Subgroups — #322×C₄₉₉ #44542552

Order 31936.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₄₉₉	C₂	1	2	yes	maximal
2	C₄×C₈×C₄₉₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₄₉₉	C₄	1	4	yes	—
4	C₂×C₈×C₄₉₉	C₄	1	2	yes	—
5	C₄²×C₄₉₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₄₉₉	C₂×C₄	1	1	yes	characteristic
7	C₂×C₄×C₄₉₉	C₂×C₄	1	2	yes	—
8	C₈×C₄₉₉	—	2	4	no	—
9	C₈×C₄₉₉	C₈	1	4	yes	complemented
10	C₂²×C₄₉₉	C₄²	1	1	yes	characteristic
11	C₄×C₄₉₉	C₂×C₈	1	2	yes	—
12	C₄×C₄₉₉	M₁₆	1	4	yes	—
13	C₂×C₄₉₉	C₄×C₈	1	1	yes	characteristic
14	C₂×C₄₉₉	#97	1	2	yes	—
15	C₄₉₉	#322	1	1	yes	characteristic, direct product factor, Sylow
16	#322	C₄₉₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₄×C₈	C₂×C₄₉₉	1	2	yes	—
18	C₄×C₈	C₂×C₄₉₉	1	1	yes	characteristic
19	C₂×C₈	C₄×C₄₉₉	1	4	yes	—
20	C₂×C₈	C₄×C₄₉₉	1	2	yes	—
21	C₄²	C₂²×C₄₉₉	1	1	yes	characteristic
22	C₂×C₄	C₂×C₄×C₄₉₉	1	1	yes	characteristic
23	C₂×C₄	C₂×C₄×C₄₉₉	1	2	yes	—
24	C₈	—	2	4	no	—
25	C₈	C₈×C₄₉₉	1	4	yes	complemented
26	C₂²	C₄²×C₄₉₉	1	1	yes	characteristic
27	C₄	C₂×C₈×C₄₉₉	1	2	yes	—
28	C₄	M₁₆×C₄₉₉	1	4	yes	—
29	C₂	C₄×C₈×C₄₉₉	1	1	yes	characteristic
30	C₂	#97×C₄₉₉	1	2	yes	—

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.

subgroup	index
C₄×C₈×C₄₉₉	2
#322	499