Subgroups — C₂×Q₈×C₁₃×C₁₆ #15719811

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 144 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	Q₈×C₁₃×C₁₆	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₁₃×C₄⋊C₁₆	C₂	1	3	yes	maximal
4	C₂×C₄×C₁₃×C₁₆	C₂	1	3	yes	maximal
5	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	3	yes	—
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₈×Q₈×C₁₃	C₄	1	4	yes	—
9	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
10	C₂×C₁₃×C₄⋊C₈	C₄	1	3	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
12	C₁₃×C₄⋊C₁₆	C₂²	1	12	yes	—
13	C₄×C₁₃×C₁₆	C₂²	1	12	yes	—
14	C₂²×Q₈×C₁₃	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
16	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₄×Q₈×C₁₃	C₈	1	4	yes	—
18	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
19	C₂×C₁₃×C₄⋊C₄	C₈	1	3	yes	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
21	C₂×C₁₃×C₁₆	—	2	6	no	—
22	C₂×C₁₃×C₁₆	Q₈	1	4	yes	direct product factor
23	C₂×C₁₃×C₁₆	C₂³	1	6	yes	—
24	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
25	C₁₃×C₄⋊C₈	C₂×C₄	1	12	yes	—
26	C₄×C₈×C₁₃	C₂×C₄	1	6	yes	—
27	C₄×C₈×C₁₃	C₂³	1	6	yes	—
28	C₂×Q₈×C₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂×Q₈×C₁₃	C₁₆	1	8	yes	direct product factor
30	C₂×Q₈×C₁₃	C₂×C₈	1	4	yes	—
31	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
32	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
33	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₃	—	2	6	no	—
35	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
36	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
38	C₂×C₈×C₁₃	#41	1	2	yes	—
39	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
40	C₁₃×C₄⋊C₄	C₂×C₈	1	12	yes	—
41	C₄²×C₁₃	C₂×C₈	1	6	yes	—
42	C₄²×C₁₃	C₂²×C₄	1	6	yes	—
43	C₁₃×C₁₆	—	2	6	no	—
44	C₁₃×C₁₆	C₂×Q₈	1	4	yes	direct product factor
45	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic
46	Q₈×C₁₆	C₂×C₁₃	1	8	yes	direct product factor
47	C₂×C₄⋊C₁₆	C₂×C₁₃	1	3	yes	—
48	C₂×C₄×C₁₆	C₂×C₁₃	1	3	yes	—
49	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
50	Q₈×C₁₃	C₂×C₁₆	1	16	yes	direct product factor
51	C₂×C₄×C₁₃	—	2	6	no	—
52	C₂×C₄×C₁₃	C₂×C₁₆	1	12	yes	—
53	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
54	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
55	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
57	C₂×C₄×C₁₃	#131	1	2	yes	—
58	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
59	C₈×C₁₃	—	2	6	no	—
60	C₈×C₁₃	C₄×Q₈	1	2	yes	—
61	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
62	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
63	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
64	C₂²×C₁₆	C₂²×C₁₃	1	3	yes	—
65	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
66	C₈×Q₈	C₄×C₁₃	1	4	yes	—
67	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
68	C₂×C₄⋊C₈	C₄×C₁₃	1	3	yes	—
69	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
70	C₄⋊C₁₆	C₂²×C₁₃	1	12	yes	—
71	C₄×C₁₆	C₂²×C₁₃	1	12	yes	—
72	C₂²×C₁₃	C₈×Q₈	1	2	yes	—
73	C₂²×C₁₃	C₂²×C₁₆	1	2	yes	—
74	C₂²×C₁₃	#504	1	2	yes	—
75	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
76	C₄×C₁₃	—	2	6	no	—
77	C₄×C₁₃	C₈×Q₈	1	2	yes	—
78	C₄×C₁₃	C₂²×C₁₆	1	12	yes	—
79	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
80	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
