Subgroups — C₁₃×#7163 #15693502

Order 3328.

238 conjugacy classes of subgroups.

The subgroup lattice has 170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×C₁₆	—	2	1	no	—
5	C₁₃×#431	C₄	1	1	yes	characteristic
6	C₄×C₁₃×M₁₆	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×C₄⋊C₁₆	C₄	1	2	yes	—
9	C₁₃×C₂²⋊C₁₆	—	2	1	no	—
10	C₄×C₁₃×C₁₆	—	2	1	no	—
11	C₄×C₁₃×C₁₆	—	2	1	no	—
12	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
13	C₁₃×#322	—	2	1	no	—
14	C₈²×C₁₃	—	2	1	no	—
15	C₂×C₁₃×M₁₆	C₈	1	2	yes	—
16	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₃×C₁₆	—	2	4	no	—
20	C₂×C₁₃×C₁₆	—	2	2	no	—
21	C₂×C₁₃×C₁₆	—	2	2	no	—
22	C₁₃×C₄⋊C₈	C₈	1	2	yes	—
23	C₁₃×C₂²⋊C₈	—	2	1	no	—
24	C₁₃×#97	—	2	1	no	—
25	C₄×C₈×C₁₃	—	2	1	no	—
26	C₄×C₈×C₁₃	—	2	1	no	—
27	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
30	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
31	#7163	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
35	C₁₃×M₁₆	—	2	2	no	—
36	C₁₃×M₁₆	C₁₆	1	4	yes	complemented
37	C₂×C₈×C₁₃	—	2	2	no	—
38	C₂×C₈×C₁₃	—	2	2	no	—
39	C₂×C₈×C₁₃	—	2	2	no	—
40	C₂×C₈×C₁₃	—	2	2	no	—
41	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
45	C₄²×C₁₃	C₄²	1	1	yes	characteristic
46	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
47	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
48	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
49	C₁₃×C₁₆	—	2	4	no	—
50	C₁₃×C₁₆	—	4	2	no	—
51	#2162	C₂×C₁₃	1	1	yes	characteristic
52	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
53	C₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic
54	C₂³×C₁₃	C₄⋊C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₃	—	2	1	no	—
56	C₂×C₄×C₁₃	—	2	1	no	—
57	C₂×C₄×C₁₃	—	2	2	no	—
58	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₃	#97	1	1	yes	characteristic
61	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
62	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
63	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
65	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
66	C₈×C₁₃	—	2	1	no	—
67	C₈×C₁₃	—	2	1	no	—
68	C₈×C₁₃	—	2	4	no	—
69	C₈×C₁₃	—	4	2	no	—
70	C₈×C₁₃	#104	1	2	yes	—
71	C₈×C₁₃	#108	1	2	yes	—
72	C₂²×C₁₆	—	2	1	no	—
73	#431	C₄×C₁₃	1	1	yes	characteristic
74	C₄×M₁₆	C₄×C₁₃	1	1	yes	characteristic
75	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
76	C₄⋊C₁₆	C₄×C₁₃	1	2	yes	—
77	C₂²⋊C₁₆	—	2	1	no	—
78	C₄×C₁₆	—	2	1	no	—
79	C₄×C₁₆	—	2	1	no	—
80	C₄×C₁₆	C₄×C₁₃	1	2	yes	—
81	#322	—	2	1	no	—
82	C₈²	—	2	1	no	—
83	C₂²×C₁₃	—	2	1	no	—
84	C₂²×C₁₃	—	2	1	no	—
85	C₂²×C₁₃	#336	1	1	yes	characteristic
86	C₂²×C₁₃	C₄⋊C₁₆	1	2	yes	—
87	C₄×C₁₃	—	2	1	no	—
88	C₄×C₁₃	—	2	1	no	—
89	C₄×C₁₃	#339	1	1	yes	characteristic
90	C₄×C₁₃	#341	1	1	yes	characteristic
91	C₄×C₁₃	C₄×C₁₆	1	1	yes	characteristic
92	C₄×C₁₃	#346	1	1	yes	characteristic
93	C₄×C₁₃	C₂²⋊C₁₆	1	2	yes	—
94	C₄×C₁₃	#350	1	2	yes	—
95	C₂×M₁₆	C₈×C₁₃	1	2	yes	—
96	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
