Subgroups — #34093929

Order 20032.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23756437	C₂	1	1	yes	maximal, characteristic
2	#23756407	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₃₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14578809	C₄	1	1	yes	characteristic
5	C₄×Dic₃₁₃	C₄	1	1	yes	characteristic
6	#19097536	C₄	1	2	yes	complemented
7	C₂×C₈×C₃₁₃	C₂²	1	1	yes	characteristic
8	C₁₆×C₃₁₃	C₄	1	2	yes	complemented
9	C₂×Dic₃₁₃	—	2	1	no	—
10	#14578809	—	2	1	no	—
11	C₂×C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₁₃	C₂×C₄	1	1	yes	characteristic
13	C₈×C₃₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₃₁₃	M₁₆	1	1	yes	characteristic
15	C₄×C₃₁₃	C₄²	1	1	yes	characteristic
16	C₄×C₃₁₃	M₁₆	1	1	yes	characteristic
17	Dic₃₁₃	—	4	1	no	—
18	C₂×C₃₁₃	—	2	1	no	—
19	C₂×C₃₁₃	#97	1	1	yes	characteristic
20	C₃₁₃	#347	1	1	yes	characteristic, complemented, Sylow
21	#347	—	313	1	no	maximal, Sylow
22	M₃₂	—	313	1	no	—
23	M₃₂	D₃₁₃	1	1	yes	characteristic
24	#97	—	313	1	no	—
25	C₂×C₈	—	313	1	no	—
26	C₂×C₈	C₂×D₃₁₃	1	1	yes	characteristic
27	C₄²	—	313	1	no	—
28	C₁₆	—	313	2	no	—
29	C₁₆	Dic₃₁₃	1	2	yes	complemented
30	C₂×C₄	—	626	1	no	—
31	C₂×C₄	C₄×D₃₁₃	1	1	yes	characteristic
32	C₈	—	626	1	no	—
33	C₈	C₄×D₃₁₃	1	1	yes	characteristic
34	C₈	C₂×Dic₃₁₃	1	1	yes	characteristic
35	C₂²	#19097544	1	1	yes	characteristic
36	C₄	—	1252	1	no	—
37	C₄	C₄×Dic₃₁₃	1	1	yes	characteristic
38	C₄	#19097544	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#23756407	1	1	yes	characteristic

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.