Subgroups — C₂×D₆₃₀₄ #38745010

Order 25216.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₁₅₂	C₂	1	2	yes	maximal, complemented
2	D₆₃₀₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₅₇₆	—	2	2	no	—
5	D₃₁₅₂	—	2	2	no	—
6	D₃₁₅₂	C₂²	1	4	yes	complemented
7	C₂×C₁₆×C₁₉₇	C₂²	1	1	yes	characteristic
8	C₃₂×C₁₉₇	C₂²	1	2	yes	complemented
9	C₂×D₇₈₈	—	4	2	no	—
10	D₁₅₇₆	—	2	4	no	—
11	D₁₅₇₆	—	4	2	no	—
12	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
13	C₁₆×C₁₉₇	D₄	1	1	yes	characteristic
14	C₁₆×C₁₉₇	C₂³	1	1	yes	characteristic
15	C₂²×D₁₉₇	—	8	2	no	—
16	D₇₈₈	—	4	4	no	—
17	D₇₈₈	—	8	2	no	—
18	C₂×C₄×C₁₉₇	D₈	1	1	yes	characteristic
19	C₈×C₁₉₇	D₈	1	1	yes	characteristic
20	C₈×C₁₉₇	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₁₉₇	D₁₆	1	1	yes	characteristic
22	C₂×D₁₉₇	—	8	4	no	—
23	C₂×D₁₉₇	—	16	4	no	—
24	C₄×C₁₉₇	D₁₆	1	1	yes	characteristic
25	C₄×C₁₉₇	C₂×D₈	1	1	yes	characteristic
26	C₂×C₁₉₇	D₃₂	1	2	yes	complemented
27	C₂×C₁₉₇	C₂×D₁₆	1	1	yes	characteristic
28	D₁₉₇	—	16	4	no	—
29	C₁₉₇	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃₂	—	197	1	no	maximal, Sylow
31	C₂×D₁₆	—	197	2	no	—
32	D₃₂	—	197	4	no	—
33	C₂×C₃₂	D₁₉₇	1	1	yes	characteristic, complemented
34	C₂×D₈	—	394	2	no	—
35	D₁₆	—	394	2	no	—
36	D₁₆	—	197	4	no	—
37	C₂×C₁₆	C₂×D₁₉₇	1	1	yes	characteristic
38	C₃₂	C₂×D₁₉₇	1	2	yes	complemented
39	C₂×D₄	—	788	2	no	—
40	D₈	—	788	2	no	—
41	D₈	—	394	4	no	—
42	C₂×C₈	D₇₈₈	1	1	yes	characteristic
43	C₁₆	D₇₈₈	1	1	yes	characteristic
44	C₁₆	C₂²×D₁₉₇	1	1	yes	characteristic
45	C₂³	—	1576	2	no	—
46	D₄	—	788	4	no	—
47	D₄	—	1576	2	no	—
48	C₂×C₄	D₁₅₇₆	1	1	yes	characteristic
49	C₈	D₁₅₇₆	1	1	yes	characteristic
50	C₈	C₂×D₇₈₈	1	1	yes	characteristic
51	C₂²	—	1576	4	no	—
52	C₂²	—	3152	4	no	—
53	C₂²	D₃₁₅₂	1	1	yes	characteristic
54	C₄	D₃₁₅₂	1	1	yes	characteristic
55	C₄	C₂×D₁₅₇₆	1	1	yes	characteristic
56	C₂	—	3152	4	no	—
57	C₂	D₆₃₀₄	1	2	yes	direct product factor
58	C₂	C₂×D₃₁₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₁₅₂
commutator, cosocle	C₁₆×C₁₉₇	C₂³
Frattini	C₁₆	C₂²×D₁₉₇
Fitting	C₂×C₃₂×C₁₉₇	C₂
socle	C₂²×C₁₉₇	D₁₆
hypercenter	C₂×C₃₂	D₁₉₇
hypocenter	C₁₉₇	C₂×D₃₂
LCS	G ▷ C₁₆×C₁₉₇ ▷ C₈×C₁₉₇ ▷ C₄×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₃₁₅₂	C₂	semidirect
2. D₆₃₀₄	C₂	direct (N × H)
3. C₂×C₃₂×C₁₉₇	C₂	semidirect
6. D₃₁₅₂	C₂²	semidirect
8. C₃₂×C₁₉₇	C₂²	semidirect
26. C₂×C₁₉₇	D₃₂	semidirect
29. C₁₉₇	C₂×D₃₂	semidirect
33. C₂×C₃₂	D₁₉₇	semidirect
38. C₃₂	C₂×D₁₉₇	semidirect
57. C₂	D₆₃₀₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₃₁₅₂	2
D₆₃₀₄	2
C₂×C₃₂×C₁₉₇	2
C₂×D₃₂	197

Subgroups — C2×D6304 #38745010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₆₃₀₄ #38745010