Subgroups — C₂×C₃⋊D₂₃₂₅ #42124458

Order 27900.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₂₃₂₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₂₅×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₃₂₅	—	3	4	no	maximal
4	C₃²×C₂₅×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₄₆₅	—	5	1	no	maximal
6	D₂₃₂₅	—	3	8	no	—
7	C₂×C₃×C₂₅×C₃₁	D₃	1	4	yes	complemented
8	C₂×D₇₇₅	—	9	1	no	Hall
9	C₃⋊D₄₆₅	—	5	2	no	—
10	C₂×C₃²×C₅×C₃₁	D₅	1	1	yes	characteristic
11	C₃×C₂₅×C₃₁	C₂×D₃	1	4	yes	complemented
12	C₂×D₄₆₅	—	15	4	no	—
13	C₂×C₂₅×C₃₁	C₃⋊D₃	1	1	yes	characteristic, complemented
14	D₇₇₅	—	9	2	no	—
15	C₃²×C₅×C₃₁	C₂×D₅	1	1	yes	characteristic
16	C₂×C₃⋊D₉₃	—	25	1	no	Hall
17	C₂×C₃×C₅×C₃₁	D₁₅	1	4	yes	—
18	D₄₆₅	—	15	8	no	—
19	C₂×C₃⋊D₇₅	—	31	1	no	maximal, Hall
20	C₂₅×C₃₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×D₁₅₅	—	45	1	no	—
22	C₂×C₃²×C₃₁	D₂₅	1	1	yes	characteristic, complemented
23	C₃⋊D₉₃	—	25	2	no	—
24	C₃×C₅×C₃₁	C₂×D₁₅	1	4	yes	—
25	C₂×C₃²×C₂₅	D₃₁	1	1	yes	characteristic, complemented
26	C₃⋊D₇₅	—	31	2	no	—
27	C₂×D₉₃	—	75	4	no	—
28	C₂×C₅×C₃₁	C₃⋊D₁₅	1	1	yes	characteristic
29	D₁₅₅	—	45	2	no	—
30	C₂×D₇₅	—	93	4	no	—
31	C₃²×C₃₁	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
32	C₃²×C₂₅	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₃₁	D₇₅	1	4	yes	complemented
34	D₉₃	—	75	8	no	—
35	C₂×C₃⋊D₁₅	—	155	1	no	—
36	C₅×C₃₁	C₂×C₃⋊D₁₅	1	1	yes	characteristic
37	C₂×C₃×C₂₅	D₉₃	1	4	yes	complemented
38	D₇₅	—	93	8	no	—
39	C₂×D₃₁	—	225	1	no	Hall
40	C₂×D₂₅	—	279	1	no	Hall
41	C₃×C₃₁	C₂×D₇₅	1	4	yes	complemented
42	C₂×C₃²×C₅	D₁₅₅	1	1	yes	characteristic
43	C₃⋊D₁₅	—	155	2	no	—
44	C₃×C₂₅	C₂×D₉₃	1	4	yes	complemented
45	C₂×C₃₁	C₃⋊D₇₅	1	1	yes	characteristic, complemented
46	D₃₁	—	225	2	no	—
47	C₂×D₁₅	—	465	4	no	—
48	C₂×C₂₅	C₃⋊D₉₃	1	1	yes	characteristic, complemented
49	D₂₅	—	279	2	no	—
50	C₃²×C₅	C₂×D₁₅₅	1	1	yes	characteristic
51	C₂×C₃⋊D₃	—	775	1	no	Hall
52	C₃₁	C₂×C₃⋊D₇₅	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃×C₅	D₄₆₅	1	4	yes	—
54	D₁₅	—	465	8	no	—
55	C₂₅	C₂×C₃⋊D₉₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₅	—	1395	1	no	—
57	C₂×C₃²	D₇₇₅	1	1	yes	characteristic, complemented
58	C₃⋊D₃	—	775	2	no	—
59	C₃×C₅	C₂×D₄₆₅	1	4	yes	—
60	C₂×D₃	—	2325	4	no	—
61	C₂×C₅	C₃⋊D₄₆₅	1	1	yes	characteristic
62	D₅	—	1395	2	no	—
63	C₃²	C₂×D₇₇₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	D₂₃₂₅	1	4	yes	complemented
65	D₃	—	2325	8	no	—
66	C₅	C₂×C₃⋊D₄₆₅	1	1	yes	characteristic
67	C₂²	—	6975	1	no	Sylow
68	C₃	C₂×D₂₃₂₅	1	4	yes	complemented
69	C₂	—	6975	2	no	—
70	C₂	C₃⋊D₂₃₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₂₃₂₅
commutator, cosocle, hypocenter	C₃²×C₂₅×C₃₁	C₂²
Frattini	C₅	C₂×C₃⋊D₄₆₅
Fitting	C₂×C₃²×C₂₅×C₃₁	C₂
socle	C₂×C₃²×C₅×C₃₁	D₅
LCS	G ▷ C₃²×C₂₅×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₂₃₂₅	C₂	direct (N × H)
2. C₂×C₃²×C₂₅×C₃₁	C₂	semidirect
4. C₃²×C₂₅×C₃₁	C₂²	semidirect
7. C₂×C₃×C₂₅×C₃₁	D₃	semidirect
11. C₃×C₂₅×C₃₁	C₂×D₃	semidirect
13. C₂×C₂₅×C₃₁	C₃⋊D₃	semidirect
20. C₂₅×C₃₁	C₂×C₃⋊D₃	semidirect
22. C₂×C₃²×C₃₁	D₂₅	semidirect
25. C₂×C₃²×C₂₅	D₃₁	semidirect
31. C₃²×C₃₁	C₂×D₂₅	semidirect
32. C₃²×C₂₅	C₂×D₃₁	semidirect
33. C₂×C₃×C₃₁	D₇₅	semidirect
37. C₂×C₃×C₂₅	D₉₃	semidirect
41. C₃×C₃₁	C₂×D₇₅	semidirect
44. C₃×C₂₅	C₂×D₉₃	semidirect
45. C₂×C₃₁	C₃⋊D₇₅	semidirect
48. C₂×C₂₅	C₃⋊D₉₃	semidirect
52. C₃₁	C₂×C₃⋊D₇₅	semidirect
55. C₂₅	C₂×C₃⋊D₉₃	semidirect
57. C₂×C₃²	D₇₇₅	semidirect
63. C₃²	C₂×D₇₇₅	semidirect
64. C₂×C₃	D₂₃₂₅	semidirect
68. C₃	C₂×D₂₃₂₅	semidirect
70. C₂	C₃⋊D₂₃₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⋊D₂₃₂₅	2
C₂×C₃²×C₂₅×C₃₁	2
C₂×D₂₃₂₅	3
C₂×C₃⋊D₄₆₅	5
C₂×C₃⋊D₇₅	31

Subgroups — C2×C3⋊D2325 #42124458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₂₃₂₅ #42124458