81	C₂²×Q₈	C₈×C₁₃	1	1	yes	characteristic
82	C₂²×C₈	C₂×C₄×C₁₃	1	3	yes	—
83	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
84	C₄×Q₈	C₈×C₁₃	1	4	yes	—
85	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
86	C₂×C₄⋊C₄	C₈×C₁₃	1	3	yes	—
87	C₂×C₄²	C₂×C₄×C₁₃	1	3	yes	—
88	C₂×C₁₆	—	2	6	no	—
89	C₂×C₁₆	Q₈×C₁₃	1	4	yes	direct product factor
90	C₂×C₁₆	C₂³×C₁₃	1	6	yes	—
91	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
92	C₄⋊C₈	C₂×C₄×C₁₃	1	12	yes	—
93	C₄×C₈	C₂×C₄×C₁₃	1	6	yes	—
94	C₄×C₈	C₂³×C₁₃	1	6	yes	—
95	C₂×C₁₃	Q₈×C₁₆	1	4	yes	direct product factor
96	C₂×C₁₃	C₂×C₈×Q₈	1	1	yes	characteristic
97	C₂×C₁₃	C₂³×C₁₆	1	1	yes	characteristic
98	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
99	C₂×Q₈	C₁₃×C₁₆	1	8	yes	direct product factor
100	C₂×Q₈	C₂×C₈×C₁₃	1	4	yes	—
101	C₂²×C₄	C₂×C₈×C₁₃	1	3	yes	—
102	C₂²×C₄	C₂×C₈×C₁₃	1	3	yes	—
103	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
104	C₂×C₈	—	2	6	no	—
105	C₂×C₈	C₂²×C₄×C₁₃	1	6	yes	—
106	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
107	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
108	C₂×C₈	C₁₃×#41	1	2	yes	—
109	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
110	C₄⋊C₄	C₂×C₈×C₁₃	1	12	yes	—
111	C₄²	C₂×C₈×C₁₃	1	6	yes	—
112	C₄²	C₂²×C₄×C₁₃	1	6	yes	—
113	C₁₆	—	2	6	no	—
114	C₁₆	C₂×Q₈×C₁₃	1	4	yes	direct product factor
115	C₁₃	C₂×Q₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
116	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
117	Q₈	C₂×C₁₃×C₁₆	1	16	yes	direct product factor
118	C₂×C₄	—	2	6	no	—
119	C₂×C₄	C₂×C₁₃×C₁₆	1	12	yes	—
120	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
121	C₂×C₄	C₂²×C₈×C₁₃	1	6	yes	—
122	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
123	C₂×C₄	C₂²×C₈×C₁₃	1	6	yes	—
124	C₂×C₄	C₁₃×#131	1	2	yes	—
125	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
126	C₈	—	2	6	no	—
127	C₈	C₄×Q₈×C₁₃	1	2	yes	—
128	C₈	C₂²×Q₈×C₁₃	1	1	yes	characteristic
129	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
130	C₂²	C₈×Q₈×C₁₃	1	2	yes	—
131	C₂²	C₂²×C₁₃×C₁₆	1	2	yes	—
132	C₂²	C₁₃×#504	1	2	yes	—
133	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
134	C₄	—	2	6	no	—
135	C₄	C₈×Q₈×C₁₃	1	2	yes	—
136	C₄	C₂²×C₁₃×C₁₆	1	12	yes	—
137	C₄	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
138	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
139	C₂	Q₈×C₁₃×C₁₆	1	4	yes	direct product factor
140	C₂	C₂×C₈×Q₈×C₁₃	1	1	yes	characteristic
141	C₂	C₂³×C₁₃×C₁₆	1	1	yes	characteristic
142	C₂	C₂×C₁₃×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃×C₁₆	C₂²
commutator	C₂	C₂³×C₁₃×C₁₆
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₃×C₁₆	C₂	direct (N × H)
22. C₂×C₁₃×C₁₆	Q₈	direct (N × H)
28. C₂×Q₈×C₁₆	C₁₃	direct (N × H)
29. C₂×Q₈×C₁₃	C₁₆	direct (N × H)
44. C₁₃×C₁₆	C₂×Q₈	direct (N × H)
46. Q₈×C₁₆	C₂×C₁₃	direct (N × H)
50. Q₈×C₁₃	C₂×C₁₆	direct (N × H)
89. C₂×C₁₆	Q₈×C₁₃	direct (N × H)
95. C₂×C₁₃	Q₈×C₁₆	direct (N × H)
99. C₂×Q₈	C₁₃×C₁₆	direct (N × H)
114. C₁₆	C₂×Q₈×C₁₃	direct (N × H)
115. C₁₃	C₂×Q₈×C₁₆	direct (N × H)
117. Q₈	C₂×C₁₃×C₁₆	direct (N × H)
139. C₂	Q₈×C₁₃×C₁₆	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
Q₈×C₁₃×C₁₆	2
C₂×C₁₃×C₄⋊C₁₆	2
C₂×C₄×C₁₃×C₁₆	2
C₂×Q₈×C₁₆	13

Subgroups — C2×Q8×C13×C16 #15719811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×C₁₃×C₁₆ #15719811