Subgroups — C₁₃×#13636 #15699975

Order 3328.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#368	C₂	1	2	yes	maximal
3	C₁₃×#1425	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₂×C₁₃×#108	—	2	2	no	—
6	C₁₃×M₆₄	C₄	1	4	yes	—
7	C₂×C₁₃×C₃₂	C₂²	1	2	yes	—
8	C₁₃×#368	—	2	2	no	—
9	C₁₃×#368	C₂²	1	4	yes	—
10	C₂×C₁₃×M₁₆	—	4	2	no	—
11	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
12	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
13	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
14	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
15	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
16	C₁₃×#108	—	2	4	no	—
17	C₁₃×#108	—	4	2	no	—
18	C₁₃×C₃₂	C₂×C₄	1	4	yes	—
19	#13636	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
21	C₁₃×M₁₆	—	4	4	no	—
22	C₁₃×M₁₆	—	8	2	no	—
23	C₂×C₈×C₁₃	—	8	2	no	—
24	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
25	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
26	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
27	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
28	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
29	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
30	C₁₃×C₁₆	C₂×Q₈	1	1	yes	characteristic
31	C₂×M₆₄	C₂×C₁₃	1	1	yes	characteristic
32	C₂×#368	C₂×C₁₃	1	2	yes	—
33	#1425	C₂×C₁₃	1	4	yes	complemented
34	C₂³×C₁₃	Q₃₂	1	1	yes	characteristic
35	C₂×C₄×C₁₃	#107	1	2	yes	—
36	C₂×C₄×C₁₃	D₁₆	1	2	yes	—
37	C₂×C₄×C₁₃	Q₃₂	1	1	yes	characteristic
38	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
39	C₈×C₁₃	—	8	4	no	—
40	C₈×C₁₃	#107	1	2	yes	—
41	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
43	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
44	C₂×#108	—	2	2	no	—
45	M₆₄	C₄×C₁₃	1	4	yes	—
46	C₂×C₃₂	C₂²×C₁₃	1	2	yes	—
47	#368	—	2	2	no	—
48	#368	C₂²×C₁₃	1	4	yes	—
49	C₂²×C₁₃	—	4	1	no	—
50	C₂²×C₁₃	#366	1	2	yes	—
51	C₂²×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
52	C₄×C₁₃	#366	1	2	yes	—
53	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
54	C₄×C₁₃	C₂×D₁₆	1	1	yes	characteristic
55	C₂×M₁₆	—	4	2	no	—
56	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
57	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
58	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
59	C₂×C₁₆	Q₈×C₁₃	1	2	yes	—
60	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
61	#108	—	2	4	no	—
62	#108	—	4	2	no	—
63	C₃₂	C₂×C₄×C₁₃	1	4	yes	—
64	C₂×C₁₃	—	2	2	no	—
65	C₂×C₁₃	—	2	1	no	—
66	C₂×C₁₃	C₂×#366	1	1	yes	characteristic
67	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
68	M₁₆	—	4	4	no	—
69	M₁₆	—	8	2	no	—
70	C₂×C₈	—	8	2	no	—
71	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
72	C₂×C₈	C₁₃×D₈	1	1	yes	characteristic
73	C₂×C₈	C₁₃×Q₁₆	1	2	yes	—
74	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
75	C₁₆	C₁₃×C₄⋊C₄	1	2	yes	—
76	C₁₆	C₂²×C₄×C₁₃	1	1	yes	characteristic
77	C₁₆	C₂×Q₈×C₁₃	1	1	yes	characteristic
78	C₁₃	#13636	1	1	yes	characteristic, direct product factor, Sylow
79	C₂³	C₁₃×Q₃₂	1	1	yes	characteristic
80	C₂×C₄	C₁₃×#107	1	2	yes	—
81	C₂×C₄	C₁₃×D₁₆	1	2	yes	—
82	C₂×C₄	C₁₃×Q₃₂	1	1	yes	characteristic
83	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
84	C₈	—	8	4	no	—
85	C₈	C₁₃×#107	1	2	yes	—
86	C₈	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
87	C₈	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
88	C₂²	—	4	1	no	—
89	C₂²	C₁₃×#366	1	2	yes	—
90	C₂²	C₂×C₁₃×Q₃₂	1	1	yes	characteristic
91	C₄	C₁₃×#366	1	2	yes	—
92	C₄	C₂×C₁₃×#107	1	1	yes	characteristic
93	C₄	C₂×C₁₃×D₁₆	1	1	yes	characteristic
94	C₂	—	2	2	no	—
95	C₂	—	2	1	no	—
96	C₂	C₂×C₁₃×#366	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	C₂×D₁₆
commutator	C₁₆	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle	C₂×C₁₃	C₂×#366
prime radical	C₂³×C₁₃	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂²×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1425	C₂	semidirect
19. #13636	C₁₃	direct (N × H)
33. #1425	C₂×C₁₃	semidirect
78. C₁₃	#13636	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×M₆₄	2
C₂×C₁₃×#368	2
C₁₃×#1425	2
#13636	13

Subgroups — C13×#13636 #15699975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13636 #15699975