Subgroups — #88150

Order 416.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#6103	C₂	1	1	yes	maximal, characteristic
5	#6103	C₂	1	1	yes	maximal, characteristic
6	#6101	C₂	1	1	yes	maximal, characteristic, complemented
7	#6101	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
15	C₄×D₁₃	—	2	2	no	—
16	Dic₂₆	—	2	2	no	—
17	C₂²×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×D₁₃	—	2	1	no	—
19	C₂×D₁₃	—	2	1	no	—
20	C₂×D₁₃	Q₈	1	2	yes	complemented
21	C₄×C₁₃	—	2	1	no	—
22	C₄×C₁₃	—	2	1	no	—
23	C₄×C₁₃	—	2	1	no	—
24	Dic₁₃	—	2	1	no	—
25	Dic₁₃	—	2	1	no	—
26	Dic₁₃	D₄	1	2	yes	—
27	C₂²⋊Q₈	—	13	1	no	maximal, Sylow
28	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₁₃	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₁₃	#41	1	1	yes	characteristic
31	D₁₃	—	2	2	no	—
32	C₂×Q₈	—	13	1	no	—
33	C₂²×C₄	—	13	1	no	—
34	C₄⋊C₄	—	13	1	no	—
35	C₄⋊C₄	—	13	1	no	—
36	C₄⋊C₄	D₁₃	1	1	yes	characteristic, complemented
37	C₂²⋊C₄	—	13	1	no	—
38	C₂²⋊C₄	—	13	1	no	—
39	C₁₃	C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
40	C₂³	—	13	1	no	—
41	Q₈	—	26	2	no	—
42	C₂×C₄	—	13	1	no	—
43	C₂×C₄	—	13	1	no	—
44	C₂×C₄	—	13	1	no	—
45	C₂×C₄	—	26	2	no	—
46	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
47	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
48	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
49	C₂²	—	13	2	no	—
50	C₂²	—	26	1	no	—
51	C₂²	—	26	1	no	—
52	C₂²	C₂²×D₁₃	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	2	1	no	—
55	C₄	—	2	1	no	—
56	C₄	—	13	2	no	—
57	C₄	—	26	1	no	—
58	C₄	—	26	1	no	—
59	C₂	—	26	2	no	—
60	C₂	#6127	1	1	yes	characteristic
61	C₂	D₄×D₁₃	1	1	yes	characteristic
62	C₂	Q₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂³
Fitting	C₁₃×C₄⋊C₄	C₂
prime radical	C₂²×D₁₃	C₂²
hypercenter	C₄⋊C₄	D₁₃
hypocenter	C₁₃	C₂²⋊Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₂₆	C₂	semidirect
3. C₁₃×C₄⋊C₄	C₂	semidirect
6. #6101	C₂	semidirect
7. #6101	C₂	semidirect
20. C₂×D₁₃	Q₈	semidirect
36. C₄⋊C₄	D₁₃	semidirect
39. C₁₃	C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₁₃	2
C₂×Dic₂₆	2
C₁₃×C₄⋊C₄	2
#6103	2
#6101	2
C₂²⋊Q₈	13