Subgroups — C₂²×C₁₃×#322 #15703650

Order 3328.

1182 conjugacy classes of subgroups.

The subgroup lattice has 130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈×C₁₃	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#322	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₈×C₁₃	C₄	1	4	yes	—
5	C₂³×C₈×C₁₃	C₄	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₄	1	12	yes	—
8	C₂×C₄×C₈×C₁₃	C₄	1	6	yes	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	12	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	6	yes	—
11	C₁₃×#322	C₂²	1	16	yes	direct product factor
12	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₁₃	—	2	16	no	—
15	C₂²×C₈×C₁₃	C₈	1	16	yes	complemented
16	C₂²×C₈×C₁₃	C₂×C₄	1	24	yes	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	12	yes	—
18	C₂×C₄²×C₁₃	C₂×C₄	1	6	yes	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
20	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	24	yes	—
22	C₄×C₈×C₁₃	C₂×C₄	1	12	yes	—
23	C₄×C₈×C₁₃	C₂³	1	8	yes	—
24	C₄×C₈×C₁₃	C₂³	1	4	yes	—
25	C₂²×#322	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
27	C₂²×C₄×C₁₃	C₄²	1	3	yes	—
28	C₂²×C₄×C₁₃	C₄²	1	6	yes	—
29	C₂²×C₄×C₁₃	C₂×C₈	1	8	yes	—
30	C₂²×C₄×C₁₃	M₁₆	1	16	yes	—
31	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
32	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
33	C₂×C₈×C₁₃	—	2	48	no	—
34	C₂×C₈×C₁₃	C₂×C₈	1	48	yes	complemented
35	C₂×C₈×C₁₃	C₂²×C₄	1	16	yes	—
36	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
37	C₄²×C₁₃	C₄²	1	6	yes	—
38	C₄²×C₁₃	C₂²×C₄	1	6	yes	—
39	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
40	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
41	C₂²×C₄×C₈	C₂×C₁₃	1	2	yes	—
42	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic
43	C₂×#322	C₂×C₁₃	1	12	yes	direct product factor
44	C₂³×C₁₃	C₄×C₈	1	4	yes	—
45	C₂³×C₁₃	#97	1	8	yes	—
46	C₂³×C₁₃	C₂×C₄²	1	3	yes	—
47	C₂×C₄×C₁₃	C₄×C₈	1	12	yes	—
48	C₂×C₄×C₁₃	#97	1	24	yes	—
49	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
50	C₂×C₄×C₁₃	C₂×C₄²	1	6	yes	—
51	C₂×C₄×C₁₃	C₂²×C₈	1	12	yes	—
52	C₂×C₄×C₁₃	C₂×M₁₆	1	24	yes	—
53	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
55	C₈×C₁₃	—	2	16	no	—
56	C₈×C₁₃	C₂²×C₈	1	16	yes	complemented
57	C₂³×C₈	C₄×C₁₃	1	4	yes	—
58	C₂³×C₈	C₄×C₁₃	1	2	yes	—
59	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
60	C₂×C₄×C₈	C₄×C₁₃	1	12	yes	—
61	C₂×C₄×C₈	C₄×C₁₃	1	6	yes	—
62	C₂×C₄×C₈	C₂²×C₁₃	1	12	yes	—
63	C₂×C₄×C₈	C₂²×C₁₃	1	6	yes	—
64	#322	C₂²×C₁₃	1	16	yes	direct product factor
65	C₂²×C₁₃	#322	1	16	yes	direct product factor
66	C₂²×C₁₃	C₂×C₄×C₈	1	6	yes	—
67	C₂²×C₁₃	C₂×#97	1	12	yes	—
68	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
69	C₄×C₁₃	C₂×C₄×C₈	1	6	yes	—
70	C₄×C₁₃	C₂×#97	1	12	yes	—
71	C₄×C₁₃	C₂³×C₈	1	2	yes	—
72	C₄×C₁₃	C₂²×M₁₆	1	4	yes	—
73	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
