Subgroups — C₁₃×#33498 #15719837

Order 3328.

494 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2183	C₂	1	6	yes	maximal, complemented
3	Q₈×C₁₃×C₁₆	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2163	C₂	1	3	yes	maximal
5	C₁₃×#2162	C₂	1	3	yes	maximal
6	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
7	C₈×Q₈×C₁₃	C₄	1	3	yes	—
8	C₈×Q₈×C₁₃	C₄	1	1	yes	characteristic
9	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₈×Q₈×C₁₃	C₂²	1	3	yes	—
11	C₂×C₁₃×C₄⋊C₈	C₄	1	3	yes	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
13	C₁₃×C₄⋊C₁₆	C₂²	1	6	yes	—
14	C₁₃×C₄⋊C₁₆	C₂²	1	6	yes	—
15	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₁₃×C₂²⋊C₁₆	C₂²	1	3	yes	—
17	C₁₃×#346	C₂²	1	6	yes	—
18	C₄×C₁₃×C₁₆	C₂²	1	6	yes	—
19	C₂²×Q₈×C₁₃	C₈	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
21	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
22	C₄×Q₈×C₁₃	C₈	1	3	yes	—
23	C₄×Q₈×C₁₃	C₈	1	1	yes	characteristic
24	C₄×Q₈×C₁₃	C₂×C₄	1	3	yes	—
25	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₄	C₈	1	3	yes	—
27	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
28	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
29	C₂×C₁₃×C₁₆	C₂³	1	6	yes	—
30	C₁₃×C₄⋊C₈	C₂×C₄	1	3	yes	—
31	C₁₃×C₄⋊C₈	C₂×C₄	1	6	yes	—
32	C₁₃×C₄⋊C₈	C₂×C₄	1	3	yes	—
33	C₄×C₈×C₁₃	C₂×C₄	1	3	yes	—
34	C₄×C₈×C₁₃	C₂×C₄	1	3	yes	—
35	C₄×C₈×C₁₃	C₂³	1	3	yes	—
36	C₄×C₈×C₁₃	C₂³	1	3	yes	—
37	#33498	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×Q₈×C₁₃	—	2	4	no	—
39	C₂×Q₈×C₁₃	C₂×C₈	1	3	yes	—
40	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
42	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
43	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₃	—	2	2	no	—
45	C₂×C₈×C₁₃	—	4	3	no	—
46	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
48	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
49	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
50	C₁₃×C₄⋊C₄	C₂×C₈	1	6	yes	—
51	C₁₃×C₄⋊C₄	C₂×C₈	1	3	yes	—
52	C₁₃×C₄⋊C₄	C₂×C₈	1	3	yes	—
53	C₄²×C₁₃	C₂×C₈	1	3	yes	—
54	C₄²×C₁₃	C₂×C₈	1	3	yes	—
55	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
56	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
57	C₁₃×C₁₆	—	2	2	no	—
58	C₁₃×C₁₆	—	2	6	no	—
59	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic
60	#2183	C₂×C₁₃	1	6	yes	complemented
61	Q₈×C₁₆	C₂×C₁₃	1	2	yes	complemented
62	#2163	C₂×C₁₃	1	3	yes	—
63	#2162	C₂×C₁₃	1	3	yes	—
64	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
65	Q₈×C₁₃	—	2	6	no	—
66	Q₈×C₁₃	M₃₂	1	4	yes	—
67	C₂×C₄×C₁₃	—	2	6	no	—
68	C₂×C₄×C₁₃	—	2	1	no	—
69	C₂×C₄×C₁₃	—	2	1	no	—
70	C₂×C₄×C₁₃	—	2	6	no	—
71	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂²×C₈	1	3	yes	—
73	C₂×C₄×C₁₃	C₂²×C₈	1	3	yes	—
74	C₂×C₄×C₁₃	C₂²×C₈	1	3	yes	—
75	C₂×C₄×C₁₃	C₂²×C₈	1	3	yes	—
76	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
77	C₈×C₁₃	—	2	1	no	—
78	C₈×C₁₃	—	2	3	no	—
79	C₈×C₁₃	—	2	3	no	—
80	C₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
81	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
82	C₈×Q₈	C₄×C₁₃	1	3	yes	—
83	C₈×Q₈	C₄×C₁₃	1	1	yes	characteristic
84	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
85	C₈×Q₈	C₂²×C₁₃	1	3	yes	—
86	C₂×C₄⋊C₈	C₄×C₁₃	1	3	yes	—
87	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
88	C₄⋊C₁₆	C₂²×C₁₃	1	6	yes	—
89	C₄⋊C₁₆	C₂²×C₁₃	1	6	yes	—
90	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
