Subgroups — C₁₃×#33500 #15719839

Order 3328.

460 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2183	C₂	1	4	yes	maximal, complemented
3	Q₈×C₁₃×C₁₆	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2164	C₂	1	4	yes	maximal
5	C₁₃×#2162	C₂	1	2	yes	maximal
6	C₁₃×#533	C₄	1	1	yes	characteristic
7	C₁₃×#446	C₄	1	4	yes	—
8	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
9	C₁₃×#424	C₄	1	2	yes	—
10	C₁₃×#423	C₄	1	1	yes	characteristic
11	C₁₃×#405	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
14	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
15	C₁₃×C₄⋊C₁₆	C₂²	1	8	yes	—
16	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	—
17	C₁₃×#346	C₂²	1	4	yes	—
18	C₄×C₁₃×C₁₆	C₂²	1	4	yes	—
19	C₄×C₁₃×C₁₆	C₂²	1	4	yes	—
20	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
23	C₁₃×C₄⋊Q₈	C₈	1	2	yes	—
24	C₁₃×#125	C₈	1	2	yes	—
25	C₁₃×C₂²⋊Q₈	C₈	1	4	yes	—
26	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
27	C₁₃×#117	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
30	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
31	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
32	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
33	C₁₃×#97	C₂×C₄	1	4	yes	—
34	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₃	C₂³	1	2	yes	—
36	C₄×C₈×C₁₃	C₂³	1	4	yes	—
37	#33500	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×Q₈×C₁₃	C₂×C₈	1	4	yes	—
39	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₁₃×M₁₆	—	4	2	no	—
42	C₂×C₈×C₁₃	—	2	2	no	—
43	C₂×C₈×C₁₃	—	4	1	no	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
46	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
47	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
48	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
49	C₁₃×C₄⋊C₄	C₂×C₈	1	8	yes	—
50	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
51	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	—
52	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
53	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
54	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
55	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
56	C₁₃×C₁₆	—	2	4	no	—
57	C₁₃×C₁₆	—	2	4	no	—
58	#2960	C₂×C₁₃	1	1	yes	characteristic
59	#2183	C₂×C₁₃	1	4	yes	complemented
60	Q₈×C₁₆	C₂×C₁₃	1	4	yes	complemented
61	#2164	C₂×C₁₃	1	4	yes	—
62	#2162	C₂×C₁₃	1	2	yes	—
63	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
64	Q₈×C₁₃	—	2	8	no	—
65	C₂×C₄×C₁₃	—	2	1	no	—
66	C₂×C₄×C₁₃	—	2	1	no	—
67	C₂×C₄×C₁₃	—	2	4	no	—
68	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
70	C₂×C₄×C₁₃	C₂²×C₈	1	8	yes	—
71	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
72	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
73	C₈×C₁₃	—	2	1	no	—
74	C₈×C₁₃	—	2	2	no	—
75	C₈×C₁₃	—	2	4	no	—
76	C₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
77	#533	C₄×C₁₃	1	1	yes	characteristic
78	#446	C₄×C₁₃	1	4	yes	—
79	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
80	#424	C₄×C₁₃	1	2	yes	—
81	#423	C₄×C₁₃	1	1	yes	characteristic
82	#405	C₂²×C₁₃	1	2	yes	—
83	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
84	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
85	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
86	C₄⋊C₁₆	C₂²×C₁₃	1	8	yes	—
87	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	—
88	#346	C₂²×C₁₃	1	4	yes	—
89	C₄×C₁₆	C₂²×C₁₃	1	4	yes	—
90	C₄×C₁₆	C₂²×C₁₃	1	4	yes	—
91	C₂²×C₁₃	—	2	2	no	—
92	C₂²×C₁₃	—	2	1	no	—
93	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
94	C₄×C₁₃	—	2	2	no	—
95	C₄×C₁₃	—	2	8	no	—
96	C₄×C₁₃	—	2	1	no	—
97	C₄×C₁₃	#504	1	4	yes	—
98	C₄×C₁₃	#519	1	1	yes	characteristic
99	C₄×C₁₃	#568	1	1	yes	characteristic
100	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
101	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
102	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
103	C₄⋊Q₈	C₈×C₁₃	1	2	yes	—
104	#125	C₈×C₁₃	1	2	yes	—
105	C₂²⋊Q₈	C₈×C₁₃	1	4	yes	—
106	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
107	#117	C₂×C₄×C₁₃	1	2	yes	—
108	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
109	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
110	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
111	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
112	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
113	#97	C₂×C₄×C₁₃	1	4	yes	—
114	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
115	C₄×C₈	C₂³×C₁₃	1	2	yes	—
116	C₄×C₈	C₂³×C₁₃	1	4	yes	—
117	C₂×C₁₃	—	4	1	no	—
118	C₂×C₁₃	#2982	1	1	yes	characteristic
119	C₂×C₁₃	C₂×#504	1	2	yes	—
120	C₂×Q₈	C₂×C₈×C₁₃	1	4	yes	—
121	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
122	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
123	M₁₆	—	4	2	no	—
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	4	1	no	—
126	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
127	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
128	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
129	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
130	C₄⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
131	C₄⋊C₄	C₂×C₈×C₁₃	1	8	yes	—
132	C₄⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
133	C₂²⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
134	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
135	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
136	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
137	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
138	C₁₆	—	2	4	no	—
139	C₁₆	—	2	4	no	—
140	C₁₃	#33500	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
142	Q₈	—	2	8	no	—
143	C₂×C₄	—	2	4	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
147	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
148	C₂×C₄	C₂²×C₈×C₁₃	1	8	yes	—
149	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
150	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
151	C₈	—	2	1	no	—
152	C₈	—	2	2	no	—
153	C₈	—	2	4	no	—
154	C₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
155	C₂²	—	2	2	no	—
156	C₂²	—	2	1	no	—
157	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
158	C₄	—	2	2	no	—
159	C₄	—	2	8	no	—
160	C₄	—	2	1	no	—
161	C₄	C₁₃×#504	1	4	yes	—
162	C₄	C₁₃×#519	1	1	yes	characteristic
163	C₄	C₁₃×#568	1	1	yes	characteristic
164	C₂	—	4	1	no	—
165	C₂	C₁₃×#2982	1	1	yes	characteristic
166	C₂	C₂×C₁₃×#504	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2183	C₂	semidirect
3. Q₈×C₁₃×C₁₆	C₂	semidirect
37. #33500	C₁₃	direct (N × H)
59. #2183	C₂×C₁₃	semidirect
60. Q₈×C₁₆	C₂×C₁₃	semidirect
140. C₁₃	#33500	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×#2960	2
C₁₃×#2183	2
Q₈×C₁₃×C₁₆	2
C₁₃×#2164	2
C₁₃×#2162	2
#33500	13

Subgroups — C13×#33500 #15719839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33500 #15719839