74	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
75	C₂²×C₈	—	2	16	no	—
76	C₂²×C₈	C₈×C₁₃	1	16	yes	complemented
77	C₂²×C₈	C₂×C₄×C₁₃	1	24	yes	—
78	C₂²×C₈	C₂×C₄×C₁₃	1	12	yes	—
79	C₂×C₄²	C₂×C₄×C₁₃	1	6	yes	—
80	C₂×C₄²	C₂×C₄×C₁₃	1	3	yes	—
81	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
82	C₄×C₈	C₂×C₄×C₁₃	1	24	yes	—
83	C₄×C₈	C₂×C₄×C₁₃	1	12	yes	—
84	C₄×C₈	C₂³×C₁₃	1	8	yes	—
85	C₄×C₈	C₂³×C₁₃	1	4	yes	—
86	C₂×C₁₃	C₂×#322	1	12	yes	direct product factor
87	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
88	C₂×C₁₃	C₂²×#97	1	2	yes	—
89	C₂⁴	C₄²×C₁₃	1	1	yes	characteristic
90	C₂²×C₄	C₄²×C₁₃	1	3	yes	—
91	C₂²×C₄	C₄²×C₁₃	1	6	yes	—
92	C₂²×C₄	C₂×C₈×C₁₃	1	8	yes	—
93	C₂²×C₄	C₁₃×M₁₆	1	16	yes	—
94	C₂²×C₄	C₂²×C₄×C₁₃	1	3	yes	—
95	C₂²×C₄	C₂²×C₄×C₁₃	1	6	yes	—
96	C₂×C₈	—	2	48	no	—
97	C₂×C₈	C₂×C₈×C₁₃	1	48	yes	complemented
98	C₂×C₈	C₂²×C₄×C₁₃	1	16	yes	—
99	C₂×C₈	C₂²×C₄×C₁₃	1	8	yes	—
100	C₄²	C₄²×C₁₃	1	6	yes	—
101	C₄²	C₂²×C₄×C₁₃	1	6	yes	—
102	C₄²	C₂²×C₄×C₁₃	1	3	yes	—
103	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
104	C₁₃	C₂²×#322	1	1	yes	characteristic, direct product factor, Sylow
105	C₂³	C₄×C₈×C₁₃	1	4	yes	—
106	C₂³	C₁₃×#97	1	8	yes	—
107	C₂³	C₂×C₄²×C₁₃	1	3	yes	—
108	C₂×C₄	C₄×C₈×C₁₃	1	12	yes	—
109	C₂×C₄	C₁₃×#97	1	24	yes	—
110	C₂×C₄	C₂×C₄²×C₁₃	1	3	yes	—
111	C₂×C₄	C₂×C₄²×C₁₃	1	6	yes	—
112	C₂×C₄	C₂²×C₈×C₁₃	1	12	yes	—
113	C₂×C₄	C₂×C₁₃×M₁₆	1	24	yes	—
114	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
115	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
116	C₈	—	2	16	no	—
117	C₈	C₂²×C₈×C₁₃	1	16	yes	complemented
118	C₂²	C₁₃×#322	1	16	yes	direct product factor
119	C₂²	C₂×C₄×C₈×C₁₃	1	6	yes	—
120	C₂²	C₂×C₁₃×#97	1	12	yes	—
121	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
122	C₄	C₂×C₄×C₈×C₁₃	1	6	yes	—
123	C₄	C₂×C₁₃×#97	1	12	yes	—
124	C₄	C₂³×C₈×C₁₃	1	2	yes	—
125	C₄	C₂²×C₁₃×M₁₆	1	4	yes	—
126	C₂	C₂×C₁₃×#322	1	12	yes	direct product factor
127	C₂	C₂²×C₄×C₈×C₁₃	1	1	yes	characteristic
128	C₂	C₂²×C₁₃×#97	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄²×C₁₃	C₂²
commutator	C₂	C₂²×C₄×C₈×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle, prime radical	C₂⁴×C₁₃	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#322	C₂	direct (N × H)
11. C₁₃×#322	C₂²	direct (N × H)
15. C₂²×C₈×C₁₃	C₈	semidirect
25. C₂²×#322	C₁₃	direct (N × H)
34. C₂×C₈×C₁₃	C₂×C₈	semidirect
43. C₂×#322	C₂×C₁₃	direct (N × H)
56. C₈×C₁₃	C₂²×C₈	semidirect
64. #322	C₂²×C₁₃	direct (N × H)
65. C₂²×C₁₃	#322	direct (N × H)
76. C₂²×C₈	C₈×C₁₃	semidirect
86. C₂×C₁₃	C₂×#322	direct (N × H)
97. C₂×C₈	C₂×C₈×C₁₃	semidirect
104. C₁₃	C₂²×#322	direct (N × H)
117. C₈	C₂²×C₈×C₁₃	semidirect
118. C₂²	C₁₃×#322	direct (N × H)
126. C₂	C₂×C₁₃×#322	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄×C₈×C₁₃	2
C₂×C₁₃×#322	2
C₂²×#322	13

Subgroups — C22×C13×#322 #15703650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#322 #15703650