Subgroups — #88121

Order 416.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	#6122	C₂	1	2	yes	maximal, complemented
3	C₂³×C₁₃	C₄	1	1	yes	characteristic
4	C₂²×D₁₃	C₄	1	1	yes	characteristic
5	C₂²⋊D₁₃	—	2	2	no	—
6	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
7	#1057	—	2	2	no	—
8	C₂²×C₁₃	—	2	1	no	—
9	C₂²×C₁₃	—	4	1	no	—
10	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂×D₁₃	—	2	1	no	—
12	C₂×D₁₃	—	4	1	no	—
13	Dic₁₃	D₄	1	2	yes	—
14	#100	—	13	1	no	maximal, Sylow
15	C₂×C₁₃	—	2	1	no	—
16	C₂×C₁₃	—	4	1	no	—
17	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
18	D₁₃	—	4	1	no	—
19	C₂×D₄	—	13	1	no	—
20	M₁₆	—	13	2	no	—
21	C₁₃	#100	1	1	yes	characteristic, complemented, Sylow
22	C₂³	—	13	1	no	—
23	C₂³	#261	1	1	yes	characteristic
24	D₄	—	26	2	no	—
25	C₂×C₄	—	13	1	no	—
26	C₈	—	26	2	no	—
27	C₂²	—	2	1	no	—
28	C₂²	—	4	1	no	—
29	C₂²	—	26	1	no	—
30	C₂²	—	52	1	no	—
31	C₂²	C₂×#261	1	1	yes	characteristic
32	C₄	—	13	2	no	—
33	C₂	—	2	1	no	—
34	C₂	—	4	1	no	—
35	C₂	—	52	1	no	—
36	C₂	C₂²⋊#261	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #6122	C₂	semidirect
21. C₁₃	#100	semidirect

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