	—
150	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
151	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
152	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
153	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
154	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
155	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
156	C₈	—	2	2	no	—
157	C₈	—	2	2	no	—
158	C₈	—	2	2	no	—
159	C₈	C₁₃×#117	1	4	yes	—
160	C₂²	—	2	2	no	—
161	C₂²	C₄×C₁₃×M₁₆	1	1	yes	characteristic
162	C₂²	C₁₃×#432	1	1	yes	characteristic
163	C₂²	C₁₃×#432	1	1	yes	characteristic
164	C₄	—	2	4	no	—
165	C₄	—	4	2	no	—
166	C₄	—	4	2	no	—
167	C₄	C₁₃×#376	1	1	yes	characteristic
168	C₄	C₄×C₁₃×M₁₆	1	1	yes	characteristic
169	C₄	C₁₃×#432	1	1	yes	characteristic
170	C₄	C₁₃×#432	1	1	yes	characteristic
171	C₂	—	2	1	no	—
172	C₂	—	2	1	no	—
173	C₂	C₁₃×#1745	1	1	yes	characteristic
174	C₂	C₁₃×#2165	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	#117
commutator	C₂×C₄	C₂×C₄²×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	#432
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

Complements

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

N	H ≅ G/N	type
13. C₁₃×#347	C₄	semidirect
31. #12595	C₁₃	direct (N × H)
85. #347	C₄×C₁₃	semidirect
142. C₁₃	#12595	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×#347	2
C₄×C₁₃×#97	2
C₁₃×#1377	2
C₁₃×#1376	2
#12595	13

Subgroups — C13×#12595 #15698934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12595 #15698934