97	C₂²×C₈	Q₈×C₁₃	1	1	yes	characteristic
98	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
99	C₂×C₁₆	—	2	4	no	—
100	C₂×C₁₆	—	2	2	no	—
101	C₂×C₁₆	—	2	2	no	—
102	C₄⋊C₈	C₈×C₁₃	1	2	yes	—
103	C₂²⋊C₈	—	2	1	no	—
104	#97	—	2	1	no	—
105	C₄×C₈	—	2	1	no	—
106	C₄×C₈	—	2	1	no	—
107	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
108	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
109	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
110	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
111	C₂×C₁₃	—	2	2	no	—
112	C₂×C₁₃	#1278	1	1	yes	characteristic
113	C₂×C₁₃	#1374	1	1	yes	characteristic
114	C₂×C₁₃	#1379	1	1	yes	characteristic
115	C₂²×C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
117	C₂²×C₄	C₁₃×M₁₆	1	1	yes	characteristic
118	M₁₆	—	2	2	no	—
119	M₁₆	C₁₃×C₁₆	1	4	yes	complemented
120	C₂×C₈	—	2	2	no	—
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	2	2	no	—
123	C₂×C₈	—	2	2	no	—
124	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
128	C₄²	C₄²×C₁₃	1	1	yes	characteristic
129	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
130	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
131	C₄²	C₁₃×M₁₆	1	1	yes	characteristic
132	C₁₆	—	2	4	no	—
133	C₁₆	—	4	2	no	—
134	C₁₃	#7163	1	1	yes	characteristic, direct product factor, Sylow
135	C₂³	C₁₃×C₄⋊C₈	1	1	yes	characteristic
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	2	1	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	C₁₃×#95	1	1	yes	characteristic
140	C₂×C₄	C₄×C₈×C₁₃	1	1	yes	characteristic
141	C₂×C₄	C₁₃×#97	1	1	yes	characteristic
142	C₂×C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
143	C₂×C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
144	C₂×C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
145	C₂×C₄	C₂×C₁₃×C₁₆	1	2	yes	—
146	C₂×C₄	C₁₃×M₃₂	1	2	yes	—
147	C₈	—	2	1	no	—
148	C₈	—	2	1	no	—
149	C₈	—	2	4	no	—
150	C₈	—	4	2	no	—
151	C₈	C₁₃×#104	1	2	yes	—
152	C₈	C₁₃×#108	1	2	yes	—
153	C₂²	—	2	1	no	—
154	C₂²	—	2	1	no	—
155	C₂²	C₁₃×#336	1	1	yes	characteristic
156	C₂²	C₁₃×C₄⋊C₁₆	1	2	yes	—
157	C₄	—	2	1	no	—
158	C₄	—	2	1	no	—
159	C₄	C₁₃×#339	1	1	yes	characteristic
160	C₄	C₁₃×#341	1	1	yes	characteristic
161	C₄	C₄×C₁₃×C₁₆	1	1	yes	characteristic
162	C₄	C₁₃×#346	1	1	yes	characteristic
163	C₄	C₁₃×C₂²⋊C₁₆	1	2	yes	—
164	C₄	C₁₃×#350	1	2	yes	—
165	C₂	—	2	2	no	—
166	C₂	C₁₃×#1278	1	1	yes	characteristic
167	C₂	C₁₃×#1374	1	1	yes	characteristic
168	C₂	C₁₃×#1379	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈×C₁₃	D₄
commutator	C₄	C₄×C₁₃×C₁₆
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₃
socle	C₂²×C₁₃	#336
prime radical	C₂³×C₁₃	C₄⋊C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
31. #7163	C₁₃	direct (N × H)
36. C₁₃×M₁₆	C₁₆	semidirect
119. M₁₆	C₁₃×C₁₆	semidirect
134. C₁₃	#7163	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×#2162	2
C₂×C₄×C₁₃×C₁₆	2
C₈×C₁₃×M₁₆	2
#7163	13

Subgroups — C13×#7163 #15693502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#7163 #15693502