91	C₂²⋊C₁₆	C₂²×C₁₃	1	3	yes	—
92	#346	C₂²×C₁₃	1	6	yes	—
93	C₄×C₁₆	C₂²×C₁₃	1	6	yes	—
94	C₂²×C₁₃	—	2	1	no	—
95	C₂²×C₁₃	—	2	1	no	—
96	C₂²×C₁₃	#504	1	2	yes	—
97	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
98	C₄×C₁₃	—	2	3	no	—
99	C₄×C₁₃	—	2	3	no	—
100	C₄×C₁₃	—	2	3	no	—
101	C₄×C₁₃	—	2	1	no	—
102	C₄×C₁₃	C₂×M₃₂	1	6	yes	—
103	C₄×C₁₃	#519	1	1	yes	characteristic
104	C₄×C₁₃	#568	1	1	yes	characteristic
105	C₂²×Q₈	C₈×C₁₃	1	1	yes	characteristic
106	C₂²×C₈	C₂×C₄×C₁₃	1	3	yes	—
107	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
108	C₄×Q₈	C₈×C₁₃	1	3	yes	—
109	C₄×Q₈	C₈×C₁₃	1	1	yes	characteristic
110	C₄×Q₈	C₂×C₄×C₁₃	1	3	yes	—
111	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
112	C₂×C₄⋊C₄	C₈×C₁₃	1	3	yes	—
113	C₂×C₄²	C₂×C₄×C₁₃	1	3	yes	—
114	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
115	C₂×C₁₆	C₂³×C₁₃	1	6	yes	—
116	C₄⋊C₈	C₂×C₄×C₁₃	1	3	yes	—
117	C₄⋊C₈	C₂×C₄×C₁₃	1	6	yes	—
118	C₄⋊C₈	C₂×C₄×C₁₃	1	3	yes	—
119	C₄×C₈	C₂×C₄×C₁₃	1	3	yes	—
120	C₄×C₈	C₂×C₄×C₁₃	1	3	yes	—
121	C₄×C₈	C₂³×C₁₃	1	3	yes	—
122	C₄×C₈	C₂³×C₁₃	1	3	yes	—
123	C₂×C₁₃	—	2	2	no	—
124	C₂×C₁₃	#2982	1	1	yes	characteristic
125	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
126	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
127	C₂×Q₈	—	2	4	no	—
128	C₂×Q₈	C₂×C₈×C₁₃	1	3	yes	—
129	C₂×Q₈	C₂×C₈×C₁₃	1	1	yes	characteristic
130	C₂²×C₄	C₂×C₈×C₁₃	1	3	yes	—
131	C₂²×C₄	C₂×C₈×C₁₃	1	3	yes	—
132	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	4	3	no	—
135	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
136	C₂×C₈	C₂²×C₄×C₁₃	1	3	yes	—
137	C₂×C₈	C₂²×C₄×C₁₃	1	3	yes	—
138	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
139	C₄⋊C₄	C₂×C₈×C₁₃	1	6	yes	—
140	C₄⋊C₄	C₂×C₈×C₁₃	1	3	yes	—
141	C₄⋊C₄	C₂×C₈×C₁₃	1	3	yes	—
142	C₄²	C₂×C₈×C₁₃	1	3	yes	—
143	C₄²	C₂×C₈×C₁₃	1	3	yes	—
144	C₄²	C₂²×C₄×C₁₃	1	3	yes	—
145	C₄²	C₂²×C₄×C₁₃	1	3	yes	—
146	C₁₆	—	2	2	no	—
147	C₁₆	—	2	6	no	—
148	C₁₃	#33498	1	1	yes	characteristic, direct product factor, Sylow
149	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
150	Q₈	—	2	6	no	—
151	Q₈	C₁₃×M₃₂	1	4	yes	—
152	C₂×C₄	—	2	6	no	—
153	C₂×C₄	—	2	6	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
157	C₂×C₄	C₂²×C₈×C₁₃	1	3	yes	—
158	C₂×C₄	C₂²×C₈×C₁₃	1	3	yes	—
159	C₂×C₄	C₂²×C₈×C₁₃	1	3	yes	—
160	C₂×C₄	C₂²×C₈×C₁₃	1	3	yes	—
161	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
162	C₈	—	2	1	no	—
163	C₈	—	2	3	no	—
164	C₈	—	2	3	no	—
165	C₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
166	C₂²	—	2	1	no	—
167	C₂²	—	2	1	no	—
168	C₂²	C₁₃×#504	1	2	yes	—
169	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
170	C₄	—	2	3	no	—
171	C₄	—	2	3	no	—
172	C₄	—	2	3	no	—
173	C₄	—	2	1	no	—
174	C₄	C₂×C₁₃×M₃₂	1	6	yes	—
175	C₄	C₁₃×#519	1	1	yes	characteristic
176	C₄	C₁₃×#568	1	1	yes	characteristic
177	C₂	—	2	2	no	—
178	C₂	C₁₃×#2982	1	1	yes	characteristic
179	C₂	C₂²×C₁₃×M₃₂	1	1	yes	characteristic
180	C₂	C₂×C₁₃×#504	1	1	yes	characteristic

	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. #33498	C₁₃	direct (N × H)
60. #2183	C₂×C₁₃	semidirect
61. Q₈×C₁₆	C₂×C₁₃	semidirect
148. C₁₃	#33498	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×C₈×Q₈×C₁₃	2
C₁₃×#2183	2
Q₈×C₁₃×C₁₆	2
C₁₃×#2163	2
C₁₃×#2162	2
#33498	13

Subgroups — C13×#33498 #15719837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33498 #15719837