Subgroups — #27163760

Order 12736.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263866	C₂	1	2	yes	maximal
2	#125×C₁₉₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉₉⋊C₈	—	2	2	no	—
4	C₄⋊C₄×C₁₉₉	—	2	2	no	—
5	C₄⋊C₄×C₁₉₉	C₄	1	2	yes	—
6	C₄²×C₁₉₉	C₂²	1	1	yes	characteristic
7	C₁₉₉⋊C₈	—	2	4	no	—
8	C₂×C₄×C₁₉₉	—	2	2	no	—
9	C₂×C₄×C₁₉₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₉₉	D₄	1	2	yes	—
11	C₂²×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
12	C₄×C₁₉₉	—	2	1	no	—
13	C₄×C₁₉₉	—	2	2	no	—
14	C₄×C₁₉₉	—	4	2	no	—
15	C₂×C₁₉₉	#101	1	1	yes	characteristic
16	C₂×C₁₉₉	#104	1	2	yes	—
17	C₁₉₉	#330	1	1	yes	characteristic, complemented, Sylow
18	#330	—	199	1	no	maximal, Sylow
19	#125	D₁₉₉	1	1	yes	characteristic
20	#97	—	199	2	no	—
21	C₂×C₈	—	398	2	no	—
22	C₄⋊C₄	—	2	2	no	—
23	C₄⋊C₄	Dic₁₉₉	1	2	yes	—
24	C₄²	C₂×D₁₉₉	1	1	yes	characteristic
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	C₂×Dic₁₉₉	1	1	yes	characteristic
27	C₂×C₄	C₂²⋊D₁₉₉	1	2	yes	—
28	C₈	—	398	4	no	—
29	C₂²	C₂²⋊Dic₁₉₉	1	1	yes	characteristic
30	C₄	—	2	1	no	—
31	C₄	—	2	2	no	—
32	C₄	—	4	2	no	—
33	C₂	#20263874	1	1	yes	characteristic
34	C₂	#20263882	1	2	yes	—

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

N	H ≅ G/N	type
17. C₁₉₉	#330	semidirect

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