Subgroups — C₁₃×#124 #88218

Order 416.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
4	C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₁₃	C₂²	1	2	yes	—
6	Q₈×C₁₃	—	2	2	no	—
7	D₄×C₁₃	—	2	2	no	—
8	C₂×C₄×C₁₃	C₂²	1	2	yes	—
9	C₂×C₄×C₁₃	C₂²	1	2	yes	—
10	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃	—	2	2	no	—
12	C₂²×C₁₃	—	2	4	no	—
13	C₂²×C₁₃	C₂³	1	1	yes	characteristic
14	C₄×C₁₃	—	2	2	no	—
15	C₄×C₁₃	—	2	2	no	—
16	C₄×C₁₃	D₄	1	2	yes	—
17	#124	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₁₃	—	4	2	no	—
19	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
20	C₂×C₁₃	#41	1	2	yes	—
21	C₂×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
22	C₂×D₄	C₂×C₁₃	1	1	yes	characteristic
23	C₂²⋊C₄	C₂×C₁₃	1	4	yes	complemented
24	C₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₁₃	#124	1	1	yes	characteristic, direct product factor, Sylow
26	C₂³	C₂²×C₁₃	1	2	yes	—
27	Q₈	—	2	2	no	—
28	D₄	—	2	2	no	—
29	C₂×C₄	C₂²×C₁₃	1	2	yes	—
30	C₂×C₄	C₂²×C₁₃	1	2	yes	—
31	C₂×C₄	C₂²×C₁₃	1	1	yes	characteristic
32	C₂²	—	2	2	no	—
33	C₂²	—	2	4	no	—
34	C₂²	C₂³×C₁₃	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	2	2	no	—
37	C₄	D₄×C₁₃	1	2	yes	—
38	C₂	—	4	2	no	—
39	C₂	C₂×D₄×C₁₃	1	1	yes	characteristic
40	C₂	C₁₃×#41	1	2	yes	—

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

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

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