Subgroups — C₁₃×#467 #11719002

Order 832.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
4	C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#103	C₂	1	2	yes	maximal, complemented
6	C₂×Q₈×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×Q₁₆	—	2	2	no	—
9	C₂×C₈×C₁₃	—	2	2	no	—
10	C₂×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×C₄⋊C₄	—	2	2	no	—
13	C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₁₃×C₂²⋊C₄	—	2	2	no	—
15	C₂³×C₁₃	D₄	1	1	yes	characteristic
16	Q₈×C₁₃	—	2	2	no	—
17	Q₈×C₁₃	—	2	2	no	—
18	C₂×C₄×C₁₃	—	2	1	no	—
19	C₂×C₄×C₁₃	—	2	1	no	—
20	C₂×C₄×C₁₃	—	2	2	no	—
21	C₂×C₄×C₁₃	—	2	2	no	—
22	C₂×C₄×C₁₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₈×C₁₃	—	2	1	no	—
25	C₈×C₁₃	D₄	1	2	yes	—
26	#467	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂²×C₁₃	—	2	1	no	—
28	C₂²×C₁₃	—	2	1	no	—
29	C₂²×C₁₃	Q₁₆	1	2	yes	complemented
30	C₂²×C₁₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₃	—	2	1	no	—
32	C₄×C₁₃	—	4	2	no	—
33	C₄×C₁₃	—	4	2	no	—
34	C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₄×C₁₃	#41	1	1	yes	characteristic
36	C₂×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
37	C₂²×C₈	C₂×C₁₃	1	1	yes	characteristic
38	C₂²⋊Q₈	C₂×C₁₃	1	2	yes	—
39	#107	C₂×C₁₃	1	1	yes	characteristic, complemented
40	#103	C₂×C₁₃	1	2	yes	complemented
41	C₂×C₁₃	—	2	2	no	—
42	C₂×C₁₃	#121	1	1	yes	characteristic
43	C₂×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
44	C₂×C₁₃	#135	1	1	yes	characteristic
45	C₂×Q₈	C₂²×C₁₃	1	2	yes	—
46	C₂²×C₄	C₂²×C₁₃	1	1	yes	characteristic
47	Q₁₆	—	2	2	no	—
48	C₂×C₈	—	2	2	no	—
49	C₂×C₈	C₂²×C₁₃	1	1	yes	characteristic
50	C₂×C₈	C₂²×C₁₃	1	1	yes	characteristic
51	C₄⋊C₄	—	2	2	no	—
52	C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
53	C₂²⋊C₄	—	2	2	no	—
54	C₁₃	#467	1	1	yes	characteristic, direct product factor, Sylow
55	C₂³	D₄×C₁₃	1	1	yes	characteristic
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	D₄×C₁₃	1	1	yes	characteristic
63	C₂×C₄	C₂³×C₁₃	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	D₄×C₁₃	1	2	yes	—
66	C₂²	—	2	1	no	—
67	C₂²	—	2	1	no	—
68	C₂²	C₁₃×Q₁₆	1	2	yes	complemented
69	C₂²	C₂×D₄×C₁₃	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	4	2	no	—
72	C₄	—	4	2	no	—
73	C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
74	C₄	C₁₃×#41	1	1	yes	characteristic
75	C₂	—	2	2	no	—
76	C₂	C₁₃×#121	1	1	yes	characteristic
77	C₂	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
78	C₂	C₁₃×#135	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₃
prime radical	C₂³×C₁₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#107	C₂	semidirect
5. C₁₃×#103	C₂	semidirect
26. #467	C₁₃	direct (N × H)
29. C₂²×C₁₃	Q₁₆	semidirect
36. C₂×Q₁₆	C₂×C₁₃	semidirect
39. #107	C₂×C₁₃	semidirect
40. #103	C₂×C₁₃	semidirect
54. C₁₃	#467	direct (N × H)
68. C₂²	C₁₃×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×Q₁₆	2
C₂²×C₈×C₁₃	2
C₁₃×C₂²⋊Q₈	2
C₁₃×#107	2
C₁₃×#103	2
#467	13

Subgroups — C13×#467 #11719002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#467 #11719002