Subgroups — C₁₃×#12899 #15699238

Order 3328.

370 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₄⋊C₁₆	C₂	1	6	yes	maximal
2	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×C₁₆	C₂²	1	4	yes	—
4	C₂×C₁₃×#97	C₄	1	3	yes	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
6	C₁₃×#376	C₄	1	1	yes	characteristic
7	C₁₃×C₄⋊C₁₆	—	2	12	no	—
8	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
9	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
10	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
11	C₂×C₁₃×C₁₆	—	2	12	no	—
12	C₁₃×#97	—	2	6	no	—
13	C₄×C₈×C₁₃	D₄	1	6	yes	—
14	C₄×C₈×C₁₃	Q₈	1	6	yes	—
15	C₁₃×#95	C₈	1	4	yes	—
16	#12899	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₄×C₁₃	C₂×C₈	1	6	yes	—
18	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₃	—	2	6	no	—
20	C₂×C₈×C₁₃	C₄⋊C₄	1	6	yes	—
21	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
22	C₂×C₈×C₁₃	C₂×Q₈	1	3	yes	—
23	C₄²×C₁₃	C₄⋊C₄	1	6	yes	—
24	C₄²×C₁₃	M₁₆	1	6	yes	—
25	C₁₃×C₁₆	—	4	4	no	—
26	C₂×C₄⋊C₁₆	C₂×C₁₃	1	6	yes	—
27	#1726	C₂×C₁₃	1	1	yes	characteristic
28	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₃	—	2	12	no	—
30	C₂×C₄×C₁₃	C₄⋊C₈	1	12	yes	—
31	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
32	C₂×C₄×C₁₃	C₂×M₁₆	1	3	yes	—
33	C₈×C₁₃	—	2	6	no	—
34	C₈×C₁₃	#127	1	1	yes	characteristic
35	C₈×C₁₃	C₄⋊Q₈	1	3	yes	—
36	C₂²×C₁₆	C₂²×C₁₃	1	4	yes	—
37	C₂×#97	C₄×C₁₃	1	3	yes	—
38	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
39	#376	C₄×C₁₃	1	1	yes	characteristic
40	C₄⋊C₁₆	—	2	12	no	—
41	C₂²×C₁₃	C₂×C₄⋊C₈	1	3	yes	—
42	C₂²×C₁₃	#504	1	4	yes	—
43	C₄×C₁₃	—	2	12	no	—
44	C₄×C₁₃	#384	1	1	yes	characteristic
45	C₄×C₁₃	#423	1	3	yes	—
46	C₂²×C₈	C₂×C₄×C₁₃	1	3	yes	—
47	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
48	C₂×C₄²	C₂×C₄×C₁₃	1	3	yes	—
49	C₂×C₁₆	—	2	12	no	—
50	#97	—	2	6	no	—
51	C₄×C₈	D₄×C₁₃	1	6	yes	—
52	C₄×C₈	Q₈×C₁₃	1	6	yes	—
53	#95	C₈×C₁₃	1	4	yes	—
54	C₂×C₁₃	#1842	1	1	yes	characteristic
55	C₂×C₁₃	#2151	1	6	yes	—
56	C₂²×C₄	C₂×C₈×C₁₃	1	6	yes	—
57	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
58	C₂×C₈	—	2	6	no	—
59	C₂×C₈	C₁₃×C₄⋊C₄	1	6	yes	—
60	C₂×C₈	C₂×D₄×C₁₃	1	3	yes	—
61	C₂×C₈	C₂×Q₈×C₁₃	1	3	yes	—
62	C₄²	C₁₃×C₄⋊C₄	1	6	yes	—
63	C₄²	C₁₃×M₁₆	1	6	yes	—
64	C₁₆	—	4	4	no	—
65	C₁₃	#12899	1	1	yes	characteristic, direct product factor, Sylow
66	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
67	C₂×C₄	—	2	12	no	—
68	C₂×C₄	C₁₃×C₄⋊C₈	1	12	yes	—
69	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	3	yes	—
70	C₂×C₄	C₂×C₁₃×M₁₆	1	3	yes	—
71	C₈	—	2	6	no	—
72	C₈	C₁₃×#127	1	1	yes	characteristic
73	C₈	C₁₃×C₄⋊Q₈	1	3	yes	—
74	C₂²	C₂×C₁₃×C₄⋊C₈	1	3	yes	—
75	C₂²	C₁₃×#504	1	4	yes	—
76	C₄	—	2	12	no	—
77	C₄	C₁₃×#384	1	1	yes	characteristic
78	C₄	C₁₃×#423	1	3	yes	—
79	C₂	C₁₃×#1842	1	1	yes	characteristic
80	C₂	C₁₃×#2151	1	6	yes	—

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

Complements

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

N	H ≅ G/N	type
16. #12899	C₁₃	direct (N × H)
65. C₁₃	#12899	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×C₁₃×C₄⋊C₁₆	2
C₁₃×#1726	2
#12899	13

Subgroups — C13×#12899 #15699238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12899 #15699238